LMFDB - Embedded newform 6025.2.a.h.1.7

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			1.7
Root			$0.0822506$ 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)

$f(q)$	$=$	$q-0.0822506 q^{2} -1.81824 q^{3} -1.99323 q^{4} +0.149552 q^{6} -0.690569 q^{7} +0.328446 q^{8} +0.306010 q^{9} +O(q^{10})$	\(q-0.0822506 q^{2} -1.81824 q^{3} -1.99323 q^{4} +0.149552 q^{6} -0.690569 q^{7} +0.328446 q^{8} +0.306010 q^{9} -2.95833 q^{11} +3.62419 q^{12} +1.93470 q^{13} +0.0567997 q^{14} +3.95945 q^{16} +2.07477 q^{17} -0.0251695 q^{18} +3.74689 q^{19} +1.25562 q^{21} +0.243324 q^{22} -4.34832 q^{23} -0.597195 q^{24} -0.159131 q^{26} +4.89833 q^{27} +1.37647 q^{28} -8.10772 q^{29} -2.80197 q^{31} -0.982559 q^{32} +5.37896 q^{33} -0.170651 q^{34} -0.609951 q^{36} +9.72312 q^{37} -0.308183 q^{38} -3.51777 q^{39} -4.09401 q^{41} -0.103276 q^{42} -3.02779 q^{43} +5.89665 q^{44} +0.357652 q^{46} -6.71240 q^{47} -7.19925 q^{48} -6.52312 q^{49} -3.77244 q^{51} -3.85632 q^{52} +0.0484656 q^{53} -0.402890 q^{54} -0.226814 q^{56} -6.81275 q^{57} +0.666864 q^{58} +4.50676 q^{59} -9.62232 q^{61} +0.230464 q^{62} -0.211321 q^{63} -7.83809 q^{64} -0.442423 q^{66} +0.964160 q^{67} -4.13551 q^{68} +7.90631 q^{69} +7.76289 q^{71} +0.100508 q^{72} -16.4250 q^{73} -0.799732 q^{74} -7.46842 q^{76} +2.04293 q^{77} +0.289338 q^{78} -6.83310 q^{79} -9.82439 q^{81} +0.336735 q^{82} +9.15477 q^{83} -2.50275 q^{84} +0.249037 q^{86} +14.7418 q^{87} -0.971651 q^{88} -2.36597 q^{89} -1.33605 q^{91} +8.66723 q^{92} +5.09467 q^{93} +0.552099 q^{94} +1.78653 q^{96} +5.25335 q^{97} +0.536530 q^{98} -0.905280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.0822506	−0.0581599	−0.0290800	−	0.999577i	$-0.509258\pi$
$2$	−0.0822506	−0.0581599	−0.0290800	+	0.999577i	$0.509258\pi$
$3$	−1.81824	−1.04976	−0.524882	−	0.851175i	$-0.675890\pi$
$3$	−1.81824	−1.04976	−0.524882	+	0.851175i	$0.675890\pi$
$4$	−1.99323	−0.996617
$5$	0	0
$5$	0	0
$6$	0.149552	0.0610542
$7$	−0.690569	−0.261010	−0.130505	−	0.991448i	$-0.541660\pi$
$7$	−0.690569	−0.261010	−0.130505	+	0.991448i	$0.541660\pi$
$8$	0.328446	0.116123
$9$	0.306010	0.102003
$10$	0	0
$11$	−2.95833	−0.891970	−0.445985	−	0.895040i	$-0.647147\pi$
$11$	−2.95833	−0.891970	−0.445985	+	0.895040i	$0.647147\pi$
$12$	3.62419	1.04621
$13$	1.93470	0.536591	0.268295	−	0.963337i	$-0.413540\pi$
$13$	1.93470	0.536591	0.268295	+	0.963337i	$0.413540\pi$
$14$	0.0567997	0.0151803
$15$	0	0
$16$	3.95945	0.989864
$17$	2.07477	0.503206	0.251603	−	0.967830i	$-0.419042\pi$
$17$	2.07477	0.503206	0.251603	+	0.967830i	$0.419042\pi$
$18$	−0.0251695	−0.00593251
$19$	3.74689	0.859595	0.429797	−	0.902925i	$-0.358585\pi$
$19$	3.74689	0.859595	0.429797	+	0.902925i	$0.358585\pi$
$20$	0	0
$21$	1.25562	0.273999
$22$	0.243324	0.0518769
$23$	−4.34832	−0.906688	−0.453344	−	0.891336i	$-0.649769\pi$
$23$	−4.34832	−0.906688	−0.453344	+	0.891336i	$0.649769\pi$
$24$	−0.597195	−0.121902
$25$	0	0
$26$	−0.159131	−0.0312081
$27$	4.89833	0.942684
$28$	1.37647	0.260127
$29$	−8.10772	−1.50557	−0.752783	−	0.658269i	$-0.771289\pi$
$29$	−8.10772	−1.50557	−0.752783	+	0.658269i	$0.771289\pi$
$30$	0	0
$31$	−2.80197	−0.503249	−0.251624	−	0.967825i	$-0.580965\pi$
$31$	−2.80197	−0.503249	−0.251624	+	0.967825i	$0.580965\pi$
$32$	−0.982559	−0.173694
$33$	5.37896	0.936358
$34$	−0.170651	−0.0292664
$35$	0	0
$36$	−0.609951	−0.101658
$37$	9.72312	1.59847	0.799236	−	0.601018i	$-0.205238\pi$
$37$	9.72312	1.59847	0.799236	+	0.601018i	$0.205238\pi$
$38$	−0.308183	−0.0499940
$39$	−3.51777	−0.563293
$40$	0	0
$41$	−4.09401	−0.639378	−0.319689	−	0.947523i	$-0.603578\pi$
$41$	−4.09401	−0.639378	−0.319689	+	0.947523i	$0.603578\pi$
$42$	−0.103276	−0.0159358
$43$	−3.02779	−0.461733	−0.230867	−	0.972985i	$-0.574156\pi$
$43$	−3.02779	−0.461733	−0.230867	+	0.972985i	$0.574156\pi$
$44$	5.89665	0.888953
$45$	0	0
$46$	0.357652	0.0527329
$47$	−6.71240	−0.979104	−0.489552	−	0.871974i	$-0.662840\pi$
$47$	−6.71240	−0.979104	−0.489552	+	0.871974i	$0.662840\pi$
$48$	−7.19925	−1.03912
$49$	−6.52312	−0.931874
$50$	0	0
$51$	−3.77244	−0.528248
$52$	−3.85632	−0.534776
$53$	0.0484656	0.00665726	0.00332863	−	0.999994i	$-0.498940\pi$
$53$	0.0484656	0.00665726	0.00332863	+	0.999994i	$0.498940\pi$
$54$	−0.402890	−0.0548264
$55$	0	0
$56$	−0.226814	−0.0303093
$57$	−6.81275	−0.902371
$58$	0.666864	0.0875636
$59$	4.50676	0.586730	0.293365	−	0.956000i	$-0.405225\pi$
$59$	4.50676	0.586730	0.293365	+	0.956000i	$0.405225\pi$
$60$	0	0
$61$	−9.62232	−1.23201	−0.616006	−	0.787742i	$-0.711250\pi$
$61$	−9.62232	−1.23201	−0.616006	+	0.787742i	$0.711250\pi$
$62$	0.230464	0.0292689
$63$	−0.211321	−0.0266240
$64$	−7.83809	−0.979762
$65$	0	0
$66$	−0.442423	−0.0544585
$67$	0.964160	0.117791	0.0588954	−	0.998264i	$-0.481242\pi$
$67$	0.964160	0.117791	0.0588954	+	0.998264i	$0.481242\pi$
$68$	−4.13551	−0.501504
$69$	7.90631	0.951808
$70$	0	0
$71$	7.76289	0.921286	0.460643	−	0.887586i	$-0.347619\pi$
$71$	7.76289	0.921286	0.460643	+	0.887586i	$0.347619\pi$
$72$	0.100508	0.0118450
$73$	−16.4250	−1.92241	−0.961203	−	0.275841i	$-0.911044\pi$
$73$	−16.4250	−1.92241	−0.961203	+	0.275841i	$0.911044\pi$
$74$	−0.799732	−0.0929670
$75$	0	0
$76$	−7.46842	−0.856687
$77$	2.04293	0.232813
$78$	0.289338	0.0327611
$79$	−6.83310	−0.768783	−0.384392	−	0.923170i	$-0.625589\pi$
$79$	−6.83310	−0.768783	−0.384392	+	0.923170i	$0.625589\pi$
$80$	0	0
$81$	−9.82439	−1.09160
$82$	0.336735	0.0371862
$83$	9.15477	1.00487	0.502433	−	0.864616i	$-0.332438\pi$
$83$	9.15477	1.00487	0.502433	+	0.864616i	$0.332438\pi$
$84$	−2.50275	−0.273072
$85$	0	0
$86$	0.249037	0.0268544
$87$	14.7418	1.58049
$88$	−0.971651	−0.103578
$89$	−2.36597	−0.250793	−0.125396	−	0.992107i	$-0.540020\pi$
$89$	−2.36597	−0.250793	−0.125396	+	0.992107i	$0.540020\pi$
$90$	0	0
$91$	−1.33605	−0.140056
$92$	8.66723	0.903621
$93$	5.09467	0.528292
$94$	0.552099	0.0569447
$95$	0	0
$96$	1.78653	0.182337
$97$	5.25335	0.533396	0.266698	−	0.963780i	$-0.414067\pi$
$97$	5.25335	0.533396	0.266698	+	0.963780i	$0.414067\pi$
$98$	0.536530	0.0541977
$99$	−0.905280	−0.0909840
$100$	0	0
$101$	9.93584	0.988653	0.494327	−	0.869276i	$-0.335415\pi$
$101$	9.93584	0.988653	0.494327	+	0.869276i	$0.335415\pi$
$102$	0.310285	0.0307228
$103$	−19.2644	−1.89818	−0.949090	−	0.315005i	$-0.897994\pi$
$103$	−19.2644	−1.89818	−0.949090	+	0.315005i	$0.897994\pi$
$104$	0.635446	0.0623106
$105$	0	0
$106$	−0.00398632	−0.000387186 0
$107$	7.88030	0.761817	0.380909	−	0.924613i	$-0.375611\pi$
$107$	7.88030	0.761817	0.380909	+	0.924613i	$0.375611\pi$
$108$	−9.76352	−0.939495
$109$	−1.72728	−0.165443	−0.0827215	−	0.996573i	$-0.526361\pi$
$109$	−1.72728	−0.165443	−0.0827215	+	0.996573i	$0.526361\pi$
$110$	0	0
$111$	−17.6790	−1.67802
$112$	−2.73427	−0.258365
$113$	−14.0431	−1.32107	−0.660533	−	0.750797i	$-0.729670\pi$
$113$	−14.0431	−1.32107	−0.660533	+	0.750797i	$0.729670\pi$
$114$	0.560353	0.0524818
$115$	0	0
$116$	16.1606	1.50047
$117$	0.592040	0.0547341
$118$	−0.370684	−0.0341242
$119$	−1.43277	−0.131342
$120$	0	0
$121$	−2.24829	−0.204390
$122$	0.791441	0.0716537
$123$	7.44392	0.671195
$124$	5.58499	0.501547
$125$	0	0
$126$	0.0173813	0.00154845
$127$	1.65498	0.146856	0.0734278	−	0.997301i	$-0.476606\pi$
$127$	1.65498	0.146856	0.0734278	+	0.997301i	$0.476606\pi$
$128$	2.60981	0.230676
$129$	5.50525	0.484711
$130$	0	0
$131$	17.1541	1.49876	0.749381	−	0.662139i	$-0.230351\pi$
$131$	17.1541	1.49876	0.749381	+	0.662139i	$0.230351\pi$
$132$	−10.7215	−0.933190
$133$	−2.58748	−0.224363
$134$	−0.0793027	−0.00685071
$135$	0	0
$136$	0.681450	0.0584339
$137$	−14.7651	−1.26147	−0.630733	−	0.776000i	$-0.717245\pi$
$137$	−14.7651	−1.26147	−0.630733	+	0.776000i	$0.717245\pi$
$138$	−0.650298	−0.0553571
$139$	20.3570	1.72666	0.863329	−	0.504641i	$-0.168375\pi$
$139$	20.3570	1.72666	0.863329	+	0.504641i	$0.168375\pi$
$140$	0	0
$141$	12.2048	1.02783
$142$	−0.638502	−0.0535819
$143$	−5.72349	−0.478623
$144$	1.21163	0.100970
$145$	0	0
$146$	1.35097	0.111807
$147$	11.8606	0.978247
$148$	−19.3805	−1.59306
$149$	8.37820	0.686369	0.343185	−	0.939268i	$-0.388494\pi$
$149$	8.37820	0.686369	0.343185	+	0.939268i	$0.388494\pi$
$150$	0	0
$151$	−22.0074	−1.79093	−0.895467	−	0.445128i	$-0.853158\pi$
$151$	−22.0074	−1.79093	−0.895467	+	0.445128i	$0.853158\pi$
$152$	1.23065	0.0998188
$153$	0.634902	0.0513288
$154$	−0.168032	−0.0135404
$155$	0	0
$156$	7.01173	0.561388
$157$	0.208187	0.0166151	0.00830757	−	0.999965i	$-0.497356\pi$
$157$	0.208187	0.0166151	0.00830757	+	0.999965i	$0.497356\pi$
$158$	0.562026	0.0447124
$159$	−0.0881222	−0.00698855
$160$	0	0
$161$	3.00281	0.236655
$162$	0.808062	0.0634873
$163$	−7.85060	−0.614906	−0.307453	−	0.951563i	$-0.599477\pi$
$163$	−7.85060	−0.614906	−0.307453	+	0.951563i	$0.599477\pi$
$164$	8.16033	0.637215
$165$	0	0
$166$	−0.752985	−0.0584430
$167$	13.8766	1.07380	0.536900	−	0.843646i	$-0.319595\pi$
$167$	13.8766	1.07380	0.536900	+	0.843646i	$0.319595\pi$
$168$	0.412404	0.0318176
$169$	−9.25692	−0.712071
$170$	0	0
$171$	1.14659	0.0876816
$172$	6.03509	0.460171
$173$	−19.3500	−1.47115	−0.735577	−	0.677441i	$-0.763089\pi$
$173$	−19.3500	−1.47115	−0.735577	+	0.677441i	$0.763089\pi$
$174$	−1.21252	−0.0919211
$175$	0	0
$176$	−11.7134	−0.882929
$177$	−8.19439	−0.615928
$178$	0.194603	0.0145861
$179$	−7.02479	−0.525057	−0.262529	−	0.964924i	$-0.584556\pi$
$179$	−7.02479	−0.525057	−0.262529	+	0.964924i	$0.584556\pi$
$180$	0	0
$181$	7.22067	0.536708	0.268354	−	0.963320i	$-0.413520\pi$
$181$	7.22067	0.536708	0.268354	+	0.963320i	$0.413520\pi$
$182$	0.109891	0.00814563
$183$	17.4957	1.29332
$184$	−1.42819	−0.105287
$185$	0	0
$186$	−0.419039	−0.0307254
$187$	−6.13786	−0.448845
$188$	13.3794	0.975793
$189$	−3.38263	−0.246050
$190$	0	0
$191$	20.7694	1.50282	0.751412	−	0.659834i	$-0.229373\pi$
$191$	20.7694	1.50282	0.751412	+	0.659834i	$0.229373\pi$
$192$	14.2516	1.02852
$193$	19.7206	1.41952	0.709762	−	0.704442i	$-0.248803\pi$
$193$	19.7206	1.41952	0.709762	+	0.704442i	$0.248803\pi$
$194$	−0.432091	−0.0310223
$195$	0	0
$196$	13.0021	0.928721
$197$	16.2977	1.16116	0.580582	−	0.814201i	$-0.302825\pi$
$197$	16.2977	1.16116	0.580582	+	0.814201i	$0.302825\pi$
$198$	0.0744598	0.00529162
$199$	4.79014	0.339564	0.169782	−	0.985482i	$-0.445694\pi$
$199$	4.79014	0.339564	0.169782	+	0.985482i	$0.445694\pi$
$200$	0	0
$201$	−1.75308	−0.123653
$202$	−0.817229	−0.0575000
$203$	5.59893	0.392968
$204$	7.51936	0.526461
$205$	0	0
$206$	1.58451	0.110398
$207$	−1.33063	−0.0924853
$208$	7.66038	0.531152
$209$	−11.0845	−0.766733
$210$	0	0
$211$	−4.30473	−0.296350	−0.148175	−	0.988961i	$-0.547340\pi$
$211$	−4.30473	−0.296350	−0.148175	+	0.988961i	$0.547340\pi$
$212$	−0.0966033	−0.00663474
$213$	−14.1148	−0.967132
$214$	−0.648159	−0.0443072
$215$	0	0
$216$	1.60884	0.109467
$217$	1.93495	0.131353
$218$	0.142069	0.00962215
$219$	29.8647	2.01807
$220$	0	0
$221$	4.01407	0.270016
$222$	1.45411	0.0975933
$223$	−14.8068	−0.991540	−0.495770	−	0.868454i	$-0.665114\pi$
$223$	−14.8068	−0.991540	−0.495770	+	0.868454i	$0.665114\pi$
$224$	0.678524	0.0453358
$225$	0	0
$226$	1.15505	0.0768331
$227$	11.9026	0.790000	0.395000	−	0.918681i	$-0.370745\pi$
$227$	11.9026	0.790000	0.395000	+	0.918681i	$0.370745\pi$
$228$	13.5794	0.899319
$229$	−5.11465	−0.337985	−0.168993	−	0.985617i	$-0.554051\pi$
$229$	−5.11465	−0.337985	−0.168993	+	0.985617i	$0.554051\pi$
$230$	0	0
$231$	−3.71454	−0.244399
$232$	−2.66295	−0.174831
$233$	14.9300	0.978097	0.489048	−	0.872257i	$-0.337344\pi$
$233$	14.9300	0.978097	0.489048	+	0.872257i	$0.337344\pi$
$234$	−0.0486956	−0.00318333
$235$	0	0
$236$	−8.98303	−0.584746
$237$	12.4242	0.807041
$238$	0.117846	0.00763884
$239$	29.8624	1.93164	0.965820	−	0.259215i	$-0.0834638\pi$
$239$	29.8624	1.93164	0.965820	+	0.259215i	$0.0834638\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	0.184923	0.0118873
$243$	3.16814	0.203237
$244$	19.1795	1.22784
$245$	0	0
$246$	−0.612266	−0.0390367
$247$	7.24912	0.461250
$248$	−0.920296	−0.0584388
$249$	−16.6456	−1.05487
$250$	0	0
$251$	13.0620	0.824464	0.412232	−	0.911079i	$-0.364749\pi$
$251$	13.0620	0.824464	0.412232	+	0.911079i	$0.364749\pi$
$252$	0.421213	0.0265339
$253$	12.8638	0.808738
$254$	−0.136123	−0.00854111
$255$	0	0
$256$	15.4615	0.966346
$257$	−6.35830	−0.396620	−0.198310	−	0.980139i	$-0.563545\pi$
$257$	−6.35830	−0.396620	−0.198310	+	0.980139i	$0.563545\pi$
$258$	−0.452810	−0.0281907
$259$	−6.71448	−0.417218
$260$	0	0
$261$	−2.48105	−0.153573
$262$	−1.41094	−0.0871679
$263$	−4.66189	−0.287465	−0.143732	−	0.989617i	$-0.545910\pi$
$263$	−4.66189	−0.287465	−0.143732	+	0.989617i	$0.545910\pi$
$264$	1.76670	0.108733
$265$	0	0
$266$	0.212822	0.0130489
$267$	4.30192	0.263273
$268$	−1.92180	−0.117392
$269$	−10.5251	−0.641728	−0.320864	−	0.947125i	$-0.603973\pi$
$269$	−10.5251	−0.641728	−0.320864	+	0.947125i	$0.603973\pi$
$270$	0	0
$271$	10.3212	0.626968	0.313484	−	0.949593i	$-0.398504\pi$
$271$	10.3212	0.626968	0.313484	+	0.949593i	$0.398504\pi$
$272$	8.21497	0.498106
$273$	2.42926	0.147025
$274$	1.21444	0.0733667
$275$	0	0
$276$	−15.7591	−0.948588
$277$	−22.1023	−1.32800	−0.663999	−	0.747734i	$-0.731142\pi$
$277$	−22.1023	−1.32800	−0.663999	+	0.747734i	$0.731142\pi$
$278$	−1.67437	−0.100422
$279$	−0.857432	−0.0513331
$280$	0	0
$281$	4.22803	0.252223	0.126111	−	0.992016i	$-0.459750\pi$
$281$	4.22803	0.252223	0.126111	+	0.992016i	$0.459750\pi$
$282$	−1.00385	−0.0597784
$283$	3.06769	0.182355	0.0911776	−	0.995835i	$-0.470937\pi$
$283$	3.06769	0.182355	0.0911776	+	0.995835i	$0.470937\pi$
$284$	−15.4733	−0.918169
$285$	0	0
$286$	0.470761	0.0278367
$287$	2.82720	0.166884
$288$	−0.300673	−0.0177173
$289$	−12.6953	−0.746783
$290$	0	0
$291$	−9.55186	−0.559940
$292$	32.7390	1.91590
$293$	15.4694	0.903735	0.451867	−	0.892085i	$-0.350758\pi$
$293$	15.4694	0.903735	0.451867	+	0.892085i	$0.350758\pi$
$294$	−0.975542	−0.0568948
$295$	0	0
$296$	3.19352	0.185619
$297$	−14.4909	−0.840846
$298$	−0.689112	−0.0399192
$299$	−8.41272	−0.486520
$300$	0	0
$301$	2.09089	0.120517
$302$	1.81012	0.104161
$303$	−18.0658	−1.03785
$304$	14.8356	0.850881
$305$	0	0
$306$	−0.0522210	−0.00298528
$307$	20.2412	1.15523	0.577614	−	0.816310i	$-0.303984\pi$
$307$	20.2412	1.15523	0.577614	+	0.816310i	$0.303984\pi$
$308$	−4.07204	−0.232026
$309$	35.0274	1.99264
$310$	0	0
$311$	1.49434	0.0847363	0.0423681	−	0.999102i	$-0.486510\pi$
$311$	1.49434	0.0847363	0.0423681	+	0.999102i	$0.486510\pi$
$312$	−1.15540	−0.0654114
$313$	21.6470	1.22356	0.611780	−	0.791028i	$-0.290454\pi$
$313$	21.6470	1.22356	0.611780	+	0.791028i	$0.290454\pi$
$314$	−0.0171235	−0.000966335 0
$315$	0	0
$316$	13.6200	0.766183
$317$	−28.9329	−1.62504	−0.812518	−	0.582936i	$-0.801904\pi$
$317$	−28.9329	−1.62504	−0.812518	+	0.582936i	$0.801904\pi$
$318$	0.00724810	0.000406453 0
$319$	23.9853	1.34292
$320$	0	0
$321$	−14.3283	−0.799728
$322$	−0.246983	−0.0137638
$323$	7.77394	0.432553
$324$	19.5823	1.08791
$325$	0	0
$326$	0.645716	0.0357629
$327$	3.14061	0.173676
$328$	−1.34466	−0.0742465
$329$	4.63537	0.255556
$330$	0	0
$331$	−27.5701	−1.51539	−0.757695	−	0.652609i	$-0.773675\pi$
$331$	−27.5701	−1.51539	−0.757695	+	0.652609i	$0.773675\pi$
$332$	−18.2476	−1.00147
$333$	2.97538	0.163050
$334$	−1.14135	−0.0624521
$335$	0	0
$336$	4.97158	0.271222
$337$	8.25450	0.449651	0.224826	−	0.974399i	$-0.427819\pi$
$337$	8.25450	0.449651	0.224826	+	0.974399i	$0.427819\pi$
$338$	0.761387	0.0414140
$339$	25.5338	1.38681
$340$	0	0
$341$	8.28915	0.448883
$342$	−0.0943074	−0.00509956
$343$	9.33864	0.504239
$344$	−0.994464	−0.0536179
$345$	0	0
$346$	1.59155	0.0855622
$347$	−21.2018	−1.13817	−0.569085	−	0.822278i	$-0.692703\pi$
$347$	−21.2018	−1.13817	−0.569085	+	0.822278i	$0.692703\pi$
$348$	−29.3839	−1.57514
$349$	21.3257	1.14154	0.570770	−	0.821110i	$-0.306645\pi$
$349$	21.3257	1.14154	0.570770	+	0.821110i	$0.306645\pi$
$350$	0	0
$351$	9.47682	0.505835
$352$	2.90673	0.154929
$353$	−2.80184	−0.149127	−0.0745635	−	0.997216i	$-0.523756\pi$
$353$	−2.80184	−0.149127	−0.0745635	+	0.997216i	$0.523756\pi$
$354$	0.673993	0.0358223
$355$	0	0
$356$	4.71594	0.249944
$357$	2.60513	0.137878
$358$	0.577793	0.0305373
$359$	4.62788	0.244250	0.122125	−	0.992515i	$-0.461029\pi$
$359$	4.62788	0.244250	0.122125	+	0.992515i	$0.461029\pi$
$360$	0	0
$361$	−4.96085	−0.261097
$362$	−0.593904	−0.0312149
$363$	4.08793	0.214561
$364$	2.66305	0.139582
$365$	0	0
$366$	−1.43903	−0.0752194
$367$	0.106183	0.00554270	0.00277135	−	0.999996i	$-0.499118\pi$
$367$	0.106183	0.00554270	0.00277135	+	0.999996i	$0.499118\pi$
$368$	−17.2170	−0.897497
$369$	−1.25281	−0.0652187
$370$	0	0
$371$	−0.0334688	−0.00173761
$372$	−10.1549	−0.526505
$373$	16.6703	0.863157	0.431579	−	0.902075i	$-0.357957\pi$
$373$	16.6703	0.863157	0.431579	+	0.902075i	$0.357957\pi$
$374$	0.504843	0.0261048
$375$	0	0
$376$	−2.20466	−0.113697
$377$	−15.6860	−0.807872
$378$	0.278223	0.0143103
$379$	−16.5660	−0.850939	−0.425469	−	0.904973i	$-0.639891\pi$
$379$	−16.5660	−0.850939	−0.425469	+	0.904973i	$0.639891\pi$
$380$	0	0
$381$	−3.00915	−0.154164
$382$	−1.70830	−0.0874041
$383$	25.0198	1.27845	0.639226	−	0.769019i	$-0.279255\pi$
$383$	25.0198	1.27845	0.639226	+	0.769019i	$0.279255\pi$
$384$	−4.74526	−0.242156
$385$	0	0
$386$	−1.62203	−0.0825594
$387$	−0.926534	−0.0470984
$388$	−10.4712	−0.531592
$389$	−32.6696	−1.65641	−0.828207	−	0.560423i	$-0.810639\pi$
$389$	−32.6696	−1.65641	−0.828207	+	0.560423i	$0.810639\pi$
$390$	0	0
$391$	−9.02178	−0.456251
$392$	−2.14249	−0.108212
$393$	−31.1904	−1.57335
$394$	−1.34050	−0.0675333
$395$	0	0
$396$	1.80443	0.0906763
$397$	21.9103	1.09964	0.549822	−	0.835282i	$-0.314695\pi$
$397$	21.9103	1.09964	0.549822	+	0.835282i	$0.314695\pi$
$398$	−0.393992	−0.0197490
$399$	4.70467	0.235528
$400$	0	0
$401$	10.2229	0.510508	0.255254	−	0.966874i	$-0.417841\pi$
$401$	10.2229	0.510508	0.255254	+	0.966874i	$0.417841\pi$
$402$	0.144192	0.00719162
$403$	−5.42099	−0.270039
$404$	−19.8045	−0.985309
$405$	0	0
$406$	−0.460516	−0.0228550
$407$	−28.7642	−1.42579
$408$	−1.23904	−0.0613418
$409$	−16.7739	−0.829417	−0.414709	−	0.909954i	$-0.636117\pi$
$409$	−16.7739	−0.829417	−0.414709	+	0.909954i	$0.636117\pi$
$410$	0	0
$411$	26.8465	1.32424
$412$	38.3985	1.89176
$413$	−3.11223	−0.153143
$414$	0.109445	0.00537894
$415$	0	0
$416$	−1.90096	−0.0932023
$417$	−37.0140	−1.81258
$418$	0.911708	0.0445931
$419$	32.5790	1.59159	0.795793	−	0.605569i	$-0.207054\pi$
$419$	32.5790	1.59159	0.795793	+	0.605569i	$0.207054\pi$
$420$	0	0
$421$	11.5346	0.562163	0.281082	−	0.959684i	$-0.409307\pi$
$421$	11.5346	0.562163	0.281082	+	0.959684i	$0.409307\pi$
$422$	0.354066	0.0172357
$423$	−2.05406	−0.0998721
$424$	0.0159183	0.000773062 0
$425$	0	0
$426$	1.16095	0.0562483
$427$	6.64487	0.321568
$428$	−15.7073	−0.759240
$429$	10.4067	0.502441
$430$	0	0
$431$	15.2713	0.735590	0.367795	−	0.929907i	$-0.380113\pi$
$431$	15.2713	0.735590	0.367795	+	0.929907i	$0.380113\pi$
$432$	19.3947	0.933129
$433$	−8.69941	−0.418067	−0.209034	−	0.977908i	$-0.567032\pi$
$433$	−8.69941	−0.418067	−0.209034	+	0.977908i	$0.567032\pi$
$434$	−0.159151	−0.00763949
$435$	0	0
$436$	3.44287	0.164883
$437$	−16.2927	−0.779384
$438$	−2.45639	−0.117371
$439$	29.4040	1.40338	0.701689	−	0.712484i	$-0.252430\pi$
$439$	29.4040	1.40338	0.701689	+	0.712484i	$0.252430\pi$
$440$	0	0
$441$	−1.99614	−0.0950543
$442$	−0.330160	−0.0157041
$443$	35.7878	1.70033	0.850164	−	0.526518i	$-0.176503\pi$
$443$	35.7878	1.70033	0.850164	+	0.526518i	$0.176503\pi$
$444$	35.2384	1.67234
$445$	0	0
$446$	1.21787	0.0576679
$447$	−15.2336	−0.720525
$448$	5.41274	0.255728
$449$	−7.50777	−0.354314	−0.177157	−	0.984183i	$-0.556690\pi$
$449$	−7.50777	−0.354314	−0.177157	+	0.984183i	$0.556690\pi$
$450$	0	0
$451$	12.1114	0.570306
$452$	27.9912	1.31660
$453$	40.0147	1.88006
$454$	−0.978992	−0.0459464
$455$	0	0
$456$	−2.23762	−0.104786
$457$	31.7902	1.48708	0.743540	−	0.668691i	$-0.233145\pi$
$457$	31.7902	1.48708	0.743540	+	0.668691i	$0.233145\pi$
$458$	0.420683	0.0196572
$459$	10.1629	0.474364
$460$	0	0
$461$	−12.8715	−0.599487	−0.299743	−	0.954020i	$-0.596901\pi$
$461$	−12.8715	−0.599487	−0.299743	+	0.954020i	$0.596901\pi$
$462$	0.305523	0.0142142
$463$	11.8687	0.551587	0.275794	−	0.961217i	$-0.411059\pi$
$463$	11.8687	0.551587	0.275794	+	0.961217i	$0.411059\pi$
$464$	−32.1021	−1.49030
$465$	0	0
$466$	−1.22800	−0.0568860
$467$	18.9191	0.875473	0.437736	−	0.899103i	$-0.355780\pi$
$467$	18.9191	0.875473	0.437736	+	0.899103i	$0.355780\pi$
$468$	−1.18007	−0.0545490
$469$	−0.665818	−0.0307446
$470$	0	0
$471$	−0.378535	−0.0174420
$472$	1.48023	0.0681329
$473$	8.95719	0.411852
$474$	−1.02190	−0.0469374
$475$	0	0
$476$	2.85585	0.130898
$477$	0.0148310	0.000679063 0
$478$	−2.45620	−0.112344
$479$	23.7911	1.08704	0.543522	−	0.839395i	$-0.317091\pi$
$479$	23.7911	1.08704	0.543522	+	0.839395i	$0.317091\pi$
$480$	0	0
$481$	18.8114	0.857725
$482$	−0.0822506	−0.00374641
$483$	−5.45985	−0.248432
$484$	4.48136	0.203698
$485$	0	0
$486$	−0.260582	−0.0118202
$487$	−1.59589	−0.0723165	−0.0361583	−	0.999346i	$-0.511512\pi$
$487$	−1.59589	−0.0723165	−0.0361583	+	0.999346i	$0.511512\pi$
$488$	−3.16041	−0.143065
$489$	14.2743	0.645506
$490$	0	0
$491$	−31.8604	−1.43784	−0.718920	−	0.695093i	$-0.755363\pi$
$491$	−31.8604	−1.43784	−0.718920	+	0.695093i	$0.755363\pi$
$492$	−14.8375	−0.668925
$493$	−16.8217	−0.757610
$494$	−0.596244	−0.0268263
$495$	0	0
$496$	−11.0943	−0.498148
$497$	−5.36081	−0.240465
$498$	1.36911	0.0613513
$499$	17.3389	0.776194	0.388097	−	0.921619i	$-0.373133\pi$
$499$	17.3389	0.776194	0.388097	+	0.921619i	$0.373133\pi$
$500$	0	0
$501$	−25.2310	−1.12724
$502$	−1.07435	−0.0479508
$503$	13.8066	0.615607	0.307803	−	0.951450i	$-0.400406\pi$
$503$	13.8066	0.615607	0.307803	+	0.951450i	$0.400406\pi$
$504$	−0.0694076	−0.00309166
$505$	0	0
$506$	−1.05805	−0.0470362
$507$	16.8313	0.747506
$508$	−3.29876	−0.146359
$509$	37.2876	1.65274	0.826372	−	0.563124i	$-0.190401\pi$
$509$	37.2876	1.65274	0.826372	+	0.563124i	$0.190401\pi$
$510$	0	0
$511$	11.3426	0.501768
$512$	−6.49133	−0.286879
$513$	18.3535	0.810326
$514$	0.522974	0.0230674
$515$	0	0
$516$	−10.9733	−0.483071
$517$	19.8575	0.873332
$518$	0.552270	0.0242653
$519$	35.1830	1.54436
$520$	0	0
$521$	35.4359	1.55248	0.776238	−	0.630439i	$-0.217125\pi$
$521$	35.4359	1.55248	0.776238	+	0.630439i	$0.217125\pi$
$522$	0.204067	0.00893179
$523$	22.2983	0.975036	0.487518	−	0.873113i	$-0.337902\pi$
$523$	22.2983	0.975036	0.487518	+	0.873113i	$0.337902\pi$
$524$	−34.1922	−1.49369
$525$	0	0
$526$	0.383443	0.0167189
$527$	−5.81345	−0.253238
$528$	21.2978	0.926866
$529$	−4.09210	−0.177917
$530$	0	0
$531$	1.37912	0.0598485
$532$	5.15746	0.223604
$533$	−7.92071	−0.343084
$534$	−0.353835	−0.0153119
$535$	0	0
$536$	0.316674	0.0136782
$537$	12.7728	0.551186
$538$	0.865698	0.0373229
$539$	19.2975	0.831203
$540$	0	0
$541$	−28.0367	−1.20539	−0.602697	−	0.797970i	$-0.705907\pi$
$541$	−28.0367	−1.20539	−0.602697	+	0.797970i	$0.705907\pi$
$542$	−0.848925	−0.0364644
$543$	−13.1289	−0.563416
$544$	−2.03859	−0.0874037
$545$	0	0
$546$	−0.199808	−0.00855099
$547$	13.1556	0.562491	0.281245	−	0.959636i	$-0.409253\pi$
$547$	13.1556	0.562491	0.281245	+	0.959636i	$0.409253\pi$
$548$	29.4303	1.25720
$549$	−2.94453	−0.125669
$550$	0	0
$551$	−30.3787	−1.29418
$552$	2.59679	0.110527
$553$	4.71872	0.200660
$554$	1.81793	0.0772363
$555$	0	0
$556$	−40.5763	−1.72082
$557$	20.1003	0.851678	0.425839	−	0.904799i	$-0.359979\pi$
$557$	20.1003	0.851678	0.425839	+	0.904799i	$0.359979\pi$
$558$	0.0705243	0.00298553
$559$	−5.85787	−0.247762
$560$	0	0
$561$	11.1601	0.471181
$562$	−0.347757	−0.0146693
$563$	1.97240	0.0831268	0.0415634	−	0.999136i	$-0.486766\pi$
$563$	1.97240	0.0831268	0.0415634	+	0.999136i	$0.486766\pi$
$564$	−24.3270	−1.02435
$565$	0	0
$566$	−0.252319	−0.0106058
$567$	6.78441	0.284919
$568$	2.54969	0.106983
$569$	19.0863	0.800139	0.400070	−	0.916485i	$-0.368986\pi$
$569$	19.0863	0.800139	0.400070	+	0.916485i	$0.368986\pi$
$570$	0	0
$571$	10.1484	0.424697	0.212348	−	0.977194i	$-0.431889\pi$
$571$	10.1484	0.424697	0.212348	+	0.977194i	$0.431889\pi$
$572$	11.4083	0.477004
$573$	−37.7639	−1.57761
$574$	−0.232539	−0.00970597
$575$	0	0
$576$	−2.39854	−0.0999391
$577$	−11.2993	−0.470395	−0.235198	−	0.971948i	$-0.575574\pi$
$577$	−11.2993	−0.470395	−0.235198	+	0.971948i	$0.575574\pi$
$578$	1.04420	0.0434329
$579$	−35.8569	−1.49016
$580$	0	0
$581$	−6.32200	−0.262281
$582$	0.785646	0.0325661
$583$	−0.143377	−0.00593807
$584$	−5.39474	−0.223236
$585$	0	0
$586$	−1.27237	−0.0525611
$587$	−36.1850	−1.49352	−0.746758	−	0.665095i	$-0.768391\pi$
$587$	−36.1850	−1.49352	−0.746758	+	0.665095i	$0.768391\pi$
$588$	−23.6410	−0.974938
$589$	−10.4987	−0.432590
$590$	0	0
$591$	−29.6332	−1.21895
$592$	38.4983	1.58227
$593$	28.2897	1.16172	0.580858	−	0.814005i	$-0.302717\pi$
$593$	28.2897	1.16172	0.580858	+	0.814005i	$0.302717\pi$
$594$	1.19188	0.0489035
$595$	0	0
$596$	−16.6997	−0.684047
$597$	−8.70965	−0.356462
$598$	0.691951	0.0282960
$599$	−10.9989	−0.449404	−0.224702	−	0.974427i	$-0.572141\pi$
$599$	−10.9989	−0.449404	−0.224702	+	0.974427i	$0.572141\pi$
$600$	0	0
$601$	−10.3224	−0.421058	−0.210529	−	0.977588i	$-0.567519\pi$
$601$	−10.3224	−0.421058	−0.210529	+	0.977588i	$0.567519\pi$
$602$	−0.171977	−0.00700927
$603$	0.295043	0.0120151
$604$	43.8658	1.78488
$605$	0	0
$606$	1.48592	0.0603614
$607$	26.4559	1.07381	0.536906	−	0.843642i	$-0.319593\pi$
$607$	26.4559	1.07381	0.536906	+	0.843642i	$0.319593\pi$
$608$	−3.68154	−0.149306
$609$	−10.1802	−0.412524
$610$	0	0
$611$	−12.9865	−0.525378
$612$	−1.26551	−0.0511552
$613$	−33.8484	−1.36712	−0.683561	−	0.729893i	$-0.739570\pi$
$613$	−33.8484	−1.36712	−0.683561	+	0.729893i	$0.739570\pi$
$614$	−1.66485	−0.0671879
$615$	0	0
$616$	0.670992	0.0270350
$617$	0.659865	0.0265651	0.0132826	−	0.999912i	$-0.495772\pi$
$617$	0.659865	0.0265651	0.0132826	+	0.999912i	$0.495772\pi$
$618$	−2.88103	−0.115892
$619$	−34.8866	−1.40221	−0.701106	−	0.713057i	$-0.747310\pi$
$619$	−34.8866	−1.40221	−0.701106	+	0.713057i	$0.747310\pi$
$620$	0	0
$621$	−21.2995	−0.854720
$622$	−0.122910	−0.00492826
$623$	1.63387	0.0654595
$624$	−13.9284	−0.557584
$625$	0	0
$626$	−1.78048	−0.0711622
$627$	20.1544	0.804888
$628$	−0.414966	−0.0165589
$629$	20.1733	0.804361
$630$	0	0
$631$	−6.39474	−0.254571	−0.127285	−	0.991866i	$-0.540626\pi$
$631$	−6.39474	−0.254571	−0.127285	+	0.991866i	$0.540626\pi$
$632$	−2.24430	−0.0892735
$633$	7.82705	0.311097
$634$	2.37975	0.0945120
$635$	0	0
$636$	0.175648	0.00696491
$637$	−12.6203	−0.500035
$638$	−1.97280	−0.0781041
$639$	2.37553	0.0939743
$640$	0	0
$641$	16.9466	0.669352	0.334676	−	0.942333i	$-0.391373\pi$
$641$	16.9466	0.669352	0.334676	+	0.942333i	$0.391373\pi$
$642$	1.17851	0.0465121
$643$	−14.3993	−0.567852	−0.283926	−	0.958846i	$-0.591637\pi$
$643$	−14.3993	−0.567852	−0.283926	+	0.958846i	$0.591637\pi$
$644$	−5.98531	−0.235854
$645$	0	0
$646$	−0.639411	−0.0251573
$647$	−4.38744	−0.172488	−0.0862441	−	0.996274i	$-0.527486\pi$
$647$	−4.38744	−0.172488	−0.0862441	+	0.996274i	$0.527486\pi$
$648$	−3.22678	−0.126760
$649$	−13.3325	−0.523346
$650$	0	0
$651$	−3.51822	−0.137890
$652$	15.6481	0.612826
$653$	4.56970	0.178826	0.0894132	−	0.995995i	$-0.471501\pi$
$653$	4.56970	0.178826	0.0894132	+	0.995995i	$0.471501\pi$
$654$	−0.258317	−0.0101010
$655$	0	0
$656$	−16.2101	−0.632897
$657$	−5.02624	−0.196092
$658$	−0.381262	−0.0148631
$659$	−13.6506	−0.531751	−0.265875	−	0.964007i	$-0.585661\pi$
$659$	−13.6506	−0.531751	−0.265875	+	0.964007i	$0.585661\pi$
$660$	0	0
$661$	32.4151	1.26080	0.630401	−	0.776270i	$-0.282891\pi$
$661$	32.4151	1.26080	0.630401	+	0.776270i	$0.282891\pi$
$662$	2.26766	0.0881350
$663$	−7.29856	−0.283453
$664$	3.00685	0.116688
$665$	0	0
$666$	−0.244726	−0.00948295
$667$	35.2550	1.36508
$668$	−27.6592	−1.07017
$669$	26.9225	1.04088
$670$	0	0
$671$	28.4660	1.09892
$672$	−1.23372	−0.0475919
$673$	−0.237992	−0.00917391	−0.00458696	−	0.999989i	$-0.501460\pi$
$673$	−0.237992	−0.00917391	−0.00458696	+	0.999989i	$0.501460\pi$
$674$	−0.678938	−0.0261517
$675$	0	0
$676$	18.4512	0.709662
$677$	30.9534	1.18964	0.594818	−	0.803860i	$-0.297224\pi$
$677$	30.9534	1.18964	0.594818	+	0.803860i	$0.297224\pi$
$678$	−2.10017	−0.0806566
$679$	−3.62780	−0.139222
$680$	0	0
$681$	−21.6417	−0.829313
$682$	−0.681788	−0.0261070
$683$	28.5801	1.09359	0.546794	−	0.837267i	$-0.315848\pi$
$683$	28.5801	1.09359	0.546794	+	0.837267i	$0.315848\pi$
$684$	−2.28542	−0.0873850
$685$	0	0
$686$	−0.768108	−0.0293265
$687$	9.29968	0.354805
$688$	−11.9884	−0.457053
$689$	0.0937666	0.00357222
$690$	0	0
$691$	−6.89241	−0.262200	−0.131100	−	0.991369i	$-0.541851\pi$
$691$	−6.89241	−0.262200	−0.131100	+	0.991369i	$0.541851\pi$
$692$	38.5691	1.46618
$693$	0.625158	0.0237478
$694$	1.74386	0.0661959
$695$	0	0
$696$	4.84189	0.183531
$697$	−8.49415	−0.321739
$698$	−1.75405	−0.0663919
$699$	−27.1464	−1.02677
$700$	0	0
$701$	−29.3972	−1.11032	−0.555158	−	0.831745i	$-0.687342\pi$
$701$	−29.3972	−1.11032	−0.555158	+	0.831745i	$0.687342\pi$
$702$	−0.779474	−0.0294194
$703$	36.4314	1.37404
$704$	23.1877	0.873918
$705$	0	0
$706$	0.230453	0.00867321
$707$	−6.86138	−0.258049
$708$	16.3333	0.613845
$709$	−10.8690	−0.408195	−0.204098	−	0.978951i	$-0.565426\pi$
$709$	−10.8690	−0.408195	−0.204098	+	0.978951i	$0.565426\pi$
$710$	0	0
$711$	−2.09100	−0.0784186
$712$	−0.777094	−0.0291228
$713$	12.1839	0.456290
$714$	−0.214273	−0.00801898
$715$	0	0
$716$	14.0021	0.523281
$717$	−54.2972	−2.02776
$718$	−0.380646	−0.0142056
$719$	−30.8283	−1.14970	−0.574850	−	0.818259i	$-0.694940\pi$
$719$	−30.8283	−1.14970	−0.574850	+	0.818259i	$0.694940\pi$
$720$	0	0
$721$	13.3034	0.495445
$722$	0.408032	0.0151854
$723$	−1.81824	−0.0676212
$724$	−14.3925	−0.534892
$725$	0	0
$726$	−0.336235	−0.0124788
$727$	−28.0322	−1.03966	−0.519828	−	0.854271i	$-0.674004\pi$
$727$	−28.0322	−1.03966	−0.519828	+	0.854271i	$0.674004\pi$
$728$	−0.438819	−0.0162637
$729$	23.7127	0.878248
$730$	0	0
$731$	−6.28197	−0.232347
$732$	−34.8731	−1.28895
$733$	−25.8442	−0.954578	−0.477289	−	0.878746i	$-0.658381\pi$
$733$	−25.8442	−0.954578	−0.477289	+	0.878746i	$0.658381\pi$
$734$	−0.00873360	−0.000322363 0
$735$	0	0
$736$	4.27248	0.157486
$737$	−2.85230	−0.105066
$738$	0.103044	0.00379312
$739$	−43.0752	−1.58455	−0.792273	−	0.610166i	$-0.791103\pi$
$739$	−43.0752	−1.58455	−0.792273	+	0.610166i	$0.791103\pi$
$740$	0	0
$741$	−13.1807	−0.484204
$742$	0.00275283	0.000101059 0
$743$	−13.1212	−0.481372	−0.240686	−	0.970603i	$-0.577372\pi$
$743$	−13.1212	−0.481372	−0.240686	+	0.970603i	$0.577372\pi$
$744$	1.67332	0.0613470
$745$	0	0
$746$	−1.37114	−0.0502012
$747$	2.80146	0.102500
$748$	12.2342	0.447327
$749$	−5.44189	−0.198842
$750$	0	0
$751$	33.6870	1.22926	0.614629	−	0.788817i	$-0.289306\pi$
$751$	33.6870	1.22926	0.614629	+	0.788817i	$0.289306\pi$
$752$	−26.5775	−0.969180
$753$	−23.7498	−0.865492
$754$	1.29019	0.0469858
$755$	0	0
$756$	6.74238	0.245218
$757$	46.0911	1.67521	0.837604	−	0.546278i	$-0.183956\pi$
$757$	46.0911	1.67521	0.837604	+	0.546278i	$0.183956\pi$
$758$	1.36256	0.0494905
$759$	−23.3895	−0.848984
$760$	0	0
$761$	14.2727	0.517387	0.258693	−	0.965960i	$-0.416708\pi$
$761$	14.2727	0.517387	0.258693	+	0.965960i	$0.416708\pi$
$762$	0.247505	0.00896615
$763$	1.19280	0.0431823
$764$	−41.3983	−1.49774
$765$	0	0
$766$	−2.05789	−0.0743547
$767$	8.71925	0.314834
$768$	−28.1128	−1.01443
$769$	13.0154	0.469349	0.234674	−	0.972074i	$-0.424598\pi$
$769$	13.0154	0.469349	0.234674	+	0.972074i	$0.424598\pi$
$770$	0	0
$771$	11.5609	0.416357
$772$	−39.3079	−1.41472
$773$	29.9438	1.07700	0.538502	−	0.842624i	$-0.318990\pi$
$773$	29.9438	1.07700	0.538502	+	0.842624i	$0.318990\pi$
$774$	0.0762080	0.00273924
$775$	0	0
$776$	1.72544	0.0619397
$777$	12.2086	0.437980
$778$	2.68709	0.0963369
$779$	−15.3398	−0.549606
$780$	0	0
$781$	−22.9652	−0.821759
$782$	0.742046	0.0265355
$783$	−39.7143	−1.41927
$784$	−25.8280	−0.922428
$785$	0	0
$786$	2.56542	0.0915057
$787$	−13.7932	−0.491676	−0.245838	−	0.969311i	$-0.579063\pi$
$787$	−13.7932	−0.491676	−0.245838	+	0.969311i	$0.579063\pi$
$788$	−32.4852	−1.15724
$789$	8.47646	0.301770
$790$	0	0
$791$	9.69774	0.344812
$792$	−0.297335	−0.0105654
$793$	−18.6163	−0.661086
$794$	−1.80213	−0.0639553
$795$	0	0
$796$	−9.54788	−0.338416
$797$	−18.4152	−0.652300	−0.326150	−	0.945318i	$-0.605751\pi$
$797$	−18.4152	−0.652300	−0.326150	+	0.945318i	$0.605751\pi$
$798$	−0.386962	−0.0136983
$799$	−13.9267	−0.492691
$800$	0	0
$801$	−0.724013	−0.0255817
$802$	−0.840841	−0.0296911
$803$	48.5907	1.71473
$804$	3.49429	0.123234
$805$	0	0
$806$	0.445879	0.0157054
$807$	19.1372	0.673663
$808$	3.26339	0.114806
$809$	−14.7007	−0.516849	−0.258425	−	0.966031i	$-0.583203\pi$
$809$	−14.7007	−0.516849	−0.258425	+	0.966031i	$0.583203\pi$
$810$	0	0
$811$	−46.3555	−1.62776	−0.813882	−	0.581031i	$-0.802650\pi$
$811$	−46.3555	−1.62776	−0.813882	+	0.581031i	$0.802650\pi$
$812$	−11.1600	−0.391639
$813$	−18.7665	−0.658168
$814$	2.36587	0.0829238
$815$	0	0
$816$	−14.9368	−0.522893
$817$	−11.3448	−0.396903
$818$	1.37967	0.0482389
$819$	−0.408844	−0.0142862
$820$	0	0
$821$	39.2626	1.37027	0.685137	−	0.728414i	$-0.259742\pi$
$821$	39.2626	1.37027	0.685137	+	0.728414i	$0.259742\pi$
$822$	−2.20814	−0.0770177
$823$	29.0804	1.01368	0.506839	−	0.862041i	$-0.330814\pi$
$823$	29.0804	1.01368	0.506839	+	0.862041i	$0.330814\pi$
$824$	−6.32732	−0.220423
$825$	0	0
$826$	0.255982	0.00890677
$827$	−30.7270	−1.06848	−0.534242	−	0.845332i	$-0.679403\pi$
$827$	−30.7270	−1.06848	−0.534242	+	0.845332i	$0.679403\pi$
$828$	2.65226	0.0921725
$829$	−16.4599	−0.571675	−0.285837	−	0.958278i	$-0.592272\pi$
$829$	−16.4599	−0.571675	−0.285837	+	0.958278i	$0.592272\pi$
$830$	0	0
$831$	40.1873	1.39408
$832$	−15.1644	−0.525731
$833$	−13.5340	−0.468925
$834$	3.04442	0.105420
$835$	0	0
$836$	22.0941	0.764139
$837$	−13.7250	−0.474405
$838$	−2.67964	−0.0925665
$839$	43.2285	1.49241	0.746206	−	0.665715i	$-0.231873\pi$
$839$	43.2285	1.49241	0.746206	+	0.665715i	$0.231873\pi$
$840$	0	0
$841$	36.7351	1.26673
$842$	−0.948729	−0.0326954
$843$	−7.68758	−0.264774
$844$	8.58034	0.295347
$845$	0	0
$846$	0.168948	0.00580855
$847$	1.55260	0.0533478
$848$	0.191897	0.00658978
$849$	−5.57781	−0.191430
$850$	0	0
$851$	−42.2793	−1.44931
$852$	28.1342	0.963861
$853$	−8.36996	−0.286582	−0.143291	−	0.989681i	$-0.545768\pi$
$853$	−8.36996	−0.286582	−0.143291	+	0.989681i	$0.545768\pi$
$854$	−0.546544	−0.0187024
$855$	0	0
$856$	2.58825	0.0884646
$857$	−18.3641	−0.627305	−0.313653	−	0.949538i	$-0.601553\pi$
$857$	−18.3641	−0.627305	−0.313653	+	0.949538i	$0.601553\pi$
$858$	−0.855958	−0.0292219
$859$	2.47499	0.0844457	0.0422228	−	0.999108i	$-0.486556\pi$
$859$	2.47499	0.0844457	0.0422228	+	0.999108i	$0.486556\pi$
$860$	0	0
$861$	−5.14053	−0.175189
$862$	−1.25607	−0.0427819
$863$	10.0917	0.343525	0.171762	−	0.985138i	$-0.445054\pi$
$863$	10.0917	0.343525	0.171762	+	0.985138i	$0.445054\pi$
$864$	−4.81290	−0.163738
$865$	0	0
$866$	0.715532	0.0243148
$867$	23.0832	0.783946
$868$	−3.85682	−0.130909
$869$	20.2146	0.685732
$870$	0	0
$871$	1.86536	0.0632055
$872$	−0.567316	−0.0192118
$873$	1.60758	0.0544083
$874$	1.34008	0.0453289
$875$	0	0
$876$	−59.5274	−2.01125
$877$	−53.6453	−1.81147	−0.905736	−	0.423843i	$-0.860681\pi$
$877$	−53.6453	−1.81147	−0.905736	+	0.423843i	$0.860681\pi$
$878$	−2.41850	−0.0816203
$879$	−28.1272	−0.948708
$880$	0	0
$881$	30.6985	1.03426	0.517130	−	0.855907i	$-0.327001\pi$
$881$	30.6985	1.03426	0.517130	+	0.855907i	$0.327001\pi$
$882$	0.164184	0.00552835
$883$	21.8831	0.736424	0.368212	−	0.929742i	$-0.379970\pi$
$883$	21.8831	0.736424	0.368212	+	0.929742i	$0.379970\pi$
$884$	−8.00099	−0.269102
$885$	0	0
$886$	−2.94356	−0.0988910
$887$	23.3921	0.785431	0.392715	−	0.919660i	$-0.371536\pi$
$887$	23.3921	0.785431	0.392715	+	0.919660i	$0.371536\pi$
$888$	−5.80660	−0.194857
$889$	−1.14288	−0.0383308
$890$	0	0
$891$	29.0638	0.973673
$892$	29.5135	0.988186
$893$	−25.1506	−0.841633
$894$	1.25297	0.0419057
$895$	0	0
$896$	−1.80225	−0.0602089
$897$	15.2964	0.510731
$898$	0.617518	0.0206069
$899$	22.7176	0.757674
$900$	0	0
$901$	0.100555	0.00334997
$902$	−0.996173	−0.0331689
$903$	−3.80175	−0.126514
$904$	−4.61240	−0.153406
$905$	0	0
$906$	−3.29124	−0.109344
$907$	2.98723	0.0991893	0.0495947	−	0.998769i	$-0.484207\pi$
$907$	2.98723	0.0991893	0.0495947	+	0.998769i	$0.484207\pi$
$908$	−23.7246	−0.787328
$909$	3.04047	0.100846
$910$	0	0
$911$	42.1883	1.39776	0.698880	−	0.715239i	$-0.253682\pi$
$911$	42.1883	1.39776	0.698880	+	0.715239i	$0.253682\pi$
$912$	−26.9748	−0.893224
$913$	−27.0828	−0.896311
$914$	−2.61476	−0.0864885
$915$	0	0
$916$	10.1947	0.336842
$917$	−11.8461	−0.391192
$918$	−0.835906	−0.0275890
$919$	−53.2428	−1.75632	−0.878160	−	0.478367i	$-0.841229\pi$
$919$	−53.2428	−1.75632	−0.878160	+	0.478367i	$0.841229\pi$
$920$	0	0
$921$	−36.8035	−1.21272
$922$	1.05869	0.0348661
$923$	15.0189	0.494353
$924$	7.40396	0.243572
$925$	0	0
$926$	−0.976211	−0.0320803
$927$	−5.89511	−0.193621
$928$	7.96631	0.261507
$929$	−27.2213	−0.893103	−0.446552	−	0.894758i	$-0.647348\pi$
$929$	−27.2213	−0.893103	−0.446552	+	0.894758i	$0.647348\pi$
$930$	0	0
$931$	−24.4414	−0.801033
$932$	−29.7590	−0.974788
$933$	−2.71708	−0.0889531
$934$	−1.55611	−0.0509174
$935$	0	0
$936$	0.194453	0.00635590
$937$	−7.54293	−0.246417	−0.123208	−	0.992381i	$-0.539318\pi$
$937$	−7.54293	−0.246417	−0.123208	+	0.992381i	$0.539318\pi$
$938$	0.0547639	0.00178811
$939$	−39.3595	−1.28445
$940$	0	0
$941$	35.4553	1.15581	0.577905	−	0.816104i	$-0.303870\pi$
$941$	35.4553	1.15581	0.577905	+	0.816104i	$0.303870\pi$
$942$	0.0311347	0.00101442
$943$	17.8021	0.579716
$944$	17.8443	0.580783
$945$	0	0
$946$	−0.736734	−0.0239533
$947$	−33.0630	−1.07440	−0.537202	−	0.843454i	$-0.680519\pi$
$947$	−33.0630	−1.07440	−0.537202	+	0.843454i	$0.680519\pi$
$948$	−24.7644	−0.804311
$949$	−31.7776	−1.03155
$950$	0	0
$951$	52.6071	1.70590
$952$	−0.470588	−0.0152518
$953$	5.14501	0.166663	0.0833316	−	0.996522i	$-0.473444\pi$
$953$	5.14501	0.166663	0.0833316	+	0.996522i	$0.473444\pi$
$954$	−0.00121986	−3.94943e−5 0
$955$	0	0
$956$	−59.5228	−1.92511
$957$	−43.6111	−1.40975
$958$	−1.95683	−0.0632223
$959$	10.1963	0.329255
$960$	0	0
$961$	−23.1490	−0.746741
$962$	−1.54725	−0.0498852
$963$	2.41145	0.0777080
$964$	−1.99323	−0.0641978
$965$	0	0
$966$	0.449076	0.0144488
$967$	−2.82789	−0.0909390	−0.0454695	−	0.998966i	$-0.514478\pi$
$967$	−2.82789	−0.0909390	−0.0454695	+	0.998966i	$0.514478\pi$
$968$	−0.738440	−0.0237344
$969$	−14.1349	−0.454079
$970$	0	0
$971$	−43.0152	−1.38042	−0.690211	−	0.723608i	$-0.742482\pi$
$971$	−43.0152	−1.38042	−0.690211	+	0.723608i	$0.742482\pi$
$972$	−6.31486	−0.202549
$973$	−14.0579	−0.450676
$974$	0.131263	0.00420592
$975$	0	0
$976$	−38.0991	−1.21952
$977$	5.45876	0.174641	0.0873207	−	0.996180i	$-0.472170\pi$
$977$	5.45876	0.174641	0.0873207	+	0.996180i	$0.472170\pi$
$978$	−1.17407	−0.0375426
$979$	6.99933	0.223700
$980$	0	0
$981$	−0.528564	−0.0168758
$982$	2.62054	0.0836246
$983$	−16.8518	−0.537489	−0.268745	−	0.963211i	$-0.586609\pi$
$983$	−16.8518	−0.537489	−0.268745	+	0.963211i	$0.586609\pi$
$984$	2.44492	0.0779413
$985$	0	0
$986$	1.38359	0.0440625
$987$	−8.42824	−0.268274
$988$	−14.4492	−0.459690
$989$	13.1658	0.418648
$990$	0	0
$991$	57.3144	1.82065	0.910326	−	0.413892i	$-0.135831\pi$
$991$	57.3144	1.82065	0.910326	+	0.413892i	$0.135831\pi$
$992$	2.75310	0.0874111
$993$	50.1292	1.59080
$994$	0.440929	0.0139854
$995$	0	0
$996$	33.1786	1.05130
$997$	39.3642	1.24668	0.623339	−	0.781952i	$-0.285776\pi$
$997$	39.3642	1.24668	0.623339	+	0.781952i	$0.285776\pi$
$998$	−1.42613	−0.0451434
$999$	47.6271	1.50685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.7		12
5.4	even	2		241.2.a.b.1.6	✓	12
15.14	odd	2		2169.2.a.h.1.7		12
20.19	odd	2		3856.2.a.n.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.6	✓	12	5.4	even	2
2169.2.a.h.1.7		12	15.14	odd	2
3856.2.a.n.1.4		12	20.19	odd	2
6025.2.a.h.1.7		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)

\(f(q)\)	\(=\)	\(q-0.0822506 q^{2} -1.81824 q^{3} -1.99323 q^{4} +0.149552 q^{6} -0.690569 q^{7} +0.328446 q^{8} +0.306010 q^{9} +O(q^{10})\)	\(q-0.0822506 q^{2} -1.81824 q^{3} -1.99323 q^{4} +0.149552 q^{6} -0.690569 q^{7} +0.328446 q^{8} +0.306010 q^{9} -2.95833 q^{11} +3.62419 q^{12} +1.93470 q^{13} +0.0567997 q^{14} +3.95945 q^{16} +2.07477 q^{17} -0.0251695 q^{18} +3.74689 q^{19} +1.25562 q^{21} +0.243324 q^{22} -4.34832 q^{23} -0.597195 q^{24} -0.159131 q^{26} +4.89833 q^{27} +1.37647 q^{28} -8.10772 q^{29} -2.80197 q^{31} -0.982559 q^{32} +5.37896 q^{33} -0.170651 q^{34} -0.609951 q^{36} +9.72312 q^{37} -0.308183 q^{38} -3.51777 q^{39} -4.09401 q^{41} -0.103276 q^{42} -3.02779 q^{43} +5.89665 q^{44} +0.357652 q^{46} -6.71240 q^{47} -7.19925 q^{48} -6.52312 q^{49} -3.77244 q^{51} -3.85632 q^{52} +0.0484656 q^{53} -0.402890 q^{54} -0.226814 q^{56} -6.81275 q^{57} +0.666864 q^{58} +4.50676 q^{59} -9.62232 q^{61} +0.230464 q^{62} -0.211321 q^{63} -7.83809 q^{64} -0.442423 q^{66} +0.964160 q^{67} -4.13551 q^{68} +7.90631 q^{69} +7.76289 q^{71} +0.100508 q^{72} -16.4250 q^{73} -0.799732 q^{74} -7.46842 q^{76} +2.04293 q^{77} +0.289338 q^{78} -6.83310 q^{79} -9.82439 q^{81} +0.336735 q^{82} +9.15477 q^{83} -2.50275 q^{84} +0.249037 q^{86} +14.7418 q^{87} -0.971651 q^{88} -2.36597 q^{89} -1.33605 q^{91} +8.66723 q^{92} +5.09467 q^{93} +0.552099 q^{94} +1.78653 q^{96} +5.25335 q^{97} +0.536530 q^{98} -0.905280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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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