LMFDB - Embedded newform 6025.2.a.h.1.6

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			1.6
Root			$0.115670$ 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)

$f(q)$	$=$	$q-0.115670 q^{2} +3.28295 q^{3} -1.98662 q^{4} -0.379739 q^{6} -3.19647 q^{7} +0.461133 q^{8} +7.77775 q^{9} +O(q^{10})$	\(q-0.115670 q^{2} +3.28295 q^{3} -1.98662 q^{4} -0.379739 q^{6} -3.19647 q^{7} +0.461133 q^{8} +7.77775 q^{9} +1.38968 q^{11} -6.52197 q^{12} +5.87704 q^{13} +0.369736 q^{14} +3.91990 q^{16} -5.28927 q^{17} -0.899653 q^{18} +4.99913 q^{19} -10.4938 q^{21} -0.160744 q^{22} -3.07207 q^{23} +1.51387 q^{24} -0.679798 q^{26} +15.6851 q^{27} +6.35017 q^{28} +3.28657 q^{29} +0.672296 q^{31} -1.37568 q^{32} +4.56225 q^{33} +0.611810 q^{34} -15.4514 q^{36} +3.79547 q^{37} -0.578249 q^{38} +19.2940 q^{39} +0.970489 q^{41} +1.21382 q^{42} -7.93946 q^{43} -2.76077 q^{44} +0.355346 q^{46} -2.82021 q^{47} +12.8688 q^{48} +3.21740 q^{49} -17.3644 q^{51} -11.6754 q^{52} -8.45419 q^{53} -1.81430 q^{54} -1.47400 q^{56} +16.4119 q^{57} -0.380158 q^{58} +5.70844 q^{59} +0.717980 q^{61} -0.0777646 q^{62} -24.8613 q^{63} -7.68068 q^{64} -0.527716 q^{66} -8.81215 q^{67} +10.5078 q^{68} -10.0854 q^{69} +15.8552 q^{71} +3.58657 q^{72} +8.75018 q^{73} -0.439022 q^{74} -9.93137 q^{76} -4.44207 q^{77} -2.23174 q^{78} +11.4452 q^{79} +28.1601 q^{81} -0.112256 q^{82} +11.9246 q^{83} +20.8473 q^{84} +0.918358 q^{86} +10.7896 q^{87} +0.640827 q^{88} -11.9996 q^{89} -18.7858 q^{91} +6.10304 q^{92} +2.20711 q^{93} +0.326214 q^{94} -4.51629 q^{96} -1.18886 q^{97} -0.372157 q^{98} +10.8086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.115670	−0.0817911	−0.0408955	−	0.999163i	$-0.513021\pi$
$2$	−0.115670	−0.0817911	−0.0408955	+	0.999163i	$0.513021\pi$
$3$	3.28295	1.89541	0.947705	−	0.319146i	$-0.103396\pi$
$3$	3.28295	1.89541	0.947705	+	0.319146i	$0.103396\pi$
$4$	−1.98662	−0.993310
$5$	0	0
$5$	0	0
$6$	−0.379739	−0.155028
$7$	−3.19647	−1.20815	−0.604076	−	0.796927i	$-0.706457\pi$
$7$	−3.19647	−1.20815	−0.604076	+	0.796927i	$0.706457\pi$
$8$	0.461133	0.163035
$9$	7.77775	2.59258
$10$	0	0
$11$	1.38968	0.419005	0.209502	−	0.977808i	$-0.432816\pi$
$11$	1.38968	0.419005	0.209502	+	0.977808i	$0.432816\pi$
$12$	−6.52197	−1.88273
$13$	5.87704	1.63000	0.814999	−	0.579463i	$-0.196738\pi$
$13$	5.87704	1.63000	0.814999	+	0.579463i	$0.196738\pi$
$14$	0.369736	0.0988160
$15$	0	0
$16$	3.91990	0.979975
$17$	−5.28927	−1.28284	−0.641418	−	0.767191i	$-0.721654\pi$
$17$	−5.28927	−1.28284	−0.641418	+	0.767191i	$0.721654\pi$
$18$	−0.899653	−0.212050
$19$	4.99913	1.14688	0.573439	−	0.819248i	$-0.305609\pi$
$19$	4.99913	1.14688	0.573439	+	0.819248i	$0.305609\pi$
$20$	0	0
$21$	−10.4938	−2.28994
$22$	−0.160744	−0.0342708
$23$	−3.07207	−0.640571	−0.320285	−	0.947321i	$-0.603779\pi$
$23$	−3.07207	−0.640571	−0.320285	+	0.947321i	$0.603779\pi$
$24$	1.51387	0.309018
$25$	0	0
$26$	−0.679798	−0.133319
$27$	15.6851	3.01860
$28$	6.35017	1.20007
$29$	3.28657	0.610301	0.305150	−	0.952304i	$-0.401293\pi$
$29$	3.28657	0.610301	0.305150	+	0.952304i	$0.401293\pi$
$30$	0	0
$31$	0.672296	0.120748	0.0603740	−	0.998176i	$-0.480771\pi$
$31$	0.672296	0.120748	0.0603740	+	0.998176i	$0.480771\pi$
$32$	−1.37568	−0.243188
$33$	4.56225	0.794186
$34$	0.611810	0.104925
$35$	0	0
$36$	−15.4514	−2.57524
$37$	3.79547	0.623971	0.311986	−	0.950087i	$-0.399006\pi$
$37$	3.79547	0.623971	0.311986	+	0.950087i	$0.399006\pi$
$38$	−0.578249	−0.0938044
$39$	19.2940	3.08952
$40$	0	0
$41$	0.970489	0.151565	0.0757824	−	0.997124i	$-0.475855\pi$
$41$	0.970489	0.151565	0.0757824	+	0.997124i	$0.475855\pi$
$42$	1.21382	0.187297
$43$	−7.93946	−1.21076	−0.605378	−	0.795938i	$-0.706978\pi$
$43$	−7.93946	−1.21076	−0.605378	+	0.795938i	$0.706978\pi$
$44$	−2.76077	−0.416201
$45$	0	0
$46$	0.355346	0.0523930
$47$	−2.82021	−0.411370	−0.205685	−	0.978618i	$-0.565942\pi$
$47$	−2.82021	−0.411370	−0.205685	+	0.978618i	$0.565942\pi$
$48$	12.8688	1.85746
$49$	3.21740	0.459629
$50$	0	0
$51$	−17.3644	−2.43150
$52$	−11.6754	−1.61909
$53$	−8.45419	−1.16127	−0.580636	−	0.814163i	$-0.697196\pi$
$53$	−8.45419	−1.16127	−0.580636	+	0.814163i	$0.697196\pi$
$54$	−1.81430	−0.246894
$55$	0	0
$56$	−1.47400	−0.196971
$57$	16.4119	2.17381
$58$	−0.380158	−0.0499172
$59$	5.70844	0.743176	0.371588	−	0.928398i	$-0.378813\pi$
$59$	5.70844	0.743176	0.371588	+	0.928398i	$0.378813\pi$
$60$	0	0
$61$	0.717980	0.0919279	0.0459639	−	0.998943i	$-0.485364\pi$
$61$	0.717980	0.0919279	0.0459639	+	0.998943i	$0.485364\pi$
$62$	−0.0777646	−0.00987611
$63$	−24.8613	−3.13223
$64$	−7.68068	−0.960085
$65$	0	0
$66$	−0.527716	−0.0649573
$67$	−8.81215	−1.07658	−0.538288	−	0.842761i	$-0.680929\pi$
$67$	−8.81215	−1.07658	−0.538288	+	0.842761i	$0.680929\pi$
$68$	10.5078	1.27425
$69$	−10.0854	−1.21414
$70$	0	0
$71$	15.8552	1.88166	0.940832	−	0.338874i	$-0.110046\pi$
$71$	15.8552	1.88166	0.940832	+	0.338874i	$0.110046\pi$
$72$	3.58657	0.422682
$73$	8.75018	1.02413	0.512066	−	0.858946i	$-0.328880\pi$
$73$	8.75018	1.02413	0.512066	+	0.858946i	$0.328880\pi$
$74$	−0.439022	−0.0510353
$75$	0	0
$76$	−9.93137	−1.13921
$77$	−4.44207	−0.506221
$78$	−2.23174	−0.252695
$79$	11.4452	1.28769	0.643843	−	0.765158i	$-0.277339\pi$
$79$	11.4452	1.28769	0.643843	+	0.765158i	$0.277339\pi$
$80$	0	0
$81$	28.1601	3.12890
$82$	−0.112256	−0.0123967
$83$	11.9246	1.30889	0.654446	−	0.756109i	$-0.272902\pi$
$83$	11.9246	1.30889	0.654446	+	0.756109i	$0.272902\pi$
$84$	20.8473	2.27462
$85$	0	0
$86$	0.918358	0.0990291
$87$	10.7896	1.15677
$88$	0.640827	0.0683124
$89$	−11.9996	−1.27195	−0.635975	−	0.771709i	$-0.719402\pi$
$89$	−11.9996	−1.27195	−0.635975	+	0.771709i	$0.719402\pi$
$90$	0	0
$91$	−18.7858	−1.96928
$92$	6.10304	0.636285
$93$	2.20711	0.228867
$94$	0.326214	0.0336464
$95$	0	0
$96$	−4.51629	−0.460942
$97$	−1.18886	−0.120710	−0.0603550	−	0.998177i	$-0.519223\pi$
$97$	−1.18886	−0.120710	−0.0603550	+	0.998177i	$0.519223\pi$
$98$	−0.372157	−0.0375936
$99$	10.8086	1.08630
$100$	0	0
$101$	19.9051	1.98064	0.990318	−	0.138820i	$-0.0443311\pi$
$101$	19.9051	1.98064	0.990318	+	0.138820i	$0.0443311\pi$
$102$	2.00854	0.198875
$103$	2.74129	0.270108	0.135054	−	0.990838i	$-0.456879\pi$
$103$	2.74129	0.270108	0.135054	+	0.990838i	$0.456879\pi$
$104$	2.71010	0.265747
$105$	0	0
$106$	0.977897	0.0949817
$107$	9.95829	0.962704	0.481352	−	0.876527i	$-0.340146\pi$
$107$	9.95829	0.962704	0.481352	+	0.876527i	$0.340146\pi$
$108$	−31.1603	−2.99840
$109$	−5.65622	−0.541768	−0.270884	−	0.962612i	$-0.587316\pi$
$109$	−5.65622	−0.541768	−0.270884	+	0.962612i	$0.587316\pi$
$110$	0	0
$111$	12.4603	1.18268
$112$	−12.5298	−1.18396
$113$	12.9604	1.21921	0.609604	−	0.792706i	$-0.291329\pi$
$113$	12.9604	1.21921	0.609604	+	0.792706i	$0.291329\pi$
$114$	−1.89836	−0.177798
$115$	0	0
$116$	−6.52917	−0.606218
$117$	45.7101	4.22590
$118$	−0.660296	−0.0607852
$119$	16.9070	1.54986
$120$	0	0
$121$	−9.06879	−0.824435
$122$	−0.0830488	−0.00751888
$123$	3.18606	0.287278
$124$	−1.33560	−0.119940
$125$	0	0
$126$	2.87571	0.256189
$127$	10.4647	0.928593	0.464297	−	0.885680i	$-0.346307\pi$
$127$	10.4647	0.928593	0.464297	+	0.885680i	$0.346307\pi$
$128$	3.63979	0.321715
$129$	−26.0648	−2.29488
$130$	0	0
$131$	12.9607	1.13238	0.566190	−	0.824275i	$-0.308417\pi$
$131$	12.9607	1.13238	0.566190	+	0.824275i	$0.308417\pi$
$132$	−9.06346	−0.788873
$133$	−15.9795	−1.38560
$134$	1.01930	0.0880543
$135$	0	0
$136$	−2.43906	−0.209147
$137$	−14.1420	−1.20824	−0.604118	−	0.796895i	$-0.706474\pi$
$137$	−14.1420	−1.20824	−0.604118	+	0.796895i	$0.706474\pi$
$138$	1.16658	0.0993062
$139$	−16.8589	−1.42996	−0.714978	−	0.699147i	$-0.753563\pi$
$139$	−16.8589	−1.42996	−0.714978	+	0.699147i	$0.753563\pi$
$140$	0	0
$141$	−9.25861	−0.779716
$142$	−1.83397	−0.153903
$143$	8.16721	0.682976
$144$	30.4880	2.54067
$145$	0	0
$146$	−1.01213	−0.0837648
$147$	10.5626	0.871186
$148$	−7.54015	−0.619797
$149$	16.2523	1.33144	0.665722	−	0.746200i	$-0.268124\pi$
$149$	16.2523	1.33144	0.665722	+	0.746200i	$0.268124\pi$
$150$	0	0
$151$	−10.4085	−0.847035	−0.423517	−	0.905888i	$-0.639205\pi$
$151$	−10.4085	−0.847035	−0.423517	+	0.905888i	$0.639205\pi$
$152$	2.30526	0.186981
$153$	−41.1386	−3.32586
$154$	0.513814	0.0414043
$155$	0	0
$156$	−38.3299	−3.06885
$157$	18.9894	1.51552	0.757758	−	0.652535i	$-0.226295\pi$
$157$	18.9894	1.51552	0.757758	+	0.652535i	$0.226295\pi$
$158$	−1.32387	−0.105321
$159$	−27.7547	−2.20109
$160$	0	0
$161$	9.81977	0.773906
$162$	−3.25728	−0.255916
$163$	−7.43947	−0.582704	−0.291352	−	0.956616i	$-0.594105\pi$
$163$	−7.43947	−0.582704	−0.291352	+	0.956616i	$0.594105\pi$
$164$	−1.92799	−0.150551
$165$	0	0
$166$	−1.37932	−0.107056
$167$	−13.4159	−1.03815	−0.519076	−	0.854728i	$-0.673724\pi$
$167$	−13.4159	−1.03815	−0.519076	+	0.854728i	$0.673724\pi$
$168$	−4.83905	−0.373341
$169$	21.5396	1.65689
$170$	0	0
$171$	38.8819	2.97338
$172$	15.7727	1.20266
$173$	3.18442	0.242107	0.121053	−	0.992646i	$-0.461373\pi$
$173$	3.18442	0.242107	0.121053	+	0.992646i	$0.461373\pi$
$174$	−1.24804	−0.0946135
$175$	0	0
$176$	5.44741	0.410614
$177$	18.7405	1.40862
$178$	1.38799	0.104034
$179$	11.8290	0.884142	0.442071	−	0.896980i	$-0.354244\pi$
$179$	11.8290	0.884142	0.442071	+	0.896980i	$0.354244\pi$
$180$	0	0
$181$	−3.92038	−0.291399	−0.145700	−	0.989329i	$-0.546543\pi$
$181$	−3.92038	−0.291399	−0.145700	+	0.989329i	$0.546543\pi$
$182$	2.17295	0.161070
$183$	2.35709	0.174241
$184$	−1.41663	−0.104435
$185$	0	0
$186$	−0.255297	−0.0187193
$187$	−7.35040	−0.537514
$188$	5.60269	0.408618
$189$	−50.1369	−3.64692
$190$	0	0
$191$	1.27094	0.0919617	0.0459809	−	0.998942i	$-0.485359\pi$
$191$	1.27094	0.0919617	0.0459809	+	0.998942i	$0.485359\pi$
$192$	−25.2153	−1.81976
$193$	7.18460	0.517159	0.258580	−	0.965990i	$-0.416746\pi$
$193$	7.18460	0.517159	0.258580	+	0.965990i	$0.416746\pi$
$194$	0.137515	0.00987300
$195$	0	0
$196$	−6.39176	−0.456554
$197$	−6.64645	−0.473540	−0.236770	−	0.971566i	$-0.576089\pi$
$197$	−6.64645	−0.473540	−0.236770	+	0.971566i	$0.576089\pi$
$198$	−1.25023	−0.0888500
$199$	12.7358	0.902819	0.451410	−	0.892317i	$-0.350921\pi$
$199$	12.7358	0.902819	0.451410	+	0.892317i	$0.350921\pi$
$200$	0	0
$201$	−28.9298	−2.04055
$202$	−2.30243	−0.161998
$203$	−10.5054	−0.737336
$204$	34.4965	2.41524
$205$	0	0
$206$	−0.317085	−0.0220924
$207$	−23.8938	−1.66073
$208$	23.0374	1.59736
$209$	6.94719	0.480547
$210$	0	0
$211$	5.22527	0.359722	0.179861	−	0.983692i	$-0.442435\pi$
$211$	5.22527	0.359722	0.179861	+	0.983692i	$0.442435\pi$
$212$	16.7953	1.15350
$213$	52.0517	3.56653
$214$	−1.15188	−0.0787406
$215$	0	0
$216$	7.23291	0.492137
$217$	−2.14897	−0.145882
$218$	0.654256	0.0443118
$219$	28.7264	1.94115
$220$	0	0
$221$	−31.0853	−2.09102
$222$	−1.44129	−0.0967328
$223$	1.68503	0.112838	0.0564191	−	0.998407i	$-0.482032\pi$
$223$	1.68503	0.112838	0.0564191	+	0.998407i	$0.482032\pi$
$224$	4.39732	0.293808
$225$	0	0
$226$	−1.49913	−0.0997203
$227$	1.27020	0.0843064	0.0421532	−	0.999111i	$-0.486578\pi$
$227$	1.27020	0.0843064	0.0421532	+	0.999111i	$0.486578\pi$
$228$	−32.6042	−2.15926
$229$	24.4833	1.61790	0.808950	−	0.587877i	$-0.200036\pi$
$229$	24.4833	1.61790	0.808950	+	0.587877i	$0.200036\pi$
$230$	0	0
$231$	−14.5831	−0.959496
$232$	1.51554	0.0995004
$233$	−3.58351	−0.234764	−0.117382	−	0.993087i	$-0.537450\pi$
$233$	−3.58351	−0.234764	−0.117382	+	0.993087i	$0.537450\pi$
$234$	−5.28729	−0.345641
$235$	0	0
$236$	−11.3405	−0.738204
$237$	37.5740	2.44069
$238$	−1.95563	−0.126765
$239$	−27.0261	−1.74817	−0.874087	−	0.485769i	$-0.838540\pi$
$239$	−27.0261	−1.74817	−0.874087	+	0.485769i	$0.838540\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	1.04899	0.0674315
$243$	45.3929	2.91195
$244$	−1.42635	−0.0913129
$245$	0	0
$246$	−0.368532	−0.0234968
$247$	29.3801	1.86941
$248$	0.310018	0.0196862
$249$	39.1478	2.48089
$250$	0	0
$251$	−19.0710	−1.20375	−0.601874	−	0.798591i	$-0.705579\pi$
$251$	−19.0710	−1.20375	−0.601874	+	0.798591i	$0.705579\pi$
$252$	49.3900	3.11128
$253$	−4.26920	−0.268402
$254$	−1.21045	−0.0759506
$255$	0	0
$256$	14.9403	0.933771
$257$	29.8662	1.86300	0.931502	−	0.363736i	$-0.118499\pi$
$257$	29.8662	1.86300	0.931502	+	0.363736i	$0.118499\pi$
$258$	3.01492	0.187701
$259$	−12.1321	−0.753851
$260$	0	0
$261$	25.5621	1.58225
$262$	−1.49916	−0.0926186
$263$	14.4912	0.893563	0.446781	−	0.894643i	$-0.352570\pi$
$263$	14.4912	0.893563	0.446781	+	0.894643i	$0.352570\pi$
$264$	2.10380	0.129480
$265$	0	0
$266$	1.84835	0.113330
$267$	−39.3939	−2.41087
$268$	17.5064	1.06937
$269$	9.73320	0.593444	0.296722	−	0.954964i	$-0.404107\pi$
$269$	9.73320	0.593444	0.296722	+	0.954964i	$0.404107\pi$
$270$	0	0
$271$	17.7984	1.08117	0.540587	−	0.841288i	$-0.318202\pi$
$271$	17.7984	1.08117	0.540587	+	0.841288i	$0.318202\pi$
$272$	−20.7334	−1.25715
$273$	−61.6727	−3.73260
$274$	1.63581	0.0988229
$275$	0	0
$276$	20.0359	1.20602
$277$	−2.28565	−0.137332	−0.0686658	−	0.997640i	$-0.521874\pi$
$277$	−2.28565	−0.137332	−0.0686658	+	0.997640i	$0.521874\pi$
$278$	1.95007	0.116958
$279$	5.22895	0.313049
$280$	0	0
$281$	9.34433	0.557436	0.278718	−	0.960373i	$-0.410090\pi$
$281$	9.34433	0.557436	0.278718	+	0.960373i	$0.410090\pi$
$282$	1.07094	0.0637738
$283$	−8.86628	−0.527045	−0.263523	−	0.964653i	$-0.584884\pi$
$283$	−8.86628	−0.527045	−0.263523	+	0.964653i	$0.584884\pi$
$284$	−31.4982	−1.86908
$285$	0	0
$286$	−0.944702	−0.0558614
$287$	−3.10214	−0.183113
$288$	−10.6997	−0.630486
$289$	10.9764	0.645670
$290$	0	0
$291$	−3.90295	−0.228795
$292$	−17.3833	−1.01728
$293$	−17.1228	−1.00032	−0.500161	−	0.865932i	$-0.666726\pi$
$293$	−17.1228	−1.00032	−0.500161	+	0.865932i	$0.666726\pi$
$294$	−1.22177	−0.0712552
$295$	0	0
$296$	1.75021	0.101729
$297$	21.7973	1.26481
$298$	−1.87991	−0.108900
$299$	−18.0547	−1.04413
$300$	0	0
$301$	25.3782	1.46278
$302$	1.20396	0.0692799
$303$	65.3475	3.75412
$304$	19.5961	1.12391
$305$	0	0
$306$	4.75851	0.272026
$307$	−5.03009	−0.287082	−0.143541	−	0.989644i	$-0.545849\pi$
$307$	−5.03009	−0.287082	−0.143541	+	0.989644i	$0.545849\pi$
$308$	8.82471	0.502834
$309$	8.99952	0.511965
$310$	0	0
$311$	9.99750	0.566906	0.283453	−	0.958986i	$-0.408520\pi$
$311$	9.99750	0.566906	0.283453	+	0.958986i	$0.408520\pi$
$312$	8.89710	0.503699
$313$	−28.1466	−1.59094	−0.795471	−	0.605992i	$-0.792776\pi$
$313$	−28.1466	−1.59094	−0.795471	+	0.605992i	$0.792776\pi$
$314$	−2.19650	−0.123956
$315$	0	0
$316$	−22.7373	−1.27907
$317$	5.66871	0.318387	0.159193	−	0.987247i	$-0.449111\pi$
$317$	5.66871	0.318387	0.159193	+	0.987247i	$0.449111\pi$
$318$	3.21038	0.180029
$319$	4.56728	0.255719
$320$	0	0
$321$	32.6925	1.82472
$322$	−1.13585	−0.0632986
$323$	−26.4417	−1.47126
$324$	−55.9434	−3.10797
$325$	0	0
$326$	0.860524	0.0476600
$327$	−18.5691	−1.02687
$328$	0.447524	0.0247104
$329$	9.01472	0.496998
$330$	0	0
$331$	−14.8950	−0.818701	−0.409350	−	0.912377i	$-0.634245\pi$
$331$	−14.8950	−0.818701	−0.409350	+	0.912377i	$0.634245\pi$
$332$	−23.6896	−1.30014
$333$	29.5202	1.61770
$334$	1.55181	0.0849115
$335$	0	0
$336$	−41.1348	−2.24409
$337$	−21.4134	−1.16646	−0.583231	−	0.812306i	$-0.698212\pi$
$337$	−21.4134	−1.16646	−0.583231	+	0.812306i	$0.698212\pi$
$338$	−2.49149	−0.135519
$339$	42.5482	2.31090
$340$	0	0
$341$	0.934278	0.0505940
$342$	−4.49748	−0.243196
$343$	12.0909	0.652850
$344$	−3.66115	−0.197396
$345$	0	0
$346$	−0.368342	−0.0198022
$347$	6.12740	0.328936	0.164468	−	0.986382i	$-0.447409\pi$
$347$	6.12740	0.328936	0.164468	+	0.986382i	$0.447409\pi$
$348$	−21.4349	−1.14903
$349$	−7.15661	−0.383085	−0.191542	−	0.981484i	$-0.561349\pi$
$349$	−7.15661	−0.383085	−0.191542	+	0.981484i	$0.561349\pi$
$350$	0	0
$351$	92.1819	4.92031
$352$	−1.91176	−0.101897
$353$	9.47379	0.504239	0.252120	−	0.967696i	$-0.418872\pi$
$353$	9.47379	0.504239	0.252120	+	0.967696i	$0.418872\pi$
$354$	−2.16772	−0.115213
$355$	0	0
$356$	23.8386	1.26344
$357$	55.5047	2.93762
$358$	−1.36826	−0.0723149
$359$	7.14694	0.377201	0.188601	−	0.982054i	$-0.439605\pi$
$359$	7.14694	0.377201	0.188601	+	0.982054i	$0.439605\pi$
$360$	0	0
$361$	5.99126	0.315330
$362$	0.453470	0.0238339
$363$	−29.7724	−1.56264
$364$	37.3202	1.95611
$365$	0	0
$366$	−0.272645	−0.0142514
$367$	−2.63925	−0.137767	−0.0688837	−	0.997625i	$-0.521944\pi$
$367$	−2.63925	−0.137767	−0.0688837	+	0.997625i	$0.521944\pi$
$368$	−12.0422	−0.627744
$369$	7.54822	0.392944
$370$	0	0
$371$	27.0235	1.40299
$372$	−4.38470	−0.227336
$373$	−20.5114	−1.06204	−0.531020	−	0.847360i	$-0.678191\pi$
$373$	−20.5114	−1.06204	−0.531020	+	0.847360i	$0.678191\pi$
$374$	0.850221	0.0439639
$375$	0	0
$376$	−1.30049	−0.0670678
$377$	19.3153	0.994789
$378$	5.79934	0.298286
$379$	−24.7263	−1.27010	−0.635051	−	0.772470i	$-0.719021\pi$
$379$	−24.7263	−1.27010	−0.635051	+	0.772470i	$0.719021\pi$
$380$	0	0
$381$	34.3551	1.76007
$382$	−0.147009	−0.00752165
$383$	33.2690	1.69997	0.849983	−	0.526810i	$-0.176612\pi$
$383$	33.2690	1.69997	0.849983	+	0.526810i	$0.176612\pi$
$384$	11.9492	0.609781
$385$	0	0
$386$	−0.831044	−0.0422990
$387$	−61.7511	−3.13899
$388$	2.36181	0.119902
$389$	−11.2024	−0.567985	−0.283992	−	0.958827i	$-0.591659\pi$
$389$	−11.2024	−0.567985	−0.283992	+	0.958827i	$0.591659\pi$
$390$	0	0
$391$	16.2490	0.821748
$392$	1.48365	0.0749356
$393$	42.5493	2.14633
$394$	0.768796	0.0387314
$395$	0	0
$396$	−21.4726	−1.07904
$397$	−5.20629	−0.261296	−0.130648	−	0.991429i	$-0.541706\pi$
$397$	−5.20629	−0.261296	−0.130648	+	0.991429i	$0.541706\pi$
$398$	−1.47315	−0.0738426
$399$	−52.4600	−2.62629
$400$	0	0
$401$	−2.79646	−0.139649	−0.0698243	−	0.997559i	$-0.522244\pi$
$401$	−2.79646	−0.139649	−0.0698243	+	0.997559i	$0.522244\pi$
$402$	3.34632	0.166899
$403$	3.95111	0.196819
$404$	−39.5440	−1.96739
$405$	0	0
$406$	1.21516	0.0603075
$407$	5.27449	0.261447
$408$	−8.00729	−0.396420
$409$	0.743107	0.0367443	0.0183721	−	0.999831i	$-0.494152\pi$
$409$	0.743107	0.0367443	0.0183721	+	0.999831i	$0.494152\pi$
$410$	0	0
$411$	−46.4276	−2.29010
$412$	−5.44591	−0.268301
$413$	−18.2469	−0.897869
$414$	2.76379	0.135833
$415$	0	0
$416$	−8.08493	−0.396396
$417$	−55.3470	−2.71035
$418$	−0.803582	−0.0393045
$419$	−11.8016	−0.576544	−0.288272	−	0.957549i	$-0.593081\pi$
$419$	−11.8016	−0.576544	−0.288272	+	0.957549i	$0.593081\pi$
$420$	0	0
$421$	−9.89956	−0.482475	−0.241237	−	0.970466i	$-0.577553\pi$
$421$	−9.89956	−0.482475	−0.241237	+	0.970466i	$0.577553\pi$
$422$	−0.604407	−0.0294221
$423$	−21.9349	−1.06651
$424$	−3.89850	−0.189328
$425$	0	0
$426$	−6.02083	−0.291710
$427$	−2.29500	−0.111063
$428$	−19.7833	−0.956264
$429$	26.8125	1.29452
$430$	0	0
$431$	9.64934	0.464793	0.232396	−	0.972621i	$-0.425343\pi$
$431$	9.64934	0.464793	0.232396	+	0.972621i	$0.425343\pi$
$432$	61.4840	2.95815
$433$	38.9496	1.87180	0.935900	−	0.352265i	$-0.114588\pi$
$433$	38.9496	1.87180	0.935900	+	0.352265i	$0.114588\pi$
$434$	0.248572	0.0119318
$435$	0	0
$436$	11.2368	0.538144
$437$	−15.3577	−0.734657
$438$	−3.32278	−0.158769
$439$	−16.8089	−0.802243	−0.401121	−	0.916025i	$-0.631379\pi$
$439$	−16.8089	−0.802243	−0.401121	+	0.916025i	$0.631379\pi$
$440$	0	0
$441$	25.0241	1.19163
$442$	3.59563	0.171027
$443$	0.438324	0.0208254	0.0104127	−	0.999946i	$-0.496685\pi$
$443$	0.438324	0.0208254	0.0104127	+	0.999946i	$0.496685\pi$
$444$	−24.7539	−1.17477
$445$	0	0
$446$	−0.194908	−0.00922917
$447$	53.3556	2.52363
$448$	24.5510	1.15993
$449$	−31.7722	−1.49942	−0.749711	−	0.661766i	$-0.769807\pi$
$449$	−31.7722	−1.49942	−0.749711	+	0.661766i	$0.769807\pi$
$450$	0	0
$451$	1.34867	0.0635064
$452$	−25.7473	−1.21105
$453$	−34.1707	−1.60548
$454$	−0.146925	−0.00689551
$455$	0	0
$456$	7.56805	0.354406
$457$	−17.1543	−0.802444	−0.401222	−	0.915981i	$-0.631414\pi$
$457$	−17.1543	−0.802444	−0.401222	+	0.915981i	$0.631414\pi$
$458$	−2.83198	−0.132330
$459$	−82.9627	−3.87237
$460$	0	0
$461$	−30.9242	−1.44028	−0.720141	−	0.693827i	$-0.755923\pi$
$461$	−30.9242	−1.44028	−0.720141	+	0.693827i	$0.755923\pi$
$462$	1.68683	0.0784783
$463$	−15.6931	−0.729319	−0.364659	−	0.931141i	$-0.618815\pi$
$463$	−15.6931	−0.729319	−0.364659	+	0.931141i	$0.618815\pi$
$464$	12.8830	0.598080
$465$	0	0
$466$	0.414505	0.0192016
$467$	−21.3617	−0.988501	−0.494250	−	0.869320i	$-0.664557\pi$
$467$	−21.3617	−0.988501	−0.494250	+	0.869320i	$0.664557\pi$
$468$	−90.8087	−4.19763
$469$	28.1678	1.30067
$470$	0	0
$471$	62.3411	2.87253
$472$	2.63235	0.121164
$473$	−11.0333	−0.507313
$474$	−4.34619	−0.199627
$475$	0	0
$476$	−33.5878	−1.53949
$477$	−65.7545	−3.01069
$478$	3.12611	0.142985
$479$	27.3633	1.25026	0.625130	−	0.780521i	$-0.285046\pi$
$479$	27.3633	1.25026	0.625130	+	0.780521i	$0.285046\pi$
$480$	0	0
$481$	22.3061	1.01707
$482$	−0.115670	−0.00526863
$483$	32.2378	1.46687
$484$	18.0162	0.818920
$485$	0	0
$486$	−5.25060	−0.238172
$487$	9.12015	0.413274	0.206637	−	0.978418i	$-0.433748\pi$
$487$	9.12015	0.413274	0.206637	+	0.978418i	$0.433748\pi$
$488$	0.331084	0.0149875
$489$	−24.4234	−1.10446
$490$	0	0
$491$	−7.29684	−0.329302	−0.164651	−	0.986352i	$-0.552650\pi$
$491$	−7.29684	−0.329302	−0.164651	+	0.986352i	$0.552650\pi$
$492$	−6.32950	−0.285356
$493$	−17.3836	−0.782916
$494$	−3.39839	−0.152901
$495$	0	0
$496$	2.63534	0.118330
$497$	−50.6806	−2.27333
$498$	−4.52822	−0.202915
$499$	1.98278	0.0887613	0.0443807	−	0.999015i	$-0.485869\pi$
$499$	1.98278	0.0887613	0.0443807	+	0.999015i	$0.485869\pi$
$500$	0	0
$501$	−44.0436	−1.96772
$502$	2.20594	0.0984559
$503$	−7.01318	−0.312702	−0.156351	−	0.987702i	$-0.549973\pi$
$503$	−7.01318	−0.312702	−0.156351	+	0.987702i	$0.549973\pi$
$504$	−11.4644	−0.510663
$505$	0	0
$506$	0.493818	0.0219529
$507$	70.7134	3.14049
$508$	−20.7894	−0.922381
$509$	−28.5738	−1.26651	−0.633256	−	0.773943i	$-0.718282\pi$
$509$	−28.5738	−1.26651	−0.633256	+	0.773943i	$0.718282\pi$
$510$	0	0
$511$	−27.9697	−1.23731
$512$	−9.00772	−0.398089
$513$	78.4118	3.46196
$514$	−3.45463	−0.152377
$515$	0	0
$516$	51.7809	2.27953
$517$	−3.91920	−0.172366
$518$	1.40332	0.0616583
$519$	10.4543	0.458892
$520$	0	0
$521$	−13.1589	−0.576501	−0.288250	−	0.957555i	$-0.593074\pi$
$521$	−13.1589	−0.576501	−0.288250	+	0.957555i	$0.593074\pi$
$522$	−2.95677	−0.129414
$523$	−23.8792	−1.04416	−0.522082	−	0.852895i	$-0.674845\pi$
$523$	−23.8792	−1.04416	−0.522082	+	0.852895i	$0.674845\pi$
$524$	−25.7480	−1.12480
$525$	0	0
$526$	−1.67619	−0.0730855
$527$	−3.55596	−0.154900
$528$	17.8836	0.778282
$529$	−13.5624	−0.589669
$530$	0	0
$531$	44.3988	1.92674
$532$	31.7453	1.37633
$533$	5.70360	0.247050
$534$	4.55670	0.197188
$535$	0	0
$536$	−4.06357	−0.175520
$537$	38.8340	1.67581
$538$	−1.12584	−0.0485384
$539$	4.47116	0.192587
$540$	0	0
$541$	−7.11389	−0.305850	−0.152925	−	0.988238i	$-0.548869\pi$
$541$	−7.11389	−0.305850	−0.152925	+	0.988238i	$0.548869\pi$
$542$	−2.05874	−0.0884304
$543$	−12.8704	−0.552321
$544$	7.27635	0.311971
$545$	0	0
$546$	7.13368	0.305294
$547$	−2.10736	−0.0901044	−0.0450522	−	0.998985i	$-0.514345\pi$
$547$	−2.10736	−0.0901044	−0.0450522	+	0.998985i	$0.514345\pi$
$548$	28.0949	1.20015
$549$	5.58426	0.238331
$550$	0	0
$551$	16.4300	0.699941
$552$	−4.65073	−0.197948
$553$	−36.5842	−1.55572
$554$	0.264382	0.0112325
$555$	0	0
$556$	33.4923	1.42039
$557$	9.69468	0.410777	0.205388	−	0.978681i	$-0.434154\pi$
$557$	9.69468	0.410777	0.205388	+	0.978681i	$0.434154\pi$
$558$	−0.604833	−0.0256046
$559$	−46.6605	−1.97353
$560$	0	0
$561$	−24.1310	−1.01881
$562$	−1.08086	−0.0455933
$563$	12.6385	0.532647	0.266324	−	0.963884i	$-0.414191\pi$
$563$	12.6385	0.532647	0.266324	+	0.963884i	$0.414191\pi$
$564$	18.3933	0.774500
$565$	0	0
$566$	1.02556	0.0431076
$567$	−90.0129	−3.78018
$568$	7.31134	0.306777
$569$	17.6815	0.741245	0.370622	−	0.928784i	$-0.379144\pi$
$569$	17.6815	0.741245	0.370622	+	0.928784i	$0.379144\pi$
$570$	0	0
$571$	−24.5248	−1.02633	−0.513166	−	0.858289i	$-0.671527\pi$
$571$	−24.5248	−1.02633	−0.513166	+	0.858289i	$0.671527\pi$
$572$	−16.2251	−0.678407
$573$	4.17242	0.174305
$574$	0.358824	0.0149770
$575$	0	0
$576$	−59.7384	−2.48910
$577$	35.7883	1.48988	0.744942	−	0.667129i	$-0.232477\pi$
$577$	35.7883	1.48988	0.744942	+	0.667129i	$0.232477\pi$
$578$	−1.26964	−0.0528101
$579$	23.5867	0.980229
$580$	0	0
$581$	−38.1165	−1.58134
$582$	0.451455	0.0187134
$583$	−11.7486	−0.486578
$584$	4.03500	0.166969
$585$	0	0
$586$	1.98059	0.0818175
$587$	42.4486	1.75204	0.876021	−	0.482273i	$-0.160189\pi$
$587$	42.4486	1.75204	0.876021	+	0.482273i	$0.160189\pi$
$588$	−20.9838	−0.865358
$589$	3.36089	0.138483
$590$	0	0
$591$	−21.8200	−0.897553
$592$	14.8779	0.611476
$593$	−17.8382	−0.732527	−0.366263	−	0.930511i	$-0.619363\pi$
$593$	−17.8382	−0.732527	−0.366263	+	0.930511i	$0.619363\pi$
$594$	−2.52129	−0.103450
$595$	0	0
$596$	−32.2872	−1.32254
$597$	41.8111	1.71121
$598$	2.08839	0.0854004
$599$	21.3734	0.873291	0.436646	−	0.899634i	$-0.356166\pi$
$599$	21.3734	0.873291	0.436646	+	0.899634i	$0.356166\pi$
$600$	0	0
$601$	−42.3095	−1.72584	−0.862920	−	0.505341i	$-0.831367\pi$
$601$	−42.3095	−1.72584	−0.862920	+	0.505341i	$0.831367\pi$
$602$	−2.93550	−0.119642
$603$	−68.5387	−2.79111
$604$	20.6778	0.841368
$605$	0	0
$606$	−7.55875	−0.307053
$607$	−1.51410	−0.0614552	−0.0307276	−	0.999528i	$-0.509782\pi$
$607$	−1.51410	−0.0614552	−0.0307276	+	0.999528i	$0.509782\pi$
$608$	−6.87720	−0.278907
$609$	−34.4887	−1.39755
$610$	0	0
$611$	−16.5745	−0.670533
$612$	81.7268	3.30361
$613$	15.4991	0.626001	0.313000	−	0.949753i	$-0.398666\pi$
$613$	15.4991	0.626001	0.313000	+	0.949753i	$0.398666\pi$
$614$	0.581830	0.0234808
$615$	0	0
$616$	−2.04838	−0.0825317
$617$	−22.9695	−0.924718	−0.462359	−	0.886693i	$-0.652997\pi$
$617$	−22.9695	−0.924718	−0.462359	+	0.886693i	$0.652997\pi$
$618$	−1.04097	−0.0418742
$619$	36.7503	1.47712	0.738559	−	0.674189i	$-0.235507\pi$
$619$	36.7503	1.47712	0.738559	+	0.674189i	$0.235507\pi$
$620$	0	0
$621$	−48.1857	−1.93363
$622$	−1.15641	−0.0463679
$623$	38.3562	1.53671
$624$	75.6306	3.02765
$625$	0	0
$626$	3.25572	0.130125
$627$	22.8073	0.910834
$628$	−37.7247	−1.50538
$629$	−20.0753	−0.800453
$630$	0	0
$631$	−16.5412	−0.658494	−0.329247	−	0.944244i	$-0.606795\pi$
$631$	−16.5412	−0.658494	−0.329247	+	0.944244i	$0.606795\pi$
$632$	5.27775	0.209938
$633$	17.1543	0.681821
$634$	−0.655700	−0.0260412
$635$	0	0
$636$	55.1380	2.18636
$637$	18.9088	0.749194
$638$	−0.528298	−0.0209155
$639$	123.318	4.87837
$640$	0	0
$641$	1.70611	0.0673873	0.0336937	−	0.999432i	$-0.489273\pi$
$641$	1.70611	0.0673873	0.0336937	+	0.999432i	$0.489273\pi$
$642$	−3.78155	−0.149246
$643$	12.2046	0.481302	0.240651	−	0.970612i	$-0.422639\pi$
$643$	12.2046	0.481302	0.240651	+	0.970612i	$0.422639\pi$
$644$	−19.5082	−0.768729
$645$	0	0
$646$	3.05852	0.120336
$647$	−28.0548	−1.10295	−0.551473	−	0.834193i	$-0.685934\pi$
$647$	−28.0548	−1.10295	−0.551473	+	0.834193i	$0.685934\pi$
$648$	12.9855	0.510120
$649$	7.93291	0.311394
$650$	0	0
$651$	−7.05497	−0.276506
$652$	14.7794	0.578806
$653$	−5.68400	−0.222432	−0.111216	−	0.993796i	$-0.535475\pi$
$653$	−5.68400	−0.222432	−0.111216	+	0.993796i	$0.535475\pi$
$654$	2.14789	0.0839891
$655$	0	0
$656$	3.80422	0.148530
$657$	68.0567	2.65515
$658$	−1.04273	−0.0406500
$659$	−30.6811	−1.19517	−0.597584	−	0.801806i	$-0.703873\pi$
$659$	−30.6811	−1.19517	−0.597584	+	0.801806i	$0.703873\pi$
$660$	0	0
$661$	−13.8208	−0.537568	−0.268784	−	0.963200i	$-0.586622\pi$
$661$	−13.8208	−0.537568	−0.268784	+	0.963200i	$0.586622\pi$
$662$	1.72290	0.0669624
$663$	−102.051	−3.96334
$664$	5.49881	0.213395
$665$	0	0
$666$	−3.41460	−0.132313
$667$	−10.0966	−0.390941
$668$	26.6522	1.03121
$669$	5.53188	0.213875
$670$	0	0
$671$	0.997763	0.0385182
$672$	14.4362	0.556887
$673$	−19.2294	−0.741240	−0.370620	−	0.928785i	$-0.620855\pi$
$673$	−19.2294	−0.741240	−0.370620	+	0.928785i	$0.620855\pi$
$674$	2.47689	0.0954062
$675$	0	0
$676$	−42.7910	−1.64581
$677$	−34.7093	−1.33399	−0.666994	−	0.745063i	$-0.732419\pi$
$677$	−34.7093	−1.33399	−0.666994	+	0.745063i	$0.732419\pi$
$678$	−4.92155	−0.189011
$679$	3.80014	0.145836
$680$	0	0
$681$	4.17001	0.159795
$682$	−0.108068	−0.00413814
$683$	−2.16428	−0.0828139	−0.0414069	−	0.999142i	$-0.513184\pi$
$683$	−2.16428	−0.0828139	−0.0414069	+	0.999142i	$0.513184\pi$
$684$	−77.2437	−2.95348
$685$	0	0
$686$	−1.39856	−0.0533973
$687$	80.3773	3.06659
$688$	−31.1219	−1.18651
$689$	−49.6856	−1.89287
$690$	0	0
$691$	22.7388	0.865025	0.432513	−	0.901628i	$-0.357627\pi$
$691$	22.7388	0.865025	0.432513	+	0.901628i	$0.357627\pi$
$692$	−6.32623	−0.240487
$693$	−34.5493	−1.31242
$694$	−0.708756	−0.0269040
$695$	0	0
$696$	4.97545	0.188594
$697$	−5.13318	−0.194433
$698$	0.827806	0.0313329
$699$	−11.7645	−0.444974
$700$	0	0
$701$	−21.4836	−0.811424	−0.405712	−	0.914001i	$-0.632976\pi$
$701$	−21.4836	−0.811424	−0.405712	+	0.914001i	$0.632976\pi$
$702$	−10.6627	−0.402437
$703$	18.9740	0.715619
$704$	−10.6737	−0.402280
$705$	0	0
$706$	−1.09583	−0.0412423
$707$	−63.6261	−2.39291
$708$	−37.2303	−1.39920
$709$	−4.43026	−0.166382	−0.0831910	−	0.996534i	$-0.526511\pi$
$709$	−4.43026	−0.166382	−0.0831910	+	0.996534i	$0.526511\pi$
$710$	0	0
$711$	89.0178	3.33843
$712$	−5.53339	−0.207373
$713$	−2.06534	−0.0773476
$714$	−6.42024	−0.240271
$715$	0	0
$716$	−23.4998	−0.878227
$717$	−88.7254	−3.31351
$718$	−0.826688	−0.0308517
$719$	37.8736	1.41245	0.706224	−	0.707989i	$-0.250397\pi$
$719$	37.8736	1.41245	0.706224	+	0.707989i	$0.250397\pi$
$720$	0	0
$721$	−8.76245	−0.326331
$722$	−0.693010	−0.0257912
$723$	3.28295	0.122094
$724$	7.78830	0.289450
$725$	0	0
$726$	3.44377	0.127810
$727$	0.346692	0.0128581	0.00642904	−	0.999979i	$-0.497954\pi$
$727$	0.346692	0.0128581	0.00642904	+	0.999979i	$0.497954\pi$
$728$	−8.66273	−0.321062
$729$	64.5421	2.39045
$730$	0	0
$731$	41.9940	1.55320
$732$	−4.68264	−0.173075
$733$	−4.28244	−0.158176	−0.0790878	−	0.996868i	$-0.525201\pi$
$733$	−4.28244	−0.158176	−0.0790878	+	0.996868i	$0.525201\pi$
$734$	0.305282	0.0112682
$735$	0	0
$736$	4.22619	0.155779
$737$	−12.2461	−0.451090
$738$	−0.873103	−0.0321394
$739$	4.52351	0.166400	0.0832000	−	0.996533i	$-0.473486\pi$
$739$	4.52351	0.166400	0.0832000	+	0.996533i	$0.473486\pi$
$740$	0	0
$741$	96.4532	3.54330
$742$	−3.12581	−0.114752
$743$	−14.4360	−0.529606	−0.264803	−	0.964303i	$-0.585307\pi$
$743$	−14.4360	−0.529606	−0.264803	+	0.964303i	$0.585307\pi$
$744$	1.01777	0.0373133
$745$	0	0
$746$	2.37255	0.0868653
$747$	92.7463	3.39341
$748$	14.6025	0.533919
$749$	−31.8313	−1.16309
$750$	0	0
$751$	−18.6022	−0.678804	−0.339402	−	0.940641i	$-0.610225\pi$
$751$	−18.6022	−0.678804	−0.339402	+	0.940641i	$0.610225\pi$
$752$	−11.0550	−0.403133
$753$	−62.6090	−2.28160
$754$	−2.23420	−0.0813649
$755$	0	0
$756$	99.6030	3.62252
$757$	−1.36472	−0.0496015	−0.0248007	−	0.999692i	$-0.507895\pi$
$757$	−1.36472	−0.0496015	−0.0248007	+	0.999692i	$0.507895\pi$
$758$	2.86009	0.103883
$759$	−14.0155	−0.508732
$760$	0	0
$761$	−32.0391	−1.16142	−0.580709	−	0.814111i	$-0.697224\pi$
$761$	−32.0391	−1.16142	−0.580709	+	0.814111i	$0.697224\pi$
$762$	−3.97386	−0.143958
$763$	18.0799	0.654538
$764$	−2.52487	−0.0913465
$765$	0	0
$766$	−3.84823	−0.139042
$767$	33.5487	1.21138
$768$	49.0484	1.76988
$769$	−7.53070	−0.271564	−0.135782	−	0.990739i	$-0.543355\pi$
$769$	−7.53070	−0.271564	−0.135782	+	0.990739i	$0.543355\pi$
$770$	0	0
$771$	98.0493	3.53116
$772$	−14.2731	−0.513699
$773$	23.1144	0.831368	0.415684	−	0.909509i	$-0.363542\pi$
$773$	23.1144	0.831368	0.415684	+	0.909509i	$0.363542\pi$
$774$	7.14276	0.256741
$775$	0	0
$776$	−0.548220	−0.0196800
$777$	−39.8290	−1.42886
$778$	1.29578	0.0464561
$779$	4.85160	0.173826
$780$	0	0
$781$	22.0336	0.788426
$782$	−1.87952	−0.0672116
$783$	51.5502	1.84225
$784$	12.6119	0.450425
$785$	0	0
$786$	−4.92167	−0.175550
$787$	−14.4891	−0.516479	−0.258240	−	0.966081i	$-0.583142\pi$
$787$	−14.4891	−0.516479	−0.258240	+	0.966081i	$0.583142\pi$
$788$	13.2040	0.470372
$789$	47.5737	1.69367
$790$	0	0
$791$	−41.4274	−1.47299
$792$	4.98419	0.177106
$793$	4.21960	0.149842
$794$	0.602212	0.0213717
$795$	0	0
$796$	−25.3013	−0.896780
$797$	13.1633	0.466267	0.233133	−	0.972445i	$-0.425102\pi$
$797$	13.1633	0.466267	0.233133	+	0.972445i	$0.425102\pi$
$798$	6.06805	0.214807
$799$	14.9169	0.527721
$800$	0	0
$801$	−93.3296	−3.29764
$802$	0.323467	0.0114220
$803$	12.1600	0.429116
$804$	57.4726	2.02690
$805$	0	0
$806$	−0.457026	−0.0160980
$807$	31.9536	1.12482
$808$	9.17891	0.322913
$809$	−33.0845	−1.16319	−0.581595	−	0.813479i	$-0.697571\pi$
$809$	−33.0845	−1.16319	−0.581595	+	0.813479i	$0.697571\pi$
$810$	0	0
$811$	−4.74569	−0.166644	−0.0833219	−	0.996523i	$-0.526553\pi$
$811$	−4.74569	−0.166644	−0.0833219	+	0.996523i	$0.526553\pi$
$812$	20.8703	0.732403
$813$	58.4311	2.04927
$814$	−0.610101	−0.0213840
$815$	0	0
$816$	−68.0668	−2.38281
$817$	−39.6904	−1.38859
$818$	−0.0859553	−0.00300536
$819$	−146.111	−5.10553
$820$	0	0
$821$	−33.6149	−1.17317	−0.586584	−	0.809888i	$-0.699528\pi$
$821$	−33.6149	−1.17317	−0.586584	+	0.809888i	$0.699528\pi$
$822$	5.37028	0.187310
$823$	−45.7636	−1.59522	−0.797609	−	0.603175i	$-0.793902\pi$
$823$	−45.7636	−1.59522	−0.797609	+	0.603175i	$0.793902\pi$
$824$	1.26410	0.0440370
$825$	0	0
$826$	2.11061	0.0734377
$827$	−29.9837	−1.04264	−0.521318	−	0.853363i	$-0.674559\pi$
$827$	−29.9837	−1.04264	−0.521318	+	0.853363i	$0.674559\pi$
$828$	47.4679	1.64962
$829$	−2.23933	−0.0777753	−0.0388876	−	0.999244i	$-0.512381\pi$
$829$	−2.23933	−0.0777753	−0.0388876	+	0.999244i	$0.512381\pi$
$830$	0	0
$831$	−7.50368	−0.260300
$832$	−45.1397	−1.56494
$833$	−17.0177	−0.589629
$834$	6.40199	0.221683
$835$	0	0
$836$	−13.8014	−0.477332
$837$	10.5450	0.364490
$838$	1.36509	0.0471561
$839$	−31.0203	−1.07094	−0.535469	−	0.844555i	$-0.679865\pi$
$839$	−31.0203	−1.07094	−0.535469	+	0.844555i	$0.679865\pi$
$840$	0	0
$841$	−18.1985	−0.627533
$842$	1.14508	0.0394621
$843$	30.6770	1.05657
$844$	−10.3806	−0.357316
$845$	0	0
$846$	2.53721	0.0872311
$847$	28.9881	0.996042
$848$	−33.1396	−1.13802
$849$	−29.1075	−0.998968
$850$	0	0
$851$	−11.6599	−0.399698
$852$	−103.407	−3.54267
$853$	13.7603	0.471142	0.235571	−	0.971857i	$-0.424304\pi$
$853$	13.7603	0.471142	0.235571	+	0.971857i	$0.424304\pi$
$854$	0.265463	0.00908395
$855$	0	0
$856$	4.59209	0.156954
$857$	−31.2228	−1.06655	−0.533276	−	0.845941i	$-0.679039\pi$
$857$	−31.2228	−1.06655	−0.533276	+	0.845941i	$0.679039\pi$
$858$	−3.10141	−0.105880
$859$	−55.8137	−1.90434	−0.952170	−	0.305569i	$-0.901153\pi$
$859$	−55.8137	−1.90434	−0.952170	+	0.305569i	$0.901153\pi$
$860$	0	0
$861$	−10.1841	−0.347075
$862$	−1.11614	−0.0380159
$863$	0.720056	0.0245110	0.0122555	−	0.999925i	$-0.496099\pi$
$863$	0.720056	0.0245110	0.0122555	+	0.999925i	$0.496099\pi$
$864$	−21.5777	−0.734088
$865$	0	0
$866$	−4.50531	−0.153097
$867$	36.0349	1.22381
$868$	4.26920	0.144906
$869$	15.9052	0.539546
$870$	0	0
$871$	−51.7894	−1.75482
$872$	−2.60827	−0.0883272
$873$	−9.24662	−0.312951
$874$	1.77642	0.0600884
$875$	0	0
$876$	−57.0685	−1.92816
$877$	−48.3619	−1.63307	−0.816533	−	0.577298i	$-0.804107\pi$
$877$	−48.3619	−1.63307	−0.816533	+	0.577298i	$0.804107\pi$
$878$	1.94428	0.0656163
$879$	−56.2132	−1.89602
$880$	0	0
$881$	36.2946	1.22279	0.611397	−	0.791324i	$-0.290608\pi$
$881$	36.2946	1.22279	0.611397	+	0.791324i	$0.290608\pi$
$882$	−2.89454	−0.0974644
$883$	26.8840	0.904718	0.452359	−	0.891836i	$-0.350583\pi$
$883$	26.8840	0.904718	0.452359	+	0.891836i	$0.350583\pi$
$884$	61.7546	2.07703
$885$	0	0
$886$	−0.0507010	−0.00170333
$887$	−13.4296	−0.450923	−0.225461	−	0.974252i	$-0.572389\pi$
$887$	−13.4296	−0.450923	−0.225461	+	0.974252i	$0.572389\pi$
$888$	5.74586	0.192819
$889$	−33.4501	−1.12188
$890$	0	0
$891$	39.1336	1.31102
$892$	−3.34752	−0.112083
$893$	−14.0986	−0.471792
$894$	−6.17165	−0.206411
$895$	0	0
$896$	−11.6345	−0.388680
$897$	−59.2726	−1.97905
$898$	3.67509	0.122639
$899$	2.20955	0.0736926
$900$	0	0
$901$	44.7165	1.48972
$902$	−0.156001	−0.00519426
$903$	83.3154	2.77256
$904$	5.97644	0.198774
$905$	0	0
$906$	3.95253	0.131314
$907$	−7.62089	−0.253047	−0.126524	−	0.991964i	$-0.540382\pi$
$907$	−7.62089	−0.253047	−0.126524	+	0.991964i	$0.540382\pi$
$908$	−2.52341	−0.0837424
$909$	154.817	5.13496
$910$	0	0
$911$	−14.0113	−0.464214	−0.232107	−	0.972690i	$-0.574562\pi$
$911$	−14.0113	−0.464214	−0.232107	+	0.972690i	$0.574562\pi$
$912$	64.3329	2.13028
$913$	16.5714	0.548432
$914$	1.98424	0.0656327
$915$	0	0
$916$	−48.6390	−1.60708
$917$	−41.4284	−1.36809
$918$	9.59630	0.316725
$919$	12.5233	0.413107	0.206553	−	0.978435i	$-0.433775\pi$
$919$	12.5233	0.413107	0.206553	+	0.978435i	$0.433775\pi$
$920$	0	0
$921$	−16.5135	−0.544139
$922$	3.57700	0.117802
$923$	93.1815	3.06711
$924$	28.9710	0.953078
$925$	0	0
$926$	1.81522	0.0596518
$927$	21.3211	0.700276
$928$	−4.52127	−0.148418
$929$	14.3668	0.471359	0.235680	−	0.971831i	$-0.424268\pi$
$929$	14.3668	0.471359	0.235680	+	0.971831i	$0.424268\pi$
$930$	0	0
$931$	16.0842	0.527138
$932$	7.11908	0.233193
$933$	32.8213	1.07452
$934$	2.47091	0.0808505
$935$	0	0
$936$	21.0784	0.688970
$937$	−57.2739	−1.87106	−0.935528	−	0.353253i	$-0.885075\pi$
$937$	−57.2739	−1.87106	−0.935528	+	0.353253i	$0.885075\pi$
$938$	−3.25817	−0.106383
$939$	−92.4039	−3.01549
$940$	0	0
$941$	−2.50683	−0.0817202	−0.0408601	−	0.999165i	$-0.513010\pi$
$941$	−2.50683	−0.0817202	−0.0408601	+	0.999165i	$0.513010\pi$
$942$	−7.21100	−0.234947
$943$	−2.98141	−0.0970880
$944$	22.3765	0.728294
$945$	0	0
$946$	1.27622	0.0414936
$947$	53.8904	1.75120	0.875601	−	0.483036i	$-0.160466\pi$
$947$	53.8904	1.75120	0.875601	+	0.483036i	$0.160466\pi$
$948$	−74.6452	−2.42436
$949$	51.4252	1.66933
$950$	0	0
$951$	18.6101	0.603473
$952$	7.79636	0.252682
$953$	20.7256	0.671369	0.335684	−	0.941975i	$-0.391032\pi$
$953$	20.7256	0.671369	0.335684	+	0.941975i	$0.391032\pi$
$954$	7.60583	0.246248
$955$	0	0
$956$	53.6907	1.73648
$957$	14.9942	0.484692
$958$	−3.16511	−0.102260
$959$	45.2046	1.45973
$960$	0	0
$961$	−30.5480	−0.985420
$962$	−2.58015	−0.0831874
$963$	77.4530	2.49589
$964$	−1.98662	−0.0639847
$965$	0	0
$966$	−3.72895	−0.119977
$967$	−12.2723	−0.394652	−0.197326	−	0.980338i	$-0.563226\pi$
$967$	−12.2723	−0.394652	−0.197326	+	0.980338i	$0.563226\pi$
$968$	−4.18191	−0.134412
$969$	−86.8068	−2.78864
$970$	0	0
$971$	48.8599	1.56799	0.783994	−	0.620768i	$-0.213179\pi$
$971$	48.8599	1.56799	0.783994	+	0.620768i	$0.213179\pi$
$972$	−90.1784	−2.89247
$973$	53.8890	1.72760
$974$	−1.05493	−0.0338021
$975$	0	0
$976$	2.81441	0.0900871
$977$	29.7335	0.951260	0.475630	−	0.879645i	$-0.342220\pi$
$977$	29.7335	0.951260	0.475630	+	0.879645i	$0.342220\pi$
$978$	2.82506	0.0903353
$979$	−16.6756	−0.532953
$980$	0	0
$981$	−43.9927	−1.40458
$982$	0.844026	0.0269339
$983$	−26.3255	−0.839655	−0.419827	−	0.907604i	$-0.637909\pi$
$983$	−26.3255	−0.839655	−0.419827	+	0.907604i	$0.637909\pi$
$984$	1.46920	0.0468363
$985$	0	0
$986$	2.01076	0.0640356
$987$	29.5949	0.942015
$988$	−58.3670	−1.85690
$989$	24.3906	0.775575
$990$	0	0
$991$	44.7423	1.42129	0.710643	−	0.703552i	$-0.248404\pi$
$991$	44.7423	1.42129	0.710643	+	0.703552i	$0.248404\pi$
$992$	−0.924865	−0.0293645
$993$	−48.8994	−1.55177
$994$	5.86222	0.185938
$995$	0	0
$996$	−77.7717	−2.46429
$997$	39.5818	1.25357	0.626784	−	0.779193i	$-0.284371\pi$
$997$	39.5818	1.25357	0.626784	+	0.779193i	$0.284371\pi$
$998$	−0.229348	−0.00725988
$999$	59.5323	1.88352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.6		12
5.4	even	2		241.2.a.b.1.7	✓	12
15.14	odd	2		2169.2.a.h.1.6		12
20.19	odd	2		3856.2.a.n.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.7	✓	12	5.4	even	2
2169.2.a.h.1.6		12	15.14	odd	2
3856.2.a.n.1.12		12	20.19	odd	2
6025.2.a.h.1.6		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)

\(f(q)\)	\(=\)	\(q-0.115670 q^{2} +3.28295 q^{3} -1.98662 q^{4} -0.379739 q^{6} -3.19647 q^{7} +0.461133 q^{8} +7.77775 q^{9} +O(q^{10})\)	\(q-0.115670 q^{2} +3.28295 q^{3} -1.98662 q^{4} -0.379739 q^{6} -3.19647 q^{7} +0.461133 q^{8} +7.77775 q^{9} +1.38968 q^{11} -6.52197 q^{12} +5.87704 q^{13} +0.369736 q^{14} +3.91990 q^{16} -5.28927 q^{17} -0.899653 q^{18} +4.99913 q^{19} -10.4938 q^{21} -0.160744 q^{22} -3.07207 q^{23} +1.51387 q^{24} -0.679798 q^{26} +15.6851 q^{27} +6.35017 q^{28} +3.28657 q^{29} +0.672296 q^{31} -1.37568 q^{32} +4.56225 q^{33} +0.611810 q^{34} -15.4514 q^{36} +3.79547 q^{37} -0.578249 q^{38} +19.2940 q^{39} +0.970489 q^{41} +1.21382 q^{42} -7.93946 q^{43} -2.76077 q^{44} +0.355346 q^{46} -2.82021 q^{47} +12.8688 q^{48} +3.21740 q^{49} -17.3644 q^{51} -11.6754 q^{52} -8.45419 q^{53} -1.81430 q^{54} -1.47400 q^{56} +16.4119 q^{57} -0.380158 q^{58} +5.70844 q^{59} +0.717980 q^{61} -0.0777646 q^{62} -24.8613 q^{63} -7.68068 q^{64} -0.527716 q^{66} -8.81215 q^{67} +10.5078 q^{68} -10.0854 q^{69} +15.8552 q^{71} +3.58657 q^{72} +8.75018 q^{73} -0.439022 q^{74} -9.93137 q^{76} -4.44207 q^{77} -2.23174 q^{78} +11.4452 q^{79} +28.1601 q^{81} -0.112256 q^{82} +11.9246 q^{83} +20.8473 q^{84} +0.918358 q^{86} +10.7896 q^{87} +0.640827 q^{88} -11.9996 q^{89} -18.7858 q^{91} +6.10304 q^{92} +2.20711 q^{93} +0.326214 q^{94} -4.51629 q^{96} -1.18886 q^{97} -0.372157 q^{98} +10.8086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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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