LMFDB - Embedded newform 294.4.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(1,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, 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("294.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.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:	$17.3465615417$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.58579 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.58579 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} -9.17157 q^{10} -6.48528 q^{11} -12.0000 q^{12} -45.2132 q^{13} +13.7574 q^{15} +16.0000 q^{16} -81.5563 q^{17} +18.0000 q^{18} +5.05382 q^{19} -18.3431 q^{20} -12.9706 q^{22} +106.250 q^{23} -24.0000 q^{24} -103.971 q^{25} -90.4264 q^{26} -27.0000 q^{27} -268.132 q^{29} +27.5147 q^{30} -292.368 q^{31} +32.0000 q^{32} +19.4558 q^{33} -163.113 q^{34} +36.0000 q^{36} +114.558 q^{37} +10.1076 q^{38} +135.640 q^{39} -36.6863 q^{40} +161.605 q^{41} -471.294 q^{43} -25.9411 q^{44} -41.2721 q^{45} +212.500 q^{46} -346.004 q^{47} -48.0000 q^{48} -207.941 q^{50} +244.669 q^{51} -180.853 q^{52} +405.529 q^{53} -54.0000 q^{54} +29.7401 q^{55} -15.1615 q^{57} -536.264 q^{58} +253.436 q^{59} +55.0294 q^{60} +751.217 q^{61} -584.735 q^{62} +64.0000 q^{64} +207.338 q^{65} +38.9117 q^{66} +11.6468 q^{67} -326.225 q^{68} -318.749 q^{69} -681.661 q^{71} +72.0000 q^{72} -685.457 q^{73} +229.117 q^{74} +311.912 q^{75} +20.2153 q^{76} +271.279 q^{78} +0.264069 q^{79} -73.3726 q^{80} +81.0000 q^{81} +323.210 q^{82} +437.137 q^{83} +374.000 q^{85} -942.587 q^{86} +804.396 q^{87} -51.8823 q^{88} +58.5126 q^{89} -82.5442 q^{90} +424.999 q^{92} +877.103 q^{93} -692.008 q^{94} -23.1758 q^{95} -96.0000 q^{96} +1280.09 q^{97} -58.3675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 12 q^{5} - 12 q^{6} + 16 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 12 * q^5 - 12 * q^6 + 16 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 12 q^{5} - 12 q^{6} + 16 q^{8} + 18 q^{9} - 24 q^{10} + 4 q^{11} - 24 q^{12} - 48 q^{13} + 36 q^{15} + 32 q^{16} - 132 q^{17} + 36 q^{18} - 120 q^{19} - 48 q^{20} + 8 q^{22} - 76 q^{23} - 48 q^{24} - 174 q^{25} - 96 q^{26} - 54 q^{27} - 112 q^{29} + 72 q^{30} - 432 q^{31} + 64 q^{32} - 12 q^{33} - 264 q^{34} + 72 q^{36} - 280 q^{37} - 240 q^{38} + 144 q^{39} - 96 q^{40} - 36 q^{41} - 128 q^{43} + 16 q^{44} - 108 q^{45} - 152 q^{46} + 264 q^{47} - 96 q^{48} - 348 q^{50} + 396 q^{51} - 192 q^{52} + 268 q^{53} - 108 q^{54} - 48 q^{55} + 360 q^{57} - 224 q^{58} - 336 q^{59} + 144 q^{60} + 504 q^{61} - 864 q^{62} + 128 q^{64} + 228 q^{65} - 24 q^{66} - 384 q^{67} - 528 q^{68} + 228 q^{69} - 396 q^{71} + 144 q^{72} + 312 q^{73} - 560 q^{74} + 522 q^{75} - 480 q^{76} + 288 q^{78} - 848 q^{79} - 192 q^{80} + 162 q^{81} - 72 q^{82} + 648 q^{83} + 748 q^{85} - 256 q^{86} + 336 q^{87} + 32 q^{88} + 612 q^{89} - 216 q^{90} - 304 q^{92} + 1296 q^{93} + 528 q^{94} + 904 q^{95} - 192 q^{96} + 2184 q^{97} + 36 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 12 * q^5 - 12 * q^6 + 16 * q^8 + 18 * q^9 - 24 * q^10 + 4 * q^11 - 24 * q^12 - 48 * q^13 + 36 * q^15 + 32 * q^16 - 132 * q^17 + 36 * q^18 - 120 * q^19 - 48 * q^20 + 8 * q^22 - 76 * q^23 - 48 * q^24 - 174 * q^25 - 96 * q^26 - 54 * q^27 - 112 * q^29 + 72 * q^30 - 432 * q^31 + 64 * q^32 - 12 * q^33 - 264 * q^34 + 72 * q^36 - 280 * q^37 - 240 * q^38 + 144 * q^39 - 96 * q^40 - 36 * q^41 - 128 * q^43 + 16 * q^44 - 108 * q^45 - 152 * q^46 + 264 * q^47 - 96 * q^48 - 348 * q^50 + 396 * q^51 - 192 * q^52 + 268 * q^53 - 108 * q^54 - 48 * q^55 + 360 * q^57 - 224 * q^58 - 336 * q^59 + 144 * q^60 + 504 * q^61 - 864 * q^62 + 128 * q^64 + 228 * q^65 - 24 * q^66 - 384 * q^67 - 528 * q^68 + 228 * q^69 - 396 * q^71 + 144 * q^72 + 312 * q^73 - 560 * q^74 + 522 * q^75 - 480 * q^76 + 288 * q^78 - 848 * q^79 - 192 * q^80 + 162 * q^81 - 72 * q^82 + 648 * q^83 + 748 * q^85 - 256 * q^86 + 336 * q^87 + 32 * q^88 + 612 * q^89 - 216 * q^90 - 304 * q^92 + 1296 * q^93 + 528 * q^94 + 904 * q^95 - 192 * q^96 + 2184 * q^97 + 36 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−4.58579	−0.410165	−0.205083	−	0.978745i	$-0.565746\pi$
$5$	−4.58579	−0.410165	−0.205083	+	0.978745i	$0.565746\pi$
$6$	−6.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−9.17157	−0.290031
$11$	−6.48528	−0.177762	−0.0888812	−	0.996042i	$-0.528329\pi$
$11$	−6.48528	−0.177762	−0.0888812	+	0.996042i	$0.528329\pi$
$12$	−12.0000	−0.288675
$13$	−45.2132	−0.964607	−0.482303	−	0.876004i	$-0.660200\pi$
$13$	−45.2132	−0.964607	−0.482303	+	0.876004i	$0.660200\pi$
$14$	0	0
$15$	13.7574	0.236809
$16$	16.0000	0.250000
$17$	−81.5563	−1.16355	−0.581774	−	0.813350i	$-0.697641\pi$
$17$	−81.5563	−1.16355	−0.581774	+	0.813350i	$0.697641\pi$
$18$	18.0000	0.235702
$19$	5.05382	0.0610225	0.0305112	−	0.999534i	$-0.490286\pi$
$19$	5.05382	0.0610225	0.0305112	+	0.999534i	$0.490286\pi$
$20$	−18.3431	−0.205083
$21$	0	0
$22$	−12.9706	−0.125697
$23$	106.250	0.963244	0.481622	−	0.876379i	$-0.340048\pi$
$23$	106.250	0.963244	0.481622	+	0.876379i	$0.340048\pi$
$24$	−24.0000	−0.204124
$25$	−103.971	−0.831765
$26$	−90.4264	−0.682080
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−268.132	−1.71693	−0.858463	−	0.512875i	$-0.828580\pi$
$29$	−268.132	−1.71693	−0.858463	+	0.512875i	$0.828580\pi$
$30$	27.5147	0.167449
$31$	−292.368	−1.69390	−0.846948	−	0.531676i	$-0.821562\pi$
$31$	−292.368	−1.69390	−0.846948	+	0.531676i	$0.821562\pi$
$32$	32.0000	0.176777
$33$	19.4558	0.102631
$34$	−163.113	−0.822753
$35$	0	0
$36$	36.0000	0.166667
$37$	114.558	0.509008	0.254504	−	0.967072i	$-0.418088\pi$
$37$	114.558	0.509008	0.254504	+	0.967072i	$0.418088\pi$
$38$	10.1076	0.0431494
$39$	135.640	0.556916
$40$	−36.6863	−0.145015
$41$	161.605	0.615573	0.307786	−	0.951456i	$-0.400412\pi$
$41$	161.605	0.615573	0.307786	+	0.951456i	$0.400412\pi$
$42$	0	0
$43$	−471.294	−1.67143	−0.835716	−	0.549162i	$-0.814947\pi$
$43$	−471.294	−1.67143	−0.835716	+	0.549162i	$0.814947\pi$
$44$	−25.9411	−0.0888812
$45$	−41.2721	−0.136722
$46$	212.500	0.681116
$47$	−346.004	−1.07383	−0.536914	−	0.843637i	$-0.680410\pi$
$47$	−346.004	−1.07383	−0.536914	+	0.843637i	$0.680410\pi$
$48$	−48.0000	−0.144338
$49$	0	0
$50$	−207.941	−0.588146
$51$	244.669	0.671775
$52$	−180.853	−0.482303
$53$	405.529	1.05101	0.525507	−	0.850790i	$-0.323876\pi$
$53$	405.529	1.05101	0.525507	+	0.850790i	$0.323876\pi$
$54$	−54.0000	−0.136083
$55$	29.7401	0.0729119
$56$	0	0
$57$	−15.1615	−0.0352313
$58$	−536.264	−1.21405
$59$	253.436	0.559229	0.279614	−	0.960112i	$-0.409793\pi$
$59$	253.436	0.559229	0.279614	+	0.960112i	$0.409793\pi$
$60$	55.0294	0.118404
$61$	751.217	1.57678	0.788390	−	0.615176i	$-0.210915\pi$
$61$	751.217	1.57678	0.788390	+	0.615176i	$0.210915\pi$
$62$	−584.735	−1.19776
$63$	0	0
$64$	64.0000	0.125000
$65$	207.338	0.395648
$66$	38.9117	0.0725712
$67$	11.6468	0.0212370	0.0106185	−	0.999944i	$-0.496620\pi$
$67$	11.6468	0.0212370	0.0106185	+	0.999944i	$0.496620\pi$
$68$	−326.225	−0.581774
$69$	−318.749	−0.556129
$70$	0	0
$71$	−681.661	−1.13941	−0.569706	−	0.821848i	$-0.692943\pi$
$71$	−681.661	−1.13941	−0.569706	+	0.821848i	$0.692943\pi$
$72$	72.0000	0.117851
$73$	−685.457	−1.09900	−0.549498	−	0.835495i	$-0.685181\pi$
$73$	−685.457	−1.09900	−0.549498	+	0.835495i	$0.685181\pi$
$74$	229.117	0.359923
$75$	311.912	0.480219
$76$	20.2153	0.0305112
$77$	0	0
$78$	271.279	0.393799
$79$	0.264069	0.000376077 0	0.000188038	−	1.00000i	$-0.499940\pi$
$79$	0.264069	0.000376077 0	0.000188038		1.00000i	$0.499940\pi$
$80$	−73.3726	−0.102541
$81$	81.0000	0.111111
$82$	323.210	0.435276
$83$	437.137	0.578097	0.289048	−	0.957314i	$-0.406661\pi$
$83$	437.137	0.578097	0.289048	+	0.957314i	$0.406661\pi$
$84$	0	0
$85$	374.000	0.477247
$86$	−942.587	−1.18188
$87$	804.396	0.991268
$88$	−51.8823	−0.0628485
$89$	58.5126	0.0696891	0.0348445	−	0.999393i	$-0.488906\pi$
$89$	58.5126	0.0696891	0.0348445	+	0.999393i	$0.488906\pi$
$90$	−82.5442	−0.0966769
$91$	0	0
$92$	424.999	0.481622
$93$	877.103	0.977971
$94$	−692.008	−0.759311
$95$	−23.1758	−0.0250293
$96$	−96.0000	−0.102062
$97$	1280.09	1.33993	0.669966	−	0.742391i	$-0.266308\pi$
$97$	1280.09	1.33993	0.669966	+	0.742391i	$0.266308\pi$
$98$	0	0
$99$	−58.3675	−0.0592541
$100$	−415.882	−0.415882
$101$	1306.39	1.28704	0.643518	−	0.765431i	$-0.277474\pi$
$101$	1306.39	1.28704	0.643518	+	0.765431i	$0.277474\pi$
$102$	489.338	0.475017
$103$	758.975	0.726058	0.363029	−	0.931778i	$-0.381743\pi$
$103$	758.975	0.726058	0.363029	+	0.931778i	$0.381743\pi$
$104$	−361.706	−0.341040
$105$	0	0
$106$	811.058	0.743178
$107$	1262.51	1.14067	0.570336	−	0.821412i	$-0.306813\pi$
$107$	1262.51	1.14067	0.570336	+	0.821412i	$0.306813\pi$
$108$	−108.000	−0.0962250
$109$	−2105.53	−1.85021	−0.925105	−	0.379711i	$-0.876023\pi$
$109$	−2105.53	−1.85021	−0.925105	+	0.379711i	$0.876023\pi$
$110$	59.4802	0.0515565
$111$	−343.675	−0.293876
$112$	0	0
$113$	1535.76	1.27852	0.639258	−	0.768992i	$-0.279241\pi$
$113$	1535.76	1.27852	0.639258	+	0.768992i	$0.279241\pi$
$114$	−30.3229	−0.0249123
$115$	−487.239	−0.395089
$116$	−1072.53	−0.858463
$117$	−406.919	−0.321536
$118$	506.871	0.395435
$119$	0	0
$120$	110.059	0.0837246
$121$	−1288.94	−0.968401
$122$	1502.43	1.11495
$123$	−484.815	−0.355401
$124$	−1169.47	−0.846948
$125$	1050.01	0.751326
$126$	0	0
$127$	24.1749	0.0168911	0.00844557	−	0.999964i	$-0.497312\pi$
$127$	24.1749	0.0168911	0.00844557	+	0.999964i	$0.497312\pi$
$128$	128.000	0.0883883
$129$	1413.88	0.965002
$130$	414.676	0.279765
$131$	−1581.53	−1.05480	−0.527400	−	0.849617i	$-0.676833\pi$
$131$	−1581.53	−1.05480	−0.527400	+	0.849617i	$0.676833\pi$
$132$	77.8234	0.0513156
$133$	0	0
$134$	23.2935	0.0150168
$135$	123.816	0.0789363
$136$	−652.451	−0.411376
$137$	−745.188	−0.464713	−0.232357	−	0.972631i	$-0.574644\pi$
$137$	−745.188	−0.464713	−0.232357	+	0.972631i	$0.574644\pi$
$138$	−637.499	−0.393243
$139$	1373.60	0.838179	0.419090	−	0.907945i	$-0.362349\pi$
$139$	1373.60	0.838179	0.419090	+	0.907945i	$0.362349\pi$
$140$	0	0
$141$	1038.01	0.619975
$142$	−1363.32	−0.805686
$143$	293.220	0.171471
$144$	144.000	0.0833333
$145$	1229.60	0.704224
$146$	−1370.91	−0.777107
$147$	0	0
$148$	458.234	0.254504
$149$	620.530	0.341180	0.170590	−	0.985342i	$-0.445433\pi$
$149$	620.530	0.341180	0.170590	+	0.985342i	$0.445433\pi$
$150$	623.823	0.339566
$151$	−1939.26	−1.04513	−0.522567	−	0.852598i	$-0.675025\pi$
$151$	−1939.26	−1.04513	−0.522567	+	0.852598i	$0.675025\pi$
$152$	40.4306	0.0215747
$153$	−734.007	−0.387849
$154$	0	0
$155$	1340.74	0.694777
$156$	542.558	0.278458
$157$	412.843	0.209863	0.104931	−	0.994479i	$-0.466538\pi$
$157$	412.843	0.209863	0.104931	+	0.994479i	$0.466538\pi$
$158$	0.528137	0.000265926 0
$159$	−1216.59	−0.606803
$160$	−146.745	−0.0725077
$161$	0	0
$162$	162.000	0.0785674
$163$	−3907.44	−1.87763	−0.938817	−	0.344417i	$-0.888077\pi$
$163$	−3907.44	−1.87763	−0.938817	+	0.344417i	$0.888077\pi$
$164$	646.420	0.307786
$165$	−89.2203	−0.0420957
$166$	874.274	0.408776
$167$	1286.41	0.596082	0.298041	−	0.954553i	$-0.403667\pi$
$167$	1286.41	0.596082	0.298041	+	0.954553i	$0.403667\pi$
$168$	0	0
$169$	−152.766	−0.0695340
$170$	748.000	0.337465
$171$	45.4844	0.0203408
$172$	−1885.17	−0.835716
$173$	1251.26	0.549892	0.274946	−	0.961460i	$-0.411340\pi$
$173$	1251.26	0.549892	0.274946	+	0.961460i	$0.411340\pi$
$174$	1608.79	0.700932
$175$	0	0
$176$	−103.765	−0.0444406
$177$	−760.307	−0.322871
$178$	117.025	0.0492776
$179$	3623.51	1.51304	0.756520	−	0.653971i	$-0.226898\pi$
$179$	3623.51	1.51304	0.756520	+	0.653971i	$0.226898\pi$
$180$	−165.088	−0.0683609
$181$	−181.727	−0.0746280	−0.0373140	−	0.999304i	$-0.511880\pi$
$181$	−181.727	−0.0746280	−0.0373140	+	0.999304i	$0.511880\pi$
$182$	0	0
$183$	−2253.65	−0.910354
$184$	849.998	0.340558
$185$	−525.341	−0.208777
$186$	1754.21	0.691530
$187$	528.916	0.206835
$188$	−1384.02	−0.536914
$189$	0	0
$190$	−46.3515	−0.0176984
$191$	1481.28	0.561160	0.280580	−	0.959831i	$-0.409473\pi$
$191$	1481.28	0.561160	0.280580	+	0.959831i	$0.409473\pi$
$192$	−192.000	−0.0721688
$193$	−356.708	−0.133038	−0.0665192	−	0.997785i	$-0.521189\pi$
$193$	−356.708	−0.133038	−0.0665192	+	0.997785i	$0.521189\pi$
$194$	2560.18	0.947476
$195$	−622.014	−0.228428
$196$	0	0
$197$	4890.53	1.76871	0.884355	−	0.466816i	$-0.154599\pi$
$197$	4890.53	1.76871	0.884355	+	0.466816i	$0.154599\pi$
$198$	−116.735	−0.0418990
$199$	−3542.85	−1.26204	−0.631020	−	0.775766i	$-0.717364\pi$
$199$	−3542.85	−1.26204	−0.631020	+	0.775766i	$0.717364\pi$
$200$	−831.765	−0.294073
$201$	−34.9403	−0.0122612
$202$	2612.78	0.910071
$203$	0	0
$204$	978.676	0.335887
$205$	−741.087	−0.252486
$206$	1517.95	0.513401
$207$	956.248	0.321081
$208$	−723.411	−0.241152
$209$	−32.7755	−0.0108475
$210$	0	0
$211$	−4289.50	−1.39953	−0.699765	−	0.714373i	$-0.746712\pi$
$211$	−4289.50	−1.39953	−0.699765	+	0.714373i	$0.746712\pi$
$212$	1622.12	0.525507
$213$	2044.98	0.657840
$214$	2525.03	0.806576
$215$	2161.25	0.685563
$216$	−216.000	−0.0680414
$217$	0	0
$218$	−4211.05	−1.30830
$219$	2056.37	0.634505
$220$	118.960	0.0364560
$221$	3687.42	1.12237
$222$	−687.351	−0.207802
$223$	−5795.73	−1.74041	−0.870204	−	0.492692i	$-0.836013\pi$
$223$	−5795.73	−1.74041	−0.870204	+	0.492692i	$0.836013\pi$
$224$	0	0
$225$	−935.735	−0.277255
$226$	3071.53	0.904048
$227$	−4104.04	−1.19998	−0.599989	−	0.800008i	$-0.704828\pi$
$227$	−4104.04	−1.19998	−0.599989	+	0.800008i	$0.704828\pi$
$228$	−60.6459	−0.0176157
$229$	1296.83	0.374223	0.187111	−	0.982339i	$-0.440087\pi$
$229$	1296.83	0.374223	0.187111	+	0.982339i	$0.440087\pi$
$230$	−974.478	−0.279370
$231$	0	0
$232$	−2145.06	−0.607025
$233$	−1478.33	−0.415660	−0.207830	−	0.978165i	$-0.566640\pi$
$233$	−1478.33	−0.415660	−0.207830	+	0.978165i	$0.566640\pi$
$234$	−813.838	−0.227360
$235$	1586.70	0.440447
$236$	1013.74	0.279614
$237$	−0.792206	−0.000217128 0
$238$	0	0
$239$	−3776.92	−1.02221	−0.511106	−	0.859518i	$-0.670764\pi$
$239$	−3776.92	−1.02221	−0.511106	+	0.859518i	$0.670764\pi$
$240$	220.118	0.0592022
$241$	3996.38	1.06817	0.534086	−	0.845430i	$-0.320656\pi$
$241$	3996.38	1.06817	0.534086	+	0.845430i	$0.320656\pi$
$242$	−2577.88	−0.684763
$243$	−243.000	−0.0641500
$244$	3004.87	0.788390
$245$	0	0
$246$	−969.631	−0.251306
$247$	−228.500	−0.0588627
$248$	−2338.94	−0.598882
$249$	−1311.41	−0.333764
$250$	2100.02	0.531268
$251$	−5423.58	−1.36388	−0.681939	−	0.731409i	$-0.738863\pi$
$251$	−5423.58	−1.36388	−0.681939	+	0.731409i	$0.738863\pi$
$252$	0	0
$253$	−689.060	−0.171229
$254$	48.3498	0.0119438
$255$	−1122.00	−0.275539
$256$	256.000	0.0625000
$257$	−5964.22	−1.44762	−0.723809	−	0.690000i	$-0.757611\pi$
$257$	−5964.22	−1.44762	−0.723809	+	0.690000i	$0.757611\pi$
$258$	2827.76	0.682359
$259$	0	0
$260$	829.352	0.197824
$261$	−2413.19	−0.572309
$262$	−3163.05	−0.745856
$263$	5166.01	1.21122	0.605608	−	0.795763i	$-0.292930\pi$
$263$	5166.01	1.21122	0.605608	+	0.795763i	$0.292930\pi$
$264$	155.647	0.0362856
$265$	−1859.67	−0.431089
$266$	0	0
$267$	−175.538	−0.0402350
$268$	46.5870	0.0106185
$269$	−3883.29	−0.880180	−0.440090	−	0.897954i	$-0.645054\pi$
$269$	−3883.29	−0.880180	−0.440090	+	0.897954i	$0.645054\pi$
$270$	247.632	0.0558164
$271$	−5527.65	−1.23904	−0.619522	−	0.784979i	$-0.712674\pi$
$271$	−5527.65	−1.23904	−0.619522	+	0.784979i	$0.712674\pi$
$272$	−1304.90	−0.290887
$273$	0	0
$274$	−1490.38	−0.328602
$275$	674.278	0.147856
$276$	−1275.00	−0.278065
$277$	2268.12	0.491979	0.245989	−	0.969273i	$-0.420887\pi$
$277$	2268.12	0.491979	0.245989	+	0.969273i	$0.420887\pi$
$278$	2747.19	0.592682
$279$	−2631.31	−0.564632
$280$	0	0
$281$	725.656	0.154053	0.0770267	−	0.997029i	$-0.475457\pi$
$281$	725.656	0.154053	0.0770267	+	0.997029i	$0.475457\pi$
$282$	2076.03	0.438388
$283$	−4237.00	−0.889976	−0.444988	−	0.895536i	$-0.646792\pi$
$283$	−4237.00	−0.889976	−0.444988	+	0.895536i	$0.646792\pi$
$284$	−2726.64	−0.569706
$285$	69.5273	0.0144507
$286$	586.441	0.121248
$287$	0	0
$288$	288.000	0.0589256
$289$	1738.44	0.353845
$290$	2459.19	0.497961
$291$	−3840.27	−0.773611
$292$	−2741.83	−0.549498
$293$	4373.78	0.872079	0.436039	−	0.899928i	$-0.356381\pi$
$293$	4373.78	0.872079	0.436039	+	0.899928i	$0.356381\pi$
$294$	0	0
$295$	−1162.20	−0.229376
$296$	916.468	0.179961
$297$	175.103	0.0342104
$298$	1241.06	0.241251
$299$	−4803.89	−0.929152
$300$	1247.65	0.240110
$301$	0	0
$302$	−3878.53	−0.739021
$303$	−3919.17	−0.743070
$304$	80.8612	0.0152556
$305$	−3444.92	−0.646740
$306$	−1468.01	−0.274251
$307$	−4133.47	−0.768435	−0.384217	−	0.923243i	$-0.625529\pi$
$307$	−4133.47	−0.768435	−0.384217	+	0.923243i	$0.625529\pi$
$308$	0	0
$309$	−2276.92	−0.419190
$310$	2681.47	0.491282
$311$	−5063.23	−0.923182	−0.461591	−	0.887093i	$-0.652721\pi$
$311$	−5063.23	−0.923182	−0.461591	+	0.887093i	$0.652721\pi$
$312$	1085.12	0.196900
$313$	−7411.56	−1.33842	−0.669211	−	0.743073i	$-0.733368\pi$
$313$	−7411.56	−1.33842	−0.669211	+	0.743073i	$0.733368\pi$
$314$	825.686	0.148395
$315$	0	0
$316$	1.05627	0.000188038 0
$317$	−6737.05	−1.19366	−0.596831	−	0.802367i	$-0.703574\pi$
$317$	−6737.05	−1.19366	−0.596831	+	0.802367i	$0.703574\pi$
$318$	−2433.17	−0.429074
$319$	1738.91	0.305205
$320$	−293.490	−0.0512707
$321$	−3787.54	−0.658567
$322$	0	0
$323$	−412.171	−0.0710026
$324$	324.000	0.0555556
$325$	4700.84	0.802326
$326$	−7814.88	−1.32769
$327$	6316.58	1.06822
$328$	1292.84	0.217638
$329$	0	0
$330$	−178.441	−0.0297662
$331$	11175.9	1.85585	0.927923	−	0.372771i	$-0.121592\pi$
$331$	11175.9	1.85585	0.927923	+	0.372771i	$0.121592\pi$
$332$	1748.55	0.289048
$333$	1031.03	0.169669
$334$	2572.83	0.421494
$335$	−53.4095	−0.00871067
$336$	0	0
$337$	9379.78	1.51617	0.758085	−	0.652156i	$-0.226135\pi$
$337$	9379.78	1.51617	0.758085	+	0.652156i	$0.226135\pi$
$338$	−305.532	−0.0491680
$339$	−4607.29	−0.738152
$340$	1496.00	0.238624
$341$	1896.09	0.301111
$342$	90.9688	0.0143831
$343$	0	0
$344$	−3770.35	−0.590941
$345$	1461.72	0.228105
$346$	2502.51	0.388832
$347$	5681.46	0.878953	0.439476	−	0.898254i	$-0.355164\pi$
$347$	5681.46	0.878953	0.439476	+	0.898254i	$0.355164\pi$
$348$	3217.58	0.495634
$349$	704.250	0.108016	0.0540080	−	0.998541i	$-0.482800\pi$
$349$	704.250	0.108016	0.0540080	+	0.998541i	$0.482800\pi$
$350$	0	0
$351$	1220.76	0.185639
$352$	−207.529	−0.0314242
$353$	4284.96	0.646078	0.323039	−	0.946386i	$-0.395295\pi$
$353$	4284.96	0.646078	0.323039	+	0.946386i	$0.395295\pi$
$354$	−1520.61	−0.228304
$355$	3125.95	0.467347
$356$	234.051	0.0348445
$357$	0	0
$358$	7247.03	1.06988
$359$	4661.27	0.685272	0.342636	−	0.939468i	$-0.388680\pi$
$359$	4661.27	0.685272	0.342636	+	0.939468i	$0.388680\pi$
$360$	−330.177	−0.0483384
$361$	−6833.46	−0.996276
$362$	−363.454	−0.0527700
$363$	3866.82	0.559106
$364$	0	0
$365$	3143.36	0.450770
$366$	−4507.30	−0.643717
$367$	6935.30	0.986430	0.493215	−	0.869907i	$-0.335822\pi$
$367$	6935.30	0.986430	0.493215	+	0.869907i	$0.335822\pi$
$368$	1700.00	0.240811
$369$	1454.45	0.205191
$370$	−1050.68	−0.147628
$371$	0	0
$372$	3508.41	0.488985
$373$	−3081.10	−0.427704	−0.213852	−	0.976866i	$-0.568601\pi$
$373$	−3081.10	−0.427704	−0.213852	+	0.976866i	$0.568601\pi$
$374$	1057.83	0.146254
$375$	−3150.03	−0.433778
$376$	−2768.03	−0.379655
$377$	12123.1	1.65616
$378$	0	0
$379$	941.827	0.127647	0.0638237	−	0.997961i	$-0.479670\pi$
$379$	941.827	0.127647	0.0638237	+	0.997961i	$0.479670\pi$
$380$	−92.7030	−0.0125146
$381$	−72.5247	−0.00975210
$382$	2962.56	0.396800
$383$	677.526	0.0903915	0.0451958	−	0.998978i	$-0.485609\pi$
$383$	677.526	0.0903915	0.0451958	+	0.998978i	$0.485609\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−713.416	−0.0940724
$387$	−4241.64	−0.557144
$388$	5120.36	0.669966
$389$	−11865.4	−1.54653	−0.773266	−	0.634082i	$-0.781378\pi$
$389$	−11865.4	−1.54653	−0.773266	+	0.634082i	$0.781378\pi$
$390$	−1244.03	−0.161523
$391$	−8665.34	−1.12078
$392$	0	0
$393$	4744.58	0.608989
$394$	9781.06	1.25067
$395$	−1.21096	−0.000154254 0
$396$	−233.470	−0.0296271
$397$	5140.76	0.649893	0.324947	−	0.945732i	$-0.394654\pi$
$397$	5140.76	0.649893	0.324947	+	0.945732i	$0.394654\pi$
$398$	−7085.70	−0.892397
$399$	0	0
$400$	−1663.53	−0.207941
$401$	−12382.0	−1.54196	−0.770981	−	0.636858i	$-0.780234\pi$
$401$	−12382.0	−1.54196	−0.770981	+	0.636858i	$0.780234\pi$
$402$	−69.8805	−0.00866996
$403$	13218.9	1.63394
$404$	5225.56	0.643518
$405$	−371.449	−0.0455739
$406$	0	0
$407$	−742.944	−0.0904824
$408$	1957.35	0.237508
$409$	15875.6	1.91931	0.959657	−	0.281173i	$-0.0907235\pi$
$409$	15875.6	1.91931	0.959657	+	0.281173i	$0.0907235\pi$
$410$	−1482.17	−0.178535
$411$	2235.56	0.268302
$412$	3035.90	0.363029
$413$	0	0
$414$	1912.50	0.227039
$415$	−2004.62	−0.237115
$416$	−1446.82	−0.170520
$417$	−4120.79	−0.483923
$418$	−65.5509	−0.00767034
$419$	16111.9	1.87857	0.939283	−	0.343145i	$-0.111492\pi$
$419$	16111.9	1.87857	0.939283	+	0.343145i	$0.111492\pi$
$420$	0	0
$421$	8691.58	1.00618	0.503090	−	0.864234i	$-0.332197\pi$
$421$	8691.58	1.00618	0.503090	+	0.864234i	$0.332197\pi$
$422$	−8578.99	−0.989618
$423$	−3114.04	−0.357943
$424$	3244.23	0.371589
$425$	8479.46	0.967798
$426$	4089.97	0.465163
$427$	0	0
$428$	5050.06	0.570336
$429$	−879.661	−0.0989987
$430$	4322.50	0.484766
$431$	−4195.10	−0.468842	−0.234421	−	0.972135i	$-0.575319\pi$
$431$	−4195.10	−0.468842	−0.234421	+	0.972135i	$0.575319\pi$
$432$	−432.000	−0.0481125
$433$	5426.54	0.602270	0.301135	−	0.953582i	$-0.402635\pi$
$433$	5426.54	0.602270	0.301135	+	0.953582i	$0.402635\pi$
$434$	0	0
$435$	−3688.79	−0.406584
$436$	−8422.11	−0.925105
$437$	536.968	0.0587795
$438$	4112.74	0.448663
$439$	3771.24	0.410003	0.205002	−	0.978762i	$-0.434280\pi$
$439$	3771.24	0.410003	0.205002	+	0.978762i	$0.434280\pi$
$440$	237.921	0.0257783
$441$	0	0
$442$	7374.85	0.793633
$443$	−5930.30	−0.636020	−0.318010	−	0.948087i	$-0.603015\pi$
$443$	−5930.30	−0.636020	−0.318010	+	0.948087i	$0.603015\pi$
$444$	−1374.70	−0.146938
$445$	−268.326	−0.0285840
$446$	−11591.5	−1.23065
$447$	−1861.59	−0.196980
$448$	0	0
$449$	−529.065	−0.0556083	−0.0278041	−	0.999613i	$-0.508851\pi$
$449$	−529.065	−0.0556083	−0.0278041	+	0.999613i	$0.508851\pi$
$450$	−1871.47	−0.196049
$451$	−1048.05	−0.109426
$452$	6143.05	0.639258
$453$	5817.79	0.603408
$454$	−8208.09	−0.848512
$455$	0	0
$456$	−121.292	−0.0124562
$457$	10057.2	1.02944	0.514721	−	0.857358i	$-0.327896\pi$
$457$	10057.2	1.02944	0.514721	+	0.857358i	$0.327896\pi$
$458$	2593.66	0.264616
$459$	2202.02	0.223925
$460$	−1948.96	−0.197545
$461$	5010.31	0.506190	0.253095	−	0.967441i	$-0.418552\pi$
$461$	5010.31	0.506190	0.253095	+	0.967441i	$0.418552\pi$
$462$	0	0
$463$	−7124.38	−0.715114	−0.357557	−	0.933891i	$-0.616390\pi$
$463$	−7124.38	−0.715114	−0.357557	+	0.933891i	$0.616390\pi$
$464$	−4290.11	−0.429232
$465$	−4022.21	−0.401130
$466$	−2956.67	−0.293916
$467$	−7501.44	−0.743309	−0.371654	−	0.928371i	$-0.621209\pi$
$467$	−7501.44	−0.743309	−0.371654	+	0.928371i	$0.621209\pi$
$468$	−1627.68	−0.160768
$469$	0	0
$470$	3173.40	0.311443
$471$	−1238.53	−0.121164
$472$	2027.49	0.197717
$473$	3056.47	0.297118
$474$	−1.58441	−0.000153533 0
$475$	−525.449	−0.0507563
$476$	0	0
$477$	3649.76	0.350338
$478$	−7553.84	−0.722813
$479$	8173.80	0.779688	0.389844	−	0.920881i	$-0.372529\pi$
$479$	8173.80	0.779688	0.389844	+	0.920881i	$0.372529\pi$
$480$	440.235	0.0418623
$481$	−5179.55	−0.490992
$482$	7992.76	0.755312
$483$	0	0
$484$	−5155.76	−0.484200
$485$	−5870.22	−0.549594
$486$	−486.000	−0.0453609
$487$	−11968.8	−1.11367	−0.556835	−	0.830623i	$-0.687985\pi$
$487$	−11968.8	−1.11367	−0.556835	+	0.830623i	$0.687985\pi$
$488$	6009.74	0.557476
$489$	11722.3	1.08405
$490$	0	0
$491$	2079.96	0.191176	0.0955878	−	0.995421i	$-0.469527\pi$
$491$	2079.96	0.191176	0.0955878	+	0.995421i	$0.469527\pi$
$492$	−1939.26	−0.177701
$493$	21867.9	1.99773
$494$	−456.999	−0.0416222
$495$	267.661	0.0243040
$496$	−4677.88	−0.423474
$497$	0	0
$498$	−2622.82	−0.236007
$499$	12834.4	1.15140	0.575699	−	0.817662i	$-0.304730\pi$
$499$	12834.4	1.15140	0.575699	+	0.817662i	$0.304730\pi$
$500$	4200.04	0.375663
$501$	−3859.24	−0.344148
$502$	−10847.2	−0.964408
$503$	−16808.8	−1.48999	−0.744997	−	0.667068i	$-0.767549\pi$
$503$	−16808.8	−1.48999	−0.744997	+	0.667068i	$0.767549\pi$
$504$	0	0
$505$	−5990.82	−0.527897
$506$	−1378.12	−0.121077
$507$	458.299	0.0401455
$508$	96.6996	0.00844557
$509$	4270.26	0.371859	0.185929	−	0.982563i	$-0.440470\pi$
$509$	4270.26	0.371859	0.185929	+	0.982563i	$0.440470\pi$
$510$	−2244.00	−0.194835
$511$	0	0
$512$	512.000	0.0441942
$513$	−136.453	−0.0117438
$514$	−11928.4	−1.02362
$515$	−3480.50	−0.297804
$516$	5655.52	0.482501
$517$	2243.93	0.190886
$518$	0	0
$519$	−3753.77	−0.317480
$520$	1658.70	0.139883
$521$	−15283.3	−1.28517	−0.642584	−	0.766215i	$-0.722138\pi$
$521$	−15283.3	−1.28517	−0.642584	+	0.766215i	$0.722138\pi$
$522$	−4826.38	−0.404683
$523$	4499.33	0.376180	0.188090	−	0.982152i	$-0.439770\pi$
$523$	4499.33	0.376180	0.188090	+	0.982152i	$0.439770\pi$
$524$	−6326.11	−0.527400
$525$	0	0
$526$	10332.0	0.856459
$527$	23844.4	1.97093
$528$	311.294	0.0256578
$529$	−877.984	−0.0721611
$530$	−3719.34	−0.304826
$531$	2280.92	0.186410
$532$	0	0
$533$	−7306.69	−0.593785
$534$	−351.076	−0.0284504
$535$	−5789.62	−0.467864
$536$	93.1740	0.00750840
$537$	−10870.5	−0.873554
$538$	−7766.59	−0.622382
$539$	0	0
$540$	495.265	0.0394682
$541$	3970.82	0.315561	0.157781	−	0.987474i	$-0.449566\pi$
$541$	3970.82	0.315561	0.157781	+	0.987474i	$0.449566\pi$
$542$	−11055.3	−0.876137
$543$	545.181	0.0430865
$544$	−2609.80	−0.205688
$545$	9655.50	0.758892
$546$	0	0
$547$	−2703.90	−0.211353	−0.105677	−	0.994401i	$-0.533701\pi$
$547$	−2703.90	−0.211353	−0.105677	+	0.994401i	$0.533701\pi$
$548$	−2980.75	−0.232357
$549$	6760.96	0.525593
$550$	1348.56	0.104550
$551$	−1355.09	−0.104771
$552$	−2549.99	−0.196621
$553$	0	0
$554$	4536.24	0.347881
$555$	1576.02	0.120538
$556$	5494.38	0.419090
$557$	790.824	0.0601585	0.0300793	−	0.999548i	$-0.490424\pi$
$557$	790.824	0.0601585	0.0300793	+	0.999548i	$0.490424\pi$
$558$	−5262.62	−0.399255
$559$	21308.7	1.61227
$560$	0	0
$561$	−1586.75	−0.119416
$562$	1451.31	0.108932
$563$	−7517.15	−0.562718	−0.281359	−	0.959603i	$-0.590785\pi$
$563$	−7517.15	−0.562718	−0.281359	+	0.959603i	$0.590785\pi$
$564$	4152.05	0.309987
$565$	−7042.68	−0.524403
$566$	−8473.99	−0.629308
$567$	0	0
$568$	−5453.29	−0.402843
$569$	13945.4	1.02746	0.513728	−	0.857953i	$-0.328264\pi$
$569$	13945.4	1.02746	0.513728	+	0.857953i	$0.328264\pi$
$570$	139.055	0.0102182
$571$	−2118.49	−0.155265	−0.0776323	−	0.996982i	$-0.524736\pi$
$571$	−2118.49	−0.155265	−0.0776323	+	0.996982i	$0.524736\pi$
$572$	1172.88	0.0857354
$573$	−4443.84	−0.323986
$574$	0	0
$575$	−11046.8	−0.801192
$576$	576.000	0.0416667
$577$	−22857.7	−1.64918	−0.824592	−	0.565728i	$-0.808595\pi$
$577$	−22857.7	−1.64918	−0.824592	+	0.565728i	$0.808595\pi$
$578$	3476.88	0.250206
$579$	1070.12	0.0768098
$580$	4918.38	0.352112
$581$	0	0
$582$	−7680.54	−0.547025
$583$	−2629.97	−0.186831
$584$	−5483.66	−0.388554
$585$	1866.04	0.131883
$586$	8747.56	0.616653
$587$	−23955.3	−1.68440	−0.842199	−	0.539167i	$-0.818739\pi$
$587$	−23955.3	−1.68440	−0.842199	+	0.539167i	$0.818739\pi$
$588$	0	0
$589$	−1477.57	−0.103366
$590$	−2324.40	−0.162194
$591$	−14671.6	−1.02116
$592$	1832.94	0.127252
$593$	10778.0	0.746373	0.373186	−	0.927756i	$-0.378265\pi$
$593$	10778.0	0.746373	0.373186	+	0.927756i	$0.378265\pi$
$594$	350.205	0.0241904
$595$	0	0
$596$	2482.12	0.170590
$597$	10628.6	0.728639
$598$	−9607.79	−0.657009
$599$	7597.58	0.518245	0.259122	−	0.965845i	$-0.416567\pi$
$599$	7597.58	0.518245	0.259122	+	0.965845i	$0.416567\pi$
$600$	2495.29	0.169783
$601$	−19956.1	−1.35445	−0.677225	−	0.735776i	$-0.736818\pi$
$601$	−19956.1	−1.35445	−0.677225	+	0.735776i	$0.736818\pi$
$602$	0	0
$603$	104.821	0.00707899
$604$	−7757.06	−0.522567
$605$	5910.81	0.397204
$606$	−7838.33	−0.525430
$607$	236.311	0.0158016	0.00790079	−	0.999969i	$-0.497485\pi$
$607$	236.311	0.0158016	0.00790079	+	0.999969i	$0.497485\pi$
$608$	161.722	0.0107873
$609$	0	0
$610$	−6889.85	−0.457314
$611$	15644.0	1.03582
$612$	−2936.03	−0.193925
$613$	26414.9	1.74044	0.870219	−	0.492664i	$-0.163977\pi$
$613$	26414.9	1.74044	0.870219	+	0.492664i	$0.163977\pi$
$614$	−8266.94	−0.543365
$615$	2223.26	0.145773
$616$	0	0
$617$	18473.6	1.20538	0.602689	−	0.797976i	$-0.294096\pi$
$617$	18473.6	1.20538	0.602689	+	0.797976i	$0.294096\pi$
$618$	−4553.85	−0.296412
$619$	−16047.9	−1.04204	−0.521018	−	0.853546i	$-0.674448\pi$
$619$	−16047.9	−1.04204	−0.521018	+	0.853546i	$0.674448\pi$
$620$	5362.94	0.347388
$621$	−2868.74	−0.185376
$622$	−10126.5	−0.652788
$623$	0	0
$624$	2170.23	0.139229
$625$	8181.20	0.523597
$626$	−14823.1	−0.946407
$627$	98.3264	0.00626280
$628$	1651.37	0.104931
$629$	−9342.97	−0.592255
$630$	0	0
$631$	−15065.7	−0.950487	−0.475243	−	0.879854i	$-0.657640\pi$
$631$	−15065.7	−0.950487	−0.475243	+	0.879854i	$0.657640\pi$
$632$	2.11255	0.000132963 0
$633$	12868.5	0.808020
$634$	−13474.1	−0.844046
$635$	−110.861	−0.00692816
$636$	−4866.35	−0.303401
$637$	0	0
$638$	3477.82	0.215812
$639$	−6134.95	−0.379804
$640$	−586.981	−0.0362538
$641$	−31198.4	−1.92241	−0.961203	−	0.275842i	$-0.911043\pi$
$641$	−31198.4	−1.92241	−0.961203	+	0.275842i	$0.911043\pi$
$642$	−7575.08	−0.465677
$643$	12497.9	0.766517	0.383259	−	0.923641i	$-0.374802\pi$
$643$	12497.9	0.766517	0.383259	+	0.923641i	$0.374802\pi$
$644$	0	0
$645$	−6483.75	−0.395810
$646$	−824.343	−0.0502064
$647$	9929.72	0.603366	0.301683	−	0.953408i	$-0.402452\pi$
$647$	9929.72	0.603366	0.301683	+	0.953408i	$0.402452\pi$
$648$	648.000	0.0392837
$649$	−1643.60	−0.0994099
$650$	9401.68	0.567330
$651$	0	0
$652$	−15629.8	−0.938817
$653$	−8145.58	−0.488149	−0.244075	−	0.969756i	$-0.578484\pi$
$653$	−8145.58	−0.488149	−0.244075	+	0.969756i	$0.578484\pi$
$654$	12633.2	0.755345
$655$	7252.55	0.432642
$656$	2585.68	0.153893
$657$	−6169.11	−0.366332
$658$	0	0
$659$	−16975.8	−1.00347	−0.501733	−	0.865022i	$-0.667304\pi$
$659$	−16975.8	−1.00347	−0.501733	+	0.865022i	$0.667304\pi$
$660$	−356.881	−0.0210479
$661$	−20637.8	−1.21440	−0.607199	−	0.794550i	$-0.707707\pi$
$661$	−20637.8	−1.21440	−0.607199	+	0.794550i	$0.707707\pi$
$662$	22351.9	1.31228
$663$	−11062.3	−0.647999
$664$	3497.10	0.204388
$665$	0	0
$666$	2062.05	0.119974
$667$	−28489.0	−1.65382
$668$	5145.66	0.298041
$669$	17387.2	1.00482
$670$	−106.819	−0.00615937
$671$	−4871.86	−0.280292
$672$	0	0
$673$	−2150.29	−0.123161	−0.0615807	−	0.998102i	$-0.519614\pi$
$673$	−2150.29	−0.123161	−0.0615807	+	0.998102i	$0.519614\pi$
$674$	18759.6	1.07209
$675$	2807.21	0.160073
$676$	−611.065	−0.0347670
$677$	27783.4	1.57726	0.788628	−	0.614871i	$-0.210792\pi$
$677$	27783.4	1.57726	0.788628	+	0.614871i	$0.210792\pi$
$678$	−9214.58	−0.521952
$679$	0	0
$680$	2992.00	0.168732
$681$	12312.1	0.692807
$682$	3792.17	0.212918
$683$	18181.8	1.01860	0.509302	−	0.860588i	$-0.329904\pi$
$683$	18181.8	1.01860	0.509302	+	0.860588i	$0.329904\pi$
$684$	181.938	0.0101704
$685$	3417.27	0.190609
$686$	0	0
$687$	−3890.49	−0.216058
$688$	−7540.70	−0.417858
$689$	−18335.3	−1.01381
$690$	2923.43	0.161294
$691$	−23935.1	−1.31771	−0.658853	−	0.752272i	$-0.728958\pi$
$691$	−23935.1	−1.31771	−0.658853	+	0.752272i	$0.728958\pi$
$692$	5005.02	0.274946
$693$	0	0
$694$	11362.9	0.621513
$695$	−6299.02	−0.343792
$696$	6435.17	0.350466
$697$	−13179.9	−0.716249
$698$	1408.50	0.0763789
$699$	4435.00	0.239982
$700$	0	0
$701$	−20627.2	−1.11138	−0.555691	−	0.831389i	$-0.687546\pi$
$701$	−20627.2	−1.11138	−0.555691	+	0.831389i	$0.687546\pi$
$702$	2441.51	0.131266
$703$	578.958	0.0310609
$704$	−415.058	−0.0222203
$705$	−4760.10	−0.254292
$706$	8569.93	0.456846
$707$	0	0
$708$	−3041.23	−0.161436
$709$	−6584.64	−0.348789	−0.174394	−	0.984676i	$-0.555797\pi$
$709$	−6584.64	−0.348789	−0.174394	+	0.984676i	$0.555797\pi$
$710$	6251.90	0.330464
$711$	2.37662	0.000125359 0
$712$	468.101	0.0246388
$713$	−31064.0	−1.63163
$714$	0	0
$715$	−1344.65	−0.0703313
$716$	14494.1	0.756520
$717$	11330.8	0.590174
$718$	9322.54	0.484560
$719$	−170.886	−0.00886366	−0.00443183	−	0.999990i	$-0.501411\pi$
$719$	−170.886	−0.00886366	−0.00443183	+	0.999990i	$0.501411\pi$
$720$	−660.353	−0.0341804
$721$	0	0
$722$	−13666.9	−0.704474
$723$	−11989.1	−0.616710
$724$	−726.908	−0.0373140
$725$	27877.8	1.42808
$726$	7733.65	0.395348
$727$	11127.5	0.567671	0.283836	−	0.958873i	$-0.408393\pi$
$727$	11127.5	0.567671	0.283836	+	0.958873i	$0.408393\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	6286.72	0.318742
$731$	38437.0	1.94479
$732$	−9014.61	−0.455177
$733$	22575.9	1.13760	0.568800	−	0.822476i	$-0.307408\pi$
$733$	22575.9	1.13760	0.568800	+	0.822476i	$0.307408\pi$
$734$	13870.6	0.697511
$735$	0	0
$736$	3399.99	0.170279
$737$	−75.5325	−0.00377513
$738$	2908.89	0.145092
$739$	−22936.4	−1.14172	−0.570860	−	0.821048i	$-0.693390\pi$
$739$	−22936.4	−1.14172	−0.570860	+	0.821048i	$0.693390\pi$
$740$	−2101.36	−0.104389
$741$	685.499	0.0339844
$742$	0	0
$743$	16973.4	0.838081	0.419041	−	0.907967i	$-0.362366\pi$
$743$	16973.4	0.838081	0.419041	+	0.907967i	$0.362366\pi$
$744$	7016.82	0.345765
$745$	−2845.62	−0.139940
$746$	−6162.21	−0.302432
$747$	3934.23	0.192699
$748$	2115.66	0.103418
$749$	0	0
$750$	−6300.06	−0.306728
$751$	−21197.9	−1.02999	−0.514994	−	0.857194i	$-0.672206\pi$
$751$	−21197.9	−1.02999	−0.514994	+	0.857194i	$0.672206\pi$
$752$	−5536.07	−0.268457
$753$	16270.8	0.787436
$754$	24246.2	1.17108
$755$	8893.05	0.428677
$756$	0	0
$757$	−7962.24	−0.382289	−0.191144	−	0.981562i	$-0.561220\pi$
$757$	−7962.24	−0.382289	−0.191144	+	0.981562i	$0.561220\pi$
$758$	1883.65	0.0902604
$759$	2067.18	0.0988588
$760$	−185.406	−0.00884919
$761$	−26856.2	−1.27928	−0.639642	−	0.768673i	$-0.720917\pi$
$761$	−26856.2	−1.27928	−0.639642	+	0.768673i	$0.720917\pi$
$762$	−145.049	−0.00689578
$763$	0	0
$764$	5925.12	0.280580
$765$	3366.00	0.159082
$766$	1355.05	0.0639165
$767$	−11458.6	−0.539436
$768$	−768.000	−0.0360844
$769$	12183.6	0.571331	0.285666	−	0.958329i	$-0.407785\pi$
$769$	12183.6	0.571331	0.285666	+	0.958329i	$0.407785\pi$
$770$	0	0
$771$	17892.7	0.835783
$772$	−1426.83	−0.0665192
$773$	17455.2	0.812187	0.406093	−	0.913832i	$-0.366891\pi$
$773$	17455.2	0.812187	0.406093	+	0.913832i	$0.366891\pi$
$774$	−8483.28	−0.393960
$775$	30397.6	1.40892
$776$	10240.7	0.473738
$777$	0	0
$778$	−23730.8	−1.09356
$779$	816.724	0.0375638
$780$	−2488.06	−0.114214
$781$	4420.76	0.202545
$782$	−17330.7	−0.792512
$783$	7239.56	0.330423
$784$	0	0
$785$	−1893.21	−0.0860785
$786$	9489.16	0.430620
$787$	−30981.0	−1.40324	−0.701622	−	0.712549i	$-0.747540\pi$
$787$	−30981.0	−1.40324	−0.701622	+	0.712549i	$0.747540\pi$
$788$	19562.1	0.884355
$789$	−15498.0	−0.699296
$790$	−2.42193	−0.000109074 0
$791$	0	0
$792$	−466.940	−0.0209495
$793$	−33964.9	−1.52097
$794$	10281.5	0.459544
$795$	5579.01	0.248889
$796$	−14171.4	−0.631020
$797$	10517.6	0.467446	0.233723	−	0.972303i	$-0.424909\pi$
$797$	10517.6	0.467446	0.233723	+	0.972303i	$0.424909\pi$
$798$	0	0
$799$	28218.8	1.24945
$800$	−3327.06	−0.147037
$801$	526.614	0.0232297
$802$	−24764.0	−1.09033
$803$	4445.38	0.195360
$804$	−139.761	−0.00613059
$805$	0	0
$806$	26437.7	1.15537
$807$	11649.9	0.508172
$808$	10451.1	0.455036
$809$	−41778.4	−1.81564	−0.907819	−	0.419361i	$-0.862254\pi$
$809$	−41778.4	−1.81564	−0.907819	+	0.419361i	$0.862254\pi$
$810$	−742.897	−0.0322256
$811$	12935.4	0.560079	0.280039	−	0.959988i	$-0.409652\pi$
$811$	12935.4	0.560079	0.280039	+	0.959988i	$0.409652\pi$
$812$	0	0
$813$	16583.0	0.715363
$814$	−1485.89	−0.0639807
$815$	17918.7	0.770140
$816$	3914.70	0.167944
$817$	−2381.83	−0.101995
$818$	31751.3	1.35716
$819$	0	0
$820$	−2964.35	−0.126243
$821$	−14499.2	−0.616354	−0.308177	−	0.951329i	$-0.599719\pi$
$821$	−14499.2	−0.616354	−0.308177	+	0.951329i	$0.599719\pi$
$822$	4471.13	0.189718
$823$	−11977.1	−0.507287	−0.253643	−	0.967298i	$-0.581629\pi$
$823$	−11977.1	−0.507287	−0.253643	+	0.967298i	$0.581629\pi$
$824$	6071.80	0.256700
$825$	−2022.84	−0.0853649
$826$	0	0
$827$	27613.5	1.16108	0.580541	−	0.814231i	$-0.302841\pi$
$827$	27613.5	1.16108	0.580541	+	0.814231i	$0.302841\pi$
$828$	3824.99	0.160541
$829$	677.836	0.0283983	0.0141992	−	0.999899i	$-0.495480\pi$
$829$	677.836	0.0283983	0.0141992	+	0.999899i	$0.495480\pi$
$830$	−4009.23	−0.167666
$831$	−6804.36	−0.284044
$832$	−2893.65	−0.120576
$833$	0	0
$834$	−8241.58	−0.342185
$835$	−5899.22	−0.244492
$836$	−131.102	−0.00542375
$837$	7893.92	0.325990
$838$	32223.8	1.32835
$839$	−42209.6	−1.73687	−0.868436	−	0.495801i	$-0.834874\pi$
$839$	−42209.6	−1.73687	−0.868436	+	0.495801i	$0.834874\pi$
$840$	0	0
$841$	47505.8	1.94784
$842$	17383.2	0.711476
$843$	−2176.97	−0.0889428
$844$	−17158.0	−0.699765
$845$	700.553	0.0285204
$846$	−6228.08	−0.253104
$847$	0	0
$848$	6488.46	0.262753
$849$	12711.0	0.513828
$850$	16958.9	0.684337
$851$	12171.8	0.490299
$852$	8179.93	0.328920
$853$	2796.45	0.112249	0.0561247	−	0.998424i	$-0.482126\pi$
$853$	2796.45	0.112249	0.0561247	+	0.998424i	$0.482126\pi$
$854$	0	0
$855$	−208.582	−0.00834310
$856$	10100.1	0.403288
$857$	−23181.1	−0.923979	−0.461989	−	0.886886i	$-0.652864\pi$
$857$	−23181.1	−0.923979	−0.461989	+	0.886886i	$0.652864\pi$
$858$	−1759.32	−0.0700026
$859$	11897.5	0.472569	0.236285	−	0.971684i	$-0.424070\pi$
$859$	11897.5	0.472569	0.236285	+	0.971684i	$0.424070\pi$
$860$	8645.01	0.342782
$861$	0	0
$862$	−8390.21	−0.331521
$863$	−29815.9	−1.17607	−0.588033	−	0.808837i	$-0.700098\pi$
$863$	−29815.9	−1.17607	−0.588033	+	0.808837i	$0.700098\pi$
$864$	−864.000	−0.0340207
$865$	−5737.99	−0.225546
$866$	10853.1	0.425869
$867$	−5215.31	−0.204292
$868$	0	0
$869$	−1.71256	−6.68523e−5 0
$870$	−7377.58	−0.287498
$871$	−526.587	−0.0204853
$872$	−16844.2	−0.654148
$873$	11520.8	0.446644
$874$	1073.94	0.0415634
$875$	0	0
$876$	8225.48	0.317253
$877$	−10338.8	−0.398082	−0.199041	−	0.979991i	$-0.563783\pi$
$877$	−10338.8	−0.398082	−0.199041	+	0.979991i	$0.563783\pi$
$878$	7542.48	0.289916
$879$	−13121.3	−0.503495
$880$	475.842	0.0182280
$881$	−24140.2	−0.923160	−0.461580	−	0.887099i	$-0.652717\pi$
$881$	−24140.2	−0.923160	−0.461580	+	0.887099i	$0.652717\pi$
$882$	0	0
$883$	12997.6	0.495361	0.247681	−	0.968842i	$-0.420332\pi$
$883$	12997.6	0.495361	0.247681	+	0.968842i	$0.420332\pi$
$884$	14749.7	0.561183
$885$	3486.61	0.132430
$886$	−11860.6	−0.449734
$887$	−45266.6	−1.71353	−0.856766	−	0.515705i	$-0.827530\pi$
$887$	−45266.6	−1.71353	−0.856766	+	0.515705i	$0.827530\pi$
$888$	−2749.40	−0.103901
$889$	0	0
$890$	−536.653	−0.0202120
$891$	−525.308	−0.0197514
$892$	−23182.9	−0.870204
$893$	−1748.64	−0.0655276
$894$	−3723.18	−0.139286
$895$	−16616.7	−0.620596
$896$	0	0
$897$	14411.7	0.536446
$898$	−1058.13	−0.0393210
$899$	78393.1	2.90829
$900$	−3742.94	−0.138627
$901$	−33073.5	−1.22290
$902$	−2096.11	−0.0773756
$903$	0	0
$904$	12286.1	0.452024
$905$	833.361	0.0306098
$906$	11635.6	0.426674
$907$	−27766.5	−1.01651	−0.508253	−	0.861208i	$-0.669708\pi$
$907$	−27766.5	−1.01651	−0.508253	+	0.861208i	$0.669708\pi$
$908$	−16416.2	−0.599989
$909$	11757.5	0.429012
$910$	0	0
$911$	18531.2	0.673948	0.336974	−	0.941514i	$-0.390597\pi$
$911$	18531.2	0.673948	0.336974	+	0.941514i	$0.390597\pi$
$912$	−242.584	−0.00880783
$913$	−2834.96	−0.102764
$914$	20114.4	0.727925
$915$	10334.8	0.373395
$916$	5187.33	0.187111
$917$	0	0
$918$	4404.04	0.158339
$919$	−18093.4	−0.649452	−0.324726	−	0.945808i	$-0.605272\pi$
$919$	−18093.4	−0.649452	−0.324726	+	0.945808i	$0.605272\pi$
$920$	−3897.91	−0.139685
$921$	12400.4	0.443656
$922$	10020.6	0.357930
$923$	30820.1	1.09908
$924$	0	0
$925$	−11910.7	−0.423375
$926$	−14248.8	−0.505662
$927$	6830.77	0.242019
$928$	−8580.23	−0.303513
$929$	−10622.5	−0.375149	−0.187574	−	0.982250i	$-0.560063\pi$
$929$	−10622.5	−0.375149	−0.187574	+	0.982250i	$0.560063\pi$
$930$	−8044.41	−0.283642
$931$	0	0
$932$	−5913.34	−0.207830
$933$	15189.7	0.532999
$934$	−15002.9	−0.525599
$935$	−2425.50	−0.0848366
$936$	−3255.35	−0.113680
$937$	−16057.6	−0.559851	−0.279925	−	0.960022i	$-0.590310\pi$
$937$	−16057.6	−0.559851	−0.279925	+	0.960022i	$0.590310\pi$
$938$	0	0
$939$	22234.7	0.772738
$940$	6346.81	0.220223
$941$	−55153.3	−1.91068	−0.955338	−	0.295516i	$-0.904508\pi$
$941$	−55153.3	−1.91068	−0.955338	+	0.295516i	$0.904508\pi$
$942$	−2477.06	−0.0856762
$943$	17170.5	0.592947
$944$	4054.97	0.139807
$945$	0	0
$946$	6112.94	0.210094
$947$	18785.7	0.644619	0.322309	−	0.946634i	$-0.395541\pi$
$947$	18785.7	0.644619	0.322309	+	0.946634i	$0.395541\pi$
$948$	−3.16882	−0.000108564 0
$949$	30991.7	1.06010
$950$	−1050.90	−0.0358901
$951$	20211.2	0.689161
$952$	0	0
$953$	−36499.4	−1.24064	−0.620321	−	0.784348i	$-0.712998\pi$
$953$	−36499.4	−1.24064	−0.620321	+	0.784348i	$0.712998\pi$
$954$	7299.52	0.247726
$955$	−6792.83	−0.230168
$956$	−15107.7	−0.511106
$957$	−5216.74	−0.176210
$958$	16347.6	0.551323
$959$	0	0
$960$	880.471	0.0296011
$961$	55687.8	1.86928
$962$	−10359.1	−0.347184
$963$	11362.6	0.380224
$964$	15985.5	0.534086
$965$	1635.79	0.0545677
$966$	0	0
$967$	26059.9	0.866627	0.433314	−	0.901243i	$-0.357344\pi$
$967$	26059.9	0.866627	0.433314	+	0.901243i	$0.357344\pi$
$968$	−10311.5	−0.342381
$969$	1236.51	0.0409934
$970$	−11740.4	−0.388622
$971$	−21689.0	−0.716820	−0.358410	−	0.933564i	$-0.616681\pi$
$971$	−21689.0	−0.716820	−0.358410	+	0.933564i	$0.616681\pi$
$972$	−972.000	−0.0320750
$973$	0	0
$974$	−23937.6	−0.787484
$975$	−14102.5	−0.463223
$976$	12019.5	0.394195
$977$	2119.19	0.0693950	0.0346975	−	0.999398i	$-0.488953\pi$
$977$	2119.19	0.0693950	0.0346975	+	0.999398i	$0.488953\pi$
$978$	23444.6	0.766541
$979$	−379.471	−0.0123881
$980$	0	0
$981$	−18949.7	−0.616737
$982$	4159.92	0.135182
$983$	48504.1	1.57380	0.786898	−	0.617083i	$-0.211686\pi$
$983$	48504.1	1.57380	0.786898	+	0.617083i	$0.211686\pi$
$984$	−3878.52	−0.125653
$985$	−22426.9	−0.725463
$986$	43735.7	1.41261
$987$	0	0
$988$	−913.998	−0.0294313
$989$	−50074.8	−1.61000
$990$	535.322	0.0171855
$991$	2043.84	0.0655144	0.0327572	−	0.999463i	$-0.489571\pi$
$991$	2043.84	0.0655144	0.0327572	+	0.999463i	$0.489571\pi$
$992$	−9355.76	−0.299441
$993$	−33527.8	−1.07147
$994$	0	0
$995$	16246.8	0.517645
$996$	−5245.65	−0.166882
$997$	26738.9	0.849378	0.424689	−	0.905339i	$-0.360383\pi$
$997$	26738.9	0.849378	0.424689	+	0.905339i	$0.360383\pi$
$998$	25668.8	0.814161
$999$	−3093.08	−0.0979586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.a.l.1.2	✓	2
3.2	odd	2		882.4.a.bb.1.1		2
4.3	odd	2		2352.4.a.bw.1.2		2
7.2	even	3		294.4.e.m.67.1		4
7.3	odd	6		294.4.e.k.79.2		4
7.4	even	3		294.4.e.m.79.1		4
7.5	odd	6		294.4.e.k.67.2		4
7.6	odd	2		294.4.a.o.1.1	yes	2
21.2	odd	6		882.4.g.be.361.2		4
21.5	even	6		882.4.g.bk.361.1		4
21.11	odd	6		882.4.g.be.667.2		4
21.17	even	6		882.4.g.bk.667.1		4
21.20	even	2		882.4.a.t.1.2		2
28.27	even	2		2352.4.a.bu.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.l.1.2	✓	2	1.1	even	1	trivial
294.4.a.o.1.1	yes	2	7.6	odd	2
294.4.e.k.67.2		4	7.5	odd	6
294.4.e.k.79.2		4	7.3	odd	6
294.4.e.m.67.1		4	7.2	even	3
294.4.e.m.79.1		4	7.4	even	3
882.4.a.t.1.2		2	21.20	even	2
882.4.a.bb.1.1		2	3.2	odd	2
882.4.g.be.361.2		4	21.2	odd	6
882.4.g.be.667.2		4	21.11	odd	6
882.4.g.bk.361.1		4	21.5	even	6
882.4.g.bk.667.1		4	21.17	even	6
2352.4.a.bu.1.1		2	28.27	even	2
2352.4.a.bw.1.2		2	4.3	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.58579 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -4.58579 q^{5} -6.00000 q^{6} +8.00000 q^{8} +9.00000 q^{9} -9.17157 q^{10} -6.48528 q^{11} -12.0000 q^{12} -45.2132 q^{13} +13.7574 q^{15} +16.0000 q^{16} -81.5563 q^{17} +18.0000 q^{18} +5.05382 q^{19} -18.3431 q^{20} -12.9706 q^{22} +106.250 q^{23} -24.0000 q^{24} -103.971 q^{25} -90.4264 q^{26} -27.0000 q^{27} -268.132 q^{29} +27.5147 q^{30} -292.368 q^{31} +32.0000 q^{32} +19.4558 q^{33} -163.113 q^{34} +36.0000 q^{36} +114.558 q^{37} +10.1076 q^{38} +135.640 q^{39} -36.6863 q^{40} +161.605 q^{41} -471.294 q^{43} -25.9411 q^{44} -41.2721 q^{45} +212.500 q^{46} -346.004 q^{47} -48.0000 q^{48} -207.941 q^{50} +244.669 q^{51} -180.853 q^{52} +405.529 q^{53} -54.0000 q^{54} +29.7401 q^{55} -15.1615 q^{57} -536.264 q^{58} +253.436 q^{59} +55.0294 q^{60} +751.217 q^{61} -584.735 q^{62} +64.0000 q^{64} +207.338 q^{65} +38.9117 q^{66} +11.6468 q^{67} -326.225 q^{68} -318.749 q^{69} -681.661 q^{71} +72.0000 q^{72} -685.457 q^{73} +229.117 q^{74} +311.912 q^{75} +20.2153 q^{76} +271.279 q^{78} +0.264069 q^{79} -73.3726 q^{80} +81.0000 q^{81} +323.210 q^{82} +437.137 q^{83} +374.000 q^{85} -942.587 q^{86} +804.396 q^{87} -51.8823 q^{88} +58.5126 q^{89} -82.5442 q^{90} +424.999 q^{92} +877.103 q^{93} -692.008 q^{94} -23.1758 q^{95} -96.0000 q^{96} +1280.09 q^{97} -58.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 12 q^{5} - 12 q^{6} + 16 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 12 * q^5 - 12 * q^6 + 16 * q^8 + 18 * q^9	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 12 q^{5} - 12 q^{6} + 16 q^{8} + 18 q^{9} - 24 q^{10} + 4 q^{11} - 24 q^{12} - 48 q^{13} + 36 q^{15} + 32 q^{16} - 132 q^{17} + 36 q^{18} - 120 q^{19} - 48 q^{20} + 8 q^{22} - 76 q^{23} - 48 q^{24} - 174 q^{25} - 96 q^{26} - 54 q^{27} - 112 q^{29} + 72 q^{30} - 432 q^{31} + 64 q^{32} - 12 q^{33} - 264 q^{34} + 72 q^{36} - 280 q^{37} - 240 q^{38} + 144 q^{39} - 96 q^{40} - 36 q^{41} - 128 q^{43} + 16 q^{44} - 108 q^{45} - 152 q^{46} + 264 q^{47} - 96 q^{48} - 348 q^{50} + 396 q^{51} - 192 q^{52} + 268 q^{53} - 108 q^{54} - 48 q^{55} + 360 q^{57} - 224 q^{58} - 336 q^{59} + 144 q^{60} + 504 q^{61} - 864 q^{62} + 128 q^{64} + 228 q^{65} - 24 q^{66} - 384 q^{67} - 528 q^{68} + 228 q^{69} - 396 q^{71} + 144 q^{72} + 312 q^{73} - 560 q^{74} + 522 q^{75} - 480 q^{76} + 288 q^{78} - 848 q^{79} - 192 q^{80} + 162 q^{81} - 72 q^{82} + 648 q^{83} + 748 q^{85} - 256 q^{86} + 336 q^{87} + 32 q^{88} + 612 q^{89} - 216 q^{90} - 304 q^{92} + 1296 q^{93} + 528 q^{94} + 904 q^{95} - 192 q^{96} + 2184 q^{97} + 36 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 12 * q^5 - 12 * q^6 + 16 * q^8 + 18 * q^9 - 24 * q^10 + 4 * q^11 - 24 * q^12 - 48 * q^13 + 36 * q^15 + 32 * q^16 - 132 * q^17 + 36 * q^18 - 120 * q^19 - 48 * q^20 + 8 * q^22 - 76 * q^23 - 48 * q^24 - 174 * q^25 - 96 * q^26 - 54 * q^27 - 112 * q^29 + 72 * q^30 - 432 * q^31 + 64 * q^32 - 12 * q^33 - 264 * q^34 + 72 * q^36 - 280 * q^37 - 240 * q^38 + 144 * q^39 - 96 * q^40 - 36 * q^41 - 128 * q^43 + 16 * q^44 - 108 * q^45 - 152 * q^46 + 264 * q^47 - 96 * q^48 - 348 * q^50 + 396 * q^51 - 192 * q^52 + 268 * q^53 - 108 * q^54 - 48 * q^55 + 360 * q^57 - 224 * q^58 - 336 * q^59 + 144 * q^60 + 504 * q^61 - 864 * q^62 + 128 * q^64 + 228 * q^65 - 24 * q^66 - 384 * q^67 - 528 * q^68 + 228 * q^69 - 396 * q^71 + 144 * q^72 + 312 * q^73 - 560 * q^74 + 522 * q^75 - 480 * q^76 + 288 * q^78 - 848 * q^79 - 192 * q^80 + 162 * q^81 - 72 * q^82 + 648 * q^83 + 748 * q^85 - 256 * q^86 + 336 * q^87 + 32 * q^88 + 612 * q^89 - 216 * q^90 - 304 * q^92 + 1296 * q^93 + 528 * q^94 + 904 * q^95 - 192 * q^96 + 2184 * q^97 + 36 * q^99

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