LMFDB - Embedded newform 201.4.a.b.1.6

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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 28x^{4} + 22x^{3} + 202x^{2} - 96x - 384 $ x^6 - x^5 - 28x^4 + 22x^3 + 202x^2 - 96x - 384
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$4.33036$ 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)

$f(q)$	$=$	$q+3.33036 q^{2} +3.00000 q^{3} +3.09132 q^{4} -17.6168 q^{5} +9.99109 q^{6} -17.3029 q^{7} -16.3477 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.33036 q^{2} +3.00000 q^{3} +3.09132 q^{4} -17.6168 q^{5} +9.99109 q^{6} -17.3029 q^{7} -16.3477 q^{8} +9.00000 q^{9} -58.6704 q^{10} -20.9004 q^{11} +9.27397 q^{12} +5.65965 q^{13} -57.6249 q^{14} -52.8505 q^{15} -79.1743 q^{16} +69.7817 q^{17} +29.9733 q^{18} -77.0844 q^{19} -54.4593 q^{20} -51.9086 q^{21} -69.6061 q^{22} +6.50326 q^{23} -49.0430 q^{24} +185.353 q^{25} +18.8487 q^{26} +27.0000 q^{27} -53.4888 q^{28} +31.7567 q^{29} -176.011 q^{30} -134.506 q^{31} -132.898 q^{32} -62.7013 q^{33} +232.398 q^{34} +304.822 q^{35} +27.8219 q^{36} -24.7518 q^{37} -256.719 q^{38} +16.9789 q^{39} +287.994 q^{40} +473.148 q^{41} -172.875 q^{42} +24.5301 q^{43} -64.6101 q^{44} -158.551 q^{45} +21.6582 q^{46} -614.310 q^{47} -237.523 q^{48} -43.6107 q^{49} +617.292 q^{50} +209.345 q^{51} +17.4958 q^{52} -208.897 q^{53} +89.9198 q^{54} +368.200 q^{55} +282.862 q^{56} -231.253 q^{57} +105.761 q^{58} -217.046 q^{59} -163.378 q^{60} -84.4339 q^{61} -447.954 q^{62} -155.726 q^{63} +190.796 q^{64} -99.7050 q^{65} -208.818 q^{66} -67.0000 q^{67} +215.718 q^{68} +19.5098 q^{69} +1015.17 q^{70} -1038.00 q^{71} -147.129 q^{72} -967.120 q^{73} -82.4324 q^{74} +556.058 q^{75} -238.293 q^{76} +361.638 q^{77} +56.5461 q^{78} +429.533 q^{79} +1394.80 q^{80} +81.0000 q^{81} +1575.75 q^{82} +1372.00 q^{83} -160.466 q^{84} -1229.33 q^{85} +81.6941 q^{86} +95.2702 q^{87} +341.674 q^{88} +277.435 q^{89} -528.034 q^{90} -97.9281 q^{91} +20.1037 q^{92} -403.518 q^{93} -2045.88 q^{94} +1357.98 q^{95} -398.694 q^{96} -839.028 q^{97} -145.240 q^{98} -188.104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9} - 111 q^{10} - 72 q^{11} + 39 q^{12} - 192 q^{13} + 3 q^{14} - 36 q^{15} - 27 q^{16} - 100 q^{17} - 45 q^{18} - 266 q^{19} + 255 q^{20} - 186 q^{21} + 44 q^{22} + 50 q^{23} - 225 q^{24} - 6 q^{25} + 472 q^{26} + 162 q^{27} - 333 q^{28} - 242 q^{29} - 333 q^{30} - 438 q^{31} + 35 q^{32} - 216 q^{33} - 150 q^{34} - 258 q^{35} + 117 q^{36} - 596 q^{37} + 664 q^{38} - 576 q^{39} - 831 q^{40} + 54 q^{41} + 9 q^{42} - 360 q^{43} - 714 q^{44} - 108 q^{45} - 871 q^{46} - 720 q^{47} - 81 q^{48} - 302 q^{49} + 4 q^{50} - 300 q^{51} - 1118 q^{52} + 694 q^{53} - 135 q^{54} - 990 q^{55} + 1917 q^{56} - 798 q^{57} + 1354 q^{58} - 378 q^{59} + 765 q^{60} - 1396 q^{61} + 1475 q^{62} - 558 q^{63} + 1225 q^{64} - 348 q^{65} + 132 q^{66} - 402 q^{67} + 2032 q^{68} + 150 q^{69} + 2415 q^{70} - 964 q^{71} - 675 q^{72} - 192 q^{73} + 2751 q^{74} - 18 q^{75} - 2306 q^{76} + 2724 q^{77} + 1416 q^{78} - 802 q^{79} + 4221 q^{80} + 486 q^{81} + 1735 q^{82} + 2126 q^{83} - 999 q^{84} - 1206 q^{85} - 609 q^{86} - 726 q^{87} + 3656 q^{88} + 432 q^{89} - 999 q^{90} + 1258 q^{91} + 3163 q^{92} - 1314 q^{93} + 1742 q^{94} + 936 q^{95} + 105 q^{96} + 1290 q^{97} + 2492 q^{98} - 648 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9 - 111 * q^10 - 72 * q^11 + 39 * q^12 - 192 * q^13 + 3 * q^14 - 36 * q^15 - 27 * q^16 - 100 * q^17 - 45 * q^18 - 266 * q^19 + 255 * q^20 - 186 * q^21 + 44 * q^22 + 50 * q^23 - 225 * q^24 - 6 * q^25 + 472 * q^26 + 162 * q^27 - 333 * q^28 - 242 * q^29 - 333 * q^30 - 438 * q^31 + 35 * q^32 - 216 * q^33 - 150 * q^34 - 258 * q^35 + 117 * q^36 - 596 * q^37 + 664 * q^38 - 576 * q^39 - 831 * q^40 + 54 * q^41 + 9 * q^42 - 360 * q^43 - 714 * q^44 - 108 * q^45 - 871 * q^46 - 720 * q^47 - 81 * q^48 - 302 * q^49 + 4 * q^50 - 300 * q^51 - 1118 * q^52 + 694 * q^53 - 135 * q^54 - 990 * q^55 + 1917 * q^56 - 798 * q^57 + 1354 * q^58 - 378 * q^59 + 765 * q^60 - 1396 * q^61 + 1475 * q^62 - 558 * q^63 + 1225 * q^64 - 348 * q^65 + 132 * q^66 - 402 * q^67 + 2032 * q^68 + 150 * q^69 + 2415 * q^70 - 964 * q^71 - 675 * q^72 - 192 * q^73 + 2751 * q^74 - 18 * q^75 - 2306 * q^76 + 2724 * q^77 + 1416 * q^78 - 802 * q^79 + 4221 * q^80 + 486 * q^81 + 1735 * q^82 + 2126 * q^83 - 999 * q^84 - 1206 * q^85 - 609 * q^86 - 726 * q^87 + 3656 * q^88 + 432 * q^89 - 999 * q^90 + 1258 * q^91 + 3163 * q^92 - 1314 * q^93 + 1742 * q^94 + 936 * q^95 + 105 * q^96 + 1290 * q^97 + 2492 * 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 $

$2$	3.33036	1.17746	0.588731	−	0.808329i	$-0.299628\pi$
$2$	3.33036	1.17746	0.588731	+	0.808329i	$0.299628\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	3.09132	0.386416
$5$	−17.6168	−1.57570	−0.787848	−	0.615869i	$-0.788805\pi$
$5$	−17.6168	−1.57570	−0.787848	+	0.615869i	$0.788805\pi$
$6$	9.99109	0.679808
$7$	−17.3029	−0.934267	−0.467134	−	0.884187i	$-0.654713\pi$
$7$	−17.3029	−0.934267	−0.467134	+	0.884187i	$0.654713\pi$
$8$	−16.3477	−0.722472
$9$	9.00000	0.333333
$10$	−58.6704	−1.85532
$11$	−20.9004	−0.572884	−0.286442	−	0.958098i	$-0.592473\pi$
$11$	−20.9004	−0.572884	−0.286442	+	0.958098i	$0.592473\pi$
$12$	9.27397	0.223097
$13$	5.65965	0.120746	0.0603732	−	0.998176i	$-0.480771\pi$
$13$	5.65965	0.120746	0.0603732	+	0.998176i	$0.480771\pi$
$14$	−57.6249	−1.10006
$15$	−52.8505	−0.909729
$16$	−79.1743	−1.23710
$17$	69.7817	0.995561	0.497781	−	0.867303i	$-0.334148\pi$
$17$	69.7817	0.995561	0.497781	+	0.867303i	$0.334148\pi$
$18$	29.9733	0.392487
$19$	−77.0844	−0.930757	−0.465378	−	0.885112i	$-0.654082\pi$
$19$	−77.0844	−0.930757	−0.465378	+	0.885112i	$0.654082\pi$
$20$	−54.4593	−0.608874
$21$	−51.9086	−0.539399
$22$	−69.6061	−0.674549
$23$	6.50326	0.0589575	0.0294788	−	0.999565i	$-0.490615\pi$
$23$	6.50326	0.0589575	0.0294788	+	0.999565i	$0.490615\pi$
$24$	−49.0430	−0.417119
$25$	185.353	1.48282
$26$	18.8487	0.142174
$27$	27.0000	0.192450
$28$	−53.4888	−0.361015
$29$	31.7567	0.203347	0.101674	−	0.994818i	$-0.467580\pi$
$29$	31.7567	0.203347	0.101674	+	0.994818i	$0.467580\pi$
$30$	−176.011	−1.07117
$31$	−134.506	−0.779290	−0.389645	−	0.920965i	$-0.627402\pi$
$31$	−134.506	−0.779290	−0.389645	+	0.920965i	$0.627402\pi$
$32$	−132.898	−0.734164
$33$	−62.7013	−0.330755
$34$	232.398	1.17223
$35$	304.822	1.47212
$36$	27.8219	0.128805
$37$	−24.7518	−0.109977	−0.0549887	−	0.998487i	$-0.517512\pi$
$37$	−24.7518	−0.109977	−0.0549887	+	0.998487i	$0.517512\pi$
$38$	−256.719	−1.09593
$39$	16.9789	0.0697130
$40$	287.994	1.13840
$41$	473.148	1.80227	0.901137	−	0.433534i	$-0.142734\pi$
$41$	473.148	1.80227	0.901137	+	0.433534i	$0.142734\pi$
$42$	−172.875	−0.635122
$43$	24.5301	0.0869954	0.0434977	−	0.999054i	$-0.486150\pi$
$43$	24.5301	0.0869954	0.0434977	+	0.999054i	$0.486150\pi$
$44$	−64.6101	−0.221371
$45$	−158.551	−0.525232
$46$	21.6582	0.0694202
$47$	−614.310	−1.90652	−0.953259	−	0.302153i	$-0.902295\pi$
$47$	−614.310	−1.90652	−0.953259	+	0.302153i	$0.902295\pi$
$48$	−237.523	−0.714239
$49$	−43.6107	−0.127145
$50$	617.292	1.74596
$51$	209.345	0.574788
$52$	17.4958	0.0466583
$53$	−208.897	−0.541399	−0.270700	−	0.962664i	$-0.587255\pi$
$53$	−208.897	−0.541399	−0.270700	+	0.962664i	$0.587255\pi$
$54$	89.9198	0.226603
$55$	368.200	0.902691
$56$	282.862	0.674982
$57$	−231.253	−0.537373
$58$	105.761	0.239434
$59$	−217.046	−0.478931	−0.239466	−	0.970905i	$-0.576972\pi$
$59$	−217.046	−0.478931	−0.239466	+	0.970905i	$0.576972\pi$
$60$	−163.378	−0.351533
$61$	−84.4339	−0.177224	−0.0886119	−	0.996066i	$-0.528243\pi$
$61$	−84.4339	−0.177224	−0.0886119	+	0.996066i	$0.528243\pi$
$62$	−447.954	−0.917583
$63$	−155.726	−0.311422
$64$	190.796	0.372649
$65$	−99.7050	−0.190260
$66$	−208.818	−0.389451
$67$	−67.0000	−0.122169
$67$	−67.0000	−0.122169
$68$	215.718	0.384700
$69$	19.5098	0.0340391
$70$	1015.17	1.73337
$71$	−1038.00	−1.73505	−0.867523	−	0.497397i	$-0.834289\pi$
$71$	−1038.00	−1.73505	−0.867523	+	0.497397i	$0.834289\pi$
$72$	−147.129	−0.240824
$73$	−967.120	−1.55059	−0.775293	−	0.631601i	$-0.782398\pi$
$73$	−967.120	−1.55059	−0.775293	+	0.631601i	$0.782398\pi$
$74$	−82.4324	−0.129494
$75$	556.058	0.856107
$76$	−238.293	−0.359659
$77$	361.638	0.535226
$78$	56.5461	0.0820844
$79$	429.533	0.611725	0.305862	−	0.952076i	$-0.401055\pi$
$79$	429.533	0.611725	0.305862	+	0.952076i	$0.401055\pi$
$80$	1394.80	1.94929
$81$	81.0000	0.111111
$82$	1575.75	2.12211
$83$	1372.00	1.81442	0.907211	−	0.420676i	$-0.138207\pi$
$83$	1372.00	1.81442	0.907211	+	0.420676i	$0.138207\pi$
$84$	−160.466	−0.208432
$85$	−1229.33	−1.56870
$86$	81.6941	0.102434
$87$	95.2702	0.117403
$88$	341.674	0.413893
$89$	277.435	0.330428	0.165214	−	0.986258i	$-0.447169\pi$
$89$	277.435	0.330428	0.165214	+	0.986258i	$0.447169\pi$
$90$	−528.034	−0.618441
$91$	−97.9281	−0.112809
$92$	20.1037	0.0227821
$93$	−403.518	−0.449923
$94$	−2045.88	−2.24485
$95$	1357.98	1.46659
$96$	−398.694	−0.423870
$97$	−839.028	−0.878252	−0.439126	−	0.898426i	$-0.644712\pi$
$97$	−839.028	−0.878252	−0.439126	+	0.898426i	$0.644712\pi$
$98$	−145.240	−0.149708
$99$	−188.104	−0.190961
$100$	572.985	0.572985
$101$	600.643	0.591745	0.295872	−	0.955227i	$-0.404390\pi$
$101$	600.643	0.591745	0.295872	+	0.955227i	$0.404390\pi$
$102$	697.195	0.676790
$103$	−1340.67	−1.28253	−0.641264	−	0.767320i	$-0.721590\pi$
$103$	−1340.67	−1.28253	−0.641264	+	0.767320i	$0.721590\pi$
$104$	−92.5221	−0.0872359
$105$	914.465	0.849930
$106$	−695.702	−0.637477
$107$	1284.68	1.16070	0.580348	−	0.814368i	$-0.302916\pi$
$107$	1284.68	1.16070	0.580348	+	0.814368i	$0.302916\pi$
$108$	83.4658	0.0743657
$109$	−669.821	−0.588598	−0.294299	−	0.955713i	$-0.595086\pi$
$109$	−669.821	−0.588598	−0.294299	+	0.955713i	$0.595086\pi$
$110$	1226.24	1.06288
$111$	−74.2553	−0.0634955
$112$	1369.94	1.15578
$113$	907.593	0.755568	0.377784	−	0.925894i	$-0.376686\pi$
$113$	907.593	0.755568	0.377784	+	0.925894i	$0.376686\pi$
$114$	−770.158	−0.632736
$115$	−114.567	−0.0928992
$116$	98.1703	0.0785766
$117$	50.9368	0.0402488
$118$	−722.841	−0.563923
$119$	−1207.42	−0.930120
$120$	863.983	0.657254
$121$	−894.171	−0.671804
$122$	−281.196	−0.208674
$123$	1419.44	1.04054
$124$	−415.801	−0.301130
$125$	−1063.22	−0.760779
$126$	−518.624	−0.366688
$127$	622.160	0.434707	0.217353	−	0.976093i	$-0.430258\pi$
$127$	622.160	0.434707	0.217353	+	0.976093i	$0.430258\pi$
$128$	1698.60	1.17294
$129$	73.5903	0.0502268
$130$	−332.054	−0.224024
$131$	419.313	0.279661	0.139830	−	0.990175i	$-0.455344\pi$
$131$	419.313	0.279661	0.139830	+	0.990175i	$0.455344\pi$
$132$	−193.830	−0.127809
$133$	1333.78	0.869576
$134$	−223.134	−0.143850
$135$	−475.654	−0.303243
$136$	−1140.77	−0.719265
$137$	−1497.55	−0.933899	−0.466950	−	0.884284i	$-0.654647\pi$
$137$	−1497.55	−0.933899	−0.466950	+	0.884284i	$0.654647\pi$
$138$	64.9747	0.0400798
$139$	713.655	0.435478	0.217739	−	0.976007i	$-0.430132\pi$
$139$	713.655	0.435478	0.217739	+	0.976007i	$0.430132\pi$
$140$	942.303	0.568851
$141$	−1842.93	−1.10073
$142$	−3456.93	−2.04295
$143$	−118.289	−0.0691737
$144$	−712.569	−0.412366
$145$	−559.453	−0.320414
$146$	−3220.86	−1.82576
$147$	−130.832	−0.0734072
$148$	−76.5157	−0.0424970
$149$	2475.02	1.36082	0.680408	−	0.732833i	$-0.261802\pi$
$149$	2475.02	1.36082	0.680408	+	0.732833i	$0.261802\pi$
$150$	1851.87	1.00803
$151$	1370.79	0.738765	0.369383	−	0.929277i	$-0.379569\pi$
$151$	1370.79	0.738765	0.369383	+	0.929277i	$0.379569\pi$
$152$	1260.15	0.672446
$153$	628.035	0.331854
$154$	1204.39	0.630209
$155$	2369.57	1.22792
$156$	52.4874	0.0269382
$157$	413.042	0.209964	0.104982	−	0.994474i	$-0.466522\pi$
$157$	413.042	0.209964	0.104982	+	0.994474i	$0.466522\pi$
$158$	1430.50	0.720282
$159$	−626.690	−0.312577
$160$	2341.24	1.15682
$161$	−112.525	−0.0550821
$162$	269.759	0.130829
$163$	−3994.35	−1.91940	−0.959698	−	0.281034i	$-0.909323\pi$
$163$	−3994.35	−1.91940	−0.959698	+	0.281034i	$0.909323\pi$
$164$	1462.65	0.696427
$165$	1104.60	0.521169
$166$	4569.27	2.13641
$167$	2828.02	1.31041	0.655206	−	0.755450i	$-0.272582\pi$
$167$	2828.02	1.31041	0.655206	+	0.755450i	$0.272582\pi$
$168$	848.585	0.389701
$169$	−2164.97	−0.985420
$170$	−4094.12	−1.84709
$171$	−693.760	−0.310252
$172$	75.8305	0.0336164
$173$	−259.803	−0.114176	−0.0570879	−	0.998369i	$-0.518182\pi$
$173$	−259.803	−0.114176	−0.0570879	+	0.998369i	$0.518182\pi$
$174$	317.284	0.138237
$175$	−3207.13	−1.38535
$176$	1654.78	0.708714
$177$	−651.137	−0.276511
$178$	923.960	0.389066
$179$	−4276.69	−1.78578	−0.892891	−	0.450272i	$-0.851327\pi$
$179$	−4276.69	−1.78578	−0.892891	+	0.450272i	$0.851327\pi$
$180$	−490.134	−0.202958
$181$	−406.624	−0.166984	−0.0834920	−	0.996508i	$-0.526607\pi$
$181$	−406.624	−0.166984	−0.0834920	+	0.996508i	$0.526607\pi$
$182$	−326.136	−0.132829
$183$	−253.302	−0.102320
$184$	−106.313	−0.0425952
$185$	436.047	0.173291
$186$	−1343.86	−0.529767
$187$	−1458.47	−0.570341
$188$	−1899.03	−0.736709
$189$	−467.177	−0.179800
$190$	4522.58	1.72685
$191$	−2987.54	−1.13178	−0.565892	−	0.824479i	$-0.691468\pi$
$191$	−2987.54	−1.13178	−0.565892	+	0.824479i	$0.691468\pi$
$192$	572.389	0.215149
$193$	−3594.72	−1.34069	−0.670346	−	0.742049i	$-0.733854\pi$
$193$	−3594.72	−1.34069	−0.670346	+	0.742049i	$0.733854\pi$
$194$	−2794.27	−1.03411
$195$	−299.115	−0.109847
$196$	−134.815	−0.0491308
$197$	−2714.16	−0.981602	−0.490801	−	0.871272i	$-0.663296\pi$
$197$	−2714.16	−0.981602	−0.490801	+	0.871272i	$0.663296\pi$
$198$	−626.455	−0.224850
$199$	−2517.27	−0.896705	−0.448352	−	0.893857i	$-0.647989\pi$
$199$	−2517.27	−0.896705	−0.448352	+	0.893857i	$0.647989\pi$
$200$	−3030.08	−1.07130
$201$	−201.000	−0.0705346
$202$	2000.36	0.696757
$203$	−549.482	−0.189981
$204$	647.153	0.222107
$205$	−8335.36	−2.83984
$206$	−4464.93	−1.51013
$207$	58.5293	0.0196525
$208$	−448.099	−0.149375
$209$	1611.10	0.533216
$210$	3045.50	1.00076
$211$	2468.48	0.805389	0.402695	−	0.915334i	$-0.368074\pi$
$211$	2468.48	0.805389	0.402695	+	0.915334i	$0.368074\pi$
$212$	−645.767	−0.209205
$213$	−3114.01	−1.00173
$214$	4278.45	1.36668
$215$	−432.142	−0.137078
$216$	−441.387	−0.139040
$217$	2327.34	0.728065
$218$	−2230.75	−0.693052
$219$	−2901.36	−0.895232
$220$	1138.22	0.348814
$221$	394.940	0.120210
$222$	−247.297	−0.0747635
$223$	−185.045	−0.0555674	−0.0277837	−	0.999614i	$-0.508845\pi$
$223$	−185.045	−0.0555674	−0.0277837	+	0.999614i	$0.508845\pi$
$224$	2299.51	0.685905
$225$	1668.17	0.494274
$226$	3022.62	0.889652
$227$	−1941.12	−0.567562	−0.283781	−	0.958889i	$-0.591589\pi$
$227$	−1941.12	−0.567562	−0.283781	+	0.958889i	$0.591589\pi$
$228$	−714.879	−0.207649
$229$	3835.20	1.10671	0.553357	−	0.832944i	$-0.313347\pi$
$229$	3835.20	1.10671	0.553357	+	0.832944i	$0.313347\pi$
$230$	−381.549	−0.109385
$231$	1084.91	0.309013
$232$	−519.149	−0.146913
$233$	−1020.32	−0.286881	−0.143440	−	0.989659i	$-0.545817\pi$
$233$	−1020.32	−0.286881	−0.143440	+	0.989659i	$0.545817\pi$
$234$	169.638	0.0473914
$235$	10822.2	3.00410
$236$	−670.959	−0.185067
$237$	1288.60	0.353179
$238$	−4021.16	−1.09518
$239$	−5192.84	−1.40543	−0.702714	−	0.711473i	$-0.748029\pi$
$239$	−5192.84	−1.40543	−0.702714	+	0.711473i	$0.748029\pi$
$240$	4184.40	1.12542
$241$	−726.201	−0.194103	−0.0970513	−	0.995279i	$-0.530941\pi$
$241$	−726.201	−0.194103	−0.0970513	+	0.995279i	$0.530941\pi$
$242$	−2977.92	−0.791024
$243$	243.000	0.0641500
$244$	−261.013	−0.0684820
$245$	768.282	0.200342
$246$	4727.26	1.22520
$247$	−436.271	−0.112386
$248$	2198.86	0.563015
$249$	4116.01	1.04756
$250$	−3540.91	−0.895788
$251$	5384.99	1.35417	0.677087	−	0.735903i	$-0.263242\pi$
$251$	5384.99	1.35417	0.677087	+	0.735903i	$0.263242\pi$
$252$	−481.399	−0.120338
$253$	−135.921	−0.0337758
$254$	2072.02	0.511851
$255$	−3687.99	−0.905691
$256$	4130.60	1.00845
$257$	4709.99	1.14320	0.571598	−	0.820534i	$-0.306324\pi$
$257$	4709.99	1.14320	0.571598	+	0.820534i	$0.306324\pi$
$258$	245.082	0.0591402
$259$	428.276	0.102748
$260$	−308.221	−0.0735193
$261$	285.811	0.0677825
$262$	1396.46	0.329290
$263$	−1408.81	−0.330309	−0.165154	−	0.986268i	$-0.552812\pi$
$263$	−1408.81	−0.330309	−0.165154	+	0.986268i	$0.552812\pi$
$264$	1025.02	0.238961
$265$	3680.10	0.853081
$266$	4441.98	1.02389
$267$	832.306	0.190773
$268$	−207.119	−0.0472082
$269$	4333.72	0.982275	0.491137	−	0.871082i	$-0.336581\pi$
$269$	4333.72	0.982275	0.491137	+	0.871082i	$0.336581\pi$
$270$	−1584.10	−0.357057
$271$	928.543	0.208137	0.104068	−	0.994570i	$-0.466814\pi$
$271$	928.543	0.208137	0.104068	+	0.994570i	$0.466814\pi$
$272$	−5524.92	−1.23161
$273$	−293.784	−0.0651306
$274$	−4987.38	−1.09963
$275$	−3873.95	−0.849484
$276$	60.3110	0.0131533
$277$	3584.00	0.777407	0.388703	−	0.921363i	$-0.372923\pi$
$277$	3584.00	0.777407	0.388703	+	0.921363i	$0.372923\pi$
$278$	2376.73	0.512758
$279$	−1210.55	−0.259763
$280$	−4983.13	−1.06357
$281$	7269.60	1.54330	0.771651	−	0.636046i	$-0.219431\pi$
$281$	7269.60	1.54330	0.771651	+	0.636046i	$0.219431\pi$
$282$	−6137.63	−1.29607
$283$	−3504.77	−0.736173	−0.368087	−	0.929791i	$-0.619987\pi$
$283$	−3504.77	−0.736173	−0.368087	+	0.929791i	$0.619987\pi$
$284$	−3208.80	−0.670449
$285$	4073.95	0.846737
$286$	−393.946	−0.0814493
$287$	−8186.81	−1.68381
$288$	−1196.08	−0.244721
$289$	−43.5186	−0.00885784
$290$	−1863.18	−0.377275
$291$	−2517.09	−0.507059
$292$	−2989.68	−0.599171
$293$	5603.62	1.11729	0.558647	−	0.829406i	$-0.311321\pi$
$293$	5603.62	1.11729	0.558647	+	0.829406i	$0.311321\pi$
$294$	−435.719	−0.0864341
$295$	3823.66	0.754651
$296$	404.634	0.0794556
$297$	−564.312	−0.110252
$298$	8242.73	1.60231
$299$	36.8062	0.00711891
$300$	1718.95	0.330813
$301$	−424.441	−0.0812770
$302$	4565.24	0.869867
$303$	1801.93	0.341644
$304$	6103.11	1.15144
$305$	1487.46	0.279251
$306$	2091.59	0.390745
$307$	1843.52	0.342721	0.171361	−	0.985208i	$-0.445184\pi$
$307$	1843.52	0.342721	0.171361	+	0.985208i	$0.445184\pi$
$308$	1117.94	0.206820
$309$	−4022.02	−0.740468
$310$	7891.52	1.44583
$311$	5006.84	0.912900	0.456450	−	0.889749i	$-0.349121\pi$
$311$	5006.84	0.912900	0.456450	+	0.889749i	$0.349121\pi$
$312$	−277.566	−0.0503657
$313$	2780.92	0.502194	0.251097	−	0.967962i	$-0.419209\pi$
$313$	2780.92	0.502194	0.251097	+	0.967962i	$0.419209\pi$
$314$	1375.58	0.247225
$315$	2743.39	0.490707
$316$	1327.83	0.236380
$317$	−6641.61	−1.17675	−0.588375	−	0.808588i	$-0.700232\pi$
$317$	−6641.61	−1.17675	−0.588375	+	0.808588i	$0.700232\pi$
$318$	−2087.11	−0.368048
$319$	−663.730	−0.116494
$320$	−3361.22	−0.587182
$321$	3854.04	0.670129
$322$	−374.749	−0.0648570
$323$	−5379.08	−0.926626
$324$	250.397	0.0429351
$325$	1049.03	0.179045
$326$	−13302.6	−2.26001
$327$	−2009.46	−0.339827
$328$	−7734.86	−1.30209
$329$	10629.3	1.78120
$330$	3678.72	0.613656
$331$	7810.77	1.29704	0.648518	−	0.761199i	$-0.275389\pi$
$331$	7810.77	1.29704	0.648518	+	0.761199i	$0.275389\pi$
$332$	4241.31	0.701121
$333$	−222.766	−0.0366591
$334$	9418.34	1.54296
$335$	1180.33	0.192502
$336$	4109.83	0.667290
$337$	9725.88	1.57211	0.786057	−	0.618154i	$-0.212119\pi$
$337$	9725.88	1.57211	0.786057	+	0.618154i	$0.212119\pi$
$338$	−7210.13	−1.16029
$339$	2722.78	0.436227
$340$	−3800.26	−0.606171
$341$	2811.23	0.446442
$342$	−2310.47	−0.365310
$343$	6689.47	1.05305
$344$	−401.010	−0.0628518
$345$	−343.700	−0.0536354
$346$	−865.237	−0.134438
$347$	−6462.88	−0.999843	−0.499922	−	0.866071i	$-0.666638\pi$
$347$	−6462.88	−0.999843	−0.499922	+	0.866071i	$0.666638\pi$
$348$	294.511	0.0453662
$349$	−7577.45	−1.16221	−0.581106	−	0.813828i	$-0.697380\pi$
$349$	−7577.45	−1.16221	−0.581106	+	0.813828i	$0.697380\pi$
$350$	−10680.9	−1.63120
$351$	152.810	0.0232377
$352$	2777.62	0.420591
$353$	1596.92	0.240781	0.120390	−	0.992727i	$-0.461585\pi$
$353$	1596.92	0.240781	0.120390	+	0.992727i	$0.461585\pi$
$354$	−2168.52	−0.325581
$355$	18286.3	2.73391
$356$	857.642	0.127682
$357$	−3622.27	−0.537005
$358$	−14242.9	−2.10269
$359$	−12987.4	−1.90933	−0.954664	−	0.297686i	$-0.903785\pi$
$359$	−12987.4	−1.90933	−0.954664	+	0.297686i	$0.903785\pi$
$360$	2591.95	0.379466
$361$	−916.990	−0.133691
$362$	−1354.21	−0.196617
$363$	−2682.51	−0.387866
$364$	−302.728	−0.0435913
$365$	17037.6	2.44325
$366$	−843.587	−0.120478
$367$	−9684.24	−1.37742	−0.688710	−	0.725037i	$-0.741823\pi$
$367$	−9684.24	−1.37742	−0.688710	+	0.725037i	$0.741823\pi$
$368$	−514.891	−0.0729363
$369$	4258.33	0.600758
$370$	1452.20	0.204044
$371$	3614.51	0.505812
$372$	−1247.40	−0.173857
$373$	943.381	0.130956	0.0654778	−	0.997854i	$-0.479143\pi$
$373$	943.381	0.130956	0.0654778	+	0.997854i	$0.479143\pi$
$374$	−4857.23	−0.671554
$375$	−3189.66	−0.439236
$376$	10042.5	1.37741
$377$	179.732	0.0245535
$378$	−1555.87	−0.211707
$379$	−11102.8	−1.50478	−0.752392	−	0.658716i	$-0.771100\pi$
$379$	−11102.8	−1.50478	−0.752392	+	0.658716i	$0.771100\pi$
$380$	4197.97	0.566713
$381$	1866.48	0.250978
$382$	−9949.59	−1.33263
$383$	13580.3	1.81181	0.905903	−	0.423485i	$-0.139193\pi$
$383$	13580.3	1.81181	0.905903	+	0.423485i	$0.139193\pi$
$384$	5095.81	0.677199
$385$	−6370.91	−0.843355
$386$	−11971.7	−1.57861
$387$	220.771	0.0289985
$388$	−2593.71	−0.339370
$389$	−5571.03	−0.726124	−0.363062	−	0.931765i	$-0.618269\pi$
$389$	−5571.03	−0.726124	−0.363062	+	0.931765i	$0.618269\pi$
$390$	−996.162	−0.129340
$391$	453.808	0.0586958
$392$	712.934	0.0918587
$393$	1257.94	0.161462
$394$	−9039.12	−1.15580
$395$	−7567.01	−0.963893
$396$	−581.490	−0.0737904
$397$	−6563.09	−0.829703	−0.414851	−	0.909889i	$-0.636166\pi$
$397$	−6563.09	−0.829703	−0.414851	+	0.909889i	$0.636166\pi$
$398$	−8383.41	−1.05584
$399$	4001.35	0.502050
$400$	−14675.2	−1.83440
$401$	11408.7	1.42075	0.710376	−	0.703823i	$-0.248525\pi$
$401$	11408.7	1.42075	0.710376	+	0.703823i	$0.248525\pi$
$402$	−669.403	−0.0830517
$403$	−761.256	−0.0940964
$404$	1856.78	0.228659
$405$	−1426.96	−0.175077
$406$	−1829.98	−0.223695
$407$	517.323	0.0630043
$408$	−3422.30	−0.415268
$409$	2360.50	0.285377	0.142689	−	0.989768i	$-0.454425\pi$
$409$	2360.50	0.285377	0.142689	+	0.989768i	$0.454425\pi$
$410$	−27759.8	−3.34380
$411$	−4492.64	−0.539187
$412$	−4144.45	−0.495589
$413$	3755.51	0.447450
$414$	194.924	0.0231401
$415$	−24170.4	−2.85898
$416$	−752.155	−0.0886477
$417$	2140.97	0.251423
$418$	5365.55	0.627841
$419$	−8416.72	−0.981346	−0.490673	−	0.871344i	$-0.663249\pi$
$419$	−8416.72	−0.981346	−0.490673	+	0.871344i	$0.663249\pi$
$420$	2826.91	0.328426
$421$	10851.3	1.25620	0.628102	−	0.778131i	$-0.283832\pi$
$421$	10851.3	1.25620	0.628102	+	0.778131i	$0.283832\pi$
$422$	8220.94	0.948315
$423$	−5528.79	−0.635506
$424$	3414.98	0.391146
$425$	12934.2	1.47624
$426$	−10370.8	−1.17950
$427$	1460.95	0.165574
$428$	3971.36	0.448511
$429$	−354.867	−0.0399374
$430$	−1439.19	−0.161405
$431$	−5278.27	−0.589896	−0.294948	−	0.955513i	$-0.595302\pi$
$431$	−5278.27	−0.589896	−0.294948	+	0.955513i	$0.595302\pi$
$432$	−2137.71	−0.238080
$433$	−2129.63	−0.236359	−0.118179	−	0.992992i	$-0.537706\pi$
$433$	−2129.63	−0.236359	−0.118179	+	0.992992i	$0.537706\pi$
$434$	7750.88	0.857268
$435$	−1678.36	−0.184991
$436$	−2070.63	−0.227443
$437$	−501.300	−0.0548751
$438$	−9662.58	−1.05410
$439$	−12818.2	−1.39357	−0.696785	−	0.717280i	$-0.745387\pi$
$439$	−12818.2	−1.39357	−0.696785	+	0.717280i	$0.745387\pi$
$440$	−6019.21	−0.652169
$441$	−392.496	−0.0423816
$442$	1315.29	0.141543
$443$	4408.35	0.472793	0.236396	−	0.971657i	$-0.424034\pi$
$443$	4408.35	0.472793	0.236396	+	0.971657i	$0.424034\pi$
$444$	−229.547	−0.0245356
$445$	−4887.53	−0.520654
$446$	−616.267	−0.0654285
$447$	7425.07	0.785668
$448$	−3301.32	−0.348154
$449$	−8544.35	−0.898068	−0.449034	−	0.893515i	$-0.648232\pi$
$449$	−8544.35	−0.898068	−0.449034	+	0.893515i	$0.648232\pi$
$450$	5555.62	0.581988
$451$	−9888.99	−1.03249
$452$	2805.66	0.291963
$453$	4112.38	0.426526
$454$	−6464.63	−0.668283
$455$	1725.18	0.177753
$456$	3780.45	0.388237
$457$	4985.74	0.510335	0.255168	−	0.966897i	$-0.417869\pi$
$457$	4985.74	0.510335	0.255168	+	0.966897i	$0.417869\pi$
$458$	12772.6	1.30311
$459$	1884.11	0.191596
$460$	−354.163	−0.0358977
$461$	12340.4	1.24674	0.623372	−	0.781925i	$-0.285762\pi$
$461$	12340.4	1.24674	0.623372	+	0.781925i	$0.285762\pi$
$462$	3613.16	0.363851
$463$	−2611.14	−0.262095	−0.131048	−	0.991376i	$-0.541834\pi$
$463$	−2611.14	−0.262095	−0.131048	+	0.991376i	$0.541834\pi$
$464$	−2514.32	−0.251561
$465$	7108.70	0.708942
$466$	−3398.03	−0.337791
$467$	18734.0	1.85633	0.928164	−	0.372171i	$-0.121387\pi$
$467$	18734.0	1.85633	0.928164	+	0.372171i	$0.121387\pi$
$468$	157.462	0.0155528
$469$	1159.29	0.114139
$470$	36041.9	3.53721
$471$	1239.13	0.121223
$472$	3548.19	0.346015
$473$	−512.690	−0.0498383
$474$	4291.50	0.415855
$475$	−14287.8	−1.38015
$476$	−3732.54	−0.359413
$477$	−1880.07	−0.180466
$478$	−17294.1	−1.65484
$479$	3393.75	0.323725	0.161863	−	0.986813i	$-0.448250\pi$
$479$	3393.75	0.323725	0.161863	+	0.986813i	$0.448250\pi$
$480$	7023.72	0.667890
$481$	−140.086	−0.0132794
$482$	−2418.51	−0.228548
$483$	−337.575	−0.0318017
$484$	−2764.17	−0.259596
$485$	14781.0	1.38386
$486$	809.278	0.0755342
$487$	−10560.5	−0.982633	−0.491316	−	0.870981i	$-0.663484\pi$
$487$	−10560.5	−0.982633	−0.491316	+	0.870981i	$0.663484\pi$
$488$	1380.30	0.128039
$489$	−11983.0	−1.10816
$490$	2558.66	0.235895
$491$	5298.74	0.487024	0.243512	−	0.969898i	$-0.421700\pi$
$491$	5298.74	0.487024	0.243512	+	0.969898i	$0.421700\pi$
$492$	4387.96	0.402082
$493$	2216.04	0.202445
$494$	−1452.94	−0.132330
$495$	3313.80	0.300897
$496$	10649.4	0.964058
$497$	17960.4	1.62100
$498$	13707.8	1.23346
$499$	18767.6	1.68367	0.841835	−	0.539735i	$-0.181476\pi$
$499$	18767.6	1.68367	0.841835	+	0.539735i	$0.181476\pi$
$500$	−3286.76	−0.293977
$501$	8484.07	0.756567
$502$	17934.0	1.59449
$503$	−14859.6	−1.31721	−0.658604	−	0.752490i	$-0.728853\pi$
$503$	−14859.6	−1.31721	−0.658604	+	0.752490i	$0.728853\pi$
$504$	2545.76	0.224994
$505$	−10581.4	−0.932410
$506$	−452.666	−0.0397697
$507$	−6494.91	−0.568933
$508$	1923.30	0.167977
$509$	−21258.5	−1.85121	−0.925607	−	0.378486i	$-0.876445\pi$
$509$	−21258.5	−1.85121	−0.925607	+	0.378486i	$0.876445\pi$
$510$	−12282.4	−1.06642
$511$	16733.9	1.44866
$512$	167.567	0.0144638
$513$	−2081.28	−0.179124
$514$	15686.0	1.34607
$515$	23618.4	2.02088
$516$	227.491	0.0194084
$517$	12839.4	1.09221
$518$	1426.32	0.120982
$519$	−779.408	−0.0659195
$520$	1629.95	0.137457
$521$	−17250.1	−1.45056	−0.725280	−	0.688454i	$-0.758290\pi$
$521$	−17250.1	−1.45056	−0.725280	+	0.688454i	$0.758290\pi$
$522$	951.853	0.0798113
$523$	4389.13	0.366966	0.183483	−	0.983023i	$-0.441263\pi$
$523$	4389.13	0.366966	0.183483	+	0.983023i	$0.441263\pi$
$524$	1296.23	0.108065
$525$	−9621.39	−0.799833
$526$	−4691.87	−0.388926
$527$	−9386.05	−0.775830
$528$	4964.34	0.409176
$529$	−12124.7	−0.996524
$530$	12256.1	1.00447
$531$	−1953.41	−0.159644
$532$	4123.15	0.336018
$533$	2677.85	0.217618
$534$	2771.88	0.224627
$535$	−22632.0	−1.82891
$536$	1095.29	0.0882640
$537$	−12830.1	−1.03102
$538$	14432.9	1.15659
$539$	911.483	0.0728393
$540$	−1470.40	−0.117178
$541$	13410.6	1.06574	0.532870	−	0.846197i	$-0.321114\pi$
$541$	13410.6	1.06574	0.532870	+	0.846197i	$0.321114\pi$
$542$	3092.39	0.245073
$543$	−1219.87	−0.0964083
$544$	−9273.83	−0.730905
$545$	11800.1	0.927452
$546$	−978.409	−0.0766887
$547$	−13774.8	−1.07673	−0.538363	−	0.842713i	$-0.680957\pi$
$547$	−13774.8	−1.07673	−0.538363	+	0.842713i	$0.680957\pi$
$548$	−4629.41	−0.360873
$549$	−759.905	−0.0590746
$550$	−12901.7	−1.00023
$551$	−2447.95	−0.189267
$552$	−318.940	−0.0245923
$553$	−7432.16	−0.571514
$554$	11936.0	0.915367
$555$	1308.14	0.100050
$556$	2206.14	0.168275
$557$	−13121.9	−0.998194	−0.499097	−	0.866546i	$-0.666335\pi$
$557$	−13121.9	−0.998194	−0.499097	+	0.866546i	$0.666335\pi$
$558$	−4031.58	−0.305861
$559$	138.832	0.0105044
$560$	−24134.0	−1.82116
$561$	−4375.40	−0.329286
$562$	24210.4	1.81718
$563$	3599.38	0.269442	0.134721	−	0.990884i	$-0.456986\pi$
$563$	3599.38	0.269442	0.134721	+	0.990884i	$0.456986\pi$
$564$	−5697.10	−0.425339
$565$	−15988.9	−1.19055
$566$	−11672.2	−0.866816
$567$	−1401.53	−0.103807
$568$	16968.9	1.25352
$569$	−26237.0	−1.93306	−0.966529	−	0.256557i	$-0.917412\pi$
$569$	−26237.0	−1.93306	−0.966529	+	0.256557i	$0.917412\pi$
$570$	13567.7	0.997000
$571$	24662.6	1.80753	0.903763	−	0.428032i	$-0.140793\pi$
$571$	24662.6	1.80753	0.903763	+	0.428032i	$0.140793\pi$
$572$	−365.670	−0.0267298
$573$	−8962.62	−0.653436
$574$	−27265.1	−1.98262
$575$	1205.40	0.0874235
$576$	1717.17	0.124216
$577$	12455.2	0.898643	0.449322	−	0.893370i	$-0.351666\pi$
$577$	12455.2	0.898643	0.449322	+	0.893370i	$0.351666\pi$
$578$	−144.933	−0.0104298
$579$	−10784.2	−0.774049
$580$	−1729.45	−0.123813
$581$	−23739.6	−1.69515
$582$	−8382.81	−0.597042
$583$	4366.03	0.310159
$584$	15810.2	1.12026
$585$	−897.345	−0.0634199
$586$	18662.1	1.31557
$587$	3744.36	0.263282	0.131641	−	0.991297i	$-0.457975\pi$
$587$	3744.36	0.263282	0.131641	+	0.991297i	$0.457975\pi$
$588$	−404.445	−0.0283657
$589$	10368.3	0.725329
$590$	12734.2	0.888572
$591$	−8142.47	−0.566728
$592$	1959.70	0.136053
$593$	27392.4	1.89691	0.948457	−	0.316905i	$-0.102644\pi$
$593$	27392.4	1.89691	0.948457	+	0.316905i	$0.102644\pi$
$594$	−1879.36	−0.129817
$595$	21271.0	1.46559
$596$	7651.10	0.525841
$597$	−7551.80	−0.517713
$598$	122.578	0.00838225
$599$	−4639.32	−0.316457	−0.158228	−	0.987403i	$-0.550578\pi$
$599$	−4639.32	−0.316457	−0.158228	+	0.987403i	$0.550578\pi$
$600$	−9090.25	−0.618513
$601$	5158.02	0.350083	0.175042	−	0.984561i	$-0.443994\pi$
$601$	5158.02	0.350083	0.175042	+	0.984561i	$0.443994\pi$
$602$	−1413.54	−0.0957005
$603$	−603.000	−0.0407231
$604$	4237.56	0.285470
$605$	15752.5	1.05856
$606$	6001.08	0.402273
$607$	−960.155	−0.0642035	−0.0321017	−	0.999485i	$-0.510220\pi$
$607$	−960.155	−0.0642035	−0.0321017	+	0.999485i	$0.510220\pi$
$608$	10244.4	0.683328
$609$	−1648.45	−0.109685
$610$	4953.78	0.328807
$611$	−3476.78	−0.230205
$612$	1941.46	0.128233
$613$	−9144.77	−0.602535	−0.301267	−	0.953540i	$-0.597410\pi$
$613$	−9144.77	−0.602535	−0.301267	+	0.953540i	$0.597410\pi$
$614$	6139.61	0.403541
$615$	−25006.1	−1.63958
$616$	−5911.94	−0.386686
$617$	17009.9	1.10988	0.554938	−	0.831892i	$-0.312742\pi$
$617$	17009.9	1.10988	0.554938	+	0.831892i	$0.312742\pi$
$618$	−13394.8	−0.871873
$619$	12368.0	0.803091	0.401546	−	0.915839i	$-0.368473\pi$
$619$	12368.0	0.803091	0.401546	+	0.915839i	$0.368473\pi$
$620$	7325.10	0.474489
$621$	175.588	0.0113464
$622$	16674.6	1.07490
$623$	−4800.43	−0.308708
$624$	−1344.30	−0.0862418
$625$	−4438.49	−0.284064
$626$	9261.46	0.591314
$627$	4833.30	0.307852
$628$	1276.85	0.0811334
$629$	−1727.22	−0.109489
$630$	9136.50	0.577789
$631$	4001.36	0.252443	0.126222	−	0.992002i	$-0.459715\pi$
$631$	4001.36	0.252443	0.126222	+	0.992002i	$0.459715\pi$
$632$	−7021.87	−0.441954
$633$	7405.44	0.464992
$634$	−22119.0	−1.38558
$635$	−10960.5	−0.684966
$636$	−1937.30	−0.120785
$637$	−246.821	−0.0153523
$638$	−2210.46	−0.137168
$639$	−9342.03	−0.578349
$640$	−29924.0	−1.84820
$641$	17896.9	1.10278	0.551391	−	0.834247i	$-0.314097\pi$
$641$	17896.9	1.10278	0.551391	+	0.834247i	$0.314097\pi$
$642$	12835.3	0.789051
$643$	−3913.31	−0.240009	−0.120005	−	0.992773i	$-0.538291\pi$
$643$	−3913.31	−0.240009	−0.120005	+	0.992773i	$0.538291\pi$
$644$	−347.851	−0.0212846
$645$	−1296.43	−0.0791423
$646$	−17914.3	−1.09107
$647$	7111.43	0.432116	0.216058	−	0.976381i	$-0.430680\pi$
$647$	7111.43	0.432116	0.216058	+	0.976381i	$0.430680\pi$
$648$	−1324.16	−0.0802747
$649$	4536.35	0.274372
$650$	3493.65	0.210819
$651$	6982.01	0.420348
$652$	−12347.8	−0.741684
$653$	−18578.4	−1.11336	−0.556682	−	0.830725i	$-0.687926\pi$
$653$	−18578.4	−1.11336	−0.556682	+	0.830725i	$0.687926\pi$
$654$	−6692.24	−0.400134
$655$	−7386.96	−0.440660
$656$	−37461.1	−2.22959
$657$	−8704.08	−0.516862
$658$	35399.6	2.09729
$659$	1449.70	0.0856942	0.0428471	−	0.999082i	$-0.486357\pi$
$659$	1449.70	0.0856942	0.0428471	+	0.999082i	$0.486357\pi$
$660$	3414.67	0.201388
$661$	7546.42	0.444057	0.222028	−	0.975040i	$-0.428732\pi$
$661$	7546.42	0.444057	0.222028	+	0.975040i	$0.428732\pi$
$662$	26012.7	1.52721
$663$	1184.82	0.0694036
$664$	−22429.1	−1.31087
$665$	−23497.0	−1.37019
$666$	−741.891	−0.0431647
$667$	206.522	0.0119889
$668$	8742.33	0.506364
$669$	−555.135	−0.0320819
$670$	3930.92	0.226664
$671$	1764.71	0.101529
$672$	6898.54	0.396008
$673$	−29243.6	−1.67497	−0.837486	−	0.546458i	$-0.815976\pi$
$673$	−29243.6	−1.67497	−0.837486	+	0.546458i	$0.815976\pi$
$674$	32390.7	1.85110
$675$	5004.52	0.285369
$676$	−6692.62	−0.380782
$677$	−20383.5	−1.15717	−0.578583	−	0.815624i	$-0.696394\pi$
$677$	−20383.5	−1.15717	−0.578583	+	0.815624i	$0.696394\pi$
$678$	9067.85	0.513641
$679$	14517.6	0.820522
$680$	20096.7	1.13334
$681$	−5823.36	−0.327682
$682$	9362.43	0.525669
$683$	−32841.0	−1.83986	−0.919932	−	0.392077i	$-0.871757\pi$
$683$	−32841.0	−1.83986	−0.919932	+	0.392077i	$0.871757\pi$
$684$	−2144.64	−0.119886
$685$	26382.0	1.47154
$686$	22278.4	1.23993
$687$	11505.6	0.638961
$688$	−1942.15	−0.107622
$689$	−1182.28	−0.0653721
$690$	−1144.65	−0.0631536
$691$	−15355.3	−0.845358	−0.422679	−	0.906280i	$-0.638910\pi$
$691$	−15355.3	−0.845358	−0.422679	+	0.906280i	$0.638910\pi$
$692$	−803.134	−0.0441193
$693$	3254.74	0.178409
$694$	−21523.7	−1.17728
$695$	−12572.3	−0.686181
$696$	−1557.45	−0.0848202
$697$	33017.0	1.79427
$698$	−25235.7	−1.36846
$699$	−3060.95	−0.165631
$700$	−9914.28	−0.535321
$701$	−2755.20	−0.148449	−0.0742243	−	0.997242i	$-0.523648\pi$
$701$	−2755.20	−0.148449	−0.0742243	+	0.997242i	$0.523648\pi$
$702$	508.915	0.0273615
$703$	1907.98	0.102362
$704$	−3987.73	−0.213485
$705$	32466.6	1.73442
$706$	5318.33	0.283510
$707$	−10392.8	−0.552848
$708$	−2012.88	−0.106848
$709$	24545.8	1.30019	0.650097	−	0.759851i	$-0.274728\pi$
$709$	24545.8	1.30019	0.650097	+	0.759851i	$0.274728\pi$
$710$	60900.1	3.21907
$711$	3865.80	0.203908
$712$	−4535.42	−0.238725
$713$	−874.727	−0.0459450
$714$	−12063.5	−0.632303
$715$	2083.88	0.108997
$716$	−13220.6	−0.690054
$717$	−15578.5	−0.811424
$718$	−43252.8	−2.24816
$719$	−35113.1	−1.82128	−0.910639	−	0.413204i	$-0.864410\pi$
$719$	−35113.1	−1.82128	−0.910639	+	0.413204i	$0.864410\pi$
$720$	12553.2	0.649764
$721$	23197.5	1.19822
$722$	−3053.91	−0.157417
$723$	−2178.60	−0.112065
$724$	−1257.01	−0.0645252
$725$	5886.19	0.301528
$726$	−8933.75	−0.456698
$727$	16983.3	0.866403	0.433201	−	0.901297i	$-0.357384\pi$
$727$	16983.3	0.866403	0.433201	+	0.901297i	$0.357384\pi$
$728$	1600.90	0.0815017
$729$	729.000	0.0370370
$730$	56741.4	2.87684
$731$	1711.75	0.0866093
$732$	−783.038	−0.0395381
$733$	−14914.9	−0.751562	−0.375781	−	0.926709i	$-0.622625\pi$
$733$	−14914.9	−0.751562	−0.375781	+	0.926709i	$0.622625\pi$
$734$	−32252.1	−1.62186
$735$	2304.85	0.115667
$736$	−864.269	−0.0432845
$737$	1400.33	0.0699889
$738$	14181.8	0.707369
$739$	14675.3	0.730500	0.365250	−	0.930909i	$-0.380983\pi$
$739$	14675.3	0.730500	0.365250	+	0.930909i	$0.380983\pi$
$740$	1347.96	0.0669624
$741$	−1308.81	−0.0648859
$742$	12037.6	0.595574
$743$	30825.3	1.52203	0.761017	−	0.648732i	$-0.224700\pi$
$743$	30825.3	1.52203	0.761017	+	0.648732i	$0.224700\pi$
$744$	6596.58	0.325057
$745$	−43602.0	−2.14424
$746$	3141.80	0.154195
$747$	12348.0	0.604807
$748$	−4508.60	−0.220389
$749$	−22228.6	−1.08440
$750$	−10622.7	−0.517183
$751$	−33900.0	−1.64718	−0.823588	−	0.567188i	$-0.808031\pi$
$751$	−33900.0	−1.64718	−0.823588	+	0.567188i	$0.808031\pi$
$752$	48637.6	2.35855
$753$	16155.0	0.781833
$754$	598.573	0.0289108
$755$	−24149.0	−1.16407
$756$	−1444.20	−0.0694774
$757$	18721.2	0.898855	0.449428	−	0.893317i	$-0.351628\pi$
$757$	18721.2	0.898855	0.449428	+	0.893317i	$0.351628\pi$
$758$	−36976.4	−1.77182
$759$	−407.763	−0.0195005
$760$	−22199.9	−1.05957
$761$	−10654.7	−0.507534	−0.253767	−	0.967265i	$-0.581670\pi$
$761$	−10654.7	−0.507534	−0.253767	+	0.967265i	$0.581670\pi$
$762$	6216.06	0.295517
$763$	11589.8	0.549908
$764$	−9235.45	−0.437339
$765$	−11064.0	−0.522901
$766$	45227.4	2.13333
$767$	−1228.40	−0.0578293
$768$	12391.8	0.582227
$769$	11457.0	0.537255	0.268628	−	0.963244i	$-0.413430\pi$
$769$	11457.0	0.537255	0.268628	+	0.963244i	$0.413430\pi$
$770$	−21217.4	−0.993018
$771$	14130.0	0.660024
$772$	−11112.4	−0.518064
$773$	−23462.9	−1.09172	−0.545861	−	0.837876i	$-0.683797\pi$
$773$	−23462.9	−1.09172	−0.545861	+	0.837876i	$0.683797\pi$
$774$	735.247	0.0341446
$775$	−24931.0	−1.15555
$776$	13716.2	0.634512
$777$	1284.83	0.0593217
$778$	−18553.5	−0.854983
$779$	−36472.3	−1.67748
$780$	−924.662	−0.0424464
$781$	21694.7	0.993980
$782$	1511.35	0.0691121
$783$	857.432	0.0391342
$784$	3452.85	0.157291
$785$	−7276.49	−0.330840
$786$	4189.39	0.190115
$787$	−6587.43	−0.298369	−0.149184	−	0.988809i	$-0.547665\pi$
$787$	−6587.43	−0.298369	−0.149184	+	0.988809i	$0.547665\pi$
$788$	−8390.33	−0.379306
$789$	−4226.44	−0.190704
$790$	−25200.9	−1.13495
$791$	−15704.0	−0.705902
$792$	3075.06	0.137964
$793$	−477.866	−0.0213992
$794$	−21857.5	−0.976943
$795$	11040.3	0.492527
$796$	−7781.69	−0.346501
$797$	18515.7	0.822911	0.411456	−	0.911430i	$-0.365020\pi$
$797$	18515.7	0.822911	0.411456	+	0.911430i	$0.365020\pi$
$798$	13325.9	0.591144
$799$	−42867.6	−1.89806
$800$	−24633.0	−1.08863
$801$	2496.92	0.110143
$802$	37995.0	1.67288
$803$	20213.2	0.888306
$804$	−621.356	−0.0272556
$805$	1982.33	0.0867927
$806$	−2535.26	−0.110795
$807$	13001.2	0.567116
$808$	−9819.12	−0.427519
$809$	−6310.42	−0.274243	−0.137121	−	0.990554i	$-0.543785\pi$
$809$	−6310.42	−0.274243	−0.137121	+	0.990554i	$0.543785\pi$
$810$	−4752.31	−0.206147
$811$	6139.16	0.265814	0.132907	−	0.991129i	$-0.457569\pi$
$811$	6139.16	0.265814	0.132907	+	0.991129i	$0.457569\pi$
$812$	−1698.63	−0.0734115
$813$	2785.63	0.120168
$814$	1722.87	0.0741851
$815$	70367.7	3.02439
$816$	−16574.7	−0.711069
$817$	−1890.89	−0.0809716
$818$	7861.33	0.336021
$819$	−881.353	−0.0376031
$820$	−25767.3	−1.09736
$821$	−28378.9	−1.20637	−0.603185	−	0.797601i	$-0.706102\pi$
$821$	−28378.9	−1.20637	−0.603185	+	0.797601i	$0.706102\pi$
$822$	−14962.1	−0.634872
$823$	−166.774	−0.00706365	−0.00353183	−	0.999994i	$-0.501124\pi$
$823$	−166.774	−0.00706365	−0.00353183	+	0.999994i	$0.501124\pi$
$824$	21916.9	0.926591
$825$	−11621.9	−0.490450
$826$	12507.2	0.526855
$827$	−26260.1	−1.10418	−0.552088	−	0.833786i	$-0.686169\pi$
$827$	−26260.1	−1.10418	−0.552088	+	0.833786i	$0.686169\pi$
$828$	180.933	0.00759404
$829$	43751.4	1.83299	0.916495	−	0.400046i	$-0.131006\pi$
$829$	43751.4	1.83299	0.916495	+	0.400046i	$0.131006\pi$
$830$	−80496.1	−3.36634
$831$	10752.0	0.448836
$832$	1079.84	0.0449960
$833$	−3043.23	−0.126581
$834$	7130.19	0.296041
$835$	−49820.8	−2.06481
$836$	4980.43	0.206043
$837$	−3631.66	−0.149974
$838$	−28030.8	−1.15550
$839$	−17888.8	−0.736102	−0.368051	−	0.929806i	$-0.619975\pi$
$839$	−17888.8	−0.736102	−0.368051	+	0.929806i	$0.619975\pi$
$840$	−14949.4	−0.614051
$841$	−23380.5	−0.958650
$842$	36138.9	1.47913
$843$	21808.8	0.891026
$844$	7630.87	0.311215
$845$	38139.9	1.55272
$846$	−18412.9	−0.748284
$847$	15471.7	0.627645
$848$	16539.3	0.669764
$849$	−10514.3	−0.425030
$850$	43075.6	1.73821
$851$	−160.967	−0.00648400
$852$	−9626.41	−0.387084
$853$	−846.836	−0.0339919	−0.0169960	−	0.999856i	$-0.505410\pi$
$853$	−846.836	−0.0339919	−0.0169960	+	0.999856i	$0.505410\pi$
$854$	4865.49	0.194957
$855$	12221.8	0.488864
$856$	−21001.5	−0.838571
$857$	49327.2	1.96614	0.983071	−	0.183225i	$-0.0586538\pi$
$857$	49327.2	1.96614	0.983071	+	0.183225i	$0.0586538\pi$
$858$	−1181.84	−0.0470248
$859$	−35238.5	−1.39967	−0.699837	−	0.714302i	$-0.746744\pi$
$859$	−35238.5	−1.39967	−0.699837	+	0.714302i	$0.746744\pi$
$860$	−1335.89	−0.0529692
$861$	−24560.4	−0.972145
$862$	−17578.5	−0.694580
$863$	11754.3	0.463640	0.231820	−	0.972759i	$-0.425532\pi$
$863$	11754.3	0.463640	0.231820	+	0.972759i	$0.425532\pi$
$864$	−3588.24	−0.141290
$865$	4576.90	0.179907
$866$	−7092.43	−0.278303
$867$	−130.556	−0.00511408
$868$	7194.56	0.281335
$869$	−8977.43	−0.350447
$870$	−5589.54	−0.217820
$871$	−379.196	−0.0147515
$872$	10950.0	0.425246
$873$	−7551.26	−0.292751
$874$	−1669.51	−0.0646134
$875$	18396.8	0.710771
$876$	−8969.04	−0.345931
$877$	−11624.0	−0.447564	−0.223782	−	0.974639i	$-0.571840\pi$
$877$	−11624.0	−0.447564	−0.223782	+	0.974639i	$0.571840\pi$
$878$	−42689.2	−1.64088
$879$	16810.9	0.645070
$880$	−29151.9	−1.11672
$881$	30928.6	1.18276	0.591380	−	0.806393i	$-0.298583\pi$
$881$	30928.6	1.18276	0.591380	+	0.806393i	$0.298583\pi$
$882$	−1307.16	−0.0499028
$883$	−7894.03	−0.300855	−0.150428	−	0.988621i	$-0.548065\pi$
$883$	−7894.03	−0.300855	−0.150428	+	0.988621i	$0.548065\pi$
$884$	1220.89	0.0464512
$885$	11471.0	0.435698
$886$	14681.4	0.556695
$887$	3157.99	0.119543	0.0597717	−	0.998212i	$-0.480963\pi$
$887$	3157.99	0.119543	0.0597717	+	0.998212i	$0.480963\pi$
$888$	1213.90	0.0458737
$889$	−10765.2	−0.406132
$890$	−16277.2	−0.613050
$891$	−1692.94	−0.0636538
$892$	−572.034	−0.0214721
$893$	47353.8	1.77451
$894$	24728.2	0.925094
$895$	75341.8	2.81385
$896$	−29390.7	−1.09584
$897$	110.418	0.00411011
$898$	−28455.8	−1.05744
$899$	−4271.47	−0.158467
$900$	5156.86	0.190995
$901$	−14577.2	−0.538996
$902$	−32934.0	−1.21572
$903$	−1273.32	−0.0469253
$904$	−14837.0	−0.545877
$905$	7163.42	0.263116
$906$	13695.7	0.502218
$907$	−5766.64	−0.211111	−0.105556	−	0.994413i	$-0.533662\pi$
$907$	−5766.64	−0.211111	−0.105556	+	0.994413i	$0.533662\pi$
$908$	−6000.63	−0.219315
$909$	5405.79	0.197248
$910$	5745.49	0.209298
$911$	−51948.1	−1.88926	−0.944631	−	0.328135i	$-0.893580\pi$
$911$	−51948.1	−1.88926	−0.944631	+	0.328135i	$0.893580\pi$
$912$	18309.3	0.664783
$913$	−28675.5	−1.03945
$914$	16604.3	0.600900
$915$	4462.37	0.161226
$916$	11855.9	0.427651
$917$	−7255.32	−0.261278
$918$	6274.76	0.225597
$919$	−46366.0	−1.66428	−0.832140	−	0.554565i	$-0.812885\pi$
$919$	−46366.0	−1.66428	−0.832140	+	0.554565i	$0.812885\pi$
$920$	1872.90	0.0671171
$921$	5530.57	0.197870
$922$	41098.0	1.46799
$923$	−5874.73	−0.209501
$924$	3353.82	0.119407
$925$	−4587.80	−0.163077
$926$	−8696.05	−0.308607
$927$	−12066.1	−0.427509
$928$	−4220.40	−0.149290
$929$	−16829.2	−0.594346	−0.297173	−	0.954824i	$-0.596044\pi$
$929$	−16829.2	−0.594346	−0.297173	+	0.954824i	$0.596044\pi$
$930$	23674.6	0.834752
$931$	3361.71	0.118341
$932$	−3154.13	−0.110855
$933$	15020.5	0.527063
$934$	62391.0	2.18575
$935$	25693.6	0.898684
$936$	−832.699	−0.0290786
$937$	689.913	0.0240539	0.0120269	−	0.999928i	$-0.496172\pi$
$937$	689.913	0.0240539	0.0120269	+	0.999928i	$0.496172\pi$
$938$	3860.87	0.134394
$939$	8342.75	0.289942
$940$	33454.9	1.16083
$941$	−37882.7	−1.31237	−0.656186	−	0.754599i	$-0.727831\pi$
$941$	−37882.7	−1.31237	−0.656186	+	0.754599i	$0.727831\pi$
$942$	4126.74	0.142735
$943$	3077.00	0.106258
$944$	17184.4	0.592485
$945$	8230.18	0.283310
$946$	−1707.44	−0.0586827
$947$	−38489.2	−1.32073	−0.660365	−	0.750944i	$-0.729599\pi$
$947$	−38489.2	−1.32073	−0.660365	+	0.750944i	$0.729599\pi$
$948$	3983.48	0.136474
$949$	−5473.56	−0.187228
$950$	−47583.6	−1.62507
$951$	−19924.8	−0.679397
$952$	19738.6	0.671986
$953$	3857.98	0.131136	0.0655678	−	0.997848i	$-0.479114\pi$
$953$	3857.98	0.131136	0.0655678	+	0.997848i	$0.479114\pi$
$954$	−6261.32	−0.212492
$955$	52631.0	1.78335
$956$	−16052.8	−0.543079
$957$	−1991.19	−0.0672581
$958$	11302.4	0.381174
$959$	25911.9	0.872511
$960$	−10083.7	−0.339010
$961$	−11699.2	−0.392708
$962$	−466.538	−0.0156360
$963$	11562.1	0.386899
$964$	−2244.92	−0.0750043
$965$	63327.6	2.11252
$966$	−1124.25	−0.0374452
$967$	−39397.5	−1.31018	−0.655088	−	0.755553i	$-0.727368\pi$
$967$	−39397.5	−1.31018	−0.655088	+	0.755553i	$0.727368\pi$
$968$	14617.6	0.485360
$969$	−16137.2	−0.534988
$970$	49226.2	1.62944
$971$	9367.03	0.309580	0.154790	−	0.987947i	$-0.450530\pi$
$971$	9367.03	0.309580	0.154790	+	0.987947i	$0.450530\pi$
$972$	751.192	0.0247886
$973$	−12348.3	−0.406853
$974$	−35170.3	−1.15701
$975$	3147.09	0.103372
$976$	6685.00	0.219243
$977$	−48197.3	−1.57827	−0.789135	−	0.614220i	$-0.789471\pi$
$977$	−48197.3	−1.57827	−0.789135	+	0.614220i	$0.789471\pi$
$978$	−39907.9	−1.30482
$979$	−5798.52	−0.189297
$980$	2375.01	0.0774152
$981$	−6028.39	−0.196199
$982$	17646.7	0.573452
$983$	−22701.1	−0.736575	−0.368288	−	0.929712i	$-0.620056\pi$
$983$	−22701.1	−0.736575	−0.368288	+	0.929712i	$0.620056\pi$
$984$	−23204.6	−0.751764
$985$	47814.8	1.54671
$986$	7380.21	0.238371
$987$	31888.0	1.02838
$988$	−1348.65	−0.0434275
$989$	159.526	0.00512904
$990$	11036.1	0.354295
$991$	1735.57	0.0556330	0.0278165	−	0.999613i	$-0.491145\pi$
$991$	1735.57	0.0556330	0.0278165	+	0.999613i	$0.491145\pi$
$992$	17875.5	0.572126
$993$	23432.3	0.748844
$994$	59814.8	1.90866
$995$	44346.2	1.41294
$996$	12723.9	0.404792
$997$	30114.7	0.956613	0.478306	−	0.878193i	$-0.341251\pi$
$997$	30114.7	0.956613	0.478306	+	0.878193i	$0.341251\pi$
$998$	62502.8	1.98246
$999$	−668.297	−0.0211652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.b.1.6	✓	6
3.2	odd	2		603.4.a.b.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.b.1.6	✓	6	1.1	even	1	trivial
603.4.a.b.1.1		6	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)

\(f(q)\)	\(=\)	\(q+3.33036 q^{2} +3.00000 q^{3} +3.09132 q^{4} -17.6168 q^{5} +9.99109 q^{6} -17.3029 q^{7} -16.3477 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.33036 q^{2} +3.00000 q^{3} +3.09132 q^{4} -17.6168 q^{5} +9.99109 q^{6} -17.3029 q^{7} -16.3477 q^{8} +9.00000 q^{9} -58.6704 q^{10} -20.9004 q^{11} +9.27397 q^{12} +5.65965 q^{13} -57.6249 q^{14} -52.8505 q^{15} -79.1743 q^{16} +69.7817 q^{17} +29.9733 q^{18} -77.0844 q^{19} -54.4593 q^{20} -51.9086 q^{21} -69.6061 q^{22} +6.50326 q^{23} -49.0430 q^{24} +185.353 q^{25} +18.8487 q^{26} +27.0000 q^{27} -53.4888 q^{28} +31.7567 q^{29} -176.011 q^{30} -134.506 q^{31} -132.898 q^{32} -62.7013 q^{33} +232.398 q^{34} +304.822 q^{35} +27.8219 q^{36} -24.7518 q^{37} -256.719 q^{38} +16.9789 q^{39} +287.994 q^{40} +473.148 q^{41} -172.875 q^{42} +24.5301 q^{43} -64.6101 q^{44} -158.551 q^{45} +21.6582 q^{46} -614.310 q^{47} -237.523 q^{48} -43.6107 q^{49} +617.292 q^{50} +209.345 q^{51} +17.4958 q^{52} -208.897 q^{53} +89.9198 q^{54} +368.200 q^{55} +282.862 q^{56} -231.253 q^{57} +105.761 q^{58} -217.046 q^{59} -163.378 q^{60} -84.4339 q^{61} -447.954 q^{62} -155.726 q^{63} +190.796 q^{64} -99.7050 q^{65} -208.818 q^{66} -67.0000 q^{67} +215.718 q^{68} +19.5098 q^{69} +1015.17 q^{70} -1038.00 q^{71} -147.129 q^{72} -967.120 q^{73} -82.4324 q^{74} +556.058 q^{75} -238.293 q^{76} +361.638 q^{77} +56.5461 q^{78} +429.533 q^{79} +1394.80 q^{80} +81.0000 q^{81} +1575.75 q^{82} +1372.00 q^{83} -160.466 q^{84} -1229.33 q^{85} +81.6941 q^{86} +95.2702 q^{87} +341.674 q^{88} +277.435 q^{89} -528.034 q^{90} -97.9281 q^{91} +20.1037 q^{92} -403.518 q^{93} -2045.88 q^{94} +1357.98 q^{95} -398.694 q^{96} -839.028 q^{97} -145.240 q^{98} -188.104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9} - 111 q^{10} - 72 q^{11} + 39 q^{12} - 192 q^{13} + 3 q^{14} - 36 q^{15} - 27 q^{16} - 100 q^{17} - 45 q^{18} - 266 q^{19} + 255 q^{20} - 186 q^{21} + 44 q^{22} + 50 q^{23} - 225 q^{24} - 6 q^{25} + 472 q^{26} + 162 q^{27} - 333 q^{28} - 242 q^{29} - 333 q^{30} - 438 q^{31} + 35 q^{32} - 216 q^{33} - 150 q^{34} - 258 q^{35} + 117 q^{36} - 596 q^{37} + 664 q^{38} - 576 q^{39} - 831 q^{40} + 54 q^{41} + 9 q^{42} - 360 q^{43} - 714 q^{44} - 108 q^{45} - 871 q^{46} - 720 q^{47} - 81 q^{48} - 302 q^{49} + 4 q^{50} - 300 q^{51} - 1118 q^{52} + 694 q^{53} - 135 q^{54} - 990 q^{55} + 1917 q^{56} - 798 q^{57} + 1354 q^{58} - 378 q^{59} + 765 q^{60} - 1396 q^{61} + 1475 q^{62} - 558 q^{63} + 1225 q^{64} - 348 q^{65} + 132 q^{66} - 402 q^{67} + 2032 q^{68} + 150 q^{69} + 2415 q^{70} - 964 q^{71} - 675 q^{72} - 192 q^{73} + 2751 q^{74} - 18 q^{75} - 2306 q^{76} + 2724 q^{77} + 1416 q^{78} - 802 q^{79} + 4221 q^{80} + 486 q^{81} + 1735 q^{82} + 2126 q^{83} - 999 q^{84} - 1206 q^{85} - 609 q^{86} - 726 q^{87} + 3656 q^{88} + 432 q^{89} - 999 q^{90} + 1258 q^{91} + 3163 q^{92} - 1314 q^{93} + 1742 q^{94} + 936 q^{95} + 105 q^{96} + 1290 q^{97} + 2492 q^{98} - 648 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9 - 111 * q^10 - 72 * q^11 + 39 * q^12 - 192 * q^13 + 3 * q^14 - 36 * q^15 - 27 * q^16 - 100 * q^17 - 45 * q^18 - 266 * q^19 + 255 * q^20 - 186 * q^21 + 44 * q^22 + 50 * q^23 - 225 * q^24 - 6 * q^25 + 472 * q^26 + 162 * q^27 - 333 * q^28 - 242 * q^29 - 333 * q^30 - 438 * q^31 + 35 * q^32 - 216 * q^33 - 150 * q^34 - 258 * q^35 + 117 * q^36 - 596 * q^37 + 664 * q^38 - 576 * q^39 - 831 * q^40 + 54 * q^41 + 9 * q^42 - 360 * q^43 - 714 * q^44 - 108 * q^45 - 871 * q^46 - 720 * q^47 - 81 * q^48 - 302 * q^49 + 4 * q^50 - 300 * q^51 - 1118 * q^52 + 694 * q^53 - 135 * q^54 - 990 * q^55 + 1917 * q^56 - 798 * q^57 + 1354 * q^58 - 378 * q^59 + 765 * q^60 - 1396 * q^61 + 1475 * q^62 - 558 * q^63 + 1225 * q^64 - 348 * q^65 + 132 * q^66 - 402 * q^67 + 2032 * q^68 + 150 * q^69 + 2415 * q^70 - 964 * q^71 - 675 * q^72 - 192 * q^73 + 2751 * q^74 - 18 * q^75 - 2306 * q^76 + 2724 * q^77 + 1416 * q^78 - 802 * q^79 + 4221 * q^80 + 486 * q^81 + 1735 * q^82 + 2126 * q^83 - 999 * q^84 - 1206 * q^85 - 609 * q^86 - 726 * q^87 + 3656 * q^88 + 432 * q^89 - 999 * q^90 + 1258 * q^91 + 3163 * q^92 - 1314 * q^93 + 1742 * q^94 + 936 * q^95 + 105 * q^96 + 1290 * q^97 + 2492 * q^98 - 648 * q^99

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