LMFDB - Embedded newform 983.4.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,4,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	983.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:	$57.9988775356$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.54428 q^{2} -2.38245 q^{3} +12.6505 q^{4} -17.0184 q^{5} +10.8265 q^{6} -0.746020 q^{7} -21.1331 q^{8} -21.3239 q^{9} +O(q^{10})$	\(q-4.54428 q^{2} -2.38245 q^{3} +12.6505 q^{4} -17.0184 q^{5} +10.8265 q^{6} -0.746020 q^{7} -21.1331 q^{8} -21.3239 q^{9} +77.3363 q^{10} -35.3169 q^{11} -30.1392 q^{12} -1.19409 q^{13} +3.39012 q^{14} +40.5455 q^{15} -5.16908 q^{16} +107.640 q^{17} +96.9018 q^{18} -119.550 q^{19} -215.291 q^{20} +1.77736 q^{21} +160.490 q^{22} -25.1970 q^{23} +50.3487 q^{24} +164.626 q^{25} +5.42627 q^{26} +115.130 q^{27} -9.43751 q^{28} +148.616 q^{29} -184.250 q^{30} -160.935 q^{31} +192.555 q^{32} +84.1410 q^{33} -489.148 q^{34} +12.6961 q^{35} -269.758 q^{36} -100.003 q^{37} +543.268 q^{38} +2.84486 q^{39} +359.652 q^{40} -201.335 q^{41} -8.07682 q^{42} +465.730 q^{43} -446.776 q^{44} +362.899 q^{45} +114.502 q^{46} +447.714 q^{47} +12.3151 q^{48} -342.443 q^{49} -748.105 q^{50} -256.448 q^{51} -15.1058 q^{52} +136.888 q^{53} -523.181 q^{54} +601.037 q^{55} +15.7657 q^{56} +284.822 q^{57} -675.353 q^{58} +184.437 q^{59} +512.921 q^{60} -225.460 q^{61} +731.335 q^{62} +15.9081 q^{63} -833.670 q^{64} +20.3215 q^{65} -382.360 q^{66} +40.3819 q^{67} +1361.70 q^{68} +60.0306 q^{69} -57.6944 q^{70} +954.712 q^{71} +450.641 q^{72} +293.706 q^{73} +454.441 q^{74} -392.213 q^{75} -1512.36 q^{76} +26.3471 q^{77} -12.9278 q^{78} -122.020 q^{79} +87.9695 q^{80} +301.455 q^{81} +914.924 q^{82} +146.365 q^{83} +22.4844 q^{84} -1831.87 q^{85} -2116.41 q^{86} -354.071 q^{87} +746.357 q^{88} +486.617 q^{89} -1649.11 q^{90} +0.890814 q^{91} -318.754 q^{92} +383.421 q^{93} -2034.54 q^{94} +2034.55 q^{95} -458.753 q^{96} +497.281 q^{97} +1556.16 q^{98} +753.095 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) $ 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9} - 243 q^{10} - 126 q^{11} - 280 q^{12} - 458 q^{13} - 177 q^{14} - 314 q^{15} + 1009 q^{16} - 594 q^{17} - 671 q^{18} - 491 q^{19} - 500 q^{20} - 660 q^{21} - 899 q^{22} - 487 q^{23} - 811 q^{24} + 705 q^{25} - 104 q^{26} - 842 q^{27} - 2648 q^{28} - 820 q^{29} - 728 q^{30} - 965 q^{31} - 1669 q^{32} - 2196 q^{33} - 508 q^{34} - 846 q^{35} + 1358 q^{36} - 3209 q^{37} - 1136 q^{38} - 1326 q^{39} - 3234 q^{40} - 1961 q^{41} - 2240 q^{42} - 2999 q^{43} - 1922 q^{44} - 2234 q^{45} - 2962 q^{46} - 1903 q^{47} - 2787 q^{48} + 1186 q^{49} - 2309 q^{50} - 2436 q^{51} - 4897 q^{52} - 1825 q^{53} - 3306 q^{54} - 2888 q^{55} - 1820 q^{56} - 6684 q^{57} - 4813 q^{58} - 1537 q^{59} - 3869 q^{60} - 2276 q^{61} - 1950 q^{62} - 6491 q^{63} - 89 q^{64} - 5546 q^{65} - 3527 q^{66} - 5005 q^{67} - 4183 q^{68} - 3018 q^{69} - 2993 q^{70} - 2014 q^{71} - 9549 q^{72} - 12904 q^{73} - 2714 q^{74} - 3379 q^{75} - 6293 q^{76} - 3258 q^{77} - 4593 q^{78} - 5005 q^{79} - 3988 q^{80} + 249 q^{81} - 5116 q^{82} - 2854 q^{83} - 4158 q^{84} - 11742 q^{85} - 2709 q^{86} - 2412 q^{87} - 10451 q^{88} - 2519 q^{89} - 8095 q^{90} - 2438 q^{91} - 6660 q^{92} - 10668 q^{93} - 4281 q^{94} - 4482 q^{95} - 6515 q^{96} - 16628 q^{97} - 5708 q^{98} - 6308 q^{99}+O(q^{100}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9 - 243 * q^10 - 126 * q^11 - 280 * q^12 - 458 * q^13 - 177 * q^14 - 314 * q^15 + 1009 * q^16 - 594 * q^17 - 671 * q^18 - 491 * q^19 - 500 * q^20 - 660 * q^21 - 899 * q^22 - 487 * q^23 - 811 * q^24 + 705 * q^25 - 104 * q^26 - 842 * q^27 - 2648 * q^28 - 820 * q^29 - 728 * q^30 - 965 * q^31 - 1669 * q^32 - 2196 * q^33 - 508 * q^34 - 846 * q^35 + 1358 * q^36 - 3209 * q^37 - 1136 * q^38 - 1326 * q^39 - 3234 * q^40 - 1961 * q^41 - 2240 * q^42 - 2999 * q^43 - 1922 * q^44 - 2234 * q^45 - 2962 * q^46 - 1903 * q^47 - 2787 * q^48 + 1186 * q^49 - 2309 * q^50 - 2436 * q^51 - 4897 * q^52 - 1825 * q^53 - 3306 * q^54 - 2888 * q^55 - 1820 * q^56 - 6684 * q^57 - 4813 * q^58 - 1537 * q^59 - 3869 * q^60 - 2276 * q^61 - 1950 * q^62 - 6491 * q^63 - 89 * q^64 - 5546 * q^65 - 3527 * q^66 - 5005 * q^67 - 4183 * q^68 - 3018 * q^69 - 2993 * q^70 - 2014 * q^71 - 9549 * q^72 - 12904 * q^73 - 2714 * q^74 - 3379 * q^75 - 6293 * q^76 - 3258 * q^77 - 4593 * q^78 - 5005 * q^79 - 3988 * q^80 + 249 * q^81 - 5116 * q^82 - 2854 * q^83 - 4158 * q^84 - 11742 * q^85 - 2709 * q^86 - 2412 * q^87 - 10451 * q^88 - 2519 * q^89 - 8095 * q^90 - 2438 * q^91 - 6660 * q^92 - 10668 * q^93 - 4281 * q^94 - 4482 * q^95 - 6515 * q^96 - 16628 * q^97 - 5708 * q^98 - 6308 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.54428	−1.60665	−0.803323	−	0.595544i	$-0.796937\pi$
$2$	−4.54428	−1.60665	−0.803323	+	0.595544i	$0.796937\pi$
$3$	−2.38245	−0.458504	−0.229252	−	0.973367i	$-0.573628\pi$
$3$	−2.38245	−0.458504	−0.229252	+	0.973367i	$0.573628\pi$
$4$	12.6505	1.58131
$5$	−17.0184	−1.52217	−0.761085	−	0.648652i	$-0.775333\pi$
$5$	−17.0184	−1.52217	−0.761085	+	0.648652i	$0.775333\pi$
$6$	10.8265	0.736653
$7$	−0.746020	−0.0402813	−0.0201406	−	0.999797i	$-0.506411\pi$
$7$	−0.746020	−0.0402813	−0.0201406	+	0.999797i	$0.506411\pi$
$8$	−21.1331	−0.933961
$9$	−21.3239	−0.789774
$10$	77.3363	2.44559
$11$	−35.3169	−0.968042	−0.484021	−	0.875056i	$-0.660824\pi$
$11$	−35.3169	−0.968042	−0.484021	+	0.875056i	$0.660824\pi$
$12$	−30.1392	−0.725037
$13$	−1.19409	−0.0254754	−0.0127377	−	0.999919i	$-0.504055\pi$
$13$	−1.19409	−0.0254754	−0.0127377	+	0.999919i	$0.504055\pi$
$14$	3.39012	0.0647178
$15$	40.5455	0.697921
$16$	−5.16908	−0.0807669
$17$	107.640	1.53568	0.767842	−	0.640640i	$-0.221331\pi$
$17$	107.640	1.53568	0.767842	+	0.640640i	$0.221331\pi$
$18$	96.9018	1.26889
$19$	−119.550	−1.44351	−0.721753	−	0.692150i	$-0.756664\pi$
$19$	−119.550	−1.44351	−0.721753	+	0.692150i	$0.756664\pi$
$20$	−215.291	−2.40703
$21$	1.77736	0.0184691
$22$	160.490	1.55530
$23$	−25.1970	−0.228432	−0.114216	−	0.993456i	$-0.536436\pi$
$23$	−25.1970	−0.228432	−0.114216	+	0.993456i	$0.536436\pi$
$24$	50.3487	0.428224
$25$	164.626	1.31700
$26$	5.42627	0.0409300
$27$	115.130	0.820618
$28$	−9.43751	−0.0636972
$29$	148.616	0.951631	0.475816	−	0.879545i	$-0.342153\pi$
$29$	148.616	0.951631	0.475816	+	0.879545i	$0.342153\pi$
$30$	−184.250	−1.12131
$31$	−160.935	−0.932414	−0.466207	−	0.884676i	$-0.654380\pi$
$31$	−160.935	−0.932414	−0.466207	+	0.884676i	$0.654380\pi$
$32$	192.555	1.06372
$33$	84.1410	0.443851
$34$	−489.148	−2.46730
$35$	12.6961	0.0613150
$36$	−269.758	−1.24888
$37$	−100.003	−0.444334	−0.222167	−	0.975009i	$-0.571313\pi$
$37$	−100.003	−0.444334	−0.222167	+	0.975009i	$0.571313\pi$
$38$	543.268	2.31920
$39$	2.84486	0.0116806
$40$	359.652	1.42165
$41$	−201.335	−0.766910	−0.383455	−	0.923560i	$-0.625266\pi$
$41$	−201.335	−0.766910	−0.383455	+	0.923560i	$0.625266\pi$
$42$	−8.07682	−0.0296733
$43$	465.730	1.65170	0.825850	−	0.563889i	$-0.190695\pi$
$43$	465.730	1.65170	0.825850	+	0.563889i	$0.190695\pi$
$44$	−446.776	−1.53077
$45$	362.899	1.20217
$46$	114.502	0.367009
$47$	447.714	1.38948	0.694742	−	0.719259i	$-0.255519\pi$
$47$	447.714	1.38948	0.694742	+	0.719259i	$0.255519\pi$
$48$	12.3151	0.0370319
$49$	−342.443	−0.998377
$50$	−748.105	−2.11596
$51$	−256.448	−0.704116
$52$	−15.1058	−0.0402846
$53$	136.888	0.354774	0.177387	−	0.984141i	$-0.443236\pi$
$53$	136.888	0.354774	0.177387	+	0.984141i	$0.443236\pi$
$54$	−523.181	−1.31844
$55$	601.037	1.47352
$56$	15.7657	0.0376211
$57$	284.822	0.661853
$58$	−675.353	−1.52893
$59$	184.437	0.406976	0.203488	−	0.979077i	$-0.434772\pi$
$59$	184.437	0.406976	0.203488	+	0.979077i	$0.434772\pi$
$60$	512.921	1.10363
$61$	−225.460	−0.473233	−0.236617	−	0.971603i	$-0.576039\pi$
$61$	−225.460	−0.473233	−0.236617	+	0.971603i	$0.576039\pi$
$62$	731.335	1.49806
$63$	15.9081	0.0318131
$64$	−833.670	−1.62826
$65$	20.3215	0.0387780
$66$	−382.360	−0.713111
$67$	40.3819	0.0736333	0.0368166	−	0.999322i	$-0.488278\pi$
$67$	40.3819	0.0736333	0.0368166	+	0.999322i	$0.488278\pi$
$68$	1361.70	2.42839
$69$	60.0306	0.104737
$70$	−57.6944	−0.0985115
$71$	954.712	1.59582	0.797912	−	0.602774i	$-0.205938\pi$
$71$	954.712	1.59582	0.797912	+	0.602774i	$0.205938\pi$
$72$	450.641	0.737618
$73$	293.706	0.470899	0.235450	−	0.971887i	$-0.424344\pi$
$73$	293.706	0.470899	0.235450	+	0.971887i	$0.424344\pi$
$74$	454.441	0.713888
$75$	−392.213	−0.603851
$76$	−1512.36	−2.28263
$77$	26.3471	0.0389940
$78$	−12.9278	−0.0187665
$79$	−122.020	−0.173777	−0.0868883	−	0.996218i	$-0.527692\pi$
$79$	−122.020	−0.173777	−0.0868883	+	0.996218i	$0.527692\pi$
$80$	87.9695	0.122941
$81$	301.455	0.413518
$82$	914.924	1.23215
$83$	146.365	0.193561	0.0967807	−	0.995306i	$-0.469145\pi$
$83$	146.365	0.193561	0.0967807	+	0.995306i	$0.469145\pi$
$84$	22.4844	0.0292054
$85$	−1831.87	−2.33757
$86$	−2116.41	−2.65370
$87$	−354.071	−0.436326
$88$	746.357	0.904113
$89$	486.617	0.579565	0.289782	−	0.957093i	$-0.406417\pi$
$89$	486.617	0.579565	0.289782	+	0.957093i	$0.406417\pi$
$90$	−1649.11	−1.93146
$91$	0.890814	0.00102618
$92$	−318.754	−0.361222
$93$	383.421	0.427515
$94$	−2034.54	−2.23241
$95$	2034.55	2.19726
$96$	−458.753	−0.487722
$97$	497.281	0.520528	0.260264	−	0.965537i	$-0.416190\pi$
$97$	497.281	0.520528	0.260264	+	0.965537i	$0.416190\pi$
$98$	1556.16	1.60404
$99$	753.095	0.764535
$100$	2082.59	2.08259
$101$	638.567	0.629107	0.314553	−	0.949240i	$-0.398145\pi$
$101$	638.567	0.629107	0.314553	+	0.949240i	$0.398145\pi$
$102$	1165.37	1.13127
$103$	308.737	0.295348	0.147674	−	0.989036i	$-0.452821\pi$
$103$	308.737	0.295348	0.147674	+	0.989036i	$0.452821\pi$
$104$	25.2348	0.0237930
$105$	−30.2478	−0.0281131
$106$	−622.058	−0.569996
$107$	−661.625	−0.597773	−0.298887	−	0.954289i	$-0.596615\pi$
$107$	−661.625	−0.597773	−0.298887	+	0.954289i	$0.596615\pi$
$108$	1456.44	1.29765
$109$	1919.79	1.68700	0.843500	−	0.537130i	$-0.180491\pi$
$109$	1919.79	1.68700	0.843500	+	0.537130i	$0.180491\pi$
$110$	−2731.28	−2.36743
$111$	238.252	0.203729
$112$	3.85624	0.00325340
$113$	272.416	0.226786	0.113393	−	0.993550i	$-0.463828\pi$
$113$	272.416	0.226786	0.113393	+	0.993550i	$0.463828\pi$
$114$	−1294.31	−1.06336
$115$	428.812	0.347712
$116$	1880.07	1.50482
$117$	25.4626	0.0201198
$118$	−838.131	−0.653867
$119$	−80.3018	−0.0618593
$120$	−856.854	−0.651831
$121$	−83.7137	−0.0628954
$122$	1024.55	0.760318
$123$	479.672	0.351631
$124$	−2035.91	−1.47444
$125$	−674.363	−0.482535
$126$	−72.2907	−0.0511124
$127$	−1300.26	−0.908499	−0.454250	−	0.890874i	$-0.650093\pi$
$127$	−1300.26	−0.908499	−0.454250	+	0.890874i	$0.650093\pi$
$128$	2247.99	1.55232
$129$	−1109.58	−0.757311
$130$	−92.3464	−0.0623024
$131$	2236.56	1.49167	0.745835	−	0.666131i	$-0.232051\pi$
$131$	2236.56	1.49167	0.745835	+	0.666131i	$0.232051\pi$
$132$	1064.42	0.701866
$133$	89.1866	0.0581463
$134$	−183.507	−0.118303
$135$	−1959.32	−1.24912
$136$	−2274.78	−1.43427
$137$	−2288.68	−1.42726	−0.713631	−	0.700522i	$-0.752950\pi$
$137$	−2288.68	−1.42726	−0.713631	+	0.700522i	$0.752950\pi$
$138$	−272.796	−0.168275
$139$	2029.01	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$139$	2029.01	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$140$	160.611	0.0969581
$141$	−1066.66	−0.637083
$142$	−4338.48	−2.56392
$143$	42.1715	0.0246613
$144$	110.225	0.0637877
$145$	−2529.21	−1.44855
$146$	−1334.68	−0.756568
$147$	815.856	0.457760
$148$	−1265.08	−0.702631
$149$	−1333.83	−0.733367	−0.366683	−	0.930346i	$-0.619507\pi$
$149$	−1333.83	−0.733367	−0.366683	+	0.930346i	$0.619507\pi$
$150$	1782.33	0.970175
$151$	78.0243	0.0420499	0.0210249	−	0.999779i	$-0.493307\pi$
$151$	78.0243	0.0420499	0.0210249	+	0.999779i	$0.493307\pi$
$152$	2526.46	1.34818
$153$	−2295.31	−1.21284
$154$	−119.729	−0.0626495
$155$	2738.86	1.41929
$156$	35.9889	0.0184706
$157$	−1572.35	−0.799281	−0.399640	−	0.916672i	$-0.630865\pi$
$157$	−1572.35	−0.799281	−0.399640	+	0.916672i	$0.630865\pi$
$158$	554.494	0.279197
$159$	−326.130	−0.162665
$160$	−3276.97	−1.61917
$161$	18.7974	0.00920153
$162$	−1369.89	−0.664377
$163$	−2621.91	−1.25990	−0.629951	−	0.776635i	$-0.716925\pi$
$163$	−2621.91	−1.25990	−0.629951	+	0.776635i	$0.716925\pi$
$164$	−2546.99	−1.21272
$165$	−1431.94	−0.675617
$166$	−665.121	−0.310985
$167$	−2490.30	−1.15392	−0.576961	−	0.816772i	$-0.695762\pi$
$167$	−2490.30	−1.15392	−0.576961	+	0.816772i	$0.695762\pi$
$168$	−37.5611	−0.0172494
$169$	−2195.57	−0.999351
$170$	8324.51	3.75565
$171$	2549.27	1.14004
$172$	5891.71	2.61185
$173$	−225.134	−0.0989401	−0.0494701	−	0.998776i	$-0.515753\pi$
$173$	−225.134	−0.0989401	−0.0494701	+	0.998776i	$0.515753\pi$
$174$	1609.00	0.701022
$175$	−122.814	−0.0530506
$176$	182.556	0.0781858
$177$	−439.412	−0.186600
$178$	−2211.32	−0.931155
$179$	4367.53	1.82371	0.911856	−	0.410510i	$-0.134649\pi$
$179$	4367.53	1.82371	0.911856	+	0.410510i	$0.134649\pi$
$180$	4590.84	1.90101
$181$	1111.32	0.456376	0.228188	−	0.973617i	$-0.426720\pi$
$181$	1111.32	0.456376	0.228188	+	0.973617i	$0.426720\pi$
$182$	−4.04811	−0.00164871
$183$	537.149	0.216979
$184$	532.490	0.213346
$185$	1701.89	0.676353
$186$	−1742.37	−0.686865
$187$	−3801.53	−1.48661
$188$	5663.80	2.19721
$189$	−85.8889	−0.0330555
$190$	−9245.55	−3.53023
$191$	−3628.20	−1.37449	−0.687244	−	0.726427i	$-0.741180\pi$
$191$	−3628.20	−1.37449	−0.687244	+	0.726427i	$0.741180\pi$
$192$	1986.18	0.746564
$193$	−2050.56	−0.764781	−0.382391	−	0.924001i	$-0.624899\pi$
$193$	−2050.56	−0.764781	−0.382391	+	0.924001i	$0.624899\pi$
$194$	−2259.78	−0.836304
$195$	−48.4150	−0.0177798
$196$	−4332.08	−1.57875
$197$	2328.72	0.842207	0.421103	−	0.907013i	$-0.361643\pi$
$197$	2328.72	0.842207	0.421103	+	0.907013i	$0.361643\pi$
$198$	−3422.28	−1.22834
$199$	−4587.82	−1.63428	−0.817140	−	0.576439i	$-0.804442\pi$
$199$	−4587.82	−1.63428	−0.817140	+	0.576439i	$0.804442\pi$
$200$	−3479.05	−1.23003
$201$	−96.2080	−0.0337611
$202$	−2901.83	−1.01075
$203$	−110.871	−0.0383329
$204$	−3244.20	−1.11343
$205$	3426.40	1.16737
$206$	−1402.99	−0.474519
$207$	537.298	0.180410
$208$	6.17234	0.00205757
$209$	4222.14	1.39737
$210$	137.454	0.0451679
$211$	3238.05	1.05648	0.528239	−	0.849096i	$-0.322853\pi$
$211$	3238.05	1.05648	0.528239	+	0.849096i	$0.322853\pi$
$212$	1731.70	0.561008
$213$	−2274.56	−0.731691
$214$	3006.61	0.960410
$215$	−7925.97	−2.51417
$216$	−2433.05	−0.766425
$217$	120.061	0.0375588
$218$	−8724.08	−2.71041
$219$	−699.740	−0.215909
$220$	7603.42	2.33010
$221$	−128.532	−0.0391222
$222$	−1082.69	−0.327320
$223$	−4525.65	−1.35901	−0.679506	−	0.733670i	$-0.737806\pi$
$223$	−4525.65	−1.35901	−0.679506	+	0.733670i	$0.737806\pi$
$224$	−143.650	−0.0428482
$225$	−3510.46	−1.04014
$226$	−1237.94	−0.364364
$227$	−5947.03	−1.73885	−0.869424	−	0.494067i	$-0.835510\pi$
$227$	−5947.03	−1.73885	−0.869424	+	0.494067i	$0.835510\pi$
$228$	3603.14	1.04660
$229$	−4626.76	−1.33513	−0.667565	−	0.744552i	$-0.732663\pi$
$229$	−4626.76	−1.33513	−0.667565	+	0.744552i	$0.732663\pi$
$230$	−1948.64	−0.558650
$231$	−62.7709	−0.0178789
$232$	−3140.72	−0.888786
$233$	2820.24	0.792961	0.396480	−	0.918043i	$-0.370231\pi$
$233$	2820.24	0.792961	0.396480	+	0.918043i	$0.370231\pi$
$234$	−115.709	−0.0323255
$235$	−7619.37	−2.11503
$236$	2333.21	0.643556
$237$	290.708	0.0796772
$238$	364.914	0.0993860
$239$	−3154.25	−0.853687	−0.426844	−	0.904325i	$-0.640375\pi$
$239$	−3154.25	−0.853687	−0.426844	+	0.904325i	$0.640375\pi$
$240$	−209.583	−0.0563689
$241$	156.845	0.0419223	0.0209611	−	0.999780i	$-0.493327\pi$
$241$	156.845	0.0419223	0.0209611	+	0.999780i	$0.493327\pi$
$242$	380.419	0.101051
$243$	−3826.70	−1.01022
$244$	−2852.18	−0.748329
$245$	5827.84	1.51970
$246$	−2179.77	−0.564946
$247$	142.753	0.0367739
$248$	3401.06	0.870838
$249$	−348.707	−0.0887486
$250$	3064.50	0.775263
$251$	−5082.64	−1.27814	−0.639070	−	0.769149i	$-0.720681\pi$
$251$	−5082.64	−1.27814	−0.639070	+	0.769149i	$0.720681\pi$
$252$	201.245	0.0503064
$253$	889.880	0.221131
$254$	5908.74	1.45964
$255$	4364.34	1.07179
$256$	−3546.15	−0.865759
$257$	−761.560	−0.184844	−0.0924218	−	0.995720i	$-0.529461\pi$
$257$	−761.560	−0.184844	−0.0924218	+	0.995720i	$0.529461\pi$
$258$	5042.24	1.21673
$259$	74.6041	0.0178984
$260$	257.076	0.0613200
$261$	−3169.08	−0.751574
$262$	−10163.5	−2.39659
$263$	1377.61	0.322992	0.161496	−	0.986873i	$-0.448368\pi$
$263$	1377.61	0.322992	0.161496	+	0.986873i	$0.448368\pi$
$264$	−1778.16	−0.414539
$265$	−2329.61	−0.540027
$266$	−405.289	−0.0934205
$267$	−1159.34	−0.265733
$268$	510.850	0.116437
$269$	−5677.00	−1.28674	−0.643369	−	0.765556i	$-0.722464\pi$
$269$	−5677.00	−1.28674	−0.643369	+	0.765556i	$0.722464\pi$
$270$	8903.70	2.00690
$271$	3116.99	0.698686	0.349343	−	0.936995i	$-0.386405\pi$
$271$	3116.99	0.698686	0.349343	+	0.936995i	$0.386405\pi$
$272$	−556.402	−0.124032
$273$	−2.12232	−0.000470509 0
$274$	10400.4	2.29310
$275$	−5814.07	−1.27492
$276$	759.417	0.165621
$277$	−97.3574	−0.0211178	−0.0105589	−	0.999944i	$-0.503361\pi$
$277$	−97.3574	−0.0211178	−0.0105589	+	0.999944i	$0.503361\pi$
$278$	−9220.39	−1.98922
$279$	3431.77	0.736396
$280$	−268.307	−0.0572658
$281$	−6997.15	−1.48546	−0.742731	−	0.669589i	$-0.766470\pi$
$281$	−6997.15	−1.48546	−0.742731	+	0.669589i	$0.766470\pi$
$282$	4847.19	1.02357
$283$	7395.21	1.55336	0.776678	−	0.629898i	$-0.216903\pi$
$283$	7395.21	1.55336	0.776678	+	0.629898i	$0.216903\pi$
$284$	12077.6	2.52349
$285$	−4847.22	−1.00745
$286$	−191.639	−0.0396219
$287$	150.200	0.0308921
$288$	−4106.02	−0.840102
$289$	6673.44	1.35832
$290$	11493.4	2.32730
$291$	−1184.75	−0.238664
$292$	3715.52	0.744638
$293$	4124.65	0.822405	0.411202	−	0.911544i	$-0.365109\pi$
$293$	4124.65	0.822405	0.411202	+	0.911544i	$0.365109\pi$
$294$	−3707.48	−0.735458
$295$	−3138.81	−0.619487
$296$	2113.37	0.414991
$297$	−4066.02	−0.794392
$298$	6061.30	1.17826
$299$	30.0874	0.00581940
$300$	−4961.68	−0.954877
$301$	−347.444	−0.0665326
$302$	−354.564	−0.0675592
$303$	−1521.36	−0.288448
$304$	617.963	0.116588
$305$	3836.97	0.720342
$306$	10430.5	1.94861
$307$	4665.85	0.867408	0.433704	−	0.901055i	$-0.357206\pi$
$307$	4665.85	0.867408	0.433704	+	0.901055i	$0.357206\pi$
$308$	333.304	0.0616616
$309$	−735.553	−0.135418
$310$	−12446.1	−2.28030
$311$	2147.13	0.391488	0.195744	−	0.980655i	$-0.437288\pi$
$311$	2147.13	0.391488	0.195744	+	0.980655i	$0.437288\pi$
$312$	−60.1208	−0.0109092
$313$	401.606	0.0725243	0.0362622	−	0.999342i	$-0.488455\pi$
$313$	401.606	0.0725243	0.0362622	+	0.999342i	$0.488455\pi$
$314$	7145.19	1.28416
$315$	−270.730	−0.0484250
$316$	−1543.62	−0.274795
$317$	3764.50	0.666988	0.333494	−	0.942752i	$-0.391772\pi$
$317$	3764.50	0.666988	0.333494	+	0.942752i	$0.391772\pi$
$318$	1482.02	0.261345
$319$	−5248.66	−0.921219
$320$	14187.7	2.47849
$321$	1576.29	0.274081
$322$	−85.4208	−0.0147836
$323$	−12868.4	−2.21677
$324$	3813.55	0.653901
$325$	−196.577	−0.0335513
$326$	11914.7	2.02422
$327$	−4573.82	−0.773495
$328$	4254.84	0.716264
$329$	−334.003	−0.0559702
$330$	6507.16	1.08548
$331$	380.738	0.0632244	0.0316122	−	0.999500i	$-0.489936\pi$
$331$	380.738	0.0632244	0.0316122	+	0.999500i	$0.489936\pi$
$332$	1851.58	0.306081
$333$	2132.45	0.350924
$334$	11316.6	1.85394
$335$	−687.234	−0.112082
$336$	−9.18731	−0.00149169
$337$	−2459.18	−0.397507	−0.198753	−	0.980050i	$-0.563689\pi$
$337$	−2459.18	−0.397507	−0.198753	+	0.980050i	$0.563689\pi$
$338$	9977.31	1.60560
$339$	−649.020	−0.103982
$340$	−23174.0	−3.69643
$341$	5683.74	0.902615
$342$	−11584.6	−1.83165
$343$	511.354	0.0804972
$344$	−9842.32	−1.54262
$345$	−1021.62	−0.159427
$346$	1023.07	0.158962
$347$	−1207.49	−0.186806	−0.0934030	−	0.995628i	$-0.529774\pi$
$347$	−1207.49	−0.186806	−0.0934030	+	0.995628i	$0.529774\pi$
$348$	−4479.17	−0.689968
$349$	6056.20	0.928885	0.464442	−	0.885603i	$-0.346255\pi$
$349$	6056.20	0.928885	0.464442	+	0.885603i	$0.346255\pi$
$350$	558.101	0.0852336
$351$	−137.475	−0.0209056
$352$	−6800.44	−1.02973
$353$	12601.4	1.90002	0.950009	−	0.312222i	$-0.101073\pi$
$353$	12601.4	1.90002	0.950009	+	0.312222i	$0.101073\pi$
$354$	1996.81	0.299800
$355$	−16247.7	−2.42912
$356$	6155.94	0.916472
$357$	191.315	0.0283627
$358$	−19847.3	−2.93006
$359$	−524.495	−0.0771081	−0.0385541	−	0.999257i	$-0.512275\pi$
$359$	−524.495	−0.0771081	−0.0385541	+	0.999257i	$0.512275\pi$
$360$	−7669.18	−1.12278
$361$	7433.18	1.08371
$362$	−5050.17	−0.733235
$363$	199.444	0.0288378
$364$	11.2692	0.00162271
$365$	−4998.40	−0.716789
$366$	−2440.95	−0.348609
$367$	10015.4	1.42453	0.712263	−	0.701913i	$-0.247671\pi$
$367$	10015.4	1.42453	0.712263	+	0.701913i	$0.247671\pi$
$368$	130.245	0.0184497
$369$	4293.26	0.605686
$370$	−7733.85	−1.08666
$371$	−102.121	−0.0142908
$372$	4850.46	0.676034
$373$	947.769	0.131565	0.0657823	−	0.997834i	$-0.479046\pi$
$373$	947.769	0.131565	0.0657823	+	0.997834i	$0.479046\pi$
$374$	17275.2	2.38845
$375$	1606.64	0.221244
$376$	−9461.58	−1.29772
$377$	−177.461	−0.0242432
$378$	390.303	0.0531086
$379$	−6075.76	−0.823459	−0.411729	−	0.911306i	$-0.635075\pi$
$379$	−6075.76	−0.823459	−0.411729	+	0.911306i	$0.635075\pi$
$380$	25738.0	3.47456
$381$	3097.81	0.416550
$382$	16487.5	2.20832
$383$	5554.81	0.741090	0.370545	−	0.928815i	$-0.379171\pi$
$383$	5554.81	0.741090	0.370545	+	0.928815i	$0.379171\pi$
$384$	−5355.74	−0.711742
$385$	−448.386	−0.0593555
$386$	9318.34	1.22873
$387$	−9931.18	−1.30447
$388$	6290.84	0.823117
$389$	2306.94	0.300686	0.150343	−	0.988634i	$-0.451962\pi$
$389$	2306.94	0.300686	0.150343	+	0.988634i	$0.451962\pi$
$390$	220.011	0.0285659
$391$	−2712.21	−0.350799
$392$	7236.90	0.932445
$393$	−5328.49	−0.683936
$394$	−10582.4	−1.35313
$395$	2076.59	0.264518
$396$	9527.02	1.20897
$397$	5173.06	0.653976	0.326988	−	0.945029i	$-0.393966\pi$
$397$	5173.06	0.653976	0.326988	+	0.945029i	$0.393966\pi$
$398$	20848.3	2.62571
$399$	−212.483	−0.0266603
$400$	−850.963	−0.106370
$401$	−9420.32	−1.17314	−0.586569	−	0.809899i	$-0.699522\pi$
$401$	−9420.32	−1.17314	−0.586569	+	0.809899i	$0.699522\pi$
$402$	437.196	0.0542422
$403$	192.171	0.0237536
$404$	8078.18	0.994813
$405$	−5130.27	−0.629445
$406$	503.827	0.0615874
$407$	3531.79	0.430134
$408$	5419.55	0.657617
$409$	4469.61	0.540362	0.270181	−	0.962810i	$-0.412917\pi$
$409$	4469.61	0.540362	0.270181	+	0.962810i	$0.412917\pi$
$410$	−15570.5	−1.87555
$411$	5452.67	0.654404
$412$	3905.68	0.467036
$413$	−137.593	−0.0163935
$414$	−2441.63	−0.289854
$415$	−2490.89	−0.294633
$416$	−229.927	−0.0270988
$417$	−4834.02	−0.567682
$418$	−19186.6	−2.24509
$419$	3208.26	0.374066	0.187033	−	0.982354i	$-0.440113\pi$
$419$	3208.26	0.374066	0.187033	+	0.982354i	$0.440113\pi$
$420$	−382.649	−0.0444556
$421$	4826.97	0.558793	0.279397	−	0.960176i	$-0.409866\pi$
$421$	4826.97	0.558793	0.279397	+	0.960176i	$0.409866\pi$
$422$	−14714.6	−1.69739
$423$	−9547.01	−1.09738
$424$	−2892.87	−0.331345
$425$	17720.4	2.02250
$426$	10336.2	1.17557
$427$	168.198	0.0190624
$428$	−8369.88	−0.945265
$429$	−100.472	−0.0113073
$430$	36017.8	4.03938
$431$	12682.2	1.41735	0.708675	−	0.705535i	$-0.249293\pi$
$431$	12682.2	1.41735	0.708675	+	0.705535i	$0.249293\pi$
$432$	−595.114	−0.0662788
$433$	7286.16	0.808661	0.404331	−	0.914613i	$-0.367505\pi$
$433$	7286.16	0.808661	0.404331	+	0.914613i	$0.367505\pi$
$434$	−545.590	−0.0603437
$435$	6025.72	0.664163
$436$	24286.3	2.66767
$437$	3012.30	0.329743
$438$	3179.82	0.346889
$439$	−2555.21	−0.277799	−0.138899	−	0.990306i	$-0.544356\pi$
$439$	−2555.21	−0.277799	−0.138899	+	0.990306i	$0.544356\pi$
$440$	−12701.8	−1.37621
$441$	7302.23	0.788493
$442$	584.086	0.0628555
$443$	6971.91	0.747733	0.373866	−	0.927483i	$-0.378032\pi$
$443$	6971.91	0.747733	0.373866	+	0.927483i	$0.378032\pi$
$444$	3014.01	0.322159
$445$	−8281.43	−0.882197
$446$	20565.8	2.18345
$447$	3177.79	0.336251
$448$	621.934	0.0655885
$449$	−13441.3	−1.41277	−0.706387	−	0.707826i	$-0.749676\pi$
$449$	−13441.3	−1.41277	−0.706387	+	0.707826i	$0.749676\pi$
$450$	15952.5	1.67113
$451$	7110.55	0.742401
$452$	3446.20	0.358619
$453$	−185.889	−0.0192800
$454$	27025.0	2.79371
$455$	−15.1602	−0.00156203
$456$	−6019.18	−0.618145
$457$	16615.2	1.70071	0.850356	−	0.526208i	$-0.176387\pi$
$457$	16615.2	1.70071	0.850356	+	0.526208i	$0.176387\pi$
$458$	21025.3	2.14508
$459$	12392.6	1.26021
$460$	5424.68	0.549841
$461$	609.903	0.0616182	0.0308091	−	0.999525i	$-0.490192\pi$
$461$	609.903	0.0616182	0.0308091	+	0.999525i	$0.490192\pi$
$462$	285.248	0.0287250
$463$	−13505.4	−1.35562	−0.677808	−	0.735239i	$-0.737070\pi$
$463$	−13505.4	−1.35562	−0.677808	+	0.735239i	$0.737070\pi$
$464$	−768.209	−0.0768603
$465$	−6525.21	−0.650751
$466$	−12815.9	−1.27401
$467$	−7392.29	−0.732494	−0.366247	−	0.930518i	$-0.619357\pi$
$467$	−7392.29	−0.732494	−0.366247	+	0.930518i	$0.619357\pi$
$468$	322.115	0.0318157
$469$	−30.1257	−0.00296604
$470$	34624.5	3.39811
$471$	3746.05	0.366473
$472$	−3897.72	−0.380100
$473$	−16448.2	−1.59892
$474$	−1321.06	−0.128013
$475$	−19681.0	−1.90110
$476$	−1015.86	−0.0978188
$477$	−2918.99	−0.280191
$478$	14333.8	1.37157
$479$	2207.84	0.210603	0.105302	−	0.994440i	$-0.466419\pi$
$479$	2207.84	0.210603	0.105302	+	0.994440i	$0.466419\pi$
$480$	7807.23	0.742396
$481$	119.412	0.0113196
$482$	−712.748	−0.0673543
$483$	−44.7840	−0.00421893
$484$	−1059.02	−0.0994571
$485$	−8462.92	−0.792333
$486$	17389.6	1.62306
$487$	506.538	0.0471323	0.0235661	−	0.999722i	$-0.492498\pi$
$487$	506.538	0.0471323	0.0235661	+	0.999722i	$0.492498\pi$
$488$	4764.68	0.441981
$489$	6246.58	0.577669
$490$	−26483.3	−2.44162
$491$	11293.7	1.03804	0.519018	−	0.854763i	$-0.326298\pi$
$491$	11293.7	1.03804	0.519018	+	0.854763i	$0.326298\pi$
$492$	6068.09	0.556038
$493$	15997.1	1.46140
$494$	−648.710	−0.0590827
$495$	−12816.5	−1.16375
$496$	831.888	0.0753082
$497$	−712.234	−0.0642818
$498$	1584.62	0.142588
$499$	−21106.7	−1.89352	−0.946759	−	0.321942i	$-0.895664\pi$
$499$	−21106.7	−1.89352	−0.946759	+	0.321942i	$0.895664\pi$
$500$	−8531.02	−0.763038
$501$	5933.02	0.529077
$502$	23096.9	2.05352
$503$	−9254.98	−0.820396	−0.410198	−	0.911997i	$-0.634540\pi$
$503$	−9254.98	−0.820396	−0.410198	+	0.911997i	$0.634540\pi$
$504$	−336.187	−0.0297122
$505$	−10867.4	−0.957608
$506$	−4043.86	−0.355280
$507$	5230.86	0.458206
$508$	−16448.9	−1.43662
$509$	−19431.9	−1.69215	−0.846075	−	0.533063i	$-0.821041\pi$
$509$	−19431.9	−1.69215	−0.846075	+	0.533063i	$0.821041\pi$
$510$	−19832.8	−1.72198
$511$	−219.110	−0.0189684
$512$	−1869.24	−0.161347
$513$	−13763.7	−1.18457
$514$	3460.74	0.296978
$515$	−5254.21	−0.449570
$516$	−14036.7	−1.19754
$517$	−15811.9	−1.34508
$518$	−339.022	−0.0287563
$519$	536.372	0.0453644
$520$	−429.456	−0.0362171
$521$	−14251.8	−1.19843	−0.599216	−	0.800588i	$-0.704521\pi$
$521$	−14251.8	−1.19843	−0.599216	+	0.800588i	$0.704521\pi$
$522$	14401.2	1.20751
$523$	6701.05	0.560261	0.280130	−	0.959962i	$-0.409622\pi$
$523$	6701.05	0.560261	0.280130	+	0.959962i	$0.409622\pi$
$524$	28293.5	2.35879
$525$	292.599	0.0243239
$526$	−6260.23	−0.518933
$527$	−17323.1	−1.43189
$528$	−434.932	−0.0358485
$529$	−11532.1	−0.947819
$530$	10586.4	0.867632
$531$	−3932.91	−0.321419
$532$	1128.25	0.0919474
$533$	240.412	0.0195374
$534$	5268.38	0.426938
$535$	11259.8	0.909913
$536$	−853.395	−0.0687706
$537$	−10405.4	−0.836179
$538$	25797.9	2.06733
$539$	12094.1	0.966471
$540$	−24786.3	−1.97525
$541$	−4180.96	−0.332261	−0.166131	−	0.986104i	$-0.553127\pi$
$541$	−4180.96	−0.332261	−0.166131	+	0.986104i	$0.553127\pi$
$542$	−14164.5	−1.12254
$543$	−2647.68	−0.209250
$544$	20726.7	1.63354
$545$	−32671.8	−2.56790
$546$	9.64443	0.000755941 0
$547$	17371.9	1.35789	0.678946	−	0.734188i	$-0.262437\pi$
$547$	17371.9	1.35789	0.678946	+	0.734188i	$0.262437\pi$
$548$	−28952.9	−2.25694
$549$	4807.69	0.373747
$550$	26420.8	2.04834
$551$	−17767.0	−1.37369
$552$	−1268.63	−0.0978200
$553$	91.0295	0.00699994
$554$	442.420	0.0339289
$555$	−4054.67	−0.310110
$556$	25668.0	1.95785
$557$	17655.6	1.34307	0.671535	−	0.740972i	$-0.265635\pi$
$557$	17655.6	1.34307	0.671535	+	0.740972i	$0.265635\pi$
$558$	−15594.9	−1.18313
$559$	−556.123	−0.0420778
$560$	−65.6270	−0.00495222
$561$	9056.97	0.681614
$562$	31797.0	2.38661
$563$	−5126.08	−0.383727	−0.191864	−	0.981422i	$-0.561453\pi$
$563$	−5126.08	−0.383727	−0.191864	+	0.981422i	$0.561453\pi$
$564$	−13493.7	−1.00743
$565$	−4636.09	−0.345207
$566$	−33605.9	−2.49569
$567$	−224.891	−0.0166570
$568$	−20176.0	−1.49044
$569$	−10564.6	−0.778368	−0.389184	−	0.921160i	$-0.627243\pi$
$569$	−10564.6	−0.778368	−0.389184	+	0.921160i	$0.627243\pi$
$570$	22027.1	1.61862
$571$	5940.75	0.435398	0.217699	−	0.976016i	$-0.430145\pi$
$571$	5940.75	0.435398	0.217699	+	0.976016i	$0.430145\pi$
$572$	533.491	0.0389971
$573$	8644.02	0.630208
$574$	−682.552	−0.0496327
$575$	−4148.07	−0.300846
$576$	17777.1	1.28596
$577$	−21023.4	−1.51684	−0.758418	−	0.651769i	$-0.774027\pi$
$577$	−21023.4	−1.51684	−0.758418	+	0.651769i	$0.774027\pi$
$578$	−30326.0	−2.18235
$579$	4885.38	0.350655
$580$	−31995.7	−2.29060
$581$	−109.191	−0.00779690
$582$	5383.83	0.383448
$583$	−4834.47	−0.343436
$584$	−6206.92	−0.439801
$585$	−433.333	−0.0306258
$586$	−18743.6	−1.32131
$587$	10736.4	0.754921	0.377460	−	0.926026i	$-0.376797\pi$
$587$	10736.4	0.754921	0.377460	+	0.926026i	$0.376797\pi$
$588$	10321.0	0.723860
$589$	19239.8	1.34595
$590$	14263.6	0.995297
$591$	−5548.08	−0.386155
$592$	516.923	0.0358875
$593$	−18090.1	−1.25273	−0.626366	−	0.779529i	$-0.715458\pi$
$593$	−18090.1	−1.25273	−0.626366	+	0.779529i	$0.715458\pi$
$594$	18477.1	1.27631
$595$	1366.61	0.0941604
$596$	−16873.6	−1.15968
$597$	10930.3	0.749323
$598$	−136.726	−0.00934971
$599$	−2776.25	−0.189373	−0.0946867	−	0.995507i	$-0.530185\pi$
$599$	−2776.25	−0.189373	−0.0946867	+	0.995507i	$0.530185\pi$
$600$	8288.68	0.563973
$601$	746.379	0.0506580	0.0253290	−	0.999679i	$-0.491937\pi$
$601$	746.379	0.0506580	0.0253290	+	0.999679i	$0.491937\pi$
$602$	1578.88	0.106894
$603$	−861.099	−0.0581537
$604$	987.046	0.0664939
$605$	1424.67	0.0957375
$606$	6913.47	0.463433
$607$	17345.5	1.15985	0.579926	−	0.814669i	$-0.303081\pi$
$607$	17345.5	1.15985	0.579926	+	0.814669i	$0.303081\pi$
$608$	−23019.9	−1.53549
$609$	264.144	0.0175758
$610$	−17436.3	−1.15733
$611$	−534.610	−0.0353977
$612$	−29036.8	−1.91788
$613$	−17978.5	−1.18457	−0.592287	−	0.805727i	$-0.701775\pi$
$613$	−17978.5	−1.18457	−0.592287	+	0.805727i	$0.701775\pi$
$614$	−21202.9	−1.39362
$615$	−8163.25	−0.535242
$616$	−556.797	−0.0364188
$617$	10479.0	0.683745	0.341872	−	0.939746i	$-0.388939\pi$
$617$	10479.0	0.683745	0.341872	+	0.939746i	$0.388939\pi$
$618$	3342.56	0.217569
$619$	−16772.3	−1.08907	−0.544535	−	0.838738i	$-0.683294\pi$
$619$	−16772.3	−1.08907	−0.544535	+	0.838738i	$0.683294\pi$
$620$	34647.9	2.24434
$621$	−2900.92	−0.187455
$622$	−9757.17	−0.628982
$623$	−363.026	−0.0233456
$624$	−14.7053	−0.000943404 0
$625$	−9101.62	−0.582504
$626$	−1825.01	−0.116521
$627$	−10059.0	−0.640701
$628$	−19891.0	−1.26391
$629$	−10764.3	−0.682357
$630$	1230.27	0.0778019
$631$	−13767.1	−0.868559	−0.434280	−	0.900778i	$-0.642997\pi$
$631$	−13767.1	−0.868559	−0.434280	+	0.900778i	$0.642997\pi$
$632$	2578.67	0.162300
$633$	−7714.51	−0.484399
$634$	−17106.9	−1.07161
$635$	22128.3	1.38289
$636$	−4125.70	−0.257224
$637$	408.908	0.0254341
$638$	23851.4	1.48007
$639$	−20358.2	−1.26034
$640$	−38257.2	−2.36289
$641$	31243.4	1.92518	0.962590	−	0.270961i	$-0.0873415\pi$
$641$	31243.4	1.92518	0.962590	+	0.270961i	$0.0873415\pi$
$642$	−7163.11	−0.440351
$643$	15633.9	0.958849	0.479425	−	0.877583i	$-0.340845\pi$
$643$	15633.9	0.958849	0.479425	+	0.877583i	$0.340845\pi$
$644$	237.797	0.0145505
$645$	18883.3	1.15276
$646$	58477.6	3.56156
$647$	−750.330	−0.0455927	−0.0227964	−	0.999740i	$-0.507257\pi$
$647$	−750.330	−0.0455927	−0.0227964	+	0.999740i	$0.507257\pi$
$648$	−6370.68	−0.386210
$649$	−6513.73	−0.393970
$650$	893.303	0.0539050
$651$	−286.040	−0.0172209
$652$	−33168.4	−1.99230
$653$	5138.56	0.307944	0.153972	−	0.988075i	$-0.450793\pi$
$653$	5138.56	0.307944	0.153972	+	0.988075i	$0.450793\pi$
$654$	20784.7	1.24273
$655$	−38062.6	−2.27058
$656$	1040.72	0.0619410
$657$	−6262.95	−0.371904
$658$	1517.80	0.0899243
$659$	22568.1	1.33403	0.667017	−	0.745043i	$-0.267571\pi$
$659$	22568.1	1.33403	0.667017	+	0.745043i	$0.267571\pi$
$660$	−18114.8	−1.06836
$661$	−25601.9	−1.50650	−0.753251	−	0.657733i	$-0.771515\pi$
$661$	−25601.9	−1.50650	−0.753251	+	0.657733i	$0.771515\pi$
$662$	−1730.18	−0.101579
$663$	306.222	0.0179377
$664$	−3093.14	−0.180779
$665$	−1517.81	−0.0885086
$666$	−9690.46	−0.563810
$667$	−3744.67	−0.217383
$668$	−31503.5	−1.82471
$669$	10782.2	0.623112
$670$	3122.99	0.180077
$671$	7962.56	0.458109
$672$	342.239	0.0196460
$673$	−18191.1	−1.04193	−0.520963	−	0.853579i	$-0.674427\pi$
$673$	−18191.1	−1.04193	−0.520963	+	0.853579i	$0.674427\pi$
$674$	11175.2	0.638653
$675$	18953.3	1.08076
$676$	−27775.1	−1.58028
$677$	9398.21	0.533534	0.266767	−	0.963761i	$-0.414045\pi$
$677$	9398.21	0.533534	0.266767	+	0.963761i	$0.414045\pi$
$678$	2949.33	0.167062
$679$	−370.981	−0.0209675
$680$	38713.0	2.18320
$681$	14168.5	0.797268
$682$	−25828.5	−1.45018
$683$	−26389.8	−1.47844	−0.739221	−	0.673462i	$-0.764806\pi$
$683$	−26389.8	−1.47844	−0.739221	+	0.673462i	$0.764806\pi$
$684$	32249.5	1.80277
$685$	38949.6	2.17254
$686$	−2323.74	−0.129330
$687$	11023.0	0.612162
$688$	−2407.40	−0.133403
$689$	−163.456	−0.00903802
$690$	4642.55	0.256143
$691$	−1373.11	−0.0755942	−0.0377971	−	0.999285i	$-0.512034\pi$
$691$	−1373.11	−0.0755942	−0.0377971	+	0.999285i	$0.512034\pi$
$692$	−2848.06	−0.156455
$693$	−561.824	−0.0307964
$694$	5487.19	0.300131
$695$	−34530.5	−1.88463
$696$	7482.62	0.407512
$697$	−21671.8	−1.17773
$698$	−27521.1	−1.49239
$699$	−6719.09	−0.363575
$700$	−1553.66	−0.0838895
$701$	−8905.75	−0.479836	−0.239918	−	0.970793i	$-0.577121\pi$
$701$	−8905.75	−0.479836	−0.239918	+	0.970793i	$0.577121\pi$
$702$	624.724	0.0335879
$703$	11955.3	0.641400
$704$	29442.7	1.57622
$705$	18152.8	0.969750
$706$	−57264.4	−3.05266
$707$	−476.384	−0.0253412
$708$	−5558.77	−0.295073
$709$	28394.7	1.50407	0.752034	−	0.659124i	$-0.229073\pi$
$709$	28394.7	1.50407	0.752034	+	0.659124i	$0.229073\pi$
$710$	73834.0	3.90273
$711$	2601.95	0.137244
$712$	−10283.7	−0.541291
$713$	4055.08	0.212993
$714$	−869.391	−0.0455688
$715$	−717.692	−0.0375387
$716$	55251.4	2.88386
$717$	7514.85	0.391419
$718$	2383.45	0.123885
$719$	22919.0	1.18878	0.594390	−	0.804177i	$-0.297393\pi$
$719$	22919.0	1.18878	0.594390	+	0.804177i	$0.297393\pi$
$720$	−1875.85	−0.0970957
$721$	−230.324	−0.0118970
$722$	−33778.5	−1.74114
$723$	−373.676	−0.0192215
$724$	14058.8	0.721672
$725$	24466.0	1.25330
$726$	−906.330	−0.0463321
$727$	25642.3	1.30814	0.654072	−	0.756433i	$-0.273059\pi$
$727$	25642.3	1.30814	0.654072	+	0.756433i	$0.273059\pi$
$728$	−18.8257	−0.000958414 0
$729$	977.662	0.0496704
$730$	22714.1	1.15163
$731$	50131.3	2.53649
$732$	6795.19	0.343111
$733$	−9677.65	−0.487657	−0.243828	−	0.969818i	$-0.578403\pi$
$733$	−9677.65	−0.487657	−0.243828	+	0.969818i	$0.578403\pi$
$734$	−45512.9	−2.28871
$735$	−13884.6	−0.696788
$736$	−4851.79	−0.242988
$737$	−1426.16	−0.0712801
$738$	−19509.8	−0.973122
$739$	29826.4	1.48468	0.742342	−	0.670022i	$-0.233715\pi$
$739$	29826.4	1.48468	0.742342	+	0.670022i	$0.233715\pi$
$740$	21529.7	1.06952
$741$	−340.103	−0.0168610
$742$	464.067	0.0229602
$743$	30288.5	1.49553	0.747765	−	0.663964i	$-0.231127\pi$
$743$	30288.5	1.49553	0.747765	+	0.663964i	$0.231127\pi$
$744$	−8102.88	−0.399282
$745$	22699.6	1.11631
$746$	−4306.93	−0.211378
$747$	−3121.06	−0.152870
$748$	−48091.2	−2.35079
$749$	493.586	0.0240791
$750$	−7301.02	−0.355461
$751$	−7206.83	−0.350174	−0.175087	−	0.984553i	$-0.556021\pi$
$751$	−7206.83	−0.350174	−0.175087	+	0.984553i	$0.556021\pi$
$752$	−2314.27	−0.112224
$753$	12109.1	0.586032
$754$	806.431	0.0389503
$755$	−1327.85	−0.0640071
$756$	−1086.54	−0.0522711
$757$	−11672.4	−0.560423	−0.280212	−	0.959938i	$-0.590405\pi$
$757$	−11672.4	−0.560423	−0.280212	+	0.959938i	$0.590405\pi$
$758$	27610.0	1.32301
$759$	−2120.10	−0.101390
$760$	−42996.3	−2.05216
$761$	−7514.48	−0.357950	−0.178975	−	0.983854i	$-0.557278\pi$
$761$	−7514.48	−0.357950	−0.178975	+	0.983854i	$0.557278\pi$
$762$	−14077.3	−0.669249
$763$	−1432.20	−0.0679545
$764$	−45898.5	−2.17349
$765$	39062.5	1.84616
$766$	−25242.6	−1.19067
$767$	−220.234	−0.0103679
$768$	8448.54	0.396954
$769$	−22427.8	−1.05171	−0.525855	−	0.850574i	$-0.676255\pi$
$769$	−22427.8	−1.05171	−0.525855	+	0.850574i	$0.676255\pi$
$770$	2037.59	0.0953632
$771$	1814.38	0.0847515
$772$	−25940.6	−1.20936
$773$	7216.53	0.335783	0.167892	−	0.985805i	$-0.446304\pi$
$773$	7216.53	0.335783	0.167892	+	0.985805i	$0.446304\pi$
$774$	45130.1	2.09582
$775$	−26494.1	−1.22799
$776$	−10509.1	−0.486153
$777$	−177.741	−0.00820646
$778$	−10483.4	−0.483095
$779$	24069.6	1.10704
$780$	−612.473	−0.0281154
$781$	−33717.5	−1.54482
$782$	12325.0	0.563610
$783$	17110.1	0.780926
$784$	1770.12	0.0806359
$785$	26758.8	1.21664
$786$	24214.2	1.09884
$787$	16535.4	0.748950	0.374475	−	0.927237i	$-0.377823\pi$
$787$	16535.4	0.748950	0.374475	+	0.927237i	$0.377823\pi$
$788$	29459.5	1.33179
$789$	−3282.08	−0.148093
$790$	−9436.60	−0.424986
$791$	−203.228	−0.00913522
$792$	−15915.2	−0.714045
$793$	269.219	0.0120558
$794$	−23507.8	−1.05071
$795$	5550.20	0.247604
$796$	−58038.1	−2.58430
$797$	15933.5	0.708147	0.354073	−	0.935218i	$-0.384796\pi$
$797$	15933.5	0.708147	0.354073	+	0.935218i	$0.384796\pi$
$798$	965.582	0.0428336
$799$	48192.1	2.13381
$800$	31699.4	1.40093
$801$	−10376.6	−0.457725
$802$	42808.6	1.88482
$803$	−10372.8	−0.455850
$804$	−1217.08	−0.0533868
$805$	−319.902	−0.0140063
$806$	−873.278	−0.0381637
$807$	13525.2	0.589974
$808$	−13494.9	−0.587561
$809$	13988.8	0.607936	0.303968	−	0.952682i	$-0.401688\pi$
$809$	13988.8	0.607936	0.303968	+	0.952682i	$0.401688\pi$
$810$	23313.4	1.01130
$811$	−1431.66	−0.0619880	−0.0309940	−	0.999520i	$-0.509867\pi$
$811$	−1431.66	−0.0619880	−0.0309940	+	0.999520i	$0.509867\pi$
$812$	−1402.57	−0.0606163
$813$	−7426.10	−0.320350
$814$	−16049.5	−0.691073
$815$	44620.7	1.91779
$816$	1325.60	0.0568693
$817$	−55678.0	−2.38424
$818$	−20311.2	−0.868170
$819$	−18.9956	−0.000810453 0
$820$	43345.7	1.84597
$821$	29412.8	1.25032	0.625160	−	0.780497i	$-0.285034\pi$
$821$	29412.8	1.25032	0.625160	+	0.780497i	$0.285034\pi$
$822$	−24778.4	−1.05140
$823$	−35688.7	−1.51158	−0.755789	−	0.654815i	$-0.772746\pi$
$823$	−35688.7	−1.51158	−0.755789	+	0.654815i	$0.772746\pi$
$824$	−6524.58	−0.275843
$825$	13851.8	0.584553
$826$	625.263	0.0263386
$827$	5713.47	0.240238	0.120119	−	0.992760i	$-0.461672\pi$
$827$	5713.47	0.240238	0.120119	+	0.992760i	$0.461672\pi$
$828$	6797.08	0.285284
$829$	629.525	0.0263743	0.0131872	−	0.999913i	$-0.495802\pi$
$829$	629.525	0.0263743	0.0131872	+	0.999913i	$0.495802\pi$
$830$	11319.3	0.473372
$831$	231.950	0.00968261
$832$	995.476	0.0414807
$833$	−36860.7	−1.53319
$834$	21967.2	0.912063
$835$	42380.8	1.75647
$836$	53412.1	2.20968
$837$	−18528.4	−0.765155
$838$	−14579.2	−0.600991
$839$	−37233.4	−1.53211	−0.766055	−	0.642776i	$-0.777783\pi$
$839$	−37233.4	−1.53211	−0.766055	+	0.642776i	$0.777783\pi$
$840$	639.230	0.0262566
$841$	−2302.27	−0.0943977
$842$	−21935.1	−0.897783
$843$	16670.4	0.681090
$844$	40962.9	1.67062
$845$	37365.1	1.52118
$846$	43384.3	1.76310
$847$	62.4521	0.00253351
$848$	−707.586	−0.0286540
$849$	−17618.8	−0.712219
$850$	−80526.3	−3.24944
$851$	2519.77	0.101500
$852$	−28774.3	−1.15703
$853$	−15350.1	−0.616153	−0.308077	−	0.951362i	$-0.599685\pi$
$853$	−15350.1	−0.616153	−0.308077	+	0.951362i	$0.599685\pi$
$854$	−764.338	−0.0306266
$855$	−43384.5	−1.73534
$856$	13982.2	0.558297
$857$	−6167.82	−0.245844	−0.122922	−	0.992416i	$-0.539227\pi$
$857$	−6167.82	−0.245844	−0.122922	+	0.992416i	$0.539227\pi$
$858$	456.572	0.0181668
$859$	−1983.40	−0.0787807	−0.0393904	−	0.999224i	$-0.512542\pi$
$859$	−1983.40	−0.0787807	−0.0393904	+	0.999224i	$0.512542\pi$
$860$	−100267.	−3.97569
$861$	−357.845	−0.0141641
$862$	−57631.3	−2.27718
$863$	−6441.24	−0.254070	−0.127035	−	0.991898i	$-0.540546\pi$
$863$	−6441.24	−0.254070	−0.127035	+	0.991898i	$0.540546\pi$
$864$	22168.7	0.872911
$865$	3831.42	0.150604
$866$	−33110.3	−1.29923
$867$	−15899.2	−0.622796
$868$	1518.83	0.0593922
$869$	4309.38	0.168223
$870$	−27382.6	−1.06708
$871$	−48.2195	−0.00187584
$872$	−40571.2	−1.57559
$873$	−10604.0	−0.411100
$874$	−13688.7	−0.529780
$875$	503.088	0.0194371
$876$	−8852.06	−0.341419
$877$	−21175.4	−0.815326	−0.407663	−	0.913132i	$-0.633656\pi$
$877$	−21175.4	−0.815326	−0.407663	+	0.913132i	$0.633656\pi$
$878$	11611.6	0.446324
$879$	−9826.79	−0.377076
$880$	−3106.81	−0.119012
$881$	−24393.8	−0.932858	−0.466429	−	0.884559i	$-0.654460\pi$
$881$	−24393.8	−0.932858	−0.466429	+	0.884559i	$0.654460\pi$
$882$	−33183.4	−1.26683
$883$	−16608.9	−0.632994	−0.316497	−	0.948594i	$-0.602507\pi$
$883$	−16608.9	−0.632994	−0.316497	+	0.948594i	$0.602507\pi$
$884$	−1625.99	−0.0618643
$885$	7478.08	0.284037
$886$	−31682.3	−1.20134
$887$	−21960.7	−0.831307	−0.415654	−	0.909523i	$-0.636447\pi$
$887$	−21960.7	−0.831307	−0.415654	+	0.909523i	$0.636447\pi$
$888$	−5035.01	−0.190275
$889$	970.019	0.0365955
$890$	37633.1	1.41738
$891$	−10646.5	−0.400303
$892$	−57251.7	−2.14902
$893$	−53524.1	−2.00573
$894$	−14440.8	−0.540237
$895$	−74328.3	−2.77600
$896$	−1677.05	−0.0625292
$897$	−71.6819	−0.00266821
$898$	61081.1	2.26983
$899$	−23917.6	−0.887314
$900$	−44409.0	−1.64478
$901$	14734.7	0.544821
$902$	−32312.3	−1.19277
$903$	827.769	0.0305055
$904$	−5757.01	−0.211809
$905$	−18912.9	−0.694682
$906$	844.734	0.0309762
$907$	291.604	0.0106754	0.00533768	−	0.999986i	$-0.498301\pi$
$907$	291.604	0.0106754	0.00533768	+	0.999986i	$0.498301\pi$
$908$	−75232.8	−2.74966
$909$	−13616.7	−0.496852
$910$	68.8923	0.00250962
$911$	37244.3	1.35451	0.677255	−	0.735749i	$-0.263170\pi$
$911$	37244.3	1.35451	0.677255	+	0.735749i	$0.263170\pi$
$912$	−1472.27	−0.0534558
$913$	−5169.15	−0.187375
$914$	−75504.0	−2.73244
$915$	−9141.41	−0.330279
$916$	−58530.7	−2.11126
$917$	−1668.51	−0.0600864
$918$	−56315.4	−2.02471
$919$	40789.4	1.46411	0.732056	−	0.681244i	$-0.238561\pi$
$919$	40789.4	1.46411	0.732056	+	0.681244i	$0.238561\pi$
$920$	−9062.13	−0.324750
$921$	−11116.2	−0.397710
$922$	−2771.57	−0.0989987
$923$	−1140.01	−0.0406543
$924$	−794.082	−0.0282721
$925$	−16463.0	−0.585190
$926$	61372.4	2.17800
$927$	−6583.49	−0.233258
$928$	28616.7	1.01227
$929$	21994.5	0.776765	0.388383	−	0.921498i	$-0.373034\pi$
$929$	21994.5	0.776765	0.388383	+	0.921498i	$0.373034\pi$
$930$	29652.4	1.04553
$931$	40939.1	1.44116
$932$	35677.4	1.25392
$933$	−5115.45	−0.179499
$934$	33592.7	1.17686
$935$	64695.9	2.26287
$936$	−538.105	−0.0187911
$937$	31638.7	1.10309	0.551543	−	0.834147i	$-0.314039\pi$
$937$	31638.7	1.10309	0.551543	+	0.834147i	$0.314039\pi$
$938$	136.900	0.00476538
$939$	−956.808	−0.0332527
$940$	−96388.7	−3.34452
$941$	−22659.7	−0.785000	−0.392500	−	0.919752i	$-0.628390\pi$
$941$	−22659.7	−0.785000	−0.392500	+	0.919752i	$0.628390\pi$
$942$	−17023.1	−0.588792
$943$	5073.04	0.175187
$944$	−953.368	−0.0328702
$945$	1461.69	0.0503162
$946$	74745.0	2.56889
$947$	−42964.9	−1.47431	−0.737155	−	0.675724i	$-0.763831\pi$
$947$	−42964.9	−1.47431	−0.737155	+	0.675724i	$0.763831\pi$
$948$	3677.59	0.125994
$949$	−350.711	−0.0119964
$950$	89435.9	3.05440
$951$	−8968.74	−0.305816
$952$	1697.03	0.0577741
$953$	49222.7	1.67312	0.836559	−	0.547877i	$-0.184564\pi$
$953$	49222.7	1.67312	0.836559	+	0.547877i	$0.184564\pi$
$954$	13264.7	0.450168
$955$	61746.1	2.09221
$956$	−39902.8	−1.34994
$957$	12504.7	0.422382
$958$	−10033.1	−0.338365
$959$	1707.40	0.0574919
$960$	−33801.6	−1.13640
$961$	−3890.85	−0.130605
$962$	−542.643	−0.0181866
$963$	14108.4	0.472106
$964$	1984.17	0.0662922
$965$	34897.3	1.16413
$966$	203.511	0.00677833
$967$	−6249.37	−0.207824	−0.103912	−	0.994586i	$-0.533136\pi$
$967$	−6249.37	−0.207824	−0.103912	+	0.994586i	$0.533136\pi$
$968$	1769.13	0.0587418
$969$	30658.4	1.01640
$970$	38457.9	1.27300
$971$	30024.2	0.992298	0.496149	−	0.868237i	$-0.334747\pi$
$971$	30024.2	0.992298	0.496149	+	0.868237i	$0.334747\pi$
$972$	−48409.6	−1.59747
$973$	−1513.68	−0.0498730
$974$	−2301.85	−0.0757249
$975$	468.337	0.0153834
$976$	1165.42	0.0382216
$977$	28226.7	0.924310	0.462155	−	0.886799i	$-0.347076\pi$
$977$	28226.7	0.924310	0.462155	+	0.886799i	$0.347076\pi$
$978$	−28386.2	−0.928110
$979$	−17185.8	−0.561043
$980$	73725.0	2.40312
$981$	−40937.5	−1.33235
$982$	−51321.5	−1.66776
$983$	983.000	0.0318950
$983$	983.000	0.0318950
$984$	−10137.0	−0.328409
$985$	−39631.1	−1.28198
$986$	−72695.2	−2.34796
$987$	795.748	0.0256625
$988$	1805.90	0.0581510
$989$	−11735.0	−0.377301
$990$	58241.6	1.86974
$991$	−33165.0	−1.06309	−0.531544	−	0.847030i	$-0.678388\pi$
$991$	−33165.0	−1.06309	−0.531544	+	0.847030i	$0.678388\pi$
$992$	−30988.8	−0.991831
$993$	−907.092	−0.0289886
$994$	3236.59	0.103278
$995$	78077.3	2.48765
$996$	−4411.31	−0.140339
$997$	20278.2	0.644148	0.322074	−	0.946714i	$-0.395620\pi$
$997$	20278.2	0.644148	0.322074	+	0.946714i	$0.395620\pi$
$998$	95914.8	3.04221
$999$	−11513.3	−0.364629

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.a.1.15	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.a.1.15	✓	109	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-4.54428 q^{2} -2.38245 q^{3} +12.6505 q^{4} -17.0184 q^{5} +10.8265 q^{6} -0.746020 q^{7} -21.1331 q^{8} -21.3239 q^{9} +O(q^{10})\)	\(q-4.54428 q^{2} -2.38245 q^{3} +12.6505 q^{4} -17.0184 q^{5} +10.8265 q^{6} -0.746020 q^{7} -21.1331 q^{8} -21.3239 q^{9} +77.3363 q^{10} -35.3169 q^{11} -30.1392 q^{12} -1.19409 q^{13} +3.39012 q^{14} +40.5455 q^{15} -5.16908 q^{16} +107.640 q^{17} +96.9018 q^{18} -119.550 q^{19} -215.291 q^{20} +1.77736 q^{21} +160.490 q^{22} -25.1970 q^{23} +50.3487 q^{24} +164.626 q^{25} +5.42627 q^{26} +115.130 q^{27} -9.43751 q^{28} +148.616 q^{29} -184.250 q^{30} -160.935 q^{31} +192.555 q^{32} +84.1410 q^{33} -489.148 q^{34} +12.6961 q^{35} -269.758 q^{36} -100.003 q^{37} +543.268 q^{38} +2.84486 q^{39} +359.652 q^{40} -201.335 q^{41} -8.07682 q^{42} +465.730 q^{43} -446.776 q^{44} +362.899 q^{45} +114.502 q^{46} +447.714 q^{47} +12.3151 q^{48} -342.443 q^{49} -748.105 q^{50} -256.448 q^{51} -15.1058 q^{52} +136.888 q^{53} -523.181 q^{54} +601.037 q^{55} +15.7657 q^{56} +284.822 q^{57} -675.353 q^{58} +184.437 q^{59} +512.921 q^{60} -225.460 q^{61} +731.335 q^{62} +15.9081 q^{63} -833.670 q^{64} +20.3215 q^{65} -382.360 q^{66} +40.3819 q^{67} +1361.70 q^{68} +60.0306 q^{69} -57.6944 q^{70} +954.712 q^{71} +450.641 q^{72} +293.706 q^{73} +454.441 q^{74} -392.213 q^{75} -1512.36 q^{76} +26.3471 q^{77} -12.9278 q^{78} -122.020 q^{79} +87.9695 q^{80} +301.455 q^{81} +914.924 q^{82} +146.365 q^{83} +22.4844 q^{84} -1831.87 q^{85} -2116.41 q^{86} -354.071 q^{87} +746.357 q^{88} +486.617 q^{89} -1649.11 q^{90} +0.890814 q^{91} -318.754 q^{92} +383.421 q^{93} -2034.54 q^{94} +2034.55 q^{95} -458.753 q^{96} +497.281 q^{97} +1556.16 q^{98} +753.095 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9} - 243 q^{10} - 126 q^{11} - 280 q^{12} - 458 q^{13} - 177 q^{14} - 314 q^{15} + 1009 q^{16} - 594 q^{17} - 671 q^{18} - 491 q^{19} - 500 q^{20} - 660 q^{21} - 899 q^{22} - 487 q^{23} - 811 q^{24} + 705 q^{25} - 104 q^{26} - 842 q^{27} - 2648 q^{28} - 820 q^{29} - 728 q^{30} - 965 q^{31} - 1669 q^{32} - 2196 q^{33} - 508 q^{34} - 846 q^{35} + 1358 q^{36} - 3209 q^{37} - 1136 q^{38} - 1326 q^{39} - 3234 q^{40} - 1961 q^{41} - 2240 q^{42} - 2999 q^{43} - 1922 q^{44} - 2234 q^{45} - 2962 q^{46} - 1903 q^{47} - 2787 q^{48} + 1186 q^{49} - 2309 q^{50} - 2436 q^{51} - 4897 q^{52} - 1825 q^{53} - 3306 q^{54} - 2888 q^{55} - 1820 q^{56} - 6684 q^{57} - 4813 q^{58} - 1537 q^{59} - 3869 q^{60} - 2276 q^{61} - 1950 q^{62} - 6491 q^{63} - 89 q^{64} - 5546 q^{65} - 3527 q^{66} - 5005 q^{67} - 4183 q^{68} - 3018 q^{69} - 2993 q^{70} - 2014 q^{71} - 9549 q^{72} - 12904 q^{73} - 2714 q^{74} - 3379 q^{75} - 6293 q^{76} - 3258 q^{77} - 4593 q^{78} - 5005 q^{79} - 3988 q^{80} + 249 q^{81} - 5116 q^{82} - 2854 q^{83} - 4158 q^{84} - 11742 q^{85} - 2709 q^{86} - 2412 q^{87} - 10451 q^{88} - 2519 q^{89} - 8095 q^{90} - 2438 q^{91} - 6660 q^{92} - 10668 q^{93} - 4281 q^{94} - 4482 q^{95} - 6515 q^{96} - 16628 q^{97} - 5708 q^{98} - 6308 q^{99}+O(q^{100}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9 - 243 * q^10 - 126 * q^11 - 280 * q^12 - 458 * q^13 - 177 * q^14 - 314 * q^15 + 1009 * q^16 - 594 * q^17 - 671 * q^18 - 491 * q^19 - 500 * q^20 - 660 * q^21 - 899 * q^22 - 487 * q^23 - 811 * q^24 + 705 * q^25 - 104 * q^26 - 842 * q^27 - 2648 * q^28 - 820 * q^29 - 728 * q^30 - 965 * q^31 - 1669 * q^32 - 2196 * q^33 - 508 * q^34 - 846 * q^35 + 1358 * q^36 - 3209 * q^37 - 1136 * q^38 - 1326 * q^39 - 3234 * q^40 - 1961 * q^41 - 2240 * q^42 - 2999 * q^43 - 1922 * q^44 - 2234 * q^45 - 2962 * q^46 - 1903 * q^47 - 2787 * q^48 + 1186 * q^49 - 2309 * q^50 - 2436 * q^51 - 4897 * q^52 - 1825 * q^53 - 3306 * q^54 - 2888 * q^55 - 1820 * q^56 - 6684 * q^57 - 4813 * q^58 - 1537 * q^59 - 3869 * q^60 - 2276 * q^61 - 1950 * q^62 - 6491 * q^63 - 89 * q^64 - 5546 * q^65 - 3527 * q^66 - 5005 * q^67 - 4183 * q^68 - 3018 * q^69 - 2993 * q^70 - 2014 * q^71 - 9549 * q^72 - 12904 * q^73 - 2714 * q^74 - 3379 * q^75 - 6293 * q^76 - 3258 * q^77 - 4593 * q^78 - 5005 * q^79 - 3988 * q^80 + 249 * q^81 - 5116 * q^82 - 2854 * q^83 - 4158 * q^84 - 11742 * q^85 - 2709 * q^86 - 2412 * q^87 - 10451 * q^88 - 2519 * q^89 - 8095 * q^90 - 2438 * q^91 - 6660 * q^92 - 10668 * q^93 - 4281 * q^94 - 4482 * q^95 - 6515 * q^96 - 16628 * q^97 - 5708 * q^98 - 6308 * q^99

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