LMFDB - Embedded newform 110.6.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,6,Mod(1,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("110.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	110.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:	$17.6422201794$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{889}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 222 $ x^2 - x - 222
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$15.4081$ of defining polynomial
Character	$\chi$	$=$	110.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000 q^{2} -4.40805 q^{3} +16.0000 q^{4} -25.0000 q^{5} +17.6322 q^{6} +92.0403 q^{7} -64.0000 q^{8} -223.569 q^{9} +100.000 q^{10} +121.000 q^{11} -70.5288 q^{12} -64.2415 q^{13} -368.161 q^{14} +110.201 q^{15} +256.000 q^{16} -1394.03 q^{17} +894.276 q^{18} +813.224 q^{19} -400.000 q^{20} -405.718 q^{21} -484.000 q^{22} +2668.06 q^{23} +282.115 q^{24} +625.000 q^{25} +256.966 q^{26} +2056.66 q^{27} +1472.64 q^{28} +1880.55 q^{29} -440.805 q^{30} +3679.50 q^{31} -1024.00 q^{32} -533.374 q^{33} +5576.12 q^{34} -2301.01 q^{35} -3577.11 q^{36} +15375.8 q^{37} -3252.90 q^{38} +283.180 q^{39} +1600.00 q^{40} +2875.24 q^{41} +1622.87 q^{42} +20405.3 q^{43} +1936.00 q^{44} +5589.23 q^{45} -10672.2 q^{46} +26141.6 q^{47} -1128.46 q^{48} -8335.59 q^{49} -2500.00 q^{50} +6144.95 q^{51} -1027.86 q^{52} +491.587 q^{53} -8226.64 q^{54} -3025.00 q^{55} -5890.58 q^{56} -3584.73 q^{57} -7522.18 q^{58} -30775.7 q^{59} +1763.22 q^{60} -12688.8 q^{61} -14718.0 q^{62} -20577.4 q^{63} +4096.00 q^{64} +1606.04 q^{65} +2133.50 q^{66} +3915.60 q^{67} -22304.5 q^{68} -11760.9 q^{69} +9204.03 q^{70} -23656.8 q^{71} +14308.4 q^{72} +49810.0 q^{73} -61503.2 q^{74} -2755.03 q^{75} +13011.6 q^{76} +11136.9 q^{77} -1132.72 q^{78} +5846.55 q^{79} -6400.00 q^{80} +45261.4 q^{81} -11501.0 q^{82} -29846.2 q^{83} -6491.49 q^{84} +34850.7 q^{85} -81621.4 q^{86} -8289.54 q^{87} -7744.00 q^{88} -110688. q^{89} -22356.9 q^{90} -5912.81 q^{91} +42688.9 q^{92} -16219.4 q^{93} -104566. q^{94} -20330.6 q^{95} +4513.84 q^{96} -65866.2 q^{97} +33342.4 q^{98} -27051.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} + 21 q^{3} + 32 q^{4} - 50 q^{5} - 84 q^{6} + 35 q^{7} - 128 q^{8} + 179 q^{9} + 200 q^{10} + 242 q^{11} + 336 q^{12} + 766 q^{13} - 140 q^{14} - 525 q^{15} + 512 q^{16} + 283 q^{17} - 716 q^{18}+ \cdots + 21659 q^{99}+O(q^{100}) $ 2 * q - 8 * q^2 + 21 * q^3 + 32 * q^4 - 50 * q^5 - 84 * q^6 + 35 * q^7 - 128 * q^8 + 179 * q^9 + 200 * q^10 + 242 * q^11 + 336 * q^12 + 766 * q^13 - 140 * q^14 - 525 * q^15 + 512 * q^16 + 283 * q^17 - 716 * q^18 + 1537 * q^19 - 800 * q^20 - 1855 * q^21 - 968 * q^22 - 806 * q^23 - 1344 * q^24 + 1250 * q^25 - 3064 * q^26 + 6111 * q^27 + 560 * q^28 + 7667 * q^29 + 2100 * q^30 + 4765 * q^31 - 2048 * q^32 + 2541 * q^33 - 1132 * q^34 - 875 * q^35 + 2864 * q^36 + 28575 * q^37 - 6148 * q^38 + 21378 * q^39 + 3200 * q^40 + 10044 * q^41 + 7420 * q^42 + 19522 * q^43 + 3872 * q^44 - 4475 * q^45 + 3224 * q^46 + 22646 * q^47 + 5376 * q^48 - 21889 * q^49 - 5000 * q^50 + 48755 * q^51 + 12256 * q^52 - 33037 * q^53 - 24444 * q^54 - 6050 * q^55 - 2240 * q^56 + 14805 * q^57 - 30668 * q^58 - 15098 * q^59 - 8400 * q^60 + 4349 * q^61 - 19060 * q^62 - 43540 * q^63 + 8192 * q^64 - 19150 * q^65 - 10164 * q^66 + 32996 * q^67 + 4528 * q^68 - 100030 * q^69 + 3500 * q^70 - 87297 * q^71 - 11456 * q^72 + 38974 * q^73 - 114300 * q^74 + 13125 * q^75 + 24592 * q^76 + 4235 * q^77 - 85512 * q^78 - 48118 * q^79 - 12800 * q^80 + 50450 * q^81 - 40176 * q^82 + 59572 * q^83 - 29680 * q^84 - 7075 * q^85 - 78088 * q^86 + 138733 * q^87 - 15488 * q^88 - 158673 * q^89 + 17900 * q^90 - 53270 * q^91 - 12896 * q^92 + 11361 * q^93 - 90584 * q^94 - 38425 * q^95 - 21504 * q^96 + 109122 * q^97 + 87556 * q^98 + 21659 * q^99

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−4.40805	−0.282777	−0.141388	−	0.989954i	$-0.545157\pi$
$3$	−4.40805	−0.282777	−0.141388	+	0.989954i	$0.545157\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	17.6322	0.199953
$7$	92.0403	0.709958	0.354979	−	0.934874i	$-0.384488\pi$
$7$	92.0403	0.709958	0.354979	+	0.934874i	$0.384488\pi$
$8$	−64.0000	−0.353553
$9$	−223.569	−0.920037
$10$	100.000	0.316228
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−70.5288	−0.141388
$13$	−64.2415	−0.105428	−0.0527142	−	0.998610i	$-0.516787\pi$
$13$	−64.2415	−0.105428	−0.0527142	+	0.998610i	$0.516787\pi$
$14$	−368.161	−0.502016
$15$	110.201	0.126462
$16$	256.000	0.250000
$17$	−1394.03	−1.16990	−0.584951	−	0.811069i	$-0.698886\pi$
$17$	−1394.03	−1.16990	−0.584951	+	0.811069i	$0.698886\pi$
$18$	894.276	0.650565
$19$	813.224	0.516804	0.258402	−	0.966037i	$-0.416804\pi$
$19$	813.224	0.516804	0.258402	+	0.966037i	$0.416804\pi$
$20$	−400.000	−0.223607
$21$	−405.718	−0.200760
$22$	−484.000	−0.213201
$23$	2668.06	1.05166	0.525831	−	0.850589i	$-0.323755\pi$
$23$	2668.06	1.05166	0.525831	+	0.850589i	$0.323755\pi$
$24$	282.115	0.0999766
$25$	625.000	0.200000
$26$	256.966	0.0745491
$27$	2056.66	0.542942
$28$	1472.64	0.354979
$29$	1880.55	0.415230	0.207615	−	0.978211i	$-0.433430\pi$
$29$	1880.55	0.415230	0.207615	+	0.978211i	$0.433430\pi$
$30$	−440.805	−0.0894218
$31$	3679.50	0.687677	0.343839	−	0.939029i	$-0.388273\pi$
$31$	3679.50	0.687677	0.343839	+	0.939029i	$0.388273\pi$
$32$	−1024.00	−0.176777
$33$	−533.374	−0.0852604
$34$	5576.12	0.827246
$35$	−2301.01	−0.317503
$36$	−3577.11	−0.460019
$37$	15375.8	1.84643	0.923215	−	0.384283i	$-0.125551\pi$
$37$	15375.8	1.84643	0.923215	+	0.384283i	$0.125551\pi$
$38$	−3252.90	−0.365436
$39$	283.180	0.0298127
$40$	1600.00	0.158114
$41$	2875.24	0.267125	0.133563	−	0.991040i	$-0.457358\pi$
$41$	2875.24	0.267125	0.133563	+	0.991040i	$0.457358\pi$
$42$	1622.87	0.141958
$43$	20405.3	1.68296	0.841478	−	0.540291i	$-0.181686\pi$
$43$	20405.3	1.68296	0.841478	+	0.540291i	$0.181686\pi$
$44$	1936.00	0.150756
$45$	5589.23	0.411453
$46$	−10672.2	−0.743637
$47$	26141.6	1.72619	0.863093	−	0.505045i	$-0.168524\pi$
$47$	26141.6	1.72619	0.863093	+	0.505045i	$0.168524\pi$
$48$	−1128.46	−0.0706942
$49$	−8335.59	−0.495959
$50$	−2500.00	−0.141421
$51$	6144.95	0.330821
$52$	−1027.86	−0.0527142
$53$	491.587	0.0240387	0.0120193	−	0.999928i	$-0.496174\pi$
$53$	491.587	0.0240387	0.0120193	+	0.999928i	$0.496174\pi$
$54$	−8226.64	−0.383918
$55$	−3025.00	−0.134840
$56$	−5890.58	−0.251008
$57$	−3584.73	−0.146140
$58$	−7522.18	−0.293612
$59$	−30775.7	−1.15101	−0.575504	−	0.817799i	$-0.695194\pi$
$59$	−30775.7	−1.15101	−0.575504	+	0.817799i	$0.695194\pi$
$60$	1763.22	0.0632308
$61$	−12688.8	−0.436613	−0.218307	−	0.975880i	$-0.570053\pi$
$61$	−12688.8	−0.436613	−0.218307	+	0.975880i	$0.570053\pi$
$62$	−14718.0	−0.486261
$63$	−20577.4	−0.653188
$64$	4096.00	0.125000
$65$	1606.04	0.0471490
$66$	2133.50	0.0602882
$67$	3915.60	0.106564	0.0532822	−	0.998579i	$-0.483032\pi$
$67$	3915.60	0.106564	0.0532822	+	0.998579i	$0.483032\pi$
$68$	−22304.5	−0.584951
$69$	−11760.9	−0.297385
$70$	9204.03	0.224508
$71$	−23656.8	−0.556942	−0.278471	−	0.960445i	$-0.589828\pi$
$71$	−23656.8	−0.556942	−0.278471	+	0.960445i	$0.589828\pi$
$72$	14308.4	0.325282
$73$	49810.0	1.09398	0.546990	−	0.837139i	$-0.315774\pi$
$73$	49810.0	1.09398	0.546990	+	0.837139i	$0.315774\pi$
$74$	−61503.2	−1.30562
$75$	−2755.03	−0.0565553
$76$	13011.6	0.258402
$77$	11136.9	0.214060
$78$	−1132.72	−0.0210808
$79$	5846.55	0.105398	0.0526990	−	0.998610i	$-0.483218\pi$
$79$	5846.55	0.105398	0.0526990	+	0.998610i	$0.483218\pi$
$80$	−6400.00	−0.111803
$81$	45261.4	0.766506
$82$	−11501.0	−0.188886
$83$	−29846.2	−0.475547	−0.237774	−	0.971321i	$-0.576418\pi$
$83$	−29846.2	−0.475547	−0.237774	+	0.971321i	$0.576418\pi$
$84$	−6491.49	−0.100380
$85$	34850.7	0.523196
$86$	−81621.4	−1.19003
$87$	−8289.54	−0.117417
$88$	−7744.00	−0.106600
$89$	−110688.	−1.48124	−0.740621	−	0.671923i	$-0.765469\pi$
$89$	−110688.	−1.48124	−0.740621	+	0.671923i	$0.765469\pi$
$90$	−22356.9	−0.290941
$91$	−5912.81	−0.0748497
$92$	42688.9	0.525831
$93$	−16219.4	−0.194459
$94$	−104566.	−1.22060
$95$	−20330.6	−0.231122
$96$	4513.84	0.0499883
$97$	−65866.2	−0.710777	−0.355389	−	0.934719i	$-0.615651\pi$
$97$	−65866.2	−0.710777	−0.355389	+	0.934719i	$0.615651\pi$
$98$	33342.4	0.350696
$99$	−27051.9	−0.277402
$100$	10000.0	0.100000
$101$	170816.	1.66619	0.833097	−	0.553127i	$-0.186565\pi$
$101$	170816.	1.66619	0.833097	+	0.553127i	$0.186565\pi$
$102$	−24579.8	−0.233926
$103$	−3350.44	−0.0311178	−0.0155589	−	0.999879i	$-0.504953\pi$
$103$	−3350.44	−0.0311178	−0.0155589	+	0.999879i	$0.504953\pi$
$104$	4111.46	0.0372746
$105$	10143.0	0.0897824
$106$	−1966.35	−0.0169979
$107$	−43688.4	−0.368898	−0.184449	−	0.982842i	$-0.559050\pi$
$107$	−43688.4	−0.368898	−0.184449	+	0.982842i	$0.559050\pi$
$108$	32906.6	0.271471
$109$	49375.4	0.398056	0.199028	−	0.979994i	$-0.436222\pi$
$109$	49375.4	0.398056	0.199028	+	0.979994i	$0.436222\pi$
$110$	12100.0	0.0953463
$111$	−67777.3	−0.522128
$112$	23562.3	0.177490
$113$	113388.	0.835356	0.417678	−	0.908595i	$-0.362844\pi$
$113$	113388.	0.835356	0.417678	+	0.908595i	$0.362844\pi$
$114$	14338.9	0.103337
$115$	−66701.5	−0.470317
$116$	30088.7	0.207615
$117$	14362.4	0.0969981
$118$	123103.	0.813886
$119$	−128307.	−0.830582
$120$	−7052.88	−0.0447109
$121$	14641.0	0.0909091
$122$	50755.3	0.308732
$123$	−12674.2	−0.0755367
$124$	58872.0	0.343839
$125$	−15625.0	−0.0894427
$126$	82309.4	0.461874
$127$	315137.	1.73377	0.866883	−	0.498512i	$-0.166120\pi$
$127$	315137.	1.73377	0.866883	+	0.498512i	$0.166120\pi$
$128$	−16384.0	−0.0883883
$129$	−89947.8	−0.475901
$130$	−6424.15	−0.0333394
$131$	263284.	1.34044	0.670218	−	0.742165i	$-0.266201\pi$
$131$	263284.	1.34044	0.670218	+	0.742165i	$0.266201\pi$
$132$	−8533.99	−0.0426302
$133$	74849.4	0.366910
$134$	−15662.4	−0.0753524
$135$	−51416.5	−0.242811
$136$	89217.9	0.413623
$137$	101284.	0.461039	0.230519	−	0.973068i	$-0.425957\pi$
$137$	101284.	0.461039	0.230519	+	0.973068i	$0.425957\pi$
$138$	47043.8	0.210283
$139$	−156014.	−0.684897	−0.342449	−	0.939537i	$-0.611256\pi$
$139$	−156014.	−0.684897	−0.342449	+	0.939537i	$0.611256\pi$
$140$	−36816.1	−0.158751
$141$	−115234.	−0.488125
$142$	94627.2	0.393818
$143$	−7773.23	−0.0317879
$144$	−57233.7	−0.230009
$145$	−47013.6	−0.185697
$146$	−199240.	−0.773560
$147$	36743.7	0.140246
$148$	246013.	0.923215
$149$	−132795.	−0.490024	−0.245012	−	0.969520i	$-0.578792\pi$
$149$	−132795.	−0.490024	−0.245012	+	0.969520i	$0.578792\pi$
$150$	11020.1	0.0399907
$151$	224845.	0.802491	0.401245	−	0.915971i	$-0.368577\pi$
$151$	224845.	0.802491	0.401245	+	0.915971i	$0.368577\pi$
$152$	−52046.3	−0.182718
$153$	311662.	1.07635
$154$	−44547.5	−0.151364
$155$	−91987.5	−0.307539
$156$	4530.88	0.0149063
$157$	200959.	0.650667	0.325333	−	0.945599i	$-0.394524\pi$
$157$	200959.	0.650667	0.325333	+	0.945599i	$0.394524\pi$
$158$	−23386.2	−0.0745276
$159$	−2166.94	−0.00679758
$160$	25600.0	0.0790569
$161$	245569.	0.746635
$162$	−181046.	−0.542002
$163$	−315221.	−0.929278	−0.464639	−	0.885500i	$-0.653816\pi$
$163$	−315221.	−0.929278	−0.464639	+	0.885500i	$0.653816\pi$
$164$	46003.8	0.133563
$165$	13334.4	0.0381296
$166$	119385.	0.336263
$167$	−461946.	−1.28174	−0.640870	−	0.767650i	$-0.721426\pi$
$167$	−461946.	−1.28174	−0.640870	+	0.767650i	$0.721426\pi$
$168$	25966.0	0.0709792
$169$	−367166.	−0.988885
$170$	−139403.	−0.369956
$171$	−181812.	−0.475479
$172$	326486.	0.841478
$173$	−284609.	−0.722992	−0.361496	−	0.932374i	$-0.617734\pi$
$173$	−284609.	−0.722992	−0.361496	+	0.932374i	$0.617734\pi$
$174$	33158.2	0.0830266
$175$	57525.2	0.141992
$176$	30976.0	0.0753778
$177$	135661.	0.325478
$178$	442753.	1.04740
$179$	−616210.	−1.43746	−0.718731	−	0.695289i	$-0.755277\pi$
$179$	−616210.	−1.43746	−0.718731	+	0.695289i	$0.755277\pi$
$180$	89427.6	0.205727
$181$	156628.	0.355364	0.177682	−	0.984088i	$-0.443140\pi$
$181$	156628.	0.355364	0.177682	+	0.984088i	$0.443140\pi$
$182$	23651.2	0.0529268
$183$	55933.0	0.123464
$184$	−170756.	−0.371818
$185$	−384395.	−0.825749
$186$	64877.7	0.137503
$187$	−168678.	−0.352739
$188$	418266.	0.863093
$189$	189296.	0.385466
$190$	81322.4	0.163428
$191$	95586.9	0.189590	0.0947949	−	0.995497i	$-0.469780\pi$
$191$	95586.9	0.189590	0.0947949	+	0.995497i	$0.469780\pi$
$192$	−18055.4	−0.0353471
$193$	748658.	1.44674	0.723370	−	0.690461i	$-0.242592\pi$
$193$	748658.	1.44674	0.723370	+	0.690461i	$0.242592\pi$
$194$	263465.	0.502595
$195$	−7079.50	−0.0133326
$196$	−133369.	−0.247980
$197$	−456491.	−0.838043	−0.419022	−	0.907976i	$-0.637627\pi$
$197$	−456491.	−0.838043	−0.419022	+	0.907976i	$0.637627\pi$
$198$	108207.	0.196153
$199$	591303.	1.05847	0.529234	−	0.848476i	$-0.322479\pi$
$199$	591303.	1.05847	0.529234	+	0.848476i	$0.322479\pi$
$200$	−40000.0	−0.0707107
$201$	−17260.2	−0.0301339
$202$	−683265.	−1.17818
$203$	173086.	0.294796
$204$	98319.2	0.165411
$205$	−71881.0	−0.119462
$206$	13401.7	0.0220036
$207$	−596495.	−0.967567
$208$	−16445.8	−0.0263571
$209$	98400.1	0.155822
$210$	−40571.8	−0.0634857
$211$	−568294.	−0.878754	−0.439377	−	0.898303i	$-0.644801\pi$
$211$	−568294.	−0.878754	−0.439377	+	0.898303i	$0.644801\pi$
$212$	7865.39	0.0120193
$213$	104280.	0.157490
$214$	174754.	0.260850
$215$	−510134.	−0.752641
$216$	−131626.	−0.191959
$217$	338662.	0.488222
$218$	−197501.	−0.281468
$219$	−219565.	−0.309352
$220$	−48400.0	−0.0674200
$221$	89554.6	0.123341
$222$	271109.	0.369200
$223$	355316.	0.478468	0.239234	−	0.970962i	$-0.423104\pi$
$223$	355316.	0.478468	0.239234	+	0.970962i	$0.423104\pi$
$224$	−94249.2	−0.125504
$225$	−139731.	−0.184007
$226$	−453553.	−0.590686
$227$	627531.	0.808297	0.404148	−	0.914693i	$-0.367568\pi$
$227$	627531.	0.808297	0.404148	+	0.914693i	$0.367568\pi$
$228$	−57355.7	−0.0730701
$229$	−987980.	−1.24497	−0.622486	−	0.782631i	$-0.713877\pi$
$229$	−987980.	−1.24497	−0.622486	+	0.782631i	$0.713877\pi$
$230$	266806.	0.332564
$231$	−49091.9	−0.0605313
$232$	−120355.	−0.146806
$233$	−147032.	−0.177428	−0.0887139	−	0.996057i	$-0.528276\pi$
$233$	−147032.	−0.177428	−0.0887139	+	0.996057i	$0.528276\pi$
$234$	−57449.7	−0.0685880
$235$	−653540.	−0.771974
$236$	−492412.	−0.575504
$237$	−25771.9	−0.0298041
$238$	513227.	0.587310
$239$	−1.36202e6	−1.54237	−0.771186	−	0.636610i	$-0.780336\pi$
$239$	−1.36202e6	−1.54237	−0.771186	+	0.636610i	$0.780336\pi$
$240$	28211.5	0.0316154
$241$	1.54270e6	1.71096	0.855478	−	0.517839i	$-0.173263\pi$
$241$	1.54270e6	1.71096	0.855478	+	0.517839i	$0.173263\pi$
$242$	−58564.0	−0.0642824
$243$	−699283.	−0.759692
$244$	−203021.	−0.218307
$245$	208390.	0.221800
$246$	50696.8	0.0534125
$247$	−52242.8	−0.0544859
$248$	−235488.	−0.243131
$249$	131564.	0.134474
$250$	62500.0	0.0632456
$251$	−551214.	−0.552250	−0.276125	−	0.961122i	$-0.589050\pi$
$251$	−551214.	−0.552250	−0.276125	+	0.961122i	$0.589050\pi$
$252$	−329238.	−0.326594
$253$	322835.	0.317088
$254$	−1.26055e6	−1.22596
$255$	−153624.	−0.147948
$256$	65536.0	0.0625000
$257$	−1.50798e6	−1.42417	−0.712085	−	0.702094i	$-0.752249\pi$
$257$	−1.50798e6	−1.42417	−0.712085	+	0.702094i	$0.752249\pi$
$258$	359791.	0.336513
$259$	1.41519e6	1.31089
$260$	25696.6	0.0235745
$261$	−420432.	−0.382027
$262$	−1.05313e6	−0.947831
$263$	413554.	0.368675	0.184337	−	0.982863i	$-0.440986\pi$
$263$	413554.	0.368675	0.184337	+	0.982863i	$0.440986\pi$
$264$	34136.0	0.0301441
$265$	−12289.7	−0.0107504
$266$	−299397.	−0.259444
$267$	487919.	0.418861
$268$	62649.7	0.0532822
$269$	1.92394e6	1.62110	0.810551	−	0.585668i	$-0.199168\pi$
$269$	1.92394e6	1.62110	0.810551	+	0.585668i	$0.199168\pi$
$270$	205666.	0.171693
$271$	1.36505e6	1.12908	0.564540	−	0.825405i	$-0.309053\pi$
$271$	1.36505e6	1.12908	0.564540	+	0.825405i	$0.309053\pi$
$272$	−356872.	−0.292476
$273$	26064.0	0.0211658
$274$	−405134.	−0.326004
$275$	75625.0	0.0603023
$276$	−188175.	−0.148693
$277$	462704.	0.362330	0.181165	−	0.983453i	$-0.442013\pi$
$277$	462704.	0.362330	0.181165	+	0.983453i	$0.442013\pi$
$278$	624055.	0.484296
$279$	−822623.	−0.632689
$280$	147264.	0.112254
$281$	1.31617e6	0.994367	0.497183	−	0.867645i	$-0.334368\pi$
$281$	1.31617e6	0.994367	0.497183	+	0.867645i	$0.334368\pi$
$282$	460934.	0.345157
$283$	−1.19241e6	−0.885035	−0.442517	−	0.896760i	$-0.645914\pi$
$283$	−1.19241e6	−0.885035	−0.442517	+	0.896760i	$0.645914\pi$
$284$	−378509.	−0.278471
$285$	89618.3	0.0653559
$286$	31092.9	0.0224774
$287$	264638.	0.189648
$288$	228935.	0.162641
$289$	523461.	0.368671
$290$	188055.	0.131307
$291$	290342.	0.200991
$292$	796960.	0.546990
$293$	−644118.	−0.438325	−0.219163	−	0.975688i	$-0.570332\pi$
$293$	−644118.	−0.438325	−0.219163	+	0.975688i	$0.570332\pi$
$294$	−146975.	−0.0991687
$295$	769394.	0.514747
$296$	−984050.	−0.652812
$297$	248856.	0.163703
$298$	531181.	0.346499
$299$	−171400.	−0.110875
$300$	−44080.5	−0.0282777
$301$	1.87811e6	1.19483
$302$	−899379.	−0.567447
$303$	−752967.	−0.471161
$304$	208185.	0.129201
$305$	317221.	0.195259
$306$	−1.24665e6	−0.761097
$307$	1.19044e6	0.720875	0.360437	−	0.932783i	$-0.382627\pi$
$307$	1.19044e6	0.720875	0.360437	+	0.932783i	$0.382627\pi$
$308$	178190.	0.107030
$309$	14768.9	0.00879938
$310$	367950.	0.217463
$311$	1.25938e6	0.738341	0.369170	−	0.929362i	$-0.379642\pi$
$311$	1.25938e6	0.738341	0.369170	+	0.929362i	$0.379642\pi$
$312$	−18123.5	−0.0105404
$313$	2.23658e6	1.29040	0.645200	−	0.764014i	$-0.276774\pi$
$313$	2.23658e6	1.29040	0.645200	+	0.764014i	$0.276774\pi$
$314$	−803836.	−0.460091
$315$	514434.	0.292115
$316$	93544.8	0.0526990
$317$	2.36125e6	1.31976	0.659878	−	0.751373i	$-0.270608\pi$
$317$	2.36125e6	1.31976	0.659878	+	0.751373i	$0.270608\pi$
$318$	8667.76	0.00480661
$319$	227546.	0.125197
$320$	−102400.	−0.0559017
$321$	192581.	0.104316
$322$	−982275.	−0.527951
$323$	−1.13366e6	−0.604611
$324$	724183.	0.383253
$325$	−40151.0	−0.0210857
$326$	1.26088e6	0.657099
$327$	−217649.	−0.112561
$328$	−184015.	−0.0944430
$329$	2.40608e6	1.22552
$330$	−53337.4	−0.0269617
$331$	−3.06002e6	−1.53516	−0.767580	−	0.640953i	$-0.778539\pi$
$331$	−3.06002e6	−1.53516	−0.767580	+	0.640953i	$0.778539\pi$
$332$	−477539.	−0.237774
$333$	−3.43755e6	−1.69879
$334$	1.84778e6	0.906327
$335$	−97890.1	−0.0476570
$336$	−103864.	−0.0501899
$337$	4.08324e6	1.95853	0.979264	−	0.202588i	$-0.0649351\pi$
$337$	4.08324e6	1.95853	0.979264	+	0.202588i	$0.0649351\pi$
$338$	1.46866e6	0.699247
$339$	−499821.	−0.236219
$340$	557612.	0.261598
$341$	445220.	0.207342
$342$	727247.	0.336215
$343$	−2.31413e6	−1.06207
$344$	−1.30594e6	−0.595015
$345$	294023.	0.132995
$346$	1.13844e6	0.511232
$347$	2.25118e6	1.00366	0.501830	−	0.864966i	$-0.332660\pi$
$347$	2.25118e6	1.00366	0.501830	+	0.864966i	$0.332660\pi$
$348$	−132633.	−0.0587087
$349$	1.09341e6	0.480531	0.240265	−	0.970707i	$-0.422766\pi$
$349$	1.09341e6	0.480531	0.240265	+	0.970707i	$0.422766\pi$
$350$	−230101.	−0.100403
$351$	−132123.	−0.0572415
$352$	−123904.	−0.0533002
$353$	−1.73879e6	−0.742694	−0.371347	−	0.928494i	$-0.621104\pi$
$353$	−1.73879e6	−0.742694	−0.371347	+	0.928494i	$0.621104\pi$
$354$	−542644.	−0.230148
$355$	591420.	0.249072
$356$	−1.77101e6	−0.740621
$357$	565583.	0.234869
$358$	2.46484e6	1.01644
$359$	1.93636e6	0.792959	0.396480	−	0.918044i	$-0.370232\pi$
$359$	1.93636e6	0.792959	0.396480	+	0.918044i	$0.370232\pi$
$360$	−357711.	−0.145471
$361$	−1.81477e6	−0.732913
$362$	−626513.	−0.251280
$363$	−64538.3	−0.0257070
$364$	−94604.9	−0.0374249
$365$	−1.24525e6	−0.489243
$366$	−223732.	−0.0873022
$367$	−1.36996e6	−0.530937	−0.265469	−	0.964119i	$-0.585527\pi$
$367$	−1.36996e6	−0.530937	−0.265469	+	0.964119i	$0.585527\pi$
$368$	683023.	0.262915
$369$	−642815.	−0.245765
$370$	1.53758e6	0.583893
$371$	45245.8	0.0170665
$372$	−259511.	−0.0972295
$373$	1.02270e6	0.380608	0.190304	−	0.981725i	$-0.439053\pi$
$373$	1.02270e6	0.380608	0.190304	+	0.981725i	$0.439053\pi$
$374$	674710.	0.249424
$375$	68875.8	0.0252923
$376$	−1.67306e6	−0.610299
$377$	−120809.	−0.0437770
$378$	−757182.	−0.272566
$379$	2.30604e6	0.824650	0.412325	−	0.911037i	$-0.364717\pi$
$379$	2.30604e6	0.824650	0.412325	+	0.911037i	$0.364717\pi$
$380$	−325290.	−0.115561
$381$	−1.38914e6	−0.490269
$382$	−382348.	−0.134060
$383$	−4.44660e6	−1.54893	−0.774464	−	0.632618i	$-0.781980\pi$
$383$	−4.44660e6	−1.54893	−0.774464	+	0.632618i	$0.781980\pi$
$384$	72221.5	0.0249942
$385$	−278422.	−0.0957307
$386$	−2.99463e6	−1.02300
$387$	−4.56201e6	−1.54838
$388$	−1.05386e6	−0.355389
$389$	−3.04391e6	−1.01990	−0.509951	−	0.860204i	$-0.670336\pi$
$389$	−3.04391e6	−1.01990	−0.509951	+	0.860204i	$0.670336\pi$
$390$	28318.0	0.00942760
$391$	−3.71935e6	−1.23034
$392$	533478.	0.175348
$393$	−1.16057e6	−0.379044
$394$	1.82596e6	0.592586
$395$	−146164.	−0.0471354
$396$	−432830.	−0.138701
$397$	−2.97167e6	−0.946289	−0.473145	−	0.880985i	$-0.656881\pi$
$397$	−2.97167e6	−0.946289	−0.473145	+	0.880985i	$0.656881\pi$
$398$	−2.36521e6	−0.748450
$399$	−329940.	−0.103753
$400$	160000.	0.0500000
$401$	4.34955e6	1.35078	0.675388	−	0.737463i	$-0.263976\pi$
$401$	4.34955e6	1.35078	0.675388	+	0.737463i	$0.263976\pi$
$402$	69040.7	0.0213079
$403$	−236377.	−0.0725007
$404$	2.73306e6	0.833097
$405$	−1.13154e6	−0.342792
$406$	−692343.	−0.208452
$407$	1.86047e6	0.556720
$408$	−393277.	−0.116963
$409$	89191.8	0.0263643	0.0131822	−	0.999913i	$-0.495804\pi$
$409$	89191.8	0.0263643	0.0131822	+	0.999913i	$0.495804\pi$
$410$	287524.	0.0844723
$411$	−446463.	−0.130371
$412$	−53607.0	−0.0155589
$413$	−2.83261e6	−0.817168
$414$	2.38598e6	0.684173
$415$	746155.	0.212671
$416$	65783.3	0.0186373
$417$	687716.	0.193673
$418$	−393600.	−0.110183
$419$	−4.18567e6	−1.16474	−0.582371	−	0.812923i	$-0.697875\pi$
$419$	−4.18567e6	−1.16474	−0.582371	+	0.812923i	$0.697875\pi$
$420$	162287.	0.0448912
$421$	1.96388e6	0.540020	0.270010	−	0.962857i	$-0.412973\pi$
$421$	1.96388e6	0.540020	0.270010	+	0.962857i	$0.412973\pi$
$422$	2.27318e6	0.621373
$423$	−5.84445e6	−1.58816
$424$	−31461.6	−0.00849895
$425$	−871268.	−0.233980
$426$	−417122.	−0.111362
$427$	−1.16788e6	−0.309977
$428$	−699014.	−0.184449
$429$	34264.8	0.00898886
$430$	2.04053e6	0.532198
$431$	−1.32562e6	−0.343736	−0.171868	−	0.985120i	$-0.554980\pi$
$431$	−1.32562e6	−0.343736	−0.171868	+	0.985120i	$0.554980\pi$
$432$	526505.	0.135735
$433$	−5.16016e6	−1.32265	−0.661323	−	0.750101i	$-0.730005\pi$
$433$	−5.16016e6	−1.32265	−0.661323	+	0.750101i	$0.730005\pi$
$434$	−1.35465e6	−0.345225
$435$	207239.	0.0525106
$436$	790006.	0.199028
$437$	2.16973e6	0.543503
$438$	878260.	0.218745
$439$	3.93148e6	0.973632	0.486816	−	0.873504i	$-0.338158\pi$
$439$	3.93148e6	0.973632	0.486816	+	0.873504i	$0.338158\pi$
$440$	193600.	0.0476731
$441$	1.86358e6	0.456301
$442$	−358218.	−0.0872152
$443$	3.06674e6	0.742452	0.371226	−	0.928543i	$-0.378938\pi$
$443$	3.06674e6	0.742452	0.371226	+	0.928543i	$0.378938\pi$
$444$	−1.08444e6	−0.261064
$445$	2.76720e6	0.662432
$446$	−1.42126e6	−0.338328
$447$	585369.	0.138567
$448$	376997.	0.0887448
$449$	4.68097e6	1.09577	0.547886	−	0.836553i	$-0.315433\pi$
$449$	4.68097e6	1.09577	0.547886	+	0.836553i	$0.315433\pi$
$450$	558923.	0.130113
$451$	347904.	0.0805412
$452$	1.81421e6	0.417678
$453$	−991127.	−0.226926
$454$	−2.51013e6	−0.571552
$455$	147820.	0.0334738
$456$	229423.	0.0516684
$457$	−6.86401e6	−1.53740	−0.768701	−	0.639608i	$-0.779097\pi$
$457$	−6.86401e6	−1.53740	−0.768701	+	0.639608i	$0.779097\pi$
$458$	3.95192e6	0.880328
$459$	−2.86705e6	−0.635189
$460$	−1.06722e6	−0.235159
$461$	−3.85378e6	−0.844569	−0.422284	−	0.906463i	$-0.638772\pi$
$461$	−3.85378e6	−0.844569	−0.422284	+	0.906463i	$0.638772\pi$
$462$	196368.	0.0428021
$463$	−3.15825e6	−0.684689	−0.342345	−	0.939574i	$-0.611221\pi$
$463$	−3.15825e6	−0.684689	−0.342345	+	0.939574i	$0.611221\pi$
$464$	481420.	0.103808
$465$	405486.	0.0869647
$466$	588127.	0.125460
$467$	196109.	0.0416107	0.0208054	−	0.999784i	$-0.493377\pi$
$467$	196109.	0.0416107	0.0208054	+	0.999784i	$0.493377\pi$
$468$	229799.	0.0484990
$469$	360393.	0.0756562
$470$	2.61416e6	0.545868
$471$	−885838.	−0.183993
$472$	1.96965e6	0.406943
$473$	2.46905e6	0.507430
$474$	103088.	0.0210747
$475$	508265.	0.103361
$476$	−2.05291e6	−0.415291
$477$	−109904.	−0.0221165
$478$	5.44808e6	1.09062
$479$	5.13528e6	1.02265	0.511323	−	0.859389i	$-0.329156\pi$
$479$	5.13528e6	1.02265	0.511323	+	0.859389i	$0.329156\pi$
$480$	−112846.	−0.0223555
$481$	−987764.	−0.194666
$482$	−6.17080e6	−1.20983
$483$	−1.08248e6	−0.211131
$484$	234256.	0.0454545
$485$	1.64666e6	0.317869
$486$	2.79713e6	0.537183
$487$	2.43868e6	0.465943	0.232971	−	0.972484i	$-0.425155\pi$
$487$	2.43868e6	0.465943	0.232971	+	0.972484i	$0.425155\pi$
$488$	812085.	0.154366
$489$	1.38951e6	0.262778
$490$	−833559.	−0.156836
$491$	4.07687e6	0.763173	0.381587	−	0.924333i	$-0.375378\pi$
$491$	4.07687e6	0.763173	0.381587	+	0.924333i	$0.375378\pi$
$492$	−202787.	−0.0377684
$493$	−2.62154e6	−0.485779
$494$	208971.	0.0385273
$495$	676296.	0.124058
$496$	941952.	0.171919
$497$	−2.17738e6	−0.395406
$498$	−526254.	−0.0950873
$499$	878791.	0.157992	0.0789958	−	0.996875i	$-0.474829\pi$
$499$	878791.	0.157992	0.0789958	+	0.996875i	$0.474829\pi$
$500$	−250000.	−0.0447214
$501$	2.03628e6	0.362446
$502$	2.20486e6	0.390500
$503$	7.00187e6	1.23394	0.616970	−	0.786987i	$-0.288360\pi$
$503$	7.00187e6	1.23394	0.616970	+	0.786987i	$0.288360\pi$
$504$	1.31695e6	0.230937
$505$	−4.27040e6	−0.745145
$506$	−1.29134e6	−0.224215
$507$	1.61849e6	0.279634
$508$	5.04220e6	0.866883
$509$	5.54203e6	0.948144	0.474072	−	0.880486i	$-0.342784\pi$
$509$	5.54203e6	0.948144	0.474072	+	0.880486i	$0.342784\pi$
$510$	614495.	0.104615
$511$	4.58452e6	0.776680
$512$	−262144.	−0.0441942
$513$	1.67253e6	0.280595
$514$	6.03190e6	1.00704
$515$	83760.9	0.0139163
$516$	−1.43917e6	−0.237950
$517$	3.16313e6	0.520465
$518$	−5.66077e6	−0.926938
$519$	1.25457e6	0.204445
$520$	−102786.	−0.0166697
$521$	−5.22863e6	−0.843905	−0.421953	−	0.906618i	$-0.638655\pi$
$521$	−5.22863e6	−0.843905	−0.421953	+	0.906618i	$0.638655\pi$
$522$	1.68173e6	0.270134
$523$	2.80925e6	0.449092	0.224546	−	0.974463i	$-0.427910\pi$
$523$	2.80925e6	0.449092	0.224546	+	0.974463i	$0.427910\pi$
$524$	4.21254e6	0.670218
$525$	−253574.	−0.0401519
$526$	−1.65422e6	−0.260692
$527$	−5.12933e6	−0.804515
$528$	−136544.	−0.0213151
$529$	682194.	0.105991
$530$	49158.7	0.00760170
$531$	6.88050e6	1.05897
$532$	1.19759e6	0.183455
$533$	−184710.	−0.0281626
$534$	−1.95168e6	−0.296179
$535$	1.09221e6	0.164976
$536$	−250599.	−0.0376762
$537$	2.71629e6	0.406480
$538$	−7.69575e6	−1.14629
$539$	−1.00861e6	−0.149537
$540$	−822664.	−0.121405
$541$	−7.28856e6	−1.07065	−0.535326	−	0.844645i	$-0.679811\pi$
$541$	−7.28856e6	−1.07065	−0.535326	+	0.844645i	$0.679811\pi$
$542$	−5.46020e6	−0.798381
$543$	−690425.	−0.100489
$544$	1.42749e6	0.206811
$545$	−1.23438e6	−0.178016
$546$	−104256.	−0.0149665
$547$	−9.33502e6	−1.33397	−0.666986	−	0.745070i	$-0.732416\pi$
$547$	−9.33502e6	−1.33397	−0.666986	+	0.745070i	$0.732416\pi$
$548$	1.62054e6	0.230519
$549$	2.83683e6	0.401700
$550$	−302500.	−0.0426401
$551$	1.52930e6	0.214593
$552$	752700.	0.105142
$553$	538118.	0.0748281
$554$	−1.85082e6	−0.256206
$555$	1.69443e6	0.233503
$556$	−2.49622e6	−0.342449
$557$	−87187.2	−0.0119073	−0.00595367	−	0.999982i	$-0.501895\pi$
$557$	−87187.2	−0.0119073	−0.00595367	+	0.999982i	$0.501895\pi$
$558$	3.29049e6	0.447378
$559$	−1.31087e6	−0.177431
$560$	−589058.	−0.0793757
$561$	743539.	0.0997463
$562$	−5.26468e6	−0.703123
$563$	1.99082e6	0.264705	0.132352	−	0.991203i	$-0.457747\pi$
$563$	1.99082e6	0.264705	0.132352	+	0.991203i	$0.457747\pi$
$564$	−1.84374e6	−0.244063
$565$	−2.83470e6	−0.373583
$566$	4.76965e6	0.625814
$567$	4.16587e6	0.544187
$568$	1.51404e6	0.196909
$569$	955969.	0.123784	0.0618918	−	0.998083i	$-0.480287\pi$
$569$	955969.	0.123784	0.0618918	+	0.998083i	$0.480287\pi$
$570$	−358473.	−0.0462136
$571$	1.17829e7	1.51239	0.756193	−	0.654349i	$-0.227057\pi$
$571$	1.17829e7	1.51239	0.756193	+	0.654349i	$0.227057\pi$
$572$	−124372.	−0.0158939
$573$	−421352.	−0.0536116
$574$	−1.05855e6	−0.134101
$575$	1.66754e6	0.210332
$576$	−915739.	−0.115005
$577$	−7.62998e6	−0.954078	−0.477039	−	0.878882i	$-0.658290\pi$
$577$	−7.62998e6	−0.954078	−0.477039	+	0.878882i	$0.658290\pi$
$578$	−2.09384e6	−0.260690
$579$	−3.30013e6	−0.409104
$580$	−752218.	−0.0928483
$581$	−2.74705e6	−0.337619
$582$	−1.16137e6	−0.142122
$583$	59482.0	0.00724793
$584$	−3.18784e6	−0.386780
$585$	−359061.	−0.0433789
$586$	2.57647e6	0.309943
$587$	5.31020e6	0.636086	0.318043	−	0.948076i	$-0.396974\pi$
$587$	5.31020e6	0.636086	0.318043	+	0.948076i	$0.396974\pi$
$588$	587899.	0.0701229
$589$	2.99226e6	0.355395
$590$	−3.07757e6	−0.363981
$591$	2.01223e6	0.236979
$592$	3.93620e6	0.461608
$593$	9.44509e6	1.10298	0.551492	−	0.834180i	$-0.314059\pi$
$593$	9.44509e6	1.10298	0.551492	+	0.834180i	$0.314059\pi$
$594$	−995424.	−0.115756
$595$	3.20767e6	0.371447
$596$	−2.12472e6	−0.245012
$597$	−2.60649e6	−0.299310
$598$	685601.	0.0784004
$599$	8.27369e6	0.942177	0.471088	−	0.882086i	$-0.343861\pi$
$599$	8.27369e6	0.942177	0.471088	+	0.882086i	$0.343861\pi$
$600$	176322.	0.0199953
$601$	−1.28982e7	−1.45661	−0.728304	−	0.685254i	$-0.759691\pi$
$601$	−1.28982e7	−1.45661	−0.728304	+	0.685254i	$0.759691\pi$
$602$	−7.51245e6	−0.844871
$603$	−875408.	−0.0980432
$604$	3.59751e6	0.401245
$605$	−366025.	−0.0406558
$606$	3.01187e6	0.333161
$607$	−884063.	−0.0973893	−0.0486947	−	0.998814i	$-0.515506\pi$
$607$	−884063.	−0.0973893	−0.0486947	+	0.998814i	$0.515506\pi$
$608$	−832742.	−0.0913590
$609$	−762971.	−0.0833614
$610$	−1.26888e6	−0.138069
$611$	−1.67938e6	−0.181989
$612$	4.98659e6	0.538177
$613$	7.44165e6	0.799868	0.399934	−	0.916544i	$-0.369033\pi$
$613$	7.44165e6	0.799868	0.399934	+	0.916544i	$0.369033\pi$
$614$	−4.76174e6	−0.509735
$615$	316855.	0.0337810
$616$	−712760.	−0.0756818
$617$	1.54607e6	0.163499	0.0817496	−	0.996653i	$-0.473949\pi$
$617$	1.54607e6	0.163499	0.0817496	+	0.996653i	$0.473949\pi$
$618$	−59075.6	−0.00622210
$619$	−337532.	−0.0354069	−0.0177035	−	0.999843i	$-0.505635\pi$
$619$	−337532.	−0.0354069	−0.0177035	+	0.999843i	$0.505635\pi$
$620$	−1.47180e6	−0.153769
$621$	5.48729e6	0.570991
$622$	−5.03753e6	−0.522086
$623$	−1.01878e7	−1.05162
$624$	72494.1	0.00745317
$625$	390625.	0.0400000
$626$	−8.94633e6	−0.912450
$627$	−433753.	−0.0440629
$628$	3.21535e6	0.325333
$629$	−2.14343e7	−2.16014
$630$	−2.05774e6	−0.206556
$631$	−2.60561e6	−0.260517	−0.130259	−	0.991480i	$-0.541581\pi$
$631$	−2.60561e6	−0.260517	−0.130259	+	0.991480i	$0.541581\pi$
$632$	−374179.	−0.0372638
$633$	2.50507e6	0.248491
$634$	−9.44499e6	−0.933208
$635$	−7.87843e6	−0.775364
$636$	−34671.0	−0.00339879
$637$	535491.	0.0522882
$638$	−910184.	−0.0885273
$639$	5.28893e6	0.512408
$640$	409600.	0.0395285
$641$	1.37962e7	1.32622	0.663108	−	0.748523i	$-0.269237\pi$
$641$	1.37962e7	1.32622	0.663108	+	0.748523i	$0.269237\pi$
$642$	−770323.	−0.0737624
$643$	4.97213e6	0.474258	0.237129	−	0.971478i	$-0.423794\pi$
$643$	4.97213e6	0.474258	0.237129	+	0.971478i	$0.423794\pi$
$644$	3.92910e6	0.373318
$645$	2.24870e6	0.212829
$646$	4.53463e6	0.427524
$647$	1.75328e7	1.64661	0.823304	−	0.567601i	$-0.192128\pi$
$647$	1.75328e7	1.64661	0.823304	+	0.567601i	$0.192128\pi$
$648$	−2.89673e6	−0.271001
$649$	−3.72387e6	−0.347042
$650$	160604.	0.0149098
$651$	−1.49284e6	−0.138058
$652$	−5.04353e6	−0.464639
$653$	−1.67551e6	−0.153768	−0.0768838	−	0.997040i	$-0.524497\pi$
$653$	−1.67551e6	−0.153768	−0.0768838	+	0.997040i	$0.524497\pi$
$654$	870596.	0.0795926
$655$	−6.58209e6	−0.599461
$656$	736062.	0.0667813
$657$	−1.11360e7	−1.00650
$658$	−9.62432e6	−0.866573
$659$	−4.27468e6	−0.383434	−0.191717	−	0.981450i	$-0.561406\pi$
$659$	−4.27468e6	−0.383434	−0.191717	+	0.981450i	$0.561406\pi$
$660$	213350.	0.0190648
$661$	−1.01563e7	−0.904131	−0.452066	−	0.891985i	$-0.649313\pi$
$661$	−1.01563e7	−0.904131	−0.452066	+	0.891985i	$0.649313\pi$
$662$	1.22401e7	1.08552
$663$	−394761.	−0.0348779
$664$	1.91016e6	0.168131
$665$	−1.87123e6	−0.164087
$666$	1.37502e7	1.20122
$667$	5.01740e6	0.436681
$668$	−7.39113e6	−0.640870
$669$	−1.56625e6	−0.135299
$670$	391560.	0.0336986
$671$	−1.53535e6	−0.131644
$672$	415455.	0.0354896
$673$	1.09681e7	0.933454	0.466727	−	0.884402i	$-0.345433\pi$
$673$	1.09681e7	0.933454	0.466727	+	0.884402i	$0.345433\pi$
$674$	−1.63329e7	−1.38489
$675$	1.28541e6	0.108588
$676$	−5.87466e6	−0.494442
$677$	−8.84010e6	−0.741286	−0.370643	−	0.928775i	$-0.620863\pi$
$677$	−8.84010e6	−0.741286	−0.370643	+	0.928775i	$0.620863\pi$
$678$	1.99928e6	0.167032
$679$	−6.06235e6	−0.504622
$680$	−2.23045e6	−0.184978
$681$	−2.76619e6	−0.228567
$682$	−1.78088e6	−0.146613
$683$	5.98047e6	0.490551	0.245275	−	0.969453i	$-0.421122\pi$
$683$	5.98047e6	0.490551	0.245275	+	0.969453i	$0.421122\pi$
$684$	−2.90899e6	−0.237740
$685$	−2.53209e6	−0.206183
$686$	9.25652e6	0.750996
$687$	4.35507e6	0.352049
$688$	5.22377e6	0.420739
$689$	−31580.3	−0.00253436
$690$	−1.17609e6	−0.0940414
$691$	3.64212e6	0.290175	0.145087	−	0.989419i	$-0.453654\pi$
$691$	3.64212e6	0.290175	0.145087	+	0.989419i	$0.453654\pi$
$692$	−4.55374e6	−0.361496
$693$	−2.48986e6	−0.196944
$694$	−9.00473e6	−0.709695
$695$	3.90034e6	0.306295
$696$	530531.	0.0415133
$697$	−4.00817e6	−0.312510
$698$	−4.37365e6	−0.339786
$699$	648124.	0.0501724
$700$	920403.	0.0709958
$701$	−1.44054e6	−0.110721	−0.0553607	−	0.998466i	$-0.517631\pi$
$701$	−1.44054e6	−0.110721	−0.0553607	+	0.998466i	$0.517631\pi$
$702$	528492.	0.0404758
$703$	1.25040e7	0.954244
$704$	495616.	0.0376889
$705$	2.88084e6	0.218296
$706$	6.95515e6	0.525164
$707$	1.57220e7	1.18293
$708$	2.17058e6	0.162739
$709$	−2.44669e7	−1.82795	−0.913975	−	0.405771i	$-0.867003\pi$
$709$	−2.44669e7	−1.82795	−0.913975	+	0.405771i	$0.867003\pi$
$710$	−2.36568e6	−0.176121
$711$	−1.30711e6	−0.0969700
$712$	7.08404e6	0.523698
$713$	9.81712e6	0.723203
$714$	−2.26233e6	−0.166078
$715$	194331.	0.0142160
$716$	−9.85936e6	−0.718731
$717$	6.00386e6	0.436147
$718$	−7.74545e6	−0.560707
$719$	−2.27569e6	−0.164169	−0.0820846	−	0.996625i	$-0.526158\pi$
$719$	−2.27569e6	−0.164169	−0.0820846	+	0.996625i	$0.526158\pi$
$720$	1.43084e6	0.102863
$721$	−308375.	−0.0220923
$722$	7.25906e6	0.518248
$723$	−6.80030e6	−0.483818
$724$	2.50605e6	0.177682
$725$	1.17534e6	0.0830460
$726$	258153.	0.0181776
$727$	1.87924e7	1.31870	0.659351	−	0.751835i	$-0.270831\pi$
$727$	1.87924e7	1.31870	0.659351	+	0.751835i	$0.270831\pi$
$728$	378420.	0.0264634
$729$	−7.91605e6	−0.551683
$730$	4.98100e6	0.345947
$731$	−2.84457e7	−1.96889
$732$	894928.	0.0617320
$733$	−355042.	−0.0244073	−0.0122036	−	0.999926i	$-0.503885\pi$
$733$	−355042.	−0.0244073	−0.0122036	+	0.999926i	$0.503885\pi$
$734$	5.47985e6	0.375429
$735$	−918593.	−0.0627198
$736$	−2.73209e6	−0.185909
$737$	473788.	0.0321304
$738$	2.57126e6	0.173782
$739$	−1.97063e7	−1.32738	−0.663689	−	0.748008i	$-0.731010\pi$
$739$	−1.97063e7	−1.32738	−0.663689	+	0.748008i	$0.731010\pi$
$740$	−6.15032e6	−0.412875
$741$	230289.	0.0154073
$742$	−180983.	−0.0120678
$743$	1.74672e7	1.16078	0.580391	−	0.814338i	$-0.302900\pi$
$743$	1.74672e7	1.16078	0.580391	+	0.814338i	$0.302900\pi$
$744$	1.03804e6	0.0687517
$745$	3.31988e6	0.219145
$746$	−4.09081e6	−0.269130
$747$	6.67269e6	0.437521
$748$	−2.69884e6	−0.176369
$749$	−4.02109e6	−0.261902
$750$	−275503.	−0.0178844
$751$	−4.94160e6	−0.319718	−0.159859	−	0.987140i	$-0.551104\pi$
$751$	−4.94160e6	−0.319718	−0.159859	+	0.987140i	$0.551104\pi$
$752$	6.69225e6	0.431546
$753$	2.42978e6	0.156163
$754$	483237.	0.0309550
$755$	−5.62112e6	−0.358885
$756$	3.02873e6	0.192733
$757$	−2.46846e7	−1.56562	−0.782810	−	0.622261i	$-0.786214\pi$
$757$	−2.46846e7	−1.56562	−0.782810	+	0.622261i	$0.786214\pi$
$758$	−9.22417e6	−0.583115
$759$	−1.42307e6	−0.0896650
$760$	1.30116e6	0.0817140
$761$	2.49595e7	1.56234	0.781169	−	0.624320i	$-0.214624\pi$
$761$	2.49595e7	1.56234	0.781169	+	0.624320i	$0.214624\pi$
$762$	5.55657e6	0.346672
$763$	4.54452e6	0.282603
$764$	1.52939e6	0.0947949
$765$	−7.79155e6	−0.481360
$766$	1.77864e7	1.09526
$767$	1.97708e6	0.121349
$768$	−288886.	−0.0176735
$769$	6.12897e6	0.373742	0.186871	−	0.982384i	$-0.440165\pi$
$769$	6.12897e6	0.373742	0.186871	+	0.982384i	$0.440165\pi$
$770$	1.11369e6	0.0676918
$771$	6.64723e6	0.402722
$772$	1.19785e7	0.723370
$773$	1.14936e7	0.691842	0.345921	−	0.938264i	$-0.387566\pi$
$773$	1.14936e7	0.691842	0.345921	+	0.938264i	$0.387566\pi$
$774$	1.82480e7	1.09487
$775$	2.29969e6	0.137535
$776$	4.21544e6	0.251298
$777$	−6.23824e6	−0.370689
$778$	1.21757e7	0.721179
$779$	2.33822e6	0.138051
$780$	−113272.	−0.00666632
$781$	−2.86247e6	−0.167924
$782$	1.48774e7	0.869982
$783$	3.86764e6	0.225446
$784$	−2.13391e6	−0.123990
$785$	−5.02398e6	−0.290987
$786$	4.64227e6	0.268024
$787$	−1.34777e7	−0.775673	−0.387837	−	0.921728i	$-0.626778\pi$
$787$	−1.34777e7	−0.775673	−0.387837	+	0.921728i	$0.626778\pi$
$788$	−7.30385e6	−0.419022
$789$	−1.82297e6	−0.104253
$790$	584655.	0.0333297
$791$	1.04363e7	0.593068
$792$	1.73132e6	0.0980763
$793$	815150.	0.0460314
$794$	1.18867e7	0.669128
$795$	54173.5	0.00303997
$796$	9.46085e6	0.529234
$797$	−2.33863e7	−1.30411	−0.652056	−	0.758171i	$-0.726093\pi$
$797$	−2.33863e7	−1.30411	−0.652056	+	0.758171i	$0.726093\pi$
$798$	1.31976e6	0.0733648
$799$	−3.64422e7	−2.01947
$800$	−640000.	−0.0353553
$801$	2.47464e7	1.36280
$802$	−1.73982e7	−0.955143
$803$	6.02701e6	0.329847
$804$	−276163.	−0.0150669
$805$	−6.13922e6	−0.333905
$806$	945507.	0.0512657
$807$	−8.48082e6	−0.458410
$808$	−1.09322e7	−0.589089
$809$	3.43344e7	1.84441	0.922207	−	0.386696i	$-0.126384\pi$
$809$	3.43344e7	1.84441	0.922207	+	0.386696i	$0.126384\pi$
$810$	4.52614e6	0.242391
$811$	−3.01851e7	−1.61154	−0.805769	−	0.592231i	$-0.798247\pi$
$811$	−3.01851e7	−1.61154	−0.805769	+	0.592231i	$0.798247\pi$
$812$	2.76937e6	0.147398
$813$	−6.01721e6	−0.319278
$814$	−7.44188e6	−0.393660
$815$	7.88052e6	0.415586
$816$	1.57311e6	0.0827053
$817$	1.65941e7	0.869759
$818$	−356767.	−0.0186424
$819$	1.32192e6	0.0688646
$820$	−1.15010e6	−0.0597310
$821$	−1.75961e7	−0.911087	−0.455543	−	0.890214i	$-0.650555\pi$
$821$	−1.75961e7	−0.911087	−0.455543	+	0.890214i	$0.650555\pi$
$822$	1.78585e6	0.0921862
$823$	2.02786e7	1.04361	0.521804	−	0.853065i	$-0.325259\pi$
$823$	2.02786e7	1.04361	0.521804	+	0.853065i	$0.325259\pi$
$824$	214428.	0.0110018
$825$	−333359.	−0.0170521
$826$	1.13304e7	0.577825
$827$	3.28389e7	1.66965	0.834824	−	0.550516i	$-0.185569\pi$
$827$	3.28389e7	1.66965	0.834824	+	0.550516i	$0.185569\pi$
$828$	−9.54393e6	−0.483784
$829$	−2.40343e7	−1.21463	−0.607317	−	0.794460i	$-0.707754\pi$
$829$	−2.40343e7	−1.21463	−0.607317	+	0.794460i	$0.707754\pi$
$830$	−2.98462e6	−0.150381
$831$	−2.03962e6	−0.102458
$832$	−263133.	−0.0131785
$833$	1.16201e7	0.580224
$834$	−2.75086e6	−0.136947
$835$	1.15486e7	0.573211
$836$	1.57440e6	0.0779112
$837$	7.56748e6	0.373369
$838$	1.67427e7	0.823597
$839$	−1.85037e7	−0.907515	−0.453757	−	0.891125i	$-0.649917\pi$
$839$	−1.85037e7	−0.907515	−0.453757	+	0.891125i	$0.649917\pi$
$840$	−649149.	−0.0317429
$841$	−1.69747e7	−0.827584
$842$	−7.85553e6	−0.381852
$843$	−5.80175e6	−0.281184
$844$	−9.09271e6	−0.439377
$845$	9.17915e6	0.442243
$846$	2.33778e7	1.12300
$847$	1.34756e6	0.0645416
$848$	125846.	0.00600967
$849$	5.25621e6	0.250267
$850$	3.48507e6	0.165449
$851$	4.10235e7	1.94182
$852$	1.66849e6	0.0787451
$853$	−5.67139e6	−0.266881	−0.133440	−	0.991057i	$-0.542602\pi$
$853$	−5.67139e6	−0.266881	−0.133440	+	0.991057i	$0.542602\pi$
$854$	4.67153e6	0.219187
$855$	4.54529e6	0.212641
$856$	2.79606e6	0.130425
$857$	−69849.7	−0.00324872	−0.00162436	−	0.999999i	$-0.500517\pi$
$857$	−69849.7	−0.00324872	−0.00162436	+	0.999999i	$0.500517\pi$
$858$	−137059.	−0.00635609
$859$	1.24652e7	0.576391	0.288195	−	0.957572i	$-0.406945\pi$
$859$	1.24652e7	0.576391	0.288195	+	0.957572i	$0.406945\pi$
$860$	−8.16214e6	−0.376321
$861$	−1.16654e6	−0.0536279
$862$	5.30246e6	0.243058
$863$	−3.28985e7	−1.50366	−0.751829	−	0.659358i	$-0.770828\pi$
$863$	−3.28985e7	−1.50366	−0.751829	+	0.659358i	$0.770828\pi$
$864$	−2.10602e6	−0.0959794
$865$	7.11522e6	0.323332
$866$	2.06406e7	0.935252
$867$	−2.30744e6	−0.104252
$868$	5.41859e6	0.244111
$869$	707433.	0.0317787
$870$	−828954.	−0.0371306
$871$	−251544.	−0.0112349
$872$	−3.16002e6	−0.140734
$873$	1.47257e7	0.653942
$874$	−8.67892e6	−0.384315
$875$	−1.43813e6	−0.0635006
$876$	−3.51304e6	−0.154676
$877$	−3.07510e7	−1.35008	−0.675042	−	0.737779i	$-0.735875\pi$
$877$	−3.07510e7	−1.35008	−0.675042	+	0.737779i	$0.735875\pi$
$878$	−1.57259e7	−0.688462
$879$	2.83930e6	0.123948
$880$	−774400.	−0.0337100
$881$	−1.53544e7	−0.666489	−0.333245	−	0.942840i	$-0.608143\pi$
$881$	−1.53544e7	−0.666489	−0.333245	+	0.942840i	$0.608143\pi$
$882$	−7.45432e6	−0.322654
$883$	2.65947e7	1.14787	0.573937	−	0.818900i	$-0.305415\pi$
$883$	2.65947e7	1.14787	0.573937	+	0.818900i	$0.305415\pi$
$884$	1.43287e6	0.0616705
$885$	−3.39153e6	−0.145558
$886$	−1.22670e7	−0.524993
$887$	−4.22486e6	−0.180303	−0.0901517	−	0.995928i	$-0.528735\pi$
$887$	−4.22486e6	−0.180303	−0.0901517	+	0.995928i	$0.528735\pi$
$888$	4.33774e6	0.184600
$889$	2.90053e7	1.23090
$890$	−1.10688e7	−0.468410
$891$	5.47663e6	0.231110
$892$	5.68505e6	0.239234
$893$	2.12590e7	0.892101
$894$	−2.34147e6	−0.0979818
$895$	1.54052e7	0.642852
$896$	−1.50799e6	−0.0627520
$897$	755541.	0.0313528
$898$	−1.87239e7	−0.774827
$899$	6.91947e6	0.285544
$900$	−2.23569e6	−0.0920037
$901$	−685286.	−0.0281229
$902$	−1.39162e6	−0.0569512
$903$	−8.27882e6	−0.337870
$904$	−7.25684e6	−0.295343
$905$	−3.91571e6	−0.158924
$906$	3.96451e6	0.160461
$907$	−1.13522e7	−0.458207	−0.229104	−	0.973402i	$-0.573579\pi$
$907$	−1.13522e7	−0.458207	−0.229104	+	0.973402i	$0.573579\pi$
$908$	1.00405e7	0.404148
$909$	−3.81892e7	−1.53296
$910$	−591281.	−0.0236696
$911$	−3.28560e7	−1.31165	−0.655826	−	0.754912i	$-0.727680\pi$
$911$	−3.28560e7	−1.31165	−0.655826	+	0.754912i	$0.727680\pi$
$912$	−917692.	−0.0365351
$913$	−3.61139e6	−0.143383
$914$	2.74560e7	1.08711
$915$	−1.39833e6	−0.0552148
$916$	−1.58077e7	−0.622486
$917$	2.42327e7	0.951653
$918$	1.14682e7	0.449146
$919$	−3.87685e7	−1.51423	−0.757113	−	0.653284i	$-0.773391\pi$
$919$	−3.87685e7	−1.51423	−0.757113	+	0.653284i	$0.773391\pi$
$920$	4.26889e6	0.166282
$921$	−5.24750e6	−0.203847
$922$	1.54151e7	0.597200
$923$	1.51975e6	0.0587175
$924$	−785470.	−0.0302656
$925$	9.60987e6	0.369286
$926$	1.26330e7	0.484148
$927$	749054.	0.0286295
$928$	−1.92568e6	−0.0734030
$929$	3.48798e7	1.32597	0.662986	−	0.748632i	$-0.269289\pi$
$929$	3.48798e7	1.32597	0.662986	+	0.748632i	$0.269289\pi$
$930$	−1.62194e6	−0.0614934
$931$	−6.77870e6	−0.256314
$932$	−2.35251e6	−0.0887139
$933$	−5.55143e6	−0.208786
$934$	−784436.	−0.0294232
$935$	4.21694e6	0.157750
$936$	−919195.	−0.0342940
$937$	−4.14192e7	−1.54118	−0.770588	−	0.637334i	$-0.780037\pi$
$937$	−4.14192e7	−1.54118	−0.770588	+	0.637334i	$0.780037\pi$
$938$	−1.44157e6	−0.0534970
$939$	−9.85897e6	−0.364895
$940$	−1.04566e7	−0.385987
$941$	−8.65196e6	−0.318523	−0.159261	−	0.987236i	$-0.550911\pi$
$941$	−8.65196e6	−0.318523	−0.159261	+	0.987236i	$0.550911\pi$
$942$	3.54335e6	0.130103
$943$	7.67131e6	0.280925
$944$	−7.87859e6	−0.287752
$945$	−4.73239e6	−0.172386
$946$	−9.87619e6	−0.358808
$947$	4.83595e7	1.75229	0.876147	−	0.482044i	$-0.160106\pi$
$947$	4.83595e7	1.75229	0.876147	+	0.482044i	$0.160106\pi$
$948$	−412350.	−0.0149020
$949$	−3.19987e6	−0.115337
$950$	−2.03306e6	−0.0730872
$951$	−1.04085e7	−0.373196
$952$	8.21164e6	0.293655
$953$	−3.85111e7	−1.37358	−0.686789	−	0.726857i	$-0.740980\pi$
$953$	−3.85111e7	−1.37358	−0.686789	+	0.726857i	$0.740980\pi$
$954$	439614.	0.0156387
$955$	−2.38967e6	−0.0847871
$956$	−2.17923e7	−0.771186
$957$	−1.00303e6	−0.0354027
$958$	−2.05411e7	−0.723120
$959$	9.32216e6	0.327318
$960$	451384.	0.0158077
$961$	−1.50904e7	−0.527100
$962$	3.95106e6	0.137650
$963$	9.76737e6	0.339400
$964$	2.46832e7	0.855478
$965$	−1.87165e7	−0.647002
$966$	4.32992e6	0.149292
$967$	−4.49114e7	−1.54451	−0.772254	−	0.635314i	$-0.780871\pi$
$967$	−4.49114e7	−1.54451	−0.772254	+	0.635314i	$0.780871\pi$
$968$	−937024.	−0.0321412
$969$	4.99722e6	0.170970
$970$	−6.58662e6	−0.224768
$971$	−5.38907e7	−1.83428	−0.917140	−	0.398565i	$-0.869508\pi$
$971$	−5.38907e7	−1.83428	−0.917140	+	0.398565i	$0.869508\pi$
$972$	−1.11885e7	−0.379846
$973$	−1.43595e7	−0.486248
$974$	−9.75472e6	−0.329471
$975$	176988.	0.00596254
$976$	−3.24834e6	−0.109153
$977$	5.38133e6	0.180365	0.0901827	−	0.995925i	$-0.471255\pi$
$977$	5.38133e6	0.180365	0.0901827	+	0.995925i	$0.471255\pi$
$978$	−5.55804e6	−0.185812
$979$	−1.33933e7	−0.446611
$980$	3.33424e6	0.110900
$981$	−1.10388e7	−0.366226
$982$	−1.63075e7	−0.539645
$983$	−4.23163e7	−1.39677	−0.698384	−	0.715724i	$-0.746097\pi$
$983$	−4.23163e7	−1.39677	−0.698384	+	0.715724i	$0.746097\pi$
$984$	811149.	0.0267063
$985$	1.14123e7	0.374784
$986$	1.04861e7	0.343497
$987$	−1.06061e7	−0.346548
$988$	−835884.	−0.0272429
$989$	5.44427e7	1.76990
$990$	−2.70519e6	−0.0877221
$991$	−1.67404e7	−0.541480	−0.270740	−	0.962652i	$-0.587268\pi$
$991$	−1.67404e7	−0.541480	−0.270740	+	0.962652i	$0.587268\pi$
$992$	−3.76781e6	−0.121565
$993$	1.34887e7	0.434108
$994$	8.70951e6	0.279594
$995$	−1.47826e7	−0.473361
$996$	2.10502e6	0.0672369
$997$	−2.98987e7	−0.952608	−0.476304	−	0.879281i	$-0.658024\pi$
$997$	−2.98987e7	−0.952608	−0.476304	+	0.879281i	$0.658024\pi$
$998$	−3.51516e6	−0.111717
$999$	3.16228e7	1.00250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.6.a.e.1.1	✓	2
3.2	odd	2		990.6.a.s.1.2		2
4.3	odd	2		880.6.a.f.1.2		2
5.2	odd	4		550.6.b.h.199.2		4
5.3	odd	4		550.6.b.h.199.3		4
5.4	even	2		550.6.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.6.a.e.1.1	✓	2	1.1	even	1	trivial
550.6.a.j.1.2		2	5.4	even	2
550.6.b.h.199.2		4	5.2	odd	4
550.6.b.h.199.3		4	5.3	odd	4
880.6.a.f.1.2		2	4.3	odd	2
990.6.a.s.1.2		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	110.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -4.40805 q^{3} +16.0000 q^{4} -25.0000 q^{5} +17.6322 q^{6} +92.0403 q^{7} -64.0000 q^{8} -223.569 q^{9} +100.000 q^{10} +121.000 q^{11} -70.5288 q^{12} -64.2415 q^{13} -368.161 q^{14} +110.201 q^{15} +256.000 q^{16} -1394.03 q^{17} +894.276 q^{18} +813.224 q^{19} -400.000 q^{20} -405.718 q^{21} -484.000 q^{22} +2668.06 q^{23} +282.115 q^{24} +625.000 q^{25} +256.966 q^{26} +2056.66 q^{27} +1472.64 q^{28} +1880.55 q^{29} -440.805 q^{30} +3679.50 q^{31} -1024.00 q^{32} -533.374 q^{33} +5576.12 q^{34} -2301.01 q^{35} -3577.11 q^{36} +15375.8 q^{37} -3252.90 q^{38} +283.180 q^{39} +1600.00 q^{40} +2875.24 q^{41} +1622.87 q^{42} +20405.3 q^{43} +1936.00 q^{44} +5589.23 q^{45} -10672.2 q^{46} +26141.6 q^{47} -1128.46 q^{48} -8335.59 q^{49} -2500.00 q^{50} +6144.95 q^{51} -1027.86 q^{52} +491.587 q^{53} -8226.64 q^{54} -3025.00 q^{55} -5890.58 q^{56} -3584.73 q^{57} -7522.18 q^{58} -30775.7 q^{59} +1763.22 q^{60} -12688.8 q^{61} -14718.0 q^{62} -20577.4 q^{63} +4096.00 q^{64} +1606.04 q^{65} +2133.50 q^{66} +3915.60 q^{67} -22304.5 q^{68} -11760.9 q^{69} +9204.03 q^{70} -23656.8 q^{71} +14308.4 q^{72} +49810.0 q^{73} -61503.2 q^{74} -2755.03 q^{75} +13011.6 q^{76} +11136.9 q^{77} -1132.72 q^{78} +5846.55 q^{79} -6400.00 q^{80} +45261.4 q^{81} -11501.0 q^{82} -29846.2 q^{83} -6491.49 q^{84} +34850.7 q^{85} -81621.4 q^{86} -8289.54 q^{87} -7744.00 q^{88} -110688. q^{89} -22356.9 q^{90} -5912.81 q^{91} +42688.9 q^{92} -16219.4 q^{93} -104566. q^{94} -20330.6 q^{95} +4513.84 q^{96} -65866.2 q^{97} +33342.4 q^{98} -27051.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} + 21 q^{3} + 32 q^{4} - 50 q^{5} - 84 q^{6} + 35 q^{7} - 128 q^{8} + 179 q^{9} + 200 q^{10} + 242 q^{11} + 336 q^{12} + 766 q^{13} - 140 q^{14} - 525 q^{15} + 512 q^{16} + 283 q^{17} - 716 q^{18}+ \cdots + 21659 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 21 * q^3 + 32 * q^4 - 50 * q^5 - 84 * q^6 + 35 * q^7 - 128 * q^8 + 179 * q^9 + 200 * q^10 + 242 * q^11 + 336 * q^12 + 766 * q^13 - 140 * q^14 - 525 * q^15 + 512 * q^16 + 283 * q^17 - 716 * q^18 + 1537 * q^19 - 800 * q^20 - 1855 * q^21 - 968 * q^22 - 806 * q^23 - 1344 * q^24 + 1250 * q^25 - 3064 * q^26 + 6111 * q^27 + 560 * q^28 + 7667 * q^29 + 2100 * q^30 + 4765 * q^31 - 2048 * q^32 + 2541 * q^33 - 1132 * q^34 - 875 * q^35 + 2864 * q^36 + 28575 * q^37 - 6148 * q^38 + 21378 * q^39 + 3200 * q^40 + 10044 * q^41 + 7420 * q^42 + 19522 * q^43 + 3872 * q^44 - 4475 * q^45 + 3224 * q^46 + 22646 * q^47 + 5376 * q^48 - 21889 * q^49 - 5000 * q^50 + 48755 * q^51 + 12256 * q^52 - 33037 * q^53 - 24444 * q^54 - 6050 * q^55 - 2240 * q^56 + 14805 * q^57 - 30668 * q^58 - 15098 * q^59 - 8400 * q^60 + 4349 * q^61 - 19060 * q^62 - 43540 * q^63 + 8192 * q^64 - 19150 * q^65 - 10164 * q^66 + 32996 * q^67 + 4528 * q^68 - 100030 * q^69 + 3500 * q^70 - 87297 * q^71 - 11456 * q^72 + 38974 * q^73 - 114300 * q^74 + 13125 * q^75 + 24592 * q^76 + 4235 * q^77 - 85512 * q^78 - 48118 * q^79 - 12800 * q^80 + 50450 * q^81 - 40176 * q^82 + 59572 * q^83 - 29680 * q^84 - 7075 * q^85 - 78088 * q^86 + 138733 * q^87 - 15488 * q^88 - 158673 * q^89 + 17900 * q^90 - 53270 * q^91 - 12896 * q^92 + 11361 * q^93 - 90584 * q^94 - 38425 * q^95 - 21504 * q^96 + 109122 * q^97 + 87556 * q^98 + 21659 * q^99

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