LMFDB - Embedded newform 2013.4.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.80221 q^{2} -3.00000 q^{3} -4.75204 q^{4} +13.7156 q^{5} +5.40663 q^{6} +7.13162 q^{7} +22.9818 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.80221 q^{2} -3.00000 q^{3} -4.75204 q^{4} +13.7156 q^{5} +5.40663 q^{6} +7.13162 q^{7} +22.9818 q^{8} +9.00000 q^{9} -24.7184 q^{10} -11.0000 q^{11} +14.2561 q^{12} -57.5672 q^{13} -12.8527 q^{14} -41.1468 q^{15} -3.40175 q^{16} +37.5058 q^{17} -16.2199 q^{18} +59.5976 q^{19} -65.1771 q^{20} -21.3949 q^{21} +19.8243 q^{22} +121.113 q^{23} -68.9455 q^{24} +63.1173 q^{25} +103.748 q^{26} -27.0000 q^{27} -33.8898 q^{28} -129.221 q^{29} +74.1551 q^{30} +126.828 q^{31} -177.724 q^{32} +33.0000 q^{33} -67.5933 q^{34} +97.8144 q^{35} -42.7684 q^{36} -153.834 q^{37} -107.407 q^{38} +172.702 q^{39} +315.209 q^{40} -141.080 q^{41} +38.5580 q^{42} -128.761 q^{43} +52.2725 q^{44} +123.440 q^{45} -218.271 q^{46} -213.302 q^{47} +10.2052 q^{48} -292.140 q^{49} -113.751 q^{50} -112.517 q^{51} +273.562 q^{52} -379.423 q^{53} +48.6596 q^{54} -150.871 q^{55} +163.898 q^{56} -178.793 q^{57} +232.884 q^{58} +35.7135 q^{59} +195.531 q^{60} +61.0000 q^{61} -228.571 q^{62} +64.1846 q^{63} +347.510 q^{64} -789.568 q^{65} -59.4729 q^{66} -275.818 q^{67} -178.229 q^{68} -363.339 q^{69} -176.282 q^{70} -146.734 q^{71} +206.837 q^{72} +663.138 q^{73} +277.241 q^{74} -189.352 q^{75} -283.210 q^{76} -78.4478 q^{77} -311.244 q^{78} -127.271 q^{79} -46.6570 q^{80} +81.0000 q^{81} +254.255 q^{82} -803.216 q^{83} +101.669 q^{84} +514.414 q^{85} +232.054 q^{86} +387.664 q^{87} -252.800 q^{88} +37.7197 q^{89} -222.465 q^{90} -410.547 q^{91} -575.534 q^{92} -380.484 q^{93} +384.414 q^{94} +817.416 q^{95} +533.172 q^{96} +1401.61 q^{97} +526.497 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.80221	−0.637177	−0.318589	−	0.947893i	$-0.603209\pi$
$2$	−1.80221	−0.637177	−0.318589	+	0.947893i	$0.603209\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−4.75204	−0.594005
$5$	13.7156	1.22676	0.613380	−	0.789788i	$-0.289810\pi$
$5$	13.7156	1.22676	0.613380	+	0.789788i	$0.289810\pi$
$6$	5.40663	0.367874
$7$	7.13162	0.385071	0.192536	−	0.981290i	$-0.438329\pi$
$7$	7.13162	0.385071	0.192536	+	0.981290i	$0.438329\pi$
$8$	22.9818	1.01566
$9$	9.00000	0.333333
$10$	−24.7184	−0.781663
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	14.2561	0.342949
$13$	−57.5672	−1.22817	−0.614087	−	0.789238i	$-0.710476\pi$
$13$	−57.5672	−1.22817	−0.614087	+	0.789238i	$0.710476\pi$
$14$	−12.8527	−0.245359
$15$	−41.1468	−0.708270
$16$	−3.40175	−0.0531523
$17$	37.5058	0.535088	0.267544	−	0.963546i	$-0.413788\pi$
$17$	37.5058	0.535088	0.267544	+	0.963546i	$0.413788\pi$
$18$	−16.2199	−0.212392
$19$	59.5976	0.719612	0.359806	−	0.933027i	$-0.382843\pi$
$19$	59.5976	0.719612	0.359806	+	0.933027i	$0.382843\pi$
$20$	−65.1771	−0.728702
$21$	−21.3949	−0.222321
$22$	19.8243	0.192116
$23$	121.113	1.09799	0.548996	−	0.835825i	$-0.315010\pi$
$23$	121.113	1.09799	0.548996	+	0.835825i	$0.315010\pi$
$24$	−68.9455	−0.586394
$25$	63.1173	0.504938
$26$	103.748	0.782565
$27$	−27.0000	−0.192450
$28$	−33.8898	−0.228734
$29$	−129.221	−0.827441	−0.413720	−	0.910404i	$-0.635771\pi$
$29$	−129.221	−0.827441	−0.413720	+	0.910404i	$0.635771\pi$
$30$	74.1551	0.451293
$31$	126.828	0.734806	0.367403	−	0.930062i	$-0.380247\pi$
$31$	126.828	0.734806	0.367403	+	0.930062i	$0.380247\pi$
$32$	−177.724	−0.981796
$33$	33.0000	0.174078
$34$	−67.5933	−0.340946
$35$	97.8144	0.472390
$36$	−42.7684	−0.198002
$37$	−153.834	−0.683517	−0.341759	−	0.939788i	$-0.611023\pi$
$37$	−153.834	−0.683517	−0.341759	+	0.939788i	$0.611023\pi$
$38$	−107.407	−0.458520
$39$	172.702	0.709087
$40$	315.209	1.24597
$41$	−141.080	−0.537389	−0.268695	−	0.963225i	$-0.586592\pi$
$41$	−141.080	−0.537389	−0.268695	+	0.963225i	$0.586592\pi$
$42$	38.5580	0.141658
$43$	−128.761	−0.456648	−0.228324	−	0.973585i	$-0.573325\pi$
$43$	−128.761	−0.456648	−0.228324	+	0.973585i	$0.573325\pi$
$44$	52.2725	0.179099
$45$	123.440	0.408920
$46$	−218.271	−0.699615
$47$	−213.302	−0.661984	−0.330992	−	0.943634i	$-0.607383\pi$
$47$	−213.302	−0.661984	−0.330992	+	0.943634i	$0.607383\pi$
$48$	10.2052	0.0306875
$49$	−292.140	−0.851720
$50$	−113.751	−0.321735
$51$	−112.517	−0.308933
$52$	273.562	0.729542
$53$	−379.423	−0.983355	−0.491677	−	0.870777i	$-0.663616\pi$
$53$	−379.423	−0.983355	−0.491677	+	0.870777i	$0.663616\pi$
$54$	48.6596	0.122625
$55$	−150.871	−0.369882
$56$	163.898	0.391103
$57$	−178.793	−0.415468
$58$	232.884	0.527226
$59$	35.7135	0.0788052	0.0394026	−	0.999223i	$-0.487455\pi$
$59$	35.7135	0.0788052	0.0394026	+	0.999223i	$0.487455\pi$
$60$	195.531	0.420716
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−228.571	−0.468202
$63$	64.1846	0.128357
$64$	347.510	0.678730
$65$	−789.568	−1.50667
$66$	−59.4729	−0.110918
$67$	−275.818	−0.502933	−0.251467	−	0.967866i	$-0.580913\pi$
$67$	−275.818	−0.502933	−0.251467	+	0.967866i	$0.580913\pi$
$68$	−178.229	−0.317845
$69$	−363.339	−0.633925
$70$	−176.282	−0.300996
$71$	−146.734	−0.245270	−0.122635	−	0.992452i	$-0.539134\pi$
$71$	−146.734	−0.245270	−0.122635	+	0.992452i	$0.539134\pi$
$72$	206.837	0.338555
$73$	663.138	1.06321	0.531606	−	0.846992i	$-0.321589\pi$
$73$	663.138	1.06321	0.531606	+	0.846992i	$0.321589\pi$
$74$	277.241	0.435521
$75$	−189.352	−0.291526
$76$	−283.210	−0.427454
$77$	−78.4478	−0.116103
$78$	−311.244	−0.451814
$79$	−127.271	−0.181255	−0.0906274	−	0.995885i	$-0.528887\pi$
$79$	−127.271	−0.181255	−0.0906274	+	0.995885i	$0.528887\pi$
$80$	−46.6570	−0.0652051
$81$	81.0000	0.111111
$82$	254.255	0.342412
$83$	−803.216	−1.06222	−0.531111	−	0.847302i	$-0.678225\pi$
$83$	−803.216	−1.06222	−0.531111	+	0.847302i	$0.678225\pi$
$84$	101.669	0.132060
$85$	514.414	0.656424
$86$	232.054	0.290966
$87$	387.664	0.477723
$88$	−252.800	−0.306234
$89$	37.7197	0.0449245	0.0224622	−	0.999748i	$-0.492849\pi$
$89$	37.7197	0.0449245	0.0224622	+	0.999748i	$0.492849\pi$
$90$	−222.465	−0.260554
$91$	−410.547	−0.472935
$92$	−575.534	−0.652213
$93$	−380.484	−0.424240
$94$	384.414	0.421801
$95$	817.416	0.882791
$96$	533.172	0.566840
$97$	1401.61	1.46714	0.733568	−	0.679616i	$-0.237854\pi$
$97$	1401.61	1.46714	0.733568	+	0.679616i	$0.237854\pi$
$98$	526.497	0.542697
$99$	−99.0000	−0.100504
$100$	−299.936	−0.299936
$101$	1203.18	1.18535	0.592677	−	0.805440i	$-0.298071\pi$
$101$	1203.18	1.18535	0.592677	+	0.805440i	$0.298071\pi$
$102$	202.780	0.196845
$103$	143.520	0.137296	0.0686478	−	0.997641i	$-0.478132\pi$
$103$	143.520	0.137296	0.0686478	+	0.997641i	$0.478132\pi$
$104$	−1323.00	−1.24741
$105$	−293.443	−0.272734
$106$	683.800	0.626571
$107$	−934.215	−0.844056	−0.422028	−	0.906583i	$-0.638682\pi$
$107$	−934.215	−0.844056	−0.422028	+	0.906583i	$0.638682\pi$
$108$	128.305	0.114316
$109$	−490.030	−0.430609	−0.215305	−	0.976547i	$-0.569074\pi$
$109$	−490.030	−0.430609	−0.215305	+	0.976547i	$0.569074\pi$
$110$	271.902	0.235680
$111$	461.502	0.394629
$112$	−24.2600	−0.0204674
$113$	1708.64	1.42243	0.711217	−	0.702973i	$-0.248144\pi$
$113$	1708.64	1.42243	0.711217	+	0.702973i	$0.248144\pi$
$114$	322.222	0.264727
$115$	1661.14	1.34697
$116$	614.065	0.491504
$117$	−518.105	−0.409392
$118$	−64.3632	−0.0502129
$119$	267.477	0.206047
$120$	−945.628	−0.719364
$121$	121.000	0.0909091
$122$	−109.935	−0.0815822
$123$	423.239	0.310262
$124$	−602.692	−0.436479
$125$	−848.758	−0.607321
$126$	−115.674	−0.0817862
$127$	2766.83	1.93320	0.966601	−	0.256287i	$-0.0824992\pi$
$127$	2766.83	1.93320	0.966601	+	0.256287i	$0.0824992\pi$
$128$	795.507	0.549325
$129$	386.283	0.263646
$130$	1422.97	0.960019
$131$	−1146.02	−0.764339	−0.382170	−	0.924092i	$-0.624823\pi$
$131$	−1146.02	−0.764339	−0.382170	+	0.924092i	$0.624823\pi$
$132$	−156.817	−0.103403
$133$	425.028	0.277102
$134$	497.082	0.320458
$135$	−370.321	−0.236090
$136$	861.952	0.543469
$137$	−1536.18	−0.957990	−0.478995	−	0.877817i	$-0.658999\pi$
$137$	−1536.18	−0.957990	−0.478995	+	0.877817i	$0.658999\pi$
$138$	654.813	0.403923
$139$	2753.56	1.68024	0.840121	−	0.542399i	$-0.182484\pi$
$139$	2753.56	1.68024	0.840121	+	0.542399i	$0.182484\pi$
$140$	−464.818	−0.280602
$141$	639.905	0.382196
$142$	264.446	0.156280
$143$	633.239	0.370309
$144$	−30.6157	−0.0177174
$145$	−1772.35	−1.01507
$146$	−1195.11	−0.677454
$147$	876.420	0.491741
$148$	731.025	0.406013
$149$	−150.813	−0.0829199	−0.0414599	−	0.999140i	$-0.513201\pi$
$149$	−150.813	−0.0829199	−0.0414599	+	0.999140i	$0.513201\pi$
$150$	341.252	0.185754
$151$	1375.66	0.741389	0.370695	−	0.928755i	$-0.379120\pi$
$151$	1375.66	0.741389	0.370695	+	0.928755i	$0.379120\pi$
$152$	1369.66	0.730884
$153$	337.552	0.178363
$154$	141.379	0.0739784
$155$	1739.52	0.901430
$156$	−820.685	−0.421201
$157$	−431.422	−0.219307	−0.109654	−	0.993970i	$-0.534974\pi$
$157$	−431.422	−0.219307	−0.109654	+	0.993970i	$0.534974\pi$
$158$	229.369	0.115491
$159$	1138.27	0.567740
$160$	−2437.59	−1.20443
$161$	863.732	0.422805
$162$	−145.979	−0.0707975
$163$	−2958.02	−1.42141	−0.710706	−	0.703489i	$-0.751625\pi$
$163$	−2958.02	−1.42141	−0.710706	+	0.703489i	$0.751625\pi$
$164$	670.417	0.319212
$165$	452.614	0.213551
$166$	1447.56	0.676824
$167$	1909.80	0.884937	0.442468	−	0.896784i	$-0.354103\pi$
$167$	1909.80	0.884937	0.442468	+	0.896784i	$0.354103\pi$
$168$	−491.693	−0.225803
$169$	1116.98	0.508413
$170$	−927.081	−0.418258
$171$	536.379	0.239871
$172$	611.878	0.271252
$173$	−534.903	−0.235075	−0.117537	−	0.993068i	$-0.537500\pi$
$173$	−534.903	−0.235075	−0.117537	+	0.993068i	$0.537500\pi$
$174$	−698.651	−0.304394
$175$	450.129	0.194437
$176$	37.4192	0.0160260
$177$	−107.141	−0.0454982
$178$	−67.9787	−0.0286248
$179$	−146.180	−0.0610392	−0.0305196	−	0.999534i	$-0.509716\pi$
$179$	−146.180	−0.0610392	−0.0305196	+	0.999534i	$0.509716\pi$
$180$	−586.593	−0.242901
$181$	−4087.63	−1.67862	−0.839312	−	0.543651i	$-0.817042\pi$
$181$	−4087.63	−1.67862	−0.839312	+	0.543651i	$0.817042\pi$
$182$	739.892	0.301343
$183$	−183.000	−0.0739221
$184$	2783.40	1.11519
$185$	−2109.92	−0.838511
$186$	685.712	0.270316
$187$	−412.564	−0.161335
$188$	1013.62	0.393222
$189$	−192.554	−0.0741070
$190$	−1473.16	−0.562494
$191$	−198.363	−0.0751468	−0.0375734	−	0.999294i	$-0.511963\pi$
$191$	−198.363	−0.0751468	−0.0375734	+	0.999294i	$0.511963\pi$
$192$	−1042.53	−0.391865
$193$	−4498.33	−1.67770	−0.838852	−	0.544360i	$-0.816773\pi$
$193$	−4498.33	−1.67770	−0.838852	+	0.544360i	$0.816773\pi$
$194$	−2526.00	−0.934825
$195$	2368.70	0.869879
$196$	1388.26	0.505926
$197$	−4911.22	−1.77619	−0.888096	−	0.459658i	$-0.847972\pi$
$197$	−4911.22	−1.77619	−0.888096	+	0.459658i	$0.847972\pi$
$198$	178.419	0.0640387
$199$	−2841.44	−1.01218	−0.506091	−	0.862480i	$-0.668910\pi$
$199$	−2841.44	−1.01218	−0.506091	+	0.862480i	$0.668910\pi$
$200$	1450.55	0.512848
$201$	827.454	0.290369
$202$	−2168.38	−0.755280
$203$	−921.557	−0.318624
$204$	534.687	0.183508
$205$	−1934.99	−0.659247
$206$	−258.653	−0.0874816
$207$	1090.02	0.365997
$208$	195.829	0.0652803
$209$	−655.574	−0.216971
$210$	528.846	0.173780
$211$	778.757	0.254084	0.127042	−	0.991897i	$-0.459452\pi$
$211$	778.757	0.254084	0.127042	+	0.991897i	$0.459452\pi$
$212$	1803.04	0.584118
$213$	440.203	0.141607
$214$	1683.65	0.537813
$215$	−1766.03	−0.560198
$216$	−620.510	−0.195465
$217$	904.489	0.282953
$218$	883.137	0.274374
$219$	−1989.41	−0.613845
$220$	716.948	0.219712
$221$	−2159.10	−0.657181
$222$	−831.722	−0.251448
$223$	−957.588	−0.287555	−0.143778	−	0.989610i	$-0.545925\pi$
$223$	−957.588	−0.287555	−0.143778	+	0.989610i	$0.545925\pi$
$224$	−1267.46	−0.378062
$225$	568.056	0.168313
$226$	−3079.32	−0.906342
$227$	−2291.83	−0.670105	−0.335053	−	0.942199i	$-0.608754\pi$
$227$	−2291.83	−0.670105	−0.335053	+	0.942199i	$0.608754\pi$
$228$	849.631	0.246790
$229$	184.275	0.0531756	0.0265878	−	0.999646i	$-0.491536\pi$
$229$	184.275	0.0531756	0.0265878	+	0.999646i	$0.491536\pi$
$230$	−2993.71	−0.858259
$231$	235.343	0.0670323
$232$	−2969.74	−0.840402
$233$	−896.543	−0.252079	−0.126040	−	0.992025i	$-0.540227\pi$
$233$	−896.543	−0.252079	−0.126040	+	0.992025i	$0.540227\pi$
$234$	933.733	0.260855
$235$	−2925.56	−0.812094
$236$	−169.712	−0.0468107
$237$	381.813	0.104647
$238$	−482.050	−0.131288
$239$	−2353.40	−0.636940	−0.318470	−	0.947933i	$-0.603169\pi$
$239$	−2353.40	−0.636940	−0.318470	+	0.947933i	$0.603169\pi$
$240$	139.971	0.0376462
$241$	4820.97	1.28857	0.644286	−	0.764784i	$-0.277155\pi$
$241$	4820.97	1.28857	0.644286	+	0.764784i	$0.277155\pi$
$242$	−218.067	−0.0579252
$243$	−243.000	−0.0641500
$244$	−289.875	−0.0760546
$245$	−4006.87	−1.04486
$246$	−762.766	−0.197692
$247$	−3430.87	−0.883810
$248$	2914.74	0.746316
$249$	2409.65	0.613274
$250$	1529.64	0.386971
$251$	6180.75	1.55429	0.777143	−	0.629324i	$-0.216668\pi$
$251$	6180.75	1.55429	0.777143	+	0.629324i	$0.216668\pi$
$252$	−305.008	−0.0762448
$253$	−1332.24	−0.331057
$254$	−4986.41	−1.23179
$255$	−1543.24	−0.378986
$256$	−4213.75	−1.02875
$257$	7132.55	1.73119	0.865596	−	0.500743i	$-0.166940\pi$
$257$	7132.55	1.73119	0.865596	+	0.500743i	$0.166940\pi$
$258$	−696.163	−0.167989
$259$	−1097.08	−0.263203
$260$	3752.06	0.894973
$261$	−1162.99	−0.275814
$262$	2065.37	0.487019
$263$	−6808.05	−1.59621	−0.798103	−	0.602521i	$-0.794163\pi$
$263$	−6808.05	−1.59621	−0.798103	+	0.602521i	$0.794163\pi$
$264$	758.401	0.176804
$265$	−5204.01	−1.20634
$266$	−765.989	−0.176563
$267$	−113.159	−0.0259372
$268$	1310.70	0.298745
$269$	−238.544	−0.0540680	−0.0270340	−	0.999635i	$-0.508606\pi$
$269$	−238.544	−0.0540680	−0.0270340	+	0.999635i	$0.508606\pi$
$270$	667.396	0.150431
$271$	−4616.71	−1.03485	−0.517427	−	0.855727i	$-0.673110\pi$
$271$	−4616.71	−1.03485	−0.517427	+	0.855727i	$0.673110\pi$
$272$	−127.585	−0.0284411
$273$	1231.64	0.273049
$274$	2768.52	0.610410
$275$	−694.290	−0.152245
$276$	1726.60	0.376555
$277$	−6323.70	−1.37168	−0.685838	−	0.727754i	$-0.740564\pi$
$277$	−6323.70	−1.37168	−0.685838	+	0.727754i	$0.740564\pi$
$278$	−4962.48	−1.07061
$279$	1141.45	0.244935
$280$	2247.95	0.479789
$281$	−438.687	−0.0931313	−0.0465656	−	0.998915i	$-0.514828\pi$
$281$	−438.687	−0.0931313	−0.0465656	+	0.998915i	$0.514828\pi$
$282$	−1153.24	−0.243527
$283$	1049.04	0.220349	0.110175	−	0.993912i	$-0.464859\pi$
$283$	1049.04	0.220349	0.110175	+	0.993912i	$0.464859\pi$
$284$	697.287	0.145691
$285$	−2452.25	−0.509680
$286$	−1141.23	−0.235952
$287$	−1006.13	−0.206933
$288$	−1599.52	−0.327265
$289$	−3506.32	−0.713681
$290$	3194.14	0.646780
$291$	−4204.84	−0.847051
$292$	−3151.26	−0.631553
$293$	6546.96	1.30538	0.652692	−	0.757623i	$-0.273639\pi$
$293$	6546.96	1.30538	0.652692	+	0.757623i	$0.273639\pi$
$294$	−1579.49	−0.313326
$295$	489.832	0.0966750
$296$	−3535.39	−0.694223
$297$	297.000	0.0580259
$298$	271.796	0.0528346
$299$	−6972.13	−1.34852
$300$	899.808	0.173168
$301$	−918.275	−0.175842
$302$	−2479.23	−0.472396
$303$	−3609.54	−0.684364
$304$	−202.736	−0.0382491
$305$	836.651	0.157070
$306$	−608.340	−0.113649
$307$	−3043.91	−0.565879	−0.282940	−	0.959138i	$-0.591310\pi$
$307$	−3043.91	−0.565879	−0.282940	+	0.959138i	$0.591310\pi$
$308$	372.787	0.0689660
$309$	−430.560	−0.0792677
$310$	−3134.98	−0.574371
$311$	−6250.90	−1.13973	−0.569865	−	0.821738i	$-0.693005\pi$
$311$	−6250.90	−1.13973	−0.569865	+	0.821738i	$0.693005\pi$
$312$	3969.00	0.720194
$313$	−330.426	−0.0596703	−0.0298352	−	0.999555i	$-0.509498\pi$
$313$	−330.426	−0.0596703	−0.0298352	+	0.999555i	$0.509498\pi$
$314$	777.513	0.139737
$315$	880.329	0.157463
$316$	604.798	0.107666
$317$	−5983.98	−1.06023	−0.530116	−	0.847925i	$-0.677852\pi$
$317$	−5983.98	−1.06023	−0.530116	+	0.847925i	$0.677852\pi$
$318$	−2051.40	−0.361751
$319$	1421.43	0.249483
$320$	4766.30	0.832639
$321$	2802.65	0.487316
$322$	−1556.62	−0.269402
$323$	2235.26	0.385056
$324$	−384.915	−0.0660006
$325$	−3633.49	−0.620153
$326$	5330.98	0.905692
$327$	1470.09	0.248612
$328$	−3242.27	−0.545807
$329$	−1521.19	−0.254911
$330$	−815.706	−0.136070
$331$	−1215.59	−0.201858	−0.100929	−	0.994894i	$-0.532181\pi$
$331$	−1215.59	−0.201858	−0.100929	+	0.994894i	$0.532181\pi$
$332$	3816.92	0.630966
$333$	−1384.50	−0.227839
$334$	−3441.85	−0.563861
$335$	−3783.01	−0.616978
$336$	72.7799	0.0118169
$337$	1459.18	0.235866	0.117933	−	0.993022i	$-0.462373\pi$
$337$	1459.18	0.235866	0.117933	+	0.993022i	$0.462373\pi$
$338$	−2013.04	−0.323949
$339$	−5125.91	−0.821242
$340$	−2444.52	−0.389919
$341$	−1395.11	−0.221552
$342$	−966.666	−0.152840
$343$	−4529.58	−0.713044
$344$	−2959.17	−0.463801
$345$	−4983.41	−0.777674
$346$	964.008	0.149784
$347$	−5278.05	−0.816543	−0.408272	−	0.912861i	$-0.633868\pi$
$347$	−5278.05	−0.816543	−0.408272	+	0.912861i	$0.633868\pi$
$348$	−1842.19	−0.283770
$349$	10987.7	1.68526	0.842631	−	0.538492i	$-0.181006\pi$
$349$	10987.7	1.68526	0.842631	+	0.538492i	$0.181006\pi$
$350$	−811.226	−0.123891
$351$	1554.31	0.236362
$352$	1954.97	0.296023
$353$	7692.05	1.15979	0.579896	−	0.814691i	$-0.303093\pi$
$353$	7692.05	1.15979	0.579896	+	0.814691i	$0.303093\pi$
$354$	193.090	0.0289904
$355$	−2012.55	−0.300887
$356$	−179.245	−0.0266854
$357$	−802.431	−0.118961
$358$	263.447	0.0388928
$359$	3247.43	0.477418	0.238709	−	0.971091i	$-0.423276\pi$
$359$	3247.43	0.477418	0.238709	+	0.971091i	$0.423276\pi$
$360$	2836.89	0.415325
$361$	−3307.12	−0.482158
$362$	7366.76	1.06958
$363$	−363.000	−0.0524864
$364$	1950.94	0.280926
$365$	9095.33	1.30430
$366$	329.804	0.0471015
$367$	4844.94	0.689111	0.344556	−	0.938766i	$-0.388030\pi$
$367$	4844.94	0.689111	0.344556	+	0.938766i	$0.388030\pi$
$368$	−411.996	−0.0583608
$369$	−1269.72	−0.179130
$370$	3802.52	0.534280
$371$	−2705.90	−0.378662
$372$	1808.08	0.252001
$373$	1809.92	0.251244	0.125622	−	0.992078i	$-0.459907\pi$
$373$	1809.92	0.251244	0.125622	+	0.992078i	$0.459907\pi$
$374$	743.526	0.102799
$375$	2546.27	0.350637
$376$	−4902.06	−0.672353
$377$	7438.91	1.01624
$378$	347.022	0.0472193
$379$	−10700.4	−1.45025	−0.725123	−	0.688619i	$-0.758217\pi$
$379$	−10700.4	−1.45025	−0.725123	+	0.688619i	$0.758217\pi$
$380$	−3884.40	−0.524383
$381$	−8300.49	−1.11613
$382$	357.491	0.0478818
$383$	5681.15	0.757946	0.378973	−	0.925408i	$-0.376277\pi$
$383$	5681.15	0.757946	0.378973	+	0.925408i	$0.376277\pi$
$384$	−2386.52	−0.317153
$385$	−1075.96	−0.142431
$386$	8106.93	1.06899
$387$	−1158.85	−0.152216
$388$	−6660.52	−0.871486
$389$	6246.74	0.814197	0.407098	−	0.913384i	$-0.366541\pi$
$389$	6246.74	0.814197	0.407098	+	0.913384i	$0.366541\pi$
$390$	−4268.90	−0.554267
$391$	4542.44	0.587522
$392$	−6713.92	−0.865061
$393$	3438.07	0.441291
$394$	8851.04	1.13175
$395$	−1745.60	−0.222356
$396$	470.452	0.0596998
$397$	−12114.4	−1.53150	−0.765751	−	0.643137i	$-0.777633\pi$
$397$	−12114.4	−1.53150	−0.765751	+	0.643137i	$0.777633\pi$
$398$	5120.87	0.644939
$399$	−1275.08	−0.159985
$400$	−214.709	−0.0268386
$401$	−9663.32	−1.20340	−0.601700	−	0.798722i	$-0.705510\pi$
$401$	−9663.32	−1.20340	−0.601700	+	0.798722i	$0.705510\pi$
$402$	−1491.25	−0.185016
$403$	−7301.14	−0.902470
$404$	−5717.56	−0.704107
$405$	1110.96	0.136307
$406$	1660.84	0.203020
$407$	1692.17	0.206088
$408$	−2585.86	−0.313772
$409$	−13009.7	−1.57284	−0.786418	−	0.617695i	$-0.788067\pi$
$409$	−13009.7	−1.57284	−0.786418	+	0.617695i	$0.788067\pi$
$410$	3487.26	0.420057
$411$	4608.54	0.553096
$412$	−682.013	−0.0815543
$413$	254.695	0.0303456
$414$	−1964.44	−0.233205
$415$	−11016.6	−1.30309
$416$	10231.1	1.20582
$417$	−8260.67	−0.970088
$418$	1181.48	0.138249
$419$	−1721.27	−0.200691	−0.100346	−	0.994953i	$-0.531995\pi$
$419$	−1721.27	−0.200691	−0.100346	+	0.994953i	$0.531995\pi$
$420$	1394.45	0.162006
$421$	6775.26	0.784337	0.392169	−	0.919893i	$-0.371725\pi$
$421$	6775.26	0.784337	0.392169	+	0.919893i	$0.371725\pi$
$422$	−1403.48	−0.161897
$423$	−1919.71	−0.220661
$424$	−8719.85	−0.998758
$425$	2367.26	0.270186
$426$	−793.337	−0.0902284
$427$	435.029	0.0493033
$428$	4439.43	0.501374
$429$	−1899.72	−0.213798
$430$	3182.76	0.356945
$431$	−4337.72	−0.484780	−0.242390	−	0.970179i	$-0.577931\pi$
$431$	−4337.72	−0.484780	−0.242390	+	0.970179i	$0.577931\pi$
$432$	91.8472	0.0102292
$433$	3923.39	0.435441	0.217721	−	0.976011i	$-0.430138\pi$
$433$	3923.39	0.435441	0.217721	+	0.976011i	$0.430138\pi$
$434$	−1630.08	−0.180291
$435$	5317.04	0.586051
$436$	2328.65	0.255784
$437$	7218.04	0.790128
$438$	3585.34	0.391128
$439$	−13138.1	−1.42836	−0.714179	−	0.699963i	$-0.753200\pi$
$439$	−13138.1	−1.42836	−0.714179	+	0.699963i	$0.753200\pi$
$440$	−3467.30	−0.375676
$441$	−2629.26	−0.283907
$442$	3891.16	0.418741
$443$	−4665.84	−0.500408	−0.250204	−	0.968193i	$-0.580498\pi$
$443$	−4665.84	−0.500408	−0.250204	+	0.968193i	$0.580498\pi$
$444$	−2193.08	−0.234412
$445$	517.347	0.0551115
$446$	1725.77	0.183224
$447$	452.438	0.0478738
$448$	2478.31	0.261360
$449$	−13078.4	−1.37463	−0.687313	−	0.726361i	$-0.741210\pi$
$449$	−13078.4	−1.37463	−0.687313	+	0.726361i	$0.741210\pi$
$450$	−1023.76	−0.107245
$451$	1551.88	0.162029
$452$	−8119.51	−0.844933
$453$	−4126.99	−0.428041
$454$	4130.35	0.426976
$455$	−5630.90	−0.580177
$456$	−4108.99	−0.421976
$457$	−3408.57	−0.348898	−0.174449	−	0.984666i	$-0.555814\pi$
$457$	−3408.57	−0.348898	−0.174449	+	0.984666i	$0.555814\pi$
$458$	−332.101	−0.0338823
$459$	−1012.66	−0.102978
$460$	−7893.78	−0.800108
$461$	5100.33	0.515284	0.257642	−	0.966240i	$-0.417054\pi$
$461$	5100.33	0.515284	0.257642	+	0.966240i	$0.417054\pi$
$462$	−424.138	−0.0427115
$463$	13821.1	1.38730	0.693651	−	0.720312i	$-0.256001\pi$
$463$	13821.1	1.38730	0.693651	+	0.720312i	$0.256001\pi$
$464$	439.578	0.0439804
$465$	−5218.56	−0.520441
$466$	1615.76	0.160619
$467$	4117.21	0.407969	0.203985	−	0.978974i	$-0.434611\pi$
$467$	4117.21	0.407969	0.203985	+	0.978974i	$0.434611\pi$
$468$	2462.06	0.243181
$469$	−1967.03	−0.193665
$470$	5272.46	0.517448
$471$	1294.27	0.126617
$472$	820.763	0.0800396
$473$	1416.37	0.137685
$474$	−688.108	−0.0666790
$475$	3761.64	0.363360
$476$	−1271.06	−0.122393
$477$	−3414.81	−0.327785
$478$	4241.31	0.405843
$479$	7208.33	0.687593	0.343797	−	0.939044i	$-0.388287\pi$
$479$	7208.33	0.687593	0.343797	+	0.939044i	$0.388287\pi$
$480$	7312.77	0.695377
$481$	8855.79	0.839478
$482$	−8688.40	−0.821049
$483$	−2591.19	−0.244107
$484$	−574.997	−0.0540005
$485$	19223.9	1.79982
$486$	437.937	0.0408749
$487$	1084.36	0.100897	0.0504487	−	0.998727i	$-0.483935\pi$
$487$	1084.36	0.100897	0.0504487	+	0.998727i	$0.483935\pi$
$488$	1401.89	0.130042
$489$	8874.07	0.820653
$490$	7221.22	0.665758
$491$	−17300.7	−1.59016	−0.795081	−	0.606504i	$-0.792571\pi$
$491$	−17300.7	−1.59016	−0.795081	+	0.606504i	$0.792571\pi$
$492$	−2011.25	−0.184297
$493$	−4846.55	−0.442753
$494$	6183.14	0.563143
$495$	−1357.84	−0.123294
$496$	−431.437	−0.0390566
$497$	−1046.45	−0.0944463
$498$	−4342.69	−0.390764
$499$	−3865.90	−0.346817	−0.173408	−	0.984850i	$-0.555478\pi$
$499$	−3865.90	−0.346817	−0.173408	+	0.984850i	$0.555478\pi$
$500$	4033.33	0.360752
$501$	−5729.39	−0.510918
$502$	−11139.0	−0.990355
$503$	11256.5	0.997822	0.498911	−	0.866653i	$-0.333733\pi$
$503$	11256.5	0.997822	0.498911	+	0.866653i	$0.333733\pi$
$504$	1475.08	0.130368
$505$	16502.3	1.45414
$506$	2400.98	0.210942
$507$	−3350.95	−0.293532
$508$	−13148.1	−1.14833
$509$	−9899.08	−0.862021	−0.431011	−	0.902347i	$-0.641843\pi$
$509$	−9899.08	−0.862021	−0.431011	+	0.902347i	$0.641843\pi$
$510$	2781.24	0.241482
$511$	4729.25	0.409412
$512$	1230.00	0.106170
$513$	−1609.14	−0.138489
$514$	−12854.3	−1.10308
$515$	1968.46	0.168429
$516$	−1835.63	−0.156607
$517$	2346.32	0.199596
$518$	1977.18	0.167707
$519$	1604.71	0.135721
$520$	−18145.7	−1.53027
$521$	−3372.95	−0.283631	−0.141816	−	0.989893i	$-0.545294\pi$
$521$	−3372.95	−0.283631	−0.141816	+	0.989893i	$0.545294\pi$
$522$	2095.95	0.175742
$523$	−11605.4	−0.970305	−0.485152	−	0.874430i	$-0.661236\pi$
$523$	−11605.4	−0.970305	−0.485152	+	0.874430i	$0.661236\pi$
$524$	5445.95	0.454021
$525$	−1350.39	−0.112258
$526$	12269.5	1.01707
$527$	4756.79	0.393186
$528$	−112.258	−0.00925263
$529$	2501.35	0.205585
$530$	9378.72	0.768652
$531$	321.422	0.0262684
$532$	−2019.75	−0.164600
$533$	8121.57	0.660008
$534$	203.936	0.0165266
$535$	−12813.3	−1.03545
$536$	−6338.81	−0.510811
$537$	438.541	0.0352410
$538$	429.906	0.0344509
$539$	3213.54	0.256803
$540$	1759.78	0.140239
$541$	−2173.91	−0.172761	−0.0863806	−	0.996262i	$-0.527530\pi$
$541$	−2173.91	−0.172761	−0.0863806	+	0.996262i	$0.527530\pi$
$542$	8320.28	0.659385
$543$	12262.9	0.969154
$544$	−6665.68	−0.525347
$545$	−6721.05	−0.528254
$546$	−2219.68	−0.173981
$547$	−8813.45	−0.688914	−0.344457	−	0.938802i	$-0.611937\pi$
$547$	−8813.45	−0.688914	−0.344457	+	0.938802i	$0.611937\pi$
$548$	7299.99	0.569051
$549$	549.000	0.0426790
$550$	1251.26	0.0970068
$551$	−7701.28	−0.595437
$552$	−8350.20	−0.643855
$553$	−907.650	−0.0697960
$554$	11396.6	0.874001
$555$	6329.76	0.484115
$556$	−13085.0	−0.998073
$557$	−6669.67	−0.507366	−0.253683	−	0.967287i	$-0.581642\pi$
$557$	−6669.67	−0.507366	−0.253683	+	0.967287i	$0.581642\pi$
$558$	−2057.14	−0.156067
$559$	7412.42	0.560844
$560$	−332.740	−0.0251086
$561$	1237.69	0.0931468
$562$	790.606	0.0593411
$563$	−6213.80	−0.465152	−0.232576	−	0.972578i	$-0.574715\pi$
$563$	−6213.80	−0.465152	−0.232576	+	0.972578i	$0.574715\pi$
$564$	−3040.85	−0.227027
$565$	23434.9	1.74498
$566$	−1890.58	−0.140401
$567$	577.661	0.0427857
$568$	−3372.22	−0.249111
$569$	16653.2	1.22695	0.613477	−	0.789713i	$-0.289770\pi$
$569$	16653.2	1.22695	0.613477	+	0.789713i	$0.289770\pi$
$570$	4419.47	0.324756
$571$	−11408.1	−0.836105	−0.418053	−	0.908423i	$-0.637287\pi$
$571$	−11408.1	−0.836105	−0.418053	+	0.908423i	$0.637287\pi$
$572$	−3009.18	−0.219965
$573$	595.088	0.0433860
$574$	1813.25	0.131853
$575$	7644.32	0.554418
$576$	3127.59	0.226243
$577$	−9805.72	−0.707483	−0.353741	−	0.935343i	$-0.615091\pi$
$577$	−9805.72	−0.707483	−0.353741	+	0.935343i	$0.615091\pi$
$578$	6319.11	0.454741
$579$	13495.0	0.968623
$580$	8422.26	0.602958
$581$	−5728.24	−0.409031
$582$	7577.99	0.539721
$583$	4173.66	0.296493
$584$	15240.1	1.07987
$585$	−7106.11	−0.502225
$586$	−11799.0	−0.831761
$587$	−278.682	−0.0195953	−0.00979764	−	0.999952i	$-0.503119\pi$
$587$	−278.682	−0.0195953	−0.00979764	+	0.999952i	$0.503119\pi$
$588$	−4164.79	−0.292097
$589$	7558.65	0.528775
$590$	−882.780	−0.0615991
$591$	14733.7	1.02549
$592$	523.304	0.0363305
$593$	5714.27	0.395712	0.197856	−	0.980231i	$-0.436602\pi$
$593$	5714.27	0.395712	0.197856	+	0.980231i	$0.436602\pi$
$594$	−535.256	−0.0369728
$595$	3668.61	0.252770
$596$	716.668	0.0492548
$597$	8524.32	0.584384
$598$	12565.2	0.859249
$599$	−11619.5	−0.792587	−0.396293	−	0.918124i	$-0.629704\pi$
$599$	−11619.5	−0.792587	−0.396293	+	0.918124i	$0.629704\pi$
$600$	−4351.66	−0.296093
$601$	−716.065	−0.0486005	−0.0243003	−	0.999705i	$-0.507736\pi$
$601$	−716.065	−0.0486005	−0.0243003	+	0.999705i	$0.507736\pi$
$602$	1654.92	0.112043
$603$	−2482.36	−0.167644
$604$	−6537.21	−0.440389
$605$	1659.59	0.111524
$606$	6505.14	0.436061
$607$	−22864.9	−1.52892	−0.764461	−	0.644670i	$-0.776995\pi$
$607$	−22864.9	−1.52892	−0.764461	+	0.644670i	$0.776995\pi$
$608$	−10591.9	−0.706513
$609$	2764.67	0.183958
$610$	−1507.82	−0.100082
$611$	12279.2	0.813031
$612$	−1604.06	−0.105948
$613$	14096.0	0.928764	0.464382	−	0.885635i	$-0.346276\pi$
$613$	14096.0	0.928764	0.464382	+	0.885635i	$0.346276\pi$
$614$	5485.76	0.360565
$615$	5804.98	0.380617
$616$	−1802.88	−0.117922
$617$	−2664.37	−0.173847	−0.0869236	−	0.996215i	$-0.527704\pi$
$617$	−2664.37	−0.173847	−0.0869236	+	0.996215i	$0.527704\pi$
$618$	775.959	0.0505075
$619$	−6104.54	−0.396385	−0.198192	−	0.980163i	$-0.563507\pi$
$619$	−6104.54	−0.396385	−0.198192	+	0.980163i	$0.563507\pi$
$620$	−8266.28	−0.535454
$621$	−3270.05	−0.211308
$622$	11265.4	0.726210
$623$	269.002	0.0172991
$624$	−587.487	−0.0376896
$625$	−19530.9	−1.24998
$626$	595.497	0.0380205
$627$	1966.72	0.125268
$628$	2050.14	0.130270
$629$	−5769.66	−0.365742
$630$	−1586.54	−0.100332
$631$	−22209.9	−1.40121	−0.700603	−	0.713552i	$-0.747085\pi$
$631$	−22209.9	−1.40121	−0.700603	+	0.713552i	$0.747085\pi$
$632$	−2924.93	−0.184094
$633$	−2336.27	−0.146696
$634$	10784.4	0.675556
$635$	37948.7	2.37157
$636$	−5409.11	−0.337241
$637$	16817.7	1.04606
$638$	−2561.72	−0.158965
$639$	−1320.61	−0.0817566
$640$	10910.8	0.673889
$641$	18058.5	1.11274	0.556371	−	0.830934i	$-0.312193\pi$
$641$	18058.5	1.11274	0.556371	+	0.830934i	$0.312193\pi$
$642$	−5050.95	−0.310507
$643$	−11409.8	−0.699782	−0.349891	−	0.936790i	$-0.613781\pi$
$643$	−11409.8	−0.699782	−0.349891	+	0.936790i	$0.613781\pi$
$644$	−4104.49	−0.251148
$645$	5298.10	0.323430
$646$	−4028.40	−0.245349
$647$	−2245.43	−0.136440	−0.0682202	−	0.997670i	$-0.521732\pi$
$647$	−2245.43	−0.136440	−0.0682202	+	0.997670i	$0.521732\pi$
$648$	1861.53	0.112852
$649$	−392.849	−0.0237607
$650$	6548.30	0.395147
$651$	−2713.47	−0.163363
$652$	14056.7	0.844327
$653$	11370.0	0.681384	0.340692	−	0.940175i	$-0.389339\pi$
$653$	11370.0	0.681384	0.340692	+	0.940175i	$0.389339\pi$
$654$	−2649.41	−0.158410
$655$	−15718.4	−0.937660
$656$	479.918	0.0285635
$657$	5968.24	0.354404
$658$	2741.49	0.162423
$659$	23972.6	1.41705	0.708527	−	0.705684i	$-0.249360\pi$
$659$	23972.6	1.41705	0.708527	+	0.705684i	$0.249360\pi$
$660$	−2150.84	−0.126851
$661$	−21053.7	−1.23887	−0.619436	−	0.785047i	$-0.712639\pi$
$661$	−21053.7	−1.23887	−0.619436	+	0.785047i	$0.712639\pi$
$662$	2190.75	0.128619
$663$	6477.31	0.379424
$664$	−18459.4	−1.07886
$665$	5829.50	0.339938
$666$	2495.17	0.145174
$667$	−15650.4	−0.908523
$668$	−9075.43	−0.525657
$669$	2872.76	0.166020
$670$	6817.77	0.393124
$671$	−671.000	−0.0386046
$672$	3802.38	0.218274
$673$	17447.0	0.999308	0.499654	−	0.866225i	$-0.333461\pi$
$673$	17447.0	0.999308	0.499654	+	0.866225i	$0.333461\pi$
$674$	−2629.75	−0.150288
$675$	−1704.17	−0.0971754
$676$	−5307.95	−0.302000
$677$	−28339.1	−1.60880	−0.804402	−	0.594085i	$-0.797514\pi$
$677$	−28339.1	−1.60880	−0.804402	+	0.594085i	$0.797514\pi$
$678$	9237.96	0.523277
$679$	9995.76	0.564952
$680$	11822.2	0.666706
$681$	6875.48	0.386885
$682$	2514.28	0.141168
$683$	−10405.5	−0.582950	−0.291475	−	0.956578i	$-0.594146\pi$
$683$	−10405.5	−0.582950	−0.291475	+	0.956578i	$0.594146\pi$
$684$	−2548.89	−0.142485
$685$	−21069.6	−1.17522
$686$	8163.25	0.454336
$687$	−552.824	−0.0307009
$688$	438.013	0.0242719
$689$	21842.3	1.20773
$690$	8981.14	0.495516
$691$	−21804.8	−1.20043	−0.600213	−	0.799840i	$-0.704918\pi$
$691$	−21804.8	−1.20043	−0.600213	+	0.799840i	$0.704918\pi$
$692$	2541.88	0.139636
$693$	−706.030	−0.0387011
$694$	9512.15	0.520283
$695$	37766.6	2.06125
$696$	8909.23	0.485206
$697$	−5291.31	−0.287550
$698$	−19802.1	−1.07381
$699$	2689.63	0.145538
$700$	−2139.03	−0.115497
$701$	−3190.99	−0.171929	−0.0859645	−	0.996298i	$-0.527397\pi$
$701$	−3190.99	−0.171929	−0.0859645	+	0.996298i	$0.527397\pi$
$702$	−2801.20	−0.150605
$703$	−9168.13	−0.491867
$704$	−3822.61	−0.204645
$705$	8776.67	0.468863
$706$	−13862.7	−0.738993
$707$	8580.61	0.456446
$708$	509.137	0.0270262
$709$	−4749.25	−0.251568	−0.125784	−	0.992058i	$-0.540145\pi$
$709$	−4749.25	−0.251568	−0.125784	+	0.992058i	$0.540145\pi$
$710$	3627.03	0.191718
$711$	−1145.44	−0.0604182
$712$	866.868	0.0456281
$713$	15360.5	0.806811
$714$	1446.15	0.0757994
$715$	8685.25	0.454279
$716$	694.655	0.0362576
$717$	7060.19	0.367737
$718$	−5852.55	−0.304200
$719$	−393.986	−0.0204356	−0.0102178	−	0.999948i	$-0.503252\pi$
$719$	−393.986	−0.0204356	−0.0102178	+	0.999948i	$0.503252\pi$
$720$	−419.913	−0.0217350
$721$	1023.53	0.0528686
$722$	5960.13	0.307220
$723$	−14462.9	−0.743958
$724$	19424.6	0.997111
$725$	−8156.10	−0.417807
$726$	654.202	0.0334431
$727$	−20398.5	−1.04063	−0.520315	−	0.853975i	$-0.674185\pi$
$727$	−20398.5	−1.04063	−0.520315	+	0.853975i	$0.674185\pi$
$728$	−9435.14	−0.480343
$729$	729.000	0.0370370
$730$	−16391.7	−0.831073
$731$	−4829.29	−0.244347
$732$	869.624	0.0439101
$733$	26010.5	1.31067	0.655334	−	0.755339i	$-0.272528\pi$
$733$	26010.5	1.31067	0.655334	+	0.755339i	$0.272528\pi$
$734$	−8731.59	−0.439086
$735$	12020.6	0.603248
$736$	−21524.7	−1.07800
$737$	3034.00	0.151640
$738$	2288.30	0.114137
$739$	−37632.3	−1.87324	−0.936622	−	0.350340i	$-0.886066\pi$
$739$	−37632.3	−1.87324	−0.936622	+	0.350340i	$0.886066\pi$
$740$	10026.4	0.498080
$741$	10292.6	0.510268
$742$	4876.60	0.241275
$743$	−14721.6	−0.726895	−0.363448	−	0.931615i	$-0.618400\pi$
$743$	−14721.6	−0.726895	−0.363448	+	0.931615i	$0.618400\pi$
$744$	−8744.23	−0.430886
$745$	−2068.48	−0.101723
$746$	−3261.86	−0.160087
$747$	−7228.95	−0.354074
$748$	1960.52	0.0958339
$749$	−6662.47	−0.325022
$750$	−4588.92	−0.223418
$751$	−8619.82	−0.418830	−0.209415	−	0.977827i	$-0.567156\pi$
$751$	−8619.82	−0.418830	−0.209415	+	0.977827i	$0.567156\pi$
$752$	725.598	0.0351860
$753$	−18542.3	−0.897367
$754$	−13406.5	−0.647526
$755$	18868.0	0.909506
$756$	915.024	0.0440200
$757$	15112.2	0.725576	0.362788	−	0.931872i	$-0.381825\pi$
$757$	15112.2	0.725576	0.362788	+	0.931872i	$0.381825\pi$
$758$	19284.4	0.924064
$759$	3996.73	0.191136
$760$	18785.7	0.896619
$761$	−11523.6	−0.548923	−0.274461	−	0.961598i	$-0.588500\pi$
$761$	−11523.6	−0.548923	−0.274461	+	0.961598i	$0.588500\pi$
$762$	14959.2	0.711175
$763$	−3494.71	−0.165815
$764$	942.629	0.0446376
$765$	4629.73	0.218808
$766$	−10238.6	−0.482946
$767$	−2055.93	−0.0967865
$768$	12641.3	0.593948
$769$	19627.4	0.920392	0.460196	−	0.887817i	$-0.347779\pi$
$769$	19627.4	0.920392	0.460196	+	0.887817i	$0.347779\pi$
$770$	1939.10	0.0907537
$771$	−21397.7	−0.999504
$772$	21376.2	0.996565
$773$	−17653.6	−0.821418	−0.410709	−	0.911767i	$-0.634719\pi$
$773$	−17653.6	−0.821418	−0.410709	+	0.911767i	$0.634719\pi$
$774$	2088.49	0.0969886
$775$	8005.04	0.371032
$776$	32211.6	1.49012
$777$	3291.25	0.151960
$778$	−11257.9	−0.518787
$779$	−8408.02	−0.386712
$780$	−11256.2	−0.516713
$781$	1614.08	0.0739516
$782$	−8186.42	−0.374355
$783$	3488.97	0.159241
$784$	993.787	0.0452709
$785$	−5917.21	−0.269037
$786$	−6196.11	−0.281181
$787$	−7365.74	−0.333622	−0.166811	−	0.985989i	$-0.553347\pi$
$787$	−7365.74	−0.333622	−0.166811	+	0.985989i	$0.553347\pi$
$788$	23338.3	1.05507
$789$	20424.2	0.921570
$790$	3145.93	0.141680
$791$	12185.3	0.547738
$792$	−2275.20	−0.102078
$793$	−3511.60	−0.157252
$794$	21832.8	0.975838
$795$	15612.0	0.696480
$796$	13502.6	0.601242
$797$	1622.94	0.0721299	0.0360650	−	0.999349i	$-0.488518\pi$
$797$	1622.94	0.0721299	0.0360650	+	0.999349i	$0.488518\pi$
$798$	2297.97	0.101939
$799$	−8000.04	−0.354219
$800$	−11217.5	−0.495747
$801$	339.477	0.0149748
$802$	17415.3	0.766779
$803$	−7294.52	−0.320570
$804$	−3932.10	−0.172481
$805$	11846.6	0.518680
$806$	13158.2	0.575033
$807$	715.632	0.0312162
$808$	27651.3	1.20392
$809$	22762.0	0.989206	0.494603	−	0.869119i	$-0.335313\pi$
$809$	22762.0	0.989206	0.494603	+	0.869119i	$0.335313\pi$
$810$	−2002.19	−0.0868514
$811$	−32627.6	−1.41271	−0.706357	−	0.707856i	$-0.749662\pi$
$811$	−32627.6	−1.41271	−0.706357	+	0.707856i	$0.749662\pi$
$812$	4379.28	0.189264
$813$	13850.1	0.597473
$814$	−3049.65	−0.131315
$815$	−40571.0	−1.74373
$816$	382.756	0.0164205
$817$	−7673.85	−0.328610
$818$	23446.3	1.00217
$819$	−3694.93	−0.157645
$820$	9195.17	0.391597
$821$	−7359.33	−0.312841	−0.156420	−	0.987691i	$-0.549995\pi$
$821$	−7359.33	−0.312841	−0.156420	+	0.987691i	$0.549995\pi$
$822$	−8305.55	−0.352420
$823$	−24881.6	−1.05385	−0.526924	−	0.849912i	$-0.676655\pi$
$823$	−24881.6	−1.05385	−0.526924	+	0.849912i	$0.676655\pi$
$824$	3298.36	0.139446
$825$	2082.87	0.0878985
$826$	−459.014	−0.0193355
$827$	20679.3	0.869516	0.434758	−	0.900547i	$-0.356834\pi$
$827$	20679.3	0.869516	0.434758	+	0.900547i	$0.356834\pi$
$828$	−5179.81	−0.217404
$829$	16751.3	0.701803	0.350902	−	0.936412i	$-0.385875\pi$
$829$	16751.3	0.701803	0.350902	+	0.936412i	$0.385875\pi$
$830$	19854.2	0.830300
$831$	18971.1	0.791938
$832$	−20005.2	−0.833599
$833$	−10956.9	−0.455745
$834$	14887.5	0.618118
$835$	26194.0	1.08560
$836$	3115.32	0.128882
$837$	−3424.36	−0.141413
$838$	3102.09	0.127876
$839$	−28021.7	−1.15306	−0.576529	−	0.817077i	$-0.695593\pi$
$839$	−28021.7	−1.15306	−0.576529	+	0.817077i	$0.695593\pi$
$840$	−6743.86	−0.277006
$841$	−7690.86	−0.315342
$842$	−12210.4	−0.499762
$843$	1316.06	0.0537694
$844$	−3700.69	−0.150928
$845$	15320.1	0.623700
$846$	3459.73	0.140600
$847$	862.926	0.0350065
$848$	1290.70	0.0522676
$849$	−3147.11	−0.127219
$850$	−4266.31	−0.172157
$851$	−18631.3	−0.750496
$852$	−2091.86	−0.0841150
$853$	−47027.2	−1.88767	−0.943834	−	0.330420i	$-0.892810\pi$
$853$	−47027.2	−1.88767	−0.943834	+	0.330420i	$0.892810\pi$
$854$	−784.013	−0.0314150
$855$	7356.75	0.294264
$856$	−21470.0	−0.857277
$857$	6181.12	0.246375	0.123187	−	0.992383i	$-0.460688\pi$
$857$	6181.12	0.246375	0.123187	+	0.992383i	$0.460688\pi$
$858$	3423.69	0.136227
$859$	−4985.72	−0.198033	−0.0990167	−	0.995086i	$-0.531570\pi$
$859$	−4985.72	−0.198033	−0.0990167	+	0.995086i	$0.531570\pi$
$860$	8392.27	0.332760
$861$	3018.38	0.119473
$862$	7817.47	0.308891
$863$	4842.66	0.191015	0.0955076	−	0.995429i	$-0.469553\pi$
$863$	4842.66	0.191015	0.0955076	+	0.995429i	$0.469553\pi$
$864$	4798.55	0.188947
$865$	−7336.51	−0.288380
$866$	−7070.77	−0.277453
$867$	10518.9	0.412044
$868$	−4298.17	−0.168075
$869$	1399.98	0.0546504
$870$	−9582.41	−0.373419
$871$	15878.1	0.617690
$872$	−11261.8	−0.437354
$873$	12614.5	0.489045
$874$	−13008.4	−0.503451
$875$	−6053.02	−0.233862
$876$	9453.78	0.364627
$877$	13290.2	0.511720	0.255860	−	0.966714i	$-0.417641\pi$
$877$	13290.2	0.511720	0.255860	+	0.966714i	$0.417641\pi$
$878$	23677.7	0.910118
$879$	−19640.9	−0.753664
$880$	513.227	0.0196601
$881$	31937.8	1.22135	0.610677	−	0.791880i	$-0.290897\pi$
$881$	31937.8	1.22135	0.610677	+	0.791880i	$0.290897\pi$
$882$	4738.48	0.180899
$883$	−26326.0	−1.00333	−0.501666	−	0.865062i	$-0.667279\pi$
$883$	−26326.0	−1.00333	−0.501666	+	0.865062i	$0.667279\pi$
$884$	10260.2	0.390369
$885$	−1469.50	−0.0558153
$886$	8408.83	0.318849
$887$	26364.5	0.998007	0.499004	−	0.866600i	$-0.333699\pi$
$887$	26364.5	0.998007	0.499004	+	0.866600i	$0.333699\pi$
$888$	10606.2	0.400810
$889$	19732.0	0.744420
$890$	−932.368	−0.0351158
$891$	−891.000	−0.0335013
$892$	4550.50	0.170809
$893$	−12712.3	−0.476371
$894$	−815.388	−0.0305041
$895$	−2004.95	−0.0748805
$896$	5673.26	0.211529
$897$	20916.4	0.778571
$898$	23570.0	0.875880
$899$	−16388.9	−0.608009
$900$	−2699.42	−0.0999787
$901$	−14230.6	−0.526181
$902$	−2796.81	−0.103241
$903$	2754.83	0.101523
$904$	39267.6	1.44471
$905$	−56064.2	−2.05927
$906$	7437.69	0.272738
$907$	22786.4	0.834188	0.417094	−	0.908863i	$-0.363049\pi$
$907$	22786.4	0.834188	0.417094	+	0.908863i	$0.363049\pi$
$908$	10890.9	0.398046
$909$	10828.6	0.395118
$910$	10148.1	0.369676
$911$	50003.9	1.81856	0.909278	−	0.416190i	$-0.136635\pi$
$911$	50003.9	1.81856	0.909278	+	0.416190i	$0.136635\pi$
$912$	608.208	0.0220831
$913$	8835.38	0.320272
$914$	6142.96	0.222310
$915$	−2509.95	−0.0906847
$916$	−875.681	−0.0315866
$917$	−8172.99	−0.294325
$918$	1825.02	0.0656150
$919$	21924.9	0.786982	0.393491	−	0.919329i	$-0.371267\pi$
$919$	21924.9	0.786982	0.393491	+	0.919329i	$0.371267\pi$
$920$	38176.0	1.36807
$921$	9131.72	0.326711
$922$	−9191.86	−0.328327
$923$	8447.08	0.301234
$924$	−1118.36	−0.0398176
$925$	−9709.58	−0.345134
$926$	−24908.5	−0.883957
$927$	1291.68	0.0457652
$928$	22965.7	0.812378
$929$	10883.7	0.384372	0.192186	−	0.981359i	$-0.438442\pi$
$929$	10883.7	0.384372	0.192186	+	0.981359i	$0.438442\pi$
$930$	9404.94	0.331613
$931$	−17410.9	−0.612908
$932$	4260.41	0.149737
$933$	18752.7	0.658024
$934$	−7420.07	−0.259949
$935$	−5658.55	−0.197919
$936$	−11907.0	−0.415804
$937$	40737.8	1.42033	0.710163	−	0.704037i	$-0.248621\pi$
$937$	40737.8	1.42033	0.710163	+	0.704037i	$0.248621\pi$
$938$	3545.00	0.123399
$939$	991.279	0.0344507
$940$	13902.4	0.482388
$941$	6446.16	0.223314	0.111657	−	0.993747i	$-0.464384\pi$
$941$	6446.16	0.223314	0.111657	+	0.993747i	$0.464384\pi$
$942$	−2332.54	−0.0806775
$943$	−17086.6	−0.590049
$944$	−121.488	−0.00418868
$945$	−2640.99	−0.0909115
$946$	−2552.60	−0.0877295
$947$	−37194.1	−1.27629	−0.638144	−	0.769917i	$-0.720298\pi$
$947$	−37194.1	−1.27629	−0.638144	+	0.769917i	$0.720298\pi$
$948$	−1814.39	−0.0621612
$949$	−38175.0	−1.30581
$950$	−6779.26	−0.231525
$951$	17951.9	0.612126
$952$	6147.12	0.209274
$953$	−8904.34	−0.302665	−0.151333	−	0.988483i	$-0.548356\pi$
$953$	−8904.34	−0.302665	−0.151333	+	0.988483i	$0.548356\pi$
$954$	6154.20	0.208857
$955$	−2720.66	−0.0921870
$956$	11183.4	0.378346
$957$	−4264.30	−0.144039
$958$	−12990.9	−0.438119
$959$	−10955.5	−0.368895
$960$	−14298.9	−0.480724
$961$	−13705.7	−0.460060
$962$	−15960.0	−0.534896
$963$	−8407.94	−0.281352
$964$	−22909.5	−0.765419
$965$	−61697.2	−2.05814
$966$	4669.87	0.155539
$967$	7029.34	0.233763	0.116881	−	0.993146i	$-0.462710\pi$
$967$	7029.34	0.233763	0.116881	+	0.993146i	$0.462710\pi$
$968$	2780.80	0.0923331
$969$	−6705.77	−0.222312
$970$	−34645.5	−1.14681
$971$	10034.1	0.331628	0.165814	−	0.986157i	$-0.446975\pi$
$971$	10034.1	0.331628	0.165814	+	0.986157i	$0.446975\pi$
$972$	1154.75	0.0381055
$973$	19637.3	0.647013
$974$	−1954.24	−0.0642895
$975$	10900.5	0.358045
$976$	−207.507	−0.00680546
$977$	−19546.2	−0.640058	−0.320029	−	0.947408i	$-0.603693\pi$
$977$	−19546.2	−0.640058	−0.320029	+	0.947408i	$0.603693\pi$
$978$	−15992.9	−0.522901
$979$	−414.916	−0.0135452
$980$	19040.8	0.620650
$981$	−4410.27	−0.143536
$982$	31179.5	1.01321
$983$	4415.03	0.143253	0.0716265	−	0.997432i	$-0.477181\pi$
$983$	4415.03	0.143253	0.0716265	+	0.997432i	$0.477181\pi$
$984$	9726.82	0.315122
$985$	−67360.3	−2.17896
$986$	8734.49	0.282112
$987$	4563.56	0.147173
$988$	16303.6	0.524988
$989$	−15594.6	−0.501396
$990$	2447.12	0.0785601
$991$	35532.7	1.13898	0.569492	−	0.821997i	$-0.307140\pi$
$991$	35532.7	1.13898	0.569492	+	0.821997i	$0.307140\pi$
$992$	−22540.4	−0.721430
$993$	3646.77	0.116543
$994$	1885.93	0.0601790
$995$	−38972.0	−1.24170
$996$	−11450.8	−0.364288
$997$	−25005.9	−0.794328	−0.397164	−	0.917748i	$-0.630006\pi$
$997$	−25005.9	−0.794328	−0.397164	+	0.917748i	$0.630006\pi$
$998$	6967.16	0.220984
$999$	4153.51	0.131543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.b.1.14	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-1.80221 q^{2} -3.00000 q^{3} -4.75204 q^{4} +13.7156 q^{5} +5.40663 q^{6} +7.13162 q^{7} +22.9818 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.80221 q^{2} -3.00000 q^{3} -4.75204 q^{4} +13.7156 q^{5} +5.40663 q^{6} +7.13162 q^{7} +22.9818 q^{8} +9.00000 q^{9} -24.7184 q^{10} -11.0000 q^{11} +14.2561 q^{12} -57.5672 q^{13} -12.8527 q^{14} -41.1468 q^{15} -3.40175 q^{16} +37.5058 q^{17} -16.2199 q^{18} +59.5976 q^{19} -65.1771 q^{20} -21.3949 q^{21} +19.8243 q^{22} +121.113 q^{23} -68.9455 q^{24} +63.1173 q^{25} +103.748 q^{26} -27.0000 q^{27} -33.8898 q^{28} -129.221 q^{29} +74.1551 q^{30} +126.828 q^{31} -177.724 q^{32} +33.0000 q^{33} -67.5933 q^{34} +97.8144 q^{35} -42.7684 q^{36} -153.834 q^{37} -107.407 q^{38} +172.702 q^{39} +315.209 q^{40} -141.080 q^{41} +38.5580 q^{42} -128.761 q^{43} +52.2725 q^{44} +123.440 q^{45} -218.271 q^{46} -213.302 q^{47} +10.2052 q^{48} -292.140 q^{49} -113.751 q^{50} -112.517 q^{51} +273.562 q^{52} -379.423 q^{53} +48.6596 q^{54} -150.871 q^{55} +163.898 q^{56} -178.793 q^{57} +232.884 q^{58} +35.7135 q^{59} +195.531 q^{60} +61.0000 q^{61} -228.571 q^{62} +64.1846 q^{63} +347.510 q^{64} -789.568 q^{65} -59.4729 q^{66} -275.818 q^{67} -178.229 q^{68} -363.339 q^{69} -176.282 q^{70} -146.734 q^{71} +206.837 q^{72} +663.138 q^{73} +277.241 q^{74} -189.352 q^{75} -283.210 q^{76} -78.4478 q^{77} -311.244 q^{78} -127.271 q^{79} -46.6570 q^{80} +81.0000 q^{81} +254.255 q^{82} -803.216 q^{83} +101.669 q^{84} +514.414 q^{85} +232.054 q^{86} +387.664 q^{87} -252.800 q^{88} +37.7197 q^{89} -222.465 q^{90} -410.547 q^{91} -575.534 q^{92} -380.484 q^{93} +384.414 q^{94} +817.416 q^{95} +533.172 q^{96} +1401.61 q^{97} +526.497 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) \) 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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