LMFDB - Embedded newform 201.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(1,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("201.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.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:	$11.8593839112$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 38x^{5} + 18x^{4} + 373x^{3} - 151x^{2} - 956x + 498 $ x^7 - x^6 - 38x^5 + 18x^4 + 373x^3 - 151x^2 - 956*x + 498
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.41567$ of defining polynomial
Character	$\chi$	$=$	201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.41567 q^{2} -3.00000 q^{3} +21.3295 q^{4} -5.98460 q^{5} +16.2470 q^{6} +0.240383 q^{7} -72.1883 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.41567 q^{2} -3.00000 q^{3} +21.3295 q^{4} -5.98460 q^{5} +16.2470 q^{6} +0.240383 q^{7} -72.1883 q^{8} +9.00000 q^{9} +32.4106 q^{10} -37.9609 q^{11} -63.9885 q^{12} +47.5308 q^{13} -1.30184 q^{14} +17.9538 q^{15} +220.312 q^{16} +135.266 q^{17} -48.7411 q^{18} -29.6275 q^{19} -127.649 q^{20} -0.721150 q^{21} +205.584 q^{22} +64.4390 q^{23} +216.565 q^{24} -89.1846 q^{25} -257.411 q^{26} -27.0000 q^{27} +5.12726 q^{28} -25.3968 q^{29} -97.2319 q^{30} +1.97461 q^{31} -615.632 q^{32} +113.883 q^{33} -732.556 q^{34} -1.43860 q^{35} +191.966 q^{36} +224.201 q^{37} +160.453 q^{38} -142.592 q^{39} +432.018 q^{40} -356.273 q^{41} +3.90551 q^{42} -312.561 q^{43} -809.688 q^{44} -53.8614 q^{45} -348.981 q^{46} -580.720 q^{47} -660.936 q^{48} -342.942 q^{49} +482.995 q^{50} -405.798 q^{51} +1013.81 q^{52} +298.900 q^{53} +146.223 q^{54} +227.181 q^{55} -17.3529 q^{56} +88.8825 q^{57} +137.541 q^{58} -409.248 q^{59} +382.946 q^{60} +192.935 q^{61} -10.6938 q^{62} +2.16345 q^{63} +1571.56 q^{64} -284.453 q^{65} -616.752 q^{66} +67.0000 q^{67} +2885.16 q^{68} -193.317 q^{69} +7.79097 q^{70} +376.462 q^{71} -649.695 q^{72} -167.148 q^{73} -1214.20 q^{74} +267.554 q^{75} -631.940 q^{76} -9.12518 q^{77} +772.233 q^{78} -1139.41 q^{79} -1318.48 q^{80} +81.0000 q^{81} +1929.46 q^{82} +21.0554 q^{83} -15.3818 q^{84} -809.513 q^{85} +1692.73 q^{86} +76.1904 q^{87} +2740.34 q^{88} +59.0821 q^{89} +291.696 q^{90} +11.4256 q^{91} +1374.45 q^{92} -5.92382 q^{93} +3144.99 q^{94} +177.309 q^{95} +1846.90 q^{96} -1504.63 q^{97} +1857.26 q^{98} -341.648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9	\( 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9} - 51 q^{10} - 130 q^{11} - 63 q^{12} + 16 q^{13} + 5 q^{14} - 33 q^{15} + 77 q^{16} + 90 q^{17} - 9 q^{18} - 132 q^{19} - 359 q^{20} + 99 q^{21} - 192 q^{22} - 399 q^{23} + 135 q^{24} - 132 q^{25} - 638 q^{26} - 189 q^{27} - 245 q^{28} - 302 q^{29} + 153 q^{30} - 555 q^{31} - 1031 q^{32} + 390 q^{33} - 832 q^{34} - 775 q^{35} + 189 q^{36} + 297 q^{37} + 98 q^{38} - 48 q^{39} + 305 q^{40} - 717 q^{41} - 15 q^{42} - 245 q^{43} - 1766 q^{44} + 99 q^{45} - 497 q^{46} - 1072 q^{47} - 231 q^{48} + 314 q^{49} + 454 q^{50} - 270 q^{51} + 1344 q^{52} + 265 q^{53} + 27 q^{54} + 1096 q^{55} - 477 q^{56} + 396 q^{57} + 1610 q^{58} - 255 q^{59} + 1077 q^{60} + 418 q^{61} - 191 q^{62} - 297 q^{63} + 1889 q^{64} + 262 q^{65} + 576 q^{66} + 469 q^{67} + 3720 q^{68} + 1197 q^{69} + 1309 q^{70} - 1194 q^{71} - 405 q^{72} + 995 q^{73} + 259 q^{74} + 396 q^{75} + 1506 q^{76} + 230 q^{77} + 1914 q^{78} - 2640 q^{79} - 1949 q^{80} + 567 q^{81} + 1535 q^{82} - 2579 q^{83} + 735 q^{84} - 562 q^{85} + 1991 q^{86} + 906 q^{87} + 3624 q^{88} - 1604 q^{89} - 459 q^{90} - 2116 q^{91} - 351 q^{92} + 1665 q^{93} + 6178 q^{94} - 3028 q^{95} + 3093 q^{96} - 808 q^{97} + 258 q^{98} - 1170 q^{99}+O(q^{100}) \) 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9 - 51 * q^10 - 130 * q^11 - 63 * q^12 + 16 * q^13 + 5 * q^14 - 33 * q^15 + 77 * q^16 + 90 * q^17 - 9 * q^18 - 132 * q^19 - 359 * q^20 + 99 * q^21 - 192 * q^22 - 399 * q^23 + 135 * q^24 - 132 * q^25 - 638 * q^26 - 189 * q^27 - 245 * q^28 - 302 * q^29 + 153 * q^30 - 555 * q^31 - 1031 * q^32 + 390 * q^33 - 832 * q^34 - 775 * q^35 + 189 * q^36 + 297 * q^37 + 98 * q^38 - 48 * q^39 + 305 * q^40 - 717 * q^41 - 15 * q^42 - 245 * q^43 - 1766 * q^44 + 99 * q^45 - 497 * q^46 - 1072 * q^47 - 231 * q^48 + 314 * q^49 + 454 * q^50 - 270 * q^51 + 1344 * q^52 + 265 * q^53 + 27 * q^54 + 1096 * q^55 - 477 * q^56 + 396 * q^57 + 1610 * q^58 - 255 * q^59 + 1077 * q^60 + 418 * q^61 - 191 * q^62 - 297 * q^63 + 1889 * q^64 + 262 * q^65 + 576 * q^66 + 469 * q^67 + 3720 * q^68 + 1197 * q^69 + 1309 * q^70 - 1194 * q^71 - 405 * q^72 + 995 * q^73 + 259 * q^74 + 396 * q^75 + 1506 * q^76 + 230 * q^77 + 1914 * q^78 - 2640 * q^79 - 1949 * q^80 + 567 * q^81 + 1535 * q^82 - 2579 * q^83 + 735 * q^84 - 562 * q^85 + 1991 * q^86 + 906 * q^87 + 3624 * q^88 - 1604 * q^89 - 459 * q^90 - 2116 * q^91 - 351 * q^92 + 1665 * q^93 + 6178 * q^94 - 3028 * q^95 + 3093 * q^96 - 808 * q^97 + 258 * q^98 - 1170 * 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 $

$2$	−5.41567	−1.91473	−0.957365	−	0.288882i	$-0.906717\pi$
$2$	−5.41567	−1.91473	−0.957365	+	0.288882i	$0.906717\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	21.3295	2.66619
$5$	−5.98460	−0.535279	−0.267639	−	0.963519i	$-0.586244\pi$
$5$	−5.98460	−0.535279	−0.267639	+	0.963519i	$0.586244\pi$
$6$	16.2470	1.10547
$7$	0.240383	0.0129795	0.00648974	−	0.999979i	$-0.497934\pi$
$7$	0.240383	0.0129795	0.00648974	+	0.999979i	$0.497934\pi$
$8$	−72.1883	−3.19030
$9$	9.00000	0.333333
$10$	32.4106	1.02491
$11$	−37.9609	−1.04051	−0.520257	−	0.854010i	$-0.674164\pi$
$11$	−37.9609	−1.04051	−0.520257	+	0.854010i	$0.674164\pi$
$12$	−63.9885	−1.53933
$13$	47.5308	1.01405	0.507026	−	0.861931i	$-0.330745\pi$
$13$	47.5308	1.01405	0.507026	+	0.861931i	$0.330745\pi$
$14$	−1.30184	−0.0248522
$15$	17.9538	0.309043
$16$	220.312	3.44238
$17$	135.266	1.92981	0.964906	−	0.262594i	$-0.0845781\pi$
$17$	135.266	1.92981	0.964906	+	0.262594i	$0.0845781\pi$
$18$	−48.7411	−0.638243
$19$	−29.6275	−0.357738	−0.178869	−	0.983873i	$-0.557244\pi$
$19$	−29.6275	−0.357738	−0.178869	+	0.983873i	$0.557244\pi$
$20$	−127.649	−1.42715
$21$	−0.721150	−0.00749370
$22$	205.584	1.99230
$23$	64.4390	0.584194	0.292097	−	0.956389i	$-0.405647\pi$
$23$	64.4390	0.584194	0.292097	+	0.956389i	$0.405647\pi$
$24$	216.565	1.84192
$25$	−89.1846	−0.713477
$26$	−257.411	−1.94163
$27$	−27.0000	−0.192450
$28$	5.12726	0.0346057
$29$	−25.3968	−0.162623	−0.0813115	−	0.996689i	$-0.525911\pi$
$29$	−25.3968	−0.162623	−0.0813115	+	0.996689i	$0.525911\pi$
$30$	−97.2319	−0.591734
$31$	1.97461	0.0114403	0.00572015	−	0.999984i	$-0.498179\pi$
$31$	1.97461	0.0114403	0.00572015	+	0.999984i	$0.498179\pi$
$32$	−615.632	−3.40092
$33$	113.883	0.600741
$34$	−732.556	−3.69507
$35$	−1.43860	−0.00694764
$36$	191.966	0.888730
$37$	224.201	0.996173	0.498086	−	0.867127i	$-0.334036\pi$
$37$	224.201	0.996173	0.498086	+	0.867127i	$0.334036\pi$
$38$	160.453	0.684971
$39$	−142.592	−0.585463
$40$	432.018	1.70770
$41$	−356.273	−1.35708	−0.678542	−	0.734562i	$-0.737388\pi$
$41$	−356.273	−1.35708	−0.678542	+	0.734562i	$0.737388\pi$
$42$	3.90551	0.0143484
$43$	−312.561	−1.10849	−0.554246	−	0.832353i	$-0.686993\pi$
$43$	−312.561	−1.10849	−0.554246	+	0.832353i	$0.686993\pi$
$44$	−809.688	−2.77421
$45$	−53.8614	−0.178426
$46$	−348.981	−1.11857
$47$	−580.720	−1.80227	−0.901136	−	0.433537i	$-0.857265\pi$
$47$	−580.720	−1.80227	−0.901136	+	0.433537i	$0.857265\pi$
$48$	−660.936	−1.98746
$49$	−342.942	−0.999832
$50$	482.995	1.36611
$51$	−405.798	−1.11418
$52$	1013.81	2.70365
$53$	298.900	0.774662	0.387331	−	0.921941i	$-0.373397\pi$
$53$	298.900	0.774662	0.387331	+	0.921941i	$0.373397\pi$
$54$	146.223	0.368490
$55$	227.181	0.556965
$56$	−17.3529	−0.0414085
$57$	88.8825	0.206540
$58$	137.541	0.311379
$59$	−409.248	−0.903043	−0.451522	−	0.892260i	$-0.649119\pi$
$59$	−409.248	−0.903043	−0.451522	+	0.892260i	$0.649119\pi$
$60$	382.946	0.823968
$61$	192.935	0.404963	0.202482	−	0.979286i	$-0.435099\pi$
$61$	192.935	0.404963	0.202482	+	0.979286i	$0.435099\pi$
$62$	−10.6938	−0.0219051
$63$	2.16345	0.00432649
$64$	1571.56	3.06946
$65$	−284.453	−0.542800
$66$	−616.752	−1.15026
$67$	67.0000	0.122169
$67$	67.0000	0.122169
$68$	2885.16	5.14525
$69$	−193.317	−0.337285
$70$	7.79097	0.0133028
$71$	376.462	0.629265	0.314633	−	0.949213i	$-0.398119\pi$
$71$	376.462	0.629265	0.314633	+	0.949213i	$0.398119\pi$
$72$	−649.695	−1.06343
$73$	−167.148	−0.267988	−0.133994	−	0.990982i	$-0.542780\pi$
$73$	−167.148	−0.267988	−0.133994	+	0.990982i	$0.542780\pi$
$74$	−1214.20	−1.90740
$75$	267.554	0.411926
$76$	−631.940	−0.953796
$77$	−9.12518	−0.0135053
$78$	772.233	1.12100
$79$	−1139.41	−1.62270	−0.811351	−	0.584559i	$-0.801267\pi$
$79$	−1139.41	−1.62270	−0.811351	+	0.584559i	$0.801267\pi$
$80$	−1318.48	−1.84263
$81$	81.0000	0.111111
$82$	1929.46	2.59845
$83$	21.0554	0.0278450	0.0139225	−	0.999903i	$-0.495568\pi$
$83$	21.0554	0.0278450	0.0139225	+	0.999903i	$0.495568\pi$
$84$	−15.3818	−0.0199796
$85$	−809.513	−1.03299
$86$	1692.73	2.12246
$87$	76.1904	0.0938904
$88$	2740.34	3.31955
$89$	59.0821	0.0703673	0.0351837	−	0.999381i	$-0.488798\pi$
$89$	59.0821	0.0703673	0.0351837	+	0.999381i	$0.488798\pi$
$90$	291.696	0.341638
$91$	11.4256	0.0131619
$92$	1374.45	1.55757
$93$	−5.92382	−0.00660506
$94$	3144.99	3.45086
$95$	177.309	0.191489
$96$	1846.90	1.96352
$97$	−1504.63	−1.57497	−0.787487	−	0.616331i	$-0.788618\pi$
$97$	−1504.63	−1.57497	−0.787487	+	0.616331i	$0.788618\pi$
$98$	1857.26	1.91441
$99$	−341.648	−0.346838
$100$	−1902.26	−1.90226
$101$	−49.8987	−0.0491595	−0.0245798	−	0.999698i	$-0.507825\pi$
$101$	−49.8987	−0.0491595	−0.0245798	+	0.999698i	$0.507825\pi$
$102$	2197.67	2.13335
$103$	−565.191	−0.540679	−0.270339	−	0.962765i	$-0.587136\pi$
$103$	−565.191	−0.540679	−0.270339	+	0.962765i	$0.587136\pi$
$104$	−3431.17	−3.23513
$105$	4.31579	0.00401122
$106$	−1618.75	−1.48327
$107$	1688.83	1.52584	0.762922	−	0.646490i	$-0.223764\pi$
$107$	1688.83	1.52584	0.762922	+	0.646490i	$0.223764\pi$
$108$	−575.897	−0.513108
$109$	−2031.16	−1.78486	−0.892430	−	0.451185i	$-0.851001\pi$
$109$	−2031.16	−1.78486	−0.892430	+	0.451185i	$0.851001\pi$
$110$	−1230.34	−1.06644
$111$	−672.603	−0.575141
$112$	52.9593	0.0446803
$113$	−1460.18	−1.21559	−0.607797	−	0.794092i	$-0.707947\pi$
$113$	−1460.18	−1.21559	−0.607797	+	0.794092i	$0.707947\pi$
$114$	−481.358	−0.395468
$115$	−385.642	−0.312707
$116$	−541.701	−0.433583
$117$	427.777	0.338017
$118$	2216.35	1.72908
$119$	32.5157	0.0250480
$120$	−1296.05	−0.985942
$121$	110.033	0.0826694
$122$	−1044.87	−0.775395
$123$	1068.82	0.783513
$124$	42.1174	0.0305020
$125$	1281.81	0.917188
$126$	−11.7165	−0.00828406
$127$	−562.989	−0.393364	−0.196682	−	0.980467i	$-0.563017\pi$
$127$	−562.989	−0.393364	−0.196682	+	0.980467i	$0.563017\pi$
$128$	−3586.03	−2.47627
$129$	937.684	0.639988
$130$	1540.50	1.03932
$131$	−1768.62	−1.17958	−0.589790	−	0.807557i	$-0.700789\pi$
$131$	−1768.62	−1.17958	−0.589790	+	0.807557i	$0.700789\pi$
$132$	2429.07	1.60169
$133$	−7.12195	−0.00464325
$134$	−362.850	−0.233921
$135$	161.584	0.103014
$136$	−9764.62	−6.15669
$137$	−1794.65	−1.11918	−0.559589	−	0.828770i	$-0.689041\pi$
$137$	−1794.65	−1.11918	−0.559589	+	0.828770i	$0.689041\pi$
$138$	1046.94	0.645809
$139$	2729.80	1.66575	0.832873	−	0.553463i	$-0.186694\pi$
$139$	2729.80	1.66575	0.832873	+	0.553463i	$0.186694\pi$
$140$	−30.6846	−0.0185237
$141$	1742.16	1.04054
$142$	−2038.80	−1.20487
$143$	−1804.31	−1.05513
$144$	1982.81	1.14746
$145$	151.990	0.0870486
$146$	905.217	0.513125
$147$	1028.83	0.577253
$148$	4782.10	2.65599
$149$	1775.23	0.976057	0.488029	−	0.872828i	$-0.337716\pi$
$149$	1775.23	0.976057	0.488029	+	0.872828i	$0.337716\pi$
$150$	−1448.98	−0.788727
$151$	585.605	0.315601	0.157801	−	0.987471i	$-0.449560\pi$
$151$	585.605	0.315601	0.157801	+	0.987471i	$0.449560\pi$
$152$	2138.76	1.14129
$153$	1217.39	0.643271
$154$	49.4190	0.0258591
$155$	−11.8172	−0.00612375
$156$	−3041.43	−1.56095
$157$	2203.90	1.12032	0.560160	−	0.828384i	$-0.310740\pi$
$157$	2203.90	1.12032	0.560160	+	0.828384i	$0.310740\pi$
$158$	6170.66	3.10704
$159$	−896.701	−0.447251
$160$	3684.31	1.82044
$161$	15.4901	0.00758254
$162$	−438.670	−0.212748
$163$	830.464	0.399061	0.199530	−	0.979892i	$-0.436058\pi$
$163$	830.464	0.399061	0.199530	+	0.979892i	$0.436058\pi$
$164$	−7599.12	−3.61824
$165$	−681.543	−0.321564
$166$	−114.029	−0.0533156
$167$	−2131.41	−0.987625	−0.493813	−	0.869568i	$-0.664397\pi$
$167$	−2131.41	−0.987625	−0.493813	+	0.869568i	$0.664397\pi$
$168$	52.0586	0.0239072
$169$	62.1744	0.0282997
$170$	4384.06	1.97789
$171$	−266.647	−0.119246
$172$	−6666.78	−2.95545
$173$	3219.12	1.41471	0.707355	−	0.706859i	$-0.249888\pi$
$173$	3219.12	1.41471	0.707355	+	0.706859i	$0.249888\pi$
$174$	−412.622	−0.179775
$175$	−21.4385	−0.00926055
$176$	−8363.26	−3.58184
$177$	1227.74	0.521372
$178$	−319.970	−0.134734
$179$	893.563	0.373118	0.186559	−	0.982444i	$-0.440267\pi$
$179$	893.563	0.373118	0.186559	+	0.982444i	$0.440267\pi$
$180$	−1148.84	−0.475718
$181$	−2604.65	−1.06963	−0.534813	−	0.844970i	$-0.679618\pi$
$181$	−2604.65	−1.06963	−0.534813	+	0.844970i	$0.679618\pi$
$182$	−61.8773	−0.0252014
$183$	−578.804	−0.233806
$184$	−4651.75	−1.86376
$185$	−1341.75	−0.533230
$186$	32.0814	0.0126469
$187$	−5134.82	−2.00800
$188$	−12386.5	−4.80520
$189$	−6.49035	−0.00249790
$190$	−960.246	−0.366650
$191$	4181.28	1.58402	0.792008	−	0.610510i	$-0.209036\pi$
$191$	4181.28	1.58402	0.792008	+	0.610510i	$0.209036\pi$
$192$	−4714.69	−1.77215
$193$	3273.90	1.22104	0.610519	−	0.792002i	$-0.290961\pi$
$193$	3273.90	1.22104	0.610519	+	0.792002i	$0.290961\pi$
$194$	8148.61	3.01565
$195$	853.358	0.313386
$196$	−7314.79	−2.66574
$197$	−1096.31	−0.396492	−0.198246	−	0.980152i	$-0.563524\pi$
$197$	−1096.31	−0.396492	−0.198246	+	0.980152i	$0.563524\pi$
$198$	1850.26	0.664101
$199$	−4008.18	−1.42780	−0.713900	−	0.700247i	$-0.753073\pi$
$199$	−4008.18	−1.42780	−0.713900	+	0.700247i	$0.753073\pi$
$200$	6438.08	2.27621
$201$	−201.000	−0.0705346
$202$	270.235	0.0941272
$203$	−6.10496	−0.00211076
$204$	−8655.47	−2.97061
$205$	2132.15	0.726418
$206$	3060.89	1.03525
$207$	579.951	0.194731
$208$	10471.6	3.49075
$209$	1124.69	0.372231
$210$	−23.3729	−0.00768040
$211$	−3924.11	−1.28032	−0.640158	−	0.768244i	$-0.721131\pi$
$211$	−3924.11	−1.28032	−0.640158	+	0.768244i	$0.721131\pi$
$212$	6375.40	2.06540
$213$	−1129.39	−0.363307
$214$	−9146.15	−2.92158
$215$	1870.55	0.593352
$216$	1949.08	0.613974
$217$	0.474662	0.000148489 0
$218$	11000.1	3.41753
$219$	501.443	0.154723
$220$	4845.66	1.48497
$221$	6429.30	1.95693
$222$	3642.60	1.10124
$223$	−810.312	−0.243329	−0.121665	−	0.992571i	$-0.538823\pi$
$223$	−810.312	−0.243329	−0.121665	+	0.992571i	$0.538823\pi$
$224$	−147.988	−0.0441421
$225$	−802.661	−0.237826
$226$	7907.86	2.32754
$227$	−6445.26	−1.88452	−0.942262	−	0.334877i	$-0.891305\pi$
$227$	−6445.26	−1.88452	−0.942262	+	0.334877i	$0.891305\pi$
$228$	1895.82	0.550674
$229$	5101.52	1.47213	0.736065	−	0.676911i	$-0.236682\pi$
$229$	5101.52	1.47213	0.736065	+	0.676911i	$0.236682\pi$
$230$	2088.51	0.598749
$231$	27.3755	0.00779730
$232$	1833.35	0.518816
$233$	−1292.39	−0.363378	−0.181689	−	0.983356i	$-0.558156\pi$
$233$	−1292.39	−0.363378	−0.181689	+	0.983356i	$0.558156\pi$
$234$	−2316.70	−0.647211
$235$	3475.38	0.964718
$236$	−8729.06	−2.40768
$237$	3418.22	0.936867
$238$	−176.094	−0.0479601
$239$	1494.55	0.404497	0.202248	−	0.979334i	$-0.435175\pi$
$239$	1494.55	0.404497	0.202248	+	0.979334i	$0.435175\pi$
$240$	3955.44	1.06384
$241$	1268.30	0.338997	0.169498	−	0.985530i	$-0.445785\pi$
$241$	1268.30	0.338997	0.169498	+	0.985530i	$0.445785\pi$
$242$	−595.903	−0.158290
$243$	−243.000	−0.0641500
$244$	4115.21	1.07971
$245$	2052.37	0.535189
$246$	−5788.37	−1.50021
$247$	−1408.22	−0.362764
$248$	−142.543	−0.0364980
$249$	−63.1663	−0.0160763
$250$	−6941.86	−1.75617
$251$	2978.74	0.749069	0.374534	−	0.927213i	$-0.377803\pi$
$251$	2978.74	0.749069	0.374534	+	0.927213i	$0.377803\pi$
$252$	46.1453	0.0115352
$253$	−2446.17	−0.607862
$254$	3048.96	0.753185
$255$	2428.54	0.596396
$256$	6848.22	1.67193
$257$	3081.16	0.747849	0.373925	−	0.927459i	$-0.378012\pi$
$257$	3081.16	0.747849	0.373925	+	0.927459i	$0.378012\pi$
$258$	−5078.19	−1.22540
$259$	53.8941	0.0129298
$260$	−6067.24	−1.44721
$261$	−228.571	−0.0542076
$262$	9578.26	2.25858
$263$	−4196.06	−0.983804	−0.491902	−	0.870651i	$-0.663698\pi$
$263$	−4196.06	−0.983804	−0.491902	+	0.870651i	$0.663698\pi$
$264$	−8221.01	−1.91655
$265$	−1788.80	−0.414660
$266$	38.5702	0.00889056
$267$	−177.246	−0.0406266
$268$	1429.08	0.325727
$269$	−7315.52	−1.65812	−0.829061	−	0.559158i	$-0.811125\pi$
$269$	−7315.52	−1.65812	−0.829061	+	0.559158i	$0.811125\pi$
$270$	−875.087	−0.197245
$271$	−3232.76	−0.724636	−0.362318	−	0.932054i	$-0.618015\pi$
$271$	−3232.76	−0.724636	−0.362318	+	0.932054i	$0.618015\pi$
$272$	29800.7	6.64314
$273$	−34.2768	−0.00759900
$274$	9719.24	2.14292
$275$	3385.53	0.742382
$276$	−4123.36	−0.899265
$277$	823.975	0.178729	0.0893644	−	0.995999i	$-0.471516\pi$
$277$	823.975	0.178729	0.0893644	+	0.995999i	$0.471516\pi$
$278$	−14783.7	−3.18946
$279$	17.7714	0.00381344
$280$	103.850	0.0221651
$281$	−7377.42	−1.56619	−0.783096	−	0.621901i	$-0.786361\pi$
$281$	−7377.42	−1.56619	−0.783096	+	0.621901i	$0.786361\pi$
$282$	−9434.98	−1.99236
$283$	−6662.25	−1.39940	−0.699699	−	0.714438i	$-0.746683\pi$
$283$	−6662.25	−1.39940	−0.699699	+	0.714438i	$0.746683\pi$
$284$	8029.76	1.67774
$285$	−531.926	−0.110556
$286$	9771.57	2.02030
$287$	−85.6420	−0.0176142
$288$	−5540.69	−1.13364
$289$	13383.9	2.72418
$290$	−823.126	−0.166675
$291$	4513.90	0.909312
$292$	−3565.18	−0.714508
$293$	−5673.40	−1.13121	−0.565603	−	0.824678i	$-0.691357\pi$
$293$	−5673.40	−1.13121	−0.565603	+	0.824678i	$0.691357\pi$
$294$	−5571.79	−1.10528
$295$	2449.18	0.483380
$296$	−16184.7	−3.17809
$297$	1024.95	0.200247
$298$	−9614.07	−1.86889
$299$	3062.84	0.592403
$300$	5706.79	1.09827
$301$	−75.1345	−0.0143876
$302$	−3171.44	−0.604291
$303$	149.696	0.0283823
$304$	−6527.30	−1.23147
$305$	−1154.64	−0.216768
$306$	−6593.01	−1.23169
$307$	−5097.46	−0.947647	−0.473823	−	0.880620i	$-0.657126\pi$
$307$	−5097.46	−0.947647	−0.473823	+	0.880620i	$0.657126\pi$
$308$	−194.636	−0.0360078
$309$	1695.57	0.312161
$310$	63.9982	0.0117253
$311$	−6044.33	−1.10207	−0.551033	−	0.834483i	$-0.685766\pi$
$311$	−6044.33	−1.10207	−0.551033	+	0.834483i	$0.685766\pi$
$312$	10293.5	1.86780
$313$	4762.15	0.859976	0.429988	−	0.902835i	$-0.358518\pi$
$313$	4762.15	0.859976	0.429988	+	0.902835i	$0.358518\pi$
$314$	−11935.6	−2.14511
$315$	−12.9474	−0.00231588
$316$	−24303.0	−4.32643
$317$	9507.37	1.68450	0.842251	−	0.539086i	$-0.181230\pi$
$317$	9507.37	1.68450	0.842251	+	0.539086i	$0.181230\pi$
$318$	4856.24	0.856366
$319$	964.086	0.169211
$320$	−9405.18	−1.64302
$321$	−5066.49	−0.880947
$322$	−83.8892	−0.0145185
$323$	−4007.59	−0.690366
$324$	1727.69	0.296243
$325$	−4239.01	−0.723502
$326$	−4497.52	−0.764094
$327$	6093.48	1.03049
$328$	25718.7	4.32951
$329$	−139.595	−0.0233925
$330$	3691.01	0.615708
$331$	1225.85	0.203561	0.101781	−	0.994807i	$-0.467546\pi$
$331$	1225.85	0.203561	0.101781	+	0.994807i	$0.467546\pi$
$332$	449.102	0.0742400
$333$	2017.81	0.332058
$334$	11543.0	1.89104
$335$	−400.968	−0.0653947
$336$	−158.878	−0.0257962
$337$	9909.18	1.60174	0.800872	−	0.598836i	$-0.204370\pi$
$337$	9909.18	1.60174	0.800872	+	0.598836i	$0.204370\pi$
$338$	−336.716	−0.0541863
$339$	4380.54	0.701824
$340$	−17266.5	−2.75414
$341$	−74.9579	−0.0119038
$342$	1444.08	0.228324
$343$	−164.889	−0.0259568
$344$	22563.3	3.53642
$345$	1156.93	0.180541
$346$	−17433.7	−2.70879
$347$	−10771.9	−1.66647	−0.833237	−	0.552916i	$-0.813515\pi$
$347$	−10771.9	−1.66647	−0.833237	+	0.552916i	$0.813515\pi$
$348$	1625.10	0.250330
$349$	947.405	0.145311	0.0726554	−	0.997357i	$-0.476853\pi$
$349$	947.405	0.145311	0.0726554	+	0.997357i	$0.476853\pi$
$350$	116.104	0.0177315
$351$	−1283.33	−0.195154
$352$	23370.0	3.53870
$353$	1458.03	0.219839	0.109920	−	0.993940i	$-0.464941\pi$
$353$	1458.03	0.219839	0.109920	+	0.993940i	$0.464941\pi$
$354$	−6649.06	−0.998287
$355$	−2252.98	−0.336832
$356$	1260.19	0.187613
$357$	−97.5470	−0.0144614
$358$	−4839.25	−0.714419
$359$	−6031.23	−0.886675	−0.443338	−	0.896355i	$-0.646206\pi$
$359$	−6031.23	−0.886675	−0.443338	+	0.896355i	$0.646206\pi$
$360$	3888.16	0.569234
$361$	−5981.21	−0.872024
$362$	14106.0	2.04805
$363$	−330.099	−0.0477292
$364$	243.703	0.0350920
$365$	1000.31	0.143449
$366$	3134.62	0.447675
$367$	−2351.86	−0.334513	−0.167256	−	0.985913i	$-0.553491\pi$
$367$	−2351.86	−0.334513	−0.167256	+	0.985913i	$0.553491\pi$
$368$	14196.7	2.01102
$369$	−3206.45	−0.452361
$370$	7266.49	1.02099
$371$	71.8506	0.0100547
$372$	−126.352	−0.0176104
$373$	−13262.4	−1.84102	−0.920512	−	0.390714i	$-0.872228\pi$
$373$	−13262.4	−1.84102	−0.920512	+	0.390714i	$0.872228\pi$
$374$	27808.5	3.84477
$375$	−3845.43	−0.529539
$376$	41921.2	5.74979
$377$	−1207.13	−0.164908
$378$	35.1496	0.00478281
$379$	−4218.46	−0.571735	−0.285867	−	0.958269i	$-0.592282\pi$
$379$	−4218.46	−0.571735	−0.285867	+	0.958269i	$0.592282\pi$
$380$	3781.91	0.510547
$381$	1688.97	0.227109
$382$	−22644.5	−3.03296
$383$	−13857.5	−1.84879	−0.924393	−	0.381442i	$-0.875427\pi$
$383$	−13857.5	−1.84879	−0.924393	+	0.381442i	$0.875427\pi$
$384$	10758.1	1.42968
$385$	54.6105	0.00722912
$386$	−17730.3	−2.33796
$387$	−2813.05	−0.369497
$388$	−32093.1	−4.19918
$389$	7793.37	1.01578	0.507891	−	0.861421i	$-0.330425\pi$
$389$	7793.37	1.01578	0.507891	+	0.861421i	$0.330425\pi$
$390$	−4621.51	−0.600049
$391$	8716.41	1.12739
$392$	24756.4	3.18976
$393$	5305.86	0.681031
$394$	5937.26	0.759175
$395$	6818.90	0.868598
$396$	−7287.20	−0.924736
$397$	7268.69	0.918904	0.459452	−	0.888203i	$-0.348046\pi$
$397$	7268.69	0.918904	0.459452	+	0.888203i	$0.348046\pi$
$398$	21707.0	2.73385
$399$	21.3659	0.00268078
$400$	−19648.4	−2.45606
$401$	3406.13	0.424175	0.212087	−	0.977251i	$-0.431974\pi$
$401$	3406.13	0.424175	0.212087	+	0.977251i	$0.431974\pi$
$402$	1088.55	0.135055
$403$	93.8545	0.0116011
$404$	−1064.32	−0.131069
$405$	−484.753	−0.0594754
$406$	33.0625	0.00404154
$407$	−8510.88	−1.03653
$408$	29293.9	3.55456
$409$	3370.02	0.407425	0.203713	−	0.979031i	$-0.434699\pi$
$409$	3370.02	0.407425	0.203713	+	0.979031i	$0.434699\pi$
$410$	−11547.0	−1.39089
$411$	5383.95	0.646158
$412$	−12055.2	−1.44155
$413$	−98.3764	−0.0117210
$414$	−3140.83	−0.372858
$415$	−126.008	−0.0149048
$416$	−29261.5	−3.44871
$417$	−8189.41	−0.961719
$418$	−6090.94	−0.712722
$419$	13405.3	1.56298	0.781491	−	0.623916i	$-0.214459\pi$
$419$	13405.3	1.56298	0.781491	+	0.623916i	$0.214459\pi$
$420$	92.0538	0.0106947
$421$	5647.26	0.653754	0.326877	−	0.945067i	$-0.394004\pi$
$421$	5647.26	0.653754	0.326877	+	0.945067i	$0.394004\pi$
$422$	21251.7	2.45146
$423$	−5226.48	−0.600757
$424$	−21577.1	−2.47141
$425$	−12063.6	−1.37688
$426$	6116.39	0.695634
$427$	46.3783	0.00525621
$428$	36021.9	4.06819
$429$	5412.94	0.609182
$430$	−10130.3	−1.13611
$431$	−4981.76	−0.556759	−0.278379	−	0.960471i	$-0.589797\pi$
$431$	−4981.76	−0.556759	−0.278379	+	0.960471i	$0.589797\pi$
$432$	−5948.43	−0.662486
$433$	10316.6	1.14500	0.572501	−	0.819904i	$-0.305973\pi$
$433$	10316.6	1.14500	0.572501	+	0.819904i	$0.305973\pi$
$434$	−2.57061	−0.000284317 0
$435$	−455.969	−0.0502575
$436$	−43323.6	−4.75878
$437$	−1909.17	−0.208988
$438$	−2715.65	−0.296253
$439$	4285.11	0.465870	0.232935	−	0.972492i	$-0.425167\pi$
$439$	4285.11	0.465870	0.232935	+	0.972492i	$0.425167\pi$
$440$	−16399.8	−1.77689
$441$	−3086.48	−0.333277
$442$	−34819.0	−3.74699
$443$	−8296.34	−0.889776	−0.444888	−	0.895586i	$-0.646757\pi$
$443$	−8296.34	−0.889776	−0.444888	+	0.895586i	$0.646757\pi$
$444$	−14346.3	−1.53343
$445$	−353.583	−0.0376661
$446$	4388.38	0.465910
$447$	−5325.69	−0.563527
$448$	377.778	0.0398400
$449$	−13124.1	−1.37944	−0.689718	−	0.724078i	$-0.742265\pi$
$449$	−13124.1	−1.37944	−0.689718	+	0.724078i	$0.742265\pi$
$450$	4346.95	0.455372
$451$	13524.4	1.41206
$452$	−31144.9	−3.24101
$453$	−1756.81	−0.182213
$454$	34905.4	3.60835
$455$	−68.3777	−0.00704526
$456$	−6416.28	−0.658925
$457$	3378.12	0.345781	0.172891	−	0.984941i	$-0.444689\pi$
$457$	3378.12	0.345781	0.172891	+	0.984941i	$0.444689\pi$
$458$	−27628.1	−2.81873
$459$	−3652.18	−0.371393
$460$	−8225.55	−0.833736
$461$	−10967.7	−1.10806	−0.554032	−	0.832495i	$-0.686912\pi$
$461$	−10967.7	−1.10806	−0.554032	+	0.832495i	$0.686912\pi$
$462$	−148.257	−0.0149297
$463$	3969.83	0.398474	0.199237	−	0.979951i	$-0.436154\pi$
$463$	3969.83	0.398474	0.199237	+	0.979951i	$0.436154\pi$
$464$	−5595.22	−0.559809
$465$	35.4517	0.00353555
$466$	6999.14	0.695770
$467$	5582.37	0.553150	0.276575	−	0.960992i	$-0.410801\pi$
$467$	5582.37	0.553150	0.276575	+	0.960992i	$0.410801\pi$
$468$	9124.28	0.901217
$469$	16.1057	0.00158570
$470$	−18821.5	−1.84717
$471$	−6611.70	−0.646817
$472$	29542.9	2.88098
$473$	11865.1	1.15340
$474$	−18512.0	−1.79385
$475$	2642.32	0.255237
$476$	693.544	0.0667826
$477$	2690.10	0.258221
$478$	−8094.02	−0.774502
$479$	13477.8	1.28563	0.642817	−	0.766020i	$-0.277766\pi$
$479$	13477.8	1.28563	0.642817	+	0.766020i	$0.277766\pi$
$480$	−11052.9	−1.05103
$481$	10656.4	1.01017
$482$	−6868.69	−0.649087
$483$	−46.4702	−0.00437778
$484$	2346.95	0.220412
$485$	9004.64	0.843050
$486$	1316.01	0.122830
$487$	11595.4	1.07893	0.539464	−	0.842009i	$-0.318627\pi$
$487$	11595.4	1.07893	0.539464	+	0.842009i	$0.318627\pi$
$488$	−13927.6	−1.29196
$489$	−2491.39	−0.230398
$490$	−11115.0	−1.02474
$491$	5241.03	0.481720	0.240860	−	0.970560i	$-0.422571\pi$
$491$	5241.03	0.481720	0.240860	+	0.970560i	$0.422571\pi$
$492$	22797.4	2.08899
$493$	−3435.32	−0.313832
$494$	7626.45	0.694595
$495$	2044.63	0.185655
$496$	435.029	0.0393818
$497$	90.4952	0.00816754
$498$	342.088	0.0307818
$499$	−8603.60	−0.771844	−0.385922	−	0.922531i	$-0.626117\pi$
$499$	−8603.60	−0.771844	−0.385922	+	0.922531i	$0.626117\pi$
$500$	27340.4	2.44540
$501$	6394.23	0.570206
$502$	−16131.9	−1.43426
$503$	10824.9	0.959557	0.479778	−	0.877390i	$-0.340717\pi$
$503$	10824.9	0.959557	0.479778	+	0.877390i	$0.340717\pi$
$504$	−156.176	−0.0138028
$505$	298.624	0.0263140
$506$	13247.6	1.16389
$507$	−186.523	−0.0163388
$508$	−12008.3	−1.04878
$509$	15663.0	1.36395	0.681973	−	0.731377i	$-0.261122\pi$
$509$	15663.0	1.36395	0.681973	+	0.731377i	$0.261122\pi$
$510$	−13152.2	−1.14194
$511$	−40.1795	−0.00347835
$512$	−8399.53	−0.725020
$513$	799.942	0.0688466
$514$	−16686.5	−1.43193
$515$	3382.44	0.289414
$516$	20000.3	1.70633
$517$	22044.7	1.87529
$518$	−291.873	−0.0247571
$519$	−9657.35	−0.816783
$520$	20534.2	1.73170
$521$	−18547.1	−1.55962	−0.779812	−	0.626014i	$-0.784685\pi$
$521$	−18547.1	−1.55962	−0.779812	+	0.626014i	$0.784685\pi$
$522$	1237.87	0.103793
$523$	−17866.9	−1.49382	−0.746909	−	0.664926i	$-0.768463\pi$
$523$	−17866.9	−1.49382	−0.746909	+	0.664926i	$0.768463\pi$
$524$	−37723.8	−3.14498
$525$	64.3154	0.00534658
$526$	22724.5	1.88372
$527$	267.097	0.0220777
$528$	25089.8	2.06798
$529$	−8014.61	−0.658717
$530$	9687.54	0.793962
$531$	−3683.23	−0.301014
$532$	−151.908	−0.0123798
$533$	−16933.9	−1.37615
$534$	959.909	0.0777890
$535$	−10107.0	−0.816752
$536$	−4836.62	−0.389757
$537$	−2680.69	−0.215420
$538$	39618.4	3.17486
$539$	13018.4	1.04034
$540$	3446.51	0.274656
$541$	−10215.9	−0.811862	−0.405931	−	0.913904i	$-0.633053\pi$
$541$	−10215.9	−0.811862	−0.405931	+	0.913904i	$0.633053\pi$
$542$	17507.6	1.38748
$543$	7813.96	0.617549
$544$	−83274.1	−6.56314
$545$	12155.7	0.955398
$546$	185.632	0.0145500
$547$	21491.5	1.67991	0.839956	−	0.542654i	$-0.182580\pi$
$547$	21491.5	1.67991	0.839956	+	0.542654i	$0.182580\pi$
$548$	−38279.0	−2.98394
$549$	1736.41	0.134988
$550$	−18334.9	−1.42146
$551$	752.443	0.0581763
$552$	13955.2	1.07604
$553$	−273.895	−0.0210618
$554$	−4462.38	−0.342217
$555$	4025.26	0.307861
$556$	58225.4	4.44120
$557$	−10007.2	−0.761256	−0.380628	−	0.924728i	$-0.624292\pi$
$557$	−10007.2	−0.761256	−0.380628	+	0.924728i	$0.624292\pi$
$558$	−96.2443	−0.00730170
$559$	−14856.3	−1.12407
$560$	−316.940	−0.0239164
$561$	15404.5	1.15932
$562$	39953.7	2.99883
$563$	7298.57	0.546355	0.273178	−	0.961964i	$-0.411925\pi$
$563$	7298.57	0.546355	0.273178	+	0.961964i	$0.411925\pi$
$564$	37159.5	2.77428
$565$	8738.59	0.650682
$566$	36080.6	2.67947
$567$	19.4710	0.00144216
$568$	−27176.2	−2.00755
$569$	−16000.7	−1.17888	−0.589441	−	0.807811i	$-0.700652\pi$
$569$	−16000.7	−1.17888	−0.589441	+	0.807811i	$0.700652\pi$
$570$	2880.74	0.211686
$571$	8565.60	0.627775	0.313887	−	0.949460i	$-0.398369\pi$
$571$	8565.60	0.627775	0.313887	+	0.949460i	$0.398369\pi$
$572$	−38485.1	−2.81319
$573$	−12543.9	−0.914532
$574$	463.809	0.0337265
$575$	−5746.97	−0.416809
$576$	14144.1	1.02315
$577$	25566.0	1.84458	0.922292	−	0.386493i	$-0.126314\pi$
$577$	25566.0	1.84458	0.922292	+	0.386493i	$0.126314\pi$
$578$	−72482.7	−5.21606
$579$	−9821.69	−0.704966
$580$	3241.86	0.232088
$581$	5.06137	0.000361413 0
$582$	−24445.8	−1.74109
$583$	−11346.5	−0.806047
$584$	12066.1	0.854964
$585$	−2560.07	−0.180933
$586$	30725.3	2.16595
$587$	15583.1	1.09571	0.547856	−	0.836573i	$-0.315444\pi$
$587$	15583.1	1.09571	0.547856	+	0.836573i	$0.315444\pi$
$588$	21944.4	1.53907
$589$	−58.5026	−0.00409263
$590$	−13264.0	−0.925542
$591$	3288.93	0.228915
$592$	49394.2	3.42920
$593$	−5236.88	−0.362653	−0.181326	−	0.983423i	$-0.558039\pi$
$593$	−5236.88	−0.362653	−0.181326	+	0.983423i	$0.558039\pi$
$594$	−5550.77	−0.383419
$595$	−194.593	−0.0134076
$596$	37864.8	2.60235
$597$	12024.5	0.824341
$598$	−16587.3	−1.13429
$599$	−23036.0	−1.57133	−0.785665	−	0.618653i	$-0.787679\pi$
$599$	−23036.0	−1.57133	−0.785665	+	0.618653i	$0.787679\pi$
$600$	−19314.2	−1.31417
$601$	−13905.9	−0.943814	−0.471907	−	0.881648i	$-0.656434\pi$
$601$	−13905.9	−0.943814	−0.471907	+	0.881648i	$0.656434\pi$
$602$	406.904	0.0275484
$603$	603.000	0.0407231
$604$	12490.7	0.841453
$605$	−658.504	−0.0442512
$606$	−810.706	−0.0543443
$607$	10503.6	0.702352	0.351176	−	0.936309i	$-0.385782\pi$
$607$	10503.6	0.702352	0.351176	+	0.936309i	$0.385782\pi$
$608$	18239.6	1.21664
$609$	18.3149	0.00121865
$610$	6253.14	0.415053
$611$	−27602.1	−1.82760
$612$	25966.4	1.71508
$613$	11120.7	0.732728	0.366364	−	0.930472i	$-0.380602\pi$
$613$	11120.7	0.732728	0.366364	+	0.930472i	$0.380602\pi$
$614$	27606.2	1.81449
$615$	−6396.45	−0.419398
$616$	658.731	0.0430861
$617$	−911.661	−0.0594847	−0.0297424	−	0.999558i	$-0.509469\pi$
$617$	−911.661	−0.0594847	−0.0297424	+	0.999558i	$0.509469\pi$
$618$	−9182.66	−0.597704
$619$	5917.03	0.384209	0.192105	−	0.981374i	$-0.438469\pi$
$619$	5917.03	0.384209	0.192105	+	0.981374i	$0.438469\pi$
$620$	−252.056	−0.0163271
$621$	−1739.85	−0.112428
$622$	32734.1	2.11016
$623$	14.2024	0.000913331 0
$624$	−31414.8	−2.01538
$625$	3476.96	0.222525
$626$	−25790.2	−1.64662
$627$	−3374.06	−0.214908
$628$	47008.1	2.98699
$629$	30326.7	1.92243
$630$	70.1188	0.00443428
$631$	5466.92	0.344904	0.172452	−	0.985018i	$-0.444831\pi$
$631$	5466.92	0.344904	0.172452	+	0.985018i	$0.444831\pi$
$632$	82251.9	5.17691
$633$	11772.3	0.739190
$634$	−51488.8	−3.22536
$635$	3369.26	0.210559
$636$	−19126.2	−1.19246
$637$	−16300.3	−1.01388
$638$	−5221.17	−0.323994
$639$	3388.16	0.209755
$640$	21460.9	1.32550
$641$	9780.66	0.602672	0.301336	−	0.953518i	$-0.402567\pi$
$641$	9780.66	0.602672	0.301336	+	0.953518i	$0.402567\pi$
$642$	27438.5	1.68677
$643$	−6795.79	−0.416796	−0.208398	−	0.978044i	$-0.566825\pi$
$643$	−6795.79	−0.416796	−0.208398	+	0.978044i	$0.566825\pi$
$644$	330.396	0.0202165
$645$	−5611.66	−0.342572
$646$	21703.8	1.32187
$647$	−4638.38	−0.281845	−0.140922	−	0.990021i	$-0.545007\pi$
$647$	−4638.38	−0.281845	−0.140922	+	0.990021i	$0.545007\pi$
$648$	−5847.25	−0.354478
$649$	15535.4	0.939629
$650$	22957.1	1.38531
$651$	−1.42399	−8.57303e−5 0
$652$	17713.4	1.06397
$653$	9616.25	0.576283	0.288142	−	0.957588i	$-0.406963\pi$
$653$	9616.25	0.576283	0.288142	+	0.957588i	$0.406963\pi$
$654$	−33000.3	−1.97311
$655$	10584.5	0.631404
$656$	−78491.2	−4.67159
$657$	−1504.33	−0.0893295
$658$	756.003	0.0447904
$659$	−13686.4	−0.809025	−0.404512	−	0.914533i	$-0.632559\pi$
$659$	−13686.4	−0.809025	−0.404512	+	0.914533i	$0.632559\pi$
$660$	−14537.0	−0.857350
$661$	8135.84	0.478741	0.239370	−	0.970928i	$-0.423059\pi$
$661$	8135.84	0.478741	0.239370	+	0.970928i	$0.423059\pi$
$662$	−6638.80	−0.389765
$663$	−19287.9	−1.12983
$664$	−1519.95	−0.0888339
$665$	42.6220	0.00248543
$666$	−10927.8	−0.635801
$667$	−1636.54	−0.0950034
$668$	−45461.9	−2.63320
$669$	2430.93	0.140486
$670$	2171.51	0.125213
$671$	−7323.99	−0.421370
$672$	443.963	0.0254855
$673$	15377.4	0.880768	0.440384	−	0.897810i	$-0.354842\pi$
$673$	15377.4	0.880768	0.440384	+	0.897810i	$0.354842\pi$
$674$	−53664.9	−3.06691
$675$	2407.98	0.137309
$676$	1326.15	0.0754523
$677$	−17861.2	−1.01398	−0.506988	−	0.861953i	$-0.669241\pi$
$677$	−17861.2	−1.01398	−0.506988	+	0.861953i	$0.669241\pi$
$678$	−23723.6	−1.34380
$679$	−361.689	−0.0204423
$680$	58437.3	3.29554
$681$	19335.8	1.08803
$682$	405.947	0.0227926
$683$	24798.4	1.38929	0.694643	−	0.719354i	$-0.255562\pi$
$683$	24798.4	1.38929	0.694643	+	0.719354i	$0.255562\pi$
$684$	−5687.46	−0.317932
$685$	10740.3	0.599072
$686$	892.985	0.0497002
$687$	−15304.6	−0.849935
$688$	−68861.0	−3.81585
$689$	14207.0	0.785547
$690$	−6265.53	−0.345688
$691$	11240.9	0.618846	0.309423	−	0.950925i	$-0.399864\pi$
$691$	11240.9	0.618846	0.309423	+	0.950925i	$0.399864\pi$
$692$	68662.2	3.77188
$693$	−82.1266	−0.00450178
$694$	58337.1	3.19085
$695$	−16336.8	−0.891639
$696$	−5500.05	−0.299539
$697$	−48191.6	−2.61892
$698$	−5130.84	−0.278231
$699$	3877.16	0.209796
$700$	−457.272	−0.0246904
$701$	−27402.4	−1.47642	−0.738212	−	0.674569i	$-0.764330\pi$
$701$	−27402.4	−1.47642	−0.738212	+	0.674569i	$0.764330\pi$
$702$	6950.10	0.373668
$703$	−6642.51	−0.356368
$704$	−59658.1	−3.19382
$705$	−10426.1	−0.556980
$706$	−7896.24	−0.420933
$707$	−11.9948	−0.000638065 0
$708$	26187.2	1.39008
$709$	−15939.0	−0.844290	−0.422145	−	0.906528i	$-0.638723\pi$
$709$	−15939.0	−0.844290	−0.422145	+	0.906528i	$0.638723\pi$
$710$	12201.4	0.644943
$711$	−10254.7	−0.540901
$712$	−4265.04	−0.224493
$713$	127.242	0.00668336
$714$	528.283	0.0276898
$715$	10798.1	0.564791
$716$	19059.3	0.994802
$717$	−4483.66	−0.233536
$718$	32663.2	1.69774
$719$	25429.3	1.31899	0.659495	−	0.751709i	$-0.270770\pi$
$719$	25429.3	1.31899	0.659495	+	0.751709i	$0.270770\pi$
$720$	−11866.3	−0.614210
$721$	−135.862	−0.00701773
$722$	32392.3	1.66969
$723$	−3804.89	−0.195720
$724$	−55556.0	−2.85183
$725$	2265.00	0.116028
$726$	1787.71	0.0913886
$727$	6240.30	0.318349	0.159175	−	0.987250i	$-0.449117\pi$
$727$	6240.30	0.318349	0.159175	+	0.987250i	$0.449117\pi$
$728$	−824.795	−0.0419903
$729$	729.000	0.0370370
$730$	−5417.36	−0.274665
$731$	−42278.9	−2.13918
$732$	−12345.6	−0.623370
$733$	18842.5	0.949474	0.474737	−	0.880128i	$-0.342543\pi$
$733$	18842.5	0.949474	0.474737	+	0.880128i	$0.342543\pi$
$734$	12736.9	0.640501
$735$	−6157.11	−0.308991
$736$	−39670.7	−1.98680
$737$	−2543.38	−0.127119
$738$	17365.1	0.866149
$739$	−12594.4	−0.626916	−0.313458	−	0.949602i	$-0.601488\pi$
$739$	−12594.4	−0.626916	−0.313458	+	0.949602i	$0.601488\pi$
$740$	−28618.9	−1.42169
$741$	4224.65	0.209442
$742$	−389.119	−0.0192521
$743$	11592.2	0.572375	0.286188	−	0.958174i	$-0.407612\pi$
$743$	11592.2	0.572375	0.286188	+	0.958174i	$0.407612\pi$
$744$	427.630	0.0210722
$745$	−10624.0	−0.522463
$746$	71824.9	3.52506
$747$	189.499	0.00928166
$748$	−109523.	−5.35370
$749$	405.966	0.0198047
$750$	20825.6	1.01392
$751$	−22113.3	−1.07447	−0.537235	−	0.843433i	$-0.680531\pi$
$751$	−22113.3	−1.07447	−0.537235	+	0.843433i	$0.680531\pi$
$752$	−127940.	−6.20410
$753$	−8936.21	−0.432475
$754$	6537.41	0.315754
$755$	−3504.61	−0.168935
$756$	−138.436	−0.00665988
$757$	13405.2	0.643620	0.321810	−	0.946804i	$-0.395709\pi$
$757$	13405.2	0.643620	0.321810	+	0.946804i	$0.395709\pi$
$758$	22845.8	1.09472
$759$	7338.50	0.350950
$760$	−12799.6	−0.610909
$761$	20111.1	0.957986	0.478993	−	0.877819i	$-0.341002\pi$
$761$	20111.1	0.957986	0.478993	+	0.877819i	$0.341002\pi$
$762$	−9146.89	−0.434852
$763$	−488.257	−0.0231666
$764$	89184.8	4.22329
$765$	−7285.61	−0.344329
$766$	75047.6	3.53992
$767$	−19451.9	−0.915732
$768$	−20544.7	−0.965289
$769$	−15298.0	−0.717373	−0.358686	−	0.933458i	$-0.616775\pi$
$769$	−15298.0	−0.717373	−0.358686	+	0.933458i	$0.616775\pi$
$770$	−295.753	−0.0138418
$771$	−9243.47	−0.431771
$772$	69830.6	3.25552
$773$	−19083.6	−0.887957	−0.443978	−	0.896037i	$-0.646433\pi$
$773$	−19083.6	−0.887957	−0.443978	+	0.896037i	$0.646433\pi$
$774$	15234.6	0.707487
$775$	−176.104	−0.00816239
$776$	108617.	5.02464
$777$	−161.682	−0.00746503
$778$	−42206.3	−1.94495
$779$	10555.5	0.485480
$780$	18201.7	0.835546
$781$	−14290.9	−0.654760
$782$	−47205.2	−2.15864
$783$	685.713	0.0312968
$784$	−75554.3	−3.44180
$785$	−13189.5	−0.599684
$786$	−28734.8	−1.30399
$787$	−6808.97	−0.308403	−0.154202	−	0.988039i	$-0.549281\pi$
$787$	−6808.97	−0.308403	−0.154202	+	0.988039i	$0.549281\pi$
$788$	−23383.8	−1.05712
$789$	12588.2	0.567999
$790$	−36928.9	−1.66313
$791$	−351.003	−0.0157778
$792$	24663.0	1.10652
$793$	9170.34	0.410654
$794$	−39364.8	−1.75945
$795$	5366.39	0.239404
$796$	−85492.5	−3.80679
$797$	−2856.16	−0.126939	−0.0634695	−	0.997984i	$-0.520217\pi$
$797$	−2856.16	−0.126939	−0.0634695	+	0.997984i	$0.520217\pi$
$798$	−115.711	−0.00513297
$799$	−78551.7	−3.47805
$800$	54904.9	2.42648
$801$	531.739	0.0234558
$802$	−18446.5	−0.812180
$803$	6345.08	0.278846
$804$	−4287.23	−0.188059
$805$	−92.7019	−0.00405877
$806$	−508.285	−0.0222129
$807$	21946.6	0.957317
$808$	3602.10	0.156834
$809$	−2363.37	−0.102709	−0.0513545	−	0.998680i	$-0.516354\pi$
$809$	−2363.37	−0.102709	−0.0513545	+	0.998680i	$0.516354\pi$
$810$	2625.26	0.113879
$811$	−2251.89	−0.0975027	−0.0487513	−	0.998811i	$-0.515524\pi$
$811$	−2251.89	−0.0975027	−0.0487513	+	0.998811i	$0.515524\pi$
$812$	−130.216	−0.00562769
$813$	9698.29	0.418369
$814$	46092.1	1.98468
$815$	−4969.99	−0.213609
$816$	−89402.2	−3.83542
$817$	9260.40	0.396549
$818$	−18250.9	−0.780109
$819$	102.830	0.00438728
$820$	45477.7	1.93677
$821$	−1774.32	−0.0754252	−0.0377126	−	0.999289i	$-0.512007\pi$
$821$	−1774.32	−0.0754252	−0.0377126	+	0.999289i	$0.512007\pi$
$822$	−29157.7	−1.23722
$823$	−29623.5	−1.25469	−0.627344	−	0.778742i	$-0.715858\pi$
$823$	−29623.5	−1.25469	−0.627344	+	0.778742i	$0.715858\pi$
$824$	40800.2	1.72493
$825$	−10156.6	−0.428615
$826$	532.774	0.0224426
$827$	−43578.0	−1.83235	−0.916175	−	0.400777i	$-0.868740\pi$
$827$	−43578.0	−1.83235	−0.916175	+	0.400777i	$0.868740\pi$
$828$	12370.1	0.519191
$829$	31465.6	1.31827	0.659134	−	0.752025i	$-0.270923\pi$
$829$	31465.6	1.31827	0.659134	+	0.752025i	$0.270923\pi$
$830$	682.419	0.0285387
$831$	−2471.92	−0.103189
$832$	74697.7	3.11259
$833$	−46388.4	−1.92949
$834$	44351.2	1.84143
$835$	12755.6	0.528655
$836$	23989.0	0.992438
$837$	−53.3143	−0.00220169
$838$	−72598.5	−2.99269
$839$	28854.9	1.18735	0.593673	−	0.804707i	$-0.297677\pi$
$839$	28854.9	1.18735	0.593673	+	0.804707i	$0.297677\pi$
$840$	−311.550	−0.0127970
$841$	−23744.0	−0.973554
$842$	−30583.7	−1.25176
$843$	22132.3	0.904242
$844$	−83699.3	−3.41356
$845$	−372.089	−0.0151482
$846$	28304.9	1.15029
$847$	26.4501	0.00107301
$848$	65851.3	2.66668
$849$	19986.8	0.807943
$850$	65332.7	2.63635
$851$	14447.3	0.581959
$852$	−24089.3	−0.968644
$853$	−12658.4	−0.508109	−0.254054	−	0.967190i	$-0.581764\pi$
$853$	−12658.4	−0.508109	−0.254054	+	0.967190i	$0.581764\pi$
$854$	−251.170	−0.0100642
$855$	1595.78	0.0638298
$856$	−121914.	−4.86790
$857$	−8416.53	−0.335476	−0.167738	−	0.985832i	$-0.553646\pi$
$857$	−8416.53	−0.335476	−0.167738	+	0.985832i	$0.553646\pi$
$858$	−29314.7	−1.16642
$859$	19828.4	0.787585	0.393793	−	0.919199i	$-0.371163\pi$
$859$	19828.4	0.787585	0.393793	+	0.919199i	$0.371163\pi$
$860$	39898.0	1.58199
$861$	256.926	0.0101696
$862$	26979.6	1.06604
$863$	35837.9	1.41360	0.706799	−	0.707414i	$-0.250138\pi$
$863$	35837.9	1.41360	0.706799	+	0.707414i	$0.250138\pi$
$864$	16622.1	0.654507
$865$	−19265.1	−0.757264
$866$	−55871.5	−2.19237
$867$	−40151.6	−1.57280
$868$	10.1243	0.000395900 0
$869$	43253.0	1.68844
$870$	2469.38	0.0962296
$871$	3184.56	0.123886
$872$	146626.	5.69424
$873$	−13541.7	−0.524992
$874$	10339.4	0.400156
$875$	308.125	0.0119046
$876$	10695.5	0.412521
$877$	−26922.7	−1.03662	−0.518310	−	0.855193i	$-0.673439\pi$
$877$	−26922.7	−1.03662	−0.518310	+	0.855193i	$0.673439\pi$
$878$	−23206.7	−0.892015
$879$	17020.2	0.653102
$880$	50050.7	1.91728
$881$	7933.01	0.303371	0.151686	−	0.988429i	$-0.451530\pi$
$881$	7933.01	0.303371	0.151686	+	0.988429i	$0.451530\pi$
$882$	16715.4	0.638136
$883$	18451.2	0.703207	0.351604	−	0.936149i	$-0.385636\pi$
$883$	18451.2	0.703207	0.351604	+	0.936149i	$0.385636\pi$
$884$	137134.	5.21754
$885$	−7347.55	−0.279079
$886$	44930.3	1.70368
$887$	−14127.3	−0.534778	−0.267389	−	0.963589i	$-0.586161\pi$
$887$	−14127.3	−0.534778	−0.267389	+	0.963589i	$0.586161\pi$
$888$	48554.0	1.83487
$889$	−135.333	−0.00510566
$890$	1914.89	0.0721205
$891$	−3074.84	−0.115613
$892$	−17283.6	−0.648763
$893$	17205.3	0.644740
$894$	28842.2	1.07900
$895$	−5347.62	−0.199722
$896$	−862.020	−0.0321407
$897$	−9188.51	−0.342024
$898$	71076.1	2.64125
$899$	−50.1486	−0.00186046
$900$	−17120.4	−0.634088
$901$	40431.0	1.49495
$902$	−73244.0	−2.70372
$903$	225.403	0.00830671
$904$	105408.	3.87811
$905$	15587.8	0.572548
$906$	9514.33	0.348888
$907$	−30362.1	−1.11153	−0.555765	−	0.831339i	$-0.687575\pi$
$907$	−30362.1	−1.11153	−0.555765	+	0.831339i	$0.687575\pi$
$908$	−137474.	−5.02450
$909$	−449.089	−0.0163865
$910$	370.311	0.0134898
$911$	2707.76	0.0984764	0.0492382	−	0.998787i	$-0.484321\pi$
$911$	2707.76	0.0984764	0.0492382	+	0.998787i	$0.484321\pi$
$912$	19581.9	0.710988
$913$	−799.284	−0.0289731
$914$	−18294.8	−0.662077
$915$	3463.91	0.125151
$916$	108813.	3.92498
$917$	−425.146	−0.0153103
$918$	19779.0	0.711116
$919$	30109.0	1.08074	0.540371	−	0.841427i	$-0.318284\pi$
$919$	30109.0	1.08074	0.540371	+	0.841427i	$0.318284\pi$
$920$	27838.8	0.997629
$921$	15292.4	0.547124
$922$	59397.6	2.12164
$923$	17893.5	0.638107
$924$	583.907	0.0207891
$925$	−19995.3	−0.710746
$926$	−21499.3	−0.762970
$927$	−5086.72	−0.180226
$928$	15635.1	0.553067
$929$	−21271.9	−0.751249	−0.375624	−	0.926772i	$-0.622572\pi$
$929$	−21271.9	−0.751249	−0.375624	+	0.926772i	$0.622572\pi$
$930$	−191.995	−0.00676962
$931$	10160.5	0.357677
$932$	−27566.0	−0.968834
$933$	18133.0	0.636278
$934$	−30232.3	−1.05913
$935$	30729.9	1.07484
$936$	−30880.5	−1.07838
$937$	8777.73	0.306036	0.153018	−	0.988223i	$-0.451101\pi$
$937$	8777.73	0.306036	0.153018	+	0.988223i	$0.451101\pi$
$938$	−87.2231	−0.00303618
$939$	−14286.4	−0.496507
$940$	74128.1	2.57212
$941$	−20055.0	−0.694767	−0.347384	−	0.937723i	$-0.612930\pi$
$941$	−20055.0	−0.694767	−0.347384	+	0.937723i	$0.612930\pi$
$942$	35806.8	1.23848
$943$	−22957.9	−0.792801
$944$	−90162.3	−3.10861
$945$	38.8421	0.00133707
$946$	−64257.6	−2.20845
$947$	49690.8	1.70510	0.852552	−	0.522643i	$-0.175054\pi$
$947$	49690.8	1.70510	0.852552	+	0.522643i	$0.175054\pi$
$948$	72909.1	2.49787
$949$	−7944.66	−0.271754
$950$	−14309.9	−0.488711
$951$	−28522.1	−0.972547
$952$	−2347.25	−0.0799106
$953$	−8709.73	−0.296050	−0.148025	−	0.988984i	$-0.547292\pi$
$953$	−8709.73	−0.296050	−0.148025	+	0.988984i	$0.547292\pi$
$954$	−14568.7	−0.494423
$955$	−25023.3	−0.847890
$956$	31878.1	1.07846
$957$	−2892.26	−0.0976943
$958$	−72991.6	−2.46164
$959$	−431.404	−0.0145263
$960$	28215.6	0.948597
$961$	−29787.1	−0.999869
$962$	−57711.8	−1.93420
$963$	15199.5	0.508615
$964$	27052.2	0.903830
$965$	−19593.0	−0.653595
$966$	251.667	0.00838227
$967$	−12008.6	−0.399349	−0.199675	−	0.979862i	$-0.563988\pi$
$967$	−12008.6	−0.399349	−0.199675	+	0.979862i	$0.563988\pi$
$968$	−7943.10	−0.263741
$969$	12022.8	0.398583
$970$	−48766.2	−1.61421
$971$	2825.30	0.0933759	0.0466880	−	0.998910i	$-0.485133\pi$
$971$	2825.30	0.0933759	0.0466880	+	0.998910i	$0.485133\pi$
$972$	−5183.07	−0.171036
$973$	656.199	0.0216205
$974$	−62796.9	−2.06585
$975$	12717.0	0.417714
$976$	42505.9	1.39404
$977$	−11885.3	−0.389194	−0.194597	−	0.980883i	$-0.562340\pi$
$977$	−11885.3	−0.389194	−0.194597	+	0.980883i	$0.562340\pi$
$978$	13492.6	0.441150
$979$	−2242.81	−0.0732182
$980$	43776.1	1.42691
$981$	−18280.4	−0.594954
$982$	−28383.7	−0.922364
$983$	−47754.7	−1.54948	−0.774739	−	0.632281i	$-0.782119\pi$
$983$	−47754.7	−1.54948	−0.774739	+	0.632281i	$0.782119\pi$
$984$	−77156.1	−2.49964
$985$	6560.98	0.212234
$986$	18604.6	0.600903
$987$	418.786	0.0135057
$988$	−30036.6	−0.967198
$989$	−20141.1	−0.647574
$990$	−11073.0	−0.355479
$991$	−15288.7	−0.490072	−0.245036	−	0.969514i	$-0.578800\pi$
$991$	−15288.7	−0.490072	−0.245036	+	0.969514i	$0.578800\pi$
$992$	−1215.63	−0.0389076
$993$	−3677.55	−0.117526
$994$	−490.093	−0.0156386
$995$	23987.3	0.764271
$996$	−1347.31	−0.0428625
$997$	38948.3	1.23722	0.618608	−	0.785700i	$-0.287697\pi$
$997$	38948.3	1.23722	0.618608	+	0.785700i	$0.287697\pi$
$998$	46594.3	1.47787
$999$	−6053.42	−0.191714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.c.1.1	✓	7
3.2	odd	2		603.4.a.c.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.c.1.1	✓	7	1.1	even	1	trivial
603.4.a.c.1.7		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)

\(f(q)\)	\(=\)	\(q-5.41567 q^{2} -3.00000 q^{3} +21.3295 q^{4} -5.98460 q^{5} +16.2470 q^{6} +0.240383 q^{7} -72.1883 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.41567 q^{2} -3.00000 q^{3} +21.3295 q^{4} -5.98460 q^{5} +16.2470 q^{6} +0.240383 q^{7} -72.1883 q^{8} +9.00000 q^{9} +32.4106 q^{10} -37.9609 q^{11} -63.9885 q^{12} +47.5308 q^{13} -1.30184 q^{14} +17.9538 q^{15} +220.312 q^{16} +135.266 q^{17} -48.7411 q^{18} -29.6275 q^{19} -127.649 q^{20} -0.721150 q^{21} +205.584 q^{22} +64.4390 q^{23} +216.565 q^{24} -89.1846 q^{25} -257.411 q^{26} -27.0000 q^{27} +5.12726 q^{28} -25.3968 q^{29} -97.2319 q^{30} +1.97461 q^{31} -615.632 q^{32} +113.883 q^{33} -732.556 q^{34} -1.43860 q^{35} +191.966 q^{36} +224.201 q^{37} +160.453 q^{38} -142.592 q^{39} +432.018 q^{40} -356.273 q^{41} +3.90551 q^{42} -312.561 q^{43} -809.688 q^{44} -53.8614 q^{45} -348.981 q^{46} -580.720 q^{47} -660.936 q^{48} -342.942 q^{49} +482.995 q^{50} -405.798 q^{51} +1013.81 q^{52} +298.900 q^{53} +146.223 q^{54} +227.181 q^{55} -17.3529 q^{56} +88.8825 q^{57} +137.541 q^{58} -409.248 q^{59} +382.946 q^{60} +192.935 q^{61} -10.6938 q^{62} +2.16345 q^{63} +1571.56 q^{64} -284.453 q^{65} -616.752 q^{66} +67.0000 q^{67} +2885.16 q^{68} -193.317 q^{69} +7.79097 q^{70} +376.462 q^{71} -649.695 q^{72} -167.148 q^{73} -1214.20 q^{74} +267.554 q^{75} -631.940 q^{76} -9.12518 q^{77} +772.233 q^{78} -1139.41 q^{79} -1318.48 q^{80} +81.0000 q^{81} +1929.46 q^{82} +21.0554 q^{83} -15.3818 q^{84} -809.513 q^{85} +1692.73 q^{86} +76.1904 q^{87} +2740.34 q^{88} +59.0821 q^{89} +291.696 q^{90} +11.4256 q^{91} +1374.45 q^{92} -5.92382 q^{93} +3144.99 q^{94} +177.309 q^{95} +1846.90 q^{96} -1504.63 q^{97} +1857.26 q^{98} -341.648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9	\( 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9} - 51 q^{10} - 130 q^{11} - 63 q^{12} + 16 q^{13} + 5 q^{14} - 33 q^{15} + 77 q^{16} + 90 q^{17} - 9 q^{18} - 132 q^{19} - 359 q^{20} + 99 q^{21} - 192 q^{22} - 399 q^{23} + 135 q^{24} - 132 q^{25} - 638 q^{26} - 189 q^{27} - 245 q^{28} - 302 q^{29} + 153 q^{30} - 555 q^{31} - 1031 q^{32} + 390 q^{33} - 832 q^{34} - 775 q^{35} + 189 q^{36} + 297 q^{37} + 98 q^{38} - 48 q^{39} + 305 q^{40} - 717 q^{41} - 15 q^{42} - 245 q^{43} - 1766 q^{44} + 99 q^{45} - 497 q^{46} - 1072 q^{47} - 231 q^{48} + 314 q^{49} + 454 q^{50} - 270 q^{51} + 1344 q^{52} + 265 q^{53} + 27 q^{54} + 1096 q^{55} - 477 q^{56} + 396 q^{57} + 1610 q^{58} - 255 q^{59} + 1077 q^{60} + 418 q^{61} - 191 q^{62} - 297 q^{63} + 1889 q^{64} + 262 q^{65} + 576 q^{66} + 469 q^{67} + 3720 q^{68} + 1197 q^{69} + 1309 q^{70} - 1194 q^{71} - 405 q^{72} + 995 q^{73} + 259 q^{74} + 396 q^{75} + 1506 q^{76} + 230 q^{77} + 1914 q^{78} - 2640 q^{79} - 1949 q^{80} + 567 q^{81} + 1535 q^{82} - 2579 q^{83} + 735 q^{84} - 562 q^{85} + 1991 q^{86} + 906 q^{87} + 3624 q^{88} - 1604 q^{89} - 459 q^{90} - 2116 q^{91} - 351 q^{92} + 1665 q^{93} + 6178 q^{94} - 3028 q^{95} + 3093 q^{96} - 808 q^{97} + 258 q^{98} - 1170 q^{99}+O(q^{100}) \) 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9 - 51 * q^10 - 130 * q^11 - 63 * q^12 + 16 * q^13 + 5 * q^14 - 33 * q^15 + 77 * q^16 + 90 * q^17 - 9 * q^18 - 132 * q^19 - 359 * q^20 + 99 * q^21 - 192 * q^22 - 399 * q^23 + 135 * q^24 - 132 * q^25 - 638 * q^26 - 189 * q^27 - 245 * q^28 - 302 * q^29 + 153 * q^30 - 555 * q^31 - 1031 * q^32 + 390 * q^33 - 832 * q^34 - 775 * q^35 + 189 * q^36 + 297 * q^37 + 98 * q^38 - 48 * q^39 + 305 * q^40 - 717 * q^41 - 15 * q^42 - 245 * q^43 - 1766 * q^44 + 99 * q^45 - 497 * q^46 - 1072 * q^47 - 231 * q^48 + 314 * q^49 + 454 * q^50 - 270 * q^51 + 1344 * q^52 + 265 * q^53 + 27 * q^54 + 1096 * q^55 - 477 * q^56 + 396 * q^57 + 1610 * q^58 - 255 * q^59 + 1077 * q^60 + 418 * q^61 - 191 * q^62 - 297 * q^63 + 1889 * q^64 + 262 * q^65 + 576 * q^66 + 469 * q^67 + 3720 * q^68 + 1197 * q^69 + 1309 * q^70 - 1194 * q^71 - 405 * q^72 + 995 * q^73 + 259 * q^74 + 396 * q^75 + 1506 * q^76 + 230 * q^77 + 1914 * q^78 - 2640 * q^79 - 1949 * q^80 + 567 * q^81 + 1535 * q^82 - 2579 * q^83 + 735 * q^84 - 562 * q^85 + 1991 * q^86 + 906 * q^87 + 3624 * q^88 - 1604 * q^89 - 459 * q^90 - 2116 * q^91 - 351 * q^92 + 1665 * q^93 + 6178 * q^94 - 3028 * q^95 + 3093 * q^96 - 808 * q^97 + 258 * q^98 - 1170 * q^99

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