LMFDB - Embedded newform 2013.4.a.b.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:	$1$
Dimension:	$36$
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)

$f(q)$	$=$	$q-4.97623 q^{2} -3.00000 q^{3} +16.7629 q^{4} -4.44765 q^{5} +14.9287 q^{6} -23.2908 q^{7} -43.6062 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.97623 q^{2} -3.00000 q^{3} +16.7629 q^{4} -4.44765 q^{5} +14.9287 q^{6} -23.2908 q^{7} -43.6062 q^{8} +9.00000 q^{9} +22.1326 q^{10} -11.0000 q^{11} -50.2887 q^{12} -53.2771 q^{13} +115.900 q^{14} +13.3430 q^{15} +82.8916 q^{16} +9.88961 q^{17} -44.7861 q^{18} +69.0130 q^{19} -74.5556 q^{20} +69.8723 q^{21} +54.7386 q^{22} -156.685 q^{23} +130.819 q^{24} -105.218 q^{25} +265.119 q^{26} -27.0000 q^{27} -390.421 q^{28} +3.00543 q^{29} -66.3977 q^{30} +66.7718 q^{31} -63.6379 q^{32} +33.0000 q^{33} -49.2130 q^{34} +103.589 q^{35} +150.866 q^{36} +143.127 q^{37} -343.425 q^{38} +159.831 q^{39} +193.945 q^{40} +141.732 q^{41} -347.701 q^{42} +33.3618 q^{43} -184.392 q^{44} -40.0289 q^{45} +779.703 q^{46} +33.0090 q^{47} -248.675 q^{48} +199.460 q^{49} +523.591 q^{50} -29.6688 q^{51} -893.078 q^{52} +182.039 q^{53} +134.358 q^{54} +48.9242 q^{55} +1015.62 q^{56} -207.039 q^{57} -14.9557 q^{58} +300.869 q^{59} +223.667 q^{60} +61.0000 q^{61} -332.272 q^{62} -209.617 q^{63} -346.455 q^{64} +236.958 q^{65} -164.216 q^{66} +450.556 q^{67} +165.779 q^{68} +470.056 q^{69} -515.485 q^{70} +224.472 q^{71} -392.456 q^{72} -489.014 q^{73} -712.234 q^{74} +315.655 q^{75} +1156.86 q^{76} +256.199 q^{77} -795.358 q^{78} -1234.64 q^{79} -368.673 q^{80} +81.0000 q^{81} -705.289 q^{82} +909.454 q^{83} +1171.26 q^{84} -43.9856 q^{85} -166.016 q^{86} -9.01628 q^{87} +479.668 q^{88} -949.770 q^{89} +199.193 q^{90} +1240.86 q^{91} -2626.50 q^{92} -200.315 q^{93} -164.260 q^{94} -306.946 q^{95} +190.914 q^{96} -537.661 q^{97} -992.561 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9 - 45 * q^10 - 396 * q^11 - 354 * q^12 - 13 * q^13 + 82 * q^14 + 15 * q^15 + 262 * q^16 + 204 * q^17 + 18 * q^18 - 431 * q^19 + 354 * q^20 + 189 * q^21 - 22 * q^22 - 179 * q^23 - 9 * q^24 + 711 * q^25 + 331 * q^26 - 972 * q^27 - 296 * q^28 + 478 * q^29 + 135 * q^30 - 574 * q^31 - 149 * q^32 + 1188 * q^33 + 276 * q^34 - 194 * q^35 + 1062 * q^36 - 12 * q^37 + 325 * q^38 + 39 * q^39 - 185 * q^40 + 900 * q^41 - 246 * q^42 - 1053 * q^43 - 1298 * q^44 - 45 * q^45 - 407 * q^46 - 653 * q^47 - 786 * q^48 + 753 * q^49 - 1520 * q^50 - 612 * q^51 + 60 * q^52 + 735 * q^53 - 54 * q^54 + 55 * q^55 - 809 * q^56 + 1293 * q^57 - 1399 * q^58 - 1127 * q^59 - 1062 * q^60 + 2196 * q^61 - 1795 * q^62 - 567 * q^63 - 2133 * q^64 + 1886 * q^65 + 66 * q^66 - 989 * q^67 + 10 * q^68 + 537 * q^69 - 2130 * q^70 + 61 * q^71 + 27 * q^72 - 1471 * q^73 - 122 * q^74 - 2133 * q^75 - 4064 * q^76 + 693 * q^77 - 993 * q^78 - 1853 * q^79 + 2197 * q^80 + 2916 * q^81 - 2566 * q^82 - 3523 * q^83 + 888 * q^84 - 449 * q^85 - 771 * q^86 - 1434 * q^87 - 33 * q^88 + 2209 * q^89 - 405 * q^90 - 1668 * q^91 - 1999 * q^92 + 1722 * q^93 - 2844 * q^94 + 1220 * q^95 + 447 * q^96 - 3622 * q^97 + 3846 * 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 $

$2$	−4.97623	−1.75936	−0.879682	−	0.475562i	$-0.842245\pi$
$2$	−4.97623	−1.75936	−0.879682	+	0.475562i	$0.842245\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	16.7629	2.09536
$5$	−4.44765	−0.397810	−0.198905	−	0.980019i	$-0.563739\pi$
$5$	−4.44765	−0.397810	−0.198905	+	0.980019i	$0.563739\pi$
$6$	14.9287	1.01577
$7$	−23.2908	−1.25758	−0.628792	−	0.777574i	$-0.716450\pi$
$7$	−23.2908	−1.25758	−0.628792	+	0.777574i	$0.716450\pi$
$8$	−43.6062	−1.92714
$9$	9.00000	0.333333
$10$	22.1326	0.699893
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−50.2887	−1.20976
$13$	−53.2771	−1.13665	−0.568323	−	0.822805i	$-0.692408\pi$
$13$	−53.2771	−1.13665	−0.568323	+	0.822805i	$0.692408\pi$
$14$	115.900	2.21255
$15$	13.3430	0.229676
$16$	82.8916	1.29518
$17$	9.88961	0.141093	0.0705466	−	0.997508i	$-0.477526\pi$
$17$	9.88961	0.141093	0.0705466	+	0.997508i	$0.477526\pi$
$18$	−44.7861	−0.586455
$19$	69.0130	0.833298	0.416649	−	0.909067i	$-0.363204\pi$
$19$	69.0130	0.833298	0.416649	+	0.909067i	$0.363204\pi$
$20$	−74.5556	−0.833557
$21$	69.8723	0.726066
$22$	54.7386	0.530468
$23$	−156.685	−1.42048	−0.710242	−	0.703957i	$-0.751415\pi$
$23$	−156.685	−1.42048	−0.710242	+	0.703957i	$0.751415\pi$
$24$	130.819	1.11264
$25$	−105.218	−0.841747
$26$	265.119	1.99978
$27$	−27.0000	−0.192450
$28$	−390.421	−2.63509
$29$	3.00543	0.0192446	0.00962231	−	0.999954i	$-0.496937\pi$
$29$	3.00543	0.0192446	0.00962231	+	0.999954i	$0.496937\pi$
$30$	−66.3977	−0.404083
$31$	66.7718	0.386857	0.193429	−	0.981114i	$-0.438039\pi$
$31$	66.7718	0.386857	0.193429	+	0.981114i	$0.438039\pi$
$32$	−63.6379	−0.351553
$33$	33.0000	0.174078
$34$	−49.2130	−0.248234
$35$	103.589	0.500280
$36$	150.866	0.698454
$37$	143.127	0.635945	0.317972	−	0.948100i	$-0.396998\pi$
$37$	143.127	0.635945	0.317972	+	0.948100i	$0.396998\pi$
$38$	−343.425	−1.46607
$39$	159.831	0.656243
$40$	193.945	0.766636
$41$	141.732	0.539872	0.269936	−	0.962878i	$-0.412997\pi$
$41$	141.732	0.539872	0.269936	+	0.962878i	$0.412997\pi$
$42$	−347.701	−1.27742
$43$	33.3618	0.118317	0.0591585	−	0.998249i	$-0.481158\pi$
$43$	33.3618	0.118317	0.0591585	+	0.998249i	$0.481158\pi$
$44$	−184.392	−0.631775
$45$	−40.0289	−0.132603
$46$	779.703	2.49915
$47$	33.0090	0.102444	0.0512218	−	0.998687i	$-0.483688\pi$
$47$	33.0090	0.102444	0.0512218	+	0.998687i	$0.483688\pi$
$48$	−248.675	−0.747773
$49$	199.460	0.581517
$50$	523.591	1.48094
$51$	−29.6688	−0.0814602
$52$	−893.078	−2.38169
$53$	182.039	0.471792	0.235896	−	0.971778i	$-0.424197\pi$
$53$	182.039	0.471792	0.235896	+	0.971778i	$0.424197\pi$
$54$	134.358	0.338590
$55$	48.9242	0.119944
$56$	1015.62	2.42354
$57$	−207.039	−0.481105
$58$	−14.9557	−0.0338583
$59$	300.869	0.663896	0.331948	−	0.943298i	$-0.392294\pi$
$59$	300.869	0.663896	0.331948	+	0.943298i	$0.392294\pi$
$60$	223.667	0.481254
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−332.272	−0.680623
$63$	−209.617	−0.419195
$64$	−346.455	−0.676670
$65$	236.958	0.452170
$66$	−164.216	−0.306266
$67$	450.556	0.821554	0.410777	−	0.911736i	$-0.365257\pi$
$67$	450.556	0.821554	0.410777	+	0.911736i	$0.365257\pi$
$68$	165.779	0.295641
$69$	470.056	0.820117
$70$	−515.485	−0.880174
$71$	224.472	0.375210	0.187605	−	0.982245i	$-0.439928\pi$
$71$	224.472	0.375210	0.187605	+	0.982245i	$0.439928\pi$
$72$	−392.456	−0.642380
$73$	−489.014	−0.784038	−0.392019	−	0.919957i	$-0.628223\pi$
$73$	−489.014	−0.784038	−0.392019	+	0.919957i	$0.628223\pi$
$74$	−712.234	−1.11886
$75$	315.655	0.485983
$76$	1156.86	1.74606
$77$	256.199	0.379176
$78$	−795.358	−1.15457
$79$	−1234.64	−1.75832	−0.879162	−	0.476522i	$-0.841897\pi$
$79$	−1234.64	−1.75832	−0.879162	+	0.476522i	$0.841897\pi$
$80$	−368.673	−0.515236
$81$	81.0000	0.111111
$82$	−705.289	−0.949832
$83$	909.454	1.20272	0.601359	−	0.798979i	$-0.294626\pi$
$83$	909.454	1.20272	0.601359	+	0.798979i	$0.294626\pi$
$84$	1171.26	1.52137
$85$	−43.9856	−0.0561283
$86$	−166.016	−0.208163
$87$	−9.01628	−0.0111109
$88$	479.668	0.581055
$89$	−949.770	−1.13118	−0.565592	−	0.824685i	$-0.691352\pi$
$89$	−949.770	−1.13118	−0.565592	+	0.824685i	$0.691352\pi$
$90$	199.193	0.233298
$91$	1240.86	1.42943
$92$	−2626.50	−2.97643
$93$	−200.315	−0.223352
$94$	−164.260	−0.180236
$95$	−306.946	−0.331495
$96$	190.914	0.202969
$97$	−537.661	−0.562796	−0.281398	−	0.959591i	$-0.590798\pi$
$97$	−537.661	−0.562796	−0.281398	+	0.959591i	$0.590798\pi$
$98$	−992.561	−1.02310
$99$	−99.0000	−0.100504
$100$	−1763.76	−1.76376
$101$	943.002	0.929032	0.464516	−	0.885565i	$-0.346228\pi$
$101$	943.002	0.929032	0.464516	+	0.885565i	$0.346228\pi$
$102$	147.639	0.143318
$103$	−1065.39	−1.01918	−0.509592	−	0.860416i	$-0.670204\pi$
$103$	−1065.39	−1.01918	−0.509592	+	0.860416i	$0.670204\pi$
$104$	2323.21	2.19048
$105$	−310.768	−0.288837
$106$	−905.869	−0.830054
$107$	922.309	0.833298	0.416649	−	0.909067i	$-0.363204\pi$
$107$	922.309	0.833298	0.416649	+	0.909067i	$0.363204\pi$
$108$	−452.598	−0.403253
$109$	1232.87	1.08338	0.541688	−	0.840580i	$-0.317786\pi$
$109$	1232.87	1.08338	0.541688	+	0.840580i	$0.317786\pi$
$110$	−243.458	−0.211026
$111$	−429.381	−0.367163
$112$	−1930.61	−1.62880
$113$	−178.659	−0.148733	−0.0743664	−	0.997231i	$-0.523693\pi$
$113$	−178.659	−0.148733	−0.0743664	+	0.997231i	$0.523693\pi$
$114$	1030.27	0.846439
$115$	696.882	0.565083
$116$	50.3797	0.0403244
$117$	−479.494	−0.378882
$118$	−1497.20	−1.16803
$119$	−230.337	−0.177436
$120$	−581.836	−0.442618
$121$	121.000	0.0909091
$122$	−303.550	−0.225263
$123$	−425.195	−0.311695
$124$	1119.29	0.810606
$125$	1023.93	0.732666
$126$	1043.10	0.737516
$127$	−515.620	−0.360267	−0.180133	−	0.983642i	$-0.557653\pi$
$127$	−515.620	−0.360267	−0.180133	+	0.983642i	$0.557653\pi$
$128$	2233.15	1.54206
$129$	−100.085	−0.0683103
$130$	−1179.16	−0.795531
$131$	2486.29	1.65823	0.829114	−	0.559079i	$-0.188845\pi$
$131$	2486.29	1.65823	0.829114	+	0.559079i	$0.188845\pi$
$132$	553.176	0.364756
$133$	−1607.37	−1.04794
$134$	−2242.07	−1.44541
$135$	120.087	0.0765586
$136$	−431.249	−0.271906
$137$	246.956	0.154006	0.0770031	−	0.997031i	$-0.475465\pi$
$137$	246.956	0.154006	0.0770031	+	0.997031i	$0.475465\pi$
$138$	−2339.11	−1.44288
$139$	386.184	0.235652	0.117826	−	0.993034i	$-0.462407\pi$
$139$	386.184	0.235652	0.117826	+	0.993034i	$0.462407\pi$
$140$	1736.46	1.04827
$141$	−99.0269	−0.0591459
$142$	−1117.02	−0.660131
$143$	586.048	0.342712
$144$	746.024	0.431727
$145$	−13.3671	−0.00765571
$146$	2433.45	1.37941
$147$	−598.381	−0.335739
$148$	2399.23	1.33253
$149$	2846.63	1.56513	0.782567	−	0.622566i	$-0.213910\pi$
$149$	2846.63	1.56513	0.782567	+	0.622566i	$0.213910\pi$
$150$	−1570.77	−0.855021
$151$	−622.237	−0.335344	−0.167672	−	0.985843i	$-0.553625\pi$
$151$	−622.237	−0.335344	−0.167672	+	0.985843i	$0.553625\pi$
$152$	−3009.40	−1.60588
$153$	89.0065	0.0470310
$154$	−1274.90	−0.667108
$155$	−296.978	−0.153896
$156$	2679.23	1.37507
$157$	1352.80	0.687679	0.343839	−	0.939028i	$-0.388272\pi$
$157$	1352.80	0.687679	0.343839	+	0.939028i	$0.388272\pi$
$158$	6143.85	3.09353
$159$	−546.117	−0.272389
$160$	283.039	0.139851
$161$	3649.32	1.78638
$162$	−403.075	−0.195485
$163$	−1962.51	−0.943043	−0.471521	−	0.881855i	$-0.656295\pi$
$163$	−1962.51	−0.943043	−0.471521	+	0.881855i	$0.656295\pi$
$164$	2375.83	1.13123
$165$	−146.773	−0.0692499
$166$	−4525.66	−2.11602
$167$	−472.438	−0.218912	−0.109456	−	0.993992i	$-0.534911\pi$
$167$	−472.438	−0.218912	−0.109456	+	0.993992i	$0.534911\pi$
$168$	−3046.87	−1.39923
$169$	641.448	0.291965
$170$	218.882	0.0987501
$171$	621.117	0.277766
$172$	559.241	0.247917
$173$	3162.67	1.38990	0.694952	−	0.719056i	$-0.255426\pi$
$173$	3162.67	1.38990	0.694952	+	0.719056i	$0.255426\pi$
$174$	44.8671	0.0195481
$175$	2450.62	1.05857
$176$	−911.807	−0.390512
$177$	−902.608	−0.383301
$178$	4726.27	1.99016
$179$	−67.9641	−0.0283792	−0.0141896	−	0.999899i	$-0.504517\pi$
$179$	−67.9641	−0.0283792	−0.0141896	+	0.999899i	$0.504517\pi$
$180$	−671.000	−0.277852
$181$	3649.59	1.49874	0.749369	−	0.662153i	$-0.230357\pi$
$181$	3649.59	1.49874	0.749369	+	0.662153i	$0.230357\pi$
$182$	−6174.83	−2.51488
$183$	−183.000	−0.0739221
$184$	6832.45	2.73747
$185$	−636.580	−0.252985
$186$	996.816	0.392958
$187$	−108.786	−0.0425412
$188$	553.326	0.214657
$189$	628.851	0.242022
$190$	1527.43	0.583220
$191$	3864.61	1.46405	0.732024	−	0.681279i	$-0.238576\pi$
$191$	3864.61	1.46405	0.732024	+	0.681279i	$0.238576\pi$
$192$	1039.37	0.390676
$193$	−3954.31	−1.47480	−0.737402	−	0.675454i	$-0.763948\pi$
$193$	−3954.31	−1.47480	−0.737402	+	0.675454i	$0.763948\pi$
$194$	2675.53	0.990164
$195$	−710.874	−0.261060
$196$	3343.53	1.21849
$197$	−1880.86	−0.680231	−0.340116	−	0.940384i	$-0.610466\pi$
$197$	−1880.86	−0.680231	−0.340116	+	0.940384i	$0.610466\pi$
$198$	492.647	0.176823
$199$	−1456.89	−0.518976	−0.259488	−	0.965746i	$-0.583554\pi$
$199$	−1456.89	−0.518976	−0.259488	+	0.965746i	$0.583554\pi$
$200$	4588.18	1.62217
$201$	−1351.67	−0.474325
$202$	−4692.60	−1.63451
$203$	−69.9988	−0.0242017
$204$	−497.336	−0.170689
$205$	−630.373	−0.214767
$206$	5301.63	1.79312
$207$	−1410.17	−0.473495
$208$	−4416.22	−1.47216
$209$	−759.143	−0.251249
$210$	1546.45	0.508169
$211$	1408.04	0.459401	0.229701	−	0.973261i	$-0.426225\pi$
$211$	1408.04	0.459401	0.229701	+	0.973261i	$0.426225\pi$
$212$	3051.50	0.988576
$213$	−673.415	−0.216627
$214$	−4589.62	−1.46608
$215$	−148.382	−0.0470677
$216$	1177.37	0.370878
$217$	−1555.17	−0.486505
$218$	−6135.07	−1.90605
$219$	1467.04	0.452665
$220$	820.111	0.251327
$221$	−526.890	−0.160373
$222$	2136.70	0.645973
$223$	2654.77	0.797204	0.398602	−	0.917124i	$-0.369495\pi$
$223$	2654.77	0.797204	0.398602	+	0.917124i	$0.369495\pi$
$224$	1482.18	0.442108
$225$	−946.965	−0.280582
$226$	889.047	0.261675
$227$	−2887.81	−0.844363	−0.422182	−	0.906511i	$-0.638736\pi$
$227$	−2887.81	−0.844363	−0.422182	+	0.906511i	$0.638736\pi$
$228$	−3470.57	−1.00809
$229$	5696.67	1.64387	0.821936	−	0.569579i	$-0.192894\pi$
$229$	5696.67	1.64387	0.821936	+	0.569579i	$0.192894\pi$
$230$	−3467.85	−0.994187
$231$	−768.596	−0.218917
$232$	−131.055	−0.0370871
$233$	2489.01	0.699831	0.349916	−	0.936781i	$-0.386210\pi$
$233$	2489.01	0.699831	0.349916	+	0.936781i	$0.386210\pi$
$234$	2386.07	0.666592
$235$	−146.812	−0.0407531
$236$	5043.44	1.39110
$237$	3703.91	1.01517
$238$	1146.21	0.312175
$239$	4922.75	1.33233	0.666164	−	0.745805i	$-0.267935\pi$
$239$	4922.75	1.33233	0.666164	+	0.745805i	$0.267935\pi$
$240$	1106.02	0.297472
$241$	6219.37	1.66234	0.831172	−	0.556016i	$-0.187671\pi$
$241$	6219.37	1.66234	0.831172	+	0.556016i	$0.187671\pi$
$242$	−602.124	−0.159942
$243$	−243.000	−0.0641500
$244$	1022.54	0.268284
$245$	−887.131	−0.231334
$246$	2115.87	0.548386
$247$	−3676.81	−0.947165
$248$	−2911.67	−0.745528
$249$	−2728.36	−0.694389
$250$	−5095.32	−1.28903
$251$	−252.658	−0.0635364	−0.0317682	−	0.999495i	$-0.510114\pi$
$251$	−252.658	−0.0635364	−0.0317682	+	0.999495i	$0.510114\pi$
$252$	−3513.79	−0.878365
$253$	1723.54	0.428292
$254$	2565.85	0.633840
$255$	131.957	0.0324057
$256$	−8341.01	−2.03638
$257$	−2985.88	−0.724724	−0.362362	−	0.932037i	$-0.618030\pi$
$257$	−2985.88	−0.724724	−0.362362	+	0.932037i	$0.618030\pi$
$258$	498.048	0.120183
$259$	−3333.54	−0.799754
$260$	3972.10	0.947459
$261$	27.0489	0.00641487
$262$	−12372.3	−2.91743
$263$	3968.57	0.930466	0.465233	−	0.885188i	$-0.345971\pi$
$263$	3968.57	0.930466	0.465233	+	0.885188i	$0.345971\pi$
$264$	−1439.01	−0.335472
$265$	−809.647	−0.187684
$266$	7998.63	1.84371
$267$	2849.31	0.653089
$268$	7552.62	1.72145
$269$	5401.63	1.22432	0.612162	−	0.790732i	$-0.290300\pi$
$269$	5401.63	1.22432	0.612162	+	0.790732i	$0.290300\pi$
$270$	−597.579	−0.134694
$271$	−1414.99	−0.317174	−0.158587	−	0.987345i	$-0.550694\pi$
$271$	−1414.99	−0.317174	−0.158587	+	0.987345i	$0.550694\pi$
$272$	819.765	0.182741
$273$	−3722.59	−0.825281
$274$	−1228.91	−0.270953
$275$	1157.40	0.253796
$276$	7879.50	1.71844
$277$	−6371.54	−1.38205	−0.691026	−	0.722830i	$-0.742841\pi$
$277$	−6371.54	−1.38205	−0.691026	+	0.722830i	$0.742841\pi$
$278$	−1921.74	−0.414599
$279$	600.946	0.128952
$280$	−4517.14	−0.964110
$281$	−2439.21	−0.517832	−0.258916	−	0.965900i	$-0.583365\pi$
$281$	−2439.21	−0.517832	−0.258916	+	0.965900i	$0.583365\pi$
$282$	492.781	0.104059
$283$	−2958.82	−0.621497	−0.310749	−	0.950492i	$-0.600580\pi$
$283$	−2958.82	−0.621497	−0.310749	+	0.950492i	$0.600580\pi$
$284$	3762.80	0.786200
$285$	920.838	0.191388
$286$	−2916.31	−0.602955
$287$	−3301.04	−0.678934
$288$	−572.741	−0.117184
$289$	−4815.20	−0.980093
$290$	66.5178	0.0134692
$291$	1612.98	0.324931
$292$	−8197.30	−1.64284
$293$	5294.09	1.05558	0.527788	−	0.849376i	$-0.323022\pi$
$293$	5294.09	1.05558	0.527788	+	0.849376i	$0.323022\pi$
$294$	2977.68	0.590687
$295$	−1338.16	−0.264105
$296$	−6241.23	−1.22556
$297$	297.000	0.0580259
$298$	−14165.5	−2.75364
$299$	8347.74	1.61459
$300$	5291.29	1.01831
$301$	−777.022	−0.148793
$302$	3096.40	0.589992
$303$	−2829.01	−0.536377
$304$	5720.59	1.07927
$305$	−271.307	−0.0509344
$306$	−442.917	−0.0827447
$307$	7070.98	1.31454	0.657268	−	0.753657i	$-0.271712\pi$
$307$	7070.98	1.31454	0.657268	+	0.753657i	$0.271712\pi$
$308$	4294.63	0.794511
$309$	3196.17	0.588426
$310$	1477.83	0.270759
$311$	−8244.64	−1.50325	−0.751625	−	0.659590i	$-0.770730\pi$
$311$	−8244.64	−1.50325	−0.751625	+	0.659590i	$0.770730\pi$
$312$	−6969.64	−1.26467
$313$	−8815.61	−1.59197	−0.795986	−	0.605314i	$-0.793047\pi$
$313$	−8815.61	−1.59197	−0.795986	+	0.605314i	$0.793047\pi$
$314$	−6731.87	−1.20988
$315$	932.304	0.166760
$316$	−20696.1	−3.68433
$317$	−6590.86	−1.16776	−0.583880	−	0.811840i	$-0.698466\pi$
$317$	−6590.86	−1.16776	−0.583880	+	0.811840i	$0.698466\pi$
$318$	2717.61	0.479232
$319$	−33.0597	−0.00580247
$320$	1540.91	0.269186
$321$	−2766.93	−0.481105
$322$	−18159.9	−3.14289
$323$	682.512	0.117573
$324$	1357.79	0.232818
$325$	5605.73	0.956769
$326$	9765.93	1.65916
$327$	−3698.62	−0.625487
$328$	−6180.38	−1.04041
$329$	−768.804	−0.128831
$330$	730.375	0.121836
$331$	−3220.18	−0.534734	−0.267367	−	0.963595i	$-0.586154\pi$
$331$	−3220.18	−0.534734	−0.267367	+	0.963595i	$0.586154\pi$
$332$	15245.1	2.52013
$333$	1288.14	0.211982
$334$	2350.96	0.385147
$335$	−2003.92	−0.326823
$336$	5791.83	0.940387
$337$	10322.4	1.66854	0.834271	−	0.551354i	$-0.185889\pi$
$337$	10322.4	1.66854	0.834271	+	0.551354i	$0.185889\pi$
$338$	−3191.99	−0.513673
$339$	535.976	0.0858709
$340$	−737.326	−0.117609
$341$	−734.490	−0.116642
$342$	−3090.82	−0.488692
$343$	3343.15	0.526277
$344$	−1454.78	−0.228013
$345$	−2090.65	−0.326251
$346$	−15738.2	−2.44535
$347$	−382.405	−0.0591601	−0.0295801	−	0.999562i	$-0.509417\pi$
$347$	−382.405	−0.0591601	−0.0295801	+	0.999562i	$0.509417\pi$
$348$	−151.139	−0.0232813
$349$	−5562.22	−0.853119	−0.426560	−	0.904459i	$-0.640275\pi$
$349$	−5562.22	−0.853119	−0.426560	+	0.904459i	$0.640275\pi$
$350$	−12194.8	−1.86241
$351$	1438.48	0.218748
$352$	700.017	0.105997
$353$	−4841.76	−0.730031	−0.365015	−	0.931001i	$-0.618936\pi$
$353$	−4841.76	−0.730031	−0.365015	+	0.931001i	$0.618936\pi$
$354$	4491.59	0.674365
$355$	−998.373	−0.149262
$356$	−15920.9	−2.37024
$357$	691.010	0.102443
$358$	338.205	0.0499294
$359$	7440.85	1.09391	0.546954	−	0.837163i	$-0.315787\pi$
$359$	7440.85	1.09391	0.546954	+	0.837163i	$0.315787\pi$
$360$	1745.51	0.255545
$361$	−2096.21	−0.305614
$362$	−18161.2	−2.63683
$363$	−363.000	−0.0524864
$364$	20800.5	2.99517
$365$	2174.97	0.311898
$366$	910.651	0.130056
$367$	1186.36	0.168740	0.0843698	−	0.996435i	$-0.473112\pi$
$367$	1186.36	0.168740	0.0843698	+	0.996435i	$0.473112\pi$
$368$	−12987.9	−1.83978
$369$	1275.58	0.179957
$370$	3167.77	0.445093
$371$	−4239.83	−0.593318
$372$	−3357.87	−0.468004
$373$	2720.55	0.377654	0.188827	−	0.982010i	$-0.439532\pi$
$373$	2720.55	0.377654	0.188827	+	0.982010i	$0.439532\pi$
$374$	541.343	0.0748454
$375$	−3071.80	−0.423005
$376$	−1439.40	−0.197423
$377$	−160.120	−0.0218743
$378$	−3129.31	−0.425805
$379$	−8306.44	−1.12579	−0.562894	−	0.826529i	$-0.690312\pi$
$379$	−8306.44	−1.12579	−0.562894	+	0.826529i	$0.690312\pi$
$380$	−5145.30	−0.694601
$381$	1546.86	0.208000
$382$	−19231.2	−2.57579
$383$	−12640.6	−1.68644	−0.843220	−	0.537568i	$-0.819343\pi$
$383$	−12640.6	−1.68644	−0.843220	+	0.537568i	$0.819343\pi$
$384$	−6699.44	−0.890310
$385$	−1139.48	−0.150840
$386$	19677.6	2.59472
$387$	300.256	0.0394390
$388$	−9012.76	−1.17926
$389$	5922.33	0.771913	0.385956	−	0.922517i	$-0.373872\pi$
$389$	5922.33	0.771913	0.385956	+	0.922517i	$0.373872\pi$
$390$	3537.48	0.459300
$391$	−1549.56	−0.200421
$392$	−8697.71	−1.12067
$393$	−7458.86	−0.957378
$394$	9359.58	1.19677
$395$	5491.24	0.699480
$396$	−1659.53	−0.210592
$397$	−7033.84	−0.889215	−0.444607	−	0.895726i	$-0.646657\pi$
$397$	−7033.84	−0.889215	−0.444607	+	0.895726i	$0.646657\pi$
$398$	7249.83	0.913069
$399$	4822.10	0.605030
$400$	−8721.71	−1.09021
$401$	−8186.27	−1.01946	−0.509729	−	0.860335i	$-0.670254\pi$
$401$	−8186.27	−1.01946	−0.509729	+	0.860335i	$0.670254\pi$
$402$	6726.21	0.834510
$403$	−3557.41	−0.439720
$404$	15807.5	1.94666
$405$	−360.260	−0.0442011
$406$	348.330	0.0425796
$407$	−1574.40	−0.191745
$408$	1293.75	0.156985
$409$	−7352.70	−0.888918	−0.444459	−	0.895799i	$-0.646604\pi$
$409$	−7352.70	−0.888918	−0.444459	+	0.895799i	$0.646604\pi$
$410$	3136.88	0.377853
$411$	−740.867	−0.0889156
$412$	−17859.0	−2.13556
$413$	−7007.48	−0.834905
$414$	7017.32	0.833050
$415$	−4044.94	−0.478453
$416$	3390.44	0.399592
$417$	−1158.55	−0.136054
$418$	3777.67	0.442038
$419$	−6301.87	−0.734765	−0.367382	−	0.930070i	$-0.619746\pi$
$419$	−6301.87	−0.734765	−0.367382	+	0.930070i	$0.619746\pi$
$420$	−5209.37	−0.605217
$421$	7003.04	0.810706	0.405353	−	0.914160i	$-0.367149\pi$
$421$	7003.04	0.810706	0.405353	+	0.914160i	$0.367149\pi$
$422$	−7006.75	−0.808254
$423$	297.081	0.0341479
$424$	−7938.04	−0.909210
$425$	−1040.57	−0.118765
$426$	3351.07	0.381127
$427$	−1420.74	−0.161017
$428$	15460.6	1.74606
$429$	−1758.14	−0.197865
$430$	738.382	0.0828092
$431$	−11085.8	−1.23894	−0.619471	−	0.785020i	$-0.712653\pi$
$431$	−11085.8	−1.23894	−0.619471	+	0.785020i	$0.712653\pi$
$432$	−2238.07	−0.249258
$433$	12506.0	1.38799	0.693995	−	0.719980i	$-0.255849\pi$
$433$	12506.0	1.38799	0.693995	+	0.719980i	$0.255849\pi$
$434$	7738.88	0.855940
$435$	40.1013	0.00442002
$436$	20666.5	2.27006
$437$	−10813.3	−1.18369
$438$	−7300.35	−0.796402
$439$	−2800.79	−0.304498	−0.152249	−	0.988342i	$-0.548652\pi$
$439$	−2800.79	−0.304498	−0.152249	+	0.988342i	$0.548652\pi$
$440$	−2133.40	−0.231150
$441$	1795.14	0.193839
$442$	2621.93	0.282155
$443$	−18221.6	−1.95425	−0.977126	−	0.212660i	$-0.931787\pi$
$443$	−18221.6	−1.95425	−0.977126	+	0.212660i	$0.931787\pi$
$444$	−7197.68	−0.769339
$445$	4224.25	0.449997
$446$	−13210.8	−1.40257
$447$	−8539.89	−0.903631
$448$	8069.21	0.850970
$449$	−11156.0	−1.17257	−0.586285	−	0.810105i	$-0.699410\pi$
$449$	−11156.0	−1.17257	−0.586285	+	0.810105i	$0.699410\pi$
$450$	4712.32	0.493646
$451$	−1559.05	−0.162778
$452$	−2994.84	−0.311649
$453$	1866.71	0.193611
$454$	14370.4	1.48554
$455$	−5518.94	−0.568641
$456$	9028.19	0.927157
$457$	3426.75	0.350758	0.175379	−	0.984501i	$-0.443885\pi$
$457$	3426.75	0.350758	0.175379	+	0.984501i	$0.443885\pi$
$458$	−28348.0	−2.89217
$459$	−267.020	−0.0271534
$460$	11681.8	1.18405
$461$	−15415.3	−1.55740	−0.778700	−	0.627397i	$-0.784120\pi$
$461$	−15415.3	−1.55740	−0.778700	+	0.627397i	$0.784120\pi$
$462$	3824.71	0.385155
$463$	12133.8	1.21794	0.608968	−	0.793195i	$-0.291584\pi$
$463$	12133.8	1.21794	0.608968	+	0.793195i	$0.291584\pi$
$464$	249.125	0.0249253
$465$	890.934	0.0888518
$466$	−12385.9	−1.23126
$467$	2868.62	0.284249	0.142124	−	0.989849i	$-0.454607\pi$
$467$	2868.62	0.284249	0.142124	+	0.989849i	$0.454607\pi$
$468$	−8037.70	−0.793895
$469$	−10493.8	−1.03317
$470$	730.573	0.0716996
$471$	−4058.41	−0.397032
$472$	−13119.8	−1.27942
$473$	−366.980	−0.0356739
$474$	−18431.5	−1.78605
$475$	−7261.43	−0.701426
$476$	−3861.11	−0.371794
$477$	1638.35	0.157264
$478$	−24496.8	−2.34405
$479$	−6080.67	−0.580027	−0.290014	−	0.957022i	$-0.593660\pi$
$479$	−6080.67	−0.580027	−0.290014	+	0.957022i	$0.593660\pi$
$480$	−849.118	−0.0807433
$481$	−7625.40	−0.722844
$482$	−30949.0	−2.92467
$483$	−10948.0	−1.03137
$484$	2028.31	0.190487
$485$	2391.33	0.223886
$486$	1209.22	0.112863
$487$	−8403.51	−0.781929	−0.390964	−	0.920406i	$-0.627858\pi$
$487$	−8403.51	−0.781929	−0.390964	+	0.920406i	$0.627858\pi$
$488$	−2659.98	−0.246745
$489$	5887.54	0.544466
$490$	4414.57	0.407000
$491$	7061.24	0.649021	0.324510	−	0.945882i	$-0.394800\pi$
$491$	7061.24	0.649021	0.324510	+	0.945882i	$0.394800\pi$
$492$	−7127.50	−0.653115
$493$	29.7225	0.00271528
$494$	18296.7	1.66641
$495$	440.318	0.0399814
$496$	5534.82	0.501050
$497$	−5228.12	−0.471858
$498$	13577.0	1.22168
$499$	−10937.2	−0.981198	−0.490599	−	0.871385i	$-0.663222\pi$
$499$	−10937.2	−0.981198	−0.490599	+	0.871385i	$0.663222\pi$
$500$	17164.1	1.53520
$501$	1417.32	0.126389
$502$	1257.28	0.111784
$503$	−2178.77	−0.193134	−0.0965669	−	0.995326i	$-0.530786\pi$
$503$	−2178.77	−0.193134	−0.0965669	+	0.995326i	$0.530786\pi$
$504$	9140.61	0.807847
$505$	−4194.15	−0.369578
$506$	−8576.73	−0.753522
$507$	−1924.34	−0.168566
$508$	−8643.28	−0.754889
$509$	−4723.99	−0.411370	−0.205685	−	0.978618i	$-0.565942\pi$
$509$	−4723.99	−0.411370	−0.205685	+	0.978618i	$0.565942\pi$
$510$	−656.647	−0.0570134
$511$	11389.5	0.985994
$512$	23641.7	2.04067
$513$	−1863.35	−0.160368
$514$	14858.4	1.27505
$515$	4738.48	0.405442
$516$	−1677.72	−0.143135
$517$	−363.099	−0.0308879
$518$	16588.5	1.40706
$519$	−9488.01	−0.802462
$520$	−10332.8	−0.871395
$521$	7743.60	0.651158	0.325579	−	0.945515i	$-0.394441\pi$
$521$	7743.60	0.651158	0.325579	+	0.945515i	$0.394441\pi$
$522$	−134.601	−0.0112861
$523$	−14538.6	−1.21554	−0.607772	−	0.794112i	$-0.707937\pi$
$523$	−14538.6	−1.21554	−0.607772	+	0.794112i	$0.707937\pi$
$524$	41677.4	3.47459
$525$	−7351.85	−0.611164
$526$	−19748.5	−1.63703
$527$	660.347	0.0545829
$528$	2735.42	0.225462
$529$	12383.3	1.01778
$530$	4028.99	0.330204
$531$	2707.82	0.221299
$532$	−26944.1	−2.19582
$533$	−7551.05	−0.613644
$534$	−14178.8	−1.14902
$535$	−4102.11	−0.331495
$536$	−19647.0	−1.58325
$537$	203.892	0.0163847
$538$	−26879.8	−2.15403
$539$	−2194.06	−0.175334
$540$	2013.00	0.160418
$541$	−3502.23	−0.278323	−0.139162	−	0.990270i	$-0.544441\pi$
$541$	−3502.23	−0.278323	−0.139162	+	0.990270i	$0.544441\pi$
$542$	7041.30	0.558025
$543$	−10948.8	−0.865297
$544$	−629.354	−0.0496017
$545$	−5483.40	−0.430978
$546$	18524.5	1.45197
$547$	−16509.3	−1.29047	−0.645236	−	0.763983i	$-0.723241\pi$
$547$	−16509.3	−1.29047	−0.645236	+	0.763983i	$0.723241\pi$
$548$	4139.69	0.322699
$549$	549.000	0.0426790
$550$	−5759.50	−0.446520
$551$	207.414	0.0160365
$552$	−20497.4	−1.58048
$553$	28755.7	2.21124
$554$	31706.3	2.43153
$555$	1909.74	0.146061
$556$	6473.56	0.493777
$557$	−6544.54	−0.497848	−0.248924	−	0.968523i	$-0.580077\pi$
$557$	−6544.54	−0.497848	−0.248924	+	0.968523i	$0.580077\pi$
$558$	−2990.45	−0.226874
$559$	−1777.42	−0.134485
$560$	8586.68	0.647953
$561$	326.357	0.0245612
$562$	12138.1	0.911055
$563$	−235.530	−0.0176313	−0.00881565	−	0.999961i	$-0.502806\pi$
$563$	−235.530	−0.0176313	−0.00881565	+	0.999961i	$0.502806\pi$
$564$	−1659.98	−0.123932
$565$	794.612	0.0591674
$566$	14723.8	1.09344
$567$	−1886.55	−0.139732
$568$	−9788.36	−0.723082
$569$	−8307.53	−0.612074	−0.306037	−	0.952020i	$-0.599003\pi$
$569$	−8307.53	−0.612074	−0.306037	+	0.952020i	$0.599003\pi$
$570$	−4582.30	−0.336722
$571$	5495.67	0.402779	0.201389	−	0.979511i	$-0.435454\pi$
$571$	5495.67	0.402779	0.201389	+	0.979511i	$0.435454\pi$
$572$	9823.86	0.718105
$573$	−11593.8	−0.845268
$574$	16426.7	1.19449
$575$	16486.2	1.19569
$576$	−3118.10	−0.225557
$577$	16180.2	1.16740	0.583702	−	0.811968i	$-0.301604\pi$
$577$	16180.2	1.16740	0.583702	+	0.811968i	$0.301604\pi$
$578$	23961.5	1.72434
$579$	11862.9	0.851479
$580$	−224.071	−0.0160415
$581$	−21181.9	−1.51252
$582$	−8026.59	−0.571671
$583$	−2002.43	−0.142251
$584$	21324.1	1.51095
$585$	2132.62	0.150723
$586$	−26344.6	−1.85714
$587$	10200.2	0.717219	0.358610	−	0.933488i	$-0.383251\pi$
$587$	10200.2	0.717219	0.358610	+	0.933488i	$0.383251\pi$
$588$	−10030.6	−0.703495
$589$	4608.12	0.322367
$590$	6659.01	0.464656
$591$	5642.57	0.392732
$592$	11864.0	0.823663
$593$	11598.5	0.803195	0.401598	−	0.915816i	$-0.368455\pi$
$593$	11598.5	0.803195	0.401598	+	0.915816i	$0.368455\pi$
$594$	−1477.94	−0.102089
$595$	1024.46	0.0705860
$596$	47717.8	3.27952
$597$	4370.67	0.299631
$598$	−41540.3	−2.84065
$599$	20121.3	1.37251	0.686256	−	0.727360i	$-0.259253\pi$
$599$	20121.3	1.37251	0.686256	+	0.727360i	$0.259253\pi$
$600$	−13764.5	−0.936557
$601$	−3030.38	−0.205677	−0.102838	−	0.994698i	$-0.532792\pi$
$601$	−3030.38	−0.205677	−0.102838	+	0.994698i	$0.532792\pi$
$602$	3866.65	0.261782
$603$	4055.00	0.273851
$604$	−10430.5	−0.702667
$605$	−538.166	−0.0361646
$606$	14077.8	0.943682
$607$	−7677.18	−0.513356	−0.256678	−	0.966497i	$-0.582628\pi$
$607$	−7677.18	−0.513356	−0.256678	+	0.966497i	$0.582628\pi$
$608$	−4391.84	−0.292949
$609$	209.996	0.0139729
$610$	1350.09	0.0896121
$611$	−1758.62	−0.116442
$612$	1492.01	0.0985471
$613$	28752.4	1.89445	0.947227	−	0.320565i	$-0.103873\pi$
$613$	28752.4	1.89445	0.947227	+	0.320565i	$0.103873\pi$
$614$	−35186.9	−2.31275
$615$	1891.12	0.123996
$616$	−11171.9	−0.730725
$617$	16911.7	1.10347	0.551735	−	0.834020i	$-0.313966\pi$
$617$	16911.7	1.10347	0.551735	+	0.834020i	$0.313966\pi$
$618$	−15904.9	−1.03526
$619$	−1108.87	−0.0720023	−0.0360011	−	0.999352i	$-0.511462\pi$
$619$	−1108.87	−0.0720023	−0.0360011	+	0.999352i	$0.511462\pi$
$620$	−4978.21	−0.322467
$621$	4230.50	0.273372
$622$	41027.3	2.64476
$623$	22120.9	1.42256
$624$	13248.7	0.849953
$625$	8598.20	0.550285
$626$	43868.5	2.80086
$627$	2277.43	0.145059
$628$	22676.9	1.44094
$629$	1415.47	0.0897274
$630$	−4639.36	−0.293391
$631$	9666.78	0.609871	0.304935	−	0.952373i	$-0.401365\pi$
$631$	9666.78	0.609871	0.304935	+	0.952373i	$0.401365\pi$
$632$	53837.9	3.38854
$633$	−4224.13	−0.265235
$634$	32797.7	2.05451
$635$	2293.30	0.143318
$636$	−9154.51	−0.570754
$637$	−10626.7	−0.660979
$638$	164.513	0.0102087
$639$	2020.25	0.125070
$640$	−9932.26	−0.613448
$641$	12810.4	0.789360	0.394680	−	0.918819i	$-0.370856\pi$
$641$	12810.4	0.789360	0.394680	+	0.918819i	$0.370856\pi$
$642$	13768.9	0.846439
$643$	26399.2	1.61910	0.809551	−	0.587050i	$-0.199711\pi$
$643$	26399.2	1.61910	0.809551	+	0.587050i	$0.199711\pi$
$644$	61173.2	3.74311
$645$	445.145	0.0271745
$646$	−3396.34	−0.206853
$647$	5432.76	0.330114	0.165057	−	0.986284i	$-0.447219\pi$
$647$	5432.76	0.330114	0.165057	+	0.986284i	$0.447219\pi$
$648$	−3532.10	−0.214127
$649$	−3309.56	−0.200172
$650$	−27895.4	−1.68330
$651$	4665.50	0.280884
$652$	−32897.4	−1.97602
$653$	6935.17	0.415612	0.207806	−	0.978170i	$-0.433368\pi$
$653$	6935.17	0.415612	0.207806	+	0.978170i	$0.433368\pi$
$654$	18405.2	1.10046
$655$	−11058.1	−0.659660
$656$	11748.4	0.699232
$657$	−4401.13	−0.261346
$658$	3825.75	0.226662
$659$	−26618.4	−1.57346	−0.786728	−	0.617300i	$-0.788226\pi$
$659$	−26618.4	−1.57346	−0.786728	+	0.617300i	$0.788226\pi$
$660$	−2460.33	−0.145104
$661$	−17133.0	−1.00816	−0.504081	−	0.863657i	$-0.668169\pi$
$661$	−17133.0	−1.00816	−0.504081	+	0.863657i	$0.668169\pi$
$662$	16024.3	0.940791
$663$	1580.67	0.0925914
$664$	−39657.9	−2.31781
$665$	7149.01	0.416882
$666$	−6410.11	−0.372953
$667$	−470.906	−0.0273367
$668$	−7919.44	−0.458701
$669$	−7964.31	−0.460266
$670$	9971.95	0.575000
$671$	−671.000	−0.0386046
$672$	−4446.53	−0.255251
$673$	−27255.2	−1.56108	−0.780542	−	0.625104i	$-0.785057\pi$
$673$	−27255.2	−1.56108	−0.780542	+	0.625104i	$0.785057\pi$
$674$	−51366.9	−2.93557
$675$	2840.90	0.161994
$676$	10752.5	0.611773
$677$	11579.9	0.657387	0.328693	−	0.944437i	$-0.393392\pi$
$677$	11579.9	0.657387	0.328693	+	0.944437i	$0.393392\pi$
$678$	−2667.14	−0.151078
$679$	12522.6	0.707764
$680$	1918.04	0.108167
$681$	8663.42	0.487493
$682$	3654.99	0.205215
$683$	−8929.26	−0.500247	−0.250123	−	0.968214i	$-0.580471\pi$
$683$	−8929.26	−0.500247	−0.250123	+	0.968214i	$0.580471\pi$
$684$	10411.7	0.582020
$685$	−1098.37	−0.0612653
$686$	−16636.3	−0.925913
$687$	−17090.0	−0.949090
$688$	2765.41	0.153242
$689$	−9698.51	−0.536261
$690$	10403.5	0.573994
$691$	−10010.1	−0.551089	−0.275544	−	0.961288i	$-0.588858\pi$
$691$	−10010.1	−0.551089	−0.275544	+	0.961288i	$0.588858\pi$
$692$	53015.5	2.91235
$693$	2305.79	0.126392
$694$	1902.94	0.104084
$695$	−1717.61	−0.0937450
$696$	393.166	0.0214122
$697$	1401.67	0.0761722
$698$	27678.9	1.50095
$699$	−7467.04	−0.404048
$700$	41079.5	2.21808
$701$	−2792.93	−0.150481	−0.0752407	−	0.997165i	$-0.523973\pi$
$701$	−2792.93	−0.150481	−0.0752407	+	0.997165i	$0.523973\pi$
$702$	−7158.22	−0.384857
$703$	9877.63	0.529932
$704$	3811.01	0.204024
$705$	440.437	0.0235288
$706$	24093.7	1.28439
$707$	−21963.3	−1.16834
$708$	−15130.3	−0.803153
$709$	−26446.8	−1.40089	−0.700444	−	0.713707i	$-0.747015\pi$
$709$	−26446.8	−1.40089	−0.700444	+	0.713707i	$0.747015\pi$
$710$	4968.14	0.262607
$711$	−11111.7	−0.586108
$712$	41415.9	2.17995
$713$	−10462.2	−0.549525
$714$	−3438.63	−0.180235
$715$	−2606.54	−0.136334
$716$	−1139.28	−0.0594647
$717$	−14768.3	−0.769220
$718$	−37027.4	−1.92458
$719$	−17686.0	−0.917351	−0.458676	−	0.888604i	$-0.651676\pi$
$719$	−17686.0	−0.917351	−0.458676	+	0.888604i	$0.651676\pi$
$720$	−3318.06	−0.171745
$721$	24813.7	1.28171
$722$	10431.2	0.537687
$723$	−18658.1	−0.959754
$724$	61177.6	3.14040
$725$	−316.226	−0.0161991
$726$	1806.37	0.0923427
$727$	−15462.3	−0.788808	−0.394404	−	0.918937i	$-0.629049\pi$
$727$	−15462.3	−0.788808	−0.394404	+	0.918937i	$0.629049\pi$
$728$	−54109.4	−2.75471
$729$	729.000	0.0370370
$730$	−10823.1	−0.548743
$731$	329.935	0.0166937
$732$	−3067.61	−0.154894
$733$	38675.3	1.94885	0.974424	−	0.224716i	$-0.0721455\pi$
$733$	38675.3	1.94885	0.974424	+	0.224716i	$0.0721455\pi$
$734$	−5903.60	−0.296874
$735$	2661.39	0.133560
$736$	9971.13	0.499376
$737$	−4956.11	−0.247708
$738$	−6347.61	−0.316611
$739$	−6924.37	−0.344678	−0.172339	−	0.985038i	$-0.555132\pi$
$739$	−6924.37	−0.344678	−0.172339	+	0.985038i	$0.555132\pi$
$740$	−10670.9	−0.530096
$741$	11030.4	0.546846
$742$	21098.4	1.04386
$743$	−11458.2	−0.565761	−0.282881	−	0.959155i	$-0.591290\pi$
$743$	−11458.2	−0.565761	−0.282881	+	0.959155i	$0.591290\pi$
$744$	8735.00	0.430431
$745$	−12660.8	−0.622626
$746$	−13538.1	−0.664430
$747$	8185.09	0.400906
$748$	−1823.56	−0.0891392
$749$	−21481.3	−1.04794
$750$	15286.0	0.744220
$751$	−13098.3	−0.636435	−0.318218	−	0.948018i	$-0.603084\pi$
$751$	−13098.3	−0.636435	−0.318218	+	0.948018i	$0.603084\pi$
$752$	2736.16	0.132683
$753$	757.974	0.0366827
$754$	796.797	0.0384849
$755$	2767.49	0.133403
$756$	10541.4	0.507124
$757$	17425.9	0.836664	0.418332	−	0.908294i	$-0.362615\pi$
$757$	17425.9	0.836664	0.418332	+	0.908294i	$0.362615\pi$
$758$	41334.8	1.98067
$759$	−5170.61	−0.247275
$760$	13384.7	0.638837
$761$	569.563	0.0271309	0.0135655	−	0.999908i	$-0.495682\pi$
$761$	569.563	0.0271309	0.0135655	+	0.999908i	$0.495682\pi$
$762$	−7697.54	−0.365948
$763$	−28714.6	−1.36244
$764$	64782.0	3.06771
$765$	−395.870	−0.0187094
$766$	62902.8	2.96706
$767$	−16029.4	−0.754615
$768$	25023.0	1.17570
$769$	17455.4	0.818541	0.409271	−	0.912413i	$-0.365783\pi$
$769$	17455.4	0.818541	0.409271	+	0.912413i	$0.365783\pi$
$770$	5670.33	0.265383
$771$	8957.64	0.418420
$772$	−66285.6	−3.09025
$773$	−15780.4	−0.734259	−0.367129	−	0.930170i	$-0.619659\pi$
$773$	−15780.4	−0.734259	−0.367129	+	0.930170i	$0.619659\pi$
$774$	−1494.15	−0.0693875
$775$	−7025.62	−0.325636
$776$	23445.4	1.08459
$777$	10000.6	0.461738
$778$	−29470.9	−1.35808
$779$	9781.32	0.449874
$780$	−11916.3	−0.547016
$781$	−2469.19	−0.113130
$782$	7710.96	0.352613
$783$	−81.1466	−0.00370363
$784$	16533.6	0.753170
$785$	−6016.81	−0.273566
$786$	37117.0	1.68438
$787$	−13783.9	−0.624326	−0.312163	−	0.950029i	$-0.601053\pi$
$787$	−13783.9	−0.624326	−0.312163	+	0.950029i	$0.601053\pi$
$788$	−31528.6	−1.42533
$789$	−11905.7	−0.537205
$790$	−27325.7	−1.23064
$791$	4161.10	0.187044
$792$	4317.02	0.193685
$793$	−3249.90	−0.145533
$794$	35002.0	1.56445
$795$	2428.94	0.108359
$796$	−24421.7	−1.08744
$797$	629.560	0.0279801	0.0139901	−	0.999902i	$-0.495547\pi$
$797$	629.560	0.0279801	0.0139901	+	0.999902i	$0.495547\pi$
$798$	−23995.9	−1.06447
$799$	326.446	0.0144541
$800$	6695.88	0.295919
$801$	−8547.93	−0.377061
$802$	40736.8	1.79360
$803$	5379.16	0.236396
$804$	−22657.9	−0.993882
$805$	−16230.9	−0.710640
$806$	17702.5	0.773627
$807$	−16204.9	−0.706864
$808$	−41120.8	−1.79038
$809$	−17317.3	−0.752588	−0.376294	−	0.926500i	$-0.622802\pi$
$809$	−17317.3	−0.752588	−0.376294	+	0.926500i	$0.622802\pi$
$810$	1792.74	0.0777659
$811$	−14581.0	−0.631331	−0.315666	−	0.948870i	$-0.602228\pi$
$811$	−14581.0	−0.631331	−0.315666	+	0.948870i	$0.602228\pi$
$812$	−1173.38	−0.0507114
$813$	4244.96	0.183121
$814$	7834.57	0.337349
$815$	8728.59	0.375152
$816$	−2459.30	−0.105506
$817$	2302.40	0.0985933
$818$	36588.8	1.56393
$819$	11167.8	0.476476
$820$	−10566.9	−0.450014
$821$	23402.2	0.994816	0.497408	−	0.867517i	$-0.334285\pi$
$821$	23402.2	0.994816	0.497408	+	0.867517i	$0.334285\pi$
$822$	3686.73	0.156435
$823$	−6806.96	−0.288306	−0.144153	−	0.989555i	$-0.546046\pi$
$823$	−6806.96	−0.288306	−0.144153	+	0.989555i	$0.546046\pi$
$824$	46457.6	1.96411
$825$	−3472.21	−0.146529
$826$	34870.9	1.46890
$827$	−39961.7	−1.68029	−0.840147	−	0.542359i	$-0.817531\pi$
$827$	−39961.7	−1.68029	−0.840147	+	0.542359i	$0.817531\pi$
$828$	−23638.5	−0.992143
$829$	−1239.99	−0.0519499	−0.0259750	−	0.999663i	$-0.508269\pi$
$829$	−1239.99	−0.0519499	−0.0259750	+	0.999663i	$0.508269\pi$
$830$	20128.6	0.841774
$831$	19114.6	0.797928
$832$	18458.1	0.769135
$833$	1972.59	0.0820481
$834$	5765.22	0.239369
$835$	2101.24	0.0870856
$836$	−12725.4	−0.526457
$837$	−1802.84	−0.0744507
$838$	31359.6	1.29272
$839$	−10452.0	−0.430086	−0.215043	−	0.976605i	$-0.568989\pi$
$839$	−10452.0	−0.430086	−0.215043	+	0.976605i	$0.568989\pi$
$840$	13551.4	0.556629
$841$	−24380.0	−0.999630
$842$	−34848.8	−1.42633
$843$	7317.62	0.298970
$844$	23602.9	0.962612
$845$	−2852.94	−0.116147
$846$	−1478.34	−0.0600786
$847$	−2818.18	−0.114326
$848$	15089.5	0.611056
$849$	8876.47	0.358822
$850$	5178.11	0.208950
$851$	−22425.9	−0.903350
$852$	−11288.4	−0.453913
$853$	−7876.17	−0.316149	−0.158074	−	0.987427i	$-0.550529\pi$
$853$	−7876.17	−0.316149	−0.158074	+	0.987427i	$0.550529\pi$
$854$	7069.92	0.283288
$855$	−2762.51	−0.110498
$856$	−40218.4	−1.60588
$857$	−1331.58	−0.0530756	−0.0265378	−	0.999648i	$-0.508448\pi$
$857$	−1331.58	−0.0530756	−0.0265378	+	0.999648i	$0.508448\pi$
$858$	8748.93	0.348116
$859$	−11848.6	−0.470627	−0.235313	−	0.971920i	$-0.575612\pi$
$859$	−11848.6	−0.470627	−0.235313	+	0.971920i	$0.575612\pi$
$860$	−2487.31	−0.0986239
$861$	9903.12	0.391983
$862$	55165.5	2.17975
$863$	−22404.2	−0.883715	−0.441858	−	0.897085i	$-0.645680\pi$
$863$	−22404.2	−0.883715	−0.441858	+	0.897085i	$0.645680\pi$
$864$	1718.22	0.0676564
$865$	−14066.5	−0.552918
$866$	−62232.7	−2.44198
$867$	14445.6	0.565857
$868$	−26069.1	−1.01940
$869$	13581.0	0.530155
$870$	−199.553	−0.00777643
$871$	−24004.3	−0.933817
$872$	−53761.0	−2.08782
$873$	−4838.95	−0.187599
$874$	53809.6	2.08254
$875$	−23848.2	−0.921389
$876$	24591.9	0.948496
$877$	20449.6	0.787383	0.393691	−	0.919243i	$-0.371198\pi$
$877$	20449.6	0.787383	0.393691	+	0.919243i	$0.371198\pi$
$878$	13937.4	0.535723
$879$	−15882.3	−0.609437
$880$	4055.40	0.155350
$881$	25039.8	0.957561	0.478780	−	0.877935i	$-0.341079\pi$
$881$	25039.8	0.957561	0.478780	+	0.877935i	$0.341079\pi$
$882$	−8933.05	−0.341033
$883$	−14315.5	−0.545589	−0.272794	−	0.962072i	$-0.587948\pi$
$883$	−14315.5	−0.545589	−0.272794	+	0.962072i	$0.587948\pi$
$884$	−8832.20	−0.336040
$885$	4014.49	0.152481
$886$	90674.9	3.43824
$887$	25099.7	0.950132	0.475066	−	0.879950i	$-0.342424\pi$
$887$	25099.7	0.950132	0.475066	+	0.879950i	$0.342424\pi$
$888$	18723.7	0.707575
$889$	12009.2	0.453066
$890$	−21020.8	−0.791708
$891$	−891.000	−0.0335013
$892$	44501.6	1.67043
$893$	2278.05	0.0853661
$894$	42496.5	1.58982
$895$	302.281	0.0112895
$896$	−52011.7	−1.93927
$897$	−25043.2	−0.932183
$898$	55514.9	2.06298
$899$	200.678	0.00744492
$900$	−15873.9	−0.587922
$901$	1800.30	0.0665666
$902$	7758.18	0.286385
$903$	2331.07	0.0859059
$904$	7790.63	0.286629
$905$	−16232.1	−0.596213
$906$	−9289.19	−0.340632
$907$	−28293.7	−1.03581	−0.517903	−	0.855439i	$-0.673287\pi$
$907$	−28293.7	−1.03581	−0.517903	+	0.855439i	$0.673287\pi$
$908$	−48408.0	−1.76925
$909$	8487.02	0.309677
$910$	27463.5	1.00045
$911$	10343.0	0.376156	0.188078	−	0.982154i	$-0.439774\pi$
$911$	10343.0	0.376156	0.188078	+	0.982154i	$0.439774\pi$
$912$	−17161.8	−0.623118
$913$	−10004.0	−0.362633
$914$	−17052.3	−0.617112
$915$	813.921	0.0294070
$916$	95492.8	3.44451
$917$	−57907.6	−2.08536
$918$	1328.75	0.0477727
$919$	44987.5	1.61480	0.807400	−	0.590004i	$-0.200874\pi$
$919$	44987.5	1.61480	0.807400	+	0.590004i	$0.200874\pi$
$920$	−30388.4	−1.08900
$921$	−21213.0	−0.758947
$922$	76710.0	2.74003
$923$	−11959.2	−0.426481
$924$	−12883.9	−0.458711
$925$	−15059.6	−0.535305
$926$	−60380.5	−2.14279
$927$	−9588.50	−0.339728
$928$	−191.259	−0.00676551
$929$	−9767.39	−0.344949	−0.172475	−	0.985014i	$-0.555176\pi$
$929$	−9767.39	−0.344949	−0.172475	+	0.985014i	$0.555176\pi$
$930$	−4433.49	−0.156323
$931$	13765.4	0.484577
$932$	41723.1	1.46640
$933$	24733.9	0.867902
$934$	−14274.9	−0.500097
$935$	483.841	0.0169233
$936$	20908.9	0.730159
$937$	−13134.2	−0.457927	−0.228963	−	0.973435i	$-0.573534\pi$
$937$	−13134.2	−0.457927	−0.228963	+	0.973435i	$0.573534\pi$
$938$	52219.6	1.81773
$939$	26446.8	0.919126
$940$	−2461.00	−0.0853926
$941$	15462.9	0.535681	0.267840	−	0.963463i	$-0.413690\pi$
$941$	15462.9	0.535681	0.267840	+	0.963463i	$0.413690\pi$
$942$	20195.6	0.698523
$943$	−22207.3	−0.766880
$944$	24939.5	0.859865
$945$	−2796.91	−0.0962789
$946$	1826.18	0.0627634
$947$	−19200.3	−0.658844	−0.329422	−	0.944183i	$-0.606854\pi$
$947$	−19200.3	−0.658844	−0.329422	+	0.944183i	$0.606854\pi$
$948$	62088.3	2.12715
$949$	26053.3	0.891174
$950$	36134.6	1.23406
$951$	19772.6	0.674206
$952$	10044.1	0.341945
$953$	−39199.8	−1.33243	−0.666214	−	0.745760i	$-0.732086\pi$
$953$	−39199.8	−1.33243	−0.666214	+	0.745760i	$0.732086\pi$
$954$	−8152.82	−0.276685
$955$	−17188.4	−0.582413
$956$	82519.6	2.79171
$957$	99.1791	0.00335006
$958$	30258.9	1.02048
$959$	−5751.79	−0.193676
$960$	−4622.74	−0.155415
$961$	−25332.5	−0.850342
$962$	37945.8	1.27175
$963$	8300.78	0.277766
$964$	104255.	3.48321
$965$	17587.4	0.586692
$966$	54479.6	1.81455
$967$	9032.89	0.300391	0.150196	−	0.988656i	$-0.452010\pi$
$967$	9032.89	0.300391	0.150196	+	0.988656i	$0.452010\pi$
$968$	−5276.35	−0.175195
$969$	−2047.53	−0.0678806
$970$	−11899.8	−0.393897
$971$	−9352.88	−0.309112	−0.154556	−	0.987984i	$-0.549395\pi$
$971$	−9352.88	−0.309112	−0.154556	+	0.987984i	$0.549395\pi$
$972$	−4073.38	−0.134418
$973$	−8994.53	−0.296353
$974$	41817.8	1.37570
$975$	−16817.2	−0.552391
$976$	5056.38	0.165831
$977$	19350.8	0.633661	0.316830	−	0.948482i	$-0.397381\pi$
$977$	19350.8	0.633661	0.316830	+	0.948482i	$0.397381\pi$
$978$	−29297.8	−0.957914
$979$	10447.5	0.341065
$980$	−14870.9	−0.484727
$981$	11095.9	0.361125
$982$	−35138.4	−1.14186
$983$	36168.5	1.17355	0.586773	−	0.809752i	$-0.300398\pi$
$983$	36168.5	1.17355	0.586773	+	0.809752i	$0.300398\pi$
$984$	18541.1	0.600681
$985$	8365.40	0.270603
$986$	−147.906	−0.00477717
$987$	2306.41	0.0743809
$988$	−61634.0	−1.98465
$989$	−5227.30	−0.168067
$990$	−2191.12	−0.0703419
$991$	1065.03	0.0341389	0.0170695	−	0.999854i	$-0.494566\pi$
$991$	1065.03	0.0341389	0.0170695	+	0.999854i	$0.494566\pi$
$992$	−4249.22	−0.136001
$993$	9660.53	0.308729
$994$	26016.4	0.830170
$995$	6479.75	0.206454
$996$	−45735.3	−1.45500
$997$	17697.6	0.562175	0.281088	−	0.959682i	$-0.409305\pi$
$997$	17697.6	0.562175	0.281088	+	0.959682i	$0.409305\pi$
$998$	54426.2	1.72629
$999$	−3864.43	−0.122388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.b.1.2	✓	36

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

\(f(q)\)	\(=\)	\(q-4.97623 q^{2} -3.00000 q^{3} +16.7629 q^{4} -4.44765 q^{5} +14.9287 q^{6} -23.2908 q^{7} -43.6062 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.97623 q^{2} -3.00000 q^{3} +16.7629 q^{4} -4.44765 q^{5} +14.9287 q^{6} -23.2908 q^{7} -43.6062 q^{8} +9.00000 q^{9} +22.1326 q^{10} -11.0000 q^{11} -50.2887 q^{12} -53.2771 q^{13} +115.900 q^{14} +13.3430 q^{15} +82.8916 q^{16} +9.88961 q^{17} -44.7861 q^{18} +69.0130 q^{19} -74.5556 q^{20} +69.8723 q^{21} +54.7386 q^{22} -156.685 q^{23} +130.819 q^{24} -105.218 q^{25} +265.119 q^{26} -27.0000 q^{27} -390.421 q^{28} +3.00543 q^{29} -66.3977 q^{30} +66.7718 q^{31} -63.6379 q^{32} +33.0000 q^{33} -49.2130 q^{34} +103.589 q^{35} +150.866 q^{36} +143.127 q^{37} -343.425 q^{38} +159.831 q^{39} +193.945 q^{40} +141.732 q^{41} -347.701 q^{42} +33.3618 q^{43} -184.392 q^{44} -40.0289 q^{45} +779.703 q^{46} +33.0090 q^{47} -248.675 q^{48} +199.460 q^{49} +523.591 q^{50} -29.6688 q^{51} -893.078 q^{52} +182.039 q^{53} +134.358 q^{54} +48.9242 q^{55} +1015.62 q^{56} -207.039 q^{57} -14.9557 q^{58} +300.869 q^{59} +223.667 q^{60} +61.0000 q^{61} -332.272 q^{62} -209.617 q^{63} -346.455 q^{64} +236.958 q^{65} -164.216 q^{66} +450.556 q^{67} +165.779 q^{68} +470.056 q^{69} -515.485 q^{70} +224.472 q^{71} -392.456 q^{72} -489.014 q^{73} -712.234 q^{74} +315.655 q^{75} +1156.86 q^{76} +256.199 q^{77} -795.358 q^{78} -1234.64 q^{79} -368.673 q^{80} +81.0000 q^{81} -705.289 q^{82} +909.454 q^{83} +1171.26 q^{84} -43.9856 q^{85} -166.016 q^{86} -9.01628 q^{87} +479.668 q^{88} -949.770 q^{89} +199.193 q^{90} +1240.86 q^{91} -2626.50 q^{92} -200.315 q^{93} -164.260 q^{94} -306.946 q^{95} +190.914 q^{96} -537.661 q^{97} -992.561 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 + 118 * q^4 - 5 * q^5 - 6 * q^6 - 63 * q^7 + 3 * q^8 + 324 * q^9 - 45 * q^10 - 396 * q^11 - 354 * q^12 - 13 * q^13 + 82 * q^14 + 15 * q^15 + 262 * q^16 + 204 * q^17 + 18 * q^18 - 431 * q^19 + 354 * q^20 + 189 * q^21 - 22 * q^22 - 179 * q^23 - 9 * q^24 + 711 * q^25 + 331 * q^26 - 972 * q^27 - 296 * q^28 + 478 * q^29 + 135 * q^30 - 574 * q^31 - 149 * q^32 + 1188 * q^33 + 276 * q^34 - 194 * q^35 + 1062 * q^36 - 12 * q^37 + 325 * q^38 + 39 * q^39 - 185 * q^40 + 900 * q^41 - 246 * q^42 - 1053 * q^43 - 1298 * q^44 - 45 * q^45 - 407 * q^46 - 653 * q^47 - 786 * q^48 + 753 * q^49 - 1520 * q^50 - 612 * q^51 + 60 * q^52 + 735 * q^53 - 54 * q^54 + 55 * q^55 - 809 * q^56 + 1293 * q^57 - 1399 * q^58 - 1127 * q^59 - 1062 * q^60 + 2196 * q^61 - 1795 * q^62 - 567 * q^63 - 2133 * q^64 + 1886 * q^65 + 66 * q^66 - 989 * q^67 + 10 * q^68 + 537 * q^69 - 2130 * q^70 + 61 * q^71 + 27 * q^72 - 1471 * q^73 - 122 * q^74 - 2133 * q^75 - 4064 * q^76 + 693 * q^77 - 993 * q^78 - 1853 * q^79 + 2197 * q^80 + 2916 * q^81 - 2566 * q^82 - 3523 * q^83 + 888 * q^84 - 449 * q^85 - 771 * q^86 - 1434 * q^87 - 33 * q^88 + 2209 * q^89 - 405 * q^90 - 1668 * q^91 - 1999 * q^92 + 1722 * q^93 - 2844 * q^94 + 1220 * q^95 + 447 * q^96 - 3622 * q^97 + 3846 * q^98 - 3564 * q^99

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