LMFDB - Embedded newform 1083.4.a.t.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1083,4,Mod(1,1083)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1083, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1083.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1083 = 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1083.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:	$63.8990685362$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 120 x^{16} - 19 x^{15} + 5904 x^{14} + 1731 x^{13} - 153482 x^{12} - 62307 x^{11} + \cdots - 49519296 $ x^18 - 120x^16 - 19x^15 + 5904x^14 + 1731x^13 - 153482x^12 - 62307x^11 + 2264487x^10 + 1134069x^9 - 18914886x^8 - 10997190x^7 + 83975016x^6 + 53300700x^5 - 174155400x^4 - 101642904x^3 + 157450608x^2 + 62731584x - 49519296
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3}\cdot 19^{3} $
Twist minimal:	no (minimal twist has level 57)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$3.36651$ of defining polynomial
Character	$\chi$	$=$	1083.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.36651 q^{2} +3.00000 q^{3} +3.33337 q^{4} -9.34862 q^{5} -10.0995 q^{6} -20.4088 q^{7} +15.7102 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.36651 q^{2} +3.00000 q^{3} +3.33337 q^{4} -9.34862 q^{5} -10.0995 q^{6} -20.4088 q^{7} +15.7102 q^{8} +9.00000 q^{9} +31.4722 q^{10} -31.9999 q^{11} +10.0001 q^{12} -71.3748 q^{13} +68.7065 q^{14} -28.0459 q^{15} -79.5556 q^{16} -79.2918 q^{17} -30.2986 q^{18} -31.1625 q^{20} -61.2265 q^{21} +107.728 q^{22} -90.4822 q^{23} +47.1307 q^{24} -37.6032 q^{25} +240.284 q^{26} +27.0000 q^{27} -68.0303 q^{28} -20.9090 q^{29} +94.4166 q^{30} +134.916 q^{31} +142.143 q^{32} -95.9997 q^{33} +266.937 q^{34} +190.795 q^{35} +30.0004 q^{36} -235.126 q^{37} -214.124 q^{39} -146.869 q^{40} -322.867 q^{41} +206.120 q^{42} -344.802 q^{43} -106.668 q^{44} -84.1376 q^{45} +304.609 q^{46} +304.107 q^{47} -238.667 q^{48} +73.5206 q^{49} +126.592 q^{50} -237.876 q^{51} -237.919 q^{52} -459.824 q^{53} -90.8957 q^{54} +299.155 q^{55} -320.628 q^{56} +70.3904 q^{58} -299.795 q^{59} -93.4874 q^{60} +38.3852 q^{61} -454.196 q^{62} -183.680 q^{63} +157.920 q^{64} +667.256 q^{65} +323.184 q^{66} +650.433 q^{67} -264.309 q^{68} -271.446 q^{69} -642.311 q^{70} -629.439 q^{71} +141.392 q^{72} +373.507 q^{73} +791.554 q^{74} -112.810 q^{75} +653.081 q^{77} +720.851 q^{78} -1024.33 q^{79} +743.735 q^{80} +81.0000 q^{81} +1086.93 q^{82} +943.414 q^{83} -204.091 q^{84} +741.270 q^{85} +1160.78 q^{86} -62.7271 q^{87} -502.726 q^{88} -758.136 q^{89} +283.250 q^{90} +1456.68 q^{91} -301.611 q^{92} +404.748 q^{93} -1023.78 q^{94} +426.428 q^{96} -1064.94 q^{97} -247.508 q^{98} -287.999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 54 q^{3} + 96 q^{4} + 18 q^{5} + 48 q^{7} - 57 q^{8} + 162 q^{9}+O(q^{10}) $ 18 * q + 54 * q^3 + 96 * q^4 + 18 * q^5 + 48 * q^7 - 57 * q^8 + 162 * q^9	\( 18 q + 54 q^{3} + 96 q^{4} + 18 q^{5} + 48 q^{7} - 57 q^{8} + 162 q^{9} + 60 q^{10} + 108 q^{11} + 288 q^{12} + 42 q^{13} - 60 q^{14} + 54 q^{15} + 576 q^{16} + 300 q^{17} + 27 q^{20} + 144 q^{21} + 219 q^{22} + 174 q^{23} - 171 q^{24} + 1068 q^{25} - 72 q^{26} + 486 q^{27} + 867 q^{28} - 168 q^{29} + 180 q^{30} + 1032 q^{31} - 921 q^{32} + 324 q^{33} - 75 q^{34} + 1524 q^{35} + 864 q^{36} - 132 q^{37} + 126 q^{39} + 363 q^{40} - 120 q^{41} - 180 q^{42} + 420 q^{43} + 2328 q^{44} + 162 q^{45} + 2229 q^{46} + 810 q^{47} + 1728 q^{48} + 1122 q^{49} + 1503 q^{50} + 900 q^{51} - 228 q^{52} + 174 q^{53} + 2550 q^{55} - 1119 q^{56} + 756 q^{58} - 474 q^{59} + 81 q^{60} + 1488 q^{61} + 333 q^{62} + 432 q^{63} + 2679 q^{64} + 1716 q^{65} + 657 q^{66} + 3060 q^{67} + 4623 q^{68} + 522 q^{69} + 1383 q^{70} - 1464 q^{71} - 513 q^{72} + 1470 q^{73} - 135 q^{74} + 3204 q^{75} + 1014 q^{77} - 216 q^{78} + 2508 q^{79} - 2049 q^{80} + 1458 q^{81} + 1485 q^{82} + 4764 q^{83} + 2601 q^{84} + 804 q^{85} + 1068 q^{86} - 504 q^{87} + 3012 q^{88} - 1050 q^{89} + 540 q^{90} - 3408 q^{91} + 3306 q^{92} + 3096 q^{93} + 8205 q^{94} - 2763 q^{96} - 2070 q^{97} - 1767 q^{98} + 972 q^{99}+O(q^{100}) \) 18 * q + 54 * q^3 + 96 * q^4 + 18 * q^5 + 48 * q^7 - 57 * q^8 + 162 * q^9 + 60 * q^10 + 108 * q^11 + 288 * q^12 + 42 * q^13 - 60 * q^14 + 54 * q^15 + 576 * q^16 + 300 * q^17 + 27 * q^20 + 144 * q^21 + 219 * q^22 + 174 * q^23 - 171 * q^24 + 1068 * q^25 - 72 * q^26 + 486 * q^27 + 867 * q^28 - 168 * q^29 + 180 * q^30 + 1032 * q^31 - 921 * q^32 + 324 * q^33 - 75 * q^34 + 1524 * q^35 + 864 * q^36 - 132 * q^37 + 126 * q^39 + 363 * q^40 - 120 * q^41 - 180 * q^42 + 420 * q^43 + 2328 * q^44 + 162 * q^45 + 2229 * q^46 + 810 * q^47 + 1728 * q^48 + 1122 * q^49 + 1503 * q^50 + 900 * q^51 - 228 * q^52 + 174 * q^53 + 2550 * q^55 - 1119 * q^56 + 756 * q^58 - 474 * q^59 + 81 * q^60 + 1488 * q^61 + 333 * q^62 + 432 * q^63 + 2679 * q^64 + 1716 * q^65 + 657 * q^66 + 3060 * q^67 + 4623 * q^68 + 522 * q^69 + 1383 * q^70 - 1464 * q^71 - 513 * q^72 + 1470 * q^73 - 135 * q^74 + 3204 * q^75 + 1014 * q^77 - 216 * q^78 + 2508 * q^79 - 2049 * q^80 + 1458 * q^81 + 1485 * q^82 + 4764 * q^83 + 2601 * q^84 + 804 * q^85 + 1068 * q^86 - 504 * q^87 + 3012 * q^88 - 1050 * q^89 + 540 * q^90 - 3408 * q^91 + 3306 * q^92 + 3096 * q^93 + 8205 * q^94 - 2763 * q^96 - 2070 * q^97 - 1767 * q^98 + 972 * 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 $

$2$	−3.36651	−1.19024	−0.595120	−	0.803637i	$-0.702896\pi$
$2$	−3.36651	−1.19024	−0.595120	+	0.803637i	$0.702896\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	3.33337	0.416672
$5$	−9.34862	−0.836166	−0.418083	−	0.908409i	$-0.637298\pi$
$5$	−9.34862	−0.836166	−0.418083	+	0.908409i	$0.637298\pi$
$6$	−10.0995	−0.687185
$7$	−20.4088	−1.10197	−0.550987	−	0.834514i	$-0.685749\pi$
$7$	−20.4088	−1.10197	−0.550987	+	0.834514i	$0.685749\pi$
$8$	15.7102	0.694301
$9$	9.00000	0.333333
$10$	31.4722	0.995239
$11$	−31.9999	−0.877122	−0.438561	−	0.898702i	$-0.644512\pi$
$11$	−31.9999	−0.877122	−0.438561	+	0.898702i	$0.644512\pi$
$12$	10.0001	0.240565
$13$	−71.3748	−1.52275	−0.761377	−	0.648309i	$-0.775476\pi$
$13$	−71.3748	−1.52275	−0.761377	+	0.648309i	$0.775476\pi$
$14$	68.7065	1.31161
$15$	−28.0459	−0.482761
$16$	−79.5556	−1.24306
$17$	−79.2918	−1.13124	−0.565620	−	0.824666i	$-0.691363\pi$
$17$	−79.2918	−1.13124	−0.565620	+	0.824666i	$0.691363\pi$
$18$	−30.2986	−0.396747
$19$	0	0
$19$	0	0
$20$	−31.1625	−0.348407
$21$	−61.2265	−0.636225
$22$	107.728	1.04399
$23$	−90.4822	−0.820297	−0.410149	−	0.912019i	$-0.634523\pi$
$23$	−90.4822	−0.820297	−0.410149	+	0.912019i	$0.634523\pi$
$24$	47.1307	0.400855
$25$	−37.6032	−0.300826
$26$	240.284	1.81244
$27$	27.0000	0.192450
$28$	−68.0303	−0.459161
$29$	−20.9090	−0.133887	−0.0669433	−	0.997757i	$-0.521325\pi$
$29$	−20.9090	−0.133887	−0.0669433	+	0.997757i	$0.521325\pi$
$30$	94.4166	0.574601
$31$	134.916	0.781666	0.390833	−	0.920462i	$-0.372187\pi$
$31$	134.916	0.781666	0.390833	+	0.920462i	$0.372187\pi$
$32$	142.143	0.785235
$33$	−95.9997	−0.506406
$34$	266.937	1.34645
$35$	190.795	0.921433
$36$	30.0004	0.138891
$37$	−235.126	−1.04472	−0.522358	−	0.852726i	$-0.674947\pi$
$37$	−235.126	−1.04472	−0.522358	+	0.852726i	$0.674947\pi$
$38$	0	0
$39$	−214.124	−0.879162
$40$	−146.869	−0.580551
$41$	−322.867	−1.22984	−0.614919	−	0.788590i	$-0.710811\pi$
$41$	−322.867	−1.22984	−0.614919	+	0.788590i	$0.710811\pi$
$42$	206.120	0.757260
$43$	−344.802	−1.22283	−0.611417	−	0.791308i	$-0.709400\pi$
$43$	−344.802	−1.22283	−0.611417	+	0.791308i	$0.709400\pi$
$44$	−106.668	−0.365472
$45$	−84.1376	−0.278722
$46$	304.609	0.976351
$47$	304.107	0.943801	0.471900	−	0.881652i	$-0.343568\pi$
$47$	304.107	0.943801	0.471900	+	0.881652i	$0.343568\pi$
$48$	−238.667	−0.717679
$49$	73.5206	0.214346
$50$	126.592	0.358055
$51$	−237.876	−0.653122
$52$	−237.919	−0.634488
$53$	−459.824	−1.19173	−0.595864	−	0.803085i	$-0.703190\pi$
$53$	−459.824	−1.19173	−0.595864	+	0.803085i	$0.703190\pi$
$54$	−90.8957	−0.229062
$55$	299.155	0.733420
$56$	−320.628	−0.765101
$57$	0	0
$58$	70.3904	0.159357
$59$	−299.795	−0.661526	−0.330763	−	0.943714i	$-0.607306\pi$
$59$	−299.795	−0.661526	−0.330763	+	0.943714i	$0.607306\pi$
$60$	−93.4874	−0.201153
$61$	38.3852	0.0805693	0.0402846	−	0.999188i	$-0.487174\pi$
$61$	38.3852	0.0805693	0.0402846	+	0.999188i	$0.487174\pi$
$62$	−454.196	−0.930370
$63$	−183.680	−0.367325
$64$	157.920	0.308438
$65$	667.256	1.27328
$66$	323.184	0.602745
$67$	650.433	1.18601	0.593007	−	0.805197i	$-0.297940\pi$
$67$	650.433	1.18601	0.593007	+	0.805197i	$0.297940\pi$
$68$	−264.309	−0.471356
$69$	−271.446	−0.473599
$70$	−642.311	−1.09673
$71$	−629.439	−1.05212	−0.526061	−	0.850447i	$-0.676332\pi$
$71$	−629.439	−1.05212	−0.526061	+	0.850447i	$0.676332\pi$
$72$	141.392	0.231434
$73$	373.507	0.598846	0.299423	−	0.954121i	$-0.403206\pi$
$73$	373.507	0.598846	0.299423	+	0.954121i	$0.403206\pi$
$74$	791.554	1.24346
$75$	−112.810	−0.173682
$76$	0	0
$77$	653.081	0.966565
$78$	720.851	1.04641
$79$	−1024.33	−1.45882	−0.729409	−	0.684078i	$-0.760205\pi$
$79$	−1024.33	−1.45882	−0.729409	+	0.684078i	$0.760205\pi$
$80$	743.735	1.03940
$81$	81.0000	0.111111
$82$	1086.93	1.46380
$83$	943.414	1.24763	0.623814	−	0.781573i	$-0.285582\pi$
$83$	943.414	1.24763	0.623814	+	0.781573i	$0.285582\pi$
$84$	−204.091	−0.265097
$85$	741.270	0.945906
$86$	1160.78	1.45547
$87$	−62.7271	−0.0772994
$88$	−502.726	−0.608986
$89$	−758.136	−0.902947	−0.451473	−	0.892285i	$-0.649101\pi$
$89$	−758.136	−0.902947	−0.451473	+	0.892285i	$0.649101\pi$
$90$	283.250	0.331746
$91$	1456.68	1.67803
$92$	−301.611	−0.341795
$93$	404.748	0.451295
$94$	−1023.78	−1.12335
$95$	0	0
$96$	426.428	0.453355
$97$	−1064.94	−1.11472	−0.557362	−	0.830270i	$-0.688186\pi$
$97$	−1064.94	−1.11472	−0.557362	+	0.830270i	$0.688186\pi$
$98$	−247.508	−0.255123
$99$	−287.999	−0.292374
$100$	−125.346	−0.125346
$101$	−1905.67	−1.87744	−0.938721	−	0.344678i	$-0.887988\pi$
$101$	−1905.67	−1.87744	−0.938721	+	0.344678i	$0.887988\pi$
$102$	800.810	0.777372
$103$	1097.27	1.04968	0.524842	−	0.851199i	$-0.324124\pi$
$103$	1097.27	1.04968	0.524842	+	0.851199i	$0.324124\pi$
$104$	−1121.31	−1.05725
$105$	572.384	0.531990
$106$	1548.00	1.41844
$107$	441.293	0.398704	0.199352	−	0.979928i	$-0.436116\pi$
$107$	441.293	0.398704	0.199352	+	0.979928i	$0.436116\pi$
$108$	90.0011	0.0801885
$109$	87.9205	0.0772592	0.0386296	−	0.999254i	$-0.487701\pi$
$109$	87.9205	0.0772592	0.0386296	+	0.999254i	$0.487701\pi$
$110$	−1007.11	−0.872945
$111$	−705.378	−0.603167
$112$	1623.64	1.36982
$113$	−1352.50	−1.12595	−0.562974	−	0.826475i	$-0.690343\pi$
$113$	−1352.50	−1.12595	−0.562974	+	0.826475i	$0.690343\pi$
$114$	0	0
$115$	845.884	0.685905
$116$	−69.6976	−0.0557867
$117$	−642.373	−0.507585
$118$	1009.26	0.787375
$119$	1618.25	1.24660
$120$	−440.607	−0.335181
$121$	−307.006	−0.230658
$122$	−129.224	−0.0958968
$123$	−968.602	−0.710048
$124$	449.726	0.325698
$125$	1520.12	1.08771
$126$	618.359	0.437204
$127$	2328.59	1.62700	0.813500	−	0.581565i	$-0.197559\pi$
$127$	2328.59	1.62700	0.813500	+	0.581565i	$0.197559\pi$
$128$	−1668.78	−1.15235
$129$	−1034.41	−0.706004
$130$	−2246.32	−1.51550
$131$	−1847.41	−1.23213	−0.616063	−	0.787697i	$-0.711273\pi$
$131$	−1847.41	−1.23213	−0.616063	+	0.787697i	$0.711273\pi$
$132$	−320.003	−0.211005
$133$	0	0
$134$	−2189.69	−1.41164
$135$	−252.413	−0.160920
$136$	−1245.69	−0.785422
$137$	−531.740	−0.331603	−0.165801	−	0.986159i	$-0.553021\pi$
$137$	−531.740	−0.331603	−0.165801	+	0.986159i	$0.553021\pi$
$138$	913.827	0.563696
$139$	1562.51	0.953459	0.476729	−	0.879050i	$-0.341822\pi$
$139$	1562.51	0.953459	0.476729	+	0.879050i	$0.341822\pi$
$140$	635.989	0.383935
$141$	912.322	0.544904
$142$	2119.01	1.25228
$143$	2283.99	1.33564
$144$	−716.000	−0.414352
$145$	195.471	0.111951
$146$	−1257.42	−0.712770
$147$	220.562	0.123753
$148$	−783.763	−0.435303
$149$	−2433.76	−1.33813	−0.669065	−	0.743204i	$-0.733305\pi$
$149$	−2433.76	−1.33813	−0.669065	+	0.743204i	$0.733305\pi$
$150$	379.775	0.206723
$151$	3524.32	1.89937	0.949686	−	0.313204i	$-0.101403\pi$
$151$	3524.32	1.89937	0.949686	+	0.313204i	$0.101403\pi$
$152$	0	0
$153$	−713.627	−0.377080
$154$	−2198.60	−1.15044
$155$	−1261.28	−0.653603
$156$	−713.756	−0.366322
$157$	−108.554	−0.0551819	−0.0275910	−	0.999619i	$-0.508784\pi$
$157$	−108.554	−0.0551819	−0.0275910	+	0.999619i	$0.508784\pi$
$158$	3448.43	1.73634
$159$	−1379.47	−0.688045
$160$	−1328.84	−0.656587
$161$	1846.64	0.903946
$162$	−272.687	−0.132249
$163$	−2626.80	−1.26225	−0.631125	−	0.775681i	$-0.717406\pi$
$163$	−2626.80	−1.26225	−0.631125	+	0.775681i	$0.717406\pi$
$164$	−1076.24	−0.512439
$165$	897.465	0.423440
$166$	−3176.01	−1.48498
$167$	148.851	0.0689725	0.0344863	−	0.999405i	$-0.489021\pi$
$167$	148.851	0.0689725	0.0344863	+	0.999405i	$0.489021\pi$
$168$	−961.883	−0.441731
$169$	2897.36	1.31878
$170$	−2495.49	−1.12585
$171$	0	0
$172$	−1149.36	−0.509520
$173$	−333.335	−0.146491	−0.0732455	−	0.997314i	$-0.523336\pi$
$173$	−333.335	−0.146491	−0.0732455	+	0.997314i	$0.523336\pi$
$174$	211.171	0.0920049
$175$	767.438	0.331502
$176$	2545.77	1.09031
$177$	−899.386	−0.381932
$178$	2552.27	1.07472
$179$	−3298.55	−1.37735	−0.688673	−	0.725072i	$-0.741807\pi$
$179$	−3298.55	−1.37735	−0.688673	+	0.725072i	$0.741807\pi$
$180$	−280.462	−0.116136
$181$	3330.22	1.36759	0.683793	−	0.729676i	$-0.260329\pi$
$181$	3330.22	1.36759	0.683793	+	0.729676i	$0.260329\pi$
$182$	−4903.91	−1.99726
$183$	115.156	0.0465167
$184$	−1421.50	−0.569533
$185$	2198.10	0.873556
$186$	−1362.59	−0.537150
$187$	2537.33	0.992236
$188$	1013.70	0.393255
$189$	−551.039	−0.212075
$190$	0	0
$191$	28.5897	0.0108308	0.00541539	−	0.999985i	$-0.498276\pi$
$191$	28.5897	0.0108308	0.00541539	+	0.999985i	$0.498276\pi$
$192$	473.761	0.178077
$193$	2559.81	0.954709	0.477355	−	0.878711i	$-0.341596\pi$
$193$	2559.81	0.954709	0.477355	+	0.878711i	$0.341596\pi$
$194$	3585.13	1.32679
$195$	2001.77	0.735126
$196$	245.072	0.0893119
$197$	3380.20	1.22248	0.611242	−	0.791444i	$-0.290670\pi$
$197$	3380.20	1.22248	0.611242	+	0.791444i	$0.290670\pi$
$198$	969.552	0.347995
$199$	−2152.10	−0.766624	−0.383312	−	0.923619i	$-0.625217\pi$
$199$	−2152.10	−0.766624	−0.383312	+	0.923619i	$0.625217\pi$
$200$	−590.756	−0.208864
$201$	1951.30	0.684746
$202$	6415.47	2.23461
$203$	426.729	0.147539
$204$	−792.928	−0.272138
$205$	3018.36	1.02835
$206$	−3693.98	−1.24938
$207$	−814.339	−0.273432
$208$	5678.26	1.89287
$209$	0	0
$210$	−1926.93	−0.633196
$211$	439.732	0.143471	0.0717355	−	0.997424i	$-0.477146\pi$
$211$	439.732	0.143471	0.0717355	+	0.997424i	$0.477146\pi$
$212$	−1532.76	−0.496560
$213$	−1888.32	−0.607443
$214$	−1485.62	−0.474554
$215$	3223.43	1.02249
$216$	424.176	0.133618
$217$	−2753.48	−0.861375
$218$	−295.985	−0.0919570
$219$	1120.52	0.345744
$220$	997.196	0.305595
$221$	5659.44	1.72260
$222$	2374.66	0.717913
$223$	−4116.11	−1.23603	−0.618016	−	0.786166i	$-0.712063\pi$
$223$	−4116.11	−1.23603	−0.618016	+	0.786166i	$0.712063\pi$
$224$	−2900.97	−0.865308
$225$	−338.429	−0.100275
$226$	4553.19	1.34015
$227$	−402.574	−0.117708	−0.0588541	−	0.998267i	$-0.518745\pi$
$227$	−402.574	−0.117708	−0.0588541	+	0.998267i	$0.518745\pi$
$228$	0	0
$229$	6101.41	1.76067	0.880334	−	0.474355i	$-0.157319\pi$
$229$	6101.41	1.76067	0.880334	+	0.474355i	$0.157319\pi$
$230$	−2847.67	−0.816391
$231$	1959.24	0.558046
$232$	−328.486	−0.0929575
$233$	4588.39	1.29011	0.645055	−	0.764136i	$-0.276835\pi$
$233$	4588.39	1.29011	0.645055	+	0.764136i	$0.276835\pi$
$234$	2162.55	0.604148
$235$	−2842.99	−0.789174
$236$	−999.330	−0.275639
$237$	−3073.00	−0.842249
$238$	−5447.87	−1.48375
$239$	−2721.93	−0.736682	−0.368341	−	0.929691i	$-0.620074\pi$
$239$	−2721.93	−0.736682	−0.368341	+	0.929691i	$0.620074\pi$
$240$	2231.21	0.600099
$241$	−4092.60	−1.09389	−0.546945	−	0.837168i	$-0.684209\pi$
$241$	−4092.60	−1.09389	−0.546945	+	0.837168i	$0.684209\pi$
$242$	1033.54	0.274538
$243$	243.000	0.0641500
$244$	127.952	0.0335709
$245$	−687.317	−0.179229
$246$	3260.80	0.845127
$247$	0	0
$248$	2119.56	0.542711
$249$	2830.24	0.720319
$250$	−5117.48	−1.29463
$251$	1890.57	0.475425	0.237713	−	0.971336i	$-0.423602\pi$
$251$	1890.57	0.475425	0.237713	+	0.971336i	$0.423602\pi$
$252$	−612.272	−0.153054
$253$	2895.42	0.719500
$254$	−7839.22	−1.93652
$255$	2223.81	0.546119
$256$	4354.60	1.06314
$257$	4036.01	0.979609	0.489805	−	0.871832i	$-0.337068\pi$
$257$	4036.01	0.979609	0.489805	+	0.871832i	$0.337068\pi$
$258$	3482.34	0.840314
$259$	4798.65	1.15125
$260$	2224.21	0.530538
$261$	−188.181	−0.0446288
$262$	6219.30	1.46653
$263$	2290.71	0.537077	0.268539	−	0.963269i	$-0.413459\pi$
$263$	2290.71	0.537077	0.268539	+	0.963269i	$0.413459\pi$
$264$	−1508.18	−0.351598
$265$	4298.72	0.996484
$266$	0	0
$267$	−2274.41	−0.521317
$268$	2168.13	0.494179
$269$	5621.25	1.27410	0.637051	−	0.770822i	$-0.280154\pi$
$269$	5621.25	1.27410	0.637051	+	0.770822i	$0.280154\pi$
$270$	849.750	0.191534
$271$	8618.00	1.93176	0.965878	−	0.258996i	$-0.0833916\pi$
$271$	8618.00	1.93176	0.965878	+	0.258996i	$0.0833916\pi$
$272$	6308.11	1.40620
$273$	4370.03	0.968814
$274$	1790.11	0.394687
$275$	1203.30	0.263861
$276$	−904.832	−0.197335
$277$	−930.771	−0.201894	−0.100947	−	0.994892i	$-0.532187\pi$
$277$	−930.771	−0.201894	−0.100947	+	0.994892i	$0.532187\pi$
$278$	−5260.22	−1.13484
$279$	1214.24	0.260555
$280$	2997.43	0.639752
$281$	−7954.11	−1.68862	−0.844311	−	0.535854i	$-0.819990\pi$
$281$	−7954.11	−1.68862	−0.844311	+	0.535854i	$0.819990\pi$
$282$	−3071.34	−0.648566
$283$	4668.08	0.980524	0.490262	−	0.871575i	$-0.336901\pi$
$283$	4668.08	0.980524	0.490262	+	0.871575i	$0.336901\pi$
$284$	−2098.15	−0.438389
$285$	0	0
$286$	−7689.06	−1.58973
$287$	6589.34	1.35525
$288$	1279.28	0.261745
$289$	1374.20	0.279706
$290$	−658.053	−0.133249
$291$	−3194.82	−0.643586
$292$	1245.04	0.249522
$293$	4079.74	0.813451	0.406725	−	0.913551i	$-0.366671\pi$
$293$	4079.74	0.813451	0.406725	+	0.913551i	$0.366671\pi$
$294$	−742.523	−0.147295
$295$	2802.67	0.553146
$296$	−3693.89	−0.725347
$297$	−863.998	−0.168802
$298$	8193.27	1.59270
$299$	6458.14	1.24911
$300$	−376.037	−0.0723683
$301$	7037.02	1.34753
$302$	−11864.6	−2.26071
$303$	−5717.02	−1.08394
$304$	0	0
$305$	−358.849	−0.0673693
$306$	2402.43	0.448816
$307$	−2866.55	−0.532908	−0.266454	−	0.963848i	$-0.585852\pi$
$307$	−2866.55	−0.532908	−0.266454	+	0.963848i	$0.585852\pi$
$308$	2176.96	0.402740
$309$	3291.82	0.606036
$310$	4246.11	0.777944
$311$	−2746.65	−0.500798	−0.250399	−	0.968143i	$-0.580562\pi$
$311$	−2746.65	−0.500798	−0.250399	+	0.968143i	$0.580562\pi$
$312$	−3363.94	−0.610403
$313$	638.007	0.115215	0.0576075	−	0.998339i	$-0.481653\pi$
$313$	638.007	0.115215	0.0576075	+	0.998339i	$0.481653\pi$
$314$	365.448	0.0656797
$315$	1717.15	0.307144
$316$	−3414.49	−0.607848
$317$	−8704.98	−1.54234	−0.771168	−	0.636632i	$-0.780327\pi$
$317$	−8704.98	−1.54234	−0.771168	+	0.636632i	$0.780327\pi$
$318$	4644.00	0.818939
$319$	669.087	0.117435
$320$	−1476.34	−0.257906
$321$	1323.88	0.230192
$322$	−6216.71	−1.07591
$323$	0	0
$324$	270.003	0.0462968
$325$	2683.92	0.458084
$326$	8843.13	1.50238
$327$	263.761	0.0446056
$328$	−5072.32	−0.853878
$329$	−6206.48	−1.04004
$330$	−3021.32	−0.503995
$331$	−2487.32	−0.413037	−0.206519	−	0.978443i	$-0.566213\pi$
$331$	−2487.32	−0.413037	−0.206519	+	0.978443i	$0.566213\pi$
$332$	3144.75	0.519851
$333$	−2116.13	−0.348239
$334$	−501.107	−0.0820939
$335$	−6080.65	−0.991706
$336$	4870.91	0.790863
$337$	−3950.49	−0.638567	−0.319284	−	0.947659i	$-0.603442\pi$
$337$	−3950.49	−0.638567	−0.319284	+	0.947659i	$0.603442\pi$
$338$	−9753.98	−1.56966
$339$	−4057.49	−0.650066
$340$	2470.93	0.394132
$341$	−4317.30	−0.685616
$342$	0	0
$343$	5499.76	0.865770
$344$	−5416.93	−0.849015
$345$	2537.65	0.396007
$346$	1122.17	0.174360
$347$	−2969.48	−0.459395	−0.229697	−	0.973262i	$-0.573774\pi$
$347$	−2969.48	−0.459395	−0.229697	+	0.973262i	$0.573774\pi$
$348$	−209.093	−0.0322085
$349$	−6263.98	−0.960754	−0.480377	−	0.877062i	$-0.659500\pi$
$349$	−6263.98	−0.960754	−0.480377	+	0.877062i	$0.659500\pi$
$350$	−2583.59	−0.394567
$351$	−1927.12	−0.293054
$352$	−4548.55	−0.688746
$353$	−1776.99	−0.267931	−0.133966	−	0.990986i	$-0.542771\pi$
$353$	−1776.99	−0.267931	−0.133966	+	0.990986i	$0.542771\pi$
$354$	3027.79	0.454591
$355$	5884.39	0.879749
$356$	−2527.15	−0.376232
$357$	4854.76	0.719724
$358$	11104.6	1.63937
$359$	−2480.78	−0.364710	−0.182355	−	0.983233i	$-0.558372\pi$
$359$	−2480.78	−0.364710	−0.182355	+	0.983233i	$0.558372\pi$
$360$	−1321.82	−0.193517
$361$	0	0
$362$	−11211.2	−1.62776
$363$	−921.017	−0.133170
$364$	4855.64	0.699189
$365$	−3491.78	−0.500735
$366$	−387.673	−0.0553660
$367$	−12548.3	−1.78478	−0.892389	−	0.451267i	$-0.850972\pi$
$367$	−12548.3	−1.78478	−0.892389	+	0.451267i	$0.850972\pi$
$368$	7198.36	1.01968
$369$	−2905.80	−0.409946
$370$	−7399.94	−1.03974
$371$	9384.47	1.31325
$372$	1349.18	0.188042
$373$	2737.91	0.380063	0.190032	−	0.981778i	$-0.439141\pi$
$373$	2737.91	0.380063	0.190032	+	0.981778i	$0.439141\pi$
$374$	−8541.95	−1.18100
$375$	4560.35	0.627988
$376$	4777.60	0.655282
$377$	1492.38	0.203876
$378$	1855.08	0.252420
$379$	5003.80	0.678174	0.339087	−	0.940755i	$-0.389882\pi$
$379$	5003.80	0.678174	0.339087	+	0.940755i	$0.389882\pi$
$380$	0	0
$381$	6985.77	0.939349
$382$	−96.2475	−0.0128912
$383$	−9487.29	−1.26574	−0.632869	−	0.774259i	$-0.718123\pi$
$383$	−9487.29	−1.26574	−0.632869	+	0.774259i	$0.718123\pi$
$384$	−5006.35	−0.665310
$385$	−6105.41	−0.808209
$386$	−8617.61	−1.13633
$387$	−3103.22	−0.407611
$388$	−3549.84	−0.464474
$389$	−2607.91	−0.339914	−0.169957	−	0.985451i	$-0.554363\pi$
$389$	−2607.91	−0.339914	−0.169957	+	0.985451i	$0.554363\pi$
$390$	−6738.97	−0.874976
$391$	7174.50	0.927954
$392$	1155.03	0.148821
$393$	−5542.22	−0.711369
$394$	−11379.5	−1.45505
$395$	9576.12	1.21981
$396$	−960.009	−0.121824
$397$	−5050.82	−0.638522	−0.319261	−	0.947667i	$-0.603435\pi$
$397$	−5050.82	−0.638522	−0.319261	+	0.947667i	$0.603435\pi$
$398$	7245.05	0.912467
$399$	0	0
$400$	2991.55	0.373943
$401$	4084.04	0.508596	0.254298	−	0.967126i	$-0.418156\pi$
$401$	4084.04	0.508596	0.254298	+	0.967126i	$0.418156\pi$
$402$	−6569.06	−0.815012
$403$	−9629.61	−1.19029
$404$	−6352.32	−0.782277
$405$	−757.239	−0.0929074
$406$	−1436.59	−0.175607
$407$	7524.01	0.916343
$408$	−3737.08	−0.453463
$409$	−13455.7	−1.62675	−0.813375	−	0.581740i	$-0.802372\pi$
$409$	−13455.7	−1.62675	−0.813375	+	0.581740i	$0.802372\pi$
$410$	−10161.3	−1.22398
$411$	−1595.22	−0.191451
$412$	3657.62	0.437374
$413$	6118.47	0.728984
$414$	2741.48	0.325450
$415$	−8819.63	−1.04323
$416$	−10145.4	−1.19572
$417$	4687.54	0.550480
$418$	0	0
$419$	2157.04	0.251500	0.125750	−	0.992062i	$-0.459866\pi$
$419$	2157.04	0.251500	0.125750	+	0.992062i	$0.459866\pi$
$420$	1907.97	0.221665
$421$	−8890.52	−1.02921	−0.514605	−	0.857428i	$-0.672061\pi$
$421$	−8890.52	−1.02921	−0.514605	+	0.857428i	$0.672061\pi$
$422$	−1480.36	−0.170765
$423$	2736.97	0.314600
$424$	−7223.94	−0.827418
$425$	2981.63	0.340306
$426$	6357.03	0.723003
$427$	−783.398	−0.0887852
$428$	1470.99	0.166129
$429$	6851.96	0.771132
$430$	−10851.7	−1.21701
$431$	−1303.01	−0.145624	−0.0728119	−	0.997346i	$-0.523197\pi$
$431$	−1303.01	−0.145624	−0.0728119	+	0.997346i	$0.523197\pi$
$432$	−2148.00	−0.239226
$433$	11127.3	1.23497	0.617487	−	0.786581i	$-0.288151\pi$
$433$	11127.3	1.23497	0.617487	+	0.786581i	$0.288151\pi$
$434$	9269.61	1.02524
$435$	586.412	0.0646352
$436$	293.072	0.0321917
$437$	0	0
$438$	−3772.25	−0.411518
$439$	−290.643	−0.0315982	−0.0157991	−	0.999875i	$-0.505029\pi$
$439$	−290.643	−0.0315982	−0.0157991	+	0.999875i	$0.505029\pi$
$440$	4699.80	0.509214
$441$	661.686	0.0714486
$442$	−19052.5	−2.05031
$443$	−7621.94	−0.817448	−0.408724	−	0.912658i	$-0.634026\pi$
$443$	−7621.94	−0.817448	−0.408724	+	0.912658i	$0.634026\pi$
$444$	−2351.29	−0.251323
$445$	7087.53	0.755014
$446$	13856.9	1.47117
$447$	−7301.28	−0.772570
$448$	−3222.97	−0.339891
$449$	−18563.2	−1.95111	−0.975557	−	0.219744i	$-0.929478\pi$
$449$	−18563.2	−1.95111	−0.975557	+	0.219744i	$0.929478\pi$
$450$	1139.32	0.119352
$451$	10331.7	1.07872
$452$	−4508.37	−0.469151
$453$	10573.0	1.09660
$454$	1355.27	0.140101
$455$	−13617.9	−1.40312
$456$	0	0
$457$	6177.29	0.632301	0.316150	−	0.948709i	$-0.397610\pi$
$457$	6177.29	0.632301	0.316150	+	0.948709i	$0.397610\pi$
$458$	−20540.5	−2.09562
$459$	−2140.88	−0.217707
$460$	2819.65	0.285797
$461$	−9206.06	−0.930085	−0.465042	−	0.885288i	$-0.653961\pi$
$461$	−9206.06	−0.930085	−0.465042	+	0.885288i	$0.653961\pi$
$462$	−6595.81	−0.664209
$463$	−3181.80	−0.319375	−0.159688	−	0.987168i	$-0.551049\pi$
$463$	−3181.80	−0.319375	−0.159688	+	0.987168i	$0.551049\pi$
$464$	1663.43	0.166429
$465$	−3783.84	−0.377358
$466$	−15446.9	−1.53554
$467$	7316.86	0.725019	0.362509	−	0.931980i	$-0.381920\pi$
$467$	7316.86	0.725019	0.362509	+	0.931980i	$0.381920\pi$
$468$	−2141.27	−0.211496
$469$	−13274.6	−1.30696
$470$	9570.94	0.939307
$471$	−325.662	−0.0318593
$472$	−4709.86	−0.459298
$473$	11033.6	1.07257
$474$	10345.3	1.00248
$475$	0	0
$476$	5394.24	0.519422
$477$	−4138.41	−0.397243
$478$	9163.39	0.876828
$479$	4652.93	0.443836	0.221918	−	0.975065i	$-0.428768\pi$
$479$	4652.93	0.443836	0.221918	+	0.975065i	$0.428768\pi$
$480$	−3986.52	−0.379081
$481$	16782.1	1.59084
$482$	13777.8	1.30199
$483$	5539.91	0.521893
$484$	−1023.36	−0.0961086
$485$	9955.72	0.932095
$486$	−818.061	−0.0763539
$487$	−8811.16	−0.819860	−0.409930	−	0.912117i	$-0.634447\pi$
$487$	−8811.16	−0.819860	−0.409930	+	0.912117i	$0.634447\pi$
$488$	603.041	0.0559393
$489$	−7880.39	−0.728760
$490$	2313.86	0.213325
$491$	18261.9	1.67851	0.839253	−	0.543741i	$-0.182993\pi$
$491$	18261.9	1.67851	0.839253	+	0.543741i	$0.182993\pi$
$492$	−3228.71	−0.295857
$493$	1657.92	0.151458
$494$	0	0
$495$	2692.40	0.244473
$496$	−10733.3	−0.971655
$497$	12846.1	1.15941
$498$	−9528.03	−0.857352
$499$	−8594.90	−0.771064	−0.385532	−	0.922695i	$-0.625982\pi$
$499$	−8594.90	−0.771064	−0.385532	+	0.922695i	$0.625982\pi$
$500$	5067.12	0.453217
$501$	446.552	0.0398213
$502$	−6364.62	−0.565870
$503$	6802.83	0.603028	0.301514	−	0.953462i	$-0.402508\pi$
$503$	6802.83	0.603028	0.301514	+	0.953462i	$0.402508\pi$
$504$	−2885.65	−0.255034
$505$	17815.4	1.56985
$506$	−9747.46	−0.856378
$507$	8692.08	0.761398
$508$	7762.06	0.677925
$509$	−9601.57	−0.836114	−0.418057	−	0.908421i	$-0.637289\pi$
$509$	−9601.57	−0.836114	−0.418057	+	0.908421i	$0.637289\pi$
$510$	−7486.47	−0.650013
$511$	−7622.85	−0.659912
$512$	−1309.55	−0.113036
$513$	0	0
$514$	−13587.3	−1.16597
$515$	−10258.0	−0.877711
$516$	−3448.07	−0.294172
$517$	−9731.41	−0.827828
$518$	−16154.7	−1.37026
$519$	−1000.00	−0.0845767
$520$	10482.7	0.884036
$521$	−11824.9	−0.994352	−0.497176	−	0.867650i	$-0.665630\pi$
$521$	−11824.9	−0.994352	−0.497176	+	0.867650i	$0.665630\pi$
$522$	633.514	0.0531190
$523$	6477.34	0.541557	0.270779	−	0.962642i	$-0.412719\pi$
$523$	6477.34	0.541557	0.270779	+	0.962642i	$0.412719\pi$
$524$	−6158.09	−0.513392
$525$	2302.31	0.191393
$526$	−7711.70	−0.639251
$527$	−10697.7	−0.884253
$528$	7637.32	0.629492
$529$	−3979.98	−0.327113
$530$	−14471.7	−1.18605
$531$	−2698.16	−0.220509
$532$	0	0
$533$	23044.6	1.87274
$534$	7656.81	0.620492
$535$	−4125.48	−0.333383
$536$	10218.5	0.823451
$537$	−9895.64	−0.795211
$538$	−18924.0	−1.51649
$539$	−2352.65	−0.188007
$540$	−841.386	−0.0670509
$541$	−4684.56	−0.372283	−0.186141	−	0.982523i	$-0.559598\pi$
$541$	−4684.56	−0.372283	−0.186141	+	0.982523i	$0.559598\pi$
$542$	−29012.6	−2.29925
$543$	9990.65	0.789576
$544$	−11270.8	−0.888290
$545$	−821.935	−0.0646015
$546$	−14711.7	−1.15312
$547$	−21113.3	−1.65034	−0.825172	−	0.564882i	$-0.808922\pi$
$547$	−21113.3	−1.65034	−0.825172	+	0.564882i	$0.808922\pi$
$548$	−1772.49	−0.138169
$549$	345.467	0.0268564
$550$	−4050.92	−0.314058
$551$	0	0
$552$	−4264.49	−0.328820
$553$	20905.5	1.60758
$554$	3133.45	0.240302
$555$	6594.31	0.504348
$556$	5208.44	0.397279
$557$	1245.43	0.0947407	0.0473704	−	0.998877i	$-0.484916\pi$
$557$	1245.43	0.0947407	0.0473704	+	0.998877i	$0.484916\pi$
$558$	−4087.76	−0.310123
$559$	24610.2	1.86208
$560$	−15178.8	−1.14539
$561$	7612.00	0.572868
$562$	26777.6	2.00986
$563$	−16289.4	−1.21939	−0.609695	−	0.792636i	$-0.708708\pi$
$563$	−16289.4	−1.21939	−0.609695	+	0.792636i	$0.708708\pi$
$564$	3041.11	0.227046
$565$	12644.0	0.941480
$566$	−15715.1	−1.16706
$567$	−1653.12	−0.122442
$568$	−9888.63	−0.730489
$569$	−14710.3	−1.08381	−0.541905	−	0.840440i	$-0.682297\pi$
$569$	−14710.3	−1.08381	−0.541905	+	0.840440i	$0.682297\pi$
$570$	0	0
$571$	6921.05	0.507245	0.253623	−	0.967303i	$-0.418378\pi$
$571$	6921.05	0.507245	0.253623	+	0.967303i	$0.418378\pi$
$572$	7613.38	0.556523
$573$	85.7691	0.00625315
$574$	−22183.1	−1.61307
$575$	3402.42	0.246767
$576$	1421.28	0.102813
$577$	−19449.1	−1.40325	−0.701627	−	0.712545i	$-0.747543\pi$
$577$	−19449.1	−1.40325	−0.701627	+	0.712545i	$0.747543\pi$
$578$	−4626.24	−0.332917
$579$	7679.42	0.551202
$580$	651.577	0.0466470
$581$	−19254.0	−1.37485
$582$	10755.4	0.766022
$583$	14714.3	1.04529
$584$	5867.89	0.415779
$585$	6005.30	0.424425
$586$	−13734.5	−0.968201
$587$	−20781.8	−1.46126	−0.730629	−	0.682775i	$-0.760773\pi$
$587$	−20781.8	−1.46126	−0.730629	+	0.682775i	$0.760773\pi$
$588$	735.215	0.0515642
$589$	0	0
$590$	−9435.22	−0.658376
$591$	10140.6	0.705802
$592$	18705.6	1.29864
$593$	−9595.12	−0.664459	−0.332230	−	0.943199i	$-0.607801\pi$
$593$	−9595.12	−0.664459	−0.332230	+	0.943199i	$0.607801\pi$
$594$	2908.65	0.200915
$595$	−15128.5	−1.04236
$596$	−8112.63	−0.557561
$597$	−6456.29	−0.442611
$598$	−21741.4	−1.48674
$599$	−1895.74	−0.129312	−0.0646558	−	0.997908i	$-0.520595\pi$
$599$	−1895.74	−0.129312	−0.0646558	+	0.997908i	$0.520595\pi$
$600$	−1772.27	−0.120587
$601$	14471.2	0.982185	0.491093	−	0.871107i	$-0.336598\pi$
$601$	14471.2	0.982185	0.491093	+	0.871107i	$0.336598\pi$
$602$	−23690.2	−1.60389
$603$	5853.89	0.395338
$604$	11747.9	0.791414
$605$	2870.08	0.192868
$606$	19246.4	1.29015
$607$	−3966.32	−0.265219	−0.132609	−	0.991168i	$-0.542336\pi$
$607$	−3966.32	−0.265219	−0.132609	+	0.991168i	$0.542336\pi$
$608$	0	0
$609$	1280.19	0.0851819
$610$	1208.07	0.0801857
$611$	−21705.6	−1.43718
$612$	−2378.78	−0.157119
$613$	18417.1	1.21347	0.606736	−	0.794904i	$-0.292479\pi$
$613$	18417.1	1.21347	0.606736	+	0.794904i	$0.292479\pi$
$614$	9650.26	0.634288
$615$	9055.09	0.593718
$616$	10260.1	0.671087
$617$	6381.90	0.416411	0.208205	−	0.978085i	$-0.433238\pi$
$617$	6381.90	0.416411	0.208205	+	0.978085i	$0.433238\pi$
$618$	−11081.9	−0.721328
$619$	1311.25	0.0851428	0.0425714	−	0.999093i	$-0.486445\pi$
$619$	1311.25	0.0851428	0.0425714	+	0.999093i	$0.486445\pi$
$620$	−4204.32	−0.272338
$621$	−2443.02	−0.157866
$622$	9246.61	0.596070
$623$	15472.7	0.995023
$624$	17034.8	1.09285
$625$	−9510.59	−0.608678
$626$	−2147.85	−0.137133
$627$	0	0
$628$	−361.851	−0.0229927
$629$	18643.6	1.18183
$630$	−5780.80	−0.365576
$631$	−14711.1	−0.928111	−0.464056	−	0.885806i	$-0.653606\pi$
$631$	−14711.1	−0.928111	−0.464056	+	0.885806i	$0.653606\pi$
$632$	−16092.5	−1.01286
$633$	1319.20	0.0828331
$634$	29305.4	1.83575
$635$	−21769.1	−1.36044
$636$	−4598.29	−0.286689
$637$	−5247.52	−0.326396
$638$	−2252.49	−0.139776
$639$	−5664.95	−0.350707
$640$	15600.8	0.963557
$641$	−20002.9	−1.23255	−0.616277	−	0.787529i	$-0.711360\pi$
$641$	−20002.9	−1.23255	−0.616277	+	0.787529i	$0.711360\pi$
$642$	−4456.85	−0.273984
$643$	6750.64	0.414027	0.207013	−	0.978338i	$-0.433626\pi$
$643$	6750.64	0.414027	0.207013	+	0.978338i	$0.433626\pi$
$644$	6155.53	0.376649
$645$	9670.29	0.590337
$646$	0	0
$647$	10225.5	0.621338	0.310669	−	0.950518i	$-0.399447\pi$
$647$	10225.5	0.621338	0.310669	+	0.950518i	$0.399447\pi$
$648$	1272.53	0.0771445
$649$	9593.43	0.580239
$650$	−9035.44	−0.545230
$651$	−8260.44	−0.497315
$652$	−8756.10	−0.525944
$653$	−28306.9	−1.69638	−0.848190	−	0.529692i	$-0.822308\pi$
$653$	−28306.9	−1.69638	−0.848190	+	0.529692i	$0.822308\pi$
$654$	−887.955	−0.0530914
$655$	17270.7	1.03026
$656$	25685.9	1.52876
$657$	3361.57	0.199615
$658$	20894.2	1.23790
$659$	−14409.6	−0.851772	−0.425886	−	0.904777i	$-0.640037\pi$
$659$	−14409.6	−0.851772	−0.425886	+	0.904777i	$0.640037\pi$
$660$	2991.59	0.176435
$661$	−20704.1	−1.21830	−0.609150	−	0.793055i	$-0.708489\pi$
$661$	−20704.1	−1.21830	−0.609150	+	0.793055i	$0.708489\pi$
$662$	8373.58	0.491614
$663$	16978.3	0.994544
$664$	14821.3	0.866230
$665$	0	0
$666$	7123.98	0.414488
$667$	1891.89	0.109827
$668$	496.175	0.0287389
$669$	−12348.3	−0.713623
$670$	20470.6	1.18037
$671$	−1228.32	−0.0706691
$672$	−8702.90	−0.499586
$673$	−16689.6	−0.955924	−0.477962	−	0.878381i	$-0.658624\pi$
$673$	−16689.6	−0.955924	−0.477962	+	0.878381i	$0.658624\pi$
$674$	13299.4	0.760048
$675$	−1015.29	−0.0578940
$676$	9657.98	0.549498
$677$	−2416.80	−0.137201	−0.0686004	−	0.997644i	$-0.521853\pi$
$677$	−2416.80	−0.137201	−0.0686004	+	0.997644i	$0.521853\pi$
$678$	13659.6	0.773735
$679$	21734.2	1.22840
$680$	11645.5	0.656743
$681$	−1207.72	−0.0679589
$682$	14534.2	0.816048
$683$	13279.3	0.743950	0.371975	−	0.928243i	$-0.378681\pi$
$683$	13279.3	0.743950	0.371975	+	0.928243i	$0.378681\pi$
$684$	0	0
$685$	4971.03	0.277275
$686$	−18515.0	−1.03047
$687$	18304.2	1.01652
$688$	27431.0	1.52005
$689$	32819.8	1.81471
$690$	−8543.02	−0.471344
$691$	−19856.5	−1.09317	−0.546583	−	0.837405i	$-0.684072\pi$
$691$	−19856.5	−1.09317	−0.546583	+	0.837405i	$0.684072\pi$
$692$	−1111.13	−0.0610387
$693$	5877.73	0.322188
$694$	9996.77	0.546790
$695$	−14607.4	−0.797250
$696$	−985.457	−0.0536691
$697$	25600.7	1.39124
$698$	21087.7	1.14353
$699$	13765.2	0.744845
$700$	2558.16	0.138128
$701$	−2317.66	−0.124874	−0.0624371	−	0.998049i	$-0.519887\pi$
$701$	−2317.66	−0.124874	−0.0624371	+	0.998049i	$0.519887\pi$
$702$	6487.66	0.348805
$703$	0	0
$704$	−5053.44	−0.270538
$705$	−8528.96	−0.455630
$706$	5982.26	0.318903
$707$	38892.6	2.06889
$708$	−2997.99	−0.159140
$709$	−4630.73	−0.245290	−0.122645	−	0.992451i	$-0.539138\pi$
$709$	−4630.73	−0.245290	−0.122645	+	0.992451i	$0.539138\pi$
$710$	−19809.8	−1.04711
$711$	−9219.01	−0.486273
$712$	−11910.5	−0.626917
$713$	−12207.5	−0.641198
$714$	−16343.6	−0.856644
$715$	−21352.1	−1.11682
$716$	−10995.3	−0.573901
$717$	−8165.79	−0.425323
$718$	8351.58	0.434092
$719$	3708.42	0.192352	0.0961758	−	0.995364i	$-0.469339\pi$
$719$	3708.42	0.192352	0.0961758	+	0.995364i	$0.469339\pi$
$720$	6693.62	0.346467
$721$	−22394.1	−1.15673
$722$	0	0
$723$	−12277.8	−0.631558
$724$	11100.9	0.569834
$725$	786.247	0.0402765
$726$	3100.61	0.158505
$727$	35686.8	1.82056	0.910282	−	0.413988i	$-0.135865\pi$
$727$	35686.8	1.82056	0.910282	+	0.413988i	$0.135865\pi$
$728$	22884.7	1.16506
$729$	729.000	0.0370370
$730$	11755.1	0.595994
$731$	27340.0	1.38332
$732$	383.857	0.0193822
$733$	−22753.0	−1.14652	−0.573261	−	0.819373i	$-0.694322\pi$
$733$	−22753.0	−1.14652	−0.573261	+	0.819373i	$0.694322\pi$
$734$	42243.8	2.12431
$735$	−2061.95	−0.103478
$736$	−12861.4	−0.644126
$737$	−20813.8	−1.04028
$738$	9782.41	0.487934
$739$	−30158.3	−1.50121	−0.750603	−	0.660753i	$-0.770237\pi$
$739$	−30158.3	−1.50121	−0.750603	+	0.660753i	$0.770237\pi$
$740$	7327.10	0.363986
$741$	0	0
$742$	−31592.9	−1.56309
$743$	791.434	0.0390779	0.0195390	−	0.999809i	$-0.493780\pi$
$743$	791.434	0.0390779	0.0195390	+	0.999809i	$0.493780\pi$
$744$	6358.69	0.313335
$745$	22752.3	1.11890
$746$	−9217.19	−0.452366
$747$	8490.73	0.415876
$748$	8457.87	0.413436
$749$	−9006.27	−0.439362
$750$	−15352.5	−0.747456
$751$	17416.0	0.846231	0.423116	−	0.906076i	$-0.360936\pi$
$751$	17416.0	0.846231	0.423116	+	0.906076i	$0.360936\pi$
$752$	−24193.5	−1.17320
$753$	5671.71	0.274487
$754$	−5024.10	−0.242662
$755$	−32947.5	−1.58819
$756$	−1836.82	−0.0883656
$757$	1822.36	0.0874963	0.0437481	−	0.999043i	$-0.486070\pi$
$757$	1822.36	0.0874963	0.0437481	+	0.999043i	$0.486070\pi$
$758$	−16845.3	−0.807190
$759$	8686.26	0.415404
$760$	0	0
$761$	−33405.5	−1.59126	−0.795629	−	0.605785i	$-0.792859\pi$
$761$	−33405.5	−1.59126	−0.795629	+	0.605785i	$0.792859\pi$
$762$	−23517.7	−1.11805
$763$	−1794.35	−0.0851376
$764$	95.3002	0.00451288
$765$	6671.43	0.315302
$766$	31939.0	1.50653
$767$	21397.8	1.00734
$768$	13063.8	0.613802
$769$	−20196.2	−0.947066	−0.473533	−	0.880776i	$-0.657022\pi$
$769$	−20196.2	−0.947066	−0.473533	+	0.880776i	$0.657022\pi$
$770$	20553.9	0.961963
$771$	12108.0	0.565578
$772$	8532.79	0.397800
$773$	8715.42	0.405526	0.202763	−	0.979228i	$-0.435008\pi$
$773$	8715.42	0.405526	0.202763	+	0.979228i	$0.435008\pi$
$774$	10447.0	0.485156
$775$	−5073.28	−0.235145
$776$	−16730.5	−0.773954
$777$	14395.9	0.664674
$778$	8779.57	0.404579
$779$	0	0
$780$	6672.64	0.306306
$781$	20142.0	0.922839
$782$	−24153.0	−1.10449
$783$	−564.544	−0.0257665
$784$	−5848.98	−0.266444
$785$	1014.83	0.0461413
$786$	18657.9	0.846699
$787$	−27349.5	−1.23876	−0.619380	−	0.785091i	$-0.712616\pi$
$787$	−27349.5	−1.23876	−0.619380	+	0.785091i	$0.712616\pi$
$788$	11267.5	0.509374
$789$	6872.13	0.310082
$790$	−32238.1	−1.45187
$791$	27602.9	1.24076
$792$	−4524.54	−0.202995
$793$	−2739.74	−0.122687
$794$	17003.6	0.759995
$795$	12896.2	0.575320
$796$	−7173.74	−0.319430
$797$	8187.05	0.363865	0.181932	−	0.983311i	$-0.441765\pi$
$797$	8187.05	0.363865	0.181932	+	0.983311i	$0.441765\pi$
$798$	0	0
$799$	−24113.2	−1.06767
$800$	−5345.02	−0.236219
$801$	−6823.22	−0.300982
$802$	−13748.9	−0.605351
$803$	−11952.2	−0.525260
$804$	6504.40	0.285314
$805$	−17263.5	−0.755849
$806$	32418.1	1.41673
$807$	16863.7	0.735603
$808$	−29938.6	−1.30351
$809$	23903.4	1.03881	0.519406	−	0.854527i	$-0.326153\pi$
$809$	23903.4	1.03881	0.519406	+	0.854527i	$0.326153\pi$
$810$	2549.25	0.110582
$811$	4439.30	0.192213	0.0961066	−	0.995371i	$-0.469361\pi$
$811$	4439.30	0.192213	0.0961066	+	0.995371i	$0.469361\pi$
$812$	1422.45	0.0614755
$813$	25854.0	1.11530
$814$	−25329.6	−1.09067
$815$	24556.9	1.05545
$816$	18924.3	0.811868
$817$	0	0
$818$	45298.6	1.93622
$819$	13110.1	0.559345
$820$	10061.3	0.428484
$821$	32465.1	1.38007	0.690036	−	0.723775i	$-0.257595\pi$
$821$	32465.1	1.38007	0.690036	+	0.723775i	$0.257595\pi$
$822$	5370.32	0.227873
$823$	19416.5	0.822379	0.411189	−	0.911550i	$-0.365113\pi$
$823$	19416.5	0.822379	0.411189	+	0.911550i	$0.365113\pi$
$824$	17238.4	0.728797
$825$	3609.90	0.152340
$826$	−20597.9	−0.867666
$827$	−21555.0	−0.906337	−0.453169	−	0.891425i	$-0.649706\pi$
$827$	−21555.0	−0.906337	−0.453169	+	0.891425i	$0.649706\pi$
$828$	−2714.50	−0.113932
$829$	5587.97	0.234111	0.117056	−	0.993125i	$-0.462654\pi$
$829$	5587.97	0.234111	0.117056	+	0.993125i	$0.462654\pi$
$830$	29691.3	1.24169
$831$	−2792.31	−0.116564
$832$	−11271.5	−0.469676
$833$	−5829.59	−0.242477
$834$	−15780.7	−0.655203
$835$	−1391.55	−0.0576725
$836$	0	0
$837$	3642.73	0.150432
$838$	−7261.70	−0.299345
$839$	9893.46	0.407104	0.203552	−	0.979064i	$-0.434751\pi$
$839$	9893.46	0.407104	0.203552	+	0.979064i	$0.434751\pi$
$840$	8992.28	0.369361
$841$	−23951.8	−0.982074
$842$	29930.0	1.22501
$843$	−23862.3	−0.974926
$844$	1465.79	0.0597803
$845$	−27086.3	−1.10272
$846$	−9214.02	−0.374450
$847$	6265.63	0.254179
$848$	36581.5	1.48139
$849$	14004.2	0.566106
$850$	−10037.7	−0.405046
$851$	21274.7	0.856977
$852$	−6294.46	−0.253104
$853$	44111.9	1.77065	0.885325	−	0.464973i	$-0.153936\pi$
$853$	44111.9	1.77065	0.885325	+	0.464973i	$0.153936\pi$
$854$	2637.32	0.105676
$855$	0	0
$856$	6932.81	0.276821
$857$	−14226.2	−0.567045	−0.283522	−	0.958966i	$-0.591503\pi$
$857$	−14226.2	−0.567045	−0.283522	+	0.958966i	$0.591503\pi$
$858$	−23067.2	−0.917833
$859$	−22116.8	−0.878481	−0.439240	−	0.898370i	$-0.644752\pi$
$859$	−22116.8	−0.878481	−0.439240	+	0.898370i	$0.644752\pi$
$860$	10744.9	0.426044
$861$	19768.0	0.782454
$862$	4386.60	0.173327
$863$	−44389.4	−1.75091	−0.875454	−	0.483301i	$-0.839438\pi$
$863$	−44389.4	−1.75091	−0.875454	+	0.483301i	$0.839438\pi$
$864$	3837.85	0.151118
$865$	3116.22	0.122491
$866$	−37460.1	−1.46991
$867$	4122.59	0.161488
$868$	−9178.38	−0.358911
$869$	32778.6	1.27956
$870$	−1974.16	−0.0769314
$871$	−46424.5	−1.80601
$872$	1381.25	0.0536411
$873$	−9584.46	−0.371575
$874$	0	0
$875$	−31023.8	−1.19862
$876$	3735.12	0.144062
$877$	−6633.03	−0.255395	−0.127698	−	0.991813i	$-0.540759\pi$
$877$	−6633.03	−0.255395	−0.127698	+	0.991813i	$0.540759\pi$
$878$	978.450	0.0376095
$879$	12239.2	0.469646
$880$	−23799.5	−0.911682
$881$	−9003.10	−0.344293	−0.172146	−	0.985071i	$-0.555070\pi$
$881$	−9003.10	−0.344293	−0.172146	+	0.985071i	$0.555070\pi$
$882$	−2227.57	−0.0850410
$883$	14884.5	0.567274	0.283637	−	0.958932i	$-0.408459\pi$
$883$	14884.5	0.567274	0.283637	+	0.958932i	$0.408459\pi$
$884$	18865.0	0.717759
$885$	8408.02	0.319359
$886$	25659.3	0.972959
$887$	3422.45	0.129554	0.0647771	−	0.997900i	$-0.479366\pi$
$887$	3422.45	0.129554	0.0647771	+	0.997900i	$0.479366\pi$
$888$	−11081.7	−0.418779
$889$	−47523.8	−1.79291
$890$	−23860.2	−0.898648
$891$	−2591.99	−0.0974580
$892$	−13720.5	−0.515019
$893$	0	0
$894$	24579.8	0.919544
$895$	30836.9	1.15169
$896$	34057.9	1.26986
$897$	19374.4	0.721174
$898$	62493.1	2.32230
$899$	−2820.97	−0.104655
$900$	−1128.11	−0.0417819
$901$	36460.3	1.34813
$902$	−34781.8	−1.28393
$903$	21111.1	0.777998
$904$	−21248.0	−0.781747
$905$	−31133.0	−1.14353
$906$	−35593.9	−1.30522
$907$	1800.74	0.0659236	0.0329618	−	0.999457i	$-0.489506\pi$
$907$	1800.74	0.0659236	0.0329618	+	0.999457i	$0.489506\pi$
$908$	−1341.93	−0.0490457
$909$	−17151.1	−0.625814
$910$	45844.8	1.67005
$911$	−5096.53	−0.185352	−0.0926759	−	0.995696i	$-0.529542\pi$
$911$	−5096.53	−0.185352	−0.0926759	+	0.995696i	$0.529542\pi$
$912$	0	0
$913$	−30189.2	−1.09432
$914$	−20795.9	−0.752590
$915$	−1076.55	−0.0388957
$916$	20338.3	0.733620
$917$	37703.4	1.35777
$918$	7207.29	0.259124
$919$	28779.5	1.03302	0.516512	−	0.856280i	$-0.327230\pi$
$919$	28779.5	1.03302	0.516512	+	0.856280i	$0.327230\pi$
$920$	13289.0	0.476224
$921$	−8599.65	−0.307674
$922$	30992.3	1.10702
$923$	44926.0	1.60212
$924$	6530.89	0.232522
$925$	8841.50	0.314277
$926$	10711.5	0.380133
$927$	9875.46	0.349895
$928$	−2972.07	−0.105132
$929$	38819.0	1.37095	0.685474	−	0.728097i	$-0.259595\pi$
$929$	38819.0	1.37095	0.685474	+	0.728097i	$0.259595\pi$
$930$	12738.3	0.449146
$931$	0	0
$932$	15294.8	0.537552
$933$	−8239.94	−0.289136
$934$	−24632.3	−0.862947
$935$	−23720.6	−0.829674
$936$	−10091.8	−0.352416
$937$	16019.0	0.558504	0.279252	−	0.960218i	$-0.409914\pi$
$937$	16019.0	0.558504	0.279252	+	0.960218i	$0.409914\pi$
$938$	44689.0	1.55559
$939$	1914.02	0.0665194
$940$	−9476.73	−0.328827
$941$	37470.0	1.29807	0.649036	−	0.760758i	$-0.275172\pi$
$941$	37470.0	1.29807	0.649036	+	0.760758i	$0.275172\pi$
$942$	1096.34	0.0379202
$943$	29213.7	1.00883
$944$	23850.4	0.822314
$945$	5151.45	0.177330
$946$	−37144.9	−1.27662
$947$	43079.4	1.47824	0.739120	−	0.673574i	$-0.235242\pi$
$947$	43079.4	1.47824	0.739120	+	0.673574i	$0.235242\pi$
$948$	−10243.5	−0.350941
$949$	−26659.0	−0.911895
$950$	0	0
$951$	−26114.9	−0.890468
$952$	25423.2	0.865514
$953$	17616.4	0.598793	0.299397	−	0.954129i	$-0.403215\pi$
$953$	17616.4	0.598793	0.299397	+	0.954129i	$0.403215\pi$
$954$	13932.0	0.472815
$955$	−267.274	−0.00905633
$956$	−9073.20	−0.306954
$957$	2007.26	0.0678010
$958$	−15664.1	−0.528272
$959$	10852.2	0.365417
$960$	−4429.02	−0.148902
$961$	−11588.6	−0.388998
$962$	−56497.0	−1.89349
$963$	3971.63	0.132901
$964$	−13642.2	−0.455793
$965$	−23930.7	−0.798296
$966$	−18650.1	−0.621178
$967$	−21038.3	−0.699633	−0.349816	−	0.936818i	$-0.613756\pi$
$967$	−21038.3	−0.699633	−0.349816	+	0.936818i	$0.613756\pi$
$968$	−4823.13	−0.160146
$969$	0	0
$970$	−33516.0	−1.10942
$971$	−6911.94	−0.228440	−0.114220	−	0.993456i	$-0.536437\pi$
$971$	−6911.94	−0.228440	−0.114220	+	0.993456i	$0.536437\pi$
$972$	810.010	0.0267295
$973$	−31889.1	−1.05069
$974$	29662.8	0.975830
$975$	8051.77	0.264475
$976$	−3053.76	−0.100152
$977$	29166.0	0.955071	0.477535	−	0.878612i	$-0.341530\pi$
$977$	29166.0	0.955071	0.477535	+	0.878612i	$0.341530\pi$
$978$	26529.4	0.867400
$979$	24260.3	0.791994
$980$	−2291.08	−0.0746796
$981$	791.284	0.0257531
$982$	−61478.7	−1.99783
$983$	−27820.9	−0.902694	−0.451347	−	0.892349i	$-0.649056\pi$
$983$	−27820.9	−0.902694	−0.451347	+	0.892349i	$0.649056\pi$
$984$	−15217.0	−0.492987
$985$	−31600.2	−1.02220
$986$	−5581.39	−0.180271
$987$	−18619.4	−0.600469
$988$	0	0
$989$	31198.5	1.00309
$990$	−9063.97	−0.290982
$991$	−38803.2	−1.24382	−0.621909	−	0.783090i	$-0.713643\pi$
$991$	−38803.2	−1.24382	−0.621909	+	0.783090i	$0.713643\pi$
$992$	19177.3	0.613791
$993$	−7461.96	−0.238467
$994$	−43246.5	−1.37998
$995$	20119.2	0.641025
$996$	9434.26	0.300136
$997$	15467.3	0.491329	0.245665	−	0.969355i	$-0.420994\pi$
$997$	15467.3	0.491329	0.245665	+	0.969355i	$0.420994\pi$
$998$	28934.8	0.917751
$999$	−6348.40	−0.201056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1083.4.a.t.1.6		18
19.14	odd	18		57.4.i.b.25.5	yes	36
19.15	odd	18		57.4.i.b.16.5	✓	36
19.18	odd	2		1083.4.a.s.1.13		18
57.14	even	18		171.4.u.c.82.2		36
57.53	even	18		171.4.u.c.73.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.4.i.b.16.5	✓	36	19.15	odd	18
57.4.i.b.25.5	yes	36	19.14	odd	18
171.4.u.c.73.2		36	57.53	even	18
171.4.u.c.82.2		36	57.14	even	18
1083.4.a.s.1.13		18	19.18	odd	2
1083.4.a.t.1.6		18	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:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1083.a (trivial)

\(f(q)\)	\(=\)	\(q-3.36651 q^{2} +3.00000 q^{3} +3.33337 q^{4} -9.34862 q^{5} -10.0995 q^{6} -20.4088 q^{7} +15.7102 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.36651 q^{2} +3.00000 q^{3} +3.33337 q^{4} -9.34862 q^{5} -10.0995 q^{6} -20.4088 q^{7} +15.7102 q^{8} +9.00000 q^{9} +31.4722 q^{10} -31.9999 q^{11} +10.0001 q^{12} -71.3748 q^{13} +68.7065 q^{14} -28.0459 q^{15} -79.5556 q^{16} -79.2918 q^{17} -30.2986 q^{18} -31.1625 q^{20} -61.2265 q^{21} +107.728 q^{22} -90.4822 q^{23} +47.1307 q^{24} -37.6032 q^{25} +240.284 q^{26} +27.0000 q^{27} -68.0303 q^{28} -20.9090 q^{29} +94.4166 q^{30} +134.916 q^{31} +142.143 q^{32} -95.9997 q^{33} +266.937 q^{34} +190.795 q^{35} +30.0004 q^{36} -235.126 q^{37} -214.124 q^{39} -146.869 q^{40} -322.867 q^{41} +206.120 q^{42} -344.802 q^{43} -106.668 q^{44} -84.1376 q^{45} +304.609 q^{46} +304.107 q^{47} -238.667 q^{48} +73.5206 q^{49} +126.592 q^{50} -237.876 q^{51} -237.919 q^{52} -459.824 q^{53} -90.8957 q^{54} +299.155 q^{55} -320.628 q^{56} +70.3904 q^{58} -299.795 q^{59} -93.4874 q^{60} +38.3852 q^{61} -454.196 q^{62} -183.680 q^{63} +157.920 q^{64} +667.256 q^{65} +323.184 q^{66} +650.433 q^{67} -264.309 q^{68} -271.446 q^{69} -642.311 q^{70} -629.439 q^{71} +141.392 q^{72} +373.507 q^{73} +791.554 q^{74} -112.810 q^{75} +653.081 q^{77} +720.851 q^{78} -1024.33 q^{79} +743.735 q^{80} +81.0000 q^{81} +1086.93 q^{82} +943.414 q^{83} -204.091 q^{84} +741.270 q^{85} +1160.78 q^{86} -62.7271 q^{87} -502.726 q^{88} -758.136 q^{89} +283.250 q^{90} +1456.68 q^{91} -301.611 q^{92} +404.748 q^{93} -1023.78 q^{94} +426.428 q^{96} -1064.94 q^{97} -247.508 q^{98} -287.999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 54 q^{3} + 96 q^{4} + 18 q^{5} + 48 q^{7} - 57 q^{8} + 162 q^{9}+O(q^{10}) \) 18 * q + 54 * q^3 + 96 * q^4 + 18 * q^5 + 48 * q^7 - 57 * q^8 + 162 * q^9	\( 18 q + 54 q^{3} + 96 q^{4} + 18 q^{5} + 48 q^{7} - 57 q^{8} + 162 q^{9} + 60 q^{10} + 108 q^{11} + 288 q^{12} + 42 q^{13} - 60 q^{14} + 54 q^{15} + 576 q^{16} + 300 q^{17} + 27 q^{20} + 144 q^{21} + 219 q^{22} + 174 q^{23} - 171 q^{24} + 1068 q^{25} - 72 q^{26} + 486 q^{27} + 867 q^{28} - 168 q^{29} + 180 q^{30} + 1032 q^{31} - 921 q^{32} + 324 q^{33} - 75 q^{34} + 1524 q^{35} + 864 q^{36} - 132 q^{37} + 126 q^{39} + 363 q^{40} - 120 q^{41} - 180 q^{42} + 420 q^{43} + 2328 q^{44} + 162 q^{45} + 2229 q^{46} + 810 q^{47} + 1728 q^{48} + 1122 q^{49} + 1503 q^{50} + 900 q^{51} - 228 q^{52} + 174 q^{53} + 2550 q^{55} - 1119 q^{56} + 756 q^{58} - 474 q^{59} + 81 q^{60} + 1488 q^{61} + 333 q^{62} + 432 q^{63} + 2679 q^{64} + 1716 q^{65} + 657 q^{66} + 3060 q^{67} + 4623 q^{68} + 522 q^{69} + 1383 q^{70} - 1464 q^{71} - 513 q^{72} + 1470 q^{73} - 135 q^{74} + 3204 q^{75} + 1014 q^{77} - 216 q^{78} + 2508 q^{79} - 2049 q^{80} + 1458 q^{81} + 1485 q^{82} + 4764 q^{83} + 2601 q^{84} + 804 q^{85} + 1068 q^{86} - 504 q^{87} + 3012 q^{88} - 1050 q^{89} + 540 q^{90} - 3408 q^{91} + 3306 q^{92} + 3096 q^{93} + 8205 q^{94} - 2763 q^{96} - 2070 q^{97} - 1767 q^{98} + 972 q^{99}+O(q^{100}) \) 18 * q + 54 * q^3 + 96 * q^4 + 18 * q^5 + 48 * q^7 - 57 * q^8 + 162 * q^9 + 60 * q^10 + 108 * q^11 + 288 * q^12 + 42 * q^13 - 60 * q^14 + 54 * q^15 + 576 * q^16 + 300 * q^17 + 27 * q^20 + 144 * q^21 + 219 * q^22 + 174 * q^23 - 171 * q^24 + 1068 * q^25 - 72 * q^26 + 486 * q^27 + 867 * q^28 - 168 * q^29 + 180 * q^30 + 1032 * q^31 - 921 * q^32 + 324 * q^33 - 75 * q^34 + 1524 * q^35 + 864 * q^36 - 132 * q^37 + 126 * q^39 + 363 * q^40 - 120 * q^41 - 180 * q^42 + 420 * q^43 + 2328 * q^44 + 162 * q^45 + 2229 * q^46 + 810 * q^47 + 1728 * q^48 + 1122 * q^49 + 1503 * q^50 + 900 * q^51 - 228 * q^52 + 174 * q^53 + 2550 * q^55 - 1119 * q^56 + 756 * q^58 - 474 * q^59 + 81 * q^60 + 1488 * q^61 + 333 * q^62 + 432 * q^63 + 2679 * q^64 + 1716 * q^65 + 657 * q^66 + 3060 * q^67 + 4623 * q^68 + 522 * q^69 + 1383 * q^70 - 1464 * q^71 - 513 * q^72 + 1470 * q^73 - 135 * q^74 + 3204 * q^75 + 1014 * q^77 - 216 * q^78 + 2508 * q^79 - 2049 * q^80 + 1458 * q^81 + 1485 * q^82 + 4764 * q^83 + 2601 * q^84 + 804 * q^85 + 1068 * q^86 - 504 * q^87 + 3012 * q^88 - 1050 * q^89 + 540 * q^90 - 3408 * q^91 + 3306 * q^92 + 3096 * q^93 + 8205 * q^94 - 2763 * q^96 - 2070 * q^97 - 1767 * q^98 + 972 * q^99

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