LMFDB - Embedded newform 3750.2.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3750,2,Mod(1,3750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3750, 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("3750.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3750 = 2 \cdot 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3750.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:	$29.9439007580$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.32625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 19x^{2} + 4x + 76 $ x^4 - x^3 - 19x^2 + 4x + 76
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.92807$ of defining polynomial
Character	$\chi$	$=$	3750.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.92807 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.92807 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.190355 q^{11} -1.00000 q^{12} -0.310033 q^{13} -2.92807 q^{14} +1.00000 q^{16} -6.04775 q^{17} +1.00000 q^{18} +3.23607 q^{19} +2.92807 q^{21} +0.190355 q^{22} -4.47214 q^{23} -1.00000 q^{24} -0.310033 q^{26} -1.00000 q^{27} -2.92807 q^{28} +6.81168 q^{29} -1.69200 q^{31} +1.00000 q^{32} -0.190355 q^{33} -6.04775 q^{34} +1.00000 q^{36} +9.75595 q^{37} +3.23607 q^{38} +0.310033 q^{39} +5.07397 q^{41} +2.92807 q^{42} +10.2394 q^{43} +0.190355 q^{44} -4.47214 q^{46} +10.7115 q^{47} -1.00000 q^{48} +1.57358 q^{49} +6.04775 q^{51} -0.310033 q^{52} -9.97175 q^{53} -1.00000 q^{54} -2.92807 q^{56} -3.23607 q^{57} +6.81168 q^{58} +7.42642 q^{59} -5.54610 q^{61} -1.69200 q^{62} -2.92807 q^{63} +1.00000 q^{64} -0.190355 q^{66} +15.0922 q^{67} -6.04775 q^{68} +4.47214 q^{69} +6.85536 q^{71} +1.00000 q^{72} -11.6375 q^{73} +9.75595 q^{74} +3.23607 q^{76} -0.557372 q^{77} +0.310033 q^{78} +1.57029 q^{79} +1.00000 q^{81} +5.07397 q^{82} -13.0195 q^{83} +2.92807 q^{84} +10.2394 q^{86} -6.81168 q^{87} +0.190355 q^{88} -9.28381 q^{89} +0.907798 q^{91} -4.47214 q^{92} +1.69200 q^{93} +10.7115 q^{94} -1.00000 q^{96} -1.73974 q^{97} +1.57358 q^{98} +0.190355 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} + 5 q^{11} - 4 q^{12} + 7 q^{13} + q^{14} + 4 q^{16} + q^{17} + 4 q^{18} + 4 q^{19} - q^{21} + 5 q^{22} - 4 q^{24} + 7 q^{26} - 4 q^{27} + q^{28} + 11 q^{29} - 3 q^{31} + 4 q^{32} - 5 q^{33} + q^{34} + 4 q^{36} - 13 q^{37} + 4 q^{38} - 7 q^{39} + 21 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} - 4 q^{48} + 11 q^{49} - q^{51} + 7 q^{52} - 26 q^{53} - 4 q^{54} + q^{56} - 4 q^{57} + 11 q^{58} + 25 q^{59} - 5 q^{61} - 3 q^{62} + q^{63} + 4 q^{64} - 5 q^{66} + 26 q^{67} + q^{68} + 10 q^{71} + 4 q^{72} - 3 q^{73} - 13 q^{74} + 4 q^{76} - 30 q^{77} - 7 q^{78} + 27 q^{79} + 4 q^{81} + 21 q^{82} - 13 q^{83} - q^{84} + 16 q^{86} - 11 q^{87} + 5 q^{88} - 3 q^{89} + 38 q^{91} + 3 q^{93} - 4 q^{96} + 22 q^{97} + 11 q^{98} + 5 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9 + 5 * q^11 - 4 * q^12 + 7 * q^13 + q^14 + 4 * q^16 + q^17 + 4 * q^18 + 4 * q^19 - q^21 + 5 * q^22 - 4 * q^24 + 7 * q^26 - 4 * q^27 + q^28 + 11 * q^29 - 3 * q^31 + 4 * q^32 - 5 * q^33 + q^34 + 4 * q^36 - 13 * q^37 + 4 * q^38 - 7 * q^39 + 21 * q^41 - q^42 + 16 * q^43 + 5 * q^44 - 4 * q^48 + 11 * q^49 - q^51 + 7 * q^52 - 26 * q^53 - 4 * q^54 + q^56 - 4 * q^57 + 11 * q^58 + 25 * q^59 - 5 * q^61 - 3 * q^62 + q^63 + 4 * q^64 - 5 * q^66 + 26 * q^67 + q^68 + 10 * q^71 + 4 * q^72 - 3 * q^73 - 13 * q^74 + 4 * q^76 - 30 * q^77 - 7 * q^78 + 27 * q^79 + 4 * q^81 + 21 * q^82 - 13 * q^83 - q^84 + 16 * q^86 - 11 * q^87 + 5 * q^88 - 3 * q^89 + 38 * q^91 + 3 * q^93 - 4 * q^96 + 22 * q^97 + 11 * q^98 + 5 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	−2.92807	−1.10671	−0.553353	−	0.832947i	$-0.686652\pi$
$7$	−2.92807	−1.10671	−0.553353	+	0.832947i	$0.686652\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	0.190355	0.0573942	0.0286971	−	0.999588i	$-0.490864\pi$
$11$	0.190355	0.0573942	0.0286971	+	0.999588i	$0.490864\pi$
$12$	−1.00000	−0.288675
$13$	−0.310033	−0.0859877	−0.0429939	−	0.999075i	$-0.513690\pi$
$13$	−0.310033	−0.0859877	−0.0429939	+	0.999075i	$0.513690\pi$
$14$	−2.92807	−0.782559
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.04775	−1.46679	−0.733397	−	0.679801i	$-0.762066\pi$
$17$	−6.04775	−1.46679	−0.733397	+	0.679801i	$0.762066\pi$
$18$	1.00000	0.235702
$19$	3.23607	0.742405	0.371202	−	0.928552i	$-0.378946\pi$
$19$	3.23607	0.742405	0.371202	+	0.928552i	$0.378946\pi$
$20$	0	0
$21$	2.92807	0.638957
$22$	0.190355	0.0405838
$23$	−4.47214	−0.932505	−0.466252	−	0.884652i	$-0.654396\pi$
$23$	−4.47214	−0.932505	−0.466252	+	0.884652i	$0.654396\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−0.310033	−0.0608025
$27$	−1.00000	−0.192450
$28$	−2.92807	−0.553353
$29$	6.81168	1.26490	0.632448	−	0.774603i	$-0.282050\pi$
$29$	6.81168	1.26490	0.632448	+	0.774603i	$0.282050\pi$
$30$	0	0
$31$	−1.69200	−0.303892	−0.151946	−	0.988389i	$-0.548554\pi$
$31$	−1.69200	−0.303892	−0.151946	+	0.988389i	$0.548554\pi$
$32$	1.00000	0.176777
$33$	−0.190355	−0.0331366
$34$	−6.04775	−1.03718
$35$	0	0
$36$	1.00000	0.166667
$37$	9.75595	1.60387	0.801934	−	0.597413i	$-0.203804\pi$
$37$	9.75595	1.60387	0.801934	+	0.597413i	$0.203804\pi$
$38$	3.23607	0.524960
$39$	0.310033	0.0496450
$40$	0	0
$41$	5.07397	0.792420	0.396210	−	0.918160i	$-0.370325\pi$
$41$	5.07397	0.792420	0.396210	+	0.918160i	$0.370325\pi$
$42$	2.92807	0.451811
$43$	10.2394	1.56149	0.780744	−	0.624852i	$-0.214841\pi$
$43$	10.2394	1.56149	0.780744	+	0.624852i	$0.214841\pi$
$44$	0.190355	0.0286971
$45$	0	0
$46$	−4.47214	−0.659380
$47$	10.7115	1.56243	0.781216	−	0.624261i	$-0.214600\pi$
$47$	10.7115	1.56243	0.781216	+	0.624261i	$0.214600\pi$
$48$	−1.00000	−0.144338
$49$	1.57358	0.224797
$50$	0	0
$51$	6.04775	0.846854
$52$	−0.310033	−0.0429939
$53$	−9.97175	−1.36972	−0.684862	−	0.728672i	$-0.740138\pi$
$53$	−9.97175	−1.36972	−0.684862	+	0.728672i	$0.740138\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−2.92807	−0.391279
$57$	−3.23607	−0.428628
$58$	6.81168	0.894417
$59$	7.42642	0.966838	0.483419	−	0.875389i	$-0.339395\pi$
$59$	7.42642	0.966838	0.483419	+	0.875389i	$0.339395\pi$
$60$	0	0
$61$	−5.54610	−0.710105	−0.355053	−	0.934846i	$-0.615537\pi$
$61$	−5.54610	−0.710105	−0.355053	+	0.934846i	$0.615537\pi$
$62$	−1.69200	−0.214884
$63$	−2.92807	−0.368902
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.190355	−0.0234311
$67$	15.0922	1.84381	0.921903	−	0.387421i	$-0.126634\pi$
$67$	15.0922	1.84381	0.921903	+	0.387421i	$0.126634\pi$
$68$	−6.04775	−0.733397
$69$	4.47214	0.538382
$70$	0	0
$71$	6.85536	0.813581	0.406791	−	0.913521i	$-0.366648\pi$
$71$	6.85536	0.813581	0.406791	+	0.913521i	$0.366648\pi$
$72$	1.00000	0.117851
$73$	−11.6375	−1.36207	−0.681035	−	0.732251i	$-0.738470\pi$
$73$	−11.6375	−1.36207	−0.681035	+	0.732251i	$0.738470\pi$
$74$	9.75595	1.13411
$75$	0	0
$76$	3.23607	0.371202
$77$	−0.557372	−0.0635185
$78$	0.310033	0.0351043
$79$	1.57029	0.176671	0.0883356	−	0.996091i	$-0.471845\pi$
$79$	1.57029	0.176671	0.0883356	+	0.996091i	$0.471845\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.07397	0.560326
$83$	−13.0195	−1.42908	−0.714538	−	0.699597i	$-0.753363\pi$
$83$	−13.0195	−1.42908	−0.714538	+	0.699597i	$0.753363\pi$
$84$	2.92807	0.319478
$85$	0	0
$86$	10.2394	1.10414
$87$	−6.81168	−0.730288
$88$	0.190355	0.0202919
$89$	−9.28381	−0.984082	−0.492041	−	0.870572i	$-0.663749\pi$
$89$	−9.28381	−0.984082	−0.492041	+	0.870572i	$0.663749\pi$
$90$	0	0
$91$	0.907798	0.0951631
$92$	−4.47214	−0.466252
$93$	1.69200	0.175452
$94$	10.7115	1.10481
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−1.73974	−0.176644	−0.0883221	−	0.996092i	$-0.528150\pi$
$97$	−1.73974	−0.176644	−0.0883221	+	0.996092i	$0.528150\pi$
$98$	1.57358	0.158955
$99$	0.190355	0.0191314
$100$	0	0
$101$	−0.765188	−0.0761391	−0.0380695	−	0.999275i	$-0.512121\pi$
$101$	−0.765188	−0.0761391	−0.0380695	+	0.999275i	$0.512121\pi$
$102$	6.04775	0.598816
$103$	−5.63298	−0.555034	−0.277517	−	0.960721i	$-0.589512\pi$
$103$	−5.63298	−0.555034	−0.277517	+	0.960721i	$0.589512\pi$
$104$	−0.310033	−0.0304012
$105$	0	0
$106$	−9.97175	−0.968542
$107$	8.81042	0.851736	0.425868	−	0.904785i	$-0.359969\pi$
$107$	8.81042	0.851736	0.425868	+	0.904785i	$0.359969\pi$
$108$	−1.00000	−0.0962250
$109$	15.8769	1.52073	0.760365	−	0.649496i	$-0.225020\pi$
$109$	15.8769	1.52073	0.760365	+	0.649496i	$0.225020\pi$
$110$	0	0
$111$	−9.75595	−0.925994
$112$	−2.92807	−0.276676
$113$	19.1399	1.80053	0.900267	−	0.435337i	$-0.143371\pi$
$113$	19.1399	1.80053	0.900267	+	0.435337i	$0.143371\pi$
$114$	−3.23607	−0.303086
$115$	0	0
$116$	6.81168	0.632448
$117$	−0.310033	−0.0286626
$118$	7.42642	0.683658
$119$	17.7082	1.62331
$120$	0	0
$121$	−10.9638	−0.996706
$122$	−5.54610	−0.502120
$123$	−5.07397	−0.457504
$124$	−1.69200	−0.151946
$125$	0	0
$126$	−2.92807	−0.260853
$127$	8.13792	0.722123	0.361062	−	0.932542i	$-0.382414\pi$
$127$	8.13792	0.722123	0.361062	+	0.932542i	$0.382414\pi$
$128$	1.00000	0.0883883
$129$	−10.2394	−0.901525
$130$	0	0
$131$	16.6201	1.45210	0.726051	−	0.687641i	$-0.241354\pi$
$131$	16.6201	1.45210	0.726051	+	0.687641i	$0.241354\pi$
$132$	−0.190355	−0.0165683
$133$	−9.47542	−0.821623
$134$	15.0922	1.30377
$135$	0	0
$136$	−6.04775	−0.518590
$137$	10.6383	0.908892	0.454446	−	0.890774i	$-0.349837\pi$
$137$	10.6383	0.908892	0.454446	+	0.890774i	$0.349837\pi$
$138$	4.47214	0.380693
$139$	22.8918	1.94166	0.970830	−	0.239769i	$-0.0770718\pi$
$139$	22.8918	1.94166	0.970830	+	0.239769i	$0.0770718\pi$
$140$	0	0
$141$	−10.7115	−0.902070
$142$	6.85536	0.575289
$143$	−0.0590164	−0.00493520
$144$	1.00000	0.0833333
$145$	0	0
$146$	−11.6375	−0.963129
$147$	−1.57358	−0.129786
$148$	9.75595	0.801934
$149$	1.40819	0.115363	0.0576815	−	0.998335i	$-0.481629\pi$
$149$	1.40819	0.115363	0.0576815	+	0.998335i	$0.481629\pi$
$150$	0	0
$151$	−7.87234	−0.640642	−0.320321	−	0.947309i	$-0.603791\pi$
$151$	−7.87234	−0.640642	−0.320321	+	0.947309i	$0.603791\pi$
$152$	3.23607	0.262480
$153$	−6.04775	−0.488931
$154$	−0.557372	−0.0449143
$155$	0	0
$156$	0.310033	0.0248225
$157$	6.95554	0.555113	0.277556	−	0.960709i	$-0.410475\pi$
$157$	6.95554	0.555113	0.277556	+	0.960709i	$0.410475\pi$
$158$	1.57029	0.124925
$159$	9.97175	0.790811
$160$	0	0
$161$	13.0947	1.03201
$162$	1.00000	0.0785674
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	5.07397	0.396210
$165$	0	0
$166$	−13.0195	−1.01051
$167$	−1.37742	−0.106588	−0.0532940	−	0.998579i	$-0.516972\pi$
$167$	−1.37742	−0.106588	−0.0532940	+	0.998579i	$0.516972\pi$
$168$	2.92807	0.225905
$169$	−12.9039	−0.992606
$170$	0	0
$171$	3.23607	0.247468
$172$	10.2394	0.780744
$173$	4.12297	0.313463	0.156732	−	0.987641i	$-0.449904\pi$
$173$	4.12297	0.313463	0.156732	+	0.987641i	$0.449904\pi$
$174$	−6.81168	−0.516392
$175$	0	0
$176$	0.190355	0.0143485
$177$	−7.42642	−0.558204
$178$	−9.28381	−0.695851
$179$	4.30800	0.321995	0.160998	−	0.986955i	$-0.448529\pi$
$179$	4.30800	0.321995	0.160998	+	0.986955i	$0.448529\pi$
$180$	0	0
$181$	12.9920	0.965689	0.482845	−	0.875706i	$-0.339604\pi$
$181$	12.9920	0.965689	0.482845	+	0.875706i	$0.339604\pi$
$182$	0.907798	0.0672904
$183$	5.54610	0.409980
$184$	−4.47214	−0.329690
$185$	0	0
$186$	1.69200	0.124063
$187$	−1.15122	−0.0841854
$188$	10.7115	0.781216
$189$	2.92807	0.212986
$190$	0	0
$191$	−1.23607	−0.0894387	−0.0447194	−	0.999000i	$-0.514239\pi$
$191$	−1.23607	−0.0894387	−0.0447194	+	0.999000i	$0.514239\pi$
$192$	−1.00000	−0.0721688
$193$	−17.4250	−1.25428	−0.627140	−	0.778906i	$-0.715775\pi$
$193$	−17.4250	−1.25428	−0.627140	+	0.778906i	$0.715775\pi$
$194$	−1.73974	−0.124906
$195$	0	0
$196$	1.57358	0.112398
$197$	−14.9422	−1.06459	−0.532295	−	0.846559i	$-0.678670\pi$
$197$	−14.9422	−1.06459	−0.532295	+	0.846559i	$0.678670\pi$
$198$	0.190355	0.0135279
$199$	−4.90436	−0.347661	−0.173830	−	0.984776i	$-0.555614\pi$
$199$	−4.90436	−0.347661	−0.173830	+	0.984776i	$0.555614\pi$
$200$	0	0
$201$	−15.0922	−1.06452
$202$	−0.765188	−0.0538384
$203$	−19.9450	−1.39987
$204$	6.04775	0.423427
$205$	0	0
$206$	−5.63298	−0.392469
$207$	−4.47214	−0.310835
$208$	−0.310033	−0.0214969
$209$	0.616002	0.0426097
$210$	0	0
$211$	−1.23200	−0.0848146	−0.0424073	−	0.999100i	$-0.513503\pi$
$211$	−1.23200	−0.0848146	−0.0424073	+	0.999100i	$0.513503\pi$
$212$	−9.97175	−0.684862
$213$	−6.85536	−0.469721
$214$	8.81042	0.602268
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	4.95429	0.336319
$218$	15.8769	1.07532
$219$	11.6375	0.786391
$220$	0	0
$221$	1.87500	0.126126
$222$	−9.75595	−0.654776
$223$	−4.66249	−0.312223	−0.156112	−	0.987739i	$-0.549896\pi$
$223$	−4.66249	−0.312223	−0.156112	+	0.987739i	$0.549896\pi$
$224$	−2.92807	−0.195640
$225$	0	0
$226$	19.1399	1.27317
$227$	−0.573577	−0.0380696	−0.0190348	−	0.999819i	$-0.506059\pi$
$227$	−0.573577	−0.0380696	−0.0190348	+	0.999819i	$0.506059\pi$
$228$	−3.23607	−0.214314
$229$	29.7330	1.96481	0.982407	−	0.186755i	$-0.0597970\pi$
$229$	29.7330	1.96481	0.982407	+	0.186755i	$0.0597970\pi$
$230$	0	0
$231$	0.557372	0.0366724
$232$	6.81168	0.447209
$233$	13.8769	0.909105	0.454552	−	0.890720i	$-0.349799\pi$
$233$	13.8769	0.909105	0.454552	+	0.890720i	$0.349799\pi$
$234$	−0.310033	−0.0202675
$235$	0	0
$236$	7.42642	0.483419
$237$	−1.57029	−0.102001
$238$	17.7082	1.14785
$239$	−2.14387	−0.138675	−0.0693376	−	0.997593i	$-0.522089\pi$
$239$	−2.14387	−0.138675	−0.0693376	+	0.997593i	$0.522089\pi$
$240$	0	0
$241$	1.73974	0.112067	0.0560334	−	0.998429i	$-0.482155\pi$
$241$	1.73974	0.112067	0.0560334	+	0.998429i	$0.482155\pi$
$242$	−10.9638	−0.704778
$243$	−1.00000	−0.0641500
$244$	−5.54610	−0.355053
$245$	0	0
$246$	−5.07397	−0.323504
$247$	−1.00329	−0.0638377
$248$	−1.69200	−0.107442
$249$	13.0195	0.825077
$250$	0	0
$251$	−6.39691	−0.403770	−0.201885	−	0.979409i	$-0.564707\pi$
$251$	−6.39691	−0.403770	−0.201885	+	0.979409i	$0.564707\pi$
$252$	−2.92807	−0.184451
$253$	−0.851293	−0.0535204
$254$	8.13792	0.510618
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.31003	0.393609	0.196805	−	0.980443i	$-0.436944\pi$
$257$	6.31003	0.393609	0.196805	+	0.980443i	$0.436944\pi$
$258$	−10.2394	−0.637474
$259$	−28.5661	−1.77501
$260$	0	0
$261$	6.81168	0.421632
$262$	16.6201	1.02679
$263$	−2.85942	−0.176320	−0.0881598	−	0.996106i	$-0.528099\pi$
$263$	−2.85942	−0.176320	−0.0881598	+	0.996106i	$0.528099\pi$
$264$	−0.190355	−0.0117155
$265$	0	0
$266$	−9.47542	−0.580976
$267$	9.28381	0.568160
$268$	15.0922	0.921903
$269$	−9.70617	−0.591796	−0.295898	−	0.955220i	$-0.595619\pi$
$269$	−9.70617	−0.591796	−0.295898	+	0.955220i	$0.595619\pi$
$270$	0	0
$271$	17.1674	1.04285	0.521423	−	0.853298i	$-0.325401\pi$
$271$	17.1674	1.04285	0.521423	+	0.853298i	$0.325401\pi$
$272$	−6.04775	−0.366698
$273$	−0.907798	−0.0549424
$274$	10.6383	0.642683
$275$	0	0
$276$	4.47214	0.269191
$277$	2.04368	0.122793	0.0613964	−	0.998113i	$-0.480445\pi$
$277$	2.04368	0.122793	0.0613964	+	0.998113i	$0.480445\pi$
$278$	22.8918	1.37296
$279$	−1.69200	−0.101297
$280$	0	0
$281$	5.15881	0.307749	0.153875	−	0.988090i	$-0.450825\pi$
$281$	5.15881	0.307749	0.153875	+	0.988090i	$0.450825\pi$
$282$	−10.7115	−0.637860
$283$	9.38651	0.557970	0.278985	−	0.960295i	$-0.410002\pi$
$283$	9.38651	0.557970	0.278985	+	0.960295i	$0.410002\pi$
$284$	6.85536	0.406791
$285$	0	0
$286$	−0.0590164	−0.00348971
$287$	−14.8569	−0.876976
$288$	1.00000	0.0589256
$289$	19.5752	1.15148
$290$	0	0
$291$	1.73974	0.101986
$292$	−11.6375	−0.681035
$293$	8.18160	0.477974	0.238987	−	0.971023i	$-0.423185\pi$
$293$	8.18160	0.477974	0.238987	+	0.971023i	$0.423185\pi$
$294$	−1.57358	−0.0917729
$295$	0	0
$296$	9.75595	0.567053
$297$	−0.190355	−0.0110455
$298$	1.40819	0.0815740
$299$	1.38651	0.0801840
$300$	0	0
$301$	−29.9815	−1.72811
$302$	−7.87234	−0.453002
$303$	0.765188	0.0439589
$304$	3.23607	0.185601
$305$	0	0
$306$	−6.04775	−0.345727
$307$	−5.85865	−0.334371	−0.167185	−	0.985925i	$-0.553468\pi$
$307$	−5.85865	−0.334371	−0.167185	+	0.985925i	$0.553468\pi$
$308$	−0.557372	−0.0317592
$309$	5.63298	0.320449
$310$	0	0
$311$	−19.0398	−1.07965	−0.539823	−	0.841779i	$-0.681509\pi$
$311$	−19.0398	−1.07965	−0.539823	+	0.841779i	$0.681509\pi$
$312$	0.310033	0.0175522
$313$	11.9966	0.678086	0.339043	−	0.940771i	$-0.389897\pi$
$313$	11.9966	0.678086	0.339043	+	0.940771i	$0.389897\pi$
$314$	6.95554	0.392524
$315$	0	0
$316$	1.57029	0.0883356
$317$	−32.6126	−1.83170	−0.915852	−	0.401516i	$-0.868483\pi$
$317$	−32.6126	−1.83170	−0.915852	+	0.401516i	$0.868483\pi$
$318$	9.97175	0.559188
$319$	1.29664	0.0725977
$320$	0	0
$321$	−8.81042	−0.491750
$322$	13.0947	0.729740
$323$	−19.5709	−1.08895
$324$	1.00000	0.0555556
$325$	0	0
$326$	14.0000	0.775388
$327$	−15.8769	−0.877994
$328$	5.07397	0.280163
$329$	−31.3640	−1.72915
$330$	0	0
$331$	3.23200	0.177647	0.0888235	−	0.996047i	$-0.471689\pi$
$331$	3.23200	0.177647	0.0888235	+	0.996047i	$0.471689\pi$
$332$	−13.0195	−0.714538
$333$	9.75595	0.534623
$334$	−1.37742	−0.0753692
$335$	0	0
$336$	2.92807	0.159739
$337$	−21.3154	−1.16112	−0.580561	−	0.814217i	$-0.697167\pi$
$337$	−21.3154	−1.16112	−0.580561	+	0.814217i	$0.697167\pi$
$338$	−12.9039	−0.701879
$339$	−19.1399	−1.03954
$340$	0	0
$341$	−0.322080	−0.0174416
$342$	3.23607	0.174987
$343$	15.8889	0.857922
$344$	10.2394	0.552069
$345$	0	0
$346$	4.12297	0.221652
$347$	−19.1412	−1.02755	−0.513777	−	0.857924i	$-0.671754\pi$
$347$	−19.1412	−1.02755	−0.513777	+	0.857924i	$0.671754\pi$
$348$	−6.81168	−0.365144
$349$	14.3745	0.769447	0.384724	−	0.923032i	$-0.374297\pi$
$349$	14.3745	0.769447	0.384724	+	0.923032i	$0.374297\pi$
$350$	0	0
$351$	0.310033	0.0165483
$352$	0.190355	0.0101460
$353$	−24.3873	−1.29800	−0.649002	−	0.760787i	$-0.724813\pi$
$353$	−24.3873	−1.29800	−0.649002	+	0.760787i	$0.724813\pi$
$354$	−7.42642	−0.394710
$355$	0	0
$356$	−9.28381	−0.492041
$357$	−17.7082	−0.937218
$358$	4.30800	0.227685
$359$	−21.3316	−1.12584	−0.562918	−	0.826513i	$-0.690321\pi$
$359$	−21.3316	−1.12584	−0.562918	+	0.826513i	$0.690321\pi$
$360$	0	0
$361$	−8.52786	−0.448835
$362$	12.9920	0.682845
$363$	10.9638	0.575448
$364$	0.907798	0.0475815
$365$	0	0
$366$	5.54610	0.289899
$367$	10.6322	0.554997	0.277498	−	0.960726i	$-0.410495\pi$
$367$	10.6322	0.554997	0.277498	+	0.960726i	$0.410495\pi$
$368$	−4.47214	−0.233126
$369$	5.07397	0.264140
$370$	0	0
$371$	29.1979	1.51588
$372$	1.69200	0.0877261
$373$	−1.23356	−0.0638711	−0.0319356	−	0.999490i	$-0.510167\pi$
$373$	−1.23356	−0.0638711	−0.0319356	+	0.999490i	$0.510167\pi$
$374$	−1.15122	−0.0595281
$375$	0	0
$376$	10.7115	0.552403
$377$	−2.11185	−0.108766
$378$	2.92807	0.150604
$379$	25.3250	1.30086	0.650428	−	0.759568i	$-0.274589\pi$
$379$	25.3250	1.30086	0.650428	+	0.759568i	$0.274589\pi$
$380$	0	0
$381$	−8.13792	−0.416918
$382$	−1.23607	−0.0632427
$383$	−19.1796	−0.980030	−0.490015	−	0.871714i	$-0.663009\pi$
$383$	−19.1796	−0.980030	−0.490015	+	0.871714i	$0.663009\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−17.4250	−0.886910
$387$	10.2394	0.520496
$388$	−1.73974	−0.0883221
$389$	−8.29751	−0.420700	−0.210350	−	0.977626i	$-0.567460\pi$
$389$	−8.29751	−0.420700	−0.210350	+	0.977626i	$0.567460\pi$
$390$	0	0
$391$	27.0463	1.36779
$392$	1.57358	0.0794776
$393$	−16.6201	−0.838371
$394$	−14.9422	−0.752779
$395$	0	0
$396$	0.190355	0.00956570
$397$	31.5160	1.58174	0.790870	−	0.611984i	$-0.209628\pi$
$397$	31.5160	1.58174	0.790870	+	0.611984i	$0.209628\pi$
$398$	−4.90436	−0.245833
$399$	9.47542	0.474365
$400$	0	0
$401$	−13.6940	−0.683847	−0.341924	−	0.939728i	$-0.611078\pi$
$401$	−13.6940	−0.683847	−0.341924	+	0.939728i	$0.611078\pi$
$402$	−15.0922	−0.752731
$403$	0.524576	0.0261310
$404$	−0.765188	−0.0380695
$405$	0	0
$406$	−19.9450	−0.989856
$407$	1.85709	0.0920527
$408$	6.04775	0.299408
$409$	−30.0967	−1.48819	−0.744094	−	0.668075i	$-0.767119\pi$
$409$	−30.0967	−1.48819	−0.744094	+	0.668075i	$0.767119\pi$
$410$	0	0
$411$	−10.6383	−0.524749
$412$	−5.63298	−0.277517
$413$	−21.7451	−1.07000
$414$	−4.47214	−0.219793
$415$	0	0
$416$	−0.310033	−0.0152006
$417$	−22.8918	−1.12102
$418$	0.616002	0.0301296
$419$	10.6388	0.519739	0.259869	−	0.965644i	$-0.416321\pi$
$419$	10.6388	0.519739	0.259869	+	0.965644i	$0.416321\pi$
$420$	0	0
$421$	12.1002	0.589727	0.294863	−	0.955539i	$-0.404726\pi$
$421$	12.1002	0.589727	0.294863	+	0.955539i	$0.404726\pi$
$422$	−1.23200	−0.0599730
$423$	10.7115	0.520811
$424$	−9.97175	−0.484271
$425$	0	0
$426$	−6.85536	−0.332143
$427$	16.2394	0.785878
$428$	8.81042	0.425868
$429$	0.0590164	0.00284934
$430$	0	0
$431$	−1.09220	−0.0526095	−0.0263048	−	0.999654i	$-0.508374\pi$
$431$	−1.09220	−0.0526095	−0.0263048	+	0.999654i	$0.508374\pi$
$432$	−1.00000	−0.0481125
$433$	−12.1263	−0.582751	−0.291375	−	0.956609i	$-0.594113\pi$
$433$	−12.1263	−0.582751	−0.291375	+	0.956609i	$0.594113\pi$
$434$	4.95429	0.237813
$435$	0	0
$436$	15.8769	0.760365
$437$	−14.4721	−0.692296
$438$	11.6375	0.556063
$439$	13.8945	0.663148	0.331574	−	0.943429i	$-0.392420\pi$
$439$	13.8945	0.663148	0.331574	+	0.943429i	$0.392420\pi$
$440$	0	0
$441$	1.57358	0.0749322
$442$	1.87500	0.0891847
$443$	38.2047	1.81516	0.907579	−	0.419880i	$-0.137928\pi$
$443$	38.2047	1.81516	0.907579	+	0.419880i	$0.137928\pi$
$444$	−9.75595	−0.462997
$445$	0	0
$446$	−4.66249	−0.220775
$447$	−1.40819	−0.0666049
$448$	−2.92807	−0.138338
$449$	14.8092	0.698888	0.349444	−	0.936957i	$-0.386371\pi$
$449$	14.8092	0.698888	0.349444	+	0.936957i	$0.386371\pi$
$450$	0	0
$451$	0.965855	0.0454803
$452$	19.1399	0.900267
$453$	7.87234	0.369875
$454$	−0.573577	−0.0269193
$455$	0	0
$456$	−3.23607	−0.151543
$457$	−4.86286	−0.227475	−0.113738	−	0.993511i	$-0.536282\pi$
$457$	−4.86286	−0.227475	−0.113738	+	0.993511i	$0.536282\pi$
$458$	29.7330	1.38933
$459$	6.04775	0.282285
$460$	0	0
$461$	−20.3058	−0.945736	−0.472868	−	0.881133i	$-0.656781\pi$
$461$	−20.3058	−0.945736	−0.472868	+	0.881133i	$0.656781\pi$
$462$	0.557372	0.0259313
$463$	−39.9825	−1.85814	−0.929072	−	0.369900i	$-0.879392\pi$
$463$	−39.9825	−1.85814	−0.929072	+	0.369900i	$0.879392\pi$
$464$	6.81168	0.316224
$465$	0	0
$466$	13.8769	0.642834
$467$	15.9416	0.737690	0.368845	−	0.929491i	$-0.379753\pi$
$467$	15.9416	0.737690	0.368845	+	0.929491i	$0.379753\pi$
$468$	−0.310033	−0.0143313
$469$	−44.1910	−2.04055
$470$	0	0
$471$	−6.95554	−0.320495
$472$	7.42642	0.341829
$473$	1.94911	0.0896203
$474$	−1.57029	−0.0721258
$475$	0	0
$476$	17.7082	0.811654
$477$	−9.97175	−0.456575
$478$	−2.14387	−0.0980581
$479$	−7.85613	−0.358956	−0.179478	−	0.983762i	$-0.557441\pi$
$479$	−7.85613	−0.358956	−0.179478	+	0.983762i	$0.557441\pi$
$480$	0	0
$481$	−3.02467	−0.137913
$482$	1.73974	0.0792432
$483$	−13.0947	−0.595830
$484$	−10.9638	−0.498353
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	40.9465	1.85546	0.927730	−	0.373251i	$-0.121757\pi$
$487$	40.9465	1.85546	0.927730	+	0.373251i	$0.121757\pi$
$488$	−5.54610	−0.251060
$489$	−14.0000	−0.633102
$490$	0	0
$491$	−7.51824	−0.339293	−0.169647	−	0.985505i	$-0.554263\pi$
$491$	−7.51824	−0.339293	−0.169647	+	0.985505i	$0.554263\pi$
$492$	−5.07397	−0.228752
$493$	−41.1953	−1.85534
$494$	−1.00329	−0.0451401
$495$	0	0
$496$	−1.69200	−0.0759730
$497$	−20.0729	−0.900395
$498$	13.0195	0.583417
$499$	15.7513	0.705123	0.352561	−	0.935789i	$-0.385311\pi$
$499$	15.7513	0.705123	0.352561	+	0.935789i	$0.385311\pi$
$500$	0	0
$501$	1.37742	0.0615387
$502$	−6.39691	−0.285508
$503$	−0.818884	−0.0365122	−0.0182561	−	0.999833i	$-0.505811\pi$
$503$	−0.818884	−0.0365122	−0.0182561	+	0.999833i	$0.505811\pi$
$504$	−2.92807	−0.130426
$505$	0	0
$506$	−0.851293	−0.0378446
$507$	12.9039	0.573081
$508$	8.13792	0.361062
$509$	26.9521	1.19463	0.597316	−	0.802006i	$-0.296234\pi$
$509$	26.9521	1.19463	0.597316	+	0.802006i	$0.296234\pi$
$510$	0	0
$511$	34.0755	1.50741
$512$	1.00000	0.0441942
$513$	−3.23607	−0.142876
$514$	6.31003	0.278324
$515$	0	0
$516$	−10.2394	−0.450763
$517$	2.03899	0.0896745
$518$	−28.5661	−1.25512
$519$	−4.12297	−0.180978
$520$	0	0
$521$	−15.4572	−0.677192	−0.338596	−	0.940932i	$-0.609952\pi$
$521$	−15.4572	−0.677192	−0.338596	+	0.940932i	$0.609952\pi$
$522$	6.81168	0.298139
$523$	−10.3308	−0.451734	−0.225867	−	0.974158i	$-0.572521\pi$
$523$	−10.3308	−0.451734	−0.225867	+	0.974158i	$0.572521\pi$
$524$	16.6201	0.726051
$525$	0	0
$526$	−2.85942	−0.124677
$527$	10.2328	0.445747
$528$	−0.190355	−0.00828414
$529$	−3.00000	−0.130435
$530$	0	0
$531$	7.42642	0.322279
$532$	−9.47542	−0.410812
$533$	−1.57310	−0.0681384
$534$	9.28381	0.401750
$535$	0	0
$536$	15.0922	0.651884
$537$	−4.30800	−0.185904
$538$	−9.70617	−0.418463
$539$	0.299538	0.0129020
$540$	0	0
$541$	−37.0351	−1.59226	−0.796131	−	0.605124i	$-0.793123\pi$
$541$	−37.0351	−1.59226	−0.796131	+	0.605124i	$0.793123\pi$
$542$	17.1674	0.737404
$543$	−12.9920	−0.557541
$544$	−6.04775	−0.259295
$545$	0	0
$546$	−0.907798	−0.0388502
$547$	24.2168	1.03544	0.517718	−	0.855551i	$-0.326782\pi$
$547$	24.2168	1.03544	0.517718	+	0.855551i	$0.326782\pi$
$548$	10.6383	0.454446
$549$	−5.54610	−0.236702
$550$	0	0
$551$	22.0431	0.939066
$552$	4.47214	0.190347
$553$	−4.59791	−0.195523
$554$	2.04368	0.0868277
$555$	0	0
$556$	22.8918	0.970830
$557$	−26.3623	−1.11701	−0.558504	−	0.829502i	$-0.688624\pi$
$557$	−26.3623	−1.11701	−0.558504	+	0.829502i	$0.688624\pi$
$558$	−1.69200	−0.0716280
$559$	−3.17454	−0.134269
$560$	0	0
$561$	1.15122	0.0486045
$562$	5.15881	0.217611
$563$	−15.1043	−0.636572	−0.318286	−	0.947995i	$-0.603107\pi$
$563$	−15.1043	−0.636572	−0.318286	+	0.947995i	$0.603107\pi$
$564$	−10.7115	−0.451035
$565$	0	0
$566$	9.38651	0.394544
$567$	−2.92807	−0.122967
$568$	6.85536	0.287644
$569$	−11.5125	−0.482630	−0.241315	−	0.970447i	$-0.577579\pi$
$569$	−11.5125	−0.482630	−0.241315	+	0.970447i	$0.577579\pi$
$570$	0	0
$571$	−31.5185	−1.31901	−0.659504	−	0.751701i	$-0.729233\pi$
$571$	−31.5185	−1.31901	−0.659504	+	0.751701i	$0.729233\pi$
$572$	−0.0590164	−0.00246760
$573$	1.23607	0.0516375
$574$	−14.8569	−0.620115
$575$	0	0
$576$	1.00000	0.0416667
$577$	13.1973	0.549412	0.274706	−	0.961528i	$-0.411420\pi$
$577$	13.1973	0.549412	0.274706	+	0.961528i	$0.411420\pi$
$578$	19.5752	0.814222
$579$	17.4250	0.724159
$580$	0	0
$581$	38.1219	1.58156
$582$	1.73974	0.0721147
$583$	−1.89817	−0.0786143
$584$	−11.6375	−0.481564
$585$	0	0
$586$	8.18160	0.337979
$587$	−30.8818	−1.27463	−0.637314	−	0.770604i	$-0.719955\pi$
$587$	−30.8818	−1.27463	−0.637314	+	0.770604i	$0.719955\pi$
$588$	−1.57358	−0.0648932
$589$	−5.47542	−0.225611
$590$	0	0
$591$	14.9422	0.614642
$592$	9.75595	0.400967
$593$	−5.13588	−0.210905	−0.105453	−	0.994424i	$-0.533629\pi$
$593$	−5.13588	−0.210905	−0.105453	+	0.994424i	$0.533629\pi$
$594$	−0.190355	−0.00781036
$595$	0	0
$596$	1.40819	0.0576815
$597$	4.90436	0.200722
$598$	1.38651	0.0566986
$599$	−42.2558	−1.72653	−0.863263	−	0.504755i	$-0.831583\pi$
$599$	−42.2558	−1.72653	−0.863263	+	0.504755i	$0.831583\pi$
$600$	0	0
$601$	4.38893	0.179028	0.0895141	−	0.995986i	$-0.471469\pi$
$601$	4.38893	0.179028	0.0895141	+	0.995986i	$0.471469\pi$
$602$	−29.9815	−1.22196
$603$	15.0922	0.614602
$604$	−7.87234	−0.320321
$605$	0	0
$606$	0.765188	0.0310836
$607$	30.0265	1.21874	0.609368	−	0.792887i	$-0.291423\pi$
$607$	30.0265	1.21874	0.609368	+	0.792887i	$0.291423\pi$
$608$	3.23607	0.131240
$609$	19.9450	0.808214
$610$	0	0
$611$	−3.32092	−0.134350
$612$	−6.04775	−0.244466
$613$	−4.48090	−0.180982	−0.0904908	−	0.995897i	$-0.528844\pi$
$613$	−4.48090	−0.180982	−0.0904908	+	0.995897i	$0.528844\pi$
$614$	−5.85865	−0.236436
$615$	0	0
$616$	−0.557372	−0.0224572
$617$	13.9699	0.562405	0.281203	−	0.959648i	$-0.409267\pi$
$617$	13.9699	0.562405	0.281203	+	0.959648i	$0.409267\pi$
$618$	5.63298	0.226592
$619$	24.4263	0.981775	0.490887	−	0.871223i	$-0.336673\pi$
$619$	24.4263	0.981775	0.490887	+	0.871223i	$0.336673\pi$
$620$	0	0
$621$	4.47214	0.179461
$622$	−19.0398	−0.763425
$623$	27.1836	1.08909
$624$	0.310033	0.0124113
$625$	0	0
$626$	11.9966	0.479479
$627$	−0.616002	−0.0246007
$628$	6.95554	0.277556
$629$	−59.0015	−2.35254
$630$	0	0
$631$	9.91109	0.394554	0.197277	−	0.980348i	$-0.436790\pi$
$631$	9.91109	0.394554	0.197277	+	0.980348i	$0.436790\pi$
$632$	1.57029	0.0624627
$633$	1.23200	0.0489677
$634$	−32.6126	−1.29521
$635$	0	0
$636$	9.97175	0.395406
$637$	−0.487861	−0.0193298
$638$	1.29664	0.0513343
$639$	6.85536	0.271194
$640$	0	0
$641$	39.5160	1.56079	0.780393	−	0.625289i	$-0.215019\pi$
$641$	39.5160	1.56079	0.780393	+	0.625289i	$0.215019\pi$
$642$	−8.81042	−0.347720
$643$	−22.9508	−0.905093	−0.452547	−	0.891741i	$-0.649484\pi$
$643$	−22.9508	−0.905093	−0.452547	+	0.891741i	$0.649484\pi$
$644$	13.0947	0.516004
$645$	0	0
$646$	−19.5709	−0.770007
$647$	2.46556	0.0969311	0.0484656	−	0.998825i	$-0.484567\pi$
$647$	2.46556	0.0969311	0.0484656	+	0.998825i	$0.484567\pi$
$648$	1.00000	0.0392837
$649$	1.41366	0.0554909
$650$	0	0
$651$	−4.95429	−0.194174
$652$	14.0000	0.548282
$653$	26.7780	1.04790	0.523951	−	0.851748i	$-0.324457\pi$
$653$	26.7780	1.04790	0.523951	+	0.851748i	$0.324457\pi$
$654$	−15.8769	−0.620835
$655$	0	0
$656$	5.07397	0.198105
$657$	−11.6375	−0.454023
$658$	−31.3640	−1.22269
$659$	28.5945	1.11388	0.556941	−	0.830552i	$-0.311975\pi$
$659$	28.5945	1.11388	0.556941	+	0.830552i	$0.311975\pi$
$660$	0	0
$661$	−2.34830	−0.0913383	−0.0456692	−	0.998957i	$-0.514542\pi$
$661$	−2.34830	−0.0913383	−0.0456692	+	0.998957i	$0.514542\pi$
$662$	3.23200	0.125615
$663$	−1.87500	−0.0728190
$664$	−13.0195	−0.505254
$665$	0	0
$666$	9.75595	0.378035
$667$	−30.4627	−1.17952
$668$	−1.37742	−0.0532940
$669$	4.66249	0.180262
$670$	0	0
$671$	−1.05573	−0.0407559
$672$	2.92807	0.112953
$673$	35.0672	1.35174	0.675871	−	0.737020i	$-0.263767\pi$
$673$	35.0672	1.35174	0.675871	+	0.737020i	$0.263767\pi$
$674$	−21.3154	−0.821037
$675$	0	0
$676$	−12.9039	−0.496303
$677$	−32.2056	−1.23776	−0.618882	−	0.785484i	$-0.712414\pi$
$677$	−32.2056	−1.23776	−0.618882	+	0.785484i	$0.712414\pi$
$678$	−19.1399	−0.735065
$679$	5.09409	0.195493
$680$	0	0
$681$	0.573577	0.0219795
$682$	−0.322080	−0.0123331
$683$	−13.8137	−0.528567	−0.264283	−	0.964445i	$-0.585135\pi$
$683$	−13.8137	−0.528567	−0.264283	+	0.964445i	$0.585135\pi$
$684$	3.23607	0.123734
$685$	0	0
$686$	15.8889	0.606642
$687$	−29.7330	−1.13439
$688$	10.2394	0.390372
$689$	3.09157	0.117780
$690$	0	0
$691$	−25.9501	−0.987187	−0.493594	−	0.869693i	$-0.664317\pi$
$691$	−25.9501	−0.987187	−0.493594	+	0.869693i	$0.664317\pi$
$692$	4.12297	0.156732
$693$	−0.557372	−0.0211728
$694$	−19.1412	−0.726590
$695$	0	0
$696$	−6.81168	−0.258196
$697$	−30.6860	−1.16232
$698$	14.3745	0.544081
$699$	−13.8769	−0.524872
$700$	0	0
$701$	37.4437	1.41423	0.707115	−	0.707098i	$-0.249996\pi$
$701$	37.4437	1.41423	0.707115	+	0.707098i	$0.249996\pi$
$702$	0.310033	0.0117014
$703$	31.5709	1.19072
$704$	0.190355	0.00717427
$705$	0	0
$706$	−24.3873	−0.917828
$707$	2.24052	0.0842635
$708$	−7.42642	−0.279102
$709$	−17.4281	−0.654525	−0.327262	−	0.944933i	$-0.606126\pi$
$709$	−17.4281	−0.654525	−0.327262	+	0.944933i	$0.606126\pi$
$710$	0	0
$711$	1.57029	0.0588904
$712$	−9.28381	−0.347926
$713$	7.56685	0.283381
$714$	−17.7082	−0.662713
$715$	0	0
$716$	4.30800	0.160998
$717$	2.14387	0.0800641
$718$	−21.3316	−0.796087
$719$	−35.4836	−1.32331	−0.661657	−	0.749807i	$-0.730146\pi$
$719$	−35.4836	−1.32331	−0.661657	+	0.749807i	$0.730146\pi$
$720$	0	0
$721$	16.4938	0.614259
$722$	−8.52786	−0.317374
$723$	−1.73974	−0.0647018
$724$	12.9920	0.482845
$725$	0	0
$726$	10.9638	0.406903
$727$	19.0922	0.708091	0.354045	−	0.935228i	$-0.384806\pi$
$727$	19.0922	0.708091	0.354045	+	0.935228i	$0.384806\pi$
$728$	0.907798	0.0336452
$729$	1.00000	0.0370370
$730$	0	0
$731$	−61.9250	−2.29038
$732$	5.54610	0.204990
$733$	−10.9493	−0.404421	−0.202211	−	0.979342i	$-0.564813\pi$
$733$	−10.9493	−0.404421	−0.202211	+	0.979342i	$0.564813\pi$
$734$	10.6322	0.392442
$735$	0	0
$736$	−4.47214	−0.164845
$737$	2.87288	0.105824
$738$	5.07397	0.186775
$739$	47.9058	1.76224	0.881121	−	0.472891i	$-0.156790\pi$
$739$	47.9058	1.76224	0.881121	+	0.472891i	$0.156790\pi$
$740$	0	0
$741$	1.00329	0.0368567
$742$	29.1979	1.07189
$743$	−38.6016	−1.41615	−0.708077	−	0.706135i	$-0.750437\pi$
$743$	−38.6016	−1.41615	−0.708077	+	0.706135i	$0.750437\pi$
$744$	1.69200	0.0620317
$745$	0	0
$746$	−1.23356	−0.0451637
$747$	−13.0195	−0.476358
$748$	−1.15122	−0.0420927
$749$	−25.7975	−0.942620
$750$	0	0
$751$	−29.2670	−1.06797	−0.533984	−	0.845495i	$-0.679306\pi$
$751$	−29.2670	−1.06797	−0.533984	+	0.845495i	$0.679306\pi$
$752$	10.7115	0.390608
$753$	6.39691	0.233117
$754$	−2.11185	−0.0769089
$755$	0	0
$756$	2.92807	0.106493
$757$	12.0788	0.439012	0.219506	−	0.975611i	$-0.429556\pi$
$757$	12.0788	0.439012	0.219506	+	0.975611i	$0.429556\pi$
$758$	25.3250	0.919845
$759$	0.851293	0.0309000
$760$	0	0
$761$	−2.12718	−0.0771103	−0.0385551	−	0.999256i	$-0.512276\pi$
$761$	−2.12718	−0.0771103	−0.0385551	+	0.999256i	$0.512276\pi$
$762$	−8.13792	−0.294806
$763$	−46.4886	−1.68300
$764$	−1.23607	−0.0447194
$765$	0	0
$766$	−19.1796	−0.692986
$767$	−2.30244	−0.0831362
$768$	−1.00000	−0.0360844
$769$	−8.97393	−0.323608	−0.161804	−	0.986823i	$-0.551731\pi$
$769$	−8.97393	−0.323608	−0.161804	+	0.986823i	$0.551731\pi$
$770$	0	0
$771$	−6.31003	−0.227250
$772$	−17.4250	−0.627140
$773$	−28.7479	−1.03399	−0.516995	−	0.855989i	$-0.672949\pi$
$773$	−28.7479	−1.03399	−0.516995	+	0.855989i	$0.672949\pi$
$774$	10.2394	0.368046
$775$	0	0
$776$	−1.73974	−0.0624532
$777$	28.5661	1.02480
$778$	−8.29751	−0.297480
$779$	16.4197	0.588297
$780$	0	0
$781$	1.30495	0.0466948
$782$	27.0463	0.967175
$783$	−6.81168	−0.243429
$784$	1.57358	0.0561992
$785$	0	0
$786$	−16.6201	−0.592818
$787$	49.3599	1.75949	0.879745	−	0.475445i	$-0.157713\pi$
$787$	49.3599	1.75949	0.879745	+	0.475445i	$0.157713\pi$
$788$	−14.9422	−0.532295
$789$	2.85942	0.101798
$790$	0	0
$791$	−56.0431	−1.99266
$792$	0.190355	0.00676397
$793$	1.71948	0.0610603
$794$	31.5160	1.11846
$795$	0	0
$796$	−4.90436	−0.173830
$797$	−2.93605	−0.104000	−0.0520001	−	0.998647i	$-0.516560\pi$
$797$	−2.93605	−0.104000	−0.0520001	+	0.998647i	$0.516560\pi$
$798$	9.47542	0.335426
$799$	−64.7804	−2.29176
$800$	0	0
$801$	−9.28381	−0.328027
$802$	−13.6940	−0.483553
$803$	−2.21526	−0.0781749
$804$	−15.0922	−0.532261
$805$	0	0
$806$	0.524576	0.0184774
$807$	9.70617	0.341673
$808$	−0.765188	−0.0269192
$809$	−36.1822	−1.27210	−0.636050	−	0.771648i	$-0.719433\pi$
$809$	−36.1822	−1.27210	−0.636050	+	0.771648i	$0.719433\pi$
$810$	0	0
$811$	−45.1968	−1.58707	−0.793537	−	0.608522i	$-0.791763\pi$
$811$	−45.1968	−1.58707	−0.793537	+	0.608522i	$0.791763\pi$
$812$	−19.9450	−0.699934
$813$	−17.1674	−0.602088
$814$	1.85709	0.0650911
$815$	0	0
$816$	6.04775	0.211713
$817$	33.1353	1.15926
$818$	−30.0967	−1.05231
$819$	0.907798	0.0317210
$820$	0	0
$821$	−19.5441	−0.682093	−0.341046	−	0.940046i	$-0.610781\pi$
$821$	−19.5441	−0.682093	−0.341046	+	0.940046i	$0.610781\pi$
$822$	−10.6383	−0.371053
$823$	17.5219	0.610776	0.305388	−	0.952228i	$-0.401214\pi$
$823$	17.5219	0.610776	0.305388	+	0.952228i	$0.401214\pi$
$824$	−5.63298	−0.196234
$825$	0	0
$826$	−21.7451	−0.756608
$827$	24.8781	0.865098	0.432549	−	0.901611i	$-0.357614\pi$
$827$	24.8781	0.865098	0.432549	+	0.901611i	$0.357614\pi$
$828$	−4.47214	−0.155417
$829$	−15.9777	−0.554928	−0.277464	−	0.960736i	$-0.589494\pi$
$829$	−15.9777	−0.554928	−0.277464	+	0.960736i	$0.589494\pi$
$830$	0	0
$831$	−2.04368	−0.0708945
$832$	−0.310033	−0.0107485
$833$	−9.51659	−0.329730
$834$	−22.8918	−0.792679
$835$	0	0
$836$	0.616002	0.0213049
$837$	1.69200	0.0584840
$838$	10.6388	0.367511
$839$	−40.4496	−1.39648	−0.698238	−	0.715866i	$-0.746032\pi$
$839$	−40.4496	−1.39648	−0.698238	+	0.715866i	$0.746032\pi$
$840$	0	0
$841$	17.3989	0.599964
$842$	12.1002	0.417000
$843$	−5.15881	−0.177679
$844$	−1.23200	−0.0424073
$845$	0	0
$846$	10.7115	0.368269
$847$	32.1026	1.10306
$848$	−9.97175	−0.342431
$849$	−9.38651	−0.322144
$850$	0	0
$851$	−43.6299	−1.49561
$852$	−6.85536	−0.234861
$853$	43.2044	1.47929	0.739645	−	0.672997i	$-0.234993\pi$
$853$	43.2044	1.47929	0.739645	+	0.672997i	$0.234993\pi$
$854$	16.2394	0.555699
$855$	0	0
$856$	8.81042	0.301134
$857$	−21.6193	−0.738501	−0.369250	−	0.929330i	$-0.620386\pi$
$857$	−21.6193	−0.738501	−0.369250	+	0.929330i	$0.620386\pi$
$858$	0.0590164	0.00201479
$859$	−39.0438	−1.33216	−0.666079	−	0.745881i	$-0.732029\pi$
$859$	−39.0438	−1.33216	−0.666079	+	0.745881i	$0.732029\pi$
$860$	0	0
$861$	14.8569	0.506322
$862$	−1.09220	−0.0372006
$863$	21.4189	0.729109	0.364554	−	0.931182i	$-0.381221\pi$
$863$	21.4189	0.729109	0.364554	+	0.931182i	$0.381221\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−12.1263	−0.412067
$867$	−19.5752	−0.664809
$868$	4.95429	0.168159
$869$	0.298912	0.0101399
$870$	0	0
$871$	−4.67908	−0.158545
$872$	15.8769	0.537659
$873$	−1.73974	−0.0588814
$874$	−14.4721	−0.489527
$875$	0	0
$876$	11.6375	0.393196
$877$	−46.9531	−1.58549	−0.792747	−	0.609551i	$-0.791350\pi$
$877$	−46.9531	−1.58549	−0.792747	+	0.609551i	$0.791350\pi$
$878$	13.8945	0.468916
$879$	−8.18160	−0.275958
$880$	0	0
$881$	0.326718	0.0110074	0.00550370	−	0.999985i	$-0.498248\pi$
$881$	0.326718	0.0110074	0.00550370	+	0.999985i	$0.498248\pi$
$882$	1.57358	0.0529851
$883$	13.8911	0.467471	0.233736	−	0.972300i	$-0.424905\pi$
$883$	13.8911	0.467471	0.233736	+	0.972300i	$0.424905\pi$
$884$	1.87500	0.0630631
$885$	0	0
$886$	38.2047	1.28351
$887$	5.43237	0.182401	0.0912006	−	0.995833i	$-0.470930\pi$
$887$	5.43237	0.182401	0.0912006	+	0.995833i	$0.470930\pi$
$888$	−9.75595	−0.327388
$889$	−23.8284	−0.799178
$890$	0	0
$891$	0.190355	0.00637713
$892$	−4.66249	−0.156112
$893$	34.6631	1.15996
$894$	−1.40819	−0.0470968
$895$	0	0
$896$	−2.92807	−0.0978199
$897$	−1.38651	−0.0462942
$898$	14.8092	0.494188
$899$	−11.5254	−0.384392
$900$	0	0
$901$	60.3066	2.00910
$902$	0.965855	0.0321594
$903$	29.9815	0.997723
$904$	19.1399	0.636585
$905$	0	0
$906$	7.87234	0.261541
$907$	48.3381	1.60504	0.802521	−	0.596624i	$-0.203492\pi$
$907$	48.3381	1.60504	0.802521	+	0.596624i	$0.203492\pi$
$908$	−0.573577	−0.0190348
$909$	−0.765188	−0.0253797
$910$	0	0
$911$	8.41563	0.278822	0.139411	−	0.990235i	$-0.455479\pi$
$911$	8.41563	0.278822	0.139411	+	0.990235i	$0.455479\pi$
$912$	−3.23607	−0.107157
$913$	−2.47833	−0.0820206
$914$	−4.86286	−0.160849
$915$	0	0
$916$	29.7330	0.982407
$917$	−48.6647	−1.60705
$918$	6.04775	0.199605
$919$	28.7074	0.946971	0.473485	−	0.880802i	$-0.342996\pi$
$919$	28.7074	0.946971	0.473485	+	0.880802i	$0.342996\pi$
$920$	0	0
$921$	5.85865	0.193049
$922$	−20.3058	−0.668737
$923$	−2.12539	−0.0699580
$924$	0.557372	0.0183362
$925$	0	0
$926$	−39.9825	−1.31391
$927$	−5.63298	−0.185011
$928$	6.81168	0.223604
$929$	−6.94897	−0.227988	−0.113994	−	0.993481i	$-0.536364\pi$
$929$	−6.94897	−0.227988	−0.113994	+	0.993481i	$0.536364\pi$
$930$	0	0
$931$	5.09220	0.166890
$932$	13.8769	0.454552
$933$	19.0398	0.623334
$934$	15.9416	0.521625
$935$	0	0
$936$	−0.310033	−0.0101337
$937$	−24.8603	−0.812150	−0.406075	−	0.913840i	$-0.633103\pi$
$937$	−24.8603	−0.812150	−0.406075	+	0.913840i	$0.633103\pi$
$938$	−44.1910	−1.44289
$939$	−11.9966	−0.391493
$940$	0	0
$941$	−0.470493	−0.0153376	−0.00766882	−	0.999971i	$-0.502441\pi$
$941$	−0.470493	−0.0153376	−0.00766882	+	0.999971i	$0.502441\pi$
$942$	−6.95554	−0.226624
$943$	−22.6915	−0.738936
$944$	7.42642	0.241709
$945$	0	0
$946$	1.94911	0.0633711
$947$	32.8498	1.06747	0.533737	−	0.845650i	$-0.320787\pi$
$947$	32.8498	1.06747	0.533737	+	0.845650i	$0.320787\pi$
$948$	−1.57029	−0.0510006
$949$	3.60802	0.117121
$950$	0	0
$951$	32.6126	1.05753
$952$	17.7082	0.573926
$953$	43.7035	1.41570	0.707848	−	0.706365i	$-0.249666\pi$
$953$	43.7035	1.41570	0.707848	+	0.706365i	$0.249666\pi$
$954$	−9.97175	−0.322847
$955$	0	0
$956$	−2.14387	−0.0693376
$957$	−1.29664	−0.0419143
$958$	−7.85613	−0.253820
$959$	−31.1497	−1.00588
$960$	0	0
$961$	−28.1371	−0.907650
$962$	−3.02467	−0.0975192
$963$	8.81042	0.283912
$964$	1.73974	0.0560334
$965$	0	0
$966$	−13.0947	−0.421316
$967$	43.3478	1.39397	0.696985	−	0.717086i	$-0.254524\pi$
$967$	43.3478	1.39397	0.696985	+	0.717086i	$0.254524\pi$
$968$	−10.9638	−0.352389
$969$	19.5709	0.628708
$970$	0	0
$971$	−30.1142	−0.966411	−0.483205	−	0.875507i	$-0.660528\pi$
$971$	−30.1142	−0.966411	−0.483205	+	0.875507i	$0.660528\pi$
$972$	−1.00000	−0.0320750
$973$	−67.0288	−2.14885
$974$	40.9465	1.31201
$975$	0	0
$976$	−5.54610	−0.177526
$977$	1.41132	0.0451523	0.0225761	−	0.999745i	$-0.492813\pi$
$977$	1.41132	0.0451523	0.0225761	+	0.999745i	$0.492813\pi$
$978$	−14.0000	−0.447671
$979$	−1.76722	−0.0564806
$980$	0	0
$981$	15.8769	0.506910
$982$	−7.51824	−0.239917
$983$	−9.71633	−0.309903	−0.154951	−	0.987922i	$-0.549522\pi$
$983$	−9.71633	−0.309903	−0.154951	+	0.987922i	$0.549522\pi$
$984$	−5.07397	−0.161752
$985$	0	0
$986$	−41.1953	−1.31193
$987$	31.3640	0.998326
$988$	−1.00329	−0.0319189
$989$	−45.7918	−1.45609
$990$	0	0
$991$	19.0154	0.604045	0.302022	−	0.953301i	$-0.402338\pi$
$991$	19.0154	0.604045	0.302022	+	0.953301i	$0.402338\pi$
$992$	−1.69200	−0.0537210
$993$	−3.23200	−0.102565
$994$	−20.0729	−0.636675
$995$	0	0
$996$	13.0195	0.412538
$997$	11.0373	0.349553	0.174777	−	0.984608i	$-0.444080\pi$
$997$	11.0373	0.349553	0.174777	+	0.984608i	$0.444080\pi$
$998$	15.7513	0.498597
$999$	−9.75595	−0.308665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3750.2.a.q.1.1		4
5.2	odd	4		3750.2.c.h.1249.5		8
5.3	odd	4		3750.2.c.h.1249.4		8
5.4	even	2		3750.2.a.l.1.4		4
25.3	odd	20		750.2.h.e.49.2		16
25.4	even	10		150.2.g.c.91.1	yes	8
25.6	even	5		750.2.g.d.301.1		8
25.8	odd	20		750.2.h.e.199.4		16
25.17	odd	20		750.2.h.e.199.1		16
25.19	even	10		150.2.g.c.61.1	✓	8
25.21	even	5		750.2.g.d.451.1		8
25.22	odd	20		750.2.h.e.49.3		16
75.29	odd	10		450.2.h.d.91.2		8
75.44	odd	10		450.2.h.d.361.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.c.61.1	✓	8	25.19	even	10
150.2.g.c.91.1	yes	8	25.4	even	10
450.2.h.d.91.2		8	75.29	odd	10
450.2.h.d.361.2		8	75.44	odd	10
750.2.g.d.301.1		8	25.6	even	5
750.2.g.d.451.1		8	25.21	even	5
750.2.h.e.49.2		16	25.3	odd	20
750.2.h.e.49.3		16	25.22	odd	20
750.2.h.e.199.1		16	25.17	odd	20
750.2.h.e.199.4		16	25.8	odd	20
3750.2.a.l.1.4		4	5.4	even	2
3750.2.a.q.1.1		4	1.1	even	1	trivial
3750.2.c.h.1249.4		8	5.3	odd	4
3750.2.c.h.1249.5		8	5.2	odd	4

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:	\( N \)	\(=\)	\( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3750.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.92807 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.92807 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.190355 q^{11} -1.00000 q^{12} -0.310033 q^{13} -2.92807 q^{14} +1.00000 q^{16} -6.04775 q^{17} +1.00000 q^{18} +3.23607 q^{19} +2.92807 q^{21} +0.190355 q^{22} -4.47214 q^{23} -1.00000 q^{24} -0.310033 q^{26} -1.00000 q^{27} -2.92807 q^{28} +6.81168 q^{29} -1.69200 q^{31} +1.00000 q^{32} -0.190355 q^{33} -6.04775 q^{34} +1.00000 q^{36} +9.75595 q^{37} +3.23607 q^{38} +0.310033 q^{39} +5.07397 q^{41} +2.92807 q^{42} +10.2394 q^{43} +0.190355 q^{44} -4.47214 q^{46} +10.7115 q^{47} -1.00000 q^{48} +1.57358 q^{49} +6.04775 q^{51} -0.310033 q^{52} -9.97175 q^{53} -1.00000 q^{54} -2.92807 q^{56} -3.23607 q^{57} +6.81168 q^{58} +7.42642 q^{59} -5.54610 q^{61} -1.69200 q^{62} -2.92807 q^{63} +1.00000 q^{64} -0.190355 q^{66} +15.0922 q^{67} -6.04775 q^{68} +4.47214 q^{69} +6.85536 q^{71} +1.00000 q^{72} -11.6375 q^{73} +9.75595 q^{74} +3.23607 q^{76} -0.557372 q^{77} +0.310033 q^{78} +1.57029 q^{79} +1.00000 q^{81} +5.07397 q^{82} -13.0195 q^{83} +2.92807 q^{84} +10.2394 q^{86} -6.81168 q^{87} +0.190355 q^{88} -9.28381 q^{89} +0.907798 q^{91} -4.47214 q^{92} +1.69200 q^{93} +10.7115 q^{94} -1.00000 q^{96} -1.73974 q^{97} +1.57358 q^{98} +0.190355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} + 5 q^{11} - 4 q^{12} + 7 q^{13} + q^{14} + 4 q^{16} + q^{17} + 4 q^{18} + 4 q^{19} - q^{21} + 5 q^{22} - 4 q^{24} + 7 q^{26} - 4 q^{27} + q^{28} + 11 q^{29} - 3 q^{31} + 4 q^{32} - 5 q^{33} + q^{34} + 4 q^{36} - 13 q^{37} + 4 q^{38} - 7 q^{39} + 21 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} - 4 q^{48} + 11 q^{49} - q^{51} + 7 q^{52} - 26 q^{53} - 4 q^{54} + q^{56} - 4 q^{57} + 11 q^{58} + 25 q^{59} - 5 q^{61} - 3 q^{62} + q^{63} + 4 q^{64} - 5 q^{66} + 26 q^{67} + q^{68} + 10 q^{71} + 4 q^{72} - 3 q^{73} - 13 q^{74} + 4 q^{76} - 30 q^{77} - 7 q^{78} + 27 q^{79} + 4 q^{81} + 21 q^{82} - 13 q^{83} - q^{84} + 16 q^{86} - 11 q^{87} + 5 q^{88} - 3 q^{89} + 38 q^{91} + 3 q^{93} - 4 q^{96} + 22 q^{97} + 11 q^{98} + 5 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9 + 5 * q^11 - 4 * q^12 + 7 * q^13 + q^14 + 4 * q^16 + q^17 + 4 * q^18 + 4 * q^19 - q^21 + 5 * q^22 - 4 * q^24 + 7 * q^26 - 4 * q^27 + q^28 + 11 * q^29 - 3 * q^31 + 4 * q^32 - 5 * q^33 + q^34 + 4 * q^36 - 13 * q^37 + 4 * q^38 - 7 * q^39 + 21 * q^41 - q^42 + 16 * q^43 + 5 * q^44 - 4 * q^48 + 11 * q^49 - q^51 + 7 * q^52 - 26 * q^53 - 4 * q^54 + q^56 - 4 * q^57 + 11 * q^58 + 25 * q^59 - 5 * q^61 - 3 * q^62 + q^63 + 4 * q^64 - 5 * q^66 + 26 * q^67 + q^68 + 10 * q^71 + 4 * q^72 - 3 * q^73 - 13 * q^74 + 4 * q^76 - 30 * q^77 - 7 * q^78 + 27 * q^79 + 4 * q^81 + 21 * q^82 - 13 * q^83 - q^84 + 16 * q^86 - 11 * q^87 + 5 * q^88 - 3 * q^89 + 38 * q^91 + 3 * q^93 - 4 * q^96 + 22 * q^97 + 11 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more