LMFDB - Embedded newform 275.6.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,6,Mod(1,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("275.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	275.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:	$44.1055504486$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 129x^{3} + 45x^{2} + 2924x - 5216 $ x^5 - x^4 - 129x^3 + 45x^2 + 2924*x - 5216
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.83289$ of defining polynomial
Character	$\chi$	$=$	275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83289 q^{2} -28.4084 q^{3} -28.6405 q^{4} -52.0695 q^{6} -92.2140 q^{7} -111.147 q^{8} +564.037 q^{9} +O(q^{10})$	\(q+1.83289 q^{2} -28.4084 q^{3} -28.6405 q^{4} -52.0695 q^{6} -92.2140 q^{7} -111.147 q^{8} +564.037 q^{9} -121.000 q^{11} +813.631 q^{12} +325.094 q^{13} -169.018 q^{14} +712.776 q^{16} -1245.73 q^{17} +1033.82 q^{18} +2290.92 q^{19} +2619.65 q^{21} -221.780 q^{22} +3929.24 q^{23} +3157.52 q^{24} +595.861 q^{26} -9120.16 q^{27} +2641.06 q^{28} +4414.55 q^{29} -6321.41 q^{31} +4863.15 q^{32} +3437.42 q^{33} -2283.28 q^{34} -16154.3 q^{36} -1016.44 q^{37} +4199.00 q^{38} -9235.39 q^{39} -17852.3 q^{41} +4801.53 q^{42} +4742.68 q^{43} +3465.50 q^{44} +7201.86 q^{46} +12272.3 q^{47} -20248.8 q^{48} -8303.58 q^{49} +35389.1 q^{51} -9310.85 q^{52} +6965.89 q^{53} -16716.2 q^{54} +10249.3 q^{56} -65081.3 q^{57} +8091.39 q^{58} +2609.62 q^{59} -52063.8 q^{61} -11586.4 q^{62} -52012.1 q^{63} -13895.2 q^{64} +6300.40 q^{66} +28472.0 q^{67} +35678.3 q^{68} -111623. q^{69} +61776.9 q^{71} -62691.3 q^{72} -27809.5 q^{73} -1863.03 q^{74} -65613.1 q^{76} +11157.9 q^{77} -16927.5 q^{78} +35035.8 q^{79} +122028. q^{81} -32721.3 q^{82} -86352.7 q^{83} -75028.2 q^{84} +8692.82 q^{86} -125410. q^{87} +13448.8 q^{88} -46993.8 q^{89} -29978.2 q^{91} -112535. q^{92} +179581. q^{93} +22493.8 q^{94} -138154. q^{96} +127650. q^{97} -15219.5 q^{98} -68248.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 9 q^{2} + 115 q^{4} - 237 q^{6} - 70 q^{7} - 753 q^{8} + 1059 q^{9}+O(q^{10}) $ 5 * q - 9 * q^2 + 115 * q^4 - 237 * q^6 - 70 * q^7 - 753 * q^8 + 1059 * q^9	\( 5 q - 9 q^{2} + 115 q^{4} - 237 q^{6} - 70 q^{7} - 753 q^{8} + 1059 q^{9} - 605 q^{11} + 1605 q^{12} - 1498 q^{13} + 2113 q^{14} + 4883 q^{16} - 3874 q^{17} - 5838 q^{18} + 882 q^{19} + 1092 q^{21} + 1089 q^{22} + 5344 q^{23} - 13119 q^{24} - 4478 q^{26} + 2160 q^{27} - 12565 q^{28} + 5318 q^{29} - 7916 q^{31} - 21385 q^{32} - 18605 q^{34} + 5628 q^{36} + 1788 q^{37} + 34421 q^{38} - 29760 q^{39} + 5854 q^{41} + 46725 q^{42} + 4364 q^{43} - 13915 q^{44} - 33834 q^{46} - 46452 q^{47} + 127545 q^{48} - 34217 q^{49} + 19842 q^{51} - 3222 q^{52} - 4412 q^{53} - 86535 q^{54} + 115575 q^{56} - 137160 q^{57} + 58221 q^{58} + 17896 q^{59} - 35930 q^{61} + 19627 q^{62} - 100980 q^{63} + 14779 q^{64} + 28677 q^{66} - 73136 q^{67} + 83409 q^{68} + 34296 q^{69} + 43612 q^{71} - 372276 q^{72} - 142306 q^{73} - 95609 q^{74} - 6617 q^{76} + 8470 q^{77} - 15750 q^{78} - 46504 q^{79} + 79101 q^{81} - 175798 q^{82} - 81604 q^{83} - 532533 q^{84} - 101788 q^{86} - 219750 q^{87} + 91113 q^{88} + 8664 q^{89} - 203380 q^{91} - 251174 q^{92} + 46470 q^{93} - 71458 q^{94} - 925479 q^{96} + 22230 q^{97} - 59962 q^{98} - 128139 q^{99}+O(q^{100}) \) 5 * q - 9 * q^2 + 115 * q^4 - 237 * q^6 - 70 * q^7 - 753 * q^8 + 1059 * q^9 - 605 * q^11 + 1605 * q^12 - 1498 * q^13 + 2113 * q^14 + 4883 * q^16 - 3874 * q^17 - 5838 * q^18 + 882 * q^19 + 1092 * q^21 + 1089 * q^22 + 5344 * q^23 - 13119 * q^24 - 4478 * q^26 + 2160 * q^27 - 12565 * q^28 + 5318 * q^29 - 7916 * q^31 - 21385 * q^32 - 18605 * q^34 + 5628 * q^36 + 1788 * q^37 + 34421 * q^38 - 29760 * q^39 + 5854 * q^41 + 46725 * q^42 + 4364 * q^43 - 13915 * q^44 - 33834 * q^46 - 46452 * q^47 + 127545 * q^48 - 34217 * q^49 + 19842 * q^51 - 3222 * q^52 - 4412 * q^53 - 86535 * q^54 + 115575 * q^56 - 137160 * q^57 + 58221 * q^58 + 17896 * q^59 - 35930 * q^61 + 19627 * q^62 - 100980 * q^63 + 14779 * q^64 + 28677 * q^66 - 73136 * q^67 + 83409 * q^68 + 34296 * q^69 + 43612 * q^71 - 372276 * q^72 - 142306 * q^73 - 95609 * q^74 - 6617 * q^76 + 8470 * q^77 - 15750 * q^78 - 46504 * q^79 + 79101 * q^81 - 175798 * q^82 - 81604 * q^83 - 532533 * q^84 - 101788 * q^86 - 219750 * q^87 + 91113 * q^88 + 8664 * q^89 - 203380 * q^91 - 251174 * q^92 + 46470 * q^93 - 71458 * q^94 - 925479 * q^96 + 22230 * q^97 - 59962 * q^98 - 128139 * 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 $

$2$	1.83289	0.324012	0.162006	−	0.986790i	$-0.448204\pi$
$2$	1.83289	0.324012	0.162006	+	0.986790i	$0.448204\pi$
$3$	−28.4084	−1.82240	−0.911200	−	0.411964i	$-0.864843\pi$
$3$	−28.4084	−1.82240	−0.911200	+	0.411964i	$0.864843\pi$
$4$	−28.6405	−0.895016
$5$	0	0
$5$	0	0
$6$	−52.0695	−0.590480
$7$	−92.2140	−0.711298	−0.355649	−	0.934620i	$-0.615740\pi$
$7$	−92.2140	−0.711298	−0.355649	+	0.934620i	$0.615740\pi$
$8$	−111.147	−0.614008
$9$	564.037	2.32114
$10$	0	0
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	813.631	1.63108
$13$	325.094	0.533519	0.266760	−	0.963763i	$-0.414047\pi$
$13$	325.094	0.533519	0.266760	+	0.963763i	$0.414047\pi$
$14$	−169.018	−0.230469
$15$	0	0
$16$	712.776	0.696070
$17$	−1245.73	−1.04544	−0.522722	−	0.852503i	$-0.675083\pi$
$17$	−1245.73	−1.04544	−0.522722	+	0.852503i	$0.675083\pi$
$18$	1033.82	0.752078
$19$	2290.92	1.45588	0.727940	−	0.685641i	$-0.240478\pi$
$19$	2290.92	1.45588	0.727940	+	0.685641i	$0.240478\pi$
$20$	0	0
$21$	2619.65	1.29627
$22$	−221.780	−0.0976933
$23$	3929.24	1.54878	0.774389	−	0.632710i	$-0.218058\pi$
$23$	3929.24	1.54878	0.774389	+	0.632710i	$0.218058\pi$
$24$	3157.52	1.11897
$25$	0	0
$26$	595.861	0.172867
$27$	−9120.16	−2.40765
$28$	2641.06	0.636623
$29$	4414.55	0.974746	0.487373	−	0.873194i	$-0.337955\pi$
$29$	4414.55	0.974746	0.487373	+	0.873194i	$0.337955\pi$
$30$	0	0
$31$	−6321.41	−1.18143	−0.590717	−	0.806879i	$-0.701155\pi$
$31$	−6321.41	−1.18143	−0.590717	+	0.806879i	$0.701155\pi$
$32$	4863.15	0.839543
$33$	3437.42	0.549474
$34$	−2283.28	−0.338737
$35$	0	0
$36$	−16154.3	−2.07746
$37$	−1016.44	−0.122061	−0.0610307	−	0.998136i	$-0.519439\pi$
$37$	−1016.44	−0.122061	−0.0610307	+	0.998136i	$0.519439\pi$
$38$	4199.00	0.471723
$39$	−9235.39	−0.972286
$40$	0	0
$41$	−17852.3	−1.65858	−0.829288	−	0.558822i	$-0.811253\pi$
$41$	−17852.3	−1.65858	−0.829288	+	0.558822i	$0.811253\pi$
$42$	4801.53	0.420007
$43$	4742.68	0.391159	0.195579	−	0.980688i	$-0.437341\pi$
$43$	4742.68	0.391159	0.195579	+	0.980688i	$0.437341\pi$
$44$	3465.50	0.269858
$45$	0	0
$46$	7201.86	0.501823
$47$	12272.3	0.810368	0.405184	−	0.914235i	$-0.367207\pi$
$47$	12272.3	0.810368	0.405184	+	0.914235i	$0.367207\pi$
$48$	−20248.8	−1.26852
$49$	−8303.58	−0.494055
$50$	0	0
$51$	35389.1	1.90522
$52$	−9310.85	−0.477508
$53$	6965.89	0.340633	0.170317	−	0.985389i	$-0.445521\pi$
$53$	6965.89	0.340633	0.170317	+	0.985389i	$0.445521\pi$
$54$	−16716.2	−0.780107
$55$	0	0
$56$	10249.3	0.436743
$57$	−65081.3	−2.65319
$58$	8091.39	0.315830
$59$	2609.62	0.0975993	0.0487997	−	0.998809i	$-0.484460\pi$
$59$	2609.62	0.0975993	0.0487997	+	0.998809i	$0.484460\pi$
$60$	0	0
$61$	−52063.8	−1.79148	−0.895739	−	0.444581i	$-0.853353\pi$
$61$	−52063.8	−1.79148	−0.895739	+	0.444581i	$0.853353\pi$
$62$	−11586.4	−0.382799
$63$	−52012.1	−1.65102
$64$	−13895.2	−0.424048
$65$	0	0
$66$	6300.40	0.178036
$67$	28472.0	0.774874	0.387437	−	0.921896i	$-0.373361\pi$
$67$	28472.0	0.774874	0.387437	+	0.921896i	$0.373361\pi$
$68$	35678.3	0.935690
$69$	−111623.	−2.82249
$70$	0	0
$71$	61776.9	1.45439	0.727194	−	0.686432i	$-0.240824\pi$
$71$	61776.9	1.45439	0.727194	+	0.686432i	$0.240824\pi$
$72$	−62691.3	−1.42520
$73$	−27809.5	−0.610782	−0.305391	−	0.952227i	$-0.598787\pi$
$73$	−27809.5	−0.610782	−0.305391	+	0.952227i	$0.598787\pi$
$74$	−1863.03	−0.0395494
$75$	0	0
$76$	−65613.1	−1.30304
$77$	11157.9	0.214465
$78$	−16927.5	−0.315032
$79$	35035.8	0.631603	0.315801	−	0.948825i	$-0.397727\pi$
$79$	35035.8	0.631603	0.315801	+	0.948825i	$0.397727\pi$
$80$	0	0
$81$	122028.	2.06656
$82$	−32721.3	−0.537398
$83$	−86352.7	−1.37588	−0.687940	−	0.725767i	$-0.741485\pi$
$83$	−86352.7	−1.37588	−0.687940	+	0.725767i	$0.741485\pi$
$84$	−75028.2	−1.16018
$85$	0	0
$86$	8692.82	0.126740
$87$	−125410.	−1.77638
$88$	13448.8	0.185130
$89$	−46993.8	−0.628877	−0.314439	−	0.949278i	$-0.601816\pi$
$89$	−46993.8	−0.628877	−0.314439	+	0.949278i	$0.601816\pi$
$90$	0	0
$91$	−29978.2	−0.379491
$92$	−112535.	−1.38618
$93$	179581.	2.15304
$94$	22493.8	0.262569
$95$	0	0
$96$	−138154.	−1.52998
$97$	127650.	1.37750	0.688752	−	0.724997i	$-0.258159\pi$
$97$	127650.	1.37750	0.688752	+	0.724997i	$0.258159\pi$
$98$	−15219.5	−0.160080
$99$	−68248.5	−0.699850
$100$	0	0
$101$	90175.9	0.879604	0.439802	−	0.898095i	$-0.355049\pi$
$101$	90175.9	0.879604	0.439802	+	0.898095i	$0.355049\pi$
$102$	64864.4	0.617314
$103$	162102.	1.50555	0.752774	−	0.658279i	$-0.228715\pi$
$103$	162102.	1.50555	0.752774	+	0.658279i	$0.228715\pi$
$104$	−36133.3	−0.327585
$105$	0	0
$106$	12767.7	0.110369
$107$	−72380.8	−0.611172	−0.305586	−	0.952164i	$-0.598852\pi$
$107$	−72380.8	−0.611172	−0.305586	+	0.952164i	$0.598852\pi$
$108$	261206.	2.15488
$109$	127763.	1.03000	0.515001	−	0.857189i	$-0.327791\pi$
$109$	127763.	1.03000	0.515001	+	0.857189i	$0.327791\pi$
$110$	0	0
$111$	28875.5	0.222445
$112$	−65727.9	−0.495113
$113$	−180703.	−1.33128	−0.665638	−	0.746275i	$-0.731841\pi$
$113$	−180703.	−1.33128	−0.665638	+	0.746275i	$0.731841\pi$
$114$	−119287.	−0.859667
$115$	0	0
$116$	−126435.	−0.872414
$117$	183365.	1.23837
$118$	4783.14	0.0316234
$119$	114874.	0.743623
$120$	0	0
$121$	14641.0	0.0909091
$122$	−95427.2	−0.580460
$123$	507156.	3.02259
$124$	181048.	1.05740
$125$	0	0
$126$	−95332.5	−0.534952
$127$	88020.8	0.484257	0.242129	−	0.970244i	$-0.422154\pi$
$127$	88020.8	0.484257	0.242129	+	0.970244i	$0.422154\pi$
$128$	−181089.	−0.976940
$129$	−134732.	−0.712848
$130$	0	0
$131$	167874.	0.854684	0.427342	−	0.904090i	$-0.359450\pi$
$131$	167874.	0.854684	0.427342	+	0.904090i	$0.359450\pi$
$132$	−98449.4	−0.491788
$133$	−211255.	−1.03556
$134$	52186.0	0.251068
$135$	0	0
$136$	138459.	0.641911
$137$	−6114.39	−0.0278325	−0.0139162	−	0.999903i	$-0.504430\pi$
$137$	−6114.39	−0.0278325	−0.0139162	+	0.999903i	$0.504430\pi$
$138$	−204593.	−0.914522
$139$	82189.4	0.360810	0.180405	−	0.983592i	$-0.442259\pi$
$139$	82189.4	0.360810	0.180405	+	0.983592i	$0.442259\pi$
$140$	0	0
$141$	−348637.	−1.47681
$142$	113230.	0.471239
$143$	−39336.3	−0.160862
$144$	402032.	1.61568
$145$	0	0
$146$	−50971.8	−0.197901
$147$	235891.	0.900365
$148$	29111.4	0.109247
$149$	−316056.	−1.16627	−0.583133	−	0.812376i	$-0.698174\pi$
$149$	−316056.	−1.16627	−0.583133	+	0.812376i	$0.698174\pi$
$150$	0	0
$151$	−427258.	−1.52492	−0.762461	−	0.647034i	$-0.776009\pi$
$151$	−427258.	−1.52492	−0.762461	+	0.647034i	$0.776009\pi$
$152$	−254629.	−0.893922
$153$	−702637.	−2.42662
$154$	20451.2	0.0694891
$155$	0	0
$156$	264506.	0.870211
$157$	−109820.	−0.355577	−0.177789	−	0.984069i	$-0.556894\pi$
$157$	−109820.	−0.355577	−0.177789	+	0.984069i	$0.556894\pi$
$158$	64216.7	0.204647
$159$	−197890.	−0.620770
$160$	0	0
$161$	−362331.	−1.10164
$162$	223664.	0.669589
$163$	−68168.1	−0.200961	−0.100481	−	0.994939i	$-0.532038\pi$
$163$	−68168.1	−0.200961	−0.100481	+	0.994939i	$0.532038\pi$
$164$	511300.	1.48445
$165$	0	0
$166$	−158275.	−0.445802
$167$	−261496.	−0.725561	−0.362781	−	0.931875i	$-0.618173\pi$
$167$	−261496.	−0.725561	−0.362781	+	0.931875i	$0.618173\pi$
$168$	−291167.	−0.795920
$169$	−265607.	−0.715357
$170$	0	0
$171$	1.29216e6	3.37930
$172$	−135833.	−0.350093
$173$	292694.	0.743530	0.371765	−	0.928327i	$-0.378753\pi$
$173$	292694.	0.743530	0.371765	+	0.928327i	$0.378753\pi$
$174$	−229863.	−0.575568
$175$	0	0
$176$	−86245.9	−0.209873
$177$	−74135.1	−0.177865
$178$	−86134.5	−0.203764
$179$	−138393.	−0.322836	−0.161418	−	0.986886i	$-0.551607\pi$
$179$	−138393.	−0.322836	−0.161418	+	0.986886i	$0.551607\pi$
$180$	0	0
$181$	320903.	0.728077	0.364039	−	0.931384i	$-0.381398\pi$
$181$	320903.	0.728077	0.364039	+	0.931384i	$0.381398\pi$
$182$	−54946.7	−0.122960
$183$	1.47905e6	3.26479
$184$	−436725.	−0.950962
$185$	0	0
$186$	329152.	0.697613
$187$	150733.	0.315213
$188$	−351486.	−0.725293
$189$	841006.	1.71256
$190$	0	0
$191$	188577.	0.374029	0.187014	−	0.982357i	$-0.440119\pi$
$191$	188577.	0.374029	0.187014	+	0.982357i	$0.440119\pi$
$192$	394740.	0.772785
$193$	−719046.	−1.38952	−0.694758	−	0.719244i	$-0.744488\pi$
$193$	−719046.	−1.38952	−0.694758	+	0.719244i	$0.744488\pi$
$194$	233969.	0.446328
$195$	0	0
$196$	237819.	0.442187
$197$	−75338.0	−0.138308	−0.0691542	−	0.997606i	$-0.522030\pi$
$197$	−75338.0	−0.138308	−0.0691542	+	0.997606i	$0.522030\pi$
$198$	−125092.	−0.226760
$199$	46802.6	0.0837793	0.0418897	−	0.999122i	$-0.486662\pi$
$199$	46802.6	0.0837793	0.0418897	+	0.999122i	$0.486662\pi$
$200$	0	0
$201$	−808844.	−1.41213
$202$	165282.	0.285002
$203$	−407084.	−0.693335
$204$	−1.01356e6	−1.70520
$205$	0	0
$206$	297114.	0.487816
$207$	2.21624e6	3.59493
$208$	231719.	0.371367
$209$	−277201.	−0.438964
$210$	0	0
$211$	−1.08846e6	−1.68309	−0.841544	−	0.540189i	$-0.818353\pi$
$211$	−1.08846e6	−1.68309	−0.841544	+	0.540189i	$0.818353\pi$
$212$	−199507.	−0.304872
$213$	−1.75498e6	−2.65048
$214$	−132666.	−0.198027
$215$	0	0
$216$	1.01368e6	1.47832
$217$	582922.	0.840352
$218$	234175.	0.333733
$219$	790024.	1.11309
$220$	0	0
$221$	−404978.	−0.557765
$222$	52925.6	0.0720748
$223$	477312.	0.642747	0.321374	−	0.946952i	$-0.395855\pi$
$223$	477312.	0.642747	0.321374	+	0.946952i	$0.395855\pi$
$224$	−448451.	−0.597166
$225$	0	0
$226$	−331208.	−0.431350
$227$	1726.55	0.00222389	0.00111195	−	0.999999i	$-0.499646\pi$
$227$	1726.55	0.00222389	0.00111195	+	0.999999i	$0.499646\pi$
$228$	1.86396e6	2.37465
$229$	914022.	1.15178	0.575888	−	0.817528i	$-0.304656\pi$
$229$	914022.	1.15178	0.575888	+	0.817528i	$0.304656\pi$
$230$	0	0
$231$	−316978.	−0.390840
$232$	−490666.	−0.598502
$233$	−794728.	−0.959022	−0.479511	−	0.877536i	$-0.659186\pi$
$233$	−794728.	−0.959022	−0.479511	+	0.877536i	$0.659186\pi$
$234$	336088.	0.401248
$235$	0	0
$236$	−74740.8	−0.0873530
$237$	−995311.	−1.15103
$238$	210551.	0.240943
$239$	785295.	0.889279	0.444640	−	0.895710i	$-0.353332\pi$
$239$	785295.	0.889279	0.444640	+	0.895710i	$0.353332\pi$
$240$	0	0
$241$	−1.69165e6	−1.87615	−0.938075	−	0.346432i	$-0.887393\pi$
$241$	−1.69165e6	−1.87615	−0.938075	+	0.346432i	$0.887393\pi$
$242$	26835.3	0.0294556
$243$	−1.25042e6	−1.35844
$244$	1.49113e6	1.60340
$245$	0	0
$246$	929561.	0.979355
$247$	744763.	0.776740
$248$	702607.	0.725410
$249$	2.45314e6	2.50740
$250$	0	0
$251$	−1.74509e6	−1.74837	−0.874184	−	0.485594i	$-0.838603\pi$
$251$	−1.74509e6	−1.74837	−0.874184	+	0.485594i	$0.838603\pi$
$252$	1.48965e6	1.47769
$253$	−475438.	−0.466974
$254$	161332.	0.156905
$255$	0	0
$256$	112730.	0.107507
$257$	−1.86805e6	−1.76423	−0.882115	−	0.471034i	$-0.843881\pi$
$257$	−1.86805e6	−1.76423	−0.882115	+	0.471034i	$0.843881\pi$
$258$	−246949.	−0.230971
$259$	93730.2	0.0868221
$260$	0	0
$261$	2.48997e6	2.26252
$262$	307695.	0.276928
$263$	1.36420e6	1.21616	0.608079	−	0.793877i	$-0.291941\pi$
$263$	1.36420e6	1.21616	0.608079	+	0.793877i	$0.291941\pi$
$264$	−382060.	−0.337382
$265$	0	0
$266$	−387206.	−0.335536
$267$	1.33502e6	1.14607
$268$	−815453.	−0.693524
$269$	1.39535e6	1.17571	0.587857	−	0.808965i	$-0.299972\pi$
$269$	1.39535e6	1.17571	0.587857	+	0.808965i	$0.299972\pi$
$270$	0	0
$271$	750872.	0.621073	0.310536	−	0.950561i	$-0.399491\pi$
$271$	750872.	0.621073	0.310536	+	0.950561i	$0.399491\pi$
$272$	−887925.	−0.727702
$273$	851633.	0.691585
$274$	−11207.0	−0.00901806
$275$	0	0
$276$	3.19695e6	2.52618
$277$	−432426.	−0.338620	−0.169310	−	0.985563i	$-0.554154\pi$
$277$	−432426.	−0.338620	−0.169310	+	0.985563i	$0.554154\pi$
$278$	150644.	0.116907
$279$	−3.56551e6	−2.74227
$280$	0	0
$281$	1.44797e6	1.09394	0.546972	−	0.837151i	$-0.315780\pi$
$281$	1.44797e6	1.09394	0.546972	+	0.837151i	$0.315780\pi$
$282$	−639014.	−0.478506
$283$	268970.	0.199636	0.0998178	−	0.995006i	$-0.468174\pi$
$283$	268970.	0.199636	0.0998178	+	0.995006i	$0.468174\pi$
$284$	−1.76932e6	−1.30170
$285$	0	0
$286$	−72099.2	−0.0521213
$287$	1.64623e6	1.17974
$288$	2.74300e6	1.94870
$289$	131981.	0.0929539
$290$	0	0
$291$	−3.62634e6	−2.51036
$292$	796479.	0.546660
$293$	1.50374e6	1.02330	0.511652	−	0.859193i	$-0.329034\pi$
$293$	1.50374e6	1.02330	0.511652	+	0.859193i	$0.329034\pi$
$294$	432363.	0.291729
$295$	0	0
$296$	112975.	0.0749467
$297$	1.10354e6	0.725933
$298$	−579295.	−0.377885
$299$	1.27737e6	0.826303
$300$	0	0
$301$	−437342.	−0.278231
$302$	−783116.	−0.494093
$303$	−2.56175e6	−1.60299
$304$	1.63291e6	1.01339
$305$	0	0
$306$	−1.28786e6	−0.786256
$307$	−3.06733e6	−1.85744	−0.928718	−	0.370786i	$-0.879088\pi$
$307$	−3.06733e6	−1.85744	−0.928718	+	0.370786i	$0.879088\pi$
$308$	−319568.	−0.191949
$309$	−4.60505e6	−2.74371
$310$	0	0
$311$	−2.28974e6	−1.34241	−0.671206	−	0.741271i	$-0.734224\pi$
$311$	−2.28974e6	−1.34241	−0.671206	+	0.741271i	$0.734224\pi$
$312$	1.02649e6	0.596991
$313$	−2.79124e6	−1.61041	−0.805205	−	0.592997i	$-0.797945\pi$
$313$	−2.79124e6	−1.61041	−0.805205	+	0.592997i	$0.797945\pi$
$314$	−201289.	−0.115211
$315$	0	0
$316$	−1.00344e6	−0.565295
$317$	−2.12565e6	−1.18808	−0.594038	−	0.804437i	$-0.702467\pi$
$317$	−2.12565e6	−1.18808	−0.594038	+	0.804437i	$0.702467\pi$
$318$	−362710.	−0.201137
$319$	−534161.	−0.293897
$320$	0	0
$321$	2.05622e6	1.11380
$322$	−664113.	−0.356946
$323$	−2.85386e6	−1.52204
$324$	−3.49495e6	−1.84960
$325$	0	0
$326$	−124945.	−0.0651139
$327$	−3.62954e6	−1.87708
$328$	1.98424e6	1.01838
$329$	−1.13168e6	−0.576413
$330$	0	0
$331$	1.11723e6	0.560498	0.280249	−	0.959927i	$-0.409583\pi$
$331$	1.11723e6	0.560498	0.280249	+	0.959927i	$0.409583\pi$
$332$	2.47319e6	1.23144
$333$	−573312.	−0.283322
$334$	−479294.	−0.235091
$335$	0	0
$336$	1.86722e6	0.902295
$337$	1.33038e6	0.638117	0.319058	−	0.947735i	$-0.396633\pi$
$337$	1.33038e6	0.638117	0.319058	+	0.947735i	$0.396633\pi$
$338$	−486828.	−0.231784
$339$	5.13347e6	2.42612
$340$	0	0
$341$	764890.	0.356216
$342$	2.36839e6	1.09493
$343$	2.31555e6	1.06272
$344$	−527137.	−0.240175
$345$	0	0
$346$	536475.	0.240913
$347$	−2.20966e6	−0.985149	−0.492574	−	0.870270i	$-0.663944\pi$
$347$	−2.20966e6	−0.985149	−0.492574	+	0.870270i	$0.663944\pi$
$348$	3.59182e6	1.58989
$349$	−3.65330e6	−1.60554	−0.802772	−	0.596286i	$-0.796642\pi$
$349$	−3.65330e6	−1.60554	−0.802772	+	0.596286i	$0.796642\pi$
$350$	0	0
$351$	−2.96491e6	−1.28453
$352$	−588442.	−0.253132
$353$	1.65317e6	0.706122	0.353061	−	0.935600i	$-0.385141\pi$
$353$	1.65317e6	0.706122	0.353061	+	0.935600i	$0.385141\pi$
$354$	−135881.	−0.0576304
$355$	0	0
$356$	1.34593e6	0.562855
$357$	−3.26337e6	−1.35518
$358$	−253659.	−0.104603
$359$	−910273.	−0.372766	−0.186383	−	0.982477i	$-0.559676\pi$
$359$	−910273.	−0.372766	−0.186383	+	0.982477i	$0.559676\pi$
$360$	0	0
$361$	2.77220e6	1.11959
$362$	588180.	0.235906
$363$	−415927.	−0.165673
$364$	858591.	0.339651
$365$	0	0
$366$	2.71093e6	1.05783
$367$	−2.26044e6	−0.876049	−0.438025	−	0.898963i	$-0.644322\pi$
$367$	−2.26044e6	−0.876049	−0.438025	+	0.898963i	$0.644322\pi$
$368$	2.80067e6	1.07806
$369$	−1.00694e7	−3.84979
$370$	0	0
$371$	−642353.	−0.242292
$372$	−5.14329e6	−1.92701
$373$	422911.	0.157390	0.0786949	−	0.996899i	$-0.474925\pi$
$373$	422911.	0.157390	0.0786949	+	0.996899i	$0.474925\pi$
$374$	276277.	0.102133
$375$	0	0
$376$	−1.36404e6	−0.497573
$377$	1.43514e6	0.520046
$378$	1.54147e6	0.554889
$379$	−783048.	−0.280021	−0.140010	−	0.990150i	$-0.544714\pi$
$379$	−783048.	−0.280021	−0.140010	+	0.990150i	$0.544714\pi$
$380$	0	0
$381$	−2.50053e6	−0.882510
$382$	345641.	0.121190
$383$	−989127.	−0.344552	−0.172276	−	0.985049i	$-0.555112\pi$
$383$	−989127.	−0.344552	−0.172276	+	0.985049i	$0.555112\pi$
$384$	5.14446e6	1.78038
$385$	0	0
$386$	−1.31793e6	−0.450220
$387$	2.67505e6	0.907935
$388$	−3.65597e6	−1.23289
$389$	−3.74594e6	−1.25513	−0.627563	−	0.778566i	$-0.715947\pi$
$389$	−3.74594e6	−1.25513	−0.627563	+	0.778566i	$0.715947\pi$
$390$	0	0
$391$	−4.89476e6	−1.61916
$392$	922921.	0.303354
$393$	−4.76903e6	−1.55758
$394$	−138086.	−0.0448136
$395$	0	0
$396$	1.95467e6	0.626377
$397$	−4.49593e6	−1.43167	−0.715836	−	0.698268i	$-0.753954\pi$
$397$	−4.49593e6	−1.43167	−0.715836	+	0.698268i	$0.753954\pi$
$398$	85783.9	0.0271455
$399$	6.00141e6	1.88721
$400$	0	0
$401$	2.86867e6	0.890881	0.445441	−	0.895311i	$-0.353047\pi$
$401$	2.86867e6	0.890881	0.445441	+	0.895311i	$0.353047\pi$
$402$	−1.48252e6	−0.457547
$403$	−2.05505e6	−0.630318
$404$	−2.58268e6	−0.787260
$405$	0	0
$406$	−746139.	−0.224649
$407$	122990.	0.0368029
$408$	−3.93341e6	−1.16982
$409$	4.83531e6	1.42928	0.714638	−	0.699495i	$-0.246592\pi$
$409$	4.83531e6	1.42928	0.714638	+	0.699495i	$0.246592\pi$
$410$	0	0
$411$	173700.	0.0507219
$412$	−4.64268e6	−1.34749
$413$	−240643.	−0.0694222
$414$	4.06212e6	1.16480
$415$	0	0
$416$	1.58098e6	0.447913
$417$	−2.33487e6	−0.657541
$418$	−508079.	−0.142230
$419$	660364.	0.183759	0.0918794	−	0.995770i	$-0.470713\pi$
$419$	660364.	0.183759	0.0918794	+	0.995770i	$0.470713\pi$
$420$	0	0
$421$	−2.69471e6	−0.740979	−0.370490	−	0.928837i	$-0.620810\pi$
$421$	−2.69471e6	−0.740979	−0.370490	+	0.928837i	$0.620810\pi$
$422$	−1.99503e6	−0.545341
$423$	6.92205e6	1.88098
$424$	−774241.	−0.209152
$425$	0	0
$426$	−3.21669e6	−0.858786
$427$	4.80101e6	1.27427
$428$	2.07302e6	0.547009
$429$	1.11748e6	0.293155
$430$	0	0
$431$	−2.55858e6	−0.663446	−0.331723	−	0.943377i	$-0.607630\pi$
$431$	−2.55858e6	−0.663446	−0.331723	+	0.943377i	$0.607630\pi$
$432$	−6.50063e6	−1.67589
$433$	−4.17832e6	−1.07098	−0.535491	−	0.844541i	$-0.679874\pi$
$433$	−4.17832e6	−1.07098	−0.535491	+	0.844541i	$0.679874\pi$
$434$	1.06843e6	0.272284
$435$	0	0
$436$	−3.65919e6	−0.921869
$437$	9.00156e6	2.25483
$438$	1.44803e6	0.360655
$439$	−3.31965e6	−0.822112	−0.411056	−	0.911610i	$-0.634840\pi$
$439$	−3.31965e6	−0.822112	−0.411056	+	0.911610i	$0.634840\pi$
$440$	0	0
$441$	−4.68353e6	−1.14677
$442$	−742281.	−0.180723
$443$	−257758.	−0.0624026	−0.0312013	−	0.999513i	$-0.509933\pi$
$443$	−257758.	−0.0624026	−0.0312013	+	0.999513i	$0.509933\pi$
$444$	−827010.	−0.199092
$445$	0	0
$446$	874860.	0.208258
$447$	8.97864e6	2.12540
$448$	1.28133e6	0.301624
$449$	−682765.	−0.159829	−0.0799145	−	0.996802i	$-0.525465\pi$
$449$	−682765.	−0.159829	−0.0799145	+	0.996802i	$0.525465\pi$
$450$	0	0
$451$	2.16013e6	0.500079
$452$	5.17542e6	1.19151
$453$	1.21377e7	2.77902
$454$	3164.57	0.000720567 0
$455$	0	0
$456$	7.23362e6	1.62908
$457$	5.91577e6	1.32502	0.662508	−	0.749055i	$-0.269492\pi$
$457$	5.91577e6	1.32502	0.662508	+	0.749055i	$0.269492\pi$
$458$	1.67530e6	0.373190
$459$	1.13612e7	2.51706
$460$	0	0
$461$	3.22869e6	0.707577	0.353789	−	0.935325i	$-0.384893\pi$
$461$	3.22869e6	0.707577	0.353789	+	0.935325i	$0.384893\pi$
$462$	−580986.	−0.126637
$463$	2.13583e6	0.463034	0.231517	−	0.972831i	$-0.425631\pi$
$463$	2.13583e6	0.463034	0.231517	+	0.972831i	$0.425631\pi$
$464$	3.14659e6	0.678492
$465$	0	0
$466$	−1.45665e6	−0.310735
$467$	−4.84133e6	−1.02724	−0.513621	−	0.858017i	$-0.671696\pi$
$467$	−4.84133e6	−1.02724	−0.513621	+	0.858017i	$0.671696\pi$
$468$	−5.25167e6	−1.10836
$469$	−2.62552e6	−0.551166
$470$	0	0
$471$	3.11982e6	0.648004
$472$	−290052.	−0.0599268
$473$	−573865.	−0.117939
$474$	−1.82429e6	−0.372949
$475$	0	0
$476$	−3.29004e6	−0.665554
$477$	3.92902e6	0.790658
$478$	1.43936e6	0.288137
$479$	−3.10279e6	−0.617894	−0.308947	−	0.951079i	$-0.599977\pi$
$479$	−3.10279e6	−0.617894	−0.308947	+	0.951079i	$0.599977\pi$
$480$	0	0
$481$	−330439.	−0.0651222
$482$	−3.10061e6	−0.607895
$483$	1.02932e7	2.00763
$484$	−419326.	−0.0813651
$485$	0	0
$486$	−2.29189e6	−0.440152
$487$	7.85531e6	1.50086	0.750431	−	0.660948i	$-0.229846\pi$
$487$	7.85531e6	1.50086	0.750431	+	0.660948i	$0.229846\pi$
$488$	5.78675e6	1.09998
$489$	1.93655e6	0.366232
$490$	0	0
$491$	773956.	0.144881	0.0724407	−	0.997373i	$-0.476921\pi$
$491$	773956.	0.144881	0.0724407	+	0.997373i	$0.476921\pi$
$492$	−1.45252e7	−2.70526
$493$	−5.49933e6	−1.01904
$494$	1.36507e6	0.251673
$495$	0	0
$496$	−4.50574e6	−0.822361
$497$	−5.69670e6	−1.03450
$498$	4.49634e6	0.812429
$499$	4.11846e6	0.740429	0.370214	−	0.928946i	$-0.379284\pi$
$499$	4.11846e6	0.740429	0.370214	+	0.928946i	$0.379284\pi$
$500$	0	0
$501$	7.42869e6	1.32226
$502$	−3.19855e6	−0.566493
$503$	−4.95526e6	−0.873265	−0.436633	−	0.899640i	$-0.643829\pi$
$503$	−4.95526e6	−0.873265	−0.436633	+	0.899640i	$0.643829\pi$
$504$	5.78101e6	1.01374
$505$	0	0
$506$	−871425.	−0.151305
$507$	7.54547e6	1.30367
$508$	−2.52096e6	−0.433418
$509$	−737336.	−0.126145	−0.0630726	−	0.998009i	$-0.520090\pi$
$509$	−737336.	−0.126145	−0.0630726	+	0.998009i	$0.520090\pi$
$510$	0	0
$511$	2.56443e6	0.434448
$512$	6.00148e6	1.01177
$513$	−2.08935e7	−3.50525
$514$	−3.42392e6	−0.571632
$515$	0	0
$516$	3.85880e6	0.638010
$517$	−1.48495e6	−0.244335
$518$	171797.	0.0281314
$519$	−8.31496e6	−1.35501
$520$	0	0
$521$	5.05918e6	0.816556	0.408278	−	0.912858i	$-0.366129\pi$
$521$	5.05918e6	0.816556	0.408278	+	0.912858i	$0.366129\pi$
$522$	4.56384e6	0.733085
$523$	5.42579e6	0.867378	0.433689	−	0.901063i	$-0.357212\pi$
$523$	5.42579e6	0.867378	0.433689	+	0.901063i	$0.357212\pi$
$524$	−4.80800e6	−0.764956
$525$	0	0
$526$	2.50043e6	0.394050
$527$	7.87475e6	1.23512
$528$	2.45011e6	0.382473
$529$	9.00258e6	1.39871
$530$	0	0
$531$	1.47192e6	0.226542
$532$	6.05044e6	0.926847
$533$	−5.80368e6	−0.884882
$534$	2.44694e6	0.371339
$535$	0	0
$536$	−3.16459e6	−0.475779
$537$	3.93153e6	0.588336
$538$	2.55752e6	0.380946
$539$	1.00473e6	0.148963
$540$	0	0
$541$	−120135.	−0.0176472	−0.00882359	−	0.999961i	$-0.502809\pi$
$541$	−120135.	−0.0176472	−0.00882359	+	0.999961i	$0.502809\pi$
$542$	1.37626e6	0.201235
$543$	−9.11634e6	−1.32685
$544$	−6.05817e6	−0.877696
$545$	0	0
$546$	1.56095e6	0.224082
$547$	−3.02121e6	−0.431730	−0.215865	−	0.976423i	$-0.569257\pi$
$547$	−3.02121e6	−0.431730	−0.215865	+	0.976423i	$0.569257\pi$
$548$	175119.	0.0249105
$549$	−2.93659e7	−4.15827
$550$	0	0
$551$	1.01134e7	1.41911
$552$	1.24066e7	1.73303
$553$	−3.23079e6	−0.449258
$554$	−792590.	−0.109717
$555$	0	0
$556$	−2.35395e6	−0.322931
$557$	−4.83695e6	−0.660592	−0.330296	−	0.943877i	$-0.607149\pi$
$557$	−4.83695e6	−0.660592	−0.330296	+	0.943877i	$0.607149\pi$
$558$	−6.53518e6	−0.888530
$559$	1.54182e6	0.208691
$560$	0	0
$561$	−4.28209e6	−0.574445
$562$	2.65398e6	0.354451
$563$	−1.28574e7	−1.70955	−0.854774	−	0.519000i	$-0.826305\pi$
$563$	−1.28574e7	−1.70955	−0.854774	+	0.519000i	$0.826305\pi$
$564$	9.98515e6	1.32177
$565$	0	0
$566$	492993.	0.0646844
$567$	−1.12527e7	−1.46994
$568$	−6.86634e6	−0.893006
$569$	3.12635e6	0.404816	0.202408	−	0.979301i	$-0.435123\pi$
$569$	3.12635e6	0.404816	0.202408	+	0.979301i	$0.435123\pi$
$570$	0	0
$571$	−4.35759e6	−0.559315	−0.279657	−	0.960100i	$-0.590221\pi$
$571$	−4.35759e6	−0.559315	−0.279657	+	0.960100i	$0.590221\pi$
$572$	1.12661e6	0.143974
$573$	−5.35717e6	−0.681630
$574$	3.01737e6	0.382251
$575$	0	0
$576$	−7.83741e6	−0.984275
$577$	8.42315e6	1.05326	0.526629	−	0.850095i	$-0.323456\pi$
$577$	8.42315e6	1.05326	0.526629	+	0.850095i	$0.323456\pi$
$578$	241907.	0.0301182
$579$	2.04269e7	2.53225
$580$	0	0
$581$	7.96293e6	0.978661
$582$	−6.64668e6	−0.813388
$583$	−842873.	−0.102705
$584$	3.09096e6	0.375025
$585$	0	0
$586$	2.75619e6	0.331563
$587$	−6.25439e6	−0.749187	−0.374593	−	0.927189i	$-0.622218\pi$
$587$	−6.25439e6	−0.749187	−0.374593	+	0.927189i	$0.622218\pi$
$588$	−6.75605e6	−0.805841
$589$	−1.44818e7	−1.72003
$590$	0	0
$591$	2.14023e6	0.252053
$592$	−724496.	−0.0849633
$593$	2.94276e6	0.343652	0.171826	−	0.985127i	$-0.445033\pi$
$593$	2.94276e6	0.343652	0.171826	+	0.985127i	$0.445033\pi$
$594$	2.02267e6	0.235211
$595$	0	0
$596$	9.05200e6	1.04383
$597$	−1.32959e6	−0.152679
$598$	2.34128e6	0.267732
$599$	4.61509e6	0.525549	0.262774	−	0.964857i	$-0.415363\pi$
$599$	4.61509e6	0.525549	0.262774	+	0.964857i	$0.415363\pi$
$600$	0	0
$601$	1.22293e7	1.38107	0.690537	−	0.723297i	$-0.257374\pi$
$601$	1.22293e7	1.38107	0.690537	+	0.723297i	$0.257374\pi$
$602$	−801599.	−0.0901501
$603$	1.60593e7	1.79859
$604$	1.22369e7	1.36483
$605$	0	0
$606$	−4.69541e6	−0.519388
$607$	−7.54646e6	−0.831327	−0.415663	−	0.909518i	$-0.636451\pi$
$607$	−7.54646e6	−0.831327	−0.415663	+	0.909518i	$0.636451\pi$
$608$	1.11411e7	1.22227
$609$	1.15646e7	1.26353
$610$	0	0
$611$	3.98966e6	0.432347
$612$	2.01239e7	2.17187
$613$	298042.	0.0320351	0.0160175	−	0.999872i	$-0.494901\pi$
$613$	298042.	0.0320351	0.0160175	+	0.999872i	$0.494901\pi$
$614$	−5.62207e6	−0.601832
$615$	0	0
$616$	−1.24017e6	−0.131683
$617$	2.05792e6	0.217629	0.108814	−	0.994062i	$-0.465295\pi$
$617$	2.05792e6	0.217629	0.108814	+	0.994062i	$0.465295\pi$
$618$	−8.44055e6	−0.888995
$619$	−1.26482e7	−1.32679	−0.663396	−	0.748269i	$-0.730885\pi$
$619$	−1.26482e7	−1.32679	−0.663396	+	0.748269i	$0.730885\pi$
$620$	0	0
$621$	−3.58353e7	−3.72891
$622$	−4.19685e6	−0.434958
$623$	4.33349e6	0.447319
$624$	−6.58276e6	−0.676779
$625$	0	0
$626$	−5.11603e6	−0.521792
$627$	7.87484e6	0.799968
$628$	3.14531e6	0.318247
$629$	1.26621e6	0.127608
$630$	0	0
$631$	−1.10828e7	−1.10809	−0.554044	−	0.832487i	$-0.686916\pi$
$631$	−1.10828e7	−1.10809	−0.554044	+	0.832487i	$0.686916\pi$
$632$	−3.89414e6	−0.387809
$633$	3.09214e7	3.06726
$634$	−3.89609e6	−0.384951
$635$	0	0
$636$	5.66767e6	0.555599
$637$	−2.69944e6	−0.263588
$638$	−979058.	−0.0952262
$639$	3.48445e7	3.37584
$640$	0	0
$641$	1.19812e7	1.15175	0.575873	−	0.817539i	$-0.304662\pi$
$641$	1.19812e7	1.15175	0.575873	+	0.817539i	$0.304662\pi$
$642$	3.76883e6	0.360885
$643$	−1.41713e7	−1.35170	−0.675852	−	0.737038i	$-0.736224\pi$
$643$	−1.41713e7	−1.35170	−0.675852	+	0.737038i	$0.736224\pi$
$644$	1.03773e7	0.985988
$645$	0	0
$646$	−5.23081e6	−0.493160
$647$	8.19642e6	0.769775	0.384887	−	0.922964i	$-0.374240\pi$
$647$	8.19642e6	0.769775	0.384887	+	0.922964i	$0.374240\pi$
$648$	−1.35631e7	−1.26888
$649$	−315764.	−0.0294273
$650$	0	0
$651$	−1.65599e7	−1.53146
$652$	1.95237e6	0.179864
$653$	1.43541e7	1.31733	0.658663	−	0.752438i	$-0.271122\pi$
$653$	1.43541e7	1.31733	0.658663	+	0.752438i	$0.271122\pi$
$654$	−6.65254e6	−0.608196
$655$	0	0
$656$	−1.27247e7	−1.15448
$657$	−1.56856e7	−1.41771
$658$	−2.07425e6	−0.186765
$659$	6.88464e6	0.617543	0.308772	−	0.951136i	$-0.400082\pi$
$659$	6.88464e6	0.617543	0.308772	+	0.951136i	$0.400082\pi$
$660$	0	0
$661$	−1.00760e7	−0.896981	−0.448491	−	0.893788i	$-0.648038\pi$
$661$	−1.00760e7	−0.896981	−0.448491	+	0.893788i	$0.648038\pi$
$662$	2.04776e6	0.181608
$663$	1.15048e7	1.01647
$664$	9.59787e6	0.844802
$665$	0	0
$666$	−1.05082e6	−0.0917997
$667$	1.73458e7	1.50967
$668$	7.48939e6	0.649389
$669$	−1.35597e7	−1.17134
$670$	0	0
$671$	6.29972e6	0.540151
$672$	1.27398e7	1.08827
$673$	−2.18143e7	−1.85654	−0.928269	−	0.371909i	$-0.878703\pi$
$673$	−2.18143e7	−1.85654	−0.928269	+	0.371909i	$0.878703\pi$
$674$	2.43844e6	0.206758
$675$	0	0
$676$	7.60712e6	0.640256
$677$	−1.40137e7	−1.17512	−0.587560	−	0.809181i	$-0.699911\pi$
$677$	−1.40137e7	−1.17512	−0.587560	+	0.809181i	$0.699911\pi$
$678$	9.40909e6	0.786092
$679$	−1.17711e7	−0.979816
$680$	0	0
$681$	−49048.4	−0.00405282
$682$	1.40196e6	0.115418
$683$	1.11846e7	0.917418	0.458709	−	0.888587i	$-0.348312\pi$
$683$	1.11846e7	0.917418	0.458709	+	0.888587i	$0.348312\pi$
$684$	−3.70082e7	−3.02453
$685$	0	0
$686$	4.24414e6	0.344334
$687$	−2.59659e7	−2.09900
$688$	3.38047e6	0.272274
$689$	2.26457e6	0.181734
$690$	0	0
$691$	−1.07831e7	−0.859109	−0.429555	−	0.903041i	$-0.641329\pi$
$691$	−1.07831e7	−0.859109	−0.429555	+	0.903041i	$0.641329\pi$
$692$	−8.38290e6	−0.665471
$693$	6.29347e6	0.497802
$694$	−4.05006e6	−0.319200
$695$	0	0
$696$	1.39390e7	1.09071
$697$	2.22391e7	1.73395
$698$	−6.69610e6	−0.520216
$699$	2.25769e7	1.74772
$700$	0	0
$701$	1.77077e7	1.36103	0.680513	−	0.732736i	$-0.261757\pi$
$701$	1.77077e7	1.36103	0.680513	+	0.732736i	$0.261757\pi$
$702$	−5.43435e6	−0.416202
$703$	−2.32859e6	−0.177707
$704$	1.68132e6	0.127855
$705$	0	0
$706$	3.03007e6	0.228792
$707$	−8.31548e6	−0.625661
$708$	2.12327e6	0.159192
$709$	−1.23538e6	−0.0922967	−0.0461484	−	0.998935i	$-0.514695\pi$
$709$	−1.23538e6	−0.0922967	−0.0461484	+	0.998935i	$0.514695\pi$
$710$	0	0
$711$	1.97615e7	1.46604
$712$	5.22324e6	0.386136
$713$	−2.48383e7	−1.82978
$714$	−5.98140e6	−0.439094
$715$	0	0
$716$	3.96365e6	0.288943
$717$	−2.23090e7	−1.62062
$718$	−1.66843e6	−0.120781
$719$	1.93573e7	1.39644	0.698222	−	0.715882i	$-0.253975\pi$
$719$	1.93573e7	1.39644	0.698222	+	0.715882i	$0.253975\pi$
$720$	0	0
$721$	−1.49480e7	−1.07089
$722$	5.08114e6	0.362759
$723$	4.80570e7	3.41910
$724$	−9.19083e6	−0.651641
$725$	0	0
$726$	−762349.	−0.0536800
$727$	2.27826e7	1.59870	0.799352	−	0.600863i	$-0.205176\pi$
$727$	2.27826e7	1.59870	0.799352	+	0.600863i	$0.205176\pi$
$728$	3.33200e6	0.233011
$729$	5.86972e6	0.409071
$730$	0	0
$731$	−5.90809e6	−0.408935
$732$	−4.23607e7	−2.92204
$733$	−5.61113e6	−0.385736	−0.192868	−	0.981225i	$-0.561779\pi$
$733$	−5.61113e6	−0.385736	−0.192868	+	0.981225i	$0.561779\pi$
$734$	−4.14314e6	−0.283851
$735$	0	0
$736$	1.91085e7	1.30027
$737$	−3.44511e6	−0.233633
$738$	−1.84561e7	−1.24738
$739$	−1.15596e7	−0.778632	−0.389316	−	0.921104i	$-0.627289\pi$
$739$	−1.15596e7	−0.778632	−0.389316	+	0.921104i	$0.627289\pi$
$740$	0	0
$741$	−2.11575e7	−1.41553
$742$	−1.17736e6	−0.0785055
$743$	7.78091e6	0.517081	0.258541	−	0.966000i	$-0.416758\pi$
$743$	7.78091e6	0.517081	0.258541	+	0.966000i	$0.416758\pi$
$744$	−1.99600e7	−1.32199
$745$	0	0
$746$	775149.	0.0509962
$747$	−4.87061e7	−3.19361
$748$	−4.31707e6	−0.282121
$749$	6.67452e6	0.434726
$750$	0	0
$751$	8.97488e6	0.580669	0.290335	−	0.956925i	$-0.406233\pi$
$751$	8.97488e6	0.580669	0.290335	+	0.956925i	$0.406233\pi$
$752$	8.74742e6	0.564073
$753$	4.95752e7	3.18623
$754$	2.63046e6	0.168501
$755$	0	0
$756$	−2.40869e7	−1.53277
$757$	−1.43633e7	−0.910994	−0.455497	−	0.890237i	$-0.650538\pi$
$757$	−1.43633e7	−0.910994	−0.455497	+	0.890237i	$0.650538\pi$
$758$	−1.43524e6	−0.0907301
$759$	1.35064e7	0.851013
$760$	0	0
$761$	5.71391e6	0.357661	0.178831	−	0.983880i	$-0.442769\pi$
$761$	5.71391e6	0.357661	0.178831	+	0.983880i	$0.442769\pi$
$762$	−4.58320e6	−0.285944
$763$	−1.17815e7	−0.732639
$764$	−5.40094e6	−0.334762
$765$	0	0
$766$	−1.81296e6	−0.111639
$767$	848370.	0.0520711
$768$	−3.20247e6	−0.195921
$769$	1.25504e6	0.0765320	0.0382660	−	0.999268i	$-0.487817\pi$
$769$	1.25504e6	0.0765320	0.0382660	+	0.999268i	$0.487817\pi$
$770$	0	0
$771$	5.30682e7	3.21513
$772$	2.05938e7	1.24364
$773$	1.45209e6	0.0874064	0.0437032	−	0.999045i	$-0.486084\pi$
$773$	1.45209e6	0.0874064	0.0437032	+	0.999045i	$0.486084\pi$
$774$	4.90307e6	0.294182
$775$	0	0
$776$	−1.41880e7	−0.845798
$777$	−2.66273e6	−0.158225
$778$	−6.86590e6	−0.406676
$779$	−4.08982e7	−2.41469
$780$	0	0
$781$	−7.47500e6	−0.438514
$782$	−8.97156e6	−0.524628
$783$	−4.02614e7	−2.34685
$784$	−5.91859e6	−0.343897
$785$	0	0
$786$	−8.74111e6	−0.504673
$787$	1.81411e7	1.04407	0.522033	−	0.852925i	$-0.325174\pi$
$787$	1.81411e7	1.04407	0.522033	+	0.852925i	$0.325174\pi$
$788$	2.15772e6	0.123788
$789$	−3.87548e7	−2.21632
$790$	0	0
$791$	1.66633e7	0.946935
$792$	7.58564e6	0.429714
$793$	−1.69256e7	−0.955788
$794$	−8.24055e6	−0.463879
$795$	0	0
$796$	−1.34045e6	−0.0749839
$797$	−2.08034e7	−1.16008	−0.580041	−	0.814587i	$-0.696964\pi$
$797$	−2.08034e7	−1.16008	−0.580041	+	0.814587i	$0.696964\pi$
$798$	1.09999e7	0.611480
$799$	−1.52880e7	−0.847195
$800$	0	0
$801$	−2.65063e7	−1.45971
$802$	5.25796e6	0.288656
$803$	3.36495e6	0.184158
$804$	2.31657e7	1.26388
$805$	0	0
$806$	−3.76668e6	−0.204231
$807$	−3.96396e7	−2.14262
$808$	−1.00228e7	−0.540084
$809$	−4.44702e6	−0.238890	−0.119445	−	0.992841i	$-0.538111\pi$
$809$	−4.44702e6	−0.238890	−0.119445	+	0.992841i	$0.538111\pi$
$810$	0	0
$811$	−2.53695e7	−1.35444	−0.677220	−	0.735780i	$-0.736816\pi$
$811$	−2.53695e7	−1.35444	−0.677220	+	0.735780i	$0.736816\pi$
$812$	1.16591e7	0.620546
$813$	−2.13311e7	−1.13184
$814$	225426.	0.0119246
$815$	0	0
$816$	2.52245e7	1.32616
$817$	1.08651e7	0.569480
$818$	8.86258e6	0.463102
$819$	−1.69088e7	−0.880853
$820$	0	0
$821$	1.75554e7	0.908977	0.454488	−	0.890753i	$-0.349822\pi$
$821$	1.75554e7	0.908977	0.454488	+	0.890753i	$0.349822\pi$
$822$	318373.	0.0164345
$823$	−1.44478e7	−0.743535	−0.371767	−	0.928326i	$-0.621248\pi$
$823$	−1.44478e7	−0.743535	−0.371767	+	0.928326i	$0.621248\pi$
$824$	−1.80172e7	−0.924418
$825$	0	0
$826$	−441072.	−0.0224936
$827$	−3.83600e6	−0.195036	−0.0975179	−	0.995234i	$-0.531090\pi$
$827$	−3.83600e6	−0.195036	−0.0975179	+	0.995234i	$0.531090\pi$
$828$	−6.34742e7	−3.21752
$829$	−5.41674e6	−0.273748	−0.136874	−	0.990588i	$-0.543706\pi$
$829$	−5.41674e6	−0.273748	−0.136874	+	0.990588i	$0.543706\pi$
$830$	0	0
$831$	1.22845e7	0.617101
$832$	−4.51724e6	−0.226238
$833$	1.03440e7	0.516507
$834$	−4.27956e6	−0.213051
$835$	0	0
$836$	7.93918e6	0.392880
$837$	5.76522e7	2.84448
$838$	1.21037e6	0.0595401
$839$	8.69662e6	0.426526	0.213263	−	0.976995i	$-0.431591\pi$
$839$	8.69662e6	0.426526	0.213263	+	0.976995i	$0.431591\pi$
$840$	0	0
$841$	−1.02288e6	−0.0498694
$842$	−4.93910e6	−0.240086
$843$	−4.11346e7	−1.99360
$844$	3.11741e7	1.50639
$845$	0	0
$846$	1.26874e7	0.609460
$847$	−1.35011e6	−0.0646635
$848$	4.96512e6	0.237105
$849$	−7.64101e6	−0.363816
$850$	0	0
$851$	−3.99385e6	−0.189046
$852$	5.02636e7	2.37222
$853$	2.03666e7	0.958400	0.479200	−	0.877706i	$-0.340927\pi$
$853$	2.03666e7	0.958400	0.479200	+	0.877706i	$0.340927\pi$
$854$	8.79972e6	0.412881
$855$	0	0
$856$	8.04493e6	0.375265
$857$	1.14010e7	0.530262	0.265131	−	0.964212i	$-0.414585\pi$
$857$	1.14010e7	0.530262	0.265131	+	0.964212i	$0.414585\pi$
$858$	2.04822e6	0.0949858
$859$	8.13091e6	0.375972	0.187986	−	0.982172i	$-0.439804\pi$
$859$	8.13091e6	0.375972	0.187986	+	0.982172i	$0.439804\pi$
$860$	0	0
$861$	−4.67669e7	−2.14996
$862$	−4.68959e6	−0.214964
$863$	3.54656e7	1.62099	0.810496	−	0.585744i	$-0.199198\pi$
$863$	3.54656e7	1.62099	0.810496	+	0.585744i	$0.199198\pi$
$864$	−4.43527e7	−2.02132
$865$	0	0
$866$	−7.65841e6	−0.347011
$867$	−3.74938e6	−0.169399
$868$	−1.66952e7	−0.752128
$869$	−4.23933e6	−0.190435
$870$	0	0
$871$	9.25607e6	0.413410
$872$	−1.42005e7	−0.632430
$873$	7.19996e7	3.19738
$874$	1.64989e7	0.730593
$875$	0	0
$876$	−2.26267e7	−0.996233
$877$	−2.51374e7	−1.10362	−0.551812	−	0.833969i	$-0.686063\pi$
$877$	−2.51374e7	−1.10362	−0.551812	+	0.833969i	$0.686063\pi$
$878$	−6.08455e6	−0.266374
$879$	−4.27189e7	−1.86487
$880$	0	0
$881$	−3.06274e7	−1.32945	−0.664723	−	0.747090i	$-0.731450\pi$
$881$	−3.06274e7	−1.32945	−0.664723	+	0.747090i	$0.731450\pi$
$882$	−8.58439e6	−0.371568
$883$	1.92011e7	0.828750	0.414375	−	0.910106i	$-0.364000\pi$
$883$	1.92011e7	0.828750	0.414375	+	0.910106i	$0.364000\pi$
$884$	1.15988e7	0.499209
$885$	0	0
$886$	−472442.	−0.0202192
$887$	3.21106e7	1.37038	0.685188	−	0.728366i	$-0.259720\pi$
$887$	3.21106e7	1.37038	0.685188	+	0.728366i	$0.259720\pi$
$888$	−3.20944e6	−0.136583
$889$	−8.11675e6	−0.344451
$890$	0	0
$891$	−1.47654e7	−0.623090
$892$	−1.36705e7	−0.575269
$893$	2.81149e7	1.17980
$894$	1.64568e7	0.688657
$895$	0	0
$896$	1.66990e7	0.694896
$897$	−3.62881e7	−1.50585
$898$	−1.25143e6	−0.0517865
$899$	−2.79062e7	−1.15160
$900$	0	0
$901$	−8.67761e6	−0.356113
$902$	3.95928e6	0.162032
$903$	1.24242e7	0.507047
$904$	2.00846e7	0.817415
$905$	0	0
$906$	2.22471e7	0.900436
$907$	−1.90654e7	−0.769533	−0.384766	−	0.923014i	$-0.625718\pi$
$907$	−1.90654e7	−0.769533	−0.384766	+	0.923014i	$0.625718\pi$
$908$	−49449.2	−0.00199042
$909$	5.08626e7	2.04168
$910$	0	0
$911$	5.97496e6	0.238528	0.119264	−	0.992863i	$-0.461947\pi$
$911$	5.97496e6	0.238528	0.119264	+	0.992863i	$0.461947\pi$
$912$	−4.63884e7	−1.84681
$913$	1.04487e7	0.414844
$914$	1.08430e7	0.429321
$915$	0	0
$916$	−2.61781e7	−1.03086
$917$	−1.54803e7	−0.607935
$918$	2.08239e7	0.815559
$919$	3.56831e7	1.39371	0.696856	−	0.717211i	$-0.254582\pi$
$919$	3.56831e7	1.39371	0.696856	+	0.717211i	$0.254582\pi$
$920$	0	0
$921$	8.71378e7	3.38499
$922$	5.91783e6	0.229264
$923$	2.00833e7	0.775944
$924$	9.07841e6	0.349808
$925$	0	0
$926$	3.91473e6	0.150029
$927$	9.14314e7	3.49459
$928$	2.14686e7	0.818342
$929$	−9.05400e6	−0.344193	−0.172096	−	0.985080i	$-0.555054\pi$
$929$	−9.05400e6	−0.344193	−0.172096	+	0.985080i	$0.555054\pi$
$930$	0	0
$931$	−1.90228e7	−0.719284
$932$	2.27614e7	0.858340
$933$	6.50480e7	2.44641
$934$	−8.87363e6	−0.332839
$935$	0	0
$936$	−2.03805e7	−0.760372
$937$	−3.49597e7	−1.30082	−0.650411	−	0.759582i	$-0.725404\pi$
$937$	−3.49597e7	−1.30082	−0.650411	+	0.759582i	$0.725404\pi$
$938$	−4.81228e6	−0.178585
$939$	7.92946e7	2.93481
$940$	0	0
$941$	4.58686e6	0.168866	0.0844328	−	0.996429i	$-0.473092\pi$
$941$	4.58686e6	0.168866	0.0844328	+	0.996429i	$0.473092\pi$
$942$	5.71829e6	0.209961
$943$	−7.01461e7	−2.56876
$944$	1.86007e6	0.0679360
$945$	0	0
$946$	−1.05183e6	−0.0382136
$947$	−1.01783e6	−0.0368809	−0.0184404	−	0.999830i	$-0.505870\pi$
$947$	−1.01783e6	−0.0368809	−0.0184404	+	0.999830i	$0.505870\pi$
$948$	2.85062e7	1.03019
$949$	−9.04070e6	−0.325864
$950$	0	0
$951$	6.03864e7	2.16515
$952$	−1.27679e7	−0.456591
$953$	−7.34796e6	−0.262080	−0.131040	−	0.991377i	$-0.541832\pi$
$953$	−7.34796e6	−0.262080	−0.131040	+	0.991377i	$0.541832\pi$
$954$	7.20147e6	0.256183
$955$	0	0
$956$	−2.24913e7	−0.795919
$957$	1.51747e7	0.535598
$958$	−5.68708e6	−0.200205
$959$	563832.	0.0197972
$960$	0	0
$961$	1.13310e7	0.395786
$962$	−605658.	−0.0211004
$963$	−4.08255e7	−1.41862
$964$	4.84497e7	1.67918
$965$	0	0
$966$	1.88664e7	0.650498
$967$	2.26230e7	0.778010	0.389005	−	0.921236i	$-0.372819\pi$
$967$	2.26230e7	0.778010	0.389005	+	0.921236i	$0.372819\pi$
$968$	−1.62731e6	−0.0558189
$969$	8.10736e7	2.77377
$970$	0	0
$971$	−7.92071e6	−0.269598	−0.134799	−	0.990873i	$-0.543039\pi$
$971$	−7.92071e6	−0.269598	−0.134799	+	0.990873i	$0.543039\pi$
$972$	3.58128e7	1.21583
$973$	−7.57902e6	−0.256644
$974$	1.43979e7	0.486298
$975$	0	0
$976$	−3.71098e7	−1.24699
$977$	873078.	0.0292628	0.0146314	−	0.999893i	$-0.495343\pi$
$977$	873078.	0.0292628	0.0146314	+	0.999893i	$0.495343\pi$
$978$	3.54948e6	0.118663
$979$	5.68625e6	0.189614
$980$	0	0
$981$	7.20630e7	2.39078
$982$	1.41858e6	0.0469433
$983$	−3.89588e7	−1.28594	−0.642971	−	0.765890i	$-0.722299\pi$
$983$	−3.89588e7	−1.28594	−0.642971	+	0.765890i	$0.722299\pi$
$984$	−5.63691e7	−1.85589
$985$	0	0
$986$	−1.00797e7	−0.330182
$987$	3.21492e7	1.05046
$988$	−2.13304e7	−0.695195
$989$	1.86351e7	0.605818
$990$	0	0
$991$	−3.86937e7	−1.25157	−0.625786	−	0.779995i	$-0.715222\pi$
$991$	−3.86937e7	−1.25157	−0.625786	+	0.779995i	$0.715222\pi$
$992$	−3.07420e7	−0.991865
$993$	−3.17388e7	−1.02145
$994$	−1.04414e7	−0.335192
$995$	0	0
$996$	−7.02593e7	−2.24417
$997$	−2.80793e7	−0.894640	−0.447320	−	0.894374i	$-0.647621\pi$
$997$	−2.80793e7	−0.894640	−0.447320	+	0.894374i	$0.647621\pi$
$998$	7.54868e6	0.239908
$999$	9.27012e6	0.293881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.6.a.e.1.4		5
5.2	odd	4		275.6.b.e.199.7		10
5.3	odd	4		275.6.b.e.199.4		10
5.4	even	2		55.6.a.c.1.2	✓	5
15.14	odd	2		495.6.a.h.1.4		5
20.19	odd	2		880.6.a.r.1.1		5
55.54	odd	2		605.6.a.d.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.a.c.1.2	✓	5	5.4	even	2
275.6.a.e.1.4		5	1.1	even	1	trivial
275.6.b.e.199.4		10	5.3	odd	4
275.6.b.e.199.7		10	5.2	odd	4
495.6.a.h.1.4		5	15.14	odd	2
605.6.a.d.1.4		5	55.54	odd	2
880.6.a.r.1.1		5	20.19	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	275.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83289 q^{2} -28.4084 q^{3} -28.6405 q^{4} -52.0695 q^{6} -92.2140 q^{7} -111.147 q^{8} +564.037 q^{9} +O(q^{10})\)	\(q+1.83289 q^{2} -28.4084 q^{3} -28.6405 q^{4} -52.0695 q^{6} -92.2140 q^{7} -111.147 q^{8} +564.037 q^{9} -121.000 q^{11} +813.631 q^{12} +325.094 q^{13} -169.018 q^{14} +712.776 q^{16} -1245.73 q^{17} +1033.82 q^{18} +2290.92 q^{19} +2619.65 q^{21} -221.780 q^{22} +3929.24 q^{23} +3157.52 q^{24} +595.861 q^{26} -9120.16 q^{27} +2641.06 q^{28} +4414.55 q^{29} -6321.41 q^{31} +4863.15 q^{32} +3437.42 q^{33} -2283.28 q^{34} -16154.3 q^{36} -1016.44 q^{37} +4199.00 q^{38} -9235.39 q^{39} -17852.3 q^{41} +4801.53 q^{42} +4742.68 q^{43} +3465.50 q^{44} +7201.86 q^{46} +12272.3 q^{47} -20248.8 q^{48} -8303.58 q^{49} +35389.1 q^{51} -9310.85 q^{52} +6965.89 q^{53} -16716.2 q^{54} +10249.3 q^{56} -65081.3 q^{57} +8091.39 q^{58} +2609.62 q^{59} -52063.8 q^{61} -11586.4 q^{62} -52012.1 q^{63} -13895.2 q^{64} +6300.40 q^{66} +28472.0 q^{67} +35678.3 q^{68} -111623. q^{69} +61776.9 q^{71} -62691.3 q^{72} -27809.5 q^{73} -1863.03 q^{74} -65613.1 q^{76} +11157.9 q^{77} -16927.5 q^{78} +35035.8 q^{79} +122028. q^{81} -32721.3 q^{82} -86352.7 q^{83} -75028.2 q^{84} +8692.82 q^{86} -125410. q^{87} +13448.8 q^{88} -46993.8 q^{89} -29978.2 q^{91} -112535. q^{92} +179581. q^{93} +22493.8 q^{94} -138154. q^{96} +127650. q^{97} -15219.5 q^{98} -68248.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 9 q^{2} + 115 q^{4} - 237 q^{6} - 70 q^{7} - 753 q^{8} + 1059 q^{9}+O(q^{10}) \) 5 * q - 9 * q^2 + 115 * q^4 - 237 * q^6 - 70 * q^7 - 753 * q^8 + 1059 * q^9	\( 5 q - 9 q^{2} + 115 q^{4} - 237 q^{6} - 70 q^{7} - 753 q^{8} + 1059 q^{9} - 605 q^{11} + 1605 q^{12} - 1498 q^{13} + 2113 q^{14} + 4883 q^{16} - 3874 q^{17} - 5838 q^{18} + 882 q^{19} + 1092 q^{21} + 1089 q^{22} + 5344 q^{23} - 13119 q^{24} - 4478 q^{26} + 2160 q^{27} - 12565 q^{28} + 5318 q^{29} - 7916 q^{31} - 21385 q^{32} - 18605 q^{34} + 5628 q^{36} + 1788 q^{37} + 34421 q^{38} - 29760 q^{39} + 5854 q^{41} + 46725 q^{42} + 4364 q^{43} - 13915 q^{44} - 33834 q^{46} - 46452 q^{47} + 127545 q^{48} - 34217 q^{49} + 19842 q^{51} - 3222 q^{52} - 4412 q^{53} - 86535 q^{54} + 115575 q^{56} - 137160 q^{57} + 58221 q^{58} + 17896 q^{59} - 35930 q^{61} + 19627 q^{62} - 100980 q^{63} + 14779 q^{64} + 28677 q^{66} - 73136 q^{67} + 83409 q^{68} + 34296 q^{69} + 43612 q^{71} - 372276 q^{72} - 142306 q^{73} - 95609 q^{74} - 6617 q^{76} + 8470 q^{77} - 15750 q^{78} - 46504 q^{79} + 79101 q^{81} - 175798 q^{82} - 81604 q^{83} - 532533 q^{84} - 101788 q^{86} - 219750 q^{87} + 91113 q^{88} + 8664 q^{89} - 203380 q^{91} - 251174 q^{92} + 46470 q^{93} - 71458 q^{94} - 925479 q^{96} + 22230 q^{97} - 59962 q^{98} - 128139 q^{99}+O(q^{100}) \) 5 * q - 9 * q^2 + 115 * q^4 - 237 * q^6 - 70 * q^7 - 753 * q^8 + 1059 * q^9 - 605 * q^11 + 1605 * q^12 - 1498 * q^13 + 2113 * q^14 + 4883 * q^16 - 3874 * q^17 - 5838 * q^18 + 882 * q^19 + 1092 * q^21 + 1089 * q^22 + 5344 * q^23 - 13119 * q^24 - 4478 * q^26 + 2160 * q^27 - 12565 * q^28 + 5318 * q^29 - 7916 * q^31 - 21385 * q^32 - 18605 * q^34 + 5628 * q^36 + 1788 * q^37 + 34421 * q^38 - 29760 * q^39 + 5854 * q^41 + 46725 * q^42 + 4364 * q^43 - 13915 * q^44 - 33834 * q^46 - 46452 * q^47 + 127545 * q^48 - 34217 * q^49 + 19842 * q^51 - 3222 * q^52 - 4412 * q^53 - 86535 * q^54 + 115575 * q^56 - 137160 * q^57 + 58221 * q^58 + 17896 * q^59 - 35930 * q^61 + 19627 * q^62 - 100980 * q^63 + 14779 * q^64 + 28677 * q^66 - 73136 * q^67 + 83409 * q^68 + 34296 * q^69 + 43612 * q^71 - 372276 * q^72 - 142306 * q^73 - 95609 * q^74 - 6617 * q^76 + 8470 * q^77 - 15750 * q^78 - 46504 * q^79 + 79101 * q^81 - 175798 * q^82 - 81604 * q^83 - 532533 * q^84 - 101788 * q^86 - 219750 * q^87 + 91113 * q^88 + 8664 * q^89 - 203380 * q^91 - 251174 * q^92 + 46470 * q^93 - 71458 * q^94 - 925479 * q^96 + 22230 * q^97 - 59962 * q^98 - 128139 * q^99

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