LMFDB - Embedded newform 3850.2.a.br.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, 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("3850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.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:	$30.7424047782$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.940.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 7x - 4 $ x^3 - 7*x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.602705$ of defining polynomial
Character	$\chi$	$=$	3850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.60270 q^{3} +1.00000 q^{4} +1.60270 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.431337 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.60270 q^{3} +1.00000 q^{4} +1.60270 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.431337 q^{9} +1.00000 q^{11} -1.60270 q^{12} -1.39730 q^{13} +1.00000 q^{14} +1.00000 q^{16} -7.67079 q^{17} +0.431337 q^{18} +3.63675 q^{19} +1.60270 q^{21} -1.00000 q^{22} +5.46538 q^{23} +1.60270 q^{24} +1.39730 q^{26} +5.49942 q^{27} -1.00000 q^{28} +8.43134 q^{29} -3.00000 q^{31} -1.00000 q^{32} -1.60270 q^{33} +7.67079 q^{34} -0.431337 q^{36} +5.84216 q^{37} -3.63675 q^{38} +2.23945 q^{39} -3.20541 q^{41} -1.60270 q^{42} -0.0340418 q^{43} +1.00000 q^{44} -5.46538 q^{46} -6.22593 q^{47} -1.60270 q^{48} +1.00000 q^{49} +12.2940 q^{51} -1.39730 q^{52} -3.67079 q^{53} -5.49942 q^{54} +1.00000 q^{56} -5.82863 q^{57} -8.43134 q^{58} -1.36325 q^{59} +4.06808 q^{61} +3.00000 q^{62} +0.431337 q^{63} +1.00000 q^{64} +1.60270 q^{66} +5.10213 q^{67} -7.67079 q^{68} -8.75939 q^{69} -14.7389 q^{71} +0.431337 q^{72} -2.63675 q^{73} -5.84216 q^{74} +3.63675 q^{76} -1.00000 q^{77} -2.23945 q^{78} +8.01352 q^{79} -7.51994 q^{81} +3.20541 q^{82} +11.7048 q^{83} +1.60270 q^{84} +0.0340418 q^{86} -13.5129 q^{87} -1.00000 q^{88} +3.01352 q^{89} +1.39730 q^{91} +5.46538 q^{92} +4.80811 q^{93} +6.22593 q^{94} +1.60270 q^{96} -19.1226 q^{97} -1.00000 q^{98} -0.431337 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 8 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 8 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 3 q^{16} + q^{17} - 8 q^{18} - 2 q^{19} + 3 q^{21} - 3 q^{22} - 4 q^{23} + 3 q^{24} + 6 q^{26} - 15 q^{27} - 3 q^{28} + 16 q^{29} - 9 q^{31} - 3 q^{32} - 3 q^{33} - q^{34} + 8 q^{36} + q^{37} + 2 q^{38} - 8 q^{39} - 6 q^{41} - 3 q^{42} + 11 q^{43} + 3 q^{44} + 4 q^{46} - 13 q^{47} - 3 q^{48} + 3 q^{49} + 9 q^{51} - 6 q^{52} + 13 q^{53} + 15 q^{54} + 3 q^{56} - 10 q^{57} - 16 q^{58} - 17 q^{59} - 10 q^{61} + 9 q^{62} - 8 q^{63} + 3 q^{64} + 3 q^{66} - 18 q^{67} + q^{68} + 22 q^{69} + 2 q^{71} - 8 q^{72} + 5 q^{73} - q^{74} - 2 q^{76} - 3 q^{77} + 8 q^{78} + 15 q^{79} + 11 q^{81} + 6 q^{82} + 3 q^{84} - 11 q^{86} - 3 q^{88} + 6 q^{91} - 4 q^{92} + 9 q^{93} + 13 q^{94} + 3 q^{96} - 22 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 8 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 3 * q^16 + q^17 - 8 * q^18 - 2 * q^19 + 3 * q^21 - 3 * q^22 - 4 * q^23 + 3 * q^24 + 6 * q^26 - 15 * q^27 - 3 * q^28 + 16 * q^29 - 9 * q^31 - 3 * q^32 - 3 * q^33 - q^34 + 8 * q^36 + q^37 + 2 * q^38 - 8 * q^39 - 6 * q^41 - 3 * q^42 + 11 * q^43 + 3 * q^44 + 4 * q^46 - 13 * q^47 - 3 * q^48 + 3 * q^49 + 9 * q^51 - 6 * q^52 + 13 * q^53 + 15 * q^54 + 3 * q^56 - 10 * q^57 - 16 * q^58 - 17 * q^59 - 10 * q^61 + 9 * q^62 - 8 * q^63 + 3 * q^64 + 3 * q^66 - 18 * q^67 + q^68 + 22 * q^69 + 2 * q^71 - 8 * q^72 + 5 * q^73 - q^74 - 2 * q^76 - 3 * q^77 + 8 * q^78 + 15 * q^79 + 11 * q^81 + 6 * q^82 + 3 * q^84 - 11 * q^86 - 3 * q^88 + 6 * q^91 - 4 * q^92 + 9 * q^93 + 13 * q^94 + 3 * q^96 - 22 * q^97 - 3 * q^98 + 8 * 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
$3$	−1.60270	−0.925322	−0.462661	−	0.886535i	$-0.653105\pi$
$3$	−1.60270	−0.925322	−0.462661	+	0.886535i	$0.653105\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.60270	0.654302
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−0.431337	−0.143779
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.60270	−0.462661
$13$	−1.39730	−0.387540	−0.193770	−	0.981047i	$-0.562072\pi$
$13$	−1.39730	−0.387540	−0.193770	+	0.981047i	$0.562072\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−7.67079	−1.86044	−0.930220	−	0.367003i	$-0.880384\pi$
$17$	−7.67079	−1.86044	−0.930220	+	0.367003i	$0.880384\pi$
$18$	0.431337	0.101667
$19$	3.63675	0.834327	0.417163	−	0.908831i	$-0.363024\pi$
$19$	3.63675	0.834327	0.417163	+	0.908831i	$0.363024\pi$
$20$	0	0
$21$	1.60270	0.349739
$22$	−1.00000	−0.213201
$23$	5.46538	1.13961	0.569805	−	0.821780i	$-0.307019\pi$
$23$	5.46538	1.13961	0.569805	+	0.821780i	$0.307019\pi$
$24$	1.60270	0.327151
$25$	0	0
$26$	1.39730	0.274032
$27$	5.49942	1.05836
$28$	−1.00000	−0.188982
$29$	8.43134	1.56566	0.782830	−	0.622236i	$-0.213775\pi$
$29$	8.43134	1.56566	0.782830	+	0.622236i	$0.213775\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	−1.00000	−0.176777
$33$	−1.60270	−0.278995
$34$	7.67079	1.31553
$35$	0	0
$36$	−0.431337	−0.0718895
$37$	5.84216	0.960445	0.480222	−	0.877147i	$-0.340556\pi$
$37$	5.84216	0.960445	0.480222	+	0.877147i	$0.340556\pi$
$38$	−3.63675	−0.589958
$39$	2.23945	0.358599
$40$	0	0
$41$	−3.20541	−0.500601	−0.250300	−	0.968168i	$-0.580529\pi$
$41$	−3.20541	−0.500601	−0.250300	+	0.968168i	$0.580529\pi$
$42$	−1.60270	−0.247303
$43$	−0.0340418	−0.00519133	−0.00259567	−	0.999997i	$-0.500826\pi$
$43$	−0.0340418	−0.00519133	−0.00259567	+	0.999997i	$0.500826\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	−5.46538	−0.805826
$47$	−6.22593	−0.908145	−0.454072	−	0.890965i	$-0.650029\pi$
$47$	−6.22593	−0.908145	−0.454072	+	0.890965i	$0.650029\pi$
$48$	−1.60270	−0.231331
$49$	1.00000	0.142857
$50$	0	0
$51$	12.2940	1.72151
$52$	−1.39730	−0.193770
$53$	−3.67079	−0.504222	−0.252111	−	0.967698i	$-0.581125\pi$
$53$	−3.67079	−0.504222	−0.252111	+	0.967698i	$0.581125\pi$
$54$	−5.49942	−0.748376
$55$	0	0
$56$	1.00000	0.133631
$57$	−5.82863	−0.772021
$58$	−8.43134	−1.10709
$59$	−1.36325	−0.177480	−0.0887402	−	0.996055i	$-0.528284\pi$
$59$	−1.36325	−0.177480	−0.0887402	+	0.996055i	$0.528284\pi$
$60$	0	0
$61$	4.06808	0.520865	0.260432	−	0.965492i	$-0.416135\pi$
$61$	4.06808	0.520865	0.260432	+	0.965492i	$0.416135\pi$
$62$	3.00000	0.381000
$63$	0.431337	0.0543433
$64$	1.00000	0.125000
$65$	0	0
$66$	1.60270	0.197279
$67$	5.10213	0.623324	0.311662	−	0.950193i	$-0.399114\pi$
$67$	5.10213	0.623324	0.311662	+	0.950193i	$0.399114\pi$
$68$	−7.67079	−0.930220
$69$	−8.75939	−1.05451
$70$	0	0
$71$	−14.7389	−1.74918	−0.874591	−	0.484861i	$-0.838870\pi$
$71$	−14.7389	−1.74918	−0.874591	+	0.484861i	$0.838870\pi$
$72$	0.431337	0.0508335
$73$	−2.63675	−0.308608	−0.154304	−	0.988023i	$-0.549313\pi$
$73$	−2.63675	−0.308608	−0.154304	+	0.988023i	$0.549313\pi$
$74$	−5.84216	−0.679137
$75$	0	0
$76$	3.63675	0.417163
$77$	−1.00000	−0.113961
$78$	−2.23945	−0.253568
$79$	8.01352	0.901592	0.450796	−	0.892627i	$-0.351140\pi$
$79$	8.01352	0.901592	0.450796	+	0.892627i	$0.351140\pi$
$80$	0	0
$81$	−7.51994	−0.835549
$82$	3.20541	0.353978
$83$	11.7048	1.28477	0.642386	−	0.766381i	$-0.277945\pi$
$83$	11.7048	1.28477	0.642386	+	0.766381i	$0.277945\pi$
$84$	1.60270	0.174869
$85$	0	0
$86$	0.0340418	0.00367083
$87$	−13.5129	−1.44874
$88$	−1.00000	−0.106600
$89$	3.01352	0.319433	0.159716	−	0.987163i	$-0.448942\pi$
$89$	3.01352	0.319433	0.159716	+	0.987163i	$0.448942\pi$
$90$	0	0
$91$	1.39730	0.146476
$92$	5.46538	0.569805
$93$	4.80811	0.498578
$94$	6.22593	0.642155
$95$	0	0
$96$	1.60270	0.163575
$97$	−19.1226	−1.94161	−0.970805	−	0.239870i	$-0.922895\pi$
$97$	−19.1226	−1.94161	−0.970805	+	0.239870i	$0.922895\pi$
$98$	−1.00000	−0.101015
$99$	−0.431337	−0.0433510
$100$	0	0
$101$	9.69131	0.964321	0.482160	−	0.876083i	$-0.339852\pi$
$101$	9.69131	0.964321	0.482160	+	0.876083i	$0.339852\pi$
$102$	−12.2940	−1.21729
$103$	−11.0681	−1.09057	−0.545285	−	0.838250i	$-0.683579\pi$
$103$	−11.0681	−1.09057	−0.545285	+	0.838250i	$0.683579\pi$
$104$	1.39730	0.137016
$105$	0	0
$106$	3.67079	0.356539
$107$	1.58219	0.152956	0.0764779	−	0.997071i	$-0.475633\pi$
$107$	1.58219	0.152956	0.0764779	+	0.997071i	$0.475633\pi$
$108$	5.49942	0.529182
$109$	13.2259	1.26681	0.633407	−	0.773819i	$-0.281656\pi$
$109$	13.2259	1.26681	0.633407	+	0.773819i	$0.281656\pi$
$110$	0	0
$111$	−9.36325	−0.888721
$112$	−1.00000	−0.0944911
$113$	11.9102	1.12042	0.560211	−	0.828350i	$-0.310720\pi$
$113$	11.9102	1.12042	0.560211	+	0.828350i	$0.310720\pi$
$114$	5.82863	0.545901
$115$	0	0
$116$	8.43134	0.782830
$117$	0.602705	0.0557201
$118$	1.36325	0.125498
$119$	7.67079	0.703180
$120$	0	0
$121$	1.00000	0.0909091
$122$	−4.06808	−0.368307
$123$	5.13733	0.463217
$124$	−3.00000	−0.269408
$125$	0	0
$126$	−0.431337	−0.0384265
$127$	−12.2530	−1.08728	−0.543638	−	0.839320i	$-0.682954\pi$
$127$	−12.2530	−1.08728	−0.543638	+	0.839320i	$0.682954\pi$
$128$	−1.00000	−0.0883883
$129$	0.0545590	0.00480365
$130$	0	0
$131$	−4.36325	−0.381219	−0.190610	−	0.981666i	$-0.561046\pi$
$131$	−4.36325	−0.381219	−0.190610	+	0.981666i	$0.561046\pi$
$132$	−1.60270	−0.139498
$133$	−3.63675	−0.315346
$134$	−5.10213	−0.440757
$135$	0	0
$136$	7.67079	0.657765
$137$	−16.4313	−1.40382	−0.701912	−	0.712264i	$-0.747670\pi$
$137$	−16.4313	−1.40382	−0.701912	+	0.712264i	$0.747670\pi$
$138$	8.75939	0.745649
$139$	1.97948	0.167898	0.0839488	−	0.996470i	$-0.473247\pi$
$139$	1.97948	0.167898	0.0839488	+	0.996470i	$0.473247\pi$
$140$	0	0
$141$	9.97832	0.840326
$142$	14.7389	1.23686
$143$	−1.39730	−0.116848
$144$	−0.431337	−0.0359447
$145$	0	0
$146$	2.63675	0.218219
$147$	−1.60270	−0.132189
$148$	5.84216	0.480222
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−4.23945	−0.345002	−0.172501	−	0.985009i	$-0.555185\pi$
$151$	−4.23945	−0.345002	−0.172501	+	0.985009i	$0.555185\pi$
$152$	−3.63675	−0.294979
$153$	3.30869	0.267492
$154$	1.00000	0.0805823
$155$	0	0
$156$	2.23945	0.179300
$157$	22.3756	1.78577	0.892884	−	0.450286i	$-0.148678\pi$
$157$	22.3756	1.78577	0.892884	+	0.450286i	$0.148678\pi$
$158$	−8.01352	−0.637522
$159$	5.88319	0.466567
$160$	0	0
$161$	−5.46538	−0.430732
$162$	7.51994	0.590822
$163$	1.61623	0.126593	0.0632964	−	0.997995i	$-0.479839\pi$
$163$	1.61623	0.126593	0.0632964	+	0.997995i	$0.479839\pi$
$164$	−3.20541	−0.250300
$165$	0	0
$166$	−11.7048	−0.908471
$167$	5.10213	0.394814	0.197407	−	0.980322i	$-0.436748\pi$
$167$	5.10213	0.394814	0.197407	+	0.980322i	$0.436748\pi$
$168$	−1.60270	−0.123651
$169$	−11.0476	−0.849813
$170$	0	0
$171$	−1.56866	−0.119959
$172$	−0.0340418	−0.00259567
$173$	−20.3281	−1.54551	−0.772757	−	0.634702i	$-0.781123\pi$
$173$	−20.3281	−1.54551	−0.772757	+	0.634702i	$0.781123\pi$
$174$	13.5129	1.02441
$175$	0	0
$176$	1.00000	0.0753778
$177$	2.18489	0.164227
$178$	−3.01352	−0.225873
$179$	5.82863	0.435652	0.217826	−	0.975988i	$-0.430103\pi$
$179$	5.82863	0.435652	0.217826	+	0.975988i	$0.430103\pi$
$180$	0	0
$181$	−7.34158	−0.545695	−0.272848	−	0.962057i	$-0.587965\pi$
$181$	−7.34158	−0.545695	−0.272848	+	0.962057i	$0.587965\pi$
$182$	−1.39730	−0.103574
$183$	−6.51994	−0.481968
$184$	−5.46538	−0.402913
$185$	0	0
$186$	−4.80811	−0.352548
$187$	−7.67079	−0.560944
$188$	−6.22593	−0.454072
$189$	−5.49942	−0.400024
$190$	0	0
$191$	−15.1497	−1.09619	−0.548097	−	0.836415i	$-0.684647\pi$
$191$	−15.1497	−1.09619	−0.548097	+	0.836415i	$0.684647\pi$
$192$	−1.60270	−0.115665
$193$	15.3416	1.10431	0.552155	−	0.833741i	$-0.313805\pi$
$193$	15.3416	1.10431	0.552155	+	0.833741i	$0.313805\pi$
$194$	19.1226	1.37293
$195$	0	0
$196$	1.00000	0.0714286
$197$	−23.7048	−1.68890	−0.844450	−	0.535635i	$-0.820072\pi$
$197$	−23.7048	−1.68890	−0.844450	+	0.535635i	$0.820072\pi$
$198$	0.431337	0.0306538
$199$	−8.84216	−0.626804	−0.313402	−	0.949621i	$-0.601469\pi$
$199$	−8.84216	−0.626804	−0.313402	+	0.949621i	$0.601469\pi$
$200$	0	0
$201$	−8.17720	−0.576775
$202$	−9.69131	−0.681878
$203$	−8.43134	−0.591764
$204$	12.2940	0.860753
$205$	0	0
$206$	11.0681	0.771150
$207$	−2.35742	−0.163852
$208$	−1.39730	−0.0968850
$209$	3.63675	0.251559
$210$	0	0
$211$	−17.0476	−1.17360	−0.586801	−	0.809731i	$-0.699613\pi$
$211$	−17.0476	−1.17360	−0.586801	+	0.809731i	$0.699613\pi$
$212$	−3.67079	−0.252111
$213$	23.6221	1.61856
$214$	−1.58219	−0.108156
$215$	0	0
$216$	−5.49942	−0.374188
$217$	3.00000	0.203653
$218$	−13.2259	−0.895773
$219$	4.22593	0.285562
$220$	0	0
$221$	10.7184	0.720995
$222$	9.36325	0.628420
$223$	8.72651	0.584370	0.292185	−	0.956362i	$-0.405618\pi$
$223$	8.72651	0.584370	0.292185	+	0.956362i	$0.405618\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−11.9102	−0.792257
$227$	−9.15784	−0.607827	−0.303914	−	0.952700i	$-0.598293\pi$
$227$	−9.15784	−0.607827	−0.303914	+	0.952700i	$0.598293\pi$
$228$	−5.82863	−0.386011
$229$	−16.8627	−1.11432	−0.557158	−	0.830406i	$-0.688108\pi$
$229$	−16.8627	−1.11432	−0.557158	+	0.830406i	$0.688108\pi$
$230$	0	0
$231$	1.60270	0.105450
$232$	−8.43134	−0.553544
$233$	22.6503	1.48387	0.741934	−	0.670473i	$-0.233909\pi$
$233$	22.6503	1.48387	0.741934	+	0.670473i	$0.233909\pi$
$234$	−0.602705	−0.0394001
$235$	0	0
$236$	−1.36325	−0.0887402
$237$	−12.8433	−0.834263
$238$	−7.67079	−0.497223
$239$	−10.7048	−0.692438	−0.346219	−	0.938154i	$-0.612535\pi$
$239$	−10.7048	−0.692438	−0.346219	+	0.938154i	$0.612535\pi$
$240$	0	0
$241$	−16.6367	−1.07167	−0.535834	−	0.844324i	$-0.680003\pi$
$241$	−16.6367	−1.07167	−0.535834	+	0.844324i	$0.680003\pi$
$242$	−1.00000	−0.0642824
$243$	−4.44602	−0.285212
$244$	4.06808	0.260432
$245$	0	0
$246$	−5.13733	−0.327544
$247$	−5.08161	−0.323335
$248$	3.00000	0.190500
$249$	−18.7594	−1.18883
$250$	0	0
$251$	−25.3551	−1.60040	−0.800200	−	0.599733i	$-0.795273\pi$
$251$	−25.3551	−1.60040	−0.800200	+	0.599733i	$0.795273\pi$
$252$	0.431337	0.0271717
$253$	5.46538	0.343605
$254$	12.2530	0.768820
$255$	0	0
$256$	1.00000	0.0625000
$257$	26.0124	1.62261	0.811303	−	0.584625i	$-0.198758\pi$
$257$	26.0124	1.62261	0.811303	+	0.584625i	$0.198758\pi$
$258$	−0.0545590	−0.00339670
$259$	−5.84216	−0.363014
$260$	0	0
$261$	−3.63675	−0.225109
$262$	4.36325	0.269563
$263$	−1.60270	−0.0988270	−0.0494135	−	0.998778i	$-0.515735\pi$
$263$	−1.60270	−0.0988270	−0.0494135	+	0.998778i	$0.515735\pi$
$264$	1.60270	0.0986397
$265$	0	0
$266$	3.63675	0.222983
$267$	−4.82979	−0.295578
$268$	5.10213	0.311662
$269$	−29.1292	−1.77604	−0.888019	−	0.459808i	$-0.847918\pi$
$269$	−29.1292	−1.77604	−0.888019	+	0.459808i	$0.847918\pi$
$270$	0	0
$271$	15.1021	0.917389	0.458694	−	0.888594i	$-0.348317\pi$
$271$	15.1021	0.917389	0.458694	+	0.888594i	$0.348317\pi$
$272$	−7.67079	−0.465110
$273$	−2.23945	−0.135538
$274$	16.4313	0.992653
$275$	0	0
$276$	−8.75939	−0.527253
$277$	−14.2043	−0.853451	−0.426725	−	0.904381i	$-0.640333\pi$
$277$	−14.2043	−0.853451	−0.426725	+	0.904381i	$0.640333\pi$
$278$	−1.97948	−0.118721
$279$	1.29401	0.0774704
$280$	0	0
$281$	−23.9918	−1.43123	−0.715617	−	0.698493i	$-0.753854\pi$
$281$	−23.9918	−1.43123	−0.715617	+	0.698493i	$0.753854\pi$
$282$	−9.97832	−0.594201
$283$	19.7253	1.17255	0.586275	−	0.810112i	$-0.300594\pi$
$283$	19.7253	1.17255	0.586275	+	0.810112i	$0.300594\pi$
$284$	−14.7389	−0.874591
$285$	0	0
$286$	1.39730	0.0826238
$287$	3.20541	0.189209
$288$	0.431337	0.0254168
$289$	41.8410	2.46124
$290$	0	0
$291$	30.6480	1.79661
$292$	−2.63675	−0.154304
$293$	5.88319	0.343700	0.171850	−	0.985123i	$-0.445026\pi$
$293$	5.88319	0.343700	0.171850	+	0.985123i	$0.445026\pi$
$294$	1.60270	0.0934716
$295$	0	0
$296$	−5.84216	−0.339568
$297$	5.49942	0.319109
$298$	0	0
$299$	−7.63675	−0.441644
$300$	0	0
$301$	0.0340418	0.00196214
$302$	4.23945	0.243953
$303$	−15.5323	−0.892308
$304$	3.63675	0.208582
$305$	0	0
$306$	−3.30869	−0.189145
$307$	−12.1362	−0.692648	−0.346324	−	0.938115i	$-0.612570\pi$
$307$	−12.1362	−0.692648	−0.346324	+	0.938115i	$0.612570\pi$
$308$	−1.00000	−0.0569803
$309$	17.7389	1.00913
$310$	0	0
$311$	−12.5892	−0.713867	−0.356933	−	0.934130i	$-0.616178\pi$
$311$	−12.5892	−0.713867	−0.356933	+	0.934130i	$0.616178\pi$
$312$	−2.23945	−0.126784
$313$	16.5880	0.937610	0.468805	−	0.883302i	$-0.344685\pi$
$313$	16.5880	0.937610	0.468805	+	0.883302i	$0.344685\pi$
$314$	−22.3756	−1.26273
$315$	0	0
$316$	8.01352	0.450796
$317$	−20.5605	−1.15479	−0.577397	−	0.816464i	$-0.695931\pi$
$317$	−20.5605	−1.15479	−0.577397	+	0.816464i	$0.695931\pi$
$318$	−5.88319	−0.329913
$319$	8.43134	0.472064
$320$	0	0
$321$	−2.53578	−0.141533
$322$	5.46538	0.304574
$323$	−27.8967	−1.55221
$324$	−7.51994	−0.417774
$325$	0	0
$326$	−1.61623	−0.0895147
$327$	−21.1973	−1.17221
$328$	3.20541	0.176989
$329$	6.22593	0.343246
$330$	0	0
$331$	−5.93192	−0.326048	−0.163024	−	0.986622i	$-0.552125\pi$
$331$	−5.93192	−0.326048	−0.163024	+	0.986622i	$0.552125\pi$
$332$	11.7048	0.642386
$333$	−2.51994	−0.138092
$334$	−5.10213	−0.279176
$335$	0	0
$336$	1.60270	0.0874347
$337$	28.2395	1.53830	0.769150	−	0.639068i	$-0.220680\pi$
$337$	28.2395	1.53830	0.769150	+	0.639068i	$0.220680\pi$
$338$	11.0476	0.600908
$339$	−19.0886	−1.03675
$340$	0	0
$341$	−3.00000	−0.162459
$342$	1.56866	0.0848236
$343$	−1.00000	−0.0539949
$344$	0.0340418	0.00183541
$345$	0	0
$346$	20.3281	1.09284
$347$	−36.3891	−1.95347	−0.976736	−	0.214446i	$-0.931205\pi$
$347$	−36.3891	−1.95347	−0.976736	+	0.214446i	$0.931205\pi$
$348$	−13.5129	−0.724370
$349$	−16.4449	−0.880273	−0.440137	−	0.897931i	$-0.645070\pi$
$349$	−16.4449	−0.880273	−0.440137	+	0.897931i	$0.645070\pi$
$350$	0	0
$351$	−7.68431	−0.410158
$352$	−1.00000	−0.0533002
$353$	−17.4243	−0.927404	−0.463702	−	0.885991i	$-0.653479\pi$
$353$	−17.4243	−0.927404	−0.463702	+	0.885991i	$0.653479\pi$
$354$	−2.18489	−0.116126
$355$	0	0
$356$	3.01352	0.159716
$357$	−12.2940	−0.650668
$358$	−5.82863	−0.308053
$359$	11.2325	0.592827	0.296413	−	0.955060i	$-0.404209\pi$
$359$	11.2325	0.592827	0.296413	+	0.955060i	$0.404209\pi$
$360$	0	0
$361$	−5.77407	−0.303899
$362$	7.34158	0.385865
$363$	−1.60270	−0.0841202
$364$	1.39730	0.0732382
$365$	0	0
$366$	6.51994	0.340803
$367$	−16.5946	−0.866229	−0.433114	−	0.901339i	$-0.642585\pi$
$367$	−16.5946	−0.866229	−0.433114	+	0.901339i	$0.642585\pi$
$368$	5.46538	0.284903
$369$	1.38261	0.0719759
$370$	0	0
$371$	3.67079	0.190578
$372$	4.80811	0.249289
$373$	20.9578	1.08515	0.542577	−	0.840006i	$-0.317449\pi$
$373$	20.9578	1.08515	0.542577	+	0.840006i	$0.317449\pi$
$374$	7.67079	0.396647
$375$	0	0
$376$	6.22593	0.321078
$377$	−11.7811	−0.606756
$378$	5.49942	0.282860
$379$	−11.0340	−0.566781	−0.283390	−	0.959005i	$-0.591459\pi$
$379$	−11.0340	−0.566781	−0.283390	+	0.959005i	$0.591459\pi$
$380$	0	0
$381$	19.6379	1.00608
$382$	15.1497	0.775126
$383$	−24.2054	−1.23684	−0.618419	−	0.785848i	$-0.712227\pi$
$383$	−24.2054	−1.23684	−0.618419	+	0.785848i	$0.712227\pi$
$384$	1.60270	0.0817877
$385$	0	0
$386$	−15.3416	−0.780866
$387$	0.0146835	0.000746404 0
$388$	−19.1226	−0.970805
$389$	0.0816083	0.00413771	0.00206885	−	0.999998i	$-0.499341\pi$
$389$	0.0816083	0.00413771	0.00206885	+	0.999998i	$0.499341\pi$
$390$	0	0
$391$	−41.9238	−2.12018
$392$	−1.00000	−0.0505076
$393$	6.99301	0.352751
$394$	23.7048	1.19423
$395$	0	0
$396$	−0.431337	−0.0216755
$397$	28.2043	1.41553	0.707765	−	0.706448i	$-0.249703\pi$
$397$	28.2043	1.41553	0.707765	+	0.706448i	$0.249703\pi$
$398$	8.84216	0.443217
$399$	5.82863	0.291797
$400$	0	0
$401$	13.4519	0.671754	0.335877	−	0.941906i	$-0.390967\pi$
$401$	13.4519	0.671754	0.335877	+	0.941906i	$0.390967\pi$
$402$	8.17720	0.407842
$403$	4.19189	0.208813
$404$	9.69131	0.482160
$405$	0	0
$406$	8.43134	0.418440
$407$	5.84216	0.289585
$408$	−12.2940	−0.608644
$409$	−14.8762	−0.735581	−0.367790	−	0.929909i	$-0.619886\pi$
$409$	−14.8762	−0.735581	−0.367790	+	0.929909i	$0.619886\pi$
$410$	0	0
$411$	26.3346	1.29899
$412$	−11.0681	−0.545285
$413$	1.36325	0.0670813
$414$	2.35742	0.115861
$415$	0	0
$416$	1.39730	0.0685080
$417$	−3.17253	−0.155359
$418$	−3.63675	−0.177879
$419$	−16.1578	−0.789362	−0.394681	−	0.918818i	$-0.629145\pi$
$419$	−16.1578	−0.789362	−0.394681	+	0.918818i	$0.629145\pi$
$420$	0	0
$421$	3.44486	0.167892	0.0839461	−	0.996470i	$-0.473248\pi$
$421$	3.44486	0.167892	0.0839461	+	0.996470i	$0.473248\pi$
$422$	17.0476	0.829863
$423$	2.68547	0.130572
$424$	3.67079	0.178269
$425$	0	0
$426$	−23.6221	−1.14449
$427$	−4.06808	−0.196868
$428$	1.58219	0.0764779
$429$	2.23945	0.108122
$430$	0	0
$431$	−32.0194	−1.54232	−0.771159	−	0.636642i	$-0.780323\pi$
$431$	−32.0194	−1.54232	−0.771159	+	0.636642i	$0.780323\pi$
$432$	5.49942	0.264591
$433$	9.83516	0.472648	0.236324	−	0.971674i	$-0.424057\pi$
$433$	9.83516	0.472648	0.236324	+	0.971674i	$0.424057\pi$
$434$	−3.00000	−0.144005
$435$	0	0
$436$	13.2259	0.633407
$437$	19.8762	0.950808
$438$	−4.22593	−0.201923
$439$	−23.4777	−1.12053	−0.560266	−	0.828313i	$-0.689301\pi$
$439$	−23.4777	−1.12053	−0.560266	+	0.828313i	$0.689301\pi$
$440$	0	0
$441$	−0.431337	−0.0205399
$442$	−10.7184	−0.509820
$443$	−13.5892	−0.645641	−0.322821	−	0.946460i	$-0.604631\pi$
$443$	−13.5892	−0.645641	−0.322821	+	0.946460i	$0.604631\pi$
$444$	−9.36325	−0.444360
$445$	0	0
$446$	−8.72651	−0.413212
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−13.0951	−0.617998	−0.308999	−	0.951062i	$-0.599994\pi$
$449$	−13.0951	−0.617998	−0.308999	+	0.951062i	$0.599994\pi$
$450$	0	0
$451$	−3.20541	−0.150937
$452$	11.9102	0.560211
$453$	6.79459	0.319238
$454$	9.15784	0.429799
$455$	0	0
$456$	5.82863	0.272951
$457$	16.7594	0.783971	0.391986	−	0.919971i	$-0.371788\pi$
$457$	16.7594	0.783971	0.391986	+	0.919971i	$0.371788\pi$
$458$	16.8627	0.787941
$459$	−42.1849	−1.96902
$460$	0	0
$461$	12.0464	0.561057	0.280529	−	0.959846i	$-0.409490\pi$
$461$	12.0464	0.561057	0.280529	+	0.959846i	$0.409490\pi$
$462$	−1.60270	−0.0745646
$463$	−36.7659	−1.70866	−0.854329	−	0.519733i	$-0.826031\pi$
$463$	−36.7659	−1.70866	−0.854329	+	0.519733i	$0.826031\pi$
$464$	8.43134	0.391415
$465$	0	0
$466$	−22.6503	−1.04925
$467$	−7.86921	−0.364143	−0.182072	−	0.983285i	$-0.558280\pi$
$467$	−7.86921	−0.364143	−0.182072	+	0.983285i	$0.558280\pi$
$468$	0.602705	0.0278600
$469$	−5.10213	−0.235594
$470$	0	0
$471$	−35.8615	−1.65241
$472$	1.36325	0.0627488
$473$	−0.0340418	−0.00156525
$474$	12.8433	0.589913
$475$	0	0
$476$	7.67079	0.351590
$477$	1.58335	0.0724965
$478$	10.7048	0.489628
$479$	−22.4789	−1.02709	−0.513544	−	0.858063i	$-0.671668\pi$
$479$	−22.4789	−1.02709	−0.513544	+	0.858063i	$0.671668\pi$
$480$	0	0
$481$	−8.16322	−0.372211
$482$	16.6367	0.757783
$483$	8.75939	0.398566
$484$	1.00000	0.0454545
$485$	0	0
$486$	4.44602	0.201676
$487$	−35.7377	−1.61943	−0.809715	−	0.586823i	$-0.800378\pi$
$487$	−35.7377	−1.61943	−0.809715	+	0.586823i	$0.800378\pi$
$488$	−4.06808	−0.184153
$489$	−2.59034	−0.117139
$490$	0	0
$491$	−7.17137	−0.323639	−0.161820	−	0.986820i	$-0.551736\pi$
$491$	−7.17137	−0.323639	−0.161820	+	0.986820i	$0.551736\pi$
$492$	5.13733	0.231609
$493$	−64.6750	−2.91282
$494$	5.08161	0.228632
$495$	0	0
$496$	−3.00000	−0.134704
$497$	14.7389	0.661129
$498$	18.7594	0.840628
$499$	1.06924	0.0478659	0.0239329	−	0.999714i	$-0.492381\pi$
$499$	1.06924	0.0478659	0.0239329	+	0.999714i	$0.492381\pi$
$500$	0	0
$501$	−8.17720	−0.365330
$502$	25.3551	1.13165
$503$	−17.5481	−0.782433	−0.391217	−	0.920299i	$-0.627946\pi$
$503$	−17.5481	−0.782433	−0.391217	+	0.920299i	$0.627946\pi$
$504$	−0.431337	−0.0192133
$505$	0	0
$506$	−5.46538	−0.242966
$507$	17.7060	0.786351
$508$	−12.2530	−0.543638
$509$	11.0340	0.489075	0.244538	−	0.969640i	$-0.421364\pi$
$509$	11.0340	0.489075	0.244538	+	0.969640i	$0.421364\pi$
$510$	0	0
$511$	2.63675	0.116643
$512$	−1.00000	−0.0441942
$513$	20.0000	0.883022
$514$	−26.0124	−1.14736
$515$	0	0
$516$	0.0545590	0.00240183
$517$	−6.22593	−0.273816
$518$	5.84216	0.256690
$519$	32.5799	1.43010
$520$	0	0
$521$	21.4654	0.940415	0.470208	−	0.882556i	$-0.344179\pi$
$521$	21.4654	0.940415	0.470208	+	0.882556i	$0.344179\pi$
$522$	3.63675	0.159176
$523$	4.43134	0.193769	0.0968844	−	0.995296i	$-0.469112\pi$
$523$	4.43134	0.193769	0.0968844	+	0.995296i	$0.469112\pi$
$524$	−4.36325	−0.190610
$525$	0	0
$526$	1.60270	0.0698813
$527$	23.0124	1.00243
$528$	−1.60270	−0.0697488
$529$	6.87036	0.298712
$530$	0	0
$531$	0.588021	0.0255180
$532$	−3.63675	−0.157673
$533$	4.47890	0.194003
$534$	4.82979	0.209005
$535$	0	0
$536$	−5.10213	−0.220378
$537$	−9.34158	−0.403119
$538$	29.1292	1.25585
$539$	1.00000	0.0430730
$540$	0	0
$541$	17.2940	0.743528	0.371764	−	0.928327i	$-0.378753\pi$
$541$	17.2940	0.743528	0.371764	+	0.928327i	$0.378753\pi$
$542$	−15.1021	−0.648692
$543$	11.7664	0.504944
$544$	7.67079	0.328882
$545$	0	0
$546$	2.23945	0.0958397
$547$	16.1292	0.689634	0.344817	−	0.938670i	$-0.387941\pi$
$547$	16.1292	0.689634	0.344817	+	0.938670i	$0.387941\pi$
$548$	−16.4313	−0.701912
$549$	−1.75471	−0.0748894
$550$	0	0
$551$	30.6626	1.30627
$552$	8.75939	0.372824
$553$	−8.01352	−0.340770
$554$	14.2043	0.603481
$555$	0	0
$556$	1.97948	0.0839488
$557$	−13.9524	−0.591184	−0.295592	−	0.955314i	$-0.595517\pi$
$557$	−13.9524	−0.591184	−0.295592	+	0.955314i	$0.595517\pi$
$558$	−1.29401	−0.0547798
$559$	0.0475665	0.00201185
$560$	0	0
$561$	12.2940	0.519054
$562$	23.9918	1.01204
$563$	−3.58918	−0.151266	−0.0756330	−	0.997136i	$-0.524098\pi$
$563$	−3.58918	−0.151266	−0.0756330	+	0.997136i	$0.524098\pi$
$564$	9.97832	0.420163
$565$	0	0
$566$	−19.7253	−0.829118
$567$	7.51994	0.315808
$568$	14.7389	0.618429
$569$	−0.0352007	−0.00147569	−0.000737845	−	1.00000i	$-0.500235\pi$
$569$	−0.0352007	−0.00147569	−0.000737845		1.00000i	$0.500235\pi$
$570$	0	0
$571$	−22.6708	−0.948743	−0.474371	−	0.880325i	$-0.657325\pi$
$571$	−22.6708	−0.948743	−0.474371	+	0.880325i	$0.657325\pi$
$572$	−1.39730	−0.0584238
$573$	24.2805	1.01433
$574$	−3.20541	−0.133791
$575$	0	0
$576$	−0.431337	−0.0179724
$577$	11.1644	0.464779	0.232390	−	0.972623i	$-0.425346\pi$
$577$	11.1644	0.464779	0.232390	+	0.972623i	$0.425346\pi$
$578$	−41.8410	−1.74036
$579$	−24.5880	−1.02184
$580$	0	0
$581$	−11.7048	−0.485598
$582$	−30.6480	−1.27040
$583$	−3.67079	−0.152029
$584$	2.63675	0.109109
$585$	0	0
$586$	−5.88319	−0.243032
$587$	42.3404	1.74758	0.873788	−	0.486307i	$-0.161656\pi$
$587$	42.3404	1.74758	0.873788	+	0.486307i	$0.161656\pi$
$588$	−1.60270	−0.0660944
$589$	−10.9102	−0.449549
$590$	0	0
$591$	37.9918	1.56278
$592$	5.84216	0.240111
$593$	−35.1973	−1.44538	−0.722689	−	0.691173i	$-0.757094\pi$
$593$	−35.1973	−1.44538	−0.722689	+	0.691173i	$0.757094\pi$
$594$	−5.49942	−0.225644
$595$	0	0
$596$	0	0
$597$	14.1714	0.579995
$598$	7.63675	0.312290
$599$	−33.8886	−1.38465	−0.692325	−	0.721586i	$-0.743413\pi$
$599$	−33.8886	−1.38465	−0.692325	+	0.721586i	$0.743413\pi$
$600$	0	0
$601$	21.0476	0.858548	0.429274	−	0.903174i	$-0.358769\pi$
$601$	21.0476	0.858548	0.429274	+	0.903174i	$0.358769\pi$
$602$	−0.0340418	−0.00138744
$603$	−2.20074	−0.0896209
$604$	−4.23945	−0.172501
$605$	0	0
$606$	15.5323	0.630957
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	−3.63675	−0.147490
$609$	13.5129	0.547572
$610$	0	0
$611$	8.69946	0.351942
$612$	3.30869	0.133746
$613$	27.1621	1.09707	0.548533	−	0.836129i	$-0.315187\pi$
$613$	27.1621	1.09707	0.548533	+	0.836129i	$0.315187\pi$
$614$	12.1362	0.489776
$615$	0	0
$616$	1.00000	0.0402911
$617$	−37.8874	−1.52529	−0.762645	−	0.646818i	$-0.776100\pi$
$617$	−37.8874	−1.52529	−0.762645	+	0.646818i	$0.776100\pi$
$618$	−17.7389	−0.713562
$619$	−10.9172	−0.438801	−0.219400	−	0.975635i	$-0.570410\pi$
$619$	−10.9172	−0.438801	−0.219400	+	0.975635i	$0.570410\pi$
$620$	0	0
$621$	30.0564	1.20612
$622$	12.5892	0.504780
$623$	−3.01352	−0.120734
$624$	2.23945	0.0896498
$625$	0	0
$626$	−16.5880	−0.662991
$627$	−5.82863	−0.232773
$628$	22.3756	0.892884
$629$	−44.8139	−1.78685
$630$	0	0
$631$	3.48006	0.138539	0.0692695	−	0.997598i	$-0.477933\pi$
$631$	3.48006	0.138539	0.0692695	+	0.997598i	$0.477933\pi$
$632$	−8.01352	−0.318761
$633$	27.3222	1.08596
$634$	20.5605	0.816562
$635$	0	0
$636$	5.88319	0.233284
$637$	−1.39730	−0.0553628
$638$	−8.43134	−0.333800
$639$	6.35742	0.251496
$640$	0	0
$641$	48.5869	1.91907	0.959533	−	0.281597i	$-0.0908640\pi$
$641$	48.5869	1.91907	0.959533	+	0.281597i	$0.0908640\pi$
$642$	2.53578	0.100079
$643$	−16.5605	−0.653083	−0.326541	−	0.945183i	$-0.605883\pi$
$643$	−16.5605	−0.653083	−0.326541	+	0.945183i	$0.605883\pi$
$644$	−5.46538	−0.215366
$645$	0	0
$646$	27.8967	1.09758
$647$	35.7718	1.40633	0.703166	−	0.711025i	$-0.251769\pi$
$647$	35.7718	1.40633	0.703166	+	0.711025i	$0.251769\pi$
$648$	7.51994	0.295411
$649$	−1.36325	−0.0535124
$650$	0	0
$651$	−4.80811	−0.188445
$652$	1.61623	0.0632964
$653$	24.0135	0.939722	0.469861	−	0.882740i	$-0.344304\pi$
$653$	24.0135	0.939722	0.469861	+	0.882740i	$0.344304\pi$
$654$	21.1973	0.828878
$655$	0	0
$656$	−3.20541	−0.125150
$657$	1.13733	0.0443713
$658$	−6.22593	−0.242712
$659$	38.8070	1.51170	0.755852	−	0.654742i	$-0.227223\pi$
$659$	38.8070	1.51170	0.755852	+	0.654742i	$0.227223\pi$
$660$	0	0
$661$	13.8557	0.538924	0.269462	−	0.963011i	$-0.413154\pi$
$661$	13.8557	0.538924	0.269462	+	0.963011i	$0.413154\pi$
$662$	5.93192	0.230550
$663$	−17.1784	−0.667152
$664$	−11.7048	−0.454236
$665$	0	0
$666$	2.51994	0.0976456
$667$	46.0804	1.78424
$668$	5.10213	0.197407
$669$	−13.9860	−0.540731
$670$	0	0
$671$	4.06808	0.157047
$672$	−1.60270	−0.0618257
$673$	−24.5880	−0.947799	−0.473899	−	0.880579i	$-0.657154\pi$
$673$	−24.5880	−0.947799	−0.473899	+	0.880579i	$0.657154\pi$
$674$	−28.2395	−1.08774
$675$	0	0
$676$	−11.0476	−0.424906
$677$	−7.34857	−0.282428	−0.141214	−	0.989979i	$-0.545101\pi$
$677$	−7.34857	−0.282428	−0.141214	+	0.989979i	$0.545101\pi$
$678$	19.0886	0.733093
$679$	19.1226	0.733860
$680$	0	0
$681$	14.6773	0.562436
$682$	3.00000	0.114876
$683$	−14.1984	−0.543287	−0.271644	−	0.962398i	$-0.587567\pi$
$683$	−14.1984	−0.543287	−0.271644	+	0.962398i	$0.587567\pi$
$684$	−1.56866	−0.0599793
$685$	0	0
$686$	1.00000	0.0381802
$687$	27.0259	1.03110
$688$	−0.0340418	−0.00129783
$689$	5.12917	0.195406
$690$	0	0
$691$	−49.5265	−1.88408	−0.942038	−	0.335507i	$-0.891093\pi$
$691$	−49.5265	−1.88408	−0.942038	+	0.335507i	$0.891093\pi$
$692$	−20.3281	−0.772757
$693$	0.431337	0.0163851
$694$	36.3891	1.38131
$695$	0	0
$696$	13.5129	0.512207
$697$	24.5880	0.931338
$698$	16.4449	0.622447
$699$	−36.3017	−1.37306
$700$	0	0
$701$	48.0452	1.81464	0.907322	−	0.420436i	$-0.138123\pi$
$701$	48.0452	1.81464	0.907322	+	0.420436i	$0.138123\pi$
$702$	7.68431	0.290026
$703$	21.2464	0.801325
$704$	1.00000	0.0376889
$705$	0	0
$706$	17.4243	0.655774
$707$	−9.69131	−0.364479
$708$	2.18489	0.0821133
$709$	26.1226	0.981056	0.490528	−	0.871425i	$-0.336804\pi$
$709$	26.1226	0.981056	0.490528	+	0.871425i	$0.336804\pi$
$710$	0	0
$711$	−3.45653	−0.129630
$712$	−3.01352	−0.112937
$713$	−16.3961	−0.614040
$714$	12.2940	0.460092
$715$	0	0
$716$	5.82863	0.217826
$717$	17.1567	0.640728
$718$	−11.2325	−0.419192
$719$	−20.1772	−0.752483	−0.376241	−	0.926522i	$-0.622784\pi$
$719$	−20.1772	−0.752483	−0.376241	+	0.926522i	$0.622784\pi$
$720$	0	0
$721$	11.0681	0.412197
$722$	5.77407	0.214889
$723$	26.6638	0.991637
$724$	−7.34158	−0.272848
$725$	0	0
$726$	1.60270	0.0594820
$727$	6.57520	0.243860	0.121930	−	0.992539i	$-0.461092\pi$
$727$	6.57520	0.243860	0.121930	+	0.992539i	$0.461092\pi$
$728$	−1.39730	−0.0517872
$729$	29.6855	1.09946
$730$	0	0
$731$	0.261128	0.00965816
$732$	−6.51994	−0.240984
$733$	−19.1984	−0.709110	−0.354555	−	0.935035i	$-0.615368\pi$
$733$	−19.1984	−0.709110	−0.354555	+	0.935035i	$0.615368\pi$
$734$	16.5946	0.612516
$735$	0	0
$736$	−5.46538	−0.201457
$737$	5.10213	0.187939
$738$	−1.38261	−0.0508946
$739$	43.5242	1.60106	0.800531	−	0.599291i	$-0.204551\pi$
$739$	43.5242	1.60106	0.800531	+	0.599291i	$0.204551\pi$
$740$	0	0
$741$	8.14432	0.299189
$742$	−3.67079	−0.134759
$743$	23.5323	0.863316	0.431658	−	0.902037i	$-0.357929\pi$
$743$	23.5323	0.863316	0.431658	+	0.902037i	$0.357929\pi$
$744$	−4.80811	−0.176274
$745$	0	0
$746$	−20.9578	−0.767320
$747$	−5.04873	−0.184723
$748$	−7.67079	−0.280472
$749$	−1.58219	−0.0578119
$750$	0	0
$751$	−24.3281	−0.887743	−0.443872	−	0.896090i	$-0.646395\pi$
$751$	−24.3281	−0.887743	−0.443872	+	0.896090i	$0.646395\pi$
$752$	−6.22593	−0.227036
$753$	40.6367	1.48089
$754$	11.7811	0.429041
$755$	0	0
$756$	−5.49942	−0.200012
$757$	53.4561	1.94289	0.971447	−	0.237257i	$-0.0762483\pi$
$757$	53.4561	1.94289	0.971447	+	0.237257i	$0.0762483\pi$
$758$	11.0340	0.400774
$759$	−8.75939	−0.317946
$760$	0	0
$761$	5.46654	0.198162	0.0990809	−	0.995079i	$-0.468410\pi$
$761$	5.46654	0.198162	0.0990809	+	0.995079i	$0.468410\pi$
$762$	−19.6379	−0.711406
$763$	−13.2259	−0.478811
$764$	−15.1497	−0.548097
$765$	0	0
$766$	24.2054	0.874577
$767$	1.90487	0.0687808
$768$	−1.60270	−0.0578326
$769$	−33.2653	−1.19958	−0.599789	−	0.800158i	$-0.704749\pi$
$769$	−33.2653	−1.19958	−0.599789	+	0.800158i	$0.704749\pi$
$770$	0	0
$771$	−41.6901	−1.50143
$772$	15.3416	0.552155
$773$	−8.36979	−0.301040	−0.150520	−	0.988607i	$-0.548095\pi$
$773$	−8.36979	−0.301040	−0.150520	+	0.988607i	$0.548095\pi$
$774$	−0.0146835	−0.000527788 0
$775$	0	0
$776$	19.1226	0.686463
$777$	9.36325	0.335905
$778$	−0.0816083	−0.00292580
$779$	−11.6573	−0.417665
$780$	0	0
$781$	−14.7389	−0.527398
$782$	41.9238	1.49919
$783$	46.3675	1.65704
$784$	1.00000	0.0357143
$785$	0	0
$786$	−6.99301	−0.249432
$787$	0.590339	0.0210433	0.0105217	−	0.999945i	$-0.496651\pi$
$787$	0.590339	0.0210433	0.0105217	+	0.999945i	$0.496651\pi$
$788$	−23.7048	−0.844450
$789$	2.56866	0.0914468
$790$	0	0
$791$	−11.9102	−0.423479
$792$	0.431337	0.0153269
$793$	−5.68431	−0.201856
$794$	−28.2043	−1.00093
$795$	0	0
$796$	−8.84216	−0.313402
$797$	−52.5118	−1.86006	−0.930031	−	0.367480i	$-0.880221\pi$
$797$	−52.5118	−1.86006	−0.930031	+	0.367480i	$0.880221\pi$
$798$	−5.82863	−0.206331
$799$	47.7578	1.68955
$800$	0	0
$801$	−1.29984	−0.0459277
$802$	−13.4519	−0.475001
$803$	−2.63675	−0.0930488
$804$	−8.17720	−0.288388
$805$	0	0
$806$	−4.19189	−0.147653
$807$	46.6855	1.64341
$808$	−9.69131	−0.340939
$809$	−14.7594	−0.518912	−0.259456	−	0.965755i	$-0.583543\pi$
$809$	−14.7594	−0.518912	−0.259456	+	0.965755i	$0.583543\pi$
$810$	0	0
$811$	−11.1373	−0.391084	−0.195542	−	0.980695i	$-0.562647\pi$
$811$	−11.1373	−0.391084	−0.195542	+	0.980695i	$0.562647\pi$
$812$	−8.43134	−0.295882
$813$	−24.2043	−0.848880
$814$	−5.84216	−0.204767
$815$	0	0
$816$	12.2940	0.430376
$817$	−0.123802	−0.00433127
$818$	14.8762	0.520134
$819$	−0.602705	−0.0210602
$820$	0	0
$821$	41.6638	1.45408	0.727038	−	0.686597i	$-0.240896\pi$
$821$	41.6638	1.45408	0.727038	+	0.686597i	$0.240896\pi$
$822$	−26.3346	−0.918524
$823$	34.6832	1.20898	0.604489	−	0.796613i	$-0.293377\pi$
$823$	34.6832	1.20898	0.604489	+	0.796613i	$0.293377\pi$
$824$	11.0681	0.385575
$825$	0	0
$826$	−1.36325	−0.0474336
$827$	50.6901	1.76267	0.881335	−	0.472493i	$-0.156646\pi$
$827$	50.6901	1.76267	0.881335	+	0.472493i	$0.156646\pi$
$828$	−2.35742	−0.0819260
$829$	3.72535	0.129387	0.0646933	−	0.997905i	$-0.479393\pi$
$829$	3.72535	0.129387	0.0646933	+	0.997905i	$0.479393\pi$
$830$	0	0
$831$	22.7652	0.789717
$832$	−1.39730	−0.0484425
$833$	−7.67079	−0.265777
$834$	3.17253	0.109856
$835$	0	0
$836$	3.63675	0.125780
$837$	−16.4983	−0.570263
$838$	16.1578	0.558163
$839$	17.6843	0.610530	0.305265	−	0.952267i	$-0.401255\pi$
$839$	17.6843	0.610530	0.305265	+	0.952267i	$0.401255\pi$
$840$	0	0
$841$	42.0874	1.45129
$842$	−3.44486	−0.118718
$843$	38.4519	1.32435
$844$	−17.0476	−0.586801
$845$	0	0
$846$	−2.68547	−0.0923284
$847$	−1.00000	−0.0343604
$848$	−3.67079	−0.126055
$849$	−31.6139	−1.08499
$850$	0	0
$851$	31.9296	1.09453
$852$	23.6221	0.809279
$853$	25.2952	0.866090	0.433045	−	0.901372i	$-0.357439\pi$
$853$	25.2952	0.866090	0.433045	+	0.901372i	$0.357439\pi$
$854$	4.06808	0.139207
$855$	0	0
$856$	−1.58219	−0.0540781
$857$	−41.5129	−1.41806	−0.709028	−	0.705181i	$-0.750866\pi$
$857$	−41.5129	−1.41806	−0.709028	+	0.705181i	$0.750866\pi$
$858$	−2.23945	−0.0764536
$859$	49.1896	1.67833	0.839163	−	0.543880i	$-0.183045\pi$
$859$	49.1896	1.67833	0.839163	+	0.543880i	$0.183045\pi$
$860$	0	0
$861$	−5.13733	−0.175080
$862$	32.0194	1.09058
$863$	−37.7648	−1.28553	−0.642764	−	0.766064i	$-0.722212\pi$
$863$	−37.7648	−1.28553	−0.642764	+	0.766064i	$0.722212\pi$
$864$	−5.49942	−0.187094
$865$	0	0
$866$	−9.83516	−0.334212
$867$	−67.0588	−2.27744
$868$	3.00000	0.101827
$869$	8.01352	0.271840
$870$	0	0
$871$	−7.12917	−0.241563
$872$	−13.2259	−0.447886
$873$	8.24830	0.279163
$874$	−19.8762	−0.672322
$875$	0	0
$876$	4.22593	0.142781
$877$	10.6789	0.360602	0.180301	−	0.983611i	$-0.442293\pi$
$877$	10.6789	0.360602	0.180301	+	0.983611i	$0.442293\pi$
$878$	23.4777	0.792336
$879$	−9.42902	−0.318033
$880$	0	0
$881$	−48.6274	−1.63830	−0.819150	−	0.573579i	$-0.805554\pi$
$881$	−48.6274	−1.63830	−0.819150	+	0.573579i	$0.805554\pi$
$882$	0.431337	0.0145239
$883$	−33.7524	−1.13586	−0.567929	−	0.823077i	$-0.692255\pi$
$883$	−33.7524	−1.13586	−0.567929	+	0.823077i	$0.692255\pi$
$884$	10.7184	0.360497
$885$	0	0
$886$	13.5892	0.456537
$887$	−19.4097	−0.651713	−0.325856	−	0.945419i	$-0.605653\pi$
$887$	−19.4097	−0.651713	−0.325856	+	0.945419i	$0.605653\pi$
$888$	9.36325	0.314210
$889$	12.2530	0.410952
$890$	0	0
$891$	−7.51994	−0.251927
$892$	8.72651	0.292185
$893$	−22.6421	−0.757690
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	12.2395	0.408663
$898$	13.0951	0.436990
$899$	−25.2940	−0.843602
$900$	0	0
$901$	28.1578	0.938074
$902$	3.20541	0.106728
$903$	−0.0545590	−0.00181561
$904$	−11.9102	−0.396129
$905$	0	0
$906$	−6.79459	−0.225735
$907$	−1.33574	−0.0443526	−0.0221763	−	0.999754i	$-0.507060\pi$
$907$	−1.33574	−0.0443526	−0.0221763	+	0.999754i	$0.507060\pi$
$908$	−9.15784	−0.303914
$909$	−4.18022	−0.138649
$910$	0	0
$911$	57.2982	1.89837	0.949187	−	0.314711i	$-0.101908\pi$
$911$	57.2982	1.89837	0.949187	+	0.314711i	$0.101908\pi$
$912$	−5.82863	−0.193005
$913$	11.7048	0.387373
$914$	−16.7594	−0.554351
$915$	0	0
$916$	−16.8627	−0.557158
$917$	4.36325	0.144087
$918$	42.1849	1.39231
$919$	−12.3621	−0.407788	−0.203894	−	0.978993i	$-0.565360\pi$
$919$	−12.3621	−0.407788	−0.203894	+	0.978993i	$0.565360\pi$
$920$	0	0
$921$	19.4507	0.640922
$922$	−12.0464	−0.396727
$923$	20.5946	0.677878
$924$	1.60270	0.0527251
$925$	0	0
$926$	36.7659	1.20820
$927$	4.77407	0.156801
$928$	−8.43134	−0.276772
$929$	−19.6286	−0.643993	−0.321997	−	0.946741i	$-0.604354\pi$
$929$	−19.6286	−0.643993	−0.321997	+	0.946741i	$0.604354\pi$
$930$	0	0
$931$	3.63675	0.119190
$932$	22.6503	0.741934
$933$	20.1767	0.660557
$934$	7.86921	0.257488
$935$	0	0
$936$	−0.602705	−0.0197000
$937$	28.5335	0.932148	0.466074	−	0.884746i	$-0.345668\pi$
$937$	28.5335	0.932148	0.466074	+	0.884746i	$0.345668\pi$
$938$	5.10213	0.166590
$939$	−26.5857	−0.867592
$940$	0	0
$941$	4.84332	0.157888	0.0789438	−	0.996879i	$-0.474845\pi$
$941$	4.84332	0.157888	0.0789438	+	0.996879i	$0.474845\pi$
$942$	35.8615	1.16843
$943$	−17.5188	−0.570490
$944$	−1.36325	−0.0443701
$945$	0	0
$946$	0.0340418	0.00110680
$947$	42.1420	1.36943	0.684716	−	0.728810i	$-0.259926\pi$
$947$	42.1420	1.36943	0.684716	+	0.728810i	$0.259926\pi$
$948$	−12.8433	−0.417131
$949$	3.68431	0.119598
$950$	0	0
$951$	32.9524	1.06856
$952$	−7.67079	−0.248612
$953$	21.8286	0.707099	0.353549	−	0.935416i	$-0.384975\pi$
$953$	21.8286	0.707099	0.353549	+	0.935416i	$0.384975\pi$
$954$	−1.58335	−0.0512627
$955$	0	0
$956$	−10.7048	−0.346219
$957$	−13.5129	−0.436811
$958$	22.4789	0.726260
$959$	16.4313	0.530596
$960$	0	0
$961$	−22.0000	−0.709677
$962$	8.16322	0.263193
$963$	−0.682456	−0.0219918
$964$	−16.6367	−0.535834
$965$	0	0
$966$	−8.75939	−0.281829
$967$	−31.5129	−1.01339	−0.506694	−	0.862126i	$-0.669133\pi$
$967$	−31.5129	−1.01339	−0.506694	+	0.862126i	$0.669133\pi$
$968$	−1.00000	−0.0321412
$969$	44.7102	1.43630
$970$	0	0
$971$	−24.3675	−0.781989	−0.390995	−	0.920393i	$-0.627869\pi$
$971$	−24.3675	−0.781989	−0.390995	+	0.920393i	$0.627869\pi$
$972$	−4.44602	−0.142606
$973$	−1.97948	−0.0634593
$974$	35.7377	1.14511
$975$	0	0
$976$	4.06808	0.130216
$977$	−32.7946	−1.04919	−0.524596	−	0.851351i	$-0.675784\pi$
$977$	−32.7946	−1.04919	−0.524596	+	0.851351i	$0.675784\pi$
$978$	2.59034	0.0828299
$979$	3.01352	0.0963127
$980$	0	0
$981$	−5.70483	−0.182141
$982$	7.17137	0.228848
$983$	−2.88856	−0.0921309	−0.0460654	−	0.998938i	$-0.514668\pi$
$983$	−2.88856	−0.0921309	−0.0460654	+	0.998938i	$0.514668\pi$
$984$	−5.13733	−0.163772
$985$	0	0
$986$	64.6750	2.05967
$987$	−9.97832	−0.317614
$988$	−5.08161	−0.161667
$989$	−0.186052	−0.00591609
$990$	0	0
$991$	−4.45185	−0.141418	−0.0707089	−	0.997497i	$-0.522526\pi$
$991$	−4.45185	−0.141418	−0.0707089	+	0.997497i	$0.522526\pi$
$992$	3.00000	0.0952501
$993$	9.50711	0.301699
$994$	−14.7389	−0.467489
$995$	0	0
$996$	−18.7594	−0.594414
$997$	26.6778	0.844894	0.422447	−	0.906388i	$-0.361171\pi$
$997$	26.6778	0.844894	0.422447	+	0.906388i	$0.361171\pi$
$998$	−1.06924	−0.0338463
$999$	32.1285	1.01650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.br.1.2	✓	3
5.2	odd	4		3850.2.c.bc.1849.2		6
5.3	odd	4		3850.2.c.bc.1849.5		6
5.4	even	2		3850.2.a.bw.1.2	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3850.2.a.br.1.2	✓	3	1.1	even	1	trivial
3850.2.a.bw.1.2	yes	3	5.4	even	2
3850.2.c.bc.1849.2		6	5.2	odd	4
3850.2.c.bc.1849.5		6	5.3	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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.60270 q^{3} +1.00000 q^{4} +1.60270 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.431337 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.60270 q^{3} +1.00000 q^{4} +1.60270 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.431337 q^{9} +1.00000 q^{11} -1.60270 q^{12} -1.39730 q^{13} +1.00000 q^{14} +1.00000 q^{16} -7.67079 q^{17} +0.431337 q^{18} +3.63675 q^{19} +1.60270 q^{21} -1.00000 q^{22} +5.46538 q^{23} +1.60270 q^{24} +1.39730 q^{26} +5.49942 q^{27} -1.00000 q^{28} +8.43134 q^{29} -3.00000 q^{31} -1.00000 q^{32} -1.60270 q^{33} +7.67079 q^{34} -0.431337 q^{36} +5.84216 q^{37} -3.63675 q^{38} +2.23945 q^{39} -3.20541 q^{41} -1.60270 q^{42} -0.0340418 q^{43} +1.00000 q^{44} -5.46538 q^{46} -6.22593 q^{47} -1.60270 q^{48} +1.00000 q^{49} +12.2940 q^{51} -1.39730 q^{52} -3.67079 q^{53} -5.49942 q^{54} +1.00000 q^{56} -5.82863 q^{57} -8.43134 q^{58} -1.36325 q^{59} +4.06808 q^{61} +3.00000 q^{62} +0.431337 q^{63} +1.00000 q^{64} +1.60270 q^{66} +5.10213 q^{67} -7.67079 q^{68} -8.75939 q^{69} -14.7389 q^{71} +0.431337 q^{72} -2.63675 q^{73} -5.84216 q^{74} +3.63675 q^{76} -1.00000 q^{77} -2.23945 q^{78} +8.01352 q^{79} -7.51994 q^{81} +3.20541 q^{82} +11.7048 q^{83} +1.60270 q^{84} +0.0340418 q^{86} -13.5129 q^{87} -1.00000 q^{88} +3.01352 q^{89} +1.39730 q^{91} +5.46538 q^{92} +4.80811 q^{93} +6.22593 q^{94} +1.60270 q^{96} -19.1226 q^{97} -1.00000 q^{98} -0.431337 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 8 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 8 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 3 q^{16} + q^{17} - 8 q^{18} - 2 q^{19} + 3 q^{21} - 3 q^{22} - 4 q^{23} + 3 q^{24} + 6 q^{26} - 15 q^{27} - 3 q^{28} + 16 q^{29} - 9 q^{31} - 3 q^{32} - 3 q^{33} - q^{34} + 8 q^{36} + q^{37} + 2 q^{38} - 8 q^{39} - 6 q^{41} - 3 q^{42} + 11 q^{43} + 3 q^{44} + 4 q^{46} - 13 q^{47} - 3 q^{48} + 3 q^{49} + 9 q^{51} - 6 q^{52} + 13 q^{53} + 15 q^{54} + 3 q^{56} - 10 q^{57} - 16 q^{58} - 17 q^{59} - 10 q^{61} + 9 q^{62} - 8 q^{63} + 3 q^{64} + 3 q^{66} - 18 q^{67} + q^{68} + 22 q^{69} + 2 q^{71} - 8 q^{72} + 5 q^{73} - q^{74} - 2 q^{76} - 3 q^{77} + 8 q^{78} + 15 q^{79} + 11 q^{81} + 6 q^{82} + 3 q^{84} - 11 q^{86} - 3 q^{88} + 6 q^{91} - 4 q^{92} + 9 q^{93} + 13 q^{94} + 3 q^{96} - 22 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 8 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 3 * q^16 + q^17 - 8 * q^18 - 2 * q^19 + 3 * q^21 - 3 * q^22 - 4 * q^23 + 3 * q^24 + 6 * q^26 - 15 * q^27 - 3 * q^28 + 16 * q^29 - 9 * q^31 - 3 * q^32 - 3 * q^33 - q^34 + 8 * q^36 + q^37 + 2 * q^38 - 8 * q^39 - 6 * q^41 - 3 * q^42 + 11 * q^43 + 3 * q^44 + 4 * q^46 - 13 * q^47 - 3 * q^48 + 3 * q^49 + 9 * q^51 - 6 * q^52 + 13 * q^53 + 15 * q^54 + 3 * q^56 - 10 * q^57 - 16 * q^58 - 17 * q^59 - 10 * q^61 + 9 * q^62 - 8 * q^63 + 3 * q^64 + 3 * q^66 - 18 * q^67 + q^68 + 22 * q^69 + 2 * q^71 - 8 * q^72 + 5 * q^73 - q^74 - 2 * q^76 - 3 * q^77 + 8 * q^78 + 15 * q^79 + 11 * q^81 + 6 * q^82 + 3 * q^84 - 11 * q^86 - 3 * q^88 + 6 * q^91 - 4 * q^92 + 9 * q^93 + 13 * q^94 + 3 * q^96 - 22 * q^97 - 3 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more