LMFDB - Embedded newform 105.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(1,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{65}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 16 $ x^2 - x - 16
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.53113$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.53113 q^{2} +3.00000 q^{3} +4.46887 q^{4} +5.00000 q^{5} -10.5934 q^{6} -7.00000 q^{7} +12.4689 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.53113 q^{2} +3.00000 q^{3} +4.46887 q^{4} +5.00000 q^{5} -10.5934 q^{6} -7.00000 q^{7} +12.4689 q^{8} +9.00000 q^{9} -17.6556 q^{10} -2.93774 q^{11} +13.4066 q^{12} -19.0623 q^{13} +24.7179 q^{14} +15.0000 q^{15} -79.7802 q^{16} +122.498 q^{17} -31.7802 q^{18} +107.436 q^{19} +22.3444 q^{20} -21.0000 q^{21} +10.3735 q^{22} +210.623 q^{23} +37.4066 q^{24} +25.0000 q^{25} +67.3113 q^{26} +27.0000 q^{27} -31.2821 q^{28} +95.4942 q^{29} -52.9669 q^{30} -94.3074 q^{31} +181.963 q^{32} -8.81323 q^{33} -432.556 q^{34} -35.0000 q^{35} +40.2198 q^{36} +97.1206 q^{37} -379.370 q^{38} -57.1868 q^{39} +62.3444 q^{40} -491.113 q^{41} +74.1537 q^{42} -43.0039 q^{43} -13.1284 q^{44} +45.0000 q^{45} -743.735 q^{46} +473.494 q^{47} -239.340 q^{48} +49.0000 q^{49} -88.2782 q^{50} +367.494 q^{51} -85.1868 q^{52} -183.677 q^{53} -95.3405 q^{54} -14.6887 q^{55} -87.2821 q^{56} +322.307 q^{57} -337.202 q^{58} -760.615 q^{59} +67.0331 q^{60} -198.747 q^{61} +333.012 q^{62} -63.0000 q^{63} -4.29373 q^{64} -95.3113 q^{65} +31.1206 q^{66} -309.992 q^{67} +547.428 q^{68} +631.868 q^{69} +123.590 q^{70} +665.693 q^{71} +112.220 q^{72} +621.288 q^{73} -342.945 q^{74} +75.0000 q^{75} +480.117 q^{76} +20.5642 q^{77} +201.934 q^{78} -24.7626 q^{79} -398.901 q^{80} +81.0000 q^{81} +1734.18 q^{82} -406.724 q^{83} -93.8463 q^{84} +612.490 q^{85} +151.852 q^{86} +286.483 q^{87} -36.6303 q^{88} +261.751 q^{89} -158.901 q^{90} +133.436 q^{91} +941.245 q^{92} -282.922 q^{93} -1671.97 q^{94} +537.179 q^{95} +545.889 q^{96} -1004.77 q^{97} -173.025 q^{98} -26.4397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 6 q^{3} + 17 q^{4} + 10 q^{5} + 3 q^{6} - 14 q^{7} + 33 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + q^2 + 6 * q^3 + 17 * q^4 + 10 * q^5 + 3 * q^6 - 14 * q^7 + 33 * q^8 + 18 * q^9	\( 2 q + q^{2} + 6 q^{3} + 17 q^{4} + 10 q^{5} + 3 q^{6} - 14 q^{7} + 33 q^{8} + 18 q^{9} + 5 q^{10} - 22 q^{11} + 51 q^{12} - 22 q^{13} - 7 q^{14} + 30 q^{15} - 87 q^{16} + 116 q^{17} + 9 q^{18} + 102 q^{19} + 85 q^{20} - 42 q^{21} - 76 q^{22} + 260 q^{23} + 99 q^{24} + 50 q^{25} + 54 q^{26} + 54 q^{27} - 119 q^{28} - 196 q^{29} + 15 q^{30} + 150 q^{31} - 15 q^{32} - 66 q^{33} - 462 q^{34} - 70 q^{35} + 153 q^{36} - 96 q^{37} - 404 q^{38} - 66 q^{39} + 165 q^{40} - 176 q^{41} - 21 q^{42} - 344 q^{43} - 252 q^{44} + 90 q^{45} - 520 q^{46} + 560 q^{47} - 261 q^{48} + 98 q^{49} + 25 q^{50} + 348 q^{51} - 122 q^{52} + 326 q^{53} + 27 q^{54} - 110 q^{55} - 231 q^{56} + 306 q^{57} - 1658 q^{58} - 844 q^{59} + 255 q^{60} - 204 q^{61} + 1440 q^{62} - 126 q^{63} - 839 q^{64} - 110 q^{65} - 228 q^{66} - 104 q^{67} + 466 q^{68} + 780 q^{69} - 35 q^{70} + 1670 q^{71} + 297 q^{72} - 386 q^{73} - 1218 q^{74} + 150 q^{75} + 412 q^{76} + 154 q^{77} + 162 q^{78} - 888 q^{79} - 435 q^{80} + 162 q^{81} + 3162 q^{82} + 928 q^{83} - 357 q^{84} + 580 q^{85} - 1212 q^{86} - 588 q^{87} - 428 q^{88} + 588 q^{89} + 45 q^{90} + 154 q^{91} + 1560 q^{92} + 450 q^{93} - 1280 q^{94} + 510 q^{95} - 45 q^{96} + 522 q^{97} + 49 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 + 6 * q^3 + 17 * q^4 + 10 * q^5 + 3 * q^6 - 14 * q^7 + 33 * q^8 + 18 * q^9 + 5 * q^10 - 22 * q^11 + 51 * q^12 - 22 * q^13 - 7 * q^14 + 30 * q^15 - 87 * q^16 + 116 * q^17 + 9 * q^18 + 102 * q^19 + 85 * q^20 - 42 * q^21 - 76 * q^22 + 260 * q^23 + 99 * q^24 + 50 * q^25 + 54 * q^26 + 54 * q^27 - 119 * q^28 - 196 * q^29 + 15 * q^30 + 150 * q^31 - 15 * q^32 - 66 * q^33 - 462 * q^34 - 70 * q^35 + 153 * q^36 - 96 * q^37 - 404 * q^38 - 66 * q^39 + 165 * q^40 - 176 * q^41 - 21 * q^42 - 344 * q^43 - 252 * q^44 + 90 * q^45 - 520 * q^46 + 560 * q^47 - 261 * q^48 + 98 * q^49 + 25 * q^50 + 348 * q^51 - 122 * q^52 + 326 * q^53 + 27 * q^54 - 110 * q^55 - 231 * q^56 + 306 * q^57 - 1658 * q^58 - 844 * q^59 + 255 * q^60 - 204 * q^61 + 1440 * q^62 - 126 * q^63 - 839 * q^64 - 110 * q^65 - 228 * q^66 - 104 * q^67 + 466 * q^68 + 780 * q^69 - 35 * q^70 + 1670 * q^71 + 297 * q^72 - 386 * q^73 - 1218 * q^74 + 150 * q^75 + 412 * q^76 + 154 * q^77 + 162 * q^78 - 888 * q^79 - 435 * q^80 + 162 * q^81 + 3162 * q^82 + 928 * q^83 - 357 * q^84 + 580 * q^85 - 1212 * q^86 - 588 * q^87 - 428 * q^88 + 588 * q^89 + 45 * q^90 + 154 * q^91 + 1560 * q^92 + 450 * q^93 - 1280 * q^94 + 510 * q^95 - 45 * q^96 + 522 * q^97 + 49 * q^98 - 198 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.53113	−1.24844	−0.624221	−	0.781248i	$-0.714584\pi$
$2$	−3.53113	−1.24844	−0.624221	+	0.781248i	$0.714584\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.46887	0.558609
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−10.5934	−0.720789
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	12.4689	0.551051
$9$	9.00000	0.333333
$10$	−17.6556	−0.558320
$11$	−2.93774	−0.0805239	−0.0402619	−	0.999189i	$-0.512819\pi$
$11$	−2.93774	−0.0805239	−0.0402619	+	0.999189i	$0.512819\pi$
$12$	13.4066	0.322513
$13$	−19.0623	−0.406686	−0.203343	−	0.979108i	$-0.565181\pi$
$13$	−19.0623	−0.406686	−0.203343	+	0.979108i	$0.565181\pi$
$14$	24.7179	0.471867
$15$	15.0000	0.258199
$16$	−79.7802	−1.24656
$17$	122.498	1.74766	0.873828	−	0.486236i	$-0.161630\pi$
$17$	122.498	1.74766	0.873828	+	0.486236i	$0.161630\pi$
$18$	−31.7802	−0.416148
$19$	107.436	1.29723	0.648617	−	0.761115i	$-0.275348\pi$
$19$	107.436	1.29723	0.648617	+	0.761115i	$0.275348\pi$
$20$	22.3444	0.249817
$21$	−21.0000	−0.218218
$22$	10.3735	0.100529
$23$	210.623	1.90947	0.954736	−	0.297455i	$-0.0961379\pi$
$23$	210.623	1.90947	0.954736	+	0.297455i	$0.0961379\pi$
$24$	37.4066	0.318150
$25$	25.0000	0.200000
$26$	67.3113	0.507724
$27$	27.0000	0.192450
$28$	−31.2821	−0.211134
$29$	95.4942	0.611477	0.305738	−	0.952116i	$-0.401097\pi$
$29$	95.4942	0.611477	0.305738	+	0.952116i	$0.401097\pi$
$30$	−52.9669	−0.322346
$31$	−94.3074	−0.546391	−0.273195	−	0.961959i	$-0.588081\pi$
$31$	−94.3074	−0.546391	−0.273195	+	0.961959i	$0.588081\pi$
$32$	181.963	1.00521
$33$	−8.81323	−0.0464905
$34$	−432.556	−2.18185
$35$	−35.0000	−0.169031
$36$	40.2198	0.186203
$37$	97.1206	0.431528	0.215764	−	0.976446i	$-0.430776\pi$
$37$	97.1206	0.431528	0.215764	+	0.976446i	$0.430776\pi$
$38$	−379.370	−1.61952
$39$	−57.1868	−0.234800
$40$	62.3444	0.246438
$41$	−491.113	−1.87071	−0.935353	−	0.353716i	$-0.884918\pi$
$41$	−491.113	−1.87071	−0.935353	+	0.353716i	$0.884918\pi$
$42$	74.1537	0.272433
$43$	−43.0039	−0.152512	−0.0762562	−	0.997088i	$-0.524297\pi$
$43$	−43.0039	−0.152512	−0.0762562	+	0.997088i	$0.524297\pi$
$44$	−13.1284	−0.0449814
$45$	45.0000	0.149071
$46$	−743.735	−2.38387
$47$	473.494	1.46949	0.734747	−	0.678341i	$-0.237301\pi$
$47$	473.494	1.46949	0.734747	+	0.678341i	$0.237301\pi$
$48$	−239.340	−0.719705
$49$	49.0000	0.142857
$50$	−88.2782	−0.249689
$51$	367.494	1.00901
$52$	−85.1868	−0.227178
$53$	−183.677	−0.476038	−0.238019	−	0.971261i	$-0.576498\pi$
$53$	−183.677	−0.476038	−0.238019	+	0.971261i	$0.576498\pi$
$54$	−95.3405	−0.240263
$55$	−14.6887	−0.0360114
$56$	−87.2821	−0.208278
$57$	322.307	0.748959
$58$	−337.202	−0.763394
$59$	−760.615	−1.67837	−0.839183	−	0.543849i	$-0.816966\pi$
$59$	−760.615	−1.67837	−0.839183	+	0.543849i	$0.816966\pi$
$60$	67.0331	0.144232
$61$	−198.747	−0.417163	−0.208582	−	0.978005i	$-0.566885\pi$
$61$	−198.747	−0.417163	−0.208582	+	0.978005i	$0.566885\pi$
$62$	333.012	0.682137
$63$	−63.0000	−0.125988
$64$	−4.29373	−0.00838618
$65$	−95.3113	−0.181876
$66$	31.1206	0.0580407
$67$	−309.992	−0.565247	−0.282624	−	0.959231i	$-0.591205\pi$
$67$	−309.992	−0.565247	−0.282624	+	0.959231i	$0.591205\pi$
$68$	547.428	0.976256
$69$	631.868	1.10243
$70$	123.590	0.211025
$71$	665.693	1.11272	0.556360	−	0.830941i	$-0.312197\pi$
$71$	665.693	1.11272	0.556360	+	0.830941i	$0.312197\pi$
$72$	112.220	0.183684
$73$	621.288	0.996113	0.498057	−	0.867145i	$-0.334047\pi$
$73$	621.288	0.996113	0.498057	+	0.867145i	$0.334047\pi$
$74$	−342.945	−0.538738
$75$	75.0000	0.115470
$76$	480.117	0.724647
$77$	20.5642	0.0304352
$78$	201.934	0.293135
$79$	−24.7626	−0.0352659	−0.0176330	−	0.999845i	$-0.505613\pi$
$79$	−24.7626	−0.0352659	−0.0176330	+	0.999845i	$0.505613\pi$
$80$	−398.901	−0.557481
$81$	81.0000	0.111111
$82$	1734.18	2.33547
$83$	−406.724	−0.537876	−0.268938	−	0.963157i	$-0.586673\pi$
$83$	−406.724	−0.537876	−0.268938	+	0.963157i	$0.586673\pi$
$84$	−93.8463	−0.121898
$85$	612.490	0.781575
$86$	151.852	0.190403
$87$	286.483	0.353036
$88$	−36.6303	−0.0443728
$89$	261.751	0.311748	0.155874	−	0.987777i	$-0.450181\pi$
$89$	261.751	0.311748	0.155874	+	0.987777i	$0.450181\pi$
$90$	−158.901	−0.186107
$91$	133.436	0.153713
$92$	941.245	1.06665
$93$	−282.922	−0.315459
$94$	−1671.97	−1.83458
$95$	537.179	0.580141
$96$	545.889	0.580360
$97$	−1004.77	−1.05175	−0.525873	−	0.850563i	$-0.676261\pi$
$97$	−1004.77	−1.05175	−0.525873	+	0.850563i	$0.676261\pi$
$98$	−173.025	−0.178349
$99$	−26.4397	−0.0268413
$100$	111.722	0.111722
$101$	−128.872	−0.126962	−0.0634812	−	0.997983i	$-0.520220\pi$
$101$	−128.872	−0.126962	−0.0634812	+	0.997983i	$0.520220\pi$
$102$	−1297.67	−1.25969
$103$	806.008	0.771051	0.385526	−	0.922697i	$-0.374020\pi$
$103$	806.008	0.771051	0.385526	+	0.922697i	$0.374020\pi$
$104$	−237.685	−0.224105
$105$	−105.000	−0.0975900
$106$	648.587	0.594305
$107$	−769.712	−0.695429	−0.347714	−	0.937600i	$-0.613042\pi$
$107$	−769.712	−0.695429	−0.347714	+	0.937600i	$0.613042\pi$
$108$	120.660	0.107504
$109$	−780.856	−0.686169	−0.343085	−	0.939304i	$-0.611472\pi$
$109$	−780.856	−0.686169	−0.343085	+	0.939304i	$0.611472\pi$
$110$	51.8677	0.0449581
$111$	291.362	0.249143
$112$	558.461	0.471157
$113$	−1115.65	−0.928771	−0.464386	−	0.885633i	$-0.653725\pi$
$113$	−1115.65	−0.928771	−0.464386	+	0.885633i	$0.653725\pi$
$114$	−1138.11	−0.935032
$115$	1053.11	0.853942
$116$	426.751	0.341576
$117$	−171.560	−0.135562
$118$	2685.83	2.09534
$119$	−857.486	−0.660552
$120$	187.033	0.142281
$121$	−1322.37	−0.993516
$122$	701.802	0.520804
$123$	−1473.34	−1.08005
$124$	−421.448	−0.305219
$125$	125.000	0.0894427
$126$	222.461	0.157289
$127$	−1875.98	−1.31076	−0.655381	−	0.755299i	$-0.727492\pi$
$127$	−1875.98	−1.31076	−0.655381	+	0.755299i	$0.727492\pi$
$128$	−1440.54	−0.994744
$129$	−129.012	−0.0880530
$130$	336.556	0.227061
$131$	364.203	0.242905	0.121452	−	0.992597i	$-0.461245\pi$
$131$	364.203	0.242905	0.121452	+	0.992597i	$0.461245\pi$
$132$	−39.3852	−0.0259700
$133$	−752.051	−0.490309
$134$	1094.62	0.705679
$135$	135.000	0.0860663
$136$	1527.41	0.963048
$137$	1603.13	0.999743	0.499872	−	0.866099i	$-0.333380\pi$
$137$	1603.13	0.999743	0.499872	+	0.866099i	$0.333380\pi$
$138$	−2231.21	−1.37633
$139$	2431.12	1.48349	0.741746	−	0.670681i	$-0.233998\pi$
$139$	2431.12	1.48349	0.741746	+	0.670681i	$0.233998\pi$
$140$	−156.410	−0.0944221
$141$	1420.48	0.848413
$142$	−2350.65	−1.38917
$143$	56.0000	0.0327479
$144$	−718.021	−0.415522
$145$	477.471	0.273461
$146$	−2193.85	−1.24359
$147$	147.000	0.0824786
$148$	434.020	0.241055
$149$	2341.57	1.28744	0.643722	−	0.765260i	$-0.277389\pi$
$149$	2341.57	1.28744	0.643722	+	0.765260i	$0.277389\pi$
$150$	−264.835	−0.144158
$151$	−2104.07	−1.13395	−0.566976	−	0.823734i	$-0.691887\pi$
$151$	−2104.07	−1.13395	−0.566976	+	0.823734i	$0.691887\pi$
$152$	1339.60	0.714843
$153$	1102.48	0.582552
$154$	−72.6148	−0.0379966
$155$	−471.537	−0.244353
$156$	−255.560	−0.131162
$157$	−593.467	−0.301680	−0.150840	−	0.988558i	$-0.548198\pi$
$157$	−593.467	−0.301680	−0.150840	+	0.988558i	$0.548198\pi$
$158$	87.4399	0.0440275
$159$	−551.031	−0.274840
$160$	909.815	0.449545
$161$	−1474.36	−0.721712
$162$	−286.021	−0.138716
$163$	2178.71	1.04693	0.523465	−	0.852047i	$-0.324639\pi$
$163$	2178.71	1.04693	0.523465	+	0.852047i	$0.324639\pi$
$164$	−2194.72	−1.04499
$165$	−44.0661	−0.0207912
$166$	1436.19	0.671508
$167$	799.502	0.370463	0.185231	−	0.982695i	$-0.440697\pi$
$167$	799.502	0.370463	0.185231	+	0.982695i	$0.440697\pi$
$168$	−261.846	−0.120249
$169$	−1833.63	−0.834606
$170$	−2162.78	−0.975752
$171$	966.922	0.432412
$172$	−192.179	−0.0851947
$173$	−1444.36	−0.634754	−0.317377	−	0.948299i	$-0.602802\pi$
$173$	−1444.36	−0.634754	−0.317377	+	0.948299i	$0.602802\pi$
$174$	−1011.61	−0.440745
$175$	−175.000	−0.0755929
$176$	234.374	0.100378
$177$	−2281.84	−0.969005
$178$	−924.276	−0.389199
$179$	3343.49	1.39611	0.698056	−	0.716043i	$-0.254048\pi$
$179$	3343.49	1.39611	0.698056	+	0.716043i	$0.254048\pi$
$180$	201.099	0.0832725
$181$	2251.81	0.924729	0.462365	−	0.886690i	$-0.347001\pi$
$181$	2251.81	0.924729	0.462365	+	0.886690i	$0.347001\pi$
$182$	−471.179	−0.191902
$183$	−596.241	−0.240849
$184$	2626.23	1.05222
$185$	485.603	0.192985
$186$	999.035	0.393832
$187$	−359.868	−0.140728
$188$	2115.98	0.820873
$189$	−189.000	−0.0727393
$190$	−1896.85	−0.724273
$191$	−1001.93	−0.379565	−0.189782	−	0.981826i	$-0.560778\pi$
$191$	−1001.93	−0.379565	−0.189782	+	0.981826i	$0.560778\pi$
$192$	−12.8812	−0.00484177
$193$	−4054.97	−1.51235	−0.756173	−	0.654372i	$-0.772933\pi$
$193$	−4054.97	−1.51235	−0.756173	+	0.654372i	$0.772933\pi$
$194$	3547.99	1.31304
$195$	−285.934	−0.105006
$196$	218.975	0.0798013
$197$	−5140.23	−1.85902	−0.929508	−	0.368802i	$-0.879768\pi$
$197$	−5140.23	−1.85902	−0.929508	+	0.368802i	$0.879768\pi$
$198$	93.3619	0.0335098
$199$	585.631	0.208614	0.104307	−	0.994545i	$-0.466737\pi$
$199$	585.631	0.208614	0.104307	+	0.994545i	$0.466737\pi$
$200$	311.722	0.110210
$201$	−929.977	−0.326346
$202$	455.062	0.158505
$203$	−668.459	−0.231116
$204$	1642.28	0.563642
$205$	−2455.56	−0.836605
$206$	−2846.12	−0.962614
$207$	1895.60	0.636490
$208$	1520.79	0.506961
$209$	−315.619	−0.104458
$210$	370.769	0.121836
$211$	−1055.16	−0.344266	−0.172133	−	0.985074i	$-0.555066\pi$
$211$	−1055.16	−0.344266	−0.172133	+	0.985074i	$0.555066\pi$
$212$	−820.829	−0.265919
$213$	1997.08	0.642430
$214$	2717.95	0.868203
$215$	−215.019	−0.0682056
$216$	336.660	0.106050
$217$	660.152	0.206516
$218$	2757.30	0.856643
$219$	1863.86	0.575106
$220$	−65.6420	−0.0201163
$221$	−2335.09	−0.710747
$222$	−1028.84	−0.311040
$223$	4675.85	1.40412	0.702059	−	0.712119i	$-0.252264\pi$
$223$	4675.85	1.40412	0.702059	+	0.712119i	$0.252264\pi$
$224$	−1273.74	−0.379935
$225$	225.000	0.0666667
$226$	3939.49	1.15952
$227$	5443.11	1.59151	0.795754	−	0.605621i	$-0.207075\pi$
$227$	5443.11	1.59151	0.795754	+	0.605621i	$0.207075\pi$
$228$	1440.35	0.418375
$229$	−536.303	−0.154759	−0.0773797	−	0.997002i	$-0.524655\pi$
$229$	−536.303	−0.154759	−0.0773797	+	0.997002i	$0.524655\pi$
$230$	−3718.68	−1.06610
$231$	61.6926	0.0175717
$232$	1190.70	0.336955
$233$	−183.490	−0.0515916	−0.0257958	−	0.999667i	$-0.508212\pi$
$233$	−183.490	−0.0515916	−0.0257958	+	0.999667i	$0.508212\pi$
$234$	605.802	0.169241
$235$	2367.47	0.657178
$236$	−3399.09	−0.937550
$237$	−74.2878	−0.0203608
$238$	3027.90	0.824661
$239$	643.218	0.174085	0.0870425	−	0.996205i	$-0.472258\pi$
$239$	643.218	0.174085	0.0870425	+	0.996205i	$0.472258\pi$
$240$	−1196.70	−0.321862
$241$	−5755.61	−1.53839	−0.769194	−	0.639015i	$-0.779342\pi$
$241$	−5755.61	−1.53839	−0.769194	+	0.639015i	$0.779342\pi$
$242$	4669.46	1.24035
$243$	243.000	0.0641500
$244$	−888.175	−0.233031
$245$	245.000	0.0638877
$246$	5202.55	1.34838
$247$	−2047.97	−0.527567
$248$	−1175.91	−0.301089
$249$	−1220.17	−0.310543
$250$	−441.391	−0.111664
$251$	−5132.27	−1.29062	−0.645311	−	0.763920i	$-0.723272\pi$
$251$	−5132.27	−1.29062	−0.645311	+	0.763920i	$0.723272\pi$
$252$	−281.539	−0.0703781
$253$	−618.755	−0.153758
$254$	6624.34	1.63641
$255$	1837.47	0.451243
$256$	5121.09	1.25027
$257$	5041.74	1.22372	0.611859	−	0.790967i	$-0.290422\pi$
$257$	5041.74	1.22372	0.611859	+	0.790967i	$0.290422\pi$
$258$	455.557	0.109929
$259$	−679.844	−0.163102
$260$	−425.934	−0.101597
$261$	859.448	0.203826
$262$	−1286.05	−0.303253
$263$	7577.00	1.77649	0.888246	−	0.459367i	$-0.151924\pi$
$263$	7577.00	1.77649	0.888246	+	0.459367i	$0.151924\pi$
$264$	−109.891	−0.0256186
$265$	−918.385	−0.212890
$266$	2655.59	0.612122
$267$	785.253	0.179988
$268$	−1385.32	−0.315752
$269$	1023.10	0.231893	0.115947	−	0.993255i	$-0.463010\pi$
$269$	1023.10	0.231893	0.115947	+	0.993255i	$0.463010\pi$
$270$	−476.702	−0.107449
$271$	−2251.98	−0.504790	−0.252395	−	0.967624i	$-0.581218\pi$
$271$	−2251.98	−0.504790	−0.252395	+	0.967624i	$0.581218\pi$
$272$	−9772.91	−2.17857
$273$	400.307	0.0887462
$274$	−5660.87	−1.24812
$275$	−73.4436	−0.0161048
$276$	2823.74	0.615829
$277$	−8630.72	−1.87209	−0.936047	−	0.351875i	$-0.885544\pi$
$277$	−8630.72	−1.87209	−0.936047	+	0.351875i	$0.885544\pi$
$278$	−8584.61	−1.85205
$279$	−848.767	−0.182130
$280$	−436.410	−0.0931447
$281$	−7521.62	−1.59680	−0.798402	−	0.602124i	$-0.794321\pi$
$281$	−7521.62	−1.59680	−0.798402	+	0.602124i	$0.794321\pi$
$282$	−5015.91	−1.05919
$283$	14.8169	0.00311226	0.00155613	−	0.999999i	$-0.499505\pi$
$283$	14.8169	0.00311226	0.00155613	+	0.999999i	$0.499505\pi$
$284$	2974.89	0.621576
$285$	1611.54	0.334945
$286$	−197.743	−0.0408839
$287$	3437.79	0.707060
$288$	1637.67	0.335071
$289$	10092.8	2.05430
$290$	−1686.01	−0.341400
$291$	−3014.32	−0.607226
$292$	2776.46	0.556438
$293$	6913.39	1.37844	0.689222	−	0.724550i	$-0.257952\pi$
$293$	6913.39	1.37844	0.689222	+	0.724550i	$0.257952\pi$
$294$	−519.076	−0.102970
$295$	−3803.07	−0.750588
$296$	1210.98	0.237794
$297$	−79.3190	−0.0154968
$298$	−8268.39	−1.60730
$299$	−4014.94	−0.776555
$300$	335.165	0.0645026
$301$	301.027	0.0576442
$302$	7429.74	1.41567
$303$	−386.615	−0.0733018
$304$	−8571.25	−1.61709
$305$	−993.735	−0.186561
$306$	−3893.01	−0.727283
$307$	−7644.12	−1.42108	−0.710542	−	0.703655i	$-0.751550\pi$
$307$	−7644.12	−1.42108	−0.710542	+	0.703655i	$0.751550\pi$
$308$	91.8987	0.0170014
$309$	2418.02	0.445167
$310$	1665.06	0.305061
$311$	7593.99	1.38462	0.692308	−	0.721602i	$-0.256594\pi$
$311$	7593.99	1.38462	0.692308	+	0.721602i	$0.256594\pi$
$312$	−713.055	−0.129387
$313$	−9127.84	−1.64836	−0.824179	−	0.566329i	$-0.808363\pi$
$313$	−9127.84	−1.64836	−0.824179	+	0.566329i	$0.808363\pi$
$314$	2095.61	0.376631
$315$	−315.000	−0.0563436
$316$	−110.661	−0.0196999
$317$	−4929.81	−0.873456	−0.436728	−	0.899593i	$-0.643863\pi$
$317$	−4929.81	−0.873456	−0.436728	+	0.899593i	$0.643863\pi$
$318$	1945.76	0.343122
$319$	−280.537	−0.0492385
$320$	−21.4686	−0.00375042
$321$	−2309.14	−0.401506
$322$	5206.15	0.901016
$323$	13160.7	2.26712
$324$	361.979	0.0620677
$325$	−476.556	−0.0813372
$326$	−7693.30	−1.30703
$327$	−2342.57	−0.396160
$328$	−6123.62	−1.03086
$329$	−3314.46	−0.555417
$330$	155.603	0.0259566
$331$	1221.67	0.202867	0.101433	−	0.994842i	$-0.467657\pi$
$331$	1221.67	0.202867	0.101433	+	0.994842i	$0.467657\pi$
$332$	−1817.60	−0.300463
$333$	874.086	0.143843
$334$	−2823.14	−0.462502
$335$	−1549.96	−0.252786
$336$	1675.38	0.272023
$337$	−8744.83	−1.41354	−0.706768	−	0.707446i	$-0.749847\pi$
$337$	−8744.83	−1.41354	−0.706768	+	0.707446i	$0.749847\pi$
$338$	6474.79	1.04196
$339$	−3346.94	−0.536226
$340$	2737.14	0.436595
$341$	277.051	0.0439975
$342$	−3414.33	−0.539841
$343$	−343.000	−0.0539949
$344$	−536.210	−0.0840421
$345$	3159.34	0.493023
$346$	5100.21	0.792454
$347$	4589.56	0.710031	0.355015	−	0.934860i	$-0.384476\pi$
$347$	4589.56	0.710031	0.355015	+	0.934860i	$0.384476\pi$
$348$	1280.25	0.197209
$349$	−3989.89	−0.611960	−0.305980	−	0.952038i	$-0.598984\pi$
$349$	−3989.89	−0.611960	−0.305980	+	0.952038i	$0.598984\pi$
$350$	617.948	0.0943734
$351$	−514.681	−0.0782668
$352$	−534.561	−0.0809437
$353$	2416.35	0.364333	0.182166	−	0.983268i	$-0.441689\pi$
$353$	2416.35	0.364333	0.182166	+	0.983268i	$0.441689\pi$
$354$	8057.49	1.20975
$355$	3328.46	0.497624
$356$	1169.73	0.174145
$357$	−2572.46	−0.381370
$358$	−11806.3	−1.74297
$359$	−2756.24	−0.405206	−0.202603	−	0.979261i	$-0.564940\pi$
$359$	−2756.24	−0.405206	−0.202603	+	0.979261i	$0.564940\pi$
$360$	561.099	0.0821459
$361$	4683.45	0.682818
$362$	−7951.44	−1.15447
$363$	−3967.11	−0.573607
$364$	596.307	0.0858654
$365$	3106.44	0.445475
$366$	2105.40	0.300687
$367$	11112.8	1.58061	0.790307	−	0.612711i	$-0.209921\pi$
$367$	11112.8	1.58061	0.790307	+	0.612711i	$0.209921\pi$
$368$	−16803.5	−2.38028
$369$	−4420.02	−0.623569
$370$	−1714.73	−0.240931
$371$	1285.74	0.179925
$372$	−1264.34	−0.176218
$373$	6091.09	0.845535	0.422768	−	0.906238i	$-0.361059\pi$
$373$	6091.09	0.845535	0.422768	+	0.906238i	$0.361059\pi$
$374$	1270.74	0.175691
$375$	375.000	0.0516398
$376$	5903.94	0.809767
$377$	−1820.33	−0.248679
$378$	667.383	0.0908108
$379$	3984.29	0.539998	0.269999	−	0.962861i	$-0.412977\pi$
$379$	3984.29	0.539998	0.269999	+	0.962861i	$0.412977\pi$
$380$	2400.58	0.324072
$381$	−5627.95	−0.756768
$382$	3537.93	0.473865
$383$	318.475	0.0424890	0.0212445	−	0.999774i	$-0.493237\pi$
$383$	318.475	0.0424890	0.0212445	+	0.999774i	$0.493237\pi$
$384$	−4321.63	−0.574316
$385$	102.821	0.0136110
$386$	14318.6	1.88808
$387$	−387.035	−0.0508374
$388$	−4490.21	−0.587515
$389$	3885.46	0.506429	0.253214	−	0.967410i	$-0.418512\pi$
$389$	3885.46	0.506429	0.253214	+	0.967410i	$0.418512\pi$
$390$	1009.67	0.131094
$391$	25800.9	3.33710
$392$	610.975	0.0787216
$393$	1092.61	0.140241
$394$	18150.8	2.32088
$395$	−123.813	−0.0157714
$396$	−118.156	−0.0149938
$397$	4806.04	0.607578	0.303789	−	0.952739i	$-0.401748\pi$
$397$	4806.04	0.607578	0.303789	+	0.952739i	$0.401748\pi$
$398$	−2067.94	−0.260443
$399$	−2256.15	−0.283080
$400$	−1994.50	−0.249313
$401$	3618.59	0.450633	0.225316	−	0.974286i	$-0.427658\pi$
$401$	3618.59	0.450633	0.225316	+	0.974286i	$0.427658\pi$
$402$	3283.87	0.407424
$403$	1797.71	0.222209
$404$	−575.911	−0.0709223
$405$	405.000	0.0496904
$406$	2360.42	0.288536
$407$	−285.315	−0.0347483
$408$	4582.24	0.556016
$409$	−2109.05	−0.254978	−0.127489	−	0.991840i	$-0.540692\pi$
$409$	−2109.05	−0.254978	−0.127489	+	0.991840i	$0.540692\pi$
$410$	8670.91	1.04445
$411$	4809.40	0.577202
$412$	3601.94	0.430716
$413$	5324.30	0.634363
$414$	−6693.62	−0.794622
$415$	−2033.62	−0.240546
$416$	−3468.63	−0.408806
$417$	7293.37	0.856494
$418$	1114.49	0.130410
$419$	−6905.91	−0.805193	−0.402597	−	0.915377i	$-0.631892\pi$
$419$	−6905.91	−0.805193	−0.402597	+	0.915377i	$0.631892\pi$
$420$	−469.231	−0.0545146
$421$	−9647.54	−1.11685	−0.558423	−	0.829556i	$-0.688593\pi$
$421$	−9647.54	−1.11685	−0.558423	+	0.829556i	$0.688593\pi$
$422$	3725.91	0.429797
$423$	4261.45	0.489831
$424$	−2290.25	−0.262321
$425$	3062.45	0.349531
$426$	−7051.94	−0.802037
$427$	1391.23	0.157673
$428$	−3439.74	−0.388473
$429$	168.000	0.0189070
$430$	759.261	0.0851508
$431$	−13002.7	−1.45318	−0.726589	−	0.687073i	$-0.758895\pi$
$431$	−13002.7	−1.45318	−0.726589	+	0.687073i	$0.758895\pi$
$432$	−2154.06	−0.239902
$433$	7356.07	0.816420	0.408210	−	0.912888i	$-0.366153\pi$
$433$	7356.07	0.816420	0.408210	+	0.912888i	$0.366153\pi$
$434$	−2331.08	−0.257824
$435$	1432.41	0.157883
$436$	−3489.55	−0.383300
$437$	22628.4	2.47703
$438$	−6581.54	−0.717987
$439$	6909.21	0.751159	0.375579	−	0.926790i	$-0.377444\pi$
$439$	6909.21	0.751159	0.375579	+	0.926790i	$0.377444\pi$
$440$	−183.152	−0.0198441
$441$	441.000	0.0476190
$442$	8245.50	0.887327
$443$	−14812.6	−1.58864	−0.794318	−	0.607502i	$-0.792172\pi$
$443$	−14812.6	−1.58864	−0.794318	+	0.607502i	$0.792172\pi$
$444$	1302.06	0.139173
$445$	1308.75	0.139418
$446$	−16511.0	−1.75296
$447$	7024.72	0.743306
$448$	30.0561	0.00316968
$449$	−10654.5	−1.11986	−0.559932	−	0.828538i	$-0.689173\pi$
$449$	−10654.5	−1.11986	−0.559932	+	0.828538i	$0.689173\pi$
$450$	−794.504	−0.0832295
$451$	1442.76	0.150636
$452$	−4985.68	−0.518820
$453$	−6312.21	−0.654688
$454$	−19220.3	−1.98691
$455$	667.179	0.0687425
$456$	4018.81	0.412715
$457$	−5855.16	−0.599328	−0.299664	−	0.954045i	$-0.596875\pi$
$457$	−5855.16	−0.599328	−0.299664	+	0.954045i	$0.596875\pi$
$458$	1893.76	0.193208
$459$	3307.45	0.336336
$460$	4706.23	0.477019
$461$	3204.74	0.323774	0.161887	−	0.986809i	$-0.448242\pi$
$461$	3204.74	0.323774	0.161887	+	0.986809i	$0.448242\pi$
$462$	−217.844	−0.0219373
$463$	371.658	0.0373054	0.0186527	−	0.999826i	$-0.494062\pi$
$463$	371.658	0.0373054	0.0186527	+	0.999826i	$0.494062\pi$
$464$	−7618.54	−0.762245
$465$	−1414.61	−0.141077
$466$	647.927	0.0644091
$467$	−19752.3	−1.95723	−0.978614	−	0.205703i	$-0.934052\pi$
$467$	−19752.3	−1.95723	−0.978614	+	0.205703i	$0.934052\pi$
$468$	−766.681	−0.0757262
$469$	2169.95	0.213643
$470$	−8359.84	−0.820449
$471$	−1780.40	−0.174175
$472$	−9484.01	−0.924866
$473$	126.334	0.0122809
$474$	262.320	0.0254193
$475$	2685.90	0.259447
$476$	−3832.00	−0.368990
$477$	−1653.09	−0.158679
$478$	−2271.28	−0.217335
$479$	−20762.0	−1.98046	−0.990232	−	0.139433i	$-0.955472\pi$
$479$	−20762.0	−1.98046	−0.990232	+	0.139433i	$0.955472\pi$
$480$	2729.45	0.259545
$481$	−1851.34	−0.175496
$482$	20323.8	1.92059
$483$	−4423.07	−0.416681
$484$	−5909.50	−0.554987
$485$	−5023.87	−0.470355
$486$	−858.064	−0.0800876
$487$	17647.6	1.64207	0.821035	−	0.570878i	$-0.193397\pi$
$487$	17647.6	1.64207	0.821035	+	0.570878i	$0.193397\pi$
$488$	−2478.15	−0.229878
$489$	6536.12	0.604445
$490$	−865.127	−0.0797601
$491$	−5637.46	−0.518157	−0.259078	−	0.965856i	$-0.583419\pi$
$491$	−5637.46	−0.518157	−0.259078	+	0.965856i	$0.583419\pi$
$492$	−6584.16	−0.603327
$493$	11697.9	1.06865
$494$	7231.64	0.658638
$495$	−132.198	−0.0120038
$496$	7523.86	0.681112
$497$	−4659.85	−0.420569
$498$	4308.58	0.387695
$499$	−17474.1	−1.56764	−0.783818	−	0.620991i	$-0.786730\pi$
$499$	−17474.1	−1.56764	−0.783818	+	0.620991i	$0.786730\pi$
$500$	558.609	0.0499635
$501$	2398.51	0.213887
$502$	18122.7	1.61127
$503$	7444.81	0.659936	0.329968	−	0.943992i	$-0.392962\pi$
$503$	7444.81	0.659936	0.329968	+	0.943992i	$0.392962\pi$
$504$	−785.539	−0.0694260
$505$	−644.358	−0.0567793
$506$	2184.90	0.191958
$507$	−5500.89	−0.481860
$508$	−8383.53	−0.732203
$509$	−3384.48	−0.294724	−0.147362	−	0.989083i	$-0.547078\pi$
$509$	−3384.48	−0.294724	−0.147362	+	0.989083i	$0.547078\pi$
$510$	−6488.35	−0.563351
$511$	−4349.02	−0.376495
$512$	−6558.89	−0.566142
$513$	2900.77	0.249653
$514$	−17803.0	−1.52774
$515$	4030.04	0.344825
$516$	−576.536	−0.0491872
$517$	−1391.00	−0.118329
$518$	2400.62	0.203624
$519$	−4333.07	−0.366476
$520$	−1188.42	−0.100223
$521$	2973.12	0.250009	0.125005	−	0.992156i	$-0.460105\pi$
$521$	2973.12	0.250009	0.125005	+	0.992156i	$0.460105\pi$
$522$	−3034.82	−0.254465
$523$	2689.02	0.224823	0.112412	−	0.993662i	$-0.464142\pi$
$523$	2689.02	0.224823	0.112412	+	0.993662i	$0.464142\pi$
$524$	1627.57	0.135689
$525$	−525.000	−0.0436436
$526$	−26755.3	−2.21785
$527$	−11552.5	−0.954903
$528$	703.121	0.0579534
$529$	32194.9	2.64608
$530$	3242.94	0.265781
$531$	−6845.53	−0.559455
$532$	−3360.82	−0.273891
$533$	9361.72	0.760790
$534$	−2772.83	−0.224704
$535$	−3848.56	−0.311005
$536$	−3865.25	−0.311480
$537$	10030.5	0.806046
$538$	−3612.69	−0.289506
$539$	−143.949	−0.0115034
$540$	603.298	0.0480774
$541$	−14429.5	−1.14671	−0.573356	−	0.819306i	$-0.694359\pi$
$541$	−14429.5	−1.14671	−0.573356	+	0.819306i	$0.694359\pi$
$542$	7952.03	0.630201
$543$	6755.44	0.533893
$544$	22290.1	1.75677
$545$	−3904.28	−0.306864
$546$	−1413.54	−0.110795
$547$	13811.2	1.07957	0.539784	−	0.841804i	$-0.318506\pi$
$547$	13811.2	1.07957	0.539784	+	0.841804i	$0.318506\pi$
$548$	7164.19	0.558466
$549$	−1788.72	−0.139054
$550$	259.339	0.0201059
$551$	10259.5	0.793229
$552$	7878.68	0.607498
$553$	173.338	0.0133293
$554$	30476.2	2.33720
$555$	1456.81	0.111420
$556$	10864.4	0.828692
$557$	−6033.26	−0.458954	−0.229477	−	0.973314i	$-0.573702\pi$
$557$	−6033.26	−0.458954	−0.229477	+	0.973314i	$0.573702\pi$
$558$	2997.10	0.227379
$559$	819.751	0.0620246
$560$	2792.31	0.210708
$561$	−1079.60	−0.0812493
$562$	26559.8	1.99352
$563$	−6958.47	−0.520896	−0.260448	−	0.965488i	$-0.583870\pi$
$563$	−6958.47	−0.520896	−0.260448	+	0.965488i	$0.583870\pi$
$564$	6347.95	0.473931
$565$	−5578.23	−0.415359
$566$	−52.3202	−0.00388548
$567$	−567.000	−0.0419961
$568$	8300.44	0.613166
$569$	−13396.4	−0.987009	−0.493505	−	0.869743i	$-0.664284\pi$
$569$	−13396.4	−0.987009	−0.493505	+	0.869743i	$0.664284\pi$
$570$	−5690.55	−0.418159
$571$	−8055.84	−0.590414	−0.295207	−	0.955433i	$-0.595389\pi$
$571$	−8055.84	−0.590414	−0.295207	+	0.955433i	$0.595389\pi$
$572$	250.257	0.0182933
$573$	−3005.78	−0.219142
$574$	−12139.3	−0.882724
$575$	5265.56	0.381894
$576$	−38.6435	−0.00279539
$577$	−21456.9	−1.54812	−0.774059	−	0.633114i	$-0.781777\pi$
$577$	−21456.9	−1.54812	−0.774059	+	0.633114i	$0.781777\pi$
$578$	−35638.9	−2.56468
$579$	−12164.9	−0.873153
$580$	2133.76	0.152758
$581$	2847.07	0.203298
$582$	10644.0	0.758087
$583$	539.596	0.0383324
$584$	7746.76	0.548910
$585$	−857.802	−0.0606252
$586$	−24412.1	−1.72091
$587$	20156.3	1.41728	0.708638	−	0.705572i	$-0.249310\pi$
$587$	20156.3	1.41728	0.708638	+	0.705572i	$0.249310\pi$
$588$	656.924	0.0460733
$589$	−10132.0	−0.708797
$590$	13429.1	0.937066
$591$	−15420.7	−1.07330
$592$	−7748.30	−0.537928
$593$	599.307	0.0415018	0.0207509	−	0.999785i	$-0.493394\pi$
$593$	599.307	0.0415018	0.0207509	+	0.999785i	$0.493394\pi$
$594$	280.086	0.0193469
$595$	−4287.43	−0.295408
$596$	10464.2	0.719177
$597$	1756.89	0.120444
$598$	14177.3	0.969485
$599$	−5493.05	−0.374691	−0.187346	−	0.982294i	$-0.559988\pi$
$599$	−5493.05	−0.374691	−0.187346	+	0.982294i	$0.559988\pi$
$600$	935.165	0.0636299
$601$	24292.8	1.64879	0.824396	−	0.566014i	$-0.191515\pi$
$601$	24292.8	1.64879	0.824396	+	0.566014i	$0.191515\pi$
$602$	−1062.97	−0.0719655
$603$	−2789.93	−0.188416
$604$	−9402.82	−0.633436
$605$	−6611.85	−0.444314
$606$	1365.19	0.0915131
$607$	3029.50	0.202576	0.101288	−	0.994857i	$-0.467704\pi$
$607$	3029.50	0.202576	0.101288	+	0.994857i	$0.467704\pi$
$608$	19549.3	1.30400
$609$	−2005.38	−0.133435
$610$	3509.01	0.232911
$611$	−9025.87	−0.597623
$612$	4926.85	0.325419
$613$	−19339.6	−1.27426	−0.637129	−	0.770757i	$-0.719878\pi$
$613$	−19339.6	−1.27426	−0.637129	+	0.770757i	$0.719878\pi$
$614$	26992.4	1.77414
$615$	−7366.69	−0.483014
$616$	256.412	0.0167713
$617$	−5743.91	−0.374783	−0.187391	−	0.982285i	$-0.560003\pi$
$617$	−5743.91	−0.374783	−0.187391	+	0.982285i	$0.560003\pi$
$618$	−8538.35	−0.555765
$619$	−8243.35	−0.535264	−0.267632	−	0.963521i	$-0.586241\pi$
$619$	−8243.35	−0.535264	−0.267632	+	0.963521i	$0.586241\pi$
$620$	−2107.24	−0.136498
$621$	5686.81	0.367478
$622$	−26815.4	−1.72861
$623$	−1832.26	−0.117830
$624$	4562.37	0.292694
$625$	625.000	0.0400000
$626$	32231.6	2.05788
$627$	−946.856	−0.0603091
$628$	−2652.13	−0.168521
$629$	11897.1	0.754162
$630$	1112.31	0.0703418
$631$	−4376.56	−0.276114	−0.138057	−	0.990424i	$-0.544086\pi$
$631$	−4376.56	−0.276114	−0.138057	+	0.990424i	$0.544086\pi$
$632$	−308.762	−0.0194334
$633$	−3165.48	−0.198762
$634$	17407.8	1.09046
$635$	−9379.92	−0.586190
$636$	−2462.49	−0.153528
$637$	−934.051	−0.0580980
$638$	990.613	0.0614714
$639$	5991.23	0.370907
$640$	−7202.71	−0.444863
$641$	11836.6	0.729357	0.364678	−	0.931133i	$-0.381179\pi$
$641$	11836.6	0.729357	0.364678	+	0.931133i	$0.381179\pi$
$642$	8153.86	0.501257
$643$	1448.21	0.0888209	0.0444104	−	0.999013i	$-0.485859\pi$
$643$	1448.21	0.0888209	0.0444104	+	0.999013i	$0.485859\pi$
$644$	−6588.72	−0.403155
$645$	−645.058	−0.0393785
$646$	−46472.0	−2.83037
$647$	−8732.95	−0.530646	−0.265323	−	0.964160i	$-0.585479\pi$
$647$	−8732.95	−0.530646	−0.265323	+	0.964160i	$0.585479\pi$
$648$	1009.98	0.0612279
$649$	2234.49	0.135149
$650$	1682.78	0.101545
$651$	1980.46	0.119232
$652$	9736.37	0.584824
$653$	−21978.4	−1.31712	−0.658562	−	0.752527i	$-0.728835\pi$
$653$	−21978.4	−1.31712	−0.658562	+	0.752527i	$0.728835\pi$
$654$	8271.91	0.494583
$655$	1821.01	0.108630
$656$	39181.1	2.33196
$657$	5591.59	0.332038
$658$	11703.8	0.693406
$659$	−27761.7	−1.64103	−0.820516	−	0.571623i	$-0.806314\pi$
$659$	−27761.7	−1.64103	−0.820516	+	0.571623i	$0.806314\pi$
$660$	−196.926	−0.0116141
$661$	−8573.72	−0.504507	−0.252254	−	0.967661i	$-0.581172\pi$
$661$	−8573.72	−0.504507	−0.252254	+	0.967661i	$0.581172\pi$
$662$	−4313.86	−0.253267
$663$	−7005.27	−0.410350
$664$	−5071.39	−0.296398
$665$	−3760.25	−0.219273
$666$	−3086.51	−0.179579
$667$	20113.2	1.16760
$668$	3572.87	0.206944
$669$	14027.6	0.810668
$670$	5473.11	0.315589
$671$	583.868	0.0335916
$672$	−3821.22	−0.219356
$673$	27159.2	1.55559	0.777795	−	0.628518i	$-0.216338\pi$
$673$	27159.2	1.55559	0.777795	+	0.628518i	$0.216338\pi$
$674$	30879.1	1.76472
$675$	675.000	0.0384900
$676$	−8194.26	−0.466219
$677$	−1392.30	−0.0790404	−0.0395202	−	0.999219i	$-0.512583\pi$
$677$	−1392.30	−0.0790404	−0.0395202	+	0.999219i	$0.512583\pi$
$678$	11818.5	0.669448
$679$	7033.42	0.397523
$680$	7637.06	0.430688
$681$	16329.3	0.918857
$682$	−978.302	−0.0549283
$683$	−8675.09	−0.486007	−0.243004	−	0.970025i	$-0.578133\pi$
$683$	−8675.09	−0.486007	−0.243004	+	0.970025i	$0.578133\pi$
$684$	4321.05	0.241549
$685$	8015.66	0.447099
$686$	1211.18	0.0674096
$687$	−1608.91	−0.0893504
$688$	3430.86	0.190117
$689$	3501.30	0.193598
$690$	−11156.0	−0.615511
$691$	−21426.0	−1.17957	−0.589785	−	0.807561i	$-0.700787\pi$
$691$	−21426.0	−1.17957	−0.589785	+	0.807561i	$0.700787\pi$
$692$	−6454.65	−0.354579
$693$	185.078	0.0101451
$694$	−16206.3	−0.886433
$695$	12155.6	0.663438
$696$	3572.11	0.194541
$697$	−60160.4	−3.26935
$698$	14088.8	0.763997
$699$	−550.470	−0.0297864
$700$	−782.052	−0.0422269
$701$	24840.5	1.33839	0.669197	−	0.743085i	$-0.266638\pi$
$701$	24840.5	1.33839	0.669197	+	0.743085i	$0.266638\pi$
$702$	1817.40	0.0977116
$703$	10434.2	0.559793
$704$	12.6139	0.000675288 0
$705$	7102.41	0.379422
$706$	−8532.45	−0.454848
$707$	902.101	0.0479873
$708$	−10197.3	−0.541295
$709$	12525.0	0.663450	0.331725	−	0.943376i	$-0.392369\pi$
$709$	12525.0	0.663450	0.331725	+	0.943376i	$0.392369\pi$
$710$	−11753.2	−0.621255
$711$	−222.863	−0.0117553
$712$	3263.74	0.171789
$713$	−19863.3	−1.04332
$714$	9083.69	0.476118
$715$	280.000	0.0146453
$716$	14941.6	0.779881
$717$	1929.65	0.100508
$718$	9732.66	0.505877
$719$	28085.0	1.45674	0.728369	−	0.685185i	$-0.240279\pi$
$719$	28085.0	1.45674	0.728369	+	0.685185i	$0.240279\pi$
$720$	−3590.11	−0.185827
$721$	−5642.05	−0.291430
$722$	−16537.9	−0.852460
$723$	−17266.8	−0.888189
$724$	10063.1	0.516562
$725$	2387.35	0.122295
$726$	14008.4	0.716115
$727$	−14326.2	−0.730851	−0.365426	−	0.930841i	$-0.619077\pi$
$727$	−14326.2	−0.730851	−0.365426	+	0.930841i	$0.619077\pi$
$728$	1663.79	0.0847037
$729$	729.000	0.0370370
$730$	−10969.2	−0.556150
$731$	−5267.89	−0.266539
$732$	−2664.53	−0.134541
$733$	6727.85	0.339016	0.169508	−	0.985529i	$-0.445782\pi$
$733$	6727.85	0.339016	0.169508	+	0.985529i	$0.445782\pi$
$734$	−39240.8	−1.97331
$735$	735.000	0.0368856
$736$	38325.5	1.91943
$737$	910.677	0.0455159
$738$	15607.6	0.778490
$739$	−3418.51	−0.170165	−0.0850826	−	0.996374i	$-0.527115\pi$
$739$	−3418.51	−0.170165	−0.0850826	+	0.996374i	$0.527115\pi$
$740$	2170.10	0.107803
$741$	−6143.91	−0.304591
$742$	−4540.11	−0.224626
$743$	8095.50	0.399724	0.199862	−	0.979824i	$-0.435951\pi$
$743$	8095.50	0.399724	0.199862	+	0.979824i	$0.435951\pi$
$744$	−3527.72	−0.173834
$745$	11707.9	0.575762
$746$	−21508.4	−1.05560
$747$	−3660.51	−0.179292
$748$	−1608.20	−0.0786119
$749$	5387.99	0.262847
$750$	−1324.17	−0.0644693
$751$	13446.8	0.653371	0.326686	−	0.945133i	$-0.394068\pi$
$751$	13446.8	0.653371	0.326686	+	0.945133i	$0.394068\pi$
$752$	−37775.4	−1.83182
$753$	−15396.8	−0.745141
$754$	6427.84	0.310462
$755$	−10520.4	−0.507119
$756$	−844.617	−0.0406328
$757$	−2593.24	−0.124508	−0.0622541	−	0.998060i	$-0.519829\pi$
$757$	−2593.24	−0.124508	−0.0622541	+	0.998060i	$0.519829\pi$
$758$	−14069.0	−0.674156
$759$	−1856.26	−0.0887722
$760$	6698.02	0.319688
$761$	27079.4	1.28992	0.644959	−	0.764217i	$-0.276875\pi$
$761$	27079.4	1.28992	0.644959	+	0.764217i	$0.276875\pi$
$762$	19873.0	0.944782
$763$	5465.99	0.259348
$764$	−4477.48	−0.212028
$765$	5512.41	0.260525
$766$	−1124.58	−0.0530451
$767$	14499.0	0.682568
$768$	15363.3	0.721842
$769$	2138.72	0.100292	0.0501458	−	0.998742i	$-0.484031\pi$
$769$	2138.72	0.100292	0.0501458	+	0.998742i	$0.484031\pi$
$770$	−363.074	−0.0169926
$771$	15125.2	0.706513
$772$	−18121.1	−0.844810
$773$	25864.0	1.20345	0.601724	−	0.798704i	$-0.294481\pi$
$773$	25864.0	1.20345	0.601724	+	0.798704i	$0.294481\pi$
$774$	1366.67	0.0634676
$775$	−2357.69	−0.109278
$776$	−12528.4	−0.579566
$777$	−2039.53	−0.0941671
$778$	−13720.1	−0.632247
$779$	−52763.1	−2.42675
$780$	−1277.80	−0.0586572
$781$	−1955.63	−0.0896006
$782$	−91106.2	−4.16618
$783$	2578.34	0.117679
$784$	−3909.23	−0.178081
$785$	−2967.33	−0.134916
$786$	−3858.14	−0.175083
$787$	−32371.3	−1.46621	−0.733107	−	0.680113i	$-0.761931\pi$
$787$	−32371.3	−1.46621	−0.733107	+	0.680113i	$0.761931\pi$
$788$	−22971.0	−1.03846
$789$	22731.0	1.02566
$790$	437.200	0.0196897
$791$	7809.52	0.351043
$792$	−329.673	−0.0147909
$793$	3788.57	0.169654
$794$	−16970.8	−0.758526
$795$	−2755.16	−0.122912
$796$	2617.11	0.116534
$797$	2024.33	0.0899691	0.0449845	−	0.998988i	$-0.485676\pi$
$797$	2024.33	0.0899691	0.0449845	+	0.998988i	$0.485676\pi$
$798$	7966.76	0.353409
$799$	58002.1	2.56817
$800$	4549.08	0.201043
$801$	2355.76	0.103916
$802$	−12777.7	−0.562589
$803$	−1825.18	−0.0802109
$804$	−4155.95	−0.182300
$805$	−7371.79	−0.322760
$806$	−6347.95	−0.277416
$807$	3069.29	0.133884
$808$	−1606.88	−0.0699628
$809$	12391.7	0.538526	0.269263	−	0.963067i	$-0.413220\pi$
$809$	12391.7	0.538526	0.269263	+	0.963067i	$0.413220\pi$
$810$	−1430.11	−0.0620356
$811$	14654.5	0.634511	0.317256	−	0.948340i	$-0.397239\pi$
$811$	14654.5	0.634511	0.317256	+	0.948340i	$0.397239\pi$
$812$	−2987.26	−0.129104
$813$	−6755.94	−0.291441
$814$	1007.49	0.0433813
$815$	10893.5	0.468201
$816$	−29318.7	−1.25780
$817$	−4620.16	−0.197844
$818$	7447.33	0.318325
$819$	1200.92	0.0512376
$820$	−10973.6	−0.467335
$821$	23887.9	1.01546	0.507731	−	0.861516i	$-0.330485\pi$
$821$	23887.9	1.01546	0.507731	+	0.861516i	$0.330485\pi$
$822$	−16982.6	−0.720604
$823$	−4008.41	−0.169774	−0.0848871	−	0.996391i	$-0.527053\pi$
$823$	−4008.41	−0.169774	−0.0848871	+	0.996391i	$0.527053\pi$
$824$	10050.0	0.424889
$825$	−220.331	−0.00929810
$826$	−18800.8	−0.791966
$827$	−45110.4	−1.89679	−0.948394	−	0.317096i	$-0.897292\pi$
$827$	−45110.4	−1.89679	−0.948394	+	0.317096i	$0.897292\pi$
$828$	8471.21	0.355549
$829$	16165.4	0.677260	0.338630	−	0.940920i	$-0.390036\pi$
$829$	16165.4	0.677260	0.338630	+	0.940920i	$0.390036\pi$
$830$	7180.97	0.300307
$831$	−25892.2	−1.08085
$832$	81.8481	0.00341054
$833$	6002.41	0.249665
$834$	−25753.8	−1.06928
$835$	3997.51	0.165676
$836$	−1410.46	−0.0583514
$837$	−2546.30	−0.105153
$838$	24385.7	1.00524
$839$	−25244.4	−1.03878	−0.519388	−	0.854538i	$-0.673840\pi$
$839$	−25244.4	−1.03878	−0.519388	+	0.854538i	$0.673840\pi$
$840$	−1309.23	−0.0537771
$841$	−15269.9	−0.626096
$842$	34066.7	1.39432
$843$	−22564.9	−0.921916
$844$	−4715.37	−0.192310
$845$	−9168.15	−0.373247
$846$	−15047.7	−0.611526
$847$	9256.59	0.375514
$848$	14653.8	0.593412
$849$	44.4506	0.00179687
$850$	−10813.9	−0.436370
$851$	20455.8	0.823990
$852$	8924.68	0.358867
$853$	−30168.1	−1.21094	−0.605472	−	0.795867i	$-0.707016\pi$
$853$	−30168.1	−1.21094	−0.605472	+	0.795867i	$0.707016\pi$
$854$	−4912.61	−0.196846
$855$	4834.61	0.193380
$856$	−9597.44	−0.383217
$857$	−13393.6	−0.533857	−0.266929	−	0.963716i	$-0.586009\pi$
$857$	−13393.6	−0.533857	−0.266929	+	0.963716i	$0.586009\pi$
$858$	−593.230	−0.0236043
$859$	19060.4	0.757081	0.378541	−	0.925585i	$-0.376426\pi$
$859$	19060.4	0.757081	0.378541	+	0.925585i	$0.376426\pi$
$860$	−960.894	−0.0381002
$861$	10313.4	0.408222
$862$	45914.3	1.81421
$863$	−9466.86	−0.373413	−0.186707	−	0.982416i	$-0.559781\pi$
$863$	−9466.86	−0.373413	−0.186707	+	0.982416i	$0.559781\pi$
$864$	4913.00	0.193453
$865$	−7221.79	−0.283871
$866$	−25975.2	−1.01925
$867$	30278.3	1.18605
$868$	2950.13	0.115362
$869$	72.7461	0.00283975
$870$	−5058.03	−0.197107
$871$	5909.15	0.229878
$872$	−9736.39	−0.378115
$873$	−9042.97	−0.350582
$874$	−79903.8	−3.09243
$875$	−875.000	−0.0338062
$876$	8329.37	0.321259
$877$	37740.6	1.45315	0.726573	−	0.687090i	$-0.241112\pi$
$877$	37740.6	1.45315	0.726573	+	0.687090i	$0.241112\pi$
$878$	−24397.3	−0.937778
$879$	20740.2	0.795845
$880$	1171.87	0.0448905
$881$	25991.5	0.993957	0.496979	−	0.867763i	$-0.334443\pi$
$881$	25991.5	0.993957	0.496979	+	0.867763i	$0.334443\pi$
$882$	−1557.23	−0.0594496
$883$	39420.3	1.50238	0.751189	−	0.660087i	$-0.229481\pi$
$883$	39420.3	1.50238	0.751189	+	0.660087i	$0.229481\pi$
$884$	−10435.2	−0.397030
$885$	−11409.2	−0.433352
$886$	52305.0	1.98332
$887$	46005.2	1.74149	0.870745	−	0.491735i	$-0.163637\pi$
$887$	46005.2	1.74149	0.870745	+	0.491735i	$0.163637\pi$
$888$	3632.95	0.137290
$889$	13131.9	0.495421
$890$	−4621.38	−0.174055
$891$	−237.957	−0.00894710
$892$	20895.8	0.784353
$893$	50870.2	1.90628
$894$	−24805.2	−0.927975
$895$	16717.5	0.624361
$896$	10083.8	0.375978
$897$	−12044.8	−0.448345
$898$	37622.6	1.39809
$899$	−9005.81	−0.334105
$900$	1005.50	0.0372406
$901$	−22500.1	−0.831950
$902$	−5094.58	−0.188061
$903$	903.081	0.0332809
$904$	−13910.8	−0.511801
$905$	11259.1	0.413551
$906$	22289.2	0.817340
$907$	−2838.97	−0.103932	−0.0519661	−	0.998649i	$-0.516549\pi$
$907$	−2838.97	−0.103932	−0.0519661	+	0.998649i	$0.516549\pi$
$908$	24324.6	0.889030
$909$	−1159.84	−0.0423208
$910$	−2355.90	−0.0858211
$911$	39890.9	1.45076	0.725382	−	0.688347i	$-0.241663\pi$
$911$	39890.9	1.45076	0.725382	+	0.688347i	$0.241663\pi$
$912$	−25713.7	−0.933626
$913$	1194.85	0.0433119
$914$	20675.3	0.748226
$915$	−2981.21	−0.107711
$916$	−2396.67	−0.0864500
$917$	−2549.42	−0.0918094
$918$	−11679.0	−0.419897
$919$	−646.475	−0.0232048	−0.0116024	−	0.999933i	$-0.503693\pi$
$919$	−646.475	−0.0232048	−0.0116024	+	0.999933i	$0.503693\pi$
$920$	13131.1	0.470566
$921$	−22932.4	−0.820463
$922$	−11316.3	−0.404213
$923$	−12689.6	−0.452528
$924$	275.696	0.00981574
$925$	2428.02	0.0863056
$926$	−1312.37	−0.0465737
$927$	7254.07	0.257017
$928$	17376.4	0.614665
$929$	51188.2	1.80778	0.903892	−	0.427760i	$-0.140697\pi$
$929$	51188.2	1.80778	0.903892	+	0.427760i	$0.140697\pi$
$930$	4995.17	0.176127
$931$	5264.35	0.185319
$932$	−819.993	−0.0288195
$933$	22782.0	0.799409
$934$	69747.8	2.44349
$935$	−1799.34	−0.0629355
$936$	−2139.16	−0.0747017
$937$	29786.1	1.03849	0.519247	−	0.854624i	$-0.326212\pi$
$937$	29786.1	1.03849	0.519247	+	0.854624i	$0.326212\pi$
$938$	−7662.36	−0.266722
$939$	−27383.5	−0.951680
$940$	10579.9	0.367105
$941$	−44817.4	−1.55261	−0.776304	−	0.630358i	$-0.782908\pi$
$941$	−44817.4	−1.55261	−0.776304	+	0.630358i	$0.782908\pi$
$942$	6286.82	0.217448
$943$	−103439.	−3.57206
$944$	60682.0	2.09219
$945$	−945.000	−0.0325300
$946$	−446.103	−0.0153320
$947$	54697.1	1.87689	0.938446	−	0.345425i	$-0.112265\pi$
$947$	54697.1	1.87689	0.938446	+	0.345425i	$0.112265\pi$
$948$	−331.983	−0.0113737
$949$	−11843.2	−0.405105
$950$	−9484.24	−0.323905
$951$	−14789.4	−0.504290
$952$	−10691.9	−0.363998
$953$	−7577.51	−0.257565	−0.128783	−	0.991673i	$-0.541107\pi$
$953$	−7577.51	−0.257565	−0.128783	+	0.991673i	$0.541107\pi$
$954$	5837.29	0.198102
$955$	−5009.63	−0.169746
$956$	2874.46	0.0972454
$957$	−841.612	−0.0284278
$958$	73313.4	2.47249
$959$	−11221.9	−0.377868
$960$	−64.4059	−0.00216530
$961$	−20897.1	−0.701457
$962$	6537.32	0.219097
$963$	−6927.41	−0.231810
$964$	−25721.1	−0.859357
$965$	−20274.8	−0.676342
$966$	15618.4	0.520202
$967$	50779.0	1.68867	0.844334	−	0.535817i	$-0.179996\pi$
$967$	50779.0	1.68867	0.844334	+	0.535817i	$0.179996\pi$
$968$	−16488.5	−0.547478
$969$	39482.0	1.30892
$970$	17739.9	0.587212
$971$	−15313.2	−0.506102	−0.253051	−	0.967453i	$-0.581434\pi$
$971$	−15313.2	−0.506102	−0.253051	+	0.967453i	$0.581434\pi$
$972$	1085.94	0.0358348
$973$	−17017.9	−0.560707
$974$	−62315.9	−2.05003
$975$	−1429.67	−0.0469601
$976$	15856.1	0.520021
$977$	46620.4	1.52663	0.763316	−	0.646025i	$-0.223570\pi$
$977$	46620.4	1.52663	0.763316	+	0.646025i	$0.223570\pi$
$978$	−23079.9	−0.754615
$979$	−768.957	−0.0251031
$980$	1094.87	0.0356882
$981$	−7027.70	−0.228723
$982$	19906.6	0.646889
$983$	−2824.37	−0.0916414	−0.0458207	−	0.998950i	$-0.514590\pi$
$983$	−2824.37	−0.0916414	−0.0458207	+	0.998950i	$0.514590\pi$
$984$	−18370.9	−0.595165
$985$	−25701.1	−0.831377
$986$	−41306.6	−1.33415
$987$	−9943.38	−0.320670
$988$	−9152.11	−0.294704
$989$	−9057.59	−0.291218
$990$	466.810	0.0149860
$991$	16951.4	0.543370	0.271685	−	0.962386i	$-0.412419\pi$
$991$	16951.4	0.543370	0.271685	+	0.962386i	$0.412419\pi$
$992$	−17160.5	−0.549239
$993$	3665.00	0.117125
$994$	16454.5	0.525056
$995$	2928.15	0.0932952
$996$	−5452.79	−0.173472
$997$	23847.8	0.757540	0.378770	−	0.925491i	$-0.376347\pi$
$997$	23847.8	0.757540	0.378770	+	0.925491i	$0.376347\pi$
$998$	61703.4	1.95710
$999$	2622.26	0.0830476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.a.f.1.1	✓	2
3.2	odd	2		315.4.a.i.1.2		2
4.3	odd	2		1680.4.a.bg.1.1		2
5.2	odd	4		525.4.d.h.274.2		4
5.3	odd	4		525.4.d.h.274.3		4
5.4	even	2		525.4.a.k.1.2		2
7.6	odd	2		735.4.a.p.1.1		2
15.14	odd	2		1575.4.a.w.1.1		2
21.20	even	2		2205.4.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.f.1.1	✓	2	1.1	even	1	trivial
315.4.a.i.1.2		2	3.2	odd	2
525.4.a.k.1.2		2	5.4	even	2
525.4.d.h.274.2		4	5.2	odd	4
525.4.d.h.274.3		4	5.3	odd	4
735.4.a.p.1.1		2	7.6	odd	2
1575.4.a.w.1.1		2	15.14	odd	2
1680.4.a.bg.1.1		2	4.3	odd	2
2205.4.a.z.1.2		2	21.20	even	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q-3.53113 q^{2} +3.00000 q^{3} +4.46887 q^{4} +5.00000 q^{5} -10.5934 q^{6} -7.00000 q^{7} +12.4689 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.53113 q^{2} +3.00000 q^{3} +4.46887 q^{4} +5.00000 q^{5} -10.5934 q^{6} -7.00000 q^{7} +12.4689 q^{8} +9.00000 q^{9} -17.6556 q^{10} -2.93774 q^{11} +13.4066 q^{12} -19.0623 q^{13} +24.7179 q^{14} +15.0000 q^{15} -79.7802 q^{16} +122.498 q^{17} -31.7802 q^{18} +107.436 q^{19} +22.3444 q^{20} -21.0000 q^{21} +10.3735 q^{22} +210.623 q^{23} +37.4066 q^{24} +25.0000 q^{25} +67.3113 q^{26} +27.0000 q^{27} -31.2821 q^{28} +95.4942 q^{29} -52.9669 q^{30} -94.3074 q^{31} +181.963 q^{32} -8.81323 q^{33} -432.556 q^{34} -35.0000 q^{35} +40.2198 q^{36} +97.1206 q^{37} -379.370 q^{38} -57.1868 q^{39} +62.3444 q^{40} -491.113 q^{41} +74.1537 q^{42} -43.0039 q^{43} -13.1284 q^{44} +45.0000 q^{45} -743.735 q^{46} +473.494 q^{47} -239.340 q^{48} +49.0000 q^{49} -88.2782 q^{50} +367.494 q^{51} -85.1868 q^{52} -183.677 q^{53} -95.3405 q^{54} -14.6887 q^{55} -87.2821 q^{56} +322.307 q^{57} -337.202 q^{58} -760.615 q^{59} +67.0331 q^{60} -198.747 q^{61} +333.012 q^{62} -63.0000 q^{63} -4.29373 q^{64} -95.3113 q^{65} +31.1206 q^{66} -309.992 q^{67} +547.428 q^{68} +631.868 q^{69} +123.590 q^{70} +665.693 q^{71} +112.220 q^{72} +621.288 q^{73} -342.945 q^{74} +75.0000 q^{75} +480.117 q^{76} +20.5642 q^{77} +201.934 q^{78} -24.7626 q^{79} -398.901 q^{80} +81.0000 q^{81} +1734.18 q^{82} -406.724 q^{83} -93.8463 q^{84} +612.490 q^{85} +151.852 q^{86} +286.483 q^{87} -36.6303 q^{88} +261.751 q^{89} -158.901 q^{90} +133.436 q^{91} +941.245 q^{92} -282.922 q^{93} -1671.97 q^{94} +537.179 q^{95} +545.889 q^{96} -1004.77 q^{97} -173.025 q^{98} -26.4397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 6 q^{3} + 17 q^{4} + 10 q^{5} + 3 q^{6} - 14 q^{7} + 33 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + q^2 + 6 * q^3 + 17 * q^4 + 10 * q^5 + 3 * q^6 - 14 * q^7 + 33 * q^8 + 18 * q^9	\( 2 q + q^{2} + 6 q^{3} + 17 q^{4} + 10 q^{5} + 3 q^{6} - 14 q^{7} + 33 q^{8} + 18 q^{9} + 5 q^{10} - 22 q^{11} + 51 q^{12} - 22 q^{13} - 7 q^{14} + 30 q^{15} - 87 q^{16} + 116 q^{17} + 9 q^{18} + 102 q^{19} + 85 q^{20} - 42 q^{21} - 76 q^{22} + 260 q^{23} + 99 q^{24} + 50 q^{25} + 54 q^{26} + 54 q^{27} - 119 q^{28} - 196 q^{29} + 15 q^{30} + 150 q^{31} - 15 q^{32} - 66 q^{33} - 462 q^{34} - 70 q^{35} + 153 q^{36} - 96 q^{37} - 404 q^{38} - 66 q^{39} + 165 q^{40} - 176 q^{41} - 21 q^{42} - 344 q^{43} - 252 q^{44} + 90 q^{45} - 520 q^{46} + 560 q^{47} - 261 q^{48} + 98 q^{49} + 25 q^{50} + 348 q^{51} - 122 q^{52} + 326 q^{53} + 27 q^{54} - 110 q^{55} - 231 q^{56} + 306 q^{57} - 1658 q^{58} - 844 q^{59} + 255 q^{60} - 204 q^{61} + 1440 q^{62} - 126 q^{63} - 839 q^{64} - 110 q^{65} - 228 q^{66} - 104 q^{67} + 466 q^{68} + 780 q^{69} - 35 q^{70} + 1670 q^{71} + 297 q^{72} - 386 q^{73} - 1218 q^{74} + 150 q^{75} + 412 q^{76} + 154 q^{77} + 162 q^{78} - 888 q^{79} - 435 q^{80} + 162 q^{81} + 3162 q^{82} + 928 q^{83} - 357 q^{84} + 580 q^{85} - 1212 q^{86} - 588 q^{87} - 428 q^{88} + 588 q^{89} + 45 q^{90} + 154 q^{91} + 1560 q^{92} + 450 q^{93} - 1280 q^{94} + 510 q^{95} - 45 q^{96} + 522 q^{97} + 49 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 + 6 * q^3 + 17 * q^4 + 10 * q^5 + 3 * q^6 - 14 * q^7 + 33 * q^8 + 18 * q^9 + 5 * q^10 - 22 * q^11 + 51 * q^12 - 22 * q^13 - 7 * q^14 + 30 * q^15 - 87 * q^16 + 116 * q^17 + 9 * q^18 + 102 * q^19 + 85 * q^20 - 42 * q^21 - 76 * q^22 + 260 * q^23 + 99 * q^24 + 50 * q^25 + 54 * q^26 + 54 * q^27 - 119 * q^28 - 196 * q^29 + 15 * q^30 + 150 * q^31 - 15 * q^32 - 66 * q^33 - 462 * q^34 - 70 * q^35 + 153 * q^36 - 96 * q^37 - 404 * q^38 - 66 * q^39 + 165 * q^40 - 176 * q^41 - 21 * q^42 - 344 * q^43 - 252 * q^44 + 90 * q^45 - 520 * q^46 + 560 * q^47 - 261 * q^48 + 98 * q^49 + 25 * q^50 + 348 * q^51 - 122 * q^52 + 326 * q^53 + 27 * q^54 - 110 * q^55 - 231 * q^56 + 306 * q^57 - 1658 * q^58 - 844 * q^59 + 255 * q^60 - 204 * q^61 + 1440 * q^62 - 126 * q^63 - 839 * q^64 - 110 * q^65 - 228 * q^66 - 104 * q^67 + 466 * q^68 + 780 * q^69 - 35 * q^70 + 1670 * q^71 + 297 * q^72 - 386 * q^73 - 1218 * q^74 + 150 * q^75 + 412 * q^76 + 154 * q^77 + 162 * q^78 - 888 * q^79 - 435 * q^80 + 162 * q^81 + 3162 * q^82 + 928 * q^83 - 357 * q^84 + 580 * q^85 - 1212 * q^86 - 588 * q^87 - 428 * q^88 + 588 * q^89 + 45 * q^90 + 154 * q^91 + 1560 * q^92 + 450 * q^93 - 1280 * q^94 + 510 * q^95 - 45 * q^96 + 522 * q^97 + 49 * q^98 - 198 * q^99

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