LMFDB - Embedded newform 1045.4.a.h.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.46816 q^{2} +0.999287 q^{3} -5.84451 q^{4} +5.00000 q^{5} -1.46711 q^{6} +27.4651 q^{7} +20.3259 q^{8} -26.0014 q^{9} +O(q^{10})$	\(q-1.46816 q^{2} +0.999287 q^{3} -5.84451 q^{4} +5.00000 q^{5} -1.46711 q^{6} +27.4651 q^{7} +20.3259 q^{8} -26.0014 q^{9} -7.34079 q^{10} -11.0000 q^{11} -5.84034 q^{12} +0.949891 q^{13} -40.3232 q^{14} +4.99643 q^{15} +16.9145 q^{16} -5.50905 q^{17} +38.1742 q^{18} +19.0000 q^{19} -29.2226 q^{20} +27.4455 q^{21} +16.1497 q^{22} +129.850 q^{23} +20.3114 q^{24} +25.0000 q^{25} -1.39459 q^{26} -52.9636 q^{27} -160.520 q^{28} +74.3341 q^{29} -7.33555 q^{30} +38.6646 q^{31} -187.440 q^{32} -10.9922 q^{33} +8.08815 q^{34} +137.326 q^{35} +151.966 q^{36} -155.865 q^{37} -27.8950 q^{38} +0.949214 q^{39} +101.630 q^{40} +138.008 q^{41} -40.2944 q^{42} +377.536 q^{43} +64.2897 q^{44} -130.007 q^{45} -190.640 q^{46} +41.3581 q^{47} +16.9024 q^{48} +411.334 q^{49} -36.7039 q^{50} -5.50512 q^{51} -5.55165 q^{52} -269.904 q^{53} +77.7589 q^{54} -55.0000 q^{55} +558.254 q^{56} +18.9864 q^{57} -109.134 q^{58} -492.457 q^{59} -29.2017 q^{60} -210.420 q^{61} -56.7657 q^{62} -714.133 q^{63} +139.877 q^{64} +4.74946 q^{65} +16.1382 q^{66} -871.951 q^{67} +32.1977 q^{68} +129.757 q^{69} -201.616 q^{70} -512.428 q^{71} -528.503 q^{72} +23.1747 q^{73} +228.834 q^{74} +24.9822 q^{75} -111.046 q^{76} -302.117 q^{77} -1.39360 q^{78} +872.732 q^{79} +84.5723 q^{80} +649.113 q^{81} -202.618 q^{82} +36.2788 q^{83} -160.406 q^{84} -27.5453 q^{85} -554.282 q^{86} +74.2811 q^{87} -223.585 q^{88} +1272.99 q^{89} +190.871 q^{90} +26.0889 q^{91} -758.908 q^{92} +38.6370 q^{93} -60.7201 q^{94} +95.0000 q^{95} -187.307 q^{96} -797.313 q^{97} -603.903 q^{98} +286.016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.46816	−0.519072	−0.259536	−	0.965733i	$-0.583570\pi$
$2$	−1.46816	−0.519072	−0.259536	+	0.965733i	$0.583570\pi$
$3$	0.999287	0.192313	0.0961564	−	0.995366i	$-0.469345\pi$
$3$	0.999287	0.192313	0.0961564	+	0.995366i	$0.469345\pi$
$4$	−5.84451	−0.730564
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−1.46711	−0.0998242
$7$	27.4651	1.48298	0.741489	−	0.670965i	$-0.234120\pi$
$7$	27.4651	1.48298	0.741489	+	0.670965i	$0.234120\pi$
$8$	20.3259	0.898287
$9$	−26.0014	−0.963016
$10$	−7.34079	−0.232136
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−5.84034	−0.140497
$13$	0.949891	0.0202656	0.0101328	−	0.999949i	$-0.496775\pi$
$13$	0.949891	0.0202656	0.0101328	+	0.999949i	$0.496775\pi$
$14$	−40.3232	−0.769773
$15$	4.99643	0.0860049
$16$	16.9145	0.264288
$17$	−5.50905	−0.0785965	−0.0392983	−	0.999228i	$-0.512512\pi$
$17$	−5.50905	−0.0785965	−0.0392983	+	0.999228i	$0.512512\pi$
$18$	38.1742	0.499875
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−29.2226	−0.326718
$21$	27.4455	0.285196
$22$	16.1497	0.156506
$23$	129.850	1.17720	0.588598	−	0.808426i	$-0.299680\pi$
$23$	129.850	1.17720	0.588598	+	0.808426i	$0.299680\pi$
$24$	20.3114	0.172752
$25$	25.0000	0.200000
$26$	−1.39459	−0.0105193
$27$	−52.9636	−0.377513
$28$	−160.520	−1.08341
$29$	74.3341	0.475983	0.237991	−	0.971267i	$-0.423511\pi$
$29$	74.3341	0.475983	0.237991	+	0.971267i	$0.423511\pi$
$30$	−7.33555	−0.0446427
$31$	38.6646	0.224012	0.112006	−	0.993708i	$-0.464272\pi$
$31$	38.6646	0.224012	0.112006	+	0.993708i	$0.464272\pi$
$32$	−187.440	−1.03547
$33$	−10.9922	−0.0579845
$34$	8.08815	0.0407973
$35$	137.326	0.663208
$36$	151.966	0.703545
$37$	−155.865	−0.692542	−0.346271	−	0.938135i	$-0.612552\pi$
$37$	−155.865	−0.692542	−0.346271	+	0.938135i	$0.612552\pi$
$38$	−27.8950	−0.119083
$39$	0.949214	0.00389733
$40$	101.630	0.401726
$41$	138.008	0.525690	0.262845	−	0.964838i	$-0.415339\pi$
$41$	138.008	0.525690	0.262845	+	0.964838i	$0.415339\pi$
$42$	−40.2944	−0.148037
$43$	377.536	1.33892	0.669461	−	0.742847i	$-0.266525\pi$
$43$	377.536	1.33892	0.669461	+	0.742847i	$0.266525\pi$
$44$	64.2897	0.220273
$45$	−130.007	−0.430674
$46$	−190.640	−0.611050
$47$	41.3581	0.128355	0.0641776	−	0.997938i	$-0.479558\pi$
$47$	41.3581	0.128355	0.0641776	+	0.997938i	$0.479558\pi$
$48$	16.9024	0.0508260
$49$	411.334	1.19922
$50$	−36.7039	−0.103814
$51$	−5.50512	−0.0151151
$52$	−5.55165	−0.0148053
$53$	−269.904	−0.699512	−0.349756	−	0.936841i	$-0.613736\pi$
$53$	−269.904	−0.699512	−0.349756	+	0.936841i	$0.613736\pi$
$54$	77.7589	0.195956
$55$	−55.0000	−0.134840
$56$	558.254	1.33214
$57$	18.9864	0.0441196
$58$	−109.134	−0.247069
$59$	−492.457	−1.08665	−0.543326	−	0.839522i	$-0.682835\pi$
$59$	−492.457	−1.08665	−0.543326	+	0.839522i	$0.682835\pi$
$60$	−29.2017	−0.0628321
$61$	−210.420	−0.441664	−0.220832	−	0.975312i	$-0.570877\pi$
$61$	−210.420	−0.441664	−0.220832	+	0.975312i	$0.570877\pi$
$62$	−56.7657	−0.116278
$63$	−714.133	−1.42813
$64$	139.877	0.273196
$65$	4.74946	0.00906304
$66$	16.1382	0.0300981
$67$	−871.951	−1.58994	−0.794969	−	0.606650i	$-0.792513\pi$
$67$	−871.951	−1.58994	−0.794969	+	0.606650i	$0.792513\pi$
$68$	32.1977	0.0574198
$69$	129.757	0.226390
$70$	−201.616	−0.344253
$71$	−512.428	−0.856535	−0.428268	−	0.903652i	$-0.640876\pi$
$71$	−512.428	−0.856535	−0.428268	+	0.903652i	$0.640876\pi$
$72$	−528.503	−0.865065
$73$	23.1747	0.0371560	0.0185780	−	0.999827i	$-0.494086\pi$
$73$	23.1747	0.0371560	0.0185780	+	0.999827i	$0.494086\pi$
$74$	228.834	0.359479
$75$	24.9822	0.0384626
$76$	−111.046	−0.167603
$77$	−302.117	−0.447135
$78$	−1.39360	−0.00202299
$79$	872.732	1.24291	0.621456	−	0.783449i	$-0.286542\pi$
$79$	872.732	1.24291	0.621456	+	0.783449i	$0.286542\pi$
$80$	84.5723	0.118193
$81$	649.113	0.890415
$82$	−202.618	−0.272871
$83$	36.2788	0.0479773	0.0239886	−	0.999712i	$-0.492363\pi$
$83$	36.2788	0.0479773	0.0239886	+	0.999712i	$0.492363\pi$
$84$	−160.406	−0.208354
$85$	−27.5453	−0.0351494
$86$	−554.282	−0.694997
$87$	74.2811	0.0915376
$88$	−223.585	−0.270844
$89$	1272.99	1.51614	0.758071	−	0.652172i	$-0.226142\pi$
$89$	1272.99	1.51614	0.758071	+	0.652172i	$0.226142\pi$
$90$	190.871	0.223551
$91$	26.0889	0.0300534
$92$	−758.908	−0.860018
$93$	38.6370	0.0430803
$94$	−60.7201	−0.0666256
$95$	95.0000	0.102598
$96$	−187.307	−0.199135
$97$	−797.313	−0.834586	−0.417293	−	0.908772i	$-0.637021\pi$
$97$	−797.313	−0.834586	−0.417293	+	0.908772i	$0.637021\pi$
$98$	−603.903	−0.622484
$99$	286.016	0.290360
$100$	−146.113	−0.146113
$101$	1779.44	1.75308	0.876541	−	0.481327i	$-0.159845\pi$
$101$	1779.44	1.75308	0.876541	+	0.481327i	$0.159845\pi$
$102$	8.08238	0.00784584
$103$	129.027	0.123431	0.0617157	−	0.998094i	$-0.480343\pi$
$103$	129.027	0.123431	0.0617157	+	0.998094i	$0.480343\pi$
$104$	19.3074	0.0182043
$105$	137.228	0.127543
$106$	396.261	0.363097
$107$	1384.43	1.25082	0.625412	−	0.780295i	$-0.284931\pi$
$107$	1384.43	1.25082	0.625412	+	0.780295i	$0.284931\pi$
$108$	309.547	0.275798
$109$	1848.94	1.62474	0.812370	−	0.583142i	$-0.198177\pi$
$109$	1848.94	1.62474	0.812370	+	0.583142i	$0.198177\pi$
$110$	80.7487	0.0699917
$111$	−155.754	−0.133185
$112$	464.558	0.391934
$113$	344.635	0.286907	0.143453	−	0.989657i	$-0.454179\pi$
$113$	344.635	0.286907	0.143453	+	0.989657i	$0.454179\pi$
$114$	−27.8751	−0.0229012
$115$	649.248	0.526458
$116$	−434.447	−0.347736
$117$	−24.6985	−0.0195161
$118$	723.004	0.564050
$119$	−151.307	−0.116557
$120$	101.557	0.0772571
$121$	121.000	0.0909091
$122$	308.929	0.229255
$123$	137.910	0.101097
$124$	−225.976	−0.163655
$125$	125.000	0.0894427
$126$	1048.46	0.741303
$127$	−545.874	−0.381406	−0.190703	−	0.981648i	$-0.561077\pi$
$127$	−545.874	−0.381406	−0.190703	+	0.981648i	$0.561077\pi$
$128$	1294.16	0.893664
$129$	377.266	0.257492
$130$	−6.97295	−0.00470437
$131$	425.277	0.283638	0.141819	−	0.989893i	$-0.454705\pi$
$131$	425.277	0.283638	0.141819	+	0.989893i	$0.454705\pi$
$132$	64.2438	0.0423614
$133$	521.838	0.340219
$134$	1280.16	0.825292
$135$	−264.818	−0.168829
$136$	−111.977	−0.0706023
$137$	−868.742	−0.541764	−0.270882	−	0.962613i	$-0.587315\pi$
$137$	−868.742	−0.541764	−0.270882	+	0.962613i	$0.587315\pi$
$138$	−190.504	−0.117513
$139$	−1778.19	−1.08507	−0.542533	−	0.840034i	$-0.682535\pi$
$139$	−1778.19	−1.08507	−0.542533	+	0.840034i	$0.682535\pi$
$140$	−802.602	−0.484516
$141$	41.3285	0.0246843
$142$	752.325	0.444603
$143$	−10.4488	−0.00611030
$144$	−439.800	−0.254514
$145$	371.671	0.212866
$146$	−34.0241	−0.0192867
$147$	411.041	0.230626
$148$	910.955	0.505946
$149$	3375.04	1.85566	0.927832	−	0.372998i	$-0.121670\pi$
$149$	3375.04	1.85566	0.927832	+	0.372998i	$0.121670\pi$
$150$	−36.6777	−0.0199648
$151$	313.175	0.168780	0.0843902	−	0.996433i	$-0.473106\pi$
$151$	313.175	0.168780	0.0843902	+	0.996433i	$0.473106\pi$
$152$	386.193	0.206081
$153$	143.243	0.0756897
$154$	443.555	0.232095
$155$	193.323	0.100181
$156$	−5.54769	−0.00284725
$157$	1837.22	0.933924	0.466962	−	0.884277i	$-0.345348\pi$
$157$	1837.22	0.933924	0.466962	+	0.884277i	$0.345348\pi$
$158$	−1281.31	−0.645161
$159$	−269.711	−0.134525
$160$	−937.202	−0.463077
$161$	3566.34	1.74576
$162$	−953.000	−0.462190
$163$	3901.40	1.87473	0.937365	−	0.348349i	$-0.113258\pi$
$163$	3901.40	1.87473	0.937365	+	0.348349i	$0.113258\pi$
$164$	−806.592	−0.384050
$165$	−54.9608	−0.0259315
$166$	−53.2630	−0.0249037
$167$	3170.82	1.46926	0.734628	−	0.678470i	$-0.237357\pi$
$167$	3170.82	1.46926	0.734628	+	0.678470i	$0.237357\pi$
$168$	557.856	0.256188
$169$	−2196.10	−0.999589
$170$	40.4408	0.0182451
$171$	−494.027	−0.220931
$172$	−2206.51	−0.978169
$173$	−861.694	−0.378690	−0.189345	−	0.981911i	$-0.560636\pi$
$173$	−861.694	−0.378690	−0.189345	+	0.981911i	$0.560636\pi$
$174$	−109.056	−0.0475146
$175$	686.629	0.296596
$176$	−186.059	−0.0796859
$177$	−492.106	−0.208977
$178$	−1868.95	−0.786987
$179$	2490.28	1.03984	0.519922	−	0.854214i	$-0.325961\pi$
$179$	2490.28	1.03984	0.519922	+	0.854214i	$0.325961\pi$
$180$	759.828	0.314635
$181$	−335.209	−0.137657	−0.0688283	−	0.997629i	$-0.521926\pi$
$181$	−335.209	−0.137657	−0.0688283	+	0.997629i	$0.521926\pi$
$182$	−38.3026	−0.0155999
$183$	−210.270	−0.0849375
$184$	2639.31	1.05746
$185$	−779.325	−0.309714
$186$	−56.7252	−0.0223618
$187$	60.5996	0.0236977
$188$	−241.718	−0.0937717
$189$	−1454.65	−0.559844
$190$	−139.475	−0.0532557
$191$	−4150.26	−1.57226	−0.786131	−	0.618060i	$-0.787919\pi$
$191$	−4150.26	−1.57226	−0.786131	+	0.618060i	$0.787919\pi$
$192$	139.777	0.0525391
$193$	3316.91	1.23708	0.618539	−	0.785754i	$-0.287725\pi$
$193$	3316.91	1.23708	0.618539	+	0.785754i	$0.287725\pi$
$194$	1170.58	0.433210
$195$	4.74607	0.00174294
$196$	−2404.05	−0.876110
$197$	1351.31	0.488716	0.244358	−	0.969685i	$-0.421423\pi$
$197$	1351.31	0.488716	0.244358	+	0.969685i	$0.421423\pi$
$198$	−419.916	−0.150718
$199$	2323.05	0.827521	0.413761	−	0.910386i	$-0.364215\pi$
$199$	2323.05	0.827521	0.413761	+	0.910386i	$0.364215\pi$
$200$	508.148	0.179657
$201$	−871.329	−0.305765
$202$	−2612.50	−0.909976
$203$	2041.60	0.705872
$204$	32.1748	0.0110426
$205$	690.042	0.235096
$206$	−189.432	−0.0640698
$207$	−3376.28	−1.13366
$208$	16.0669	0.00535595
$209$	−209.000	−0.0691714
$210$	−201.472	−0.0662042
$211$	2366.42	0.772089	0.386045	−	0.922480i	$-0.373841\pi$
$211$	2366.42	0.772089	0.386045	+	0.922480i	$0.373841\pi$
$212$	1577.46	0.511039
$213$	−512.062	−0.164723
$214$	−2032.56	−0.649267
$215$	1887.68	0.598784
$216$	−1076.53	−0.339115
$217$	1061.93	0.332205
$218$	−2714.54	−0.843357
$219$	23.1581	0.00714558
$220$	321.448	0.0985093
$221$	−5.23300	−0.00159280
$222$	228.671	0.0691324
$223$	−3157.89	−0.948288	−0.474144	−	0.880447i	$-0.657242\pi$
$223$	−3157.89	−0.948288	−0.474144	+	0.880447i	$0.657242\pi$
$224$	−5148.08	−1.53558
$225$	−650.036	−0.192603
$226$	−505.978	−0.148925
$227$	−1657.86	−0.484739	−0.242370	−	0.970184i	$-0.577925\pi$
$227$	−1657.86	−0.484739	−0.242370	+	0.970184i	$0.577925\pi$
$228$	−110.967	−0.0322322
$229$	508.933	0.146861	0.0734306	−	0.997300i	$-0.476605\pi$
$229$	508.933	0.146861	0.0734306	+	0.997300i	$0.476605\pi$
$230$	−953.198	−0.273270
$231$	−301.901	−0.0859897
$232$	1510.91	0.427569
$233$	2857.06	0.803314	0.401657	−	0.915790i	$-0.368434\pi$
$233$	2857.06	0.803314	0.401657	+	0.915790i	$0.368434\pi$
$234$	36.2613	0.0101302
$235$	206.790	0.0574022
$236$	2878.17	0.793869
$237$	872.109	0.239028
$238$	222.142	0.0605015
$239$	−5340.10	−1.44528	−0.722640	−	0.691224i	$-0.757072\pi$
$239$	−5340.10	−1.44528	−0.722640	+	0.691224i	$0.757072\pi$
$240$	84.5119	0.0227301
$241$	5574.54	1.48999	0.744995	−	0.667070i	$-0.232452\pi$
$241$	5574.54	1.48999	0.744995	+	0.667070i	$0.232452\pi$
$242$	−177.647	−0.0471884
$243$	2078.67	0.548751
$244$	1229.80	0.322664
$245$	2056.67	0.536309
$246$	−202.473	−0.0524766
$247$	18.0479	0.00464924
$248$	785.893	0.201227
$249$	36.2529	0.00922664
$250$	−183.520	−0.0464272
$251$	3401.23	0.855313	0.427656	−	0.903941i	$-0.359339\pi$
$251$	3401.23	0.855313	0.427656	+	0.903941i	$0.359339\pi$
$252$	4173.76	1.04334
$253$	−1428.35	−0.354938
$254$	801.429	0.197977
$255$	−27.5256	−0.00675969
$256$	−3019.05	−0.737072
$257$	−6956.03	−1.68835	−0.844173	−	0.536070i	$-0.819908\pi$
$257$	−6956.03	−1.68835	−0.844173	+	0.536070i	$0.819908\pi$
$258$	−553.886	−0.133657
$259$	−4280.85	−1.02702
$260$	−27.7583	−0.00662113
$261$	−1932.79	−0.458379
$262$	−624.373	−0.147229
$263$	−276.795	−0.0648971	−0.0324485	−	0.999473i	$-0.510331\pi$
$263$	−276.795	−0.0648971	−0.0324485	+	0.999473i	$0.510331\pi$
$264$	−223.426	−0.0520867
$265$	−1349.52	−0.312831
$266$	−766.140	−0.176598
$267$	1272.08	0.291573
$268$	5096.13	1.16155
$269$	2950.20	0.668687	0.334344	−	0.942451i	$-0.391485\pi$
$269$	2950.20	0.668687	0.334344	+	0.942451i	$0.391485\pi$
$270$	388.795	0.0876344
$271$	8394.98	1.88177	0.940883	−	0.338732i	$-0.109998\pi$
$271$	8394.98	1.88177	0.940883	+	0.338732i	$0.109998\pi$
$272$	−93.1826	−0.0207721
$273$	26.0703	0.00577965
$274$	1275.45	0.281215
$275$	−275.000	−0.0603023
$276$	−758.366	−0.165392
$277$	−4775.19	−1.03579	−0.517894	−	0.855445i	$-0.673284\pi$
$277$	−4775.19	−1.03579	−0.517894	+	0.855445i	$0.673284\pi$
$278$	2610.67	0.563228
$279$	−1005.33	−0.215727
$280$	2791.27	0.595751
$281$	−3968.84	−0.842565	−0.421283	−	0.906929i	$-0.638420\pi$
$281$	−3968.84	−0.842565	−0.421283	+	0.906929i	$0.638420\pi$
$282$	−60.6768	−0.0128129
$283$	5683.26	1.19376	0.596881	−	0.802329i	$-0.296406\pi$
$283$	5683.26	1.19376	0.596881	+	0.802329i	$0.296406\pi$
$284$	2994.89	0.625754
$285$	94.9322	0.0197309
$286$	15.3405	0.00317169
$287$	3790.42	0.779586
$288$	4873.72	0.997176
$289$	−4882.65	−0.993823
$290$	−545.671	−0.110493
$291$	−796.744	−0.160502
$292$	−135.445	−0.0271449
$293$	4247.87	0.846974	0.423487	−	0.905902i	$-0.360806\pi$
$293$	4247.87	0.846974	0.423487	+	0.905902i	$0.360806\pi$
$294$	−603.472	−0.119712
$295$	−2462.28	−0.485965
$296$	−3168.10	−0.622102
$297$	582.600	0.113824
$298$	−4955.09	−0.963223
$299$	123.343	0.0238566
$300$	−146.009	−0.0280994
$301$	10369.1	1.98559
$302$	−459.790	−0.0876091
$303$	1778.17	0.337140
$304$	321.375	0.0606319
$305$	−1052.10	−0.197518
$306$	−210.304	−0.0392884
$307$	5824.49	1.08280	0.541402	−	0.840764i	$-0.317894\pi$
$307$	5824.49	1.08280	0.541402	+	0.840764i	$0.317894\pi$
$308$	1765.72	0.326661
$309$	128.935	0.0237374
$310$	−283.828	−0.0520012
$311$	−4674.13	−0.852236	−0.426118	−	0.904667i	$-0.640119\pi$
$311$	−4674.13	−0.852236	−0.426118	+	0.904667i	$0.640119\pi$
$312$	19.2936	0.00350092
$313$	9811.34	1.77179	0.885894	−	0.463888i	$-0.153546\pi$
$313$	9811.34	1.77179	0.885894	+	0.463888i	$0.153546\pi$
$314$	−2697.33	−0.484774
$315$	−3570.66	−0.638680
$316$	−5100.69	−0.908027
$317$	445.411	0.0789172	0.0394586	−	0.999221i	$-0.487437\pi$
$317$	445.411	0.0789172	0.0394586	+	0.999221i	$0.487437\pi$
$318$	395.979	0.0698282
$319$	−817.676	−0.143514
$320$	699.383	0.122177
$321$	1383.44	0.240549
$322$	−5235.95	−0.906173
$323$	−104.672	−0.0180313
$324$	−3793.75	−0.650506
$325$	23.7473	0.00405312
$326$	−5727.86	−0.973120
$327$	1847.62	0.312458
$328$	2805.15	0.472221
$329$	1135.90	0.190348
$330$	80.6910	0.0134603
$331$	−3569.06	−0.592668	−0.296334	−	0.955084i	$-0.595764\pi$
$331$	−3569.06	−0.592668	−0.296334	+	0.955084i	$0.595764\pi$
$332$	−212.032	−0.0350505
$333$	4052.71	0.666929
$334$	−4655.27	−0.762650
$335$	−4359.76	−0.711042
$336$	464.226	0.0753739
$337$	9309.15	1.50475	0.752376	−	0.658734i	$-0.228908\pi$
$337$	9309.15	1.50475	0.752376	+	0.658734i	$0.228908\pi$
$338$	3224.22	0.518859
$339$	344.389	0.0551759
$340$	160.989	0.0256789
$341$	−425.310	−0.0675421
$342$	725.310	0.114679
$343$	1876.80	0.295446
$344$	7673.76	1.20274
$345$	648.785	0.101245
$346$	1265.10	0.196567
$347$	−7243.49	−1.12061	−0.560304	−	0.828287i	$-0.689316\pi$
$347$	−7243.49	−1.12061	−0.560304	+	0.828287i	$0.689316\pi$
$348$	−434.137	−0.0668741
$349$	−6364.57	−0.976182	−0.488091	−	0.872793i	$-0.662307\pi$
$349$	−6364.57	−0.976182	−0.488091	+	0.872793i	$0.662307\pi$
$350$	−1008.08	−0.153955
$351$	−50.3097	−0.00765052
$352$	2061.85	0.312207
$353$	10638.7	1.60408	0.802042	−	0.597268i	$-0.203747\pi$
$353$	10638.7	1.60408	0.802042	+	0.597268i	$0.203747\pi$
$354$	722.488	0.108474
$355$	−2562.14	−0.383054
$356$	−7440.01	−1.10764
$357$	−151.199	−0.0224154
$358$	−3656.12	−0.539754
$359$	1082.99	0.159215	0.0796074	−	0.996826i	$-0.474633\pi$
$359$	1082.99	0.159215	0.0796074	+	0.996826i	$0.474633\pi$
$360$	−2642.52	−0.386869
$361$	361.000	0.0526316
$362$	492.139	0.0714537
$363$	120.914	0.0174830
$364$	−152.477	−0.0219559
$365$	115.873	0.0166167
$366$	308.709	0.0440887
$367$	−3288.73	−0.467767	−0.233883	−	0.972265i	$-0.575143\pi$
$367$	−3288.73	−0.467767	−0.233883	+	0.972265i	$0.575143\pi$
$368$	2196.34	0.311119
$369$	−3588.41	−0.506248
$370$	1144.17	0.160764
$371$	−7412.95	−1.03736
$372$	−225.814	−0.0314729
$373$	3224.99	0.447678	0.223839	−	0.974626i	$-0.428141\pi$
$373$	3224.99	0.447678	0.223839	+	0.974626i	$0.428141\pi$
$374$	−88.9697	−0.0123008
$375$	124.911	0.0172010
$376$	840.641	0.115300
$377$	70.6094	0.00964607
$378$	2135.66	0.290599
$379$	−3475.11	−0.470988	−0.235494	−	0.971876i	$-0.575671\pi$
$379$	−3475.11	−0.470988	−0.235494	+	0.971876i	$0.575671\pi$
$380$	−555.229	−0.0749543
$381$	−545.485	−0.0733492
$382$	6093.23	0.816117
$383$	−4049.69	−0.540286	−0.270143	−	0.962820i	$-0.587071\pi$
$383$	−4049.69	−0.540286	−0.270143	+	0.962820i	$0.587071\pi$
$384$	1293.24	0.171863
$385$	−1510.58	−0.199965
$386$	−4869.74	−0.642133
$387$	−9816.47	−1.28940
$388$	4659.91	0.609719
$389$	4760.34	0.620460	0.310230	−	0.950661i	$-0.399594\pi$
$389$	4760.34	0.620460	0.310230	+	0.950661i	$0.399594\pi$
$390$	−6.96798	−0.000904711 0
$391$	−715.348	−0.0925236
$392$	8360.74	1.07725
$393$	424.973	0.0545472
$394$	−1983.94	−0.253679
$395$	4363.66	0.555847
$396$	−1671.62	−0.212127
$397$	−2855.98	−0.361052	−0.180526	−	0.983570i	$-0.557780\pi$
$397$	−2855.98	−0.361052	−0.180526	+	0.983570i	$0.557780\pi$
$398$	−3410.61	−0.429543
$399$	521.465	0.0654284
$400$	422.861	0.0528577
$401$	11554.3	1.43889	0.719444	−	0.694550i	$-0.244397\pi$
$401$	11554.3	1.43889	0.719444	+	0.694550i	$0.244397\pi$
$402$	1279.25	0.158714
$403$	36.7272	0.00453973
$404$	−10400.0	−1.28074
$405$	3245.56	0.398206
$406$	−2997.39	−0.366399
$407$	1714.52	0.208809
$408$	−111.897	−0.0135777
$409$	−12734.6	−1.53957	−0.769786	−	0.638302i	$-0.779637\pi$
$409$	−12734.6	−1.53957	−0.769786	+	0.638302i	$0.779637\pi$
$410$	−1013.09	−0.122032
$411$	−868.122	−0.104188
$412$	−754.101	−0.0901745
$413$	−13525.4	−1.61148
$414$	4956.90	0.588451
$415$	181.394	0.0214561
$416$	−178.048	−0.0209844
$417$	−1776.92	−0.208672
$418$	306.845	0.0359050
$419$	−570.293	−0.0664931	−0.0332466	−	0.999447i	$-0.510585\pi$
$419$	−570.293	−0.0664931	−0.0332466	+	0.999447i	$0.510585\pi$
$420$	−802.029	−0.0931786
$421$	8162.00	0.944873	0.472437	−	0.881365i	$-0.343375\pi$
$421$	8162.00	0.944873	0.472437	+	0.881365i	$0.343375\pi$
$422$	−3474.27	−0.400770
$423$	−1075.37	−0.123608
$424$	−5486.05	−0.628363
$425$	−137.726	−0.0157193
$426$	751.788	0.0855029
$427$	−5779.21	−0.654977
$428$	−8091.33	−0.913807
$429$	−10.4414	−0.00117509
$430$	−2771.41	−0.310812
$431$	−7827.12	−0.874755	−0.437377	−	0.899278i	$-0.644093\pi$
$431$	−7827.12	−0.874755	−0.437377	+	0.899278i	$0.644093\pi$
$432$	−895.851	−0.0997723
$433$	−9972.80	−1.10684	−0.553420	−	0.832902i	$-0.686678\pi$
$433$	−9972.80	−1.10684	−0.553420	+	0.832902i	$0.686678\pi$
$434$	−1559.08	−0.172438
$435$	371.406	0.0409369
$436$	−10806.2	−1.18698
$437$	2467.14	0.270067
$438$	−33.9998	−0.00370907
$439$	−13895.3	−1.51067	−0.755337	−	0.655336i	$-0.772527\pi$
$439$	−13895.3	−1.51067	−0.755337	+	0.655336i	$0.772527\pi$
$440$	−1117.93	−0.121125
$441$	−10695.3	−1.15487
$442$	7.68287	0.000826780 0
$443$	462.220	0.0495728	0.0247864	−	0.999693i	$-0.492109\pi$
$443$	462.220	0.0495728	0.0247864	+	0.999693i	$0.492109\pi$
$444$	910.305	0.0972999
$445$	6364.95	0.678039
$446$	4636.29	0.492230
$447$	3372.63	0.356868
$448$	3841.73	0.405144
$449$	−9422.16	−0.990333	−0.495166	−	0.868798i	$-0.664893\pi$
$449$	−9422.16	−0.990333	−0.495166	+	0.868798i	$0.664893\pi$
$450$	954.355	0.0999749
$451$	−1518.09	−0.158501
$452$	−2014.22	−0.209604
$453$	312.952	0.0324586
$454$	2433.99	0.251615
$455$	130.445	0.0134403
$456$	385.917	0.0396321
$457$	−16201.5	−1.65837	−0.829184	−	0.558975i	$-0.811195\pi$
$457$	−16201.5	−1.65837	−0.829184	+	0.558975i	$0.811195\pi$
$458$	−747.194	−0.0762316
$459$	291.779	0.0296712
$460$	−3794.54	−0.384612
$461$	12564.5	1.26938	0.634691	−	0.772766i	$-0.281127\pi$
$461$	12564.5	1.26938	0.634691	+	0.772766i	$0.281127\pi$
$462$	443.238	0.0446349
$463$	6140.02	0.616309	0.308154	−	0.951336i	$-0.400289\pi$
$463$	6140.02	0.616309	0.308154	+	0.951336i	$0.400289\pi$
$464$	1257.32	0.125797
$465$	193.185	0.0192661
$466$	−4194.61	−0.416978
$467$	−5064.23	−0.501808	−0.250904	−	0.968012i	$-0.580728\pi$
$467$	−5064.23	−0.501808	−0.250904	+	0.968012i	$0.580728\pi$
$468$	144.351	0.0142577
$469$	−23948.3	−2.35784
$470$	−303.601	−0.0297959
$471$	1835.91	0.179606
$472$	−10009.6	−0.976125
$473$	−4152.89	−0.403700
$474$	−1280.39	−0.124073
$475$	475.000	0.0458831
$476$	884.315	0.0851523
$477$	7017.89	0.673641
$478$	7840.10	0.750205
$479$	18459.1	1.76079	0.880393	−	0.474245i	$-0.157279\pi$
$479$	18459.1	1.76079	0.880393	+	0.474245i	$0.157279\pi$
$480$	−936.534	−0.0890557
$481$	−148.055	−0.0140348
$482$	−8184.30	−0.773412
$483$	3563.79	0.335731
$484$	−707.186	−0.0664149
$485$	−3986.56	−0.373238
$486$	−3051.81	−0.284841
$487$	5767.97	0.536697	0.268349	−	0.963322i	$-0.413522\pi$
$487$	5767.97	0.536697	0.268349	+	0.963322i	$0.413522\pi$
$488$	−4276.97	−0.396741
$489$	3898.61	0.360535
$490$	−3019.52	−0.278383
$491$	−5789.31	−0.532114	−0.266057	−	0.963957i	$-0.585721\pi$
$491$	−5789.31	−0.532114	−0.266057	+	0.963957i	$0.585721\pi$
$492$	−806.016	−0.0738577
$493$	−409.511	−0.0374106
$494$	−26.4972	−0.00241329
$495$	1430.08	0.129853
$496$	653.990	0.0592037
$497$	−14073.9	−1.27022
$498$	−53.2250	−0.00478929
$499$	−14813.4	−1.32894	−0.664470	−	0.747315i	$-0.731343\pi$
$499$	−14813.4	−1.32894	−0.664470	+	0.747315i	$0.731343\pi$
$500$	−730.564	−0.0653437
$501$	3168.56	0.282557
$502$	−4993.53	−0.443969
$503$	21117.0	1.87189	0.935946	−	0.352144i	$-0.114547\pi$
$503$	21117.0	1.87189	0.935946	+	0.352144i	$0.114547\pi$
$504$	−14515.4	−1.28287
$505$	8897.22	0.784002
$506$	2097.04	0.184238
$507$	−2194.53	−0.192234
$508$	3190.37	0.278641
$509$	14008.3	1.21986	0.609928	−	0.792457i	$-0.291198\pi$
$509$	14008.3	1.21986	0.609928	+	0.792457i	$0.291198\pi$
$510$	40.4119	0.00350876
$511$	636.496	0.0551016
$512$	−5920.87	−0.511070
$513$	−1006.31	−0.0866074
$514$	10212.5	0.876373
$515$	645.136	0.0552002
$516$	−2204.94	−0.188114
$517$	−454.939	−0.0387005
$518$	6284.97	0.533100
$519$	−861.079	−0.0728269
$520$	96.5371	0.00814122
$521$	2736.24	0.230090	0.115045	−	0.993360i	$-0.463299\pi$
$521$	2736.24	0.230090	0.115045	+	0.993360i	$0.463299\pi$
$522$	2837.65	0.237932
$523$	−17940.9	−1.50000	−0.750002	−	0.661436i	$-0.769947\pi$
$523$	−17940.9	−1.50000	−0.750002	+	0.661436i	$0.769947\pi$
$524$	−2485.53	−0.207216
$525$	686.139	0.0570391
$526$	406.379	0.0336863
$527$	−213.005	−0.0176065
$528$	−185.926	−0.0153246
$529$	4693.92	0.385791
$530$	1981.31	0.162382
$531$	12804.6	1.04646
$532$	−3049.89	−0.248551
$533$	131.093	0.0106534
$534$	−1867.62	−0.151348
$535$	6922.16	0.559385
$536$	−17723.2	−1.42822
$537$	2488.50	0.199975
$538$	−4331.36	−0.347097
$539$	−4524.67	−0.361580
$540$	1547.73	0.123340
$541$	−14189.7	−1.12766	−0.563830	−	0.825891i	$-0.690673\pi$
$541$	−14189.7	−1.12766	−0.563830	+	0.825891i	$0.690673\pi$
$542$	−12325.1	−0.976772
$543$	−334.969	−0.0264731
$544$	1032.62	0.0813845
$545$	9244.72	0.726606
$546$	−38.2753	−0.00300006
$547$	−12478.2	−0.975374	−0.487687	−	0.873019i	$-0.662159\pi$
$547$	−12478.2	−0.975374	−0.487687	+	0.873019i	$0.662159\pi$
$548$	5077.38	0.395793
$549$	5471.21	0.425329
$550$	403.743	0.0313012
$551$	1412.35	0.109198
$552$	2637.43	0.203363
$553$	23969.7	1.84321
$554$	7010.73	0.537649
$555$	−778.769	−0.0595620
$556$	10392.7	0.792711
$557$	7471.85	0.568389	0.284194	−	0.958767i	$-0.408274\pi$
$557$	7471.85	0.568389	0.284194	+	0.958767i	$0.408274\pi$
$558$	1475.99	0.111978
$559$	358.618	0.0271340
$560$	2322.79	0.175278
$561$	60.5563	0.00455738
$562$	5826.88	0.437352
$563$	−9496.59	−0.710895	−0.355447	−	0.934696i	$-0.615671\pi$
$563$	−9496.59	−0.710895	−0.355447	+	0.934696i	$0.615671\pi$
$564$	−241.545	−0.0180335
$565$	1723.17	0.128309
$566$	−8343.92	−0.619649
$567$	17828.0	1.32047
$568$	−10415.6	−0.769415
$569$	7966.13	0.586920	0.293460	−	0.955971i	$-0.405193\pi$
$569$	7966.13	0.586920	0.293460	+	0.955971i	$0.405193\pi$
$570$	−139.375	−0.0102417
$571$	609.893	0.0446992	0.0223496	−	0.999750i	$-0.492885\pi$
$571$	609.893	0.0446992	0.0223496	+	0.999750i	$0.492885\pi$
$572$	61.0682	0.00446397
$573$	−4147.30	−0.302366
$574$	−5564.93	−0.404662
$575$	3246.24	0.235439
$576$	−3636.99	−0.263092
$577$	−8934.58	−0.644630	−0.322315	−	0.946633i	$-0.604461\pi$
$577$	−8934.58	−0.644630	−0.322315	+	0.946633i	$0.604461\pi$
$578$	7168.50	0.515866
$579$	3314.54	0.237906
$580$	−2172.23	−0.155512
$581$	996.402	0.0711493
$582$	1169.75	0.0833119
$583$	2968.94	0.210911
$584$	471.047	0.0333768
$585$	−123.493	−0.00872785
$586$	−6236.54	−0.439640
$587$	7111.59	0.500045	0.250023	−	0.968240i	$-0.419562\pi$
$587$	7111.59	0.500045	0.250023	+	0.968240i	$0.419562\pi$
$588$	−2402.33	−0.168487
$589$	734.627	0.0513918
$590$	3615.02	0.252251
$591$	1350.35	0.0939863
$592$	−2636.37	−0.183031
$593$	−13508.6	−0.935465	−0.467733	−	0.883870i	$-0.654929\pi$
$593$	−13508.6	−0.935465	−0.467733	+	0.883870i	$0.654929\pi$
$594$	−855.348	−0.0590831
$595$	−756.534	−0.0521259
$596$	−19725.5	−1.35568
$597$	2321.39	0.159143
$598$	−181.087	−0.0123833
$599$	−9603.94	−0.655102	−0.327551	−	0.944833i	$-0.606223\pi$
$599$	−9603.94	−0.655102	−0.327551	+	0.944833i	$0.606223\pi$
$600$	507.786	0.0345504
$601$	−22522.2	−1.52862	−0.764308	−	0.644851i	$-0.776919\pi$
$601$	−22522.2	−1.52862	−0.764308	+	0.644851i	$0.776919\pi$
$602$	−15223.4	−1.03067
$603$	22672.0	1.53114
$604$	−1830.36	−0.123305
$605$	605.000	0.0406558
$606$	−2610.64	−0.175000
$607$	4.23892	0.000283447 0	0.000141724	−	1.00000i	$-0.499955\pi$
$607$	4.23892	0.000283447 0	0.000141724		1.00000i	$0.499955\pi$
$608$	−3561.37	−0.237554
$609$	2040.14	0.135748
$610$	1544.65	0.102526
$611$	39.2857	0.00260119
$612$	−837.187	−0.0552962
$613$	−2668.81	−0.175844	−0.0879220	−	0.996127i	$-0.528023\pi$
$613$	−2668.81	−0.175844	−0.0879220	+	0.996127i	$0.528023\pi$
$614$	−8551.26	−0.562054
$615$	689.549	0.0452119
$616$	−6140.80	−0.401656
$617$	−21377.4	−1.39485	−0.697423	−	0.716660i	$-0.745670\pi$
$617$	−21377.4	−1.39485	−0.697423	+	0.716660i	$0.745670\pi$
$618$	−189.297	−0.0123214
$619$	−15210.8	−0.987680	−0.493840	−	0.869553i	$-0.664407\pi$
$619$	−15210.8	−0.987680	−0.493840	+	0.869553i	$0.664407\pi$
$620$	−1129.88	−0.0731887
$621$	−6877.30	−0.444407
$622$	6862.36	0.442372
$623$	34962.8	2.24841
$624$	16.0554	0.00103002
$625$	625.000	0.0400000
$626$	−14404.6	−0.919685
$627$	−208.851	−0.0133026
$628$	−10737.7	−0.682292
$629$	858.668	0.0544314
$630$	5242.30	0.331521
$631$	10927.8	0.689427	0.344714	−	0.938708i	$-0.387976\pi$
$631$	10927.8	0.689427	0.344714	+	0.938708i	$0.387976\pi$
$632$	17739.1	1.11649
$633$	2364.73	0.148483
$634$	−653.933	−0.0409637
$635$	−2729.37	−0.170570
$636$	1576.33	0.0982793
$637$	390.723	0.0243030
$638$	1200.48	0.0744942
$639$	13323.9	0.824857
$640$	6470.82	0.399659
$641$	10053.4	0.619481	0.309740	−	0.950821i	$-0.399758\pi$
$641$	10053.4	0.619481	0.309740	+	0.950821i	$0.399758\pi$
$642$	−2031.11	−0.124862
$643$	−4999.32	−0.306616	−0.153308	−	0.988178i	$-0.548993\pi$
$643$	−4999.32	−0.306616	−0.153308	+	0.988178i	$0.548993\pi$
$644$	−20843.5	−1.27539
$645$	1886.33	0.115154
$646$	153.675	0.00935953
$647$	800.105	0.0486173	0.0243086	−	0.999705i	$-0.492262\pi$
$647$	800.105	0.0486173	0.0243086	+	0.999705i	$0.492262\pi$
$648$	13193.8	0.799849
$649$	5417.03	0.327638
$650$	−34.8648	−0.00210386
$651$	1061.17	0.0638872
$652$	−22801.8	−1.36961
$653$	−1865.37	−0.111788	−0.0558939	−	0.998437i	$-0.517801\pi$
$653$	−1865.37	−0.111788	−0.0558939	+	0.998437i	$0.517801\pi$
$654$	−2712.60	−0.162188
$655$	2126.38	0.126847
$656$	2334.34	0.138934
$657$	−602.574	−0.0357818
$658$	−1667.69	−0.0988043
$659$	3945.42	0.233220	0.116610	−	0.993178i	$-0.462797\pi$
$659$	3945.42	0.233220	0.116610	+	0.993178i	$0.462797\pi$
$660$	321.219	0.0189446
$661$	−10405.0	−0.612265	−0.306133	−	0.951989i	$-0.599035\pi$
$661$	−10405.0	−0.612265	−0.306133	+	0.951989i	$0.599035\pi$
$662$	5239.94	0.307637
$663$	−5.22927	−0.000306317 0
$664$	737.400	0.0430974
$665$	2609.19	0.152150
$666$	−5950.02	−0.346184
$667$	9652.26	0.560325
$668$	−18531.9	−1.07339
$669$	−3155.64	−0.182368
$670$	6400.81	0.369082
$671$	2314.62	0.133167
$672$	−5144.41	−0.295312
$673$	−27651.3	−1.58377	−0.791886	−	0.610669i	$-0.790901\pi$
$673$	−27651.3	−1.58377	−0.791886	+	0.610669i	$0.790901\pi$
$674$	−13667.3	−0.781075
$675$	−1324.09	−0.0755026
$676$	12835.1	0.730264
$677$	9932.92	0.563890	0.281945	−	0.959431i	$-0.409020\pi$
$677$	9932.92	0.563890	0.281945	+	0.959431i	$0.409020\pi$
$678$	−505.617	−0.0286403
$679$	−21898.3	−1.23767
$680$	−559.883	−0.0315743
$681$	−1656.67	−0.0932215
$682$	624.423	0.0350592
$683$	−14535.6	−0.814335	−0.407168	−	0.913353i	$-0.633484\pi$
$683$	−14535.6	−0.814335	−0.407168	+	0.913353i	$0.633484\pi$
$684$	2887.35	0.161404
$685$	−4343.71	−0.242284
$686$	−2755.44	−0.153358
$687$	508.570	0.0282433
$688$	6385.81	0.353862
$689$	−256.379	−0.0141760
$690$	−952.518	−0.0525533
$691$	62.2591	0.00342756	0.00171378	−	0.999999i	$-0.499454\pi$
$691$	62.2591	0.00342756	0.00171378	+	0.999999i	$0.499454\pi$
$692$	5036.18	0.276657
$693$	7855.46	0.430598
$694$	10634.6	0.581677
$695$	−8890.96	−0.485257
$696$	1509.83	0.0822271
$697$	−760.295	−0.0413174
$698$	9344.18	0.506709
$699$	2855.02	0.154488
$700$	−4013.01	−0.216682
$701$	22424.4	1.20822	0.604108	−	0.796902i	$-0.293530\pi$
$701$	22424.4	1.20822	0.604108	+	0.796902i	$0.293530\pi$
$702$	73.8625	0.00397117
$703$	−2961.44	−0.158880
$704$	−1538.64	−0.0823718
$705$	206.643	0.0110392
$706$	−15619.3	−0.832635
$707$	48872.7	2.59978
$708$	2876.12	0.152671
$709$	22285.4	1.18046	0.590231	−	0.807235i	$-0.299037\pi$
$709$	22285.4	1.18046	0.590231	+	0.807235i	$0.299037\pi$
$710$	3761.62	0.198833
$711$	−22692.3	−1.19694
$712$	25874.7	1.36193
$713$	5020.58	0.263706
$714$	221.984	0.0116352
$715$	−52.2440	−0.00273261
$716$	−14554.5	−0.759673
$717$	−5336.29	−0.277946
$718$	−1590.00	−0.0826440
$719$	23676.7	1.22809	0.614043	−	0.789273i	$-0.289542\pi$
$719$	23676.7	1.22809	0.614043	+	0.789273i	$0.289542\pi$
$720$	−2199.00	−0.113822
$721$	3543.75	0.183046
$722$	−530.005	−0.0273196
$723$	5570.56	0.286544
$724$	1959.13	0.100567
$725$	1858.35	0.0951966
$726$	−177.520	−0.00907493
$727$	−34021.9	−1.73563	−0.867814	−	0.496889i	$-0.834475\pi$
$727$	−34021.9	−1.73563	−0.867814	+	0.496889i	$0.834475\pi$
$728$	530.281	0.0269966
$729$	−15448.9	−0.784883
$730$	−170.120	−0.00862525
$731$	−2079.86	−0.105235
$732$	1228.92	0.0620523
$733$	−15018.8	−0.756799	−0.378399	−	0.925642i	$-0.623525\pi$
$733$	−15018.8	−0.756799	−0.378399	+	0.925642i	$0.623525\pi$
$734$	4828.38	0.242805
$735$	2055.20	0.103139
$736$	−24339.1	−1.21895
$737$	9591.47	0.479384
$738$	5268.36	0.262779
$739$	14623.9	0.727941	0.363971	−	0.931410i	$-0.381421\pi$
$739$	14623.9	0.727941	0.363971	+	0.931410i	$0.381421\pi$
$740$	4554.78	0.226266
$741$	18.0351	0.000894109 0
$742$	10883.4	0.538465
$743$	6946.02	0.342967	0.171484	−	0.985187i	$-0.445144\pi$
$743$	6946.02	0.342967	0.171484	+	0.985187i	$0.445144\pi$
$744$	785.333	0.0386985
$745$	16875.2	0.829878
$746$	−4734.80	−0.232377
$747$	−943.300	−0.0462029
$748$	−354.175	−0.0173127
$749$	38023.6	1.85494
$750$	−183.389	−0.00892855
$751$	22467.2	1.09167	0.545833	−	0.837894i	$-0.316213\pi$
$751$	22467.2	1.09167	0.545833	+	0.837894i	$0.316213\pi$
$752$	699.549	0.0339228
$753$	3398.80	0.164488
$754$	−103.666	−0.00500700
$755$	1565.88	0.0754808
$756$	8501.74	0.409002
$757$	9254.70	0.444343	0.222172	−	0.975008i	$-0.428685\pi$
$757$	9254.70	0.444343	0.222172	+	0.975008i	$0.428685\pi$
$758$	5102.01	0.244477
$759$	−1427.33	−0.0682591
$760$	1930.96	0.0921624
$761$	15482.0	0.737479	0.368739	−	0.929533i	$-0.379790\pi$
$761$	15482.0	0.737479	0.368739	+	0.929533i	$0.379790\pi$
$762$	800.857	0.0380735
$763$	50781.5	2.40945
$764$	24256.2	1.14864
$765$	716.216	0.0338495
$766$	5945.58	0.280447
$767$	−467.781	−0.0220216
$768$	−3016.89	−0.141748
$769$	−14148.0	−0.663448	−0.331724	−	0.943377i	$-0.607630\pi$
$769$	−14148.0	−0.663448	−0.331724	+	0.943377i	$0.607630\pi$
$770$	2217.77	0.103796
$771$	−6951.06	−0.324691
$772$	−19385.7	−0.903765
$773$	14157.1	0.658725	0.329362	−	0.944204i	$-0.393166\pi$
$773$	14157.1	0.658725	0.329362	+	0.944204i	$0.393166\pi$
$774$	14412.1	0.669293
$775$	966.615	0.0448024
$776$	−16206.1	−0.749698
$777$	−4277.80	−0.197510
$778$	−6988.94	−0.322064
$779$	2622.16	0.120602
$780$	−27.7385	−0.00127333
$781$	5636.71	0.258255
$782$	1050.24	0.0480264
$783$	−3937.00	−0.179690
$784$	6957.49	0.316941
$785$	9186.10	0.417664
$786$	−623.927	−0.0283139
$787$	−36498.1	−1.65313	−0.826567	−	0.562839i	$-0.809709\pi$
$787$	−36498.1	−1.65313	−0.826567	+	0.562839i	$0.809709\pi$
$788$	−7897.76	−0.357038
$789$	−276.598	−0.0124805
$790$	−6406.54	−0.288525
$791$	9465.44	0.425477
$792$	5813.53	0.260827
$793$	−199.876	−0.00895057
$794$	4193.03	0.187412
$795$	−1348.56	−0.0601615
$796$	−13577.1	−0.604558
$797$	20745.1	0.921993	0.460997	−	0.887402i	$-0.347492\pi$
$797$	20745.1	0.921993	0.460997	+	0.887402i	$0.347492\pi$
$798$	−765.593	−0.0339620
$799$	−227.844	−0.0100883
$800$	−4686.01	−0.207094
$801$	−33099.5	−1.46007
$802$	−16963.5	−0.746887
$803$	−254.921	−0.0112030
$804$	5092.50	0.223381
$805$	17831.7	0.780726
$806$	−53.9212	−0.00235645
$807$	2948.10	0.128597
$808$	36168.9	1.57477
$809$	−16878.4	−0.733513	−0.366757	−	0.930317i	$-0.619532\pi$
$809$	−16878.4	−0.733513	−0.366757	+	0.930317i	$0.619532\pi$
$810$	−4765.00	−0.206697
$811$	−6831.84	−0.295806	−0.147903	−	0.989002i	$-0.547252\pi$
$811$	−6831.84	−0.295806	−0.147903	+	0.989002i	$0.547252\pi$
$812$	−11932.1	−0.515685
$813$	8388.99	0.361888
$814$	−2517.18	−0.108387
$815$	19507.0	0.838405
$816$	−93.1161	−0.00399475
$817$	7173.18	0.307170
$818$	18696.4	0.799149
$819$	−678.349	−0.0289419
$820$	−4032.96	−0.171752
$821$	−14559.4	−0.618912	−0.309456	−	0.950914i	$-0.600147\pi$
$821$	−14559.4	−0.618912	−0.309456	+	0.950914i	$0.600147\pi$
$822$	1274.54	0.0540811
$823$	23405.6	0.991333	0.495667	−	0.868513i	$-0.334924\pi$
$823$	23405.6	0.991333	0.495667	+	0.868513i	$0.334924\pi$
$824$	2622.60	0.110877
$825$	−274.804	−0.0115969
$826$	19857.4	0.836474
$827$	7001.52	0.294398	0.147199	−	0.989107i	$-0.452974\pi$
$827$	7001.52	0.294398	0.147199	+	0.989107i	$0.452974\pi$
$828$	19732.7	0.828210
$829$	19603.5	0.821298	0.410649	−	0.911793i	$-0.365302\pi$
$829$	19603.5	0.821298	0.410649	+	0.911793i	$0.365302\pi$
$830$	−266.315	−0.0111373
$831$	−4771.79	−0.199195
$832$	132.867	0.00553648
$833$	−2266.06	−0.0942549
$834$	2608.80	0.108316
$835$	15854.1	0.657071
$836$	1221.50	0.0505342
$837$	−2047.82	−0.0845674
$838$	837.279	0.0345147
$839$	13398.8	0.551346	0.275673	−	0.961251i	$-0.411099\pi$
$839$	13398.8	0.551346	0.275673	+	0.961251i	$0.411099\pi$
$840$	2789.28	0.114571
$841$	−18863.4	−0.773440
$842$	−11983.1	−0.490457
$843$	−3966.00	−0.162036
$844$	−13830.6	−0.564061
$845$	−10980.5	−0.447030
$846$	1578.81	0.0641615
$847$	3323.28	0.134816
$848$	−4565.28	−0.184873
$849$	5679.21	0.229576
$850$	202.204	0.00815945
$851$	−20239.0	−0.815258
$852$	2992.75	0.120340
$853$	11175.1	0.448569	0.224284	−	0.974524i	$-0.427996\pi$
$853$	11175.1	0.448569	0.224284	+	0.974524i	$0.427996\pi$
$854$	8484.78	0.339980
$855$	−2470.14	−0.0988033
$856$	28139.9	1.12360
$857$	30444.6	1.21350	0.606748	−	0.794894i	$-0.292474\pi$
$857$	30444.6	1.21350	0.606748	+	0.794894i	$0.292474\pi$
$858$	15.3295	0.000609956 0
$859$	18409.9	0.731244	0.365622	−	0.930763i	$-0.380856\pi$
$859$	18409.9	0.731244	0.365622	+	0.930763i	$0.380856\pi$
$860$	−11032.6	−0.437450
$861$	3787.71	0.149924
$862$	11491.4	0.454061
$863$	3982.68	0.157094	0.0785468	−	0.996910i	$-0.474972\pi$
$863$	3982.68	0.157094	0.0785468	+	0.996910i	$0.474972\pi$
$864$	9927.52	0.390904
$865$	−4308.47	−0.169355
$866$	14641.6	0.574530
$867$	−4879.17	−0.191125
$868$	−6206.45	−0.242697
$869$	−9600.05	−0.374752
$870$	−545.282	−0.0212492
$871$	−828.259	−0.0322210
$872$	37581.5	1.45948
$873$	20731.3	0.803720
$874$	−3622.15	−0.140184
$875$	3433.14	0.132642
$876$	−135.348	−0.00522030
$877$	45406.3	1.74830	0.874151	−	0.485655i	$-0.161419\pi$
$877$	45406.3	1.74830	0.874151	+	0.485655i	$0.161419\pi$
$878$	20400.5	0.784149
$879$	4244.84	0.162884
$880$	−930.295	−0.0356366
$881$	−10197.7	−0.389977	−0.194989	−	0.980805i	$-0.562467\pi$
$881$	−10197.7	−0.389977	−0.194989	+	0.980805i	$0.562467\pi$
$882$	15702.3	0.599462
$883$	7588.55	0.289213	0.144607	−	0.989489i	$-0.453808\pi$
$883$	7588.55	0.289213	0.144607	+	0.989489i	$0.453808\pi$
$884$	30.5843	0.00116365
$885$	−2460.53	−0.0934573
$886$	−678.612	−0.0257319
$887$	−17626.5	−0.667237	−0.333618	−	0.942708i	$-0.608270\pi$
$887$	−17626.5	−0.667237	−0.333618	+	0.942708i	$0.608270\pi$
$888$	−3165.84	−0.119638
$889$	−14992.5	−0.565616
$890$	−9344.75	−0.351951
$891$	−7140.24	−0.268470
$892$	18456.4	0.692785
$893$	785.803	0.0294467
$894$	−4951.55	−0.185240
$895$	12451.4	0.465032
$896$	35544.4	1.32528
$897$	123.255	0.00458792
$898$	13833.2	0.514054
$899$	2874.10	0.106626
$900$	3799.14	0.140709
$901$	1486.91	0.0549792
$902$	2228.80	0.0822737
$903$	10361.7	0.381855
$904$	7005.02	0.257725
$905$	−1676.04	−0.0615619
$906$	−459.462	−0.0168484
$907$	−35631.0	−1.30442	−0.652209	−	0.758040i	$-0.726157\pi$
$907$	−35631.0	−1.30442	−0.652209	+	0.758040i	$0.726157\pi$
$908$	9689.36	0.354133
$909$	−46268.1	−1.68825
$910$	−191.513	−0.00697648
$911$	23992.4	0.872561	0.436281	−	0.899811i	$-0.356296\pi$
$911$	23992.4	0.872561	0.436281	+	0.899811i	$0.356296\pi$
$912$	321.145	0.0116603
$913$	−399.067	−0.0144657
$914$	23786.4	0.860813
$915$	−1051.35	−0.0379852
$916$	−2974.47	−0.107292
$917$	11680.3	0.420629
$918$	−428.378	−0.0154015
$919$	41244.8	1.48046	0.740229	−	0.672355i	$-0.234717\pi$
$919$	41244.8	1.48046	0.740229	+	0.672355i	$0.234717\pi$
$920$	13196.6	0.472911
$921$	5820.33	0.208237
$922$	−18446.6	−0.658901
$923$	−486.751	−0.0173582
$924$	1764.46	0.0628210
$925$	−3896.63	−0.138508
$926$	−9014.52	−0.319909
$927$	−3354.89	−0.118866
$928$	−13933.2	−0.492867
$929$	−45369.4	−1.60229	−0.801143	−	0.598473i	$-0.795774\pi$
$929$	−45369.4	−1.60229	−0.801143	+	0.598473i	$0.795774\pi$
$930$	−283.626	−0.0100005
$931$	7815.35	0.275121
$932$	−16698.1	−0.586873
$933$	−4670.79	−0.163896
$934$	7435.08	0.260475
$935$	302.998	0.0105980
$936$	−502.021	−0.0175310
$937$	5150.15	0.179560	0.0897802	−	0.995962i	$-0.471384\pi$
$937$	5150.15	0.179560	0.0897802	+	0.995962i	$0.471384\pi$
$938$	35159.8	1.22389
$939$	9804.34	0.340737
$940$	−1208.59	−0.0419360
$941$	9951.44	0.344748	0.172374	−	0.985032i	$-0.444856\pi$
$941$	9951.44	0.344748	0.172374	+	0.985032i	$0.444856\pi$
$942$	−2695.40	−0.0932282
$943$	17920.3	0.618840
$944$	−8329.64	−0.287189
$945$	−7273.27	−0.250370
$946$	6097.10	0.209550
$947$	32172.3	1.10397	0.551984	−	0.833854i	$-0.313871\pi$
$947$	32172.3	1.10397	0.551984	+	0.833854i	$0.313871\pi$
$948$	−5097.05	−0.174625
$949$	22.0134	0.000752988 0
$950$	−697.375	−0.0238167
$951$	445.093	0.0151768
$952$	−3075.45	−0.104702
$953$	−39981.3	−1.35899	−0.679497	−	0.733678i	$-0.737802\pi$
$953$	−39981.3	−1.35899	−0.679497	+	0.733678i	$0.737802\pi$
$954$	−10303.4	−0.349668
$955$	−20751.3	−0.703137
$956$	31210.3	1.05587
$957$	−817.092	−0.0275996
$958$	−27100.8	−0.913974
$959$	−23860.1	−0.803424
$960$	698.884	0.0234962
$961$	−28296.0	−0.949819
$962$	217.368	0.00728505
$963$	−35997.2	−1.20456
$964$	−32580.5	−1.08853
$965$	16584.5	0.553238
$966$	−5232.21	−0.174269
$967$	−26637.2	−0.885828	−0.442914	−	0.896564i	$-0.646055\pi$
$967$	−26637.2	−0.885828	−0.442914	+	0.896564i	$0.646055\pi$
$968$	2459.44	0.0816625
$969$	−104.597	−0.00346765
$970$	5852.90	0.193738
$971$	−47474.8	−1.56904	−0.784520	−	0.620104i	$-0.787090\pi$
$971$	−47474.8	−1.56904	−0.784520	+	0.620104i	$0.787090\pi$
$972$	−12148.8	−0.400898
$973$	−48838.3	−1.60913
$974$	−8468.28	−0.278584
$975$	23.7303	0.000779466 0
$976$	−3559.13	−0.116727
$977$	−1905.99	−0.0624136	−0.0312068	−	0.999513i	$-0.509935\pi$
$977$	−1905.99	−0.0624136	−0.0312068	+	0.999513i	$0.509935\pi$
$978$	−5723.78	−0.187143
$979$	−14002.9	−0.457134
$980$	−12020.2	−0.391809
$981$	−48075.2	−1.56465
$982$	8499.63	0.276206
$983$	33336.4	1.08166	0.540828	−	0.841133i	$-0.318111\pi$
$983$	33336.4	1.08166	0.540828	+	0.841133i	$0.318111\pi$
$984$	2803.15	0.0908140
$985$	6756.56	0.218560
$986$	601.226	0.0194188
$987$	1135.09	0.0366063
$988$	−105.481	−0.00339657
$989$	49022.9	1.57617
$990$	−2099.58	−0.0674031
$991$	−17080.5	−0.547506	−0.273753	−	0.961800i	$-0.588265\pi$
$991$	−17080.5	−0.547506	−0.273753	+	0.961800i	$0.588265\pi$
$992$	−7247.31	−0.231958
$993$	−3566.51	−0.113978
$994$	20662.7	0.659337
$995$	11615.3	0.370079
$996$	−211.881	−0.00674066
$997$	2113.88	0.0671486	0.0335743	−	0.999436i	$-0.489311\pi$
$997$	2113.88	0.0671486	0.0335743	+	0.999436i	$0.489311\pi$
$998$	21748.5	0.689815
$999$	8255.17	0.261444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.h.1.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.h.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.46816 q^{2} +0.999287 q^{3} -5.84451 q^{4} +5.00000 q^{5} -1.46711 q^{6} +27.4651 q^{7} +20.3259 q^{8} -26.0014 q^{9} +O(q^{10})\)	\(q-1.46816 q^{2} +0.999287 q^{3} -5.84451 q^{4} +5.00000 q^{5} -1.46711 q^{6} +27.4651 q^{7} +20.3259 q^{8} -26.0014 q^{9} -7.34079 q^{10} -11.0000 q^{11} -5.84034 q^{12} +0.949891 q^{13} -40.3232 q^{14} +4.99643 q^{15} +16.9145 q^{16} -5.50905 q^{17} +38.1742 q^{18} +19.0000 q^{19} -29.2226 q^{20} +27.4455 q^{21} +16.1497 q^{22} +129.850 q^{23} +20.3114 q^{24} +25.0000 q^{25} -1.39459 q^{26} -52.9636 q^{27} -160.520 q^{28} +74.3341 q^{29} -7.33555 q^{30} +38.6646 q^{31} -187.440 q^{32} -10.9922 q^{33} +8.08815 q^{34} +137.326 q^{35} +151.966 q^{36} -155.865 q^{37} -27.8950 q^{38} +0.949214 q^{39} +101.630 q^{40} +138.008 q^{41} -40.2944 q^{42} +377.536 q^{43} +64.2897 q^{44} -130.007 q^{45} -190.640 q^{46} +41.3581 q^{47} +16.9024 q^{48} +411.334 q^{49} -36.7039 q^{50} -5.50512 q^{51} -5.55165 q^{52} -269.904 q^{53} +77.7589 q^{54} -55.0000 q^{55} +558.254 q^{56} +18.9864 q^{57} -109.134 q^{58} -492.457 q^{59} -29.2017 q^{60} -210.420 q^{61} -56.7657 q^{62} -714.133 q^{63} +139.877 q^{64} +4.74946 q^{65} +16.1382 q^{66} -871.951 q^{67} +32.1977 q^{68} +129.757 q^{69} -201.616 q^{70} -512.428 q^{71} -528.503 q^{72} +23.1747 q^{73} +228.834 q^{74} +24.9822 q^{75} -111.046 q^{76} -302.117 q^{77} -1.39360 q^{78} +872.732 q^{79} +84.5723 q^{80} +649.113 q^{81} -202.618 q^{82} +36.2788 q^{83} -160.406 q^{84} -27.5453 q^{85} -554.282 q^{86} +74.2811 q^{87} -223.585 q^{88} +1272.99 q^{89} +190.871 q^{90} +26.0889 q^{91} -758.908 q^{92} +38.6370 q^{93} -60.7201 q^{94} +95.0000 q^{95} -187.307 q^{96} -797.313 q^{97} -603.903 q^{98} +286.016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) \) 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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