LMFDB - Embedded newform 201.4.a.d.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:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 54x^{7} + 138x^{6} + 949x^{5} - 2039x^{4} - 5472x^{3} + 10352x^{2} + 3808x - 6656 $ x^9 - 3x^8 - 54x^7 + 138x^6 + 949x^5 - 2039x^4 - 5472x^3 + 10352x^2 + 3808x - 6656
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.46691$ 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)

$f(q)$	$=$	$q-4.46691 q^{2} -3.00000 q^{3} +11.9533 q^{4} -5.77925 q^{5} +13.4007 q^{6} -31.2412 q^{7} -17.6590 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.46691 q^{2} -3.00000 q^{3} +11.9533 q^{4} -5.77925 q^{5} +13.4007 q^{6} -31.2412 q^{7} -17.6590 q^{8} +9.00000 q^{9} +25.8154 q^{10} +16.7852 q^{11} -35.8599 q^{12} -84.1751 q^{13} +139.552 q^{14} +17.3377 q^{15} -16.7453 q^{16} -57.1887 q^{17} -40.2022 q^{18} -40.6729 q^{19} -69.0810 q^{20} +93.7237 q^{21} -74.9778 q^{22} -110.272 q^{23} +52.9769 q^{24} -91.6003 q^{25} +376.003 q^{26} -27.0000 q^{27} -373.435 q^{28} +293.536 q^{29} -77.4461 q^{30} +65.2333 q^{31} +216.071 q^{32} -50.3555 q^{33} +255.457 q^{34} +180.551 q^{35} +107.580 q^{36} +164.408 q^{37} +181.682 q^{38} +252.525 q^{39} +102.056 q^{40} -170.062 q^{41} -418.655 q^{42} +256.183 q^{43} +200.638 q^{44} -52.0132 q^{45} +492.573 q^{46} +278.135 q^{47} +50.2358 q^{48} +633.014 q^{49} +409.170 q^{50} +171.566 q^{51} -1006.17 q^{52} -89.5766 q^{53} +120.607 q^{54} -97.0056 q^{55} +551.688 q^{56} +122.019 q^{57} -1311.20 q^{58} -366.525 q^{59} +207.243 q^{60} -401.633 q^{61} -291.391 q^{62} -281.171 q^{63} -831.209 q^{64} +486.469 q^{65} +224.933 q^{66} -67.0000 q^{67} -683.593 q^{68} +330.815 q^{69} -806.504 q^{70} +441.953 q^{71} -158.931 q^{72} +865.464 q^{73} -734.394 q^{74} +274.801 q^{75} -486.175 q^{76} -524.389 q^{77} -1128.01 q^{78} -69.9382 q^{79} +96.7750 q^{80} +81.0000 q^{81} +759.650 q^{82} +1012.95 q^{83} +1120.31 q^{84} +330.508 q^{85} -1144.35 q^{86} -880.609 q^{87} -296.409 q^{88} -1514.64 q^{89} +232.338 q^{90} +2629.73 q^{91} -1318.11 q^{92} -195.700 q^{93} -1242.40 q^{94} +235.059 q^{95} -648.214 q^{96} -1250.94 q^{97} -2827.62 q^{98} +151.067 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{2} - 27 q^{3} + 45 q^{4} + 12 q^{5} - 9 q^{6} + 8 q^{7} + 51 q^{8} + 81 q^{9}+O(q^{10}) $ 9 * q + 3 * q^2 - 27 * q^3 + 45 * q^4 + 12 * q^5 - 9 * q^6 + 8 * q^7 + 51 * q^8 + 81 * q^9	\( 9 q + 3 q^{2} - 27 q^{3} + 45 q^{4} + 12 q^{5} - 9 q^{6} + 8 q^{7} + 51 q^{8} + 81 q^{9} + 45 q^{10} + 72 q^{11} - 135 q^{12} - 166 q^{13} + 93 q^{14} - 36 q^{15} + 173 q^{16} + 146 q^{17} + 27 q^{18} + 154 q^{19} + 763 q^{20} - 24 q^{21} + 244 q^{22} + 476 q^{23} - 153 q^{24} + 465 q^{25} + 502 q^{26} - 243 q^{27} - 141 q^{28} + 432 q^{29} - 135 q^{30} + 248 q^{31} + 1171 q^{32} - 216 q^{33} + 146 q^{34} + 178 q^{35} + 405 q^{36} - 240 q^{37} + 1182 q^{38} + 498 q^{39} + 1409 q^{40} + 406 q^{41} - 279 q^{42} + 154 q^{43} + 892 q^{44} + 108 q^{45} + 273 q^{46} + 494 q^{47} - 519 q^{48} + 431 q^{49} + 1658 q^{50} - 438 q^{51} - 1258 q^{52} - 450 q^{53} - 81 q^{54} - 346 q^{55} - 659 q^{56} - 462 q^{57} - 2114 q^{58} + 732 q^{59} - 2289 q^{60} - 914 q^{61} - 1265 q^{62} + 72 q^{63} - 467 q^{64} - 536 q^{65} - 732 q^{66} - 603 q^{67} - 3314 q^{68} - 1428 q^{69} - 4805 q^{70} + 2990 q^{71} + 459 q^{72} - 1384 q^{73} - 2043 q^{74} - 1395 q^{75} + 450 q^{76} + 1660 q^{77} - 1506 q^{78} + 2438 q^{79} + 995 q^{80} + 729 q^{81} - 3561 q^{82} + 972 q^{83} + 423 q^{84} - 2706 q^{85} - 21 q^{86} - 1296 q^{87} - 3796 q^{88} + 1034 q^{89} + 405 q^{90} + 1898 q^{91} + 1827 q^{92} - 744 q^{93} - 3502 q^{94} + 6040 q^{95} - 3513 q^{96} - 1516 q^{97} - 3996 q^{98} + 648 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 - 27 * q^3 + 45 * q^4 + 12 * q^5 - 9 * q^6 + 8 * q^7 + 51 * q^8 + 81 * q^9 + 45 * q^10 + 72 * q^11 - 135 * q^12 - 166 * q^13 + 93 * q^14 - 36 * q^15 + 173 * q^16 + 146 * q^17 + 27 * q^18 + 154 * q^19 + 763 * q^20 - 24 * q^21 + 244 * q^22 + 476 * q^23 - 153 * q^24 + 465 * q^25 + 502 * q^26 - 243 * q^27 - 141 * q^28 + 432 * q^29 - 135 * q^30 + 248 * q^31 + 1171 * q^32 - 216 * q^33 + 146 * q^34 + 178 * q^35 + 405 * q^36 - 240 * q^37 + 1182 * q^38 + 498 * q^39 + 1409 * q^40 + 406 * q^41 - 279 * q^42 + 154 * q^43 + 892 * q^44 + 108 * q^45 + 273 * q^46 + 494 * q^47 - 519 * q^48 + 431 * q^49 + 1658 * q^50 - 438 * q^51 - 1258 * q^52 - 450 * q^53 - 81 * q^54 - 346 * q^55 - 659 * q^56 - 462 * q^57 - 2114 * q^58 + 732 * q^59 - 2289 * q^60 - 914 * q^61 - 1265 * q^62 + 72 * q^63 - 467 * q^64 - 536 * q^65 - 732 * q^66 - 603 * q^67 - 3314 * q^68 - 1428 * q^69 - 4805 * q^70 + 2990 * q^71 + 459 * q^72 - 1384 * q^73 - 2043 * q^74 - 1395 * q^75 + 450 * q^76 + 1660 * q^77 - 1506 * q^78 + 2438 * q^79 + 995 * q^80 + 729 * q^81 - 3561 * q^82 + 972 * q^83 + 423 * q^84 - 2706 * q^85 - 21 * q^86 - 1296 * q^87 - 3796 * q^88 + 1034 * q^89 + 405 * q^90 + 1898 * q^91 + 1827 * q^92 - 744 * q^93 - 3502 * q^94 + 6040 * q^95 - 3513 * q^96 - 1516 * q^97 - 3996 * q^98 + 648 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.46691	−1.57929	−0.789646	−	0.613563i	$-0.789736\pi$
$2$	−4.46691	−1.57929	−0.789646	+	0.613563i	$0.789736\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	11.9533	1.49416
$5$	−5.77925	−0.516912	−0.258456	−	0.966023i	$-0.583214\pi$
$5$	−5.77925	−0.516912	−0.258456	+	0.966023i	$0.583214\pi$
$6$	13.4007	0.911804
$7$	−31.2412	−1.68687	−0.843434	−	0.537233i	$-0.819470\pi$
$7$	−31.2412	−1.68687	−0.843434	+	0.537233i	$0.819470\pi$
$8$	−17.6590	−0.780424
$9$	9.00000	0.333333
$10$	25.8154	0.816354
$11$	16.7852	0.460083	0.230042	−	0.973181i	$-0.426114\pi$
$11$	16.7852	0.460083	0.230042	+	0.973181i	$0.426114\pi$
$12$	−35.8599	−0.862654
$13$	−84.1751	−1.79584	−0.897922	−	0.440154i	$-0.854924\pi$
$13$	−84.1751	−1.79584	−0.897922	+	0.440154i	$0.854924\pi$
$14$	139.552	2.66406
$15$	17.3377	0.298439
$16$	−16.7453	−0.261645
$17$	−57.1887	−0.815899	−0.407950	−	0.913004i	$-0.633756\pi$
$17$	−57.1887	−0.815899	−0.407950	+	0.913004i	$0.633756\pi$
$18$	−40.2022	−0.526430
$19$	−40.6729	−0.491105	−0.245553	−	0.969383i	$-0.578969\pi$
$19$	−40.6729	−0.491105	−0.245553	+	0.969383i	$0.578969\pi$
$20$	−69.0810	−0.772349
$21$	93.7237	0.973913
$22$	−74.9778	−0.726606
$23$	−110.272	−0.999705	−0.499853	−	0.866110i	$-0.666613\pi$
$23$	−110.272	−0.999705	−0.499853	+	0.866110i	$0.666613\pi$
$24$	52.9769	0.450578
$25$	−91.6003	−0.732802
$26$	376.003	2.83616
$27$	−27.0000	−0.192450
$28$	−373.435	−2.52045
$29$	293.536	1.87960	0.939799	−	0.341728i	$-0.111012\pi$
$29$	293.536	1.87960	0.939799	+	0.341728i	$0.111012\pi$
$30$	−77.4461	−0.471322
$31$	65.2333	0.377943	0.188972	−	0.981983i	$-0.439485\pi$
$31$	65.2333	0.377943	0.188972	+	0.981983i	$0.439485\pi$
$32$	216.071	1.19364
$33$	−50.3555	−0.265629
$34$	255.457	1.28854
$35$	180.551	0.871961
$36$	107.580	0.498054
$37$	164.408	0.730498	0.365249	−	0.930910i	$-0.380984\pi$
$37$	164.408	0.730498	0.365249	+	0.930910i	$0.380984\pi$
$38$	181.682	0.775598
$39$	252.525	1.03683
$40$	102.056	0.403410
$41$	−170.062	−0.647784	−0.323892	−	0.946094i	$-0.604991\pi$
$41$	−170.062	−0.647784	−0.323892	+	0.946094i	$0.604991\pi$
$42$	−418.655	−1.53809
$43$	256.183	0.908549	0.454274	−	0.890862i	$-0.349899\pi$
$43$	256.183	0.908549	0.454274	+	0.890862i	$0.349899\pi$
$44$	200.638	0.687439
$45$	−52.0132	−0.172304
$46$	492.573	1.57883
$47$	278.135	0.863193	0.431597	−	0.902067i	$-0.357950\pi$
$47$	278.135	0.863193	0.431597	+	0.902067i	$0.357950\pi$
$48$	50.2358	0.151061
$49$	633.014	1.84552
$50$	409.170	1.15731
$51$	171.566	0.471060
$52$	−1006.17	−2.68328
$53$	−89.5766	−0.232157	−0.116078	−	0.993240i	$-0.537032\pi$
$53$	−89.5766	−0.232157	−0.116078	+	0.993240i	$0.537032\pi$
$54$	120.607	0.303935
$55$	−97.0056	−0.237823
$56$	551.688	1.31647
$57$	122.019	0.283540
$58$	−1311.20	−2.96843
$59$	−366.525	−0.808772	−0.404386	−	0.914588i	$-0.632515\pi$
$59$	−366.525	−0.808772	−0.404386	+	0.914588i	$0.632515\pi$
$60$	207.243	0.445916
$61$	−401.633	−0.843013	−0.421506	−	0.906825i	$-0.638499\pi$
$61$	−401.633	−0.843013	−0.421506	+	0.906825i	$0.638499\pi$
$62$	−291.391	−0.596883
$63$	−281.171	−0.562289
$64$	−831.209	−1.62346
$65$	486.469	0.928293
$66$	224.933	0.419506
$67$	−67.0000	−0.122169
$67$	−67.0000	−0.122169
$68$	−683.593	−1.21908
$69$	330.815	0.577180
$70$	−806.504	−1.37708
$71$	441.953	0.738735	0.369367	−	0.929284i	$-0.379574\pi$
$71$	441.953	0.738735	0.369367	+	0.929284i	$0.379574\pi$
$72$	−158.931	−0.260141
$73$	865.464	1.38760	0.693801	−	0.720167i	$-0.255935\pi$
$73$	865.464	1.38760	0.693801	+	0.720167i	$0.255935\pi$
$74$	−734.394	−1.15367
$75$	274.801	0.423084
$76$	−486.175	−0.733790
$77$	−524.389	−0.776100
$78$	−1128.01	−1.63746
$79$	−69.9382	−0.0996033	−0.0498017	−	0.998759i	$-0.515859\pi$
$79$	−69.9382	−0.0996033	−0.0498017	+	0.998759i	$0.515859\pi$
$80$	96.7750	0.135247
$81$	81.0000	0.111111
$82$	759.650	1.02304
$83$	1012.95	1.33958	0.669792	−	0.742549i	$-0.266383\pi$
$83$	1012.95	1.33958	0.669792	+	0.742549i	$0.266383\pi$
$84$	1120.31	1.45518
$85$	330.508	0.421748
$86$	−1144.35	−1.43486
$87$	−880.609	−1.08519
$88$	−296.409	−0.359060
$89$	−1514.64	−1.80396	−0.901978	−	0.431783i	$-0.857885\pi$
$89$	−1514.64	−1.80396	−0.901978	+	0.431783i	$0.857885\pi$
$90$	232.338	0.272118
$91$	2629.73	3.02935
$92$	−1318.11	−1.49372
$93$	−195.700	−0.218206
$94$	−1242.40	−1.36323
$95$	235.059	0.253858
$96$	−648.214	−0.689146
$97$	−1250.94	−1.30942	−0.654712	−	0.755878i	$-0.727210\pi$
$97$	−1250.94	−1.30942	−0.654712	+	0.755878i	$0.727210\pi$
$98$	−2827.62	−2.91462
$99$	151.067	0.153361
$100$	−1094.92	−1.09492
$101$	1547.67	1.52474	0.762371	−	0.647140i	$-0.224035\pi$
$101$	1547.67	1.52474	0.762371	+	0.647140i	$0.224035\pi$
$102$	−766.370	−0.743941
$103$	−722.713	−0.691370	−0.345685	−	0.938351i	$-0.612353\pi$
$103$	−722.713	−0.691370	−0.345685	+	0.938351i	$0.612353\pi$
$104$	1486.45	1.40152
$105$	−541.652	−0.503427
$106$	400.131	0.366643
$107$	896.097	0.809617	0.404808	−	0.914402i	$-0.367338\pi$
$107$	896.097	0.809617	0.404808	+	0.914402i	$0.367338\pi$
$108$	−322.739	−0.287551
$109$	−1793.96	−1.57643	−0.788213	−	0.615402i	$-0.788994\pi$
$109$	−1793.96	−1.57643	−0.788213	+	0.615402i	$0.788994\pi$
$110$	433.315	0.375591
$111$	−493.223	−0.421753
$112$	523.142	0.441360
$113$	−1151.81	−0.958878	−0.479439	−	0.877575i	$-0.659160\pi$
$113$	−1151.81	−0.958878	−0.479439	+	0.877575i	$0.659160\pi$
$114$	−545.046	−0.447792
$115$	637.287	0.516759
$116$	3508.72	2.80842
$117$	−757.576	−0.598615
$118$	1637.24	1.27729
$119$	1786.64	1.37631
$120$	−306.167	−0.232909
$121$	−1049.26	−0.788323
$122$	1794.06	1.33136
$123$	510.185	0.373998
$124$	779.752	0.564708
$125$	1251.79	0.895706
$126$	1255.97	0.888018
$127$	2572.83	1.79765	0.898825	−	0.438309i	$-0.144422\pi$
$127$	2572.83	1.79765	0.898825	+	0.438309i	$0.144422\pi$
$128$	1984.37	1.37027
$129$	−768.550	−0.524551
$130$	−2173.01	−1.46604
$131$	−1103.04	−0.735671	−0.367835	−	0.929891i	$-0.619901\pi$
$131$	−1103.04	−0.735671	−0.367835	+	0.929891i	$0.619901\pi$
$132$	−601.914	−0.396893
$133$	1270.67	0.828430
$134$	299.283	0.192941
$135$	156.040	0.0994797
$136$	1009.89	0.636747
$137$	−950.271	−0.592607	−0.296303	−	0.955094i	$-0.595754\pi$
$137$	−950.271	−0.592607	−0.296303	+	0.955094i	$0.595754\pi$
$138$	−1477.72	−0.911535
$139$	−1655.01	−1.00990	−0.504949	−	0.863149i	$-0.668489\pi$
$139$	−1655.01	−1.00990	−0.504949	+	0.863149i	$0.668489\pi$
$140$	2158.17	1.30285
$141$	−834.404	−0.498365
$142$	−1974.16	−1.16668
$143$	−1412.89	−0.826238
$144$	−150.707	−0.0872149
$145$	−1696.42	−0.971586
$146$	−3865.95	−2.19143
$147$	−1899.04	−1.06551
$148$	1965.21	1.09148
$149$	3050.54	1.67725	0.838625	−	0.544709i	$-0.183360\pi$
$149$	3050.54	1.67725	0.838625	+	0.544709i	$0.183360\pi$
$150$	−1227.51	−0.668172
$151$	3232.83	1.74228	0.871140	−	0.491035i	$-0.163381\pi$
$151$	3232.83	1.74228	0.871140	+	0.491035i	$0.163381\pi$
$152$	718.241	0.383270
$153$	−514.698	−0.271966
$154$	2342.40	1.22569
$155$	−376.999	−0.195363
$156$	3018.51	1.54919
$157$	880.492	0.447585	0.223793	−	0.974637i	$-0.428156\pi$
$157$	880.492	0.447585	0.223793	+	0.974637i	$0.428156\pi$
$158$	312.408	0.157303
$159$	268.730	0.134036
$160$	−1248.73	−0.617005
$161$	3445.02	1.68637
$162$	−361.820	−0.175477
$163$	−1698.84	−0.816338	−0.408169	−	0.912906i	$-0.633833\pi$
$163$	−1698.84	−0.816338	−0.408169	+	0.912906i	$0.633833\pi$
$164$	−2032.79	−0.967894
$165$	291.017	0.137307
$166$	−4524.75	−2.11559
$167$	830.954	0.385037	0.192519	−	0.981293i	$-0.438334\pi$
$167$	830.954	0.385037	0.192519	+	0.981293i	$0.438334\pi$
$168$	−1655.06	−0.760065
$169$	4888.45	2.22506
$170$	−1476.35	−0.666063
$171$	−366.056	−0.163702
$172$	3062.23	1.35752
$173$	−1377.01	−0.605157	−0.302579	−	0.953124i	$-0.597848\pi$
$173$	−1377.01	−0.605157	−0.302579	+	0.953124i	$0.597848\pi$
$174$	3933.60	1.71383
$175$	2861.71	1.23614
$176$	−281.072	−0.120378
$177$	1099.58	0.466945
$178$	6765.78	2.84897
$179$	−1275.04	−0.532406	−0.266203	−	0.963917i	$-0.585769\pi$
$179$	−1275.04	−0.532406	−0.266203	+	0.963917i	$0.585769\pi$
$180$	−621.729	−0.257450
$181$	−1741.06	−0.714984	−0.357492	−	0.933916i	$-0.616368\pi$
$181$	−1741.06	−0.714984	−0.357492	+	0.933916i	$0.616368\pi$
$182$	−11746.8	−4.78423
$183$	1204.90	0.486714
$184$	1947.28	0.780194
$185$	−950.152	−0.377603
$186$	874.174	0.344610
$187$	−959.922	−0.375382
$188$	3324.62	1.28975
$189$	843.513	0.324638
$190$	−1049.99	−0.400916
$191$	221.362	0.0838596	0.0419298	−	0.999121i	$-0.486649\pi$
$191$	221.362	0.0838596	0.0419298	+	0.999121i	$0.486649\pi$
$192$	2493.63	0.937302
$193$	−1441.62	−0.537670	−0.268835	−	0.963186i	$-0.586639\pi$
$193$	−1441.62	−0.537670	−0.268835	+	0.963186i	$0.586639\pi$
$194$	5587.85	2.06796
$195$	−1459.41	−0.535950
$196$	7566.60	2.75751
$197$	−237.623	−0.0859386	−0.0429693	−	0.999076i	$-0.513682\pi$
$197$	−237.623	−0.0859386	−0.0429693	+	0.999076i	$0.513682\pi$
$198$	−674.800	−0.242202
$199$	3657.12	1.30275	0.651373	−	0.758757i	$-0.274193\pi$
$199$	3657.12	1.30275	0.651373	+	0.758757i	$0.274193\pi$
$200$	1617.57	0.571896
$201$	201.000	0.0705346
$202$	−6913.30	−2.40801
$203$	−9170.44	−3.17063
$204$	2050.78	0.703839
$205$	982.828	0.334847
$206$	3228.30	1.09187
$207$	−992.445	−0.333235
$208$	1409.53	0.469873
$209$	−682.701	−0.225949
$210$	2419.51	0.795058
$211$	−337.326	−0.110059	−0.0550296	−	0.998485i	$-0.517525\pi$
$211$	−337.326	−0.110059	−0.0550296	+	0.998485i	$0.517525\pi$
$212$	−1070.74	−0.346879
$213$	−1325.86	−0.426509
$214$	−4002.78	−1.27862
$215$	−1480.55	−0.469639
$216$	476.792	0.150193
$217$	−2037.97	−0.637540
$218$	8013.47	2.48964
$219$	−2596.39	−0.801132
$220$	−1159.54	−0.355345
$221$	4813.86	1.46523
$222$	2203.18	0.666071
$223$	−381.611	−0.114594	−0.0572972	−	0.998357i	$-0.518248\pi$
$223$	−381.611	−0.114594	−0.0572972	+	0.998357i	$0.518248\pi$
$224$	−6750.33	−2.01351
$225$	−824.403	−0.244267
$226$	5145.04	1.51435
$227$	2687.64	0.785837	0.392919	−	0.919573i	$-0.371465\pi$
$227$	2687.64	0.785837	0.392919	+	0.919573i	$0.371465\pi$
$228$	1458.52	0.423654
$229$	−5189.23	−1.49744	−0.748721	−	0.662885i	$-0.769332\pi$
$229$	−5189.23	−1.49744	−0.748721	+	0.662885i	$0.769332\pi$
$230$	−2846.70	−0.816113
$231$	1573.17	0.448081
$232$	−5183.55	−1.46688
$233$	3031.15	0.852262	0.426131	−	0.904662i	$-0.359876\pi$
$233$	3031.15	0.852262	0.426131	+	0.904662i	$0.359876\pi$
$234$	3384.02	0.945387
$235$	−1607.41	−0.446195
$236$	−4381.18	−1.20844
$237$	209.815	0.0575060
$238$	−7980.78	−2.17360
$239$	−3833.48	−1.03752	−0.518760	−	0.854920i	$-0.673606\pi$
$239$	−3833.48	−1.03752	−0.518760	+	0.854920i	$0.673606\pi$
$240$	−290.325	−0.0780850
$241$	37.2005	0.00994314	0.00497157	−	0.999988i	$-0.498417\pi$
$241$	37.2005	0.00994314	0.00497157	+	0.999988i	$0.498417\pi$
$242$	4686.94	1.24499
$243$	−243.000	−0.0641500
$244$	−4800.83	−1.25960
$245$	−3658.35	−0.953972
$246$	−2278.95	−0.590652
$247$	3423.64	0.881949
$248$	−1151.95	−0.294956
$249$	−3038.84	−0.773409
$250$	−5591.62	−1.41458
$251$	−945.577	−0.237786	−0.118893	−	0.992907i	$-0.537935\pi$
$251$	−945.577	−0.237786	−0.118893	+	0.992907i	$0.537935\pi$
$252$	−3360.92	−0.840150
$253$	−1850.93	−0.459948
$254$	−11492.6	−2.83901
$255$	−991.523	−0.243496
$256$	−2214.31	−0.540603
$257$	−6891.04	−1.67257	−0.836286	−	0.548294i	$-0.815278\pi$
$257$	−6891.04	−1.67257	−0.836286	+	0.548294i	$0.815278\pi$
$258$	3433.04	0.828419
$259$	−5136.29	−1.23225
$260$	5814.90	1.38702
$261$	2641.83	0.626533
$262$	4927.17	1.16184
$263$	−536.230	−0.125724	−0.0628618	−	0.998022i	$-0.520023\pi$
$263$	−536.230	−0.125724	−0.0628618	+	0.998022i	$0.520023\pi$
$264$	889.226	0.207303
$265$	517.686	0.120004
$266$	−5675.97	−1.30833
$267$	4543.93	1.04151
$268$	−800.870	−0.182541
$269$	1493.61	0.338540	0.169270	−	0.985570i	$-0.445859\pi$
$269$	1493.61	0.338540	0.169270	+	0.985570i	$0.445859\pi$
$270$	−697.015	−0.157107
$271$	5285.92	1.18486	0.592430	−	0.805622i	$-0.298169\pi$
$271$	5285.92	1.18486	0.592430	+	0.805622i	$0.298169\pi$
$272$	957.639	0.213476
$273$	−7889.20	−1.74900
$274$	4244.77	0.935899
$275$	−1537.53	−0.337150
$276$	3954.32	0.862400
$277$	3530.38	0.765776	0.382888	−	0.923795i	$-0.374930\pi$
$277$	3530.38	0.765776	0.382888	+	0.923795i	$0.374930\pi$
$278$	7392.77	1.59492
$279$	587.100	0.125981
$280$	−3188.34	−0.680499
$281$	−1014.39	−0.215350	−0.107675	−	0.994186i	$-0.534341\pi$
$281$	−1014.39	−0.215350	−0.107675	+	0.994186i	$0.534341\pi$
$282$	3727.21	0.787063
$283$	693.775	0.145727	0.0728633	−	0.997342i	$-0.476786\pi$
$283$	693.775	0.145727	0.0728633	+	0.997342i	$0.476786\pi$
$284$	5282.79	1.10379
$285$	−705.176	−0.146565
$286$	6311.27	1.30487
$287$	5312.93	1.09273
$288$	1944.64	0.397879
$289$	−1642.46	−0.334308
$290$	7577.75	1.53442
$291$	3752.83	0.755996
$292$	10345.1	2.07330
$293$	5927.10	1.18179	0.590896	−	0.806748i	$-0.298774\pi$
$293$	5927.10	1.18179	0.590896	+	0.806748i	$0.298774\pi$
$294$	8482.85	1.68275
$295$	2118.24	0.418064
$296$	−2903.27	−0.570098
$297$	−453.200	−0.0885431
$298$	−13626.5	−2.64887
$299$	9282.13	1.79531
$300$	3284.77	0.632155
$301$	−8003.48	−1.53260
$302$	−14440.8	−2.75157
$303$	−4643.01	−0.880310
$304$	681.078	0.128495
$305$	2321.13	0.435763
$306$	2299.11	0.429514
$307$	−4149.65	−0.771443	−0.385722	−	0.922615i	$-0.626047\pi$
$307$	−4149.65	−0.771443	−0.385722	+	0.922615i	$0.626047\pi$
$308$	−6268.17	−1.15962
$309$	2168.14	0.399162
$310$	1684.02	0.308536
$311$	1865.76	0.340184	0.170092	−	0.985428i	$-0.445593\pi$
$311$	1865.76	0.340184	0.170092	+	0.985428i	$0.445593\pi$
$312$	−4459.34	−0.809167
$313$	368.456	0.0665379	0.0332689	−	0.999446i	$-0.489408\pi$
$313$	368.456	0.0665379	0.0332689	+	0.999446i	$0.489408\pi$
$314$	−3933.08	−0.706868
$315$	1624.96	0.290654
$316$	−835.991	−0.148823
$317$	4366.06	0.773573	0.386786	−	0.922169i	$-0.373585\pi$
$317$	4366.06	0.773573	0.386786	+	0.922169i	$0.373585\pi$
$318$	−1200.39	−0.211681
$319$	4927.06	0.864772
$320$	4803.76	0.839183
$321$	−2688.29	−0.467432
$322$	−15388.6	−2.66327
$323$	2326.03	0.400693
$324$	968.216	0.166018
$325$	7710.46	1.31600
$326$	7588.55	1.28924
$327$	5381.89	0.910150
$328$	3003.11	0.505546
$329$	−8689.26	−1.45609
$330$	−1299.95	−0.216848
$331$	7331.75	1.21749	0.608746	−	0.793365i	$-0.291673\pi$
$331$	7331.75	1.21749	0.608746	+	0.793365i	$0.291673\pi$
$332$	12108.1	2.00155
$333$	1479.67	0.243499
$334$	−3711.80	−0.608086
$335$	387.210	0.0631508
$336$	−1569.43	−0.254819
$337$	−2656.36	−0.429381	−0.214690	−	0.976682i	$-0.568874\pi$
$337$	−2656.36	−0.429381	−0.214690	+	0.976682i	$0.568874\pi$
$338$	−21836.3	−3.51401
$339$	3455.43	0.553609
$340$	3950.65	0.630159
$341$	1094.95	0.173886
$342$	1635.14	0.258533
$343$	−9060.40	−1.42628
$344$	−4523.93	−0.709053
$345$	−1911.86	−0.298351
$346$	6150.99	0.955720
$347$	1387.51	0.214655	0.107327	−	0.994224i	$-0.465771\pi$
$347$	1387.51	0.214655	0.107327	+	0.994224i	$0.465771\pi$
$348$	−10526.2	−1.62144
$349$	−7889.46	−1.21007	−0.605033	−	0.796201i	$-0.706840\pi$
$349$	−7889.46	−1.21007	−0.605033	+	0.796201i	$0.706840\pi$
$350$	−12783.0	−1.95223
$351$	2272.73	0.345610
$352$	3626.79	0.549172
$353$	10212.0	1.53974	0.769872	−	0.638198i	$-0.220320\pi$
$353$	10212.0	1.53974	0.769872	+	0.638198i	$0.220320\pi$
$354$	−4911.71	−0.737442
$355$	−2554.15	−0.381860
$356$	−18105.0	−2.69540
$357$	−5359.93	−0.794615
$358$	5695.48	0.840825
$359$	2128.56	0.312927	0.156464	−	0.987684i	$-0.449991\pi$
$359$	2128.56	0.312927	0.156464	+	0.987684i	$0.449991\pi$
$360$	918.500	0.134470
$361$	−5204.72	−0.758816
$362$	7777.17	1.12917
$363$	3147.77	0.455139
$364$	31434.0	4.52634
$365$	−5001.73	−0.717267
$366$	−5382.17	−0.768663
$367$	−8999.03	−1.27996	−0.639980	−	0.768392i	$-0.721057\pi$
$367$	−8999.03	−1.27996	−0.639980	+	0.768392i	$0.721057\pi$
$368$	1846.53	0.261567
$369$	−1530.55	−0.215928
$370$	4244.24	0.596345
$371$	2798.48	0.391617
$372$	−2339.26	−0.326034
$373$	−10142.5	−1.40794	−0.703968	−	0.710231i	$-0.748590\pi$
$373$	−10142.5	−1.40794	−0.703968	+	0.710231i	$0.748590\pi$
$374$	4287.88	0.592837
$375$	−3755.36	−0.517136
$376$	−4911.57	−0.673657
$377$	−24708.5	−3.37546
$378$	−3767.90	−0.512698
$379$	11811.8	1.60087	0.800435	−	0.599420i	$-0.204602\pi$
$379$	11811.8	1.60087	0.800435	+	0.599420i	$0.204602\pi$
$380$	2809.72	0.379305
$381$	−7718.48	−1.03787
$382$	−988.804	−0.132439
$383$	9598.45	1.28057	0.640284	−	0.768138i	$-0.278817\pi$
$383$	9598.45	1.28057	0.640284	+	0.768138i	$0.278817\pi$
$384$	−5953.10	−0.791127
$385$	3030.57	0.401175
$386$	6439.61	0.849138
$387$	2305.65	0.302850
$388$	−14952.9	−1.95649
$389$	−10932.3	−1.42491	−0.712455	−	0.701718i	$-0.752417\pi$
$389$	−10932.3	−1.42491	−0.712455	+	0.701718i	$0.752417\pi$
$390$	6519.04	0.846421
$391$	6306.29	0.815659
$392$	−11178.4	−1.44029
$393$	3309.11	0.424740
$394$	1061.44	0.135722
$395$	404.190	0.0514861
$396$	1805.74	0.229146
$397$	−2392.19	−0.302419	−0.151210	−	0.988502i	$-0.548317\pi$
$397$	−2392.19	−0.302419	−0.151210	+	0.988502i	$0.548317\pi$
$398$	−16336.0	−2.05742
$399$	−3812.01	−0.478294
$400$	1533.87	0.191734
$401$	12786.0	1.59227	0.796135	−	0.605119i	$-0.206874\pi$
$401$	12786.0	1.59227	0.796135	+	0.605119i	$0.206874\pi$
$402$	−897.849	−0.111395
$403$	−5491.02	−0.678727
$404$	18499.7	2.27821
$405$	−468.119	−0.0574346
$406$	40963.5	5.00735
$407$	2759.61	0.336090
$408$	−3029.68	−0.367626
$409$	−2441.83	−0.295209	−0.147605	−	0.989046i	$-0.547156\pi$
$409$	−2441.83	−0.295209	−0.147605	+	0.989046i	$0.547156\pi$
$410$	−4390.20	−0.528821
$411$	2850.81	0.342142
$412$	−8638.80	−1.03302
$413$	11450.7	1.36429
$414$	4433.16	0.526275
$415$	−5854.07	−0.692446
$416$	−18187.8	−2.14359
$417$	4965.02	0.583065
$418$	3049.57	0.356840
$419$	−11349.2	−1.32326	−0.661631	−	0.749829i	$-0.730136\pi$
$419$	−11349.2	−1.32326	−0.661631	+	0.749829i	$0.730136\pi$
$420$	−6474.52	−0.752201
$421$	−4281.69	−0.495670	−0.247835	−	0.968802i	$-0.579719\pi$
$421$	−4281.69	−0.495670	−0.247835	+	0.968802i	$0.579719\pi$
$422$	1506.80	0.173815
$423$	2503.21	0.287731
$424$	1581.83	0.181180
$425$	5238.50	0.597893
$426$	5922.49	0.673581
$427$	12547.5	1.42205
$428$	10711.3	1.20970
$429$	4238.68	0.477029
$430$	6613.47	0.741697
$431$	15245.5	1.70382	0.851911	−	0.523686i	$-0.175443\pi$
$431$	15245.5	1.70382	0.851911	+	0.523686i	$0.175443\pi$
$432$	452.122	0.0503535
$433$	6101.90	0.677226	0.338613	−	0.940926i	$-0.390042\pi$
$433$	6101.90	0.677226	0.338613	+	0.940926i	$0.390042\pi$
$434$	9103.42	1.00686
$435$	5089.26	0.560945
$436$	−21443.7	−2.35543
$437$	4485.07	0.490961
$438$	11597.9	1.26522
$439$	12737.1	1.38476	0.692379	−	0.721534i	$-0.256562\pi$
$439$	12737.1	1.38476	0.692379	+	0.721534i	$0.256562\pi$
$440$	1713.02	0.185602
$441$	5697.13	0.615174
$442$	−21503.1	−2.31402
$443$	−2054.43	−0.220336	−0.110168	−	0.993913i	$-0.535139\pi$
$443$	−2054.43	−0.220336	−0.110168	+	0.993913i	$0.535139\pi$
$444$	−5895.63	−0.630167
$445$	8753.51	0.932485
$446$	1704.62	0.180978
$447$	−9151.63	−0.968361
$448$	25968.0	2.73855
$449$	774.960	0.0814535	0.0407268	−	0.999170i	$-0.487033\pi$
$449$	774.960	0.0814535	0.0407268	+	0.999170i	$0.487033\pi$
$450$	3682.53	0.385769
$451$	−2854.51	−0.298035
$452$	−13767.9	−1.43272
$453$	−9698.50	−1.00591
$454$	−12005.5	−1.24107
$455$	−15197.9	−1.56591
$456$	−2154.72	−0.221281
$457$	−11825.6	−1.21045	−0.605227	−	0.796053i	$-0.706918\pi$
$457$	−11825.6	−1.21045	−0.605227	+	0.796053i	$0.706918\pi$
$458$	23179.8	2.36490
$459$	1544.09	0.157020
$460$	7617.67	0.772121
$461$	4667.33	0.471539	0.235769	−	0.971809i	$-0.424239\pi$
$461$	4667.33	0.471539	0.235769	+	0.971809i	$0.424239\pi$
$462$	−7027.20	−0.707651
$463$	12512.7	1.25597	0.627986	−	0.778225i	$-0.283880\pi$
$463$	12512.7	1.25597	0.627986	+	0.778225i	$0.283880\pi$
$464$	−4915.34	−0.491787
$465$	1131.00	0.112793
$466$	−13539.9	−1.34597
$467$	−9885.94	−0.979587	−0.489793	−	0.871839i	$-0.662928\pi$
$467$	−9885.94	−0.979587	−0.489793	+	0.871839i	$0.662928\pi$
$468$	−9055.52	−0.894427
$469$	2093.16	0.206084
$470$	7180.15	0.704671
$471$	−2641.48	−0.258413
$472$	6472.46	0.631185
$473$	4300.08	0.418008
$474$	−937.223	−0.0908187
$475$	3725.65	0.359883
$476$	21356.3	2.05643
$477$	−806.190	−0.0773855
$478$	17123.8	1.63855
$479$	−6083.64	−0.580310	−0.290155	−	0.956980i	$-0.593707\pi$
$479$	−6083.64	−0.580310	−0.290155	+	0.956980i	$0.593707\pi$
$480$	3746.19	0.356228
$481$	−13839.0	−1.31186
$482$	−166.171	−0.0157031
$483$	−10335.1	−0.973626
$484$	−12542.1	−1.17788
$485$	7229.52	0.676856
$486$	1085.46	0.101312
$487$	10888.8	1.01318	0.506590	−	0.862187i	$-0.330906\pi$
$487$	10888.8	1.01318	0.506590	+	0.862187i	$0.330906\pi$
$488$	7092.42	0.657907
$489$	5096.51	0.471313
$490$	16341.5	1.50660
$491$	2882.06	0.264899	0.132450	−	0.991190i	$-0.457716\pi$
$491$	2882.06	0.264899	0.132450	+	0.991190i	$0.457716\pi$
$492$	6098.38	0.558814
$493$	−16787.0	−1.53356
$494$	−15293.1	−1.39285
$495$	−873.051	−0.0792742
$496$	−1092.35	−0.0988868
$497$	−13807.1	−1.24615
$498$	13574.2	1.22144
$499$	8893.51	0.797852	0.398926	−	0.916983i	$-0.369383\pi$
$499$	8893.51	0.797852	0.398926	+	0.916983i	$0.369383\pi$
$500$	14963.0	1.33833
$501$	−2492.86	−0.222301
$502$	4223.81	0.375533
$503$	−5532.18	−0.490393	−0.245196	−	0.969473i	$-0.578852\pi$
$503$	−5532.18	−0.490393	−0.245196	+	0.969473i	$0.578852\pi$
$504$	4965.19	0.438824
$505$	−8944.37	−0.788157
$506$	8267.93	0.726392
$507$	−14665.3	−1.28464
$508$	30753.7	2.68598
$509$	854.845	0.0744407	0.0372204	−	0.999307i	$-0.488150\pi$
$509$	854.845	0.0744407	0.0372204	+	0.999307i	$0.488150\pi$
$510$	4429.04	0.384552
$511$	−27038.2	−2.34070
$512$	−5983.80	−0.516502
$513$	1098.17	0.0945133
$514$	30781.6	2.64148
$515$	4176.74	0.357377
$516$	−9186.70	−0.783763
$517$	4668.53	0.397141
$518$	22943.4	1.94609
$519$	4131.03	0.349388
$520$	−8590.54	−0.724462
$521$	8604.94	0.723588	0.361794	−	0.932258i	$-0.382164\pi$
$521$	8604.94	0.723588	0.361794	+	0.932258i	$0.382164\pi$
$522$	−11800.8	−0.989477
$523$	−9932.87	−0.830467	−0.415233	−	0.909715i	$-0.636300\pi$
$523$	−9932.87	−0.830467	−0.415233	+	0.909715i	$0.636300\pi$
$524$	−13184.9	−1.09921
$525$	−8585.12	−0.713686
$526$	2395.29	0.198554
$527$	−3730.61	−0.308364
$528$	843.216	0.0695005
$529$	−7.17001	−0.000589300 0
$530$	−2312.45	−0.189522
$531$	−3298.73	−0.269591
$532$	15188.7	1.23781
$533$	14314.9	1.16332
$534$	−20297.3	−1.64485
$535$	−5178.77	−0.418500
$536$	1183.15	0.0953439
$537$	3825.11	0.307385
$538$	−6671.84	−0.534653
$539$	10625.2	0.849094
$540$	1865.19	0.148639
$541$	−3651.71	−0.290202	−0.145101	−	0.989417i	$-0.546351\pi$
$541$	−3651.71	−0.290202	−0.145101	+	0.989417i	$0.546351\pi$
$542$	−23611.7	−1.87124
$543$	5223.19	0.412796
$544$	−12356.8	−0.973887
$545$	10367.8	0.814873
$546$	35240.3	2.76218
$547$	−19019.4	−1.48667	−0.743337	−	0.668917i	$-0.766758\pi$
$547$	−19019.4	−1.48667	−0.743337	+	0.668917i	$0.766758\pi$
$548$	−11358.9	−0.885450
$549$	−3614.69	−0.281004
$550$	6867.99	0.532458
$551$	−11939.0	−0.923080
$552$	−5841.85	−0.450445
$553$	2184.95	0.168018
$554$	−15769.9	−1.20938
$555$	2850.46	0.218009
$556$	−19782.8	−1.50895
$557$	11750.9	0.893895	0.446948	−	0.894560i	$-0.352511\pi$
$557$	11750.9	0.893895	0.446948	+	0.894560i	$0.352511\pi$
$558$	−2622.52	−0.198961
$559$	−21564.3	−1.63161
$560$	−3023.37	−0.228144
$561$	2879.76	0.216727
$562$	4531.19	0.340101
$563$	25643.4	1.91961	0.959806	−	0.280665i	$-0.0905551\pi$
$563$	25643.4	1.91961	0.959806	+	0.280665i	$0.0905551\pi$
$564$	−9973.86	−0.744637
$565$	6656.60	0.495655
$566$	−3099.03	−0.230145
$567$	−2530.54	−0.187430
$568$	−7804.43	−0.576526
$569$	−20661.2	−1.52225	−0.761127	−	0.648603i	$-0.775354\pi$
$569$	−20661.2	−1.52225	−0.761127	+	0.648603i	$0.775354\pi$
$570$	3149.96	0.231469
$571$	18295.4	1.34087	0.670437	−	0.741966i	$-0.266106\pi$
$571$	18295.4	1.34087	0.670437	+	0.741966i	$0.266106\pi$
$572$	−16888.7	−1.23453
$573$	−664.086	−0.0484164
$574$	−23732.4	−1.72573
$575$	10100.9	0.732586
$576$	−7480.88	−0.541152
$577$	190.550	0.0137482	0.00687408	−	0.999976i	$-0.497812\pi$
$577$	190.550	0.0137482	0.00687408	+	0.999976i	$0.497812\pi$
$578$	7336.70	0.527970
$579$	4324.87	0.310424
$580$	−20277.8	−1.45171
$581$	−31645.7	−2.25970
$582$	−16763.6	−1.19394
$583$	−1503.56	−0.106811
$584$	−15283.2	−1.08292
$585$	4378.22	0.309431
$586$	−26475.8	−1.86639
$587$	10347.9	0.727606	0.363803	−	0.931476i	$-0.381478\pi$
$587$	10347.9	0.727606	0.363803	+	0.931476i	$0.381478\pi$
$588$	−22699.8	−1.59205
$589$	−2653.23	−0.185610
$590$	−9461.99	−0.660244
$591$	712.868	0.0496167
$592$	−2753.05	−0.191131
$593$	17698.5	1.22562	0.612809	−	0.790231i	$-0.290040\pi$
$593$	17698.5	1.22562	0.612809	+	0.790231i	$0.290040\pi$
$594$	2024.40	0.139835
$595$	−10325.5	−0.711433
$596$	36464.0	2.50608
$597$	−10971.4	−0.752141
$598$	−41462.4	−2.83533
$599$	22021.7	1.50214	0.751070	−	0.660223i	$-0.229538\pi$
$599$	22021.7	1.50214	0.751070	+	0.660223i	$0.229538\pi$
$600$	−4852.70	−0.330184
$601$	−7048.48	−0.478392	−0.239196	−	0.970971i	$-0.576884\pi$
$601$	−7048.48	−0.478392	−0.239196	+	0.970971i	$0.576884\pi$
$602$	35750.8	2.42042
$603$	−603.000	−0.0407231
$604$	38643.0	2.60325
$605$	6063.92	0.407493
$606$	20739.9	1.39027
$607$	−29245.5	−1.95558	−0.977790	−	0.209588i	$-0.932788\pi$
$607$	−29245.5	−1.95558	−0.977790	+	0.209588i	$0.932788\pi$
$608$	−8788.24	−0.586201
$609$	27511.3	1.83057
$610$	−10368.3	−0.688197
$611$	−23412.0	−1.55016
$612$	−6152.33	−0.406362
$613$	5909.25	0.389351	0.194676	−	0.980868i	$-0.437635\pi$
$613$	5909.25	0.389351	0.194676	+	0.980868i	$0.437635\pi$
$614$	18536.1	1.21833
$615$	−2948.48	−0.193324
$616$	9260.17	0.605687
$617$	−8323.26	−0.543082	−0.271541	−	0.962427i	$-0.587533\pi$
$617$	−8323.26	−0.543082	−0.271541	+	0.962427i	$0.587533\pi$
$618$	−9684.89	−0.630394
$619$	−371.387	−0.0241152	−0.0120576	−	0.999927i	$-0.503838\pi$
$619$	−371.387	−0.0241152	−0.0120576	+	0.999927i	$0.503838\pi$
$620$	−4506.38	−0.291904
$621$	2977.33	0.192393
$622$	−8334.16	−0.537250
$623$	47319.4	3.04303
$624$	−4228.60	−0.271281
$625$	4215.65	0.269802
$626$	−1645.86	−0.105083
$627$	2048.10	0.130452
$628$	10524.8	0.668764
$629$	−9402.25	−0.596013
$630$	−7258.54	−0.459027
$631$	−2152.18	−0.135779	−0.0678897	−	0.997693i	$-0.521627\pi$
$631$	−2152.18	−0.135779	−0.0678897	+	0.997693i	$0.521627\pi$
$632$	1235.04	0.0777328
$633$	1011.98	0.0635427
$634$	−19502.8	−1.22170
$635$	−14869.0	−0.929226
$636$	3212.21	0.200271
$637$	−53284.0	−3.31427
$638$	−22008.7	−1.36573
$639$	3977.58	0.246245
$640$	−11468.1	−0.708309
$641$	−752.960	−0.0463965	−0.0231982	−	0.999731i	$-0.507385\pi$
$641$	−752.960	−0.0463965	−0.0231982	+	0.999731i	$0.507385\pi$
$642$	12008.4	0.738212
$643$	−13943.7	−0.855190	−0.427595	−	0.903971i	$-0.640639\pi$
$643$	−13943.7	−0.855190	−0.427595	+	0.903971i	$0.640639\pi$
$644$	41179.3	2.51971
$645$	4441.64	0.271146
$646$	−10390.2	−0.632810
$647$	13936.9	0.846859	0.423429	−	0.905929i	$-0.360826\pi$
$647$	13936.9	0.846859	0.423429	+	0.905929i	$0.360826\pi$
$648$	−1430.38	−0.0867137
$649$	−6152.19	−0.372103
$650$	−34442.0	−2.07835
$651$	6113.90	0.368084
$652$	−20306.7	−1.21974
$653$	−14995.7	−0.898662	−0.449331	−	0.893365i	$-0.648338\pi$
$653$	−14995.7	−0.898662	−0.449331	+	0.893365i	$0.648338\pi$
$654$	−24040.4	−1.43739
$655$	6374.73	0.380277
$656$	2847.72	0.169489
$657$	7789.18	0.462534
$658$	38814.2	2.29959
$659$	−13021.1	−0.769697	−0.384848	−	0.922980i	$-0.625746\pi$
$659$	−13021.1	−0.769697	−0.384848	+	0.922980i	$0.625746\pi$
$660$	3478.61	0.205159
$661$	23715.9	1.39552	0.697761	−	0.716330i	$-0.254180\pi$
$661$	23715.9	1.39552	0.697761	+	0.716330i	$0.254180\pi$
$662$	−32750.3	−1.92277
$663$	−14441.6	−0.845950
$664$	−17887.6	−1.04544
$665$	−7343.52	−0.428225
$666$	−6609.54	−0.384556
$667$	−32368.7	−1.87904
$668$	9932.64	0.575307
$669$	1144.83	0.0661611
$670$	−1729.63	−0.0997335
$671$	−6741.47	−0.387856
$672$	20251.0	1.16250
$673$	29548.6	1.69244	0.846222	−	0.532831i	$-0.178872\pi$
$673$	29548.6	1.69244	0.846222	+	0.532831i	$0.178872\pi$
$674$	11865.7	0.678117
$675$	2473.21	0.141028
$676$	58433.0	3.32459
$677$	31164.0	1.76917	0.884587	−	0.466375i	$-0.154440\pi$
$677$	31164.0	1.76917	0.884587	+	0.466375i	$0.154440\pi$
$678$	−15435.1	−0.874309
$679$	39081.0	2.20882
$680$	−5836.42	−0.329142
$681$	−8062.92	−0.453703
$682$	−4891.05	−0.274616
$683$	27771.3	1.55584	0.777919	−	0.628364i	$-0.216275\pi$
$683$	27771.3	1.55584	0.777919	+	0.628364i	$0.216275\pi$
$684$	−4375.57	−0.244597
$685$	5491.85	0.306325
$686$	40472.0	2.25252
$687$	15567.7	0.864548
$688$	−4289.85	−0.237717
$689$	7540.12	0.416917
$690$	8540.11	0.471183
$691$	10424.8	0.573921	0.286960	−	0.957942i	$-0.407355\pi$
$691$	10424.8	0.573921	0.286960	+	0.957942i	$0.407355\pi$
$692$	−16459.8	−0.904202
$693$	−4719.50	−0.258700
$694$	−6197.86	−0.339002
$695$	9564.70	0.522028
$696$	15550.6	0.846905
$697$	9725.59	0.528527
$698$	35241.5	1.91105
$699$	−9093.44	−0.492054
$700$	34206.8	1.84699
$701$	−16916.2	−0.911433	−0.455716	−	0.890125i	$-0.650617\pi$
$701$	−16916.2	−0.911433	−0.455716	+	0.890125i	$0.650617\pi$
$702$	−10152.1	−0.545819
$703$	−6686.93	−0.358752
$704$	−13952.0	−0.746925
$705$	4822.23	0.257611
$706$	−45616.1	−2.43171
$707$	−48351.1	−2.57204
$708$	13143.6	0.697690
$709$	−17448.7	−0.924258	−0.462129	−	0.886813i	$-0.652914\pi$
$709$	−17448.7	−0.924258	−0.462129	+	0.886813i	$0.652914\pi$
$710$	11409.2	0.603069
$711$	−629.444	−0.0332011
$712$	26747.1	1.40785
$713$	−7193.38	−0.377832
$714$	23942.3	1.25493
$715$	8165.46	0.427092
$716$	−15240.9	−0.795501
$717$	11500.4	0.599012
$718$	−9508.07	−0.494203
$719$	10272.8	0.532841	0.266420	−	0.963857i	$-0.414159\pi$
$719$	10272.8	0.532841	0.266420	+	0.963857i	$0.414159\pi$
$720$	870.975	0.0450824
$721$	22578.5	1.16625
$722$	23249.0	1.19839
$723$	−111.602	−0.00574068
$724$	−20811.4	−1.06830
$725$	−26888.0	−1.37737
$726$	−14060.8	−0.718796
$727$	−27031.1	−1.37899	−0.689495	−	0.724290i	$-0.742168\pi$
$727$	−27031.1	−1.37899	−0.689495	+	0.724290i	$0.742168\pi$
$728$	−46438.4	−2.36418
$729$	729.000	0.0370370
$730$	22342.3	1.13277
$731$	−14650.8	−0.741284
$732$	14402.5	0.727228
$733$	−6174.80	−0.311148	−0.155574	−	0.987824i	$-0.549723\pi$
$733$	−6174.80	−0.311148	−0.155574	+	0.987824i	$0.549723\pi$
$734$	40197.8	2.02143
$735$	10975.0	0.550776
$736$	−23826.5	−1.19328
$737$	−1124.61	−0.0562081
$738$	6836.85	0.341013
$739$	18160.2	0.903967	0.451984	−	0.892026i	$-0.350717\pi$
$739$	18160.2	0.903967	0.451984	+	0.892026i	$0.350717\pi$
$740$	−11357.4	−0.564200
$741$	−10270.9	−0.509193
$742$	−12500.6	−0.618478
$743$	−17560.1	−0.867050	−0.433525	−	0.901142i	$-0.642730\pi$
$743$	−17560.1	−0.867050	−0.433525	+	0.901142i	$0.642730\pi$
$744$	3455.86	0.170293
$745$	−17629.8	−0.866990
$746$	45305.8	2.22354
$747$	9116.53	0.446528
$748$	−11474.2	−0.560881
$749$	−27995.2	−1.36572
$750$	16774.9	0.816708
$751$	1568.79	0.0762263	0.0381131	−	0.999273i	$-0.487865\pi$
$751$	1568.79	0.0762263	0.0381131	+	0.999273i	$0.487865\pi$
$752$	−4657.43	−0.225850
$753$	2836.73	0.137286
$754$	110370.	5.33084
$755$	−18683.3	−0.900605
$756$	10082.8	0.485061
$757$	6187.46	0.297077	0.148538	−	0.988907i	$-0.452543\pi$
$757$	6187.46	0.297077	0.148538	+	0.988907i	$0.452543\pi$
$758$	−52762.1	−2.52824
$759$	5552.78	0.265551
$760$	−4150.89	−0.198117
$761$	27885.1	1.32830	0.664149	−	0.747600i	$-0.268794\pi$
$761$	27885.1	1.32830	0.664149	+	0.747600i	$0.268794\pi$
$762$	34477.8	1.63910
$763$	56045.6	2.65922
$764$	2646.00	0.125300
$765$	2974.57	0.140583
$766$	−42875.4	−2.02239
$767$	30852.3	1.45243
$768$	6642.93	0.312117
$769$	31052.7	1.45616	0.728081	−	0.685491i	$-0.240412\pi$
$769$	31052.7	1.45616	0.728081	+	0.685491i	$0.240412\pi$
$770$	−13537.3	−0.633572
$771$	20673.1	0.965660
$772$	−17232.1	−0.803366
$773$	−14314.4	−0.666045	−0.333023	−	0.942919i	$-0.608069\pi$
$773$	−14314.4	−0.666045	−0.333023	+	0.942919i	$0.608069\pi$
$774$	−10299.1	−0.478288
$775$	−5975.39	−0.276958
$776$	22090.4	1.02191
$777$	15408.9	0.711442
$778$	48833.6	2.25035
$779$	6916.89	0.318130
$780$	−17444.7	−0.800795
$781$	7418.25	0.339880
$782$	−28169.6	−1.28816
$783$	−7925.48	−0.361729
$784$	−10600.0	−0.482871
$785$	−5088.58	−0.231362
$786$	−14781.5	−0.670788
$787$	33367.2	1.51132	0.755661	−	0.654963i	$-0.227316\pi$
$787$	33367.2	1.51132	0.755661	+	0.654963i	$0.227316\pi$
$788$	−2840.37	−0.128406
$789$	1608.69	0.0725866
$790$	−1805.48	−0.0813116
$791$	35984.0	1.61750
$792$	−2667.68	−0.119687
$793$	33807.5	1.51392
$794$	10685.7	0.477608
$795$	−1553.06	−0.0692846
$796$	43714.6	1.94651
$797$	42915.3	1.90732	0.953662	−	0.300880i	$-0.0972802\pi$
$797$	42915.3	1.90732	0.953662	+	0.300880i	$0.0972802\pi$
$798$	17027.9	0.755366
$799$	−15906.1	−0.704279
$800$	−19792.2	−0.874700
$801$	−13631.8	−0.601318
$802$	−57113.8	−2.51466
$803$	14527.0	0.638413
$804$	2402.61	0.105390
$805$	−19909.6	−0.871704
$806$	24527.9	1.07191
$807$	−4480.84	−0.195456
$808$	−27330.3	−1.18994
$809$	18195.7	0.790763	0.395381	−	0.918517i	$-0.370612\pi$
$809$	18195.7	0.790763	0.395381	+	0.918517i	$0.370612\pi$
$810$	2091.05	0.0907060
$811$	29378.3	1.27202	0.636011	−	0.771680i	$-0.280583\pi$
$811$	29378.3	1.27202	0.636011	+	0.771680i	$0.280583\pi$
$812$	−109617.	−4.73743
$813$	−15857.8	−0.684079
$814$	−12326.9	−0.530784
$815$	9818.00	0.421975
$816$	−2872.92	−0.123250
$817$	−10419.7	−0.446193
$818$	10907.4	0.466221
$819$	23667.6	1.00978
$820$	11748.0	0.500315
$821$	2323.24	0.0987594	0.0493797	−	0.998780i	$-0.484276\pi$
$821$	2323.24	0.0987594	0.0493797	+	0.998780i	$0.484276\pi$
$822$	−12734.3	−0.540341
$823$	38424.4	1.62745	0.813725	−	0.581250i	$-0.197436\pi$
$823$	38424.4	1.62745	0.813725	+	0.581250i	$0.197436\pi$
$824$	12762.4	0.539561
$825$	4612.58	0.194654
$826$	−51149.3	−2.15461
$827$	−19383.6	−0.815037	−0.407518	−	0.913197i	$-0.633606\pi$
$827$	−19383.6	−0.815037	−0.407518	+	0.913197i	$0.633606\pi$
$828$	−11863.0	−0.497907
$829$	43849.1	1.83708	0.918542	−	0.395324i	$-0.129368\pi$
$829$	43849.1	1.83708	0.918542	+	0.395324i	$0.129368\pi$
$830$	26149.6	1.09357
$831$	−10591.1	−0.442121
$832$	69967.1	2.91547
$833$	−36201.2	−1.50576
$834$	−22178.3	−0.920830
$835$	−4802.29	−0.199030
$836$	−8160.52	−0.337605
$837$	−1761.30	−0.0727352
$838$	50696.1	2.08982
$839$	−4929.53	−0.202844	−0.101422	−	0.994843i	$-0.532339\pi$
$839$	−4929.53	−0.202844	−0.101422	+	0.994843i	$0.532339\pi$
$840$	9565.02	0.392886
$841$	61774.6	2.53289
$842$	19125.9	0.782807
$843$	3043.17	0.124333
$844$	−4032.15	−0.164446
$845$	−28251.6	−1.15016
$846$	−11181.6	−0.454411
$847$	32780.1	1.32980
$848$	1499.98	0.0607425
$849$	−2081.33	−0.0841353
$850$	−23399.9	−0.944247
$851$	−18129.5	−0.730283
$852$	−15848.4	−0.637272
$853$	39986.7	1.60506	0.802531	−	0.596610i	$-0.203486\pi$
$853$	39986.7	1.60506	0.802531	+	0.596610i	$0.203486\pi$
$854$	−56048.5	−2.24583
$855$	2115.53	0.0846193
$856$	−15824.2	−0.631844
$857$	−14582.9	−0.581262	−0.290631	−	0.956835i	$-0.593865\pi$
$857$	−14582.9	−0.581262	−0.290631	+	0.956835i	$0.593865\pi$
$858$	−18933.8	−0.753367
$859$	−38965.2	−1.54770	−0.773850	−	0.633369i	$-0.781672\pi$
$859$	−38965.2	−1.54770	−0.773850	+	0.633369i	$0.781672\pi$
$860$	−17697.4	−0.701717
$861$	−15938.8	−0.630886
$862$	−68100.1	−2.69083
$863$	−1615.74	−0.0637317	−0.0318659	−	0.999492i	$-0.510145\pi$
$863$	−1615.74	−0.0637317	−0.0318659	+	0.999492i	$0.510145\pi$
$864$	−5833.92	−0.229715
$865$	7958.09	0.312813
$866$	−27256.7	−1.06954
$867$	4927.37	0.193013
$868$	−24360.4	−0.952588
$869$	−1173.92	−0.0458258
$870$	−22733.3	−0.885896
$871$	5639.73	0.219397
$872$	31679.5	1.23028
$873$	−11258.5	−0.436475
$874$	−20034.4	−0.775370
$875$	−39107.4	−1.51094
$876$	−31035.4	−1.19702
$877$	−38257.2	−1.47304	−0.736519	−	0.676417i	$-0.763532\pi$
$877$	−38257.2	−1.47304	−0.736519	+	0.676417i	$0.763532\pi$
$878$	−56895.5	−2.18694
$879$	−17781.3	−0.682308
$880$	1624.38	0.0622250
$881$	39568.9	1.51318	0.756588	−	0.653891i	$-0.226865\pi$
$881$	39568.9	1.51318	0.756588	+	0.653891i	$0.226865\pi$
$882$	−25448.6	−0.971539
$883$	−36027.9	−1.37309	−0.686543	−	0.727089i	$-0.740873\pi$
$883$	−36027.9	−1.37309	−0.686543	+	0.727089i	$0.740873\pi$
$884$	57541.5	2.18929
$885$	−6354.72	−0.241369
$886$	9176.96	0.347975
$887$	17386.2	0.658140	0.329070	−	0.944306i	$-0.393265\pi$
$887$	17386.2	0.658140	0.329070	+	0.944306i	$0.393265\pi$
$888$	8709.80	0.329146
$889$	−80378.2	−3.03240
$890$	−39101.1	−1.47267
$891$	1359.60	0.0511204
$892$	−4561.50	−0.171222
$893$	−11312.5	−0.423919
$894$	40879.5	1.52932
$895$	7368.76	0.275207
$896$	−61994.0	−2.31147
$897$	−27846.4	−1.03653
$898$	−3461.68	−0.128639
$899$	19148.3	0.710381
$900$	−9854.32	−0.364975
$901$	5122.77	0.189416
$902$	12750.8	0.470684
$903$	24010.4	0.884848
$904$	20339.8	0.748331
$905$	10062.0	0.369584
$906$	43322.3	1.58862
$907$	28554.1	1.04534	0.522670	−	0.852535i	$-0.324936\pi$
$907$	28554.1	1.04534	0.522670	+	0.852535i	$0.324936\pi$
$908$	32126.1	1.17417
$909$	13929.0	0.508247
$910$	67887.6	2.47302
$911$	1708.56	0.0621373	0.0310687	−	0.999517i	$-0.490109\pi$
$911$	1708.56	0.0621373	0.0310687	+	0.999517i	$0.490109\pi$
$912$	−2043.23	−0.0741866
$913$	17002.5	0.616320
$914$	52823.8	1.91166
$915$	−6963.40	−0.251588
$916$	−62028.4	−2.23742
$917$	34460.3	1.24098
$918$	−6897.33	−0.247980
$919$	1139.24	0.0408924	0.0204462	−	0.999791i	$-0.493491\pi$
$919$	1139.24	0.0408924	0.0204462	+	0.999791i	$0.493491\pi$
$920$	−11253.8	−0.403291
$921$	12448.9	0.445393
$922$	−20848.6	−0.744697
$923$	−37201.4	−1.32665
$924$	18804.5	0.669506
$925$	−15059.8	−0.535311
$926$	−55893.1	−1.98354
$927$	−6504.42	−0.230457
$928$	63424.8	2.24356
$929$	−32991.5	−1.16514	−0.582570	−	0.812780i	$-0.697953\pi$
$929$	−32991.5	−1.16514	−0.582570	+	0.812780i	$0.697953\pi$
$930$	−5052.07	−0.178133
$931$	−25746.5	−0.906346
$932$	36232.2	1.27342
$933$	−5597.27	−0.196405
$934$	44159.6	1.54705
$935$	5547.62	0.194039
$936$	13378.0	0.467173
$937$	−16468.3	−0.574169	−0.287085	−	0.957905i	$-0.592686\pi$
$937$	−16468.3	−0.574169	−0.287085	+	0.957905i	$0.592686\pi$
$938$	−9349.97	−0.325466
$939$	−1105.37	−0.0384156
$940$	−19213.8	−0.666687
$941$	−51112.4	−1.77069	−0.885344	−	0.464936i	$-0.846077\pi$
$941$	−51112.4	−1.77069	−0.885344	+	0.464936i	$0.846077\pi$
$942$	11799.2	0.408110
$943$	18753.0	0.647593
$944$	6137.56	0.211611
$945$	−4874.87	−0.167809
$946$	−19208.1	−0.660157
$947$	26895.2	0.922891	0.461445	−	0.887169i	$-0.347331\pi$
$947$	26895.2	0.922891	0.461445	+	0.887169i	$0.347331\pi$
$948$	2507.97	0.0859232
$949$	−72850.5	−2.49192
$950$	−16642.1	−0.568360
$951$	−13098.2	−0.446622
$952$	−31550.3	−1.07411
$953$	−14931.3	−0.507525	−0.253763	−	0.967266i	$-0.581668\pi$
$953$	−14931.3	−0.507525	−0.253763	+	0.967266i	$0.581668\pi$
$954$	3601.18	0.122214
$955$	−1279.31	−0.0433480
$956$	−45822.7	−1.55022
$957$	−14781.2	−0.499276
$958$	27175.1	0.916478
$959$	29687.6	0.999649
$960$	−14411.3	−0.484502
$961$	−25535.6	−0.857159
$962$	61817.7	2.07181
$963$	8064.87	0.269872
$964$	444.669	0.0148567
$965$	8331.51	0.277928
$966$	46165.8	1.53764
$967$	55044.4	1.83052	0.915258	−	0.402869i	$-0.131987\pi$
$967$	55044.4	1.83052	0.915258	+	0.402869i	$0.131987\pi$
$968$	18528.8	0.615226
$969$	−6978.09	−0.231340
$970$	−32293.6	−1.06895
$971$	9134.25	0.301887	0.150943	−	0.988542i	$-0.451769\pi$
$971$	9134.25	0.301887	0.150943	+	0.988542i	$0.451769\pi$
$972$	−2904.65	−0.0958505
$973$	51704.5	1.70357
$974$	−48639.3	−1.60011
$975$	−23131.4	−0.759792
$976$	6725.44	0.220570
$977$	39035.3	1.27825	0.639124	−	0.769104i	$-0.279297\pi$
$977$	39035.3	1.27825	0.639124	+	0.769104i	$0.279297\pi$
$978$	−22765.7	−0.744341
$979$	−25423.6	−0.829970
$980$	−43729.2	−1.42539
$981$	−16145.7	−0.525475
$982$	−12873.9	−0.418353
$983$	30985.3	1.00537	0.502684	−	0.864470i	$-0.332346\pi$
$983$	30985.3	1.00537	0.502684	+	0.864470i	$0.332346\pi$
$984$	−9009.34	−0.291877
$985$	1373.28	0.0444227
$986$	74985.8	2.42194
$987$	26067.8	0.840676
$988$	40923.8	1.31777
$989$	−28249.8	−0.908281
$990$	3899.84	0.125197
$991$	−43209.8	−1.38507	−0.692536	−	0.721384i	$-0.743506\pi$
$991$	−43209.8	−1.38507	−0.692536	+	0.721384i	$0.743506\pi$
$992$	14095.0	0.451127
$993$	−21995.3	−0.702919
$994$	61675.3	1.96803
$995$	−21135.4	−0.673405
$996$	−36324.2	−1.15560
$997$	−17703.6	−0.562367	−0.281183	−	0.959654i	$-0.590727\pi$
$997$	−17703.6	−0.562367	−0.281183	+	0.959654i	$0.590727\pi$
$998$	−39726.5	−1.26004
$999$	−4439.00	−0.140584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.d.1.1	✓	9
3.2	odd	2		603.4.a.f.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.d.1.1	✓	9	1.1	even	1	trivial
603.4.a.f.1.9		9	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)

\(f(q)\)	\(=\)	\(q-4.46691 q^{2} -3.00000 q^{3} +11.9533 q^{4} -5.77925 q^{5} +13.4007 q^{6} -31.2412 q^{7} -17.6590 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.46691 q^{2} -3.00000 q^{3} +11.9533 q^{4} -5.77925 q^{5} +13.4007 q^{6} -31.2412 q^{7} -17.6590 q^{8} +9.00000 q^{9} +25.8154 q^{10} +16.7852 q^{11} -35.8599 q^{12} -84.1751 q^{13} +139.552 q^{14} +17.3377 q^{15} -16.7453 q^{16} -57.1887 q^{17} -40.2022 q^{18} -40.6729 q^{19} -69.0810 q^{20} +93.7237 q^{21} -74.9778 q^{22} -110.272 q^{23} +52.9769 q^{24} -91.6003 q^{25} +376.003 q^{26} -27.0000 q^{27} -373.435 q^{28} +293.536 q^{29} -77.4461 q^{30} +65.2333 q^{31} +216.071 q^{32} -50.3555 q^{33} +255.457 q^{34} +180.551 q^{35} +107.580 q^{36} +164.408 q^{37} +181.682 q^{38} +252.525 q^{39} +102.056 q^{40} -170.062 q^{41} -418.655 q^{42} +256.183 q^{43} +200.638 q^{44} -52.0132 q^{45} +492.573 q^{46} +278.135 q^{47} +50.2358 q^{48} +633.014 q^{49} +409.170 q^{50} +171.566 q^{51} -1006.17 q^{52} -89.5766 q^{53} +120.607 q^{54} -97.0056 q^{55} +551.688 q^{56} +122.019 q^{57} -1311.20 q^{58} -366.525 q^{59} +207.243 q^{60} -401.633 q^{61} -291.391 q^{62} -281.171 q^{63} -831.209 q^{64} +486.469 q^{65} +224.933 q^{66} -67.0000 q^{67} -683.593 q^{68} +330.815 q^{69} -806.504 q^{70} +441.953 q^{71} -158.931 q^{72} +865.464 q^{73} -734.394 q^{74} +274.801 q^{75} -486.175 q^{76} -524.389 q^{77} -1128.01 q^{78} -69.9382 q^{79} +96.7750 q^{80} +81.0000 q^{81} +759.650 q^{82} +1012.95 q^{83} +1120.31 q^{84} +330.508 q^{85} -1144.35 q^{86} -880.609 q^{87} -296.409 q^{88} -1514.64 q^{89} +232.338 q^{90} +2629.73 q^{91} -1318.11 q^{92} -195.700 q^{93} -1242.40 q^{94} +235.059 q^{95} -648.214 q^{96} -1250.94 q^{97} -2827.62 q^{98} +151.067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{2} - 27 q^{3} + 45 q^{4} + 12 q^{5} - 9 q^{6} + 8 q^{7} + 51 q^{8} + 81 q^{9}+O(q^{10}) \) 9 * q + 3 * q^2 - 27 * q^3 + 45 * q^4 + 12 * q^5 - 9 * q^6 + 8 * q^7 + 51 * q^8 + 81 * q^9	\( 9 q + 3 q^{2} - 27 q^{3} + 45 q^{4} + 12 q^{5} - 9 q^{6} + 8 q^{7} + 51 q^{8} + 81 q^{9} + 45 q^{10} + 72 q^{11} - 135 q^{12} - 166 q^{13} + 93 q^{14} - 36 q^{15} + 173 q^{16} + 146 q^{17} + 27 q^{18} + 154 q^{19} + 763 q^{20} - 24 q^{21} + 244 q^{22} + 476 q^{23} - 153 q^{24} + 465 q^{25} + 502 q^{26} - 243 q^{27} - 141 q^{28} + 432 q^{29} - 135 q^{30} + 248 q^{31} + 1171 q^{32} - 216 q^{33} + 146 q^{34} + 178 q^{35} + 405 q^{36} - 240 q^{37} + 1182 q^{38} + 498 q^{39} + 1409 q^{40} + 406 q^{41} - 279 q^{42} + 154 q^{43} + 892 q^{44} + 108 q^{45} + 273 q^{46} + 494 q^{47} - 519 q^{48} + 431 q^{49} + 1658 q^{50} - 438 q^{51} - 1258 q^{52} - 450 q^{53} - 81 q^{54} - 346 q^{55} - 659 q^{56} - 462 q^{57} - 2114 q^{58} + 732 q^{59} - 2289 q^{60} - 914 q^{61} - 1265 q^{62} + 72 q^{63} - 467 q^{64} - 536 q^{65} - 732 q^{66} - 603 q^{67} - 3314 q^{68} - 1428 q^{69} - 4805 q^{70} + 2990 q^{71} + 459 q^{72} - 1384 q^{73} - 2043 q^{74} - 1395 q^{75} + 450 q^{76} + 1660 q^{77} - 1506 q^{78} + 2438 q^{79} + 995 q^{80} + 729 q^{81} - 3561 q^{82} + 972 q^{83} + 423 q^{84} - 2706 q^{85} - 21 q^{86} - 1296 q^{87} - 3796 q^{88} + 1034 q^{89} + 405 q^{90} + 1898 q^{91} + 1827 q^{92} - 744 q^{93} - 3502 q^{94} + 6040 q^{95} - 3513 q^{96} - 1516 q^{97} - 3996 q^{98} + 648 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 - 27 * q^3 + 45 * q^4 + 12 * q^5 - 9 * q^6 + 8 * q^7 + 51 * q^8 + 81 * q^9 + 45 * q^10 + 72 * q^11 - 135 * q^12 - 166 * q^13 + 93 * q^14 - 36 * q^15 + 173 * q^16 + 146 * q^17 + 27 * q^18 + 154 * q^19 + 763 * q^20 - 24 * q^21 + 244 * q^22 + 476 * q^23 - 153 * q^24 + 465 * q^25 + 502 * q^26 - 243 * q^27 - 141 * q^28 + 432 * q^29 - 135 * q^30 + 248 * q^31 + 1171 * q^32 - 216 * q^33 + 146 * q^34 + 178 * q^35 + 405 * q^36 - 240 * q^37 + 1182 * q^38 + 498 * q^39 + 1409 * q^40 + 406 * q^41 - 279 * q^42 + 154 * q^43 + 892 * q^44 + 108 * q^45 + 273 * q^46 + 494 * q^47 - 519 * q^48 + 431 * q^49 + 1658 * q^50 - 438 * q^51 - 1258 * q^52 - 450 * q^53 - 81 * q^54 - 346 * q^55 - 659 * q^56 - 462 * q^57 - 2114 * q^58 + 732 * q^59 - 2289 * q^60 - 914 * q^61 - 1265 * q^62 + 72 * q^63 - 467 * q^64 - 536 * q^65 - 732 * q^66 - 603 * q^67 - 3314 * q^68 - 1428 * q^69 - 4805 * q^70 + 2990 * q^71 + 459 * q^72 - 1384 * q^73 - 2043 * q^74 - 1395 * q^75 + 450 * q^76 + 1660 * q^77 - 1506 * q^78 + 2438 * q^79 + 995 * q^80 + 729 * q^81 - 3561 * q^82 + 972 * q^83 + 423 * q^84 - 2706 * q^85 - 21 * q^86 - 1296 * q^87 - 3796 * q^88 + 1034 * q^89 + 405 * q^90 + 1898 * q^91 + 1827 * q^92 - 744 * q^93 - 3502 * q^94 + 6040 * q^95 - 3513 * q^96 - 1516 * q^97 - 3996 * q^98 + 648 * q^99

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