LMFDB - Embedded newform 2013.4.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.18056 q^{2} -3.00000 q^{3} +2.11597 q^{4} +11.4382 q^{5} +9.54169 q^{6} +18.3064 q^{7} +18.7145 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.18056 q^{2} -3.00000 q^{3} +2.11597 q^{4} +11.4382 q^{5} +9.54169 q^{6} +18.3064 q^{7} +18.7145 q^{8} +9.00000 q^{9} -36.3799 q^{10} -11.0000 q^{11} -6.34792 q^{12} -77.4266 q^{13} -58.2246 q^{14} -34.3146 q^{15} -76.4504 q^{16} +59.7610 q^{17} -28.6251 q^{18} -128.347 q^{19} +24.2029 q^{20} -54.9191 q^{21} +34.9862 q^{22} -124.902 q^{23} -56.1435 q^{24} +5.83220 q^{25} +246.260 q^{26} -27.0000 q^{27} +38.7358 q^{28} -103.551 q^{29} +109.140 q^{30} -255.368 q^{31} +93.4392 q^{32} +33.0000 q^{33} -190.074 q^{34} +209.392 q^{35} +19.0438 q^{36} +7.48216 q^{37} +408.215 q^{38} +232.280 q^{39} +214.060 q^{40} +64.1265 q^{41} +174.674 q^{42} -76.3895 q^{43} -23.2757 q^{44} +102.944 q^{45} +397.259 q^{46} -43.2434 q^{47} +229.351 q^{48} -7.87650 q^{49} -18.5497 q^{50} -179.283 q^{51} -163.833 q^{52} +180.093 q^{53} +85.8752 q^{54} -125.820 q^{55} +342.595 q^{56} +385.041 q^{57} +329.352 q^{58} +257.538 q^{59} -72.6087 q^{60} -61.0000 q^{61} +812.213 q^{62} +164.757 q^{63} +314.414 q^{64} -885.620 q^{65} -104.959 q^{66} +500.595 q^{67} +126.453 q^{68} +374.706 q^{69} -665.984 q^{70} +1110.19 q^{71} +168.431 q^{72} -555.772 q^{73} -23.7975 q^{74} -17.4966 q^{75} -271.579 q^{76} -201.370 q^{77} -738.780 q^{78} +816.011 q^{79} -874.455 q^{80} +81.0000 q^{81} -203.958 q^{82} +248.989 q^{83} -116.207 q^{84} +683.558 q^{85} +242.962 q^{86} +310.654 q^{87} -205.860 q^{88} +382.309 q^{89} -327.419 q^{90} -1417.40 q^{91} -264.289 q^{92} +766.104 q^{93} +137.538 q^{94} -1468.06 q^{95} -280.318 q^{96} +296.876 q^{97} +25.0517 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * 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 $

$2$	−3.18056	−1.12450	−0.562249	−	0.826968i	$-0.690064\pi$
$2$	−3.18056	−1.12450	−0.562249	+	0.826968i	$0.690064\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	2.11597	0.264497
$5$	11.4382	1.02306	0.511531	−	0.859265i	$-0.329078\pi$
$5$	11.4382	1.02306	0.511531	+	0.859265i	$0.329078\pi$
$6$	9.54169	0.649229
$7$	18.3064	0.988452	0.494226	−	0.869334i	$-0.335452\pi$
$7$	18.3064	0.988452	0.494226	+	0.869334i	$0.335452\pi$
$8$	18.7145	0.827072
$9$	9.00000	0.333333
$10$	−36.3799	−1.15043
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−6.34792	−0.152707
$13$	−77.4266	−1.65187	−0.825934	−	0.563767i	$-0.809351\pi$
$13$	−77.4266	−1.65187	−0.825934	+	0.563767i	$0.809351\pi$
$14$	−58.2246	−1.11151
$15$	−34.3146	−0.590666
$16$	−76.4504	−1.19454
$17$	59.7610	0.852599	0.426299	−	0.904582i	$-0.359817\pi$
$17$	59.7610	0.852599	0.426299	+	0.904582i	$0.359817\pi$
$18$	−28.6251	−0.374833
$19$	−128.347	−1.54973	−0.774863	−	0.632129i	$-0.782181\pi$
$19$	−128.347	−1.54973	−0.774863	+	0.632129i	$0.782181\pi$
$20$	24.2029	0.270597
$21$	−54.9191	−0.570683
$22$	34.9862	0.339049
$23$	−124.902	−1.13234	−0.566171	−	0.824288i	$-0.691576\pi$
$23$	−124.902	−1.13234	−0.566171	+	0.824288i	$0.691576\pi$
$24$	−56.1435	−0.477510
$25$	5.83220	0.0466576
$26$	246.260	1.85752
$27$	−27.0000	−0.192450
$28$	38.7358	0.261442
$29$	−103.551	−0.663070	−0.331535	−	0.943443i	$-0.607566\pi$
$29$	−103.551	−0.663070	−0.331535	+	0.943443i	$0.607566\pi$
$30$	109.140	0.664203
$31$	−255.368	−1.47953	−0.739765	−	0.672866i	$-0.765063\pi$
$31$	−255.368	−1.47953	−0.739765	+	0.672866i	$0.765063\pi$
$32$	93.4392	0.516184
$33$	33.0000	0.174078
$34$	−190.074	−0.958746
$35$	209.392	1.01125
$36$	19.0438	0.0881655
$37$	7.48216	0.0332449	0.0166224	−	0.999862i	$-0.494709\pi$
$37$	7.48216	0.0332449	0.0166224	+	0.999862i	$0.494709\pi$
$38$	408.215	1.74267
$39$	232.280	0.953706
$40$	214.060	0.846147
$41$	64.1265	0.244265	0.122133	−	0.992514i	$-0.461027\pi$
$41$	64.1265	0.244265	0.122133	+	0.992514i	$0.461027\pi$
$42$	174.674	0.641732
$43$	−76.3895	−0.270914	−0.135457	−	0.990783i	$-0.543250\pi$
$43$	−76.3895	−0.270914	−0.135457	+	0.990783i	$0.543250\pi$
$44$	−23.2757	−0.0797487
$45$	102.944	0.341021
$46$	397.259	1.27332
$47$	−43.2434	−0.134206	−0.0671031	−	0.997746i	$-0.521376\pi$
$47$	−43.2434	−0.134206	−0.0671031	+	0.997746i	$0.521376\pi$
$48$	229.351	0.689667
$49$	−7.87650	−0.0229636
$50$	−18.5497	−0.0524664
$51$	−179.283	−0.492248
$52$	−163.833	−0.436913
$53$	180.093	0.466747	0.233374	−	0.972387i	$-0.425023\pi$
$53$	180.093	0.466747	0.233374	+	0.972387i	$0.425023\pi$
$54$	85.8752	0.216410
$55$	−125.820	−0.308465
$56$	342.595	0.817521
$57$	385.041	0.894735
$58$	329.352	0.745621
$59$	257.538	0.568281	0.284140	−	0.958783i	$-0.408292\pi$
$59$	257.538	0.568281	0.284140	+	0.958783i	$0.408292\pi$
$60$	−72.6087	−0.156229
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	812.213	1.66373
$63$	164.757	0.329484
$64$	314.414	0.614090
$65$	−885.620	−1.68996
$66$	−104.959	−0.195750
$67$	500.595	0.912798	0.456399	−	0.889775i	$-0.349139\pi$
$67$	500.595	0.912798	0.456399	+	0.889775i	$0.349139\pi$
$68$	126.453	0.225509
$69$	374.706	0.653758
$70$	−665.984	−1.13715
$71$	1110.19	1.85571	0.927855	−	0.372941i	$-0.121650\pi$
$71$	1110.19	1.85571	0.927855	+	0.372941i	$0.121650\pi$
$72$	168.431	0.275691
$73$	−555.772	−0.891071	−0.445535	−	0.895264i	$-0.646987\pi$
$73$	−555.772	−0.891071	−0.445535	+	0.895264i	$0.646987\pi$
$74$	−23.7975	−0.0373838
$75$	−17.4966	−0.0269378
$76$	−271.579	−0.409897
$77$	−201.370	−0.298029
$78$	−738.780	−1.07244
$79$	816.011	1.16213	0.581066	−	0.813857i	$-0.302636\pi$
$79$	816.011	1.16213	0.581066	+	0.813857i	$0.302636\pi$
$80$	−874.455	−1.22209
$81$	81.0000	0.111111
$82$	−203.958	−0.274676
$83$	248.989	0.329279	0.164639	−	0.986354i	$-0.447354\pi$
$83$	248.989	0.329279	0.164639	+	0.986354i	$0.447354\pi$
$84$	−116.207	−0.150944
$85$	683.558	0.872262
$86$	242.962	0.304642
$87$	310.654	0.382823
$88$	−205.860	−0.249372
$89$	382.309	0.455333	0.227666	−	0.973739i	$-0.426890\pi$
$89$	382.309	0.455333	0.227666	+	0.973739i	$0.426890\pi$
$90$	−327.419	−0.383478
$91$	−1417.40	−1.63279
$92$	−264.289	−0.299501
$93$	766.104	0.854207
$94$	137.538	0.150915
$95$	−1468.06	−1.58547
$96$	−280.318	−0.298019
$97$	296.876	0.310754	0.155377	−	0.987855i	$-0.450341\pi$
$97$	296.876	0.310754	0.155377	+	0.987855i	$0.450341\pi$
$98$	25.0517	0.0258225
$99$	−99.0000	−0.100504
$100$	12.3408	0.0123408
$101$	995.334	0.980588	0.490294	−	0.871557i	$-0.336889\pi$
$101$	995.334	0.980588	0.490294	+	0.871557i	$0.336889\pi$
$102$	570.221	0.553532
$103$	−137.845	−0.131867	−0.0659335	−	0.997824i	$-0.521003\pi$
$103$	−137.845	−0.131867	−0.0659335	+	0.997824i	$0.521003\pi$
$104$	−1449.00	−1.36621
$105$	−628.176	−0.583844
$106$	−572.796	−0.524857
$107$	−54.4752	−0.0492179	−0.0246089	−	0.999697i	$-0.507834\pi$
$107$	−54.4752	−0.0492179	−0.0246089	+	0.999697i	$0.507834\pi$
$108$	−57.1313	−0.0509024
$109$	1364.96	1.19945	0.599724	−	0.800207i	$-0.295277\pi$
$109$	1364.96	1.19945	0.599724	+	0.800207i	$0.295277\pi$
$110$	400.179	0.346868
$111$	−22.4465	−0.0191939
$112$	−1399.53	−1.18074
$113$	−1971.25	−1.64106	−0.820531	−	0.571602i	$-0.806322\pi$
$113$	−1971.25	−1.64106	−0.820531	+	0.571602i	$0.806322\pi$
$114$	−1224.65	−1.00613
$115$	−1428.65	−1.15846
$116$	−219.112	−0.175380
$117$	−696.839	−0.550622
$118$	−819.115	−0.639031
$119$	1094.01	0.842753
$120$	−642.180	−0.488523
$121$	121.000	0.0909091
$122$	194.014	0.143977
$123$	−192.379	−0.141027
$124$	−540.351	−0.391331
$125$	−1363.06	−0.975329
$126$	−524.021	−0.370504
$127$	1997.70	1.39581	0.697904	−	0.716192i	$-0.254116\pi$
$127$	1997.70	1.39581	0.697904	+	0.716192i	$0.254116\pi$
$128$	−1747.53	−1.20673
$129$	229.169	0.156412
$130$	2816.77	1.90036
$131$	2203.94	1.46992	0.734960	−	0.678111i	$-0.237201\pi$
$131$	2203.94	1.46992	0.734960	+	0.678111i	$0.237201\pi$
$132$	69.8271	0.0460429
$133$	−2349.57	−1.53183
$134$	−1592.17	−1.02644
$135$	−308.831	−0.196889
$136$	1118.40	0.705161
$137$	−1304.10	−0.813263	−0.406632	−	0.913592i	$-0.633297\pi$
$137$	−1304.10	−0.813263	−0.406632	+	0.913592i	$0.633297\pi$
$138$	−1191.78	−0.735150
$139$	−712.064	−0.434507	−0.217253	−	0.976115i	$-0.569710\pi$
$139$	−712.064	−0.434507	−0.217253	+	0.976115i	$0.569710\pi$
$140$	443.067	0.267472
$141$	129.730	0.0774840
$142$	−3531.03	−2.08674
$143$	851.692	0.498057
$144$	−688.054	−0.398179
$145$	−1184.44	−0.678362
$146$	1767.67	1.00201
$147$	23.6295	0.0132580
$148$	15.8321	0.00879315
$149$	−1265.37	−0.695727	−0.347864	−	0.937545i	$-0.613093\pi$
$149$	−1265.37	−0.695727	−0.347864	+	0.937545i	$0.613093\pi$
$150$	55.6490	0.0302915
$151$	−3286.92	−1.77143	−0.885716	−	0.464228i	$-0.846332\pi$
$151$	−3286.92	−1.77143	−0.885716	+	0.464228i	$0.846332\pi$
$152$	−2401.95	−1.28174
$153$	537.849	0.284200
$154$	640.470	0.335134
$155$	−2920.95	−1.51365
$156$	491.498	0.252252
$157$	−376.760	−0.191521	−0.0957603	−	0.995404i	$-0.530528\pi$
$157$	−376.760	−0.191521	−0.0957603	+	0.995404i	$0.530528\pi$
$158$	−2595.37	−1.30682
$159$	−540.278	−0.269477
$160$	1068.78	0.528088
$161$	−2286.50	−1.11927
$162$	−257.625	−0.124944
$163$	1400.66	0.673057	0.336528	−	0.941673i	$-0.390747\pi$
$163$	1400.66	0.673057	0.336528	+	0.941673i	$0.390747\pi$
$164$	135.690	0.0646073
$165$	377.460	0.178092
$166$	−791.926	−0.370273
$167$	2787.52	1.29164	0.645822	−	0.763488i	$-0.276515\pi$
$167$	2787.52	1.29164	0.645822	+	0.763488i	$0.276515\pi$
$168$	−1027.78	−0.471996
$169$	3797.88	1.72866
$170$	−2174.10	−0.980857
$171$	−1155.12	−0.516576
$172$	−161.638	−0.0716558
$173$	1009.57	0.443679	0.221839	−	0.975083i	$-0.428794\pi$
$173$	1009.57	0.443679	0.221839	+	0.975083i	$0.428794\pi$
$174$	−988.055	−0.430484
$175$	106.766	0.0461188
$176$	840.955	0.360167
$177$	−772.613	−0.328097
$178$	−1215.96	−0.512021
$179$	3056.47	1.27627	0.638133	−	0.769926i	$-0.279707\pi$
$179$	3056.47	1.27627	0.638133	+	0.769926i	$0.279707\pi$
$180$	217.826	0.0901989
$181$	1441.60	0.592007	0.296003	−	0.955187i	$-0.404346\pi$
$181$	1441.60	0.592007	0.296003	+	0.955187i	$0.404346\pi$
$182$	4508.13	1.83607
$183$	183.000	0.0739221
$184$	−2337.48	−0.936529
$185$	85.5824	0.0340116
$186$	−2436.64	−0.960554
$187$	−657.371	−0.257068
$188$	−91.5018	−0.0354971
$189$	−494.272	−0.190228
$190$	4669.25	1.78286
$191$	1260.30	0.477446	0.238723	−	0.971088i	$-0.423271\pi$
$191$	1260.30	0.477446	0.238723	+	0.971088i	$0.423271\pi$
$192$	−943.243	−0.354545
$193$	3128.50	1.16681	0.583405	−	0.812181i	$-0.301720\pi$
$193$	3128.50	1.16681	0.583405	+	0.812181i	$0.301720\pi$
$194$	−944.231	−0.349442
$195$	2656.86	0.975701
$196$	−16.6665	−0.00607378
$197$	4093.88	1.48059	0.740297	−	0.672280i	$-0.234685\pi$
$197$	4093.88	1.48059	0.740297	+	0.672280i	$0.234685\pi$
$198$	314.876	0.113016
$199$	2152.29	0.766694	0.383347	−	0.923604i	$-0.374771\pi$
$199$	2152.29	0.766694	0.383347	+	0.923604i	$0.374771\pi$
$200$	109.147	0.0385892
$201$	−1501.79	−0.527004
$202$	−3165.72	−1.10267
$203$	−1895.65	−0.655412
$204$	−379.358	−0.130198
$205$	733.491	0.249899
$206$	438.425	0.148284
$207$	−1124.12	−0.377448
$208$	5919.30	1.97322
$209$	1411.82	0.467260
$210$	1997.95	0.656532
$211$	1965.90	0.641412	0.320706	−	0.947179i	$-0.396080\pi$
$211$	1965.90	0.641412	0.320706	+	0.947179i	$0.396080\pi$
$212$	381.071	0.123453
$213$	−3330.57	−1.07139
$214$	173.262	0.0553454
$215$	−873.758	−0.277162
$216$	−505.292	−0.159170
$217$	−4674.86	−1.46244
$218$	−4341.35	−1.34878
$219$	1667.32	0.514460
$220$	−266.232	−0.0815880
$221$	−4627.09	−1.40838
$222$	71.3924	0.0215835
$223$	2151.28	0.646012	0.323006	−	0.946397i	$-0.395307\pi$
$223$	2151.28	0.646012	0.323006	+	0.946397i	$0.395307\pi$
$224$	1710.53	0.510223
$225$	52.4898	0.0155525
$226$	6269.69	1.84537
$227$	−1752.29	−0.512352	−0.256176	−	0.966630i	$-0.582463\pi$
$227$	−1752.29	−0.512352	−0.256176	+	0.966630i	$0.582463\pi$
$228$	814.736	0.236654
$229$	5957.88	1.71925	0.859624	−	0.510927i	$-0.170698\pi$
$229$	5957.88	1.71925	0.859624	+	0.510927i	$0.170698\pi$
$230$	4543.92	1.30268
$231$	604.110	0.172067
$232$	−1937.91	−0.548407
$233$	−1241.08	−0.348953	−0.174476	−	0.984661i	$-0.555823\pi$
$233$	−1241.08	−0.348953	−0.174476	+	0.984661i	$0.555823\pi$
$234$	2216.34	0.619174
$235$	−494.626	−0.137301
$236$	544.943	0.150308
$237$	−2448.03	−0.670957
$238$	−3479.56	−0.947674
$239$	1714.87	0.464123	0.232062	−	0.972701i	$-0.425453\pi$
$239$	1714.87	0.464123	0.232062	+	0.972701i	$0.425453\pi$
$240$	2623.36	0.705573
$241$	−4191.58	−1.12035	−0.560173	−	0.828376i	$-0.689265\pi$
$241$	−4191.58	−1.12035	−0.560173	+	0.828376i	$0.689265\pi$
$242$	−384.848	−0.102227
$243$	−243.000	−0.0641500
$244$	−129.074	−0.0338653
$245$	−90.0929	−0.0234932
$246$	611.875	0.158584
$247$	9937.47	2.55994
$248$	−4779.08	−1.22368
$249$	−746.968	−0.190109
$250$	4335.31	1.09676
$251$	2490.88	0.626386	0.313193	−	0.949690i	$-0.398601\pi$
$251$	2490.88	0.626386	0.313193	+	0.949690i	$0.398601\pi$
$252$	348.622	0.0871474
$253$	1373.92	0.341414
$254$	−6353.82	−1.56958
$255$	−2050.67	−0.503601
$256$	3042.81	0.742873
$257$	4187.65	1.01641	0.508207	−	0.861235i	$-0.330308\pi$
$257$	4187.65	1.01641	0.508207	+	0.861235i	$0.330308\pi$
$258$	−728.885	−0.175885
$259$	136.971	0.0328609
$260$	−1873.95	−0.446990
$261$	−931.963	−0.221023
$262$	−7009.78	−1.65292
$263$	−2559.50	−0.600097	−0.300048	−	0.953924i	$-0.597003\pi$
$263$	−2559.50	−0.600097	−0.300048	+	0.953924i	$0.597003\pi$
$264$	617.579	0.143975
$265$	2059.93	0.477512
$266$	7472.95	1.72254
$267$	−1146.93	−0.262887
$268$	1059.25	0.241432
$269$	3120.55	0.707298	0.353649	−	0.935378i	$-0.384941\pi$
$269$	3120.55	0.707298	0.353649	+	0.935378i	$0.384941\pi$
$270$	982.257	0.221401
$271$	7656.51	1.71623	0.858117	−	0.513454i	$-0.171634\pi$
$271$	7656.51	1.71623	0.858117	+	0.513454i	$0.171634\pi$
$272$	−4568.76	−1.01846
$273$	4252.20	0.942692
$274$	4147.78	0.914513
$275$	−64.1542	−0.0140678
$276$	792.868	0.172917
$277$	1204.49	0.261267	0.130633	−	0.991431i	$-0.458299\pi$
$277$	1204.49	0.261267	0.130633	+	0.991431i	$0.458299\pi$
$278$	2264.76	0.488602
$279$	−2298.31	−0.493177
$280$	3918.67	0.836375
$281$	−4251.72	−0.902620	−0.451310	−	0.892367i	$-0.649043\pi$
$281$	−4251.72	−0.902620	−0.451310	+	0.892367i	$0.649043\pi$
$282$	−412.615	−0.0871306
$283$	−2811.55	−0.590562	−0.295281	−	0.955410i	$-0.595413\pi$
$283$	−2811.55	−0.590562	−0.295281	+	0.955410i	$0.595413\pi$
$284$	2349.13	0.490829
$285$	4404.17	0.915370
$286$	−2708.86	−0.560064
$287$	1173.92	0.241444
$288$	840.953	0.172061
$289$	−1341.62	−0.273075
$290$	3767.19	0.762817
$291$	−890.627	−0.179414
$292$	−1176.00	−0.235685
$293$	−5125.07	−1.02188	−0.510938	−	0.859618i	$-0.670702\pi$
$293$	−5125.07	−1.02188	−0.510938	+	0.859618i	$0.670702\pi$
$294$	−75.1551	−0.0149086
$295$	2945.77	0.581387
$296$	140.025	0.0274959
$297$	297.000	0.0580259
$298$	4024.60	0.782344
$299$	9670.74	1.87048
$300$	−37.0223	−0.00712495
$301$	−1398.42	−0.267785
$302$	10454.3	1.99197
$303$	−2986.00	−0.566143
$304$	9812.18	1.85121
$305$	−697.730	−0.130990
$306$	−1710.66	−0.319582
$307$	4041.57	0.751350	0.375675	−	0.926752i	$-0.377411\pi$
$307$	4041.57	0.751350	0.375675	+	0.926752i	$0.377411\pi$
$308$	−426.094	−0.0788277
$309$	413.536	0.0761334
$310$	9290.25	1.70210
$311$	391.526	0.0713872	0.0356936	−	0.999363i	$-0.488636\pi$
$311$	391.526	0.0713872	0.0356936	+	0.999363i	$0.488636\pi$
$312$	4347.00	0.788784
$313$	333.912	0.0602997	0.0301499	−	0.999545i	$-0.490402\pi$
$313$	333.912	0.0602997	0.0301499	+	0.999545i	$0.490402\pi$
$314$	1198.31	0.215364
$315$	1884.53	0.337083
$316$	1726.66	0.307380
$317$	−835.393	−0.148014	−0.0740069	−	0.997258i	$-0.523579\pi$
$317$	−835.393	−0.148014	−0.0740069	+	0.997258i	$0.523579\pi$
$318$	1718.39	0.303026
$319$	1139.07	0.199923
$320$	3596.33	0.628253
$321$	163.426	0.0284160
$322$	7272.37	1.25861
$323$	−7670.15	−1.32130
$324$	171.394	0.0293885
$325$	−451.567	−0.0770722
$326$	−4454.89	−0.756851
$327$	−4094.89	−0.692502
$328$	1200.10	0.202025
$329$	−791.629	−0.132656
$330$	−1200.54	−0.200265
$331$	−11832.2	−1.96483	−0.982414	−	0.186718i	$-0.940215\pi$
$331$	−11832.2	−1.96483	−0.982414	+	0.186718i	$0.940215\pi$
$332$	526.854	0.0870931
$333$	67.3395	0.0110816
$334$	−8865.87	−1.45245
$335$	5725.91	0.933850
$336$	4198.59	0.681702
$337$	−631.323	−0.102049	−0.0510243	−	0.998697i	$-0.516249\pi$
$337$	−631.323	−0.102049	−0.0510243	+	0.998697i	$0.516249\pi$
$338$	−12079.4	−1.94388
$339$	5913.76	0.947467
$340$	1446.39	0.230710
$341$	2809.05	0.446095
$342$	3673.94	0.580888
$343$	−6423.28	−1.01115
$344$	−1429.59	−0.224065
$345$	4285.96	0.668836
$346$	−3211.01	−0.498916
$347$	1639.45	0.253631	0.126816	−	0.991926i	$-0.459524\pi$
$347$	1639.45	0.253631	0.126816	+	0.991926i	$0.459524\pi$
$348$	657.336	0.101255
$349$	−8444.61	−1.29521	−0.647607	−	0.761974i	$-0.724230\pi$
$349$	−8444.61	−1.29521	−0.647607	+	0.761974i	$0.724230\pi$
$350$	−339.577	−0.0518605
$351$	2090.52	0.317902
$352$	−1027.83	−0.155635
$353$	−1549.24	−0.233592	−0.116796	−	0.993156i	$-0.537262\pi$
$353$	−1549.24	−0.233592	−0.116796	+	0.993156i	$0.537262\pi$
$354$	2457.34	0.368945
$355$	12698.6	1.89851
$356$	808.955	0.120434
$357$	−3282.02	−0.486563
$358$	−9721.31	−1.43516
$359$	−2065.76	−0.303695	−0.151848	−	0.988404i	$-0.548522\pi$
$359$	−2065.76	−0.303695	−0.151848	+	0.988404i	$0.548522\pi$
$360$	1926.54	0.282049
$361$	9613.94	1.40165
$362$	−4585.09	−0.665710
$363$	−363.000	−0.0524864
$364$	−2999.18	−0.431868
$365$	−6357.02	−0.911621
$366$	−582.043	−0.0831253
$367$	4138.00	0.588561	0.294280	−	0.955719i	$-0.404920\pi$
$367$	4138.00	0.588561	0.294280	+	0.955719i	$0.404920\pi$
$368$	9548.82	1.35263
$369$	577.138	0.0814217
$370$	−272.200	−0.0382460
$371$	3296.84	0.461357
$372$	1621.05	0.225935
$373$	4013.61	0.557150	0.278575	−	0.960414i	$-0.410138\pi$
$373$	4013.61	0.557150	0.278575	+	0.960414i	$0.410138\pi$
$374$	2090.81	0.289073
$375$	4089.19	0.563107
$376$	−809.278	−0.110998
$377$	8017.63	1.09530
$378$	1572.06	0.213911
$379$	−3912.22	−0.530231	−0.265115	−	0.964217i	$-0.585410\pi$
$379$	−3912.22	−0.530231	−0.265115	+	0.964217i	$0.585410\pi$
$380$	−3106.37	−0.419351
$381$	−5993.11	−0.805870
$382$	−4008.46	−0.536887
$383$	1325.53	0.176844	0.0884222	−	0.996083i	$-0.471818\pi$
$383$	1325.53	0.176844	0.0884222	+	0.996083i	$0.471818\pi$
$384$	5242.58	0.696704
$385$	−2303.31	−0.304903
$386$	−9950.39	−1.31208
$387$	−687.506	−0.0903046
$388$	628.181	0.0821934
$389$	9357.22	1.21961	0.609807	−	0.792550i	$-0.291247\pi$
$389$	9357.22	1.21961	0.609807	+	0.792550i	$0.291247\pi$
$390$	−8450.31	−1.09717
$391$	−7464.28	−0.965434
$392$	−147.405	−0.0189925
$393$	−6611.83	−0.848658
$394$	−13020.8	−1.66493
$395$	9333.69	1.18893
$396$	−209.481	−0.0265829
$397$	2337.88	0.295554	0.147777	−	0.989021i	$-0.452788\pi$
$397$	2337.88	0.295554	0.147777	+	0.989021i	$0.452788\pi$
$398$	−6845.51	−0.862146
$399$	7048.70	0.884402
$400$	−445.874	−0.0557343
$401$	6365.73	0.792742	0.396371	−	0.918090i	$-0.370269\pi$
$401$	6365.73	0.792742	0.396371	+	0.918090i	$0.370269\pi$
$402$	4776.52	0.592615
$403$	19772.3	2.44399
$404$	2106.10	0.259362
$405$	926.493	0.113674
$406$	6029.24	0.737010
$407$	−82.3038	−0.0100237
$408$	−3355.20	−0.407125
$409$	6812.78	0.823644	0.411822	−	0.911264i	$-0.364893\pi$
$409$	6812.78	0.823644	0.411822	+	0.911264i	$0.364893\pi$
$410$	−2332.91	−0.281011
$411$	3912.31	0.469538
$412$	−291.677	−0.0348784
$413$	4714.58	0.561718
$414$	3575.33	0.424439
$415$	2847.99	0.336873
$416$	−7234.68	−0.852667
$417$	2136.19	0.250863
$418$	−4490.37	−0.525433
$419$	−11764.9	−1.37172	−0.685861	−	0.727733i	$-0.740574\pi$
$419$	−11764.9	−1.37172	−0.685861	+	0.727733i	$0.740574\pi$
$420$	−1329.20	−0.154425
$421$	4136.34	0.478843	0.239422	−	0.970916i	$-0.423042\pi$
$421$	4136.34	0.478843	0.239422	+	0.970916i	$0.423042\pi$
$422$	−6252.66	−0.721267
$423$	−389.190	−0.0447354
$424$	3370.34	0.386034
$425$	348.538	0.0397802
$426$	10593.1	1.20478
$427$	−1116.69	−0.126558
$428$	−115.268	−0.0130180
$429$	−2555.08	−0.287553
$430$	2779.04	0.311668
$431$	−873.612	−0.0976344	−0.0488172	−	0.998808i	$-0.515545\pi$
$431$	−873.612	−0.0976344	−0.0488172	+	0.998808i	$0.515545\pi$
$432$	2064.16	0.229889
$433$	−10929.8	−1.21306	−0.606529	−	0.795061i	$-0.707439\pi$
$433$	−10929.8	−1.21306	−0.606529	+	0.795061i	$0.707439\pi$
$434$	14868.7	1.64452
$435$	3553.32	0.391652
$436$	2888.23	0.317250
$437$	16030.8	1.75482
$438$	−5303.00	−0.578509
$439$	−6805.53	−0.739886	−0.369943	−	0.929054i	$-0.620623\pi$
$439$	−6805.53	−0.739886	−0.369943	+	0.929054i	$0.620623\pi$
$440$	−2354.66	−0.255123
$441$	−70.8885	−0.00765452
$442$	14716.8	1.58372
$443$	−1637.86	−0.175659	−0.0878294	−	0.996136i	$-0.527993\pi$
$443$	−1637.86	−0.175659	−0.0878294	+	0.996136i	$0.527993\pi$
$444$	−47.4962	−0.00507673
$445$	4372.92	0.465834
$446$	−6842.29	−0.726439
$447$	3796.12	0.401678
$448$	5755.79	0.606998
$449$	−14419.0	−1.51554	−0.757768	−	0.652524i	$-0.773710\pi$
$449$	−14419.0	−1.51554	−0.757768	+	0.652524i	$0.773710\pi$
$450$	−166.947	−0.0174888
$451$	−705.391	−0.0736487
$452$	−4171.12	−0.434055
$453$	9860.77	1.02274
$454$	5573.28	0.576139
$455$	−16212.5	−1.67045
$456$	7205.85	0.740011
$457$	16179.6	1.65613	0.828065	−	0.560632i	$-0.189442\pi$
$457$	16179.6	1.65613	0.828065	+	0.560632i	$0.189442\pi$
$458$	−18949.4	−1.93329
$459$	−1613.55	−0.164083
$460$	−3022.99	−0.306408
$461$	5314.68	0.536940	0.268470	−	0.963288i	$-0.413482\pi$
$461$	5314.68	0.536940	0.268470	+	0.963288i	$0.413482\pi$
$462$	−1921.41	−0.193489
$463$	15801.3	1.58607	0.793034	−	0.609178i	$-0.208500\pi$
$463$	15801.3	1.58607	0.793034	+	0.609178i	$0.208500\pi$
$464$	7916.55	0.792062
$465$	8762.84	0.873907
$466$	3947.34	0.392397
$467$	−3294.12	−0.326410	−0.163205	−	0.986592i	$-0.552183\pi$
$467$	−3294.12	−0.326410	−0.163205	+	0.986592i	$0.552183\pi$
$468$	−1474.49	−0.145638
$469$	9164.09	0.902257
$470$	1573.19	0.154395
$471$	1130.28	0.110574
$472$	4819.69	0.470009
$473$	840.285	0.0816836
$474$	7786.12	0.754490
$475$	−748.545	−0.0723066
$476$	2314.89	0.222905
$477$	1620.83	0.155582
$478$	−5454.24	−0.521906
$479$	6131.60	0.584885	0.292443	−	0.956283i	$-0.405532\pi$
$479$	6131.60	0.584885	0.292443	+	0.956283i	$0.405532\pi$
$480$	−3206.33	−0.304892
$481$	−579.318	−0.0549161
$482$	13331.6	1.25983
$483$	6859.51	0.646208
$484$	256.033	0.0240451
$485$	3395.72	0.317921
$486$	772.876	0.0721366
$487$	−896.272	−0.0833962	−0.0416981	−	0.999130i	$-0.513277\pi$
$487$	−896.272	−0.0833962	−0.0416981	+	0.999130i	$0.513277\pi$
$488$	−1141.59	−0.105896
$489$	−4201.98	−0.388590
$490$	286.546	0.0264180
$491$	1916.68	0.176168	0.0880838	−	0.996113i	$-0.471926\pi$
$491$	1916.68	0.176168	0.0880838	+	0.996113i	$0.471926\pi$
$492$	−407.070	−0.0373010
$493$	−6188.34	−0.565332
$494$	−31606.7	−2.87865
$495$	−1132.38	−0.102822
$496$	19523.0	1.76735
$497$	20323.6	1.83428
$498$	2375.78	0.213777
$499$	10294.5	0.923539	0.461770	−	0.887000i	$-0.347215\pi$
$499$	10294.5	0.923539	0.461770	+	0.887000i	$0.347215\pi$
$500$	−2884.21	−0.257971
$501$	−8362.55	−0.745731
$502$	−7922.39	−0.704370
$503$	−15077.0	−1.33649	−0.668243	−	0.743943i	$-0.732953\pi$
$503$	−15077.0	−1.33649	−0.668243	+	0.743943i	$0.732953\pi$
$504$	3083.35	0.272507
$505$	11384.8	1.00320
$506$	−4369.85	−0.383920
$507$	−11393.6	−0.998045
$508$	4227.09	0.369186
$509$	3145.39	0.273903	0.136952	−	0.990578i	$-0.456269\pi$
$509$	3145.39	0.273903	0.136952	+	0.990578i	$0.456269\pi$
$510$	6522.30	0.566298
$511$	−10174.2	−0.880780
$512$	4302.39	0.371368
$513$	3465.37	0.298245
$514$	−13319.1	−1.14296
$515$	−1576.70	−0.134908
$516$	484.914	0.0413705
$517$	475.677	0.0404647
$518$	−435.646	−0.0369521
$519$	−3028.72	−0.256158
$520$	−16573.9	−1.39772
$521$	−15180.9	−1.27656	−0.638281	−	0.769803i	$-0.720354\pi$
$521$	−15180.9	−1.27656	−0.638281	+	0.769803i	$0.720354\pi$
$522$	2964.17	0.248540
$523$	3142.94	0.262775	0.131387	−	0.991331i	$-0.458057\pi$
$523$	3142.94	0.262775	0.131387	+	0.991331i	$0.458057\pi$
$524$	4663.48	0.388789
$525$	−320.299	−0.0266267
$526$	8140.64	0.674808
$527$	−15261.0	−1.26145
$528$	−2522.86	−0.207942
$529$	3433.52	0.282200
$530$	−6551.74	−0.536961
$531$	2317.84	0.189427
$532$	−4971.62	−0.405164
$533$	−4965.09	−0.403494
$534$	3647.87	0.295616
$535$	−623.097	−0.0503530
$536$	9368.40	0.754950
$537$	−9169.42	−0.736853
$538$	−9925.09	−0.795355
$539$	86.6415	0.00692377
$540$	−653.478	−0.0520763
$541$	23052.8	1.83201	0.916005	−	0.401166i	$-0.131395\pi$
$541$	23052.8	1.83201	0.916005	+	0.401166i	$0.131395\pi$
$542$	−24352.0	−1.92990
$543$	−4324.80	−0.341795
$544$	5584.03	0.440098
$545$	15612.7	1.22711
$546$	−13524.4	−1.06006
$547$	−13096.3	−1.02369	−0.511844	−	0.859078i	$-0.671037\pi$
$547$	−13096.3	−1.02369	−0.511844	+	0.859078i	$0.671037\pi$
$548$	−2759.45	−0.215105
$549$	−549.000	−0.0426790
$550$	204.046	0.0158192
$551$	13290.5	1.02758
$552$	7012.44	0.540705
$553$	14938.2	1.14871
$554$	−3830.96	−0.293794
$555$	−256.747	−0.0196366
$556$	−1506.71	−0.114926
$557$	−25527.4	−1.94189	−0.970944	−	0.239306i	$-0.923080\pi$
$557$	−25527.4	−1.94189	−0.970944	+	0.239306i	$0.923080\pi$
$558$	7309.92	0.554576
$559$	5914.58	0.447514
$560$	−16008.1	−1.20797
$561$	1972.11	0.148418
$562$	13522.9	1.01499
$563$	−907.211	−0.0679119	−0.0339559	−	0.999423i	$-0.510811\pi$
$563$	−907.211	−0.0679119	−0.0339559	+	0.999423i	$0.510811\pi$
$564$	274.505	0.0204943
$565$	−22547.6	−1.67891
$566$	8942.29	0.664086
$567$	1482.82	0.109828
$568$	20776.7	1.53481
$569$	−19752.2	−1.45528	−0.727641	−	0.685958i	$-0.759383\pi$
$569$	−19752.2	−1.45528	−0.727641	+	0.685958i	$0.759383\pi$
$570$	−14007.7	−1.02933
$571$	6720.12	0.492519	0.246259	−	0.969204i	$-0.420798\pi$
$571$	6720.12	0.492519	0.246259	+	0.969204i	$0.420798\pi$
$572$	1802.16	0.131734
$573$	−3780.90	−0.275654
$574$	−3733.74	−0.271504
$575$	−728.454	−0.0528324
$576$	2829.73	0.204697
$577$	26008.4	1.87650	0.938252	−	0.345952i	$-0.112444\pi$
$577$	26008.4	1.87650	0.938252	+	0.345952i	$0.112444\pi$
$578$	4267.10	0.307073
$579$	−9385.50	−0.673658
$580$	−2506.24	−0.179424
$581$	4558.09	0.325476
$582$	2832.69	0.201751
$583$	−1981.02	−0.140730
$584$	−10401.0	−0.736980
$585$	−7970.58	−0.563321
$586$	16300.6	1.14910
$587$	8894.84	0.625434	0.312717	−	0.949846i	$-0.398761\pi$
$587$	8894.84	0.625434	0.312717	+	0.949846i	$0.398761\pi$
$588$	49.9994	0.00350670
$589$	32775.7	2.29287
$590$	−9369.19	−0.653769
$591$	−12281.6	−0.854822
$592$	−572.015	−0.0397123
$593$	2595.41	0.179731	0.0898657	−	0.995954i	$-0.471356\pi$
$593$	2595.41	0.179731	0.0898657	+	0.995954i	$0.471356\pi$
$594$	−944.627	−0.0652500
$595$	12513.5	0.862189
$596$	−2677.49	−0.184017
$597$	−6456.88	−0.442651
$598$	−30758.4	−2.10335
$599$	−18436.4	−1.25758	−0.628791	−	0.777574i	$-0.716450\pi$
$599$	−18436.4	−1.25758	−0.628791	+	0.777574i	$0.716450\pi$
$600$	−327.440	−0.0222795
$601$	4762.25	0.323222	0.161611	−	0.986855i	$-0.448331\pi$
$601$	4762.25	0.323222	0.161611	+	0.986855i	$0.448331\pi$
$602$	4447.75	0.301124
$603$	4505.36	0.304266
$604$	−6955.04	−0.468538
$605$	1384.02	0.0930057
$606$	9497.16	0.636627
$607$	12206.3	0.816206	0.408103	−	0.912936i	$-0.366190\pi$
$607$	12206.3	0.816206	0.408103	+	0.912936i	$0.366190\pi$
$608$	−11992.6	−0.799944
$609$	5686.95	0.378402
$610$	2219.17	0.147298
$611$	3348.19	0.221691
$612$	1138.07	0.0751698
$613$	−18425.8	−1.21405	−0.607023	−	0.794684i	$-0.707636\pi$
$613$	−18425.8	−1.21405	−0.607023	+	0.794684i	$0.707636\pi$
$614$	−12854.4	−0.844891
$615$	−2200.47	−0.144279
$616$	−3768.54	−0.246492
$617$	1219.88	0.0795956	0.0397978	−	0.999208i	$-0.487329\pi$
$617$	1219.88	0.0795956	0.0397978	+	0.999208i	$0.487329\pi$
$618$	−1315.28	−0.0856119
$619$	−9407.07	−0.610827	−0.305414	−	0.952220i	$-0.598795\pi$
$619$	−9407.07	−0.610827	−0.305414	+	0.952220i	$0.598795\pi$
$620$	−6180.64	−0.400356
$621$	3372.36	0.217919
$622$	−1245.27	−0.0802748
$623$	6998.69	0.450075
$624$	−17757.9	−1.13924
$625$	−16320.0	−1.04448
$626$	−1062.03	−0.0678070
$627$	−4235.45	−0.269773
$628$	−797.214	−0.0506565
$629$	447.142	0.0283445
$630$	−5993.85	−0.379049
$631$	−27165.3	−1.71384	−0.856922	−	0.515446i	$-0.827626\pi$
$631$	−27165.3	−1.71384	−0.856922	+	0.515446i	$0.827626\pi$
$632$	15271.2	0.961167
$633$	−5897.69	−0.370319
$634$	2657.02	0.166441
$635$	22850.1	1.42800
$636$	−1143.21	−0.0712757
$637$	609.851	0.0379327
$638$	−3622.87	−0.224813
$639$	9991.72	0.618570
$640$	−19988.6	−1.23456
$641$	10884.3	0.670675	0.335337	−	0.942098i	$-0.391150\pi$
$641$	10884.3	0.670675	0.335337	+	0.942098i	$0.391150\pi$
$642$	−519.785	−0.0319537
$643$	−14847.4	−0.910615	−0.455307	−	0.890334i	$-0.650471\pi$
$643$	−14847.4	−0.910615	−0.455307	+	0.890334i	$0.650471\pi$
$644$	−4838.18	−0.296042
$645$	2621.27	0.160019
$646$	24395.4	1.48579
$647$	3.89282	0.000236542 0	0.000118271	−	1.00000i	$-0.499962\pi$
$647$	3.89282	0.000236542 0	0.000118271		1.00000i	$0.499962\pi$
$648$	1515.88	0.0918969
$649$	−2832.92	−0.171343
$650$	1436.24	0.0866675
$651$	14024.6	0.844342
$652$	2963.76	0.178021
$653$	−22288.3	−1.33570	−0.667849	−	0.744297i	$-0.732785\pi$
$653$	−22288.3	−1.33570	−0.667849	+	0.744297i	$0.732785\pi$
$654$	13024.1	0.778717
$655$	25209.1	1.50382
$656$	−4902.50	−0.291784
$657$	−5001.95	−0.297024
$658$	2517.83	0.149172
$659$	26075.6	1.54137	0.770684	−	0.637217i	$-0.219915\pi$
$659$	26075.6	1.54137	0.770684	+	0.637217i	$0.219915\pi$
$660$	798.696	0.0471048
$661$	−15129.8	−0.890287	−0.445144	−	0.895459i	$-0.646847\pi$
$661$	−15129.8	−0.890287	−0.445144	+	0.895459i	$0.646847\pi$
$662$	37633.1	2.20944
$663$	13881.3	0.813129
$664$	4659.71	0.272337
$665$	−26874.8	−1.56716
$666$	−214.177	−0.0124613
$667$	12933.8	0.750822
$668$	5898.31	0.341635
$669$	−6453.85	−0.372975
$670$	−18211.6	−1.05011
$671$	671.000	0.0386046
$672$	−5131.60	−0.294577
$673$	5428.08	0.310902	0.155451	−	0.987844i	$-0.450317\pi$
$673$	5428.08	0.310902	0.155451	+	0.987844i	$0.450317\pi$
$674$	2007.96	0.114753
$675$	−157.469	−0.00897926
$676$	8036.20	0.457226
$677$	−15631.2	−0.887382	−0.443691	−	0.896180i	$-0.646331\pi$
$677$	−15631.2	−0.887382	−0.443691	+	0.896180i	$0.646331\pi$
$678$	−18809.1	−1.06543
$679$	5434.72	0.307165
$680$	12792.5	0.721424
$681$	5256.88	0.295806
$682$	−8934.34	−0.501633
$683$	16050.7	0.899214	0.449607	−	0.893226i	$-0.351564\pi$
$683$	16050.7	0.899214	0.449607	+	0.893226i	$0.351564\pi$
$684$	−2444.21	−0.136632
$685$	−14916.6	−0.832020
$686$	20429.6	1.13704
$687$	−17873.6	−0.992609
$688$	5840.01	0.323617
$689$	−13944.0	−0.771005
$690$	−13631.8	−0.752105
$691$	4038.44	0.222329	0.111165	−	0.993802i	$-0.464542\pi$
$691$	4038.44	0.222329	0.111165	+	0.993802i	$0.464542\pi$
$692$	2136.23	0.117352
$693$	−1812.33	−0.0993431
$694$	−5214.36	−0.285208
$695$	−8144.72	−0.444528
$696$	5813.74	0.316623
$697$	3832.26	0.208260
$698$	26858.6	1.45647
$699$	3723.25	0.201468
$700$	225.915	0.0121983
$701$	1029.43	0.0554653	0.0277327	−	0.999615i	$-0.491171\pi$
$701$	1029.43	0.0554653	0.0277327	+	0.999615i	$0.491171\pi$
$702$	−6649.02	−0.357480
$703$	−960.313	−0.0515205
$704$	−3458.56	−0.185155
$705$	1483.88	0.0792710
$706$	4927.46	0.262673
$707$	18221.0	0.969264
$708$	−1634.83	−0.0867806
$709$	−5812.48	−0.307887	−0.153944	−	0.988080i	$-0.549197\pi$
$709$	−5812.48	−0.307887	−0.153944	+	0.988080i	$0.549197\pi$
$710$	−40388.6	−2.13487
$711$	7344.10	0.387377
$712$	7154.72	0.376593
$713$	31896.0	1.67533
$714$	10438.7	0.547140
$715$	9741.82	0.509543
$716$	6467.42	0.337568
$717$	−5144.60	−0.267962
$718$	6570.28	0.341505
$719$	−14196.6	−0.736360	−0.368180	−	0.929755i	$-0.620019\pi$
$719$	−14196.6	−0.736360	−0.368180	+	0.929755i	$0.620019\pi$
$720$	−7870.09	−0.407363
$721$	−2523.45	−0.130344
$722$	−30577.7	−1.57616
$723$	12574.7	0.646832
$724$	3050.38	0.156584
$725$	−603.933	−0.0309372
$726$	1154.54	0.0590209
$727$	30992.0	1.58106	0.790529	−	0.612424i	$-0.209806\pi$
$727$	30992.0	1.58106	0.790529	+	0.612424i	$0.209806\pi$
$728$	−26526.0	−1.35044
$729$	729.000	0.0370370
$730$	20218.9	1.02512
$731$	−4565.12	−0.230981
$732$	387.223	0.0195522
$733$	−20543.0	−1.03516	−0.517580	−	0.855635i	$-0.673167\pi$
$733$	−20543.0	−1.03516	−0.517580	+	0.855635i	$0.673167\pi$
$734$	−13161.2	−0.661836
$735$	270.279	0.0135638
$736$	−11670.8	−0.584497
$737$	−5506.55	−0.275219
$738$	−1835.62	−0.0915586
$739$	−172.490	−0.00858613	−0.00429307	−	0.999991i	$-0.501367\pi$
$739$	−172.490	−0.00858613	−0.00429307	+	0.999991i	$0.501367\pi$
$740$	181.090	0.00899595
$741$	−29812.4	−1.47798
$742$	−10485.8	−0.518796
$743$	−32436.0	−1.60156	−0.800782	−	0.598956i	$-0.795582\pi$
$743$	−32436.0	−1.60156	−0.800782	+	0.598956i	$0.795582\pi$
$744$	14337.3	0.706491
$745$	−14473.6	−0.711773
$746$	−12765.5	−0.626514
$747$	2240.90	0.109760
$748$	−1390.98	−0.0679937
$749$	−997.243	−0.0486495
$750$	−13005.9	−0.633212
$751$	−36975.2	−1.79660	−0.898298	−	0.439387i	$-0.855196\pi$
$751$	−36975.2	−1.79660	−0.898298	+	0.439387i	$0.855196\pi$
$752$	3305.97	0.160314
$753$	−7472.63	−0.361644
$754$	−25500.6	−1.23167
$755$	−37596.5	−1.81229
$756$	−1045.87	−0.0503145
$757$	36825.9	1.76811	0.884056	−	0.467382i	$-0.154803\pi$
$757$	36825.9	1.76811	0.884056	+	0.467382i	$0.154803\pi$
$758$	12443.1	0.596243
$759$	−4121.77	−0.197116
$760$	−27474.0	−1.31130
$761$	−21563.9	−1.02719	−0.513594	−	0.858034i	$-0.671686\pi$
$761$	−21563.9	−1.02719	−0.513594	+	0.858034i	$0.671686\pi$
$762$	19061.5	0.906199
$763$	24987.5	1.18560
$764$	2666.76	0.126283
$765$	6152.02	0.290754
$766$	−4215.93	−0.198861
$767$	−19940.3	−0.938724
$768$	−9128.42	−0.428898
$769$	−9012.82	−0.422640	−0.211320	−	0.977417i	$-0.567776\pi$
$769$	−9012.82	−0.422640	−0.211320	+	0.977417i	$0.567776\pi$
$770$	7325.82	0.342863
$771$	−12563.0	−0.586827
$772$	6619.82	0.308617
$773$	18464.3	0.859142	0.429571	−	0.903033i	$-0.358665\pi$
$773$	18464.3	0.859142	0.429571	+	0.903033i	$0.358665\pi$
$774$	2186.65	0.101547
$775$	−1489.36	−0.0690313
$776$	5555.88	0.257016
$777$	−410.914	−0.0189723
$778$	−29761.2	−1.37145
$779$	−8230.44	−0.378544
$780$	5621.84	0.258070
$781$	−12212.1	−0.559518
$782$	23740.6	1.08563
$783$	2795.89	0.127608
$784$	602.162	0.0274308
$785$	−4309.45	−0.195938
$786$	21029.3	0.954315
$787$	25763.8	1.16694	0.583469	−	0.812135i	$-0.301695\pi$
$787$	25763.8	1.16694	0.583469	+	0.812135i	$0.301695\pi$
$788$	8662.55	0.391612
$789$	7678.50	0.346466
$790$	−29686.4	−1.33695
$791$	−36086.5	−1.62211
$792$	−1852.74	−0.0831239
$793$	4723.02	0.211500
$794$	−7435.77	−0.332350
$795$	−6179.80	−0.275692
$796$	4554.20	0.202788
$797$	−7079.54	−0.314642	−0.157321	−	0.987547i	$-0.550286\pi$
$797$	−7079.54	−0.314642	−0.157321	+	0.987547i	$0.550286\pi$
$798$	−22418.8	−0.994509
$799$	−2584.27	−0.114424
$800$	544.957	0.0240839
$801$	3440.78	0.151778
$802$	−20246.6	−0.891437
$803$	6113.49	0.268668
$804$	−3177.74	−0.139391
$805$	−26153.5	−1.14508
$806$	−62886.9	−2.74826
$807$	−9361.64	−0.408359
$808$	18627.2	0.811018
$809$	19606.5	0.852074	0.426037	−	0.904706i	$-0.359909\pi$
$809$	19606.5	0.852074	0.426037	+	0.904706i	$0.359909\pi$
$810$	−2946.77	−0.127826
$811$	43998.3	1.90504	0.952520	−	0.304475i	$-0.0984809\pi$
$811$	43998.3	1.90504	0.952520	+	0.304475i	$0.0984809\pi$
$812$	−4011.15	−0.173354
$813$	−22969.5	−0.990869
$814$	261.772	0.0112716
$815$	16021.0	0.688580
$816$	13706.3	0.588009
$817$	9804.36	0.419842
$818$	−21668.5	−0.926186
$819$	−12756.6	−0.544264
$820$	1552.05	0.0660973
$821$	−14618.2	−0.621411	−0.310706	−	0.950506i	$-0.600565\pi$
$821$	−14618.2	−0.621411	−0.310706	+	0.950506i	$0.600565\pi$
$822$	−12443.3	−0.527995
$823$	−5468.89	−0.231632	−0.115816	−	0.993271i	$-0.536948\pi$
$823$	−5468.89	−0.231632	−0.115816	+	0.993271i	$0.536948\pi$
$824$	−2579.71	−0.109064
$825$	192.463	0.00812205
$826$	−14995.0	−0.631651
$827$	8377.56	0.352257	0.176128	−	0.984367i	$-0.443643\pi$
$827$	8377.56	0.352257	0.176128	+	0.984367i	$0.443643\pi$
$828$	−2378.60	−0.0998336
$829$	22436.3	0.939982	0.469991	−	0.882671i	$-0.344257\pi$
$829$	22436.3	0.939982	0.469991	+	0.882671i	$0.344257\pi$
$830$	−9058.20	−0.378813
$831$	−3613.47	−0.150842
$832$	−24344.0	−1.01440
$833$	−470.708	−0.0195787
$834$	−6794.29	−0.282095
$835$	31884.1	1.32143
$836$	2987.37	0.123589
$837$	6894.93	0.284736
$838$	37418.9	1.54250
$839$	4864.32	0.200161	0.100081	−	0.994979i	$-0.468090\pi$
$839$	4864.32	0.200161	0.100081	+	0.994979i	$0.468090\pi$
$840$	−11756.0	−0.482882
$841$	−13666.1	−0.560339
$842$	−13155.9	−0.538458
$843$	12755.2	0.521128
$844$	4159.78	0.169651
$845$	43440.8	1.76853
$846$	1237.84	0.0503049
$847$	2215.07	0.0898592
$848$	−13768.2	−0.557548
$849$	8434.64	0.340961
$850$	−1108.55	−0.0447328
$851$	−934.538	−0.0376446
$852$	−7047.40	−0.283380
$853$	−4030.92	−0.161801	−0.0809005	−	0.996722i	$-0.525780\pi$
$853$	−4030.92	−0.161801	−0.0809005	+	0.996722i	$0.525780\pi$
$854$	3551.70	0.142315
$855$	−13212.5	−0.528489
$856$	−1019.48	−0.0407068
$857$	−12268.0	−0.488994	−0.244497	−	0.969650i	$-0.578623\pi$
$857$	−12268.0	−0.488994	−0.244497	+	0.969650i	$0.578623\pi$
$858$	8126.58	0.323353
$859$	−2228.42	−0.0885131	−0.0442565	−	0.999020i	$-0.514092\pi$
$859$	−2228.42	−0.0885131	−0.0442565	+	0.999020i	$0.514092\pi$
$860$	−1848.85	−0.0733083
$861$	−3521.77	−0.139398
$862$	2778.58	0.109790
$863$	6219.80	0.245336	0.122668	−	0.992448i	$-0.460855\pi$
$863$	6219.80	0.245336	0.122668	+	0.992448i	$0.460855\pi$
$864$	−2522.86	−0.0993396
$865$	11547.7	0.453911
$866$	34763.0	1.36408
$867$	4024.85	0.157660
$868$	−9891.88	−0.386811
$869$	−8976.12	−0.350396
$870$	−11301.6	−0.440412
$871$	−38759.4	−1.50782
$872$	25544.6	0.992030
$873$	2671.88	0.103585
$874$	−50986.9	−1.97329
$875$	−24952.8	−0.964066
$876$	3527.99	0.136073
$877$	6797.32	0.261721	0.130860	−	0.991401i	$-0.458226\pi$
$877$	6797.32	0.261721	0.130860	+	0.991401i	$0.458226\pi$
$878$	21645.4	0.832001
$879$	15375.2	0.589980
$880$	9619.00	0.368473
$881$	34483.2	1.31869	0.659346	−	0.751840i	$-0.270833\pi$
$881$	34483.2	1.31869	0.659346	+	0.751840i	$0.270833\pi$
$882$	225.465	0.00860749
$883$	45407.7	1.73057	0.865284	−	0.501283i	$-0.167138\pi$
$883$	45407.7	1.73057	0.865284	+	0.501283i	$0.167138\pi$
$884$	−9790.80	−0.372512
$885$	−8837.30	−0.335664
$886$	5209.30	0.197528
$887$	−43333.7	−1.64036	−0.820182	−	0.572102i	$-0.806128\pi$
$887$	−43333.7	−1.64036	−0.820182	+	0.572102i	$0.806128\pi$
$888$	−420.075	−0.0158748
$889$	36570.7	1.37969
$890$	−13908.3	−0.523830
$891$	−891.000	−0.0335013
$892$	4552.06	0.170868
$893$	5550.15	0.207983
$894$	−12073.8	−0.451687
$895$	34960.5	1.30570
$896$	−31990.9	−1.19279
$897$	−29012.2	−1.07992
$898$	45860.6	1.70422
$899$	26443.7	0.981031
$900$	111.067	0.00411359
$901$	10762.5	0.397948
$902$	2243.54	0.0828179
$903$	4195.25	0.154606
$904$	−36891.1	−1.35728
$905$	16489.3	0.605660
$906$	−31362.8	−1.15007
$907$	−17376.4	−0.636136	−0.318068	−	0.948068i	$-0.603034\pi$
$907$	−17376.4	−0.636136	−0.318068	+	0.948068i	$0.603034\pi$
$908$	−3707.81	−0.135515
$909$	8958.01	0.326863
$910$	51564.8	1.87842
$911$	−28177.3	−1.02476	−0.512379	−	0.858759i	$-0.671236\pi$
$911$	−28177.3	−1.02476	−0.512379	+	0.858759i	$0.671236\pi$
$912$	−29436.5	−1.06880
$913$	−2738.88	−0.0992812
$914$	−51460.3	−1.86232
$915$	2093.19	0.0756270
$916$	12606.7	0.454735
$917$	40346.2	1.45294
$918$	5131.99	0.184511
$919$	−36646.1	−1.31539	−0.657695	−	0.753285i	$-0.728468\pi$
$919$	−36646.1	−1.31539	−0.657695	+	0.753285i	$0.728468\pi$
$920$	−26736.6	−0.958128
$921$	−12124.7	−0.433792
$922$	−16903.7	−0.603788
$923$	−85958.3	−3.06539
$924$	1278.28	0.0455112
$925$	43.6375	0.00155113
$926$	−50257.1	−1.78353
$927$	−1240.61	−0.0439557
$928$	−9675.77	−0.342266
$929$	11822.8	0.417538	0.208769	−	0.977965i	$-0.433054\pi$
$929$	11822.8	0.417538	0.208769	+	0.977965i	$0.433054\pi$
$930$	−27870.7	−0.982707
$931$	1010.92	0.0355872
$932$	−2626.10	−0.0922969
$933$	−1174.58	−0.0412154
$934$	10477.1	0.367048
$935$	−7519.14	−0.262997
$936$	−13041.0	−0.455405
$937$	7571.31	0.263974	0.131987	−	0.991251i	$-0.457864\pi$
$937$	7571.31	0.263974	0.131987	+	0.991251i	$0.457864\pi$
$938$	−29147.0	−1.01459
$939$	−1001.74	−0.0348141
$940$	−1046.61	−0.0363158
$941$	34777.4	1.20479	0.602396	−	0.798197i	$-0.294213\pi$
$941$	34777.4	1.20479	0.602396	+	0.798197i	$0.294213\pi$
$942$	−3594.92	−0.124341
$943$	−8009.53	−0.276592
$944$	−19688.9	−0.678833
$945$	−5653.58	−0.194615
$946$	−2672.58	−0.0918530
$947$	−8104.07	−0.278085	−0.139043	−	0.990286i	$-0.544403\pi$
$947$	−8104.07	−0.278085	−0.139043	+	0.990286i	$0.544403\pi$
$948$	−5179.97	−0.177466
$949$	43031.5	1.47193
$950$	2380.79	0.0813086
$951$	2506.18	0.0854558
$952$	20473.8	0.697017
$953$	−41220.9	−1.40113	−0.700565	−	0.713588i	$-0.747069\pi$
$953$	−41220.9	−1.40113	−0.700565	+	0.713588i	$0.747069\pi$
$954$	−5155.16	−0.174952
$955$	14415.6	0.488457
$956$	3628.61	0.122759
$957$	−3417.20	−0.115426
$958$	−19501.9	−0.657702
$959$	−23873.4	−0.803872
$960$	−10789.0	−0.362722
$961$	35421.7	1.18901
$962$	1842.56	0.0617531
$963$	−490.277	−0.0164060
$964$	−8869.26	−0.296327
$965$	35784.4	1.19372
$966$	−21817.1	−0.726660
$967$	26009.6	0.864957	0.432478	−	0.901644i	$-0.357639\pi$
$967$	26009.6	0.864957	0.432478	+	0.901644i	$0.357639\pi$
$968$	2264.46	0.0751884
$969$	23010.4	0.762850
$970$	−10800.3	−0.357502
$971$	42703.8	1.41136	0.705679	−	0.708531i	$-0.250642\pi$
$971$	42703.8	1.41136	0.705679	+	0.708531i	$0.250642\pi$
$972$	−514.181	−0.0169675
$973$	−13035.3	−0.429489
$974$	2850.65	0.0937789
$975$	1354.70	0.0444976
$976$	4663.48	0.152945
$977$	48598.5	1.59141	0.795703	−	0.605687i	$-0.207101\pi$
$977$	48598.5	1.59141	0.795703	+	0.605687i	$0.207101\pi$
$978$	13364.7	0.436968
$979$	−4205.39	−0.137288
$980$	−190.634	−0.00621386
$981$	12284.7	0.399816
$982$	−6096.10	−0.198100
$983$	43607.4	1.41491	0.707457	−	0.706756i	$-0.249842\pi$
$983$	43607.4	1.41491	0.707457	+	0.706756i	$0.249842\pi$
$984$	−3600.29	−0.116639
$985$	46826.6	1.51474
$986$	19682.4	0.635715
$987$	2374.89	0.0765892
$988$	21027.4	0.677096
$989$	9541.21	0.306767
$990$	3601.61	0.115623
$991$	−49491.8	−1.58644	−0.793218	−	0.608938i	$-0.791596\pi$
$991$	−49491.8	−1.58644	−0.793218	+	0.608938i	$0.791596\pi$
$992$	−23861.4	−0.763709
$993$	35496.7	1.13439
$994$	−64640.4	−2.06264
$995$	24618.4	0.784376
$996$	−1580.56	−0.0502832
$997$	−61075.4	−1.94010	−0.970049	−	0.242908i	$-0.921899\pi$
$997$	−61075.4	−1.94010	−0.970049	+	0.242908i	$0.921899\pi$
$998$	−32742.4	−1.03852
$999$	−202.018	−0.00639798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.e.1.9	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.e.1.9	✓	38	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-3.18056 q^{2} -3.00000 q^{3} +2.11597 q^{4} +11.4382 q^{5} +9.54169 q^{6} +18.3064 q^{7} +18.7145 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.18056 q^{2} -3.00000 q^{3} +2.11597 q^{4} +11.4382 q^{5} +9.54169 q^{6} +18.3064 q^{7} +18.7145 q^{8} +9.00000 q^{9} -36.3799 q^{10} -11.0000 q^{11} -6.34792 q^{12} -77.4266 q^{13} -58.2246 q^{14} -34.3146 q^{15} -76.4504 q^{16} +59.7610 q^{17} -28.6251 q^{18} -128.347 q^{19} +24.2029 q^{20} -54.9191 q^{21} +34.9862 q^{22} -124.902 q^{23} -56.1435 q^{24} +5.83220 q^{25} +246.260 q^{26} -27.0000 q^{27} +38.7358 q^{28} -103.551 q^{29} +109.140 q^{30} -255.368 q^{31} +93.4392 q^{32} +33.0000 q^{33} -190.074 q^{34} +209.392 q^{35} +19.0438 q^{36} +7.48216 q^{37} +408.215 q^{38} +232.280 q^{39} +214.060 q^{40} +64.1265 q^{41} +174.674 q^{42} -76.3895 q^{43} -23.2757 q^{44} +102.944 q^{45} +397.259 q^{46} -43.2434 q^{47} +229.351 q^{48} -7.87650 q^{49} -18.5497 q^{50} -179.283 q^{51} -163.833 q^{52} +180.093 q^{53} +85.8752 q^{54} -125.820 q^{55} +342.595 q^{56} +385.041 q^{57} +329.352 q^{58} +257.538 q^{59} -72.6087 q^{60} -61.0000 q^{61} +812.213 q^{62} +164.757 q^{63} +314.414 q^{64} -885.620 q^{65} -104.959 q^{66} +500.595 q^{67} +126.453 q^{68} +374.706 q^{69} -665.984 q^{70} +1110.19 q^{71} +168.431 q^{72} -555.772 q^{73} -23.7975 q^{74} -17.4966 q^{75} -271.579 q^{76} -201.370 q^{77} -738.780 q^{78} +816.011 q^{79} -874.455 q^{80} +81.0000 q^{81} -203.958 q^{82} +248.989 q^{83} -116.207 q^{84} +683.558 q^{85} +242.962 q^{86} +310.654 q^{87} -205.860 q^{88} +382.309 q^{89} -327.419 q^{90} -1417.40 q^{91} -264.289 q^{92} +766.104 q^{93} +137.538 q^{94} -1468.06 q^{95} -280.318 q^{96} +296.876 q^{97} +25.0517 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9} + 95 q^{10} - 418 q^{11} - 426 q^{12} + 13 q^{13} + 26 q^{14} - 45 q^{15} + 486 q^{16} - 224 q^{17} - 18 q^{18} + 367 q^{19} + 18 q^{20} - 189 q^{21} + 22 q^{22} + 51 q^{23} + 135 q^{24} + 773 q^{25} - 439 q^{26} - 1026 q^{27} + 22 q^{28} - 462 q^{29} - 285 q^{30} + 234 q^{31} - 597 q^{32} + 1254 q^{33} + 956 q^{34} - 522 q^{35} + 1278 q^{36} + 954 q^{37} + 705 q^{38} - 39 q^{39} + 1495 q^{40} - 740 q^{41} - 78 q^{42} + 1441 q^{43} - 1562 q^{44} + 135 q^{45} + 581 q^{46} + 1003 q^{47} - 1458 q^{48} + 2707 q^{49} + 388 q^{50} + 672 q^{51} + 788 q^{52} + 735 q^{53} + 54 q^{54} - 165 q^{55} + 1059 q^{56} - 1101 q^{57} + 177 q^{58} + 261 q^{59} - 54 q^{60} - 2318 q^{61} + 1251 q^{62} + 567 q^{63} + 5571 q^{64} - 1354 q^{65} - 66 q^{66} + 3495 q^{67} - 1856 q^{68} - 153 q^{69} + 542 q^{70} - 873 q^{71} - 405 q^{72} + 989 q^{73} - 3406 q^{74} - 2319 q^{75} + 1712 q^{76} - 693 q^{77} + 1317 q^{78} + 2313 q^{79} + 1593 q^{80} + 3078 q^{81} + 5170 q^{82} + 569 q^{83} - 66 q^{84} - 1271 q^{85} + 3065 q^{86} + 1386 q^{87} + 495 q^{88} - 2917 q^{89} + 855 q^{90} + 2740 q^{91} + 1083 q^{92} - 702 q^{93} + 3272 q^{94} + 2696 q^{95} + 1791 q^{96} + 4250 q^{97} + 5952 q^{98} - 3762 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 - 114 * q^3 + 142 * q^4 + 15 * q^5 + 6 * q^6 + 63 * q^7 - 45 * q^8 + 342 * q^9 + 95 * q^10 - 418 * q^11 - 426 * q^12 + 13 * q^13 + 26 * q^14 - 45 * q^15 + 486 * q^16 - 224 * q^17 - 18 * q^18 + 367 * q^19 + 18 * q^20 - 189 * q^21 + 22 * q^22 + 51 * q^23 + 135 * q^24 + 773 * q^25 - 439 * q^26 - 1026 * q^27 + 22 * q^28 - 462 * q^29 - 285 * q^30 + 234 * q^31 - 597 * q^32 + 1254 * q^33 + 956 * q^34 - 522 * q^35 + 1278 * q^36 + 954 * q^37 + 705 * q^38 - 39 * q^39 + 1495 * q^40 - 740 * q^41 - 78 * q^42 + 1441 * q^43 - 1562 * q^44 + 135 * q^45 + 581 * q^46 + 1003 * q^47 - 1458 * q^48 + 2707 * q^49 + 388 * q^50 + 672 * q^51 + 788 * q^52 + 735 * q^53 + 54 * q^54 - 165 * q^55 + 1059 * q^56 - 1101 * q^57 + 177 * q^58 + 261 * q^59 - 54 * q^60 - 2318 * q^61 + 1251 * q^62 + 567 * q^63 + 5571 * q^64 - 1354 * q^65 - 66 * q^66 + 3495 * q^67 - 1856 * q^68 - 153 * q^69 + 542 * q^70 - 873 * q^71 - 405 * q^72 + 989 * q^73 - 3406 * q^74 - 2319 * q^75 + 1712 * q^76 - 693 * q^77 + 1317 * q^78 + 2313 * q^79 + 1593 * q^80 + 3078 * q^81 + 5170 * q^82 + 569 * q^83 - 66 * q^84 - 1271 * q^85 + 3065 * q^86 + 1386 * q^87 + 495 * q^88 - 2917 * q^89 + 855 * q^90 + 2740 * q^91 + 1083 * q^92 - 702 * q^93 + 3272 * q^94 + 2696 * q^95 + 1791 * q^96 + 4250 * q^97 + 5952 * q^98 - 3762 * q^99

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