LMFDB - Embedded newform 4235.2.a.bb.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.580017.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 4x^{2} + 6x + 3 $ x^5 - 7x^3 - 4x^2 + 6*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.27779$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.27779 q^{2} +2.68935 q^{3} -0.367260 q^{4} -1.00000 q^{5} +3.43642 q^{6} +1.00000 q^{7} -3.02485 q^{8} +4.23262 q^{9} +O(q^{10})$	\(q+1.27779 q^{2} +2.68935 q^{3} -0.367260 q^{4} -1.00000 q^{5} +3.43642 q^{6} +1.00000 q^{7} -3.02485 q^{8} +4.23262 q^{9} -1.27779 q^{10} -0.987692 q^{12} -5.71421 q^{13} +1.27779 q^{14} -2.68935 q^{15} -3.13060 q^{16} +0.114328 q^{17} +5.40839 q^{18} -6.33354 q^{19} +0.367260 q^{20} +2.68935 q^{21} -5.42928 q^{23} -8.13490 q^{24} +1.00000 q^{25} -7.30154 q^{26} +3.31495 q^{27} -0.367260 q^{28} -3.52986 q^{29} -3.43642 q^{30} -7.76248 q^{31} +2.04947 q^{32} +0.146086 q^{34} -1.00000 q^{35} -1.55447 q^{36} +10.9880 q^{37} -8.09291 q^{38} -15.3675 q^{39} +3.02485 q^{40} +2.05057 q^{41} +3.43642 q^{42} -3.25834 q^{43} -4.23262 q^{45} -6.93746 q^{46} -0.743888 q^{47} -8.41929 q^{48} +1.00000 q^{49} +1.27779 q^{50} +0.307468 q^{51} +2.09860 q^{52} +0.656155 q^{53} +4.23580 q^{54} -3.02485 q^{56} -17.0331 q^{57} -4.51041 q^{58} -5.88567 q^{59} +0.987692 q^{60} -7.98055 q^{61} -9.91879 q^{62} +4.23262 q^{63} +8.87998 q^{64} +5.71421 q^{65} +12.0477 q^{67} -0.0419880 q^{68} -14.6012 q^{69} -1.27779 q^{70} -0.829397 q^{71} -12.8031 q^{72} +1.17180 q^{73} +14.0403 q^{74} +2.68935 q^{75} +2.32606 q^{76} -19.6364 q^{78} +0.699582 q^{79} +3.13060 q^{80} -3.78279 q^{81} +2.62019 q^{82} +8.74733 q^{83} -0.987692 q^{84} -0.114328 q^{85} -4.16346 q^{86} -9.49303 q^{87} +8.44787 q^{89} -5.40839 q^{90} -5.71421 q^{91} +1.99396 q^{92} -20.8760 q^{93} -0.950530 q^{94} +6.33354 q^{95} +5.51175 q^{96} -7.68221 q^{97} +1.27779 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 + 5 * q^7 - 12 * q^8 + 11 * q^9	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9} - 23 q^{12} - 10 q^{13} + 2 q^{15} + 10 q^{16} - 2 q^{17} - 5 q^{18} + 3 q^{19} - 4 q^{20} - 2 q^{21} + 3 q^{23} + 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} + 4 q^{28} - q^{29} - 5 q^{30} - 12 q^{31} - 29 q^{32} - 20 q^{34} - 5 q^{35} + 45 q^{36} + 9 q^{38} + 2 q^{39} + 12 q^{40} + 11 q^{41} + 5 q^{42} - 10 q^{43} - 11 q^{45} - 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} - 6 q^{51} - 30 q^{52} + 4 q^{53} + 34 q^{54} - 12 q^{56} - 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} - 40 q^{61} - q^{62} + 11 q^{63} + 38 q^{64} + 10 q^{65} + 7 q^{67} + 19 q^{68} - 24 q^{69} + 10 q^{71} - 72 q^{72} - 11 q^{73} + 37 q^{74} - 2 q^{75} - 3 q^{76} - 87 q^{78} - 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} - 26 q^{83} - 23 q^{84} + 2 q^{85} - 17 q^{86} - 14 q^{87} + 5 q^{89} + 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} - 44 q^{94} - 3 q^{95} + 84 q^{96} - 5 q^{97}+O(q^{100}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 + 5 * q^7 - 12 * q^8 + 11 * q^9 - 23 * q^12 - 10 * q^13 + 2 * q^15 + 10 * q^16 - 2 * q^17 - 5 * q^18 + 3 * q^19 - 4 * q^20 - 2 * q^21 + 3 * q^23 + 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 + 4 * q^28 - q^29 - 5 * q^30 - 12 * q^31 - 29 * q^32 - 20 * q^34 - 5 * q^35 + 45 * q^36 + 9 * q^38 + 2 * q^39 + 12 * q^40 + 11 * q^41 + 5 * q^42 - 10 * q^43 - 11 * q^45 - 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 - 6 * q^51 - 30 * q^52 + 4 * q^53 + 34 * q^54 - 12 * q^56 - 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 - 40 * q^61 - q^62 + 11 * q^63 + 38 * q^64 + 10 * q^65 + 7 * q^67 + 19 * q^68 - 24 * q^69 + 10 * q^71 - 72 * q^72 - 11 * q^73 + 37 * q^74 - 2 * q^75 - 3 * q^76 - 87 * q^78 - 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 - 26 * q^83 - 23 * q^84 + 2 * q^85 - 17 * q^86 - 14 * q^87 + 5 * q^89 + 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 - 44 * q^94 - 3 * q^95 + 84 * q^96 - 5 * q^97

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 $

$2$	1.27779	0.903532	0.451766	−	0.892136i	$-0.350794\pi$
$2$	1.27779	0.903532	0.451766	+	0.892136i	$0.350794\pi$
$3$	2.68935	1.55270	0.776349	−	0.630303i	$-0.217069\pi$
$3$	2.68935	1.55270	0.776349	+	0.630303i	$0.217069\pi$
$4$	−0.367260	−0.183630
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.43642	1.40291
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.02485	−1.06945
$9$	4.23262	1.41087
$10$	−1.27779	−0.404072
$11$	0	0
$11$	0	0
$12$	−0.987692	−0.285122
$13$	−5.71421	−1.58484	−0.792418	−	0.609978i	$-0.791178\pi$
$13$	−5.71421	−1.58484	−0.792418	+	0.609978i	$0.791178\pi$
$14$	1.27779	0.341503
$15$	−2.68935	−0.694388
$16$	−3.13060	−0.782650
$17$	0.114328	0.0277285	0.0138643	−	0.999904i	$-0.495587\pi$
$17$	0.114328	0.0277285	0.0138643	+	0.999904i	$0.495587\pi$
$18$	5.40839	1.27477
$19$	−6.33354	−1.45301	−0.726507	−	0.687159i	$-0.758857\pi$
$19$	−6.33354	−1.45301	−0.726507	+	0.687159i	$0.758857\pi$
$20$	0.367260	0.0821219
$21$	2.68935	0.586865
$22$	0	0
$23$	−5.42928	−1.13208	−0.566041	−	0.824377i	$-0.691526\pi$
$23$	−5.42928	−1.13208	−0.566041	+	0.824377i	$0.691526\pi$
$24$	−8.13490	−1.66053
$25$	1.00000	0.200000
$26$	−7.30154	−1.43195
$27$	3.31495	0.637962
$28$	−0.367260	−0.0694057
$29$	−3.52986	−0.655478	−0.327739	−	0.944768i	$-0.606287\pi$
$29$	−3.52986	−0.655478	−0.327739	+	0.944768i	$0.606287\pi$
$30$	−3.43642	−0.627402
$31$	−7.76248	−1.39418	−0.697091	−	0.716983i	$-0.745523\pi$
$31$	−7.76248	−1.39418	−0.697091	+	0.716983i	$0.745523\pi$
$32$	2.04947	0.362298
$33$	0	0
$34$	0.146086	0.0250536
$35$	−1.00000	−0.169031
$36$	−1.55447	−0.259079
$37$	10.9880	1.80641	0.903204	−	0.429211i	$-0.141208\pi$
$37$	10.9880	1.80641	0.903204	+	0.429211i	$0.141208\pi$
$38$	−8.09291	−1.31284
$39$	−15.3675	−2.46077
$40$	3.02485	0.478271
$41$	2.05057	0.320245	0.160123	−	0.987097i	$-0.448811\pi$
$41$	2.05057	0.320245	0.160123	+	0.987097i	$0.448811\pi$
$42$	3.43642	0.530251
$43$	−3.25834	−0.496892	−0.248446	−	0.968646i	$-0.579920\pi$
$43$	−3.25834	−0.496892	−0.248446	+	0.968646i	$0.579920\pi$
$44$	0	0
$45$	−4.23262	−0.630962
$46$	−6.93746	−1.02287
$47$	−0.743888	−0.108507	−0.0542536	−	0.998527i	$-0.517278\pi$
$47$	−0.743888	−0.108507	−0.0542536	+	0.998527i	$0.517278\pi$
$48$	−8.41929	−1.21522
$49$	1.00000	0.142857
$50$	1.27779	0.180706
$51$	0.307468	0.0430541
$52$	2.09860	0.291024
$53$	0.656155	0.0901298	0.0450649	−	0.998984i	$-0.485651\pi$
$53$	0.656155	0.0901298	0.0450649	+	0.998984i	$0.485651\pi$
$54$	4.23580	0.576419
$55$	0	0
$56$	−3.02485	−0.404213
$57$	−17.0331	−2.25609
$58$	−4.51041	−0.592245
$59$	−5.88567	−0.766249	−0.383125	−	0.923697i	$-0.625152\pi$
$59$	−5.88567	−0.766249	−0.383125	+	0.923697i	$0.625152\pi$
$60$	0.987692	0.127511
$61$	−7.98055	−1.02180	−0.510902	−	0.859639i	$-0.670689\pi$
$61$	−7.98055	−1.02180	−0.510902	+	0.859639i	$0.670689\pi$
$62$	−9.91879	−1.25969
$63$	4.23262	0.533260
$64$	8.87998	1.11000
$65$	5.71421	0.708760
$66$	0	0
$67$	12.0477	1.47187	0.735933	−	0.677054i	$-0.236744\pi$
$67$	12.0477	1.47187	0.735933	+	0.677054i	$0.236744\pi$
$68$	−0.0419880	−0.00509179
$69$	−14.6012	−1.75778
$70$	−1.27779	−0.152725
$71$	−0.829397	−0.0984313	−0.0492157	−	0.998788i	$-0.515672\pi$
$71$	−0.829397	−0.0984313	−0.0492157	+	0.998788i	$0.515672\pi$
$72$	−12.8031	−1.50885
$73$	1.17180	0.137149	0.0685746	−	0.997646i	$-0.478155\pi$
$73$	1.17180	0.137149	0.0685746	+	0.997646i	$0.478155\pi$
$74$	14.0403	1.63215
$75$	2.68935	0.310540
$76$	2.32606	0.266817
$77$	0	0
$78$	−19.6364	−2.22339
$79$	0.699582	0.0787092	0.0393546	−	0.999225i	$-0.487470\pi$
$79$	0.699582	0.0787092	0.0393546	+	0.999225i	$0.487470\pi$
$80$	3.13060	0.350012
$81$	−3.78279	−0.420310
$82$	2.62019	0.289352
$83$	8.74733	0.960144	0.480072	−	0.877229i	$-0.340611\pi$
$83$	8.74733	0.960144	0.480072	+	0.877229i	$0.340611\pi$
$84$	−0.987692	−0.107766
$85$	−0.114328	−0.0124006
$86$	−4.16346	−0.448957
$87$	−9.49303	−1.01776
$88$	0	0
$89$	8.44787	0.895472	0.447736	−	0.894166i	$-0.352230\pi$
$89$	8.44787	0.895472	0.447736	+	0.894166i	$0.352230\pi$
$90$	−5.40839	−0.570094
$91$	−5.71421	−0.599012
$92$	1.99396	0.207884
$93$	−20.8760	−2.16474
$94$	−0.950530	−0.0980397
$95$	6.33354	0.649807
$96$	5.51175	0.562540
$97$	−7.68221	−0.780010	−0.390005	−	0.920813i	$-0.627527\pi$
$97$	−7.68221	−0.780010	−0.390005	+	0.920813i	$0.627527\pi$
$98$	1.27779	0.129076
$99$	0	0
$100$	−0.367260	−0.0367260
$101$	−19.1938	−1.90986	−0.954929	−	0.296835i	$-0.904069\pi$
$101$	−19.1938	−1.90986	−0.954929	+	0.296835i	$0.904069\pi$
$102$	0.392878	0.0389007
$103$	−8.84677	−0.871698	−0.435849	−	0.900020i	$-0.643552\pi$
$103$	−8.84677	−0.871698	−0.435849	+	0.900020i	$0.643552\pi$
$104$	17.2846	1.69490
$105$	−2.68935	−0.262454
$106$	0.838427	0.0814352
$107$	15.4018	1.48895	0.744475	−	0.667650i	$-0.232700\pi$
$107$	15.4018	1.48895	0.744475	+	0.667650i	$0.232700\pi$
$108$	−1.21745	−0.117149
$109$	−3.91449	−0.374940	−0.187470	−	0.982270i	$-0.560029\pi$
$109$	−3.91449	−0.374940	−0.187470	+	0.982270i	$0.560029\pi$
$110$	0	0
$111$	29.5505	2.80481
$112$	−3.13060	−0.295814
$113$	17.7729	1.67193	0.835967	−	0.548780i	$-0.184908\pi$
$113$	17.7729	1.67193	0.835967	+	0.548780i	$0.184908\pi$
$114$	−21.7647	−2.03845
$115$	5.42928	0.506283
$116$	1.29638	0.120366
$117$	−24.1861	−2.23600
$118$	−7.52064	−0.692331
$119$	0.114328	0.0104804
$120$	8.13490	0.742612
$121$	0	0
$122$	−10.1974	−0.923233
$123$	5.51471	0.497245
$124$	2.85085	0.256014
$125$	−1.00000	−0.0894427
$126$	5.40839	0.481817
$127$	−3.11741	−0.276626	−0.138313	−	0.990389i	$-0.544168\pi$
$127$	−3.11741	−0.276626	−0.138313	+	0.990389i	$0.544168\pi$
$128$	7.24779	0.640620
$129$	−8.76282	−0.771523
$130$	7.30154	0.640387
$131$	−12.4579	−1.08845	−0.544225	−	0.838939i	$-0.683176\pi$
$131$	−12.4579	−1.08845	−0.544225	+	0.838939i	$0.683176\pi$
$132$	0	0
$133$	−6.33354	−0.549187
$134$	15.3945	1.32988
$135$	−3.31495	−0.285305
$136$	−0.345825	−0.0296542
$137$	−20.5066	−1.75200	−0.876000	−	0.482312i	$-0.839797\pi$
$137$	−20.5066	−1.75200	−0.876000	+	0.482312i	$0.839797\pi$
$138$	−18.6573	−1.58821
$139$	21.4970	1.82335	0.911675	−	0.410913i	$-0.134790\pi$
$139$	21.4970	1.82335	0.911675	+	0.410913i	$0.134790\pi$
$140$	0.367260	0.0310392
$141$	−2.00058	−0.168479
$142$	−1.05979	−0.0889358
$143$	0	0
$144$	−13.2506	−1.10422
$145$	3.52986	0.293139
$146$	1.49731	0.123919
$147$	2.68935	0.221814
$148$	−4.03544	−0.331711
$149$	−15.0366	−1.23185	−0.615925	−	0.787805i	$-0.711217\pi$
$149$	−15.0366	−1.23185	−0.615925	+	0.787805i	$0.711217\pi$
$150$	3.43642	0.280583
$151$	18.4655	1.50270	0.751351	−	0.659903i	$-0.229403\pi$
$151$	18.4655	1.50270	0.751351	+	0.659903i	$0.229403\pi$
$152$	19.1580	1.55392
$153$	0.483906	0.0391215
$154$	0	0
$155$	7.76248	0.623497
$156$	5.64388	0.451872
$157$	−3.80016	−0.303286	−0.151643	−	0.988435i	$-0.548456\pi$
$157$	−3.80016	−0.303286	−0.151643	+	0.988435i	$0.548456\pi$
$158$	0.893917	0.0711162
$159$	1.76463	0.139944
$160$	−2.04947	−0.162025
$161$	−5.42928	−0.427887
$162$	−4.83360	−0.379764
$163$	4.68279	0.366784	0.183392	−	0.983040i	$-0.441292\pi$
$163$	4.68279	0.366784	0.183392	+	0.983040i	$0.441292\pi$
$164$	−0.753093	−0.0588067
$165$	0	0
$166$	11.1772	0.867521
$167$	−19.7979	−1.53201	−0.766004	−	0.642836i	$-0.777758\pi$
$167$	−19.7979	−1.53201	−0.766004	+	0.642836i	$0.777758\pi$
$168$	−8.13490	−0.627621
$169$	19.6522	1.51171
$170$	−0.146086	−0.0112043
$171$	−26.8075	−2.05002
$172$	1.19666	0.0912443
$173$	5.03852	0.383072	0.191536	−	0.981486i	$-0.438653\pi$
$173$	5.03852	0.383072	0.191536	+	0.981486i	$0.438653\pi$
$174$	−12.1301	−0.919579
$175$	1.00000	0.0755929
$176$	0	0
$177$	−15.8287	−1.18975
$178$	10.7946	0.809088
$179$	3.48467	0.260457	0.130228	−	0.991484i	$-0.458429\pi$
$179$	3.48467	0.260457	0.130228	+	0.991484i	$0.458429\pi$
$180$	1.55447	0.115864
$181$	18.4355	1.37030	0.685149	−	0.728403i	$-0.259737\pi$
$181$	18.4355	1.37030	0.685149	+	0.728403i	$0.259737\pi$
$182$	−7.30154	−0.541226
$183$	−21.4625	−1.58655
$184$	16.4228	1.21070
$185$	−10.9880	−0.807850
$186$	−26.6751	−1.95592
$187$	0	0
$188$	0.273200	0.0199252
$189$	3.31495	0.241127
$190$	8.09291	0.587122
$191$	12.3915	0.896618	0.448309	−	0.893879i	$-0.352026\pi$
$191$	12.3915	0.896618	0.448309	+	0.893879i	$0.352026\pi$
$192$	23.8814	1.72349
$193$	−13.3250	−0.959151	−0.479576	−	0.877501i	$-0.659209\pi$
$193$	−13.3250	−0.959151	−0.479576	+	0.877501i	$0.659209\pi$
$194$	−9.81623	−0.704764
$195$	15.3675	1.10049
$196$	−0.367260	−0.0262329
$197$	−14.3676	−1.02365	−0.511824	−	0.859090i	$-0.671030\pi$
$197$	−14.3676	−1.02365	−0.511824	+	0.859090i	$0.671030\pi$
$198$	0	0
$199$	4.88790	0.346494	0.173247	−	0.984878i	$-0.444574\pi$
$199$	4.88790	0.346494	0.173247	+	0.984878i	$0.444574\pi$
$200$	−3.02485	−0.213890
$201$	32.4006	2.28537
$202$	−24.5256	−1.72562
$203$	−3.52986	−0.247747
$204$	−0.112921	−0.00790602
$205$	−2.05057	−0.143218
$206$	−11.3043	−0.787607
$207$	−22.9801	−1.59722
$208$	17.8889	1.24037
$209$	0	0
$210$	−3.43642	−0.237136
$211$	−19.7242	−1.35787	−0.678935	−	0.734199i	$-0.737558\pi$
$211$	−19.7242	−1.35787	−0.678935	+	0.734199i	$0.737558\pi$
$212$	−0.240980	−0.0165506
$213$	−2.23054	−0.152834
$214$	19.6802	1.34531
$215$	3.25834	0.222217
$216$	−10.0272	−0.682267
$217$	−7.76248	−0.526951
$218$	−5.00189	−0.338770
$219$	3.15139	0.212951
$220$	0	0
$221$	−0.653292	−0.0439452
$222$	37.7592	2.53423
$223$	18.8686	1.26353	0.631767	−	0.775159i	$-0.282330\pi$
$223$	18.8686	1.26353	0.631767	+	0.775159i	$0.282330\pi$
$224$	2.04947	0.136936
$225$	4.23262	0.282175
$226$	22.7100	1.51065
$227$	14.6125	0.969868	0.484934	−	0.874551i	$-0.338844\pi$
$227$	14.6125	0.969868	0.484934	+	0.874551i	$0.338844\pi$
$228$	6.25559	0.414286
$229$	19.1789	1.26738	0.633689	−	0.773588i	$-0.281540\pi$
$229$	19.1789	1.26738	0.633689	+	0.773588i	$0.281540\pi$
$230$	6.93746	0.457443
$231$	0	0
$232$	10.6773	0.700999
$233$	−20.6605	−1.35352	−0.676758	−	0.736206i	$-0.736615\pi$
$233$	−20.6605	−1.35352	−0.676758	+	0.736206i	$0.736615\pi$
$234$	−30.9046	−2.02030
$235$	0.743888	0.0485259
$236$	2.16157	0.140706
$237$	1.88142	0.122212
$238$	0.146086	0.00946938
$239$	−18.4967	−1.19645	−0.598227	−	0.801327i	$-0.704128\pi$
$239$	−18.4967	−1.19645	−0.598227	+	0.801327i	$0.704128\pi$
$240$	8.41929	0.543463
$241$	−22.3243	−1.43804	−0.719018	−	0.694992i	$-0.755408\pi$
$241$	−22.3243	−1.43804	−0.719018	+	0.694992i	$0.755408\pi$
$242$	0	0
$243$	−20.1181	−1.29058
$244$	2.93094	0.187634
$245$	−1.00000	−0.0638877
$246$	7.04662	0.449276
$247$	36.1912	2.30279
$248$	23.4804	1.49100
$249$	23.5247	1.49081
$250$	−1.27779	−0.0808143
$251$	−29.5965	−1.86812	−0.934058	−	0.357121i	$-0.883758\pi$
$251$	−29.5965	−1.86812	−0.934058	+	0.357121i	$0.883758\pi$
$252$	−1.55447	−0.0979226
$253$	0	0
$254$	−3.98339	−0.249940
$255$	−0.307468	−0.0192544
$256$	−8.49884	−0.531177
$257$	24.8642	1.55099	0.775494	−	0.631355i	$-0.217501\pi$
$257$	24.8642	1.55099	0.775494	+	0.631355i	$0.217501\pi$
$258$	−11.1970	−0.697096
$259$	10.9880	0.682758
$260$	−2.09860	−0.130150
$261$	−14.9405	−0.924797
$262$	−15.9185	−0.983449
$263$	10.2318	0.630917	0.315459	−	0.948939i	$-0.397842\pi$
$263$	10.2318	0.630917	0.315459	+	0.948939i	$0.397842\pi$
$264$	0	0
$265$	−0.656155	−0.0403073
$266$	−8.09291	−0.496208
$267$	22.7193	1.39040
$268$	−4.42466	−0.270279
$269$	5.45707	0.332724	0.166362	−	0.986065i	$-0.446798\pi$
$269$	5.45707	0.332724	0.166362	+	0.986065i	$0.446798\pi$
$270$	−4.23580	−0.257783
$271$	−6.88897	−0.418475	−0.209237	−	0.977865i	$-0.567098\pi$
$271$	−6.88897	−0.418475	−0.209237	+	0.977865i	$0.567098\pi$
$272$	−0.357914	−0.0217017
$273$	−15.3675	−0.930085
$274$	−26.2031	−1.58299
$275$	0	0
$276$	5.36246	0.322782
$277$	−25.1238	−1.50954	−0.754772	−	0.655988i	$-0.772252\pi$
$277$	−25.1238	−1.50954	−0.754772	+	0.655988i	$0.772252\pi$
$278$	27.4686	1.64745
$279$	−32.8556	−1.96701
$280$	3.02485	0.180770
$281$	16.4407	0.980771	0.490386	−	0.871506i	$-0.336856\pi$
$281$	16.4407	0.980771	0.490386	+	0.871506i	$0.336856\pi$
$282$	−2.55631	−0.152226
$283$	−6.27657	−0.373103	−0.186552	−	0.982445i	$-0.559731\pi$
$283$	−6.27657	−0.373103	−0.186552	+	0.982445i	$0.559731\pi$
$284$	0.304605	0.0180750
$285$	17.0331	1.00895
$286$	0	0
$287$	2.05057	0.121041
$288$	8.67463	0.511157
$289$	−16.9869	−0.999231
$290$	4.51041	0.264860
$291$	−20.6602	−1.21112
$292$	−0.430357	−0.0251847
$293$	5.98463	0.349626	0.174813	−	0.984602i	$-0.444068\pi$
$293$	5.98463	0.349626	0.174813	+	0.984602i	$0.444068\pi$
$294$	3.43642	0.200416
$295$	5.88567	0.342677
$296$	−33.2370	−1.93186
$297$	0	0
$298$	−19.2136	−1.11302
$299$	31.0240	1.79417
$300$	−0.987692	−0.0570245
$301$	−3.25834	−0.187807
$302$	23.5950	1.35774
$303$	−51.6190	−2.96543
$304$	19.8278	1.13720
$305$	7.98055	0.456965
$306$	0.618328	0.0353475
$307$	−24.1958	−1.38093	−0.690465	−	0.723366i	$-0.742594\pi$
$307$	−24.1958	−1.38093	−0.690465	+	0.723366i	$0.742594\pi$
$308$	0	0
$309$	−23.7921	−1.35348
$310$	9.91879	0.563350
$311$	−8.26385	−0.468600	−0.234300	−	0.972164i	$-0.575280\pi$
$311$	−8.26385	−0.468600	−0.234300	+	0.972164i	$0.575280\pi$
$312$	46.4845	2.63167
$313$	−3.32802	−0.188111	−0.0940554	−	0.995567i	$-0.529983\pi$
$313$	−3.32802	−0.188111	−0.0940554	+	0.995567i	$0.529983\pi$
$314$	−4.85580	−0.274029
$315$	−4.23262	−0.238481
$316$	−0.256929	−0.0144534
$317$	−4.42285	−0.248412	−0.124206	−	0.992256i	$-0.539638\pi$
$317$	−4.42285	−0.248412	−0.124206	+	0.992256i	$0.539638\pi$
$318$	2.25482	0.126444
$319$	0	0
$320$	−8.87998	−0.496406
$321$	41.4209	2.31189
$322$	−6.93746	−0.386610
$323$	−0.724099	−0.0402899
$324$	1.38927	0.0771816
$325$	−5.71421	−0.316967
$326$	5.98360	0.331401
$327$	−10.5274	−0.582169
$328$	−6.20268	−0.342486
$329$	−0.743888	−0.0410119
$330$	0	0
$331$	−35.1681	−1.93301	−0.966506	−	0.256644i	$-0.917383\pi$
$331$	−35.1681	−1.93301	−0.966506	+	0.256644i	$0.917383\pi$
$332$	−3.21255	−0.176311
$333$	46.5078	2.54861
$334$	−25.2975	−1.38422
$335$	−12.0477	−0.658239
$336$	−8.41929	−0.459310
$337$	14.5648	0.793397	0.396699	−	0.917949i	$-0.370156\pi$
$337$	14.5648	0.793397	0.396699	+	0.917949i	$0.370156\pi$
$338$	25.1113	1.36587
$339$	47.7976	2.59601
$340$	0.0419880	0.00227712
$341$	0	0
$342$	−34.2542	−1.85226
$343$	1.00000	0.0539949
$344$	9.85599	0.531399
$345$	14.6012	0.786104
$346$	6.43816	0.346118
$347$	36.7525	1.97298	0.986488	−	0.163834i	$-0.0523861\pi$
$347$	36.7525	1.97298	0.986488	+	0.163834i	$0.0523861\pi$
$348$	3.48641	0.186891
$349$	−6.07415	−0.325142	−0.162571	−	0.986697i	$-0.551979\pi$
$349$	−6.07415	−0.325142	−0.162571	+	0.986697i	$0.551979\pi$
$350$	1.27779	0.0683006
$351$	−18.9423	−1.01107
$352$	0	0
$353$	−25.7569	−1.37090	−0.685451	−	0.728119i	$-0.740395\pi$
$353$	−25.7569	−1.37090	−0.685451	+	0.728119i	$0.740395\pi$
$354$	−20.2256	−1.07498
$355$	0.829397	0.0440198
$356$	−3.10257	−0.164436
$357$	0.307468	0.0162729
$358$	4.45267	0.235331
$359$	−24.8162	−1.30975	−0.654876	−	0.755737i	$-0.727279\pi$
$359$	−24.8162	−1.30975	−0.654876	+	0.755737i	$0.727279\pi$
$360$	12.8031	0.674780
$361$	21.1137	1.11125
$362$	23.5566	1.23811
$363$	0	0
$364$	2.09860	0.109997
$365$	−1.17180	−0.0613350
$366$	−27.4245	−1.43350
$367$	−27.3679	−1.42859	−0.714296	−	0.699844i	$-0.753253\pi$
$367$	−27.3679	−1.42859	−0.714296	+	0.699844i	$0.753253\pi$
$368$	16.9969	0.886024
$369$	8.67929	0.451826
$370$	−14.0403	−0.729919
$371$	0.656155	0.0340659
$372$	7.66694	0.397512
$373$	10.7019	0.554125	0.277063	−	0.960852i	$-0.410639\pi$
$373$	10.7019	0.554125	0.277063	+	0.960852i	$0.410639\pi$
$374$	0	0
$375$	−2.68935	−0.138878
$376$	2.25015	0.116043
$377$	20.1703	1.03883
$378$	4.23580	0.217866
$379$	−1.03501	−0.0531647	−0.0265824	−	0.999647i	$-0.508462\pi$
$379$	−1.03501	−0.0531647	−0.0265824	+	0.999647i	$0.508462\pi$
$380$	−2.32606	−0.119324
$381$	−8.38382	−0.429516
$382$	15.8337	0.810123
$383$	−26.0652	−1.33187	−0.665935	−	0.746010i	$-0.731967\pi$
$383$	−26.0652	−1.33187	−0.665935	+	0.746010i	$0.731967\pi$
$384$	19.4919	0.994690
$385$	0	0
$386$	−17.0265	−0.866624
$387$	−13.7913	−0.701051
$388$	2.82137	0.143233
$389$	−12.3040	−0.623837	−0.311918	−	0.950109i	$-0.600972\pi$
$389$	−12.3040	−0.623837	−0.311918	+	0.950109i	$0.600972\pi$
$390$	19.6364	0.994329
$391$	−0.620717	−0.0313910
$392$	−3.02485	−0.152778
$393$	−33.5036	−1.69003
$394$	−18.3587	−0.924900
$395$	−0.699582	−0.0351998
$396$	0	0
$397$	30.3190	1.52167	0.760834	−	0.648946i	$-0.224790\pi$
$397$	30.3190	1.52167	0.760834	+	0.648946i	$0.224790\pi$
$398$	6.24569	0.313068
$399$	−17.0331	−0.852723
$400$	−3.13060	−0.156530
$401$	5.72615	0.285950	0.142975	−	0.989726i	$-0.454333\pi$
$401$	5.72615	0.285950	0.142975	+	0.989726i	$0.454333\pi$
$402$	41.4011	2.06490
$403$	44.3564	2.20955
$404$	7.04913	0.350707
$405$	3.78279	0.187968
$406$	−4.51041	−0.223848
$407$	0	0
$408$	−0.930045	−0.0460441
$409$	9.18023	0.453933	0.226967	−	0.973903i	$-0.427119\pi$
$409$	9.18023	0.453933	0.226967	+	0.973903i	$0.427119\pi$
$410$	−2.62019	−0.129402
$411$	−55.1496	−2.72033
$412$	3.24907	0.160070
$413$	−5.88567	−0.289615
$414$	−29.3636	−1.44314
$415$	−8.74733	−0.429389
$416$	−11.7111	−0.574184
$417$	57.8130	2.83111
$418$	0	0
$419$	19.3924	0.947380	0.473690	−	0.880692i	$-0.342922\pi$
$419$	19.3924	0.947380	0.473690	+	0.880692i	$0.342922\pi$
$420$	0.987692	0.0481945
$421$	−17.6613	−0.860759	−0.430379	−	0.902648i	$-0.641620\pi$
$421$	−17.6613	−0.860759	−0.430379	+	0.902648i	$0.641620\pi$
$422$	−25.2033	−1.22688
$423$	−3.14859	−0.153090
$424$	−1.98477	−0.0963891
$425$	0.114328	0.00554571
$426$	−2.85016	−0.138091
$427$	−7.98055	−0.386206
$428$	−5.65648	−0.273416
$429$	0	0
$430$	4.16346	0.200780
$431$	13.8924	0.669175	0.334588	−	0.942365i	$-0.391403\pi$
$431$	13.8924	0.669175	0.334588	+	0.942365i	$0.391403\pi$
$432$	−10.3778	−0.499301
$433$	21.5969	1.03788	0.518941	−	0.854810i	$-0.326326\pi$
$433$	21.5969	1.03788	0.518941	+	0.854810i	$0.326326\pi$
$434$	−9.91879	−0.476117
$435$	9.49303	0.455156
$436$	1.43764	0.0688503
$437$	34.3865	1.64493
$438$	4.02681	0.192408
$439$	−4.59245	−0.219186	−0.109593	−	0.993977i	$-0.534955\pi$
$439$	−4.59245	−0.219186	−0.109593	+	0.993977i	$0.534955\pi$
$440$	0	0
$441$	4.23262	0.201553
$442$	−0.834768	−0.0397059
$443$	18.0085	0.855609	0.427805	−	0.903871i	$-0.359287\pi$
$443$	18.0085	0.855609	0.427805	+	0.903871i	$0.359287\pi$
$444$	−10.8527	−0.515047
$445$	−8.44787	−0.400467
$446$	24.1100	1.14164
$447$	−40.4388	−1.91269
$448$	8.87998	0.419540
$449$	14.4902	0.683836	0.341918	−	0.939730i	$-0.388924\pi$
$449$	14.4902	0.683836	0.341918	+	0.939730i	$0.388924\pi$
$450$	5.40839	0.254954
$451$	0	0
$452$	−6.52728	−0.307017
$453$	49.6602	2.33324
$454$	18.6717	0.876307
$455$	5.71421	0.267886
$456$	51.5227	2.41277
$457$	−15.8719	−0.742455	−0.371228	−	0.928542i	$-0.621063\pi$
$457$	−15.8719	−0.742455	−0.371228	+	0.928542i	$0.621063\pi$
$458$	24.5066	1.14512
$459$	0.378990	0.0176898
$460$	−1.99396	−0.0929687
$461$	12.8746	0.599629	0.299815	−	0.953998i	$-0.403075\pi$
$461$	12.8746	0.599629	0.299815	+	0.953998i	$0.403075\pi$
$462$	0	0
$463$	24.7254	1.14909	0.574543	−	0.818475i	$-0.305180\pi$
$463$	24.7254	1.14909	0.574543	+	0.818475i	$0.305180\pi$
$464$	11.0506	0.513010
$465$	20.8760	0.968103
$466$	−26.3997	−1.22294
$467$	10.6779	0.494116	0.247058	−	0.969001i	$-0.420536\pi$
$467$	10.6779	0.494116	0.247058	+	0.969001i	$0.420536\pi$
$468$	8.88258	0.410597
$469$	12.0477	0.556313
$470$	0.950530	0.0438447
$471$	−10.2200	−0.470912
$472$	17.8033	0.819463
$473$	0	0
$474$	2.40406	0.110422
$475$	−6.33354	−0.290603
$476$	−0.0419880	−0.00192452
$477$	2.77726	0.127162
$478$	−23.6349	−1.08103
$479$	21.0362	0.961169	0.480584	−	0.876948i	$-0.340425\pi$
$479$	21.0362	0.961169	0.480584	+	0.876948i	$0.340425\pi$
$480$	−5.51175	−0.251576
$481$	−62.7874	−2.86286
$482$	−28.5257	−1.29931
$483$	−14.6012	−0.664380
$484$	0	0
$485$	7.68221	0.348831
$486$	−25.7067	−1.16608
$487$	11.4131	0.517176	0.258588	−	0.965988i	$-0.416743\pi$
$487$	11.4131	0.517176	0.258588	+	0.965988i	$0.416743\pi$
$488$	24.1400	1.09277
$489$	12.5937	0.569505
$490$	−1.27779	−0.0577245
$491$	−3.16966	−0.143045	−0.0715225	−	0.997439i	$-0.522786\pi$
$491$	−3.16966	−0.143045	−0.0715225	+	0.997439i	$0.522786\pi$
$492$	−2.02533	−0.0913091
$493$	−0.403560	−0.0181755
$494$	46.2446	2.08064
$495$	0	0
$496$	24.3012	1.09116
$497$	−0.829397	−0.0372035
$498$	30.0595	1.34700
$499$	−1.23960	−0.0554922	−0.0277461	−	0.999615i	$-0.508833\pi$
$499$	−1.23960	−0.0554922	−0.0277461	+	0.999615i	$0.508833\pi$
$500$	0.367260	0.0164244
$501$	−53.2435	−2.37875
$502$	−37.8181	−1.68790
$503$	−1.03614	−0.0461991	−0.0230996	−	0.999733i	$-0.507353\pi$
$503$	−1.03614	−0.0461991	−0.0230996	+	0.999733i	$0.507353\pi$
$504$	−12.8031	−0.570294
$505$	19.1938	0.854114
$506$	0	0
$507$	52.8516	2.34722
$508$	1.14490	0.0507968
$509$	29.4873	1.30700	0.653501	−	0.756926i	$-0.273300\pi$
$509$	29.4873	1.30700	0.653501	+	0.756926i	$0.273300\pi$
$510$	−0.392878	−0.0173969
$511$	1.17180	0.0518375
$512$	−25.3553	−1.12056
$513$	−20.9954	−0.926968
$514$	31.7712	1.40137
$515$	8.84677	0.389835
$516$	3.21823	0.141675
$517$	0	0
$518$	14.0403	0.616894
$519$	13.5504	0.594795
$520$	−17.2846	−0.757982
$521$	14.3644	0.629315	0.314658	−	0.949205i	$-0.398110\pi$
$521$	14.3644	0.629315	0.314658	+	0.949205i	$0.398110\pi$
$522$	−19.0908	−0.835583
$523$	26.0926	1.14095	0.570475	−	0.821315i	$-0.306759\pi$
$523$	26.0926	1.14095	0.570475	+	0.821315i	$0.306759\pi$
$524$	4.57528	0.199872
$525$	2.68935	0.117373
$526$	13.0740	0.570054
$527$	−0.887466	−0.0386586
$528$	0	0
$529$	6.47705	0.281611
$530$	−0.838427	−0.0364189
$531$	−24.9118	−1.08108
$532$	2.32606	0.100847
$533$	−11.7174	−0.507536
$534$	29.0304	1.25627
$535$	−15.4018	−0.665879
$536$	−36.4427	−1.57408
$537$	9.37152	0.404411
$538$	6.97298	0.300626
$539$	0	0
$540$	1.21745	0.0523907
$541$	24.4387	1.05070	0.525351	−	0.850885i	$-0.323934\pi$
$541$	24.4387	1.05070	0.525351	+	0.850885i	$0.323934\pi$
$542$	−8.80263	−0.378105
$543$	49.5795	2.12766
$544$	0.234311	0.0100460
$545$	3.91449	0.167678
$546$	−19.6364	−0.840361
$547$	−9.64267	−0.412291	−0.206145	−	0.978521i	$-0.566092\pi$
$547$	−9.64267	−0.412291	−0.206145	+	0.978521i	$0.566092\pi$
$548$	7.53127	0.321720
$549$	−33.7786	−1.44164
$550$	0	0
$551$	22.3565	0.952419
$552$	44.1666	1.87986
$553$	0.699582	0.0297493
$554$	−32.1029	−1.36392
$555$	−29.5505	−1.25435
$556$	−7.89498	−0.334822
$557$	11.0653	0.468852	0.234426	−	0.972134i	$-0.424679\pi$
$557$	11.0653	0.468852	0.234426	+	0.972134i	$0.424679\pi$
$558$	−41.9825	−1.77726
$559$	18.6188	0.787492
$560$	3.13060	0.132292
$561$	0	0
$562$	21.0077	0.886158
$563$	6.71297	0.282918	0.141459	−	0.989944i	$-0.454821\pi$
$563$	6.71297	0.282918	0.141459	+	0.989944i	$0.454821\pi$
$564$	0.734733	0.0309378
$565$	−17.7729	−0.747711
$566$	−8.02012	−0.337111
$567$	−3.78279	−0.158862
$568$	2.50881	0.105267
$569$	33.9179	1.42191	0.710955	−	0.703237i	$-0.248263\pi$
$569$	33.9179	1.42191	0.710955	+	0.703237i	$0.248263\pi$
$570$	21.7647	0.911623
$571$	20.0707	0.839931	0.419965	−	0.907540i	$-0.362042\pi$
$571$	20.0707	0.839931	0.419965	+	0.907540i	$0.362042\pi$
$572$	0	0
$573$	33.3252	1.39218
$574$	2.62019	0.109365
$575$	−5.42928	−0.226416
$576$	37.5856	1.56607
$577$	−36.6983	−1.52777	−0.763884	−	0.645353i	$-0.776710\pi$
$577$	−36.6983	−1.52777	−0.763884	+	0.645353i	$0.776710\pi$
$578$	−21.7057	−0.902837
$579$	−35.8355	−1.48927
$580$	−1.29638	−0.0538291
$581$	8.74733	0.362900
$582$	−26.3993	−1.09429
$583$	0	0
$584$	−3.54453	−0.146674
$585$	24.1861	0.999971
$586$	7.64708	0.315898
$587$	0.710389	0.0293209	0.0146604	−	0.999893i	$-0.495333\pi$
$587$	0.710389	0.0293209	0.0146604	+	0.999893i	$0.495333\pi$
$588$	−0.987692	−0.0407318
$589$	49.1639	2.02577
$590$	7.52064	0.309620
$591$	−38.6395	−1.58942
$592$	−34.3989	−1.41379
$593$	−3.10847	−0.127650	−0.0638248	−	0.997961i	$-0.520330\pi$
$593$	−3.10847	−0.127650	−0.0638248	+	0.997961i	$0.520330\pi$
$594$	0	0
$595$	−0.114328	−0.00468698
$596$	5.52236	0.226205
$597$	13.1453	0.538000
$598$	39.6421	1.62109
$599$	−10.8079	−0.441600	−0.220800	−	0.975319i	$-0.570867\pi$
$599$	−10.8079	−0.441600	−0.220800	+	0.975319i	$0.570867\pi$
$600$	−8.13490	−0.332106
$601$	1.36180	0.0555488	0.0277744	−	0.999614i	$-0.491158\pi$
$601$	1.36180	0.0555488	0.0277744	+	0.999614i	$0.491158\pi$
$602$	−4.16346	−0.169690
$603$	50.9935	2.07662
$604$	−6.78164	−0.275941
$605$	0	0
$606$	−65.9581	−2.67936
$607$	−20.6040	−0.836291	−0.418146	−	0.908380i	$-0.637320\pi$
$607$	−20.6040	−0.836291	−0.418146	+	0.908380i	$0.637320\pi$
$608$	−12.9804	−0.526425
$609$	−9.49303	−0.384677
$610$	10.1974	0.412882
$611$	4.25073	0.171966
$612$	−0.177719	−0.00718388
$613$	−2.68962	−0.108633	−0.0543163	−	0.998524i	$-0.517298\pi$
$613$	−2.68962	−0.108633	−0.0543163	+	0.998524i	$0.517298\pi$
$614$	−30.9171	−1.24771
$615$	−5.51471	−0.222375
$616$	0	0
$617$	20.2761	0.816285	0.408143	−	0.912918i	$-0.366177\pi$
$617$	20.2761	0.816285	0.408143	+	0.912918i	$0.366177\pi$
$618$	−30.4012	−1.22292
$619$	−34.1015	−1.37066	−0.685328	−	0.728234i	$-0.740341\pi$
$619$	−34.1015	−1.37066	−0.685328	+	0.728234i	$0.740341\pi$
$620$	−2.85085	−0.114493
$621$	−17.9978	−0.722226
$622$	−10.5594	−0.423395
$623$	8.44787	0.338457
$624$	48.1096	1.92592
$625$	1.00000	0.0400000
$626$	−4.25250	−0.169964
$627$	0	0
$628$	1.39565	0.0556925
$629$	1.25623	0.0500891
$630$	−5.40839	−0.215475
$631$	17.5803	0.699861	0.349930	−	0.936776i	$-0.386205\pi$
$631$	17.5803	0.699861	0.349930	+	0.936776i	$0.386205\pi$
$632$	−2.11613	−0.0841753
$633$	−53.0453	−2.10836
$634$	−5.65146	−0.224448
$635$	3.11741	0.123711
$636$	−0.648079	−0.0256980
$637$	−5.71421	−0.226405
$638$	0	0
$639$	−3.51052	−0.138874
$640$	−7.24779	−0.286494
$641$	−20.4508	−0.807758	−0.403879	−	0.914812i	$-0.632338\pi$
$641$	−20.4508	−0.807758	−0.403879	+	0.914812i	$0.632338\pi$
$642$	52.9271	2.08887
$643$	−17.9192	−0.706665	−0.353332	−	0.935498i	$-0.614951\pi$
$643$	−17.9192	−0.706665	−0.353332	+	0.935498i	$0.614951\pi$
$644$	1.99396	0.0785729
$645$	8.76282	0.345036
$646$	−0.925244	−0.0364032
$647$	27.5048	1.08133	0.540663	−	0.841239i	$-0.318173\pi$
$647$	27.5048	1.08133	0.540663	+	0.841239i	$0.318173\pi$
$648$	11.4424	0.449500
$649$	0	0
$650$	−7.30154	−0.286390
$651$	−20.8760	−0.818197
$652$	−1.71980	−0.0673526
$653$	−44.8740	−1.75606	−0.878028	−	0.478610i	$-0.841141\pi$
$653$	−44.8740	−1.75606	−0.878028	+	0.478610i	$0.841141\pi$
$654$	−13.4518	−0.526008
$655$	12.4579	0.486769
$656$	−6.41952	−0.250640
$657$	4.95980	0.193500
$658$	−0.950530	−0.0370555
$659$	−33.2963	−1.29704	−0.648521	−	0.761197i	$-0.724612\pi$
$659$	−33.2963	−1.29704	−0.648521	+	0.761197i	$0.724612\pi$
$660$	0	0
$661$	−20.7701	−0.807863	−0.403932	−	0.914789i	$-0.632357\pi$
$661$	−20.7701	−0.807863	−0.403932	+	0.914789i	$0.632357\pi$
$662$	−44.9373	−1.74654
$663$	−1.75693	−0.0682336
$664$	−26.4594	−1.02682
$665$	6.33354	0.245604
$666$	59.4271	2.30275
$667$	19.1646	0.742055
$668$	7.27098	0.281323
$669$	50.7443	1.96189
$670$	−15.3945	−0.594740
$671$	0	0
$672$	5.51175	0.212620
$673$	−36.8748	−1.42142	−0.710710	−	0.703485i	$-0.751626\pi$
$673$	−36.8748	−1.42142	−0.710710	+	0.703485i	$0.751626\pi$
$674$	18.6108	0.716860
$675$	3.31495	0.127592
$676$	−7.21746	−0.277595
$677$	−13.3892	−0.514588	−0.257294	−	0.966333i	$-0.582831\pi$
$677$	−13.3892	−0.514588	−0.257294	+	0.966333i	$0.582831\pi$
$678$	61.0752	2.34558
$679$	−7.68221	−0.294816
$680$	0.345825	0.0132618
$681$	39.2983	1.50591
$682$	0	0
$683$	−4.46213	−0.170739	−0.0853693	−	0.996349i	$-0.527207\pi$
$683$	−4.46213	−0.170739	−0.0853693	+	0.996349i	$0.527207\pi$
$684$	9.84531	0.376445
$685$	20.5066	0.783518
$686$	1.27779	0.0487861
$687$	51.5788	1.96786
$688$	10.2005	0.388892
$689$	−3.74941	−0.142841
$690$	18.6573	0.710270
$691$	−32.9632	−1.25398	−0.626990	−	0.779027i	$-0.715713\pi$
$691$	−32.9632	−1.25398	−0.626990	+	0.779027i	$0.715713\pi$
$692$	−1.85045	−0.0703435
$693$	0	0
$694$	46.9618	1.78265
$695$	−21.4970	−0.815427
$696$	28.7150	1.08844
$697$	0.234437	0.00887994
$698$	−7.76147	−0.293776
$699$	−55.5634	−2.10160
$700$	−0.367260	−0.0138811
$701$	10.0233	0.378574	0.189287	−	0.981922i	$-0.439382\pi$
$701$	10.0233	0.378574	0.189287	+	0.981922i	$0.439382\pi$
$702$	−24.2042	−0.913530
$703$	−69.5926	−2.62474
$704$	0	0
$705$	2.00058	0.0753461
$706$	−32.9118	−1.23865
$707$	−19.1938	−0.721858
$708$	5.81323	0.218475
$709$	−35.3012	−1.32576	−0.662882	−	0.748724i	$-0.730667\pi$
$709$	−35.3012	−1.32576	−0.662882	+	0.748724i	$0.730667\pi$
$710$	1.05979	0.0397733
$711$	2.96107	0.111049
$712$	−25.5536	−0.957660
$713$	42.1446	1.57833
$714$	0.392878	0.0147031
$715$	0	0
$716$	−1.27978	−0.0478277
$717$	−49.7442	−1.85773
$718$	−31.7099	−1.18340
$719$	−15.8441	−0.590886	−0.295443	−	0.955360i	$-0.595467\pi$
$719$	−15.8441	−0.590886	−0.295443	+	0.955360i	$0.595467\pi$
$720$	13.2506	0.493822
$721$	−8.84677	−0.329471
$722$	26.9788	1.00405
$723$	−60.0380	−2.23284
$724$	−6.77062	−0.251628
$725$	−3.52986	−0.131096
$726$	0	0
$727$	41.9381	1.55540	0.777699	−	0.628636i	$-0.216387\pi$
$727$	41.9381	1.55540	0.777699	+	0.628636i	$0.216387\pi$
$728$	17.2846	0.640612
$729$	−42.7563	−1.58357
$730$	−1.49731	−0.0554181
$731$	−0.372518	−0.0137781
$732$	7.88233	0.291339
$733$	−15.6164	−0.576806	−0.288403	−	0.957509i	$-0.593124\pi$
$733$	−15.6164	−0.576806	−0.288403	+	0.957509i	$0.593124\pi$
$734$	−34.9703	−1.29078
$735$	−2.68935	−0.0991983
$736$	−11.1271	−0.410152
$737$	0	0
$738$	11.0903	0.408239
$739$	2.15862	0.0794060	0.0397030	−	0.999212i	$-0.487359\pi$
$739$	2.15862	0.0794060	0.0397030	+	0.999212i	$0.487359\pi$
$740$	4.03544	0.148346
$741$	97.3308	3.57554
$742$	0.838427	0.0307796
$743$	23.1867	0.850638	0.425319	−	0.905044i	$-0.360162\pi$
$743$	23.1867	0.850638	0.425319	+	0.905044i	$0.360162\pi$
$744$	63.1470	2.31508
$745$	15.0366	0.550900
$746$	13.6748	0.500670
$747$	37.0241	1.35464
$748$	0	0
$749$	15.4018	0.562770
$750$	−3.43642	−0.125480
$751$	−32.8301	−1.19799	−0.598993	−	0.800754i	$-0.704432\pi$
$751$	−32.8301	−1.19799	−0.598993	+	0.800754i	$0.704432\pi$
$752$	2.32882	0.0849232
$753$	−79.5955	−2.90062
$754$	25.7734	0.938612
$755$	−18.4655	−0.672028
$756$	−1.21745	−0.0442782
$757$	14.5746	0.529722	0.264861	−	0.964287i	$-0.414674\pi$
$757$	14.5746	0.529722	0.264861	+	0.964287i	$0.414674\pi$
$758$	−1.32252	−0.0480360
$759$	0	0
$760$	−19.1580	−0.694935
$761$	10.0458	0.364159	0.182080	−	0.983284i	$-0.441717\pi$
$761$	10.0458	0.364159	0.182080	+	0.983284i	$0.441717\pi$
$762$	−10.7127	−0.388082
$763$	−3.91449	−0.141714
$764$	−4.55091	−0.164646
$765$	−0.483906	−0.0174956
$766$	−33.3058	−1.20339
$767$	33.6320	1.21438
$768$	−22.8564	−0.824758
$769$	−21.2784	−0.767320	−0.383660	−	0.923475i	$-0.625336\pi$
$769$	−21.2784	−0.767320	−0.383660	+	0.923475i	$0.625336\pi$
$770$	0	0
$771$	66.8687	2.40822
$772$	4.89373	0.176129
$773$	6.70714	0.241239	0.120620	−	0.992699i	$-0.461512\pi$
$773$	6.70714	0.241239	0.120620	+	0.992699i	$0.461512\pi$
$774$	−17.6223	−0.633422
$775$	−7.76248	−0.278836
$776$	23.2376	0.834180
$777$	29.5505	1.06012
$778$	−15.7219	−0.563657
$779$	−12.9874	−0.465321
$780$	−5.64388	−0.202083
$781$	0	0
$782$	−0.793144	−0.0283628
$783$	−11.7013	−0.418170
$784$	−3.13060	−0.111807
$785$	3.80016	0.135634
$786$	−42.8105	−1.52700
$787$	3.15876	0.112597	0.0562987	−	0.998414i	$-0.482070\pi$
$787$	3.15876	0.112597	0.0562987	+	0.998414i	$0.482070\pi$
$788$	5.27665	0.187973
$789$	27.5168	0.979624
$790$	−0.893917	−0.0318041
$791$	17.7729	0.631932
$792$	0	0
$793$	45.6025	1.61939
$794$	38.7413	1.37488
$795$	−1.76463	−0.0625851
$796$	−1.79513	−0.0636267
$797$	−54.6066	−1.93427	−0.967133	−	0.254270i	$-0.918165\pi$
$797$	−54.6066	−1.93427	−0.967133	+	0.254270i	$0.918165\pi$
$798$	−21.7647	−0.770462
$799$	−0.0850470	−0.00300875
$800$	2.04947	0.0724597
$801$	35.7566	1.26340
$802$	7.31680	0.258365
$803$	0	0
$804$	−11.8995	−0.419662
$805$	5.42928	0.191357
$806$	56.6780	1.99640
$807$	14.6760	0.516619
$808$	58.0586	2.04249
$809$	22.3195	0.784712	0.392356	−	0.919814i	$-0.371660\pi$
$809$	22.3195	0.784712	0.392356	+	0.919814i	$0.371660\pi$
$810$	4.83360	0.169835
$811$	27.7089	0.972990	0.486495	−	0.873683i	$-0.338275\pi$
$811$	27.7089	0.972990	0.486495	+	0.873683i	$0.338275\pi$
$812$	1.29638	0.0454939
$813$	−18.5269	−0.649765
$814$	0	0
$815$	−4.68279	−0.164031
$816$	−0.962558	−0.0336963
$817$	20.6368	0.721990
$818$	11.7304	0.410143
$819$	−24.1861	−0.845130
$820$	0.753093	0.0262992
$821$	23.1125	0.806632	0.403316	−	0.915061i	$-0.367858\pi$
$821$	23.1125	0.806632	0.403316	+	0.915061i	$0.367858\pi$
$822$	−70.4694	−2.45790
$823$	25.2118	0.878827	0.439413	−	0.898285i	$-0.355186\pi$
$823$	25.2118	0.878827	0.439413	+	0.898285i	$0.355186\pi$
$824$	26.7602	0.932235
$825$	0	0
$826$	−7.52064	−0.261676
$827$	20.9598	0.728844	0.364422	−	0.931234i	$-0.381267\pi$
$827$	20.9598	0.728844	0.364422	+	0.931234i	$0.381267\pi$
$828$	8.43966	0.293299
$829$	−0.142169	−0.00493774	−0.00246887	−	0.999997i	$-0.500786\pi$
$829$	−0.142169	−0.00493774	−0.00246887	+	0.999997i	$0.500786\pi$
$830$	−11.1772	−0.387967
$831$	−67.5668	−2.34387
$832$	−50.7421	−1.75916
$833$	0.114328	0.00396122
$834$	73.8726	2.55800
$835$	19.7979	0.685135
$836$	0	0
$837$	−25.7322	−0.889436
$838$	24.7793	0.855988
$839$	−27.2849	−0.941979	−0.470989	−	0.882139i	$-0.656103\pi$
$839$	−27.2849	−0.941979	−0.470989	+	0.882139i	$0.656103\pi$
$840$	8.13490	0.280681
$841$	−16.5401	−0.570348
$842$	−22.5674	−0.777723
$843$	44.2149	1.52284
$844$	7.24391	0.249346
$845$	−19.6522	−0.676055
$846$	−4.02323	−0.138322
$847$	0	0
$848$	−2.05416	−0.0705401
$849$	−16.8799	−0.579317
$850$	0.146086	0.00501072
$851$	−59.6566	−2.04500
$852$	0.819189	0.0280650
$853$	−36.8827	−1.26284	−0.631420	−	0.775441i	$-0.717528\pi$
$853$	−36.8827	−1.26284	−0.631420	+	0.775441i	$0.717528\pi$
$854$	−10.1974	−0.348949
$855$	26.8075	0.916796
$856$	−46.5883	−1.59235
$857$	−18.6949	−0.638606	−0.319303	−	0.947653i	$-0.603449\pi$
$857$	−18.6949	−0.638606	−0.319303	+	0.947653i	$0.603449\pi$
$858$	0	0
$859$	−24.6718	−0.841790	−0.420895	−	0.907109i	$-0.638284\pi$
$859$	−24.6718	−0.841790	−0.420895	+	0.907109i	$0.638284\pi$
$860$	−1.19666	−0.0408057
$861$	5.51471	0.187941
$862$	17.7516	0.604621
$863$	−35.1893	−1.19786	−0.598930	−	0.800802i	$-0.704407\pi$
$863$	−35.1893	−1.19786	−0.598930	+	0.800802i	$0.704407\pi$
$864$	6.79389	0.231133
$865$	−5.03852	−0.171315
$866$	27.5963	0.937760
$867$	−45.6838	−1.55150
$868$	2.85085	0.0967641
$869$	0	0
$870$	12.1301	0.411248
$871$	−68.8433	−2.33267
$872$	11.8408	0.400979
$873$	−32.5159	−1.10050
$874$	43.9387	1.48625
$875$	−1.00000	−0.0338062
$876$	−1.15738	−0.0391043
$877$	−10.6113	−0.358319	−0.179160	−	0.983820i	$-0.557338\pi$
$877$	−10.6113	−0.358319	−0.179160	+	0.983820i	$0.557338\pi$
$878$	−5.86818	−0.198041
$879$	16.0948	0.542863
$880$	0	0
$881$	7.08762	0.238788	0.119394	−	0.992847i	$-0.461905\pi$
$881$	7.08762	0.238788	0.119394	+	0.992847i	$0.461905\pi$
$882$	5.40839	0.182110
$883$	−33.3327	−1.12174	−0.560868	−	0.827906i	$-0.689532\pi$
$883$	−33.3327	−1.12174	−0.560868	+	0.827906i	$0.689532\pi$
$884$	0.239928	0.00806966
$885$	15.8287	0.532074
$886$	23.0110	0.773070
$887$	6.54635	0.219805	0.109902	−	0.993942i	$-0.464946\pi$
$887$	6.54635	0.219805	0.109902	+	0.993942i	$0.464946\pi$
$888$	−89.3859	−2.99959
$889$	−3.11741	−0.104555
$890$	−10.7946	−0.361835
$891$	0	0
$892$	−6.92968	−0.232023
$893$	4.71144	0.157662
$894$	−51.6722	−1.72818
$895$	−3.48467	−0.116480
$896$	7.24779	0.242132
$897$	83.4345	2.78580
$898$	18.5154	0.617867
$899$	27.4004	0.913856
$900$	−1.55447	−0.0518158
$901$	0.0750167	0.00249917
$902$	0	0
$903$	−8.76282	−0.291608
$904$	−53.7604	−1.78805
$905$	−18.4355	−0.612816
$906$	63.4552	2.10816
$907$	48.2558	1.60231	0.801154	−	0.598458i	$-0.204220\pi$
$907$	48.2558	1.60231	0.801154	+	0.598458i	$0.204220\pi$
$908$	−5.36661	−0.178097
$909$	−81.2402	−2.69457
$910$	7.30154	0.242044
$911$	8.98748	0.297768	0.148884	−	0.988855i	$-0.452432\pi$
$911$	8.98748	0.297768	0.148884	+	0.988855i	$0.452432\pi$
$912$	53.3239	1.76573
$913$	0	0
$914$	−20.2809	−0.670832
$915$	21.4625	0.709529
$916$	−7.04365	−0.232729
$917$	−12.4579	−0.411395
$918$	0.484269	0.0159833
$919$	54.8689	1.80996	0.904979	−	0.425457i	$-0.139887\pi$
$919$	54.8689	1.80996	0.904979	+	0.425457i	$0.139887\pi$
$920$	−16.4228	−0.541443
$921$	−65.0711	−2.14417
$922$	16.4510	0.541784
$923$	4.73935	0.155997
$924$	0	0
$925$	10.9880	0.361282
$926$	31.5938	1.03824
$927$	−37.4450	−1.22986
$928$	−7.23434	−0.237479
$929$	−53.6029	−1.75866	−0.879328	−	0.476217i	$-0.842008\pi$
$929$	−53.6029	−1.75866	−0.879328	+	0.476217i	$0.842008\pi$
$930$	26.6751	0.874712
$931$	−6.33354	−0.207573
$932$	7.58778	0.248546
$933$	−22.2244	−0.727595
$934$	13.6441	0.446450
$935$	0	0
$936$	73.1593	2.39129
$937$	45.2105	1.47696	0.738482	−	0.674274i	$-0.235543\pi$
$937$	45.2105	1.47696	0.738482	+	0.674274i	$0.235543\pi$
$938$	15.3945	0.502647
$939$	−8.95022	−0.292079
$940$	−0.273200	−0.00891082
$941$	53.2174	1.73484	0.867419	−	0.497578i	$-0.165777\pi$
$941$	53.2174	1.73484	0.867419	+	0.497578i	$0.165777\pi$
$942$	−13.0590	−0.425484
$943$	−11.1331	−0.362544
$944$	18.4257	0.599705
$945$	−3.31495	−0.107835
$946$	0	0
$947$	2.16339	0.0703008	0.0351504	−	0.999382i	$-0.488809\pi$
$947$	2.16339	0.0703008	0.0351504	+	0.999382i	$0.488809\pi$
$948$	−0.690972	−0.0224417
$949$	−6.69592	−0.217359
$950$	−8.09291	−0.262569
$951$	−11.8946	−0.385709
$952$	−0.345825	−0.0112082
$953$	11.5589	0.374431	0.187215	−	0.982319i	$-0.440054\pi$
$953$	11.5589	0.374431	0.187215	+	0.982319i	$0.440054\pi$
$954$	3.54874	0.114895
$955$	−12.3915	−0.400980
$956$	6.79312	0.219705
$957$	0	0
$958$	26.8798	0.868447
$959$	−20.5066	−0.662193
$960$	−23.8814	−0.770769
$961$	29.2561	0.943744
$962$	−80.2290	−2.58669
$963$	65.1900	2.10072
$964$	8.19883	0.264067
$965$	13.3250	0.428946
$966$	−18.6573	−0.600288
$967$	27.8539	0.895721	0.447860	−	0.894104i	$-0.352186\pi$
$967$	27.8539	0.895721	0.447860	+	0.894104i	$0.352186\pi$
$968$	0	0
$969$	−1.94736	−0.0625581
$970$	9.81623	0.315180
$971$	33.5681	1.07725	0.538625	−	0.842545i	$-0.318944\pi$
$971$	33.5681	1.07725	0.538625	+	0.842545i	$0.318944\pi$
$972$	7.38858	0.236989
$973$	21.4970	0.689161
$974$	14.5835	0.467285
$975$	−15.3675	−0.492155
$976$	24.9839	0.799715
$977$	29.3005	0.937406	0.468703	−	0.883356i	$-0.344721\pi$
$977$	29.3005	0.937406	0.468703	+	0.883356i	$0.344721\pi$
$978$	16.0920	0.514566
$979$	0	0
$980$	0.367260	0.0117317
$981$	−16.5686	−0.528993
$982$	−4.05016	−0.129246
$983$	15.9995	0.510305	0.255153	−	0.966901i	$-0.417874\pi$
$983$	15.9995	0.510305	0.255153	+	0.966901i	$0.417874\pi$
$984$	−16.6812	−0.531777
$985$	14.3676	0.457790
$986$	−0.515664	−0.0164221
$987$	−2.00058	−0.0636791
$988$	−13.2916	−0.422861
$989$	17.6904	0.562522
$990$	0	0
$991$	−22.8782	−0.726749	−0.363375	−	0.931643i	$-0.618376\pi$
$991$	−22.8782	−0.726749	−0.363375	+	0.931643i	$0.618376\pi$
$992$	−15.9090	−0.505110
$993$	−94.5794	−3.00139
$994$	−1.05979	−0.0336146
$995$	−4.88790	−0.154957
$996$	−8.63967	−0.273758
$997$	−14.5120	−0.459598	−0.229799	−	0.973238i	$-0.573807\pi$
$997$	−14.5120	−0.459598	−0.229799	+	0.973238i	$0.573807\pi$
$998$	−1.58395	−0.0501389
$999$	36.4245	1.15242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bb.1.4	yes	5
11.10	odd	2		4235.2.a.ba.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.ba.1.2	✓	5	11.10	odd	2
4235.2.a.bb.1.4	yes	5	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+1.27779 q^{2} +2.68935 q^{3} -0.367260 q^{4} -1.00000 q^{5} +3.43642 q^{6} +1.00000 q^{7} -3.02485 q^{8} +4.23262 q^{9} +O(q^{10})\)	\(q+1.27779 q^{2} +2.68935 q^{3} -0.367260 q^{4} -1.00000 q^{5} +3.43642 q^{6} +1.00000 q^{7} -3.02485 q^{8} +4.23262 q^{9} -1.27779 q^{10} -0.987692 q^{12} -5.71421 q^{13} +1.27779 q^{14} -2.68935 q^{15} -3.13060 q^{16} +0.114328 q^{17} +5.40839 q^{18} -6.33354 q^{19} +0.367260 q^{20} +2.68935 q^{21} -5.42928 q^{23} -8.13490 q^{24} +1.00000 q^{25} -7.30154 q^{26} +3.31495 q^{27} -0.367260 q^{28} -3.52986 q^{29} -3.43642 q^{30} -7.76248 q^{31} +2.04947 q^{32} +0.146086 q^{34} -1.00000 q^{35} -1.55447 q^{36} +10.9880 q^{37} -8.09291 q^{38} -15.3675 q^{39} +3.02485 q^{40} +2.05057 q^{41} +3.43642 q^{42} -3.25834 q^{43} -4.23262 q^{45} -6.93746 q^{46} -0.743888 q^{47} -8.41929 q^{48} +1.00000 q^{49} +1.27779 q^{50} +0.307468 q^{51} +2.09860 q^{52} +0.656155 q^{53} +4.23580 q^{54} -3.02485 q^{56} -17.0331 q^{57} -4.51041 q^{58} -5.88567 q^{59} +0.987692 q^{60} -7.98055 q^{61} -9.91879 q^{62} +4.23262 q^{63} +8.87998 q^{64} +5.71421 q^{65} +12.0477 q^{67} -0.0419880 q^{68} -14.6012 q^{69} -1.27779 q^{70} -0.829397 q^{71} -12.8031 q^{72} +1.17180 q^{73} +14.0403 q^{74} +2.68935 q^{75} +2.32606 q^{76} -19.6364 q^{78} +0.699582 q^{79} +3.13060 q^{80} -3.78279 q^{81} +2.62019 q^{82} +8.74733 q^{83} -0.987692 q^{84} -0.114328 q^{85} -4.16346 q^{86} -9.49303 q^{87} +8.44787 q^{89} -5.40839 q^{90} -5.71421 q^{91} +1.99396 q^{92} -20.8760 q^{93} -0.950530 q^{94} +6.33354 q^{95} +5.51175 q^{96} -7.68221 q^{97} +1.27779 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 + 5 * q^7 - 12 * q^8 + 11 * q^9	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} + 5 q^{6} + 5 q^{7} - 12 q^{8} + 11 q^{9} - 23 q^{12} - 10 q^{13} + 2 q^{15} + 10 q^{16} - 2 q^{17} - 5 q^{18} + 3 q^{19} - 4 q^{20} - 2 q^{21} + 3 q^{23} + 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} + 4 q^{28} - q^{29} - 5 q^{30} - 12 q^{31} - 29 q^{32} - 20 q^{34} - 5 q^{35} + 45 q^{36} + 9 q^{38} + 2 q^{39} + 12 q^{40} + 11 q^{41} + 5 q^{42} - 10 q^{43} - 11 q^{45} - 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} - 6 q^{51} - 30 q^{52} + 4 q^{53} + 34 q^{54} - 12 q^{56} - 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} - 40 q^{61} - q^{62} + 11 q^{63} + 38 q^{64} + 10 q^{65} + 7 q^{67} + 19 q^{68} - 24 q^{69} + 10 q^{71} - 72 q^{72} - 11 q^{73} + 37 q^{74} - 2 q^{75} - 3 q^{76} - 87 q^{78} - 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} - 26 q^{83} - 23 q^{84} + 2 q^{85} - 17 q^{86} - 14 q^{87} + 5 q^{89} + 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} - 44 q^{94} - 3 q^{95} + 84 q^{96} - 5 q^{97}+O(q^{100}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 + 5 * q^6 + 5 * q^7 - 12 * q^8 + 11 * q^9 - 23 * q^12 - 10 * q^13 + 2 * q^15 + 10 * q^16 - 2 * q^17 - 5 * q^18 + 3 * q^19 - 4 * q^20 - 2 * q^21 + 3 * q^23 + 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 + 4 * q^28 - q^29 - 5 * q^30 - 12 * q^31 - 29 * q^32 - 20 * q^34 - 5 * q^35 + 45 * q^36 + 9 * q^38 + 2 * q^39 + 12 * q^40 + 11 * q^41 + 5 * q^42 - 10 * q^43 - 11 * q^45 - 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 - 6 * q^51 - 30 * q^52 + 4 * q^53 + 34 * q^54 - 12 * q^56 - 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 - 40 * q^61 - q^62 + 11 * q^63 + 38 * q^64 + 10 * q^65 + 7 * q^67 + 19 * q^68 - 24 * q^69 + 10 * q^71 - 72 * q^72 - 11 * q^73 + 37 * q^74 - 2 * q^75 - 3 * q^76 - 87 * q^78 - 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 - 26 * q^83 - 23 * q^84 + 2 * q^85 - 17 * q^86 - 14 * q^87 + 5 * q^89 + 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 - 44 * q^94 - 3 * q^95 + 84 * q^96 - 5 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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