LMFDB - Embedded newform 363.4.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,4,Mod(1,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, 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("363.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	363.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:	$21.4176933321$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	363.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.47214 q^{2} +3.00000 q^{3} +12.0000 q^{4} +5.79837 q^{5} -13.4164 q^{6} -15.2918 q^{7} -17.8885 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.47214 q^{2} +3.00000 q^{3} +12.0000 q^{4} +5.79837 q^{5} -13.4164 q^{6} -15.2918 q^{7} -17.8885 q^{8} +9.00000 q^{9} -25.9311 q^{10} +36.0000 q^{12} +46.5967 q^{13} +68.3870 q^{14} +17.3951 q^{15} -16.0000 q^{16} -113.228 q^{17} -40.2492 q^{18} -110.812 q^{19} +69.5805 q^{20} -45.8754 q^{21} +12.1935 q^{23} -53.6656 q^{24} -91.3789 q^{25} -208.387 q^{26} +27.0000 q^{27} -183.502 q^{28} +280.663 q^{29} -77.7933 q^{30} +91.5886 q^{31} +214.663 q^{32} +506.371 q^{34} -88.6676 q^{35} +108.000 q^{36} -280.597 q^{37} +495.564 q^{38} +139.790 q^{39} -103.724 q^{40} +5.98684 q^{41} +205.161 q^{42} -126.915 q^{43} +52.1854 q^{45} -54.5310 q^{46} +233.992 q^{47} -48.0000 q^{48} -109.161 q^{49} +408.659 q^{50} -339.684 q^{51} +559.161 q^{52} +9.62114 q^{53} -120.748 q^{54} +273.548 q^{56} -332.435 q^{57} -1255.16 q^{58} -311.733 q^{59} +208.741 q^{60} -889.431 q^{61} -409.597 q^{62} -137.626 q^{63} -832.000 q^{64} +270.185 q^{65} -589.717 q^{67} -1358.74 q^{68} +36.5805 q^{69} +396.533 q^{70} +263.041 q^{71} -160.997 q^{72} -168.535 q^{73} +1254.87 q^{74} -274.137 q^{75} -1329.74 q^{76} -625.161 q^{78} +498.860 q^{79} -92.7740 q^{80} +81.0000 q^{81} -26.7740 q^{82} +323.004 q^{83} -550.505 q^{84} -656.538 q^{85} +567.580 q^{86} +841.988 q^{87} -1183.82 q^{89} -233.380 q^{90} -712.548 q^{91} +146.322 q^{92} +274.766 q^{93} -1046.44 q^{94} -642.527 q^{95} +643.988 q^{96} -1159.67 q^{97} +488.183 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{3} + 24 q^{4} - 13 q^{5} - 44 q^{7} + 18 q^{9}+O(q^{10}) $ 2 * q + 6 * q^3 + 24 * q^4 - 13 * q^5 - 44 * q^7 + 18 * q^9	\( 2 q + 6 q^{3} + 24 q^{4} - 13 q^{5} - 44 q^{7} + 18 q^{9} - 110 q^{10} + 72 q^{12} + 44 q^{13} - 60 q^{14} - 39 q^{15} - 32 q^{16} - 99 q^{17} - 121 q^{19} - 156 q^{20} - 132 q^{21} - 74 q^{23} + 137 q^{25} - 220 q^{26} + 54 q^{27} - 528 q^{28} + 132 q^{29} - 330 q^{30} + 11 q^{31} + 570 q^{34} + 451 q^{35} + 216 q^{36} - 512 q^{37} + 450 q^{38} + 132 q^{39} - 440 q^{40} + 88 q^{41} - 180 q^{42} - 66 q^{43} - 117 q^{45} - 440 q^{46} + 345 q^{47} - 96 q^{48} + 372 q^{49} + 1430 q^{50} - 297 q^{51} + 528 q^{52} + 339 q^{53} - 240 q^{56} - 363 q^{57} - 1920 q^{58} + 385 q^{59} - 468 q^{60} - 1155 q^{61} - 770 q^{62} - 396 q^{63} - 1664 q^{64} + 319 q^{65} + 75 q^{67} - 1188 q^{68} - 222 q^{69} + 2810 q^{70} + 1141 q^{71} + 374 q^{73} + 220 q^{74} + 411 q^{75} - 1452 q^{76} - 660 q^{78} - 572 q^{79} + 208 q^{80} + 162 q^{81} + 340 q^{82} - 396 q^{83} - 1584 q^{84} - 924 q^{85} + 840 q^{86} + 396 q^{87} - 2712 q^{89} - 990 q^{90} - 638 q^{91} - 888 q^{92} + 33 q^{93} - 550 q^{94} - 451 q^{95} - 327 q^{97} + 2640 q^{98}+O(q^{100}) \) 2 * q + 6 * q^3 + 24 * q^4 - 13 * q^5 - 44 * q^7 + 18 * q^9 - 110 * q^10 + 72 * q^12 + 44 * q^13 - 60 * q^14 - 39 * q^15 - 32 * q^16 - 99 * q^17 - 121 * q^19 - 156 * q^20 - 132 * q^21 - 74 * q^23 + 137 * q^25 - 220 * q^26 + 54 * q^27 - 528 * q^28 + 132 * q^29 - 330 * q^30 + 11 * q^31 + 570 * q^34 + 451 * q^35 + 216 * q^36 - 512 * q^37 + 450 * q^38 + 132 * q^39 - 440 * q^40 + 88 * q^41 - 180 * q^42 - 66 * q^43 - 117 * q^45 - 440 * q^46 + 345 * q^47 - 96 * q^48 + 372 * q^49 + 1430 * q^50 - 297 * q^51 + 528 * q^52 + 339 * q^53 - 240 * q^56 - 363 * q^57 - 1920 * q^58 + 385 * q^59 - 468 * q^60 - 1155 * q^61 - 770 * q^62 - 396 * q^63 - 1664 * q^64 + 319 * q^65 + 75 * q^67 - 1188 * q^68 - 222 * q^69 + 2810 * q^70 + 1141 * q^71 + 374 * q^73 + 220 * q^74 + 411 * q^75 - 1452 * q^76 - 660 * q^78 - 572 * q^79 + 208 * q^80 + 162 * q^81 + 340 * q^82 - 396 * q^83 - 1584 * q^84 - 924 * q^85 + 840 * q^86 + 396 * q^87 - 2712 * q^89 - 990 * q^90 - 638 * q^91 - 888 * q^92 + 33 * q^93 - 550 * q^94 - 451 * q^95 - 327 * q^97 + 2640 * q^98

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 $

$2$	−4.47214	−1.58114	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	−4.47214	−1.58114	−0.790569	+	0.612372i	$0.790215\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	12.0000	1.50000
$5$	5.79837	0.518622	0.259311	−	0.965794i	$-0.416504\pi$
$5$	5.79837	0.518622	0.259311	+	0.965794i	$0.416504\pi$
$6$	−13.4164	−0.912871
$7$	−15.2918	−0.825679	−0.412840	−	0.910804i	$-0.635463\pi$
$7$	−15.2918	−0.825679	−0.412840	+	0.910804i	$0.635463\pi$
$8$	−17.8885	−0.790569
$9$	9.00000	0.333333
$10$	−25.9311	−0.820014
$11$	0	0
$11$	0	0
$12$	36.0000	0.866025
$13$	46.5967	0.994124	0.497062	−	0.867715i	$-0.334412\pi$
$13$	46.5967	0.994124	0.497062	+	0.867715i	$0.334412\pi$
$14$	68.3870	1.30551
$15$	17.3951	0.299427
$16$	−16.0000	−0.250000
$17$	−113.228	−1.61540	−0.807700	−	0.589593i	$-0.799288\pi$
$17$	−113.228	−1.61540	−0.807700	+	0.589593i	$0.799288\pi$
$18$	−40.2492	−0.527046
$19$	−110.812	−1.33800	−0.668998	−	0.743265i	$-0.733276\pi$
$19$	−110.812	−1.33800	−0.668998	+	0.743265i	$0.733276\pi$
$20$	69.5805	0.777933
$21$	−45.8754	−0.476706
$22$	0	0
$23$	12.1935	0.110544	0.0552722	−	0.998471i	$-0.482397\pi$
$23$	12.1935	0.110544	0.0552722	+	0.998471i	$0.482397\pi$
$24$	−53.6656	−0.456435
$25$	−91.3789	−0.731031
$26$	−208.387	−1.57185
$27$	27.0000	0.192450
$28$	−183.502	−1.23852
$29$	280.663	1.79716	0.898581	−	0.438807i	$-0.144599\pi$
$29$	280.663	1.79716	0.898581	+	0.438807i	$0.144599\pi$
$30$	−77.7933	−0.473435
$31$	91.5886	0.530639	0.265319	−	0.964161i	$-0.414523\pi$
$31$	91.5886	0.530639	0.265319	+	0.964161i	$0.414523\pi$
$32$	214.663	1.18585
$33$	0	0
$34$	506.371	2.55417
$35$	−88.6676	−0.428216
$36$	108.000	0.500000
$37$	−280.597	−1.24675	−0.623376	−	0.781922i	$-0.714239\pi$
$37$	−280.597	−1.24675	−0.623376	+	0.781922i	$0.714239\pi$
$38$	495.564	2.11556
$39$	139.790	0.573958
$40$	−103.724	−0.410007
$41$	5.98684	0.0228046	0.0114023	−	0.999935i	$-0.496370\pi$
$41$	5.98684	0.0228046	0.0114023	+	0.999935i	$0.496370\pi$
$42$	205.161	0.753739
$43$	−126.915	−0.450101	−0.225050	−	0.974347i	$-0.572255\pi$
$43$	−126.915	−0.450101	−0.225050	+	0.974347i	$0.572255\pi$
$44$	0	0
$45$	52.1854	0.172874
$46$	−54.5310	−0.174786
$47$	233.992	0.726196	0.363098	−	0.931751i	$-0.381719\pi$
$47$	233.992	0.726196	0.363098	+	0.931751i	$0.381719\pi$
$48$	−48.0000	−0.144338
$49$	−109.161	−0.318254
$50$	408.659	1.15586
$51$	−339.684	−0.932652
$52$	559.161	1.49119
$53$	9.62114	0.0249352	0.0124676	−	0.999922i	$-0.496031\pi$
$53$	9.62114	0.0249352	0.0124676	+	0.999922i	$0.496031\pi$
$54$	−120.748	−0.304290
$55$	0	0
$56$	273.548	0.652757
$57$	−332.435	−0.772492
$58$	−1255.16	−2.84156
$59$	−311.733	−0.687868	−0.343934	−	0.938994i	$-0.611760\pi$
$59$	−311.733	−0.687868	−0.343934	+	0.938994i	$0.611760\pi$
$60$	208.741	0.449140
$61$	−889.431	−1.86689	−0.933443	−	0.358726i	$-0.883211\pi$
$61$	−889.431	−1.86689	−0.933443	+	0.358726i	$0.883211\pi$
$62$	−409.597	−0.839014
$63$	−137.626	−0.275226
$64$	−832.000	−1.62500
$65$	270.185	0.515575
$66$	0	0
$67$	−589.717	−1.07530	−0.537652	−	0.843167i	$-0.680689\pi$
$67$	−589.717	−1.07530	−0.537652	+	0.843167i	$0.680689\pi$
$68$	−1358.74	−2.42310
$69$	36.5805	0.0638228
$70$	396.533	0.677069
$71$	263.041	0.439679	0.219839	−	0.975536i	$-0.429447\pi$
$71$	263.041	0.439679	0.219839	+	0.975536i	$0.429447\pi$
$72$	−160.997	−0.263523
$73$	−168.535	−0.270212	−0.135106	−	0.990831i	$-0.543138\pi$
$73$	−168.535	−0.270212	−0.135106	+	0.990831i	$0.543138\pi$
$74$	1254.87	1.97129
$75$	−274.137	−0.422061
$76$	−1329.74	−2.00699
$77$	0	0
$78$	−625.161	−0.907507
$79$	498.860	0.710457	0.355229	−	0.934779i	$-0.384403\pi$
$79$	498.860	0.710457	0.355229	+	0.934779i	$0.384403\pi$
$80$	−92.7740	−0.129656
$81$	81.0000	0.111111
$82$	−26.7740	−0.0360572
$83$	323.004	0.427160	0.213580	−	0.976926i	$-0.431488\pi$
$83$	323.004	0.427160	0.213580	+	0.976926i	$0.431488\pi$
$84$	−550.505	−0.715059
$85$	−656.538	−0.837783
$86$	567.580	0.711672
$87$	841.988	1.03759
$88$	0	0
$89$	−1183.82	−1.40994	−0.704972	−	0.709235i	$-0.749040\pi$
$89$	−1183.82	−1.40994	−0.704972	+	0.709235i	$0.749040\pi$
$90$	−233.380	−0.273338
$91$	−712.548	−0.820828
$92$	146.322	0.165816
$93$	274.766	0.306364
$94$	−1046.44	−1.14822
$95$	−642.527	−0.693914
$96$	643.988	0.684653
$97$	−1159.67	−1.21388	−0.606941	−	0.794747i	$-0.707603\pi$
$97$	−1159.67	−1.21388	−0.606941	+	0.794747i	$0.707603\pi$
$98$	488.183	0.503203
$99$	0	0
$100$	−1096.55	−1.09655
$101$	−962.735	−0.948472	−0.474236	−	0.880398i	$-0.657276\pi$
$101$	−962.735	−0.948472	−0.474236	+	0.880398i	$0.657276\pi$
$102$	1519.11	1.47465
$103$	−546.807	−0.523092	−0.261546	−	0.965191i	$-0.584232\pi$
$103$	−546.807	−0.523092	−0.261546	+	0.965191i	$0.584232\pi$
$104$	−833.548	−0.785924
$105$	−266.003	−0.247230
$106$	−43.0270	−0.0394260
$107$	−1559.76	−1.40923	−0.704617	−	0.709588i	$-0.748881\pi$
$107$	−1559.76	−1.40923	−0.704617	+	0.709588i	$0.748881\pi$
$108$	324.000	0.288675
$109$	784.644	0.689498	0.344749	−	0.938695i	$-0.387964\pi$
$109$	784.644	0.689498	0.344749	+	0.938695i	$0.387964\pi$
$110$	0	0
$111$	−841.790	−0.719813
$112$	244.669	0.206420
$113$	−1543.68	−1.28510	−0.642552	−	0.766242i	$-0.722125\pi$
$113$	−1543.68	−1.28510	−0.642552	+	0.766242i	$0.722125\pi$
$114$	1486.69	1.22142
$115$	70.7024	0.0573308
$116$	3367.95	2.69574
$117$	419.371	0.331375
$118$	1394.11	1.08762
$119$	1731.46	1.33380
$120$	−311.173	−0.236718
$121$	0	0
$122$	3977.66	2.95181
$123$	17.9605	0.0131662
$124$	1099.06	0.795958
$125$	−1254.65	−0.897751
$126$	615.483	0.435171
$127$	−320.225	−0.223743	−0.111872	−	0.993723i	$-0.535685\pi$
$127$	−320.225	−0.223743	−0.111872	+	0.993723i	$0.535685\pi$
$128$	2003.52	1.38350
$129$	−380.745	−0.259866
$130$	−1208.31	−0.815196
$131$	551.281	0.367676	0.183838	−	0.982957i	$-0.441148\pi$
$131$	551.281	0.367676	0.183838	+	0.982957i	$0.441148\pi$
$132$	0	0
$133$	1694.51	1.10476
$134$	2637.29	1.70021
$135$	156.556	0.0998089
$136$	2025.48	1.27709
$137$	−1703.31	−1.06221	−0.531107	−	0.847305i	$-0.678224\pi$
$137$	−1703.31	−1.06221	−0.531107	+	0.847305i	$0.678224\pi$
$138$	−163.593	−0.100913
$139$	2499.08	1.52496	0.762478	−	0.647014i	$-0.223983\pi$
$139$	2499.08	1.52496	0.762478	+	0.647014i	$0.223983\pi$
$140$	−1064.01	−0.642324
$141$	701.976	0.419270
$142$	−1176.35	−0.695193
$143$	0	0
$144$	−144.000	−0.0833333
$145$	1627.39	0.932049
$146$	753.711	0.427243
$147$	−327.483	−0.183744
$148$	−3367.16	−1.87013
$149$	74.4389	0.0409280	0.0204640	−	0.999791i	$-0.493486\pi$
$149$	74.4389	0.0409280	0.0204640	+	0.999791i	$0.493486\pi$
$150$	1225.98	0.667337
$151$	−2245.30	−1.21007	−0.605033	−	0.796201i	$-0.706840\pi$
$151$	−2245.30	−1.21007	−0.605033	+	0.796201i	$0.706840\pi$
$152$	1982.26	1.05778
$153$	−1019.05	−0.538467
$154$	0	0
$155$	531.065	0.275201
$156$	1677.48	0.860937
$157$	2597.85	1.32058	0.660291	−	0.751010i	$-0.270433\pi$
$157$	2597.85	1.32058	0.660291	+	0.751010i	$0.270433\pi$
$158$	−2230.97	−1.12333
$159$	28.8634	0.0143963
$160$	1244.69	0.615010
$161$	−186.460	−0.0912742
$162$	−362.243	−0.175682
$163$	2756.84	1.32474	0.662370	−	0.749177i	$-0.269551\pi$
$163$	2756.84	1.32474	0.662370	+	0.749177i	$0.269551\pi$
$164$	71.8421	0.0342069
$165$	0	0
$166$	−1444.52	−0.675399
$167$	826.749	0.383088	0.191544	−	0.981484i	$-0.438650\pi$
$167$	826.749	0.383088	0.191544	+	0.981484i	$0.438650\pi$
$168$	820.644	0.376869
$169$	−25.7431	−0.0117174
$170$	2936.13	1.32465
$171$	−997.304	−0.445998
$172$	−1522.98	−0.675151
$173$	−1755.84	−0.771640	−0.385820	−	0.922574i	$-0.626081\pi$
$173$	−1755.84	−0.771640	−0.385820	+	0.922574i	$0.626081\pi$
$174$	−3765.48	−1.64058
$175$	1397.35	0.603597
$176$	0	0
$177$	−935.200	−0.397141
$178$	5294.22	2.22932
$179$	687.241	0.286965	0.143483	−	0.989653i	$-0.454170\pi$
$179$	687.241	0.286965	0.143483	+	0.989653i	$0.454170\pi$
$180$	626.224	0.259311
$181$	1584.67	0.650762	0.325381	−	0.945583i	$-0.394507\pi$
$181$	1584.67	0.650762	0.325381	+	0.945583i	$0.394507\pi$
$182$	3186.61	1.29784
$183$	−2668.29	−1.07785
$184$	−218.124	−0.0873930
$185$	−1627.00	−0.646593
$186$	−1228.79	−0.484405
$187$	0	0
$188$	2807.90	1.08929
$189$	−412.878	−0.158902
$190$	2873.47	1.09717
$191$	3031.71	1.14852	0.574259	−	0.818674i	$-0.305290\pi$
$191$	3031.71	1.14852	0.574259	+	0.818674i	$0.305290\pi$
$192$	−2496.00	−0.938194
$193$	−3926.69	−1.46451	−0.732253	−	0.681033i	$-0.761531\pi$
$193$	−3926.69	−1.46451	−0.732253	+	0.681033i	$0.761531\pi$
$194$	5186.19	1.91931
$195$	810.556	0.297667
$196$	−1309.93	−0.477380
$197$	1769.43	0.639933	0.319967	−	0.947429i	$-0.396328\pi$
$197$	1769.43	0.639933	0.319967	+	0.947429i	$0.396328\pi$
$198$	0	0
$199$	−786.483	−0.280162	−0.140081	−	0.990140i	$-0.544736\pi$
$199$	−786.483	−0.280162	−0.140081	+	0.990140i	$0.544736\pi$
$200$	1634.63	0.577931
$201$	−1769.15	−0.620827
$202$	4305.48	1.49967
$203$	−4291.83	−1.48388
$204$	−4076.21	−1.39898
$205$	34.7140	0.0118270
$206$	2445.39	0.827081
$207$	109.741	0.0368481
$208$	−745.548	−0.248531
$209$	0	0
$210$	1189.60	0.390906
$211$	−3624.00	−1.18240	−0.591200	−	0.806525i	$-0.701345\pi$
$211$	−3624.00	−1.18240	−0.591200	+	0.806525i	$0.701345\pi$
$212$	115.454	0.0374028
$213$	789.122	0.253849
$214$	6975.48	2.22820
$215$	−735.900	−0.233432
$216$	−482.991	−0.152145
$217$	−1400.55	−0.438137
$218$	−3509.03	−1.09019
$219$	−505.604	−0.156007
$220$	0	0
$221$	−5276.05	−1.60591
$222$	3764.60	1.13812
$223$	−489.192	−0.146900	−0.0734500	−	0.997299i	$-0.523401\pi$
$223$	−489.192	−0.146900	−0.0734500	+	0.997299i	$0.523401\pi$
$224$	−3282.58	−0.979135
$225$	−822.410	−0.243677
$226$	6903.53	2.03193
$227$	1860.52	0.543995	0.271997	−	0.962298i	$-0.412316\pi$
$227$	1860.52	0.543995	0.271997	+	0.962298i	$0.412316\pi$
$228$	−3989.22	−1.15874
$229$	6508.16	1.87804	0.939020	−	0.343862i	$-0.111735\pi$
$229$	6508.16	1.87804	0.939020	+	0.343862i	$0.111735\pi$
$230$	−316.191	−0.0906479
$231$	0	0
$232$	−5020.64	−1.42078
$233$	−233.000	−0.0655123	−0.0327562	−	0.999463i	$-0.510428\pi$
$233$	−233.000	−0.0655123	−0.0327562	+	0.999463i	$0.510428\pi$
$234$	−1875.48	−0.523949
$235$	1356.77	0.376622
$236$	−3740.80	−1.03180
$237$	1496.58	0.410183
$238$	−7743.32	−2.10893
$239$	6356.79	1.72045	0.860223	−	0.509918i	$-0.170324\pi$
$239$	6356.79	1.72045	0.860223	+	0.509918i	$0.170324\pi$
$240$	−278.322	−0.0748567
$241$	−128.649	−0.0343860	−0.0171930	−	0.999852i	$-0.505473\pi$
$241$	−128.649	−0.0343860	−0.0171930	+	0.999852i	$0.505473\pi$
$242$	0	0
$243$	243.000	0.0641500
$244$	−10673.2	−2.80033
$245$	−632.956	−0.165053
$246$	−80.3219	−0.0208176
$247$	−5163.46	−1.33013
$248$	−1638.39	−0.419507
$249$	969.012	0.246621
$250$	5610.95	1.41947
$251$	−105.459	−0.0265199	−0.0132599	−	0.999912i	$-0.504221\pi$
$251$	−105.459	−0.0265199	−0.0132599	+	0.999912i	$0.504221\pi$
$252$	−1651.51	−0.412840
$253$	0	0
$254$	1432.09	0.353769
$255$	−1969.61	−0.483694
$256$	−2304.00	−0.562500
$257$	−260.267	−0.0631712	−0.0315856	−	0.999501i	$-0.510056\pi$
$257$	−260.267	−0.0631712	−0.0315856	+	0.999501i	$0.510056\pi$
$258$	1702.74	0.410884
$259$	4290.83	1.02942
$260$	3242.22	0.773362
$261$	2525.96	0.599054
$262$	−2465.40	−0.581347
$263$	−606.064	−0.142097	−0.0710485	−	0.997473i	$-0.522635\pi$
$263$	−606.064	−0.142097	−0.0710485	+	0.997473i	$0.522635\pi$
$264$	0	0
$265$	55.7870	0.0129319
$266$	−7578.07	−1.74677
$267$	−3551.47	−0.814031
$268$	−7076.60	−1.61296
$269$	4438.94	1.00612	0.503061	−	0.864251i	$-0.332207\pi$
$269$	4438.94	1.00612	0.503061	+	0.864251i	$0.332207\pi$
$270$	−700.140	−0.157812
$271$	−4836.88	−1.08421	−0.542103	−	0.840312i	$-0.682372\pi$
$271$	−4836.88	−1.08421	−0.542103	+	0.840312i	$0.682372\pi$
$272$	1811.65	0.403850
$273$	−2137.64	−0.473905
$274$	7617.41	1.67951
$275$	0	0
$276$	438.966	0.0957342
$277$	−4594.74	−0.996647	−0.498324	−	0.866991i	$-0.666051\pi$
$277$	−4594.74	−0.996647	−0.498324	+	0.866991i	$0.666051\pi$
$278$	−11176.2	−2.41117
$279$	824.298	0.176880
$280$	1586.13	0.338534
$281$	4571.35	0.970476	0.485238	−	0.874382i	$-0.338733\pi$
$281$	4571.35	0.970476	0.485238	+	0.874382i	$0.338733\pi$
$282$	−3139.33	−0.662923
$283$	−8072.52	−1.69562	−0.847812	−	0.530297i	$-0.822081\pi$
$283$	−8072.52	−1.69562	−0.847812	+	0.530297i	$0.822081\pi$
$284$	3156.49	0.659518
$285$	−1927.58	−0.400632
$286$	0	0
$287$	−91.5496	−0.0188293
$288$	1931.96	0.395285
$289$	7907.57	1.60952
$290$	−7277.89	−1.47370
$291$	−3479.00	−0.700835
$292$	−2022.42	−0.405319
$293$	143.830	0.0286780	0.0143390	−	0.999897i	$-0.495436\pi$
$293$	143.830	0.0286780	0.0143390	+	0.999897i	$0.495436\pi$
$294$	1464.55	0.290524
$295$	−1807.55	−0.356744
$296$	5019.47	0.985644
$297$	0	0
$298$	−332.901	−0.0647128
$299$	568.177	0.109895
$300$	−3289.64	−0.633091
$301$	1940.76	0.371639
$302$	10041.3	1.91328
$303$	−2888.20	−0.547601
$304$	1772.98	0.334499
$305$	−5157.26	−0.968209
$306$	4557.34	0.851391
$307$	−954.997	−0.177539	−0.0887697	−	0.996052i	$-0.528294\pi$
$307$	−954.997	−0.177539	−0.0887697	+	0.996052i	$0.528294\pi$
$308$	0	0
$309$	−1640.42	−0.302007
$310$	−2375.00	−0.435131
$311$	−1863.12	−0.339704	−0.169852	−	0.985470i	$-0.554329\pi$
$311$	−1863.12	−0.339704	−0.169852	+	0.985470i	$0.554329\pi$
$312$	−2500.64	−0.453753
$313$	1541.80	0.278428	0.139214	−	0.990262i	$-0.455542\pi$
$313$	1541.80	0.278428	0.139214	+	0.990262i	$0.455542\pi$
$314$	−11618.0	−2.08802
$315$	−798.008	−0.142739
$316$	5986.32	1.06569
$317$	−1794.27	−0.317906	−0.158953	−	0.987286i	$-0.550812\pi$
$317$	−1794.27	−0.317906	−0.158953	+	0.987286i	$0.550812\pi$
$318$	−129.081	−0.0227626
$319$	0	0
$320$	−4824.25	−0.842761
$321$	−4679.29	−0.813622
$322$	833.876	0.144317
$323$	12547.0	2.16140
$324$	972.000	0.166667
$325$	−4257.96	−0.726735
$326$	−12329.0	−2.09460
$327$	2353.93	0.398082
$328$	−107.096	−0.0180286
$329$	−3578.16	−0.599605
$330$	0	0
$331$	11429.1	1.89788	0.948939	−	0.315458i	$-0.102158\pi$
$331$	11429.1	1.89788	0.948939	+	0.315458i	$0.102158\pi$
$332$	3876.05	0.640740
$333$	−2525.37	−0.415584
$334$	−3697.33	−0.605716
$335$	−3419.40	−0.557677
$336$	734.006	0.119177
$337$	1599.69	0.258578	0.129289	−	0.991607i	$-0.458731\pi$
$337$	1599.69	0.258578	0.129289	+	0.991607i	$0.458731\pi$
$338$	115.127	0.0185268
$339$	−4631.03	−0.741956
$340$	−7878.45	−1.25667
$341$	0	0
$342$	4460.08	0.705185
$343$	6914.35	1.08845
$344$	2270.32	0.355836
$345$	212.107	0.0330999
$346$	7852.34	1.22007
$347$	−2233.25	−0.345496	−0.172748	−	0.984966i	$-0.555265\pi$
$347$	−2233.25	−0.345496	−0.172748	+	0.984966i	$0.555265\pi$
$348$	10103.9	1.55639
$349$	7132.33	1.09394	0.546969	−	0.837153i	$-0.315781\pi$
$349$	7132.33	1.09394	0.546969	+	0.837153i	$0.315781\pi$
$350$	−6249.13	−0.954371
$351$	1258.11	0.191319
$352$	0	0
$353$	5585.03	0.842100	0.421050	−	0.907037i	$-0.361662\pi$
$353$	5585.03	0.842100	0.421050	+	0.907037i	$0.361662\pi$
$354$	4182.34	0.627935
$355$	1525.21	0.228027
$356$	−14205.9	−2.11492
$357$	5194.38	0.770071
$358$	−3073.43	−0.453732
$359$	−8606.08	−1.26521	−0.632606	−	0.774473i	$-0.718015\pi$
$359$	−8606.08	−1.26521	−0.632606	+	0.774473i	$0.718015\pi$
$360$	−933.520	−0.136669
$361$	5420.20	0.790231
$362$	−7086.88	−1.02895
$363$	0	0
$364$	−8550.58	−1.23124
$365$	−977.228	−0.140138
$366$	11933.0	1.70423
$367$	−2057.83	−0.292692	−0.146346	−	0.989233i	$-0.546751\pi$
$367$	−2057.83	−0.292692	−0.146346	+	0.989233i	$0.546751\pi$
$368$	−195.096	−0.0276361
$369$	53.8816	0.00760153
$370$	7276.19	1.02235
$371$	−147.125	−0.0205885
$372$	3297.19	0.459547
$373$	−10090.3	−1.40069	−0.700344	−	0.713805i	$-0.746970\pi$
$373$	−10090.3	−1.40069	−0.700344	+	0.713805i	$0.746970\pi$
$374$	0	0
$375$	−3763.94	−0.518317
$376$	−4185.77	−0.574109
$377$	13078.0	1.78660
$378$	1846.45	0.251246
$379$	7133.10	0.966762	0.483381	−	0.875410i	$-0.339409\pi$
$379$	7133.10	0.966762	0.483381	+	0.875410i	$0.339409\pi$
$380$	−7710.32	−1.04087
$381$	−960.676	−0.129178
$382$	−13558.2	−1.81596
$383$	6671.03	0.890010	0.445005	−	0.895528i	$-0.353202\pi$
$383$	6671.03	0.890010	0.445005	+	0.895528i	$0.353202\pi$
$384$	6010.55	0.798762
$385$	0	0
$386$	17560.7	2.31559
$387$	−1142.23	−0.150034
$388$	−13916.0	−1.82082
$389$	3346.33	0.436159	0.218079	−	0.975931i	$-0.430021\pi$
$389$	3346.33	0.436159	0.218079	+	0.975931i	$0.430021\pi$
$390$	−3624.92	−0.470653
$391$	−1380.64	−0.178573
$392$	1952.73	0.251602
$393$	1653.84	0.212278
$394$	−7913.14	−1.01182
$395$	2892.58	0.368459
$396$	0	0
$397$	8174.27	1.03339	0.516694	−	0.856170i	$-0.327163\pi$
$397$	8174.27	1.03339	0.516694	+	0.856170i	$0.327163\pi$
$398$	3517.26	0.442975
$399$	5083.52	0.637831
$400$	1462.06	0.182758
$401$	−12303.6	−1.53220	−0.766101	−	0.642721i	$-0.777806\pi$
$401$	−12303.6	−1.53220	−0.766101	+	0.642721i	$0.777806\pi$
$402$	7911.88	0.981614
$403$	4267.73	0.527521
$404$	−11552.8	−1.42271
$405$	469.668	0.0576247
$406$	19193.7	2.34622
$407$	0	0
$408$	6076.45	0.737326
$409$	631.506	0.0763471	0.0381736	−	0.999271i	$-0.487846\pi$
$409$	631.506	0.0763471	0.0381736	+	0.999271i	$0.487846\pi$
$410$	−155.246	−0.0187001
$411$	−5109.92	−0.613269
$412$	−6561.68	−0.784638
$413$	4766.96	0.567959
$414$	−490.779	−0.0582620
$415$	1872.90	0.221535
$416$	10002.6	1.17889
$417$	7497.23	0.880433
$418$	0	0
$419$	−3416.77	−0.398378	−0.199189	−	0.979961i	$-0.563831\pi$
$419$	−3416.77	−0.398378	−0.199189	+	0.979961i	$0.563831\pi$
$420$	−3192.03	−0.370846
$421$	3775.61	0.437083	0.218541	−	0.975828i	$-0.429870\pi$
$421$	3775.61	0.437083	0.218541	+	0.975828i	$0.429870\pi$
$422$	16207.0	1.86954
$423$	2105.93	0.242065
$424$	−172.108	−0.0197130
$425$	10346.6	1.18091
$426$	−3529.06	−0.401370
$427$	13601.0	1.54145
$428$	−18717.2	−2.11385
$429$	0	0
$430$	3291.04	0.369089
$431$	−453.515	−0.0506845	−0.0253423	−	0.999679i	$-0.508068\pi$
$431$	−453.515	−0.0506845	−0.0253423	+	0.999679i	$0.508068\pi$
$432$	−432.000	−0.0481125
$433$	−9814.08	−1.08923	−0.544613	−	0.838688i	$-0.683323\pi$
$433$	−9814.08	−1.08923	−0.544613	+	0.838688i	$0.683323\pi$
$434$	6263.47	0.692756
$435$	4882.16	0.538119
$436$	9415.73	1.03425
$437$	−1351.18	−0.147908
$438$	2261.13	0.246669
$439$	−614.875	−0.0668483	−0.0334241	−	0.999441i	$-0.510641\pi$
$439$	−614.875	−0.0668483	−0.0334241	+	0.999441i	$0.510641\pi$
$440$	0	0
$441$	−982.449	−0.106085
$442$	23595.2	2.53916
$443$	−12488.8	−1.33941	−0.669706	−	0.742626i	$-0.733580\pi$
$443$	−12488.8	−1.33941	−0.669706	+	0.742626i	$0.733580\pi$
$444$	−10101.5	−1.07972
$445$	−6864.25	−0.731228
$446$	2187.73	0.232269
$447$	223.317	0.0236298
$448$	12722.8	1.34173
$449$	−9113.67	−0.957908	−0.478954	−	0.877840i	$-0.658984\pi$
$449$	−9113.67	−0.957908	−0.478954	+	0.877840i	$0.658984\pi$
$450$	3677.93	0.385287
$451$	0	0
$452$	−18524.1	−1.92766
$453$	−6735.90	−0.698631
$454$	−8320.48	−0.860131
$455$	−4131.62	−0.425700
$456$	5946.77	0.610708
$457$	1749.99	0.179127	0.0895637	−	0.995981i	$-0.471453\pi$
$457$	1749.99	0.179127	0.0895637	+	0.995981i	$0.471453\pi$
$458$	−29105.4	−2.96944
$459$	−3057.15	−0.310884
$460$	848.429	0.0859961
$461$	−1394.82	−0.140918	−0.0704589	−	0.997515i	$-0.522446\pi$
$461$	−1394.82	−0.140918	−0.0704589	+	0.997515i	$0.522446\pi$
$462$	0	0
$463$	9007.16	0.904099	0.452050	−	0.891993i	$-0.350693\pi$
$463$	9007.16	0.904099	0.452050	+	0.891993i	$0.350693\pi$
$464$	−4490.60	−0.449291
$465$	1593.20	0.158887
$466$	1042.01	0.103584
$467$	9585.69	0.949835	0.474917	−	0.880030i	$-0.342478\pi$
$467$	9585.69	0.949835	0.474917	+	0.880030i	$0.342478\pi$
$468$	5032.45	0.497062
$469$	9017.83	0.887857
$470$	−6067.67	−0.595491
$471$	7793.56	0.762438
$472$	5576.46	0.543808
$473$	0	0
$474$	−6692.91	−0.648556
$475$	10125.8	0.978116
$476$	20777.5	2.00070
$477$	86.5903	0.00831173
$478$	−28428.4	−2.72026
$479$	5639.55	0.537949	0.268975	−	0.963147i	$-0.413315\pi$
$479$	5639.55	0.537949	0.268975	+	0.963147i	$0.413315\pi$
$480$	3734.08	0.355076
$481$	−13074.9	−1.23943
$482$	575.337	0.0543690
$483$	−559.381	−0.0526972
$484$	0	0
$485$	−6724.19	−0.629546
$486$	−1086.73	−0.101430
$487$	−16926.0	−1.57493	−0.787464	−	0.616360i	$-0.788606\pi$
$487$	−16926.0	−1.57493	−0.787464	+	0.616360i	$0.788606\pi$
$488$	15910.6	1.47590
$489$	8270.53	0.764839
$490$	2830.67	0.260972
$491$	5204.75	0.478385	0.239192	−	0.970972i	$-0.423117\pi$
$491$	5204.75	0.478385	0.239192	+	0.970972i	$0.423117\pi$
$492$	215.526	0.0197494
$493$	−31778.8	−2.90314
$494$	23091.7	2.10313
$495$	0	0
$496$	−1465.42	−0.132660
$497$	−4022.36	−0.363034
$498$	−4333.55	−0.389942
$499$	1658.77	0.148811	0.0744056	−	0.997228i	$-0.476294\pi$
$499$	1658.77	0.148811	0.0744056	+	0.997228i	$0.476294\pi$
$500$	−15055.7	−1.34663
$501$	2480.25	0.221176
$502$	471.625	0.0419316
$503$	15317.7	1.35782	0.678911	−	0.734221i	$-0.262452\pi$
$503$	15317.7	1.35782	0.678911	+	0.734221i	$0.262452\pi$
$504$	2461.93	0.217586
$505$	−5582.29	−0.491899
$506$	0	0
$507$	−77.2293	−0.00676504
$508$	−3842.70	−0.335615
$509$	13232.2	1.15227	0.576136	−	0.817354i	$-0.304560\pi$
$509$	13232.2	1.15227	0.576136	+	0.817354i	$0.304560\pi$
$510$	8808.38	0.764788
$511$	2577.20	0.223109
$512$	−5724.33	−0.494106
$513$	−2991.91	−0.257497
$514$	1163.95	0.0998824
$515$	−3170.59	−0.271287
$516$	−4568.93	−0.389799
$517$	0	0
$518$	−19189.2	−1.62765
$519$	−5267.51	−0.445507
$520$	−4833.22	−0.407598
$521$	13364.4	1.12381	0.561907	−	0.827201i	$-0.310068\pi$
$521$	13364.4	1.12381	0.561907	+	0.827201i	$0.310068\pi$
$522$	−11296.4	−0.947188
$523$	−8393.85	−0.701793	−0.350896	−	0.936414i	$-0.614123\pi$
$523$	−8393.85	−0.701793	−0.350896	+	0.936414i	$0.614123\pi$
$524$	6615.37	0.551515
$525$	4192.04	0.348487
$526$	2710.40	0.224675
$527$	−10370.4	−0.857194
$528$	0	0
$529$	−12018.3	−0.987780
$530$	−249.487	−0.0204472
$531$	−2805.60	−0.229289
$532$	20334.1	1.65713
$533$	278.967	0.0226706
$534$	15882.6	1.28710
$535$	−9044.09	−0.730860
$536$	10549.2	0.850103
$537$	2061.72	0.165679
$538$	−19851.5	−1.59082
$539$	0	0
$540$	1878.67	0.149713
$541$	−1822.20	−0.144810	−0.0724052	−	0.997375i	$-0.523067\pi$
$541$	−1822.20	−0.144810	−0.0724052	+	0.997375i	$0.523067\pi$
$542$	21631.2	1.71428
$543$	4754.02	0.375718
$544$	−24305.8	−1.91563
$545$	4549.66	0.357589
$546$	9559.83	0.749310
$547$	11200.3	0.875488	0.437744	−	0.899100i	$-0.355778\pi$
$547$	11200.3	0.875488	0.437744	+	0.899100i	$0.355778\pi$
$548$	−20439.7	−1.59332
$549$	−8004.88	−0.622295
$550$	0	0
$551$	−31100.6	−2.40460
$552$	−654.372	−0.0504564
$553$	−7628.46	−0.586610
$554$	20548.3	1.57584
$555$	−4881.01	−0.373311
$556$	29988.9	2.28743
$557$	−6746.81	−0.513234	−0.256617	−	0.966513i	$-0.582608\pi$
$557$	−6746.81	−0.513234	−0.256617	+	0.966513i	$0.582608\pi$
$558$	−3686.37	−0.279671
$559$	−5913.82	−0.447456
$560$	1418.68	0.107054
$561$	0	0
$562$	−20443.7	−1.53446
$563$	21625.8	1.61886	0.809432	−	0.587214i	$-0.199775\pi$
$563$	21625.8	1.61886	0.809432	+	0.587214i	$0.199775\pi$
$564$	8423.71	0.628904
$565$	−8950.81	−0.666484
$566$	36101.4	2.68102
$567$	−1238.64	−0.0917422
$568$	−4705.41	−0.347596
$569$	1089.30	0.0802560	0.0401280	−	0.999195i	$-0.487223\pi$
$569$	1089.30	0.0802560	0.0401280	+	0.999195i	$0.487223\pi$
$570$	8620.40	0.633454
$571$	19919.7	1.45992	0.729960	−	0.683490i	$-0.239539\pi$
$571$	19919.7	1.45992	0.729960	+	0.683490i	$0.239539\pi$
$572$	0	0
$573$	9095.13	0.663097
$574$	409.422	0.0297717
$575$	−1114.23	−0.0808113
$576$	−7488.00	−0.541667
$577$	11535.6	0.832297	0.416148	−	0.909297i	$-0.363380\pi$
$577$	11535.6	0.832297	0.416148	+	0.909297i	$0.363380\pi$
$578$	−35363.7	−2.54487
$579$	−11780.1	−0.845533
$580$	19528.6	1.39807
$581$	−4939.31	−0.352697
$582$	15558.6	1.10812
$583$	0	0
$584$	3014.84	0.213622
$585$	2431.67	0.171858
$586$	−643.229	−0.0453440
$587$	−12561.0	−0.883216	−0.441608	−	0.897208i	$-0.645592\pi$
$587$	−12561.0	−0.883216	−0.441608	+	0.897208i	$0.645592\pi$
$588$	−3929.80	−0.275616
$589$	−10149.1	−0.709992
$590$	8083.59	0.564061
$591$	5308.30	0.369466
$592$	4489.55	0.311688
$593$	7070.92	0.489659	0.244830	−	0.969566i	$-0.421268\pi$
$593$	7070.92	0.489659	0.244830	+	0.969566i	$0.421268\pi$
$594$	0	0
$595$	10039.6	0.691740
$596$	893.267	0.0613920
$597$	−2359.45	−0.161752
$598$	−2540.97	−0.173759
$599$	−18863.0	−1.28668	−0.643341	−	0.765580i	$-0.722452\pi$
$599$	−18863.0	−1.28668	−0.643341	+	0.765580i	$0.722452\pi$
$600$	4903.90	0.333668
$601$	−3331.71	−0.226128	−0.113064	−	0.993588i	$-0.536067\pi$
$601$	−3331.71	−0.226128	−0.113064	+	0.993588i	$0.536067\pi$
$602$	−8679.33	−0.587613
$603$	−5307.45	−0.358435
$604$	−26943.6	−1.81510
$605$	0	0
$606$	12916.4	0.865832
$607$	−5855.20	−0.391524	−0.195762	−	0.980651i	$-0.562718\pi$
$607$	−5855.20	−0.391524	−0.195762	+	0.980651i	$0.562718\pi$
$608$	−23787.1	−1.58667
$609$	−12875.5	−0.856719
$610$	23064.0	1.53087
$611$	10903.3	0.721929
$612$	−12228.6	−0.807700
$613$	−11903.9	−0.784330	−0.392165	−	0.919895i	$-0.628274\pi$
$613$	−11903.9	−0.784330	−0.392165	+	0.919895i	$0.628274\pi$
$614$	4270.88	0.280714
$615$	104.142	0.00682830
$616$	0	0
$617$	−7655.61	−0.499519	−0.249759	−	0.968308i	$-0.580352\pi$
$617$	−7655.61	−0.499519	−0.249759	+	0.968308i	$0.580352\pi$
$618$	7336.18	0.477515
$619$	−6230.38	−0.404556	−0.202278	−	0.979328i	$-0.564834\pi$
$619$	−6230.38	−0.404556	−0.202278	+	0.979328i	$0.564834\pi$
$620$	6372.78	0.412802
$621$	329.224	0.0212743
$622$	8332.14	0.537120
$623$	18102.8	1.16416
$624$	−2236.64	−0.143489
$625$	4147.45	0.265437
$626$	−6895.15	−0.440233
$627$	0	0
$628$	31174.2	1.98087
$629$	31771.4	2.01400
$630$	3568.80	0.225690
$631$	−8238.80	−0.519780	−0.259890	−	0.965638i	$-0.583686\pi$
$631$	−8238.80	−0.519780	−0.259890	+	0.965638i	$0.583686\pi$
$632$	−8923.88	−0.561666
$633$	−10872.0	−0.682659
$634$	8024.23	0.502654
$635$	−1856.79	−0.116038
$636$	346.361	0.0215945
$637$	−5086.55	−0.316384
$638$	0	0
$639$	2367.37	0.146560
$640$	11617.1	0.717512
$641$	7106.80	0.437912	0.218956	−	0.975735i	$-0.429735\pi$
$641$	7106.80	0.437912	0.218956	+	0.975735i	$0.429735\pi$
$642$	20926.4	1.28645
$643$	−973.624	−0.0597138	−0.0298569	−	0.999554i	$-0.509505\pi$
$643$	−973.624	−0.0597138	−0.0298569	+	0.999554i	$0.509505\pi$
$644$	−2237.53	−0.136911
$645$	−2207.70	−0.134772
$646$	−56111.7	−3.41747
$647$	−7689.42	−0.467237	−0.233619	−	0.972328i	$-0.575057\pi$
$647$	−7689.42	−0.467237	−0.233619	+	0.972328i	$0.575057\pi$
$648$	−1448.97	−0.0878410
$649$	0	0
$650$	19042.2	1.14907
$651$	−4201.66	−0.252959
$652$	33082.1	1.98711
$653$	−29850.9	−1.78891	−0.894453	−	0.447161i	$-0.852435\pi$
$653$	−29850.9	−1.78891	−0.894453	+	0.447161i	$0.852435\pi$
$654$	−10527.1	−0.629422
$655$	3196.53	0.190685
$656$	−95.7895	−0.00570115
$657$	−1516.81	−0.0900708
$658$	16002.0	0.948059
$659$	30312.9	1.79184	0.895921	−	0.444213i	$-0.146517\pi$
$659$	30312.9	1.79184	0.895921	+	0.444213i	$0.146517\pi$
$660$	0	0
$661$	16789.0	0.987922	0.493961	−	0.869484i	$-0.335549\pi$
$661$	16789.0	0.987922	0.493961	+	0.869484i	$0.335549\pi$
$662$	−51112.3	−3.00081
$663$	−15828.2	−0.927172
$664$	−5778.07	−0.337700
$665$	9825.39	0.572951
$666$	11293.8	0.657096
$667$	3422.26	0.198666
$668$	9920.99	0.574632
$669$	−1467.58	−0.0848128
$670$	15292.0	0.881765
$671$	0	0
$672$	−9847.73	−0.565304
$673$	2891.55	0.165618	0.0828092	−	0.996565i	$-0.473611\pi$
$673$	2891.55	0.165618	0.0828092	+	0.996565i	$0.473611\pi$
$674$	−7154.04	−0.408848
$675$	−2467.23	−0.140687
$676$	−308.917	−0.0175761
$677$	−1781.70	−0.101147	−0.0505733	−	0.998720i	$-0.516105\pi$
$677$	−1781.70	−0.101147	−0.0505733	+	0.998720i	$0.516105\pi$
$678$	20710.6	1.17313
$679$	17733.4	1.00228
$680$	11744.5	0.662325
$681$	5581.55	0.314076
$682$	0	0
$683$	30297.1	1.69734	0.848672	−	0.528920i	$-0.177403\pi$
$683$	30297.1	1.69734	0.848672	+	0.528920i	$0.177403\pi$
$684$	−11967.6	−0.668998
$685$	−9876.40	−0.550888
$686$	−30921.9	−1.72100
$687$	19524.5	1.08429
$688$	2030.64	0.112525
$689$	448.314	0.0247887
$690$	−948.573	−0.0523356
$691$	27418.0	1.50945	0.754725	−	0.656042i	$-0.227770\pi$
$691$	27418.0	1.50945	0.754725	+	0.656042i	$0.227770\pi$
$692$	−21070.0	−1.15746
$693$	0	0
$694$	9987.39	0.546277
$695$	14490.6	0.790876
$696$	−15061.9	−0.820289
$697$	−677.878	−0.0368385
$698$	−31896.7	−1.72967
$699$	−699.001	−0.0378235
$700$	16768.2	0.905396
$701$	−21650.3	−1.16651	−0.583253	−	0.812291i	$-0.698220\pi$
$701$	−21650.3	−1.16651	−0.583253	+	0.812291i	$0.698220\pi$
$702$	−5626.45	−0.302502
$703$	31093.4	1.66815
$704$	0	0
$705$	4070.32	0.217443
$706$	−24977.0	−1.33148
$707$	14721.9	0.783134
$708$	−11222.4	−0.595711
$709$	27915.8	1.47870	0.739350	−	0.673321i	$-0.235133\pi$
$709$	27915.8	1.47870	0.739350	+	0.673321i	$0.235133\pi$
$710$	−6820.94	−0.360543
$711$	4489.74	0.236819
$712$	21176.9	1.11466
$713$	1116.79	0.0586591
$714$	−23230.0	−1.21759
$715$	0	0
$716$	8246.89	0.430448
$717$	19070.4	0.993300
$718$	38487.6	2.00048
$719$	24112.3	1.25068	0.625338	−	0.780354i	$-0.284961\pi$
$719$	24112.3	1.25068	0.625338	+	0.780354i	$0.284961\pi$
$720$	−834.966	−0.0432185
$721$	8361.65	0.431906
$722$	−24239.8	−1.24947
$723$	−385.948	−0.0198528
$724$	19016.1	0.976143
$725$	−25646.6	−1.31378
$726$	0	0
$727$	−27063.6	−1.38065	−0.690327	−	0.723498i	$-0.742533\pi$
$727$	−27063.6	−1.38065	−0.690327	+	0.723498i	$0.742533\pi$
$728$	12746.4	0.648921
$729$	729.000	0.0370370
$730$	4370.30	0.221578
$731$	14370.3	0.727093
$732$	−32019.5	−1.61677
$733$	2047.13	0.103155	0.0515774	−	0.998669i	$-0.483575\pi$
$733$	2047.13	0.103155	0.0515774	+	0.998669i	$0.483575\pi$
$734$	9202.91	0.462787
$735$	−1898.87	−0.0952936
$736$	2617.49	0.131089
$737$	0	0
$738$	−240.966	−0.0120191
$739$	−17653.6	−0.878753	−0.439376	−	0.898303i	$-0.644801\pi$
$739$	−17653.6	−0.878753	−0.439376	+	0.898303i	$0.644801\pi$
$740$	−19524.1	−0.969890
$741$	−15490.4	−0.767953
$742$	657.961	0.0325532
$743$	−6356.78	−0.313873	−0.156937	−	0.987609i	$-0.550162\pi$
$743$	−6356.78	−0.313873	−0.156937	+	0.987609i	$0.550162\pi$
$744$	−4915.16	−0.242202
$745$	431.624	0.0212262
$746$	45125.3	2.21468
$747$	2907.03	0.142387
$748$	0	0
$749$	23851.6	1.16358
$750$	16832.8	0.819531
$751$	27165.3	1.31994	0.659970	−	0.751292i	$-0.270569\pi$
$751$	27165.3	1.31994	0.659970	+	0.751292i	$0.270569\pi$
$752$	−3743.87	−0.181549
$753$	−316.376	−0.0153112
$754$	−58486.4	−2.82487
$755$	−13019.1	−0.627567
$756$	−4954.54	−0.238353
$757$	−12663.6	−0.608015	−0.304007	−	0.952670i	$-0.598325\pi$
$757$	−12663.6	−0.608015	−0.304007	+	0.952670i	$0.598325\pi$
$758$	−31900.2	−1.52859
$759$	0	0
$760$	11493.9	0.548587
$761$	−13176.6	−0.627665	−0.313833	−	0.949478i	$-0.601613\pi$
$761$	−13176.6	−0.627665	−0.313833	+	0.949478i	$0.601613\pi$
$762$	4296.27	0.204249
$763$	−11998.6	−0.569304
$764$	36380.5	1.72278
$765$	−5908.84	−0.279261
$766$	−29833.7	−1.40723
$767$	−14525.8	−0.683826
$768$	−6912.00	−0.324760
$769$	−28039.9	−1.31488	−0.657442	−	0.753505i	$-0.728361\pi$
$769$	−28039.9	−1.31488	−0.657442	+	0.753505i	$0.728361\pi$
$770$	0	0
$771$	−780.800	−0.0364719
$772$	−47120.3	−2.19676
$773$	−29247.3	−1.36087	−0.680435	−	0.732809i	$-0.738209\pi$
$773$	−29247.3	−1.36087	−0.680435	+	0.732809i	$0.738209\pi$
$774$	5108.22	0.237224
$775$	−8369.26	−0.387913
$776$	20744.8	0.959657
$777$	12872.5	0.594334
$778$	−14965.2	−0.689627
$779$	−663.411	−0.0305124
$780$	9726.67	0.446501
$781$	0	0
$782$	6174.43	0.282349
$783$	7577.89	0.345864
$784$	1746.58	0.0795634
$785$	15063.3	0.684883
$786$	−7396.20	−0.335641
$787$	10317.3	0.467309	0.233655	−	0.972320i	$-0.424932\pi$
$787$	10317.3	0.467309	0.233655	+	0.972320i	$0.424932\pi$
$788$	21233.2	0.959900
$789$	−1818.19	−0.0820397
$790$	−12936.0	−0.582585
$791$	23605.6	1.06108
$792$	0	0
$793$	−41444.6	−1.85592
$794$	−36556.4	−1.63393
$795$	167.361	0.00746626
$796$	−9437.80	−0.420243
$797$	−24248.0	−1.07768	−0.538838	−	0.842410i	$-0.681136\pi$
$797$	−24248.0	−1.07768	−0.538838	+	0.842410i	$0.681136\pi$
$798$	−22734.2	−1.00850
$799$	−26494.4	−1.17310
$800$	−19615.6	−0.866896
$801$	−10654.4	−0.469981
$802$	55023.4	2.42262
$803$	0	0
$804$	−21229.8	−0.931241
$805$	−1081.17	−0.0473368
$806$	−19085.9	−0.834084
$807$	13316.8	0.580885
$808$	17221.9	0.749833
$809$	−14488.2	−0.629641	−0.314820	−	0.949151i	$-0.601944\pi$
$809$	−14488.2	−0.629641	−0.314820	+	0.949151i	$0.601944\pi$
$810$	−2100.42	−0.0911127
$811$	42949.0	1.85961	0.929805	−	0.368052i	$-0.119975\pi$
$811$	42949.0	1.85961	0.929805	+	0.368052i	$0.119975\pi$
$812$	−51502.0	−2.22582
$813$	−14510.6	−0.625966
$814$	0	0
$815$	15985.2	0.687040
$816$	5434.94	0.233163
$817$	14063.6	0.602233
$818$	−2824.18	−0.120715
$819$	−6412.93	−0.273609
$820$	416.568	0.0177405
$821$	5842.42	0.248358	0.124179	−	0.992260i	$-0.460370\pi$
$821$	5842.42	0.248358	0.124179	+	0.992260i	$0.460370\pi$
$822$	22852.2	0.969664
$823$	−29418.5	−1.24601	−0.623005	−	0.782218i	$-0.714088\pi$
$823$	−29418.5	−1.24601	−0.623005	+	0.782218i	$0.714088\pi$
$824$	9781.57	0.413540
$825$	0	0
$826$	−21318.5	−0.898021
$827$	38253.8	1.60848	0.804241	−	0.594303i	$-0.202572\pi$
$827$	38253.8	1.60848	0.804241	+	0.594303i	$0.202572\pi$
$828$	1316.90	0.0552722
$829$	12591.2	0.527515	0.263757	−	0.964589i	$-0.415038\pi$
$829$	12591.2	0.527515	0.263757	+	0.964589i	$0.415038\pi$
$830$	−8375.85	−0.350277
$831$	−13784.2	−0.575415
$832$	−38768.5	−1.61545
$833$	12360.1	0.514107
$834$	−33528.6	−1.39209
$835$	4793.80	0.198678
$836$	0	0
$837$	2472.89	0.102121
$838$	15280.3	0.629891
$839$	−31476.0	−1.29520	−0.647600	−	0.761980i	$-0.724227\pi$
$839$	−31476.0	−1.29520	−0.647600	+	0.761980i	$0.724227\pi$
$840$	4758.40	0.195453
$841$	54382.5	2.22979
$842$	−16885.0	−0.691088
$843$	13714.0	0.560305
$844$	−43488.0	−1.77360
$845$	−149.268	−0.00607690
$846$	−9417.99	−0.382739
$847$	0	0
$848$	−153.938	−0.00623380
$849$	−24217.6	−0.978969
$850$	−46271.6	−1.86718
$851$	−3421.46	−0.137821
$852$	9469.46	0.380773
$853$	16806.3	0.674602	0.337301	−	0.941397i	$-0.390486\pi$
$853$	16806.3	0.674602	0.337301	+	0.941397i	$0.390486\pi$
$854$	−60825.5	−2.43724
$855$	−5782.74	−0.231305
$856$	27901.9	1.11410
$857$	−42475.1	−1.69302	−0.846512	−	0.532369i	$-0.821302\pi$
$857$	−42475.1	−1.69302	−0.846512	+	0.532369i	$0.821302\pi$
$858$	0	0
$859$	−25306.4	−1.00517	−0.502586	−	0.864527i	$-0.667618\pi$
$859$	−25306.4	−1.00517	−0.502586	+	0.864527i	$0.667618\pi$
$860$	−8830.80	−0.350148
$861$	−274.649	−0.0108711
$862$	2028.18	0.0801393
$863$	13195.8	0.520497	0.260249	−	0.965542i	$-0.416195\pi$
$863$	13195.8	0.520497	0.260249	+	0.965542i	$0.416195\pi$
$864$	5795.89	0.228218
$865$	−10181.0	−0.400190
$866$	43889.9	1.72222
$867$	23722.7	0.929256
$868$	−16806.7	−0.657206
$869$	0	0
$870$	−21833.7	−0.850840
$871$	−27478.9	−1.06899
$872$	−14036.1	−0.545096
$873$	−10437.0	−0.404627
$874$	6042.66	0.233863
$875$	19185.8	0.741255
$876$	−6067.25	−0.234011
$877$	28994.0	1.11637	0.558185	−	0.829716i	$-0.311498\pi$
$877$	28994.0	1.11637	0.558185	+	0.829716i	$0.311498\pi$
$878$	2749.80	0.105696
$879$	431.491	0.0165573
$880$	0	0
$881$	9676.79	0.370056	0.185028	−	0.982733i	$-0.440762\pi$
$881$	9676.79	0.370056	0.185028	+	0.982733i	$0.440762\pi$
$882$	4393.64	0.167734
$883$	−21664.9	−0.825686	−0.412843	−	0.910802i	$-0.635464\pi$
$883$	−21664.9	−0.825686	−0.412843	+	0.910802i	$0.635464\pi$
$884$	−63312.6	−2.40886
$885$	−5422.64	−0.205966
$886$	55851.5	2.11780
$887$	27086.0	1.02532	0.512661	−	0.858591i	$-0.328660\pi$
$887$	27086.0	1.02532	0.512661	+	0.858591i	$0.328660\pi$
$888$	15058.4	0.569062
$889$	4896.82	0.184740
$890$	30697.8	1.15617
$891$	0	0
$892$	−5870.30	−0.220350
$893$	−25929.0	−0.971647
$894$	−998.702	−0.0373620
$895$	3984.88	0.148827
$896$	−30637.4	−1.14232
$897$	1704.53	0.0634478
$898$	40757.6	1.51459
$899$	25705.5	0.953644
$900$	−9868.92	−0.365515
$901$	−1089.38	−0.0402803
$902$	0	0
$903$	5822.27	0.214566
$904$	27614.1	1.01596
$905$	9188.54	0.337500
$906$	30123.8	1.10463
$907$	−37853.9	−1.38580	−0.692898	−	0.721035i	$-0.743667\pi$
$907$	−37853.9	−1.38580	−0.692898	+	0.721035i	$0.743667\pi$
$908$	22326.2	0.815992
$909$	−8664.61	−0.316157
$910$	18477.2	0.673090
$911$	19800.0	0.720091	0.360045	−	0.932935i	$-0.382761\pi$
$911$	19800.0	0.720091	0.360045	+	0.932935i	$0.382761\pi$
$912$	5318.95	0.193123
$913$	0	0
$914$	−7826.21	−0.283225
$915$	−15471.8	−0.558996
$916$	78097.9	2.81706
$917$	−8430.07	−0.303583
$918$	13672.0	0.491551
$919$	5261.57	0.188861	0.0944305	−	0.995531i	$-0.469897\pi$
$919$	5261.57	0.188861	0.0944305	+	0.995531i	$0.469897\pi$
$920$	−1264.76	−0.0453239
$921$	−2864.99	−0.102502
$922$	6237.81	0.222811
$923$	12256.8	0.437095
$924$	0	0
$925$	25640.6	0.911414
$926$	−40281.2	−1.42951
$927$	−4921.26	−0.174364
$928$	60247.7	2.13117
$929$	−44402.4	−1.56813	−0.784066	−	0.620677i	$-0.786858\pi$
$929$	−44402.4	−1.56813	−0.784066	+	0.620677i	$0.786858\pi$
$930$	−7124.99	−0.251223
$931$	12096.3	0.425822
$932$	−2796.01	−0.0982685
$933$	−5589.37	−0.196128
$934$	−42868.5	−1.50182
$935$	0	0
$936$	−7501.93	−0.261975
$937$	−30250.3	−1.05468	−0.527339	−	0.849655i	$-0.676810\pi$
$937$	−30250.3	−1.05468	−0.527339	+	0.849655i	$0.676810\pi$
$938$	−40329.0	−1.40382
$939$	4625.41	0.160750
$940$	16281.3	0.564932
$941$	51716.6	1.79162	0.895809	−	0.444439i	$-0.146597\pi$
$941$	51716.6	1.79162	0.895809	+	0.444439i	$0.146597\pi$
$942$	−34853.9	−1.20552
$943$	73.0006	0.00252092
$944$	4987.73	0.171967
$945$	−2394.02	−0.0824102
$946$	0	0
$947$	−8455.69	−0.290151	−0.145075	−	0.989421i	$-0.546342\pi$
$947$	−8455.69	−0.290151	−0.145075	+	0.989421i	$0.546342\pi$
$948$	17959.0	0.615274
$949$	−7853.17	−0.268625
$950$	−45284.1	−1.54654
$951$	−5382.81	−0.183543
$952$	−30973.3	−1.05446
$953$	23867.6	0.811278	0.405639	−	0.914033i	$-0.367049\pi$
$953$	23867.6	0.811278	0.405639	+	0.914033i	$0.367049\pi$
$954$	−387.243	−0.0131420
$955$	17579.0	0.595647
$956$	76281.5	2.58067
$957$	0	0
$958$	−25220.8	−0.850572
$959$	26046.6	0.877048
$960$	−14472.7	−0.486568
$961$	−21402.5	−0.718423
$962$	58472.7	1.95970
$963$	−14037.9	−0.469745
$964$	−1543.79	−0.0515790
$965$	−22768.4	−0.759525
$966$	2501.63	0.0833215
$967$	9812.37	0.326313	0.163156	−	0.986600i	$-0.447832\pi$
$967$	9812.37	0.326313	0.163156	+	0.986600i	$0.447832\pi$
$968$	0	0
$969$	37640.9	1.24788
$970$	30071.5	0.995399
$971$	23725.4	0.784124	0.392062	−	0.919939i	$-0.371762\pi$
$971$	23725.4	0.784124	0.392062	+	0.919939i	$0.371762\pi$
$972$	2916.00	0.0962250
$973$	−38215.4	−1.25912
$974$	75695.4	2.49018
$975$	−12773.9	−0.419581
$976$	14230.9	0.466721
$977$	−14576.8	−0.477332	−0.238666	−	0.971102i	$-0.576710\pi$
$977$	−14576.8	−0.477332	−0.238666	+	0.971102i	$0.576710\pi$
$978$	−36986.9	−1.20932
$979$	0	0
$980$	−7595.47	−0.247580
$981$	7061.80	0.229833
$982$	−23276.3	−0.756393
$983$	47504.3	1.54136	0.770678	−	0.637225i	$-0.219918\pi$
$983$	47504.3	1.54136	0.770678	+	0.637225i	$0.219918\pi$
$984$	−321.288	−0.0104088
$985$	10259.8	0.331884
$986$	142119.	4.59026
$987$	−10734.5	−0.346182
$988$	−61961.5	−1.99520
$989$	−1547.54	−0.0497561
$990$	0	0
$991$	−3389.37	−0.108645	−0.0543224	−	0.998523i	$-0.517300\pi$
$991$	−3389.37	−0.108645	−0.0543224	+	0.998523i	$0.517300\pi$
$992$	19660.6	0.629260
$993$	34287.2	1.09574
$994$	17988.6	0.574006
$995$	−4560.32	−0.145298
$996$	11628.1	0.369931
$997$	−33416.1	−1.06148	−0.530742	−	0.847533i	$-0.678087\pi$
$997$	−33416.1	−1.06148	−0.530742	+	0.847533i	$0.678087\pi$
$998$	−7418.25	−0.235291
$999$	−7576.11	−0.239938

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.4.a.n.1.1		2
3.2	odd	2		1089.4.a.p.1.2		2
11.5	even	5		33.4.e.a.25.1	yes	4
11.9	even	5		33.4.e.a.4.1	✓	4
11.10	odd	2		363.4.a.o.1.2		2
33.5	odd	10		99.4.f.a.91.1		4
33.20	odd	10		99.4.f.a.37.1		4
33.32	even	2		1089.4.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.a.4.1	✓	4	11.9	even	5
33.4.e.a.25.1	yes	4	11.5	even	5
99.4.f.a.37.1		4	33.20	odd	10
99.4.f.a.91.1		4	33.5	odd	10
363.4.a.n.1.1		2	1.1	even	1	trivial
363.4.a.o.1.2		2	11.10	odd	2
1089.4.a.p.1.2		2	3.2	odd	2
1089.4.a.q.1.1		2	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	363.a (trivial)

\(f(q)\)	\(=\)	\(q-4.47214 q^{2} +3.00000 q^{3} +12.0000 q^{4} +5.79837 q^{5} -13.4164 q^{6} -15.2918 q^{7} -17.8885 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.47214 q^{2} +3.00000 q^{3} +12.0000 q^{4} +5.79837 q^{5} -13.4164 q^{6} -15.2918 q^{7} -17.8885 q^{8} +9.00000 q^{9} -25.9311 q^{10} +36.0000 q^{12} +46.5967 q^{13} +68.3870 q^{14} +17.3951 q^{15} -16.0000 q^{16} -113.228 q^{17} -40.2492 q^{18} -110.812 q^{19} +69.5805 q^{20} -45.8754 q^{21} +12.1935 q^{23} -53.6656 q^{24} -91.3789 q^{25} -208.387 q^{26} +27.0000 q^{27} -183.502 q^{28} +280.663 q^{29} -77.7933 q^{30} +91.5886 q^{31} +214.663 q^{32} +506.371 q^{34} -88.6676 q^{35} +108.000 q^{36} -280.597 q^{37} +495.564 q^{38} +139.790 q^{39} -103.724 q^{40} +5.98684 q^{41} +205.161 q^{42} -126.915 q^{43} +52.1854 q^{45} -54.5310 q^{46} +233.992 q^{47} -48.0000 q^{48} -109.161 q^{49} +408.659 q^{50} -339.684 q^{51} +559.161 q^{52} +9.62114 q^{53} -120.748 q^{54} +273.548 q^{56} -332.435 q^{57} -1255.16 q^{58} -311.733 q^{59} +208.741 q^{60} -889.431 q^{61} -409.597 q^{62} -137.626 q^{63} -832.000 q^{64} +270.185 q^{65} -589.717 q^{67} -1358.74 q^{68} +36.5805 q^{69} +396.533 q^{70} +263.041 q^{71} -160.997 q^{72} -168.535 q^{73} +1254.87 q^{74} -274.137 q^{75} -1329.74 q^{76} -625.161 q^{78} +498.860 q^{79} -92.7740 q^{80} +81.0000 q^{81} -26.7740 q^{82} +323.004 q^{83} -550.505 q^{84} -656.538 q^{85} +567.580 q^{86} +841.988 q^{87} -1183.82 q^{89} -233.380 q^{90} -712.548 q^{91} +146.322 q^{92} +274.766 q^{93} -1046.44 q^{94} -642.527 q^{95} +643.988 q^{96} -1159.67 q^{97} +488.183 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{3} + 24 q^{4} - 13 q^{5} - 44 q^{7} + 18 q^{9}+O(q^{10}) \) 2 * q + 6 * q^3 + 24 * q^4 - 13 * q^5 - 44 * q^7 + 18 * q^9	\( 2 q + 6 q^{3} + 24 q^{4} - 13 q^{5} - 44 q^{7} + 18 q^{9} - 110 q^{10} + 72 q^{12} + 44 q^{13} - 60 q^{14} - 39 q^{15} - 32 q^{16} - 99 q^{17} - 121 q^{19} - 156 q^{20} - 132 q^{21} - 74 q^{23} + 137 q^{25} - 220 q^{26} + 54 q^{27} - 528 q^{28} + 132 q^{29} - 330 q^{30} + 11 q^{31} + 570 q^{34} + 451 q^{35} + 216 q^{36} - 512 q^{37} + 450 q^{38} + 132 q^{39} - 440 q^{40} + 88 q^{41} - 180 q^{42} - 66 q^{43} - 117 q^{45} - 440 q^{46} + 345 q^{47} - 96 q^{48} + 372 q^{49} + 1430 q^{50} - 297 q^{51} + 528 q^{52} + 339 q^{53} - 240 q^{56} - 363 q^{57} - 1920 q^{58} + 385 q^{59} - 468 q^{60} - 1155 q^{61} - 770 q^{62} - 396 q^{63} - 1664 q^{64} + 319 q^{65} + 75 q^{67} - 1188 q^{68} - 222 q^{69} + 2810 q^{70} + 1141 q^{71} + 374 q^{73} + 220 q^{74} + 411 q^{75} - 1452 q^{76} - 660 q^{78} - 572 q^{79} + 208 q^{80} + 162 q^{81} + 340 q^{82} - 396 q^{83} - 1584 q^{84} - 924 q^{85} + 840 q^{86} + 396 q^{87} - 2712 q^{89} - 990 q^{90} - 638 q^{91} - 888 q^{92} + 33 q^{93} - 550 q^{94} - 451 q^{95} - 327 q^{97} + 2640 q^{98}+O(q^{100}) \) 2 * q + 6 * q^3 + 24 * q^4 - 13 * q^5 - 44 * q^7 + 18 * q^9 - 110 * q^10 + 72 * q^12 + 44 * q^13 - 60 * q^14 - 39 * q^15 - 32 * q^16 - 99 * q^17 - 121 * q^19 - 156 * q^20 - 132 * q^21 - 74 * q^23 + 137 * q^25 - 220 * q^26 + 54 * q^27 - 528 * q^28 + 132 * q^29 - 330 * q^30 + 11 * q^31 + 570 * q^34 + 451 * q^35 + 216 * q^36 - 512 * q^37 + 450 * q^38 + 132 * q^39 - 440 * q^40 + 88 * q^41 - 180 * q^42 - 66 * q^43 - 117 * q^45 - 440 * q^46 + 345 * q^47 - 96 * q^48 + 372 * q^49 + 1430 * q^50 - 297 * q^51 + 528 * q^52 + 339 * q^53 - 240 * q^56 - 363 * q^57 - 1920 * q^58 + 385 * q^59 - 468 * q^60 - 1155 * q^61 - 770 * q^62 - 396 * q^63 - 1664 * q^64 + 319 * q^65 + 75 * q^67 - 1188 * q^68 - 222 * q^69 + 2810 * q^70 + 1141 * q^71 + 374 * q^73 + 220 * q^74 + 411 * q^75 - 1452 * q^76 - 660 * q^78 - 572 * q^79 + 208 * q^80 + 162 * q^81 + 340 * q^82 - 396 * q^83 - 1584 * q^84 - 924 * q^85 + 840 * q^86 + 396 * q^87 - 2712 * q^89 - 990 * q^90 - 638 * q^91 - 888 * q^92 + 33 * q^93 - 550 * q^94 - 451 * q^95 - 327 * q^97 + 2640 * q^98

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