LMFDB - Embedded newform 6025.2.a.i.1.13

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:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 $ x^15 - 2x^14 - 16x^13 + 31x^12 + 99x^11 - 184x^10 - 296x^9 + 519x^8 + 437x^7 - 699x^6 - 297x^5 + 394x^4 + 89x^3 - 57x^2 - 17x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-1.93741$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.93741 q^{2} +1.04448 q^{3} +1.75357 q^{4} +2.02359 q^{6} +2.21578 q^{7} -0.477443 q^{8} -1.90906 q^{9} +O(q^{10})$	\(q+1.93741 q^{2} +1.04448 q^{3} +1.75357 q^{4} +2.02359 q^{6} +2.21578 q^{7} -0.477443 q^{8} -1.90906 q^{9} -0.841836 q^{11} +1.83157 q^{12} -4.89587 q^{13} +4.29288 q^{14} -4.43214 q^{16} -3.85883 q^{17} -3.69863 q^{18} -0.266070 q^{19} +2.31434 q^{21} -1.63098 q^{22} +2.96732 q^{23} -0.498681 q^{24} -9.48533 q^{26} -5.12742 q^{27} +3.88552 q^{28} +10.1115 q^{29} -8.28075 q^{31} -7.63199 q^{32} -0.879283 q^{33} -7.47614 q^{34} -3.34766 q^{36} -8.35609 q^{37} -0.515487 q^{38} -5.11366 q^{39} -7.10678 q^{41} +4.48384 q^{42} +4.67348 q^{43} -1.47622 q^{44} +5.74892 q^{46} -0.450157 q^{47} -4.62929 q^{48} -2.09032 q^{49} -4.03048 q^{51} -8.58524 q^{52} -2.94547 q^{53} -9.93394 q^{54} -1.05791 q^{56} -0.277905 q^{57} +19.5902 q^{58} +6.86623 q^{59} -0.893170 q^{61} -16.0432 q^{62} -4.23004 q^{63} -5.92204 q^{64} -1.70353 q^{66} -4.58394 q^{67} -6.76672 q^{68} +3.09931 q^{69} -3.54355 q^{71} +0.911465 q^{72} +3.33619 q^{73} -16.1892 q^{74} -0.466571 q^{76} -1.86532 q^{77} -9.90726 q^{78} -8.22313 q^{79} +0.371659 q^{81} -13.7688 q^{82} -4.23611 q^{83} +4.05835 q^{84} +9.05446 q^{86} +10.5613 q^{87} +0.401929 q^{88} +0.158230 q^{89} -10.8482 q^{91} +5.20339 q^{92} -8.64910 q^{93} -0.872139 q^{94} -7.97148 q^{96} +5.91542 q^{97} -4.04982 q^{98} +1.60711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.93741	1.36996	0.684979	−	0.728563i	$-0.259811\pi$
$2$	1.93741	1.36996	0.684979	+	0.728563i	$0.259811\pi$
$3$	1.04448	0.603032	0.301516	−	0.953461i	$-0.402507\pi$
$3$	1.04448	0.603032	0.301516	+	0.953461i	$0.402507\pi$
$4$	1.75357	0.876783
$5$	0	0
$5$	0	0
$6$	2.02359	0.826129
$7$	2.21578	0.837486	0.418743	−	0.908105i	$-0.362471\pi$
$7$	2.21578	0.837486	0.418743	+	0.908105i	$0.362471\pi$
$8$	−0.477443	−0.168802
$9$	−1.90906	−0.636352
$10$	0	0
$11$	−0.841836	−0.253823	−0.126912	−	0.991914i	$-0.540506\pi$
$11$	−0.841836	−0.253823	−0.126912	+	0.991914i	$0.540506\pi$
$12$	1.83157	0.528729
$13$	−4.89587	−1.35787	−0.678936	−	0.734198i	$-0.737558\pi$
$13$	−4.89587	−1.35787	−0.678936	+	0.734198i	$0.737558\pi$
$14$	4.29288	1.14732
$15$	0	0
$16$	−4.43214	−1.10803
$17$	−3.85883	−0.935904	−0.467952	−	0.883754i	$-0.655008\pi$
$17$	−3.85883	−0.935904	−0.467952	+	0.883754i	$0.655008\pi$
$18$	−3.69863	−0.871775
$19$	−0.266070	−0.0610406	−0.0305203	−	0.999534i	$-0.509716\pi$
$19$	−0.266070	−0.0610406	−0.0305203	+	0.999534i	$0.509716\pi$
$20$	0	0
$21$	2.31434	0.505031
$22$	−1.63098	−0.347727
$23$	2.96732	0.618728	0.309364	−	0.950944i	$-0.399884\pi$
$23$	2.96732	0.618728	0.309364	+	0.950944i	$0.399884\pi$
$24$	−0.498681	−0.101793
$25$	0	0
$26$	−9.48533	−1.86023
$27$	−5.12742	−0.986773
$28$	3.88552	0.734293
$29$	10.1115	1.87767	0.938833	−	0.344372i	$-0.111908\pi$
$29$	10.1115	1.87767	0.938833	+	0.344372i	$0.111908\pi$
$30$	0	0
$31$	−8.28075	−1.48727	−0.743633	−	0.668588i	$-0.766899\pi$
$31$	−8.28075	−1.48727	−0.743633	+	0.668588i	$0.766899\pi$
$32$	−7.63199	−1.34916
$33$	−0.879283	−0.153064
$34$	−7.47614	−1.28215
$35$	0	0
$36$	−3.34766	−0.557943
$37$	−8.35609	−1.37373	−0.686866	−	0.726784i	$-0.741014\pi$
$37$	−8.35609	−1.37373	−0.686866	+	0.726784i	$0.741014\pi$
$38$	−0.515487	−0.0836230
$39$	−5.11366	−0.818840
$40$	0	0
$41$	−7.10678	−1.10989	−0.554946	−	0.831886i	$-0.687261\pi$
$41$	−7.10678	−1.10989	−0.554946	+	0.831886i	$0.687261\pi$
$42$	4.48384	0.691871
$43$	4.67348	0.712699	0.356350	−	0.934353i	$-0.384021\pi$
$43$	4.67348	0.712699	0.356350	+	0.934353i	$0.384021\pi$
$44$	−1.47622	−0.222548
$45$	0	0
$46$	5.74892	0.847631
$47$	−0.450157	−0.0656621	−0.0328310	−	0.999461i	$-0.510452\pi$
$47$	−0.450157	−0.0656621	−0.0328310	+	0.999461i	$0.510452\pi$
$48$	−4.62929	−0.668181
$49$	−2.09032	−0.298618
$50$	0	0
$51$	−4.03048	−0.564380
$52$	−8.58524	−1.19056
$53$	−2.94547	−0.404591	−0.202296	−	0.979324i	$-0.564840\pi$
$53$	−2.94547	−0.404591	−0.202296	+	0.979324i	$0.564840\pi$
$54$	−9.93394	−1.35184
$55$	0	0
$56$	−1.05791	−0.141369
$57$	−0.277905	−0.0368094
$58$	19.5902	2.57232
$59$	6.86623	0.893907	0.446953	−	0.894557i	$-0.352509\pi$
$59$	6.86623	0.893907	0.446953	+	0.894557i	$0.352509\pi$
$60$	0	0
$61$	−0.893170	−0.114359	−0.0571794	−	0.998364i	$-0.518211\pi$
$61$	−0.893170	−0.114359	−0.0571794	+	0.998364i	$0.518211\pi$
$62$	−16.0432	−2.03749
$63$	−4.23004	−0.532936
$64$	−5.92204	−0.740255
$65$	0	0
$66$	−1.70353	−0.209691
$67$	−4.58394	−0.560017	−0.280008	−	0.959998i	$-0.590337\pi$
$67$	−4.58394	−0.560017	−0.280008	+	0.959998i	$0.590337\pi$
$68$	−6.76672	−0.820585
$69$	3.09931	0.373113
$70$	0	0
$71$	−3.54355	−0.420542	−0.210271	−	0.977643i	$-0.567435\pi$
$71$	−3.54355	−0.420542	−0.210271	+	0.977643i	$0.567435\pi$
$72$	0.911465	0.107417
$73$	3.33619	0.390471	0.195236	−	0.980756i	$-0.437453\pi$
$73$	3.33619	0.390471	0.195236	+	0.980756i	$0.437453\pi$
$74$	−16.1892	−1.88196
$75$	0	0
$76$	−0.466571	−0.0535193
$77$	−1.86532	−0.212573
$78$	−9.90726	−1.12178
$79$	−8.22313	−0.925175	−0.462587	−	0.886574i	$-0.653079\pi$
$79$	−8.22313	−0.925175	−0.462587	+	0.886574i	$0.653079\pi$
$80$	0	0
$81$	0.371659	0.0412955
$82$	−13.7688	−1.52051
$83$	−4.23611	−0.464973	−0.232486	−	0.972600i	$-0.574686\pi$
$83$	−4.23611	−0.464973	−0.232486	+	0.972600i	$0.574686\pi$
$84$	4.05835	0.442803
$85$	0	0
$86$	9.05446	0.976368
$87$	10.5613	1.13229
$88$	0.401929	0.0428458
$89$	0.158230	0.0167724	0.00838619	−	0.999965i	$-0.497331\pi$
$89$	0.158230	0.0167724	0.00838619	+	0.999965i	$0.497331\pi$
$90$	0	0
$91$	−10.8482	−1.13720
$92$	5.20339	0.542491
$93$	−8.64910	−0.896870
$94$	−0.872139	−0.0899542
$95$	0	0
$96$	−7.97148	−0.813586
$97$	5.91542	0.600620	0.300310	−	0.953842i	$-0.402910\pi$
$97$	5.91542	0.600620	0.300310	+	0.953842i	$0.402910\pi$
$98$	−4.04982	−0.409094
$99$	1.60711	0.161521
$100$	0	0
$101$	−8.45542	−0.841346	−0.420673	−	0.907212i	$-0.638206\pi$
$101$	−8.45542	−0.841346	−0.420673	+	0.907212i	$0.638206\pi$
$102$	−7.80871	−0.773177
$103$	18.2416	1.79740	0.898701	−	0.438562i	$-0.144512\pi$
$103$	18.2416	1.79740	0.898701	+	0.438562i	$0.144512\pi$
$104$	2.33750	0.229211
$105$	0	0
$106$	−5.70659	−0.554273
$107$	16.0529	1.55190	0.775948	−	0.630797i	$-0.217272\pi$
$107$	16.0529	1.55190	0.775948	+	0.630797i	$0.217272\pi$
$108$	−8.99128	−0.865186
$109$	−13.7735	−1.31926	−0.659632	−	0.751589i	$-0.729288\pi$
$109$	−13.7735	−1.31926	−0.659632	+	0.751589i	$0.729288\pi$
$110$	0	0
$111$	−8.72779	−0.828405
$112$	−9.82064	−0.927963
$113$	−2.24065	−0.210783	−0.105391	−	0.994431i	$-0.533610\pi$
$113$	−2.24065	−0.210783	−0.105391	+	0.994431i	$0.533610\pi$
$114$	−0.538417	−0.0504274
$115$	0	0
$116$	17.7313	1.64631
$117$	9.34650	0.864084
$118$	13.3027	1.22461
$119$	−8.55031	−0.783806
$120$	0	0
$121$	−10.2913	−0.935574
$122$	−1.73044	−0.156667
$123$	−7.42291	−0.669301
$124$	−14.5208	−1.30401
$125$	0	0
$126$	−8.19534	−0.730099
$127$	8.96779	0.795763	0.397882	−	0.917437i	$-0.369746\pi$
$127$	8.96779	0.795763	0.397882	+	0.917437i	$0.369746\pi$
$128$	3.79055	0.335040
$129$	4.88137	0.429781
$130$	0	0
$131$	9.43843	0.824639	0.412320	−	0.911039i	$-0.364719\pi$
$131$	9.43843	0.824639	0.412320	+	0.911039i	$0.364719\pi$
$132$	−1.54188	−0.134204
$133$	−0.589551	−0.0511206
$134$	−8.88097	−0.767199
$135$	0	0
$136$	1.84237	0.157982
$137$	−2.15225	−0.183879	−0.0919394	−	0.995765i	$-0.529307\pi$
$137$	−2.15225	−0.183879	−0.0919394	+	0.995765i	$0.529307\pi$
$138$	6.00464	0.511149
$139$	−9.11427	−0.773062	−0.386531	−	0.922276i	$-0.626327\pi$
$139$	−9.11427	−0.773062	−0.386531	+	0.922276i	$0.626327\pi$
$140$	0	0
$141$	−0.470181	−0.0395964
$142$	−6.86532	−0.576124
$143$	4.12152	0.344659
$144$	8.46120	0.705100
$145$	0	0
$146$	6.46357	0.534929
$147$	−2.18331	−0.180076
$148$	−14.6530	−1.20447
$149$	−16.3597	−1.34024	−0.670121	−	0.742252i	$-0.733758\pi$
$149$	−16.3597	−1.34024	−0.670121	+	0.742252i	$0.733758\pi$
$150$	0	0
$151$	−6.58297	−0.535715	−0.267857	−	0.963459i	$-0.586316\pi$
$151$	−6.58297	−0.535715	−0.267857	+	0.963459i	$0.586316\pi$
$152$	0.127033	0.0103037
$153$	7.36672	0.595564
$154$	−3.61390	−0.291216
$155$	0	0
$156$	−8.96714	−0.717946
$157$	2.90475	0.231824	0.115912	−	0.993259i	$-0.463021\pi$
$157$	2.90475	0.231824	0.115912	+	0.993259i	$0.463021\pi$
$158$	−15.9316	−1.26745
$159$	−3.07649	−0.243982
$160$	0	0
$161$	6.57492	0.518176
$162$	0.720057	0.0565731
$163$	−15.0409	−1.17810	−0.589048	−	0.808098i	$-0.700497\pi$
$163$	−15.0409	−1.17810	−0.589048	+	0.808098i	$0.700497\pi$
$164$	−12.4622	−0.973135
$165$	0	0
$166$	−8.20708	−0.636993
$167$	−20.4587	−1.58314	−0.791571	−	0.611078i	$-0.790736\pi$
$167$	−20.4587	−1.58314	−0.791571	+	0.611078i	$0.790736\pi$
$168$	−1.10497	−0.0852500
$169$	10.9696	0.843814
$170$	0	0
$171$	0.507942	0.0388433
$172$	8.19526	0.624883
$173$	10.9861	0.835257	0.417629	−	0.908618i	$-0.362861\pi$
$173$	10.9861	0.835257	0.417629	+	0.908618i	$0.362861\pi$
$174$	20.4617	1.55119
$175$	0	0
$176$	3.73113	0.281245
$177$	7.17166	0.539055
$178$	0.306557	0.0229775
$179$	11.0028	0.822385	0.411192	−	0.911549i	$-0.365112\pi$
$179$	11.0028	0.822385	0.411192	+	0.911549i	$0.365112\pi$
$180$	0	0
$181$	−7.57651	−0.563158	−0.281579	−	0.959538i	$-0.590858\pi$
$181$	−7.57651	−0.563158	−0.281579	+	0.959538i	$0.590858\pi$
$182$	−21.0174	−1.55791
$183$	−0.932901	−0.0689620
$184$	−1.41672	−0.104442
$185$	0	0
$186$	−16.7569	−1.22867
$187$	3.24850	0.237554
$188$	−0.789379	−0.0575714
$189$	−11.3612	−0.826408
$190$	0	0
$191$	−15.3019	−1.10721	−0.553603	−	0.832781i	$-0.686747\pi$
$191$	−15.3019	−1.10721	−0.553603	+	0.832781i	$0.686747\pi$
$192$	−6.18547	−0.446398
$193$	5.64119	0.406062	0.203031	−	0.979172i	$-0.434921\pi$
$193$	5.64119	0.406062	0.203031	+	0.979172i	$0.434921\pi$
$194$	11.4606	0.822824
$195$	0	0
$196$	−3.66552	−0.261823
$197$	2.39891	0.170915	0.0854575	−	0.996342i	$-0.472765\pi$
$197$	2.39891	0.170915	0.0854575	+	0.996342i	$0.472765\pi$
$198$	3.11364	0.221277
$199$	12.8446	0.910533	0.455267	−	0.890355i	$-0.349544\pi$
$199$	12.8446	0.910533	0.455267	+	0.890355i	$0.349544\pi$
$200$	0	0
$201$	−4.78784	−0.337708
$202$	−16.3816	−1.15261
$203$	22.4049	1.57252
$204$	−7.06772	−0.494839
$205$	0	0
$206$	35.3416	2.46236
$207$	−5.66477	−0.393729
$208$	21.6992	1.50457
$209$	0.223987	0.0154935
$210$	0	0
$211$	−8.91417	−0.613677	−0.306838	−	0.951762i	$-0.599271\pi$
$211$	−8.91417	−0.613677	−0.306838	+	0.951762i	$0.599271\pi$
$212$	−5.16508	−0.354739
$213$	−3.70118	−0.253600
$214$	31.1012	2.12603
$215$	0	0
$216$	2.44805	0.166569
$217$	−18.3483	−1.24556
$218$	−26.6850	−1.80734
$219$	3.48459	0.235467
$220$	0	0
$221$	18.8923	1.27084
$222$	−16.9093	−1.13488
$223$	13.9643	0.935118	0.467559	−	0.883962i	$-0.345134\pi$
$223$	13.9643	0.935118	0.467559	+	0.883962i	$0.345134\pi$
$224$	−16.9108	−1.12990
$225$	0	0
$226$	−4.34106	−0.288763
$227$	10.8998	0.723448	0.361724	−	0.932285i	$-0.382188\pi$
$227$	10.8998	0.723448	0.361724	+	0.932285i	$0.382188\pi$
$228$	−0.487325	−0.0322739
$229$	3.03714	0.200700	0.100350	−	0.994952i	$-0.468004\pi$
$229$	3.03714	0.200700	0.100350	+	0.994952i	$0.468004\pi$
$230$	0	0
$231$	−1.94830	−0.128189
$232$	−4.82769	−0.316953
$233$	−9.08021	−0.594864	−0.297432	−	0.954743i	$-0.596130\pi$
$233$	−9.08021	−0.594864	−0.297432	+	0.954743i	$0.596130\pi$
$234$	18.1080	1.18376
$235$	0	0
$236$	12.0404	0.783763
$237$	−8.58892	−0.557911
$238$	−16.5655	−1.07378
$239$	19.6463	1.27081	0.635406	−	0.772178i	$-0.280833\pi$
$239$	19.6463	1.27081	0.635406	+	0.772178i	$0.280833\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−19.9385	−1.28170
$243$	15.7705	1.01168
$244$	−1.56623	−0.100268
$245$	0	0
$246$	−14.3812	−0.916914
$247$	1.30264	0.0828852
$248$	3.95359	0.251053
$249$	−4.42454	−0.280394
$250$	0	0
$251$	13.1121	0.827630	0.413815	−	0.910361i	$-0.364196\pi$
$251$	13.1121	0.827630	0.413815	+	0.910361i	$0.364196\pi$
$252$	−7.41766	−0.467269
$253$	−2.49799	−0.157048
$254$	17.3743	1.09016
$255$	0	0
$256$	19.1879	1.19925
$257$	19.7916	1.23457	0.617283	−	0.786741i	$-0.288233\pi$
$257$	19.7916	1.23457	0.617283	+	0.786741i	$0.288233\pi$
$258$	9.45723	0.588781
$259$	−18.5152	−1.15048
$260$	0	0
$261$	−19.3035	−1.19486
$262$	18.2861	1.12972
$263$	17.2344	1.06272	0.531359	−	0.847147i	$-0.321682\pi$
$263$	17.2344	1.06272	0.531359	+	0.847147i	$0.321682\pi$
$264$	0.419808	0.0258374
$265$	0	0
$266$	−1.14220	−0.0700330
$267$	0.165269	0.0101143
$268$	−8.03824	−0.491013
$269$	27.8008	1.69505	0.847523	−	0.530759i	$-0.178093\pi$
$269$	27.8008	1.69505	0.847523	+	0.530759i	$0.178093\pi$
$270$	0	0
$271$	5.87605	0.356945	0.178472	−	0.983945i	$-0.442884\pi$
$271$	5.87605	0.356945	0.178472	+	0.983945i	$0.442884\pi$
$272$	17.1029	1.03701
$273$	−11.3307	−0.685767
$274$	−4.16979	−0.251906
$275$	0	0
$276$	5.43485	0.327139
$277$	−16.8511	−1.01249	−0.506244	−	0.862390i	$-0.668966\pi$
$277$	−16.8511	−1.01249	−0.506244	+	0.862390i	$0.668966\pi$
$278$	−17.6581	−1.05906
$279$	15.8084	0.946425
$280$	0	0
$281$	11.6236	0.693409	0.346704	−	0.937974i	$-0.387301\pi$
$281$	11.6236	0.693409	0.346704	+	0.937974i	$0.387301\pi$
$282$	−0.910934	−0.0542453
$283$	25.1649	1.49590	0.747949	−	0.663756i	$-0.231039\pi$
$283$	25.1649	1.49590	0.747949	+	0.663756i	$0.231039\pi$
$284$	−6.21385	−0.368724
$285$	0	0
$286$	7.98509	0.472168
$287$	−15.7470	−0.929519
$288$	14.5699	0.858539
$289$	−2.10943	−0.124084
$290$	0	0
$291$	6.17856	0.362194
$292$	5.85023	0.342359
$293$	−7.23794	−0.422845	−0.211423	−	0.977395i	$-0.567810\pi$
$293$	−7.23794	−0.422845	−0.211423	+	0.977395i	$0.567810\pi$
$294$	−4.22997	−0.246697
$295$	0	0
$296$	3.98956	0.231888
$297$	4.31645	0.250466
$298$	−31.6956	−1.83607
$299$	−14.5276	−0.840153
$300$	0	0
$301$	10.3554	0.596875
$302$	−12.7539	−0.733906
$303$	−8.83154	−0.507359
$304$	1.17926	0.0676350
$305$	0	0
$306$	14.2724	0.815897
$307$	−0.450426	−0.0257072	−0.0128536	−	0.999917i	$-0.504092\pi$
$307$	−0.450426	−0.0257072	−0.0128536	+	0.999917i	$0.504092\pi$
$308$	−3.27097	−0.186381
$309$	19.0531	1.08389
$310$	0	0
$311$	−7.67190	−0.435034	−0.217517	−	0.976057i	$-0.569796\pi$
$311$	−7.67190	−0.435034	−0.217517	+	0.976057i	$0.569796\pi$
$312$	2.44148	0.138222
$313$	−33.3880	−1.88720	−0.943602	−	0.331082i	$-0.892586\pi$
$313$	−33.3880	−1.88720	−0.943602	+	0.331082i	$0.892586\pi$
$314$	5.62769	0.317589
$315$	0	0
$316$	−14.4198	−0.811178
$317$	−16.3568	−0.918691	−0.459345	−	0.888258i	$-0.651916\pi$
$317$	−16.3568	−0.918691	−0.459345	+	0.888258i	$0.651916\pi$
$318$	−5.96043	−0.334245
$319$	−8.51226	−0.476595
$320$	0	0
$321$	16.7670	0.935844
$322$	12.7383	0.709879
$323$	1.02672	0.0571281
$324$	0.651729	0.0362072
$325$	0	0
$326$	−29.1405	−1.61394
$327$	−14.3862	−0.795559
$328$	3.39308	0.187352
$329$	−0.997447	−0.0549910
$330$	0	0
$331$	−2.14773	−0.118050	−0.0590249	−	0.998257i	$-0.518799\pi$
$331$	−2.14773	−0.118050	−0.0590249	+	0.998257i	$0.518799\pi$
$332$	−7.42829	−0.407681
$333$	15.9522	0.874177
$334$	−39.6369	−2.16884
$335$	0	0
$336$	−10.2575	−0.559592
$337$	16.1735	0.881025	0.440512	−	0.897747i	$-0.354797\pi$
$337$	16.1735	0.881025	0.440512	+	0.897747i	$0.354797\pi$
$338$	21.2526	1.15599
$339$	−2.34032	−0.127109
$340$	0	0
$341$	6.97103	0.377503
$342$	0.984093	0.0532136
$343$	−20.1421	−1.08757
$344$	−2.23132	−0.120305
$345$	0	0
$346$	21.2846	1.14427
$347$	−30.1784	−1.62006	−0.810030	−	0.586389i	$-0.800549\pi$
$347$	−30.1784	−1.62006	−0.810030	+	0.586389i	$0.800549\pi$
$348$	18.5200	0.992777
$349$	13.0279	0.697368	0.348684	−	0.937240i	$-0.386629\pi$
$349$	13.0279	0.697368	0.348684	+	0.937240i	$0.386629\pi$
$350$	0	0
$351$	25.1032	1.33991
$352$	6.42489	0.342448
$353$	−3.68729	−0.196255	−0.0981273	−	0.995174i	$-0.531285\pi$
$353$	−3.68729	−0.196255	−0.0981273	+	0.995174i	$0.531285\pi$
$354$	13.8945	0.738482
$355$	0	0
$356$	0.277468	0.0147057
$357$	−8.93066	−0.472660
$358$	21.3169	1.12663
$359$	11.0989	0.585779	0.292890	−	0.956146i	$-0.405383\pi$
$359$	11.0989	0.585779	0.292890	+	0.956146i	$0.405383\pi$
$360$	0	0
$361$	−18.9292	−0.996274
$362$	−14.6788	−0.771502
$363$	−10.7491	−0.564181
$364$	−19.0230	−0.997076
$365$	0	0
$366$	−1.80741	−0.0944750
$367$	26.8323	1.40063	0.700317	−	0.713832i	$-0.253042\pi$
$367$	26.8323	1.40063	0.700317	+	0.713832i	$0.253042\pi$
$368$	−13.1516	−0.685572
$369$	13.5672	0.706282
$370$	0	0
$371$	−6.52651	−0.338839
$372$	−15.1668	−0.786360
$373$	34.9560	1.80995	0.904976	−	0.425462i	$-0.139888\pi$
$373$	34.9560	1.80995	0.904976	+	0.425462i	$0.139888\pi$
$374$	6.29369	0.325439
$375$	0	0
$376$	0.214924	0.0110839
$377$	−49.5049	−2.54963
$378$	−22.0114	−1.13214
$379$	−15.4702	−0.794651	−0.397325	−	0.917678i	$-0.630062\pi$
$379$	−15.4702	−0.794651	−0.397325	+	0.917678i	$0.630062\pi$
$380$	0	0
$381$	9.36671	0.479871
$382$	−29.6461	−1.51682
$383$	1.21907	0.0622914	0.0311457	−	0.999515i	$-0.490084\pi$
$383$	1.21907	0.0622914	0.0311457	+	0.999515i	$0.490084\pi$
$384$	3.95916	0.202040
$385$	0	0
$386$	10.9293	0.556288
$387$	−8.92194	−0.453527
$388$	10.3731	0.526614
$389$	−11.3545	−0.575698	−0.287849	−	0.957676i	$-0.592940\pi$
$389$	−11.3545	−0.575698	−0.287849	+	0.957676i	$0.592940\pi$
$390$	0	0
$391$	−11.4504	−0.579070
$392$	0.998011	0.0504072
$393$	9.85827	0.497284
$394$	4.64767	0.234146
$395$	0	0
$396$	2.81818	0.141619
$397$	−28.4840	−1.42957	−0.714785	−	0.699344i	$-0.753476\pi$
$397$	−28.4840	−1.42957	−0.714785	+	0.699344i	$0.753476\pi$
$398$	24.8854	1.24739
$399$	−0.615776	−0.0308274
$400$	0	0
$401$	−27.2348	−1.36004	−0.680021	−	0.733193i	$-0.738029\pi$
$401$	−27.2348	−1.36004	−0.680021	+	0.733193i	$0.738029\pi$
$402$	−9.27602	−0.462646
$403$	40.5415	2.01952
$404$	−14.8271	−0.737678
$405$	0	0
$406$	43.4076	2.15428
$407$	7.03446	0.348685
$408$	1.92433	0.0952683
$409$	−7.38479	−0.365154	−0.182577	−	0.983192i	$-0.558444\pi$
$409$	−7.38479	−0.365154	−0.182577	+	0.983192i	$0.558444\pi$
$410$	0	0
$411$	−2.24798	−0.110885
$412$	31.9879	1.57593
$413$	15.2140	0.748634
$414$	−10.9750	−0.539392
$415$	0	0
$416$	37.3653	1.83198
$417$	−9.51970	−0.466182
$418$	0.433955	0.0212254
$419$	−14.3843	−0.702718	−0.351359	−	0.936241i	$-0.614280\pi$
$419$	−14.3843	−0.702718	−0.351359	+	0.936241i	$0.614280\pi$
$420$	0	0
$421$	−15.4142	−0.751241	−0.375620	−	0.926774i	$-0.622570\pi$
$421$	−15.4142	−0.751241	−0.375620	+	0.926774i	$0.622570\pi$
$422$	−17.2704	−0.840711
$423$	0.859374	0.0417842
$424$	1.40629	0.0682957
$425$	0	0
$426$	−7.17070	−0.347422
$427$	−1.97907	−0.0957738
$428$	28.1499	1.36068
$429$	4.30486	0.207841
$430$	0	0
$431$	−13.1058	−0.631284	−0.315642	−	0.948878i	$-0.602220\pi$
$431$	−13.1058	−0.631284	−0.315642	+	0.948878i	$0.602220\pi$
$432$	22.7254	1.09338
$433$	−18.2500	−0.877038	−0.438519	−	0.898722i	$-0.644497\pi$
$433$	−18.2500	−0.877038	−0.438519	+	0.898722i	$0.644497\pi$
$434$	−35.5482	−1.70637
$435$	0	0
$436$	−24.1528	−1.15671
$437$	−0.789513	−0.0377675
$438$	6.75109	0.322579
$439$	20.7857	0.992045	0.496023	−	0.868310i	$-0.334793\pi$
$439$	20.7857	0.992045	0.496023	+	0.868310i	$0.334793\pi$
$440$	0	0
$441$	3.99055	0.190026
$442$	36.6023	1.74099
$443$	−2.63796	−0.125333	−0.0626667	−	0.998035i	$-0.519961\pi$
$443$	−2.63796	−0.125333	−0.0626667	+	0.998035i	$0.519961\pi$
$444$	−15.3048	−0.726332
$445$	0	0
$446$	27.0546	1.28107
$447$	−17.0875	−0.808209
$448$	−13.1219	−0.619953
$449$	11.0962	0.523664	0.261832	−	0.965113i	$-0.415673\pi$
$449$	11.0962	0.523664	0.261832	+	0.965113i	$0.415673\pi$
$450$	0	0
$451$	5.98274	0.281716
$452$	−3.92913	−0.184811
$453$	−6.87580	−0.323053
$454$	21.1175	0.991093
$455$	0	0
$456$	0.132684	0.00621349
$457$	10.2432	0.479158	0.239579	−	0.970877i	$-0.422991\pi$
$457$	10.2432	0.479158	0.239579	+	0.970877i	$0.422991\pi$
$458$	5.88419	0.274950
$459$	19.7859	0.923525
$460$	0	0
$461$	−33.5653	−1.56329	−0.781646	−	0.623722i	$-0.785620\pi$
$461$	−33.5653	−1.56329	−0.781646	+	0.623722i	$0.785620\pi$
$462$	−3.77466	−0.175613
$463$	36.1736	1.68113	0.840566	−	0.541709i	$-0.182223\pi$
$463$	36.1736	1.68113	0.840566	+	0.541709i	$0.182223\pi$
$464$	−44.8158	−2.08052
$465$	0	0
$466$	−17.5921	−0.814939
$467$	25.2859	1.17009	0.585046	−	0.811000i	$-0.301076\pi$
$467$	25.2859	1.17009	0.585046	+	0.811000i	$0.301076\pi$
$468$	16.3897	0.757614
$469$	−10.1570	−0.469006
$470$	0	0
$471$	3.03396	0.139797
$472$	−3.27823	−0.150893
$473$	−3.93431	−0.180900
$474$	−16.6403	−0.764314
$475$	0	0
$476$	−14.9935	−0.687228
$477$	5.62306	0.257462
$478$	38.0630	1.74096
$479$	−6.04506	−0.276206	−0.138103	−	0.990418i	$-0.544100\pi$
$479$	−6.04506	−0.276206	−0.138103	+	0.990418i	$0.544100\pi$
$480$	0	0
$481$	40.9104	1.86535
$482$	−1.93741	−0.0882467
$483$	6.86739	0.312477
$484$	−18.0465	−0.820296
$485$	0	0
$486$	30.5539	1.38595
$487$	−22.1290	−1.00276	−0.501381	−	0.865227i	$-0.667175\pi$
$487$	−22.1290	−1.00276	−0.501381	+	0.865227i	$0.667175\pi$
$488$	0.426438	0.0193039
$489$	−15.7100	−0.710430
$490$	0	0
$491$	−36.7444	−1.65825	−0.829126	−	0.559062i	$-0.811162\pi$
$491$	−36.7444	−1.65825	−0.829126	+	0.559062i	$0.811162\pi$
$492$	−13.0166	−0.586832
$493$	−39.0187	−1.75732
$494$	2.52376	0.113549
$495$	0	0
$496$	36.7014	1.64794
$497$	−7.85172	−0.352198
$498$	−8.57216	−0.384128
$499$	−18.8161	−0.842326	−0.421163	−	0.906985i	$-0.638378\pi$
$499$	−18.8161	−0.842326	−0.421163	+	0.906985i	$0.638378\pi$
$500$	0	0
$501$	−21.3688	−0.954686
$502$	25.4036	1.13382
$503$	−7.78708	−0.347209	−0.173604	−	0.984815i	$-0.555541\pi$
$503$	−7.78708	−0.347209	−0.173604	+	0.984815i	$0.555541\pi$
$504$	2.01961	0.0899604
$505$	0	0
$506$	−4.83964	−0.215148
$507$	11.4575	0.508847
$508$	15.7256	0.697712
$509$	−23.8774	−1.05835	−0.529174	−	0.848513i	$-0.677498\pi$
$509$	−23.8774	−1.05835	−0.529174	+	0.848513i	$0.677498\pi$
$510$	0	0
$511$	7.39225	0.327014
$512$	29.5938	1.30788
$513$	1.36425	0.0602332
$514$	38.3445	1.69130
$515$	0	0
$516$	8.55981	0.376825
$517$	0.378958	0.0166666
$518$	−35.8717	−1.57611
$519$	11.4748	0.503687
$520$	0	0
$521$	9.57588	0.419527	0.209763	−	0.977752i	$-0.432731\pi$
$521$	9.57588	0.419527	0.209763	+	0.977752i	$0.432731\pi$
$522$	−37.3988	−1.63690
$523$	−2.10109	−0.0918742	−0.0459371	−	0.998944i	$-0.514627\pi$
$523$	−2.10109	−0.0918742	−0.0459371	+	0.998944i	$0.514627\pi$
$524$	16.5509	0.723030
$525$	0	0
$526$	33.3901	1.45588
$527$	31.9540	1.39194
$528$	3.89710	0.169600
$529$	−14.1950	−0.617175
$530$	0	0
$531$	−13.1080	−0.568839
$532$	−1.03382	−0.0448217
$533$	34.7939	1.50709
$534$	0.320194	0.0138562
$535$	0	0
$536$	2.18857	0.0945317
$537$	11.4922	0.495925
$538$	53.8616	2.32214
$539$	1.75971	0.0757961
$540$	0	0
$541$	−7.37105	−0.316906	−0.158453	−	0.987366i	$-0.550651\pi$
$541$	−7.37105	−0.316906	−0.158453	+	0.987366i	$0.550651\pi$
$542$	11.3843	0.488999
$543$	−7.91354	−0.339602
$544$	29.4506	1.26268
$545$	0	0
$546$	−21.9523	−0.939472
$547$	−24.5743	−1.05072	−0.525362	−	0.850879i	$-0.676070\pi$
$547$	−24.5743	−1.05072	−0.525362	+	0.850879i	$0.676070\pi$
$548$	−3.77411	−0.161222
$549$	1.70511	0.0727724
$550$	0	0
$551$	−2.69038	−0.114614
$552$	−1.47974	−0.0629821
$553$	−18.2206	−0.774821
$554$	−32.6476	−1.38706
$555$	0	0
$556$	−15.9825	−0.677808
$557$	29.6935	1.25815	0.629076	−	0.777344i	$-0.283433\pi$
$557$	29.6935	1.25815	0.629076	+	0.777344i	$0.283433\pi$
$558$	30.6274	1.29656
$559$	−22.8808	−0.967754
$560$	0	0
$561$	3.39301	0.143253
$562$	22.5198	0.949940
$563$	28.6794	1.20869	0.604347	−	0.796721i	$-0.293434\pi$
$563$	28.6794	1.20869	0.604347	+	0.796721i	$0.293434\pi$
$564$	−0.824493	−0.0347174
$565$	0	0
$566$	48.7548	2.04932
$567$	0.823515	0.0345844
$568$	1.69184	0.0709881
$569$	−27.9411	−1.17135	−0.585675	−	0.810546i	$-0.699171\pi$
$569$	−27.9411	−1.17135	−0.585675	+	0.810546i	$0.699171\pi$
$570$	0	0
$571$	8.92815	0.373631	0.186816	−	0.982395i	$-0.440183\pi$
$571$	8.92815	0.373631	0.186816	+	0.982395i	$0.440183\pi$
$572$	7.22737	0.302191
$573$	−15.9826	−0.667681
$574$	−30.5085	−1.27340
$575$	0	0
$576$	11.3055	0.471063
$577$	25.0287	1.04196	0.520979	−	0.853569i	$-0.325567\pi$
$577$	25.0287	1.04196	0.520979	+	0.853569i	$0.325567\pi$
$578$	−4.08684	−0.169990
$579$	5.89213	0.244869
$580$	0	0
$581$	−9.38627	−0.389408
$582$	11.9704	0.496190
$583$	2.47960	0.102695
$584$	−1.59284	−0.0659121
$585$	0	0
$586$	−14.0229	−0.579280
$587$	−8.40095	−0.346744	−0.173372	−	0.984856i	$-0.555466\pi$
$587$	−8.40095	−0.346744	−0.173372	+	0.984856i	$0.555466\pi$
$588$	−3.82858	−0.157888
$589$	2.20326	0.0907836
$590$	0	0
$591$	2.50562	0.103067
$592$	37.0353	1.52214
$593$	−21.9331	−0.900683	−0.450342	−	0.892856i	$-0.648698\pi$
$593$	−21.9331	−0.900683	−0.450342	+	0.892856i	$0.648698\pi$
$594$	8.36275	0.343128
$595$	0	0
$596$	−28.6879	−1.17510
$597$	13.4160	0.549081
$598$	−28.1460	−1.15097
$599$	34.3385	1.40303	0.701517	−	0.712652i	$-0.252506\pi$
$599$	34.3385	1.40303	0.701517	+	0.712652i	$0.252506\pi$
$600$	0	0
$601$	5.20018	0.212120	0.106060	−	0.994360i	$-0.466177\pi$
$601$	5.20018	0.212120	0.106060	+	0.994360i	$0.466177\pi$
$602$	20.0627	0.817694
$603$	8.75099	0.356368
$604$	−11.5437	−0.469706
$605$	0	0
$606$	−17.1103	−0.695060
$607$	30.1142	1.22230	0.611150	−	0.791515i	$-0.290707\pi$
$607$	30.1142	1.22230	0.611150	+	0.791515i	$0.290707\pi$
$608$	2.03064	0.0823534
$609$	23.4016	0.948280
$610$	0	0
$611$	2.20391	0.0891606
$612$	12.9180	0.522181
$613$	−34.7505	−1.40356	−0.701780	−	0.712394i	$-0.747611\pi$
$613$	−34.7505	−1.40356	−0.701780	+	0.712394i	$0.747611\pi$
$614$	−0.872662	−0.0352178
$615$	0	0
$616$	0.890585	0.0358827
$617$	−21.4159	−0.862173	−0.431087	−	0.902311i	$-0.641870\pi$
$617$	−21.4159	−0.862173	−0.431087	+	0.902311i	$0.641870\pi$
$618$	36.9137	1.48489
$619$	−19.7088	−0.792162	−0.396081	−	0.918216i	$-0.629630\pi$
$619$	−19.7088	−0.792162	−0.396081	+	0.918216i	$0.629630\pi$
$620$	0	0
$621$	−15.2147	−0.610544
$622$	−14.8636	−0.595978
$623$	0.350603	0.0140466
$624$	22.6644	0.907303
$625$	0	0
$626$	−64.6864	−2.58539
$627$	0.233951	0.00934309
$628$	5.09367	0.203259
$629$	32.2447	1.28568
$630$	0	0
$631$	27.0539	1.07700	0.538499	−	0.842626i	$-0.318992\pi$
$631$	27.0539	1.07700	0.538499	+	0.842626i	$0.318992\pi$
$632$	3.92608	0.156171
$633$	−9.31069	−0.370067
$634$	−31.6899	−1.25857
$635$	0	0
$636$	−5.39483	−0.213919
$637$	10.2340	0.405485
$638$	−16.4918	−0.652915
$639$	6.76483	0.267613
$640$	0	0
$641$	−31.9381	−1.26148	−0.630739	−	0.775995i	$-0.717248\pi$
$641$	−31.9381	−1.26148	−0.630739	+	0.775995i	$0.717248\pi$
$642$	32.4846	1.28207
$643$	8.97974	0.354126	0.177063	−	0.984199i	$-0.443340\pi$
$643$	8.97974	0.354126	0.177063	+	0.984199i	$0.443340\pi$
$644$	11.5296	0.454328
$645$	0	0
$646$	1.98918	0.0782630
$647$	46.1104	1.81279	0.906393	−	0.422435i	$-0.138825\pi$
$647$	46.1104	1.81279	0.906393	+	0.422435i	$0.138825\pi$
$648$	−0.177446	−0.00697074
$649$	−5.78024	−0.226894
$650$	0	0
$651$	−19.1645	−0.751116
$652$	−26.3753	−1.03294
$653$	−37.8299	−1.48040	−0.740199	−	0.672388i	$-0.765269\pi$
$653$	−37.8299	−1.48040	−0.740199	+	0.672388i	$0.765269\pi$
$654$	−27.8720	−1.08988
$655$	0	0
$656$	31.4982	1.22980
$657$	−6.36897	−0.248477
$658$	−1.93247	−0.0753354
$659$	−30.8367	−1.20123	−0.600613	−	0.799540i	$-0.705077\pi$
$659$	−30.8367	−1.20123	−0.600613	+	0.799540i	$0.705077\pi$
$660$	0	0
$661$	−33.8029	−1.31478	−0.657390	−	0.753551i	$-0.728339\pi$
$661$	−33.8029	−1.31478	−0.657390	+	0.753551i	$0.728339\pi$
$662$	−4.16103	−0.161723
$663$	19.7327	0.766356
$664$	2.02250	0.0784882
$665$	0	0
$666$	30.9061	1.19759
$667$	30.0042	1.16177
$668$	−35.8757	−1.38807
$669$	14.5855	0.563906
$670$	0	0
$671$	0.751903	0.0290269
$672$	−17.6630	−0.681367
$673$	−46.0122	−1.77364	−0.886819	−	0.462116i	$-0.847090\pi$
$673$	−46.0122	−1.77364	−0.886819	+	0.462116i	$0.847090\pi$
$674$	31.3347	1.20697
$675$	0	0
$676$	19.2359	0.739842
$677$	−37.8407	−1.45433	−0.727167	−	0.686460i	$-0.759164\pi$
$677$	−37.8407	−1.45433	−0.727167	+	0.686460i	$0.759164\pi$
$678$	−4.53417	−0.174134
$679$	13.1073	0.503011
$680$	0	0
$681$	11.3847	0.436263
$682$	13.5058	0.517162
$683$	9.93679	0.380221	0.190110	−	0.981763i	$-0.439115\pi$
$683$	9.93679	0.380221	0.190110	+	0.981763i	$0.439115\pi$
$684$	0.890710	0.0340571
$685$	0	0
$686$	−39.0236	−1.48993
$687$	3.17224	0.121029
$688$	−20.7135	−0.789695
$689$	14.4206	0.549383
$690$	0	0
$691$	−40.2203	−1.53005	−0.765026	−	0.643999i	$-0.777274\pi$
$691$	−40.2203	−1.53005	−0.765026	+	0.643999i	$0.777274\pi$
$692$	19.2649	0.732340
$693$	3.56100	0.135271
$694$	−58.4679	−2.21941
$695$	0	0
$696$	−5.04244	−0.191133
$697$	27.4239	1.03875
$698$	25.2404	0.955364
$699$	−9.48412	−0.358722
$700$	0	0
$701$	−19.9044	−0.751778	−0.375889	−	0.926665i	$-0.622663\pi$
$701$	−19.9044	−0.751778	−0.375889	+	0.926665i	$0.622663\pi$
$702$	48.6353	1.83562
$703$	2.22330	0.0838534
$704$	4.98539	0.187894
$705$	0	0
$706$	−7.14380	−0.268860
$707$	−18.7353	−0.704615
$708$	12.5760	0.472634
$709$	6.54552	0.245822	0.122911	−	0.992418i	$-0.460777\pi$
$709$	6.54552	0.245822	0.122911	+	0.992418i	$0.460777\pi$
$710$	0	0
$711$	15.6984	0.588737
$712$	−0.0755460	−0.00283121
$713$	−24.5716	−0.920214
$714$	−17.3024	−0.647525
$715$	0	0
$716$	19.2941	0.721053
$717$	20.5202	0.766341
$718$	21.5032	0.802492
$719$	16.1685	0.602983	0.301492	−	0.953469i	$-0.402515\pi$
$719$	16.1685	0.602983	0.301492	+	0.953469i	$0.402515\pi$
$720$	0	0
$721$	40.4194	1.50530
$722$	−36.6737	−1.36485
$723$	−1.04448	−0.0388447
$724$	−13.2859	−0.493767
$725$	0	0
$726$	−20.8254	−0.772904
$727$	28.7008	1.06445	0.532227	−	0.846601i	$-0.321355\pi$
$727$	28.7008	1.06445	0.532227	+	0.846601i	$0.321355\pi$
$728$	5.17938	0.191961
$729$	15.3570	0.568778
$730$	0	0
$731$	−18.0342	−0.667018
$732$	−1.63590	−0.0604647
$733$	−45.8930	−1.69509	−0.847547	−	0.530720i	$-0.821922\pi$
$733$	−45.8930	−1.69509	−0.847547	+	0.530720i	$0.821922\pi$
$734$	51.9852	1.91881
$735$	0	0
$736$	−22.6465	−0.834762
$737$	3.85892	0.142145
$738$	26.2853	0.967576
$739$	−2.95907	−0.108851	−0.0544256	−	0.998518i	$-0.517333\pi$
$739$	−2.95907	−0.108851	−0.0544256	+	0.998518i	$0.517333\pi$
$740$	0	0
$741$	1.36059	0.0499825
$742$	−12.6445	−0.464196
$743$	−37.7720	−1.38572	−0.692861	−	0.721071i	$-0.743650\pi$
$743$	−37.7720	−1.38572	−0.692861	+	0.721071i	$0.743650\pi$
$744$	4.12945	0.151393
$745$	0	0
$746$	67.7242	2.47956
$747$	8.08696	0.295886
$748$	5.69647	0.208283
$749$	35.5698	1.29969
$750$	0	0
$751$	32.8614	1.19913	0.599564	−	0.800326i	$-0.295340\pi$
$751$	32.8614	1.19913	0.599564	+	0.800326i	$0.295340\pi$
$752$	1.99516	0.0727558
$753$	13.6954	0.499088
$754$	−95.9113	−3.49288
$755$	0	0
$756$	−19.9227	−0.724581
$757$	13.4112	0.487437	0.243719	−	0.969846i	$-0.421633\pi$
$757$	13.4112	0.487437	0.243719	+	0.969846i	$0.421633\pi$
$758$	−29.9722	−1.08864
$759$	−2.60911	−0.0947048
$760$	0	0
$761$	−32.7090	−1.18570	−0.592849	−	0.805313i	$-0.701997\pi$
$761$	−32.7090	−1.18570	−0.592849	+	0.805313i	$0.701997\pi$
$762$	18.1472	0.657403
$763$	−30.5191	−1.10486
$764$	−26.8329	−0.970779
$765$	0	0
$766$	2.36184	0.0853366
$767$	−33.6162	−1.21381
$768$	20.0415	0.723184
$769$	−21.5663	−0.777702	−0.388851	−	0.921301i	$-0.627128\pi$
$769$	−21.5663	−0.777702	−0.388851	+	0.921301i	$0.627128\pi$
$770$	0	0
$771$	20.6720	0.744484
$772$	9.89221	0.356028
$773$	27.3205	0.982650	0.491325	−	0.870976i	$-0.336513\pi$
$773$	27.3205	0.982650	0.491325	+	0.870976i	$0.336513\pi$
$774$	−17.2855	−0.621313
$775$	0	0
$776$	−2.82428	−0.101386
$777$	−19.3389	−0.693778
$778$	−21.9984	−0.788682
$779$	1.89090	0.0677485
$780$	0	0
$781$	2.98309	0.106743
$782$	−22.1841	−0.793301
$783$	−51.8462	−1.85283
$784$	9.26461	0.330879
$785$	0	0
$786$	19.0995	0.681258
$787$	−42.5565	−1.51698	−0.758488	−	0.651688i	$-0.774061\pi$
$787$	−42.5565	−1.51698	−0.758488	+	0.651688i	$0.774061\pi$
$788$	4.20664	0.149855
$789$	18.0010	0.640853
$790$	0	0
$791$	−4.96478	−0.176527
$792$	−0.767304	−0.0272650
$793$	4.37285	0.155284
$794$	−55.1852	−1.95845
$795$	0	0
$796$	22.5239	0.798340
$797$	−4.42037	−0.156578	−0.0782888	−	0.996931i	$-0.524946\pi$
$797$	−4.42037	−0.156578	−0.0782888	+	0.996931i	$0.524946\pi$
$798$	−1.19301	−0.0422322
$799$	1.73708	0.0614534
$800$	0	0
$801$	−0.302071	−0.0106731
$802$	−52.7650	−1.86320
$803$	−2.80852	−0.0991106
$804$	−8.39580	−0.296097
$805$	0	0
$806$	78.5456	2.76665
$807$	29.0375	1.02217
$808$	4.03698	0.142021
$809$	37.6212	1.32269	0.661345	−	0.750082i	$-0.269986\pi$
$809$	37.6212	1.32269	0.661345	+	0.750082i	$0.269986\pi$
$810$	0	0
$811$	51.2039	1.79801	0.899006	−	0.437937i	$-0.144291\pi$
$811$	51.2039	1.79801	0.899006	+	0.437937i	$0.144291\pi$
$812$	39.2886	1.37876
$813$	6.13744	0.215249
$814$	13.6286	0.477684
$815$	0	0
$816$	17.8636	0.625353
$817$	−1.24347	−0.0435036
$818$	−14.3074	−0.500246
$819$	20.7098	0.723658
$820$	0	0
$821$	4.27142	0.149074	0.0745368	−	0.997218i	$-0.476252\pi$
$821$	4.27142	0.149074	0.0745368	+	0.997218i	$0.476252\pi$
$822$	−4.35527	−0.151908
$823$	34.2678	1.19450	0.597250	−	0.802056i	$-0.296260\pi$
$823$	34.2678	1.19450	0.597250	+	0.802056i	$0.296260\pi$
$824$	−8.70934	−0.303404
$825$	0	0
$826$	29.4759	1.02560
$827$	7.16083	0.249007	0.124503	−	0.992219i	$-0.460266\pi$
$827$	7.16083	0.249007	0.124503	+	0.992219i	$0.460266\pi$
$828$	−9.93355	−0.345215
$829$	44.4222	1.54285	0.771423	−	0.636322i	$-0.219545\pi$
$829$	44.4222	1.54285	0.771423	+	0.636322i	$0.219545\pi$
$830$	0	0
$831$	−17.6007	−0.610563
$832$	28.9936	1.00517
$833$	8.06621	0.279478
$834$	−18.4436	−0.638649
$835$	0	0
$836$	0.392776	0.0135844
$837$	42.4589	1.46759
$838$	−27.8683	−0.962694
$839$	6.59204	0.227583	0.113791	−	0.993505i	$-0.463700\pi$
$839$	6.59204	0.227583	0.113791	+	0.993505i	$0.463700\pi$
$840$	0	0
$841$	73.2434	2.52563
$842$	−29.8636	−1.02917
$843$	12.1407	0.418148
$844$	−15.6316	−0.538061
$845$	0	0
$846$	1.66496	0.0572426
$847$	−22.8033	−0.783530
$848$	13.0547	0.448301
$849$	26.2843	0.902075
$850$	0	0
$851$	−24.7952	−0.849967
$852$	−6.49026	−0.222353
$853$	33.3879	1.14318	0.571591	−	0.820539i	$-0.306327\pi$
$853$	33.3879	1.14318	0.571591	+	0.820539i	$0.306327\pi$
$854$	−3.83427	−0.131206
$855$	0	0
$856$	−7.66436	−0.261963
$857$	27.3941	0.935765	0.467882	−	0.883791i	$-0.345017\pi$
$857$	27.3941	0.935765	0.467882	+	0.883791i	$0.345017\pi$
$858$	8.34029	0.284733
$859$	38.6261	1.31790	0.658952	−	0.752185i	$-0.271000\pi$
$859$	38.6261	1.31790	0.658952	+	0.752185i	$0.271000\pi$
$860$	0	0
$861$	−16.4475	−0.560530
$862$	−25.3913	−0.864832
$863$	0.684874	0.0233134	0.0116567	−	0.999932i	$-0.496289\pi$
$863$	0.684874	0.0233134	0.0116567	+	0.999932i	$0.496289\pi$
$864$	39.1325	1.33131
$865$	0	0
$866$	−35.3577	−1.20150
$867$	−2.20326	−0.0748268
$868$	−32.1750	−1.09209
$869$	6.92253	0.234831
$870$	0	0
$871$	22.4424	0.760431
$872$	6.57607	0.222694
$873$	−11.2929	−0.382206
$874$	−1.52961	−0.0517399
$875$	0	0
$876$	6.11046	0.206453
$877$	7.13189	0.240827	0.120413	−	0.992724i	$-0.461578\pi$
$877$	7.13189	0.240827	0.120413	+	0.992724i	$0.461578\pi$
$878$	40.2704	1.35906
$879$	−7.55991	−0.254989
$880$	0	0
$881$	−42.9339	−1.44648	−0.723240	−	0.690596i	$-0.757348\pi$
$881$	−42.9339	−1.44648	−0.723240	+	0.690596i	$0.757348\pi$
$882$	7.73133	0.260328
$883$	53.8191	1.81116	0.905578	−	0.424179i	$-0.139437\pi$
$883$	53.8191	1.81116	0.905578	+	0.424179i	$0.139437\pi$
$884$	33.1290	1.11425
$885$	0	0
$886$	−5.11083	−0.171702
$887$	45.3145	1.52151	0.760756	−	0.649039i	$-0.224829\pi$
$887$	45.3145	1.52151	0.760756	+	0.649039i	$0.224829\pi$
$888$	4.16702	0.139836
$889$	19.8706	0.666440
$890$	0	0
$891$	−0.312876	−0.0104817
$892$	24.4873	0.819896
$893$	0.119773	0.00400805
$894$	−33.1055	−1.10721
$895$	0	0
$896$	8.39902	0.280592
$897$	−15.1738	−0.506640
$898$	21.4980	0.717398
$899$	−83.7312	−2.79259
$900$	0	0
$901$	11.3661	0.378659
$902$	11.5910	0.385939
$903$	10.8160	0.359935
$904$	1.06978	0.0355804
$905$	0	0
$906$	−13.3213	−0.442569
$907$	16.0562	0.533136	0.266568	−	0.963816i	$-0.414110\pi$
$907$	16.0562	0.533136	0.266568	+	0.963816i	$0.414110\pi$
$908$	19.1136	0.634307
$909$	16.1419	0.535392
$910$	0	0
$911$	−47.4536	−1.57221	−0.786104	−	0.618094i	$-0.787905\pi$
$911$	−47.4536	−1.57221	−0.786104	+	0.618094i	$0.787905\pi$
$912$	1.23171	0.0407861
$913$	3.56611	0.118021
$914$	19.8453	0.656425
$915$	0	0
$916$	5.32583	0.175970
$917$	20.9135	0.690623
$918$	38.3334	1.26519
$919$	30.6116	1.00978	0.504891	−	0.863183i	$-0.331533\pi$
$919$	30.6116	1.00978	0.504891	+	0.863183i	$0.331533\pi$
$920$	0	0
$921$	−0.470463	−0.0155023
$922$	−65.0299	−2.14164
$923$	17.3488	0.571042
$924$	−3.41647	−0.112394
$925$	0	0
$926$	70.0833	2.30308
$927$	−34.8243	−1.14378
$928$	−77.1712	−2.53327
$929$	−38.5536	−1.26490	−0.632451	−	0.774600i	$-0.717951\pi$
$929$	−38.5536	−1.26490	−0.632451	+	0.774600i	$0.717951\pi$
$930$	0	0
$931$	0.556172	0.0182278
$932$	−15.9227	−0.521567
$933$	−8.01317	−0.262339
$934$	48.9893	1.60298
$935$	0	0
$936$	−4.46242	−0.145859
$937$	51.2732	1.67502	0.837511	−	0.546421i	$-0.184010\pi$
$937$	51.2732	1.67502	0.837511	+	0.546421i	$0.184010\pi$
$938$	−19.6783	−0.642518
$939$	−34.8732	−1.13805
$940$	0	0
$941$	−14.5933	−0.475727	−0.237864	−	0.971299i	$-0.576447\pi$
$941$	−14.5933	−0.475727	−0.237864	+	0.971299i	$0.576447\pi$
$942$	5.87803	0.191516
$943$	−21.0881	−0.686722
$944$	−30.4321	−0.990480
$945$	0	0
$946$	−7.62237	−0.247825
$947$	12.0362	0.391124	0.195562	−	0.980691i	$-0.437347\pi$
$947$	12.0362	0.391124	0.195562	+	0.980691i	$0.437347\pi$
$948$	−15.0612	−0.489167
$949$	−16.3335	−0.530209
$950$	0	0
$951$	−17.0844	−0.554000
$952$	4.08229	0.132308
$953$	60.5333	1.96087	0.980433	−	0.196854i	$-0.0630726\pi$
$953$	60.5333	1.96087	0.980433	+	0.196854i	$0.0630726\pi$
$954$	10.8942	0.352713
$955$	0	0
$956$	34.4511	1.11423
$957$	−8.89091	−0.287402
$958$	−11.7118	−0.378390
$959$	−4.76890	−0.153996
$960$	0	0
$961$	37.5708	1.21196
$962$	79.2602	2.55545
$963$	−30.6459	−0.987552
$964$	−1.75357	−0.0564786
$965$	0	0
$966$	13.3050	0.428080
$967$	−8.36402	−0.268969	−0.134484	−	0.990916i	$-0.542938\pi$
$967$	−8.36402	−0.268969	−0.134484	+	0.990916i	$0.542938\pi$
$968$	4.91352	0.157926
$969$	1.07239	0.0344501
$970$	0	0
$971$	11.6781	0.374768	0.187384	−	0.982287i	$-0.439999\pi$
$971$	11.6781	0.374768	0.187384	+	0.982287i	$0.439999\pi$
$972$	27.6546	0.887020
$973$	−20.1952	−0.647429
$974$	−42.8731	−1.37374
$975$	0	0
$976$	3.95865	0.126713
$977$	−4.65204	−0.148832	−0.0744160	−	0.997227i	$-0.523709\pi$
$977$	−4.65204	−0.148832	−0.0744160	+	0.997227i	$0.523709\pi$
$978$	−30.4367	−0.973259
$979$	−0.133204	−0.00425722
$980$	0	0
$981$	26.2944	0.839516
$982$	−71.1891	−2.27173
$983$	−8.10338	−0.258458	−0.129229	−	0.991615i	$-0.541250\pi$
$983$	−8.10338	−0.258458	−0.129229	+	0.991615i	$0.541250\pi$
$984$	3.54402	0.112979
$985$	0	0
$986$	−75.5954	−2.40745
$987$	−1.04182	−0.0331614
$988$	2.28427	0.0726724
$989$	13.8677	0.440967
$990$	0	0
$991$	−25.0488	−0.795700	−0.397850	−	0.917450i	$-0.630244\pi$
$991$	−25.0488	−0.795700	−0.397850	+	0.917450i	$0.630244\pi$
$992$	63.1986	2.00656
$993$	−2.24326	−0.0711878
$994$	−15.2120	−0.482496
$995$	0	0
$996$	−7.75872	−0.245845
$997$	8.44459	0.267443	0.133721	−	0.991019i	$-0.457307\pi$
$997$	8.44459	0.267443	0.133721	+	0.991019i	$0.457307\pi$
$998$	−36.4546	−1.15395
$999$	42.8452	1.35556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.i.1.13		15
5.4	even	2		1205.2.a.c.1.3	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.3	✓	15	5.4	even	2
6025.2.a.i.1.13		15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.93741 q^{2} +1.04448 q^{3} +1.75357 q^{4} +2.02359 q^{6} +2.21578 q^{7} -0.477443 q^{8} -1.90906 q^{9} +O(q^{10})\)	\(q+1.93741 q^{2} +1.04448 q^{3} +1.75357 q^{4} +2.02359 q^{6} +2.21578 q^{7} -0.477443 q^{8} -1.90906 q^{9} -0.841836 q^{11} +1.83157 q^{12} -4.89587 q^{13} +4.29288 q^{14} -4.43214 q^{16} -3.85883 q^{17} -3.69863 q^{18} -0.266070 q^{19} +2.31434 q^{21} -1.63098 q^{22} +2.96732 q^{23} -0.498681 q^{24} -9.48533 q^{26} -5.12742 q^{27} +3.88552 q^{28} +10.1115 q^{29} -8.28075 q^{31} -7.63199 q^{32} -0.879283 q^{33} -7.47614 q^{34} -3.34766 q^{36} -8.35609 q^{37} -0.515487 q^{38} -5.11366 q^{39} -7.10678 q^{41} +4.48384 q^{42} +4.67348 q^{43} -1.47622 q^{44} +5.74892 q^{46} -0.450157 q^{47} -4.62929 q^{48} -2.09032 q^{49} -4.03048 q^{51} -8.58524 q^{52} -2.94547 q^{53} -9.93394 q^{54} -1.05791 q^{56} -0.277905 q^{57} +19.5902 q^{58} +6.86623 q^{59} -0.893170 q^{61} -16.0432 q^{62} -4.23004 q^{63} -5.92204 q^{64} -1.70353 q^{66} -4.58394 q^{67} -6.76672 q^{68} +3.09931 q^{69} -3.54355 q^{71} +0.911465 q^{72} +3.33619 q^{73} -16.1892 q^{74} -0.466571 q^{76} -1.86532 q^{77} -9.90726 q^{78} -8.22313 q^{79} +0.371659 q^{81} -13.7688 q^{82} -4.23611 q^{83} +4.05835 q^{84} +9.05446 q^{86} +10.5613 q^{87} +0.401929 q^{88} +0.158230 q^{89} -10.8482 q^{91} +5.20339 q^{92} -8.64910 q^{93} -0.872139 q^{94} -7.97148 q^{96} +5.91542 q^{97} -4.04982 q^{98} +1.60711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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