LMFDB - Embedded newform 1875.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.44400625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 $ x^6 - 11x^4 - x^3 + 29x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.141689$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.141689 q^{2} -1.00000 q^{3} -1.97992 q^{4} +0.141689 q^{6} -0.858311 q^{7} +0.563913 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.141689 q^{2} -1.00000 q^{3} -1.97992 q^{4} +0.141689 q^{6} -0.858311 q^{7} +0.563913 q^{8} +1.00000 q^{9} -3.67993 q^{11} +1.97992 q^{12} +4.58134 q^{13} +0.121614 q^{14} +3.87995 q^{16} -5.30702 q^{17} -0.141689 q^{18} +6.36870 q^{19} +0.858311 q^{21} +0.521407 q^{22} +3.42379 q^{23} -0.563913 q^{24} -0.649128 q^{26} -1.00000 q^{27} +1.69939 q^{28} +3.73405 q^{29} +1.25290 q^{31} -1.67757 q^{32} +3.67993 q^{33} +0.751949 q^{34} -1.97992 q^{36} -7.45067 q^{37} -0.902378 q^{38} -4.58134 q^{39} -2.53168 q^{41} -0.121614 q^{42} -3.37972 q^{43} +7.28598 q^{44} -0.485114 q^{46} -8.49937 q^{47} -3.87995 q^{48} -6.26330 q^{49} +5.30702 q^{51} -9.07071 q^{52} -2.34827 q^{53} +0.141689 q^{54} -0.484013 q^{56} -6.36870 q^{57} -0.529076 q^{58} +13.1264 q^{59} +10.3476 q^{61} -0.177523 q^{62} -0.858311 q^{63} -7.52220 q^{64} -0.521407 q^{66} +3.34649 q^{67} +10.5075 q^{68} -3.42379 q^{69} -4.32289 q^{71} +0.563913 q^{72} -9.08007 q^{73} +1.05568 q^{74} -12.6095 q^{76} +3.15852 q^{77} +0.649128 q^{78} -3.24730 q^{79} +1.00000 q^{81} +0.358712 q^{82} -7.39269 q^{83} -1.69939 q^{84} +0.478870 q^{86} -3.73405 q^{87} -2.07516 q^{88} -15.4975 q^{89} -3.93221 q^{91} -6.77883 q^{92} -1.25290 q^{93} +1.20427 q^{94} +1.67757 q^{96} -10.0386 q^{97} +0.887444 q^{98} -3.67993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 3 * q^8 + 6 * q^9	$ 6 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 3 q^{8} + 6 q^{9} + 3 q^{11} - 10 q^{12} - 6 q^{13} - 22 q^{14} + 18 q^{16} - 13 q^{17} + 11 q^{19} + 6 q^{21} - 16 q^{22} - 13 q^{23} + 3 q^{24} - 28 q^{26} - 6 q^{27} - 7 q^{28} - 3 q^{29} - 11 q^{31} - 16 q^{32} - 3 q^{33} + 15 q^{34} + 10 q^{36} - 21 q^{37} + 9 q^{38} + 6 q^{39} - q^{41} + 22 q^{42} - 2 q^{43} + 9 q^{44} + 19 q^{46} - 14 q^{47} - 18 q^{48} - 14 q^{49} + 13 q^{51} - 13 q^{52} - 23 q^{53} - 35 q^{56} - 11 q^{57} - 22 q^{58} + 9 q^{59} + 11 q^{61} + 23 q^{62} - 6 q^{63} - 23 q^{64} + 16 q^{66} - 8 q^{67} - 50 q^{68} + 13 q^{69} - 8 q^{71} - 3 q^{72} - 13 q^{73} - 22 q^{74} - 26 q^{76} + 13 q^{77} + 28 q^{78} - 5 q^{79} + 6 q^{81} + 13 q^{82} + 20 q^{83} + 7 q^{84} - 37 q^{86} + 3 q^{87} - 28 q^{88} - 4 q^{89} + 34 q^{91} - 61 q^{92} + 11 q^{93} + 41 q^{94} + 16 q^{96} + 7 q^{97} + 41 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 3 * q^8 + 6 * q^9 + 3 * q^11 - 10 * q^12 - 6 * q^13 - 22 * q^14 + 18 * q^16 - 13 * q^17 + 11 * q^19 + 6 * q^21 - 16 * q^22 - 13 * q^23 + 3 * q^24 - 28 * q^26 - 6 * q^27 - 7 * q^28 - 3 * q^29 - 11 * q^31 - 16 * q^32 - 3 * q^33 + 15 * q^34 + 10 * q^36 - 21 * q^37 + 9 * q^38 + 6 * q^39 - q^41 + 22 * q^42 - 2 * q^43 + 9 * q^44 + 19 * q^46 - 14 * q^47 - 18 * q^48 - 14 * q^49 + 13 * q^51 - 13 * q^52 - 23 * q^53 - 35 * q^56 - 11 * q^57 - 22 * q^58 + 9 * q^59 + 11 * q^61 + 23 * q^62 - 6 * q^63 - 23 * q^64 + 16 * q^66 - 8 * q^67 - 50 * q^68 + 13 * q^69 - 8 * q^71 - 3 * q^72 - 13 * q^73 - 22 * q^74 - 26 * q^76 + 13 * q^77 + 28 * q^78 - 5 * q^79 + 6 * q^81 + 13 * q^82 + 20 * q^83 + 7 * q^84 - 37 * q^86 + 3 * q^87 - 28 * q^88 - 4 * q^89 + 34 * q^91 - 61 * q^92 + 11 * q^93 + 41 * q^94 + 16 * q^96 + 7 * q^97 + 41 * q^98 + 3 * 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 $

$2$	−0.141689	−0.100190	−0.0500948	−	0.998744i	$-0.515952\pi$
$2$	−0.141689	−0.100190	−0.0500948	+	0.998744i	$0.515952\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.97992	−0.989962
$5$	0	0
$5$	0	0
$6$	0.141689	0.0578445
$7$	−0.858311	−0.324411	−0.162205	−	0.986757i	$-0.551861\pi$
$7$	−0.858311	−0.324411	−0.162205	+	0.986757i	$0.551861\pi$
$8$	0.563913	0.199374
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.67993	−1.10954	−0.554770	−	0.832004i	$-0.687194\pi$
$11$	−3.67993	−1.10954	−0.554770	+	0.832004i	$0.687194\pi$
$12$	1.97992	0.571555
$13$	4.58134	1.27064	0.635318	−	0.772251i	$-0.280869\pi$
$13$	4.58134	1.27064	0.635318	+	0.772251i	$0.280869\pi$
$14$	0.121614	0.0325026
$15$	0	0
$16$	3.87995	0.969987
$17$	−5.30702	−1.28714	−0.643571	−	0.765387i	$-0.722548\pi$
$17$	−5.30702	−1.28714	−0.643571	+	0.765387i	$0.722548\pi$
$18$	−0.141689	−0.0333965
$19$	6.36870	1.46108	0.730540	−	0.682870i	$-0.239268\pi$
$19$	6.36870	1.46108	0.730540	+	0.682870i	$0.239268\pi$
$20$	0	0
$21$	0.858311	0.187299
$22$	0.521407	0.111164
$23$	3.42379	0.713909	0.356954	−	0.934122i	$-0.383815\pi$
$23$	3.42379	0.713909	0.356954	+	0.934122i	$0.383815\pi$
$24$	−0.563913	−0.115108
$25$	0	0
$26$	−0.649128	−0.127304
$27$	−1.00000	−0.192450
$28$	1.69939	0.321154
$29$	3.73405	0.693396	0.346698	−	0.937977i	$-0.387303\pi$
$29$	3.73405	0.693396	0.346698	+	0.937977i	$0.387303\pi$
$30$	0	0
$31$	1.25290	0.225028	0.112514	−	0.993650i	$-0.464110\pi$
$31$	1.25290	0.225028	0.112514	+	0.993650i	$0.464110\pi$
$32$	−1.67757	−0.296556
$33$	3.67993	0.640593
$34$	0.751949	0.128958
$35$	0	0
$36$	−1.97992	−0.329987
$37$	−7.45067	−1.22488	−0.612441	−	0.790516i	$-0.709812\pi$
$37$	−7.45067	−1.22488	−0.612441	+	0.790516i	$0.709812\pi$
$38$	−0.902378	−0.146385
$39$	−4.58134	−0.733602
$40$	0	0
$41$	−2.53168	−0.395381	−0.197691	−	0.980264i	$-0.563344\pi$
$41$	−2.53168	−0.395381	−0.197691	+	0.980264i	$0.563344\pi$
$42$	−0.121614	−0.0187654
$43$	−3.37972	−0.515402	−0.257701	−	0.966225i	$-0.582965\pi$
$43$	−3.37972	−0.515402	−0.257701	+	0.966225i	$0.582965\pi$
$44$	7.28598	1.09840
$45$	0	0
$46$	−0.485114	−0.0715262
$47$	−8.49937	−1.23976	−0.619880	−	0.784696i	$-0.712819\pi$
$47$	−8.49937	−1.23976	−0.619880	+	0.784696i	$0.712819\pi$
$48$	−3.87995	−0.560022
$49$	−6.26330	−0.894758
$50$	0	0
$51$	5.30702	0.743132
$52$	−9.07071	−1.25788
$53$	−2.34827	−0.322560	−0.161280	−	0.986909i	$-0.551562\pi$
$53$	−2.34827	−0.322560	−0.161280	+	0.986909i	$0.551562\pi$
$54$	0.141689	0.0192815
$55$	0	0
$56$	−0.484013	−0.0646789
$57$	−6.36870	−0.843555
$58$	−0.529076	−0.0694710
$59$	13.1264	1.70891	0.854455	−	0.519525i	$-0.173891\pi$
$59$	13.1264	1.70891	0.854455	+	0.519525i	$0.173891\pi$
$60$	0	0
$61$	10.3476	1.32488	0.662439	−	0.749116i	$-0.269521\pi$
$61$	10.3476	1.32488	0.662439	+	0.749116i	$0.269521\pi$
$62$	−0.177523	−0.0225454
$63$	−0.858311	−0.108137
$64$	−7.52220	−0.940275
$65$	0	0
$66$	−0.521407	−0.0641808
$67$	3.34649	0.408838	0.204419	−	0.978883i	$-0.434469\pi$
$67$	3.34649	0.408838	0.204419	+	0.978883i	$0.434469\pi$
$68$	10.5075	1.27422
$69$	−3.42379	−0.412175
$70$	0	0
$71$	−4.32289	−0.513032	−0.256516	−	0.966540i	$-0.582575\pi$
$71$	−4.32289	−0.513032	−0.256516	+	0.966540i	$0.582575\pi$
$72$	0.563913	0.0664578
$73$	−9.08007	−1.06274	−0.531371	−	0.847139i	$-0.678323\pi$
$73$	−9.08007	−1.06274	−0.531371	+	0.847139i	$0.678323\pi$
$74$	1.05568	0.122721
$75$	0	0
$76$	−12.6095	−1.44641
$77$	3.15852	0.359947
$78$	0.649128	0.0734993
$79$	−3.24730	−0.365350	−0.182675	−	0.983173i	$-0.558476\pi$
$79$	−3.24730	−0.365350	−0.182675	+	0.983173i	$0.558476\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0.358712	0.0396131
$83$	−7.39269	−0.811453	−0.405727	−	0.913994i	$-0.632981\pi$
$83$	−7.39269	−0.811453	−0.405727	+	0.913994i	$0.632981\pi$
$84$	−1.69939	−0.185419
$85$	0	0
$86$	0.478870	0.0516379
$87$	−3.73405	−0.400332
$88$	−2.07516	−0.221213
$89$	−15.4975	−1.64273	−0.821367	−	0.570400i	$-0.806788\pi$
$89$	−15.4975	−1.64273	−0.821367	+	0.570400i	$0.806788\pi$
$90$	0	0
$91$	−3.93221	−0.412208
$92$	−6.77883	−0.706742
$93$	−1.25290	−0.129920
$94$	1.20427	0.124211
$95$	0	0
$96$	1.67757	0.171217
$97$	−10.0386	−1.01926	−0.509631	−	0.860393i	$-0.670218\pi$
$97$	−10.0386	−1.01926	−0.509631	+	0.860393i	$0.670218\pi$
$98$	0.887444	0.0896454
$99$	−3.67993	−0.369847
$100$	0	0
$101$	−0.714616	−0.0711070	−0.0355535	−	0.999368i	$-0.511319\pi$
$101$	−0.714616	−0.0711070	−0.0355535	+	0.999368i	$0.511319\pi$
$102$	−0.751949	−0.0744541
$103$	0.780764	0.0769310	0.0384655	−	0.999260i	$-0.487753\pi$
$103$	0.780764	0.0769310	0.0384655	+	0.999260i	$0.487753\pi$
$104$	2.58348	0.253331
$105$	0	0
$106$	0.332725	0.0323171
$107$	11.9601	1.15623	0.578113	−	0.815957i	$-0.303789\pi$
$107$	11.9601	1.15623	0.578113	+	0.815957i	$0.303789\pi$
$108$	1.97992	0.190518
$109$	2.43384	0.233119	0.116560	−	0.993184i	$-0.462813\pi$
$109$	2.43384	0.233119	0.116560	+	0.993184i	$0.462813\pi$
$110$	0	0
$111$	7.45067	0.707186
$112$	−3.33020	−0.314674
$113$	−16.0354	−1.50848	−0.754240	−	0.656599i	$-0.771994\pi$
$113$	−16.0354	−1.50848	−0.754240	+	0.656599i	$0.771994\pi$
$114$	0.902378	0.0845154
$115$	0	0
$116$	−7.39313	−0.686435
$117$	4.58134	0.423545
$118$	−1.85987	−0.171215
$119$	4.55507	0.417563
$120$	0	0
$121$	2.54188	0.231080
$122$	−1.46615	−0.132739
$123$	2.53168	0.228274
$124$	−2.48065	−0.222769
$125$	0	0
$126$	0.121614	0.0108342
$127$	−3.83848	−0.340610	−0.170305	−	0.985391i	$-0.554475\pi$
$127$	−3.83848	−0.340610	−0.170305	+	0.985391i	$0.554475\pi$
$128$	4.42097	0.390762
$129$	3.37972	0.297568
$130$	0	0
$131$	−12.4495	−1.08771	−0.543857	−	0.839178i	$-0.683037\pi$
$131$	−12.4495	−1.08771	−0.543857	+	0.839178i	$0.683037\pi$
$132$	−7.28598	−0.634163
$133$	−5.46632	−0.473990
$134$	−0.474162	−0.0409613
$135$	0	0
$136$	−2.99270	−0.256622
$137$	−11.8589	−1.01317	−0.506587	−	0.862189i	$-0.669093\pi$
$137$	−11.8589	−1.01317	−0.506587	+	0.862189i	$0.669093\pi$
$138$	0.485114	0.0412957
$139$	−4.66089	−0.395332	−0.197666	−	0.980269i	$-0.563336\pi$
$139$	−4.66089	−0.395332	−0.197666	+	0.980269i	$0.563336\pi$
$140$	0	0
$141$	8.49937	0.715776
$142$	0.612508	0.0514005
$143$	−16.8590	−1.40982
$144$	3.87995	0.323329
$145$	0	0
$146$	1.28655	0.106476
$147$	6.26330	0.516589
$148$	14.7518	1.21259
$149$	−11.5480	−0.946053	−0.473026	−	0.881048i	$-0.656838\pi$
$149$	−11.5480	−0.946053	−0.473026	+	0.881048i	$0.656838\pi$
$150$	0	0
$151$	24.4694	1.99129	0.995646	−	0.0932103i	$-0.0297129\pi$
$151$	24.4694	1.99129	0.995646	+	0.0932103i	$0.0297129\pi$
$152$	3.59140	0.291301
$153$	−5.30702	−0.429047
$154$	−0.447529	−0.0360629
$155$	0	0
$156$	9.07071	0.726238
$157$	−22.3660	−1.78500	−0.892501	−	0.451045i	$-0.851052\pi$
$157$	−22.3660	−1.78500	−0.892501	+	0.451045i	$0.851052\pi$
$158$	0.460109	0.0366043
$159$	2.34827	0.186230
$160$	0	0
$161$	−2.93867	−0.231600
$162$	−0.141689	−0.0111322
$163$	−0.813450	−0.0637143	−0.0318572	−	0.999492i	$-0.510142\pi$
$163$	−0.813450	−0.0637143	−0.0318572	+	0.999492i	$0.510142\pi$
$164$	5.01253	0.391413
$165$	0	0
$166$	1.04747	0.0812992
$167$	−25.1660	−1.94740	−0.973700	−	0.227833i	$-0.926836\pi$
$167$	−25.1660	−1.94740	−0.973700	+	0.227833i	$0.926836\pi$
$168$	0.484013	0.0373424
$169$	7.98869	0.614515
$170$	0	0
$171$	6.36870	0.487027
$172$	6.69158	0.510229
$173$	0.410945	0.0312436	0.0156218	−	0.999878i	$-0.495027\pi$
$173$	0.410945	0.0312436	0.0156218	+	0.999878i	$0.495027\pi$
$174$	0.529076	0.0401091
$175$	0	0
$176$	−14.2779	−1.07624
$177$	−13.1264	−0.986640
$178$	2.19584	0.164585
$179$	−14.8502	−1.10996	−0.554978	−	0.831865i	$-0.687273\pi$
$179$	−14.8502	−1.10996	−0.554978	+	0.831865i	$0.687273\pi$
$180$	0	0
$181$	0.739223	0.0549460	0.0274730	−	0.999623i	$-0.491254\pi$
$181$	0.739223	0.0549460	0.0274730	+	0.999623i	$0.491254\pi$
$182$	0.557153	0.0412990
$183$	−10.3476	−0.764919
$184$	1.93072	0.142334
$185$	0	0
$186$	0.177523	0.0130166
$187$	19.5295	1.42814
$188$	16.8281	1.22732
$189$	0.858311	0.0624329
$190$	0	0
$191$	−2.72506	−0.197179	−0.0985893	−	0.995128i	$-0.531433\pi$
$191$	−2.72506	−0.197179	−0.0985893	+	0.995128i	$0.531433\pi$
$192$	7.52220	0.542868
$193$	14.2040	1.02243	0.511215	−	0.859453i	$-0.329196\pi$
$193$	14.2040	1.02243	0.511215	+	0.859453i	$0.329196\pi$
$194$	1.42236	0.102120
$195$	0	0
$196$	12.4009	0.885776
$197$	−5.54591	−0.395130	−0.197565	−	0.980290i	$-0.563303\pi$
$197$	−5.54591	−0.395130	−0.197565	+	0.980290i	$0.563303\pi$
$198$	0.521407	0.0370548
$199$	5.96371	0.422756	0.211378	−	0.977404i	$-0.432205\pi$
$199$	5.96371	0.422756	0.211378	+	0.977404i	$0.432205\pi$
$200$	0	0
$201$	−3.34649	−0.236043
$202$	0.101254	0.00712418
$203$	−3.20497	−0.224945
$204$	−10.5075	−0.735672
$205$	0	0
$206$	−0.110626	−0.00770768
$207$	3.42379	0.237970
$208$	17.7754	1.23250
$209$	−23.4364	−1.62113
$210$	0	0
$211$	−13.7183	−0.944407	−0.472204	−	0.881490i	$-0.656541\pi$
$211$	−13.7183	−0.944407	−0.472204	+	0.881490i	$0.656541\pi$
$212$	4.64940	0.319322
$213$	4.32289	0.296199
$214$	−1.69462	−0.115842
$215$	0	0
$216$	−0.563913	−0.0383694
$217$	−1.07538	−0.0730014
$218$	−0.344849	−0.0233561
$219$	9.08007	0.613574
$220$	0	0
$221$	−24.3133	−1.63549
$222$	−1.05568	−0.0708527
$223$	3.24170	0.217081	0.108540	−	0.994092i	$-0.465382\pi$
$223$	3.24170	0.217081	0.108540	+	0.994092i	$0.465382\pi$
$224$	1.43988	0.0962060
$225$	0	0
$226$	2.27204	0.151134
$227$	13.1799	0.874779	0.437390	−	0.899272i	$-0.355903\pi$
$227$	13.1799	0.874779	0.437390	+	0.899272i	$0.355903\pi$
$228$	12.6095	0.835087
$229$	5.83810	0.385793	0.192896	−	0.981219i	$-0.438212\pi$
$229$	5.83810	0.385793	0.192896	+	0.981219i	$0.438212\pi$
$230$	0	0
$231$	−3.15852	−0.207815
$232$	2.10568	0.138245
$233$	9.33453	0.611526	0.305763	−	0.952108i	$-0.401089\pi$
$233$	9.33453	0.611526	0.305763	+	0.952108i	$0.401089\pi$
$234$	−0.649128	−0.0424348
$235$	0	0
$236$	−25.9893	−1.69176
$237$	3.24730	0.210935
$238$	−0.645406	−0.0418354
$239$	17.1502	1.10935	0.554676	−	0.832066i	$-0.312842\pi$
$239$	17.1502	1.10935	0.554676	+	0.832066i	$0.312842\pi$
$240$	0	0
$241$	7.22073	0.465128	0.232564	−	0.972581i	$-0.425289\pi$
$241$	7.22073	0.465128	0.232564	+	0.972581i	$0.425289\pi$
$242$	−0.360157	−0.0231518
$243$	−1.00000	−0.0641500
$244$	−20.4875	−1.31158
$245$	0	0
$246$	−0.358712	−0.0228706
$247$	29.1772	1.85650
$248$	0.706527	0.0448645
$249$	7.39269	0.468493
$250$	0	0
$251$	−5.75708	−0.363383	−0.181692	−	0.983356i	$-0.558157\pi$
$251$	−5.75708	−0.363383	−0.181692	+	0.983356i	$0.558157\pi$
$252$	1.69939	0.107051
$253$	−12.5993	−0.792110
$254$	0.543872	0.0341256
$255$	0	0
$256$	14.4180	0.901125
$257$	26.9602	1.68173	0.840867	−	0.541242i	$-0.182046\pi$
$257$	26.9602	1.68173	0.840867	+	0.541242i	$0.182046\pi$
$258$	−0.478870	−0.0298132
$259$	6.39499	0.397365
$260$	0	0
$261$	3.73405	0.231132
$262$	1.76396	0.108978
$263$	20.6673	1.27440	0.637200	−	0.770699i	$-0.280093\pi$
$263$	20.6673	1.27440	0.637200	+	0.770699i	$0.280093\pi$
$264$	2.07516	0.127717
$265$	0	0
$266$	0.774520	0.0474889
$267$	15.4975	0.948433
$268$	−6.62579	−0.404734
$269$	−13.7435	−0.837958	−0.418979	−	0.907996i	$-0.637612\pi$
$269$	−13.7435	−0.837958	−0.418979	+	0.907996i	$0.637612\pi$
$270$	0	0
$271$	3.34392	0.203128	0.101564	−	0.994829i	$-0.467615\pi$
$271$	3.34392	0.203128	0.101564	+	0.994829i	$0.467615\pi$
$272$	−20.5910	−1.24851
$273$	3.93221	0.237988
$274$	1.68028	0.101510
$275$	0	0
$276$	6.77883	0.408038
$277$	8.90947	0.535318	0.267659	−	0.963514i	$-0.413750\pi$
$277$	8.90947	0.535318	0.267659	+	0.963514i	$0.413750\pi$
$278$	0.660400	0.0396081
$279$	1.25290	0.0750092
$280$	0	0
$281$	−22.4913	−1.34172	−0.670859	−	0.741585i	$-0.734074\pi$
$281$	−22.4913	−1.34172	−0.670859	+	0.741585i	$0.734074\pi$
$282$	−1.20427	−0.0717133
$283$	1.30694	0.0776894	0.0388447	−	0.999245i	$-0.487632\pi$
$283$	1.30694	0.0776894	0.0388447	+	0.999245i	$0.487632\pi$
$284$	8.55899	0.507883
$285$	0	0
$286$	2.38874	0.141249
$287$	2.17296	0.128266
$288$	−1.67757	−0.0988520
$289$	11.1645	0.656733
$290$	0	0
$291$	10.0386	0.588472
$292$	17.9779	1.05207
$293$	1.97058	0.115123	0.0575613	−	0.998342i	$-0.481668\pi$
$293$	1.97058	0.115123	0.0575613	+	0.998342i	$0.481668\pi$
$294$	−0.887444	−0.0517568
$295$	0	0
$296$	−4.20153	−0.244209
$297$	3.67993	0.213531
$298$	1.63624	0.0947847
$299$	15.6855	0.907118
$300$	0	0
$301$	2.90085	0.167202
$302$	−3.46706	−0.199507
$303$	0.714616	0.0410536
$304$	24.7102	1.41723
$305$	0	0
$306$	0.751949	0.0429861
$307$	−15.2544	−0.870617	−0.435308	−	0.900281i	$-0.643361\pi$
$307$	−15.2544	−0.870617	−0.435308	+	0.900281i	$0.643361\pi$
$308$	−6.25363	−0.356334
$309$	−0.780764	−0.0444161
$310$	0	0
$311$	17.7452	1.00624	0.503120	−	0.864217i	$-0.332185\pi$
$311$	17.7452	1.00624	0.503120	+	0.864217i	$0.332185\pi$
$312$	−2.58348	−0.146261
$313$	−27.3869	−1.54800	−0.773999	−	0.633187i	$-0.781747\pi$
$313$	−27.3869	−1.54800	−0.773999	+	0.633187i	$0.781747\pi$
$314$	3.16903	0.178839
$315$	0	0
$316$	6.42941	0.361683
$317$	8.64563	0.485587	0.242793	−	0.970078i	$-0.421936\pi$
$317$	8.64563	0.485587	0.242793	+	0.970078i	$0.421936\pi$
$318$	−0.332725	−0.0186583
$319$	−13.7410	−0.769350
$320$	0	0
$321$	−11.9601	−0.667547
$322$	0.416379	0.0232039
$323$	−33.7988	−1.88062
$324$	−1.97992	−0.109996
$325$	0	0
$326$	0.115257	0.00638351
$327$	−2.43384	−0.134592
$328$	−1.42765	−0.0788286
$329$	7.29510	0.402192
$330$	0	0
$331$	4.96260	0.272769	0.136385	−	0.990656i	$-0.456452\pi$
$331$	4.96260	0.272769	0.136385	+	0.990656i	$0.456452\pi$
$332$	14.6370	0.803308
$333$	−7.45067	−0.408294
$334$	3.56575	0.195109
$335$	0	0
$336$	3.33020	0.181677
$337$	−7.30529	−0.397945	−0.198972	−	0.980005i	$-0.563760\pi$
$337$	−7.30529	−0.397945	−0.198972	+	0.980005i	$0.563760\pi$
$338$	−1.13191	−0.0615680
$339$	16.0354	0.870921
$340$	0	0
$341$	−4.61058	−0.249677
$342$	−0.902378	−0.0487950
$343$	11.3840	0.614680
$344$	−1.90587	−0.102758
$345$	0	0
$346$	−0.0582266	−0.00313028
$347$	15.9374	0.855565	0.427783	−	0.903882i	$-0.359295\pi$
$347$	15.9374	0.855565	0.427783	+	0.903882i	$0.359295\pi$
$348$	7.39313	0.396314
$349$	16.5844	0.887743	0.443871	−	0.896091i	$-0.353605\pi$
$349$	16.5844	0.887743	0.443871	+	0.896091i	$0.353605\pi$
$350$	0	0
$351$	−4.58134	−0.244534
$352$	6.17336	0.329041
$353$	12.9691	0.690277	0.345138	−	0.938552i	$-0.387832\pi$
$353$	12.9691	0.690277	0.345138	+	0.938552i	$0.387832\pi$
$354$	1.85987	0.0988511
$355$	0	0
$356$	30.6839	1.62624
$357$	−4.55507	−0.241080
$358$	2.10412	0.111206
$359$	−13.4920	−0.712082	−0.356041	−	0.934470i	$-0.615874\pi$
$359$	−13.4920	−0.712082	−0.356041	+	0.934470i	$0.615874\pi$
$360$	0	0
$361$	21.5603	1.13475
$362$	−0.104740	−0.00550502
$363$	−2.54188	−0.133414
$364$	7.78549	0.408070
$365$	0	0
$366$	1.46615	0.0766369
$367$	4.57463	0.238794	0.119397	−	0.992847i	$-0.461904\pi$
$367$	4.57463	0.238794	0.119397	+	0.992847i	$0.461904\pi$
$368$	13.2841	0.692482
$369$	−2.53168	−0.131794
$370$	0	0
$371$	2.01555	0.104642
$372$	2.48065	0.128616
$373$	−20.7463	−1.07420	−0.537101	−	0.843518i	$-0.680481\pi$
$373$	−20.7463	−1.07420	−0.537101	+	0.843518i	$0.680481\pi$
$374$	−2.76712	−0.143084
$375$	0	0
$376$	−4.79291	−0.247175
$377$	17.1070	0.881053
$378$	−0.121614	−0.00625513
$379$	−5.78163	−0.296982	−0.148491	−	0.988914i	$-0.547442\pi$
$379$	−5.78163	−0.296982	−0.148491	+	0.988914i	$0.547442\pi$
$380$	0	0
$381$	3.83848	0.196651
$382$	0.386113	0.0197553
$383$	25.8124	1.31895	0.659476	−	0.751726i	$-0.270778\pi$
$383$	25.8124	1.31895	0.659476	+	0.751726i	$0.270778\pi$
$384$	−4.42097	−0.225606
$385$	0	0
$386$	−2.01256	−0.102437
$387$	−3.37972	−0.171801
$388$	19.8756	1.00903
$389$	−15.7046	−0.796254	−0.398127	−	0.917330i	$-0.630340\pi$
$389$	−15.7046	−0.796254	−0.398127	+	0.917330i	$0.630340\pi$
$390$	0	0
$391$	−18.1701	−0.918901
$392$	−3.53196	−0.178391
$393$	12.4495	0.627992
$394$	0.785797	0.0395879
$395$	0	0
$396$	7.28598	0.366134
$397$	−19.6040	−0.983895	−0.491948	−	0.870625i	$-0.663715\pi$
$397$	−19.6040	−0.983895	−0.491948	+	0.870625i	$0.663715\pi$
$398$	−0.844995	−0.0423558
$399$	5.46632	0.273658
$400$	0	0
$401$	−14.4239	−0.720297	−0.360148	−	0.932895i	$-0.617274\pi$
$401$	−14.4239	−0.720297	−0.360148	+	0.932895i	$0.617274\pi$
$402$	0.474162	0.0236490
$403$	5.73996	0.285928
$404$	1.41489	0.0703932
$405$	0	0
$406$	0.454111	0.0225372
$407$	27.4179	1.35906
$408$	2.99270	0.148161
$409$	−27.8742	−1.37829	−0.689146	−	0.724622i	$-0.742014\pi$
$409$	−27.8742	−1.37829	−0.689146	+	0.724622i	$0.742014\pi$
$410$	0	0
$411$	11.8589	0.584957
$412$	−1.54585	−0.0761588
$413$	−11.2665	−0.554389
$414$	−0.485114	−0.0238421
$415$	0	0
$416$	−7.68554	−0.376815
$417$	4.66089	0.228245
$418$	3.32069	0.162420
$419$	−36.2881	−1.77279	−0.886396	−	0.462928i	$-0.846799\pi$
$419$	−36.2881	−1.77279	−0.886396	+	0.462928i	$0.846799\pi$
$420$	0	0
$421$	−3.37600	−0.164536	−0.0822681	−	0.996610i	$-0.526216\pi$
$421$	−3.37600	−0.164536	−0.0822681	+	0.996610i	$0.526216\pi$
$422$	1.94374	0.0946198
$423$	−8.49937	−0.413254
$424$	−1.32422	−0.0643099
$425$	0	0
$426$	−0.612508	−0.0296761
$427$	−8.88148	−0.429805
$428$	−23.6801	−1.14462
$429$	16.8590	0.813961
$430$	0	0
$431$	−25.6625	−1.23612	−0.618059	−	0.786131i	$-0.712081\pi$
$431$	−25.6625	−1.23612	−0.618059	+	0.786131i	$0.712081\pi$
$432$	−3.87995	−0.186674
$433$	−39.8070	−1.91300	−0.956501	−	0.291730i	$-0.905769\pi$
$433$	−39.8070	−1.91300	−0.956501	+	0.291730i	$0.905769\pi$
$434$	0.152370	0.00731398
$435$	0	0
$436$	−4.81882	−0.230779
$437$	21.8051	1.04308
$438$	−1.28655	−0.0614738
$439$	33.9180	1.61882	0.809408	−	0.587247i	$-0.199788\pi$
$439$	33.9180	1.61882	0.809408	+	0.587247i	$0.199788\pi$
$440$	0	0
$441$	−6.26330	−0.298253
$442$	3.44494	0.163859
$443$	−28.9300	−1.37451	−0.687253	−	0.726418i	$-0.741184\pi$
$443$	−28.9300	−1.37451	−0.687253	+	0.726418i	$0.741184\pi$
$444$	−14.7518	−0.700088
$445$	0	0
$446$	−0.459315	−0.0217492
$447$	11.5480	0.546204
$448$	6.45638	0.305035
$449$	−10.2089	−0.481788	−0.240894	−	0.970551i	$-0.577441\pi$
$449$	−10.2089	−0.481788	−0.240894	+	0.970551i	$0.577441\pi$
$450$	0	0
$451$	9.31639	0.438692
$452$	31.7488	1.49334
$453$	−24.4694	−1.14967
$454$	−1.86745	−0.0876438
$455$	0	0
$456$	−3.59140	−0.168182
$457$	32.4952	1.52006	0.760030	−	0.649888i	$-0.225184\pi$
$457$	32.4952	1.52006	0.760030	+	0.649888i	$0.225184\pi$
$458$	−0.827198	−0.0386524
$459$	5.30702	0.247711
$460$	0	0
$461$	−0.700568	−0.0326287	−0.0163144	−	0.999867i	$-0.505193\pi$
$461$	−0.700568	−0.0326287	−0.0163144	+	0.999867i	$0.505193\pi$
$462$	0.447529	0.0208209
$463$	2.17126	0.100907	0.0504535	−	0.998726i	$-0.483933\pi$
$463$	2.17126	0.100907	0.0504535	+	0.998726i	$0.483933\pi$
$464$	14.4879	0.672585
$465$	0	0
$466$	−1.32261	−0.0612685
$467$	−3.87710	−0.179411	−0.0897053	−	0.995968i	$-0.528593\pi$
$467$	−3.87710	−0.179411	−0.0897053	+	0.995968i	$0.528593\pi$
$468$	−9.07071	−0.419294
$469$	−2.87232	−0.132632
$470$	0	0
$471$	22.3660	1.03057
$472$	7.40215	0.340711
$473$	12.4371	0.571859
$474$	−0.460109	−0.0211335
$475$	0	0
$476$	−9.01870	−0.413371
$477$	−2.34827	−0.107520
$478$	−2.43000	−0.111146
$479$	−21.9994	−1.00518	−0.502588	−	0.864526i	$-0.667619\pi$
$479$	−21.9994	−1.00518	−0.502588	+	0.864526i	$0.667619\pi$
$480$	0	0
$481$	−34.1341	−1.55638
$482$	−1.02310	−0.0466010
$483$	2.93867	0.133714
$484$	−5.03272	−0.228760
$485$	0	0
$486$	0.141689	0.00642717
$487$	28.3997	1.28692	0.643458	−	0.765482i	$-0.277499\pi$
$487$	28.3997	1.28692	0.643458	+	0.765482i	$0.277499\pi$
$488$	5.83517	0.264146
$489$	0.813450	0.0367855
$490$	0	0
$491$	−14.0468	−0.633925	−0.316963	−	0.948438i	$-0.602663\pi$
$491$	−14.0468	−0.633925	−0.316963	+	0.948438i	$0.602663\pi$
$492$	−5.01253	−0.225982
$493$	−19.8167	−0.892498
$494$	−4.13410	−0.186002
$495$	0	0
$496$	4.86119	0.218274
$497$	3.71038	0.166433
$498$	−1.04747	−0.0469381
$499$	13.0842	0.585731	0.292866	−	0.956154i	$-0.405391\pi$
$499$	13.0842	0.585731	0.292866	+	0.956154i	$0.405391\pi$
$500$	0	0
$501$	25.1660	1.12433
$502$	0.815717	0.0364072
$503$	12.3044	0.548625	0.274312	−	0.961641i	$-0.411550\pi$
$503$	12.3044	0.548625	0.274312	+	0.961641i	$0.411550\pi$
$504$	−0.484013	−0.0215596
$505$	0	0
$506$	1.78519	0.0793612
$507$	−7.98869	−0.354790
$508$	7.59990	0.337191
$509$	0.0783897	0.00347456	0.00173728	−	0.999998i	$-0.499447\pi$
$509$	0.0783897	0.00347456	0.00173728	+	0.999998i	$0.499447\pi$
$510$	0	0
$511$	7.79352	0.344765
$512$	−10.8848	−0.481045
$513$	−6.36870	−0.281185
$514$	−3.81998	−0.168492
$515$	0	0
$516$	−6.69158	−0.294581
$517$	31.2771	1.37556
$518$	−0.906103	−0.0398119
$519$	−0.410945	−0.0180385
$520$	0	0
$521$	18.1194	0.793824	0.396912	−	0.917857i	$-0.370082\pi$
$521$	18.1194	0.793824	0.396912	+	0.917857i	$0.370082\pi$
$522$	−0.529076	−0.0231570
$523$	11.6303	0.508558	0.254279	−	0.967131i	$-0.418162\pi$
$523$	11.6303	0.508558	0.254279	+	0.967131i	$0.418162\pi$
$524$	24.6490	1.07680
$525$	0	0
$526$	−2.92834	−0.127682
$527$	−6.64917	−0.289642
$528$	14.2779	0.621367
$529$	−11.2777	−0.490335
$530$	0	0
$531$	13.1264	0.569637
$532$	10.8229	0.469232
$533$	−11.5985	−0.502386
$534$	−2.19584	−0.0950231
$535$	0	0
$536$	1.88713	0.0815115
$537$	14.8502	0.640833
$538$	1.94732	0.0839547
$539$	23.0485	0.992770
$540$	0	0
$541$	29.2716	1.25848	0.629242	−	0.777209i	$-0.283365\pi$
$541$	29.2716	1.25848	0.629242	+	0.777209i	$0.283365\pi$
$542$	−0.473798	−0.0203514
$543$	−0.739223	−0.0317231
$544$	8.90292	0.381710
$545$	0	0
$546$	−0.557153	−0.0238440
$547$	12.0675	0.515971	0.257985	−	0.966149i	$-0.416941\pi$
$547$	12.0675	0.515971	0.257985	+	0.966149i	$0.416941\pi$
$548$	23.4797	1.00300
$549$	10.3476	0.441626
$550$	0	0
$551$	23.7810	1.01311
$552$	−1.93072	−0.0821768
$553$	2.78719	0.118524
$554$	−1.26238	−0.0536333
$555$	0	0
$556$	9.22821	0.391363
$557$	−41.4154	−1.75483	−0.877413	−	0.479737i	$-0.840732\pi$
$557$	−41.4154	−1.75483	−0.877413	+	0.479737i	$0.840732\pi$
$558$	−0.177523	−0.00751514
$559$	−15.4836	−0.654888
$560$	0	0
$561$	−19.5295	−0.824534
$562$	3.18678	0.134426
$563$	−32.1467	−1.35482	−0.677411	−	0.735604i	$-0.736898\pi$
$563$	−32.1467	−1.35482	−0.677411	+	0.735604i	$0.736898\pi$
$564$	−16.8281	−0.708591
$565$	0	0
$566$	−0.185179	−0.00778367
$567$	−0.858311	−0.0360457
$568$	−2.43773	−0.102285
$569$	21.1080	0.884893	0.442446	−	0.896795i	$-0.354111\pi$
$569$	21.1080	0.884893	0.442446	+	0.896795i	$0.354111\pi$
$570$	0	0
$571$	−24.7493	−1.03573	−0.517863	−	0.855464i	$-0.673272\pi$
$571$	−24.7493	−1.03573	−0.517863	+	0.855464i	$0.673272\pi$
$572$	33.3796	1.39567
$573$	2.72506	0.113841
$574$	−0.307886	−0.0128509
$575$	0	0
$576$	−7.52220	−0.313425
$577$	−18.7710	−0.781448	−0.390724	−	0.920508i	$-0.627775\pi$
$577$	−18.7710	−0.781448	−0.390724	+	0.920508i	$0.627775\pi$
$578$	−1.58189	−0.0657979
$579$	−14.2040	−0.590300
$580$	0	0
$581$	6.34522	0.263244
$582$	−1.42236	−0.0589587
$583$	8.64147	0.357893
$584$	−5.12037	−0.211883
$585$	0	0
$586$	−0.279211	−0.0115341
$587$	14.7572	0.609095	0.304547	−	0.952497i	$-0.401495\pi$
$587$	14.7572	0.609095	0.304547	+	0.952497i	$0.401495\pi$
$588$	−12.4009	−0.511403
$589$	7.97935	0.328783
$590$	0	0
$591$	5.54591	0.228128
$592$	−28.9082	−1.18812
$593$	8.01859	0.329284	0.164642	−	0.986353i	$-0.447353\pi$
$593$	8.01859	0.329284	0.164642	+	0.986353i	$0.447353\pi$
$594$	−0.521407	−0.0213936
$595$	0	0
$596$	22.8643	0.936556
$597$	−5.96371	−0.244078
$598$	−2.22247	−0.0908838
$599$	−1.28951	−0.0526878	−0.0263439	−	0.999653i	$-0.508386\pi$
$599$	−1.28951	−0.0526878	−0.0263439	+	0.999653i	$0.508386\pi$
$600$	0	0
$601$	−16.8813	−0.688603	−0.344302	−	0.938859i	$-0.611884\pi$
$601$	−16.8813	−0.688603	−0.344302	+	0.938859i	$0.611884\pi$
$602$	−0.411020	−0.0167519
$603$	3.34649	0.136279
$604$	−48.4476	−1.97130
$605$	0	0
$606$	−0.101254	−0.00411315
$607$	−0.499318	−0.0202667	−0.0101334	−	0.999949i	$-0.503226\pi$
$607$	−0.499318	−0.0202667	−0.0101334	+	0.999949i	$0.503226\pi$
$608$	−10.6840	−0.433292
$609$	3.20497	0.129872
$610$	0	0
$611$	−38.9385	−1.57528
$612$	10.5075	0.424740
$613$	27.4241	1.10765	0.553825	−	0.832633i	$-0.313168\pi$
$613$	27.4241	1.10765	0.553825	+	0.832633i	$0.313168\pi$
$614$	2.16139	0.0872267
$615$	0	0
$616$	1.78113	0.0717639
$617$	−28.3205	−1.14014	−0.570070	−	0.821596i	$-0.693084\pi$
$617$	−28.3205	−1.14014	−0.570070	+	0.821596i	$0.693084\pi$
$618$	0.110626	0.00445003
$619$	−0.371804	−0.0149440	−0.00747202	−	0.999972i	$-0.502378\pi$
$619$	−0.371804	−0.0149440	−0.00747202	+	0.999972i	$0.502378\pi$
$620$	0	0
$621$	−3.42379	−0.137392
$622$	−2.51431	−0.100815
$623$	13.3017	0.532921
$624$	−17.7754	−0.711584
$625$	0	0
$626$	3.88043	0.155093
$627$	23.4364	0.935958
$628$	44.2830	1.76709
$629$	39.5409	1.57660
$630$	0	0
$631$	16.4507	0.654892	0.327446	−	0.944870i	$-0.393812\pi$
$631$	16.4507	0.654892	0.327446	+	0.944870i	$0.393812\pi$
$632$	−1.83120	−0.0728411
$633$	13.7183	0.545254
$634$	−1.22499	−0.0486508
$635$	0	0
$636$	−4.64940	−0.184361
$637$	−28.6943	−1.13691
$638$	1.94696	0.0770809
$639$	−4.32289	−0.171011
$640$	0	0
$641$	−2.02604	−0.0800239	−0.0400119	−	0.999199i	$-0.512740\pi$
$641$	−2.02604	−0.0800239	−0.0400119	+	0.999199i	$0.512740\pi$
$642$	1.69462	0.0668813
$643$	−33.2034	−1.30941	−0.654706	−	0.755883i	$-0.727208\pi$
$643$	−33.2034	−1.30941	−0.654706	+	0.755883i	$0.727208\pi$
$644$	5.81834	0.229275
$645$	0	0
$646$	4.78894	0.188418
$647$	−40.5797	−1.59535	−0.797677	−	0.603085i	$-0.793938\pi$
$647$	−40.5797	−1.59535	−0.797677	+	0.603085i	$0.793938\pi$
$648$	0.563913	0.0221526
$649$	−48.3042	−1.89611
$650$	0	0
$651$	1.07538	0.0421474
$652$	1.61057	0.0630748
$653$	−9.29712	−0.363824	−0.181912	−	0.983315i	$-0.558229\pi$
$653$	−9.29712	−0.363824	−0.181912	+	0.983315i	$0.558229\pi$
$654$	0.344849	0.0134847
$655$	0	0
$656$	−9.82277	−0.383515
$657$	−9.08007	−0.354247
$658$	−1.03364	−0.0402954
$659$	−3.47563	−0.135391	−0.0676957	−	0.997706i	$-0.521565\pi$
$659$	−3.47563	−0.135391	−0.0676957	+	0.997706i	$0.521565\pi$
$660$	0	0
$661$	4.07303	0.158422	0.0792112	−	0.996858i	$-0.474760\pi$
$661$	4.07303	0.158422	0.0792112	+	0.996858i	$0.474760\pi$
$662$	−0.703148	−0.0273286
$663$	24.3133	0.944249
$664$	−4.16884	−0.161782
$665$	0	0
$666$	1.05568	0.0409068
$667$	12.7846	0.495021
$668$	49.8267	1.92785
$669$	−3.24170	−0.125332
$670$	0	0
$671$	−38.0785	−1.47001
$672$	−1.43988	−0.0555446
$673$	21.3843	0.824305	0.412153	−	0.911115i	$-0.364777\pi$
$673$	21.3843	0.824305	0.412153	+	0.911115i	$0.364777\pi$
$674$	1.03508	0.0398699
$675$	0	0
$676$	−15.8170	−0.608346
$677$	−20.3257	−0.781181	−0.390590	−	0.920565i	$-0.627729\pi$
$677$	−20.3257	−0.781181	−0.390590	+	0.920565i	$0.627729\pi$
$678$	−2.27204	−0.0872573
$679$	8.61621	0.330660
$680$	0	0
$681$	−13.1799	−0.505054
$682$	0.653271	0.0250150
$683$	−18.9591	−0.725449	−0.362725	−	0.931896i	$-0.618153\pi$
$683$	−18.9591	−0.725449	−0.362725	+	0.931896i	$0.618153\pi$
$684$	−12.6095	−0.482138
$685$	0	0
$686$	−1.61300	−0.0615845
$687$	−5.83810	−0.222737
$688$	−13.1131	−0.499933
$689$	−10.7582	−0.409856
$690$	0	0
$691$	14.8195	0.563762	0.281881	−	0.959449i	$-0.409042\pi$
$691$	14.8195	0.563762	0.281881	+	0.959449i	$0.409042\pi$
$692$	−0.813641	−0.0309300
$693$	3.15852	0.119982
$694$	−2.25816	−0.0857187
$695$	0	0
$696$	−2.10568	−0.0798156
$697$	13.4357	0.508912
$698$	−2.34984	−0.0889426
$699$	−9.33453	−0.353064
$700$	0	0
$701$	31.3996	1.18595	0.592973	−	0.805222i	$-0.297954\pi$
$701$	31.3996	1.18595	0.592973	+	0.805222i	$0.297954\pi$
$702$	0.649128	0.0244998
$703$	−47.4511	−1.78965
$704$	27.6812	1.04327
$705$	0	0
$706$	−1.83759	−0.0691586
$707$	0.613363	0.0230679
$708$	25.9893	0.976736
$709$	25.3324	0.951379	0.475690	−	0.879613i	$-0.342199\pi$
$709$	25.3324	0.951379	0.475690	+	0.879613i	$0.342199\pi$
$710$	0	0
$711$	−3.24730	−0.121783
$712$	−8.73926	−0.327518
$713$	4.28966	0.160649
$714$	0.645406	0.0241537
$715$	0	0
$716$	29.4023	1.09881
$717$	−17.1502	−0.640485
$718$	1.91168	0.0713432
$719$	−4.12711	−0.153915	−0.0769575	−	0.997034i	$-0.524521\pi$
$719$	−4.12711	−0.153915	−0.0769575	+	0.997034i	$0.524521\pi$
$720$	0	0
$721$	−0.670138	−0.0249572
$722$	−3.05487	−0.113691
$723$	−7.22073	−0.268542
$724$	−1.46361	−0.0543945
$725$	0	0
$726$	0.360157	0.0133667
$727$	23.0039	0.853168	0.426584	−	0.904448i	$-0.359717\pi$
$727$	23.0039	0.853168	0.426584	+	0.904448i	$0.359717\pi$
$728$	−2.21743	−0.0821834
$729$	1.00000	0.0370370
$730$	0	0
$731$	17.9362	0.663396
$732$	20.4875	0.757240
$733$	−9.35692	−0.345606	−0.172803	−	0.984956i	$-0.555282\pi$
$733$	−9.35692	−0.345606	−0.172803	+	0.984956i	$0.555282\pi$
$734$	−0.648176	−0.0239246
$735$	0	0
$736$	−5.74366	−0.211714
$737$	−12.3148	−0.453623
$738$	0.358712	0.0132044
$739$	−47.1754	−1.73538	−0.867688	−	0.497109i	$-0.834395\pi$
$739$	−47.1754	−1.73538	−0.867688	+	0.497109i	$0.834395\pi$
$740$	0	0
$741$	−29.1772	−1.07185
$742$	−0.285582	−0.0104840
$743$	2.39450	0.0878455	0.0439228	−	0.999035i	$-0.486014\pi$
$743$	2.39450	0.0878455	0.0439228	+	0.999035i	$0.486014\pi$
$744$	−0.706527	−0.0259025
$745$	0	0
$746$	2.93953	0.107624
$747$	−7.39269	−0.270484
$748$	−38.6668	−1.41380
$749$	−10.2655	−0.375092
$750$	0	0
$751$	−7.21632	−0.263327	−0.131664	−	0.991294i	$-0.542032\pi$
$751$	−7.21632	−0.263327	−0.131664	+	0.991294i	$0.542032\pi$
$752$	−32.9771	−1.20255
$753$	5.75708	0.209800
$754$	−2.42388	−0.0882724
$755$	0	0
$756$	−1.69939	−0.0618062
$757$	13.3742	0.486094	0.243047	−	0.970015i	$-0.421853\pi$
$757$	13.3742	0.486094	0.243047	+	0.970015i	$0.421853\pi$
$758$	0.819196	0.0297545
$759$	12.5993	0.457325
$760$	0	0
$761$	21.7541	0.788584	0.394292	−	0.918985i	$-0.370990\pi$
$761$	21.7541	0.788584	0.394292	+	0.918985i	$0.370990\pi$
$762$	−0.543872	−0.0197024
$763$	−2.08899	−0.0756265
$764$	5.39542	0.195199
$765$	0	0
$766$	−3.65735	−0.132145
$767$	60.1365	2.17140
$768$	−14.4180	−0.520265
$769$	14.2003	0.512077	0.256038	−	0.966667i	$-0.417583\pi$
$769$	14.2003	0.512077	0.256038	+	0.966667i	$0.417583\pi$
$770$	0	0
$771$	−26.9602	−0.970949
$772$	−28.1229	−1.01217
$773$	22.8365	0.821373	0.410687	−	0.911777i	$-0.365289\pi$
$773$	22.8365	0.821373	0.410687	+	0.911777i	$0.365289\pi$
$774$	0.478870	0.0172126
$775$	0	0
$776$	−5.66089	−0.203214
$777$	−6.39499	−0.229419
$778$	2.22517	0.0797763
$779$	−16.1235	−0.577684
$780$	0	0
$781$	15.9079	0.569230
$782$	2.57451	0.0920644
$783$	−3.73405	−0.133444
$784$	−24.3013	−0.867903
$785$	0	0
$786$	−1.76396	−0.0629183
$787$	−38.4761	−1.37153	−0.685763	−	0.727825i	$-0.740531\pi$
$787$	−38.4761	−1.37153	−0.685763	+	0.727825i	$0.740531\pi$
$788$	10.9805	0.391163
$789$	−20.6673	−0.735775
$790$	0	0
$791$	13.7633	0.489367
$792$	−2.07516	−0.0737376
$793$	47.4060	1.68344
$794$	2.77768	0.0985760
$795$	0	0
$796$	−11.8077	−0.418512
$797$	−1.86739	−0.0661464	−0.0330732	−	0.999453i	$-0.510529\pi$
$797$	−1.86739	−0.0661464	−0.0330732	+	0.999453i	$0.510529\pi$
$798$	−0.774520	−0.0274177
$799$	45.1063	1.59575
$800$	0	0
$801$	−15.4975	−0.547578
$802$	2.04372	0.0721662
$803$	33.4140	1.17916
$804$	6.62579	0.233673
$805$	0	0
$806$	−0.813293	−0.0286470
$807$	13.7435	0.483796
$808$	−0.402982	−0.0141768
$809$	35.1514	1.23586	0.617929	−	0.786234i	$-0.287972\pi$
$809$	35.1514	1.23586	0.617929	+	0.786234i	$0.287972\pi$
$810$	0	0
$811$	−6.59158	−0.231462	−0.115731	−	0.993281i	$-0.536921\pi$
$811$	−6.59158	−0.231462	−0.115731	+	0.993281i	$0.536921\pi$
$812$	6.34561	0.222687
$813$	−3.34392	−0.117276
$814$	−3.88483	−0.136163
$815$	0	0
$816$	20.5910	0.720828
$817$	−21.5244	−0.753044
$818$	3.94949	0.138091
$819$	−3.93221	−0.137403
$820$	0	0
$821$	5.25743	0.183486	0.0917428	−	0.995783i	$-0.470756\pi$
$821$	5.25743	0.183486	0.0917428	+	0.995783i	$0.470756\pi$
$822$	−1.68028	−0.0586066
$823$	−22.1919	−0.773560	−0.386780	−	0.922172i	$-0.626413\pi$
$823$	−22.1919	−0.773560	−0.386780	+	0.922172i	$0.626413\pi$
$824$	0.440283	0.0153380
$825$	0	0
$826$	1.59635	0.0555440
$827$	−6.56256	−0.228203	−0.114101	−	0.993469i	$-0.536399\pi$
$827$	−6.56256	−0.228203	−0.114101	+	0.993469i	$0.536399\pi$
$828$	−6.77883	−0.235581
$829$	25.0574	0.870279	0.435140	−	0.900363i	$-0.356699\pi$
$829$	25.0574	0.870279	0.435140	+	0.900363i	$0.356699\pi$
$830$	0	0
$831$	−8.90947	−0.309066
$832$	−34.4618	−1.19475
$833$	33.2395	1.15168
$834$	−0.660400	−0.0228678
$835$	0	0
$836$	46.4022	1.60485
$837$	−1.25290	−0.0433066
$838$	5.14165	0.177615
$839$	−42.1485	−1.45513	−0.727564	−	0.686040i	$-0.759348\pi$
$839$	−42.1485	−1.45513	−0.727564	+	0.686040i	$0.759348\pi$
$840$	0	0
$841$	−15.0569	−0.519203
$842$	0.478344	0.0164848
$843$	22.4913	0.774641
$844$	27.1612	0.934927
$845$	0	0
$846$	1.20427	0.0414037
$847$	−2.18172	−0.0749648
$848$	−9.11117	−0.312879
$849$	−1.30694	−0.0448540
$850$	0	0
$851$	−25.5095	−0.874454
$852$	−8.55899	−0.293226
$853$	43.2473	1.48076	0.740379	−	0.672189i	$-0.234646\pi$
$853$	43.2473	1.48076	0.740379	+	0.672189i	$0.234646\pi$
$854$	1.25841	0.0430620
$855$	0	0
$856$	6.74446	0.230521
$857$	−39.2430	−1.34052	−0.670258	−	0.742128i	$-0.733817\pi$
$857$	−39.2430	−1.34052	−0.670258	+	0.742128i	$0.733817\pi$
$858$	−2.38874	−0.0815504
$859$	52.6092	1.79500	0.897501	−	0.441013i	$-0.145381\pi$
$859$	52.6092	1.79500	0.897501	+	0.441013i	$0.145381\pi$
$860$	0	0
$861$	−2.17296	−0.0740544
$862$	3.63611	0.123846
$863$	−42.8744	−1.45946	−0.729731	−	0.683735i	$-0.760355\pi$
$863$	−42.8744	−1.45946	−0.729731	+	0.683735i	$0.760355\pi$
$864$	1.67757	0.0570722
$865$	0	0
$866$	5.64023	0.191663
$867$	−11.1645	−0.379165
$868$	2.12917	0.0722686
$869$	11.9498	0.405371
$870$	0	0
$871$	15.3314	0.519484
$872$	1.37247	0.0464778
$873$	−10.0386	−0.339754
$874$	−3.08955	−0.104506
$875$	0	0
$876$	−17.9779	−0.607415
$877$	−0.390314	−0.0131800	−0.00658999	−	0.999978i	$-0.502098\pi$
$877$	−0.390314	−0.0131800	−0.00658999	+	0.999978i	$0.502098\pi$
$878$	−4.80582	−0.162188
$879$	−1.97058	−0.0664660
$880$	0	0
$881$	44.7002	1.50599	0.752994	−	0.658028i	$-0.228609\pi$
$881$	44.7002	1.50599	0.752994	+	0.658028i	$0.228609\pi$
$882$	0.887444	0.0298818
$883$	32.7567	1.10235	0.551175	−	0.834390i	$-0.314180\pi$
$883$	32.7567	1.10235	0.551175	+	0.834390i	$0.314180\pi$
$884$	48.1384	1.61907
$885$	0	0
$886$	4.09908	0.137711
$887$	−15.7130	−0.527591	−0.263796	−	0.964579i	$-0.584974\pi$
$887$	−15.7130	−0.527591	−0.263796	+	0.964579i	$0.584974\pi$
$888$	4.20153	0.140994
$889$	3.29461	0.110498
$890$	0	0
$891$	−3.67993	−0.123282
$892$	−6.41833	−0.214902
$893$	−54.1299	−1.81139
$894$	−1.63624	−0.0547239
$895$	0	0
$896$	−3.79456	−0.126767
$897$	−15.6855	−0.523725
$898$	1.44649	0.0482701
$899$	4.67839	0.156033
$900$	0	0
$901$	12.4623	0.415180
$902$	−1.32003	−0.0439523
$903$	−2.90085	−0.0965342
$904$	−9.04256	−0.300751
$905$	0	0
$906$	3.46706	0.115185
$907$	−1.50466	−0.0499613	−0.0249806	−	0.999688i	$-0.507952\pi$
$907$	−1.50466	−0.0499613	−0.0249806	+	0.999688i	$0.507952\pi$
$908$	−26.0952	−0.865998
$909$	−0.714616	−0.0237023
$910$	0	0
$911$	11.4509	0.379386	0.189693	−	0.981843i	$-0.439251\pi$
$911$	11.4509	0.379386	0.189693	+	0.981843i	$0.439251\pi$
$912$	−24.7102	−0.818237
$913$	27.2046	0.900340
$914$	−4.60422	−0.152294
$915$	0	0
$916$	−11.5590	−0.381920
$917$	10.6855	0.352866
$918$	−0.751949	−0.0248180
$919$	−21.8001	−0.719119	−0.359559	−	0.933122i	$-0.617073\pi$
$919$	−21.8001	−0.719119	−0.359559	+	0.933122i	$0.617073\pi$
$920$	0	0
$921$	15.2544	0.502651
$922$	0.0992632	0.00326906
$923$	−19.8046	−0.651877
$924$	6.25363	0.205729
$925$	0	0
$926$	−0.307645	−0.0101098
$927$	0.780764	0.0256437
$928$	−6.26415	−0.205631
$929$	−30.7507	−1.00890	−0.504449	−	0.863442i	$-0.668304\pi$
$929$	−30.7507	−1.00890	−0.504449	+	0.863442i	$0.668304\pi$
$930$	0	0
$931$	−39.8891	−1.30731
$932$	−18.4817	−0.605387
$933$	−17.7452	−0.580953
$934$	0.549344	0.0179751
$935$	0	0
$936$	2.58348	0.0844437
$937$	−3.81060	−0.124487	−0.0622435	−	0.998061i	$-0.519826\pi$
$937$	−3.81060	−0.124487	−0.0622435	+	0.998061i	$0.519826\pi$
$938$	0.406978	0.0132883
$939$	27.3869	0.893737
$940$	0	0
$941$	−20.7043	−0.674939	−0.337470	−	0.941336i	$-0.609571\pi$
$941$	−20.7043	−0.674939	−0.337470	+	0.941336i	$0.609571\pi$
$942$	−3.16903	−0.103253
$943$	−8.66792	−0.282266
$944$	50.9297	1.65762
$945$	0	0
$946$	−1.76221	−0.0572944
$947$	15.6833	0.509639	0.254819	−	0.966989i	$-0.417984\pi$
$947$	15.6833	0.509639	0.254819	+	0.966989i	$0.417984\pi$
$948$	−6.42941	−0.208818
$949$	−41.5989	−1.35036
$950$	0	0
$951$	−8.64563	−0.280354
$952$	2.56867	0.0832509
$953$	−7.75207	−0.251114	−0.125557	−	0.992086i	$-0.540072\pi$
$953$	−7.75207	−0.251114	−0.125557	+	0.992086i	$0.540072\pi$
$954$	0.332725	0.0107724
$955$	0	0
$956$	−33.9560	−1.09822
$957$	13.7410	0.444185
$958$	3.11708	0.100708
$959$	10.1786	0.328685
$960$	0	0
$961$	−29.4302	−0.949363
$962$	4.83644	0.155933
$963$	11.9601	0.385409
$964$	−14.2965	−0.460459
$965$	0	0
$966$	−0.416379	−0.0133968
$967$	−48.4273	−1.55732	−0.778659	−	0.627447i	$-0.784100\pi$
$967$	−48.4273	−1.55732	−0.778659	+	0.627447i	$0.784100\pi$
$968$	1.43340	0.0460712
$969$	33.7988	1.08577
$970$	0	0
$971$	25.3350	0.813039	0.406520	−	0.913642i	$-0.366742\pi$
$971$	25.3350	0.813039	0.406520	+	0.913642i	$0.366742\pi$
$972$	1.97992	0.0635061
$973$	4.00049	0.128250
$974$	−4.02394	−0.128936
$975$	0	0
$976$	40.1483	1.28511
$977$	−1.16885	−0.0373948	−0.0186974	−	0.999825i	$-0.505952\pi$
$977$	−1.16885	−0.0373948	−0.0186974	+	0.999825i	$0.505952\pi$
$978$	−0.115257	−0.00368552
$979$	57.0298	1.82268
$980$	0	0
$981$	2.43384	0.0777065
$982$	1.99029	0.0635127
$983$	−23.9943	−0.765299	−0.382649	−	0.923894i	$-0.624988\pi$
$983$	−23.9943	−0.765299	−0.382649	+	0.923894i	$0.624988\pi$
$984$	1.42765	0.0455117
$985$	0	0
$986$	2.80782	0.0894190
$987$	−7.29510	−0.232206
$988$	−57.7686	−1.83786
$989$	−11.5714	−0.367950
$990$	0	0
$991$	−36.6726	−1.16494	−0.582472	−	0.812851i	$-0.697914\pi$
$991$	−36.6726	−1.16494	−0.582472	+	0.812851i	$0.697914\pi$
$992$	−2.10183	−0.0667333
$993$	−4.96260	−0.157483
$994$	−0.525722	−0.0166749
$995$	0	0
$996$	−14.6370	−0.463790
$997$	−57.0203	−1.80585	−0.902925	−	0.429798i	$-0.858585\pi$
$997$	−57.0203	−1.80585	−0.902925	+	0.429798i	$0.858585\pi$
$998$	−1.85390	−0.0586842
$999$	7.45067	0.235729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.j.1.3		6
3.2	odd	2		5625.2.a.p.1.4		6
5.2	odd	4		1875.2.b.f.1249.6		12
5.3	odd	4		1875.2.b.f.1249.7		12
5.4	even	2		1875.2.a.k.1.4		6
15.14	odd	2		5625.2.a.q.1.3		6
25.3	odd	20		375.2.i.d.49.4		24
25.4	even	10		375.2.g.c.76.2		12
25.6	even	5		75.2.g.c.61.2	yes	12
25.8	odd	20		375.2.i.d.199.3		24
25.17	odd	20		375.2.i.d.199.4		24
25.19	even	10		375.2.g.c.301.2		12
25.21	even	5		75.2.g.c.16.2	✓	12
25.22	odd	20		375.2.i.d.49.3		24
75.56	odd	10		225.2.h.d.136.2		12
75.71	odd	10		225.2.h.d.91.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.2	✓	12	25.21	even	5
75.2.g.c.61.2	yes	12	25.6	even	5
225.2.h.d.91.2		12	75.71	odd	10
225.2.h.d.136.2		12	75.56	odd	10
375.2.g.c.76.2		12	25.4	even	10
375.2.g.c.301.2		12	25.19	even	10
375.2.i.d.49.3		24	25.22	odd	20
375.2.i.d.49.4		24	25.3	odd	20
375.2.i.d.199.3		24	25.8	odd	20
375.2.i.d.199.4		24	25.17	odd	20
1875.2.a.j.1.3		6	1.1	even	1	trivial
1875.2.a.k.1.4		6	5.4	even	2
1875.2.b.f.1249.6		12	5.2	odd	4
1875.2.b.f.1249.7		12	5.3	odd	4
5625.2.a.p.1.4		6	3.2	odd	2
5625.2.a.q.1.3		6	15.14	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q-0.141689 q^{2} -1.00000 q^{3} -1.97992 q^{4} +0.141689 q^{6} -0.858311 q^{7} +0.563913 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.141689 q^{2} -1.00000 q^{3} -1.97992 q^{4} +0.141689 q^{6} -0.858311 q^{7} +0.563913 q^{8} +1.00000 q^{9} -3.67993 q^{11} +1.97992 q^{12} +4.58134 q^{13} +0.121614 q^{14} +3.87995 q^{16} -5.30702 q^{17} -0.141689 q^{18} +6.36870 q^{19} +0.858311 q^{21} +0.521407 q^{22} +3.42379 q^{23} -0.563913 q^{24} -0.649128 q^{26} -1.00000 q^{27} +1.69939 q^{28} +3.73405 q^{29} +1.25290 q^{31} -1.67757 q^{32} +3.67993 q^{33} +0.751949 q^{34} -1.97992 q^{36} -7.45067 q^{37} -0.902378 q^{38} -4.58134 q^{39} -2.53168 q^{41} -0.121614 q^{42} -3.37972 q^{43} +7.28598 q^{44} -0.485114 q^{46} -8.49937 q^{47} -3.87995 q^{48} -6.26330 q^{49} +5.30702 q^{51} -9.07071 q^{52} -2.34827 q^{53} +0.141689 q^{54} -0.484013 q^{56} -6.36870 q^{57} -0.529076 q^{58} +13.1264 q^{59} +10.3476 q^{61} -0.177523 q^{62} -0.858311 q^{63} -7.52220 q^{64} -0.521407 q^{66} +3.34649 q^{67} +10.5075 q^{68} -3.42379 q^{69} -4.32289 q^{71} +0.563913 q^{72} -9.08007 q^{73} +1.05568 q^{74} -12.6095 q^{76} +3.15852 q^{77} +0.649128 q^{78} -3.24730 q^{79} +1.00000 q^{81} +0.358712 q^{82} -7.39269 q^{83} -1.69939 q^{84} +0.478870 q^{86} -3.73405 q^{87} -2.07516 q^{88} -15.4975 q^{89} -3.93221 q^{91} -6.77883 q^{92} -1.25290 q^{93} +1.20427 q^{94} +1.67757 q^{96} -10.0386 q^{97} +0.887444 q^{98} -3.67993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 3 q^{8} + 6 q^{9} + 3 q^{11} - 10 q^{12} - 6 q^{13} - 22 q^{14} + 18 q^{16} - 13 q^{17} + 11 q^{19} + 6 q^{21} - 16 q^{22} - 13 q^{23} + 3 q^{24} - 28 q^{26} - 6 q^{27} - 7 q^{28} - 3 q^{29} - 11 q^{31} - 16 q^{32} - 3 q^{33} + 15 q^{34} + 10 q^{36} - 21 q^{37} + 9 q^{38} + 6 q^{39} - q^{41} + 22 q^{42} - 2 q^{43} + 9 q^{44} + 19 q^{46} - 14 q^{47} - 18 q^{48} - 14 q^{49} + 13 q^{51} - 13 q^{52} - 23 q^{53} - 35 q^{56} - 11 q^{57} - 22 q^{58} + 9 q^{59} + 11 q^{61} + 23 q^{62} - 6 q^{63} - 23 q^{64} + 16 q^{66} - 8 q^{67} - 50 q^{68} + 13 q^{69} - 8 q^{71} - 3 q^{72} - 13 q^{73} - 22 q^{74} - 26 q^{76} + 13 q^{77} + 28 q^{78} - 5 q^{79} + 6 q^{81} + 13 q^{82} + 20 q^{83} + 7 q^{84} - 37 q^{86} + 3 q^{87} - 28 q^{88} - 4 q^{89} + 34 q^{91} - 61 q^{92} + 11 q^{93} + 41 q^{94} + 16 q^{96} + 7 q^{97} + 41 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 3 * q^8 + 6 * q^9 + 3 * q^11 - 10 * q^12 - 6 * q^13 - 22 * q^14 + 18 * q^16 - 13 * q^17 + 11 * q^19 + 6 * q^21 - 16 * q^22 - 13 * q^23 + 3 * q^24 - 28 * q^26 - 6 * q^27 - 7 * q^28 - 3 * q^29 - 11 * q^31 - 16 * q^32 - 3 * q^33 + 15 * q^34 + 10 * q^36 - 21 * q^37 + 9 * q^38 + 6 * q^39 - q^41 + 22 * q^42 - 2 * q^43 + 9 * q^44 + 19 * q^46 - 14 * q^47 - 18 * q^48 - 14 * q^49 + 13 * q^51 - 13 * q^52 - 23 * q^53 - 35 * q^56 - 11 * q^57 - 22 * q^58 + 9 * q^59 + 11 * q^61 + 23 * q^62 - 6 * q^63 - 23 * q^64 + 16 * q^66 - 8 * q^67 - 50 * q^68 + 13 * q^69 - 8 * q^71 - 3 * q^72 - 13 * q^73 - 22 * q^74 - 26 * q^76 + 13 * q^77 + 28 * q^78 - 5 * q^79 + 6 * q^81 + 13 * q^82 + 20 * q^83 + 7 * q^84 - 37 * q^86 + 3 * q^87 - 28 * q^88 - 4 * q^89 + 34 * q^91 - 61 * q^92 + 11 * q^93 + 41 * q^94 + 16 * q^96 + 7 * q^97 + 41 * q^98 + 3 * q^99

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