LMFDB - Embedded newform 2013.4.a.a.1.11

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:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-3.06792 q^{2} +3.00000 q^{3} +1.41213 q^{4} -10.3390 q^{5} -9.20376 q^{6} -32.3876 q^{7} +20.2111 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.06792 q^{2} +3.00000 q^{3} +1.41213 q^{4} -10.3390 q^{5} -9.20376 q^{6} -32.3876 q^{7} +20.2111 q^{8} +9.00000 q^{9} +31.7193 q^{10} +11.0000 q^{11} +4.23638 q^{12} -34.5048 q^{13} +99.3625 q^{14} -31.0171 q^{15} -73.3029 q^{16} +42.1465 q^{17} -27.6113 q^{18} -107.866 q^{19} -14.6000 q^{20} -97.1628 q^{21} -33.7471 q^{22} +200.592 q^{23} +60.6332 q^{24} -18.1045 q^{25} +105.858 q^{26} +27.0000 q^{27} -45.7354 q^{28} +183.402 q^{29} +95.1579 q^{30} -216.586 q^{31} +63.1989 q^{32} +33.0000 q^{33} -129.302 q^{34} +334.856 q^{35} +12.7091 q^{36} -58.6938 q^{37} +330.924 q^{38} -103.514 q^{39} -208.963 q^{40} -79.5708 q^{41} +298.088 q^{42} +74.6099 q^{43} +15.5334 q^{44} -93.0513 q^{45} -615.400 q^{46} +77.1849 q^{47} -219.909 q^{48} +705.957 q^{49} +55.5430 q^{50} +126.440 q^{51} -48.7251 q^{52} +369.209 q^{53} -82.8338 q^{54} -113.729 q^{55} -654.588 q^{56} -323.598 q^{57} -562.662 q^{58} -638.868 q^{59} -43.8000 q^{60} +61.0000 q^{61} +664.467 q^{62} -291.488 q^{63} +392.534 q^{64} +356.746 q^{65} -101.241 q^{66} +418.980 q^{67} +59.5162 q^{68} +601.776 q^{69} -1027.31 q^{70} +1014.41 q^{71} +181.900 q^{72} +902.408 q^{73} +180.068 q^{74} -54.3134 q^{75} -152.320 q^{76} -356.264 q^{77} +317.574 q^{78} +153.565 q^{79} +757.881 q^{80} +81.0000 q^{81} +244.117 q^{82} +435.819 q^{83} -137.206 q^{84} -435.754 q^{85} -228.897 q^{86} +550.206 q^{87} +222.322 q^{88} +395.583 q^{89} +285.474 q^{90} +1117.53 q^{91} +283.261 q^{92} -649.757 q^{93} -236.797 q^{94} +1115.23 q^{95} +189.597 q^{96} +452.833 q^{97} -2165.82 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * 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 $

$2$	−3.06792	−1.08467	−0.542337	−	0.840161i	$-0.682460\pi$
$2$	−3.06792	−1.08467	−0.542337	+	0.840161i	$0.682460\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	1.41213	0.176516
$5$	−10.3390	−0.924751	−0.462375	−	0.886684i	$-0.653003\pi$
$5$	−10.3390	−0.924751	−0.462375	+	0.886684i	$0.653003\pi$
$6$	−9.20376	−0.626236
$7$	−32.3876	−1.74877	−0.874383	−	0.485236i	$-0.838734\pi$
$7$	−32.3876	−1.74877	−0.874383	+	0.485236i	$0.838734\pi$
$8$	20.2111	0.893211
$9$	9.00000	0.333333
$10$	31.7193	1.00305
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	4.23638	0.101911
$13$	−34.5048	−0.736146	−0.368073	−	0.929797i	$-0.619982\pi$
$13$	−34.5048	−0.736146	−0.368073	+	0.929797i	$0.619982\pi$
$14$	99.3625	1.89684
$15$	−31.0171	−0.533905
$16$	−73.3029	−1.14536
$17$	42.1465	0.601296	0.300648	−	0.953735i	$-0.402797\pi$
$17$	42.1465	0.601296	0.300648	+	0.953735i	$0.402797\pi$
$18$	−27.6113	−0.361558
$19$	−107.866	−1.30243	−0.651214	−	0.758894i	$-0.725740\pi$
$19$	−107.866	−1.30243	−0.651214	+	0.758894i	$0.725740\pi$
$20$	−14.6000	−0.163233
$21$	−97.1628	−1.00965
$22$	−33.7471	−0.327041
$23$	200.592	1.81854	0.909268	−	0.416211i	$-0.136642\pi$
$23$	200.592	1.81854	0.909268	+	0.416211i	$0.136642\pi$
$24$	60.6332	0.515696
$25$	−18.1045	−0.144836
$26$	105.858	0.798478
$27$	27.0000	0.192450
$28$	−45.7354	−0.308685
$29$	183.402	1.17437	0.587187	−	0.809451i	$-0.300235\pi$
$29$	183.402	1.17437	0.587187	+	0.809451i	$0.300235\pi$
$30$	95.1579	0.579113
$31$	−216.586	−1.25484	−0.627418	−	0.778683i	$-0.715888\pi$
$31$	−216.586	−1.25484	−0.627418	+	0.778683i	$0.715888\pi$
$32$	63.1989	0.349128
$33$	33.0000	0.174078
$34$	−129.302	−0.652210
$35$	334.856	1.61717
$36$	12.7091	0.0588386
$37$	−58.6938	−0.260789	−0.130395	−	0.991462i	$-0.541624\pi$
$37$	−58.6938	−0.260789	−0.130395	+	0.991462i	$0.541624\pi$
$38$	330.924	1.41271
$39$	−103.514	−0.425014
$40$	−208.963	−0.825998
$41$	−79.5708	−0.303094	−0.151547	−	0.988450i	$-0.548426\pi$
$41$	−79.5708	−0.303094	−0.151547	+	0.988450i	$0.548426\pi$
$42$	298.088	1.09514
$43$	74.6099	0.264602	0.132301	−	0.991210i	$-0.457763\pi$
$43$	74.6099	0.264602	0.132301	+	0.991210i	$0.457763\pi$
$44$	15.5334	0.0532215
$45$	−93.0513	−0.308250
$46$	−615.400	−1.97252
$47$	77.1849	0.239544	0.119772	−	0.992801i	$-0.461784\pi$
$47$	77.1849	0.239544	0.119772	+	0.992801i	$0.461784\pi$
$48$	−219.909	−0.661273
$49$	705.957	2.05818
$50$	55.5430	0.157099
$51$	126.440	0.347159
$52$	−48.7251	−0.129941
$53$	369.209	0.956882	0.478441	−	0.878120i	$-0.341202\pi$
$53$	369.209	0.956882	0.478441	+	0.878120i	$0.341202\pi$
$54$	−82.8338	−0.208745
$55$	−113.729	−0.278823
$56$	−654.588	−1.56202
$57$	−323.598	−0.751957
$58$	−562.662	−1.27381
$59$	−638.868	−1.40972	−0.704861	−	0.709346i	$-0.748991\pi$
$59$	−638.868	−1.40972	−0.704861	+	0.709346i	$0.748991\pi$
$60$	−43.8000	−0.0942427
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	664.467	1.36109
$63$	−291.488	−0.582922
$64$	392.534	0.766668
$65$	356.746	0.680752
$66$	−101.241	−0.188817
$67$	418.980	0.763978	0.381989	−	0.924167i	$-0.375239\pi$
$67$	418.980	0.763978	0.381989	+	0.924167i	$0.375239\pi$
$68$	59.5162	0.106138
$69$	601.776	1.04993
$70$	−1027.31	−1.75410
$71$	1014.41	1.69561	0.847806	−	0.530307i	$-0.177923\pi$
$71$	1014.41	1.69561	0.847806	+	0.530307i	$0.177923\pi$
$72$	181.900	0.297737
$73$	902.408	1.44683	0.723417	−	0.690412i	$-0.242571\pi$
$73$	902.408	1.44683	0.723417	+	0.690412i	$0.242571\pi$
$74$	180.068	0.282871
$75$	−54.3134	−0.0836209
$76$	−152.320	−0.229899
$77$	−356.264	−0.527273
$78$	317.574	0.461002
$79$	153.565	0.218702	0.109351	−	0.994003i	$-0.465123\pi$
$79$	153.565	0.218702	0.109351	+	0.994003i	$0.465123\pi$
$80$	757.881	1.05917
$81$	81.0000	0.111111
$82$	244.117	0.328758
$83$	435.819	0.576354	0.288177	−	0.957577i	$-0.406951\pi$
$83$	435.819	0.576354	0.288177	+	0.957577i	$0.406951\pi$
$84$	−137.206	−0.178219
$85$	−435.754	−0.556049
$86$	−228.897	−0.287007
$87$	550.206	0.678026
$88$	222.322	0.269313
$89$	395.583	0.471143	0.235572	−	0.971857i	$-0.424304\pi$
$89$	395.583	0.471143	0.235572	+	0.971857i	$0.424304\pi$
$90$	285.474	0.334351
$91$	1117.53	1.28735
$92$	283.261	0.321000
$93$	−649.757	−0.724480
$94$	−236.797	−0.259827
$95$	1115.23	1.20442
$96$	189.597	0.201569
$97$	452.833	0.474002	0.237001	−	0.971509i	$-0.423836\pi$
$97$	452.833	0.474002	0.237001	+	0.971509i	$0.423836\pi$
$98$	−2165.82	−2.23246
$99$	99.0000	0.100504
$100$	−25.5658	−0.0255658
$101$	−1808.14	−1.78135	−0.890675	−	0.454641i	$-0.849767\pi$
$101$	−1808.14	−1.78135	−0.890675	+	0.454641i	$0.849767\pi$
$102$	−387.907	−0.376554
$103$	282.948	0.270677	0.135338	−	0.990799i	$-0.456788\pi$
$103$	282.948	0.270677	0.135338	+	0.990799i	$0.456788\pi$
$104$	−697.378	−0.657534
$105$	1004.57	0.933675
$106$	−1132.70	−1.03790
$107$	−10.9710	−0.00991225	−0.00495612	−	0.999988i	$-0.501578\pi$
$107$	−10.9710	−0.00991225	−0.00495612	+	0.999988i	$0.501578\pi$
$108$	38.1274	0.0339705
$109$	1164.38	1.02319	0.511596	−	0.859226i	$-0.329055\pi$
$109$	1164.38	1.02319	0.511596	+	0.859226i	$0.329055\pi$
$110$	348.912	0.302432
$111$	−176.081	−0.150567
$112$	2374.11	2.00296
$113$	−673.052	−0.560314	−0.280157	−	0.959954i	$-0.590386\pi$
$113$	−673.052	−0.560314	−0.280157	+	0.959954i	$0.590386\pi$
$114$	992.772	0.815628
$115$	−2073.93	−1.68169
$116$	258.987	0.207296
$117$	−310.543	−0.245382
$118$	1960.00	1.52909
$119$	−1365.03	−1.05153
$120$	−626.888	−0.476890
$121$	121.000	0.0909091
$122$	−187.143	−0.138878
$123$	−238.712	−0.174992
$124$	−305.846	−0.221498
$125$	1479.56	1.05869
$126$	894.263	0.632280
$127$	−2003.80	−1.40007	−0.700033	−	0.714111i	$-0.746831\pi$
$127$	−2003.80	−1.40007	−0.700033	+	0.714111i	$0.746831\pi$
$128$	−1709.85	−1.18071
$129$	223.830	0.152768
$130$	−1094.47	−0.738393
$131$	1047.81	0.698836	0.349418	−	0.936967i	$-0.386379\pi$
$131$	1047.81	0.698836	0.349418	+	0.936967i	$0.386379\pi$
$132$	46.6002	0.0307275
$133$	3493.52	2.27764
$134$	−1285.40	−0.828666
$135$	−279.154	−0.177968
$136$	851.826	0.537085
$137$	301.572	0.188066	0.0940329	−	0.995569i	$-0.470024\pi$
$137$	301.572	0.188066	0.0940329	+	0.995569i	$0.470024\pi$
$138$	−1846.20	−1.13883
$139$	−1079.01	−0.658423	−0.329211	−	0.944256i	$-0.606783\pi$
$139$	−1079.01	−0.658423	−0.329211	+	0.944256i	$0.606783\pi$
$140$	472.859	0.285457
$141$	231.555	0.138301
$142$	−3112.13	−1.83918
$143$	−379.553	−0.221956
$144$	−659.726	−0.381786
$145$	−1896.20	−1.08600
$146$	−2768.51	−1.56934
$147$	2117.87	1.18829
$148$	−82.8831	−0.0460334
$149$	28.8891	0.0158838	0.00794190	−	0.999968i	$-0.497472\pi$
$149$	28.8891	0.0158838	0.00794190	+	0.999968i	$0.497472\pi$
$150$	166.629	0.0907013
$151$	−3671.30	−1.97858	−0.989291	−	0.145955i	$-0.953374\pi$
$151$	−3671.30	−1.97858	−0.989291	+	0.145955i	$0.953374\pi$
$152$	−2180.09	−1.16334
$153$	379.319	0.200432
$154$	1092.99	0.571919
$155$	2239.28	1.16041
$156$	−146.175	−0.0750217
$157$	240.505	0.122257	0.0611287	−	0.998130i	$-0.480530\pi$
$157$	240.505	0.122257	0.0611287	+	0.998130i	$0.480530\pi$
$158$	−471.126	−0.237220
$159$	1107.63	0.552456
$160$	−653.415	−0.322856
$161$	−6496.69	−3.18019
$162$	−248.501	−0.120519
$163$	681.241	0.327355	0.163678	−	0.986514i	$-0.447664\pi$
$163$	681.241	0.327355	0.163678	+	0.986514i	$0.447664\pi$
$164$	−112.364	−0.0535010
$165$	−341.188	−0.160978
$166$	−1337.06	−0.625155
$167$	−435.698	−0.201888	−0.100944	−	0.994892i	$-0.532186\pi$
$167$	−435.698	−0.201888	−0.100944	+	0.994892i	$0.532186\pi$
$168$	−1963.76	−0.901831
$169$	−1006.42	−0.458088
$170$	1336.86	0.603132
$171$	−970.793	−0.434143
$172$	105.359	0.0467065
$173$	3377.98	1.48452	0.742262	−	0.670109i	$-0.233753\pi$
$173$	3377.98	1.48452	0.742262	+	0.670109i	$0.233753\pi$
$174$	−1687.99	−0.735436
$175$	586.360	0.253284
$176$	−806.332	−0.345338
$177$	−1916.61	−0.813903
$178$	−1213.62	−0.511036
$179$	−576.333	−0.240655	−0.120327	−	0.992734i	$-0.538394\pi$
$179$	−576.333	−0.240655	−0.120327	+	0.992734i	$0.538394\pi$
$180$	−131.400	−0.0544110
$181$	−3428.98	−1.40814	−0.704071	−	0.710129i	$-0.748636\pi$
$181$	−3428.98	−1.40814	−0.704071	+	0.710129i	$0.748636\pi$
$182$	−3428.48	−1.39635
$183$	183.000	0.0739221
$184$	4054.18	1.62434
$185$	606.837	0.241165
$186$	1993.40	0.785824
$187$	463.612	0.181298
$188$	108.995	0.0422833
$189$	−874.465	−0.336550
$190$	−3421.43	−1.30640
$191$	2629.90	0.996299	0.498150	−	0.867091i	$-0.334013\pi$
$191$	2629.90	0.996299	0.498150	+	0.867091i	$0.334013\pi$
$192$	1177.60	0.442636
$193$	−4027.24	−1.50201	−0.751003	−	0.660299i	$-0.770429\pi$
$193$	−4027.24	−1.50201	−0.751003	+	0.660299i	$0.770429\pi$
$194$	−1389.25	−0.514137
$195$	1070.24	0.393032
$196$	996.900	0.363302
$197$	2693.34	0.974073	0.487037	−	0.873381i	$-0.338078\pi$
$197$	2693.34	0.974073	0.487037	+	0.873381i	$0.338078\pi$
$198$	−303.724	−0.109014
$199$	1200.43	0.427620	0.213810	−	0.976875i	$-0.431413\pi$
$199$	1200.43	0.427620	0.213810	+	0.976875i	$0.431413\pi$
$200$	−365.910	−0.129369
$201$	1256.94	0.441083
$202$	5547.21	1.93218
$203$	−5939.95	−2.05371
$204$	178.549	0.0612790
$205$	822.685	0.280287
$206$	−868.062	−0.293596
$207$	1805.33	0.606179
$208$	2529.30	0.843151
$209$	−1186.53	−0.392697
$210$	−3081.94	−1.01273
$211$	−3723.22	−1.21477	−0.607386	−	0.794407i	$-0.707782\pi$
$211$	−3723.22	−1.21477	−0.607386	+	0.794407i	$0.707782\pi$
$212$	521.369	0.168905
$213$	3043.23	0.978962
$214$	33.6583	0.0107515
$215$	−771.394	−0.244691
$216$	545.699	0.171899
$217$	7014.69	2.19441
$218$	−3572.24	−1.10983
$219$	2707.22	0.835330
$220$	−160.600	−0.0492166
$221$	−1454.26	−0.442642
$222$	540.204	0.163316
$223$	−1998.96	−0.600270	−0.300135	−	0.953897i	$-0.597032\pi$
$223$	−1998.96	−0.600270	−0.300135	+	0.953897i	$0.597032\pi$
$224$	−2046.86	−0.610543
$225$	−162.940	−0.0482785
$226$	2064.87	0.607757
$227$	1614.93	0.472187	0.236094	−	0.971730i	$-0.424133\pi$
$227$	1614.93	0.472187	0.236094	+	0.971730i	$0.424133\pi$
$228$	−456.961	−0.132732
$229$	4415.45	1.27415	0.637076	−	0.770801i	$-0.280144\pi$
$229$	4415.45	1.27415	0.637076	+	0.770801i	$0.280144\pi$
$230$	6362.64	1.82409
$231$	−1068.79	−0.304421
$232$	3706.75	1.04896
$233$	497.573	0.139902	0.0699508	−	0.997550i	$-0.477716\pi$
$233$	497.573	0.139902	0.0699508	+	0.997550i	$0.477716\pi$
$234$	952.721	0.266159
$235$	−798.017	−0.221519
$236$	−902.163	−0.248838
$237$	460.696	0.126268
$238$	4187.79	1.14056
$239$	−1490.61	−0.403429	−0.201715	−	0.979444i	$-0.564651\pi$
$239$	−1490.61	−0.403429	−0.201715	+	0.979444i	$0.564651\pi$
$240$	2273.64	0.611513
$241$	1104.19	0.295134	0.147567	−	0.989052i	$-0.452856\pi$
$241$	1104.19	0.295134	0.147567	+	0.989052i	$0.452856\pi$
$242$	−371.218	−0.0986066
$243$	243.000	0.0641500
$244$	86.1397	0.0226005
$245$	−7298.91	−1.90331
$246$	732.350	0.189809
$247$	3721.89	0.958778
$248$	−4377.42	−1.12083
$249$	1307.46	0.332758
$250$	−4539.17	−1.14833
$251$	−5142.26	−1.29313	−0.646566	−	0.762858i	$-0.723796\pi$
$251$	−5142.26	−1.29313	−0.646566	+	0.762858i	$0.723796\pi$
$252$	−411.618	−0.102895
$253$	2206.51	0.548309
$254$	6147.49	1.51861
$255$	−1307.26	−0.321035
$256$	2105.42	0.514019
$257$	959.014	0.232769	0.116385	−	0.993204i	$-0.462870\pi$
$257$	959.014	0.232769	0.116385	+	0.993204i	$0.462870\pi$
$258$	−686.692	−0.165704
$259$	1900.95	0.456059
$260$	503.770	0.120163
$261$	1650.62	0.391458
$262$	−3214.59	−0.758008
$263$	7586.54	1.77873	0.889365	−	0.457198i	$-0.151147\pi$
$263$	7586.54	1.77873	0.889365	+	0.457198i	$0.151147\pi$
$264$	666.965	0.155488
$265$	−3817.26	−0.884877
$266$	−10717.8	−2.47050
$267$	1186.75	0.272015
$268$	591.652	0.134854
$269$	−2294.28	−0.520017	−0.260009	−	0.965606i	$-0.583725\pi$
$269$	−2294.28	−0.520017	−0.260009	+	0.965606i	$0.583725\pi$
$270$	856.421	0.193038
$271$	−337.183	−0.0755809	−0.0377904	−	0.999286i	$-0.512032\pi$
$271$	−337.183	−0.0755809	−0.0377904	+	0.999286i	$0.512032\pi$
$272$	−3089.46	−0.688700
$273$	3352.58	0.743251
$274$	−925.198	−0.203990
$275$	−199.149	−0.0436696
$276$	849.784	0.185330
$277$	−4564.51	−0.990091	−0.495045	−	0.868867i	$-0.664849\pi$
$277$	−4564.51	−0.990091	−0.495045	+	0.868867i	$0.664849\pi$
$278$	3310.33	0.714173
$279$	−1949.27	−0.418279
$280$	6767.80	1.44448
$281$	5660.84	1.20177	0.600885	−	0.799336i	$-0.294815\pi$
$281$	5660.84	1.20177	0.600885	+	0.799336i	$0.294815\pi$
$282$	−710.391	−0.150011
$283$	−931.821	−0.195728	−0.0978640	−	0.995200i	$-0.531201\pi$
$283$	−931.821	−0.195728	−0.0978640	+	0.995200i	$0.531201\pi$
$284$	1432.48	0.299302
$285$	3345.69	0.695373
$286$	1164.44	0.240750
$287$	2577.11	0.530041
$288$	568.790	0.116376
$289$	−3136.67	−0.638443
$290$	5817.38	1.17796
$291$	1358.50	0.273665
$292$	1274.31	0.255389
$293$	−8312.10	−1.65733	−0.828666	−	0.559744i	$-0.810900\pi$
$293$	−8312.10	−1.65733	−0.828666	+	0.559744i	$0.810900\pi$
$294$	−6497.45	−1.28891
$295$	6605.28	1.30364
$296$	−1186.26	−0.232940
$297$	297.000	0.0580259
$298$	−88.6293	−0.0172287
$299$	−6921.38	−1.33871
$300$	−76.6973	−0.0147604
$301$	−2416.44	−0.462728
$302$	11263.2	2.14612
$303$	−5424.41	−1.02846
$304$	7906.89	1.49175
$305$	−630.681	−0.118402
$306$	−1163.72	−0.217403
$307$	−4697.93	−0.873372	−0.436686	−	0.899614i	$-0.643848\pi$
$307$	−4697.93	−0.873372	−0.436686	+	0.899614i	$0.643848\pi$
$308$	−503.089	−0.0930720
$309$	848.844	0.156275
$310$	−6869.94	−1.25867
$311$	8599.31	1.56792	0.783959	−	0.620813i	$-0.213197\pi$
$311$	8599.31	1.56792	0.783959	+	0.620813i	$0.213197\pi$
$312$	−2092.13	−0.379628
$313$	983.040	0.177523	0.0887615	−	0.996053i	$-0.471709\pi$
$313$	983.040	0.177523	0.0887615	+	0.996053i	$0.471709\pi$
$314$	−737.851	−0.132609
$315$	3013.71	0.539058
$316$	216.854	0.0386043
$317$	−6630.17	−1.17472	−0.587362	−	0.809325i	$-0.699833\pi$
$317$	−6630.17	−1.17472	−0.587362	+	0.809325i	$0.699833\pi$
$318$	−3398.11	−0.599234
$319$	2017.42	0.354087
$320$	−4058.42	−0.708977
$321$	−32.9131	−0.00572284
$322$	19931.3	3.44947
$323$	−4546.18	−0.783146
$324$	114.382	0.0196129
$325$	624.690	0.106620
$326$	−2089.99	−0.355073
$327$	3493.15	0.590740
$328$	−1608.21	−0.270727
$329$	−2499.83	−0.418907
$330$	1046.74	0.174609
$331$	−5485.80	−0.910958	−0.455479	−	0.890247i	$-0.650532\pi$
$331$	−5485.80	−0.910958	−0.455479	+	0.890247i	$0.650532\pi$
$332$	615.432	0.101736
$333$	−528.244	−0.0869298
$334$	1336.69	0.218983
$335$	−4331.84	−0.706489
$336$	7122.32	1.15641
$337$	−5340.00	−0.863170	−0.431585	−	0.902072i	$-0.642046\pi$
$337$	−5340.00	−0.863170	−0.431585	+	0.902072i	$0.642046\pi$
$338$	3087.62	0.496876
$339$	−2019.16	−0.323497
$340$	−615.340	−0.0981515
$341$	−2382.44	−0.378347
$342$	2978.32	0.470903
$343$	−11755.3	−1.85051
$344$	1507.95	0.236346
$345$	−6221.78	−0.970926
$346$	−10363.4	−1.61022
$347$	1251.16	0.193561	0.0967804	−	0.995306i	$-0.469146\pi$
$347$	1251.16	0.193561	0.0967804	+	0.995306i	$0.469146\pi$
$348$	776.960	0.119682
$349$	2507.76	0.384635	0.192317	−	0.981333i	$-0.438400\pi$
$349$	2507.76	0.384635	0.192317	+	0.981333i	$0.438400\pi$
$350$	−1798.90	−0.274730
$351$	−931.629	−0.141671
$352$	695.188	0.105266
$353$	−8235.25	−1.24170	−0.620848	−	0.783931i	$-0.713211\pi$
$353$	−8235.25	−1.24170	−0.620848	+	0.783931i	$0.713211\pi$
$354$	5879.99	0.882819
$355$	−10488.0	−1.56802
$356$	558.614	0.0831642
$357$	−4095.08	−0.607099
$358$	1768.14	0.261032
$359$	−4750.46	−0.698383	−0.349191	−	0.937051i	$-0.613544\pi$
$359$	−4750.46	−0.698383	−0.349191	+	0.937051i	$0.613544\pi$
$360$	−1880.67	−0.275333
$361$	4776.06	0.696320
$362$	10519.8	1.52737
$363$	363.000	0.0524864
$364$	1578.09	0.227237
$365$	−9330.02	−1.33796
$366$	−561.429	−0.0801813
$367$	4171.33	0.593301	0.296651	−	0.954986i	$-0.404130\pi$
$367$	4171.33	0.593301	0.296651	+	0.954986i	$0.404130\pi$
$368$	−14704.0	−2.08287
$369$	−716.137	−0.101031
$370$	−1861.73	−0.261585
$371$	−11957.8	−1.67336
$372$	−917.538	−0.127882
$373$	2253.61	0.312836	0.156418	−	0.987691i	$-0.450005\pi$
$373$	2253.61	0.312836	0.156418	+	0.987691i	$0.450005\pi$
$374$	−1422.32	−0.196649
$375$	4438.68	0.611234
$376$	1559.99	0.213964
$377$	−6328.24	−0.864512
$378$	2682.79	0.365047
$379$	4718.97	0.639570	0.319785	−	0.947490i	$-0.396389\pi$
$379$	4718.97	0.639570	0.319785	+	0.947490i	$0.396389\pi$
$380$	1574.84	0.212599
$381$	−6011.40	−0.808328
$382$	−8068.33	−1.08066
$383$	823.911	0.109921	0.0549607	−	0.998489i	$-0.482497\pi$
$383$	823.911	0.109921	0.0549607	+	0.998489i	$0.482497\pi$
$384$	−5129.56	−0.681685
$385$	3683.42	0.487596
$386$	12355.2	1.62918
$387$	671.489	0.0882008
$388$	639.457	0.0836688
$389$	10382.7	1.35328	0.676639	−	0.736315i	$-0.263436\pi$
$389$	10382.7	1.35328	0.676639	+	0.736315i	$0.263436\pi$
$390$	−3283.40	−0.426312
$391$	8454.26	1.09348
$392$	14268.1	1.83839
$393$	3143.43	0.403473
$394$	−8262.95	−1.05655
$395$	−1587.72	−0.202245
$396$	139.800	0.0177405
$397$	−3834.75	−0.484788	−0.242394	−	0.970178i	$-0.577933\pi$
$397$	−3834.75	−0.484788	−0.242394	+	0.970178i	$0.577933\pi$
$398$	−3682.82	−0.463827
$399$	10480.6	1.31500
$400$	1327.11	0.165889
$401$	−10501.4	−1.30776	−0.653882	−	0.756597i	$-0.726861\pi$
$401$	−10501.4	−1.30776	−0.653882	+	0.756597i	$0.726861\pi$
$402$	−3856.19	−0.478431
$403$	7473.24	0.923743
$404$	−2553.32	−0.314436
$405$	−837.461	−0.102750
$406$	18223.3	2.22760
$407$	−645.632	−0.0786309
$408$	2555.48	0.310086
$409$	−8465.63	−1.02347	−0.511734	−	0.859144i	$-0.670997\pi$
$409$	−8465.63	−1.02347	−0.511734	+	0.859144i	$0.670997\pi$
$410$	−2523.93	−0.304020
$411$	904.715	0.108580
$412$	399.558	0.0477787
$413$	20691.4	2.46527
$414$	−5538.60	−0.657506
$415$	−4505.95	−0.532984
$416$	−2180.66	−0.257009
$417$	−3237.04	−0.380140
$418$	3640.16	0.425948
$419$	−2182.50	−0.254468	−0.127234	−	0.991873i	$-0.540610\pi$
$419$	−2182.50	−0.254468	−0.127234	+	0.991873i	$0.540610\pi$
$420$	1418.58	0.164808
$421$	3077.05	0.356215	0.178107	−	0.984011i	$-0.443003\pi$
$421$	3077.05	0.356215	0.178107	+	0.984011i	$0.443003\pi$
$422$	11422.5	1.31763
$423$	694.664	0.0798481
$424$	7462.10	0.854697
$425$	−763.040	−0.0870891
$426$	−9336.39	−1.06185
$427$	−1975.64	−0.223907
$428$	−15.4925	−0.00174967
$429$	−1138.66	−0.128147
$430$	2366.57	0.265410
$431$	−4661.16	−0.520929	−0.260464	−	0.965483i	$-0.583876\pi$
$431$	−4661.16	−0.520929	−0.260464	+	0.965483i	$0.583876\pi$
$432$	−1979.18	−0.220424
$433$	508.088	0.0563907	0.0281954	−	0.999602i	$-0.491024\pi$
$433$	508.088	0.0563907	0.0281954	+	0.999602i	$0.491024\pi$
$434$	−21520.5	−2.38022
$435$	−5688.59	−0.627005
$436$	1644.26	0.180609
$437$	−21637.0	−2.36851
$438$	−8305.54	−0.906060
$439$	6703.16	0.728757	0.364379	−	0.931251i	$-0.381281\pi$
$439$	6703.16	0.728757	0.364379	+	0.931251i	$0.381281\pi$
$440$	−2298.59	−0.249048
$441$	6353.61	0.686061
$442$	4461.54	0.480122
$443$	−12813.2	−1.37420	−0.687101	−	0.726562i	$-0.741117\pi$
$443$	−12813.2	−1.37420	−0.687101	+	0.726562i	$0.741117\pi$
$444$	−248.649	−0.0265774
$445$	−4089.95	−0.435690
$446$	6132.64	0.651096
$447$	86.6672	0.00917051
$448$	−12713.2	−1.34072
$449$	9378.89	0.985784	0.492892	−	0.870091i	$-0.335940\pi$
$449$	9378.89	0.985784	0.492892	+	0.870091i	$0.335940\pi$
$450$	499.887	0.0523664
$451$	−875.279	−0.0913864
$452$	−950.435	−0.0989042
$453$	−11013.9	−1.14234
$454$	−4954.47	−0.512169
$455$	−11554.1	−1.19048
$456$	−6540.26	−0.671657
$457$	−9658.76	−0.988661	−0.494330	−	0.869274i	$-0.664587\pi$
$457$	−9658.76	−0.988661	−0.494330	+	0.869274i	$0.664587\pi$
$458$	−13546.2	−1.38204
$459$	1137.96	0.115720
$460$	−2928.65	−0.296845
$461$	−6199.78	−0.626361	−0.313181	−	0.949694i	$-0.601395\pi$
$461$	−6199.78	−0.626361	−0.313181	+	0.949694i	$0.601395\pi$
$462$	3278.96	0.330197
$463$	2917.91	0.292888	0.146444	−	0.989219i	$-0.453217\pi$
$463$	2917.91	0.292888	0.146444	+	0.989219i	$0.453217\pi$
$464$	−13443.9	−1.34508
$465$	6717.85	0.669963
$466$	−1526.51	−0.151747
$467$	−3622.73	−0.358972	−0.179486	−	0.983761i	$-0.557443\pi$
$467$	−3622.73	−0.358972	−0.179486	+	0.983761i	$0.557443\pi$
$468$	−438.526	−0.0433138
$469$	−13569.7	−1.33602
$470$	2448.25	0.240275
$471$	721.516	0.0705853
$472$	−12912.2	−1.25918
$473$	820.709	0.0797806
$474$	−1413.38	−0.136959
$475$	1952.85	0.188638
$476$	−1927.59	−0.185611
$477$	3322.88	0.318961
$478$	4573.07	0.437589
$479$	−1289.67	−0.123020	−0.0615101	−	0.998106i	$-0.519592\pi$
$479$	−1289.67	−0.123020	−0.0615101	+	0.998106i	$0.519592\pi$
$480$	−1960.25	−0.186401
$481$	2025.22	0.191979
$482$	−3387.57	−0.320124
$483$	−19490.1	−1.83609
$484$	170.867	0.0160469
$485$	−4681.85	−0.438334
$486$	−745.504	−0.0695818
$487$	−18549.2	−1.72597	−0.862984	−	0.505231i	$-0.831407\pi$
$487$	−18549.2	−1.72597	−0.862984	+	0.505231i	$0.831407\pi$
$488$	1232.87	0.114364
$489$	2043.72	0.188999
$490$	22392.5	2.06447
$491$	−15696.8	−1.44274	−0.721371	−	0.692549i	$-0.756488\pi$
$491$	−15696.8	−1.44274	−0.721371	+	0.692549i	$0.756488\pi$
$492$	−337.092	−0.0308888
$493$	7729.75	0.706147
$494$	−11418.5	−1.03996
$495$	−1023.56	−0.0929410
$496$	15876.4	1.43724
$497$	−32854.3	−2.96523
$498$	−4011.17	−0.360934
$499$	−10850.9	−0.973456	−0.486728	−	0.873554i	$-0.661810\pi$
$499$	−10850.9	−0.973456	−0.486728	+	0.873554i	$0.661810\pi$
$500$	2089.33	0.186875
$501$	−1307.09	−0.116560
$502$	15776.0	1.40263
$503$	2648.81	0.234801	0.117400	−	0.993085i	$-0.462544\pi$
$503$	2648.81	0.234801	0.117400	+	0.993085i	$0.462544\pi$
$504$	−5891.29	−0.520672
$505$	18694.4	1.64730
$506$	−6769.40	−0.594736
$507$	−3019.26	−0.264478
$508$	−2829.62	−0.247134
$509$	10932.8	0.952042	0.476021	−	0.879434i	$-0.342079\pi$
$509$	10932.8	0.952042	0.476021	+	0.879434i	$0.342079\pi$
$510$	4010.58	0.348218
$511$	−29226.8	−2.53017
$512$	7219.58	0.623170
$513$	−2912.38	−0.250652
$514$	−2942.18	−0.252478
$515$	−2925.41	−0.250308
$516$	316.076	0.0269660
$517$	849.034	0.0722253
$518$	−5831.97	−0.494675
$519$	10133.9	0.857091
$520$	7210.21	0.608055
$521$	7209.65	0.606258	0.303129	−	0.952950i	$-0.401969\pi$
$521$	7209.65	0.606258	0.303129	+	0.952950i	$0.401969\pi$
$522$	−5063.96	−0.424604
$523$	−18745.2	−1.56725	−0.783625	−	0.621234i	$-0.786631\pi$
$523$	−18745.2	−1.56725	−0.783625	+	0.621234i	$0.786631\pi$
$524$	1479.64	0.123356
$525$	1759.08	0.146233
$526$	−23274.9	−1.92934
$527$	−9128.33	−0.754528
$528$	−2419.00	−0.199381
$529$	28070.2	2.30707
$530$	11711.0	0.959802
$531$	−5749.82	−0.469907
$532$	4933.29	0.402040
$533$	2745.57	0.223122
$534$	−3640.85	−0.295047
$535$	113.430	0.00916636
$536$	8468.03	0.682394
$537$	−1729.00	−0.138942
$538$	7038.66	0.564048
$539$	7765.52	0.620565
$540$	−394.200	−0.0314142
$541$	7637.76	0.606974	0.303487	−	0.952836i	$-0.401849\pi$
$541$	7637.76	0.606974	0.303487	+	0.952836i	$0.401849\pi$
$542$	1034.45	0.0819806
$543$	−10286.9	−0.812991
$544$	2663.61	0.209929
$545$	−12038.6	−0.946197
$546$	−10285.4	−0.806184
$547$	−16674.4	−1.30337	−0.651686	−	0.758489i	$-0.725938\pi$
$547$	−16674.4	−1.30337	−0.651686	+	0.758489i	$0.725938\pi$
$548$	425.857	0.0331966
$549$	549.000	0.0426790
$550$	610.973	0.0473672
$551$	−19782.8	−1.52954
$552$	12162.5	0.937811
$553$	−4973.61	−0.382459
$554$	14003.6	1.07392
$555$	1820.51	0.139237
$556$	−1523.70	−0.116222
$557$	17552.5	1.33523	0.667615	−	0.744506i	$-0.267315\pi$
$557$	17552.5	1.33523	0.667615	+	0.744506i	$0.267315\pi$
$558$	5980.20	0.453696
$559$	−2574.40	−0.194786
$560$	−24545.9	−1.85224
$561$	1390.84	0.104672
$562$	−17367.0	−1.30353
$563$	−7203.30	−0.539223	−0.269612	−	0.962969i	$-0.586895\pi$
$563$	−7203.30	−0.539223	−0.269612	+	0.962969i	$0.586895\pi$
$564$	326.985	0.0244123
$565$	6958.71	0.518151
$566$	2858.75	0.212301
$567$	−2623.40	−0.194307
$568$	20502.3	1.51454
$569$	5834.62	0.429877	0.214939	−	0.976628i	$-0.431045\pi$
$569$	5834.62	0.429877	0.214939	+	0.976628i	$0.431045\pi$
$570$	−10264.3	−0.754253
$571$	24932.5	1.82731	0.913654	−	0.406493i	$-0.133248\pi$
$571$	24932.5	1.82731	0.913654	+	0.406493i	$0.133248\pi$
$572$	−535.976	−0.0391788
$573$	7889.71	0.575214
$574$	−7906.36	−0.574922
$575$	−3631.61	−0.263389
$576$	3532.81	0.255556
$577$	21274.2	1.53493	0.767467	−	0.641089i	$-0.221517\pi$
$577$	21274.2	1.53493	0.767467	+	0.641089i	$0.221517\pi$
$578$	9623.05	0.692502
$579$	−12081.7	−0.867183
$580$	−2677.67	−0.191697
$581$	−14115.1	−1.00791
$582$	−4167.76	−0.296837
$583$	4061.30	0.288511
$584$	18238.6	1.29233
$585$	3210.71	0.226917
$586$	25500.8	1.79766
$587$	−11575.8	−0.813940	−0.406970	−	0.913442i	$-0.633415\pi$
$587$	−11575.8	−0.813940	−0.406970	+	0.913442i	$0.633415\pi$
$588$	2990.70	0.209752
$589$	23362.2	1.63433
$590$	−20264.5	−1.41403
$591$	8080.02	0.562382
$592$	4302.43	0.298697
$593$	−3867.87	−0.267849	−0.133925	−	0.990992i	$-0.542758\pi$
$593$	−3867.87	−0.267849	−0.133925	+	0.990992i	$0.542758\pi$
$594$	−911.172	−0.0629391
$595$	14113.0	0.972400
$596$	40.7950	0.00280374
$597$	3601.29	0.246886
$598$	21234.2	1.45206
$599$	11588.4	0.790467	0.395233	−	0.918581i	$-0.370664\pi$
$599$	11588.4	0.790467	0.395233	+	0.918581i	$0.370664\pi$
$600$	−1097.73	−0.0746911
$601$	−1789.24	−0.121438	−0.0607192	−	0.998155i	$-0.519339\pi$
$601$	−1789.24	−0.121438	−0.0607192	+	0.998155i	$0.519339\pi$
$602$	7413.43	0.501908
$603$	3770.82	0.254659
$604$	−5184.34	−0.349251
$605$	−1251.02	−0.0840683
$606$	16641.6	1.11555
$607$	−10023.6	−0.670254	−0.335127	−	0.942173i	$-0.608779\pi$
$607$	−10023.6	−0.670254	−0.335127	+	0.942173i	$0.608779\pi$
$608$	−6817.01	−0.454714
$609$	−17819.8	−1.18571
$610$	1934.88	0.128428
$611$	−2663.25	−0.176340
$612$	535.646	0.0353794
$613$	−15222.5	−1.00299	−0.501493	−	0.865161i	$-0.667216\pi$
$613$	−15222.5	−1.00299	−0.501493	+	0.865161i	$0.667216\pi$
$614$	14412.9	0.947323
$615$	2468.06	0.161824
$616$	−7200.47	−0.470966
$617$	29017.1	1.89333	0.946664	−	0.322223i	$-0.104430\pi$
$617$	29017.1	1.89333	0.946664	+	0.322223i	$0.104430\pi$
$618$	−2604.18	−0.169508
$619$	−3207.07	−0.208244	−0.104122	−	0.994565i	$-0.533203\pi$
$619$	−3207.07	−0.208244	−0.104122	+	0.994565i	$0.533203\pi$
$620$	3162.15	0.204831
$621$	5415.98	0.349977
$622$	−26382.0	−1.70068
$623$	−12812.0	−0.823919
$624$	7587.90	0.486794
$625$	−13034.2	−0.834187
$626$	−3015.89	−0.192554
$627$	−3559.58	−0.226724
$628$	339.624	0.0215804
$629$	−2473.74	−0.156812
$630$	−9245.81	−0.584701
$631$	−26850.6	−1.69398	−0.846992	−	0.531606i	$-0.821589\pi$
$631$	−26850.6	−1.69398	−0.846992	+	0.531606i	$0.821589\pi$
$632$	3103.72	0.195347
$633$	−11169.7	−0.701349
$634$	20340.8	1.27419
$635$	20717.3	1.29471
$636$	1564.11	0.0975172
$637$	−24358.9	−1.51512
$638$	−6189.28	−0.384069
$639$	9129.70	0.565204
$640$	17678.2	1.09186
$641$	−23089.6	−1.42275	−0.711377	−	0.702811i	$-0.751928\pi$
$641$	−23089.6	−1.42275	−0.711377	+	0.702811i	$0.751928\pi$
$642$	100.975	0.00620741
$643$	−31346.5	−1.92253	−0.961264	−	0.275629i	$-0.911114\pi$
$643$	−31346.5	−1.92253	−0.961264	+	0.275629i	$0.911114\pi$
$644$	−9174.15	−0.561354
$645$	−2314.18	−0.141273
$646$	13947.3	0.849457
$647$	3885.68	0.236108	0.118054	−	0.993007i	$-0.462334\pi$
$647$	3885.68	0.236108	0.118054	+	0.993007i	$0.462334\pi$
$648$	1637.10	0.0992457
$649$	−7027.55	−0.425047
$650$	−1916.50	−0.115648
$651$	21044.1	1.26695
$652$	961.998	0.0577834
$653$	13977.1	0.837619	0.418809	−	0.908074i	$-0.362448\pi$
$653$	13977.1	0.837619	0.418809	+	0.908074i	$0.362448\pi$
$654$	−10716.7	−0.640759
$655$	−10833.3	−0.646249
$656$	5832.77	0.347152
$657$	8121.67	0.482278
$658$	7669.29	0.454377
$659$	14753.1	0.872080	0.436040	−	0.899927i	$-0.356381\pi$
$659$	14753.1	0.872080	0.436040	+	0.899927i	$0.356381\pi$
$660$	−481.801	−0.0284152
$661$	33107.5	1.94816	0.974078	−	0.226214i	$-0.0726347\pi$
$661$	33107.5	1.94816	0.974078	+	0.226214i	$0.0726347\pi$
$662$	16830.0	0.988091
$663$	−4362.77	−0.255560
$664$	8808.37	0.514806
$665$	−36119.6	−2.10625
$666$	1620.61	0.0942904
$667$	36788.9	2.13564
$668$	−615.261	−0.0356365
$669$	−5996.87	−0.346566
$670$	13289.7	0.766310
$671$	671.000	0.0386046
$672$	−6140.58	−0.352497
$673$	21495.6	1.23119	0.615597	−	0.788061i	$-0.288915\pi$
$673$	21495.6	1.23119	0.615597	+	0.788061i	$0.288915\pi$
$674$	16382.7	0.936257
$675$	−488.820	−0.0278736
$676$	−1421.19	−0.0808598
$677$	1075.21	0.0610393	0.0305196	−	0.999534i	$-0.490284\pi$
$677$	1075.21	0.0610393	0.0305196	+	0.999534i	$0.490284\pi$
$678$	6194.61	0.350889
$679$	−14666.2	−0.828918
$680$	−8807.06	−0.496670
$681$	4844.78	0.272617
$682$	7309.14	0.410383
$683$	−16027.8	−0.897929	−0.448964	−	0.893550i	$-0.648207\pi$
$683$	−16027.8	−0.897929	−0.448964	+	0.893550i	$0.648207\pi$
$684$	−1370.88	−0.0766331
$685$	−3117.96	−0.173914
$686$	36064.3	2.00720
$687$	13246.3	0.735632
$688$	−5469.12	−0.303065
$689$	−12739.5	−0.704405
$690$	19087.9	1.05314
$691$	12651.1	0.696485	0.348243	−	0.937404i	$-0.386779\pi$
$691$	12651.1	0.696485	0.348243	+	0.937404i	$0.386779\pi$
$692$	4770.13	0.262042
$693$	−3206.37	−0.175758
$694$	−3838.45	−0.209950
$695$	11156.0	0.608877
$696$	11120.2	0.605620
$697$	−3353.63	−0.182250
$698$	−7693.62	−0.417203
$699$	1492.72	0.0807722
$700$	828.014	0.0447086
$701$	−1399.92	−0.0754268	−0.0377134	−	0.999289i	$-0.512007\pi$
$701$	−1399.92	−0.0754268	−0.0377134	+	0.999289i	$0.512007\pi$
$702$	2858.16	0.153667
$703$	6331.06	0.339659
$704$	4317.88	0.231159
$705$	−2394.05	−0.127894
$706$	25265.1	1.34683
$707$	58561.2	3.11516
$708$	−2706.49	−0.143667
$709$	−22449.0	−1.18913	−0.594563	−	0.804049i	$-0.702675\pi$
$709$	−22449.0	−1.18913	−0.594563	+	0.804049i	$0.702675\pi$
$710$	32176.4	1.70079
$711$	1382.09	0.0729006
$712$	7995.16	0.420830
$713$	−43445.3	−2.28196
$714$	12563.4	0.658504
$715$	3924.21	0.205254
$716$	−813.856	−0.0424793
$717$	−4471.83	−0.232920
$718$	14574.0	0.757517
$719$	20150.8	1.04520	0.522600	−	0.852578i	$-0.324962\pi$
$719$	20150.8	1.04520	0.522600	+	0.852578i	$0.324962\pi$
$720$	6820.93	0.353057
$721$	−9164.01	−0.473350
$722$	−14652.6	−0.755280
$723$	3312.58	0.170396
$724$	−4842.15	−0.248559
$725$	−3320.39	−0.170091
$726$	−1113.65	−0.0569306
$727$	−15492.4	−0.790346	−0.395173	−	0.918607i	$-0.629315\pi$
$727$	−15492.4	−0.790346	−0.395173	+	0.918607i	$0.629315\pi$
$728$	22586.4	1.14987
$729$	729.000	0.0370370
$730$	28623.7	1.45125
$731$	3144.55	0.159105
$732$	258.419	0.0130484
$733$	−33087.1	−1.66726	−0.833628	−	0.552326i	$-0.813740\pi$
$733$	−33087.1	−1.66726	−0.833628	+	0.552326i	$0.813740\pi$
$734$	−12797.3	−0.643538
$735$	−21896.7	−1.09887
$736$	12677.2	0.634901
$737$	4608.78	0.230348
$738$	2197.05	0.109586
$739$	10780.7	0.536635	0.268318	−	0.963330i	$-0.413532\pi$
$739$	10780.7	0.536635	0.268318	+	0.963330i	$0.413532\pi$
$740$	856.931	0.0425695
$741$	11165.7	0.553551
$742$	36685.5	1.81505
$743$	−22502.6	−1.11109	−0.555544	−	0.831487i	$-0.687490\pi$
$743$	−22502.6	−1.11109	−0.555544	+	0.831487i	$0.687490\pi$
$744$	−13132.3	−0.647114
$745$	−298.685	−0.0146886
$746$	−6913.90	−0.339324
$747$	3922.37	0.192118
$748$	654.679	0.0320019
$749$	355.326	0.0173342
$750$	−13617.5	−0.662989
$751$	−28465.4	−1.38311	−0.691555	−	0.722324i	$-0.743074\pi$
$751$	−28465.4	−1.38311	−0.691555	+	0.722324i	$0.743074\pi$
$752$	−5657.88	−0.274364
$753$	−15426.8	−0.746591
$754$	19414.5	0.937713
$755$	37957.7	1.82970
$756$	−1234.86	−0.0594064
$757$	−2477.01	−0.118928	−0.0594639	−	0.998230i	$-0.518939\pi$
$757$	−2477.01	−0.118928	−0.0594639	+	0.998230i	$0.518939\pi$
$758$	−14477.4	−0.693725
$759$	6619.54	0.316566
$760$	22540.0	1.07580
$761$	−40805.1	−1.94374	−0.971868	−	0.235525i	$-0.924319\pi$
$761$	−40805.1	−1.94374	−0.971868	+	0.235525i	$0.924319\pi$
$762$	18442.5	0.876772
$763$	−37711.6	−1.78932
$764$	3713.76	0.175863
$765$	−3921.79	−0.185350
$766$	−2527.69	−0.119229
$767$	22044.0	1.03776
$768$	6316.26	0.296769
$769$	−25803.7	−1.21002	−0.605009	−	0.796218i	$-0.706831\pi$
$769$	−25803.7	−1.21002	−0.605009	+	0.796218i	$0.706831\pi$
$770$	−11300.4	−0.528882
$771$	2877.04	0.134389
$772$	−5686.97	−0.265128
$773$	16247.4	0.755986	0.377993	−	0.925808i	$-0.376614\pi$
$773$	16247.4	0.755986	0.377993	+	0.925808i	$0.376614\pi$
$774$	−2060.07	−0.0956691
$775$	3921.16	0.181745
$776$	9152.23	0.423384
$777$	5702.86	0.263306
$778$	−31853.4	−1.46786
$779$	8582.98	0.394759
$780$	1511.31	0.0693764
$781$	11158.5	0.511246
$782$	−25937.0	−1.18607
$783$	4951.85	0.226009
$784$	−51748.7	−2.35736
$785$	−2486.59	−0.113058
$786$	−9643.78	−0.437636
$787$	10233.8	0.463526	0.231763	−	0.972772i	$-0.425551\pi$
$787$	10233.8	0.463526	0.231763	+	0.972772i	$0.425551\pi$
$788$	3803.33	0.171939
$789$	22759.6	1.02695
$790$	4870.99	0.219370
$791$	21798.5	0.979857
$792$	2000.90	0.0897711
$793$	−2104.79	−0.0942539
$794$	11764.7	0.525836
$795$	−11451.8	−0.510884
$796$	1695.16	0.0754816
$797$	−20514.5	−0.911744	−0.455872	−	0.890045i	$-0.650672\pi$
$797$	−20514.5	−0.911744	−0.455872	+	0.890045i	$0.650672\pi$
$798$	−32153.5	−1.42634
$799$	3253.08	0.144037
$800$	−1144.18	−0.0505662
$801$	3560.25	0.157048
$802$	32217.3	1.41850
$803$	9926.49	0.436237
$804$	1774.96	0.0778581
$805$	67169.5	2.94089
$806$	−22927.3	−1.00196
$807$	−6882.83	−0.300232
$808$	−36544.3	−1.59112
$809$	6701.40	0.291234	0.145617	−	0.989341i	$-0.453483\pi$
$809$	6701.40	0.291234	0.145617	+	0.989341i	$0.453483\pi$
$810$	2569.26	0.111450
$811$	6702.72	0.290215	0.145107	−	0.989416i	$-0.453647\pi$
$811$	6702.72	0.290215	0.145107	+	0.989416i	$0.453647\pi$
$812$	−8387.95	−0.362512
$813$	−1011.55	−0.0436366
$814$	1980.75	0.0852889
$815$	−7043.37	−0.302722
$816$	−9268.39	−0.397621
$817$	−8047.87	−0.344626
$818$	25971.9	1.11013
$819$	10057.7	0.429116
$820$	1161.74	0.0494751
$821$	15911.5	0.676390	0.338195	−	0.941076i	$-0.390184\pi$
$821$	15911.5	0.676390	0.338195	+	0.941076i	$0.390184\pi$
$822$	−2775.59	−0.117774
$823$	35976.2	1.52376	0.761878	−	0.647721i	$-0.224278\pi$
$823$	35976.2	1.52376	0.761878	+	0.647721i	$0.224278\pi$
$824$	5718.68	0.241771
$825$	−597.447	−0.0252127
$826$	−63479.6	−2.67402
$827$	31995.4	1.34533	0.672665	−	0.739947i	$-0.265149\pi$
$827$	31995.4	1.34533	0.672665	+	0.739947i	$0.265149\pi$
$828$	2549.35	0.107000
$829$	−694.713	−0.0291054	−0.0145527	−	0.999894i	$-0.504632\pi$
$829$	−694.713	−0.0291054	−0.0145527	+	0.999894i	$0.504632\pi$
$830$	13823.9	0.578113
$831$	−13693.5	−0.571629
$832$	−13544.3	−0.564380
$833$	29753.6	1.23758
$834$	9930.98	0.412328
$835$	4504.70	0.186696
$836$	−1675.52	−0.0693172
$837$	−5847.81	−0.241493
$838$	6695.72	0.276014
$839$	39995.5	1.64576	0.822882	−	0.568212i	$-0.192365\pi$
$839$	39995.5	1.64576	0.822882	+	0.568212i	$0.192365\pi$
$840$	20303.4	0.833969
$841$	9247.25	0.379156
$842$	−9440.15	−0.386377
$843$	16982.5	0.693842
$844$	−5257.65	−0.214426
$845$	10405.4	0.423618
$846$	−2131.17	−0.0866091
$847$	−3918.90	−0.158979
$848$	−27064.1	−1.09597
$849$	−2795.46	−0.113004
$850$	2340.95	0.0944633
$851$	−11773.5	−0.474255
$852$	4297.43	0.172802
$853$	−16095.2	−0.646060	−0.323030	−	0.946389i	$-0.604701\pi$
$853$	−16095.2	−0.646060	−0.323030	+	0.946389i	$0.604701\pi$
$854$	6061.11	0.242865
$855$	10037.1	0.401474
$856$	−221.736	−0.00885373
$857$	23551.1	0.938729	0.469364	−	0.883005i	$-0.344483\pi$
$857$	23551.1	0.938729	0.469364	+	0.883005i	$0.344483\pi$
$858$	3493.31	0.138997
$859$	5596.80	0.222305	0.111153	−	0.993803i	$-0.464546\pi$
$859$	5596.80	0.222305	0.111153	+	0.993803i	$0.464546\pi$
$860$	−1089.31	−0.0431919
$861$	7731.32	0.306020
$862$	14300.1	0.565038
$863$	28605.1	1.12831	0.564153	−	0.825670i	$-0.309203\pi$
$863$	28605.1	1.12831	0.564153	+	0.825670i	$0.309203\pi$
$864$	1706.37	0.0671897
$865$	−34925.0	−1.37282
$866$	−1558.77	−0.0611655
$867$	−9410.01	−0.368605
$868$	9905.62	0.387349
$869$	1689.22	0.0659411
$870$	17452.1	0.680095
$871$	−14456.8	−0.562400
$872$	23533.5	0.913926
$873$	4075.49	0.158001
$874$	66380.7	2.56906
$875$	−47919.4	−1.85140
$876$	3822.94	0.147449
$877$	−38126.4	−1.46800	−0.734001	−	0.679149i	$-0.762349\pi$
$877$	−38126.4	−1.46800	−0.734001	+	0.679149i	$0.762349\pi$
$878$	−20564.8	−0.790463
$879$	−24936.3	−0.956861
$880$	8336.69	0.319352
$881$	23610.6	0.902908	0.451454	−	0.892295i	$-0.350906\pi$
$881$	23610.6	0.902908	0.451454	+	0.892295i	$0.350906\pi$
$882$	−19492.4	−0.744152
$883$	50713.3	1.93277	0.966387	−	0.257091i	$-0.0827641\pi$
$883$	50713.3	1.93277	0.966387	+	0.257091i	$0.0827641\pi$
$884$	−2053.59	−0.0781333
$885$	19815.8	0.752658
$886$	39309.7	1.49056
$887$	−29002.4	−1.09786	−0.548932	−	0.835867i	$-0.684965\pi$
$887$	−29002.4	−1.09786	−0.548932	+	0.835867i	$0.684965\pi$
$888$	−3558.79	−0.134488
$889$	64898.2	2.44839
$890$	12547.6	0.472581
$891$	891.000	0.0335013
$892$	−2822.78	−0.105957
$893$	−8325.62	−0.311989
$894$	−265.888	−0.00994701
$895$	5958.73	0.222546
$896$	55378.1	2.06479
$897$	−20764.1	−0.772904
$898$	−28773.7	−1.06925
$899$	−39722.2	−1.47365
$900$	−230.092	−0.00852193
$901$	15560.9	0.575369
$902$	2685.28	0.0991244
$903$	−7249.31	−0.267156
$904$	−13603.1	−0.500478
$905$	35452.3	1.30218
$906$	33789.7	1.23906
$907$	27680.4	1.01335	0.506676	−	0.862136i	$-0.330874\pi$
$907$	27680.4	1.01335	0.506676	+	0.862136i	$0.330874\pi$
$908$	2280.48	0.0833485
$909$	−16273.2	−0.593783
$910$	35447.2	1.29128
$911$	36231.8	1.31769	0.658843	−	0.752280i	$-0.271046\pi$
$911$	36231.8	1.31769	0.658843	+	0.752280i	$0.271046\pi$
$912$	23720.7	0.861260
$913$	4794.01	0.173777
$914$	29632.3	1.07237
$915$	−1892.04	−0.0683596
$916$	6235.17	0.224908
$917$	−33936.0	−1.22210
$918$	−3491.16	−0.125518
$919$	11995.3	0.430564	0.215282	−	0.976552i	$-0.430933\pi$
$919$	11995.3	0.430564	0.215282	+	0.976552i	$0.430933\pi$
$920$	−41916.3	−1.50211
$921$	−14093.8	−0.504242
$922$	19020.4	0.679397
$923$	−35002.0	−1.24822
$924$	−1509.27	−0.0537351
$925$	1062.62	0.0377716
$926$	−8951.92	−0.317687
$927$	2546.53	0.0902255
$928$	11590.8	0.410007
$929$	−52651.9	−1.85948	−0.929738	−	0.368221i	$-0.879967\pi$
$929$	−52651.9	−1.85948	−0.929738	+	0.368221i	$0.879967\pi$
$930$	−20609.8	−0.726691
$931$	−76148.7	−2.68064
$932$	702.635	0.0246948
$933$	25797.9	0.905237
$934$	11114.2	0.389367
$935$	−4793.30	−0.167655
$936$	−6276.40	−0.219178
$937$	−10913.3	−0.380491	−0.190246	−	0.981736i	$-0.560928\pi$
$937$	−10913.3	−0.380491	−0.190246	+	0.981736i	$0.560928\pi$
$938$	41630.9	1.44914
$939$	2949.12	0.102493
$940$	−1126.90	−0.0391016
$941$	−12636.1	−0.437752	−0.218876	−	0.975753i	$-0.570239\pi$
$941$	−12636.1	−0.437752	−0.218876	+	0.975753i	$0.570239\pi$
$942$	−2213.55	−0.0765620
$943$	−15961.3	−0.551188
$944$	46830.9	1.61464
$945$	9041.12	0.311225
$946$	−2517.87	−0.0865359
$947$	−34911.4	−1.19796	−0.598980	−	0.800764i	$-0.704427\pi$
$947$	−34911.4	−1.19796	−0.598980	+	0.800764i	$0.704427\pi$
$948$	650.561	0.0222882
$949$	−31137.4	−1.06508
$950$	−5991.20	−0.204611
$951$	−19890.5	−0.678227
$952$	−27588.6	−0.939235
$953$	10713.6	0.364164	0.182082	−	0.983283i	$-0.441716\pi$
$953$	10713.6	0.364164	0.182082	+	0.983283i	$0.441716\pi$
$954$	−10194.3	−0.345968
$955$	−27190.7	−0.921329
$956$	−2104.93	−0.0712116
$957$	6052.26	0.204432
$958$	3956.61	0.133437
$959$	−9767.19	−0.328883
$960$	−12175.3	−0.409328
$961$	17118.3	0.574613
$962$	−6213.20	−0.208235
$963$	−98.7394	−0.00330408
$964$	1559.26	0.0520958
$965$	41637.7	1.38898
$966$	59794.0	1.99155
$967$	−41620.9	−1.38411	−0.692056	−	0.721844i	$-0.743295\pi$
$967$	−41620.9	−1.38411	−0.692056	+	0.721844i	$0.743295\pi$
$968$	2445.54	0.0812010
$969$	−13638.5	−0.452149
$970$	14363.5	0.475449
$971$	−8208.89	−0.271304	−0.135652	−	0.990757i	$-0.543313\pi$
$971$	−8208.89	−0.271304	−0.135652	+	0.990757i	$0.543313\pi$
$972$	343.147	0.0113235
$973$	34946.7	1.15143
$974$	56907.6	1.87211
$975$	1874.07	0.0615572
$976$	−4471.48	−0.146648
$977$	10766.0	0.352543	0.176272	−	0.984342i	$-0.443596\pi$
$977$	10766.0	0.352543	0.176272	+	0.984342i	$0.443596\pi$
$978$	−6269.97	−0.205002
$979$	4351.42	0.142055
$980$	−10307.0	−0.335964
$981$	10479.5	0.341064
$982$	48156.5	1.56490
$983$	51104.0	1.65815	0.829076	−	0.559136i	$-0.188867\pi$
$983$	51104.0	1.65815	0.829076	+	0.559136i	$0.188867\pi$
$984$	−4824.63	−0.156305
$985$	−27846.5	−0.900775
$986$	−23714.3	−0.765939
$987$	−7499.50	−0.241856
$988$	5255.78	0.169239
$989$	14966.2	0.481189
$990$	3140.21	0.100811
$991$	28863.4	0.925202	0.462601	−	0.886567i	$-0.346916\pi$
$991$	28863.4	0.925202	0.462601	+	0.886567i	$0.346916\pi$
$992$	−13688.0	−0.438098
$993$	−16457.4	−0.525942
$994$	100794.	3.21630
$995$	−12411.3	−0.395442
$996$	1846.29	0.0587370
$997$	13032.0	0.413968	0.206984	−	0.978344i	$-0.433635\pi$
$997$	13032.0	0.413968	0.206984	+	0.978344i	$0.433635\pi$
$998$	33289.8	1.05588
$999$	−1584.73	−0.0501889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.a.1.11	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.a.1.11	✓	36	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)

\(f(q)\)	\(=\)	\(q-3.06792 q^{2} +3.00000 q^{3} +1.41213 q^{4} -10.3390 q^{5} -9.20376 q^{6} -32.3876 q^{7} +20.2111 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.06792 q^{2} +3.00000 q^{3} +1.41213 q^{4} -10.3390 q^{5} -9.20376 q^{6} -32.3876 q^{7} +20.2111 q^{8} +9.00000 q^{9} +31.7193 q^{10} +11.0000 q^{11} +4.23638 q^{12} -34.5048 q^{13} +99.3625 q^{14} -31.0171 q^{15} -73.3029 q^{16} +42.1465 q^{17} -27.6113 q^{18} -107.866 q^{19} -14.6000 q^{20} -97.1628 q^{21} -33.7471 q^{22} +200.592 q^{23} +60.6332 q^{24} -18.1045 q^{25} +105.858 q^{26} +27.0000 q^{27} -45.7354 q^{28} +183.402 q^{29} +95.1579 q^{30} -216.586 q^{31} +63.1989 q^{32} +33.0000 q^{33} -129.302 q^{34} +334.856 q^{35} +12.7091 q^{36} -58.6938 q^{37} +330.924 q^{38} -103.514 q^{39} -208.963 q^{40} -79.5708 q^{41} +298.088 q^{42} +74.6099 q^{43} +15.5334 q^{44} -93.0513 q^{45} -615.400 q^{46} +77.1849 q^{47} -219.909 q^{48} +705.957 q^{49} +55.5430 q^{50} +126.440 q^{51} -48.7251 q^{52} +369.209 q^{53} -82.8338 q^{54} -113.729 q^{55} -654.588 q^{56} -323.598 q^{57} -562.662 q^{58} -638.868 q^{59} -43.8000 q^{60} +61.0000 q^{61} +664.467 q^{62} -291.488 q^{63} +392.534 q^{64} +356.746 q^{65} -101.241 q^{66} +418.980 q^{67} +59.5162 q^{68} +601.776 q^{69} -1027.31 q^{70} +1014.41 q^{71} +181.900 q^{72} +902.408 q^{73} +180.068 q^{74} -54.3134 q^{75} -152.320 q^{76} -356.264 q^{77} +317.574 q^{78} +153.565 q^{79} +757.881 q^{80} +81.0000 q^{81} +244.117 q^{82} +435.819 q^{83} -137.206 q^{84} -435.754 q^{85} -228.897 q^{86} +550.206 q^{87} +222.322 q^{88} +395.583 q^{89} +285.474 q^{90} +1117.53 q^{91} +283.261 q^{92} -649.757 q^{93} -236.797 q^{94} +1115.23 q^{95} +189.597 q^{96} +452.833 q^{97} -2165.82 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * q^99

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