LMFDB - Embedded newform 6025.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 241)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.63125$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.63125 q^{2} +1.16790 q^{3} +0.660992 q^{4} -1.90514 q^{6} -5.06139 q^{7} +2.18426 q^{8} -1.63601 q^{9} +O(q^{10})$	\(q-1.63125 q^{2} +1.16790 q^{3} +0.660992 q^{4} -1.90514 q^{6} -5.06139 q^{7} +2.18426 q^{8} -1.63601 q^{9} +1.08118 q^{11} +0.771973 q^{12} -3.01110 q^{13} +8.25641 q^{14} -4.88507 q^{16} -2.47710 q^{17} +2.66875 q^{18} -7.12459 q^{19} -5.91119 q^{21} -1.76369 q^{22} -5.33139 q^{23} +2.55100 q^{24} +4.91187 q^{26} -5.41439 q^{27} -3.34554 q^{28} -6.80248 q^{29} -8.37871 q^{31} +3.60028 q^{32} +1.26271 q^{33} +4.04078 q^{34} -1.08139 q^{36} +2.09398 q^{37} +11.6220 q^{38} -3.51666 q^{39} -10.6564 q^{41} +9.64266 q^{42} +5.49791 q^{43} +0.714654 q^{44} +8.69686 q^{46} -4.90386 q^{47} -5.70528 q^{48} +18.6176 q^{49} -2.89301 q^{51} -1.99032 q^{52} +4.04410 q^{53} +8.83226 q^{54} -11.0554 q^{56} -8.32081 q^{57} +11.0966 q^{58} +5.64831 q^{59} -2.03784 q^{61} +13.6678 q^{62} +8.28048 q^{63} +3.89718 q^{64} -2.05981 q^{66} -7.65097 q^{67} -1.63735 q^{68} -6.22653 q^{69} +12.2631 q^{71} -3.57348 q^{72} -0.733715 q^{73} -3.41582 q^{74} -4.70930 q^{76} -5.47229 q^{77} +5.73657 q^{78} +6.86216 q^{79} -1.41544 q^{81} +17.3833 q^{82} -5.58812 q^{83} -3.90725 q^{84} -8.96849 q^{86} -7.94461 q^{87} +2.36159 q^{88} +9.62798 q^{89} +15.2403 q^{91} -3.52401 q^{92} -9.78549 q^{93} +7.99945 q^{94} +4.20476 q^{96} +10.9185 q^{97} -30.3701 q^{98} -1.76883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.63125	−1.15347	−0.576736	−	0.816931i	$-0.695674\pi$
$2$	−1.63125	−1.15347	−0.576736	+	0.816931i	$0.695674\pi$
$3$	1.16790	0.674287	0.337144	−	0.941453i	$-0.390539\pi$
$3$	1.16790	0.674287	0.337144	+	0.941453i	$0.390539\pi$
$4$	0.660992	0.330496
$5$	0	0
$5$	0	0
$6$	−1.90514	−0.777771
$7$	−5.06139	−1.91302	−0.956512	−	0.291693i	$-0.905782\pi$
$7$	−5.06139	−1.91302	−0.956512	+	0.291693i	$0.905782\pi$
$8$	2.18426	0.772253
$9$	−1.63601	−0.545337
$10$	0	0
$11$	1.08118	0.325989	0.162995	−	0.986627i	$-0.447885\pi$
$11$	1.08118	0.325989	0.162995	+	0.986627i	$0.447885\pi$
$12$	0.771973	0.222849
$13$	−3.01110	−0.835129	−0.417565	−	0.908647i	$-0.637116\pi$
$13$	−3.01110	−0.835129	−0.417565	+	0.908647i	$0.637116\pi$
$14$	8.25641	2.20662
$15$	0	0
$16$	−4.88507	−1.22127
$17$	−2.47710	−0.600785	−0.300393	−	0.953816i	$-0.597118\pi$
$17$	−2.47710	−0.600785	−0.300393	+	0.953816i	$0.597118\pi$
$18$	2.66875	0.629030
$19$	−7.12459	−1.63449	−0.817247	−	0.576287i	$-0.804501\pi$
$19$	−7.12459	−1.63449	−0.817247	+	0.576287i	$0.804501\pi$
$20$	0	0
$21$	−5.91119	−1.28993
$22$	−1.76369	−0.376019
$23$	−5.33139	−1.11167	−0.555836	−	0.831292i	$-0.687602\pi$
$23$	−5.33139	−1.11167	−0.555836	+	0.831292i	$0.687602\pi$
$24$	2.55100	0.520721
$25$	0	0
$26$	4.91187	0.963298
$27$	−5.41439	−1.04200
$28$	−3.34554	−0.632247
$29$	−6.80248	−1.26319	−0.631595	−	0.775299i	$-0.717599\pi$
$29$	−6.80248	−1.26319	−0.631595	+	0.775299i	$0.717599\pi$
$30$	0	0
$31$	−8.37871	−1.50486	−0.752430	−	0.658672i	$-0.771119\pi$
$31$	−8.37871	−1.50486	−0.752430	+	0.658672i	$0.771119\pi$
$32$	3.60028	0.636445
$33$	1.26271	0.219810
$34$	4.04078	0.692989
$35$	0	0
$36$	−1.08139	−0.180232
$37$	2.09398	0.344249	0.172124	−	0.985075i	$-0.444937\pi$
$37$	2.09398	0.344249	0.172124	+	0.985075i	$0.444937\pi$
$38$	11.6220	1.88534
$39$	−3.51666	−0.563117
$40$	0	0
$41$	−10.6564	−1.66425	−0.832124	−	0.554589i	$-0.812875\pi$
$41$	−10.6564	−1.66425	−0.832124	+	0.554589i	$0.812875\pi$
$42$	9.64266	1.48789
$43$	5.49791	0.838423	0.419211	−	0.907889i	$-0.362307\pi$
$43$	5.49791	0.838423	0.419211	+	0.907889i	$0.362307\pi$
$44$	0.714654	0.107738
$45$	0	0
$46$	8.69686	1.28228
$47$	−4.90386	−0.715302	−0.357651	−	0.933855i	$-0.616422\pi$
$47$	−4.90386	−0.715302	−0.357651	+	0.933855i	$0.616422\pi$
$48$	−5.70528	−0.823486
$49$	18.6176	2.65966
$50$	0	0
$51$	−2.89301	−0.405102
$52$	−1.99032	−0.276007
$53$	4.04410	0.555500	0.277750	−	0.960653i	$-0.410411\pi$
$53$	4.04410	0.555500	0.277750	+	0.960653i	$0.410411\pi$
$54$	8.83226	1.20192
$55$	0	0
$56$	−11.0554	−1.47734
$57$	−8.32081	−1.10212
$58$	11.0966	1.45705
$59$	5.64831	0.735347	0.367673	−	0.929955i	$-0.380154\pi$
$59$	5.64831	0.735347	0.367673	+	0.929955i	$0.380154\pi$
$60$	0	0
$61$	−2.03784	−0.260919	−0.130459	−	0.991454i	$-0.541645\pi$
$61$	−2.03784	−0.260919	−0.130459	+	0.991454i	$0.541645\pi$
$62$	13.6678	1.73581
$63$	8.28048	1.04324
$64$	3.89718	0.487148
$65$	0	0
$66$	−2.05981	−0.253545
$67$	−7.65097	−0.934715	−0.467358	−	0.884068i	$-0.654794\pi$
$67$	−7.65097	−0.934715	−0.467358	+	0.884068i	$0.654794\pi$
$68$	−1.63735	−0.198557
$69$	−6.22653	−0.749586
$70$	0	0
$71$	12.2631	1.45536	0.727682	−	0.685915i	$-0.240598\pi$
$71$	12.2631	1.45536	0.727682	+	0.685915i	$0.240598\pi$
$72$	−3.57348	−0.421138
$73$	−0.733715	−0.0858748	−0.0429374	−	0.999078i	$-0.513672\pi$
$73$	−0.733715	−0.0858748	−0.0429374	+	0.999078i	$0.513672\pi$
$74$	−3.41582	−0.397081
$75$	0	0
$76$	−4.70930	−0.540194
$77$	−5.47229	−0.623625
$78$	5.73657	0.649539
$79$	6.86216	0.772053	0.386027	−	0.922488i	$-0.373847\pi$
$79$	6.86216	0.772053	0.386027	+	0.922488i	$0.373847\pi$
$80$	0	0
$81$	−1.41544	−0.157271
$82$	17.3833	1.91966
$83$	−5.58812	−0.613376	−0.306688	−	0.951810i	$-0.599221\pi$
$83$	−5.58812	−0.613376	−0.306688	+	0.951810i	$0.599221\pi$
$84$	−3.90725	−0.426316
$85$	0	0
$86$	−8.96849	−0.967097
$87$	−7.94461	−0.851752
$88$	2.36159	0.251746
$89$	9.62798	1.02056	0.510282	−	0.860007i	$-0.329541\pi$
$89$	9.62798	1.02056	0.510282	+	0.860007i	$0.329541\pi$
$90$	0	0
$91$	15.2403	1.59762
$92$	−3.52401	−0.367403
$93$	−9.78549	−1.01471
$94$	7.99945	0.825080
$95$	0	0
$96$	4.20476	0.429147
$97$	10.9185	1.10861	0.554303	−	0.832315i	$-0.312985\pi$
$97$	10.9185	1.10861	0.554303	+	0.832315i	$0.312985\pi$
$98$	−30.3701	−3.06784
$99$	−1.76883	−0.177774
$100$	0	0
$101$	−13.9401	−1.38709	−0.693545	−	0.720413i	$-0.743952\pi$
$101$	−13.9401	−1.38709	−0.693545	+	0.720413i	$0.743952\pi$
$102$	4.71923	0.467273
$103$	7.14621	0.704137	0.352068	−	0.935974i	$-0.385478\pi$
$103$	7.14621	0.704137	0.352068	+	0.935974i	$0.385478\pi$
$104$	−6.57703	−0.644931
$105$	0	0
$106$	−6.59695	−0.640753
$107$	−17.8929	−1.72977	−0.864886	−	0.501968i	$-0.832610\pi$
$107$	−17.8929	−1.72977	−0.864886	+	0.501968i	$0.832610\pi$
$108$	−3.57887	−0.344377
$109$	−14.9297	−1.43001	−0.715004	−	0.699120i	$-0.753575\pi$
$109$	−14.9297	−1.43001	−0.715004	+	0.699120i	$0.753575\pi$
$110$	0	0
$111$	2.44556	0.232123
$112$	24.7252	2.33632
$113$	−0.859306	−0.0808367	−0.0404184	−	0.999183i	$-0.512869\pi$
$113$	−0.859306	−0.0808367	−0.0404184	+	0.999183i	$0.512869\pi$
$114$	13.5734	1.27126
$115$	0	0
$116$	−4.49639	−0.417479
$117$	4.92619	0.455427
$118$	−9.21383	−0.848201
$119$	12.5376	1.14932
$120$	0	0
$121$	−9.83104	−0.893731
$122$	3.32424	0.300962
$123$	−12.4456	−1.12218
$124$	−5.53826	−0.497351
$125$	0	0
$126$	−13.5076	−1.20335
$127$	3.01886	0.267880	0.133940	−	0.990989i	$-0.457237\pi$
$127$	3.01886	0.267880	0.133940	+	0.990989i	$0.457237\pi$
$128$	−13.5578	−1.19836
$129$	6.42100	0.565338
$130$	0	0
$131$	−2.17519	−0.190047	−0.0950234	−	0.995475i	$-0.530293\pi$
$131$	−2.17519	−0.190047	−0.0950234	+	0.995475i	$0.530293\pi$
$132$	0.834644	0.0726464
$133$	36.0603	3.12683
$134$	12.4807	1.07817
$135$	0	0
$136$	−5.41064	−0.463958
$137$	−15.9150	−1.35971	−0.679854	−	0.733347i	$-0.737957\pi$
$137$	−15.9150	−1.35971	−0.679854	+	0.733347i	$0.737957\pi$
$138$	10.1571	0.864626
$139$	−15.0721	−1.27840	−0.639201	−	0.769040i	$-0.720735\pi$
$139$	−15.0721	−1.27840	−0.639201	+	0.769040i	$0.720735\pi$
$140$	0	0
$141$	−5.72722	−0.482319
$142$	−20.0043	−1.67872
$143$	−3.25555	−0.272243
$144$	7.99203	0.666003
$145$	0	0
$146$	1.19688	0.0990542
$147$	21.7435	1.79338
$148$	1.38411	0.113773
$149$	−1.36774	−0.112050	−0.0560250	−	0.998429i	$-0.517843\pi$
$149$	−1.36774	−0.112050	−0.0560250	+	0.998429i	$0.517843\pi$
$150$	0	0
$151$	17.1854	1.39853	0.699264	−	0.714864i	$-0.253511\pi$
$151$	17.1854	1.39853	0.699264	+	0.714864i	$0.253511\pi$
$152$	−15.5620	−1.26224
$153$	4.05256	0.327630
$154$	8.92669	0.719334
$155$	0	0
$156$	−2.32449	−0.186108
$157$	−12.1279	−0.967909	−0.483955	−	0.875093i	$-0.660800\pi$
$157$	−12.1279	−0.967909	−0.483955	+	0.875093i	$0.660800\pi$
$158$	−11.1939	−0.890541
$159$	4.72310	0.374566
$160$	0	0
$161$	26.9842	2.12665
$162$	2.30894	0.181407
$163$	−10.7083	−0.838737	−0.419369	−	0.907816i	$-0.637749\pi$
$163$	−10.7083	−0.838737	−0.419369	+	0.907816i	$0.637749\pi$
$164$	−7.04379	−0.550028
$165$	0	0
$166$	9.11564	0.707511
$167$	10.5539	0.816684	0.408342	−	0.912829i	$-0.366107\pi$
$167$	10.5539	0.816684	0.408342	+	0.912829i	$0.366107\pi$
$168$	−12.9116	−0.996151
$169$	−3.93327	−0.302559
$170$	0	0
$171$	11.6559	0.891350
$172$	3.63407	0.277096
$173$	2.07621	0.157851	0.0789255	−	0.996881i	$-0.474851\pi$
$173$	2.07621	0.157851	0.0789255	+	0.996881i	$0.474851\pi$
$174$	12.9597	0.982472
$175$	0	0
$176$	−5.28166	−0.398120
$177$	6.59665	0.495835
$178$	−15.7057	−1.17719
$179$	−3.06922	−0.229405	−0.114702	−	0.993400i	$-0.536591\pi$
$179$	−3.06922	−0.229405	−0.114702	+	0.993400i	$0.536591\pi$
$180$	0	0
$181$	−0.391403	−0.0290927	−0.0145464	−	0.999894i	$-0.504630\pi$
$181$	−0.391403	−0.0290927	−0.0145464	+	0.999894i	$0.504630\pi$
$182$	−24.8609	−1.84281
$183$	−2.37999	−0.175934
$184$	−11.6452	−0.858492
$185$	0	0
$186$	15.9626	1.17044
$187$	−2.67820	−0.195849
$188$	−3.24142	−0.236405
$189$	27.4043	1.99337
$190$	0	0
$191$	4.99018	0.361077	0.180538	−	0.983568i	$-0.442216\pi$
$191$	4.99018	0.361077	0.180538	+	0.983568i	$0.442216\pi$
$192$	4.55152	0.328477
$193$	−13.5209	−0.973254	−0.486627	−	0.873610i	$-0.661773\pi$
$193$	−13.5209	−0.973254	−0.486627	+	0.873610i	$0.661773\pi$
$194$	−17.8109	−1.27874
$195$	0	0
$196$	12.3061	0.879008
$197$	−5.86751	−0.418043	−0.209021	−	0.977911i	$-0.567028\pi$
$197$	−5.86751	−0.418043	−0.209021	+	0.977911i	$0.567028\pi$
$198$	2.88541	0.205057
$199$	12.5774	0.891585	0.445792	−	0.895136i	$-0.352922\pi$
$199$	12.5774	0.891585	0.445792	+	0.895136i	$0.352922\pi$
$200$	0	0
$201$	−8.93557	−0.630266
$202$	22.7398	1.59997
$203$	34.4300	2.41651
$204$	−1.91225	−0.133885
$205$	0	0
$206$	−11.6573	−0.812201
$207$	8.72221	0.606236
$208$	14.7095	1.01992
$209$	−7.70299	−0.532827
$210$	0	0
$211$	6.00657	0.413509	0.206755	−	0.978393i	$-0.433710\pi$
$211$	6.00657	0.413509	0.206755	+	0.978393i	$0.433710\pi$
$212$	2.67312	0.183591
$213$	14.3221	0.981333
$214$	29.1879	1.99524
$215$	0	0
$216$	−11.8265	−0.804689
$217$	42.4079	2.87884
$218$	24.3542	1.64947
$219$	−0.856905	−0.0579043
$220$	0	0
$221$	7.45880	0.501733
$222$	−3.98934	−0.267747
$223$	25.7624	1.72518	0.862590	−	0.505904i	$-0.168841\pi$
$223$	25.7624	1.72518	0.862590	+	0.505904i	$0.168841\pi$
$224$	−18.2224	−1.21753
$225$	0	0
$226$	1.40175	0.0932429
$227$	−5.03720	−0.334331	−0.167165	−	0.985929i	$-0.553461\pi$
$227$	−5.03720	−0.334331	−0.167165	+	0.985929i	$0.553461\pi$
$228$	−5.49999	−0.364246
$229$	21.1245	1.39594	0.697972	−	0.716125i	$-0.254086\pi$
$229$	21.1245	1.39594	0.697972	+	0.716125i	$0.254086\pi$
$230$	0	0
$231$	−6.39108	−0.420502
$232$	−14.8584	−0.975502
$233$	−20.9468	−1.37227	−0.686135	−	0.727474i	$-0.740694\pi$
$233$	−20.9468	−1.37227	−0.686135	+	0.727474i	$0.740694\pi$
$234$	−8.03588	−0.525322
$235$	0	0
$236$	3.73349	0.243029
$237$	8.01431	0.520586
$238$	−20.4520	−1.32570
$239$	−7.83541	−0.506831	−0.253415	−	0.967358i	$-0.581554\pi$
$239$	−7.83541	−0.506831	−0.253415	+	0.967358i	$0.581554\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	16.0369	1.03089
$243$	14.5901	0.935955
$244$	−1.34700	−0.0862326
$245$	0	0
$246$	20.3019	1.29440
$247$	21.4529	1.36501
$248$	−18.3013	−1.16213
$249$	−6.52636	−0.413591
$250$	0	0
$251$	−7.01648	−0.442876	−0.221438	−	0.975174i	$-0.571075\pi$
$251$	−7.01648	−0.442876	−0.221438	+	0.975174i	$0.571075\pi$
$252$	5.47334	0.344788
$253$	−5.76421	−0.362393
$254$	−4.92453	−0.308992
$255$	0	0
$256$	14.3219	0.895121
$257$	−11.3057	−0.705229	−0.352615	−	0.935769i	$-0.614707\pi$
$257$	−11.3057	−0.705229	−0.352615	+	0.935769i	$0.614707\pi$
$258$	−10.4743	−0.652101
$259$	−10.5985	−0.658556
$260$	0	0
$261$	11.1289	0.688864
$262$	3.54828	0.219214
$263$	−19.8667	−1.22503	−0.612516	−	0.790458i	$-0.709842\pi$
$263$	−19.8667	−1.22503	−0.612516	+	0.790458i	$0.709842\pi$
$264$	2.75810	0.169749
$265$	0	0
$266$	−58.8236	−3.60671
$267$	11.2445	0.688153
$268$	−5.05724	−0.308920
$269$	−20.2533	−1.23486	−0.617431	−	0.786625i	$-0.711827\pi$
$269$	−20.2533	−1.23486	−0.617431	+	0.786625i	$0.711827\pi$
$270$	0	0
$271$	−4.23892	−0.257496	−0.128748	−	0.991677i	$-0.541096\pi$
$271$	−4.23892	−0.257496	−0.128748	+	0.991677i	$0.541096\pi$
$272$	12.1008	0.733720
$273$	17.7992	1.07726
$274$	25.9614	1.56839
$275$	0	0
$276$	−4.11569	−0.247735
$277$	0.369469	0.0221992	0.0110996	−	0.999938i	$-0.496467\pi$
$277$	0.369469	0.0221992	0.0110996	+	0.999938i	$0.496467\pi$
$278$	24.5865	1.47460
$279$	13.7077	0.820656
$280$	0	0
$281$	24.6918	1.47299	0.736494	−	0.676444i	$-0.236480\pi$
$281$	24.6918	1.47299	0.736494	+	0.676444i	$0.236480\pi$
$282$	9.34255	0.556341
$283$	−0.0696775	−0.00414190	−0.00207095	−	0.999998i	$-0.500659\pi$
$283$	−0.0696775	−0.00414190	−0.00207095	+	0.999998i	$0.500659\pi$
$284$	8.10583	0.480992
$285$	0	0
$286$	5.31064	0.314024
$287$	53.9361	3.18375
$288$	−5.89009	−0.347077
$289$	−10.8640	−0.639057
$290$	0	0
$291$	12.7517	0.747518
$292$	−0.484980	−0.0283813
$293$	7.59140	0.443494	0.221747	−	0.975104i	$-0.428824\pi$
$293$	7.59140	0.443494	0.221747	+	0.975104i	$0.428824\pi$
$294$	−35.4692	−2.06861
$295$	0	0
$296$	4.57381	0.265847
$297$	−5.85395	−0.339681
$298$	2.23114	0.129246
$299$	16.0534	0.928389
$300$	0	0
$301$	−27.8270	−1.60392
$302$	−28.0338	−1.61316
$303$	−16.2806	−0.935297
$304$	34.8042	1.99616
$305$	0	0
$306$	−6.61076	−0.377912
$307$	20.6437	1.17820	0.589100	−	0.808060i	$-0.299482\pi$
$307$	20.6437	1.17820	0.589100	+	0.808060i	$0.299482\pi$
$308$	−3.61714	−0.206106
$309$	8.34605	0.474790
$310$	0	0
$311$	24.0882	1.36592	0.682959	−	0.730456i	$-0.260693\pi$
$311$	24.0882	1.36592	0.682959	+	0.730456i	$0.260693\pi$
$312$	−7.68132	−0.434869
$313$	−16.3804	−0.925876	−0.462938	−	0.886391i	$-0.653205\pi$
$313$	−16.3804	−0.925876	−0.462938	+	0.886391i	$0.653205\pi$
$314$	19.7836	1.11646
$315$	0	0
$316$	4.53584	0.255161
$317$	1.59833	0.0897714	0.0448857	−	0.998992i	$-0.485708\pi$
$317$	1.59833	0.0897714	0.0448857	+	0.998992i	$0.485708\pi$
$318$	−7.70458	−0.432051
$319$	−7.35473	−0.411786
$320$	0	0
$321$	−20.8971	−1.16636
$322$	−44.0181	−2.45304
$323$	17.6483	0.981980
$324$	−0.935593	−0.0519774
$325$	0	0
$326$	17.4679	0.967460
$327$	−17.4364	−0.964236
$328$	−23.2764	−1.28522
$329$	24.8203	1.36839
$330$	0	0
$331$	−26.9070	−1.47894	−0.739472	−	0.673188i	$-0.764925\pi$
$331$	−26.9070	−1.47894	−0.739472	+	0.673188i	$0.764925\pi$
$332$	−3.69370	−0.202718
$333$	−3.42578	−0.187732
$334$	−17.2161	−0.942022
$335$	0	0
$336$	28.8766	1.57535
$337$	10.8794	0.592640	0.296320	−	0.955089i	$-0.404240\pi$
$337$	10.8794	0.592640	0.296320	+	0.955089i	$0.404240\pi$
$338$	6.41617	0.348994
$339$	−1.00358	−0.0545072
$340$	0	0
$341$	−9.05892	−0.490568
$342$	−19.0138	−1.02815
$343$	−58.8013	−3.17497
$344$	12.0089	0.647475
$345$	0	0
$346$	−3.38682	−0.182077
$347$	−12.9007	−0.692546	−0.346273	−	0.938134i	$-0.612553\pi$
$347$	−12.9007	−0.692546	−0.346273	+	0.938134i	$0.612553\pi$
$348$	−5.25133	−0.281501
$349$	−10.7803	−0.577058	−0.288529	−	0.957471i	$-0.593166\pi$
$349$	−10.7803	−0.577058	−0.288529	+	0.957471i	$0.593166\pi$
$350$	0	0
$351$	16.3033	0.870205
$352$	3.89256	0.207474
$353$	−6.56859	−0.349611	−0.174805	−	0.984603i	$-0.555930\pi$
$353$	−6.56859	−0.349611	−0.174805	+	0.984603i	$0.555930\pi$
$354$	−10.7608	−0.571931
$355$	0	0
$356$	6.36402	0.337292
$357$	14.6426	0.774970
$358$	5.00669	0.264612
$359$	15.8305	0.835504	0.417752	−	0.908561i	$-0.362818\pi$
$359$	15.8305	0.835504	0.417752	+	0.908561i	$0.362818\pi$
$360$	0	0
$361$	31.7598	1.67157
$362$	0.638477	0.0335576
$363$	−11.4817	−0.602631
$364$	10.0738	0.528008
$365$	0	0
$366$	3.88237	0.202935
$367$	5.63657	0.294226	0.147113	−	0.989120i	$-0.453002\pi$
$367$	5.63657	0.294226	0.147113	+	0.989120i	$0.453002\pi$
$368$	26.0442	1.35765
$369$	17.4340	0.907576
$370$	0	0
$371$	−20.4687	−1.06268
$372$	−6.46814	−0.335357
$373$	−1.29504	−0.0670548	−0.0335274	−	0.999438i	$-0.510674\pi$
$373$	−1.29504	−0.0670548	−0.0335274	+	0.999438i	$0.510674\pi$
$374$	4.36883	0.225907
$375$	0	0
$376$	−10.7113	−0.552394
$377$	20.4830	1.05493
$378$	−44.7035	−2.29930
$379$	−13.8155	−0.709656	−0.354828	−	0.934932i	$-0.615461\pi$
$379$	−13.8155	−0.709656	−0.354828	+	0.934932i	$0.615461\pi$
$380$	0	0
$381$	3.52572	0.180628
$382$	−8.14026	−0.416492
$383$	−12.0143	−0.613900	−0.306950	−	0.951726i	$-0.599308\pi$
$383$	−12.0143	−0.613900	−0.306950	+	0.951726i	$0.599308\pi$
$384$	−15.8342	−0.808036
$385$	0	0
$386$	22.0560	1.12262
$387$	−8.99463	−0.457223
$388$	7.21704	0.366390
$389$	4.86222	0.246524	0.123262	−	0.992374i	$-0.460664\pi$
$389$	4.86222	0.246524	0.123262	+	0.992374i	$0.460664\pi$
$390$	0	0
$391$	13.2064	0.667876
$392$	40.6658	2.05393
$393$	−2.54040	−0.128146
$394$	9.57141	0.482201
$395$	0	0
$396$	−1.16918	−0.0587536
$397$	−9.17854	−0.460658	−0.230329	−	0.973113i	$-0.573980\pi$
$397$	−9.17854	−0.460658	−0.230329	+	0.973113i	$0.573980\pi$
$398$	−20.5169	−1.02842
$399$	42.1148	2.10838
$400$	0	0
$401$	−28.0569	−1.40109	−0.700547	−	0.713607i	$-0.747060\pi$
$401$	−28.0569	−1.40109	−0.700547	+	0.713607i	$0.747060\pi$
$402$	14.5762	0.726994
$403$	25.2291	1.25675
$404$	−9.21429	−0.458428
$405$	0	0
$406$	−56.1641	−2.78738
$407$	2.26398	0.112221
$408$	−6.31908	−0.312841
$409$	−11.6170	−0.574422	−0.287211	−	0.957867i	$-0.592728\pi$
$409$	−11.6170	−0.574422	−0.287211	+	0.957867i	$0.592728\pi$
$410$	0	0
$411$	−18.5871	−0.916834
$412$	4.72359	0.232714
$413$	−28.5883	−1.40674
$414$	−14.2281	−0.699275
$415$	0	0
$416$	−10.8408	−0.531514
$417$	−17.6027	−0.862010
$418$	12.5655	0.614601
$419$	15.5789	0.761080	0.380540	−	0.924765i	$-0.375738\pi$
$419$	15.5789	0.761080	0.380540	+	0.924765i	$0.375738\pi$
$420$	0	0
$421$	7.53596	0.367280	0.183640	−	0.982994i	$-0.441212\pi$
$421$	7.53596	0.367280	0.183640	+	0.982994i	$0.441212\pi$
$422$	−9.79824	−0.476971
$423$	8.02277	0.390081
$424$	8.83337	0.428986
$425$	0	0
$426$	−23.3630	−1.13194
$427$	10.3143	0.499144
$428$	−11.8271	−0.571683
$429$	−3.80216	−0.183570
$430$	0	0
$431$	24.2144	1.16636	0.583182	−	0.812341i	$-0.301807\pi$
$431$	24.2144	1.16636	0.583182	+	0.812341i	$0.301807\pi$
$432$	26.4497	1.27256
$433$	−1.90821	−0.0917025	−0.0458512	−	0.998948i	$-0.514600\pi$
$433$	−1.90821	−0.0917025	−0.0458512	+	0.998948i	$0.514600\pi$
$434$	−69.1781	−3.32065
$435$	0	0
$436$	−9.86844	−0.472612
$437$	37.9840	1.81702
$438$	1.39783	0.0667910
$439$	−14.9135	−0.711784	−0.355892	−	0.934527i	$-0.615823\pi$
$439$	−14.9135	−0.711784	−0.355892	+	0.934527i	$0.615823\pi$
$440$	0	0
$441$	−30.4586	−1.45041
$442$	−12.1672	−0.578735
$443$	23.0698	1.09608	0.548039	−	0.836453i	$-0.315375\pi$
$443$	23.0698	1.09608	0.548039	+	0.836453i	$0.315375\pi$
$444$	1.61650	0.0767156
$445$	0	0
$446$	−42.0251	−1.98995
$447$	−1.59739	−0.0755539
$448$	−19.7251	−0.931925
$449$	14.5420	0.686277	0.343139	−	0.939285i	$-0.388510\pi$
$449$	14.5420	0.686277	0.343139	+	0.939285i	$0.388510\pi$
$450$	0	0
$451$	−11.5215	−0.542527
$452$	−0.567995	−0.0267162
$453$	20.0708	0.943009
$454$	8.21696	0.385641
$455$	0	0
$456$	−18.1748	−0.851115
$457$	−11.8002	−0.551991	−0.275995	−	0.961159i	$-0.589007\pi$
$457$	−11.8002	−0.551991	−0.275995	+	0.961159i	$0.589007\pi$
$458$	−34.4594	−1.61018
$459$	13.4120	0.626019
$460$	0	0
$461$	15.0722	0.701985	0.350992	−	0.936378i	$-0.385844\pi$
$461$	15.0722	0.701985	0.350992	+	0.936378i	$0.385844\pi$
$462$	10.4255	0.485037
$463$	−24.3295	−1.13069	−0.565344	−	0.824855i	$-0.691257\pi$
$463$	−24.3295	−1.13069	−0.565344	+	0.824855i	$0.691257\pi$
$464$	33.2306	1.54269
$465$	0	0
$466$	34.1695	1.58287
$467$	−29.7743	−1.37779	−0.688895	−	0.724862i	$-0.741904\pi$
$467$	−29.7743	−1.37779	−0.688895	+	0.724862i	$0.741904\pi$
$468$	3.25618	0.150517
$469$	38.7245	1.78813
$470$	0	0
$471$	−14.1641	−0.652649
$472$	12.3374	0.567874
$473$	5.94424	0.273317
$474$	−13.0734	−0.600481
$475$	0	0
$476$	8.28724	0.379845
$477$	−6.61619	−0.302934
$478$	12.7816	0.584615
$479$	−10.1987	−0.465991	−0.232996	−	0.972478i	$-0.574853\pi$
$479$	−10.1987	−0.465991	−0.232996	+	0.972478i	$0.574853\pi$
$480$	0	0
$481$	−6.30520	−0.287492
$482$	−1.63125	−0.0743016
$483$	31.5149	1.43398
$484$	−6.49825	−0.295375
$485$	0	0
$486$	−23.8002	−1.07960
$487$	24.9246	1.12944	0.564720	−	0.825282i	$-0.308984\pi$
$487$	24.9246	1.12944	0.564720	+	0.825282i	$0.308984\pi$
$488$	−4.45118	−0.201495
$489$	−12.5062	−0.565550
$490$	0	0
$491$	−26.8710	−1.21267	−0.606335	−	0.795209i	$-0.707361\pi$
$491$	−26.8710	−1.21267	−0.606335	+	0.795209i	$0.707361\pi$
$492$	−8.22644	−0.370877
$493$	16.8504	0.758905
$494$	−34.9951	−1.57450
$495$	0	0
$496$	40.9306	1.83784
$497$	−62.0684	−2.78415
$498$	10.6462	0.477066
$499$	−37.6147	−1.68387	−0.841933	−	0.539582i	$-0.818582\pi$
$499$	−37.6147	−1.68387	−0.841933	+	0.539582i	$0.818582\pi$
$500$	0	0
$501$	12.3259	0.550680
$502$	11.4457	0.510845
$503$	38.0897	1.69834	0.849168	−	0.528123i	$-0.177104\pi$
$503$	38.0897	1.69834	0.849168	+	0.528123i	$0.177104\pi$
$504$	18.0867	0.805648
$505$	0	0
$506$	9.40290	0.418010
$507$	−4.59367	−0.204012
$508$	1.99544	0.0885334
$509$	−37.4493	−1.65991	−0.829954	−	0.557831i	$-0.811634\pi$
$509$	−37.4493	−1.65991	−0.829954	+	0.557831i	$0.811634\pi$
$510$	0	0
$511$	3.71362	0.164281
$512$	3.75296	0.165859
$513$	38.5754	1.70314
$514$	18.4424	0.813462
$515$	0	0
$516$	4.24423	0.186842
$517$	−5.30198	−0.233181
$518$	17.2888	0.759626
$519$	2.42480	0.106437
$520$	0	0
$521$	14.8226	0.649391	0.324695	−	0.945819i	$-0.394738\pi$
$521$	14.8226	0.649391	0.324695	+	0.945819i	$0.394738\pi$
$522$	−18.1541	−0.794584
$523$	−23.8624	−1.04343	−0.521715	−	0.853120i	$-0.674708\pi$
$523$	−23.8624	−1.04343	−0.521715	+	0.853120i	$0.674708\pi$
$524$	−1.43778	−0.0628098
$525$	0	0
$526$	32.4076	1.41304
$527$	20.7549	0.904098
$528$	−6.16845	−0.268447
$529$	5.42372	0.235814
$530$	0	0
$531$	−9.24069	−0.401012
$532$	23.8356	1.03340
$533$	32.0875	1.38986
$534$	−18.3427	−0.793765
$535$	0	0
$536$	−16.7117	−0.721837
$537$	−3.58454	−0.154685
$538$	33.0382	1.42438
$539$	20.1291	0.867021
$540$	0	0
$541$	−12.9272	−0.555782	−0.277891	−	0.960613i	$-0.589635\pi$
$541$	−12.9272	−0.555782	−0.277891	+	0.960613i	$0.589635\pi$
$542$	6.91477	0.297015
$543$	−0.457119	−0.0196168
$544$	−8.91825	−0.382367
$545$	0	0
$546$	−29.0350	−1.24258
$547$	9.03128	0.386150	0.193075	−	0.981184i	$-0.438154\pi$
$547$	9.03128	0.386150	0.193075	+	0.981184i	$0.438154\pi$
$548$	−10.5197	−0.449379
$549$	3.33393	0.142289
$550$	0	0
$551$	48.4649	2.06467
$552$	−13.6004	−0.578870
$553$	−34.7320	−1.47696
$554$	−0.602698	−0.0256062
$555$	0	0
$556$	−9.96256	−0.422507
$557$	4.33616	0.183729	0.0918644	−	0.995772i	$-0.470717\pi$
$557$	4.33616	0.183729	0.0918644	+	0.995772i	$0.470717\pi$
$558$	−22.3607	−0.946603
$559$	−16.5547	−0.700191
$560$	0	0
$561$	−3.12787	−0.132059
$562$	−40.2786	−1.69905
$563$	−6.56701	−0.276767	−0.138383	−	0.990379i	$-0.544191\pi$
$563$	−6.56701	−0.276767	−0.138383	+	0.990379i	$0.544191\pi$
$564$	−3.78565	−0.159405
$565$	0	0
$566$	0.113662	0.00477756
$567$	7.16407	0.300863
$568$	26.7859	1.12391
$569$	18.1137	0.759366	0.379683	−	0.925117i	$-0.376033\pi$
$569$	18.1137	0.759366	0.379683	+	0.925117i	$0.376033\pi$
$570$	0	0
$571$	6.26298	0.262098	0.131049	−	0.991376i	$-0.458166\pi$
$571$	6.26298	0.262098	0.131049	+	0.991376i	$0.458166\pi$
$572$	−2.15190	−0.0899753
$573$	5.82803	0.243470
$574$	−87.9835	−3.67236
$575$	0	0
$576$	−6.37583	−0.265660
$577$	1.76988	0.0736810	0.0368405	−	0.999321i	$-0.488271\pi$
$577$	1.76988	0.0736810	0.0368405	+	0.999321i	$0.488271\pi$
$578$	17.7219	0.737134
$579$	−15.7910	−0.656253
$580$	0	0
$581$	28.2836	1.17340
$582$	−20.8013	−0.862241
$583$	4.37241	0.181087
$584$	−1.60263	−0.0663171
$585$	0	0
$586$	−12.3835	−0.511558
$587$	−11.9082	−0.491502	−0.245751	−	0.969333i	$-0.579035\pi$
$587$	−11.9082	−0.491502	−0.245751	+	0.969333i	$0.579035\pi$
$588$	14.3723	0.592704
$589$	59.6949	2.45969
$590$	0	0
$591$	−6.85266	−0.281881
$592$	−10.2293	−0.420420
$593$	34.2932	1.40825	0.704126	−	0.710075i	$-0.251339\pi$
$593$	34.2932	1.40825	0.704126	+	0.710075i	$0.251339\pi$
$594$	9.54929	0.391812
$595$	0	0
$596$	−0.904069	−0.0370321
$597$	14.6891	0.601184
$598$	−26.1871	−1.07087
$599$	−18.2245	−0.744632	−0.372316	−	0.928106i	$-0.621436\pi$
$599$	−18.2245	−0.744632	−0.372316	+	0.928106i	$0.621436\pi$
$600$	0	0
$601$	−19.2591	−0.785595	−0.392797	−	0.919625i	$-0.628493\pi$
$601$	−19.2591	−0.785595	−0.392797	+	0.919625i	$0.628493\pi$
$602$	45.3930	1.85008
$603$	12.5171	0.509735
$604$	11.3594	0.462208
$605$	0	0
$606$	26.5578	1.07884
$607$	−39.9799	−1.62273	−0.811367	−	0.584536i	$-0.801276\pi$
$607$	−39.9799	−1.62273	−0.811367	+	0.584536i	$0.801276\pi$
$608$	−25.6505	−1.04027
$609$	40.2108	1.62942
$610$	0	0
$611$	14.7660	0.597369
$612$	2.67871	0.108281
$613$	18.3233	0.740070	0.370035	−	0.929018i	$-0.379346\pi$
$613$	18.3233	0.740070	0.370035	+	0.929018i	$0.379346\pi$
$614$	−33.6752	−1.35902
$615$	0	0
$616$	−11.9529	−0.481597
$617$	−12.3769	−0.498273	−0.249137	−	0.968468i	$-0.580147\pi$
$617$	−12.3769	−0.498273	−0.249137	+	0.968468i	$0.580147\pi$
$618$	−13.6145	−0.547657
$619$	−8.87878	−0.356868	−0.178434	−	0.983952i	$-0.557103\pi$
$619$	−8.87878	−0.356868	−0.178434	+	0.983952i	$0.557103\pi$
$620$	0	0
$621$	28.8662	1.15836
$622$	−39.2941	−1.57555
$623$	−48.7309	−1.95236
$624$	17.1792	0.687717
$625$	0	0
$626$	26.7206	1.06797
$627$	−8.99632	−0.359278
$628$	−8.01643	−0.319890
$629$	−5.18701	−0.206820
$630$	0	0
$631$	34.5564	1.37567	0.687835	−	0.725867i	$-0.258561\pi$
$631$	34.5564	1.37567	0.687835	+	0.725867i	$0.258561\pi$
$632$	14.9888	0.596221
$633$	7.01507	0.278824
$634$	−2.60729	−0.103549
$635$	0	0
$636$	3.12193	0.123793
$637$	−56.0596	−2.22116
$638$	11.9974	0.474983
$639$	−20.0626	−0.793664
$640$	0	0
$641$	−1.70265	−0.0672505	−0.0336253	−	0.999435i	$-0.510705\pi$
$641$	−1.70265	−0.0672505	−0.0336253	+	0.999435i	$0.510705\pi$
$642$	34.0885	1.34537
$643$	−40.7018	−1.60512	−0.802561	−	0.596571i	$-0.796530\pi$
$643$	−40.7018	−1.60512	−0.802561	+	0.596571i	$0.796530\pi$
$644$	17.8364	0.702851
$645$	0	0
$646$	−28.7889	−1.13269
$647$	30.3915	1.19481	0.597406	−	0.801939i	$-0.296198\pi$
$647$	30.3915	1.19481	0.597406	+	0.801939i	$0.296198\pi$
$648$	−3.09169	−0.121453
$649$	6.10685	0.239715
$650$	0	0
$651$	49.5282	1.94116
$652$	−7.07809	−0.277200
$653$	−6.95225	−0.272062	−0.136031	−	0.990705i	$-0.543435\pi$
$653$	−6.95225	−0.272062	−0.136031	+	0.990705i	$0.543435\pi$
$654$	28.4432	1.11222
$655$	0	0
$656$	52.0573	2.03249
$657$	1.20037	0.0468307
$658$	−40.4883	−1.57840
$659$	−38.2304	−1.48924	−0.744622	−	0.667486i	$-0.767370\pi$
$659$	−38.2304	−1.48924	−0.744622	+	0.667486i	$0.767370\pi$
$660$	0	0
$661$	35.0225	1.36222	0.681109	−	0.732182i	$-0.261498\pi$
$661$	35.0225	1.36222	0.681109	+	0.732182i	$0.261498\pi$
$662$	43.8922	1.70592
$663$	8.71113	0.338312
$664$	−12.2059	−0.473681
$665$	0	0
$666$	5.58832	0.216543
$667$	36.2667	1.40425
$668$	6.97604	0.269911
$669$	30.0879	1.16327
$670$	0	0
$671$	−2.20328	−0.0850566
$672$	−21.2819	−0.820968
$673$	19.3765	0.746909	0.373454	−	0.927649i	$-0.378173\pi$
$673$	19.3765	0.746909	0.373454	+	0.927649i	$0.378173\pi$
$674$	−17.7471	−0.683594
$675$	0	0
$676$	−2.59986	−0.0999947
$677$	3.01738	0.115967	0.0579837	−	0.998318i	$-0.481533\pi$
$677$	3.01738	0.115967	0.0579837	+	0.998318i	$0.481533\pi$
$678$	1.63710	0.0628725
$679$	−55.2627	−2.12079
$680$	0	0
$681$	−5.88294	−0.225435
$682$	14.7774	0.565856
$683$	5.60316	0.214399	0.107199	−	0.994238i	$-0.465812\pi$
$683$	5.60316	0.214399	0.107199	+	0.994238i	$0.465812\pi$
$684$	7.70447	0.294588
$685$	0	0
$686$	95.9200	3.66224
$687$	24.6713	0.941267
$688$	−26.8577	−1.02394
$689$	−12.1772	−0.463914
$690$	0	0
$691$	49.0976	1.86776	0.933881	−	0.357583i	$-0.116399\pi$
$691$	49.0976	1.86776	0.933881	+	0.357583i	$0.116399\pi$
$692$	1.37236	0.0521691
$693$	8.95272	0.340086
$694$	21.0443	0.798832
$695$	0	0
$696$	−17.3531	−0.657768
$697$	26.3970	0.999856
$698$	17.5855	0.665619
$699$	−24.4637	−0.925304
$700$	0	0
$701$	14.0248	0.529709	0.264855	−	0.964288i	$-0.414676\pi$
$701$	14.0248	0.529709	0.264855	+	0.964288i	$0.414676\pi$
$702$	−26.5948	−1.00376
$703$	−14.9188	−0.562673
$704$	4.21357	0.158805
$705$	0	0
$706$	10.7150	0.403266
$707$	70.5561	2.65354
$708$	4.36034	0.163872
$709$	−10.0074	−0.375835	−0.187918	−	0.982185i	$-0.560174\pi$
$709$	−10.0074	−0.375835	−0.187918	+	0.982185i	$0.560174\pi$
$710$	0	0
$711$	−11.2266	−0.421029
$712$	21.0300	0.788134
$713$	44.6702	1.67291
$714$	−23.8858	−0.893905
$715$	0	0
$716$	−2.02873	−0.0758173
$717$	−9.15098	−0.341749
$718$	−25.8236	−0.963730
$719$	32.3086	1.20491	0.602454	−	0.798154i	$-0.294190\pi$
$719$	32.3086	1.20491	0.602454	+	0.798154i	$0.294190\pi$
$720$	0	0
$721$	−36.1697	−1.34703
$722$	−51.8084	−1.92811
$723$	1.16790	0.0434347
$724$	−0.258714	−0.00961504
$725$	0	0
$726$	18.7295	0.695118
$727$	−14.7153	−0.545762	−0.272881	−	0.962048i	$-0.587977\pi$
$727$	−14.7153	−0.545762	−0.272881	+	0.962048i	$0.587977\pi$
$728$	33.2889	1.23377
$729$	21.2861	0.788373
$730$	0	0
$731$	−13.6189	−0.503712
$732$	−1.57316	−0.0581455
$733$	−28.2634	−1.04393	−0.521966	−	0.852966i	$-0.674801\pi$
$733$	−28.2634	−1.04393	−0.521966	+	0.852966i	$0.674801\pi$
$734$	−9.19468	−0.339382
$735$	0	0
$736$	−19.1945	−0.707518
$737$	−8.27210	−0.304707
$738$	−28.4392	−1.04686
$739$	−34.0536	−1.25268	−0.626340	−	0.779550i	$-0.715448\pi$
$739$	−34.0536	−1.25268	−0.626340	+	0.779550i	$0.715448\pi$
$740$	0	0
$741$	25.0548	0.920411
$742$	33.3897	1.22578
$743$	47.2361	1.73293	0.866463	−	0.499241i	$-0.166388\pi$
$743$	47.2361	1.73293	0.866463	+	0.499241i	$0.166388\pi$
$744$	−21.3741	−0.783612
$745$	0	0
$746$	2.11255	0.0773458
$747$	9.14222	0.334496
$748$	−1.77027	−0.0647275
$749$	90.5629	3.30910
$750$	0	0
$751$	36.7588	1.34135	0.670674	−	0.741752i	$-0.266005\pi$
$751$	36.7588	1.34135	0.670674	+	0.741752i	$0.266005\pi$
$752$	23.9557	0.873576
$753$	−8.19454	−0.298626
$754$	−33.4129	−1.21683
$755$	0	0
$756$	18.1141	0.658802
$757$	−7.43315	−0.270162	−0.135081	−	0.990835i	$-0.543130\pi$
$757$	−7.43315	−0.270162	−0.135081	+	0.990835i	$0.543130\pi$
$758$	22.5367	0.818568
$759$	−6.73202	−0.244357
$760$	0	0
$761$	1.06982	0.0387809	0.0193905	−	0.999812i	$-0.493827\pi$
$761$	1.06982	0.0387809	0.0193905	+	0.999812i	$0.493827\pi$
$762$	−5.75135	−0.208350
$763$	75.5651	2.73564
$764$	3.29847	0.119335
$765$	0	0
$766$	19.5983	0.708116
$767$	−17.0076	−0.614109
$768$	16.7266	0.603569
$769$	−26.2212	−0.945562	−0.472781	−	0.881180i	$-0.656750\pi$
$769$	−26.2212	−0.945562	−0.472781	+	0.881180i	$0.656750\pi$
$770$	0	0
$771$	−13.2039	−0.475527
$772$	−8.93720	−0.321657
$773$	15.9051	0.572065	0.286033	−	0.958220i	$-0.407663\pi$
$773$	15.9051	0.572065	0.286033	+	0.958220i	$0.407663\pi$
$774$	14.6725	0.527394
$775$	0	0
$776$	23.8489	0.856124
$777$	−12.3779	−0.444056
$778$	−7.93152	−0.284359
$779$	75.9225	2.72020
$780$	0	0
$781$	13.2587	0.474433
$782$	−21.5430	−0.770376
$783$	36.8313	1.31624
$784$	−90.9485	−3.24816
$785$	0	0
$786$	4.14404	0.147813
$787$	44.7474	1.59507	0.797536	−	0.603272i	$-0.206137\pi$
$787$	44.7474	1.59507	0.797536	+	0.603272i	$0.206137\pi$
$788$	−3.87838	−0.138162
$789$	−23.2023	−0.826023
$790$	0	0
$791$	4.34928	0.154643
$792$	−3.86358	−0.137286
$793$	6.13614	0.217901
$794$	14.9725	0.531356
$795$	0	0
$796$	8.31354	0.294665
$797$	20.2003	0.715530	0.357765	−	0.933812i	$-0.383539\pi$
$797$	20.2003	0.715530	0.357765	+	0.933812i	$0.383539\pi$
$798$	−68.7000	−2.43195
$799$	12.1474	0.429743
$800$	0	0
$801$	−15.7515	−0.556551
$802$	45.7679	1.61612
$803$	−0.793280	−0.0279943
$804$	−5.90634	−0.208301
$805$	0	0
$806$	−41.1552	−1.44963
$807$	−23.6538	−0.832652
$808$	−30.4488	−1.07118
$809$	31.3338	1.10164	0.550818	−	0.834625i	$-0.314316\pi$
$809$	31.3338	1.10164	0.550818	+	0.834625i	$0.314316\pi$
$810$	0	0
$811$	−28.2192	−0.990909	−0.495454	−	0.868634i	$-0.664998\pi$
$811$	−28.2192	−0.990909	−0.495454	+	0.868634i	$0.664998\pi$
$812$	22.7580	0.798648
$813$	−4.95064	−0.173626
$814$	−3.69313	−0.129444
$815$	0	0
$816$	14.1325	0.494738
$817$	−39.1704	−1.37040
$818$	18.9502	0.662579
$819$	−24.9334	−0.871242
$820$	0	0
$821$	−36.8115	−1.28473	−0.642365	−	0.766399i	$-0.722047\pi$
$821$	−36.8115	−1.28473	−0.642365	+	0.766399i	$0.722047\pi$
$822$	30.3203	1.05754
$823$	34.8680	1.21542	0.607711	−	0.794158i	$-0.292088\pi$
$823$	34.8680	1.21542	0.607711	+	0.794158i	$0.292088\pi$
$824$	15.6092	0.543772
$825$	0	0
$826$	46.6347	1.62263
$827$	11.6305	0.404431	0.202216	−	0.979341i	$-0.435186\pi$
$827$	11.6305	0.404431	0.202216	+	0.979341i	$0.435186\pi$
$828$	5.76532	0.200359
$829$	−45.8232	−1.59150	−0.795752	−	0.605622i	$-0.792924\pi$
$829$	−45.8232	−1.59150	−0.795752	+	0.605622i	$0.792924\pi$
$830$	0	0
$831$	0.431502	0.0149686
$832$	−11.7348	−0.406831
$833$	−46.1178	−1.59789
$834$	28.7145	0.994303
$835$	0	0
$836$	−5.09162	−0.176097
$837$	45.3656	1.56807
$838$	−25.4132	−0.877884
$839$	−3.48632	−0.120361	−0.0601806	−	0.998188i	$-0.519168\pi$
$839$	−3.48632	−0.120361	−0.0601806	+	0.998188i	$0.519168\pi$
$840$	0	0
$841$	17.2737	0.595646
$842$	−12.2931	−0.423647
$843$	28.8375	0.993216
$844$	3.97030	0.136663
$845$	0	0
$846$	−13.0872	−0.449947
$847$	49.7587	1.70973
$848$	−19.7557	−0.678414
$849$	−0.0813764	−0.00279283
$850$	0	0
$851$	−11.1638	−0.382692
$852$	9.46679	0.324327
$853$	44.6130	1.52752	0.763760	−	0.645500i	$-0.223351\pi$
$853$	44.6130	1.52752	0.763760	+	0.645500i	$0.223351\pi$
$854$	−16.8252	−0.575748
$855$	0	0
$856$	−39.0828	−1.33582
$857$	−21.1188	−0.721404	−0.360702	−	0.932681i	$-0.617463\pi$
$857$	−21.1188	−0.721404	−0.360702	+	0.932681i	$0.617463\pi$
$858$	6.20229	0.211743
$859$	−36.4020	−1.24202	−0.621011	−	0.783802i	$-0.713278\pi$
$859$	−36.4020	−1.24202	−0.621011	+	0.783802i	$0.713278\pi$
$860$	0	0
$861$	62.9920	2.14676
$862$	−39.4998	−1.34537
$863$	4.01817	0.136780	0.0683900	−	0.997659i	$-0.478214\pi$
$863$	4.01817	0.136780	0.0683900	+	0.997659i	$0.478214\pi$
$864$	−19.4933	−0.663176
$865$	0	0
$866$	3.11277	0.105776
$867$	−12.6880	−0.430908
$868$	28.0313	0.951444
$869$	7.41925	0.251681
$870$	0	0
$871$	23.0379	0.780608
$872$	−32.6104	−1.10433
$873$	−17.8628	−0.604563
$874$	−61.9616	−2.09588
$875$	0	0
$876$	−0.566408	−0.0191372
$877$	−48.0234	−1.62163	−0.810817	−	0.585300i	$-0.800977\pi$
$877$	−48.0234	−1.62163	−0.810817	+	0.585300i	$0.800977\pi$
$878$	24.3278	0.821022
$879$	8.86599	0.299042
$880$	0	0
$881$	−56.8752	−1.91617	−0.958087	−	0.286479i	$-0.907515\pi$
$881$	−56.8752	−1.91617	−0.958087	+	0.286479i	$0.907515\pi$
$882$	49.6858	1.67301
$883$	−44.7065	−1.50449	−0.752246	−	0.658882i	$-0.771030\pi$
$883$	−44.7065	−1.50449	−0.752246	+	0.658882i	$0.771030\pi$
$884$	4.93021	0.165821
$885$	0	0
$886$	−37.6327	−1.26429
$887$	−5.64866	−0.189663	−0.0948317	−	0.995493i	$-0.530231\pi$
$887$	−5.64866	−0.189663	−0.0948317	+	0.995493i	$0.530231\pi$
$888$	5.34175	0.179257
$889$	−15.2796	−0.512462
$890$	0	0
$891$	−1.53035	−0.0512686
$892$	17.0288	0.570165
$893$	34.9380	1.16916
$894$	2.60575	0.0871492
$895$	0	0
$896$	68.6215	2.29248
$897$	18.7487	0.626001
$898$	−23.7216	−0.791601
$899$	56.9960	1.90092
$900$	0	0
$901$	−10.0176	−0.333736
$902$	18.7945	0.625789
$903$	−32.4992	−1.08150
$904$	−1.87695	−0.0624265
$905$	0	0
$906$	−32.7406	−1.08773
$907$	−25.2839	−0.839538	−0.419769	−	0.907631i	$-0.637889\pi$
$907$	−25.2839	−0.839538	−0.419769	+	0.907631i	$0.637889\pi$
$908$	−3.32955	−0.110495
$909$	22.8061	0.756431
$910$	0	0
$911$	27.3571	0.906380	0.453190	−	0.891414i	$-0.350286\pi$
$911$	27.3571	0.906380	0.453190	+	0.891414i	$0.350286\pi$
$912$	40.6478	1.34598
$913$	−6.04178	−0.199954
$914$	19.2492	0.636705
$915$	0	0
$916$	13.9631	0.461354
$917$	11.0095	0.363564
$918$	−21.8784	−0.722095
$919$	−44.3463	−1.46285	−0.731424	−	0.681923i	$-0.761144\pi$
$919$	−44.3463	−1.46285	−0.731424	+	0.681923i	$0.761144\pi$
$920$	0	0
$921$	24.1098	0.794445
$922$	−24.5867	−0.809719
$923$	−36.9255	−1.21542
$924$	−4.22446	−0.138974
$925$	0	0
$926$	39.6876	1.30422
$927$	−11.6913	−0.383992
$928$	−24.4908	−0.803950
$929$	−33.2552	−1.09107	−0.545535	−	0.838088i	$-0.683673\pi$
$929$	−33.2552	−1.09107	−0.545535	+	0.838088i	$0.683673\pi$
$930$	0	0
$931$	−132.643	−4.34720
$932$	−13.8457	−0.453530
$933$	28.1326	0.921021
$934$	48.5694	1.58924
$935$	0	0
$936$	10.7601	0.351705
$937$	51.9272	1.69639	0.848194	−	0.529686i	$-0.177690\pi$
$937$	51.9272	1.69639	0.848194	+	0.529686i	$0.177690\pi$
$938$	−63.1696	−2.06256
$939$	−19.1307	−0.624306
$940$	0	0
$941$	21.0604	0.686549	0.343274	−	0.939235i	$-0.388464\pi$
$941$	21.0604	0.686549	0.343274	+	0.939235i	$0.388464\pi$
$942$	23.1053	0.752812
$943$	56.8134	1.85010
$944$	−27.5924	−0.898056
$945$	0	0
$946$	−9.69658	−0.315263
$947$	22.4529	0.729621	0.364810	−	0.931082i	$-0.381134\pi$
$947$	22.4529	0.729621	0.364810	+	0.931082i	$0.381134\pi$
$948$	5.29740	0.172052
$949$	2.20929	0.0717166
$950$	0	0
$951$	1.86669	0.0605317
$952$	27.3853	0.887564
$953$	−29.3558	−0.950927	−0.475463	−	0.879736i	$-0.657720\pi$
$953$	−29.3558	−0.950927	−0.475463	+	0.879736i	$0.657720\pi$
$954$	10.7927	0.349426
$955$	0	0
$956$	−5.17915	−0.167506
$957$	−8.58958	−0.277662
$958$	16.6367	0.537508
$959$	80.5519	2.60116
$960$	0	0
$961$	39.2028	1.26461
$962$	10.2854	0.331614
$963$	29.2730	0.943309
$964$	0.660992	0.0212891
$965$	0	0
$966$	−51.4088	−1.65405
$967$	−26.9397	−0.866324	−0.433162	−	0.901316i	$-0.642602\pi$
$967$	−26.9397	−0.866324	−0.433162	+	0.901316i	$0.642602\pi$
$968$	−21.4736	−0.690187
$969$	20.6115	0.662136
$970$	0	0
$971$	−38.3427	−1.23047	−0.615237	−	0.788342i	$-0.710940\pi$
$971$	−38.3427	−1.23047	−0.615237	+	0.788342i	$0.710940\pi$
$972$	9.64394	0.309330
$973$	76.2859	2.44561
$974$	−40.6583	−1.30278
$975$	0	0
$976$	9.95500	0.318652
$977$	13.7841	0.440991	0.220496	−	0.975388i	$-0.429233\pi$
$977$	13.7841	0.440991	0.220496	+	0.975388i	$0.429233\pi$
$978$	20.4008	0.652346
$979$	10.4096	0.332693
$980$	0	0
$981$	24.4252	0.779836
$982$	43.8334	1.39878
$983$	−14.8201	−0.472688	−0.236344	−	0.971669i	$-0.575949\pi$
$983$	−14.8201	−0.472688	−0.236344	+	0.971669i	$0.575949\pi$
$984$	−27.1844	−0.866608
$985$	0	0
$986$	−27.4874	−0.875376
$987$	28.9877	0.922688
$988$	14.1802	0.451132
$989$	−29.3115	−0.932051
$990$	0	0
$991$	−52.3768	−1.66380	−0.831902	−	0.554923i	$-0.812748\pi$
$991$	−52.3768	−1.66380	−0.831902	+	0.554923i	$0.812748\pi$
$992$	−30.1657	−0.957761
$993$	−31.4247	−0.997233
$994$	101.249	3.21143
$995$	0	0
$996$	−4.31387	−0.136690
$997$	−23.1646	−0.733630	−0.366815	−	0.930294i	$-0.619552\pi$
$997$	−23.1646	−0.733630	−0.366815	+	0.930294i	$0.619552\pi$
$998$	61.3592	1.94229
$999$	−11.3377	−0.358708

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.4		12
5.4	even	2		241.2.a.b.1.9	✓	12
15.14	odd	2		2169.2.a.h.1.4		12
20.19	odd	2		3856.2.a.n.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.9	✓	12	5.4	even	2
2169.2.a.h.1.4		12	15.14	odd	2
3856.2.a.n.1.8		12	20.19	odd	2
6025.2.a.h.1.4		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.63125 q^{2} +1.16790 q^{3} +0.660992 q^{4} -1.90514 q^{6} -5.06139 q^{7} +2.18426 q^{8} -1.63601 q^{9} +O(q^{10})\)	\(q-1.63125 q^{2} +1.16790 q^{3} +0.660992 q^{4} -1.90514 q^{6} -5.06139 q^{7} +2.18426 q^{8} -1.63601 q^{9} +1.08118 q^{11} +0.771973 q^{12} -3.01110 q^{13} +8.25641 q^{14} -4.88507 q^{16} -2.47710 q^{17} +2.66875 q^{18} -7.12459 q^{19} -5.91119 q^{21} -1.76369 q^{22} -5.33139 q^{23} +2.55100 q^{24} +4.91187 q^{26} -5.41439 q^{27} -3.34554 q^{28} -6.80248 q^{29} -8.37871 q^{31} +3.60028 q^{32} +1.26271 q^{33} +4.04078 q^{34} -1.08139 q^{36} +2.09398 q^{37} +11.6220 q^{38} -3.51666 q^{39} -10.6564 q^{41} +9.64266 q^{42} +5.49791 q^{43} +0.714654 q^{44} +8.69686 q^{46} -4.90386 q^{47} -5.70528 q^{48} +18.6176 q^{49} -2.89301 q^{51} -1.99032 q^{52} +4.04410 q^{53} +8.83226 q^{54} -11.0554 q^{56} -8.32081 q^{57} +11.0966 q^{58} +5.64831 q^{59} -2.03784 q^{61} +13.6678 q^{62} +8.28048 q^{63} +3.89718 q^{64} -2.05981 q^{66} -7.65097 q^{67} -1.63735 q^{68} -6.22653 q^{69} +12.2631 q^{71} -3.57348 q^{72} -0.733715 q^{73} -3.41582 q^{74} -4.70930 q^{76} -5.47229 q^{77} +5.73657 q^{78} +6.86216 q^{79} -1.41544 q^{81} +17.3833 q^{82} -5.58812 q^{83} -3.90725 q^{84} -8.96849 q^{86} -7.94461 q^{87} +2.36159 q^{88} +9.62798 q^{89} +15.2403 q^{91} -3.52401 q^{92} -9.78549 q^{93} +7.99945 q^{94} +4.20476 q^{96} +10.9185 q^{97} -30.3701 q^{98} -1.76883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * q^99

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