LMFDB - Embedded newform 2013.4.a.e.1.2

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			1.2
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)

$f(q)$	$=$	$q-5.27624 q^{2} -3.00000 q^{3} +19.8387 q^{4} -1.30000 q^{5} +15.8287 q^{6} +18.3929 q^{7} -62.4637 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.27624 q^{2} -3.00000 q^{3} +19.8387 q^{4} -1.30000 q^{5} +15.8287 q^{6} +18.3929 q^{7} -62.4637 q^{8} +9.00000 q^{9} +6.85913 q^{10} -11.0000 q^{11} -59.5161 q^{12} -9.87284 q^{13} -97.0455 q^{14} +3.90001 q^{15} +170.864 q^{16} -113.404 q^{17} -47.4861 q^{18} +80.8987 q^{19} -25.7904 q^{20} -55.1788 q^{21} +58.0386 q^{22} -68.3990 q^{23} +187.391 q^{24} -123.310 q^{25} +52.0915 q^{26} -27.0000 q^{27} +364.892 q^{28} -271.577 q^{29} -20.5774 q^{30} -240.813 q^{31} -401.809 q^{32} +33.0000 q^{33} +598.349 q^{34} -23.9109 q^{35} +178.548 q^{36} -70.0256 q^{37} -426.841 q^{38} +29.6185 q^{39} +81.2031 q^{40} -322.691 q^{41} +291.137 q^{42} +153.115 q^{43} -218.226 q^{44} -11.7000 q^{45} +360.889 q^{46} -243.451 q^{47} -512.592 q^{48} -4.69982 q^{49} +650.613 q^{50} +340.213 q^{51} -195.864 q^{52} +531.213 q^{53} +142.458 q^{54} +14.3000 q^{55} -1148.89 q^{56} -242.696 q^{57} +1432.91 q^{58} -316.535 q^{59} +77.3711 q^{60} -61.0000 q^{61} +1270.58 q^{62} +165.536 q^{63} +753.129 q^{64} +12.8347 q^{65} -174.116 q^{66} -830.910 q^{67} -2249.80 q^{68} +205.197 q^{69} +126.160 q^{70} +1133.44 q^{71} -562.174 q^{72} +650.603 q^{73} +369.472 q^{74} +369.930 q^{75} +1604.92 q^{76} -202.322 q^{77} -156.274 q^{78} -534.098 q^{79} -222.124 q^{80} +81.0000 q^{81} +1702.59 q^{82} +745.929 q^{83} -1094.68 q^{84} +147.426 q^{85} -807.872 q^{86} +814.731 q^{87} +687.101 q^{88} +767.251 q^{89} +61.7321 q^{90} -181.591 q^{91} -1356.95 q^{92} +722.438 q^{93} +1284.51 q^{94} -105.169 q^{95} +1205.43 q^{96} +1175.54 q^{97} +24.7974 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.27624	−1.86543	−0.932716	−	0.360612i	$-0.882568\pi$
$2$	−5.27624	−1.86543	−0.932716	+	0.360612i	$0.882568\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	19.8387	2.47984
$5$	−1.30000	−0.116276	−0.0581379	−	0.998309i	$-0.518516\pi$
$5$	−1.30000	−0.116276	−0.0581379	+	0.998309i	$0.518516\pi$
$6$	15.8287	1.07701
$7$	18.3929	0.993125	0.496563	−	0.868001i	$-0.334595\pi$
$7$	18.3929	0.993125	0.496563	+	0.868001i	$0.334595\pi$
$8$	−62.4637	−2.76053
$9$	9.00000	0.333333
$10$	6.85913	0.216905
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−59.5161	−1.43173
$13$	−9.87284	−0.210633	−0.105317	−	0.994439i	$-0.533586\pi$
$13$	−9.87284	−0.210633	−0.105317	+	0.994439i	$0.533586\pi$
$14$	−97.0455	−1.85261
$15$	3.90001	0.0671319
$16$	170.864	2.66975
$17$	−113.404	−1.61792	−0.808960	−	0.587864i	$-0.799969\pi$
$17$	−113.404	−1.61792	−0.808960	+	0.587864i	$0.799969\pi$
$18$	−47.4861	−0.621811
$19$	80.8987	0.976813	0.488406	−	0.872616i	$-0.337578\pi$
$19$	80.8987	0.976813	0.488406	+	0.872616i	$0.337578\pi$
$20$	−25.7904	−0.288345
$21$	−55.1788	−0.573381
$22$	58.0386	0.562449
$23$	−68.3990	−0.620094	−0.310047	−	0.950721i	$-0.600345\pi$
$23$	−68.3990	−0.620094	−0.310047	+	0.950721i	$0.600345\pi$
$24$	187.391	1.59379
$25$	−123.310	−0.986480
$26$	52.0915	0.392922
$27$	−27.0000	−0.192450
$28$	364.892	2.46279
$29$	−271.577	−1.73899	−0.869493	−	0.493945i	$-0.835554\pi$
$29$	−271.577	−1.73899	−0.869493	+	0.493945i	$0.835554\pi$
$30$	−20.5774	−0.125230
$31$	−240.813	−1.39520	−0.697600	−	0.716487i	$-0.745749\pi$
$31$	−240.813	−1.39520	−0.697600	+	0.716487i	$0.745749\pi$
$32$	−401.809	−2.21970
$33$	33.0000	0.174078
$34$	598.349	3.01812
$35$	−23.9109	−0.115476
$36$	178.548	0.826612
$37$	−70.0256	−0.311139	−0.155569	−	0.987825i	$-0.549721\pi$
$37$	−70.0256	−0.311139	−0.155569	+	0.987825i	$0.549721\pi$
$38$	−426.841	−1.82218
$39$	29.6185	0.121609
$40$	81.2031	0.320983
$41$	−322.691	−1.22917	−0.614583	−	0.788852i	$-0.710676\pi$
$41$	−322.691	−1.22917	−0.614583	+	0.788852i	$0.710676\pi$
$42$	291.137	1.06960
$43$	153.115	0.543020	0.271510	−	0.962436i	$-0.412477\pi$
$43$	153.115	0.543020	0.271510	+	0.962436i	$0.412477\pi$
$44$	−218.226	−0.747699
$45$	−11.7000	−0.0387586
$46$	360.889	1.15674
$47$	−243.451	−0.755554	−0.377777	−	0.925897i	$-0.623311\pi$
$47$	−243.451	−0.755554	−0.377777	+	0.925897i	$0.623311\pi$
$48$	−512.592	−1.54138
$49$	−4.69982	−0.0137021
$50$	650.613	1.84021
$51$	340.213	0.934106
$52$	−195.864	−0.522336
$53$	531.213	1.37675	0.688375	−	0.725355i	$-0.258324\pi$
$53$	531.213	1.37675	0.688375	+	0.725355i	$0.258324\pi$
$54$	142.458	0.359003
$55$	14.3000	0.0350585
$56$	−1148.89	−2.74156
$57$	−242.696	−0.563963
$58$	1432.91	3.24396
$59$	−316.535	−0.698464	−0.349232	−	0.937036i	$-0.613557\pi$
$59$	−316.535	−0.698464	−0.349232	+	0.937036i	$0.613557\pi$
$60$	77.3711	0.166476
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	1270.58	2.60265
$63$	165.536	0.331042
$64$	753.129	1.47096
$65$	12.8347	0.0244916
$66$	−174.116	−0.324730
$67$	−830.910	−1.51510	−0.757551	−	0.652776i	$-0.773604\pi$
$67$	−830.910	−1.51510	−0.757551	+	0.652776i	$0.773604\pi$
$68$	−2249.80	−4.01217
$69$	205.197	0.358012
$70$	126.160	0.215414
$71$	1133.44	1.89457	0.947283	−	0.320398i	$-0.103817\pi$
$71$	1133.44	1.89457	0.947283	+	0.320398i	$0.103817\pi$
$72$	−562.174	−0.920178
$73$	650.603	1.04311	0.521557	−	0.853216i	$-0.325351\pi$
$73$	650.603	1.04311	0.521557	+	0.853216i	$0.325351\pi$
$74$	369.472	0.580408
$75$	369.930	0.569544
$76$	1604.92	2.42233
$77$	−202.322	−0.299439
$78$	−156.274	−0.226854
$79$	−534.098	−0.760642	−0.380321	−	0.924855i	$-0.624186\pi$
$79$	−534.098	−0.760642	−0.380321	+	0.924855i	$0.624186\pi$
$80$	−222.124	−0.310427
$81$	81.0000	0.111111
$82$	1702.59	2.29293
$83$	745.929	0.986463	0.493231	−	0.869898i	$-0.335816\pi$
$83$	745.929	0.986463	0.493231	+	0.869898i	$0.335816\pi$
$84$	−1094.68	−1.42189
$85$	147.426	0.188125
$86$	−807.872	−1.01297
$87$	814.731	1.00400
$88$	687.101	0.832332
$89$	767.251	0.913803	0.456902	−	0.889517i	$-0.348959\pi$
$89$	767.251	0.913803	0.456902	+	0.889517i	$0.348959\pi$
$90$	61.7321	0.0723016
$91$	−181.591	−0.209185
$92$	−1356.95	−1.53773
$93$	722.438	0.805519
$94$	1284.51	1.40943
$95$	−105.169	−0.113580
$96$	1205.43	1.28155
$97$	1175.54	1.23050	0.615249	−	0.788333i	$-0.289056\pi$
$97$	1175.54	1.23050	0.615249	+	0.788333i	$0.289056\pi$
$98$	24.7974	0.0255603
$99$	−99.0000	−0.100504
$100$	−2446.31	−2.44631
$101$	1425.70	1.40458	0.702289	−	0.711892i	$-0.252162\pi$
$101$	1425.70	1.40458	0.702289	+	0.711892i	$0.252162\pi$
$102$	−1795.05	−1.74251
$103$	426.980	0.408462	0.204231	−	0.978923i	$-0.434531\pi$
$103$	426.980	0.408462	0.204231	+	0.978923i	$0.434531\pi$
$104$	616.695	0.581460
$105$	71.7326	0.0666704
$106$	−2802.81	−2.56823
$107$	−1653.67	−1.49408	−0.747041	−	0.664778i	$-0.768526\pi$
$107$	−1653.67	−1.49408	−0.747041	+	0.664778i	$0.768526\pi$
$108$	−535.645	−0.477245
$109$	−461.881	−0.405873	−0.202937	−	0.979192i	$-0.565049\pi$
$109$	−461.881	−0.405873	−0.202937	+	0.979192i	$0.565049\pi$
$110$	−75.4504	−0.0653992
$111$	210.077	0.179636
$112$	3142.69	2.65140
$113$	651.788	0.542611	0.271305	−	0.962493i	$-0.412545\pi$
$113$	651.788	0.542611	0.271305	+	0.962493i	$0.412545\pi$
$114$	1280.52	1.05203
$115$	88.9189	0.0721020
$116$	−5387.73	−4.31240
$117$	−88.8556	−0.0702111
$118$	1670.12	1.30294
$119$	−2085.84	−1.60680
$120$	−243.609	−0.185320
$121$	121.000	0.0909091
$122$	321.851	0.238844
$123$	968.072	0.709660
$124$	−4777.40	−3.45987
$125$	322.804	0.230980
$126$	−873.410	−0.617536
$127$	1256.77	0.878112	0.439056	−	0.898460i	$-0.355313\pi$
$127$	1256.77	0.878112	0.439056	+	0.898460i	$0.355313\pi$
$128$	−759.215	−0.524264
$129$	−459.346	−0.313513
$130$	−67.7191	−0.0456874
$131$	−2451.86	−1.63527	−0.817635	−	0.575737i	$-0.804715\pi$
$131$	−2451.86	−1.63527	−0.817635	+	0.575737i	$0.804715\pi$
$132$	654.677	0.431684
$133$	1487.97	0.970097
$134$	4384.08	2.82632
$135$	35.1001	0.0223773
$136$	7083.67	4.46632
$137$	−867.185	−0.540793	−0.270397	−	0.962749i	$-0.587155\pi$
$137$	−867.185	−0.540793	−0.270397	+	0.962749i	$0.587155\pi$
$138$	−1082.67	−0.667846
$139$	−2446.64	−1.49296	−0.746478	−	0.665410i	$-0.768257\pi$
$139$	−2446.64	−1.49296	−0.746478	+	0.665410i	$0.768257\pi$
$140$	−474.361	−0.286363
$141$	730.354	0.436219
$142$	−5980.28	−3.53418
$143$	108.601	0.0635084
$144$	1537.78	0.889917
$145$	353.051	0.202202
$146$	−3432.74	−1.94586
$147$	14.0995	0.00791091
$148$	−1389.22	−0.771573
$149$	−1253.87	−0.689403	−0.344701	−	0.938712i	$-0.612020\pi$
$149$	−1253.87	−0.689403	−0.344701	+	0.938712i	$0.612020\pi$
$150$	−1951.84	−1.06245
$151$	1388.35	0.748227	0.374114	−	0.927383i	$-0.377947\pi$
$151$	1388.35	0.748227	0.374114	+	0.927383i	$0.377947\pi$
$152$	−5053.24	−2.69652
$153$	−1020.64	−0.539306
$154$	1067.50	0.558582
$155$	313.057	0.162228
$156$	587.593	0.301571
$157$	3262.96	1.65868	0.829339	−	0.558745i	$-0.188717\pi$
$157$	3262.96	1.65868	0.829339	+	0.558745i	$0.188717\pi$
$158$	2818.03	1.41893
$159$	−1593.64	−0.794867
$160$	522.353	0.258098
$161$	−1258.06	−0.615831
$162$	−427.375	−0.207270
$163$	632.232	0.303805	0.151902	−	0.988395i	$-0.451460\pi$
$163$	632.232	0.303805	0.151902	+	0.988395i	$0.451460\pi$
$164$	−6401.76	−3.04813
$165$	−42.9001	−0.0202410
$166$	−3935.70	−1.84018
$167$	−232.663	−0.107808	−0.0539041	−	0.998546i	$-0.517167\pi$
$167$	−232.663	−0.107808	−0.0539041	+	0.998546i	$0.517167\pi$
$168$	3446.67	1.58284
$169$	−2099.53	−0.955634
$170$	−777.856	−0.350934
$171$	728.089	0.325604
$172$	3037.60	1.34660
$173$	2341.22	1.02890	0.514449	−	0.857521i	$-0.327996\pi$
$173$	2341.22	1.02890	0.514449	+	0.857521i	$0.327996\pi$
$174$	−4298.72	−1.87290
$175$	−2268.03	−0.979698
$176$	−1879.50	−0.804960
$177$	949.606	0.403258
$178$	−4048.20	−1.70464
$179$	−2314.25	−0.966342	−0.483171	−	0.875526i	$-0.660515\pi$
$179$	−2314.25	−0.966342	−0.483171	+	0.875526i	$0.660515\pi$
$180$	−232.113	−0.0961150
$181$	3451.54	1.41741	0.708704	−	0.705506i	$-0.249280\pi$
$181$	3451.54	1.41741	0.708704	+	0.705506i	$0.249280\pi$
$182$	958.115	0.390221
$183$	183.000	0.0739221
$184$	4272.45	1.71179
$185$	91.0335	0.0361779
$186$	−3811.75	−1.50264
$187$	1247.45	0.487821
$188$	−4829.75	−1.87365
$189$	−496.609	−0.191127
$190$	554.895	0.211875
$191$	2475.27	0.937717	0.468858	−	0.883273i	$-0.344665\pi$
$191$	2475.27	0.937717	0.468858	+	0.883273i	$0.344665\pi$
$192$	−2259.39	−0.849257
$193$	3577.24	1.33417	0.667086	−	0.744981i	$-0.267541\pi$
$193$	3577.24	1.33417	0.667086	+	0.744981i	$0.267541\pi$
$194$	−6202.44	−2.29541
$195$	−38.5042	−0.0141402
$196$	−93.2383	−0.0339790
$197$	−2229.03	−0.806151	−0.403075	−	0.915167i	$-0.632059\pi$
$197$	−2229.03	−0.806151	−0.403075	+	0.915167i	$0.632059\pi$
$198$	522.348	0.187483
$199$	−547.298	−0.194959	−0.0974797	−	0.995238i	$-0.531078\pi$
$199$	−547.298	−0.194959	−0.0974797	+	0.995238i	$0.531078\pi$
$200$	7702.40	2.72321
$201$	2492.73	0.874744
$202$	−7522.33	−2.62014
$203$	−4995.10	−1.72703
$204$	6749.39	2.31643
$205$	419.499	0.142922
$206$	−2252.85	−0.761958
$207$	−615.591	−0.206698
$208$	−1686.91	−0.562339
$209$	−889.886	−0.294520
$210$	−378.479	−0.124369
$211$	−588.315	−0.191949	−0.0959746	−	0.995384i	$-0.530597\pi$
$211$	−588.315	−0.191949	−0.0959746	+	0.995384i	$0.530597\pi$
$212$	10538.6	3.41411
$213$	−3400.31	−1.09383
$214$	8725.18	2.78711
$215$	−199.050	−0.0631401
$216$	1686.52	0.531265
$217$	−4429.25	−1.38561
$218$	2436.99	0.757129
$219$	−1951.81	−0.602242
$220$	283.694	0.0869393
$221$	1119.62	0.340788
$222$	−1108.42	−0.335099
$223$	−5618.35	−1.68714	−0.843570	−	0.537019i	$-0.819550\pi$
$223$	−5618.35	−1.68714	−0.843570	+	0.537019i	$0.819550\pi$
$224$	−7390.45	−2.20444
$225$	−1109.79	−0.328827
$226$	−3438.99	−1.01220
$227$	−4226.47	−1.23577	−0.617886	−	0.786268i	$-0.712011\pi$
$227$	−4226.47	−1.23577	−0.617886	+	0.786268i	$0.712011\pi$
$228$	−4814.77	−1.39854
$229$	−5134.67	−1.48170	−0.740848	−	0.671673i	$-0.765576\pi$
$229$	−5134.67	−1.48170	−0.740848	+	0.671673i	$0.765576\pi$
$230$	−469.157	−0.134501
$231$	606.967	0.172881
$232$	16963.7	4.80053
$233$	1363.93	0.383495	0.191748	−	0.981444i	$-0.438585\pi$
$233$	1363.93	0.383495	0.191748	+	0.981444i	$0.438585\pi$
$234$	468.823	0.130974
$235$	316.488	0.0878526
$236$	−6279.64	−1.73208
$237$	1602.29	0.439157
$238$	11005.4	2.99737
$239$	4896.44	1.32521	0.662604	−	0.748970i	$-0.269451\pi$
$239$	4896.44	1.32521	0.662604	+	0.748970i	$0.269451\pi$
$240$	666.371	0.179225
$241$	−5198.60	−1.38951	−0.694753	−	0.719248i	$-0.744486\pi$
$241$	−5198.60	−1.38951	−0.694753	+	0.719248i	$0.744486\pi$
$242$	−638.425	−0.169585
$243$	−243.000	−0.0641500
$244$	−1210.16	−0.317510
$245$	6.10979	0.00159322
$246$	−5107.78	−1.32382
$247$	−798.701	−0.205749
$248$	15042.0	3.85150
$249$	−2237.79	−0.569534
$250$	−1703.19	−0.430877
$251$	6848.66	1.72224	0.861122	−	0.508398i	$-0.169762\pi$
$251$	6848.66	1.72224	0.861122	+	0.508398i	$0.169762\pi$
$252$	3284.03	0.820929
$253$	752.389	0.186966
$254$	−6631.02	−1.63806
$255$	−442.279	−0.108614
$256$	−2019.23	−0.492977
$257$	174.086	0.0422535	0.0211268	−	0.999777i	$-0.493275\pi$
$257$	174.086	0.0422535	0.0211268	+	0.999777i	$0.493275\pi$
$258$	2423.62	0.584836
$259$	−1287.98	−0.309000
$260$	254.624	0.0607351
$261$	−2444.19	−0.579662
$262$	12936.6	3.05048
$263$	288.309	0.0675965	0.0337982	−	0.999429i	$-0.489240\pi$
$263$	288.309	0.0675965	0.0337982	+	0.999429i	$0.489240\pi$
$264$	−2061.30	−0.480547
$265$	−690.579	−0.160083
$266$	−7850.86	−1.80965
$267$	−2301.75	−0.527584
$268$	−16484.2	−3.75720
$269$	−4188.65	−0.949392	−0.474696	−	0.880150i	$-0.657442\pi$
$269$	−4188.65	−0.949392	−0.474696	+	0.880150i	$0.657442\pi$
$270$	−185.196	−0.0417433
$271$	−7496.66	−1.68040	−0.840202	−	0.542274i	$-0.817564\pi$
$271$	−7496.66	−1.68040	−0.840202	+	0.542274i	$0.817564\pi$
$272$	−19376.7	−4.31944
$273$	544.772	0.120773
$274$	4575.48	1.00881
$275$	1356.41	0.297435
$276$	4070.84	0.887810
$277$	6513.07	1.41275	0.706376	−	0.707837i	$-0.250329\pi$
$277$	6513.07	1.41275	0.706376	+	0.707837i	$0.250329\pi$
$278$	12909.0	2.78501
$279$	−2167.31	−0.465067
$280$	1493.56	0.318777
$281$	3129.40	0.664357	0.332179	−	0.943217i	$-0.392216\pi$
$281$	3129.40	0.664357	0.332179	+	0.943217i	$0.392216\pi$
$282$	−3853.52	−0.813737
$283$	7496.75	1.57468	0.787342	−	0.616517i	$-0.211457\pi$
$283$	7496.75	1.57468	0.787342	+	0.616517i	$0.211457\pi$
$284$	22485.9	4.69821
$285$	315.506	0.0655753
$286$	−573.006	−0.118471
$287$	−5935.23	−1.22072
$288$	−3616.28	−0.739901
$289$	7947.58	1.61766
$290$	−1862.78	−0.377194
$291$	−3526.63	−0.710428
$292$	12907.1	2.58675
$293$	−1681.95	−0.335359	−0.167680	−	0.985842i	$-0.553627\pi$
$293$	−1681.95	−0.335359	−0.167680	+	0.985842i	$0.553627\pi$
$294$	−74.3921	−0.0147573
$295$	411.497	0.0812145
$296$	4374.06	0.858909
$297$	297.000	0.0580259
$298$	6615.71	1.28603
$299$	675.292	0.130613
$300$	7338.92	1.41238
$301$	2816.24	0.539287
$302$	−7325.27	−1.39577
$303$	−4277.10	−0.810933
$304$	13822.7	2.60785
$305$	79.3002	0.0148876
$306$	5385.14	1.00604
$307$	−2846.81	−0.529237	−0.264619	−	0.964353i	$-0.585246\pi$
$307$	−2846.81	−0.529237	−0.264619	+	0.964353i	$0.585246\pi$
$308$	−4013.81	−0.742558
$309$	−1280.94	−0.235826
$310$	−1651.76	−0.302625
$311$	2815.58	0.513366	0.256683	−	0.966496i	$-0.417370\pi$
$311$	2815.58	0.513366	0.256683	+	0.966496i	$0.417370\pi$
$312$	−1850.08	−0.335706
$313$	4762.81	0.860096	0.430048	−	0.902806i	$-0.358497\pi$
$313$	4762.81	0.860096	0.430048	+	0.902806i	$0.358497\pi$
$314$	−17216.2	−3.09415
$315$	−215.198	−0.0384922
$316$	−10595.8	−1.88627
$317$	2249.44	0.398553	0.199276	−	0.979943i	$-0.436141\pi$
$317$	2249.44	0.398553	0.199276	+	0.979943i	$0.436141\pi$
$318$	8408.42	1.48277
$319$	2987.35	0.524324
$320$	−979.071	−0.171037
$321$	4961.02	0.862609
$322$	6637.81	1.14879
$323$	−9174.28	−1.58040
$324$	1606.93	0.275537
$325$	1217.42	0.207786
$326$	−3335.80	−0.566727
$327$	1385.64	0.234331
$328$	20156.5	3.39316
$329$	−4477.78	−0.750359
$330$	226.351	0.0377583
$331$	8367.36	1.38946	0.694730	−	0.719270i	$-0.255524\pi$
$331$	8367.36	1.38946	0.694730	+	0.719270i	$0.255524\pi$
$332$	14798.3	2.44627
$333$	−630.230	−0.103713
$334$	1227.58	0.201109
$335$	1080.19	0.176170
$336$	−9428.07	−1.53078
$337$	1077.14	0.174112	0.0870558	−	0.996203i	$-0.472254\pi$
$337$	1077.14	0.174112	0.0870558	+	0.996203i	$0.472254\pi$
$338$	11077.6	1.78267
$339$	−1955.36	−0.313276
$340$	2924.74	0.466519
$341$	2648.94	0.420669
$342$	−3841.57	−0.607392
$343$	−6395.22	−1.00673
$344$	−9564.15	−1.49902
$345$	−266.757	−0.0416281
$346$	−12352.8	−1.91934
$347$	866.688	0.134081	0.0670407	−	0.997750i	$-0.478644\pi$
$347$	866.688	0.134081	0.0670407	+	0.997750i	$0.478644\pi$
$348$	16163.2	2.48977
$349$	1320.86	0.202591	0.101295	−	0.994856i	$-0.467701\pi$
$349$	1320.86	0.202591	0.101295	+	0.994856i	$0.467701\pi$
$350$	11966.7	1.82756
$351$	266.567	0.0405364
$352$	4419.90	0.669266
$353$	−4338.63	−0.654169	−0.327085	−	0.944995i	$-0.606066\pi$
$353$	−4338.63	−0.654169	−0.327085	+	0.944995i	$0.606066\pi$
$354$	−5010.35	−0.752251
$355$	−1473.47	−0.220292
$356$	15221.3	2.26608
$357$	6257.53	0.927685
$358$	12210.5	1.80264
$359$	3959.37	0.582083	0.291041	−	0.956710i	$-0.405998\pi$
$359$	3959.37	0.582083	0.291041	+	0.956710i	$0.405998\pi$
$360$	730.828	0.106994
$361$	−314.397	−0.0458371
$362$	−18211.1	−2.64408
$363$	−363.000	−0.0524864
$364$	−3602.52	−0.518745
$365$	−845.786	−0.121289
$366$	−965.552	−0.137897
$367$	6561.63	0.933282	0.466641	−	0.884447i	$-0.345464\pi$
$367$	6561.63	0.933282	0.466641	+	0.884447i	$0.345464\pi$
$368$	−11686.9	−1.65550
$369$	−2904.22	−0.409722
$370$	−480.315	−0.0674875
$371$	9770.57	1.36729
$372$	14332.2	1.99756
$373$	−11597.7	−1.60994	−0.804968	−	0.593318i	$-0.797818\pi$
$373$	−11597.7	−1.60994	−0.804968	+	0.593318i	$0.797818\pi$
$374$	−6581.84	−0.909997
$375$	−968.412	−0.133356
$376$	15206.9	2.08573
$377$	2681.24	0.366289
$378$	2620.23	0.356534
$379$	5995.96	0.812643	0.406321	−	0.913730i	$-0.366811\pi$
$379$	5995.96	0.812643	0.406321	+	0.913730i	$0.366811\pi$
$380$	−2086.41	−0.281659
$381$	−3770.31	−0.506978
$382$	−13060.1	−1.74925
$383$	4471.07	0.596504	0.298252	−	0.954487i	$-0.403596\pi$
$383$	4471.07	0.596504	0.298252	+	0.954487i	$0.403596\pi$
$384$	2277.65	0.302684
$385$	263.020	0.0348175
$386$	−18874.4	−2.48881
$387$	1378.04	0.181007
$388$	23321.2	3.05143
$389$	9150.06	1.19261	0.596306	−	0.802757i	$-0.296634\pi$
$389$	9150.06	1.19261	0.596306	+	0.802757i	$0.296634\pi$
$390$	203.157	0.0263776
$391$	7756.75	1.00326
$392$	293.568	0.0378251
$393$	7355.59	0.944124
$394$	11760.9	1.50382
$395$	694.329	0.0884443
$396$	−1964.03	−0.249233
$397$	11281.3	1.42618	0.713088	−	0.701074i	$-0.247296\pi$
$397$	11281.3	1.42618	0.713088	+	0.701074i	$0.247296\pi$
$398$	2887.67	0.363683
$399$	−4463.90	−0.560086
$400$	−21069.2	−2.63365
$401$	−8573.23	−1.06765	−0.533824	−	0.845596i	$-0.679245\pi$
$401$	−8573.23	−1.06765	−0.533824	+	0.845596i	$0.679245\pi$
$402$	−13152.2	−1.63178
$403$	2377.50	0.293876
$404$	28284.0	3.48312
$405$	−105.300	−0.0129195
$406$	26355.3	3.22166
$407$	770.282	0.0938119
$408$	−21251.0	−2.57863
$409$	9498.54	1.14834	0.574172	−	0.818735i	$-0.305324\pi$
$409$	9498.54	1.14834	0.574172	+	0.818735i	$0.305324\pi$
$410$	−2213.38	−0.266612
$411$	2601.56	0.312227
$412$	8470.72	1.01292
$413$	−5822.01	−0.693662
$414$	3248.00	0.385581
$415$	−969.711	−0.114702
$416$	3967.00	0.467544
$417$	7339.91	0.861959
$418$	4695.25	0.549407
$419$	−7892.88	−0.920269	−0.460134	−	0.887849i	$-0.652199\pi$
$419$	−7892.88	−0.920269	−0.460134	+	0.887849i	$0.652199\pi$
$420$	1423.08	0.165332
$421$	−8707.73	−1.00805	−0.504025	−	0.863689i	$-0.668148\pi$
$421$	−8707.73	−1.00805	−0.504025	+	0.863689i	$0.668148\pi$
$422$	3104.09	0.358068
$423$	−2191.06	−0.251851
$424$	−33181.6	−3.80056
$425$	13983.9	1.59605
$426$	17940.8	2.04046
$427$	−1121.97	−0.127157
$428$	−32806.7	−3.70508
$429$	−325.804	−0.0366666
$430$	1050.24	0.117784
$431$	3569.00	0.398870	0.199435	−	0.979911i	$-0.436089\pi$
$431$	3569.00	0.398870	0.199435	+	0.979911i	$0.436089\pi$
$432$	−4613.33	−0.513794
$433$	13836.6	1.53566	0.767832	−	0.640651i	$-0.221335\pi$
$433$	13836.6	1.53566	0.767832	+	0.640651i	$0.221335\pi$
$434$	23369.8	2.58476
$435$	−1059.15	−0.116741
$436$	−9163.11	−1.00650
$437$	−5533.39	−0.605716
$438$	10298.2	1.12344
$439$	6406.60	0.696515	0.348258	−	0.937399i	$-0.386773\pi$
$439$	6406.60	0.696515	0.348258	+	0.937399i	$0.386773\pi$
$440$	−893.234	−0.0967801
$441$	−42.2984	−0.00456737
$442$	−5907.41	−0.635717
$443$	7849.49	0.841853	0.420926	−	0.907095i	$-0.361705\pi$
$443$	7849.49	0.841853	0.420926	+	0.907095i	$0.361705\pi$
$444$	4167.65	0.445468
$445$	−997.429	−0.106253
$446$	29643.7	3.14724
$447$	3761.61	0.398027
$448$	13852.3	1.46084
$449$	1189.62	0.125037	0.0625183	−	0.998044i	$-0.480087\pi$
$449$	1189.62	0.125037	0.0625183	+	0.998044i	$0.480087\pi$
$450$	5855.52	0.613404
$451$	3549.60	0.370608
$452$	12930.6	1.34559
$453$	−4165.05	−0.431989
$454$	22299.8	2.30525
$455$	236.068	0.0243232
$456$	15159.7	1.55684
$457$	15229.3	1.55886	0.779430	−	0.626490i	$-0.215509\pi$
$457$	15229.3	1.55886	0.779430	+	0.626490i	$0.215509\pi$
$458$	27091.7	2.76400
$459$	3061.92	0.311369
$460$	1764.03	0.178801
$461$	−6037.18	−0.609934	−0.304967	−	0.952363i	$-0.598645\pi$
$461$	−6037.18	−0.609934	−0.304967	+	0.952363i	$0.598645\pi$
$462$	−3202.50	−0.322498
$463$	9312.59	0.934757	0.467379	−	0.884057i	$-0.345198\pi$
$463$	9312.59	0.934757	0.467379	+	0.884057i	$0.345198\pi$
$464$	−46402.8	−4.64266
$465$	−939.171	−0.0936624
$466$	−7196.44	−0.715384
$467$	−11040.0	−1.09394	−0.546968	−	0.837153i	$-0.684218\pi$
$467$	−11040.0	−1.09394	−0.546968	+	0.837153i	$0.684218\pi$
$468$	−1762.78	−0.174112
$469$	−15282.9	−1.50469
$470$	−1669.86	−0.163883
$471$	−9788.88	−0.957639
$472$	19772.0	1.92813
$473$	−1684.27	−0.163727
$474$	−8454.08	−0.819217
$475$	−9975.62	−0.963606
$476$	−41380.4	−3.98459
$477$	4780.92	0.458917
$478$	−25834.8	−2.47208
$479$	13330.6	1.27159	0.635795	−	0.771858i	$-0.280672\pi$
$479$	13330.6	1.27159	0.635795	+	0.771858i	$0.280672\pi$
$480$	−1567.06	−0.149013
$481$	691.352	0.0655362
$482$	27429.0	2.59203
$483$	3774.17	0.355550
$484$	2400.48	0.225440
$485$	−1528.21	−0.143077
$486$	1282.13	0.119668
$487$	−4211.49	−0.391870	−0.195935	−	0.980617i	$-0.562774\pi$
$487$	−4211.49	−0.391870	−0.195935	+	0.980617i	$0.562774\pi$
$488$	3810.29	0.353450
$489$	−1896.70	−0.175402
$490$	−32.2367	−0.00297205
$491$	15919.7	1.46323	0.731614	−	0.681719i	$-0.238767\pi$
$491$	15919.7	1.46323	0.731614	+	0.681719i	$0.238767\pi$
$492$	19205.3	1.75984
$493$	30798.1	2.81354
$494$	4214.13	0.383811
$495$	128.700	0.0116862
$496$	−41146.2	−3.72484
$497$	20847.2	1.88154
$498$	11807.1	1.06243
$499$	7928.78	0.711305	0.355652	−	0.934618i	$-0.384259\pi$
$499$	7928.78	0.711305	0.355652	+	0.934618i	$0.384259\pi$
$500$	6404.00	0.572792
$501$	697.988	0.0622431
$502$	−36135.1	−3.21273
$503$	−10252.0	−0.908773	−0.454386	−	0.890805i	$-0.650141\pi$
$503$	−10252.0	−0.908773	−0.454386	+	0.890805i	$0.650141\pi$
$504$	−10340.0	−0.913852
$505$	−1853.41	−0.163318
$506$	−3969.78	−0.348771
$507$	6298.58	0.551735
$508$	24932.7	2.17757
$509$	9736.38	0.847854	0.423927	−	0.905696i	$-0.360651\pi$
$509$	9736.38	0.847854	0.423927	+	0.905696i	$0.360651\pi$
$510$	2333.57	0.202612
$511$	11966.5	1.03594
$512$	16727.7	1.44388
$513$	−2184.27	−0.187988
$514$	−918.517	−0.0788211
$515$	−555.075	−0.0474942
$516$	−9112.81	−0.777460
$517$	2677.96	0.227808
$518$	6795.67	0.576418
$519$	−7023.65	−0.594035
$520$	−801.705	−0.0676098
$521$	13133.3	1.10438	0.552189	−	0.833719i	$-0.313793\pi$
$521$	13133.3	1.10438	0.552189	+	0.833719i	$0.313793\pi$
$522$	12896.1	1.08132
$523$	−22184.5	−1.85480	−0.927398	−	0.374076i	$-0.877960\pi$
$523$	−22184.5	−1.85480	−0.927398	+	0.374076i	$0.877960\pi$
$524$	−48641.8	−4.05520
$525$	6804.10	0.565629
$526$	−1521.19	−0.126097
$527$	27309.2	2.25732
$528$	5638.51	0.464744
$529$	−7488.58	−0.615483
$530$	3643.66	0.298624
$531$	−2848.82	−0.232821
$532$	29519.3	2.40568
$533$	3185.88	0.258904
$534$	12144.6	0.984173
$535$	2149.78	0.173726
$536$	51901.7	4.18249
$537$	6942.75	0.557918
$538$	22100.3	1.77103
$539$	51.6980	0.00413134
$540$	696.340	0.0554920
$541$	−18323.0	−1.45614	−0.728068	−	0.685505i	$-0.759581\pi$
$541$	−18323.0	−1.45614	−0.728068	+	0.685505i	$0.759581\pi$
$542$	39554.1	3.13468
$543$	−10354.6	−0.818341
$544$	45567.0	3.59130
$545$	600.447	0.0471932
$546$	−2874.35	−0.225294
$547$	3770.92	0.294758	0.147379	−	0.989080i	$-0.452916\pi$
$547$	3770.92	0.294758	0.147379	+	0.989080i	$0.452916\pi$
$548$	−17203.8	−1.34108
$549$	−549.000	−0.0426790
$550$	−7156.74	−0.554845
$551$	−21970.2	−1.69866
$552$	−12817.4	−0.988303
$553$	−9823.63	−0.755413
$554$	−34364.5	−2.63539
$555$	−273.101	−0.0208873
$556$	−48538.1	−3.70229
$557$	−16191.3	−1.23168	−0.615840	−	0.787871i	$-0.711183\pi$
$557$	−16191.3	−1.23168	−0.615840	+	0.787871i	$0.711183\pi$
$558$	11435.3	0.867550
$559$	−1511.68	−0.114378
$560$	−4085.51	−0.308293
$561$	−3742.35	−0.281644
$562$	−16511.5	−1.23931
$563$	6129.44	0.458836	0.229418	−	0.973328i	$-0.426318\pi$
$563$	6129.44	0.458836	0.229418	+	0.973328i	$0.426318\pi$
$564$	14489.3	1.08175
$565$	−847.326	−0.0630925
$566$	−39554.6	−2.93746
$567$	1489.83	0.110347
$568$	−70798.7	−5.23001
$569$	−2132.72	−0.157132	−0.0785661	−	0.996909i	$-0.525034\pi$
$569$	−2132.72	−0.157132	−0.0785661	+	0.996909i	$0.525034\pi$
$570$	−1664.68	−0.122326
$571$	−22249.6	−1.63067	−0.815337	−	0.578986i	$-0.803448\pi$
$571$	−22249.6	−1.63067	−0.815337	+	0.578986i	$0.803448\pi$
$572$	2154.51	0.157490
$573$	−7425.80	−0.541391
$574$	31315.7	2.27716
$575$	8434.28	0.611711
$576$	6778.16	0.490319
$577$	−20417.7	−1.47314	−0.736568	−	0.676363i	$-0.763555\pi$
$577$	−20417.7	−1.47314	−0.736568	+	0.676363i	$0.763555\pi$
$578$	−41933.3	−3.01764
$579$	−10731.7	−0.770284
$580$	7004.07	0.501428
$581$	13719.8	0.979681
$582$	18607.3	1.32525
$583$	−5843.35	−0.415106
$584$	−40639.1	−2.87955
$585$	115.513	0.00816386
$586$	8874.34	0.625590
$587$	13298.1	0.935045	0.467522	−	0.883981i	$-0.345147\pi$
$587$	13298.1	0.935045	0.467522	+	0.883981i	$0.345147\pi$
$588$	279.715	0.0196178
$589$	−19481.4	−1.36285
$590$	−2171.16	−0.151500
$591$	6687.09	0.465431
$592$	−11964.9	−0.830663
$593$	−13637.3	−0.944379	−0.472190	−	0.881497i	$-0.656536\pi$
$593$	−13637.3	−0.944379	−0.472190	+	0.881497i	$0.656536\pi$
$594$	−1567.04	−0.108243
$595$	2711.60	0.186832
$596$	−24875.1	−1.70961
$597$	1641.89	0.112560
$598$	−3563.00	−0.243649
$599$	−24456.8	−1.66824	−0.834122	−	0.551580i	$-0.814025\pi$
$599$	−24456.8	−1.66824	−0.834122	+	0.551580i	$0.814025\pi$
$600$	−23107.2	−1.57225
$601$	−24889.8	−1.68931	−0.844657	−	0.535308i	$-0.820195\pi$
$601$	−24889.8	−1.68931	−0.844657	+	0.535308i	$0.820195\pi$
$602$	−14859.1	−1.00600
$603$	−7478.19	−0.505034
$604$	27543.0	1.85548
$605$	−157.300	−0.0105705
$606$	22567.0	1.51274
$607$	−2802.55	−0.187400	−0.0937002	−	0.995600i	$-0.529870\pi$
$607$	−2802.55	−0.187400	−0.0937002	+	0.995600i	$0.529870\pi$
$608$	−32505.9	−2.16823
$609$	14985.3	0.997102
$610$	−418.407	−0.0277718
$611$	2403.56	0.159145
$612$	−20248.2	−1.33739
$613$	−8469.76	−0.558059	−0.279030	−	0.960282i	$-0.590013\pi$
$613$	−8469.76	−0.558059	−0.279030	+	0.960282i	$0.590013\pi$
$614$	15020.4	0.987256
$615$	−1258.50	−0.0825163
$616$	12637.8	0.826610
$617$	922.574	0.0601968	0.0300984	−	0.999547i	$-0.490418\pi$
$617$	922.574	0.0601968	0.0300984	+	0.999547i	$0.490418\pi$
$618$	6758.54	0.439917
$619$	27061.9	1.75721	0.878603	−	0.477554i	$-0.158476\pi$
$619$	27061.9	1.75721	0.878603	+	0.477554i	$0.158476\pi$
$620$	6210.64	0.402299
$621$	1846.77	0.119337
$622$	−14855.7	−0.957650
$623$	14112.0	0.907521
$624$	5060.74	0.324666
$625$	14994.1	0.959623
$626$	−25129.7	−1.60445
$627$	2669.66	0.170041
$628$	64732.8	4.11325
$629$	7941.22	0.503398
$630$	1135.44	0.0718045
$631$	27795.7	1.75361	0.876806	−	0.480845i	$-0.159670\pi$
$631$	27795.7	1.75361	0.876806	+	0.480845i	$0.159670\pi$
$632$	33361.7	2.09978
$633$	1764.95	0.110822
$634$	−11868.6	−0.743473
$635$	−1633.81	−0.102103
$636$	−31615.7	−1.97114
$637$	46.4006	0.00288612
$638$	−15762.0	−0.978091
$639$	10200.9	0.631522
$640$	986.983	0.0609592
$641$	−4363.20	−0.268855	−0.134427	−	0.990923i	$-0.542920\pi$
$641$	−4363.20	−0.268855	−0.134427	+	0.990923i	$0.542920\pi$
$642$	−26175.5	−1.60914
$643$	13679.5	0.838987	0.419493	−	0.907758i	$-0.362208\pi$
$643$	13679.5	0.838987	0.419493	+	0.907758i	$0.362208\pi$
$644$	−24958.2	−1.52716
$645$	597.151	0.0364539
$646$	48405.7	2.94814
$647$	21559.4	1.31003	0.655015	−	0.755616i	$-0.272662\pi$
$647$	21559.4	1.31003	0.655015	+	0.755616i	$0.272662\pi$
$648$	−5059.56	−0.306726
$649$	3481.89	0.210595
$650$	−6423.40	−0.387610
$651$	13287.7	0.799982
$652$	12542.6	0.753386
$653$	6806.44	0.407897	0.203948	−	0.978982i	$-0.434623\pi$
$653$	6806.44	0.407897	0.203948	+	0.978982i	$0.434623\pi$
$654$	−7310.98	−0.437128
$655$	3187.43	0.190142
$656$	−55136.2	−3.28157
$657$	5855.43	0.347705
$658$	23625.9	1.39974
$659$	2573.31	0.152112	0.0760560	−	0.997104i	$-0.475767\pi$
$659$	2573.31	0.152112	0.0760560	+	0.997104i	$0.475767\pi$
$660$	−851.082	−0.0501944
$661$	−22953.5	−1.35066	−0.675330	−	0.737515i	$-0.735999\pi$
$661$	−22953.5	−1.35066	−0.675330	+	0.737515i	$0.735999\pi$
$662$	−44148.2	−2.59194
$663$	−3358.87	−0.196754
$664$	−46593.5	−2.72316
$665$	−1934.36	−0.112799
$666$	3325.25	0.193469
$667$	18575.6	1.07834
$668$	−4615.72	−0.267347
$669$	16855.0	0.974071
$670$	−5699.32	−0.328633
$671$	671.000	0.0386046
$672$	22171.4	1.27274
$673$	−14299.2	−0.819012	−0.409506	−	0.912307i	$-0.634299\pi$
$673$	−14299.2	−0.819012	−0.409506	+	0.912307i	$0.634299\pi$
$674$	−5683.25	−0.324793
$675$	3329.37	0.189848
$676$	−41651.9	−2.36981
$677$	3165.78	0.179720	0.0898602	−	0.995954i	$-0.471358\pi$
$677$	3165.78	0.179720	0.0898602	+	0.995954i	$0.471358\pi$
$678$	10317.0	0.584396
$679$	21621.7	1.22204
$680$	−9208.79	−0.519325
$681$	12679.4	0.713474
$682$	−13976.4	−0.784729
$683$	8075.85	0.452436	0.226218	−	0.974077i	$-0.427364\pi$
$683$	8075.85	0.452436	0.226218	+	0.974077i	$0.427364\pi$
$684$	14444.3	0.807445
$685$	1127.34	0.0628812
$686$	33742.7	1.87799
$687$	15404.0	0.855457
$688$	26161.9	1.44973
$689$	−5244.59	−0.289990
$690$	1407.47	0.0776544
$691$	−28780.7	−1.58447	−0.792237	−	0.610214i	$-0.791083\pi$
$691$	−28780.7	−1.58447	−0.792237	+	0.610214i	$0.791083\pi$
$692$	46446.7	2.55150
$693$	−1820.90	−0.0998128
$694$	−4572.85	−0.250120
$695$	3180.64	0.173595
$696$	−50891.2	−2.77159
$697$	36594.6	1.98869
$698$	−6969.19	−0.377920
$699$	−4091.80	−0.221411
$700$	−44994.8	−2.42949
$701$	−27678.6	−1.49131	−0.745654	−	0.666333i	$-0.767863\pi$
$701$	−27678.6	−1.49131	−0.745654	+	0.666333i	$0.767863\pi$
$702$	−1406.47	−0.0756179
$703$	−5664.98	−0.303924
$704$	−8284.42	−0.443510
$705$	−949.463	−0.0507217
$706$	22891.6	1.22031
$707$	26222.8	1.39492
$708$	18838.9	1.00001
$709$	−7730.15	−0.409467	−0.204733	−	0.978818i	$-0.565633\pi$
$709$	−7730.15	−0.409467	−0.204733	+	0.978818i	$0.565633\pi$
$710$	7774.39	0.410940
$711$	−4806.88	−0.253547
$712$	−47925.4	−2.52258
$713$	16471.3	0.865156
$714$	−33016.2	−1.73053
$715$	−141.182	−0.00738449
$716$	−45911.7	−2.39637
$717$	−14689.3	−0.765109
$718$	−20890.6	−1.08584
$719$	−9259.32	−0.480271	−0.240135	−	0.970739i	$-0.577192\pi$
$719$	−9259.32	−0.480271	−0.240135	+	0.970739i	$0.577192\pi$
$720$	−1999.11	−0.103476
$721$	7853.41	0.405654
$722$	1658.83	0.0855060
$723$	15595.8	0.802232
$724$	68474.0	3.51494
$725$	33488.2	1.71548
$726$	1915.27	0.0979098
$727$	2085.38	0.106386	0.0531929	−	0.998584i	$-0.483060\pi$
$727$	2085.38	0.106386	0.0531929	+	0.998584i	$0.483060\pi$
$728$	11342.8	0.577463
$729$	729.000	0.0370370
$730$	4462.57	0.226256
$731$	−17364.0	−0.878562
$732$	3630.48	0.183315
$733$	−8607.61	−0.433737	−0.216868	−	0.976201i	$-0.569584\pi$
$733$	−8607.61	−0.433737	−0.216868	+	0.976201i	$0.569584\pi$
$734$	−34620.7	−1.74097
$735$	−18.3294	−0.000919848 0
$736$	27483.3	1.37643
$737$	9140.01	0.456820
$738$	15323.3	0.764309
$739$	−17509.4	−0.871572	−0.435786	−	0.900050i	$-0.643530\pi$
$739$	−17509.4	−0.871572	−0.435786	+	0.900050i	$0.643530\pi$
$740$	1805.99	0.0897153
$741$	2396.10	0.118789
$742$	−51551.9	−2.55058
$743$	14212.7	0.701766	0.350883	−	0.936419i	$-0.385881\pi$
$743$	14212.7	0.701766	0.350883	+	0.936419i	$0.385881\pi$
$744$	−45126.1	−2.22366
$745$	1630.03	0.0801609
$746$	61192.2	3.00323
$747$	6713.36	0.328821
$748$	24747.8	1.20972
$749$	−30415.9	−1.48381
$750$	5109.57	0.248767
$751$	−10776.7	−0.523634	−0.261817	−	0.965118i	$-0.584322\pi$
$751$	−10776.7	−0.523634	−0.261817	+	0.965118i	$0.584322\pi$
$752$	−41597.1	−2.01714
$753$	−20546.0	−0.994338
$754$	−14146.9	−0.683286
$755$	−1804.86	−0.0870008
$756$	−9852.08	−0.473964
$757$	37270.4	1.78945	0.894726	−	0.446615i	$-0.147371\pi$
$757$	37270.4	1.78945	0.894726	+	0.446615i	$0.147371\pi$
$758$	−31636.1	−1.51593
$759$	−2257.17	−0.107945
$760$	6569.22	0.313541
$761$	9109.73	0.433939	0.216969	−	0.976178i	$-0.430383\pi$
$761$	9109.73	0.433939	0.216969	+	0.976178i	$0.430383\pi$
$762$	19893.0	0.945734
$763$	−8495.35	−0.403083
$764$	49106.0	2.32538
$765$	1326.84	0.0627083
$766$	−23590.4	−1.11274
$767$	3125.10	0.147120
$768$	6057.70	0.284620
$769$	3397.38	0.159314	0.0796571	−	0.996822i	$-0.474617\pi$
$769$	3397.38	0.159314	0.0796571	+	0.996822i	$0.474617\pi$
$770$	−1387.75	−0.0649496
$771$	−522.257	−0.0243951
$772$	70967.7	3.30853
$773$	−13509.5	−0.628592	−0.314296	−	0.949325i	$-0.601768\pi$
$773$	−13509.5	−0.628592	−0.314296	+	0.949325i	$0.601768\pi$
$774$	−7270.85	−0.337655
$775$	29694.6	1.37634
$776$	−73428.8	−3.39683
$777$	3863.93	0.178401
$778$	−48277.9	−2.22474
$779$	−26105.3	−1.20067
$780$	−763.873	−0.0350654
$781$	−12467.8	−0.571233
$782$	−40926.5	−1.87152
$783$	7332.58	0.334668
$784$	−803.030	−0.0365812
$785$	−4241.86	−0.192864
$786$	−38809.9	−1.76120
$787$	37668.1	1.70613	0.853065	−	0.521804i	$-0.174741\pi$
$787$	37668.1	1.70613	0.853065	+	0.521804i	$0.174741\pi$
$788$	−44221.0	−1.99912
$789$	−864.926	−0.0390268
$790$	−3663.44	−0.164987
$791$	11988.3	0.538880
$792$	6183.91	0.277444
$793$	602.244	0.0269688
$794$	−59522.8	−2.66043
$795$	2071.74	0.0924238
$796$	−10857.7	−0.483467
$797$	31366.1	1.39403	0.697016	−	0.717056i	$-0.254511\pi$
$797$	31366.1	1.39403	0.697016	+	0.717056i	$0.254511\pi$
$798$	23552.6	1.04480
$799$	27608.5	1.22243
$800$	49547.1	2.18969
$801$	6905.26	0.304601
$802$	45234.4	1.99162
$803$	−7156.64	−0.314511
$804$	49452.5	2.16922
$805$	1635.48	0.0716063
$806$	−12544.3	−0.548205
$807$	12565.9	0.548131
$808$	−89054.4	−3.87738
$809$	−14546.9	−0.632191	−0.316096	−	0.948727i	$-0.602372\pi$
$809$	−14546.9	−0.632191	−0.316096	+	0.948727i	$0.602372\pi$
$810$	555.589	0.0241005
$811$	−4329.11	−0.187442	−0.0937211	−	0.995598i	$-0.529876\pi$
$811$	−4329.11	−0.187442	−0.0937211	+	0.995598i	$0.529876\pi$
$812$	−99096.2	−4.28275
$813$	22490.0	0.970182
$814$	−4064.19	−0.175000
$815$	−821.903	−0.0353252
$816$	58130.2	2.49383
$817$	12386.8	0.530429
$818$	−50116.5	−2.14216
$819$	−1634.32	−0.0697285
$820$	8322.31	0.354424
$821$	28383.1	1.20655	0.603275	−	0.797533i	$-0.293862\pi$
$821$	28383.1	1.20655	0.603275	+	0.797533i	$0.293862\pi$
$822$	−13726.4	−0.582438
$823$	−20840.5	−0.882690	−0.441345	−	0.897337i	$-0.645499\pi$
$823$	−20840.5	−0.882690	−0.441345	+	0.897337i	$0.645499\pi$
$824$	−26670.8	−1.12757
$825$	−4069.23	−0.171724
$826$	30718.3	1.29398
$827$	−37554.7	−1.57909	−0.789544	−	0.613694i	$-0.789683\pi$
$827$	−37554.7	−1.57909	−0.789544	+	0.613694i	$0.789683\pi$
$828$	−12212.5	−0.512577
$829$	−8279.25	−0.346864	−0.173432	−	0.984846i	$-0.555486\pi$
$829$	−8279.25	−0.346864	−0.173432	+	0.984846i	$0.555486\pi$
$830$	5116.42	0.213968
$831$	−19539.2	−0.815653
$832$	−7435.53	−0.309832
$833$	532.981	0.0221689
$834$	−38727.1	−1.60793
$835$	302.462	0.0125355
$836$	−17654.2	−0.730361
$837$	6501.94	0.268506
$838$	41644.7	1.71670
$839$	−21636.8	−0.890330	−0.445165	−	0.895449i	$-0.646855\pi$
$839$	−21636.8	−0.890330	−0.445165	+	0.895449i	$0.646855\pi$
$840$	−4480.69	−0.184046
$841$	49365.1	2.02407
$842$	45944.1	1.88045
$843$	−9388.20	−0.383567
$844$	−11671.4	−0.476003
$845$	2729.39	0.111117
$846$	11560.6	0.469811
$847$	2225.55	0.0902841
$848$	90765.2	3.67558
$849$	−22490.2	−0.909144
$850$	−73782.4	−2.97731
$851$	4789.68	0.192935
$852$	−67457.7	−2.71251
$853$	−20799.5	−0.834890	−0.417445	−	0.908702i	$-0.637074\pi$
$853$	−20799.5	−0.834890	−0.417445	+	0.908702i	$0.637074\pi$
$854$	5919.78	0.237202
$855$	−946.518	−0.0378599
$856$	103295.	4.12446
$857$	12152.5	0.484389	0.242194	−	0.970228i	$-0.422133\pi$
$857$	12152.5	0.484389	0.242194	+	0.970228i	$0.422133\pi$
$858$	1719.02	0.0683990
$859$	−40033.5	−1.59013	−0.795066	−	0.606522i	$-0.792564\pi$
$859$	−40033.5	−1.59013	−0.795066	+	0.606522i	$0.792564\pi$
$860$	−3948.90	−0.156577
$861$	17805.7	0.704781
$862$	−18830.9	−0.744064
$863$	753.174	0.0297084	0.0148542	−	0.999890i	$-0.495272\pi$
$863$	753.174	0.0297084	0.0148542	+	0.999890i	$0.495272\pi$
$864$	10848.9	0.427182
$865$	−3043.59	−0.119636
$866$	−73005.0	−2.86468
$867$	−23842.7	−0.933958
$868$	−87870.5	−3.43608
$869$	5875.08	0.229342
$870$	5588.35	0.217773
$871$	8203.45	0.319131
$872$	28850.8	1.12043
$873$	10579.9	0.410166
$874$	29195.5	1.12992
$875$	5937.31	0.229392
$876$	−38721.3	−1.49346
$877$	−20974.1	−0.807575	−0.403788	−	0.914853i	$-0.632307\pi$
$877$	−20974.1	−0.807575	−0.403788	+	0.914853i	$0.632307\pi$
$878$	−33802.7	−1.29930
$879$	5045.84	0.193620
$880$	2443.36	0.0935974
$881$	31079.0	1.18851	0.594255	−	0.804277i	$-0.297447\pi$
$881$	31079.0	1.18851	0.594255	+	0.804277i	$0.297447\pi$
$882$	223.176	0.00852011
$883$	−7344.07	−0.279895	−0.139948	−	0.990159i	$-0.544693\pi$
$883$	−7344.07	−0.279895	−0.139948	+	0.990159i	$0.544693\pi$
$884$	22211.9	0.845098
$885$	−1234.49	−0.0468892
$886$	−41415.8	−1.57042
$887$	−12917.4	−0.488977	−0.244489	−	0.969652i	$-0.578620\pi$
$887$	−12917.4	−0.488977	−0.244489	+	0.969652i	$0.578620\pi$
$888$	−13122.2	−0.495891
$889$	23115.7	0.872076
$890$	5262.67	0.198208
$891$	−891.000	−0.0335013
$892$	−111461.	−4.18383
$893$	−19694.9	−0.738034
$894$	−19847.1	−0.742492
$895$	3008.53	0.112362
$896$	−13964.2	−0.520660
$897$	−2025.88	−0.0754092
$898$	−6276.70	−0.233247
$899$	65399.2	2.42623
$900$	−22016.8	−0.815436
$901$	−60242.0	−2.22747
$902$	−18728.5	−0.691343
$903$	−8448.71	−0.311357
$904$	−40713.1	−1.49789
$905$	−4487.01	−0.164810
$906$	21975.8	0.805847
$907$	46696.7	1.70952	0.854762	−	0.519020i	$-0.173703\pi$
$907$	46696.7	1.70952	0.854762	+	0.519020i	$0.173703\pi$
$908$	−83847.5	−3.06451
$909$	12831.3	0.468192
$910$	−1245.55	−0.0453733
$911$	43586.4	1.58516	0.792581	−	0.609766i	$-0.208737\pi$
$911$	43586.4	1.58516	0.792581	+	0.609766i	$0.208737\pi$
$912$	−41468.0	−1.50564
$913$	−8205.22	−0.297430
$914$	−80353.6	−2.90795
$915$	−237.901	−0.00859536
$916$	−101865.	−3.67436
$917$	−45097.0	−1.62403
$918$	−16155.4	−0.580837
$919$	42720.5	1.53343	0.766714	−	0.641989i	$-0.221890\pi$
$919$	42720.5	1.53343	0.766714	+	0.641989i	$0.221890\pi$
$920$	−5554.21	−0.199040
$921$	8540.42	0.305555
$922$	31853.6	1.13779
$923$	−11190.2	−0.399059
$924$	12041.4	0.428716
$925$	8634.86	0.306932
$926$	−49135.4	−1.74373
$927$	3842.82	0.136154
$928$	109122.	3.86003
$929$	−30137.6	−1.06435	−0.532177	−	0.846633i	$-0.678626\pi$
$929$	−30137.6	−1.06435	−0.532177	+	0.846633i	$0.678626\pi$
$930$	4955.29	0.174721
$931$	−380.210	−0.0133844
$932$	27058.7	0.951005
$933$	−8446.74	−0.296392
$934$	58249.5	2.04066
$935$	−1621.69	−0.0567218
$936$	5550.25	0.193820
$937$	−27903.9	−0.972873	−0.486437	−	0.873716i	$-0.661704\pi$
$937$	−27903.9	−0.972873	−0.486437	+	0.873716i	$0.661704\pi$
$938$	80636.1	2.80689
$939$	−14288.4	−0.496576
$940$	6278.70	0.217860
$941$	53582.9	1.85627	0.928136	−	0.372241i	$-0.121411\pi$
$941$	53582.9	1.85627	0.928136	+	0.372241i	$0.121411\pi$
$942$	51648.5	1.78641
$943$	22071.7	0.762200
$944$	−54084.5	−1.86472
$945$	645.594	0.0222235
$946$	8886.59	0.305421
$947$	29567.8	1.01460	0.507299	−	0.861770i	$-0.330644\pi$
$947$	29567.8	1.01460	0.507299	+	0.861770i	$0.330644\pi$
$948$	31787.4	1.08904
$949$	−6423.30	−0.219715
$950$	52633.7	1.79754
$951$	−6748.33	−0.230105
$952$	130289.	4.43562
$953$	−35454.1	−1.20511	−0.602556	−	0.798077i	$-0.705851\pi$
$953$	−35454.1	−1.20511	−0.602556	+	0.798077i	$0.705851\pi$
$954$	−25225.3	−0.856078
$955$	−3217.85	−0.109034
$956$	97139.0	3.28630
$957$	−8962.04	−0.302719
$958$	−70335.6	−2.37207
$959$	−15950.1	−0.537075
$960$	2937.21	0.0987480
$961$	28199.7	0.946584
$962$	−3647.74	−0.122253
$963$	−14883.1	−0.498027
$964$	−103133.	−3.44575
$965$	−4650.42	−0.155132
$966$	−19913.4	−0.663255
$967$	−37558.7	−1.24902	−0.624512	−	0.781016i	$-0.714702\pi$
$967$	−37558.7	−1.24902	−0.624512	+	0.781016i	$0.714702\pi$
$968$	−7558.11	−0.250958
$969$	27522.8	0.912447
$970$	8063.19	0.266901
$971$	40172.1	1.32769	0.663843	−	0.747872i	$-0.268924\pi$
$971$	40172.1	1.32769	0.663843	+	0.747872i	$0.268924\pi$
$972$	−4820.80	−0.159082
$973$	−45000.8	−1.48269
$974$	22220.8	0.731007
$975$	−3652.26	−0.119965
$976$	−10422.7	−0.341826
$977$	−36720.3	−1.20244	−0.601221	−	0.799083i	$-0.705319\pi$
$977$	−36720.3	−1.20244	−0.601221	+	0.799083i	$0.705319\pi$
$978$	10007.4	0.327200
$979$	−8439.76	−0.275522
$980$	121.210	0.00395093
$981$	−4156.93	−0.135291
$982$	−83996.0	−2.72955
$983$	19413.2	0.629892	0.314946	−	0.949110i	$-0.398014\pi$
$983$	19413.2	0.629892	0.314946	+	0.949110i	$0.398014\pi$
$984$	−60469.4	−1.95904
$985$	2897.74	0.0937359
$986$	−162498.	−5.24847
$987$	13433.4	0.433220
$988$	−15845.2	−0.510225
$989$	−10472.9	−0.336724
$990$	−679.054	−0.0217997
$991$	17079.3	0.547468	0.273734	−	0.961805i	$-0.411741\pi$
$991$	17079.3	0.547468	0.273734	+	0.961805i	$0.411741\pi$
$992$	96760.7	3.09693
$993$	−25102.1	−0.802205
$994$	−109995.	−3.50989
$995$	711.489	0.0226691
$996$	−44394.8	−1.41235
$997$	53011.2	1.68393	0.841966	−	0.539530i	$-0.181398\pi$
$997$	53011.2	1.68393	0.841966	+	0.539530i	$0.181398\pi$
$998$	−41834.1	−1.32689
$999$	1890.69	0.0598787

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.e.1.2	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.e.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-5.27624 q^{2} -3.00000 q^{3} +19.8387 q^{4} -1.30000 q^{5} +15.8287 q^{6} +18.3929 q^{7} -62.4637 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.27624 q^{2} -3.00000 q^{3} +19.8387 q^{4} -1.30000 q^{5} +15.8287 q^{6} +18.3929 q^{7} -62.4637 q^{8} +9.00000 q^{9} +6.85913 q^{10} -11.0000 q^{11} -59.5161 q^{12} -9.87284 q^{13} -97.0455 q^{14} +3.90001 q^{15} +170.864 q^{16} -113.404 q^{17} -47.4861 q^{18} +80.8987 q^{19} -25.7904 q^{20} -55.1788 q^{21} +58.0386 q^{22} -68.3990 q^{23} +187.391 q^{24} -123.310 q^{25} +52.0915 q^{26} -27.0000 q^{27} +364.892 q^{28} -271.577 q^{29} -20.5774 q^{30} -240.813 q^{31} -401.809 q^{32} +33.0000 q^{33} +598.349 q^{34} -23.9109 q^{35} +178.548 q^{36} -70.0256 q^{37} -426.841 q^{38} +29.6185 q^{39} +81.2031 q^{40} -322.691 q^{41} +291.137 q^{42} +153.115 q^{43} -218.226 q^{44} -11.7000 q^{45} +360.889 q^{46} -243.451 q^{47} -512.592 q^{48} -4.69982 q^{49} +650.613 q^{50} +340.213 q^{51} -195.864 q^{52} +531.213 q^{53} +142.458 q^{54} +14.3000 q^{55} -1148.89 q^{56} -242.696 q^{57} +1432.91 q^{58} -316.535 q^{59} +77.3711 q^{60} -61.0000 q^{61} +1270.58 q^{62} +165.536 q^{63} +753.129 q^{64} +12.8347 q^{65} -174.116 q^{66} -830.910 q^{67} -2249.80 q^{68} +205.197 q^{69} +126.160 q^{70} +1133.44 q^{71} -562.174 q^{72} +650.603 q^{73} +369.472 q^{74} +369.930 q^{75} +1604.92 q^{76} -202.322 q^{77} -156.274 q^{78} -534.098 q^{79} -222.124 q^{80} +81.0000 q^{81} +1702.59 q^{82} +745.929 q^{83} -1094.68 q^{84} +147.426 q^{85} -807.872 q^{86} +814.731 q^{87} +687.101 q^{88} +767.251 q^{89} +61.7321 q^{90} -181.591 q^{91} -1356.95 q^{92} +722.438 q^{93} +1284.51 q^{94} -105.169 q^{95} +1205.43 q^{96} +1175.54 q^{97} +24.7974 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} - 114 q^{3} + 142 q^{4} + 15 q^{5} + 6 q^{6} + 63 q^{7} - 45 q^{8} + 342 q^{9}+O(q^{10}) \) 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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