LMFDB - Embedded newform 1045.4.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74596 q^{2} +10.1412 q^{3} -0.459676 q^{4} +5.00000 q^{5} -27.8474 q^{6} -22.6095 q^{7} +23.2300 q^{8} +75.8438 q^{9} +O(q^{10})$	\(q-2.74596 q^{2} +10.1412 q^{3} -0.459676 q^{4} +5.00000 q^{5} -27.8474 q^{6} -22.6095 q^{7} +23.2300 q^{8} +75.8438 q^{9} -13.7298 q^{10} -11.0000 q^{11} -4.66167 q^{12} -80.9941 q^{13} +62.0848 q^{14} +50.7060 q^{15} -60.1113 q^{16} +52.6470 q^{17} -208.264 q^{18} +19.0000 q^{19} -2.29838 q^{20} -229.287 q^{21} +30.2056 q^{22} -29.7724 q^{23} +235.580 q^{24} +25.0000 q^{25} +222.407 q^{26} +495.334 q^{27} +10.3930 q^{28} +134.743 q^{29} -139.237 q^{30} +126.470 q^{31} -20.7763 q^{32} -111.553 q^{33} -144.567 q^{34} -113.047 q^{35} -34.8636 q^{36} +198.688 q^{37} -52.1733 q^{38} -821.377 q^{39} +116.150 q^{40} -280.999 q^{41} +629.614 q^{42} +425.512 q^{43} +5.05644 q^{44} +379.219 q^{45} +81.7540 q^{46} +260.426 q^{47} -609.600 q^{48} +168.187 q^{49} -68.6491 q^{50} +533.904 q^{51} +37.2311 q^{52} -166.015 q^{53} -1360.17 q^{54} -55.0000 q^{55} -525.217 q^{56} +192.683 q^{57} -370.000 q^{58} +405.494 q^{59} -23.3083 q^{60} +775.314 q^{61} -347.283 q^{62} -1714.79 q^{63} +537.941 q^{64} -404.971 q^{65} +306.321 q^{66} +731.823 q^{67} -24.2006 q^{68} -301.928 q^{69} +310.424 q^{70} -775.258 q^{71} +1761.85 q^{72} +228.641 q^{73} -545.590 q^{74} +253.530 q^{75} -8.73385 q^{76} +248.704 q^{77} +2255.47 q^{78} -864.089 q^{79} -300.556 q^{80} +2975.50 q^{81} +771.613 q^{82} +1197.36 q^{83} +105.398 q^{84} +263.235 q^{85} -1168.44 q^{86} +1366.46 q^{87} -255.530 q^{88} +1266.08 q^{89} -1041.32 q^{90} +1831.23 q^{91} +13.6857 q^{92} +1282.56 q^{93} -715.122 q^{94} +95.0000 q^{95} -210.697 q^{96} +615.491 q^{97} -461.837 q^{98} -834.282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * 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 $

$2$	−2.74596	−0.970845	−0.485423	−	0.874280i	$-0.661334\pi$
$2$	−2.74596	−0.970845	−0.485423	+	0.874280i	$0.661334\pi$
$3$	10.1412	1.95167	0.975837	−	0.218501i	$-0.0701168\pi$
$3$	10.1412	1.95167	0.975837	+	0.218501i	$0.0701168\pi$
$4$	−0.459676	−0.0574596
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−27.8474	−1.89477
$7$	−22.6095	−1.22080	−0.610398	−	0.792095i	$-0.708990\pi$
$7$	−22.6095	−1.22080	−0.610398	+	0.792095i	$0.708990\pi$
$8$	23.2300	1.02663
$9$	75.8438	2.80903
$10$	−13.7298	−0.434175
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−4.66167	−0.112142
$13$	−80.9941	−1.72798	−0.863990	−	0.503509i	$-0.832042\pi$
$13$	−80.9941	−1.72798	−0.863990	+	0.503509i	$0.832042\pi$
$14$	62.0848	1.18520
$15$	50.7060	0.872815
$16$	−60.1113	−0.939239
$17$	52.6470	0.751105	0.375552	−	0.926801i	$-0.377453\pi$
$17$	52.6470	0.751105	0.375552	+	0.926801i	$0.377453\pi$
$18$	−208.264	−2.72713
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−2.29838	−0.0256967
$21$	−229.287	−2.38259
$22$	30.2056	0.292721
$23$	−29.7724	−0.269912	−0.134956	−	0.990852i	$-0.543089\pi$
$23$	−29.7724	−0.269912	−0.134956	+	0.990852i	$0.543089\pi$
$24$	235.580	2.00365
$25$	25.0000	0.200000
$26$	222.407	1.67760
$27$	495.334	3.53063
$28$	10.3930	0.0701464
$29$	134.743	0.862800	0.431400	−	0.902161i	$-0.358020\pi$
$29$	134.743	0.862800	0.431400	+	0.902161i	$0.358020\pi$
$30$	−139.237	−0.847368
$31$	126.470	0.732733	0.366366	−	0.930471i	$-0.380602\pi$
$31$	126.470	0.732733	0.366366	+	0.930471i	$0.380602\pi$
$32$	−20.7763	−0.114774
$33$	−111.553	−0.588452
$34$	−144.567	−0.729206
$35$	−113.047	−0.545957
$36$	−34.8636	−0.161406
$37$	198.688	0.882813	0.441407	−	0.897307i	$-0.354480\pi$
$37$	198.688	0.882813	0.441407	+	0.897307i	$0.354480\pi$
$38$	−52.1733	−0.222727
$39$	−821.377	−3.37245
$40$	116.150	0.459123
$41$	−280.999	−1.07036	−0.535179	−	0.844739i	$-0.679756\pi$
$41$	−280.999	−1.07036	−0.535179	+	0.844739i	$0.679756\pi$
$42$	629.614	2.31313
$43$	425.512	1.50907	0.754534	−	0.656261i	$-0.227863\pi$
$43$	425.512	1.50907	0.754534	+	0.656261i	$0.227863\pi$
$44$	5.05644	0.0173247
$45$	379.219	1.25624
$46$	81.7540	0.262043
$47$	260.426	0.808236	0.404118	−	0.914707i	$-0.367578\pi$
$47$	260.426	0.808236	0.404118	+	0.914707i	$0.367578\pi$
$48$	−609.600	−1.83309
$49$	168.187	0.490343
$50$	−68.6491	−0.194169
$51$	533.904	1.46591
$52$	37.2311	0.0992889
$53$	−166.015	−0.430261	−0.215131	−	0.976585i	$-0.569018\pi$
$53$	−166.015	−0.430261	−0.215131	+	0.976585i	$0.569018\pi$
$54$	−1360.17	−3.42770
$55$	−55.0000	−0.134840
$56$	−525.217	−1.25331
$57$	192.683	0.447745
$58$	−370.000	−0.837645
$59$	405.494	0.894759	0.447380	−	0.894344i	$-0.352357\pi$
$59$	405.494	0.894759	0.447380	+	0.894344i	$0.352357\pi$
$60$	−23.3083	−0.0501515
$61$	775.314	1.62736	0.813678	−	0.581316i	$-0.197462\pi$
$61$	775.314	1.62736	0.813678	+	0.581316i	$0.197462\pi$
$62$	−347.283	−0.711370
$63$	−1714.79	−3.42925
$64$	537.941	1.05067
$65$	−404.971	−0.772776
$66$	306.321	0.571295
$67$	731.823	1.33442	0.667212	−	0.744868i	$-0.267488\pi$
$67$	731.823	1.33442	0.667212	+	0.744868i	$0.267488\pi$
$68$	−24.2006	−0.0431581
$69$	−301.928	−0.526780
$70$	310.424	0.530039
$71$	−775.258	−1.29586	−0.647931	−	0.761699i	$-0.724365\pi$
$71$	−775.258	−1.29586	−0.647931	+	0.761699i	$0.724365\pi$
$72$	1761.85	2.88383
$73$	228.641	0.366581	0.183290	−	0.983059i	$-0.441325\pi$
$73$	228.641	0.366581	0.183290	+	0.983059i	$0.441325\pi$
$74$	−545.590	−0.857075
$75$	253.530	0.390335
$76$	−8.73385	−0.0131821
$77$	248.704	0.368084
$78$	2255.47	3.27413
$79$	−864.089	−1.23060	−0.615301	−	0.788292i	$-0.710966\pi$
$79$	−864.089	−1.23060	−0.615301	+	0.788292i	$0.710966\pi$
$80$	−300.556	−0.420040
$81$	2975.50	4.08161
$82$	771.613	1.03915
$83$	1197.36	1.58346	0.791728	−	0.610873i	$-0.209182\pi$
$83$	1197.36	1.58346	0.791728	+	0.610873i	$0.209182\pi$
$84$	105.398	0.136903
$85$	263.235	0.335904
$86$	−1168.44	−1.46507
$87$	1366.46	1.68390
$88$	−255.530	−0.309540
$89$	1266.08	1.50791	0.753954	−	0.656927i	$-0.228144\pi$
$89$	1266.08	1.50791	0.753954	+	0.656927i	$0.228144\pi$
$90$	−1041.32	−1.21961
$91$	1831.23	2.10951
$92$	13.6857	0.0155090
$93$	1282.56	1.43006
$94$	−715.122	−0.784672
$95$	95.0000	0.102598
$96$	−210.697	−0.224001
$97$	615.491	0.644264	0.322132	−	0.946695i	$-0.395600\pi$
$97$	615.491	0.644264	0.322132	+	0.946695i	$0.395600\pi$
$98$	−461.837	−0.476047
$99$	−834.282	−0.846954
$100$	−11.4919	−0.0114919
$101$	365.407	0.359993	0.179997	−	0.983667i	$-0.442391\pi$
$101$	365.407	0.359993	0.179997	+	0.983667i	$0.442391\pi$
$102$	−1466.08	−1.42317
$103$	991.931	0.948911	0.474456	−	0.880279i	$-0.342645\pi$
$103$	991.931	0.948911	0.474456	+	0.880279i	$0.342645\pi$
$104$	−1881.49	−1.77399
$105$	−1146.43	−1.06553
$106$	455.870	0.417717
$107$	−2035.73	−1.83926	−0.919631	−	0.392784i	$-0.871512\pi$
$107$	−2035.73	−1.83926	−0.919631	+	0.392784i	$0.871512\pi$
$108$	−227.693	−0.202869
$109$	−351.058	−0.308488	−0.154244	−	0.988033i	$-0.549294\pi$
$109$	−351.058	−0.308488	−0.154244	+	0.988033i	$0.549294\pi$
$110$	151.028	0.130909
$111$	2014.93	1.72296
$112$	1359.08	1.14662
$113$	−133.224	−0.110909	−0.0554543	−	0.998461i	$-0.517661\pi$
$113$	−133.224	−0.110909	−0.0554543	+	0.998461i	$0.517661\pi$
$114$	−529.100	−0.434691
$115$	−148.862	−0.120708
$116$	−61.9383	−0.0495761
$117$	−6142.90	−4.85394
$118$	−1113.47	−0.868673
$119$	−1190.32	−0.916946
$120$	1177.90	0.896058
$121$	121.000	0.0909091
$122$	−2128.98	−1.57991
$123$	−2849.66	−2.08899
$124$	−58.1354	−0.0421025
$125$	125.000	0.0894427
$126$	4708.74	3.32927
$127$	−1658.88	−1.15907	−0.579535	−	0.814947i	$-0.696766\pi$
$127$	−1658.88	−1.15907	−0.579535	+	0.814947i	$0.696766\pi$
$128$	−1310.96	−0.905261
$129$	4315.20	2.94521
$130$	1112.04	0.750246
$131$	−321.436	−0.214381	−0.107191	−	0.994238i	$-0.534186\pi$
$131$	−321.436	−0.214381	−0.107191	+	0.994238i	$0.534186\pi$
$132$	51.2783	0.0338122
$133$	−429.580	−0.280070
$134$	−2009.56	−1.29552
$135$	2476.67	1.57895
$136$	1222.99	0.771106
$137$	−1901.15	−1.18559	−0.592796	−	0.805353i	$-0.701976\pi$
$137$	−1901.15	−1.18559	−0.592796	+	0.805353i	$0.701976\pi$
$138$	829.083	0.511422
$139$	−2400.79	−1.46498	−0.732491	−	0.680776i	$-0.761643\pi$
$139$	−2400.79	−1.46498	−0.732491	+	0.680776i	$0.761643\pi$
$140$	51.9652	0.0313704
$141$	2641.03	1.57741
$142$	2128.83	1.25808
$143$	890.936	0.521005
$144$	−4559.07	−2.63835
$145$	673.716	0.385856
$146$	−627.840	−0.355893
$147$	1705.62	0.956988
$148$	−91.3322	−0.0507261
$149$	3444.76	1.89400	0.946999	−	0.321236i	$-0.104098\pi$
$149$	3444.76	1.89400	0.946999	+	0.321236i	$0.104098\pi$
$150$	−696.184	−0.378955
$151$	455.960	0.245732	0.122866	−	0.992423i	$-0.460791\pi$
$151$	455.960	0.245732	0.122866	+	0.992423i	$0.460791\pi$
$152$	441.370	0.235525
$153$	3992.95	2.10987
$154$	−682.933	−0.357352
$155$	632.351	0.327688
$156$	377.568	0.193780
$157$	322.388	0.163881	0.0819406	−	0.996637i	$-0.473888\pi$
$157$	322.388	0.163881	0.0819406	+	0.996637i	$0.473888\pi$
$158$	2372.76	1.19472
$159$	−1683.59	−0.839729
$160$	−103.882	−0.0513285
$161$	673.138	0.329508
$162$	−8170.61	−3.96261
$163$	−369.806	−0.177702	−0.0888509	−	0.996045i	$-0.528319\pi$
$163$	−369.806	−0.177702	−0.0888509	+	0.996045i	$0.528319\pi$
$164$	129.169	0.0615023
$165$	−557.766	−0.263164
$166$	−3287.90	−1.53729
$167$	1056.69	0.489636	0.244818	−	0.969569i	$-0.421272\pi$
$167$	1056.69	0.489636	0.244818	+	0.969569i	$0.421272\pi$
$168$	−5326.33	−2.44604
$169$	4363.05	1.98591
$170$	−722.835	−0.326111
$171$	1441.03	0.644435
$172$	−195.598	−0.0867104
$173$	−3200.78	−1.40665	−0.703327	−	0.710866i	$-0.748303\pi$
$173$	−3200.78	−1.40665	−0.703327	+	0.710866i	$0.748303\pi$
$174$	−3752.24	−1.63481
$175$	−565.236	−0.244159
$176$	661.224	0.283191
$177$	4112.19	1.74628
$178$	−3476.60	−1.46395
$179$	−1633.60	−0.682127	−0.341063	−	0.940040i	$-0.610787\pi$
$179$	−1633.60	−0.682127	−0.341063	+	0.940040i	$0.610787\pi$
$180$	−174.318	−0.0721827
$181$	−4036.19	−1.65750	−0.828751	−	0.559617i	$-0.810948\pi$
$181$	−4036.19	−1.65750	−0.828751	+	0.559617i	$0.810948\pi$
$182$	−5028.50	−2.04801
$183$	7862.60	3.17607
$184$	−691.612	−0.277100
$185$	993.440	0.394806
$186$	−3521.86	−1.38836
$187$	−579.117	−0.226467
$188$	−119.712	−0.0464409
$189$	−11199.2	−4.31018
$190$	−260.867	−0.0996066
$191$	2969.50	1.12495	0.562476	−	0.826814i	$-0.309849\pi$
$191$	2969.50	1.12495	0.562476	+	0.826814i	$0.309849\pi$
$192$	5455.37	2.05056
$193$	808.748	0.301632	0.150816	−	0.988562i	$-0.451810\pi$
$193$	808.748	0.301632	0.150816	+	0.988562i	$0.451810\pi$
$194$	−1690.12	−0.625481
$195$	−4106.89	−1.50821
$196$	−77.3118	−0.0281749
$197$	3604.04	1.30344	0.651718	−	0.758461i	$-0.274048\pi$
$197$	3604.04	1.30344	0.651718	+	0.758461i	$0.274048\pi$
$198$	2290.91	0.822261
$199$	3516.72	1.25273	0.626365	−	0.779530i	$-0.284542\pi$
$199$	3516.72	1.25273	0.626365	+	0.779530i	$0.284542\pi$
$200$	580.749	0.205326
$201$	7421.55	2.60436
$202$	−1003.39	−0.349498
$203$	−3046.47	−1.05330
$204$	−245.423	−0.0842306
$205$	−1404.99	−0.478678
$206$	−2723.81	−0.921246
$207$	−2258.05	−0.758191
$208$	4868.66	1.62299
$209$	−209.000	−0.0691714
$210$	3148.07	1.03446
$211$	1880.29	0.613480	0.306740	−	0.951793i	$-0.400762\pi$
$211$	1880.29	0.613480	0.306740	+	0.951793i	$0.400762\pi$
$212$	76.3130	0.0247226
$213$	−7862.04	−2.52910
$214$	5590.03	1.78564
$215$	2127.56	0.674876
$216$	11506.6	3.62465
$217$	−2859.42	−0.894517
$218$	963.992	0.299494
$219$	2318.69	0.715446
$220$	25.2822	0.00774784
$221$	−4264.10	−1.29789
$222$	−5532.93	−1.67273
$223$	44.3303	0.0133120	0.00665600	−	0.999978i	$-0.497881\pi$
$223$	44.3303	0.0133120	0.00665600	+	0.999978i	$0.497881\pi$
$224$	469.741	0.140116
$225$	1896.09	0.561806
$226$	365.828	0.107675
$227$	6257.70	1.82968	0.914841	−	0.403814i	$-0.132316\pi$
$227$	6257.70	1.82968	0.914841	+	0.403814i	$0.132316\pi$
$228$	−88.5717	−0.0257272
$229$	−300.458	−0.0867022	−0.0433511	−	0.999060i	$-0.513803\pi$
$229$	−300.458	−0.0867022	−0.0433511	+	0.999060i	$0.513803\pi$
$230$	408.770	0.117189
$231$	2522.16	0.718379
$232$	3130.08	0.885775
$233$	1692.21	0.475796	0.237898	−	0.971290i	$-0.423542\pi$
$233$	1692.21	0.475796	0.237898	+	0.971290i	$0.423542\pi$
$234$	16868.2	4.71243
$235$	1302.13	0.361454
$236$	−186.396	−0.0514125
$237$	−8762.89	−2.40173
$238$	3268.58	0.890212
$239$	−3006.38	−0.813669	−0.406834	−	0.913502i	$-0.633367\pi$
$239$	−3006.38	−0.813669	−0.406834	+	0.913502i	$0.633367\pi$
$240$	−3048.00	−0.819782
$241$	−891.443	−0.238269	−0.119135	−	0.992878i	$-0.538012\pi$
$241$	−891.443	−0.238269	−0.119135	+	0.992878i	$0.538012\pi$
$242$	−332.262	−0.0882587
$243$	16801.1	4.43534
$244$	−356.393	−0.0935072
$245$	840.937	0.219288
$246$	7825.08	2.02808
$247$	−1538.89	−0.396426
$248$	2937.90	0.752245
$249$	12142.6	3.09039
$250$	−343.246	−0.0868350
$251$	4569.58	1.14912	0.574560	−	0.818462i	$-0.305173\pi$
$251$	4569.58	1.14912	0.574560	+	0.818462i	$0.305173\pi$
$252$	788.247	0.197043
$253$	327.497	0.0813815
$254$	4555.23	1.12528
$255$	2669.52	0.655575
$256$	−703.687	−0.171799
$257$	2322.67	0.563753	0.281876	−	0.959451i	$-0.409043\pi$
$257$	2322.67	0.563753	0.281876	+	0.959451i	$0.409043\pi$
$258$	−11849.4	−2.85934
$259$	−4492.23	−1.07773
$260$	186.155	0.0444034
$261$	10219.4	2.42363
$262$	882.651	0.208131
$263$	−5182.26	−1.21503	−0.607513	−	0.794310i	$-0.707833\pi$
$263$	−5182.26	−1.21503	−0.607513	+	0.794310i	$0.707833\pi$
$264$	−2591.38	−0.604122
$265$	−830.073	−0.192419
$266$	1179.61	0.271904
$267$	12839.5	2.94294
$268$	−336.402	−0.0766754
$269$	−6823.41	−1.54658	−0.773291	−	0.634051i	$-0.781391\pi$
$269$	−6823.41	−1.54658	−0.773291	+	0.634051i	$0.781391\pi$
$270$	−6800.85	−1.53291
$271$	6889.32	1.54427	0.772133	−	0.635460i	$-0.219190\pi$
$271$	6889.32	1.54427	0.772133	+	0.635460i	$0.219190\pi$
$272$	−3164.68	−0.705467
$273$	18570.9	4.11707
$274$	5220.49	1.15103
$275$	−275.000	−0.0603023
$276$	138.789	0.0302685
$277$	1250.43	0.271231	0.135616	−	0.990762i	$-0.456699\pi$
$277$	1250.43	0.271231	0.135616	+	0.990762i	$0.456699\pi$
$278$	6592.49	1.42227
$279$	9591.98	2.05827
$280$	−2626.09	−0.560495
$281$	−1119.32	−0.237625	−0.118813	−	0.992917i	$-0.537909\pi$
$281$	−1119.32	−0.237625	−0.118813	+	0.992917i	$0.537909\pi$
$282$	−7252.19	−1.53142
$283$	−1524.53	−0.320226	−0.160113	−	0.987099i	$-0.551186\pi$
$283$	−1524.53	−0.320226	−0.160113	+	0.987099i	$0.551186\pi$
$284$	356.368	0.0744596
$285$	963.413	0.200237
$286$	−2446.48	−0.505816
$287$	6353.23	1.30669
$288$	−1575.75	−0.322403
$289$	−2141.29	−0.435842
$290$	−1850.00	−0.374606
$291$	6241.81	1.25739
$292$	−105.101	−0.0210636
$293$	2968.25	0.591832	0.295916	−	0.955214i	$-0.404375\pi$
$293$	2968.25	0.591832	0.295916	+	0.955214i	$0.404375\pi$
$294$	−4683.58	−0.929088
$295$	2027.47	0.400149
$296$	4615.52	0.906322
$297$	−5448.67	−1.06453
$298$	−9459.19	−1.83878
$299$	2411.39	0.466402
$300$	−116.542	−0.0224285
$301$	−9620.59	−1.84226
$302$	−1252.05	−0.238568
$303$	3705.66	0.702589
$304$	−1142.11	−0.215476
$305$	3876.57	0.727776
$306$	−10964.5	−2.04836
$307$	−6971.27	−1.29600	−0.647999	−	0.761641i	$-0.724394\pi$
$307$	−6971.27	−1.29600	−0.647999	+	0.761641i	$0.724394\pi$
$308$	−114.323	−0.0211499
$309$	10059.4	1.85196
$310$	−1736.41	−0.318134
$311$	−8838.15	−1.61146	−0.805732	−	0.592280i	$-0.798228\pi$
$311$	−8838.15	−1.61146	−0.805732	+	0.592280i	$0.798228\pi$
$312$	−19080.6	−3.46226
$313$	2475.05	0.446959	0.223480	−	0.974709i	$-0.428258\pi$
$313$	2475.05	0.446959	0.223480	+	0.974709i	$0.428258\pi$
$314$	−885.265	−0.159103
$315$	−8573.93	−1.53361
$316$	397.201	0.0707099
$317$	731.715	0.129644	0.0648221	−	0.997897i	$-0.479352\pi$
$317$	731.715	0.129644	0.0648221	+	0.997897i	$0.479352\pi$
$318$	4623.07	0.815247
$319$	−1482.18	−0.260144
$320$	2689.71	0.469872
$321$	−20644.7	−3.58964
$322$	−1848.41	−0.319901
$323$	1000.29	0.172315
$324$	−1367.77	−0.234528
$325$	−2024.85	−0.345596
$326$	1015.47	0.172521
$327$	−3560.14	−0.602069
$328$	−6527.60	−1.09886
$329$	−5888.10	−0.986691
$330$	1531.60	0.255491
$331$	9350.55	1.55273	0.776364	−	0.630285i	$-0.217062\pi$
$331$	9350.55	1.55273	0.776364	+	0.630285i	$0.217062\pi$
$332$	−550.396	−0.0909847
$333$	15069.2	2.47985
$334$	−2901.64	−0.475361
$335$	3659.11	0.596772
$336$	13782.7	2.23783
$337$	5872.04	0.949170	0.474585	−	0.880210i	$-0.342598\pi$
$337$	5872.04	0.949170	0.474585	+	0.880210i	$0.342598\pi$
$338$	−11980.8	−1.92801
$339$	−1351.05	−0.216457
$340$	−121.003	−0.0193009
$341$	−1391.17	−0.220927
$342$	−3957.02	−0.625647
$343$	3952.42	0.622188
$344$	9884.63	1.54925
$345$	−1509.64	−0.235583
$346$	8789.24	1.36564
$347$	8482.54	1.31230	0.656148	−	0.754633i	$-0.272185\pi$
$347$	8482.54	1.31230	0.656148	+	0.754633i	$0.272185\pi$
$348$	−628.128	−0.0967563
$349$	−9333.18	−1.43150	−0.715750	−	0.698357i	$-0.753915\pi$
$349$	−9333.18	−1.43150	−0.715750	+	0.698357i	$0.753915\pi$
$350$	1552.12	0.237041
$351$	−40119.2	−6.10086
$352$	228.539	0.0346057
$353$	−985.222	−0.148550	−0.0742749	−	0.997238i	$-0.523664\pi$
$353$	−985.222	−0.148550	−0.0742749	+	0.997238i	$0.523664\pi$
$354$	−11291.9	−1.69537
$355$	−3876.29	−0.579527
$356$	−581.985	−0.0866437
$357$	−12071.3	−1.78958
$358$	4485.80	0.662239
$359$	−4673.99	−0.687141	−0.343570	−	0.939127i	$-0.611636\pi$
$359$	−4673.99	−0.687141	−0.343570	+	0.939127i	$0.611636\pi$
$360$	8809.24	1.28969
$361$	361.000	0.0526316
$362$	11083.2	1.60918
$363$	1227.08	0.177425
$364$	−841.775	−0.121212
$365$	1143.20	0.163940
$366$	−21590.4	−3.08347
$367$	471.117	0.0670084	0.0335042	−	0.999439i	$-0.489333\pi$
$367$	471.117	0.0670084	0.0335042	+	0.999439i	$0.489333\pi$
$368$	1789.66	0.253512
$369$	−21312.0	−3.00666
$370$	−2727.95	−0.383296
$371$	3753.50	0.525261
$372$	−589.562	−0.0821703
$373$	7269.67	1.00914	0.504570	−	0.863371i	$-0.331651\pi$
$373$	7269.67	1.00914	0.504570	+	0.863371i	$0.331651\pi$
$374$	1590.24	0.219864
$375$	1267.65	0.174563
$376$	6049.70	0.829759
$377$	−10913.4	−1.49090
$378$	30752.7	4.18452
$379$	7353.02	0.996568	0.498284	−	0.867014i	$-0.333964\pi$
$379$	7353.02	0.996568	0.498284	+	0.867014i	$0.333964\pi$
$380$	−43.6693	−0.00589523
$381$	−16823.0	−2.26213
$382$	−8154.16	−1.09215
$383$	6371.92	0.850104	0.425052	−	0.905169i	$-0.360256\pi$
$383$	6371.92	0.850104	0.425052	+	0.905169i	$0.360256\pi$
$384$	−13294.7	−1.76677
$385$	1243.52	0.164612
$386$	−2220.79	−0.292838
$387$	32272.4	4.23902
$388$	−282.927	−0.0370191
$389$	−2327.27	−0.303334	−0.151667	−	0.988432i	$-0.548464\pi$
$389$	−2327.27	−0.303334	−0.151667	+	0.988432i	$0.548464\pi$
$390$	11277.4	1.46423
$391$	−1567.43	−0.202732
$392$	3906.99	0.503400
$393$	−3259.74	−0.418402
$394$	−9896.56	−1.26544
$395$	−4320.44	−0.550342
$396$	383.500	0.0486656
$397$	−4595.10	−0.580910	−0.290455	−	0.956889i	$-0.593807\pi$
$397$	−4595.10	−0.580910	−0.290455	+	0.956889i	$0.593807\pi$
$398$	−9656.78	−1.21621
$399$	−4356.45	−0.546605
$400$	−1502.78	−0.187848
$401$	5100.88	0.635226	0.317613	−	0.948220i	$-0.397119\pi$
$401$	5100.88	0.635226	0.317613	+	0.948220i	$0.397119\pi$
$402$	−20379.3	−2.52843
$403$	−10243.3	−1.26615
$404$	−167.969	−0.0206851
$405$	14877.5	1.82535
$406$	8365.50	1.02259
$407$	−2185.57	−0.266178
$408$	12402.6	1.50495
$409$	−3582.24	−0.433082	−0.216541	−	0.976274i	$-0.569477\pi$
$409$	−3582.24	−0.433082	−0.216541	+	0.976274i	$0.569477\pi$
$410$	3858.07	0.464723
$411$	−19279.9	−2.31389
$412$	−455.967	−0.0545240
$413$	−9168.00	−1.09232
$414$	6200.53	0.736086
$415$	5986.78	0.708143
$416$	1682.76	0.198327
$417$	−24346.9	−2.85917
$418$	573.907	0.0671548
$419$	−10191.0	−1.18821	−0.594106	−	0.804386i	$-0.702494\pi$
$419$	−10191.0	−1.18821	−0.594106	+	0.804386i	$0.702494\pi$
$420$	526.989	0.0612248
$421$	−7169.70	−0.830000	−0.415000	−	0.909821i	$-0.636218\pi$
$421$	−7169.70	−0.830000	−0.415000	+	0.909821i	$0.636218\pi$
$422$	−5163.21	−0.595595
$423$	19751.7	2.27036
$424$	−3856.51	−0.441719
$425$	1316.18	0.150221
$426$	21588.9	2.45536
$427$	−17529.4	−1.98667
$428$	935.775	0.105683
$429$	9035.15	1.01683
$430$	−5842.20	−0.655200
$431$	6718.08	0.750808	0.375404	−	0.926861i	$-0.377504\pi$
$431$	6718.08	0.750808	0.375404	+	0.926861i	$0.377504\pi$
$432$	−29775.2	−3.31611
$433$	−15051.0	−1.67045	−0.835224	−	0.549909i	$-0.814662\pi$
$433$	−15051.0	−1.67045	−0.835224	+	0.549909i	$0.814662\pi$
$434$	7851.87	0.868438
$435$	6832.28	0.753064
$436$	161.373	0.0177256
$437$	−565.676	−0.0619221
$438$	−6367.04	−0.694587
$439$	−1058.29	−0.115056	−0.0575278	−	0.998344i	$-0.518322\pi$
$439$	−1058.29	−0.115056	−0.0575278	+	0.998344i	$0.518322\pi$
$440$	−1277.65	−0.138431
$441$	12756.0	1.37739
$442$	11709.1	1.26005
$443$	−5167.60	−0.554222	−0.277111	−	0.960838i	$-0.589377\pi$
$443$	−5167.60	−0.554222	−0.277111	+	0.960838i	$0.589377\pi$
$444$	−926.217	−0.0990007
$445$	6330.38	0.674357
$446$	−121.729	−0.0129239
$447$	34934.0	3.69647
$448$	−12162.6	−1.28265
$449$	1190.29	0.125107	0.0625537	−	0.998042i	$-0.480076\pi$
$449$	1190.29	0.125107	0.0625537	+	0.998042i	$0.480076\pi$
$450$	−5206.61	−0.545426
$451$	3090.99	0.322725
$452$	61.2399	0.00637275
$453$	4623.98	0.479588
$454$	−17183.4	−1.77634
$455$	9156.17	0.943402
$456$	4476.01	0.459668
$457$	17758.2	1.81771	0.908853	−	0.417117i	$-0.136959\pi$
$457$	17758.2	1.81771	0.908853	+	0.417117i	$0.136959\pi$
$458$	825.046	0.0841744
$459$	26077.9	2.65188
$460$	68.4284	0.00693585
$461$	4856.93	0.490693	0.245347	−	0.969435i	$-0.421098\pi$
$461$	4856.93	0.490693	0.245347	+	0.969435i	$0.421098\pi$
$462$	−6925.75	−0.697435
$463$	651.775	0.0654223	0.0327112	−	0.999465i	$-0.489586\pi$
$463$	651.775	0.0654223	0.0327112	+	0.999465i	$0.489586\pi$
$464$	−8099.59	−0.810375
$465$	6412.79	0.639540
$466$	−4646.75	−0.461924
$467$	−395.800	−0.0392194	−0.0196097	−	0.999808i	$-0.506242\pi$
$467$	−395.800	−0.0392194	−0.0196097	+	0.999808i	$0.506242\pi$
$468$	2823.75	0.278905
$469$	−16546.1	−1.62906
$470$	−3575.61	−0.350916
$471$	3269.40	0.319843
$472$	9419.61	0.918586
$473$	−4680.63	−0.455001
$474$	24062.6	2.33171
$475$	475.000	0.0458831
$476$	547.162	0.0526873
$477$	−12591.2	−1.20862
$478$	8255.42	0.789946
$479$	−12889.4	−1.22950	−0.614751	−	0.788721i	$-0.710744\pi$
$479$	−12889.4	−1.22950	−0.614751	+	0.788721i	$0.710744\pi$
$480$	−1053.48	−0.100176
$481$	−16092.6	−1.52548
$482$	2447.87	0.231323
$483$	6826.42	0.643091
$484$	−55.6208	−0.00522360
$485$	3077.46	0.288124
$486$	−46135.1	−4.30603
$487$	12487.7	1.16195	0.580977	−	0.813920i	$-0.302671\pi$
$487$	12487.7	1.16195	0.580977	+	0.813920i	$0.302671\pi$
$488$	18010.5	1.67069
$489$	−3750.27	−0.346816
$490$	−2309.18	−0.212895
$491$	−1999.64	−0.183794	−0.0918968	−	0.995769i	$-0.529293\pi$
$491$	−1999.64	−0.183794	−0.0918968	+	0.995769i	$0.529293\pi$
$492$	1309.92	0.120032
$493$	7093.83	0.648053
$494$	4225.73	0.384868
$495$	−4171.41	−0.378769
$496$	−7602.29	−0.688211
$497$	17528.2	1.58198
$498$	−33343.2	−3.00029
$499$	−5990.97	−0.537460	−0.268730	−	0.963216i	$-0.586604\pi$
$499$	−5990.97	−0.537460	−0.268730	+	0.963216i	$0.586604\pi$
$500$	−57.4596	−0.00513934
$501$	10716.1	0.955609
$502$	−12547.9	−1.11562
$503$	−17702.2	−1.56919	−0.784595	−	0.620008i	$-0.787129\pi$
$503$	−17702.2	−1.56919	−0.784595	+	0.620008i	$0.787129\pi$
$504$	−39834.4	−3.52057
$505$	1827.03	0.160994
$506$	−899.294	−0.0790089
$507$	44246.5	3.87585
$508$	762.549	0.0665997
$509$	−7694.50	−0.670045	−0.335022	−	0.942210i	$-0.608744\pi$
$509$	−7694.50	−0.670045	−0.335022	+	0.942210i	$0.608744\pi$
$510$	−7330.40	−0.636462
$511$	−5169.44	−0.447520
$512$	12420.0	1.07205
$513$	9411.35	0.809983
$514$	−6377.98	−0.547317
$515$	4959.66	0.424366
$516$	−1983.59	−0.169230
$517$	−2864.69	−0.243692
$518$	12335.5	1.04631
$519$	−32459.8	−2.74533
$520$	−9407.46	−0.793355
$521$	4951.02	0.416330	0.208165	−	0.978094i	$-0.433251\pi$
$521$	4951.02	0.416330	0.208165	+	0.978094i	$0.433251\pi$
$522$	−28062.2	−2.35297
$523$	−11807.7	−0.987214	−0.493607	−	0.869685i	$-0.664322\pi$
$523$	−11807.7	−0.987214	−0.493607	+	0.869685i	$0.664322\pi$
$524$	147.756	0.0123183
$525$	−5732.17	−0.476519
$526$	14230.3	1.17960
$527$	6658.28	0.550359
$528$	6705.60	0.552697
$529$	−11280.6	−0.927147
$530$	2279.35	0.186809
$531$	30754.2	2.51340
$532$	197.468	0.0160927
$533$	22759.3	1.84956
$534$	−35256.9	−2.85714
$535$	−10178.6	−0.822543
$536$	17000.2	1.36996
$537$	−16566.6	−1.33129
$538$	18736.9	1.50149
$539$	−1850.06	−0.147844
$540$	−1138.47	−0.0907256
$541$	−12000.2	−0.953659	−0.476829	−	0.878996i	$-0.658214\pi$
$541$	−12000.2	−0.953659	−0.476829	+	0.878996i	$0.658214\pi$
$542$	−18917.8	−1.49924
$543$	−40931.8	−3.23490
$544$	−1093.81	−0.0862073
$545$	−1755.29	−0.137960
$546$	−50995.0	−3.99704
$547$	−2294.22	−0.179330	−0.0896650	−	0.995972i	$-0.528580\pi$
$547$	−2294.22	−0.179330	−0.0896650	+	0.995972i	$0.528580\pi$
$548$	873.913	0.0681236
$549$	58802.7	4.57129
$550$	755.140	0.0585442
$551$	2560.12	0.197940
$552$	−7013.77	−0.540808
$553$	19536.6	1.50231
$554$	−3433.64	−0.263324
$555$	10074.7	0.770533
$556$	1103.59	0.0841772
$557$	−22625.1	−1.72110	−0.860552	−	0.509363i	$-0.829881\pi$
$557$	−22625.1	−1.72110	−0.860552	+	0.509363i	$0.829881\pi$
$558$	−26339.2	−1.99826
$559$	−34464.0	−2.60764
$560$	6795.42	0.512784
$561$	−5872.94	−0.441989
$562$	3073.60	0.230698
$563$	−13239.0	−0.991042	−0.495521	−	0.868596i	$-0.665023\pi$
$563$	−13239.0	−0.991042	−0.495521	+	0.868596i	$0.665023\pi$
$564$	−1214.02	−0.0906374
$565$	−666.120	−0.0495998
$566$	4186.31	0.310890
$567$	−67274.3	−4.98282
$568$	−18009.2	−1.33037
$569$	5189.44	0.382342	0.191171	−	0.981557i	$-0.438771\pi$
$569$	5189.44	0.382342	0.191171	+	0.981557i	$0.438771\pi$
$570$	−2645.50	−0.194400
$571$	−14154.4	−1.03738	−0.518690	−	0.854963i	$-0.673580\pi$
$571$	−14154.4	−1.03738	−0.518690	+	0.854963i	$0.673580\pi$
$572$	−409.542	−0.0299367
$573$	30114.3	2.19554
$574$	−17445.8	−1.26859
$575$	−744.310	−0.0539824
$576$	40799.5	2.95135
$577$	−16200.8	−1.16888	−0.584442	−	0.811435i	$-0.698687\pi$
$577$	−16200.8	−1.16888	−0.584442	+	0.811435i	$0.698687\pi$
$578$	5879.91	0.423135
$579$	8201.67	0.588687
$580$	−309.691	−0.0221711
$581$	−27071.6	−1.93308
$582$	−17139.8	−1.22073
$583$	1826.16	0.129729
$584$	5311.32	0.376342
$585$	−30714.5	−2.17075
$586$	−8150.70	−0.574578
$587$	16010.0	1.12573	0.562867	−	0.826548i	$-0.309699\pi$
$587$	16010.0	1.12573	0.562867	+	0.826548i	$0.309699\pi$
$588$	−784.034	−0.0549881
$589$	2402.93	0.168100
$590$	−5567.36	−0.388482
$591$	36549.2	2.54388
$592$	−11943.4	−0.829173
$593$	2107.98	0.145977	0.0729886	−	0.997333i	$-0.476746\pi$
$593$	2107.98	0.145977	0.0729886	+	0.997333i	$0.476746\pi$
$594$	14961.9	1.03349
$595$	−5951.60	−0.410071
$596$	−1583.48	−0.108828
$597$	35663.7	2.44492
$598$	−6621.59	−0.452805
$599$	−7717.81	−0.526446	−0.263223	−	0.964735i	$-0.584785\pi$
$599$	−7717.81	−0.526446	−0.263223	+	0.964735i	$0.584785\pi$
$600$	5889.49	0.400729
$601$	13706.7	0.930293	0.465147	−	0.885234i	$-0.346002\pi$
$601$	13706.7	0.930293	0.465147	+	0.885234i	$0.346002\pi$
$602$	26417.8	1.78855
$603$	55504.2	3.74843
$604$	−209.594	−0.0141196
$605$	605.000	0.0406558
$606$	−10175.6	−0.682106
$607$	16823.5	1.12495	0.562475	−	0.826814i	$-0.309849\pi$
$607$	16823.5	1.12495	0.562475	+	0.826814i	$0.309849\pi$
$608$	−394.750	−0.0263310
$609$	−30894.8	−2.05570
$610$	−10644.9	−0.706558
$611$	−21093.0	−1.39662
$612$	−1835.46	−0.121232
$613$	28796.2	1.89734	0.948669	−	0.316270i	$-0.102431\pi$
$613$	28796.2	1.89734	0.948669	+	0.316270i	$0.102431\pi$
$614$	19142.9	1.25821
$615$	−14248.3	−0.934224
$616$	5777.39	0.377886
$617$	−6652.47	−0.434066	−0.217033	−	0.976164i	$-0.569638\pi$
$617$	−6652.47	−0.434066	−0.217033	+	0.976164i	$0.569638\pi$
$618$	−27622.7	−1.79797
$619$	−16923.1	−1.09887	−0.549434	−	0.835537i	$-0.685156\pi$
$619$	−16923.1	−1.09887	−0.549434	+	0.835537i	$0.685156\pi$
$620$	−290.677	−0.0188288
$621$	−14747.3	−0.952960
$622$	24269.2	1.56448
$623$	−28625.3	−1.84085
$624$	49374.0	3.16754
$625$	625.000	0.0400000
$626$	−6796.40	−0.433928
$627$	−2119.51	−0.135000
$628$	−148.194	−0.00941654
$629$	10460.3	0.663085
$630$	23543.7	1.48890
$631$	−6678.26	−0.421327	−0.210664	−	0.977559i	$-0.567562\pi$
$631$	−6678.26	−0.421327	−0.210664	+	0.977559i	$0.567562\pi$
$632$	−20072.8	−1.26337
$633$	19068.4	1.19731
$634$	−2009.26	−0.125865
$635$	−8294.41	−0.518352
$636$	773.904	0.0482505
$637$	−13622.2	−0.847302
$638$	4070.00	0.252559
$639$	−58798.5	−3.64011
$640$	−6554.79	−0.404845
$641$	−6722.45	−0.414229	−0.207114	−	0.978317i	$-0.566407\pi$
$641$	−6722.45	−0.414229	−0.207114	+	0.978317i	$0.566407\pi$
$642$	56689.6	3.48498
$643$	13337.5	0.818007	0.409004	−	0.912533i	$-0.365876\pi$
$643$	13337.5	0.818007	0.409004	+	0.912533i	$0.365876\pi$
$644$	−309.426	−0.0189334
$645$	21576.0	1.31714
$646$	−2746.77	−0.167291
$647$	11145.2	0.677223	0.338611	−	0.940926i	$-0.390043\pi$
$647$	11145.2	0.677223	0.338611	+	0.940926i	$0.390043\pi$
$648$	69120.7	4.19030
$649$	−4460.43	−0.269780
$650$	5560.18	0.335520
$651$	−28998.0	−1.74581
$652$	169.991	0.0102107
$653$	−31177.4	−1.86840	−0.934201	−	0.356746i	$-0.883886\pi$
$653$	−31177.4	−1.86840	−0.934201	+	0.356746i	$0.883886\pi$
$654$	9776.03	0.584515
$655$	−1607.18	−0.0958743
$656$	16891.2	1.00532
$657$	17341.0	1.02974
$658$	16168.5	0.957925
$659$	3997.85	0.236319	0.118159	−	0.992995i	$-0.462301\pi$
$659$	3997.85	0.236319	0.118159	+	0.992995i	$0.462301\pi$
$660$	256.392	0.0151213
$661$	960.851	0.0565398	0.0282699	−	0.999600i	$-0.491000\pi$
$661$	960.851	0.0565398	0.0282699	+	0.999600i	$0.491000\pi$
$662$	−25676.3	−1.50746
$663$	−43243.1	−2.53306
$664$	27814.6	1.62562
$665$	−2147.90	−0.125251
$666$	−41379.6	−2.40755
$667$	−4011.63	−0.232880
$668$	−485.736	−0.0281343
$669$	449.562	0.0259807
$670$	−10047.8	−0.579373
$671$	−8528.45	−0.490666
$672$	4763.74	0.273460
$673$	−18408.2	−1.05436	−0.527181	−	0.849753i	$-0.676751\pi$
$673$	−18408.2	−1.05436	−0.527181	+	0.849753i	$0.676751\pi$
$674$	−16124.4	−0.921497
$675$	12383.4	0.706127
$676$	−2005.59	−0.114110
$677$	9279.37	0.526788	0.263394	−	0.964688i	$-0.415158\pi$
$677$	9279.37	0.526788	0.263394	+	0.964688i	$0.415158\pi$
$678$	3709.94	0.210146
$679$	−13915.9	−0.786515
$680$	6114.95	0.344849
$681$	63460.5	3.57094
$682$	3820.11	0.214486
$683$	−18995.4	−1.06419	−0.532093	−	0.846686i	$-0.678594\pi$
$683$	−18995.4	−1.06419	−0.532093	+	0.846686i	$0.678594\pi$
$684$	−662.408	−0.0370290
$685$	−9505.75	−0.530213
$686$	−10853.2	−0.604048
$687$	−3047.00	−0.169214
$688$	−25578.1	−1.41738
$689$	13446.2	0.743483
$690$	4145.42	0.228715
$691$	5592.16	0.307867	0.153933	−	0.988081i	$-0.450806\pi$
$691$	5592.16	0.307867	0.153933	+	0.988081i	$0.450806\pi$
$692$	1471.33	0.0808257
$693$	18862.7	1.03396
$694$	−23292.7	−1.27404
$695$	−12004.0	−0.655160
$696$	31742.8	1.72874
$697$	−14793.8	−0.803951
$698$	25628.6	1.38977
$699$	17161.0	0.928598
$700$	259.826	0.0140293
$701$	−18726.7	−1.00898	−0.504491	−	0.863417i	$-0.668320\pi$
$701$	−18726.7	−1.00898	−0.504491	+	0.863417i	$0.668320\pi$
$702$	110166.	5.92299
$703$	3775.07	0.202531
$704$	−5917.35	−0.316788
$705$	13205.2	0.705441
$706$	2705.39	0.144219
$707$	−8261.65	−0.439478
$708$	−1890.28	−0.100340
$709$	−9100.44	−0.482051	−0.241026	−	0.970519i	$-0.577484\pi$
$709$	−9100.44	−0.482051	−0.241026	+	0.970519i	$0.577484\pi$
$710$	10644.2	0.562631
$711$	−65535.8	−3.45680
$712$	29410.9	1.54806
$713$	−3765.32	−0.197773
$714$	33147.3	1.73740
$715$	4454.68	0.233001
$716$	750.925	0.0391947
$717$	−30488.3	−1.58802
$718$	12834.6	0.667108
$719$	6253.77	0.324376	0.162188	−	0.986760i	$-0.448145\pi$
$719$	6253.77	0.324376	0.162188	+	0.986760i	$0.448145\pi$
$720$	−22795.3	−1.17991
$721$	−22427.0	−1.15843
$722$	−991.293	−0.0510971
$723$	−9040.30	−0.465024
$724$	1855.34	0.0952394
$725$	3368.58	0.172560
$726$	−3369.53	−0.172252
$727$	27941.3	1.42543	0.712715	−	0.701454i	$-0.247465\pi$
$727$	27941.3	1.42543	0.712715	+	0.701454i	$0.247465\pi$
$728$	42539.5	2.16569
$729$	90044.3	4.57473
$730$	−3139.20	−0.159160
$731$	22401.9	1.13347
$732$	−3614.25	−0.182495
$733$	−10161.6	−0.512040	−0.256020	−	0.966671i	$-0.582411\pi$
$733$	−10161.6	−0.512040	−0.256020	+	0.966671i	$0.582411\pi$
$734$	−1293.67	−0.0650548
$735$	8528.11	0.427978
$736$	618.561	0.0309789
$737$	−8050.05	−0.402344
$738$	58522.0	2.91901
$739$	2723.98	0.135593	0.0677965	−	0.997699i	$-0.478403\pi$
$739$	2723.98	0.135593	0.0677965	+	0.997699i	$0.478403\pi$
$740$	−456.661	−0.0226854
$741$	−15606.2	−0.773693
$742$	−10307.0	−0.509947
$743$	1524.24	0.0752609	0.0376305	−	0.999292i	$-0.488019\pi$
$743$	1524.24	0.0752609	0.0376305	+	0.999292i	$0.488019\pi$
$744$	29793.8	1.46814
$745$	17223.8	0.847022
$746$	−19962.3	−0.979719
$747$	90812.0	4.44798
$748$	266.207	0.0130127
$749$	46026.6	2.24536
$750$	−3480.92	−0.169474
$751$	−31087.2	−1.51051	−0.755253	−	0.655434i	$-0.772486\pi$
$751$	−31087.2	−1.51051	−0.755253	+	0.655434i	$0.772486\pi$
$752$	−15654.6	−0.759127
$753$	46341.0	2.24271
$754$	29967.8	1.44743
$755$	2279.80	0.109895
$756$	5148.02	0.247661
$757$	22111.2	1.06162	0.530809	−	0.847491i	$-0.321888\pi$
$757$	22111.2	1.06162	0.530809	+	0.847491i	$0.321888\pi$
$758$	−20191.1	−0.967513
$759$	3321.21	0.158830
$760$	2206.85	0.105330
$761$	1991.03	0.0948420	0.0474210	−	0.998875i	$-0.484900\pi$
$761$	1991.03	0.0948420	0.0474210	+	0.998875i	$0.484900\pi$
$762$	46195.5	2.19618
$763$	7937.22	0.376601
$764$	−1365.01	−0.0646392
$765$	19964.7	0.943565
$766$	−17497.1	−0.825319
$767$	−32842.6	−1.54613
$768$	−7136.23	−0.335295
$769$	−4210.56	−0.197447	−0.0987236	−	0.995115i	$-0.531476\pi$
$769$	−4210.56	−0.197447	−0.0987236	+	0.995115i	$0.531476\pi$
$770$	−3414.66	−0.159813
$771$	23554.7	1.10026
$772$	−371.762	−0.0173316
$773$	−36881.7	−1.71610	−0.858049	−	0.513568i	$-0.828323\pi$
$773$	−36881.7	−1.71610	−0.858049	+	0.513568i	$0.828323\pi$
$774$	−88618.9	−4.11543
$775$	3161.76	0.146547
$776$	14297.8	0.661421
$777$	−45556.5	−2.10339
$778$	6390.59	0.294491
$779$	−5338.98	−0.245557
$780$	1887.84	0.0866608
$781$	8527.83	0.390717
$782$	4304.11	0.196822
$783$	66742.9	3.04623
$784$	−10110.0	−0.460549
$785$	1611.94	0.0732899
$786$	8951.13	0.406204
$787$	−42021.6	−1.90331	−0.951657	−	0.307164i	$-0.900620\pi$
$787$	−42021.6	−1.90331	−0.951657	+	0.307164i	$0.900620\pi$
$788$	−1656.69	−0.0748949
$789$	−52554.3	−2.37133
$790$	11863.8	0.534297
$791$	3012.12	0.135397
$792$	−19380.3	−0.869508
$793$	−62795.9	−2.81204
$794$	12618.0	0.563974
$795$	−8417.93	−0.375538
$796$	−1616.55	−0.0719813
$797$	−20854.4	−0.926852	−0.463426	−	0.886136i	$-0.653380\pi$
$797$	−20854.4	−0.926852	−0.463426	+	0.886136i	$0.653380\pi$
$798$	11962.7	0.530669
$799$	13710.7	0.607070
$800$	−519.408	−0.0229548
$801$	96024.0	4.23576
$802$	−14006.8	−0.616706
$803$	−2515.05	−0.110528
$804$	−3411.51	−0.149645
$805$	3365.69	0.147360
$806$	28127.9	1.22923
$807$	−69197.5	−3.01842
$808$	8488.39	0.369580
$809$	36083.4	1.56814	0.784069	−	0.620674i	$-0.213141\pi$
$809$	36083.4	1.56814	0.784069	+	0.620674i	$0.213141\pi$
$810$	−40853.0	−1.77214
$811$	−28443.9	−1.23157	−0.615783	−	0.787916i	$-0.711160\pi$
$811$	−28443.9	−1.23157	−0.615783	+	0.787916i	$0.711160\pi$
$812$	1400.39	0.0605223
$813$	69865.9	3.01390
$814$	6001.49	0.258418
$815$	−1849.03	−0.0794707
$816$	−32093.6	−1.37684
$817$	8084.72	0.346204
$818$	9836.71	0.420455
$819$	138888.	5.92567
$820$	645.843	0.0275046
$821$	19150.1	0.814060	0.407030	−	0.913415i	$-0.366565\pi$
$821$	19150.1	0.814060	0.407030	+	0.913415i	$0.366565\pi$
$822$	52942.0	2.24643
$823$	−35629.6	−1.50908	−0.754538	−	0.656256i	$-0.772139\pi$
$823$	−35629.6	−1.50908	−0.754538	+	0.656256i	$0.772139\pi$
$824$	23042.5	0.974180
$825$	−2788.83	−0.117690
$826$	25175.0	1.06047
$827$	26748.5	1.12471	0.562356	−	0.826895i	$-0.309895\pi$
$827$	26748.5	1.12471	0.562356	+	0.826895i	$0.309895\pi$
$828$	1037.97	0.0435653
$829$	−21812.3	−0.913839	−0.456920	−	0.889508i	$-0.651047\pi$
$829$	−21812.3	−0.913839	−0.456920	+	0.889508i	$0.651047\pi$
$830$	−16439.5	−0.687498
$831$	12680.9	0.529355
$832$	−43570.1	−1.81553
$833$	8854.57	0.368299
$834$	66855.7	2.77581
$835$	5283.45	0.218972
$836$	96.0724	0.00397456
$837$	62645.0	2.58701
$838$	27984.0	1.15357
$839$	14689.6	0.604458	0.302229	−	0.953235i	$-0.402269\pi$
$839$	14689.6	0.604458	0.302229	+	0.953235i	$0.402269\pi$
$840$	−26631.6	−1.09390
$841$	−6233.27	−0.255577
$842$	19687.8	0.805801
$843$	−11351.2	−0.463767
$844$	−864.324	−0.0352503
$845$	21815.3	0.888127
$846$	−54237.5	−2.20417
$847$	−2735.74	−0.110981
$848$	9979.35	0.404118
$849$	−15460.6	−0.624977
$850$	−3614.17	−0.145841
$851$	−5915.42	−0.238282
$852$	3613.99	0.145321
$853$	−34313.4	−1.37734	−0.688668	−	0.725077i	$-0.741804\pi$
$853$	−34313.4	−1.37734	−0.688668	+	0.725077i	$0.741804\pi$
$854$	48135.2	1.92875
$855$	7205.16	0.288200
$856$	−47289.9	−1.88824
$857$	23883.9	0.951992	0.475996	−	0.879448i	$-0.342088\pi$
$857$	23883.9	0.951992	0.475996	+	0.879448i	$0.342088\pi$
$858$	−24810.2	−0.987187
$859$	−11544.7	−0.458557	−0.229278	−	0.973361i	$-0.573637\pi$
$859$	−11544.7	−0.458557	−0.229278	+	0.973361i	$0.573637\pi$
$860$	−977.989	−0.0387781
$861$	64429.3	2.55023
$862$	−18447.6	−0.728919
$863$	22776.5	0.898402	0.449201	−	0.893431i	$-0.351709\pi$
$863$	22776.5	0.898402	0.449201	+	0.893431i	$0.351709\pi$
$864$	−10291.2	−0.405225
$865$	−16003.9	−0.629075
$866$	41329.5	1.62175
$867$	−21715.2	−0.850621
$868$	1314.41	0.0513986
$869$	9504.98	0.371041
$870$	−18761.2	−0.731109
$871$	−59273.3	−2.30586
$872$	−8155.06	−0.316703
$873$	46681.2	1.80976
$874$	1553.33	0.0601167
$875$	−2826.18	−0.109191
$876$	−1065.85	−0.0411092
$877$	27439.2	1.05651	0.528253	−	0.849087i	$-0.322847\pi$
$877$	27439.2	1.05651	0.528253	+	0.849087i	$0.322847\pi$
$878$	2906.03	0.111701
$879$	30101.6	1.15506
$880$	3306.12	0.126647
$881$	42613.2	1.62960	0.814799	−	0.579744i	$-0.196848\pi$
$881$	42613.2	1.62960	0.814799	+	0.579744i	$0.196848\pi$
$882$	−35027.5	−1.33723
$883$	29883.7	1.13892	0.569460	−	0.822019i	$-0.307153\pi$
$883$	29883.7	1.13892	0.569460	+	0.822019i	$0.307153\pi$
$884$	1960.11	0.0745764
$885$	20561.0	0.780959
$886$	14190.1	0.538064
$887$	−29780.8	−1.12733	−0.563664	−	0.826004i	$-0.690609\pi$
$887$	−29780.8	−1.12733	−0.563664	+	0.826004i	$0.690609\pi$
$888$	46806.8	1.76884
$889$	37506.4	1.41499
$890$	−17383.0	−0.654696
$891$	−32730.5	−1.23065
$892$	−20.3776	−0.000764902 0
$893$	4948.10	0.185422
$894$	−95927.5	−3.58870
$895$	−8167.98	−0.305056
$896$	29640.0	1.10514
$897$	24454.4	0.910265
$898$	−3268.49	−0.121460
$899$	17041.0	0.632202
$900$	−871.590	−0.0322811
$901$	−8740.17	−0.323171
$902$	−8487.74	−0.313316
$903$	−97564.3	−3.59550
$904$	−3094.79	−0.113862
$905$	−20181.0	−0.741258
$906$	−12697.3	−0.465606
$907$	8569.29	0.313714	0.156857	−	0.987621i	$-0.449864\pi$
$907$	8569.29	0.313714	0.156857	+	0.987621i	$0.449864\pi$
$908$	−2876.52	−0.105133
$909$	27713.8	1.01123
$910$	−25142.5	−0.915897
$911$	−28747.3	−1.04549	−0.522745	−	0.852489i	$-0.675092\pi$
$911$	−28747.3	−1.04549	−0.522745	+	0.852489i	$0.675092\pi$
$912$	−11582.4	−0.420539
$913$	−13170.9	−0.477430
$914$	−48763.3	−1.76471
$915$	39313.0	1.42038
$916$	138.113	0.00498187
$917$	7267.48	0.261716
$918$	−71608.9	−2.57456
$919$	−14906.2	−0.535051	−0.267525	−	0.963551i	$-0.586206\pi$
$919$	−14906.2	−0.535051	−0.267525	+	0.963551i	$0.586206\pi$
$920$	−3458.06	−0.123923
$921$	−70697.0	−2.52936
$922$	−13336.9	−0.476387
$923$	62791.3	2.23922
$924$	−1159.38	−0.0412778
$925$	4967.20	0.176563
$926$	−1789.75	−0.0635149
$927$	75231.8	2.66552
$928$	−2799.47	−0.0990270
$929$	−21511.9	−0.759724	−0.379862	−	0.925043i	$-0.624028\pi$
$929$	−21511.9	−0.759724	−0.379862	+	0.925043i	$0.624028\pi$
$930$	−17609.3	−0.620895
$931$	3195.56	0.112492
$932$	−777.870	−0.0273390
$933$	−89629.4	−3.14505
$934$	1086.85	0.0380760
$935$	−2895.59	−0.101279
$936$	−142699.	−4.98320
$937$	32385.5	1.12912	0.564562	−	0.825391i	$-0.309045\pi$
$937$	32385.5	1.12912	0.564562	+	0.825391i	$0.309045\pi$
$938$	45435.0	1.58156
$939$	25100.0	0.872318
$940$	−598.559	−0.0207690
$941$	6092.34	0.211057	0.105529	−	0.994416i	$-0.466347\pi$
$941$	6092.34	0.211057	0.105529	+	0.994416i	$0.466347\pi$
$942$	−8977.65	−0.310518
$943$	8366.01	0.288902
$944$	−24374.8	−0.840393
$945$	−55996.2	−1.92757
$946$	12852.8	0.441736
$947$	5693.46	0.195367	0.0976835	−	0.995218i	$-0.468857\pi$
$947$	5693.46	0.195367	0.0976835	+	0.995218i	$0.468857\pi$
$948$	4028.09	0.138003
$949$	−18518.6	−0.633444
$950$	−1304.33	−0.0445454
$951$	7420.47	0.253023
$952$	−27651.1	−0.941363
$953$	−19480.2	−0.662148	−0.331074	−	0.943605i	$-0.607411\pi$
$953$	−19480.2	−0.662148	−0.331074	+	0.943605i	$0.607411\pi$
$954$	34574.9	1.17338
$955$	14847.5	0.503094
$956$	1381.96	0.0467530
$957$	−15031.0	−0.507716
$958$	35393.8	1.19366
$959$	42983.9	1.44737
$960$	27276.8	0.917037
$961$	−13796.3	−0.463102
$962$	44189.6	1.48101
$963$	−154397.	−5.16654
$964$	409.776	0.0136909
$965$	4043.74	0.134894
$966$	−18745.1	−0.624342
$967$	28152.8	0.936227	0.468114	−	0.883668i	$-0.344934\pi$
$967$	28152.8	0.936227	0.468114	+	0.883668i	$0.344934\pi$
$968$	2810.83	0.0933300
$969$	10144.2	0.336303
$970$	−8450.59	−0.279724
$971$	−49162.0	−1.62480	−0.812401	−	0.583099i	$-0.801840\pi$
$971$	−49162.0	−1.62480	−0.812401	+	0.583099i	$0.801840\pi$
$972$	−7723.05	−0.254853
$973$	54280.6	1.78844
$974$	−34290.8	−1.12808
$975$	−20534.4	−0.674490
$976$	−46605.1	−1.52848
$977$	48768.7	1.59698	0.798490	−	0.602008i	$-0.205633\pi$
$977$	48768.7	1.59698	0.798490	+	0.602008i	$0.205633\pi$
$978$	10298.1	0.336705
$979$	−13926.8	−0.454651
$980$	−386.559	−0.0126002
$981$	−26625.5	−0.866553
$982$	5490.95	0.178435
$983$	6941.15	0.225217	0.112609	−	0.993639i	$-0.464079\pi$
$983$	6941.15	0.225217	0.112609	+	0.993639i	$0.464079\pi$
$984$	−66197.6	−2.14462
$985$	18020.2	0.582915
$986$	−19479.4	−0.629159
$987$	−59712.4	−1.92570
$988$	707.391	0.0227784
$989$	−12668.5	−0.407316
$990$	11454.5	0.367726
$991$	−9793.38	−0.313922	−0.156961	−	0.987605i	$-0.550170\pi$
$991$	−9793.38	−0.313922	−0.156961	+	0.987605i	$0.550170\pi$
$992$	−2627.58	−0.0840987
$993$	94825.7	3.03042
$994$	−48131.7	−1.53586
$995$	17583.6	0.560238
$996$	−5581.68	−0.177572
$997$	−18143.5	−0.576341	−0.288170	−	0.957579i	$-0.593047\pi$
$997$	−18143.5	−0.576341	−0.288170	+	0.957579i	$0.593047\pi$
$998$	16451.0	0.521790
$999$	98416.9	3.11689

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.h.1.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.h.1.8	✓	24	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74596 q^{2} +10.1412 q^{3} -0.459676 q^{4} +5.00000 q^{5} -27.8474 q^{6} -22.6095 q^{7} +23.2300 q^{8} +75.8438 q^{9} +O(q^{10})\)	\(q-2.74596 q^{2} +10.1412 q^{3} -0.459676 q^{4} +5.00000 q^{5} -27.8474 q^{6} -22.6095 q^{7} +23.2300 q^{8} +75.8438 q^{9} -13.7298 q^{10} -11.0000 q^{11} -4.66167 q^{12} -80.9941 q^{13} +62.0848 q^{14} +50.7060 q^{15} -60.1113 q^{16} +52.6470 q^{17} -208.264 q^{18} +19.0000 q^{19} -2.29838 q^{20} -229.287 q^{21} +30.2056 q^{22} -29.7724 q^{23} +235.580 q^{24} +25.0000 q^{25} +222.407 q^{26} +495.334 q^{27} +10.3930 q^{28} +134.743 q^{29} -139.237 q^{30} +126.470 q^{31} -20.7763 q^{32} -111.553 q^{33} -144.567 q^{34} -113.047 q^{35} -34.8636 q^{36} +198.688 q^{37} -52.1733 q^{38} -821.377 q^{39} +116.150 q^{40} -280.999 q^{41} +629.614 q^{42} +425.512 q^{43} +5.05644 q^{44} +379.219 q^{45} +81.7540 q^{46} +260.426 q^{47} -609.600 q^{48} +168.187 q^{49} -68.6491 q^{50} +533.904 q^{51} +37.2311 q^{52} -166.015 q^{53} -1360.17 q^{54} -55.0000 q^{55} -525.217 q^{56} +192.683 q^{57} -370.000 q^{58} +405.494 q^{59} -23.3083 q^{60} +775.314 q^{61} -347.283 q^{62} -1714.79 q^{63} +537.941 q^{64} -404.971 q^{65} +306.321 q^{66} +731.823 q^{67} -24.2006 q^{68} -301.928 q^{69} +310.424 q^{70} -775.258 q^{71} +1761.85 q^{72} +228.641 q^{73} -545.590 q^{74} +253.530 q^{75} -8.73385 q^{76} +248.704 q^{77} +2255.47 q^{78} -864.089 q^{79} -300.556 q^{80} +2975.50 q^{81} +771.613 q^{82} +1197.36 q^{83} +105.398 q^{84} +263.235 q^{85} -1168.44 q^{86} +1366.46 q^{87} -255.530 q^{88} +1266.08 q^{89} -1041.32 q^{90} +1831.23 q^{91} +13.6857 q^{92} +1282.56 q^{93} -715.122 q^{94} +95.0000 q^{95} -210.697 q^{96} +615.491 q^{97} -461.837 q^{98} -834.282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * q^99

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