LMFDB - Embedded newform 6025.2.a.h.1.8

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			1.8
Root			$-0.342147$ 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)

$f(q)$	$=$	$q+0.342147 q^{2} -2.18519 q^{3} -1.88294 q^{4} -0.747658 q^{6} -1.82459 q^{7} -1.32853 q^{8} +1.77508 q^{9} +O(q^{10})$	\(q+0.342147 q^{2} -2.18519 q^{3} -1.88294 q^{4} -0.747658 q^{6} -1.82459 q^{7} -1.32853 q^{8} +1.77508 q^{9} +5.99218 q^{11} +4.11458 q^{12} -3.70515 q^{13} -0.624278 q^{14} +3.31132 q^{16} +1.64451 q^{17} +0.607337 q^{18} -3.15821 q^{19} +3.98709 q^{21} +2.05021 q^{22} +5.46015 q^{23} +2.90311 q^{24} -1.26771 q^{26} +2.67670 q^{27} +3.43559 q^{28} +7.24801 q^{29} -9.41700 q^{31} +3.79003 q^{32} -13.0941 q^{33} +0.562662 q^{34} -3.34236 q^{36} -1.27680 q^{37} -1.08057 q^{38} +8.09648 q^{39} -5.81239 q^{41} +1.36417 q^{42} -7.82887 q^{43} -11.2829 q^{44} +1.86817 q^{46} -2.61568 q^{47} -7.23587 q^{48} -3.67086 q^{49} -3.59356 q^{51} +6.97656 q^{52} -8.81076 q^{53} +0.915823 q^{54} +2.42403 q^{56} +6.90130 q^{57} +2.47989 q^{58} -7.78270 q^{59} +1.03194 q^{61} -3.22200 q^{62} -3.23879 q^{63} -5.32589 q^{64} -4.48010 q^{66} +8.39801 q^{67} -3.09650 q^{68} -11.9315 q^{69} +13.1691 q^{71} -2.35825 q^{72} +13.3963 q^{73} -0.436852 q^{74} +5.94670 q^{76} -10.9333 q^{77} +2.77018 q^{78} -10.6362 q^{79} -11.1743 q^{81} -1.98869 q^{82} -6.25636 q^{83} -7.50743 q^{84} -2.67862 q^{86} -15.8383 q^{87} -7.96082 q^{88} -3.94129 q^{89} +6.76039 q^{91} -10.2811 q^{92} +20.5780 q^{93} -0.894948 q^{94} -8.28195 q^{96} +2.22451 q^{97} -1.25598 q^{98} +10.6366 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.342147	0.241934	0.120967	−	0.992657i	$-0.461400\pi$
$2$	0.342147	0.241934	0.120967	+	0.992657i	$0.461400\pi$
$3$	−2.18519	−1.26162	−0.630811	−	0.775936i	$-0.717278\pi$
$3$	−2.18519	−1.26162	−0.630811	+	0.775936i	$0.717278\pi$
$4$	−1.88294	−0.941468
$5$	0	0
$5$	0	0
$6$	−0.747658	−0.305230
$7$	−1.82459	−0.689631	−0.344815	−	0.938671i	$-0.612058\pi$
$7$	−1.82459	−0.689631	−0.344815	+	0.938671i	$0.612058\pi$
$8$	−1.32853	−0.469708
$9$	1.77508	0.591692
$10$	0	0
$11$	5.99218	1.80671	0.903355	−	0.428894i	$-0.141096\pi$
$11$	5.99218	1.80671	0.903355	+	0.428894i	$0.141096\pi$
$12$	4.11458	1.18778
$13$	−3.70515	−1.02762	−0.513812	−	0.857903i	$-0.671767\pi$
$13$	−3.70515	−1.02762	−0.513812	+	0.857903i	$0.671767\pi$
$14$	−0.624278	−0.166845
$15$	0	0
$16$	3.31132	0.827829
$17$	1.64451	0.398851	0.199426	−	0.979913i	$-0.436092\pi$
$17$	1.64451	0.398851	0.199426	+	0.979913i	$0.436092\pi$
$18$	0.607337	0.143151
$19$	−3.15821	−0.724543	−0.362271	−	0.932073i	$-0.617999\pi$
$19$	−3.15821	−0.724543	−0.362271	+	0.932073i	$0.617999\pi$
$20$	0	0
$21$	3.98709	0.870054
$22$	2.05021	0.437105
$23$	5.46015	1.13852	0.569260	−	0.822158i	$-0.307230\pi$
$23$	5.46015	1.13852	0.569260	+	0.822158i	$0.307230\pi$
$24$	2.90311	0.592594
$25$	0	0
$26$	−1.26771	−0.248618
$27$	2.67670	0.515130
$28$	3.43559	0.649265
$29$	7.24801	1.34592	0.672961	−	0.739678i	$-0.265022\pi$
$29$	7.24801	1.34592	0.672961	+	0.739678i	$0.265022\pi$
$30$	0	0
$31$	−9.41700	−1.69134	−0.845672	−	0.533703i	$-0.820800\pi$
$31$	−9.41700	−1.69134	−0.845672	+	0.533703i	$0.820800\pi$
$32$	3.79003	0.669988
$33$	−13.0941	−2.27939
$34$	0.562662	0.0964958
$35$	0	0
$36$	−3.34236	−0.557059
$37$	−1.27680	−0.209904	−0.104952	−	0.994477i	$-0.533469\pi$
$37$	−1.27680	−0.209904	−0.104952	+	0.994477i	$0.533469\pi$
$38$	−1.08057	−0.175292
$39$	8.09648	1.29647
$40$	0	0
$41$	−5.81239	−0.907743	−0.453872	−	0.891067i	$-0.649958\pi$
$41$	−5.81239	−0.907743	−0.453872	+	0.891067i	$0.649958\pi$
$42$	1.36417	0.210496
$43$	−7.82887	−1.19389	−0.596946	−	0.802281i	$-0.703619\pi$
$43$	−7.82887	−1.19389	−0.596946	+	0.802281i	$0.703619\pi$
$44$	−11.2829	−1.70096
$45$	0	0
$46$	1.86817	0.275447
$47$	−2.61568	−0.381537	−0.190768	−	0.981635i	$-0.561098\pi$
$47$	−2.61568	−0.381537	−0.190768	+	0.981635i	$0.561098\pi$
$48$	−7.23587	−1.04441
$49$	−3.67086	−0.524409
$50$	0	0
$51$	−3.59356	−0.503200
$52$	6.97656	0.967475
$53$	−8.81076	−1.21025	−0.605126	−	0.796130i	$-0.706877\pi$
$53$	−8.81076	−1.21025	−0.605126	+	0.796130i	$0.706877\pi$
$54$	0.915823	0.124628
$55$	0	0
$56$	2.42403	0.323925
$57$	6.90130	0.914100
$58$	2.47989	0.325625
$59$	−7.78270	−1.01322	−0.506610	−	0.862175i	$-0.669102\pi$
$59$	−7.78270	−1.01322	−0.506610	+	0.862175i	$0.669102\pi$
$60$	0	0
$61$	1.03194	0.132127	0.0660635	−	0.997815i	$-0.478956\pi$
$61$	1.03194	0.132127	0.0660635	+	0.997815i	$0.478956\pi$
$62$	−3.22200	−0.409194
$63$	−3.23879	−0.408049
$64$	−5.32589	−0.665736
$65$	0	0
$66$	−4.48010	−0.551462
$67$	8.39801	1.02598	0.512990	−	0.858395i	$-0.328538\pi$
$67$	8.39801	1.02598	0.512990	+	0.858395i	$0.328538\pi$
$68$	−3.09650	−0.375505
$69$	−11.9315	−1.43638
$70$	0	0
$71$	13.1691	1.56288	0.781440	−	0.623981i	$-0.214486\pi$
$71$	13.1691	1.56288	0.781440	+	0.623981i	$0.214486\pi$
$72$	−2.35825	−0.277923
$73$	13.3963	1.56792	0.783959	−	0.620813i	$-0.213197\pi$
$73$	13.3963	1.56792	0.783959	+	0.620813i	$0.213197\pi$
$74$	−0.436852	−0.0507830
$75$	0	0
$76$	5.94670	0.682133
$77$	−10.9333	−1.24596
$78$	2.77018	0.313662
$79$	−10.6362	−1.19666	−0.598332	−	0.801248i	$-0.704170\pi$
$79$	−10.6362	−1.19666	−0.598332	+	0.801248i	$0.704170\pi$
$80$	0	0
$81$	−11.1743	−1.24159
$82$	−1.98869	−0.219614
$83$	−6.25636	−0.686725	−0.343362	−	0.939203i	$-0.611566\pi$
$83$	−6.25636	−0.686725	−0.343362	+	0.939203i	$0.611566\pi$
$84$	−7.50743	−0.819128
$85$	0	0
$86$	−2.67862	−0.288844
$87$	−15.8383	−1.69805
$88$	−7.96082	−0.848626
$89$	−3.94129	−0.417776	−0.208888	−	0.977940i	$-0.566984\pi$
$89$	−3.94129	−0.417776	−0.208888	+	0.977940i	$0.566984\pi$
$90$	0	0
$91$	6.76039	0.708681
$92$	−10.2811	−1.07188
$93$	20.5780	2.13384
$94$	−0.894948	−0.0923069
$95$	0	0
$96$	−8.28195	−0.845273
$97$	2.22451	0.225865	0.112933	−	0.993603i	$-0.463976\pi$
$97$	2.22451	0.225865	0.112933	+	0.993603i	$0.463976\pi$
$98$	−1.25598	−0.126873
$99$	10.6366	1.06902
$100$	0	0
$101$	−4.24027	−0.421923	−0.210962	−	0.977494i	$-0.567659\pi$
$101$	−4.24027	−0.421923	−0.210962	+	0.977494i	$0.567659\pi$
$102$	−1.22953	−0.121741
$103$	−0.164858	−0.0162439	−0.00812196	−	0.999967i	$-0.502585\pi$
$103$	−0.164858	−0.0162439	−0.00812196	+	0.999967i	$0.502585\pi$
$104$	4.92242	0.482683
$105$	0	0
$106$	−3.01458	−0.292801
$107$	−9.28536	−0.897650	−0.448825	−	0.893620i	$-0.648157\pi$
$107$	−9.28536	−0.897650	−0.448825	+	0.893620i	$0.648157\pi$
$108$	−5.04005	−0.484979
$109$	12.1952	1.16809	0.584044	−	0.811722i	$-0.301470\pi$
$109$	12.1952	1.16809	0.584044	+	0.811722i	$0.301470\pi$
$110$	0	0
$111$	2.79005	0.264820
$112$	−6.04180	−0.570897
$113$	−13.1834	−1.24019	−0.620093	−	0.784528i	$-0.712905\pi$
$113$	−13.1834	−1.24019	−0.620093	+	0.784528i	$0.712905\pi$
$114$	2.36126	0.221152
$115$	0	0
$116$	−13.6475	−1.26714
$117$	−6.57693	−0.608037
$118$	−2.66283	−0.245133
$119$	−3.00055	−0.275060
$120$	0	0
$121$	24.9062	2.26420
$122$	0.353077	0.0319661
$123$	12.7012	1.14523
$124$	17.7316	1.59235
$125$	0	0
$126$	−1.10814	−0.0987212
$127$	11.7563	1.04321	0.521603	−	0.853188i	$-0.325334\pi$
$127$	11.7563	1.04321	0.521603	+	0.853188i	$0.325334\pi$
$128$	−9.40229	−0.831053
$129$	17.1076	1.50624
$130$	0	0
$131$	14.0839	1.23051	0.615257	−	0.788326i	$-0.289052\pi$
$131$	14.0839	1.23051	0.615257	+	0.788326i	$0.289052\pi$
$132$	24.6553	2.14597
$133$	5.76244	0.499667
$134$	2.87335	0.248220
$135$	0	0
$136$	−2.18478	−0.187343
$137$	12.3993	1.05935	0.529673	−	0.848202i	$-0.322315\pi$
$137$	12.3993	1.05935	0.529673	+	0.848202i	$0.322315\pi$
$138$	−4.08232	−0.347510
$139$	−10.5456	−0.894464	−0.447232	−	0.894418i	$-0.647590\pi$
$139$	−10.5456	−0.894464	−0.447232	+	0.894418i	$0.647590\pi$
$140$	0	0
$141$	5.71578	0.481356
$142$	4.50575	0.378114
$143$	−22.2019	−1.85662
$144$	5.87784	0.489820
$145$	0	0
$146$	4.58350	0.379333
$147$	8.02156	0.661607
$148$	2.40412	0.197618
$149$	−9.30604	−0.762380	−0.381190	−	0.924497i	$-0.624486\pi$
$149$	−9.30604	−0.762380	−0.381190	+	0.924497i	$0.624486\pi$
$150$	0	0
$151$	10.2870	0.837143	0.418572	−	0.908184i	$-0.362531\pi$
$151$	10.2870	0.837143	0.418572	+	0.908184i	$0.362531\pi$
$152$	4.19579	0.340323
$153$	2.91912	0.235997
$154$	−3.74079	−0.301441
$155$	0	0
$156$	−15.2451	−1.22059
$157$	4.23848	0.338268	0.169134	−	0.985593i	$-0.445903\pi$
$157$	4.23848	0.338268	0.169134	+	0.985593i	$0.445903\pi$
$158$	−3.63914	−0.289514
$159$	19.2532	1.52688
$160$	0	0
$161$	−9.96254	−0.785159
$162$	−3.82326	−0.300384
$163$	6.42582	0.503309	0.251655	−	0.967817i	$-0.419025\pi$
$163$	6.42582	0.503309	0.251655	+	0.967817i	$0.419025\pi$
$164$	10.9444	0.854611
$165$	0	0
$166$	−2.14060	−0.166142
$167$	−3.96260	−0.306636	−0.153318	−	0.988177i	$-0.548996\pi$
$167$	−3.96260	−0.306636	−0.153318	+	0.988177i	$0.548996\pi$
$168$	−5.29698	−0.408671
$169$	0.728137	0.0560105
$170$	0	0
$171$	−5.60606	−0.428706
$172$	14.7413	1.12401
$173$	8.45221	0.642610	0.321305	−	0.946976i	$-0.395879\pi$
$173$	8.45221	0.642610	0.321305	+	0.946976i	$0.395879\pi$
$174$	−5.41903	−0.410816
$175$	0	0
$176$	19.8420	1.49565
$177$	17.0067	1.27830
$178$	−1.34850	−0.101074
$179$	−10.5847	−0.791138	−0.395569	−	0.918436i	$-0.629453\pi$
$179$	−10.5847	−0.791138	−0.395569	+	0.918436i	$0.629453\pi$
$180$	0	0
$181$	−19.4914	−1.44879	−0.724394	−	0.689387i	$-0.757880\pi$
$181$	−19.4914	−1.44879	−0.724394	+	0.689387i	$0.757880\pi$
$182$	2.31305	0.171454
$183$	−2.25500	−0.166694
$184$	−7.25400	−0.534772
$185$	0	0
$186$	7.04070	0.516249
$187$	9.85417	0.720608
$188$	4.92517	0.359205
$189$	−4.88388	−0.355250
$190$	0	0
$191$	−2.21537	−0.160298	−0.0801491	−	0.996783i	$-0.525540\pi$
$191$	−2.21537	−0.160298	−0.0801491	+	0.996783i	$0.525540\pi$
$192$	11.6381	0.839908
$193$	8.84755	0.636861	0.318430	−	0.947946i	$-0.396844\pi$
$193$	8.84755	0.636861	0.318430	+	0.947946i	$0.396844\pi$
$194$	0.761111	0.0546446
$195$	0	0
$196$	6.91200	0.493714
$197$	−6.19744	−0.441549	−0.220775	−	0.975325i	$-0.570859\pi$
$197$	−6.19744	−0.441549	−0.220775	+	0.975325i	$0.570859\pi$
$198$	3.63927	0.258632
$199$	20.2303	1.43409	0.717043	−	0.697028i	$-0.245495\pi$
$199$	20.2303	1.43409	0.717043	+	0.697028i	$0.245495\pi$
$200$	0	0
$201$	−18.3513	−1.29440
$202$	−1.45080	−0.102078
$203$	−13.2247	−0.928190
$204$	6.76645	0.473746
$205$	0	0
$206$	−0.0564056	−0.00392996
$207$	9.69219	0.673653
$208$	−12.2689	−0.850697
$209$	−18.9245	−1.30904
$210$	0	0
$211$	1.96502	0.135278	0.0676388	−	0.997710i	$-0.478453\pi$
$211$	1.96502	0.135278	0.0676388	+	0.997710i	$0.478453\pi$
$212$	16.5901	1.13941
$213$	−28.7769	−1.97176
$214$	−3.17696	−0.217172
$215$	0	0
$216$	−3.55608	−0.241961
$217$	17.1822	1.16640
$218$	4.17255	0.282600
$219$	−29.2735	−1.97812
$220$	0	0
$221$	−6.09314	−0.409869
$222$	0.954606	0.0640690
$223$	−21.4906	−1.43911	−0.719557	−	0.694433i	$-0.755655\pi$
$223$	−21.4906	−1.43911	−0.719557	+	0.694433i	$0.755655\pi$
$224$	−6.91525	−0.462045
$225$	0	0
$226$	−4.51065	−0.300044
$227$	−20.7806	−1.37925	−0.689627	−	0.724165i	$-0.742226\pi$
$227$	−20.7806	−1.37925	−0.689627	+	0.724165i	$0.742226\pi$
$228$	−12.9947	−0.860595
$229$	28.4761	1.88176	0.940878	−	0.338746i	$-0.110003\pi$
$229$	28.4761	1.88176	0.940878	+	0.338746i	$0.110003\pi$
$230$	0	0
$231$	23.8914	1.57194
$232$	−9.62924	−0.632190
$233$	2.19220	0.143616	0.0718079	−	0.997418i	$-0.477123\pi$
$233$	2.19220	0.143616	0.0718079	+	0.997418i	$0.477123\pi$
$234$	−2.25028	−0.147105
$235$	0	0
$236$	14.6543	0.953915
$237$	23.2421	1.50974
$238$	−1.02663	−0.0665465
$239$	25.2449	1.63296	0.816478	−	0.577377i	$-0.195924\pi$
$239$	25.2449	1.63296	0.816478	+	0.577377i	$0.195924\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	8.52158	0.547788
$243$	16.3880	1.05129
$244$	−1.94309	−0.124393
$245$	0	0
$246$	4.34568	0.277071
$247$	11.7016	0.744557
$248$	12.5108	0.794437
$249$	13.6714	0.866388
$250$	0	0
$251$	21.2167	1.33919	0.669593	−	0.742728i	$-0.266468\pi$
$251$	21.2167	1.33919	0.669593	+	0.742728i	$0.266468\pi$
$252$	6.09843	0.384165
$253$	32.7182	2.05698
$254$	4.02240	0.252388
$255$	0	0
$256$	7.43481	0.464676
$257$	−19.1130	−1.19224	−0.596119	−	0.802896i	$-0.703292\pi$
$257$	−19.1130	−1.19224	−0.596119	+	0.802896i	$0.703292\pi$
$258$	5.85332	0.364412
$259$	2.32963	0.144756
$260$	0	0
$261$	12.8658	0.796372
$262$	4.81876	0.297704
$263$	12.7792	0.787999	0.394000	−	0.919111i	$-0.371091\pi$
$263$	12.7792	0.787999	0.394000	+	0.919111i	$0.371091\pi$
$264$	17.3959	1.07065
$265$	0	0
$266$	1.97160	0.120887
$267$	8.61249	0.527076
$268$	−15.8129	−0.965927
$269$	1.65545	0.100934	0.0504672	−	0.998726i	$-0.483929\pi$
$269$	1.65545	0.100934	0.0504672	+	0.998726i	$0.483929\pi$
$270$	0	0
$271$	−17.0226	−1.03405	−0.517023	−	0.855971i	$-0.672960\pi$
$271$	−17.0226	−1.03405	−0.517023	+	0.855971i	$0.672960\pi$
$272$	5.44548	0.330181
$273$	−14.7728	−0.894088
$274$	4.24239	0.256292
$275$	0	0
$276$	22.4662	1.35231
$277$	−16.8245	−1.01089	−0.505443	−	0.862860i	$-0.668671\pi$
$277$	−16.8245	−1.01089	−0.505443	+	0.862860i	$0.668671\pi$
$278$	−3.60814	−0.216402
$279$	−16.7159	−1.00076
$280$	0	0
$281$	−16.1664	−0.964405	−0.482203	−	0.876060i	$-0.660163\pi$
$281$	−16.1664	−0.964405	−0.482203	+	0.876060i	$0.660163\pi$
$282$	1.95564	0.116456
$283$	−2.53878	−0.150915	−0.0754573	−	0.997149i	$-0.524042\pi$
$283$	−2.53878	−0.150915	−0.0754573	+	0.997149i	$0.524042\pi$
$284$	−24.7965	−1.47140
$285$	0	0
$286$	−7.59632	−0.449180
$287$	10.6052	0.626008
$288$	6.72759	0.396427
$289$	−14.2956	−0.840918
$290$	0	0
$291$	−4.86100	−0.284957
$292$	−25.2243	−1.47614
$293$	22.8971	1.33767	0.668833	−	0.743413i	$-0.266794\pi$
$293$	22.8971	1.33767	0.668833	+	0.743413i	$0.266794\pi$
$294$	2.74455	0.160065
$295$	0	0
$296$	1.69627	0.0985935
$297$	16.0392	0.930691
$298$	−3.18403	−0.184446
$299$	−20.2307	−1.16997
$300$	0	0
$301$	14.2845	0.823345
$302$	3.51966	0.202534
$303$	9.26583	0.532308
$304$	−10.4578	−0.599798
$305$	0	0
$306$	0.998769	0.0570958
$307$	4.71512	0.269106	0.134553	−	0.990906i	$-0.457040\pi$
$307$	4.71512	0.269106	0.134553	+	0.990906i	$0.457040\pi$
$308$	20.5867	1.17303
$309$	0.360246	0.0204937
$310$	0	0
$311$	4.63908	0.263058	0.131529	−	0.991312i	$-0.458011\pi$
$311$	4.63908	0.263058	0.131529	+	0.991312i	$0.458011\pi$
$312$	−10.7564	−0.608964
$313$	5.04057	0.284910	0.142455	−	0.989801i	$-0.454500\pi$
$313$	5.04057	0.284910	0.142455	+	0.989801i	$0.454500\pi$
$314$	1.45018	0.0818386
$315$	0	0
$316$	20.0272	1.12662
$317$	28.0992	1.57821	0.789105	−	0.614259i	$-0.210545\pi$
$317$	28.0992	1.57821	0.789105	+	0.614259i	$0.210545\pi$
$318$	6.58744	0.369405
$319$	43.4314	2.43169
$320$	0	0
$321$	20.2903	1.13250
$322$	−3.40865	−0.189957
$323$	−5.19369	−0.288985
$324$	21.0405	1.16892
$325$	0	0
$326$	2.19858	0.121768
$327$	−26.6489	−1.47369
$328$	7.72197	0.426374
$329$	4.77256	0.263120
$330$	0	0
$331$	29.6777	1.63124	0.815618	−	0.578590i	$-0.196397\pi$
$331$	29.6777	1.63124	0.815618	+	0.578590i	$0.196397\pi$
$332$	11.7803	0.646529
$333$	−2.26641	−0.124199
$334$	−1.35579	−0.0741857
$335$	0	0
$336$	13.2025	0.720256
$337$	12.2225	0.665799	0.332900	−	0.942962i	$-0.391973\pi$
$337$	12.2225	0.665799	0.332900	+	0.942962i	$0.391973\pi$
$338$	0.249130	0.0135509
$339$	28.8082	1.56465
$340$	0	0
$341$	−56.4284	−3.05577
$342$	−1.91810	−0.103719
$343$	19.4700	1.05128
$344$	10.4009	0.560780
$345$	0	0
$346$	2.89190	0.155469
$347$	17.9815	0.965296	0.482648	−	0.875814i	$-0.339675\pi$
$347$	17.9815	0.965296	0.482648	+	0.875814i	$0.339675\pi$
$348$	29.8225	1.59866
$349$	26.2848	1.40699	0.703496	−	0.710699i	$-0.251621\pi$
$349$	26.2848	1.40699	0.703496	+	0.710699i	$0.251621\pi$
$350$	0	0
$351$	−9.91756	−0.529360
$352$	22.7105	1.21047
$353$	13.7610	0.732424	0.366212	−	0.930531i	$-0.380654\pi$
$353$	13.7610	0.732424	0.366212	+	0.930531i	$0.380654\pi$
$354$	5.81879	0.309265
$355$	0	0
$356$	7.42120	0.393323
$357$	6.55679	0.347022
$358$	−3.62152	−0.191403
$359$	−1.32555	−0.0699598	−0.0349799	−	0.999388i	$-0.511137\pi$
$359$	−1.32555	−0.0699598	−0.0349799	+	0.999388i	$0.511137\pi$
$360$	0	0
$361$	−9.02572	−0.475038
$362$	−6.66894	−0.350511
$363$	−54.4249	−2.85657
$364$	−12.7294	−0.667200
$365$	0	0
$366$	−0.771541	−0.0403291
$367$	−6.05979	−0.316319	−0.158159	−	0.987414i	$-0.550556\pi$
$367$	−6.05979	−0.316319	−0.158159	+	0.987414i	$0.550556\pi$
$368$	18.0803	0.942500
$369$	−10.3174	−0.537105
$370$	0	0
$371$	16.0760	0.834627
$372$	−38.7470	−2.00894
$373$	−20.4445	−1.05858	−0.529288	−	0.848442i	$-0.677541\pi$
$373$	−20.4445	−1.05858	−0.529288	+	0.848442i	$0.677541\pi$
$374$	3.37157	0.174340
$375$	0	0
$376$	3.47503	0.179211
$377$	−26.8550	−1.38310
$378$	−1.67100	−0.0859471
$379$	35.4042	1.81859	0.909296	−	0.416150i	$-0.136621\pi$
$379$	35.4042	1.81859	0.909296	+	0.416150i	$0.136621\pi$
$380$	0	0
$381$	−25.6899	−1.31613
$382$	−0.757981	−0.0387817
$383$	−6.79327	−0.347120	−0.173560	−	0.984823i	$-0.555527\pi$
$383$	−6.79327	−0.347120	−0.173560	+	0.984823i	$0.555527\pi$
$384$	20.5458	1.04848
$385$	0	0
$386$	3.02716	0.154079
$387$	−13.8969	−0.706417
$388$	−4.18862	−0.212645
$389$	24.6869	1.25168	0.625838	−	0.779953i	$-0.284757\pi$
$389$	24.6869	1.25168	0.625838	+	0.779953i	$0.284757\pi$
$390$	0	0
$391$	8.97924	0.454100
$392$	4.87687	0.246319
$393$	−30.7760	−1.55245
$394$	−2.12043	−0.106826
$395$	0	0
$396$	−20.0280	−1.00644
$397$	−14.3804	−0.721730	−0.360865	−	0.932618i	$-0.617518\pi$
$397$	−14.3804	−0.721730	−0.360865	+	0.932618i	$0.617518\pi$
$398$	6.92173	0.346955
$399$	−12.5921	−0.630391
$400$	0	0
$401$	7.62276	0.380663	0.190331	−	0.981720i	$-0.439044\pi$
$401$	7.62276	0.380663	0.190331	+	0.981720i	$0.439044\pi$
$402$	−6.27883	−0.313160
$403$	34.8914	1.73806
$404$	7.98416	0.397227
$405$	0	0
$406$	−4.52478	−0.224561
$407$	−7.65079	−0.379236
$408$	4.77417	0.236357
$409$	5.12423	0.253377	0.126688	−	0.991943i	$-0.459565\pi$
$409$	5.12423	0.253377	0.126688	+	0.991943i	$0.459565\pi$
$410$	0	0
$411$	−27.0949	−1.33649
$412$	0.310416	0.0152931
$413$	14.2002	0.698748
$414$	3.31615	0.162980
$415$	0	0
$416$	−14.0426	−0.688496
$417$	23.0441	1.12848
$418$	−6.47498	−0.316701
$419$	13.3513	0.652254	0.326127	−	0.945326i	$-0.394256\pi$
$419$	13.3513	0.652254	0.326127	+	0.945326i	$0.394256\pi$
$420$	0	0
$421$	27.8059	1.35518	0.677588	−	0.735442i	$-0.263025\pi$
$421$	27.8059	1.35518	0.677588	+	0.735442i	$0.263025\pi$
$422$	0.672326	0.0327283
$423$	−4.64304	−0.225752
$424$	11.7054	0.568465
$425$	0	0
$426$	−9.84594	−0.477038
$427$	−1.88288	−0.0911188
$428$	17.4837	0.845109
$429$	48.5155	2.34235
$430$	0	0
$431$	18.5717	0.894567	0.447283	−	0.894392i	$-0.352392\pi$
$431$	18.5717	0.894567	0.447283	+	0.894392i	$0.352392\pi$
$432$	8.86339	0.426440
$433$	7.19376	0.345710	0.172855	−	0.984947i	$-0.444701\pi$
$433$	7.19376	0.345710	0.172855	+	0.984947i	$0.444701\pi$
$434$	5.87883	0.282193
$435$	0	0
$436$	−22.9628	−1.09972
$437$	−17.2443	−0.824906
$438$	−10.0158	−0.478575
$439$	−16.2866	−0.777315	−0.388657	−	0.921382i	$-0.627061\pi$
$439$	−16.2866	−0.777315	−0.388657	+	0.921382i	$0.627061\pi$
$440$	0	0
$441$	−6.51607	−0.310289
$442$	−2.08475	−0.0991614
$443$	37.0915	1.76227	0.881135	−	0.472864i	$-0.156780\pi$
$443$	37.0915	1.76227	0.881135	+	0.472864i	$0.156780\pi$
$444$	−5.25348	−0.249319
$445$	0	0
$446$	−7.35293	−0.348171
$447$	20.3355	0.961837
$448$	9.71757	0.459112
$449$	−17.1059	−0.807275	−0.403638	−	0.914919i	$-0.632254\pi$
$449$	−17.1059	−0.807275	−0.403638	+	0.914919i	$0.632254\pi$
$450$	0	0
$451$	−34.8289	−1.64003
$452$	24.8234	1.16760
$453$	−22.4791	−1.05616
$454$	−7.11001	−0.333689
$455$	0	0
$456$	−9.16861	−0.429360
$457$	9.35857	0.437776	0.218888	−	0.975750i	$-0.429757\pi$
$457$	9.35857	0.437776	0.218888	+	0.975750i	$0.429757\pi$
$458$	9.74302	0.455262
$459$	4.40184	0.205460
$460$	0	0
$461$	−15.8670	−0.738999	−0.369500	−	0.929231i	$-0.620471\pi$
$461$	−15.8670	−0.738999	−0.369500	+	0.929231i	$0.620471\pi$
$462$	8.17435	0.380305
$463$	6.99749	0.325201	0.162601	−	0.986692i	$-0.448012\pi$
$463$	6.99749	0.325201	0.162601	+	0.986692i	$0.448012\pi$
$464$	24.0005	1.11419
$465$	0	0
$466$	0.750055	0.0347456
$467$	24.2782	1.12346	0.561729	−	0.827321i	$-0.310136\pi$
$467$	24.2782	1.12346	0.561729	+	0.827321i	$0.310136\pi$
$468$	12.3839	0.572447
$469$	−15.3229	−0.707547
$470$	0	0
$471$	−9.26191	−0.426766
$472$	10.3396	0.475918
$473$	−46.9120	−2.15702
$474$	7.95222	0.365258
$475$	0	0
$476$	5.64984	0.258960
$477$	−15.6398	−0.716096
$478$	8.63746	0.395068
$479$	8.93171	0.408100	0.204050	−	0.978960i	$-0.434589\pi$
$479$	8.93171	0.408100	0.204050	+	0.978960i	$0.434589\pi$
$480$	0	0
$481$	4.73072	0.215702
$482$	0.342147	0.0155844
$483$	21.7701	0.990574
$484$	−46.8968	−2.13167
$485$	0	0
$486$	5.60711	0.254344
$487$	−34.5963	−1.56771	−0.783855	−	0.620944i	$-0.786750\pi$
$487$	−34.5963	−1.56771	−0.783855	+	0.620944i	$0.786750\pi$
$488$	−1.37097	−0.0620611
$489$	−14.0417	−0.634987
$490$	0	0
$491$	34.3798	1.55154	0.775770	−	0.631016i	$-0.217362\pi$
$491$	34.3798	1.55154	0.775770	+	0.631016i	$0.217362\pi$
$492$	−23.9156	−1.07820
$493$	11.9194	0.536823
$494$	4.00368	0.180134
$495$	0	0
$496$	−31.1827	−1.40014
$497$	−24.0281	−1.07781
$498$	4.67762	0.209609
$499$	38.3126	1.71511	0.857554	−	0.514394i	$-0.171983\pi$
$499$	38.3126	1.71511	0.857554	+	0.514394i	$0.171983\pi$
$500$	0	0
$501$	8.65906	0.386858
$502$	7.25923	0.323995
$503$	12.6073	0.562132	0.281066	−	0.959688i	$-0.409312\pi$
$503$	12.6073	0.562132	0.281066	+	0.959688i	$0.409312\pi$
$504$	4.30285	0.191664
$505$	0	0
$506$	11.1944	0.497653
$507$	−1.59112	−0.0706641
$508$	−22.1364	−0.982146
$509$	−19.0748	−0.845476	−0.422738	−	0.906252i	$-0.638931\pi$
$509$	−19.0748	−0.845476	−0.422738	+	0.906252i	$0.638931\pi$
$510$	0	0
$511$	−24.4428	−1.08128
$512$	21.3484	0.943474
$513$	−8.45356	−0.373234
$514$	−6.53947	−0.288444
$515$	0	0
$516$	−32.2125	−1.41808
$517$	−15.6737	−0.689326
$518$	0.797076	0.0350215
$519$	−18.4697	−0.810731
$520$	0	0
$521$	11.5960	0.508028	0.254014	−	0.967201i	$-0.418249\pi$
$521$	11.5960	0.508028	0.254014	+	0.967201i	$0.418249\pi$
$522$	4.40199	0.192670
$523$	26.2727	1.14883	0.574413	−	0.818566i	$-0.305230\pi$
$523$	26.2727	1.14883	0.574413	+	0.818566i	$0.305230\pi$
$524$	−26.5190	−1.15849
$525$	0	0
$526$	4.37236	0.190644
$527$	−15.4863	−0.674594
$528$	−43.3586	−1.88694
$529$	6.81324	0.296228
$530$	0	0
$531$	−13.8149	−0.599515
$532$	−10.8503	−0.470420
$533$	21.5358	0.932819
$534$	2.94674	0.127518
$535$	0	0
$536$	−11.1570	−0.481911
$537$	23.1296	0.998118
$538$	0.566406	0.0244195
$539$	−21.9965	−0.947455
$540$	0	0
$541$	−15.1441	−0.651097	−0.325548	−	0.945525i	$-0.605549\pi$
$541$	−15.1441	−0.651097	−0.325548	+	0.945525i	$0.605549\pi$
$542$	−5.82421	−0.250171
$543$	42.5926	1.82782
$544$	6.23272	0.267226
$545$	0	0
$546$	−5.05446	−0.216311
$547$	−34.7331	−1.48508	−0.742540	−	0.669802i	$-0.766379\pi$
$547$	−34.7331	−1.48508	−0.742540	+	0.669802i	$0.766379\pi$
$548$	−23.3471	−0.997339
$549$	1.83178	0.0781785
$550$	0	0
$551$	−22.8907	−0.975178
$552$	15.8514	0.674680
$553$	19.4067	0.825256
$554$	−5.75645	−0.244568
$555$	0	0
$556$	19.8566	0.842109
$557$	−34.1470	−1.44685	−0.723427	−	0.690401i	$-0.757434\pi$
$557$	−34.1470	−1.44685	−0.723427	+	0.690401i	$0.757434\pi$
$558$	−5.71930	−0.242117
$559$	29.0071	1.22687
$560$	0	0
$561$	−21.5333	−0.909136
$562$	−5.53128	−0.233323
$563$	19.2900	0.812975	0.406488	−	0.913656i	$-0.366753\pi$
$563$	19.2900	0.812975	0.406488	+	0.913656i	$0.366753\pi$
$564$	−10.7624	−0.453181
$565$	0	0
$566$	−0.868635	−0.0365114
$567$	20.3886	0.856241
$568$	−17.4955	−0.734097
$569$	−33.4263	−1.40130	−0.700652	−	0.713503i	$-0.747107\pi$
$569$	−33.4263	−1.40130	−0.700652	+	0.713503i	$0.747107\pi$
$570$	0	0
$571$	3.07936	0.128867	0.0644336	−	0.997922i	$-0.479476\pi$
$571$	3.07936	0.128867	0.0644336	+	0.997922i	$0.479476\pi$
$572$	41.8048	1.74795
$573$	4.84101	0.202236
$574$	3.62855	0.151453
$575$	0	0
$576$	−9.45386	−0.393911
$577$	5.95435	0.247883	0.123941	−	0.992290i	$-0.460447\pi$
$577$	5.95435	0.247883	0.123941	+	0.992290i	$0.460447\pi$
$578$	−4.89120	−0.203447
$579$	−19.3336	−0.803478
$580$	0	0
$581$	11.4153	0.473587
$582$	−1.66318	−0.0689408
$583$	−52.7957	−2.18657
$584$	−17.7974	−0.736463
$585$	0	0
$586$	7.83419	0.323627
$587$	−42.0432	−1.73531	−0.867655	−	0.497167i	$-0.834374\pi$
$587$	−42.0432	−1.73531	−0.867655	+	0.497167i	$0.834374\pi$
$588$	−15.1041	−0.622881
$589$	29.7409	1.22545
$590$	0	0
$591$	13.5426	0.557068
$592$	−4.22788	−0.173765
$593$	−40.9908	−1.68329	−0.841645	−	0.540031i	$-0.818413\pi$
$593$	−40.9908	−1.68329	−0.841645	+	0.540031i	$0.818413\pi$
$594$	5.48778	0.225166
$595$	0	0
$596$	17.5227	0.717757
$597$	−44.2071	−1.80928
$598$	−6.92186	−0.283056
$599$	−27.0862	−1.10671	−0.553356	−	0.832945i	$-0.686653\pi$
$599$	−27.0862	−1.10671	−0.553356	+	0.832945i	$0.686653\pi$
$600$	0	0
$601$	−3.03033	−0.123610	−0.0618049	−	0.998088i	$-0.519686\pi$
$601$	−3.03033	−0.123610	−0.0618049	+	0.998088i	$0.519686\pi$
$602$	4.88740	0.199195
$603$	14.9071	0.607064
$604$	−19.3697	−0.788144
$605$	0	0
$606$	3.17027	0.128784
$607$	−0.560838	−0.0227637	−0.0113818	−	0.999935i	$-0.503623\pi$
$607$	−0.560838	−0.0227637	−0.0113818	+	0.999935i	$0.503623\pi$
$608$	−11.9697	−0.485435
$609$	28.8985	1.17103
$610$	0	0
$611$	9.69150	0.392076
$612$	−5.49652	−0.222184
$613$	−23.7388	−0.958801	−0.479401	−	0.877596i	$-0.659146\pi$
$613$	−23.7388	−0.958801	−0.479401	+	0.877596i	$0.659146\pi$
$614$	1.61326	0.0651061
$615$	0	0
$616$	14.5252	0.585239
$617$	10.2411	0.412290	0.206145	−	0.978521i	$-0.433908\pi$
$617$	10.2411	0.412290	0.206145	+	0.978521i	$0.433908\pi$
$618$	0.123257	0.00495813
$619$	−27.8348	−1.11878	−0.559388	−	0.828906i	$-0.688964\pi$
$619$	−27.8348	−1.11878	−0.559388	+	0.828906i	$0.688964\pi$
$620$	0	0
$621$	14.6152	0.586486
$622$	1.58725	0.0636428
$623$	7.19125	0.288111
$624$	26.8100	1.07326
$625$	0	0
$626$	1.72462	0.0689295
$627$	41.3538	1.65151
$628$	−7.98079	−0.318468
$629$	−2.09970	−0.0837204
$630$	0	0
$631$	23.0564	0.917861	0.458931	−	0.888472i	$-0.348233\pi$
$631$	23.0564	0.917861	0.458931	+	0.888472i	$0.348233\pi$
$632$	14.1305	0.562082
$633$	−4.29396	−0.170669
$634$	9.61406	0.381823
$635$	0	0
$636$	−36.2526	−1.43751
$637$	13.6011	0.538895
$638$	14.8599	0.588310
$639$	23.3761	0.924744
$640$	0	0
$641$	35.6143	1.40668	0.703340	−	0.710853i	$-0.251691\pi$
$641$	35.6143	1.40668	0.703340	+	0.710853i	$0.251691\pi$
$642$	6.94227	0.273990
$643$	28.2806	1.11528	0.557639	−	0.830084i	$-0.311707\pi$
$643$	28.2806	1.11528	0.557639	+	0.830084i	$0.311707\pi$
$644$	18.7588	0.739201
$645$	0	0
$646$	−1.77700	−0.0699153
$647$	−14.5953	−0.573802	−0.286901	−	0.957960i	$-0.592625\pi$
$647$	−14.5953	−0.573802	−0.286901	+	0.957960i	$0.592625\pi$
$648$	14.8455	0.583186
$649$	−46.6353	−1.83060
$650$	0	0
$651$	−37.5464	−1.47156
$652$	−12.0994	−0.473850
$653$	28.0718	1.09853	0.549267	−	0.835647i	$-0.314907\pi$
$653$	28.0718	1.09853	0.549267	+	0.835647i	$0.314907\pi$
$654$	−9.11783	−0.356535
$655$	0	0
$656$	−19.2467	−0.751457
$657$	23.7794	0.927724
$658$	1.63292	0.0636577
$659$	−2.33181	−0.0908343	−0.0454172	−	0.998968i	$-0.514462\pi$
$659$	−2.33181	−0.0908343	−0.0454172	+	0.998968i	$0.514462\pi$
$660$	0	0
$661$	−21.3409	−0.830063	−0.415031	−	0.909807i	$-0.636229\pi$
$661$	−21.3409	−0.830063	−0.415031	+	0.909807i	$0.636229\pi$
$662$	10.1542	0.394652
$663$	13.3147	0.517100
$664$	8.31179	0.322560
$665$	0	0
$666$	−0.775446	−0.0300479
$667$	39.5752	1.53236
$668$	7.46133	0.288687
$669$	46.9611	1.81562
$670$	0	0
$671$	6.18360	0.238715
$672$	15.1112	0.582926
$673$	25.0948	0.967333	0.483667	−	0.875252i	$-0.339305\pi$
$673$	25.0948	0.967333	0.483667	+	0.875252i	$0.339305\pi$
$674$	4.18187	0.161080
$675$	0	0
$676$	−1.37103	−0.0527321
$677$	7.78669	0.299267	0.149633	−	0.988742i	$-0.452191\pi$
$677$	7.78669	0.299267	0.149633	+	0.988742i	$0.452191\pi$
$678$	9.85664	0.378542
$679$	−4.05883	−0.155764
$680$	0	0
$681$	45.4096	1.74010
$682$	−19.3068	−0.739295
$683$	−2.68470	−0.102727	−0.0513636	−	0.998680i	$-0.516357\pi$
$683$	−2.68470	−0.102727	−0.0513636	+	0.998680i	$0.516357\pi$
$684$	10.5559	0.403613
$685$	0	0
$686$	6.66159	0.254341
$687$	−62.2259	−2.37407
$688$	−25.9239	−0.988339
$689$	32.6452	1.24368
$690$	0	0
$691$	−46.3260	−1.76232	−0.881162	−	0.472814i	$-0.843238\pi$
$691$	−46.3260	−1.76232	−0.881162	+	0.472814i	$0.843238\pi$
$692$	−15.9150	−0.604996
$693$	−19.4074	−0.737227
$694$	6.15230	0.233538
$695$	0	0
$696$	21.0418	0.797586
$697$	−9.55851	−0.362054
$698$	8.99326	0.340400
$699$	−4.79039	−0.181189
$700$	0	0
$701$	4.33233	0.163630	0.0818150	−	0.996648i	$-0.473928\pi$
$701$	4.33233	0.163630	0.0818150	+	0.996648i	$0.473928\pi$
$702$	−3.39326	−0.128070
$703$	4.03239	0.152084
$704$	−31.9137	−1.20279
$705$	0	0
$706$	4.70829	0.177199
$707$	7.73677	0.290971
$708$	−32.0225	−1.20348
$709$	−45.2491	−1.69936	−0.849682	−	0.527295i	$-0.823206\pi$
$709$	−45.2491	−1.69936	−0.849682	+	0.527295i	$0.823206\pi$
$710$	0	0
$711$	−18.8800	−0.708057
$712$	5.23614	0.196233
$713$	−51.4182	−1.92563
$714$	2.24338	0.0839566
$715$	0	0
$716$	19.9303	0.744831
$717$	−55.1650	−2.06017
$718$	−0.453533	−0.0169257
$719$	34.3560	1.28126	0.640632	−	0.767848i	$-0.278672\pi$
$719$	34.3560	1.28126	0.640632	+	0.767848i	$0.278672\pi$
$720$	0	0
$721$	0.300798	0.0112023
$722$	−3.08812	−0.114928
$723$	−2.18519	−0.0812683
$724$	36.7011	1.36399
$725$	0	0
$726$	−18.6213	−0.691102
$727$	29.1579	1.08141	0.540703	−	0.841213i	$-0.318158\pi$
$727$	29.1579	1.08141	0.540703	+	0.841213i	$0.318158\pi$
$728$	−8.98141	−0.332873
$729$	−2.28799	−0.0847405
$730$	0	0
$731$	−12.8746	−0.476185
$732$	4.24602	0.156937
$733$	−36.8326	−1.36044	−0.680222	−	0.733007i	$-0.738116\pi$
$733$	−36.8326	−1.36044	−0.680222	+	0.733007i	$0.738116\pi$
$734$	−2.07334	−0.0765283
$735$	0	0
$736$	20.6941	0.762795
$737$	50.3224	1.85365
$738$	−3.53008	−0.129944
$739$	24.4258	0.898517	0.449258	−	0.893402i	$-0.351688\pi$
$739$	24.4258	0.898517	0.449258	+	0.893402i	$0.351688\pi$
$740$	0	0
$741$	−25.5704	−0.939350
$742$	5.50037	0.201925
$743$	24.4245	0.896049	0.448024	−	0.894021i	$-0.352128\pi$
$743$	24.4245	0.896049	0.448024	+	0.894021i	$0.352128\pi$
$744$	−27.3386	−1.00228
$745$	0	0
$746$	−6.99503	−0.256106
$747$	−11.1055	−0.406330
$748$	−18.5548	−0.678429
$749$	16.9420	0.619047
$750$	0	0
$751$	−30.0598	−1.09690	−0.548449	−	0.836184i	$-0.684781\pi$
$751$	−30.0598	−1.09690	−0.548449	+	0.836184i	$0.684781\pi$
$752$	−8.66136	−0.315847
$753$	−46.3627	−1.68955
$754$	−9.18835	−0.334620
$755$	0	0
$756$	9.19603	0.334456
$757$	−5.79087	−0.210473	−0.105236	−	0.994447i	$-0.533560\pi$
$757$	−5.79087	−0.210473	−0.105236	+	0.994447i	$0.533560\pi$
$758$	12.1134	0.439980
$759$	−71.4956	−2.59513
$760$	0	0
$761$	2.42691	0.0879754	0.0439877	−	0.999032i	$-0.485994\pi$
$761$	2.42691	0.0879754	0.0439877	+	0.999032i	$0.485994\pi$
$762$	−8.78972	−0.318418
$763$	−22.2512	−0.805549
$764$	4.17139	0.150916
$765$	0	0
$766$	−2.32430	−0.0839803
$767$	28.8361	1.04121
$768$	−16.2465	−0.586246
$769$	22.0750	0.796045	0.398022	−	0.917376i	$-0.369697\pi$
$769$	22.0750	0.796045	0.398022	+	0.917376i	$0.369697\pi$
$770$	0	0
$771$	41.7657	1.50416
$772$	−16.6594	−0.599584
$773$	−28.7802	−1.03515	−0.517576	−	0.855637i	$-0.673166\pi$
$773$	−28.7802	−1.03515	−0.517576	+	0.855637i	$0.673166\pi$
$774$	−4.75476	−0.170906
$775$	0	0
$776$	−2.95534	−0.106091
$777$	−5.09070	−0.182628
$778$	8.44655	0.302824
$779$	18.3567	0.657699
$780$	0	0
$781$	78.9113	2.82367
$782$	3.07222	0.109862
$783$	19.4007	0.693325
$784$	−12.1554	−0.434121
$785$	0	0
$786$	−10.5299	−0.375590
$787$	53.4388	1.90489	0.952443	−	0.304715i	$-0.0985613\pi$
$787$	53.4388	1.90489	0.952443	+	0.304715i	$0.0985613\pi$
$788$	11.6694	0.415704
$789$	−27.9250	−0.994158
$790$	0	0
$791$	24.0543	0.855271
$792$	−14.1311	−0.502125
$793$	−3.82351	−0.135777
$794$	−4.92020	−0.174611
$795$	0	0
$796$	−38.0923	−1.35015
$797$	−10.4149	−0.368914	−0.184457	−	0.982841i	$-0.559053\pi$
$797$	−10.4149	−0.368914	−0.184457	+	0.982841i	$0.559053\pi$
$798$	−4.30833	−0.152513
$799$	−4.30151	−0.152176
$800$	0	0
$801$	−6.99609	−0.247195
$802$	2.60810	0.0920954
$803$	80.2730	2.83277
$804$	34.5543	1.21864
$805$	0	0
$806$	11.9380	0.420498
$807$	−3.61747	−0.127341
$808$	5.63335	0.198181
$809$	−25.9467	−0.912237	−0.456118	−	0.889919i	$-0.650761\pi$
$809$	−25.9467	−0.912237	−0.456118	+	0.889919i	$0.650761\pi$
$810$	0	0
$811$	−11.1712	−0.392275	−0.196137	−	0.980576i	$-0.562840\pi$
$811$	−11.1712	−0.392275	−0.196137	+	0.980576i	$0.562840\pi$
$812$	24.9012	0.873861
$813$	37.1976	1.30458
$814$	−2.61769	−0.0917501
$815$	0	0
$816$	−11.8994	−0.416563
$817$	24.7252	0.865026
$818$	1.75324	0.0613005
$819$	12.0002	0.419321
$820$	0	0
$821$	18.3232	0.639484	0.319742	−	0.947505i	$-0.396404\pi$
$821$	18.3232	0.639484	0.319742	+	0.947505i	$0.396404\pi$
$822$	−9.27045	−0.323344
$823$	−21.1230	−0.736301	−0.368150	−	0.929766i	$-0.620009\pi$
$823$	−21.1230	−0.736301	−0.368150	+	0.929766i	$0.620009\pi$
$824$	0.219019	0.00762989
$825$	0	0
$826$	4.85857	0.169051
$827$	−47.5383	−1.65307	−0.826534	−	0.562887i	$-0.809690\pi$
$827$	−47.5383	−1.65307	−0.826534	+	0.562887i	$0.809690\pi$
$828$	−18.2498	−0.634223
$829$	15.8701	0.551190	0.275595	−	0.961274i	$-0.411125\pi$
$829$	15.8701	0.551190	0.275595	+	0.961274i	$0.411125\pi$
$830$	0	0
$831$	36.7648	1.27536
$832$	19.7332	0.684126
$833$	−6.03676	−0.209161
$834$	7.88448	0.273017
$835$	0	0
$836$	35.6337	1.23242
$837$	−25.2065	−0.871262
$838$	4.56811	0.157803
$839$	34.3114	1.18456	0.592281	−	0.805732i	$-0.298228\pi$
$839$	34.3114	1.18456	0.592281	+	0.805732i	$0.298228\pi$
$840$	0	0
$841$	23.5337	0.811507
$842$	9.51370	0.327864
$843$	35.3267	1.21672
$844$	−3.70001	−0.127360
$845$	0	0
$846$	−1.58860	−0.0546173
$847$	−45.4437	−1.56146
$848$	−29.1752	−1.00188
$849$	5.54772	0.190397
$850$	0	0
$851$	−6.97150	−0.238980
$852$	54.1851	1.85635
$853$	45.8466	1.56976	0.784879	−	0.619649i	$-0.212725\pi$
$853$	45.8466	1.56976	0.784879	+	0.619649i	$0.212725\pi$
$854$	−0.644221	−0.0220448
$855$	0	0
$856$	12.3359	0.421633
$857$	−21.7254	−0.742125	−0.371063	−	0.928608i	$-0.621007\pi$
$857$	−21.7254	−0.742125	−0.371063	+	0.928608i	$0.621007\pi$
$858$	16.5994	0.566696
$859$	52.5363	1.79252	0.896258	−	0.443534i	$-0.146275\pi$
$859$	52.5363	1.79252	0.896258	+	0.443534i	$0.146275\pi$
$860$	0	0
$861$	−23.1745	−0.789786
$862$	6.35425	0.216427
$863$	−32.9971	−1.12323	−0.561617	−	0.827397i	$-0.689821\pi$
$863$	−32.9971	−1.12323	−0.561617	+	0.827397i	$0.689821\pi$
$864$	10.1447	0.345131
$865$	0	0
$866$	2.46132	0.0836392
$867$	31.2387	1.06092
$868$	−32.3529	−1.09813
$869$	−63.7339	−2.16202
$870$	0	0
$871$	−31.1159	−1.05432
$872$	−16.2017	−0.548660
$873$	3.94868	0.133643
$874$	−5.90008	−0.199573
$875$	0	0
$876$	55.1201	1.86234
$877$	21.4221	0.723372	0.361686	−	0.932300i	$-0.382201\pi$
$877$	21.4221	0.723372	0.361686	+	0.932300i	$0.382201\pi$
$878$	−5.57239	−0.188059
$879$	−50.0347	−1.68763
$880$	0	0
$881$	−39.1162	−1.31786	−0.658929	−	0.752205i	$-0.728990\pi$
$881$	−39.1162	−1.31786	−0.658929	+	0.752205i	$0.728990\pi$
$882$	−2.22945	−0.0750696
$883$	2.84717	0.0958150	0.0479075	−	0.998852i	$-0.484745\pi$
$883$	2.84717	0.0958150	0.0479075	+	0.998852i	$0.484745\pi$
$884$	11.4730	0.385878
$885$	0	0
$886$	12.6907	0.426354
$887$	46.9262	1.57563	0.787814	−	0.615913i	$-0.211213\pi$
$887$	46.9262	1.57563	0.787814	+	0.615913i	$0.211213\pi$
$888$	−3.70667	−0.124388
$889$	−21.4505	−0.719428
$890$	0	0
$891$	−66.9586	−2.24320
$892$	40.4653	1.35488
$893$	8.26088	0.276440
$894$	6.95773	0.232701
$895$	0	0
$896$	17.1553	0.573120
$897$	44.2080	1.47606
$898$	−5.85272	−0.195308
$899$	−68.2546	−2.27642
$900$	0	0
$901$	−14.4893	−0.482710
$902$	−11.9166	−0.396779
$903$	−31.2144	−1.03875
$904$	17.5145	0.582525
$905$	0	0
$906$	−7.69115	−0.255521
$907$	−15.7164	−0.521856	−0.260928	−	0.965358i	$-0.584028\pi$
$907$	−15.7164	−0.521856	−0.260928	+	0.965358i	$0.584028\pi$
$908$	39.1285	1.29852
$909$	−7.52681	−0.249649
$910$	0	0
$911$	0.0451186	0.00149485	0.000747423	−	1.00000i	$-0.499762\pi$
$911$	0.0451186	0.00149485	0.000747423		1.00000i	$0.499762\pi$
$912$	22.8524	0.756718
$913$	−37.4892	−1.24071
$914$	3.20201	0.105913
$915$	0	0
$916$	−53.6187	−1.77161
$917$	−25.6973	−0.848601
$918$	1.50608	0.0497079
$919$	−7.88987	−0.260263	−0.130131	−	0.991497i	$-0.541540\pi$
$919$	−7.88987	−0.260263	−0.130131	+	0.991497i	$0.541540\pi$
$920$	0	0
$921$	−10.3035	−0.339511
$922$	−5.42884	−0.178789
$923$	−48.7933	−1.60605
$924$	−44.9859	−1.47993
$925$	0	0
$926$	2.39417	0.0786773
$927$	−0.292635	−0.00961140
$928$	27.4702	0.901752
$929$	25.6276	0.840815	0.420408	−	0.907335i	$-0.361887\pi$
$929$	25.6276	0.840815	0.420408	+	0.907335i	$0.361887\pi$
$930$	0	0
$931$	11.5934	0.379957
$932$	−4.12777	−0.135210
$933$	−10.1373	−0.331880
$934$	8.30670	0.271803
$935$	0	0
$936$	8.73767	0.285600
$937$	57.8627	1.89029	0.945146	−	0.326649i	$-0.105919\pi$
$937$	57.8627	1.89029	0.945146	+	0.326649i	$0.105919\pi$
$938$	−5.24269	−0.171180
$939$	−11.0146	−0.359449
$940$	0	0
$941$	−14.1272	−0.460533	−0.230266	−	0.973128i	$-0.573960\pi$
$941$	−14.1272	−0.460533	−0.230266	+	0.973128i	$0.573960\pi$
$942$	−3.16893	−0.103249
$943$	−31.7365	−1.03348
$944$	−25.7710	−0.838774
$945$	0	0
$946$	−16.0508	−0.521857
$947$	−22.5318	−0.732185	−0.366092	−	0.930578i	$-0.619305\pi$
$947$	−22.5318	−0.732185	−0.366092	+	0.930578i	$0.619305\pi$
$948$	−43.7634	−1.42137
$949$	−49.6353	−1.61123
$950$	0	0
$951$	−61.4023	−1.99110
$952$	3.98633	0.129198
$953$	34.0142	1.10183	0.550914	−	0.834562i	$-0.314279\pi$
$953$	34.0142	1.10183	0.550914	+	0.834562i	$0.314279\pi$
$954$	−5.35110	−0.173248
$955$	0	0
$956$	−47.5345	−1.53737
$957$	−94.9061	−3.06788
$958$	3.05596	0.0987335
$959$	−22.6237	−0.730557
$960$	0	0
$961$	57.6799	1.86064
$962$	1.61860	0.0521858
$963$	−16.4822	−0.531133
$964$	−1.88294	−0.0606453
$965$	0	0
$966$	7.44857	0.239654
$967$	62.1874	1.99981	0.999906	−	0.0137093i	$-0.00436394\pi$
$967$	62.1874	1.99981	0.999906	+	0.0137093i	$0.00436394\pi$
$968$	−33.0888	−1.06351
$969$	11.3492	0.364590
$970$	0	0
$971$	18.4346	0.591594	0.295797	−	0.955251i	$-0.404415\pi$
$971$	18.4346	0.591594	0.295797	+	0.955251i	$0.404415\pi$
$972$	−30.8576	−0.989757
$973$	19.2414	0.616850
$974$	−11.8370	−0.379283
$975$	0	0
$976$	3.41710	0.109379
$977$	−25.2228	−0.806949	−0.403474	−	0.914991i	$-0.632198\pi$
$977$	−25.2228	−0.806949	−0.403474	+	0.914991i	$0.632198\pi$
$978$	−4.80432	−0.153625
$979$	−23.6169	−0.754800
$980$	0	0
$981$	21.6474	0.691148
$982$	11.7630	0.375371
$983$	−12.7405	−0.406358	−0.203179	−	0.979142i	$-0.565127\pi$
$983$	−12.7405	−0.406358	−0.203179	+	0.979142i	$0.565127\pi$
$984$	−16.8740	−0.537923
$985$	0	0
$986$	4.07819	0.129876
$987$	−10.4290	−0.331958
$988$	−22.0334	−0.700977
$989$	−42.7468	−1.35927
$990$	0	0
$991$	15.6775	0.498011	0.249005	−	0.968502i	$-0.419896\pi$
$991$	15.6775	0.498011	0.249005	+	0.968502i	$0.419896\pi$
$992$	−35.6907	−1.13318
$993$	−64.8517	−2.05801
$994$	−8.22116	−0.260759
$995$	0	0
$996$	−25.7423	−0.815676
$997$	−28.1048	−0.890088	−0.445044	−	0.895509i	$-0.646812\pi$
$997$	−28.1048	−0.890088	−0.445044	+	0.895509i	$0.646812\pi$
$998$	13.1085	0.414944
$999$	−3.41759	−0.108128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.8		12
5.4	even	2		241.2.a.b.1.5	✓	12
15.14	odd	2		2169.2.a.h.1.8		12
20.19	odd	2		3856.2.a.n.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.5	✓	12	5.4	even	2
2169.2.a.h.1.8		12	15.14	odd	2
3856.2.a.n.1.3		12	20.19	odd	2
6025.2.a.h.1.8		12	1.1	even	1	trivial

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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)

\(f(q)\)	\(=\)	\(q+0.342147 q^{2} -2.18519 q^{3} -1.88294 q^{4} -0.747658 q^{6} -1.82459 q^{7} -1.32853 q^{8} +1.77508 q^{9} +O(q^{10})\)	\(q+0.342147 q^{2} -2.18519 q^{3} -1.88294 q^{4} -0.747658 q^{6} -1.82459 q^{7} -1.32853 q^{8} +1.77508 q^{9} +5.99218 q^{11} +4.11458 q^{12} -3.70515 q^{13} -0.624278 q^{14} +3.31132 q^{16} +1.64451 q^{17} +0.607337 q^{18} -3.15821 q^{19} +3.98709 q^{21} +2.05021 q^{22} +5.46015 q^{23} +2.90311 q^{24} -1.26771 q^{26} +2.67670 q^{27} +3.43559 q^{28} +7.24801 q^{29} -9.41700 q^{31} +3.79003 q^{32} -13.0941 q^{33} +0.562662 q^{34} -3.34236 q^{36} -1.27680 q^{37} -1.08057 q^{38} +8.09648 q^{39} -5.81239 q^{41} +1.36417 q^{42} -7.82887 q^{43} -11.2829 q^{44} +1.86817 q^{46} -2.61568 q^{47} -7.23587 q^{48} -3.67086 q^{49} -3.59356 q^{51} +6.97656 q^{52} -8.81076 q^{53} +0.915823 q^{54} +2.42403 q^{56} +6.90130 q^{57} +2.47989 q^{58} -7.78270 q^{59} +1.03194 q^{61} -3.22200 q^{62} -3.23879 q^{63} -5.32589 q^{64} -4.48010 q^{66} +8.39801 q^{67} -3.09650 q^{68} -11.9315 q^{69} +13.1691 q^{71} -2.35825 q^{72} +13.3963 q^{73} -0.436852 q^{74} +5.94670 q^{76} -10.9333 q^{77} +2.77018 q^{78} -10.6362 q^{79} -11.1743 q^{81} -1.98869 q^{82} -6.25636 q^{83} -7.50743 q^{84} -2.67862 q^{86} -15.8383 q^{87} -7.96082 q^{88} -3.94129 q^{89} +6.76039 q^{91} -10.2811 q^{92} +20.5780 q^{93} -0.894948 q^{94} -8.28195 q^{96} +2.22451 q^{97} -1.25598 q^{98} +10.6366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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

Introduction

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