LMFDB - Embedded newform 1441.4.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.94944 q^{2} -0.986242 q^{3} +16.4970 q^{4} -9.10214 q^{5} +4.88135 q^{6} -0.117691 q^{7} -42.0552 q^{8} -26.0273 q^{9} +O(q^{10})$	\(q-4.94944 q^{2} -0.986242 q^{3} +16.4970 q^{4} -9.10214 q^{5} +4.88135 q^{6} -0.117691 q^{7} -42.0552 q^{8} -26.0273 q^{9} +45.0505 q^{10} -11.0000 q^{11} -16.2700 q^{12} +33.7294 q^{13} +0.582504 q^{14} +8.97691 q^{15} +76.1741 q^{16} +128.842 q^{17} +128.821 q^{18} +7.38135 q^{19} -150.158 q^{20} +0.116072 q^{21} +54.4438 q^{22} +115.355 q^{23} +41.4766 q^{24} -42.1511 q^{25} -166.942 q^{26} +52.2978 q^{27} -1.94154 q^{28} -208.626 q^{29} -44.4307 q^{30} -108.981 q^{31} -40.5775 q^{32} +10.8487 q^{33} -637.698 q^{34} +1.07124 q^{35} -429.372 q^{36} +80.4118 q^{37} -36.5336 q^{38} -33.2654 q^{39} +382.792 q^{40} +250.086 q^{41} -0.574490 q^{42} -50.9010 q^{43} -181.467 q^{44} +236.904 q^{45} -570.940 q^{46} -180.683 q^{47} -75.1261 q^{48} -342.986 q^{49} +208.624 q^{50} -127.070 q^{51} +556.433 q^{52} +175.177 q^{53} -258.845 q^{54} +100.124 q^{55} +4.94952 q^{56} -7.27980 q^{57} +1032.58 q^{58} -169.673 q^{59} +148.092 q^{60} -125.136 q^{61} +539.397 q^{62} +3.06318 q^{63} -408.557 q^{64} -307.010 q^{65} -53.6948 q^{66} -917.756 q^{67} +2125.51 q^{68} -113.768 q^{69} -5.30203 q^{70} +907.010 q^{71} +1094.58 q^{72} +537.884 q^{73} -397.994 q^{74} +41.5712 q^{75} +121.770 q^{76} +1.29460 q^{77} +164.645 q^{78} +539.103 q^{79} -693.347 q^{80} +651.160 q^{81} -1237.79 q^{82} +662.269 q^{83} +1.91483 q^{84} -1172.74 q^{85} +251.931 q^{86} +205.756 q^{87} +462.607 q^{88} -1553.57 q^{89} -1172.54 q^{90} -3.96965 q^{91} +1903.00 q^{92} +107.482 q^{93} +894.280 q^{94} -67.1861 q^{95} +40.0192 q^{96} -469.571 q^{97} +1697.59 q^{98} +286.301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) $ 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * 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 $

$2$	−4.94944	−1.74989	−0.874946	−	0.484221i	$-0.839103\pi$
$2$	−4.94944	−1.74989	−0.874946	+	0.484221i	$0.839103\pi$
$3$	−0.986242	−0.189802	−0.0949012	−	0.995487i	$-0.530254\pi$
$3$	−0.986242	−0.189802	−0.0949012	+	0.995487i	$0.530254\pi$
$4$	16.4970	2.06212
$5$	−9.10214	−0.814120	−0.407060	−	0.913401i	$-0.633446\pi$
$5$	−9.10214	−0.814120	−0.407060	+	0.913401i	$0.633446\pi$
$6$	4.88135	0.332134
$7$	−0.117691	−0.00635471	−0.00317736	−	0.999995i	$-0.501011\pi$
$7$	−0.117691	−0.00635471	−0.00317736	+	0.999995i	$0.501011\pi$
$8$	−42.0552	−1.85860
$9$	−26.0273	−0.963975
$10$	45.0505	1.42462
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−16.2700	−0.391395
$13$	33.7294	0.719605	0.359803	−	0.933028i	$-0.382844\pi$
$13$	33.7294	0.719605	0.359803	+	0.933028i	$0.382844\pi$
$14$	0.582504	0.0111201
$15$	8.97691	0.154522
$16$	76.1741	1.19022
$17$	128.842	1.83817	0.919085	−	0.394059i	$-0.128930\pi$
$17$	128.842	1.83817	0.919085	+	0.394059i	$0.128930\pi$
$18$	128.821	1.68685
$19$	7.38135	0.0891262	0.0445631	−	0.999007i	$-0.485810\pi$
$19$	7.38135	0.0891262	0.0445631	+	0.999007i	$0.485810\pi$
$20$	−150.158	−1.67881
$21$	0.116072	0.00120614
$22$	54.4438	0.527612
$23$	115.355	1.04579	0.522893	−	0.852398i	$-0.324853\pi$
$23$	115.355	1.04579	0.522893	+	0.852398i	$0.324853\pi$
$24$	41.4766	0.352766
$25$	−42.1511	−0.337209
$26$	−166.942	−1.25923
$27$	52.2978	0.372767
$28$	−1.94154	−0.0131042
$29$	−208.626	−1.33589	−0.667946	−	0.744210i	$-0.732826\pi$
$29$	−208.626	−1.33589	−0.667946	+	0.744210i	$0.732826\pi$
$30$	−44.4307	−0.270397
$31$	−108.981	−0.631408	−0.315704	−	0.948858i	$-0.602241\pi$
$31$	−108.981	−0.631408	−0.315704	+	0.948858i	$0.602241\pi$
$32$	−40.5775	−0.224161
$33$	10.8487	0.0572276
$34$	−637.698	−3.21660
$35$	1.07124	0.00517350
$36$	−429.372	−1.98783
$37$	80.4118	0.357287	0.178644	−	0.983914i	$-0.442829\pi$
$37$	80.4118	0.357287	0.178644	+	0.983914i	$0.442829\pi$
$38$	−36.5336	−0.155961
$39$	−33.2654	−0.136583
$40$	382.792	1.51312
$41$	250.086	0.952607	0.476303	−	0.879281i	$-0.341976\pi$
$41$	250.086	0.952607	0.476303	+	0.879281i	$0.341976\pi$
$42$	−0.574490	−0.00211061
$43$	−50.9010	−0.180519	−0.0902596	−	0.995918i	$-0.528770\pi$
$43$	−50.9010	−0.180519	−0.0902596	+	0.995918i	$0.528770\pi$
$44$	−181.467	−0.621753
$45$	236.904	0.784791
$46$	−570.940	−1.83001
$47$	−180.683	−0.560752	−0.280376	−	0.959890i	$-0.590459\pi$
$47$	−180.683	−0.560752	−0.280376	+	0.959890i	$0.590459\pi$
$48$	−75.1261	−0.225907
$49$	−342.986	−0.999960
$50$	208.624	0.590079
$51$	−127.070	−0.348889
$52$	556.433	1.48391
$53$	175.177	0.454007	0.227003	−	0.973894i	$-0.427107\pi$
$53$	175.177	0.454007	0.227003	+	0.973894i	$0.427107\pi$
$54$	−258.845	−0.652302
$55$	100.124	0.245466
$56$	4.94952	0.0118108
$57$	−7.27980	−0.0169164
$58$	1032.58	2.33767
$59$	−169.673	−0.374399	−0.187200	−	0.982322i	$-0.559941\pi$
$59$	−169.673	−0.374399	−0.187200	+	0.982322i	$0.559941\pi$
$60$	148.092	0.318643
$61$	−125.136	−0.262656	−0.131328	−	0.991339i	$-0.541924\pi$
$61$	−125.136	−0.262656	−0.131328	+	0.991339i	$0.541924\pi$
$62$	539.397	1.10490
$63$	3.06318	0.00612578
$64$	−408.557	−0.797963
$65$	−307.010	−0.585845
$66$	−53.6948	−0.100142
$67$	−917.756	−1.67346	−0.836729	−	0.547617i	$-0.815535\pi$
$67$	−917.756	−1.67346	−0.836729	+	0.547617i	$0.815535\pi$
$68$	2125.51	3.79053
$69$	−113.768	−0.198493
$70$	−5.30203	−0.00905306
$71$	907.010	1.51609	0.758044	−	0.652203i	$-0.226155\pi$
$71$	907.010	1.51609	0.758044	+	0.652203i	$0.226155\pi$
$72$	1094.58	1.79164
$73$	537.884	0.862391	0.431196	−	0.902258i	$-0.358092\pi$
$73$	537.884	0.862391	0.431196	+	0.902258i	$0.358092\pi$
$74$	−397.994	−0.625214
$75$	41.5712	0.0640030
$76$	121.770	0.183789
$77$	1.29460	0.00191602
$78$	164.645	0.239005
$79$	539.103	0.767770	0.383885	−	0.923381i	$-0.374586\pi$
$79$	539.103	0.767770	0.383885	+	0.923381i	$0.374586\pi$
$80$	−693.347	−0.968982
$81$	651.160	0.893223
$82$	−1237.79	−1.66696
$83$	662.269	0.875825	0.437912	−	0.899018i	$-0.355718\pi$
$83$	662.269	0.875825	0.437912	+	0.899018i	$0.355718\pi$
$84$	1.91483	0.00248721
$85$	−1172.74	−1.49649
$86$	251.931	0.315889
$87$	205.756	0.253556
$88$	462.607	0.560388
$89$	−1553.57	−1.85032	−0.925158	−	0.379583i	$-0.876067\pi$
$89$	−1553.57	−1.85032	−0.925158	+	0.379583i	$0.876067\pi$
$90$	−1172.54	−1.37330
$91$	−3.96965	−0.00457288
$92$	1903.00	2.15654
$93$	107.482	0.119843
$94$	894.280	0.981254
$95$	−67.1861	−0.0725594
$96$	40.0192	0.0425463
$97$	−469.571	−0.491523	−0.245761	−	0.969330i	$-0.579038\pi$
$97$	−469.571	−0.491523	−0.245761	+	0.969330i	$0.579038\pi$
$98$	1697.59	1.74982
$99$	286.301	0.290649
$100$	−695.365	−0.695365
$101$	−682.173	−0.672067	−0.336034	−	0.941850i	$-0.609086\pi$
$101$	−682.173	−0.672067	−0.336034	+	0.941850i	$0.609086\pi$
$102$	628.925	0.610518
$103$	−1400.37	−1.33964	−0.669820	−	0.742523i	$-0.733629\pi$
$103$	−1400.37	−1.33964	−0.669820	+	0.742523i	$0.733629\pi$
$104$	−1418.50	−1.33745
$105$	−1.05650	−0.000981942 0
$106$	−867.027	−0.794463
$107$	−650.517	−0.587737	−0.293869	−	0.955846i	$-0.594943\pi$
$107$	−650.517	−0.587737	−0.293869	+	0.955846i	$0.594943\pi$
$108$	862.755	0.768691
$109$	−1147.21	−1.00810	−0.504051	−	0.863674i	$-0.668158\pi$
$109$	−1147.21	−1.00810	−0.504051	+	0.863674i	$0.668158\pi$
$110$	−495.555	−0.429540
$111$	−79.3055	−0.0678140
$112$	−8.96500	−0.00756351
$113$	344.684	0.286948	0.143474	−	0.989654i	$-0.454173\pi$
$113$	344.684	0.286948	0.143474	+	0.989654i	$0.454173\pi$
$114$	36.0309	0.0296018
$115$	−1049.97	−0.851395
$116$	−3441.70	−2.75477
$117$	−877.887	−0.693681
$118$	839.787	0.655158
$119$	−15.1636	−0.0116810
$120$	−377.526	−0.287194
$121$	121.000	0.0909091
$122$	619.353	0.459620
$123$	−246.645	−0.180807
$124$	−1797.86	−1.30204
$125$	1521.43	1.08865
$126$	−15.1610	−0.0107195
$127$	27.3197	0.0190884	0.00954420	−	0.999954i	$-0.496962\pi$
$127$	27.3197	0.0190884	0.00954420	+	0.999954i	$0.496962\pi$
$128$	2346.75	1.62051
$129$	50.2007	0.0342630
$130$	1519.53	1.02516
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	178.970	0.118010
$133$	−0.868718	−0.000566372 0
$134$	4542.38	2.92837
$135$	−476.022	−0.303477
$136$	−5418.50	−3.41642
$137$	2301.90	1.43551	0.717753	−	0.696298i	$-0.245171\pi$
$137$	2301.90	1.43551	0.717753	+	0.696298i	$0.245171\pi$
$138$	563.086	0.347341
$139$	−713.248	−0.435229	−0.217615	−	0.976035i	$-0.569828\pi$
$139$	−713.248	−0.435229	−0.217615	+	0.976035i	$0.569828\pi$
$140$	17.6722	0.0106684
$141$	178.197	0.106432
$142$	−4489.19	−2.65299
$143$	−371.024	−0.216969
$144$	−1982.61	−1.14734
$145$	1898.94	1.08758
$146$	−2662.23	−1.50909
$147$	338.267	0.189795
$148$	1326.55	0.736769
$149$	−2393.11	−1.31578	−0.657890	−	0.753114i	$-0.728551\pi$
$149$	−2393.11	−1.31578	−0.657890	+	0.753114i	$0.728551\pi$
$150$	−205.754	−0.111998
$151$	1010.37	0.544523	0.272261	−	0.962223i	$-0.412228\pi$
$151$	1010.37	0.544523	0.272261	+	0.962223i	$0.412228\pi$
$152$	−310.424	−0.165650
$153$	−3353.43	−1.77195
$154$	−6.40755	−0.00335282
$155$	991.964	0.514042
$156$	−548.778	−0.281650
$157$	1603.92	0.815329	0.407664	−	0.913132i	$-0.366343\pi$
$157$	1603.92	0.815329	0.407664	+	0.913132i	$0.366343\pi$
$158$	−2668.26	−1.34351
$159$	−172.767	−0.0861716
$160$	369.342	0.182494
$161$	−13.5762	−0.00664567
$162$	−3222.88	−1.56304
$163$	−3553.05	−1.70734	−0.853670	−	0.520814i	$-0.825629\pi$
$163$	−3553.05	−1.70734	−0.853670	+	0.520814i	$0.825629\pi$
$164$	4125.66	1.96439
$165$	−98.7460	−0.0465901
$166$	−3277.86	−1.53260
$167$	3735.78	1.73104	0.865519	−	0.500876i	$-0.166989\pi$
$167$	3735.78	1.73104	0.865519	+	0.500876i	$0.166989\pi$
$168$	−4.88142	−0.00224173
$169$	−1059.32	−0.482169
$170$	5804.42	2.61870
$171$	−192.117	−0.0859155
$172$	−839.712	−0.372252
$173$	−4102.85	−1.80308	−0.901542	−	0.432691i	$-0.857564\pi$
$173$	−4102.85	−1.80308	−0.901542	+	0.432691i	$0.857564\pi$
$174$	−1018.38	−0.443695
$175$	4.96080	0.00214286
$176$	−837.915	−0.358865
$177$	167.339	0.0710619
$178$	7689.30	3.23785
$179$	−42.2071	−0.0176241	−0.00881204	−	0.999961i	$-0.502805\pi$
$179$	−42.2071	−0.0176241	−0.00881204	+	0.999961i	$0.502805\pi$
$180$	3908.20	1.61833
$181$	−55.7708	−0.0229028	−0.0114514	−	0.999934i	$-0.503645\pi$
$181$	−55.7708	−0.0229028	−0.0114514	+	0.999934i	$0.503645\pi$
$182$	19.6475	0.00800205
$183$	123.414	0.0498528
$184$	−4851.26	−1.94369
$185$	−731.920	−0.290875
$186$	−531.976	−0.209712
$187$	−1417.27	−0.554229
$188$	−2980.72	−1.15634
$189$	−6.15497	−0.00236883
$190$	332.534	0.126971
$191$	4393.04	1.66424	0.832118	−	0.554599i	$-0.187128\pi$
$191$	4393.04	1.66424	0.832118	+	0.554599i	$0.187128\pi$
$192$	402.936	0.151455
$193$	4107.11	1.53179	0.765897	−	0.642963i	$-0.222295\pi$
$193$	4107.11	1.53179	0.765897	+	0.642963i	$0.222295\pi$
$194$	2324.11	0.860112
$195$	302.786	0.111195
$196$	−5658.23	−2.06204
$197$	−4577.92	−1.65565	−0.827825	−	0.560987i	$-0.810422\pi$
$197$	−4577.92	−1.65565	−0.827825	+	0.560987i	$0.810422\pi$
$198$	−1417.03	−0.508605
$199$	−3779.55	−1.34636	−0.673179	−	0.739480i	$-0.735072\pi$
$199$	−3779.55	−1.34636	−0.673179	+	0.739480i	$0.735072\pi$
$200$	1772.67	0.626735
$201$	905.130	0.317626
$202$	3376.38	1.17604
$203$	24.5534	0.00848921
$204$	−2096.27	−0.719451
$205$	−2276.32	−0.775536
$206$	6931.07	2.34423
$207$	−3002.37	−1.00811
$208$	2569.31	0.856489
$209$	−81.1949	−0.0268726
$210$	5.22909	0.00171829
$211$	3139.29	1.02425	0.512127	−	0.858910i	$-0.328858\pi$
$211$	3139.29	1.02425	0.512127	+	0.858910i	$0.328858\pi$
$212$	2889.88	0.936217
$213$	−894.532	−0.287757
$214$	3219.70	1.02848
$215$	463.308	0.146964
$216$	−2199.39	−0.692823
$217$	12.8261	0.00401242
$218$	5678.06	1.76407
$219$	−530.484	−0.163684
$220$	1651.73	0.506181
$221$	4345.79	1.32276
$222$	392.518	0.118667
$223$	−6312.85	−1.89569	−0.947846	−	0.318727i	$-0.896745\pi$
$223$	−6312.85	−1.89569	−0.947846	+	0.318727i	$0.896745\pi$
$224$	4.77560	0.00142448
$225$	1097.08	0.325061
$226$	−1705.99	−0.502128
$227$	4218.26	1.23337	0.616687	−	0.787208i	$-0.288474\pi$
$227$	4218.26	1.23337	0.616687	+	0.787208i	$0.288474\pi$
$228$	−120.095	−0.0348836
$229$	3766.08	1.08677	0.543383	−	0.839485i	$-0.317143\pi$
$229$	3766.08	1.08677	0.543383	+	0.839485i	$0.317143\pi$
$230$	5196.78	1.48985
$231$	−1.27679	−0.000363665 0
$232$	8773.81	2.48288
$233$	−812.989	−0.228586	−0.114293	−	0.993447i	$-0.536460\pi$
$233$	−812.989	−0.228586	−0.114293	+	0.993447i	$0.536460\pi$
$234$	4345.05	1.21387
$235$	1644.60	0.456519
$236$	−2799.09	−0.772056
$237$	−531.686	−0.145725
$238$	75.0513	0.0204406
$239$	−1142.76	−0.309285	−0.154643	−	0.987970i	$-0.549423\pi$
$239$	−1142.76	−0.309285	−0.154643	+	0.987970i	$0.549423\pi$
$240$	683.808	0.183915
$241$	4496.88	1.20195	0.600974	−	0.799269i	$-0.294780\pi$
$241$	4496.88	1.20195	0.600974	+	0.799269i	$0.294780\pi$
$242$	−598.882	−0.159081
$243$	−2054.24	−0.542303
$244$	−2064.36	−0.541629
$245$	3121.91	0.814087
$246$	1220.76	0.316393
$247$	248.969	0.0641357
$248$	4583.24	1.17353
$249$	−653.158	−0.166234
$250$	−7530.24	−1.90502
$251$	−3552.04	−0.893239	−0.446620	−	0.894724i	$-0.647372\pi$
$251$	−3552.04	−0.893239	−0.446620	+	0.894724i	$0.647372\pi$
$252$	50.5332	0.0126321
$253$	−1268.90	−0.315316
$254$	−135.217	−0.0334026
$255$	1156.61	0.284038
$256$	−8346.64	−2.03775
$257$	7788.33	1.89036	0.945181	−	0.326548i	$-0.105886\pi$
$257$	7788.33	1.89036	0.945181	+	0.326548i	$0.105886\pi$
$258$	−248.465	−0.0599565
$259$	−9.46374	−0.00227046
$260$	−5064.73	−1.20808
$261$	5429.98	1.28777
$262$	648.377	0.152889
$263$	2567.62	0.602001	0.301001	−	0.953624i	$-0.402679\pi$
$263$	2567.62	0.602001	0.301001	+	0.953624i	$0.402679\pi$
$264$	−456.243	−0.106363
$265$	−1594.48	−0.369616
$266$	4.29967	0.000991089 0
$267$	1532.20	0.351194
$268$	−15140.2	−3.45087
$269$	8469.23	1.91962	0.959810	−	0.280650i	$-0.0905499\pi$
$269$	8469.23	1.91962	0.959810	+	0.280650i	$0.0905499\pi$
$270$	2356.04	0.531052
$271$	−8139.57	−1.82451	−0.912257	−	0.409618i	$-0.865662\pi$
$271$	−8139.57	−1.82451	−0.912257	+	0.409618i	$0.865662\pi$
$272$	9814.46	2.18783
$273$	3.91504	0.000867944 0
$274$	−11393.1	−2.51198
$275$	463.662	0.101672
$276$	−1876.82	−0.409316
$277$	−223.896	−0.0485654	−0.0242827	−	0.999705i	$-0.507730\pi$
$277$	−223.896	−0.0485654	−0.0242827	+	0.999705i	$0.507730\pi$
$278$	3530.18	0.761604
$279$	2836.50	0.608661
$280$	−45.0512	−0.00961544
$281$	−7105.86	−1.50854	−0.754270	−	0.656564i	$-0.772009\pi$
$281$	−7105.86	−1.50854	−0.754270	+	0.656564i	$0.772009\pi$
$282$	−881.976	−0.186244
$283$	7784.40	1.63510	0.817552	−	0.575854i	$-0.195330\pi$
$283$	7784.40	1.63510	0.817552	+	0.575854i	$0.195330\pi$
$284$	14962.9	3.12636
$285$	66.2618	0.0137720
$286$	1836.36	0.379672
$287$	−29.4329	−0.00605354
$288$	1056.12	0.216086
$289$	11687.4	2.37887
$290$	−9398.70	−1.90314
$291$	463.111	0.0932922
$292$	8873.46	1.77836
$293$	3197.33	0.637509	0.318754	−	0.947837i	$-0.396735\pi$
$293$	3197.33	0.637509	0.318754	+	0.947837i	$0.396735\pi$
$294$	−1674.23	−0.332120
$295$	1544.39	0.304806
$296$	−3381.74	−0.664052
$297$	−575.276	−0.112394
$298$	11844.6	2.30247
$299$	3890.85	0.752553
$300$	685.798	0.131982
$301$	5.99058	0.00114715
$302$	−5000.78	−0.952856
$303$	672.788	0.127560
$304$	562.268	0.106080
$305$	1139.01	0.213834
$306$	16597.6	3.10072
$307$	3972.97	0.738596	0.369298	−	0.929311i	$-0.379598\pi$
$307$	3972.97	0.738596	0.369298	+	0.929311i	$0.379598\pi$
$308$	21.3570	0.00395106
$309$	1381.11	0.254267
$310$	−4909.67	−0.899517
$311$	8594.89	1.56711	0.783555	−	0.621322i	$-0.213404\pi$
$311$	8594.89	1.56711	0.783555	+	0.621322i	$0.213404\pi$
$312$	1398.98	0.253852
$313$	7881.16	1.42323	0.711613	−	0.702572i	$-0.247965\pi$
$313$	7881.16	1.42323	0.711613	+	0.702572i	$0.247965\pi$
$314$	−7938.50	−1.42674
$315$	−27.8815	−0.00498712
$316$	8893.57	1.58323
$317$	3478.72	0.616354	0.308177	−	0.951329i	$-0.400281\pi$
$317$	3478.72	0.616354	0.308177	+	0.951329i	$0.400281\pi$
$318$	855.098	0.150791
$319$	2294.89	0.402787
$320$	3718.74	0.649638
$321$	641.568	0.111554
$322$	67.1945	0.0116292
$323$	951.032	0.163829
$324$	10742.2	1.84193
$325$	−1421.73	−0.242657
$326$	17585.6	2.98766
$327$	1131.43	0.191340
$328$	−10517.4	−1.77051
$329$	21.2647	0.00356341
$330$	488.738	0.0815276
$331$	11811.2	1.96133	0.980664	−	0.195697i	$-0.0626968\pi$
$331$	11811.2	1.96133	0.980664	+	0.195697i	$0.0626968\pi$
$332$	10925.4	1.80606
$333$	−2092.90	−0.344416
$334$	−18490.0	−3.02913
$335$	8353.54	1.36240
$336$	8.84166	0.00143557
$337$	−8588.11	−1.38820	−0.694101	−	0.719877i	$-0.744198\pi$
$337$	−8588.11	−1.38820	−0.694101	+	0.719877i	$0.744198\pi$
$338$	5243.06	0.843743
$339$	−339.942	−0.0544635
$340$	−19346.7	−3.08594
$341$	1198.80	0.190377
$342$	950.871	0.150343
$343$	80.7343	0.0127092
$344$	2140.65	0.335512
$345$	1035.53	0.161597
$346$	20306.8	3.15520
$347$	−3796.68	−0.587367	−0.293684	−	0.955903i	$-0.594881\pi$
$347$	−3796.68	−0.587367	−0.293684	+	0.955903i	$0.594881\pi$
$348$	3394.35	0.522862
$349$	7608.57	1.16698	0.583492	−	0.812119i	$-0.301686\pi$
$349$	7608.57	1.16698	0.583492	+	0.812119i	$0.301686\pi$
$350$	−24.5532	−0.00374978
$351$	1763.98	0.268245
$352$	446.352	0.0675871
$353$	3555.58	0.536103	0.268052	−	0.963405i	$-0.413620\pi$
$353$	3555.58	0.536103	0.268052	+	0.963405i	$0.413620\pi$
$354$	−828.233	−0.124351
$355$	−8255.73	−1.23428
$356$	−25629.2	−3.81557
$357$	14.9550	0.00221709
$358$	208.902	0.0308402
$359$	−2399.05	−0.352694	−0.176347	−	0.984328i	$-0.556428\pi$
$359$	−2399.05	−0.352694	−0.176347	+	0.984328i	$0.556428\pi$
$360$	−9963.06	−1.45861
$361$	−6804.52	−0.992057
$362$	276.034	0.0400775
$363$	−119.335	−0.0172548
$364$	−65.4872	−0.00942984
$365$	−4895.90	−0.702090
$366$	−610.832	−0.0872369
$367$	3937.99	0.560112	0.280056	−	0.959984i	$-0.409647\pi$
$367$	3937.99	0.560112	0.280056	+	0.959984i	$0.409647\pi$
$368$	8787.03	1.24472
$369$	−6509.07	−0.918289
$370$	3622.59	0.508999
$371$	−20.6167	−0.00288508
$372$	1773.13	0.247130
$373$	−4367.82	−0.606319	−0.303160	−	0.952940i	$-0.598042\pi$
$373$	−4367.82	−0.606319	−0.303160	+	0.952940i	$0.598042\pi$
$374$	7014.68	0.969841
$375$	−1500.50	−0.206628
$376$	7598.66	1.04221
$377$	−7036.84	−0.961315
$378$	30.4637	0.00414519
$379$	11240.5	1.52344	0.761719	−	0.647907i	$-0.224356\pi$
$379$	11240.5	1.52344	0.761719	+	0.647907i	$0.224356\pi$
$380$	−1108.37	−0.149626
$381$	−26.9438	−0.00362302
$382$	−21743.1	−2.91223
$383$	7618.29	1.01639	0.508194	−	0.861243i	$-0.330313\pi$
$383$	7618.29	1.01639	0.508194	+	0.861243i	$0.330313\pi$
$384$	−2314.46	−0.307577
$385$	−11.7836	−0.00155987
$386$	−20327.9	−2.68047
$387$	1324.82	0.174016
$388$	−7746.50	−1.01358
$389$	5615.21	0.731884	0.365942	−	0.930638i	$-0.380747\pi$
$389$	5615.21	0.731884	0.365942	+	0.930638i	$0.380747\pi$
$390$	−1498.62	−0.194579
$391$	14862.6	1.92233
$392$	14424.4	1.85852
$393$	129.198	0.0165831
$394$	22658.1	2.89721
$395$	−4906.99	−0.625057
$396$	4723.09	0.599354
$397$	−5028.05	−0.635644	−0.317822	−	0.948150i	$-0.602951\pi$
$397$	−5028.05	−0.635644	−0.317822	+	0.948150i	$0.602951\pi$
$398$	18706.7	2.35598
$399$	0.856767	0.000107499 0
$400$	−3210.82	−0.401353
$401$	−5276.50	−0.657097	−0.328549	−	0.944487i	$-0.606559\pi$
$401$	−5276.50	−0.657097	−0.328549	+	0.944487i	$0.606559\pi$
$402$	−4479.89	−0.555812
$403$	−3675.88	−0.454364
$404$	−11253.8	−1.38588
$405$	−5926.94	−0.727191
$406$	−121.526	−0.0148552
$407$	−884.530	−0.107726
$408$	5343.95	0.648444
$409$	1949.29	0.235663	0.117831	−	0.993034i	$-0.462406\pi$
$409$	1949.29	0.235663	0.117831	+	0.993034i	$0.462406\pi$
$410$	11266.5	1.35710
$411$	−2270.23	−0.272462
$412$	−23101.9	−2.76250
$413$	19.9690	0.00237920
$414$	14860.1	1.76409
$415$	−6028.06	−0.713026
$416$	−1368.66	−0.161307
$417$	703.435	0.0826076
$418$	401.869	0.0470241
$419$	11570.5	1.34906	0.674529	−	0.738248i	$-0.264347\pi$
$419$	11570.5	1.34906	0.674529	+	0.738248i	$0.264347\pi$
$420$	−17.4291	−0.00202488
$421$	−6553.61	−0.758678	−0.379339	−	0.925258i	$-0.623849\pi$
$421$	−6553.61	−0.758678	−0.379339	+	0.925258i	$0.623849\pi$
$422$	−15537.7	−1.79233
$423$	4702.69	0.540550
$424$	−7367.09	−0.843815
$425$	−5430.85	−0.619847
$426$	4427.43	0.503544
$427$	14.7274	0.00166910
$428$	−10731.6	−1.21199
$429$	365.919	0.0411813
$430$	−2293.11	−0.257172
$431$	−2195.54	−0.245372	−0.122686	−	0.992446i	$-0.539151\pi$
$431$	−2195.54	−0.245372	−0.122686	+	0.992446i	$0.539151\pi$
$432$	3983.74	0.443675
$433$	71.6416	0.00795122	0.00397561	−	0.999992i	$-0.498735\pi$
$433$	71.6416	0.00795122	0.00397561	+	0.999992i	$0.498735\pi$
$434$	−63.4821	−0.00702129
$435$	−1872.82	−0.206425
$436$	−18925.5	−2.07883
$437$	851.473	0.0932070
$438$	2625.60	0.286429
$439$	−2316.89	−0.251888	−0.125944	−	0.992037i	$-0.540196\pi$
$439$	−2316.89	−0.251888	−0.125944	+	0.992037i	$0.540196\pi$
$440$	−4210.72	−0.456223
$441$	8927.01	0.963936
$442$	−21509.2	−2.31468
$443$	289.956	0.0310975	0.0155488	−	0.999879i	$-0.495050\pi$
$443$	289.956	0.0310975	0.0155488	+	0.999879i	$0.495050\pi$
$444$	−1308.30	−0.139841
$445$	14140.8	1.50638
$446$	31245.1	3.31726
$447$	2360.19	0.249738
$448$	48.0835	0.00507083
$449$	11801.1	1.24037	0.620185	−	0.784456i	$-0.287057\pi$
$449$	11801.1	1.24037	0.620185	+	0.784456i	$0.287057\pi$
$450$	−5429.93	−0.568821
$451$	−2750.95	−0.287222
$452$	5686.24	0.591722
$453$	−996.472	−0.103352
$454$	−20878.0	−2.15827
$455$	36.1323	0.00372288
$456$	306.154	0.0314407
$457$	4280.65	0.438163	0.219081	−	0.975707i	$-0.429694\pi$
$457$	4280.65	0.438163	0.219081	+	0.975707i	$0.429694\pi$
$458$	−18640.0	−1.90172
$459$	6738.18	0.685209
$460$	−17321.4	−1.75568
$461$	10298.7	1.04047	0.520236	−	0.854023i	$-0.325844\pi$
$461$	10298.7	1.04047	0.520236	+	0.854023i	$0.325844\pi$
$462$	6.31939	0.000636374 0
$463$	15691.2	1.57502	0.787508	−	0.616305i	$-0.211371\pi$
$463$	15691.2	1.57502	0.787508	+	0.616305i	$0.211371\pi$
$464$	−15891.9	−1.59001
$465$	−978.317	−0.0975664
$466$	4023.84	0.400002
$467$	−11221.3	−1.11190	−0.555952	−	0.831214i	$-0.687646\pi$
$467$	−11221.3	−1.11190	−0.555952	+	0.831214i	$0.687646\pi$
$468$	−14482.5	−1.43045
$469$	108.012	0.0106343
$470$	−8139.86	−0.798859
$471$	−1581.85	−0.154751
$472$	7135.64	0.695857
$473$	559.911	0.0544286
$474$	2631.55	0.255002
$475$	−311.132	−0.0300541
$476$	−250.153	−0.0240877
$477$	−4559.38	−0.437651
$478$	5656.04	0.541216
$479$	8849.52	0.844143	0.422072	−	0.906562i	$-0.361303\pi$
$479$	8849.52	0.844143	0.422072	+	0.906562i	$0.361303\pi$
$480$	−364.260	−0.0346378
$481$	2712.25	0.257106
$482$	−22257.0	−2.10328
$483$	13.3894	0.00126136
$484$	1996.13	0.187465
$485$	4274.10	0.400159
$486$	10167.3	0.948972
$487$	−6709.68	−0.624322	−0.312161	−	0.950029i	$-0.601053\pi$
$487$	−6709.68	−0.624322	−0.312161	+	0.950029i	$0.601053\pi$
$488$	5262.62	0.488172
$489$	3504.17	0.324057
$490$	−15451.7	−1.42456
$491$	−10918.8	−1.00358	−0.501792	−	0.864988i	$-0.667326\pi$
$491$	−10918.8	−1.00358	−0.501792	+	0.864988i	$0.667326\pi$
$492$	−4068.90	−0.372846
$493$	−26879.9	−2.45560
$494$	−1232.26	−0.112231
$495$	−2605.95	−0.236623
$496$	−8301.56	−0.751515
$497$	−106.747	−0.00963431
$498$	3232.76	0.290891
$499$	−4092.84	−0.367175	−0.183588	−	0.983003i	$-0.558771\pi$
$499$	−4092.84	−0.367175	−0.183588	+	0.983003i	$0.558771\pi$
$500$	25099.0	2.24492
$501$	−3684.38	−0.328555
$502$	17580.6	1.56307
$503$	−17881.5	−1.58508	−0.792542	−	0.609818i	$-0.791243\pi$
$503$	−17881.5	−1.58508	−0.792542	+	0.609818i	$0.791243\pi$
$504$	−128.823	−0.0113854
$505$	6209.23	0.547143
$506$	6280.35	0.551770
$507$	1044.75	0.0915167
$508$	450.691	0.0393626
$509$	8118.50	0.706967	0.353483	−	0.935441i	$-0.384997\pi$
$509$	8118.50	0.706967	0.353483	+	0.935441i	$0.384997\pi$
$510$	−5724.56	−0.497035
$511$	−63.3041	−0.00548025
$512$	22537.2	1.94534
$513$	386.028	0.0332233
$514$	−38547.9	−3.30793
$515$	12746.4	1.09063
$516$	828.159	0.0706544
$517$	1987.51	0.169073
$518$	46.8402	0.00397305
$519$	4046.40	0.342230
$520$	12911.4	1.08885
$521$	7007.76	0.589281	0.294640	−	0.955608i	$-0.404800\pi$
$521$	7007.76	0.589281	0.294640	+	0.955608i	$0.404800\pi$
$522$	−26875.4	−2.25345
$523$	−5916.53	−0.494669	−0.247334	−	0.968930i	$-0.579555\pi$
$523$	−5916.53	−0.494669	−0.247334	+	0.968930i	$0.579555\pi$
$524$	−2161.10	−0.180168
$525$	−4.89255	−0.000406721 0
$526$	−12708.3	−1.05344
$527$	−14041.4	−1.16064
$528$	826.387	0.0681134
$529$	1139.67	0.0936690
$530$	7891.79	0.646788
$531$	4416.14	0.360912
$532$	−14.3312	−0.00116793
$533$	8435.26	0.685501
$534$	−7583.51	−0.614552
$535$	5921.10	0.478489
$536$	38596.4	3.11028
$537$	41.6264	0.00334509
$538$	−41917.9	−3.35913
$539$	3772.85	0.301499
$540$	−7852.91	−0.625807
$541$	10236.7	0.813515	0.406757	−	0.913536i	$-0.366659\pi$
$541$	10236.7	0.813515	0.406757	+	0.913536i	$0.366659\pi$
$542$	40286.3	3.19270
$543$	55.0035	0.00434701
$544$	−5228.10	−0.412046
$545$	10442.1	0.820715
$546$	−19.3772	−0.00151881
$547$	134.734	0.0105316	0.00526581	−	0.999986i	$-0.498324\pi$
$547$	134.734	0.0105316	0.00526581	+	0.999986i	$0.498324\pi$
$548$	37974.3	2.96019
$549$	3256.96	0.253194
$550$	−2294.87	−0.177915
$551$	−1539.94	−0.119063
$552$	4784.52	0.368918
$553$	−63.4476	−0.00487896
$554$	1108.16	0.0849842
$555$	721.850	0.0552087
$556$	−11766.4	−0.897495
$557$	−5880.98	−0.447370	−0.223685	−	0.974661i	$-0.571809\pi$
$557$	−5880.98	−0.447370	−0.223685	+	0.974661i	$0.571809\pi$
$558$	−14039.1	−1.06509
$559$	−1716.86	−0.129903
$560$	81.6007	0.00615760
$561$	1397.77	0.105194
$562$	35170.0	2.63978
$563$	−15512.9	−1.16126	−0.580632	−	0.814166i	$-0.697194\pi$
$563$	−15512.9	−1.16126	−0.580632	+	0.814166i	$0.697194\pi$
$564$	2939.71	0.219476
$565$	−3137.36	−0.233610
$566$	−38528.4	−2.86126
$567$	−76.6356	−0.00567617
$568$	−38144.5	−2.81780
$569$	7669.73	0.565082	0.282541	−	0.959255i	$-0.408823\pi$
$569$	7669.73	0.565082	0.282541	+	0.959255i	$0.408823\pi$
$570$	−327.959	−0.0240994
$571$	−15208.3	−1.11462	−0.557308	−	0.830306i	$-0.688166\pi$
$571$	−15208.3	−1.11462	−0.557308	+	0.830306i	$0.688166\pi$
$572$	−6120.77	−0.447416
$573$	−4332.60	−0.315876
$574$	145.676	0.0105930
$575$	−4862.32	−0.352648
$576$	10633.6	0.769216
$577$	21510.7	1.55200	0.775999	−	0.630734i	$-0.217246\pi$
$577$	21510.7	1.55200	0.775999	+	0.630734i	$0.217246\pi$
$578$	−57846.0	−4.16276
$579$	−4050.61	−0.290738
$580$	31326.8	2.24271
$581$	−77.9430	−0.00556561
$582$	−2292.14	−0.163251
$583$	−1926.94	−0.136888
$584$	−22620.8	−1.60284
$585$	7990.65	0.564740
$586$	−15825.0	−1.11557
$587$	1370.13	0.0963397	0.0481698	−	0.998839i	$-0.484661\pi$
$587$	1370.13	0.0963397	0.0481698	+	0.998839i	$0.484661\pi$
$588$	5580.39	0.391380
$589$	−804.430	−0.0562750
$590$	−7643.86	−0.533377
$591$	4514.93	0.314246
$592$	6125.30	0.425250
$593$	−22671.2	−1.56997	−0.784986	−	0.619513i	$-0.787330\pi$
$593$	−22671.2	−1.56997	−0.784986	+	0.619513i	$0.787330\pi$
$594$	2847.29	0.196676
$595$	138.021	0.00950977
$596$	−39479.0	−2.71330
$597$	3727.55	0.255542
$598$	−19257.5	−1.31689
$599$	8111.74	0.553317	0.276658	−	0.960968i	$-0.410773\pi$
$599$	8111.74	0.553317	0.276658	+	0.960968i	$0.410773\pi$
$600$	−1748.29	−0.118956
$601$	−2391.35	−0.162305	−0.0811526	−	0.996702i	$-0.525860\pi$
$601$	−2391.35	−0.162305	−0.0811526	+	0.996702i	$0.525860\pi$
$602$	−29.6500	−0.00200738
$603$	23886.7	1.61317
$604$	16668.1	1.12287
$605$	−1101.36	−0.0740109
$606$	−3329.92	−0.223216
$607$	19592.0	1.31007	0.655036	−	0.755598i	$-0.272653\pi$
$607$	19592.0	1.31007	0.655036	+	0.755598i	$0.272653\pi$
$608$	−299.517	−0.0199786
$609$	−24.2156	−0.00161127
$610$	−5637.44	−0.374186
$611$	−6094.34	−0.403520
$612$	−55321.3	−3.65397
$613$	28914.0	1.90510	0.952549	−	0.304384i	$-0.0984507\pi$
$613$	28914.0	1.90510	0.952549	+	0.304384i	$0.0984507\pi$
$614$	−19664.0	−1.29246
$615$	2245.00	0.147199
$616$	−54.4447	−0.00356110
$617$	−9630.99	−0.628410	−0.314205	−	0.949355i	$-0.601738\pi$
$617$	−9630.99	−0.628410	−0.314205	+	0.949355i	$0.601738\pi$
$618$	−6835.71	−0.444940
$619$	−12287.3	−0.797847	−0.398923	−	0.916984i	$-0.630616\pi$
$619$	−12287.3	−0.797847	−0.398923	+	0.916984i	$0.630616\pi$
$620$	16364.4	1.06002
$621$	6032.79	0.389835
$622$	−42539.9	−2.74227
$623$	182.841	0.0117582
$624$	−2533.96	−0.162564
$625$	−8579.40	−0.549082
$626$	−39007.3	−2.49049
$627$	80.0778	0.00510048
$628$	26459.8	1.68131
$629$	10360.5	0.656755
$630$	137.998	0.00872692
$631$	−14139.5	−0.892049	−0.446024	−	0.895021i	$-0.647161\pi$
$631$	−14139.5	−0.892049	−0.446024	+	0.895021i	$0.647161\pi$
$632$	−22672.1	−1.42697
$633$	−3096.10	−0.194406
$634$	−17217.7	−1.07855
$635$	−248.667	−0.0155403
$636$	−2850.12	−0.177696
$637$	−11568.7	−0.719576
$638$	−11358.4	−0.704833
$639$	−23607.0	−1.46147
$640$	−21360.4	−1.31929
$641$	27584.9	1.69975	0.849875	−	0.526984i	$-0.176677\pi$
$641$	27584.9	1.69975	0.849875	+	0.526984i	$0.176677\pi$
$642$	−3175.40	−0.195207
$643$	6569.27	0.402903	0.201452	−	0.979498i	$-0.435434\pi$
$643$	6569.27	0.402903	0.201452	+	0.979498i	$0.435434\pi$
$644$	−223.966	−0.0137042
$645$	−456.934	−0.0278942
$646$	−4707.08	−0.286683
$647$	7775.52	0.472468	0.236234	−	0.971696i	$-0.424087\pi$
$647$	7775.52	0.472468	0.236234	+	0.971696i	$0.424087\pi$
$648$	−27384.7	−1.66014
$649$	1866.40	0.112886
$650$	7036.78	0.424624
$651$	−12.6497	−0.000761566 0
$652$	−58614.6	−3.52074
$653$	−25126.9	−1.50580	−0.752902	−	0.658132i	$-0.771347\pi$
$653$	−25126.9	−1.50580	−0.752902	+	0.658132i	$0.771347\pi$
$654$	−5599.94	−0.334824
$655$	1192.38	0.0711300
$656$	19050.1	1.13381
$657$	−13999.7	−0.831324
$658$	−105.249	−0.00623559
$659$	−7626.89	−0.450837	−0.225418	−	0.974262i	$-0.572375\pi$
$659$	−7626.89	−0.450837	−0.225418	+	0.974262i	$0.572375\pi$
$660$	−1629.01	−0.0960744
$661$	614.217	0.0361426	0.0180713	−	0.999837i	$-0.494247\pi$
$661$	614.217	0.0361426	0.0180713	+	0.999837i	$0.494247\pi$
$662$	−58458.6	−3.43211
$663$	−4286.00	−0.251062
$664$	−27851.9	−1.62780
$665$	7.90719	0.000461094 0
$666$	10358.7	0.602690
$667$	−24066.0	−1.39706
$668$	61629.0	3.56961
$669$	6226.00	0.359807
$670$	−41345.4	−2.38405
$671$	1376.50	0.0791938
$672$	−4.70990	−0.000270369 0
$673$	−27132.5	−1.55406	−0.777030	−	0.629464i	$-0.783275\pi$
$673$	−27132.5	−1.55406	−0.777030	+	0.629464i	$0.783275\pi$
$674$	42506.4	2.42920
$675$	−2204.41	−0.125700
$676$	−17475.6	−0.994290
$677$	24732.9	1.40408	0.702040	−	0.712137i	$-0.252273\pi$
$677$	24732.9	1.40408	0.702040	+	0.712137i	$0.252273\pi$
$678$	1682.52	0.0953052
$679$	55.2642	0.00312349
$680$	49319.9	2.78137
$681$	−4160.23	−0.234097
$682$	−5933.37	−0.333138
$683$	−24298.6	−1.36129	−0.680645	−	0.732614i	$-0.738300\pi$
$683$	−24298.6	−1.36129	−0.680645	+	0.732614i	$0.738300\pi$
$684$	−3169.35	−0.177168
$685$	−20952.2	−1.16867
$686$	−399.590	−0.0222397
$687$	−3714.27	−0.206271
$688$	−3877.34	−0.214858
$689$	5908.61	0.326706
$690$	−5125.28	−0.282777
$691$	28149.2	1.54971	0.774854	−	0.632141i	$-0.217823\pi$
$691$	28149.2	1.54971	0.774854	+	0.632141i	$0.217823\pi$
$692$	−67684.5	−3.71818
$693$	−33.6950	−0.00184699
$694$	18791.4	1.02783
$695$	6492.08	0.354329
$696$	−8653.10	−0.471257
$697$	32221.7	1.75105
$698$	−37658.2	−2.04210
$699$	801.804	0.0433863
$700$	81.8382	0.00441884
$701$	22022.6	1.18656	0.593281	−	0.804995i	$-0.297832\pi$
$701$	22022.6	1.18656	0.593281	+	0.804995i	$0.297832\pi$
$702$	−8730.69	−0.469400
$703$	593.548	0.0318437
$704$	4494.13	0.240595
$705$	−1621.98	−0.0866484
$706$	−17598.1	−0.938123
$707$	80.2856	0.00427079
$708$	2760.58	0.146538
$709$	14714.5	0.779428	0.389714	−	0.920936i	$-0.372574\pi$
$709$	14714.5	0.779428	0.389714	+	0.920936i	$0.372574\pi$
$710$	40861.2	2.15985
$711$	−14031.4	−0.740111
$712$	65335.7	3.43899
$713$	−12571.5	−0.660318
$714$	−74.0188	−0.00387967
$715$	3377.11	0.176639
$716$	−696.289	−0.0363430
$717$	1127.04	0.0587031
$718$	11874.0	0.617176
$719$	12711.9	0.659350	0.329675	−	0.944094i	$-0.393061\pi$
$719$	12711.9	0.659350	0.329675	+	0.944094i	$0.393061\pi$
$720$	18046.0	0.934075
$721$	164.811	0.00851303
$722$	33678.5	1.73599
$723$	−4435.01	−0.228133
$724$	−920.049	−0.0472284
$725$	8793.81	0.450475
$726$	590.643	0.0301940
$727$	6452.35	0.329167	0.164584	−	0.986363i	$-0.447372\pi$
$727$	6452.35	0.329167	0.164584	+	0.986363i	$0.447372\pi$
$728$	166.944	0.00849914
$729$	−15555.3	−0.790293
$730$	24231.9	1.22858
$731$	−6558.21	−0.331825
$732$	2035.96	0.102802
$733$	26284.5	1.32448	0.662238	−	0.749294i	$-0.269607\pi$
$733$	26284.5	1.32448	0.662238	+	0.749294i	$0.269607\pi$
$734$	−19490.8	−0.980135
$735$	−3078.96	−0.154516
$736$	−4680.79	−0.234424
$737$	10095.3	0.504567
$738$	32216.3	1.60691
$739$	4861.35	0.241986	0.120993	−	0.992653i	$-0.461392\pi$
$739$	4861.35	0.241986	0.120993	+	0.992653i	$0.461392\pi$
$740$	−12074.4	−0.599818
$741$	−245.544	−0.0121731
$742$	102.041	0.00504858
$743$	29453.7	1.45431	0.727154	−	0.686475i	$-0.240843\pi$
$743$	29453.7	1.45431	0.727154	+	0.686475i	$0.240843\pi$
$744$	−4520.18	−0.222739
$745$	21782.4	1.07120
$746$	21618.3	1.06099
$747$	−17237.1	−0.844273
$748$	−23380.6	−1.14289
$749$	76.5600	0.00373490
$750$	7426.64	0.361577
$751$	12745.1	0.619274	0.309637	−	0.950855i	$-0.399793\pi$
$751$	12745.1	0.619274	0.309637	+	0.950855i	$0.399793\pi$
$752$	−13763.4	−0.667418
$753$	3503.18	0.169539
$754$	34828.4	1.68220
$755$	−9196.55	−0.443307
$756$	−101.538	−0.00488481
$757$	11606.1	0.557239	0.278619	−	0.960402i	$-0.410123\pi$
$757$	11606.1	0.557239	0.278619	+	0.960402i	$0.410123\pi$
$758$	−55633.9	−2.66585
$759$	1251.44	0.0598478
$760$	2825.53	0.134859
$761$	7429.81	0.353916	0.176958	−	0.984218i	$-0.443374\pi$
$761$	7429.81	0.353916	0.176958	+	0.984218i	$0.443374\pi$
$762$	133.357	0.00633990
$763$	135.017	0.00640619
$764$	72471.8	3.43185
$765$	30523.3	1.44258
$766$	−37706.3	−1.77857
$767$	−5722.98	−0.269420
$768$	8231.81	0.386770
$769$	−18976.8	−0.889885	−0.444942	−	0.895559i	$-0.646776\pi$
$769$	−18976.8	−0.889885	−0.444942	+	0.895559i	$0.646776\pi$
$770$	58.3224	0.00272960
$771$	−7681.18	−0.358795
$772$	67754.9	3.15874
$773$	−8431.86	−0.392333	−0.196166	−	0.980571i	$-0.562849\pi$
$773$	−8431.86	−0.392333	−0.196166	+	0.980571i	$0.562849\pi$
$774$	−6557.10	−0.304509
$775$	4593.69	0.212916
$776$	19747.9	0.913542
$777$	9.33354	0.000430938 0
$778$	−27792.2	−1.28072
$779$	1845.97	0.0849023
$780$	4995.05	0.229297
$781$	−9977.11	−0.457118
$782$	−73561.4	−3.36387
$783$	−10910.7	−0.497977
$784$	−26126.7	−1.19017
$785$	−14599.1	−0.663775
$786$	−639.456	−0.0290186
$787$	32994.6	1.49445	0.747224	−	0.664572i	$-0.231386\pi$
$787$	32994.6	1.49445	0.747224	+	0.664572i	$0.231386\pi$
$788$	−75521.7	−3.41415
$789$	−2532.30	−0.114261
$790$	24286.9	1.09378
$791$	−40.5662	−0.00182347
$792$	−12040.4	−0.540200
$793$	−4220.77	−0.189009
$794$	24886.0	1.11231
$795$	1572.55	0.0701540
$796$	−62351.1	−2.77635
$797$	−11474.0	−0.509952	−0.254976	−	0.966947i	$-0.582068\pi$
$797$	−11474.0	−0.509952	−0.254976	+	0.966947i	$0.582068\pi$
$798$	−4.24052	−0.000188111 0
$799$	−23279.6	−1.03076
$800$	1710.38	0.0755890
$801$	40435.3	1.78366
$802$	26115.7	1.14985
$803$	−5916.73	−0.260021
$804$	14931.9	0.654984
$805$	123.572	0.00541037
$806$	18193.6	0.795088
$807$	−8352.71	−0.364349
$808$	28688.9	1.24910
$809$	−17696.5	−0.769069	−0.384535	−	0.923111i	$-0.625638\pi$
$809$	−17696.5	−0.769069	−0.384535	+	0.923111i	$0.625638\pi$
$810$	29335.1	1.27250
$811$	8589.07	0.371890	0.185945	−	0.982560i	$-0.440465\pi$
$811$	8589.07	0.371890	0.185945	+	0.982560i	$0.440465\pi$
$812$	405.056	0.0175058
$813$	8027.58	0.346297
$814$	4377.93	0.188509
$815$	32340.4	1.38998
$816$	−9679.44	−0.415255
$817$	−375.718	−0.0160890
$818$	−9647.88	−0.412384
$819$	103.319	0.00440815
$820$	−37552.3	−1.59925
$821$	40682.5	1.72939	0.864695	−	0.502298i	$-0.167512\pi$
$821$	40682.5	1.72939	0.864695	+	0.502298i	$0.167512\pi$
$822$	11236.4	0.476780
$823$	31711.4	1.34312	0.671561	−	0.740949i	$-0.265624\pi$
$823$	31711.4	1.34312	0.671561	+	0.740949i	$0.265624\pi$
$824$	58893.0	2.48985
$825$	−457.283	−0.0192976
$826$	−98.8353	−0.00416334
$827$	23864.5	1.00345	0.501724	−	0.865028i	$-0.332699\pi$
$827$	23864.5	1.00345	0.501724	+	0.865028i	$0.332699\pi$
$828$	−49530.0	−2.07885
$829$	−15055.0	−0.630739	−0.315369	−	0.948969i	$-0.602128\pi$
$829$	−15055.0	−0.630739	−0.315369	+	0.948969i	$0.602128\pi$
$830$	29835.5	1.24772
$831$	220.816	0.00921783
$832$	−13780.4	−0.574218
$833$	−44191.2	−1.83810
$834$	−3481.61	−0.144554
$835$	−34003.6	−1.40927
$836$	−1339.47	−0.0554145
$837$	−5699.49	−0.235368
$838$	−57267.5	−2.36071
$839$	−19265.5	−0.792754	−0.396377	−	0.918088i	$-0.629733\pi$
$839$	−19265.5	−0.792754	−0.396377	+	0.918088i	$0.629733\pi$
$840$	44.4314	0.00182503
$841$	19135.8	0.784608
$842$	32436.7	1.32760
$843$	7008.10	0.286325
$844$	51788.7	2.11213
$845$	9642.12	0.392543
$846$	−23275.7	−0.945905
$847$	−14.2406	−0.000577701 0
$848$	13343.9	0.540368
$849$	−7677.31	−0.310347
$850$	26879.7	1.08467
$851$	9275.87	0.373646
$852$	−14757.1	−0.593390
$853$	21969.7	0.881862	0.440931	−	0.897541i	$-0.354648\pi$
$853$	21969.7	0.881862	0.440931	+	0.897541i	$0.354648\pi$
$854$	−72.8923	−0.00292075
$855$	1748.67	0.0699455
$856$	27357.7	1.09237
$857$	13730.8	0.547299	0.273650	−	0.961829i	$-0.411769\pi$
$857$	13730.8	0.547299	0.273650	+	0.961829i	$0.411769\pi$
$858$	−1811.10	−0.0720627
$859$	24487.9	0.972662	0.486331	−	0.873775i	$-0.338335\pi$
$859$	24487.9	0.972662	0.486331	+	0.873775i	$0.338335\pi$
$860$	7643.17	0.303058
$861$	29.0279	0.00114898
$862$	10866.7	0.429374
$863$	−14948.6	−0.589638	−0.294819	−	0.955553i	$-0.595259\pi$
$863$	−14948.6	−0.589638	−0.294819	+	0.955553i	$0.595259\pi$
$864$	−2122.11	−0.0835598
$865$	37344.7	1.46793
$866$	−354.586	−0.0139138
$867$	−11526.6	−0.451515
$868$	211.592	0.00827408
$869$	−5930.14	−0.231491
$870$	9269.40	0.361221
$871$	−30955.4	−1.20423
$872$	48246.3	1.87365
$873$	12221.7	0.473816
$874$	−4214.31	−0.163102
$875$	−179.059	−0.00691805
$876$	−8751.38	−0.337536
$877$	19574.6	0.753689	0.376845	−	0.926276i	$-0.377009\pi$
$877$	19574.6	0.753689	0.376845	+	0.926276i	$0.377009\pi$
$878$	11467.3	0.440777
$879$	−3153.34	−0.121001
$880$	7626.82	0.292159
$881$	35319.3	1.35067	0.675333	−	0.737513i	$-0.264000\pi$
$881$	35319.3	1.35067	0.675333	+	0.737513i	$0.264000\pi$
$882$	−44183.7	−1.68678
$883$	−6232.19	−0.237520	−0.118760	−	0.992923i	$-0.537892\pi$
$883$	−6232.19	−0.237520	−0.118760	+	0.992923i	$0.537892\pi$
$884$	71692.3	2.72768
$885$	−1523.14	−0.0578529
$886$	−1435.12	−0.0544173
$887$	48583.2	1.83908	0.919541	−	0.392994i	$-0.128561\pi$
$887$	48583.2	1.83908	0.919541	+	0.392994i	$0.128561\pi$
$888$	3335.21	0.126039
$889$	−3.21528	−0.000121301 0
$890$	−69989.1	−2.63600
$891$	−7162.75	−0.269317
$892$	−104143.	−3.90915
$893$	−1333.68	−0.0499777
$894$	−11681.6	−0.437015
$895$	384.175	0.0143481
$896$	−276.191	−0.0102979
$897$	−3837.32	−0.142836
$898$	−58408.6	−2.17051
$899$	22736.4	0.843493
$900$	18098.5	0.670315
$901$	22570.2	0.834542
$902$	13615.6	0.502607
$903$	−5.90817	−0.000217731 0
$904$	−14495.8	−0.533321
$905$	507.633	0.0186456
$906$	4931.98	0.180854
$907$	−43904.0	−1.60729	−0.803644	−	0.595111i	$-0.797108\pi$
$907$	−43904.0	−1.60729	−0.803644	+	0.595111i	$0.797108\pi$
$908$	69588.6	2.54337
$909$	17755.1	0.647856
$910$	−178.835	−0.00651463
$911$	−30768.8	−1.11901	−0.559503	−	0.828828i	$-0.689008\pi$
$911$	−30768.8	−1.11901	−0.559503	+	0.828828i	$0.689008\pi$
$912$	−554.532	−0.0201342
$913$	−7284.96	−0.264071
$914$	−21186.8	−0.766737
$915$	−1123.33	−0.0405861
$916$	62128.9	2.24104
$917$	15.4175	0.000555214 0
$918$	−33350.2	−1.19904
$919$	13862.4	0.497584	0.248792	−	0.968557i	$-0.419967\pi$
$919$	13862.4	0.497584	0.248792	+	0.968557i	$0.419967\pi$
$920$	44156.8	1.58240
$921$	−3918.31	−0.140187
$922$	−50972.7	−1.82071
$923$	30592.9	1.09098
$924$	−21.0631	−0.000749921 0
$925$	−3389.45	−0.120480
$926$	−77662.7	−2.75611
$927$	36448.0	1.29138
$928$	8465.51	0.299455
$929$	28676.1	1.01274	0.506369	−	0.862317i	$-0.330987\pi$
$929$	28676.1	1.01274	0.506369	+	0.862317i	$0.330987\pi$
$930$	4842.12	0.170731
$931$	−2531.70	−0.0891226
$932$	−13411.8	−0.471373
$933$	−8476.64	−0.297441
$934$	55539.1	1.94571
$935$	12900.2	0.451209
$936$	36919.7	1.28927
$937$	16802.6	0.585824	0.292912	−	0.956139i	$-0.405376\pi$
$937$	16802.6	0.585824	0.292912	+	0.956139i	$0.405376\pi$
$938$	−534.597	−0.0186090
$939$	−7772.73	−0.270132
$940$	27130.9	0.941397
$941$	−11849.6	−0.410505	−0.205252	−	0.978709i	$-0.565802\pi$
$941$	−11849.6	−0.410505	−0.205252	+	0.978709i	$0.565802\pi$
$942$	7829.28	0.270798
$943$	28848.6	0.996223
$944$	−12924.7	−0.445618
$945$	56.0234	0.00192851
$946$	−2771.25	−0.0952441
$947$	−52320.7	−1.79535	−0.897673	−	0.440662i	$-0.854744\pi$
$947$	−52320.7	−1.79535	−0.897673	+	0.440662i	$0.854744\pi$
$948$	−8771.21	−0.300502
$949$	18142.5	0.620581
$950$	1539.93	0.0525915
$951$	−3430.86	−0.116986
$952$	637.708	0.0217103
$953$	−5323.66	−0.180955	−0.0904775	−	0.995898i	$-0.528839\pi$
$953$	−5323.66	−0.180955	−0.0904775	+	0.995898i	$0.528839\pi$
$954$	22566.4	0.765842
$955$	−39986.0	−1.35489
$956$	−18852.1	−0.637784
$957$	−2263.31	−0.0764499
$958$	−43800.2	−1.47716
$959$	−270.912	−0.00912223
$960$	−3667.58	−0.123303
$961$	−17914.0	−0.601324
$962$	−13424.1	−0.449907
$963$	16931.2	0.566564
$964$	74184.9	2.47856
$965$	−37383.5	−1.24706
$966$	−66.2701	−0.00220725
$967$	−3691.40	−0.122759	−0.0613793	−	0.998115i	$-0.519550\pi$
$967$	−3691.40	−0.122759	−0.0613793	+	0.998115i	$0.519550\pi$
$968$	−5088.68	−0.168963
$969$	−937.948	−0.0310952
$970$	−21154.4	−0.700234
$971$	20008.7	0.661287	0.330643	−	0.943756i	$-0.392734\pi$
$971$	20008.7	0.661287	0.330643	+	0.943756i	$0.392734\pi$
$972$	−33888.7	−1.11829
$973$	83.9428	0.00276576
$974$	33209.2	1.09250
$975$	1402.17	0.0460569
$976$	−9532.12	−0.312619
$977$	45017.1	1.47413	0.737065	−	0.675822i	$-0.236211\pi$
$977$	45017.1	1.47413	0.737065	+	0.675822i	$0.236211\pi$
$978$	−17343.7	−0.567065
$979$	17089.3	0.557891
$980$	51502.0	1.67875
$981$	29858.9	0.971785
$982$	54042.1	1.75616
$983$	3894.17	0.126353	0.0631763	−	0.998002i	$-0.479877\pi$
$983$	3894.17	0.126353	0.0631763	+	0.998002i	$0.479877\pi$
$984$	10372.7	0.336047
$985$	41668.8	1.34790
$986$	133040.	4.29703
$987$	−20.9722	−0.000676345 0
$988$	4107.23	0.132256
$989$	−5871.66	−0.188785
$990$	12898.0	0.414065
$991$	−10072.8	−0.322879	−0.161440	−	0.986883i	$-0.551614\pi$
$991$	−10072.8	−0.322879	−0.161440	+	0.986883i	$0.551614\pi$
$992$	4422.19	0.141537
$993$	−11648.7	−0.372265
$994$	528.337	0.0168590
$995$	34402.0	1.09610
$996$	−10775.1	−0.342794
$997$	−26849.1	−0.852878	−0.426439	−	0.904516i	$-0.640232\pi$
$997$	−26849.1	−0.852878	−0.426439	+	0.904516i	$0.640232\pi$
$998$	20257.2	0.642517
$999$	4205.36	0.133185

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.c.1.7	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.c.1.7	✓	84	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-4.94944 q^{2} -0.986242 q^{3} +16.4970 q^{4} -9.10214 q^{5} +4.88135 q^{6} -0.117691 q^{7} -42.0552 q^{8} -26.0273 q^{9} +O(q^{10})\)	\(q-4.94944 q^{2} -0.986242 q^{3} +16.4970 q^{4} -9.10214 q^{5} +4.88135 q^{6} -0.117691 q^{7} -42.0552 q^{8} -26.0273 q^{9} +45.0505 q^{10} -11.0000 q^{11} -16.2700 q^{12} +33.7294 q^{13} +0.582504 q^{14} +8.97691 q^{15} +76.1741 q^{16} +128.842 q^{17} +128.821 q^{18} +7.38135 q^{19} -150.158 q^{20} +0.116072 q^{21} +54.4438 q^{22} +115.355 q^{23} +41.4766 q^{24} -42.1511 q^{25} -166.942 q^{26} +52.2978 q^{27} -1.94154 q^{28} -208.626 q^{29} -44.4307 q^{30} -108.981 q^{31} -40.5775 q^{32} +10.8487 q^{33} -637.698 q^{34} +1.07124 q^{35} -429.372 q^{36} +80.4118 q^{37} -36.5336 q^{38} -33.2654 q^{39} +382.792 q^{40} +250.086 q^{41} -0.574490 q^{42} -50.9010 q^{43} -181.467 q^{44} +236.904 q^{45} -570.940 q^{46} -180.683 q^{47} -75.1261 q^{48} -342.986 q^{49} +208.624 q^{50} -127.070 q^{51} +556.433 q^{52} +175.177 q^{53} -258.845 q^{54} +100.124 q^{55} +4.94952 q^{56} -7.27980 q^{57} +1032.58 q^{58} -169.673 q^{59} +148.092 q^{60} -125.136 q^{61} +539.397 q^{62} +3.06318 q^{63} -408.557 q^{64} -307.010 q^{65} -53.6948 q^{66} -917.756 q^{67} +2125.51 q^{68} -113.768 q^{69} -5.30203 q^{70} +907.010 q^{71} +1094.58 q^{72} +537.884 q^{73} -397.994 q^{74} +41.5712 q^{75} +121.770 q^{76} +1.29460 q^{77} +164.645 q^{78} +539.103 q^{79} -693.347 q^{80} +651.160 q^{81} -1237.79 q^{82} +662.269 q^{83} +1.91483 q^{84} -1172.74 q^{85} +251.931 q^{86} +205.756 q^{87} +462.607 q^{88} -1553.57 q^{89} -1172.54 q^{90} -3.96965 q^{91} +1903.00 q^{92} +107.482 q^{93} +894.280 q^{94} -67.1861 q^{95} +40.0192 q^{96} -469.571 q^{97} +1697.59 q^{98} +286.301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * q^99

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