LMFDB - Embedded newform 105.4.a.g.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{41}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 10 $ x^2 - x - 10
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			$-2.70156$ 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)

$f(q)$	$=$	$q-1.70156 q^{2} +3.00000 q^{3} -5.10469 q^{4} -5.00000 q^{5} -5.10469 q^{6} +7.00000 q^{7} +22.2984 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.70156 q^{2} +3.00000 q^{3} -5.10469 q^{4} -5.00000 q^{5} -5.10469 q^{6} +7.00000 q^{7} +22.2984 q^{8} +9.00000 q^{9} +8.50781 q^{10} +37.4031 q^{11} -15.3141 q^{12} +29.0156 q^{13} -11.9109 q^{14} -15.0000 q^{15} +2.89531 q^{16} +58.4187 q^{17} -15.3141 q^{18} -54.5969 q^{19} +25.5234 q^{20} +21.0000 q^{21} -63.6437 q^{22} +161.675 q^{23} +66.8953 q^{24} +25.0000 q^{25} -49.3719 q^{26} +27.0000 q^{27} -35.7328 q^{28} +137.581 q^{29} +25.5234 q^{30} +154.659 q^{31} -183.314 q^{32} +112.209 q^{33} -99.4031 q^{34} -35.0000 q^{35} -45.9422 q^{36} -350.125 q^{37} +92.9000 q^{38} +87.0469 q^{39} -111.492 q^{40} +353.769 q^{41} -35.7328 q^{42} -518.156 q^{43} -190.931 q^{44} -45.0000 q^{45} -275.100 q^{46} -542.219 q^{47} +8.68594 q^{48} +49.0000 q^{49} -42.5391 q^{50} +175.256 q^{51} -148.116 q^{52} +305.309 q^{53} -45.9422 q^{54} -187.016 q^{55} +156.089 q^{56} -163.791 q^{57} -234.103 q^{58} +14.6813 q^{59} +76.5703 q^{60} -171.069 q^{61} -263.163 q^{62} +63.0000 q^{63} +288.758 q^{64} -145.078 q^{65} -190.931 q^{66} +551.956 q^{67} -298.209 q^{68} +485.025 q^{69} +59.5547 q^{70} -120.334 q^{71} +200.686 q^{72} +284.659 q^{73} +595.759 q^{74} +75.0000 q^{75} +278.700 q^{76} +261.822 q^{77} -148.116 q^{78} +941.612 q^{79} -14.4766 q^{80} +81.0000 q^{81} -601.959 q^{82} +377.150 q^{83} -107.198 q^{84} -292.094 q^{85} +881.675 q^{86} +412.744 q^{87} +834.031 q^{88} -677.725 q^{89} +76.5703 q^{90} +203.109 q^{91} -825.300 q^{92} +463.978 q^{93} +922.619 q^{94} +272.984 q^{95} -549.942 q^{96} -1225.03 q^{97} -83.3765 q^{98} +336.628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} - 10 q^{5} + 9 q^{6} + 14 q^{7} + 51 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 - 10 * q^5 + 9 * q^6 + 14 * q^7 + 51 * q^8 + 18 * q^9	\( 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} - 10 q^{5} + 9 q^{6} + 14 q^{7} + 51 q^{8} + 18 q^{9} - 15 q^{10} + 62 q^{11} + 27 q^{12} - 6 q^{13} + 21 q^{14} - 30 q^{15} + 25 q^{16} + 40 q^{17} + 27 q^{18} - 122 q^{19} - 45 q^{20} + 42 q^{21} + 52 q^{22} + 16 q^{23} + 153 q^{24} + 50 q^{25} - 214 q^{26} + 54 q^{27} + 63 q^{28} + 352 q^{29} - 45 q^{30} + 66 q^{31} - 309 q^{32} + 186 q^{33} - 186 q^{34} - 70 q^{35} + 81 q^{36} - 188 q^{37} - 224 q^{38} - 18 q^{39} - 255 q^{40} + 16 q^{41} + 63 q^{42} - 396 q^{43} + 156 q^{44} - 90 q^{45} - 960 q^{46} - 188 q^{47} + 75 q^{48} + 98 q^{49} + 75 q^{50} + 120 q^{51} - 642 q^{52} + 982 q^{53} + 81 q^{54} - 310 q^{55} + 357 q^{56} - 366 q^{57} + 774 q^{58} + 516 q^{59} - 135 q^{60} - 880 q^{61} - 680 q^{62} + 126 q^{63} - 479 q^{64} + 30 q^{65} + 156 q^{66} - 356 q^{67} - 558 q^{68} + 48 q^{69} - 105 q^{70} + 310 q^{71} + 459 q^{72} + 326 q^{73} + 1358 q^{74} + 150 q^{75} - 672 q^{76} + 434 q^{77} - 642 q^{78} + 1832 q^{79} - 125 q^{80} + 162 q^{81} - 2190 q^{82} - 680 q^{83} + 189 q^{84} - 200 q^{85} + 1456 q^{86} + 1056 q^{87} + 1540 q^{88} + 796 q^{89} - 135 q^{90} - 42 q^{91} - 2880 q^{92} + 198 q^{93} + 2588 q^{94} + 610 q^{95} - 927 q^{96} - 670 q^{97} + 147 q^{98} + 558 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 - 10 * q^5 + 9 * q^6 + 14 * q^7 + 51 * q^8 + 18 * q^9 - 15 * q^10 + 62 * q^11 + 27 * q^12 - 6 * q^13 + 21 * q^14 - 30 * q^15 + 25 * q^16 + 40 * q^17 + 27 * q^18 - 122 * q^19 - 45 * q^20 + 42 * q^21 + 52 * q^22 + 16 * q^23 + 153 * q^24 + 50 * q^25 - 214 * q^26 + 54 * q^27 + 63 * q^28 + 352 * q^29 - 45 * q^30 + 66 * q^31 - 309 * q^32 + 186 * q^33 - 186 * q^34 - 70 * q^35 + 81 * q^36 - 188 * q^37 - 224 * q^38 - 18 * q^39 - 255 * q^40 + 16 * q^41 + 63 * q^42 - 396 * q^43 + 156 * q^44 - 90 * q^45 - 960 * q^46 - 188 * q^47 + 75 * q^48 + 98 * q^49 + 75 * q^50 + 120 * q^51 - 642 * q^52 + 982 * q^53 + 81 * q^54 - 310 * q^55 + 357 * q^56 - 366 * q^57 + 774 * q^58 + 516 * q^59 - 135 * q^60 - 880 * q^61 - 680 * q^62 + 126 * q^63 - 479 * q^64 + 30 * q^65 + 156 * q^66 - 356 * q^67 - 558 * q^68 + 48 * q^69 - 105 * q^70 + 310 * q^71 + 459 * q^72 + 326 * q^73 + 1358 * q^74 + 150 * q^75 - 672 * q^76 + 434 * q^77 - 642 * q^78 + 1832 * q^79 - 125 * q^80 + 162 * q^81 - 2190 * q^82 - 680 * q^83 + 189 * q^84 - 200 * q^85 + 1456 * q^86 + 1056 * q^87 + 1540 * q^88 + 796 * q^89 - 135 * q^90 - 42 * q^91 - 2880 * q^92 + 198 * q^93 + 2588 * q^94 + 610 * q^95 - 927 * q^96 - 670 * q^97 + 147 * q^98 + 558 * 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 $

$2$	−1.70156	−0.601593	−0.300797	−	0.953688i	$-0.597253\pi$
$2$	−1.70156	−0.601593	−0.300797	+	0.953688i	$0.597253\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−5.10469	−0.638086
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−5.10469	−0.347330
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	22.2984	0.985461
$9$	9.00000	0.333333
$10$	8.50781	0.269041
$11$	37.4031	1.02522	0.512612	−	0.858620i	$-0.328678\pi$
$11$	37.4031	1.02522	0.512612	+	0.858620i	$0.328678\pi$
$12$	−15.3141	−0.368399
$13$	29.0156	0.619037	0.309519	−	0.950893i	$-0.399832\pi$
$13$	29.0156	0.619037	0.309519	+	0.950893i	$0.399832\pi$
$14$	−11.9109	−0.227381
$15$	−15.0000	−0.258199
$16$	2.89531	0.0452393
$17$	58.4187	0.833449	0.416724	−	0.909033i	$-0.363178\pi$
$17$	58.4187	0.833449	0.416724	+	0.909033i	$0.363178\pi$
$18$	−15.3141	−0.200531
$19$	−54.5969	−0.659231	−0.329615	−	0.944115i	$-0.606919\pi$
$19$	−54.5969	−0.659231	−0.329615	+	0.944115i	$0.606919\pi$
$20$	25.5234	0.285361
$21$	21.0000	0.218218
$22$	−63.6437	−0.616768
$23$	161.675	1.46572	0.732860	−	0.680379i	$-0.238185\pi$
$23$	161.675	1.46572	0.732860	+	0.680379i	$0.238185\pi$
$24$	66.8953	0.568956
$25$	25.0000	0.200000
$26$	−49.3719	−0.372409
$27$	27.0000	0.192450
$28$	−35.7328	−0.241174
$29$	137.581	0.880972	0.440486	−	0.897759i	$-0.354806\pi$
$29$	137.581	0.880972	0.440486	+	0.897759i	$0.354806\pi$
$30$	25.5234	0.155331
$31$	154.659	0.896053	0.448026	−	0.894020i	$-0.352127\pi$
$31$	154.659	0.896053	0.448026	+	0.894020i	$0.352127\pi$
$32$	−183.314	−1.01268
$33$	112.209	0.591913
$34$	−99.4031	−0.501397
$35$	−35.0000	−0.169031
$36$	−45.9422	−0.212695
$37$	−350.125	−1.55568	−0.777840	−	0.628462i	$-0.783685\pi$
$37$	−350.125	−1.55568	−0.777840	+	0.628462i	$0.783685\pi$
$38$	92.9000	0.396589
$39$	87.0469	0.357401
$40$	−111.492	−0.440712
$41$	353.769	1.34755	0.673773	−	0.738938i	$-0.264673\pi$
$41$	353.769	1.34755	0.673773	+	0.738938i	$0.264673\pi$
$42$	−35.7328	−0.131278
$43$	−518.156	−1.83763	−0.918815	−	0.394689i	$-0.870852\pi$
$43$	−518.156	−1.83763	−0.918815	+	0.394689i	$0.870852\pi$
$44$	−190.931	−0.654181
$45$	−45.0000	−0.149071
$46$	−275.100	−0.881767
$47$	−542.219	−1.68278	−0.841391	−	0.540427i	$-0.818263\pi$
$47$	−542.219	−1.68278	−0.841391	+	0.540427i	$0.818263\pi$
$48$	8.68594	0.0261189
$49$	49.0000	0.142857
$50$	−42.5391	−0.120319
$51$	175.256	0.481192
$52$	−148.116	−0.394999
$53$	305.309	0.791273	0.395637	−	0.918407i	$-0.370524\pi$
$53$	305.309	0.791273	0.395637	+	0.918407i	$0.370524\pi$
$54$	−45.9422	−0.115777
$55$	−187.016	−0.458494
$56$	156.089	0.372469
$57$	−163.791	−0.380607
$58$	−234.103	−0.529987
$59$	14.6813	0.0323956	0.0161978	−	0.999869i	$-0.494844\pi$
$59$	14.6813	0.0323956	0.0161978	+	0.999869i	$0.494844\pi$
$60$	76.5703	0.164753
$61$	−171.069	−0.359067	−0.179534	−	0.983752i	$-0.557459\pi$
$61$	−171.069	−0.359067	−0.179534	+	0.983752i	$0.557459\pi$
$62$	−263.163	−0.539059
$63$	63.0000	0.125988
$64$	288.758	0.563980
$65$	−145.078	−0.276842
$66$	−190.931	−0.356091
$67$	551.956	1.00645	0.503225	−	0.864155i	$-0.332147\pi$
$67$	551.956	1.00645	0.503225	+	0.864155i	$0.332147\pi$
$68$	−298.209	−0.531812
$69$	485.025	0.846234
$70$	59.5547	0.101688
$71$	−120.334	−0.201142	−0.100571	−	0.994930i	$-0.532067\pi$
$71$	−120.334	−0.201142	−0.100571	+	0.994930i	$0.532067\pi$
$72$	200.686	0.328487
$73$	284.659	0.456395	0.228198	−	0.973615i	$-0.426717\pi$
$73$	284.659	0.456395	0.228198	+	0.973615i	$0.426717\pi$
$74$	595.759	0.935887
$75$	75.0000	0.115470
$76$	278.700	0.420646
$77$	261.822	0.387498
$78$	−148.116	−0.215010
$79$	941.612	1.34101	0.670504	−	0.741906i	$-0.266078\pi$
$79$	941.612	1.34101	0.670504	+	0.741906i	$0.266078\pi$
$80$	−14.4766	−0.0202316
$81$	81.0000	0.111111
$82$	−601.959	−0.810674
$83$	377.150	0.498766	0.249383	−	0.968405i	$-0.419772\pi$
$83$	377.150	0.498766	0.249383	+	0.968405i	$0.419772\pi$
$84$	−107.198	−0.139242
$85$	−292.094	−0.372730
$86$	881.675	1.10551
$87$	412.744	0.508630
$88$	834.031	1.01032
$89$	−677.725	−0.807176	−0.403588	−	0.914941i	$-0.632237\pi$
$89$	−677.725	−0.807176	−0.403588	+	0.914941i	$0.632237\pi$
$90$	76.5703	0.0896802
$91$	203.109	0.233974
$92$	−825.300	−0.935255
$93$	463.978	0.517336
$94$	922.619	1.01235
$95$	272.984	0.294817
$96$	−549.942	−0.584669
$97$	−1225.03	−1.28230	−0.641151	−	0.767414i	$-0.721543\pi$
$97$	−1225.03	−1.28230	−0.641151	+	0.767414i	$0.721543\pi$
$98$	−83.3765	−0.0859419
$99$	336.628	0.341741
$100$	−127.617	−0.127617
$101$	−338.144	−0.333134	−0.166567	−	0.986030i	$-0.553268\pi$
$101$	−338.144	−0.333134	−0.166567	+	0.986030i	$0.553268\pi$
$102$	−298.209	−0.289482
$103$	−566.700	−0.542122	−0.271061	−	0.962562i	$-0.587375\pi$
$103$	−566.700	−0.542122	−0.271061	+	0.962562i	$0.587375\pi$
$104$	647.003	0.610037
$105$	−105.000	−0.0975900
$106$	−519.503	−0.476024
$107$	−562.531	−0.508242	−0.254121	−	0.967172i	$-0.581786\pi$
$107$	−562.531	−0.508242	−0.254121	+	0.967172i	$0.581786\pi$
$108$	−137.827	−0.122800
$109$	1830.79	1.60879	0.804396	−	0.594094i	$-0.202489\pi$
$109$	1830.79	1.60879	0.804396	+	0.594094i	$0.202489\pi$
$110$	318.219	0.275827
$111$	−1050.37	−0.898173
$112$	20.2672	0.0170988
$113$	−31.8032	−0.0264761	−0.0132380	−	0.999912i	$-0.504214\pi$
$113$	−31.8032	−0.0264761	−0.0132380	+	0.999912i	$0.504214\pi$
$114$	278.700	0.228971
$115$	−808.375	−0.655490
$116$	−702.309	−0.562136
$117$	261.141	0.206346
$118$	−24.9811	−0.0194890
$119$	408.931	0.315014
$120$	−334.477	−0.254445
$121$	67.9937	0.0510847
$122$	291.084	0.216012
$123$	1061.31	0.778006
$124$	−789.488	−0.571759
$125$	−125.000	−0.0894427
$126$	−107.198	−0.0757936
$127$	2220.81	1.55169	0.775847	−	0.630921i	$-0.217323\pi$
$127$	2220.81	1.55169	0.775847	+	0.630921i	$0.217323\pi$
$128$	975.173	0.673390
$129$	−1554.47	−1.06096
$130$	246.859	0.166546
$131$	646.512	0.431191	0.215596	−	0.976483i	$-0.430831\pi$
$131$	646.512	0.431191	0.215596	+	0.976483i	$0.430831\pi$
$132$	−572.794	−0.377692
$133$	−382.178	−0.249166
$134$	−939.188	−0.605474
$135$	−135.000	−0.0860663
$136$	1302.65	0.821331
$137$	−896.009	−0.558768	−0.279384	−	0.960179i	$-0.590130\pi$
$137$	−896.009	−0.558768	−0.279384	+	0.960179i	$0.590130\pi$
$138$	−825.300	−0.509088
$139$	−2313.61	−1.41178	−0.705891	−	0.708320i	$-0.749453\pi$
$139$	−2313.61	−1.41178	−0.705891	+	0.708320i	$0.749453\pi$
$140$	178.664	0.107856
$141$	−1626.66	−0.971554
$142$	204.756	0.121005
$143$	1085.27	0.634652
$144$	26.0578	0.0150798
$145$	−687.906	−0.393983
$146$	−484.366	−0.274564
$147$	147.000	0.0824786
$148$	1787.28	0.992658
$149$	819.337	0.450488	0.225244	−	0.974302i	$-0.427682\pi$
$149$	819.337	0.450488	0.225244	+	0.974302i	$0.427682\pi$
$150$	−127.617	−0.0694660
$151$	534.744	0.288191	0.144095	−	0.989564i	$-0.453973\pi$
$151$	534.744	0.288191	0.144095	+	0.989564i	$0.453973\pi$
$152$	−1217.43	−0.649646
$153$	525.769	0.277816
$154$	−445.506	−0.233116
$155$	−773.297	−0.400727
$156$	−444.347	−0.228053
$157$	1564.76	0.795423	0.397711	−	0.917511i	$-0.369805\pi$
$157$	1564.76	0.795423	0.397711	+	0.917511i	$0.369805\pi$
$158$	−1602.21	−0.806741
$159$	915.928	0.456842
$160$	916.570	0.452883
$161$	1131.72	0.553990
$162$	−137.827	−0.0668437
$163$	−1114.31	−0.535455	−0.267728	−	0.963495i	$-0.586273\pi$
$163$	−1114.31	−0.535455	−0.267728	+	0.963495i	$0.586273\pi$
$164$	−1805.88	−0.859850
$165$	−561.047	−0.264712
$166$	−641.744	−0.300054
$167$	−1774.47	−0.822231	−0.411115	−	0.911583i	$-0.634861\pi$
$167$	−1774.47	−0.822231	−0.411115	+	0.911583i	$0.634861\pi$
$168$	468.267	0.215045
$169$	−1355.09	−0.616793
$170$	497.016	0.224232
$171$	−491.372	−0.219744
$172$	2645.02	1.17257
$173$	−4215.88	−1.85276	−0.926380	−	0.376590i	$-0.877097\pi$
$173$	−4215.88	−1.85276	−0.926380	+	0.376590i	$0.877097\pi$
$174$	−702.309	−0.305988
$175$	175.000	0.0755929
$176$	108.294	0.0463804
$177$	44.0438	0.0187036
$178$	1153.19	0.485592
$179$	−2430.70	−1.01497	−0.507483	−	0.861662i	$-0.669424\pi$
$179$	−2430.70	−1.01497	−0.507483	+	0.861662i	$0.669424\pi$
$180$	229.711	0.0951202
$181$	−2700.91	−1.10916	−0.554578	−	0.832132i	$-0.687120\pi$
$181$	−2700.91	−1.10916	−0.554578	+	0.832132i	$0.687120\pi$
$182$	−345.603	−0.140757
$183$	−513.206	−0.207308
$184$	3605.10	1.44441
$185$	1750.62	0.695722
$186$	−789.488	−0.311226
$187$	2185.04	0.854472
$188$	2767.86	1.07376
$189$	189.000	0.0727393
$190$	−464.500	−0.177360
$191$	3611.10	1.36801	0.684005	−	0.729478i	$-0.260237\pi$
$191$	3611.10	1.36801	0.684005	+	0.729478i	$0.260237\pi$
$192$	866.273	0.325614
$193$	−4468.33	−1.66651	−0.833257	−	0.552886i	$-0.813526\pi$
$193$	−4468.33	−1.66651	−0.833257	+	0.552886i	$0.813526\pi$
$194$	2084.47	0.771425
$195$	−435.234	−0.159835
$196$	−250.130	−0.0911551
$197$	−434.422	−0.157113	−0.0785566	−	0.996910i	$-0.525031\pi$
$197$	−434.422	−0.157113	−0.0785566	+	0.996910i	$0.525031\pi$
$198$	−572.794	−0.205589
$199$	−468.915	−0.167038	−0.0835189	−	0.996506i	$-0.526616\pi$
$199$	−468.915	−0.167038	−0.0835189	+	0.996506i	$0.526616\pi$
$200$	557.461	0.197092
$201$	1655.87	0.581074
$202$	575.372	0.200411
$203$	963.069	0.332976
$204$	−894.628	−0.307042
$205$	−1768.84	−0.602641
$206$	964.275	0.326137
$207$	1455.07	0.488573
$208$	84.0093	0.0280048
$209$	−2042.09	−0.675859
$210$	178.664	0.0587095
$211$	3735.51	1.21878	0.609392	−	0.792869i	$-0.291414\pi$
$211$	3735.51	1.21878	0.609392	+	0.792869i	$0.291414\pi$
$212$	−1558.51	−0.504900
$213$	−361.003	−0.116129
$214$	957.182	0.305755
$215$	2590.78	0.821813
$216$	602.058	0.189652
$217$	1082.62	0.338676
$218$	−3115.21	−0.967838
$219$	853.978	0.263500
$220$	954.656	0.292559
$221$	1695.06	0.515936
$222$	1787.28	0.540334
$223$	842.806	0.253087	0.126544	−	0.991961i	$-0.459612\pi$
$223$	842.806	0.253087	0.126544	+	0.991961i	$0.459612\pi$
$224$	−1283.20	−0.382756
$225$	225.000	0.0666667
$226$	54.1152	0.0159278
$227$	992.150	0.290094	0.145047	−	0.989425i	$-0.453667\pi$
$227$	992.150	0.290094	0.145047	+	0.989425i	$0.453667\pi$
$228$	836.100	0.242860
$229$	−6411.39	−1.85012	−0.925059	−	0.379825i	$-0.875984\pi$
$229$	−6411.39	−1.85012	−0.925059	+	0.379825i	$0.875984\pi$
$230$	1375.50	0.394338
$231$	785.466	0.223722
$232$	3067.85	0.868164
$233$	−2274.35	−0.639476	−0.319738	−	0.947506i	$-0.603595\pi$
$233$	−2274.35	−0.639476	−0.319738	+	0.947506i	$0.603595\pi$
$234$	−444.347	−0.124136
$235$	2711.09	0.752563
$236$	−74.9433	−0.0206712
$237$	2824.84	0.774232
$238$	−695.822	−0.189510
$239$	2863.12	0.774893	0.387447	−	0.921892i	$-0.373357\pi$
$239$	2863.12	0.774893	0.387447	+	0.921892i	$0.373357\pi$
$240$	−43.4297	−0.0116807
$241$	−5364.23	−1.43378	−0.716889	−	0.697187i	$-0.754435\pi$
$241$	−5364.23	−1.43378	−0.716889	+	0.697187i	$0.754435\pi$
$242$	−115.696	−0.0307322
$243$	243.000	0.0641500
$244$	873.252	0.229116
$245$	−245.000	−0.0638877
$246$	−1805.88	−0.468043
$247$	−1584.16	−0.408088
$248$	3448.66	0.883025
$249$	1131.45	0.287963
$250$	212.695	0.0538081
$251$	5569.81	1.40065	0.700325	−	0.713824i	$-0.253039\pi$
$251$	5569.81	1.40065	0.700325	+	0.713824i	$0.253039\pi$
$252$	−321.595	−0.0803913
$253$	6047.15	1.50269
$254$	−3778.85	−0.933489
$255$	−876.281	−0.215196
$256$	−3969.38	−0.969087
$257$	2095.36	0.508580	0.254290	−	0.967128i	$-0.418158\pi$
$257$	2095.36	0.508580	0.254290	+	0.967128i	$0.418158\pi$
$258$	2645.02	0.638264
$259$	−2450.87	−0.587992
$260$	740.578	0.176649
$261$	1238.23	0.293657
$262$	−1100.08	−0.259402
$263$	−7465.88	−1.75044	−0.875220	−	0.483724i	$-0.839284\pi$
$263$	−7465.88	−1.75044	−0.875220	+	0.483724i	$0.839284\pi$
$264$	2502.09	0.583308
$265$	−1526.55	−0.353868
$266$	650.300	0.149896
$267$	−2033.17	−0.466023
$268$	−2817.56	−0.642202
$269$	−6521.38	−1.47812	−0.739062	−	0.673637i	$-0.764731\pi$
$269$	−6521.38	−1.47812	−0.739062	+	0.673637i	$0.764731\pi$
$270$	229.711	0.0517769
$271$	2409.70	0.540144	0.270072	−	0.962840i	$-0.412952\pi$
$271$	2409.70	0.540144	0.270072	+	0.962840i	$0.412952\pi$
$272$	169.141	0.0377046
$273$	609.328	0.135085
$274$	1524.62	0.336151
$275$	935.078	0.205045
$276$	−2475.90	−0.539970
$277$	−2219.83	−0.481503	−0.240752	−	0.970587i	$-0.577394\pi$
$277$	−2219.83	−0.481503	−0.240752	+	0.970587i	$0.577394\pi$
$278$	3936.75	0.849319
$279$	1391.93	0.298684
$280$	−780.445	−0.166573
$281$	5838.56	1.23950	0.619749	−	0.784800i	$-0.287234\pi$
$281$	5838.56	1.23950	0.619749	+	0.784800i	$0.287234\pi$
$282$	2767.86	0.584480
$283$	−3645.04	−0.765636	−0.382818	−	0.923824i	$-0.625046\pi$
$283$	−3645.04	−0.765636	−0.382818	+	0.923824i	$0.625046\pi$
$284$	614.269	0.128346
$285$	818.953	0.170213
$286$	−1846.66	−0.381802
$287$	2476.38	0.509325
$288$	−1649.83	−0.337559
$289$	−1500.25	−0.305363
$290$	1170.52	0.237017
$291$	−3675.10	−0.740338
$292$	−1453.10	−0.291219
$293$	3777.91	0.753268	0.376634	−	0.926362i	$-0.377081\pi$
$293$	3777.91	0.753268	0.376634	+	0.926362i	$0.377081\pi$
$294$	−250.130	−0.0496186
$295$	−73.4064	−0.0144877
$296$	−7807.24	−1.53306
$297$	1009.88	0.197304
$298$	−1394.15	−0.271011
$299$	4691.10	0.907336
$300$	−382.851	−0.0736798
$301$	−3627.09	−0.694559
$302$	−909.900	−0.173374
$303$	−1014.43	−0.192335
$304$	−158.075	−0.0298231
$305$	855.344	0.160580
$306$	−894.628	−0.167132
$307$	−4799.64	−0.892281	−0.446140	−	0.894963i	$-0.647202\pi$
$307$	−4799.64	−0.892281	−0.446140	+	0.894963i	$0.647202\pi$
$308$	−1336.52	−0.247257
$309$	−1700.10	−0.312994
$310$	1315.81	0.241075
$311$	580.113	0.105772	0.0528861	−	0.998601i	$-0.483158\pi$
$311$	580.113	0.105772	0.0528861	+	0.998601i	$0.483158\pi$
$312$	1941.01	0.352205
$313$	−6114.78	−1.10424	−0.552121	−	0.833764i	$-0.686182\pi$
$313$	−6114.78	−1.10424	−0.552121	+	0.833764i	$0.686182\pi$
$314$	−2662.53	−0.478521
$315$	−315.000	−0.0563436
$316$	−4806.64	−0.855679
$317$	−4300.63	−0.761979	−0.380989	−	0.924579i	$-0.624417\pi$
$317$	−4300.63	−0.761979	−0.380989	+	0.924579i	$0.624417\pi$
$318$	−1558.51	−0.274833
$319$	5145.97	0.903194
$320$	−1443.79	−0.252220
$321$	−1687.59	−0.293434
$322$	−1925.70	−0.333277
$323$	−3189.48	−0.549435
$324$	−413.480	−0.0708984
$325$	725.391	0.123807
$326$	1896.06	0.322126
$327$	5492.38	0.928836
$328$	7888.49	1.32795
$329$	−3795.53	−0.636032
$330$	954.656	0.159249
$331$	−6687.54	−1.11051	−0.555257	−	0.831679i	$-0.687380\pi$
$331$	−6687.54	−1.11051	−0.555257	+	0.831679i	$0.687380\pi$
$332$	−1925.23	−0.318256
$333$	−3151.12	−0.518560
$334$	3019.37	0.494648
$335$	−2759.78	−0.450098
$336$	60.8016	0.00987202
$337$	5869.28	0.948723	0.474362	−	0.880330i	$-0.342679\pi$
$337$	5869.28	0.948723	0.474362	+	0.880330i	$0.342679\pi$
$338$	2305.78	0.371058
$339$	−95.4097	−0.0152860
$340$	1491.05	0.237833
$341$	5784.74	0.918655
$342$	836.100	0.132196
$343$	343.000	0.0539949
$344$	−11554.1	−1.81091
$345$	−2425.12	−0.378447
$346$	7173.58	1.11461
$347$	1937.22	0.299699	0.149850	−	0.988709i	$-0.452121\pi$
$347$	1937.22	0.299699	0.149850	+	0.988709i	$0.452121\pi$
$348$	−2106.93	−0.324549
$349$	−9748.82	−1.49525	−0.747625	−	0.664121i	$-0.768806\pi$
$349$	−9748.82	−1.49525	−0.747625	+	0.664121i	$0.768806\pi$
$350$	−297.773	−0.0454762
$351$	783.422	0.119134
$352$	−6856.52	−1.03822
$353$	−4576.61	−0.690052	−0.345026	−	0.938593i	$-0.612130\pi$
$353$	−4576.61	−0.690052	−0.345026	+	0.938593i	$0.612130\pi$
$354$	−74.9433	−0.0112520
$355$	601.672	0.0899533
$356$	3459.57	0.515048
$357$	1226.79	0.181873
$358$	4135.98	0.610596
$359$	10849.9	1.59509	0.797546	−	0.603258i	$-0.206131\pi$
$359$	10849.9	1.59509	0.797546	+	0.603258i	$0.206131\pi$
$360$	−1003.43	−0.146904
$361$	−3878.18	−0.565415
$362$	4595.77	0.667261
$363$	203.981	0.0294938
$364$	−1036.81	−0.149296
$365$	−1423.30	−0.204106
$366$	873.252	0.124715
$367$	11467.7	1.63108	0.815541	−	0.578699i	$-0.196439\pi$
$367$	11467.7	1.63108	0.815541	+	0.578699i	$0.196439\pi$
$368$	468.100	0.0663081
$369$	3183.92	0.449182
$370$	−2978.80	−0.418541
$371$	2137.17	0.299073
$372$	−2368.46	−0.330105
$373$	539.982	0.0749576	0.0374788	−	0.999297i	$-0.488067\pi$
$373$	539.982	0.0749576	0.0374788	+	0.999297i	$0.488067\pi$
$374$	−3717.99	−0.514044
$375$	−375.000	−0.0516398
$376$	−12090.6	−1.65832
$377$	3992.01	0.545355
$378$	−321.595	−0.0437595
$379$	8577.57	1.16253	0.581267	−	0.813713i	$-0.302557\pi$
$379$	8577.57	1.16253	0.581267	+	0.813713i	$0.302557\pi$
$380$	−1393.50	−0.188118
$381$	6662.44	0.895871
$382$	−6144.51	−0.822985
$383$	8627.96	1.15109	0.575546	−	0.817770i	$-0.304790\pi$
$383$	8627.96	1.15109	0.575546	+	0.817770i	$0.304790\pi$
$384$	2925.52	0.388782
$385$	−1309.11	−0.173295
$386$	7603.13	1.00256
$387$	−4663.41	−0.612543
$388$	6253.42	0.818219
$389$	9234.06	1.20356	0.601781	−	0.798661i	$-0.294458\pi$
$389$	9234.06	1.20356	0.601781	+	0.798661i	$0.294458\pi$
$390$	740.578	0.0961555
$391$	9444.85	1.22160
$392$	1092.62	0.140780
$393$	1939.54	0.248948
$394$	739.196	0.0945182
$395$	−4708.06	−0.599717
$396$	−1718.38	−0.218060
$397$	11618.0	1.46874	0.734372	−	0.678747i	$-0.237477\pi$
$397$	11618.0	1.46874	0.734372	+	0.678747i	$0.237477\pi$
$398$	797.889	0.100489
$399$	−1146.53	−0.143856
$400$	72.3828	0.00904786
$401$	11157.1	1.38942	0.694711	−	0.719289i	$-0.255532\pi$
$401$	11157.1	1.38942	0.694711	+	0.719289i	$0.255532\pi$
$402$	−2817.56	−0.349570
$403$	4487.54	0.554690
$404$	1726.12	0.212568
$405$	−405.000	−0.0496904
$406$	−1638.72	−0.200316
$407$	−13095.8	−1.59492
$408$	3907.94	0.474196
$409$	−7428.08	−0.898031	−0.449015	−	0.893524i	$-0.648225\pi$
$409$	−7428.08	−0.898031	−0.449015	+	0.893524i	$0.648225\pi$
$410$	3009.80	0.362545
$411$	−2688.03	−0.322605
$412$	2892.83	0.345921
$413$	102.769	0.0122444
$414$	−2475.90	−0.293922
$415$	−1885.75	−0.223055
$416$	−5318.97	−0.626885
$417$	−6940.83	−0.815093
$418$	3474.75	0.406592
$419$	9644.74	1.12453	0.562263	−	0.826959i	$-0.309931\pi$
$419$	9644.74	1.12453	0.562263	+	0.826959i	$0.309931\pi$
$420$	535.992	0.0622708
$421$	9918.18	1.14818	0.574088	−	0.818793i	$-0.305357\pi$
$421$	9918.18	1.14818	0.574088	+	0.818793i	$0.305357\pi$
$422$	−6356.21	−0.733212
$423$	−4879.97	−0.560927
$424$	6807.92	0.779769
$425$	1460.47	0.166690
$426$	614.269	0.0698625
$427$	−1197.48	−0.135715
$428$	2871.54	0.324302
$429$	3255.82	0.366417
$430$	−4408.37	−0.494397
$431$	−16324.1	−1.82437	−0.912185	−	0.409779i	$-0.865606\pi$
$431$	−16324.1	−1.82437	−0.912185	+	0.409779i	$0.865606\pi$
$432$	78.1735	0.00870630
$433$	−5168.75	−0.573659	−0.286829	−	0.957982i	$-0.592601\pi$
$433$	−5168.75	−0.573659	−0.286829	+	0.957982i	$0.592601\pi$
$434$	−1842.14	−0.203745
$435$	−2063.72	−0.227466
$436$	−9345.63	−1.02655
$437$	−8826.95	−0.966248
$438$	−1453.10	−0.158520
$439$	18339.0	1.99378	0.996892	−	0.0787782i	$-0.0251019\pi$
$439$	18339.0	1.99378	0.996892	+	0.0787782i	$0.0251019\pi$
$440$	−4170.16	−0.451828
$441$	441.000	0.0476190
$442$	−2884.24	−0.310383
$443$	−1613.28	−0.173023	−0.0865113	−	0.996251i	$-0.527572\pi$
$443$	−1613.28	−0.173023	−0.0865113	+	0.996251i	$0.527572\pi$
$444$	5361.83	0.573111
$445$	3388.62	0.360980
$446$	−1434.09	−0.152256
$447$	2458.01	0.260089
$448$	2021.30	0.213164
$449$	−886.750	−0.0932034	−0.0466017	−	0.998914i	$-0.514839\pi$
$449$	−886.750	−0.0932034	−0.0466017	+	0.998914i	$0.514839\pi$
$450$	−382.851	−0.0401062
$451$	13232.1	1.38154
$452$	162.345	0.0168940
$453$	1604.23	0.166387
$454$	−1688.21	−0.174518
$455$	−1015.55	−0.104636
$456$	−3652.28	−0.375073
$457$	7391.22	0.756557	0.378279	−	0.925692i	$-0.376516\pi$
$457$	7391.22	0.756557	0.378279	+	0.925692i	$0.376516\pi$
$458$	10909.4	1.11302
$459$	1577.31	0.160397
$460$	4126.50	0.418259
$461$	−7133.35	−0.720679	−0.360340	−	0.932821i	$-0.617339\pi$
$461$	−7133.35	−0.720679	−0.360340	+	0.932821i	$0.617339\pi$
$462$	−1336.52	−0.134590
$463$	14461.8	1.45162	0.725808	−	0.687897i	$-0.241466\pi$
$463$	14461.8	1.45162	0.725808	+	0.687897i	$0.241466\pi$
$464$	398.341	0.0398546
$465$	−2319.89	−0.231360
$466$	3869.95	0.384704
$467$	−16393.5	−1.62441	−0.812206	−	0.583370i	$-0.801734\pi$
$467$	−16393.5	−1.62441	−0.812206	+	0.583370i	$0.801734\pi$
$468$	−1333.04	−0.131666
$469$	3863.69	0.380403
$470$	−4613.09	−0.452737
$471$	4694.28	0.459238
$472$	327.370	0.0319246
$473$	−19380.7	−1.88398
$474$	−4806.64	−0.465772
$475$	−1364.92	−0.131846
$476$	−2087.47	−0.201006
$477$	2747.78	0.263758
$478$	−4871.77	−0.466171
$479$	−12991.4	−1.23923	−0.619617	−	0.784904i	$-0.712712\pi$
$479$	−12991.4	−1.23923	−0.619617	+	0.784904i	$0.712712\pi$
$480$	2749.71	0.261472
$481$	−10159.1	−0.963025
$482$	9127.57	0.862551
$483$	3395.17	0.319846
$484$	−347.087	−0.0325964
$485$	6125.17	0.573463
$486$	−413.480	−0.0385922
$487$	−12863.5	−1.19692	−0.598461	−	0.801152i	$-0.704221\pi$
$487$	−12863.5	−1.19692	−0.598461	+	0.801152i	$0.704221\pi$
$488$	−3814.57	−0.353847
$489$	−3342.92	−0.309145
$490$	416.883	0.0384344
$491$	−4898.10	−0.450200	−0.225100	−	0.974336i	$-0.572271\pi$
$491$	−4898.10	−0.450200	−0.225100	+	0.974336i	$0.572271\pi$
$492$	−5417.63	−0.496435
$493$	8037.32	0.734245
$494$	2695.55	0.245503
$495$	−1683.14	−0.152831
$496$	447.787	0.0405368
$497$	−842.340	−0.0760244
$498$	−1925.23	−0.173236
$499$	10308.0	0.924746	0.462373	−	0.886686i	$-0.346998\pi$
$499$	10308.0	0.924746	0.462373	+	0.886686i	$0.346998\pi$
$500$	638.086	0.0570721
$501$	−5323.41	−0.474715
$502$	−9477.37	−0.842621
$503$	−15119.6	−1.34026	−0.670130	−	0.742244i	$-0.733762\pi$
$503$	−15119.6	−1.34026	−0.670130	+	0.742244i	$0.733762\pi$
$504$	1404.80	0.124156
$505$	1690.72	0.148982
$506$	−10289.6	−0.904009
$507$	−4065.28	−0.356105
$508$	−11336.6	−0.990114
$509$	14183.8	1.23514	0.617571	−	0.786515i	$-0.288117\pi$
$509$	14183.8	1.23514	0.617571	+	0.786515i	$0.288117\pi$
$510$	1491.05	0.129460
$511$	1992.62	0.172501
$512$	−1047.24	−0.0903943
$513$	−1474.12	−0.126869
$514$	−3565.39	−0.305958
$515$	2833.50	0.242444
$516$	7935.07	0.676981
$517$	−20280.7	−1.72523
$518$	4170.32	0.353732
$519$	−12647.6	−1.06969
$520$	−3235.02	−0.272817
$521$	−7464.08	−0.627653	−0.313827	−	0.949480i	$-0.601611\pi$
$521$	−7464.08	−0.627653	−0.313827	+	0.949480i	$0.601611\pi$
$522$	−2106.93	−0.176662
$523$	−16642.9	−1.39148	−0.695739	−	0.718295i	$-0.744923\pi$
$523$	−16642.9	−1.39148	−0.695739	+	0.718295i	$0.744923\pi$
$524$	−3300.24	−0.275137
$525$	525.000	0.0436436
$526$	12703.7	1.05305
$527$	9035.01	0.746814
$528$	324.881	0.0267777
$529$	13971.8	1.14834
$530$	2597.51	0.212885
$531$	132.132	0.0107985
$532$	1950.90	0.158989
$533$	10264.8	0.834181
$534$	3459.57	0.280356
$535$	2812.66	0.227293
$536$	12307.8	0.991818
$537$	−7292.09	−0.585991
$538$	11096.5	0.889230
$539$	1832.75	0.146461
$540$	689.133	0.0549177
$541$	67.8755	0.00539408	0.00269704	−	0.999996i	$-0.499142\pi$
$541$	67.8755	0.00539408	0.00269704	+	0.999996i	$0.499142\pi$
$542$	−4100.26	−0.324947
$543$	−8102.74	−0.640372
$544$	−10709.0	−0.844014
$545$	−9153.97	−0.719473
$546$	−1036.81	−0.0812662
$547$	−9212.91	−0.720138	−0.360069	−	0.932926i	$-0.617247\pi$
$547$	−9212.91	−0.720138	−0.360069	+	0.932926i	$0.617247\pi$
$548$	4573.85	0.356542
$549$	−1539.62	−0.119689
$550$	−1591.09	−0.123354
$551$	−7511.51	−0.580764
$552$	10815.3	0.833931
$553$	6591.29	0.506854
$554$	3777.17	0.289669
$555$	5251.87	0.401675
$556$	11810.2	0.900838
$557$	16699.6	1.27035	0.635173	−	0.772370i	$-0.280929\pi$
$557$	16699.6	1.27035	0.635173	+	0.772370i	$0.280929\pi$
$558$	−2368.46	−0.179686
$559$	−15034.6	−1.13756
$560$	−101.336	−0.00764683
$561$	6555.13	0.493329
$562$	−9934.67	−0.745674
$563$	14772.8	1.10586	0.552931	−	0.833227i	$-0.313509\pi$
$563$	14772.8	1.10586	0.552931	+	0.833227i	$0.313509\pi$
$564$	8303.57	0.619935
$565$	159.016	0.0118405
$566$	6202.26	0.460601
$567$	567.000	0.0419961
$568$	−2683.27	−0.198217
$569$	5663.76	0.417289	0.208644	−	0.977992i	$-0.433095\pi$
$569$	5663.76	0.417289	0.208644	+	0.977992i	$0.433095\pi$
$570$	−1393.50	−0.102399
$571$	5579.58	0.408929	0.204464	−	0.978874i	$-0.434455\pi$
$571$	5579.58	0.408929	0.204464	+	0.978874i	$0.434455\pi$
$572$	−5539.99	−0.404962
$573$	10833.3	0.789821
$574$	−4213.72	−0.306406
$575$	4041.87	0.293144
$576$	2598.82	0.187993
$577$	−2301.23	−0.166034	−0.0830170	−	0.996548i	$-0.526456\pi$
$577$	−2301.23	−0.166034	−0.0830170	+	0.996548i	$0.526456\pi$
$578$	2552.77	0.183704
$579$	−13405.0	−0.962162
$580$	3511.55	0.251395
$581$	2640.05	0.188516
$582$	6253.42	0.445382
$583$	11419.5	0.811232
$584$	6347.46	0.449760
$585$	−1305.70	−0.0922806
$586$	−6428.34	−0.453161
$587$	−16470.4	−1.15810	−0.579052	−	0.815291i	$-0.696577\pi$
$587$	−16470.4	−1.15810	−0.579052	+	0.815291i	$0.696577\pi$
$588$	−750.389	−0.0526284
$589$	−8443.92	−0.590706
$590$	124.906	0.00871573
$591$	−1303.27	−0.0907093
$592$	−1013.72	−0.0703779
$593$	−13570.0	−0.939715	−0.469858	−	0.882742i	$-0.655695\pi$
$593$	−13570.0	−0.939715	−0.469858	+	0.882742i	$0.655695\pi$
$594$	−1718.38	−0.118697
$595$	−2044.66	−0.140879
$596$	−4182.46	−0.287450
$597$	−1406.75	−0.0964393
$598$	−7982.20	−0.545847
$599$	27814.1	1.89725	0.948625	−	0.316403i	$-0.102475\pi$
$599$	27814.1	1.89725	0.948625	+	0.316403i	$0.102475\pi$
$600$	1672.38	0.113791
$601$	20646.1	1.40128	0.700641	−	0.713514i	$-0.252898\pi$
$601$	20646.1	1.40128	0.700641	+	0.713514i	$0.252898\pi$
$602$	6171.72	0.417842
$603$	4967.61	0.335483
$604$	−2729.70	−0.183891
$605$	−339.969	−0.0228458
$606$	1726.12	0.115707
$607$	3315.28	0.221686	0.110843	−	0.993838i	$-0.464645\pi$
$607$	3315.28	0.221686	0.110843	+	0.993838i	$0.464645\pi$
$608$	10008.4	0.667588
$609$	2889.21	0.192244
$610$	−1455.42	−0.0966037
$611$	−15732.8	−1.04170
$612$	−2683.88	−0.177271
$613$	−11113.9	−0.732278	−0.366139	−	0.930560i	$-0.619320\pi$
$613$	−11113.9	−0.732278	−0.366139	+	0.930560i	$0.619320\pi$
$614$	8166.89	0.536790
$615$	−5306.53	−0.347935
$616$	5838.22	0.381865
$617$	7871.34	0.513595	0.256797	−	0.966465i	$-0.417333\pi$
$617$	7871.34	0.513595	0.256797	+	0.966465i	$0.417333\pi$
$618$	2892.83	0.188295
$619$	−19107.1	−1.24068	−0.620339	−	0.784334i	$-0.713005\pi$
$619$	−19107.1	−1.24068	−0.620339	+	0.784334i	$0.713005\pi$
$620$	3947.44	0.255698
$621$	4365.22	0.282078
$622$	−987.098	−0.0636319
$623$	−4744.07	−0.305084
$624$	252.028	0.0161686
$625$	625.000	0.0400000
$626$	10404.7	0.664305
$627$	−6126.28	−0.390208
$628$	−7987.60	−0.507548
$629$	−20453.9	−1.29658
$630$	535.992	0.0338959
$631$	−25769.9	−1.62580	−0.812902	−	0.582401i	$-0.802113\pi$
$631$	−25769.9	−1.62580	−0.812902	+	0.582401i	$0.802113\pi$
$632$	20996.5	1.32151
$633$	11206.5	0.703665
$634$	7317.79	0.458401
$635$	−11104.1	−0.693939
$636$	−4675.53	−0.291504
$637$	1421.77	0.0884339
$638$	−8756.19	−0.543355
$639$	−1083.01	−0.0670472
$640$	−4875.87	−0.301149
$641$	−1954.61	−0.120440	−0.0602202	−	0.998185i	$-0.519180\pi$
$641$	−1954.61	−0.120440	−0.0602202	+	0.998185i	$0.519180\pi$
$642$	2871.54	0.176528
$643$	−19396.5	−1.18961	−0.594807	−	0.803868i	$-0.702772\pi$
$643$	−19396.5	−1.18961	−0.594807	+	0.803868i	$0.702772\pi$
$644$	−5777.10	−0.353493
$645$	7772.34	0.474474
$646$	5427.10	0.330536
$647$	31264.3	1.89973	0.949865	−	0.312661i	$-0.101220\pi$
$647$	31264.3	1.89973	0.949865	+	0.312661i	$0.101220\pi$
$648$	1806.17	0.109496
$649$	549.126	0.0332127
$650$	−1234.30	−0.0744817
$651$	3247.85	0.195535
$652$	5688.18	0.341666
$653$	6442.75	0.386102	0.193051	−	0.981189i	$-0.438162\pi$
$653$	6442.75	0.386102	0.193051	+	0.981189i	$0.438162\pi$
$654$	−9345.63	−0.558781
$655$	−3232.56	−0.192835
$656$	1024.27	0.0609620
$657$	2561.93	0.152132
$658$	6458.33	0.382632
$659$	−3584.70	−0.211897	−0.105949	−	0.994372i	$-0.533788\pi$
$659$	−3584.70	−0.211897	−0.105949	+	0.994372i	$0.533788\pi$
$660$	2863.97	0.168909
$661$	6294.43	0.370386	0.185193	−	0.982702i	$-0.440709\pi$
$661$	6294.43	0.370386	0.185193	+	0.982702i	$0.440709\pi$
$662$	11379.3	0.668078
$663$	5085.17	0.297876
$664$	8409.85	0.491514
$665$	1910.89	0.111430
$666$	5361.83	0.311962
$667$	22243.4	1.29126
$668$	9058.11	0.524654
$669$	2528.42	0.146120
$670$	4695.94	0.270776
$671$	−6398.51	−0.368125
$672$	−3849.60	−0.220984
$673$	−10233.9	−0.586162	−0.293081	−	0.956088i	$-0.594681\pi$
$673$	−10233.9	−0.586162	−0.293081	+	0.956088i	$0.594681\pi$
$674$	−9986.94	−0.570745
$675$	675.000	0.0384900
$676$	6917.33	0.393567
$677$	−7100.75	−0.403108	−0.201554	−	0.979477i	$-0.564599\pi$
$677$	−7100.75	−0.403108	−0.201554	+	0.979477i	$0.564599\pi$
$678$	162.345	0.00919593
$679$	−8575.24	−0.484665
$680$	−6513.23	−0.367310
$681$	2976.45	0.167486
$682$	−9843.10	−0.552657
$683$	−35274.6	−1.97620	−0.988100	−	0.153813i	$-0.950845\pi$
$683$	−35274.6	−1.97620	−0.988100	+	0.153813i	$0.950845\pi$
$684$	2508.30	0.140215
$685$	4480.05	0.249889
$686$	−583.636	−0.0324830
$687$	−19234.2	−1.06817
$688$	−1500.22	−0.0831330
$689$	8858.74	0.489828
$690$	4126.50	0.227671
$691$	4945.12	0.272245	0.136122	−	0.990692i	$-0.456536\pi$
$691$	4945.12	0.272245	0.136122	+	0.990692i	$0.456536\pi$
$692$	21520.8	1.18222
$693$	2356.40	0.129166
$694$	−3296.31	−0.180297
$695$	11568.0	0.631368
$696$	9203.54	0.501235
$697$	20666.7	1.12311
$698$	16588.2	0.899532
$699$	−6823.06	−0.369201
$700$	−893.320	−0.0482348
$701$	−15300.4	−0.824379	−0.412190	−	0.911098i	$-0.635236\pi$
$701$	−15300.4	−0.824379	−0.412190	+	0.911098i	$0.635236\pi$
$702$	−1333.04	−0.0716701
$703$	19115.7	1.02555
$704$	10800.4	0.578206
$705$	8133.28	0.434492
$706$	7787.38	0.415130
$707$	−2367.01	−0.125913
$708$	−224.830	−0.0119345
$709$	−28297.4	−1.49892	−0.749458	−	0.662052i	$-0.769686\pi$
$709$	−28297.4	−1.49892	−0.749458	+	0.662052i	$0.769686\pi$
$710$	−1023.78	−0.0541153
$711$	8474.51	0.447003
$712$	−15112.2	−0.795441
$713$	25004.5	1.31336
$714$	−2087.47	−0.109414
$715$	−5426.37	−0.283825
$716$	12407.9	0.647635
$717$	8589.35	0.447385
$718$	−18461.9	−0.959597
$719$	8548.96	0.443425	0.221712	−	0.975112i	$-0.428835\pi$
$719$	8548.96	0.443425	0.221712	+	0.975112i	$0.428835\pi$
$720$	−130.289	−0.00674387
$721$	−3966.90	−0.204903
$722$	6598.97	0.340150
$723$	−16092.7	−0.827792
$724$	13787.3	0.707737
$725$	3439.53	0.176194
$726$	−347.087	−0.0177432
$727$	14345.3	0.731827	0.365913	−	0.930649i	$-0.380757\pi$
$727$	14345.3	0.731827	0.365913	+	0.930649i	$0.380757\pi$
$728$	4529.02	0.230572
$729$	729.000	0.0370370
$730$	2421.83	0.122789
$731$	−30270.0	−1.53157
$732$	2619.76	0.132280
$733$	−22624.0	−1.14002	−0.570012	−	0.821637i	$-0.693061\pi$
$733$	−22624.0	−1.14002	−0.570012	+	0.821637i	$0.693061\pi$
$734$	−19512.9	−0.981248
$735$	−735.000	−0.0368856
$736$	−29637.3	−1.48430
$737$	20644.9	1.03184
$738$	−5417.63	−0.270225
$739$	14837.3	0.738566	0.369283	−	0.929317i	$-0.379603\pi$
$739$	14837.3	0.738566	0.369283	+	0.929317i	$0.379603\pi$
$740$	−8936.39	−0.443930
$741$	−4752.49	−0.235610
$742$	−3636.52	−0.179920
$743$	13073.1	0.645497	0.322749	−	0.946485i	$-0.395393\pi$
$743$	13073.1	0.645497	0.322749	+	0.946485i	$0.395393\pi$
$744$	10346.0	0.509815
$745$	−4096.69	−0.201464
$746$	−918.813	−0.0450940
$747$	3394.35	0.166255
$748$	−11154.0	−0.545226
$749$	−3937.72	−0.192098
$750$	638.086	0.0310661
$751$	16213.3	0.787791	0.393895	−	0.919155i	$-0.371127\pi$
$751$	16213.3	0.787791	0.393895	+	0.919155i	$0.371127\pi$
$752$	−1569.89	−0.0761278
$753$	16709.4	0.808665
$754$	−6792.65	−0.328082
$755$	−2673.72	−0.128883
$756$	−964.786	−0.0464139
$757$	19903.9	0.955642	0.477821	−	0.878457i	$-0.341427\pi$
$757$	19903.9	0.955642	0.477821	+	0.878457i	$0.341427\pi$
$758$	−14595.3	−0.699372
$759$	18141.4	0.867580
$760$	6087.13	0.290531
$761$	−30125.5	−1.43502	−0.717509	−	0.696549i	$-0.754718\pi$
$761$	−30125.5	−1.43502	−0.717509	+	0.696549i	$0.754718\pi$
$762$	−11336.6	−0.538950
$763$	12815.6	0.608066
$764$	−18433.5	−0.872907
$765$	−2628.84	−0.124243
$766$	−14681.0	−0.692489
$767$	425.986	0.0200541
$768$	−11908.1	−0.559503
$769$	−36049.1	−1.69046	−0.845230	−	0.534402i	$-0.820537\pi$
$769$	−36049.1	−1.69046	−0.845230	+	0.534402i	$0.820537\pi$
$770$	2227.53	0.104253
$771$	6286.09	0.293629
$772$	22809.4	1.06338
$773$	−9644.77	−0.448769	−0.224384	−	0.974501i	$-0.572037\pi$
$773$	−9644.77	−0.448769	−0.224384	+	0.974501i	$0.572037\pi$
$774$	7935.07	0.368502
$775$	3866.48	0.179211
$776$	−27316.4	−1.26366
$777$	−7352.62	−0.339477
$778$	−15712.3	−0.724054
$779$	−19314.7	−0.888344
$780$	2221.73	0.101988
$781$	−4500.88	−0.206215
$782$	−16071.0	−0.734908
$783$	3714.69	0.169543
$784$	141.870	0.00646275
$785$	−7823.80	−0.355724
$786$	−3300.24	−0.149766
$787$	−25218.6	−1.14224	−0.571122	−	0.820865i	$-0.693492\pi$
$787$	−25218.6	−1.14224	−0.571122	+	0.820865i	$0.693492\pi$
$788$	2217.59	0.100252
$789$	−22397.6	−1.01062
$790$	8011.06	0.360786
$791$	−222.623	−0.0100070
$792$	7506.28	0.336773
$793$	−4963.67	−0.222276
$794$	−19768.8	−0.883586
$795$	−4579.64	−0.204306
$796$	2393.67	0.106584
$797$	32042.3	1.42409	0.712044	−	0.702135i	$-0.247770\pi$
$797$	32042.3	1.42409	0.712044	+	0.702135i	$0.247770\pi$
$798$	1950.90	0.0865427
$799$	−31675.7	−1.40251
$800$	−4582.85	−0.202535
$801$	−6099.52	−0.269059
$802$	−18984.5	−0.835867
$803$	10647.1	0.467908
$804$	−8452.69	−0.370775
$805$	−5658.62	−0.247752
$806$	−7635.82	−0.333698
$807$	−19564.1	−0.853396
$808$	−7540.07	−0.328291
$809$	3427.90	0.148972	0.0744860	−	0.997222i	$-0.476268\pi$
$809$	3427.90	0.148972	0.0744860	+	0.997222i	$0.476268\pi$
$810$	689.133	0.0298934
$811$	23094.4	0.999943	0.499972	−	0.866042i	$-0.333344\pi$
$811$	23094.4	0.999943	0.499972	+	0.866042i	$0.333344\pi$
$812$	−4916.16	−0.212467
$813$	7229.11	0.311852
$814$	22283.3	0.959494
$815$	5571.53	0.239463
$816$	507.422	0.0217688
$817$	28289.7	1.21142
$818$	12639.3	0.540249
$819$	1827.98	0.0779914
$820$	9029.39	0.384537
$821$	474.741	0.0201810	0.0100905	−	0.999949i	$-0.496788\pi$
$821$	474.741	0.0201810	0.0100905	+	0.999949i	$0.496788\pi$
$822$	4573.85	0.194077
$823$	24159.8	1.02328	0.511638	−	0.859201i	$-0.329039\pi$
$823$	24159.8	1.02328	0.511638	+	0.859201i	$0.329039\pi$
$824$	−12636.5	−0.534240
$825$	2805.23	0.118383
$826$	−174.868	−0.00736613
$827$	−7566.35	−0.318147	−0.159074	−	0.987267i	$-0.550851\pi$
$827$	−7566.35	−0.318147	−0.159074	+	0.987267i	$0.550851\pi$
$828$	−7427.70	−0.311752
$829$	−10580.9	−0.443295	−0.221648	−	0.975127i	$-0.571143\pi$
$829$	−10580.9	−0.443295	−0.221648	+	0.975127i	$0.571143\pi$
$830$	3208.72	0.134188
$831$	−6659.48	−0.277996
$832$	8378.49	0.349125
$833$	2862.52	0.119064
$834$	11810.2	0.490354
$835$	8872.34	0.367713
$836$	10424.2	0.431256
$837$	4175.80	0.172445
$838$	−16411.1	−0.676507
$839$	15315.6	0.630218	0.315109	−	0.949055i	$-0.397959\pi$
$839$	15315.6	0.630218	0.315109	+	0.949055i	$0.397959\pi$
$840$	−2341.34	−0.0961712
$841$	−5460.40	−0.223888
$842$	−16876.4	−0.690735
$843$	17515.7	0.715625
$844$	−19068.6	−0.777688
$845$	6775.47	0.275838
$846$	8303.57	0.337450
$847$	475.956	0.0193082
$848$	883.966	0.0357966
$849$	−10935.1	−0.442040
$850$	−2485.08	−0.100279
$851$	−56606.4	−2.28019
$852$	1842.81	0.0741004
$853$	18598.2	0.746528	0.373264	−	0.927725i	$-0.378239\pi$
$853$	18598.2	0.746528	0.373264	+	0.927725i	$0.378239\pi$
$854$	2037.59	0.0816450
$855$	2456.86	0.0982723
$856$	−12543.6	−0.500853
$857$	41775.3	1.66513	0.832566	−	0.553926i	$-0.186871\pi$
$857$	41775.3	1.66513	0.832566	+	0.553926i	$0.186871\pi$
$858$	−5539.99	−0.220434
$859$	32414.7	1.28752	0.643758	−	0.765229i	$-0.277374\pi$
$859$	32414.7	1.28752	0.643758	+	0.765229i	$0.277374\pi$
$860$	−13225.1	−0.524387
$861$	7429.14	0.294059
$862$	27776.4	1.09753
$863$	−31299.7	−1.23459	−0.617297	−	0.786730i	$-0.711772\pi$
$863$	−31299.7	−1.23459	−0.617297	+	0.786730i	$0.711772\pi$
$864$	−4949.48	−0.194890
$865$	21079.4	0.828580
$866$	8794.94	0.345109
$867$	−4500.75	−0.176302
$868$	−5526.41	−0.216104
$869$	35219.2	1.37483
$870$	3511.55	0.136842
$871$	16015.4	0.623030
$872$	40823.8	1.58540
$873$	−11025.3	−0.427434
$874$	15019.6	0.581288
$875$	−875.000	−0.0338062
$876$	−4359.29	−0.168136
$877$	−19973.0	−0.769031	−0.384515	−	0.923119i	$-0.625631\pi$
$877$	−19973.0	−0.769031	−0.384515	+	0.923119i	$0.625631\pi$
$878$	−31204.9	−1.19945
$879$	11333.7	0.434900
$880$	−541.469	−0.0207419
$881$	17367.9	0.664176	0.332088	−	0.943248i	$-0.392247\pi$
$881$	17367.9	0.664176	0.332088	+	0.943248i	$0.392247\pi$
$882$	−750.389	−0.0286473
$883$	−14364.2	−0.547446	−0.273723	−	0.961809i	$-0.588255\pi$
$883$	−14364.2	−0.547446	−0.273723	+	0.961809i	$0.588255\pi$
$884$	−8652.73	−0.329211
$885$	−220.219	−0.00836450
$886$	2745.09	0.104089
$887$	−33738.1	−1.27713	−0.638564	−	0.769568i	$-0.720471\pi$
$887$	−33738.1	−1.27713	−0.638564	+	0.769568i	$0.720471\pi$
$888$	−23421.7	−0.885114
$889$	15545.7	0.586485
$890$	−5765.95	−0.217163
$891$	3029.65	0.113914
$892$	−4302.26	−0.161491
$893$	29603.4	1.10934
$894$	−4182.46	−0.156468
$895$	12153.5	0.453906
$896$	6826.21	0.254518
$897$	14073.3	0.523850
$898$	1508.86	0.0560705
$899$	21278.2	0.789398
$900$	−1148.55	−0.0425391
$901$	17835.8	0.659485
$902$	−22515.2	−0.831123
$903$	−10881.3	−0.401004
$904$	−709.162	−0.0260911
$905$	13504.6	0.496030
$906$	−2729.70	−0.100097
$907$	−32998.6	−1.20805	−0.604024	−	0.796966i	$-0.706437\pi$
$907$	−32998.6	−1.20805	−0.604024	+	0.796966i	$0.706437\pi$
$908$	−5064.62	−0.185105
$909$	−3043.29	−0.111045
$910$	1728.02	0.0629485
$911$	33446.3	1.21638	0.608192	−	0.793790i	$-0.291895\pi$
$911$	33446.3	1.21638	0.608192	+	0.793790i	$0.291895\pi$
$912$	−474.225	−0.0172184
$913$	14106.6	0.511347
$914$	−12576.6	−0.455139
$915$	2566.03	0.0927108
$916$	32728.2	1.18053
$917$	4525.59	0.162975
$918$	−2683.88	−0.0964939
$919$	41708.7	1.49711	0.748554	−	0.663074i	$-0.230748\pi$
$919$	41708.7	1.49711	0.748554	+	0.663074i	$0.230748\pi$
$920$	−18025.5	−0.645960
$921$	−14398.9	−0.515158
$922$	12137.8	0.433556
$923$	−3491.58	−0.124514
$924$	−4009.56	−0.142754
$925$	−8753.12	−0.311136
$926$	−24607.7	−0.873283
$927$	−5100.30	−0.180707
$928$	−25220.6	−0.892140
$929$	49024.6	1.73137	0.865686	−	0.500587i	$-0.166883\pi$
$929$	49024.6	1.73137	0.865686	+	0.500587i	$0.166883\pi$
$930$	3947.44	0.139184
$931$	−2675.25	−0.0941758
$932$	11609.9	0.408040
$933$	1740.34	0.0610677
$934$	27894.6	0.977235
$935$	−10925.2	−0.382131
$936$	5823.03	0.203346
$937$	−5447.58	−0.189930	−0.0949651	−	0.995481i	$-0.530274\pi$
$937$	−5447.58	−0.189930	−0.0949651	+	0.995481i	$0.530274\pi$
$938$	−6574.31	−0.228848
$939$	−18344.4	−0.637535
$940$	−13839.3	−0.480200
$941$	4125.75	0.142928	0.0714642	−	0.997443i	$-0.477233\pi$
$941$	4125.75	0.142928	0.0714642	+	0.997443i	$0.477233\pi$
$942$	−7987.60	−0.276274
$943$	57195.5	1.97513
$944$	42.5069	0.00146555
$945$	−945.000	−0.0325300
$946$	32977.4	1.13339
$947$	17332.3	0.594747	0.297374	−	0.954761i	$-0.403889\pi$
$947$	17332.3	0.594747	0.297374	+	0.954761i	$0.403889\pi$
$948$	−14419.9	−0.494026
$949$	8259.57	0.282526
$950$	2322.50	0.0793177
$951$	−12901.9	−0.439929
$952$	9118.53	0.310434
$953$	56839.4	1.93201	0.966007	−	0.258517i	$-0.0832337\pi$
$953$	56839.4	1.93201	0.966007	+	0.258517i	$0.0832337\pi$
$954$	−4675.53	−0.158675
$955$	−18055.5	−0.611792
$956$	−14615.3	−0.494449
$957$	15437.9	0.521459
$958$	22105.7	0.745515
$959$	−6272.07	−0.211195
$960$	−4331.37	−0.145619
$961$	−5871.48	−0.197089
$962$	17286.3	0.579349
$963$	−5062.78	−0.169414
$964$	27382.7	0.914873
$965$	22341.6	0.745287
$966$	−5777.10	−0.192417
$967$	−13284.2	−0.441769	−0.220884	−	0.975300i	$-0.570894\pi$
$967$	−13284.2	−0.441769	−0.220884	+	0.975300i	$0.570894\pi$
$968$	1516.15	0.0503420
$969$	−9568.44	−0.317216
$970$	−10422.4	−0.344992
$971$	12153.0	0.401658	0.200829	−	0.979626i	$-0.435636\pi$
$971$	12153.0	0.401658	0.200829	+	0.979626i	$0.435636\pi$
$972$	−1240.44	−0.0409332
$973$	−16195.3	−0.533604
$974$	21888.1	0.720060
$975$	2176.17	0.0714803
$976$	−495.298	−0.0162440
$977$	−37999.3	−1.24433	−0.622163	−	0.782888i	$-0.713746\pi$
$977$	−37999.3	−1.24433	−0.622163	+	0.782888i	$0.713746\pi$
$978$	5688.18	0.185980
$979$	−25349.0	−0.827537
$980$	1250.65	0.0407658
$981$	16477.1	0.536264
$982$	8334.42	0.270837
$983$	22375.0	0.725993	0.362996	−	0.931791i	$-0.381754\pi$
$983$	22375.0	0.725993	0.362996	+	0.931791i	$0.381754\pi$
$984$	23665.5	0.766695
$985$	2172.11	0.0702631
$986$	−13676.0	−0.441717
$987$	−11386.6	−0.367213
$988$	8086.65	0.260395
$989$	−83772.9	−2.69345
$990$	2863.97	0.0919423
$991$	18985.3	0.608564	0.304282	−	0.952582i	$-0.401583\pi$
$991$	18985.3	0.608564	0.304282	+	0.952582i	$0.401583\pi$
$992$	−28351.2	−0.907412
$993$	−20062.6	−0.641156
$994$	1433.29	0.0457358
$995$	2344.58	0.0747016
$996$	−5775.70	−0.183745
$997$	−56476.5	−1.79401	−0.897006	−	0.442019i	$-0.854262\pi$
$997$	−56476.5	−1.79401	−0.897006	+	0.442019i	$0.854262\pi$
$998$	−17539.6	−0.556321
$999$	−9453.37	−0.299391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.a.g.1.1	✓	2
3.2	odd	2		315.4.a.g.1.2		2
4.3	odd	2		1680.4.a.y.1.1		2
5.2	odd	4		525.4.d.j.274.2		4
5.3	odd	4		525.4.d.j.274.3		4
5.4	even	2		525.4.a.i.1.2		2
7.6	odd	2		735.4.a.q.1.1		2
15.14	odd	2		1575.4.a.y.1.1		2
21.20	even	2		2205.4.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.g.1.1	✓	2	1.1	even	1	trivial
315.4.a.g.1.2		2	3.2	odd	2
525.4.a.i.1.2		2	5.4	even	2
525.4.d.j.274.2		4	5.2	odd	4
525.4.d.j.274.3		4	5.3	odd	4
735.4.a.q.1.1		2	7.6	odd	2
1575.4.a.y.1.1		2	15.14	odd	2
1680.4.a.y.1.1		2	4.3	odd	2
2205.4.a.v.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)

\(f(q)\)	\(=\)	\(q-1.70156 q^{2} +3.00000 q^{3} -5.10469 q^{4} -5.00000 q^{5} -5.10469 q^{6} +7.00000 q^{7} +22.2984 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.70156 q^{2} +3.00000 q^{3} -5.10469 q^{4} -5.00000 q^{5} -5.10469 q^{6} +7.00000 q^{7} +22.2984 q^{8} +9.00000 q^{9} +8.50781 q^{10} +37.4031 q^{11} -15.3141 q^{12} +29.0156 q^{13} -11.9109 q^{14} -15.0000 q^{15} +2.89531 q^{16} +58.4187 q^{17} -15.3141 q^{18} -54.5969 q^{19} +25.5234 q^{20} +21.0000 q^{21} -63.6437 q^{22} +161.675 q^{23} +66.8953 q^{24} +25.0000 q^{25} -49.3719 q^{26} +27.0000 q^{27} -35.7328 q^{28} +137.581 q^{29} +25.5234 q^{30} +154.659 q^{31} -183.314 q^{32} +112.209 q^{33} -99.4031 q^{34} -35.0000 q^{35} -45.9422 q^{36} -350.125 q^{37} +92.9000 q^{38} +87.0469 q^{39} -111.492 q^{40} +353.769 q^{41} -35.7328 q^{42} -518.156 q^{43} -190.931 q^{44} -45.0000 q^{45} -275.100 q^{46} -542.219 q^{47} +8.68594 q^{48} +49.0000 q^{49} -42.5391 q^{50} +175.256 q^{51} -148.116 q^{52} +305.309 q^{53} -45.9422 q^{54} -187.016 q^{55} +156.089 q^{56} -163.791 q^{57} -234.103 q^{58} +14.6813 q^{59} +76.5703 q^{60} -171.069 q^{61} -263.163 q^{62} +63.0000 q^{63} +288.758 q^{64} -145.078 q^{65} -190.931 q^{66} +551.956 q^{67} -298.209 q^{68} +485.025 q^{69} +59.5547 q^{70} -120.334 q^{71} +200.686 q^{72} +284.659 q^{73} +595.759 q^{74} +75.0000 q^{75} +278.700 q^{76} +261.822 q^{77} -148.116 q^{78} +941.612 q^{79} -14.4766 q^{80} +81.0000 q^{81} -601.959 q^{82} +377.150 q^{83} -107.198 q^{84} -292.094 q^{85} +881.675 q^{86} +412.744 q^{87} +834.031 q^{88} -677.725 q^{89} +76.5703 q^{90} +203.109 q^{91} -825.300 q^{92} +463.978 q^{93} +922.619 q^{94} +272.984 q^{95} -549.942 q^{96} -1225.03 q^{97} -83.3765 q^{98} +336.628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} - 10 q^{5} + 9 q^{6} + 14 q^{7} + 51 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 - 10 * q^5 + 9 * q^6 + 14 * q^7 + 51 * q^8 + 18 * q^9	\( 2 q + 3 q^{2} + 6 q^{3} + 9 q^{4} - 10 q^{5} + 9 q^{6} + 14 q^{7} + 51 q^{8} + 18 q^{9} - 15 q^{10} + 62 q^{11} + 27 q^{12} - 6 q^{13} + 21 q^{14} - 30 q^{15} + 25 q^{16} + 40 q^{17} + 27 q^{18} - 122 q^{19} - 45 q^{20} + 42 q^{21} + 52 q^{22} + 16 q^{23} + 153 q^{24} + 50 q^{25} - 214 q^{26} + 54 q^{27} + 63 q^{28} + 352 q^{29} - 45 q^{30} + 66 q^{31} - 309 q^{32} + 186 q^{33} - 186 q^{34} - 70 q^{35} + 81 q^{36} - 188 q^{37} - 224 q^{38} - 18 q^{39} - 255 q^{40} + 16 q^{41} + 63 q^{42} - 396 q^{43} + 156 q^{44} - 90 q^{45} - 960 q^{46} - 188 q^{47} + 75 q^{48} + 98 q^{49} + 75 q^{50} + 120 q^{51} - 642 q^{52} + 982 q^{53} + 81 q^{54} - 310 q^{55} + 357 q^{56} - 366 q^{57} + 774 q^{58} + 516 q^{59} - 135 q^{60} - 880 q^{61} - 680 q^{62} + 126 q^{63} - 479 q^{64} + 30 q^{65} + 156 q^{66} - 356 q^{67} - 558 q^{68} + 48 q^{69} - 105 q^{70} + 310 q^{71} + 459 q^{72} + 326 q^{73} + 1358 q^{74} + 150 q^{75} - 672 q^{76} + 434 q^{77} - 642 q^{78} + 1832 q^{79} - 125 q^{80} + 162 q^{81} - 2190 q^{82} - 680 q^{83} + 189 q^{84} - 200 q^{85} + 1456 q^{86} + 1056 q^{87} + 1540 q^{88} + 796 q^{89} - 135 q^{90} - 42 q^{91} - 2880 q^{92} + 198 q^{93} + 2588 q^{94} + 610 q^{95} - 927 q^{96} - 670 q^{97} + 147 q^{98} + 558 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 6 * q^3 + 9 * q^4 - 10 * q^5 + 9 * q^6 + 14 * q^7 + 51 * q^8 + 18 * q^9 - 15 * q^10 + 62 * q^11 + 27 * q^12 - 6 * q^13 + 21 * q^14 - 30 * q^15 + 25 * q^16 + 40 * q^17 + 27 * q^18 - 122 * q^19 - 45 * q^20 + 42 * q^21 + 52 * q^22 + 16 * q^23 + 153 * q^24 + 50 * q^25 - 214 * q^26 + 54 * q^27 + 63 * q^28 + 352 * q^29 - 45 * q^30 + 66 * q^31 - 309 * q^32 + 186 * q^33 - 186 * q^34 - 70 * q^35 + 81 * q^36 - 188 * q^37 - 224 * q^38 - 18 * q^39 - 255 * q^40 + 16 * q^41 + 63 * q^42 - 396 * q^43 + 156 * q^44 - 90 * q^45 - 960 * q^46 - 188 * q^47 + 75 * q^48 + 98 * q^49 + 75 * q^50 + 120 * q^51 - 642 * q^52 + 982 * q^53 + 81 * q^54 - 310 * q^55 + 357 * q^56 - 366 * q^57 + 774 * q^58 + 516 * q^59 - 135 * q^60 - 880 * q^61 - 680 * q^62 + 126 * q^63 - 479 * q^64 + 30 * q^65 + 156 * q^66 - 356 * q^67 - 558 * q^68 + 48 * q^69 - 105 * q^70 + 310 * q^71 + 459 * q^72 + 326 * q^73 + 1358 * q^74 + 150 * q^75 - 672 * q^76 + 434 * q^77 - 642 * q^78 + 1832 * q^79 - 125 * q^80 + 162 * q^81 - 2190 * q^82 - 680 * q^83 + 189 * q^84 - 200 * q^85 + 1456 * q^86 + 1056 * q^87 + 1540 * q^88 + 796 * q^89 - 135 * q^90 - 42 * q^91 - 2880 * q^92 + 198 * q^93 + 2588 * q^94 + 610 * q^95 - 927 * q^96 - 670 * q^97 + 147 * q^98 + 558 * q^99

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