LMFDB - Embedded newform 3850.2.a.bv.1.3

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:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
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			1.3
Root			$-1.81361$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.81361 q^{3} +1.00000 q^{4} +2.81361 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.91638 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.81361 q^{3} +1.00000 q^{4} +2.81361 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.91638 q^{9} +1.00000 q^{11} +2.81361 q^{12} -4.91638 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.81361 q^{17} +4.91638 q^{18} +1.28917 q^{19} -2.81361 q^{21} +1.00000 q^{22} +7.49472 q^{23} +2.81361 q^{24} -4.91638 q^{26} +5.39194 q^{27} -1.00000 q^{28} -1.86751 q^{29} +9.15165 q^{31} +1.00000 q^{32} +2.81361 q^{33} +4.81361 q^{34} +4.91638 q^{36} +6.75971 q^{37} +1.28917 q^{38} -13.8328 q^{39} -12.4111 q^{41} -2.81361 q^{42} -2.62721 q^{43} +1.00000 q^{44} +7.49472 q^{46} +11.0192 q^{47} +2.81361 q^{48} +1.00000 q^{49} +13.5436 q^{51} -4.91638 q^{52} -9.74914 q^{53} +5.39194 q^{54} -1.00000 q^{56} +3.62721 q^{57} -1.86751 q^{58} +1.39194 q^{59} +6.57834 q^{61} +9.15165 q^{62} -4.91638 q^{63} +1.00000 q^{64} +2.81361 q^{66} +3.62721 q^{67} +4.81361 q^{68} +21.0872 q^{69} -0.338044 q^{71} +4.91638 q^{72} -13.6952 q^{73} +6.75971 q^{74} +1.28917 q^{76} -1.00000 q^{77} -13.8328 q^{78} -6.28917 q^{79} +0.421663 q^{81} -12.4111 q^{82} +9.75971 q^{83} -2.81361 q^{84} -2.62721 q^{86} -5.25443 q^{87} +1.00000 q^{88} -6.71083 q^{89} +4.91638 q^{91} +7.49472 q^{92} +25.7491 q^{93} +11.0192 q^{94} +2.81361 q^{96} -0.338044 q^{97} +1.00000 q^{98} +4.91638 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} - 3 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 - 3 * q^7 + 3 * q^8 + q^9	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} - 3 q^{7} + 3 q^{8} + q^{9} + 3 q^{11} + 2 q^{12} - q^{13} - 3 q^{14} + 3 q^{16} + 8 q^{17} + q^{18} + 3 q^{19} - 2 q^{21} + 3 q^{22} + 7 q^{23} + 2 q^{24} - q^{26} + 8 q^{27} - 3 q^{28} - 3 q^{29} + 9 q^{31} + 3 q^{32} + 2 q^{33} + 8 q^{34} + q^{36} + 10 q^{37} + 3 q^{38} - 14 q^{39} - 8 q^{41} - 2 q^{42} + 5 q^{43} + 3 q^{44} + 7 q^{46} + 12 q^{47} + 2 q^{48} + 3 q^{49} + 14 q^{51} - q^{52} + 12 q^{53} + 8 q^{54} - 3 q^{56} - 2 q^{57} - 3 q^{58} - 4 q^{59} + 18 q^{61} + 9 q^{62} - q^{63} + 3 q^{64} + 2 q^{66} - 2 q^{67} + 8 q^{68} + 10 q^{69} + 11 q^{71} + q^{72} + 4 q^{73} + 10 q^{74} + 3 q^{76} - 3 q^{77} - 14 q^{78} - 18 q^{79} + 3 q^{81} - 8 q^{82} + 19 q^{83} - 2 q^{84} + 5 q^{86} + 10 q^{87} + 3 q^{88} - 21 q^{89} + q^{91} + 7 q^{92} + 36 q^{93} + 12 q^{94} + 2 q^{96} + 11 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 - 3 * q^7 + 3 * q^8 + q^9 + 3 * q^11 + 2 * q^12 - q^13 - 3 * q^14 + 3 * q^16 + 8 * q^17 + q^18 + 3 * q^19 - 2 * q^21 + 3 * q^22 + 7 * q^23 + 2 * q^24 - q^26 + 8 * q^27 - 3 * q^28 - 3 * q^29 + 9 * q^31 + 3 * q^32 + 2 * q^33 + 8 * q^34 + q^36 + 10 * q^37 + 3 * q^38 - 14 * q^39 - 8 * q^41 - 2 * q^42 + 5 * q^43 + 3 * q^44 + 7 * q^46 + 12 * q^47 + 2 * q^48 + 3 * q^49 + 14 * q^51 - q^52 + 12 * q^53 + 8 * q^54 - 3 * q^56 - 2 * q^57 - 3 * q^58 - 4 * q^59 + 18 * q^61 + 9 * q^62 - q^63 + 3 * q^64 + 2 * q^66 - 2 * q^67 + 8 * q^68 + 10 * q^69 + 11 * q^71 + q^72 + 4 * q^73 + 10 * q^74 + 3 * q^76 - 3 * q^77 - 14 * q^78 - 18 * q^79 + 3 * q^81 - 8 * q^82 + 19 * q^83 - 2 * q^84 + 5 * q^86 + 10 * q^87 + 3 * q^88 - 21 * q^89 + q^91 + 7 * q^92 + 36 * q^93 + 12 * q^94 + 2 * q^96 + 11 * q^97 + 3 * q^98 + 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
$3$	2.81361	1.62444	0.812218	−	0.583354i	$-0.198260\pi$
$3$	2.81361	1.62444	0.812218	+	0.583354i	$0.198260\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.81361	1.14865
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	4.91638	1.63879
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.81361	0.812218
$13$	−4.91638	−1.36356	−0.681779	−	0.731558i	$-0.738794\pi$
$13$	−4.91638	−1.36356	−0.681779	+	0.731558i	$0.738794\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	4.81361	1.16747	0.583736	−	0.811944i	$-0.301590\pi$
$17$	4.81361	1.16747	0.583736	+	0.811944i	$0.301590\pi$
$18$	4.91638	1.15880
$19$	1.28917	0.295756	0.147878	−	0.989006i	$-0.452756\pi$
$19$	1.28917	0.295756	0.147878	+	0.989006i	$0.452756\pi$
$20$	0	0
$21$	−2.81361	−0.613979
$22$	1.00000	0.213201
$23$	7.49472	1.56276	0.781378	−	0.624057i	$-0.214517\pi$
$23$	7.49472	1.56276	0.781378	+	0.624057i	$0.214517\pi$
$24$	2.81361	0.574325
$25$	0	0
$26$	−4.91638	−0.964182
$27$	5.39194	1.03768
$28$	−1.00000	−0.188982
$29$	−1.86751	−0.346787	−0.173394	−	0.984853i	$-0.555473\pi$
$29$	−1.86751	−0.346787	−0.173394	+	0.984853i	$0.555473\pi$
$30$	0	0
$31$	9.15165	1.64369	0.821843	−	0.569715i	$-0.192946\pi$
$31$	9.15165	1.64369	0.821843	+	0.569715i	$0.192946\pi$
$32$	1.00000	0.176777
$33$	2.81361	0.489786
$34$	4.81361	0.825527
$35$	0	0
$36$	4.91638	0.819397
$37$	6.75971	1.11129	0.555645	−	0.831420i	$-0.312472\pi$
$37$	6.75971	1.11129	0.555645	+	0.831420i	$0.312472\pi$
$38$	1.28917	0.209131
$39$	−13.8328	−2.21501
$40$	0	0
$41$	−12.4111	−1.93829	−0.969144	−	0.246495i	$-0.920721\pi$
$41$	−12.4111	−1.93829	−0.969144	+	0.246495i	$0.920721\pi$
$42$	−2.81361	−0.434149
$43$	−2.62721	−0.400646	−0.200323	−	0.979730i	$-0.564199\pi$
$43$	−2.62721	−0.400646	−0.200323	+	0.979730i	$0.564199\pi$
$44$	1.00000	0.150756
$45$	0	0
$46$	7.49472	1.10504
$47$	11.0192	1.60731	0.803655	−	0.595096i	$-0.202886\pi$
$47$	11.0192	1.60731	0.803655	+	0.595096i	$0.202886\pi$
$48$	2.81361	0.406109
$49$	1.00000	0.142857
$50$	0	0
$51$	13.5436	1.89648
$52$	−4.91638	−0.681779
$53$	−9.74914	−1.33915	−0.669574	−	0.742745i	$-0.733523\pi$
$53$	−9.74914	−1.33915	−0.669574	+	0.742745i	$0.733523\pi$
$54$	5.39194	0.733751
$55$	0	0
$56$	−1.00000	−0.133631
$57$	3.62721	0.480436
$58$	−1.86751	−0.245216
$59$	1.39194	0.181216	0.0906078	−	0.995887i	$-0.471119\pi$
$59$	1.39194	0.181216	0.0906078	+	0.995887i	$0.471119\pi$
$60$	0	0
$61$	6.57834	0.842270	0.421135	−	0.906998i	$-0.361632\pi$
$61$	6.57834	0.842270	0.421135	+	0.906998i	$0.361632\pi$
$62$	9.15165	1.16226
$63$	−4.91638	−0.619406
$64$	1.00000	0.125000
$65$	0	0
$66$	2.81361	0.346331
$67$	3.62721	0.443135	0.221567	−	0.975145i	$-0.428883\pi$
$67$	3.62721	0.443135	0.221567	+	0.975145i	$0.428883\pi$
$68$	4.81361	0.583736
$69$	21.0872	2.53860
$70$	0	0
$71$	−0.338044	−0.0401185	−0.0200592	−	0.999799i	$-0.506385\pi$
$71$	−0.338044	−0.0401185	−0.0200592	+	0.999799i	$0.506385\pi$
$72$	4.91638	0.579401
$73$	−13.6952	−1.60291	−0.801454	−	0.598057i	$-0.795940\pi$
$73$	−13.6952	−1.60291	−0.801454	+	0.598057i	$0.795940\pi$
$74$	6.75971	0.785800
$75$	0	0
$76$	1.28917	0.147878
$77$	−1.00000	−0.113961
$78$	−13.8328	−1.56625
$79$	−6.28917	−0.707587	−0.353793	−	0.935324i	$-0.615108\pi$
$79$	−6.28917	−0.707587	−0.353793	+	0.935324i	$0.615108\pi$
$80$	0	0
$81$	0.421663	0.0468514
$82$	−12.4111	−1.37058
$83$	9.75971	1.07127	0.535634	−	0.844451i	$-0.320073\pi$
$83$	9.75971	1.07127	0.535634	+	0.844451i	$0.320073\pi$
$84$	−2.81361	−0.306990
$85$	0	0
$86$	−2.62721	−0.283300
$87$	−5.25443	−0.563334
$88$	1.00000	0.106600
$89$	−6.71083	−0.711347	−0.355673	−	0.934610i	$-0.615748\pi$
$89$	−6.71083	−0.711347	−0.355673	+	0.934610i	$0.615748\pi$
$90$	0	0
$91$	4.91638	0.515377
$92$	7.49472	0.781378
$93$	25.7491	2.67006
$94$	11.0192	1.13654
$95$	0	0
$96$	2.81361	0.287163
$97$	−0.338044	−0.0343232	−0.0171616	−	0.999853i	$-0.505463\pi$
$97$	−0.338044	−0.0343232	−0.0171616	+	0.999853i	$0.505463\pi$
$98$	1.00000	0.101015
$99$	4.91638	0.494115
$100$	0	0
$101$	16.5139	1.64319	0.821596	−	0.570070i	$-0.193084\pi$
$101$	16.5139	1.64319	0.821596	+	0.570070i	$0.193084\pi$
$102$	13.5436	1.34102
$103$	5.83779	0.575214	0.287607	−	0.957748i	$-0.407140\pi$
$103$	5.83779	0.575214	0.287607	+	0.957748i	$0.407140\pi$
$104$	−4.91638	−0.482091
$105$	0	0
$106$	−9.74914	−0.946921
$107$	−0.0488759	−0.00472501	−0.00236251	−	0.999997i	$-0.500752\pi$
$107$	−0.0488759	−0.00472501	−0.00236251	+	0.999997i	$0.500752\pi$
$108$	5.39194	0.518840
$109$	0.240293	0.0230159	0.0115079	−	0.999934i	$-0.496337\pi$
$109$	0.240293	0.0230159	0.0115079	+	0.999934i	$0.496337\pi$
$110$	0	0
$111$	19.0192	1.80522
$112$	−1.00000	−0.0944911
$113$	−21.0036	−1.97585	−0.987925	−	0.154934i	$-0.950484\pi$
$113$	−21.0036	−1.97585	−0.987925	+	0.154934i	$0.950484\pi$
$114$	3.62721	0.339720
$115$	0	0
$116$	−1.86751	−0.173394
$117$	−24.1708	−2.23459
$118$	1.39194	0.128139
$119$	−4.81361	−0.441263
$120$	0	0
$121$	1.00000	0.0909091
$122$	6.57834	0.595575
$123$	−34.9200	−3.14863
$124$	9.15165	0.821843
$125$	0	0
$126$	−4.91638	−0.437986
$127$	4.96526	0.440595	0.220298	−	0.975433i	$-0.429297\pi$
$127$	4.96526	0.440595	0.220298	+	0.975433i	$0.429297\pi$
$128$	1.00000	0.0883883
$129$	−7.39194	−0.650824
$130$	0	0
$131$	12.1325	1.06002	0.530010	−	0.847991i	$-0.322188\pi$
$131$	12.1325	1.06002	0.530010	+	0.847991i	$0.322188\pi$
$132$	2.81361	0.244893
$133$	−1.28917	−0.111785
$134$	3.62721	0.313343
$135$	0	0
$136$	4.81361	0.412763
$137$	−16.7491	−1.43098	−0.715488	−	0.698625i	$-0.753796\pi$
$137$	−16.7491	−1.43098	−0.715488	+	0.698625i	$0.753796\pi$
$138$	21.0872	1.79506
$139$	−22.5819	−1.91537	−0.957686	−	0.287814i	$-0.907071\pi$
$139$	−22.5819	−1.91537	−0.957686	+	0.287814i	$0.907071\pi$
$140$	0	0
$141$	31.0036	2.61097
$142$	−0.338044	−0.0283681
$143$	−4.91638	−0.411128
$144$	4.91638	0.409698
$145$	0	0
$146$	−13.6952	−1.13343
$147$	2.81361	0.232062
$148$	6.75971	0.555645
$149$	−13.4217	−1.09955	−0.549773	−	0.835314i	$-0.685286\pi$
$149$	−13.4217	−1.09955	−0.549773	+	0.835314i	$0.685286\pi$
$150$	0	0
$151$	−15.2544	−1.24139	−0.620694	−	0.784053i	$-0.713149\pi$
$151$	−15.2544	−1.24139	−0.620694	+	0.784053i	$0.713149\pi$
$152$	1.28917	0.104565
$153$	23.6655	1.91324
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	−13.8328	−1.10751
$157$	−8.50885	−0.679080	−0.339540	−	0.940592i	$-0.610271\pi$
$157$	−8.50885	−0.679080	−0.339540	+	0.940592i	$0.610271\pi$
$158$	−6.28917	−0.500339
$159$	−27.4303	−2.17536
$160$	0	0
$161$	−7.49472	−0.590667
$162$	0.421663	0.0331290
$163$	15.7250	1.23167	0.615837	−	0.787873i	$-0.288818\pi$
$163$	15.7250	1.23167	0.615837	+	0.787873i	$0.288818\pi$
$164$	−12.4111	−0.969144
$165$	0	0
$166$	9.75971	0.757500
$167$	−14.6167	−1.13107	−0.565535	−	0.824724i	$-0.691330\pi$
$167$	−14.6167	−1.13107	−0.565535	+	0.824724i	$0.691330\pi$
$168$	−2.81361	−0.217074
$169$	11.1708	0.859293
$170$	0	0
$171$	6.33804	0.484682
$172$	−2.62721	−0.200323
$173$	3.08362	0.234443	0.117222	−	0.993106i	$-0.462601\pi$
$173$	3.08362	0.234443	0.117222	+	0.993106i	$0.462601\pi$
$174$	−5.25443	−0.398337
$175$	0	0
$176$	1.00000	0.0753778
$177$	3.91638	0.294373
$178$	−6.71083	−0.502998
$179$	−17.0489	−1.27429	−0.637146	−	0.770743i	$-0.719885\pi$
$179$	−17.0489	−1.27429	−0.637146	+	0.770743i	$0.719885\pi$
$180$	0	0
$181$	−11.0872	−0.824104	−0.412052	−	0.911160i	$-0.635188\pi$
$181$	−11.0872	−0.824104	−0.412052	+	0.911160i	$0.635188\pi$
$182$	4.91638	0.364426
$183$	18.5089	1.36821
$184$	7.49472	0.552518
$185$	0	0
$186$	25.7491	1.88802
$187$	4.81361	0.352006
$188$	11.0192	0.803655
$189$	−5.39194	−0.392206
$190$	0	0
$191$	−1.55416	−0.112455	−0.0562274	−	0.998418i	$-0.517907\pi$
$191$	−1.55416	−0.112455	−0.0562274	+	0.998418i	$0.517907\pi$
$192$	2.81361	0.203055
$193$	12.9894	0.935000	0.467500	−	0.883993i	$-0.345155\pi$
$193$	12.9894	0.935000	0.467500	+	0.883993i	$0.345155\pi$
$194$	−0.338044	−0.0242702
$195$	0	0
$196$	1.00000	0.0714286
$197$	−0.710831	−0.0506446	−0.0253223	−	0.999679i	$-0.508061\pi$
$197$	−0.710831	−0.0506446	−0.0253223	+	0.999679i	$0.508061\pi$
$198$	4.91638	0.349392
$199$	15.2197	1.07889	0.539447	−	0.842019i	$-0.318633\pi$
$199$	15.2197	1.07889	0.539447	+	0.842019i	$0.318633\pi$
$200$	0	0
$201$	10.2056	0.719844
$202$	16.5139	1.16191
$203$	1.86751	0.131073
$204$	13.5436	0.948241
$205$	0	0
$206$	5.83779	0.406738
$207$	36.8469	2.56104
$208$	−4.91638	−0.340890
$209$	1.28917	0.0891737
$210$	0	0
$211$	−12.0242	−0.827779	−0.413889	−	0.910327i	$-0.635830\pi$
$211$	−12.0242	−0.827779	−0.413889	+	0.910327i	$0.635830\pi$
$212$	−9.74914	−0.669574
$213$	−0.951124	−0.0651699
$214$	−0.0488759	−0.00334109
$215$	0	0
$216$	5.39194	0.366875
$217$	−9.15165	−0.621255
$218$	0.240293	0.0162747
$219$	−38.5330	−2.60382
$220$	0	0
$221$	−23.6655	−1.59192
$222$	19.0192	1.27648
$223$	6.03831	0.404355	0.202178	−	0.979349i	$-0.435198\pi$
$223$	6.03831	0.404355	0.202178	+	0.979349i	$0.435198\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−21.0036	−1.39714
$227$	4.60303	0.305514	0.152757	−	0.988264i	$-0.451185\pi$
$227$	4.60303	0.305514	0.152757	+	0.988264i	$0.451185\pi$
$228$	3.62721	0.240218
$229$	−5.42166	−0.358274	−0.179137	−	0.983824i	$-0.557330\pi$
$229$	−5.42166	−0.358274	−0.179137	+	0.983824i	$0.557330\pi$
$230$	0	0
$231$	−2.81361	−0.185122
$232$	−1.86751	−0.122608
$233$	−2.57834	−0.168912	−0.0844562	−	0.996427i	$-0.526915\pi$
$233$	−2.57834	−0.168912	−0.0844562	+	0.996427i	$0.526915\pi$
$234$	−24.1708	−1.58010
$235$	0	0
$236$	1.39194	0.0906078
$237$	−17.6952	−1.14943
$238$	−4.81361	−0.312020
$239$	−21.0630	−1.36245	−0.681226	−	0.732073i	$-0.738553\pi$
$239$	−21.0630	−1.36245	−0.681226	+	0.732073i	$0.738553\pi$
$240$	0	0
$241$	21.0192	1.35396	0.676981	−	0.736000i	$-0.263288\pi$
$241$	21.0192	1.35396	0.676981	+	0.736000i	$0.263288\pi$
$242$	1.00000	0.0642824
$243$	−14.9894	−0.961573
$244$	6.57834	0.421135
$245$	0	0
$246$	−34.9200	−2.22641
$247$	−6.33804	−0.403280
$248$	9.15165	0.581130
$249$	27.4600	1.74021
$250$	0	0
$251$	−27.4897	−1.73513	−0.867567	−	0.497320i	$-0.834317\pi$
$251$	−27.4897	−1.73513	−0.867567	+	0.497320i	$0.834317\pi$
$252$	−4.91638	−0.309703
$253$	7.49472	0.471189
$254$	4.96526	0.311548
$255$	0	0
$256$	1.00000	0.0625000
$257$	−8.23025	−0.513389	−0.256694	−	0.966493i	$-0.582633\pi$
$257$	−8.23025	−0.513389	−0.256694	+	0.966493i	$0.582633\pi$
$258$	−7.39194	−0.460202
$259$	−6.75971	−0.420028
$260$	0	0
$261$	−9.18137	−0.568313
$262$	12.1325	0.749548
$263$	8.96526	0.552821	0.276411	−	0.961040i	$-0.410855\pi$
$263$	8.96526	0.552821	0.276411	+	0.961040i	$0.410855\pi$
$264$	2.81361	0.173166
$265$	0	0
$266$	−1.28917	−0.0790440
$267$	−18.8816	−1.15554
$268$	3.62721	0.221567
$269$	7.56777	0.461415	0.230708	−	0.973023i	$-0.425896\pi$
$269$	7.56777	0.461415	0.230708	+	0.973023i	$0.425896\pi$
$270$	0	0
$271$	20.6167	1.25237	0.626186	−	0.779674i	$-0.284615\pi$
$271$	20.6167	1.25237	0.626186	+	0.779674i	$0.284615\pi$
$272$	4.81361	0.291868
$273$	13.8328	0.837197
$274$	−16.7491	−1.01185
$275$	0	0
$276$	21.0872	1.26930
$277$	22.3517	1.34298	0.671491	−	0.741013i	$-0.265654\pi$
$277$	22.3517	1.34298	0.671491	+	0.741013i	$0.265654\pi$
$278$	−22.5819	−1.35437
$279$	44.9930	2.69366
$280$	0	0
$281$	−6.20555	−0.370192	−0.185096	−	0.982720i	$-0.559260\pi$
$281$	−6.20555	−0.370192	−0.185096	+	0.982720i	$0.559260\pi$
$282$	31.0036	1.84624
$283$	−10.6761	−0.634628	−0.317314	−	0.948321i	$-0.602781\pi$
$283$	−10.6761	−0.634628	−0.317314	+	0.948321i	$0.602781\pi$
$284$	−0.338044	−0.0200592
$285$	0	0
$286$	−4.91638	−0.290712
$287$	12.4111	0.732604
$288$	4.91638	0.289701
$289$	6.17081	0.362989
$290$	0	0
$291$	−0.951124	−0.0557559
$292$	−13.6952	−0.801454
$293$	−12.2736	−0.717030	−0.358515	−	0.933524i	$-0.616717\pi$
$293$	−12.2736	−0.717030	−0.358515	+	0.933524i	$0.616717\pi$
$294$	2.81361	0.164093
$295$	0	0
$296$	6.75971	0.392900
$297$	5.39194	0.312872
$298$	−13.4217	−0.777496
$299$	−36.8469	−2.13091
$300$	0	0
$301$	2.62721	0.151430
$302$	−15.2544	−0.877794
$303$	46.4635	2.66926
$304$	1.28917	0.0739389
$305$	0	0
$306$	23.6655	1.35287
$307$	19.2544	1.09891	0.549454	−	0.835524i	$-0.314836\pi$
$307$	19.2544	1.09891	0.549454	+	0.835524i	$0.314836\pi$
$308$	−1.00000	−0.0569803
$309$	16.4252	0.934399
$310$	0	0
$311$	−1.36725	−0.0775295	−0.0387647	−	0.999248i	$-0.512342\pi$
$311$	−1.36725	−0.0775295	−0.0387647	+	0.999248i	$0.512342\pi$
$312$	−13.8328	−0.783126
$313$	−32.2822	−1.82470	−0.912348	−	0.409415i	$-0.865733\pi$
$313$	−32.2822	−1.82470	−0.912348	+	0.409415i	$0.865733\pi$
$314$	−8.50885	−0.480182
$315$	0	0
$316$	−6.28917	−0.353793
$317$	11.3380	0.636808	0.318404	−	0.947955i	$-0.396853\pi$
$317$	11.3380	0.636808	0.318404	+	0.947955i	$0.396853\pi$
$318$	−27.4303	−1.53821
$319$	−1.86751	−0.104560
$320$	0	0
$321$	−0.137518	−0.00767548
$322$	−7.49472	−0.417664
$323$	6.20555	0.345286
$324$	0.421663	0.0234257
$325$	0	0
$326$	15.7250	0.870925
$327$	0.676089	0.0373878
$328$	−12.4111	−0.685288
$329$	−11.0192	−0.607506
$330$	0	0
$331$	−32.7144	−1.79815	−0.899073	−	0.437799i	$-0.855758\pi$
$331$	−32.7144	−1.79815	−0.899073	+	0.437799i	$0.855758\pi$
$332$	9.75971	0.535634
$333$	33.2333	1.82117
$334$	−14.6167	−0.799788
$335$	0	0
$336$	−2.81361	−0.153495
$337$	18.5472	1.01033	0.505164	−	0.863023i	$-0.331432\pi$
$337$	18.5472	1.01033	0.505164	+	0.863023i	$0.331432\pi$
$338$	11.1708	0.607612
$339$	−59.0958	−3.20964
$340$	0	0
$341$	9.15165	0.495590
$342$	6.33804	0.342722
$343$	−1.00000	−0.0539949
$344$	−2.62721	−0.141650
$345$	0	0
$346$	3.08362	0.165776
$347$	6.28917	0.337620	0.168810	−	0.985649i	$-0.446008\pi$
$347$	6.28917	0.337620	0.168810	+	0.985649i	$0.446008\pi$
$348$	−5.25443	−0.281667
$349$	−23.2283	−1.24338	−0.621691	−	0.783263i	$-0.713554\pi$
$349$	−23.2283	−1.24338	−0.621691	+	0.783263i	$0.713554\pi$
$350$	0	0
$351$	−26.5089	−1.41494
$352$	1.00000	0.0533002
$353$	−9.21968	−0.490714	−0.245357	−	0.969433i	$-0.578905\pi$
$353$	−9.21968	−0.490714	−0.245357	+	0.969433i	$0.578905\pi$
$354$	3.91638	0.208153
$355$	0	0
$356$	−6.71083	−0.355673
$357$	−13.5436	−0.716803
$358$	−17.0489	−0.901061
$359$	28.0766	1.48183	0.740914	−	0.671600i	$-0.234393\pi$
$359$	28.0766	1.48183	0.740914	+	0.671600i	$0.234393\pi$
$360$	0	0
$361$	−17.3380	−0.912529
$362$	−11.0872	−0.582730
$363$	2.81361	0.147676
$364$	4.91638	0.257688
$365$	0	0
$366$	18.5089	0.967473
$367$	6.87807	0.359032	0.179516	−	0.983755i	$-0.442547\pi$
$367$	6.87807	0.359032	0.179516	+	0.983755i	$0.442547\pi$
$368$	7.49472	0.390689
$369$	−61.0177	−3.17645
$370$	0	0
$371$	9.74914	0.506150
$372$	25.7491	1.33503
$373$	10.3627	0.536562	0.268281	−	0.963341i	$-0.413544\pi$
$373$	10.3627	0.536562	0.268281	+	0.963341i	$0.413544\pi$
$374$	4.81361	0.248906
$375$	0	0
$376$	11.0192	0.568270
$377$	9.18137	0.472865
$378$	−5.39194	−0.277332
$379$	−32.4494	−1.66681	−0.833407	−	0.552659i	$-0.813613\pi$
$379$	−32.4494	−1.66681	−0.833407	+	0.552659i	$0.813613\pi$
$380$	0	0
$381$	13.9703	0.715719
$382$	−1.55416	−0.0795176
$383$	30.7194	1.56969	0.784845	−	0.619693i	$-0.212743\pi$
$383$	30.7194	1.56969	0.784845	+	0.619693i	$0.212743\pi$
$384$	2.81361	0.143581
$385$	0	0
$386$	12.9894	0.661145
$387$	−12.9164	−0.656577
$388$	−0.338044	−0.0171616
$389$	−29.3169	−1.48643	−0.743213	−	0.669054i	$-0.766699\pi$
$389$	−29.3169	−1.48643	−0.743213	+	0.669054i	$0.766699\pi$
$390$	0	0
$391$	36.0766	1.82447
$392$	1.00000	0.0505076
$393$	34.1361	1.72194
$394$	−0.710831	−0.0358112
$395$	0	0
$396$	4.91638	0.247057
$397$	22.1955	1.11396	0.556980	−	0.830526i	$-0.311960\pi$
$397$	22.1955	1.11396	0.556980	+	0.830526i	$0.311960\pi$
$398$	15.2197	0.762894
$399$	−3.62721	−0.181588
$400$	0	0
$401$	−20.2544	−1.01146	−0.505729	−	0.862692i	$-0.668776\pi$
$401$	−20.2544	−1.01146	−0.505729	+	0.862692i	$0.668776\pi$
$402$	10.2056	0.509007
$403$	−44.9930	−2.24126
$404$	16.5139	0.821596
$405$	0	0
$406$	1.86751	0.0926827
$407$	6.75971	0.335066
$408$	13.5436	0.670508
$409$	−22.1658	−1.09603	−0.548014	−	0.836469i	$-0.684616\pi$
$409$	−22.1658	−1.09603	−0.548014	+	0.836469i	$0.684616\pi$
$410$	0	0
$411$	−47.1255	−2.32453
$412$	5.83779	0.287607
$413$	−1.39194	−0.0684931
$414$	36.8469	1.81093
$415$	0	0
$416$	−4.91638	−0.241045
$417$	−63.5366	−3.11140
$418$	1.28917	0.0630553
$419$	36.5769	1.78690	0.893449	−	0.449165i	$-0.148278\pi$
$419$	36.5769	1.78690	0.893449	+	0.449165i	$0.148278\pi$
$420$	0	0
$421$	−2.94108	−0.143339	−0.0716697	−	0.997428i	$-0.522833\pi$
$421$	−2.94108	−0.143339	−0.0716697	+	0.997428i	$0.522833\pi$
$422$	−12.0242	−0.585328
$423$	54.1744	2.63405
$424$	−9.74914	−0.473460
$425$	0	0
$426$	−0.951124	−0.0460821
$427$	−6.57834	−0.318348
$428$	−0.0488759	−0.00236251
$429$	−13.8328	−0.667852
$430$	0	0
$431$	6.53303	0.314685	0.157343	−	0.987544i	$-0.449707\pi$
$431$	6.53303	0.314685	0.157343	+	0.987544i	$0.449707\pi$
$432$	5.39194	0.259420
$433$	−16.0347	−0.770581	−0.385290	−	0.922795i	$-0.625899\pi$
$433$	−16.0347	−0.770581	−0.385290	+	0.922795i	$0.625899\pi$
$434$	−9.15165	−0.439293
$435$	0	0
$436$	0.240293	0.0115079
$437$	9.66196	0.462194
$438$	−38.5330	−1.84118
$439$	−14.2650	−0.680831	−0.340415	−	0.940275i	$-0.610568\pi$
$439$	−14.2650	−0.680831	−0.340415	+	0.940275i	$0.610568\pi$
$440$	0	0
$441$	4.91638	0.234113
$442$	−23.6655	−1.12565
$443$	13.9022	0.660516	0.330258	−	0.943891i	$-0.392864\pi$
$443$	13.9022	0.660516	0.330258	+	0.943891i	$0.392864\pi$
$444$	19.0192	0.902609
$445$	0	0
$446$	6.03831	0.285922
$447$	−37.7633	−1.78614
$448$	−1.00000	−0.0472456
$449$	11.5089	0.543136	0.271568	−	0.962419i	$-0.412458\pi$
$449$	11.5089	0.543136	0.271568	+	0.962419i	$0.412458\pi$
$450$	0	0
$451$	−12.4111	−0.584416
$452$	−21.0036	−0.987925
$453$	−42.9200	−2.01656
$454$	4.60303	0.216031
$455$	0	0
$456$	3.62721	0.169860
$457$	17.4600	0.816743	0.408372	−	0.912816i	$-0.366097\pi$
$457$	17.4600	0.816743	0.408372	+	0.912816i	$0.366097\pi$
$458$	−5.42166	−0.253338
$459$	25.9547	1.21146
$460$	0	0
$461$	9.35363	0.435642	0.217821	−	0.975989i	$-0.430105\pi$
$461$	9.35363	0.435642	0.217821	+	0.975989i	$0.430105\pi$
$462$	−2.81361	−0.130901
$463$	−16.3380	−0.759293	−0.379647	−	0.925132i	$-0.623954\pi$
$463$	−16.3380	−0.759293	−0.379647	+	0.925132i	$0.623954\pi$
$464$	−1.86751	−0.0866968
$465$	0	0
$466$	−2.57834	−0.119439
$467$	−3.55918	−0.164699	−0.0823496	−	0.996604i	$-0.526242\pi$
$467$	−3.55918	−0.164699	−0.0823496	+	0.996604i	$0.526242\pi$
$468$	−24.1708	−1.11730
$469$	−3.62721	−0.167489
$470$	0	0
$471$	−23.9406	−1.10312
$472$	1.39194	0.0640694
$473$	−2.62721	−0.120799
$474$	−17.6952	−0.812770
$475$	0	0
$476$	−4.81361	−0.220631
$477$	−47.9305	−2.19459
$478$	−21.0630	−0.963400
$479$	−38.7144	−1.76891	−0.884453	−	0.466629i	$-0.845468\pi$
$479$	−38.7144	−1.76891	−0.884453	+	0.466629i	$0.845468\pi$
$480$	0	0
$481$	−33.2333	−1.51531
$482$	21.0192	0.957396
$483$	−21.0872	−0.959500
$484$	1.00000	0.0454545
$485$	0	0
$486$	−14.9894	−0.679935
$487$	14.8781	0.674190	0.337095	−	0.941471i	$-0.390556\pi$
$487$	14.8781	0.674190	0.337095	+	0.941471i	$0.390556\pi$
$488$	6.57834	0.297787
$489$	44.2439	2.00078
$490$	0	0
$491$	12.2927	0.554764	0.277382	−	0.960760i	$-0.410533\pi$
$491$	12.2927	0.554764	0.277382	+	0.960760i	$0.410533\pi$
$492$	−34.9200	−1.57431
$493$	−8.98944	−0.404864
$494$	−6.33804	−0.285162
$495$	0	0
$496$	9.15165	0.410921
$497$	0.338044	0.0151634
$498$	27.4600	1.23051
$499$	20.0383	0.897038	0.448519	−	0.893773i	$-0.351952\pi$
$499$	20.0383	0.897038	0.448519	+	0.893773i	$0.351952\pi$
$500$	0	0
$501$	−41.1255	−1.83735
$502$	−27.4897	−1.22693
$503$	−37.6061	−1.67677	−0.838386	−	0.545077i	$-0.816501\pi$
$503$	−37.6061	−1.67677	−0.838386	+	0.545077i	$0.816501\pi$
$504$	−4.91638	−0.218993
$505$	0	0
$506$	7.49472	0.333181
$507$	31.4303	1.39587
$508$	4.96526	0.220298
$509$	−6.04836	−0.268089	−0.134044	−	0.990975i	$-0.542796\pi$
$509$	−6.04836	−0.268089	−0.134044	+	0.990975i	$0.542796\pi$
$510$	0	0
$511$	13.6952	0.605842
$512$	1.00000	0.0441942
$513$	6.95112	0.306900
$514$	−8.23025	−0.363021
$515$	0	0
$516$	−7.39194	−0.325412
$517$	11.0192	0.484622
$518$	−6.75971	−0.297004
$519$	8.67609	0.380838
$520$	0	0
$521$	7.90582	0.346360	0.173180	−	0.984890i	$-0.444596\pi$
$521$	7.90582	0.346360	0.173180	+	0.984890i	$0.444596\pi$
$522$	−9.18137	−0.401858
$523$	12.6413	0.552767	0.276384	−	0.961047i	$-0.410864\pi$
$523$	12.6413	0.552767	0.276384	+	0.961047i	$0.410864\pi$
$524$	12.1325	0.530010
$525$	0	0
$526$	8.96526	0.390904
$527$	44.0524	1.91895
$528$	2.81361	0.122447
$529$	33.1708	1.44221
$530$	0	0
$531$	6.84333	0.296975
$532$	−1.28917	−0.0558925
$533$	61.0177	2.64297
$534$	−18.8816	−0.817088
$535$	0	0
$536$	3.62721	0.156672
$537$	−47.9688	−2.07001
$538$	7.56777	0.326270
$539$	1.00000	0.0430730
$540$	0	0
$541$	−41.7980	−1.79704	−0.898519	−	0.438935i	$-0.855356\pi$
$541$	−41.7980	−1.79704	−0.898519	+	0.438935i	$0.855356\pi$
$542$	20.6167	0.885561
$543$	−31.1950	−1.33871
$544$	4.81361	0.206382
$545$	0	0
$546$	13.8328	0.591988
$547$	−3.63778	−0.155540	−0.0777700	−	0.996971i	$-0.524780\pi$
$547$	−3.63778	−0.155540	−0.0777700	+	0.996971i	$0.524780\pi$
$548$	−16.7491	−0.715488
$549$	32.3416	1.38031
$550$	0	0
$551$	−2.40753	−0.102564
$552$	21.0872	0.897530
$553$	6.28917	0.267443
$554$	22.3517	0.949631
$555$	0	0
$556$	−22.5819	−0.957686
$557$	24.8852	1.05442	0.527210	−	0.849735i	$-0.323238\pi$
$557$	24.8852	1.05442	0.527210	+	0.849735i	$0.323238\pi$
$558$	44.9930	1.90471
$559$	12.9164	0.546305
$560$	0	0
$561$	13.5436	0.571811
$562$	−6.20555	−0.261765
$563$	−5.10831	−0.215290	−0.107645	−	0.994189i	$-0.534331\pi$
$563$	−5.10831	−0.215290	−0.107645	+	0.994189i	$0.534331\pi$
$564$	31.0036	1.30549
$565$	0	0
$566$	−10.6761	−0.448749
$567$	−0.421663	−0.0177082
$568$	−0.338044	−0.0141840
$569$	21.4116	0.897622	0.448811	−	0.893627i	$-0.351848\pi$
$569$	21.4116	0.897622	0.448811	+	0.893627i	$0.351848\pi$
$570$	0	0
$571$	−9.85746	−0.412522	−0.206261	−	0.978497i	$-0.566130\pi$
$571$	−9.85746	−0.412522	−0.206261	+	0.978497i	$0.566130\pi$
$572$	−4.91638	−0.205564
$573$	−4.37279	−0.182676
$574$	12.4111	0.518029
$575$	0	0
$576$	4.91638	0.204849
$577$	5.77332	0.240347	0.120173	−	0.992753i	$-0.461655\pi$
$577$	5.77332	0.240347	0.120173	+	0.992753i	$0.461655\pi$
$578$	6.17081	0.256672
$579$	36.5472	1.51885
$580$	0	0
$581$	−9.75971	−0.404901
$582$	−0.951124	−0.0394254
$583$	−9.74914	−0.403768
$584$	−13.6952	−0.566713
$585$	0	0
$586$	−12.2736	−0.507017
$587$	28.1361	1.16130	0.580650	−	0.814153i	$-0.302799\pi$
$587$	28.1361	1.16130	0.580650	+	0.814153i	$0.302799\pi$
$588$	2.81361	0.116031
$589$	11.7980	0.486129
$590$	0	0
$591$	−2.00000	−0.0822690
$592$	6.75971	0.277822
$593$	20.8917	0.857919	0.428959	−	0.903324i	$-0.358880\pi$
$593$	20.8917	0.857919	0.428959	+	0.903324i	$0.358880\pi$
$594$	5.39194	0.221234
$595$	0	0
$596$	−13.4217	−0.549773
$597$	42.8222	1.75260
$598$	−36.8469	−1.50678
$599$	38.7839	1.58467	0.792333	−	0.610088i	$-0.208866\pi$
$599$	38.7839	1.58467	0.792333	+	0.610088i	$0.208866\pi$
$600$	0	0
$601$	41.0857	1.67592	0.837961	−	0.545730i	$-0.183748\pi$
$601$	41.0857	1.67592	0.837961	+	0.545730i	$0.183748\pi$
$602$	2.62721	0.107077
$603$	17.8328	0.726206
$604$	−15.2544	−0.620694
$605$	0	0
$606$	46.4635	1.88745
$607$	−9.36222	−0.380001	−0.190000	−	0.981784i	$-0.560849\pi$
$607$	−9.36222	−0.380001	−0.190000	+	0.981784i	$0.560849\pi$
$608$	1.28917	0.0522827
$609$	5.25443	0.212920
$610$	0	0
$611$	−54.1744	−2.19166
$612$	23.6655	0.956622
$613$	−10.4705	−0.422901	−0.211451	−	0.977389i	$-0.567819\pi$
$613$	−10.4705	−0.422901	−0.211451	+	0.977389i	$0.567819\pi$
$614$	19.2544	0.777045
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	15.9200	0.640913	0.320457	−	0.947263i	$-0.396164\pi$
$617$	15.9200	0.640913	0.320457	+	0.947263i	$0.396164\pi$
$618$	16.4252	0.660720
$619$	17.5280	0.704510	0.352255	−	0.935904i	$-0.385415\pi$
$619$	17.5280	0.704510	0.352255	+	0.935904i	$0.385415\pi$
$620$	0	0
$621$	40.4111	1.62164
$622$	−1.36725	−0.0548216
$623$	6.71083	0.268864
$624$	−13.8328	−0.553754
$625$	0	0
$626$	−32.2822	−1.29026
$627$	3.62721	0.144857
$628$	−8.50885	−0.339540
$629$	32.5386	1.29740
$630$	0	0
$631$	22.8122	0.908138	0.454069	−	0.890967i	$-0.349972\pi$
$631$	22.8122	0.908138	0.454069	+	0.890967i	$0.349972\pi$
$632$	−6.28917	−0.250170
$633$	−33.8313	−1.34467
$634$	11.3380	0.450291
$635$	0	0
$636$	−27.4303	−1.08768
$637$	−4.91638	−0.194794
$638$	−1.86751	−0.0739353
$639$	−1.66196	−0.0657459
$640$	0	0
$641$	10.7350	0.424007	0.212004	−	0.977269i	$-0.432001\pi$
$641$	10.7350	0.424007	0.212004	+	0.977269i	$0.432001\pi$
$642$	−0.137518	−0.00542739
$643$	14.2736	0.562895	0.281448	−	0.959577i	$-0.409185\pi$
$643$	14.2736	0.562895	0.281448	+	0.959577i	$0.409185\pi$
$644$	−7.49472	−0.295333
$645$	0	0
$646$	6.20555	0.244154
$647$	46.9597	1.84618	0.923089	−	0.384588i	$-0.125656\pi$
$647$	46.9597	1.84618	0.923089	+	0.384588i	$0.125656\pi$
$648$	0.421663	0.0165645
$649$	1.39194	0.0546386
$650$	0	0
$651$	−25.7491	−1.00919
$652$	15.7250	0.615837
$653$	21.9164	0.857654	0.428827	−	0.903387i	$-0.358927\pi$
$653$	21.9164	0.857654	0.428827	+	0.903387i	$0.358927\pi$
$654$	0.676089	0.0264372
$655$	0	0
$656$	−12.4111	−0.484572
$657$	−67.3311	−2.62683
$658$	−11.0192	−0.429571
$659$	12.5819	0.490122	0.245061	−	0.969508i	$-0.421192\pi$
$659$	12.5819	0.490122	0.245061	+	0.969508i	$0.421192\pi$
$660$	0	0
$661$	12.4705	0.485048	0.242524	−	0.970145i	$-0.422025\pi$
$661$	12.4705	0.485048	0.242524	+	0.970145i	$0.422025\pi$
$662$	−32.7144	−1.27148
$663$	−66.5855	−2.58597
$664$	9.75971	0.378750
$665$	0	0
$666$	33.2333	1.28776
$667$	−13.9964	−0.541944
$668$	−14.6167	−0.565535
$669$	16.9894	0.656850
$670$	0	0
$671$	6.57834	0.253954
$672$	−2.81361	−0.108537
$673$	−28.4705	−1.09746	−0.548729	−	0.836000i	$-0.684888\pi$
$673$	−28.4705	−1.09746	−0.548729	+	0.836000i	$0.684888\pi$
$674$	18.5472	0.714410
$675$	0	0
$676$	11.1708	0.429646
$677$	−42.1411	−1.61961	−0.809807	−	0.586697i	$-0.800428\pi$
$677$	−42.1411	−1.61961	−0.809807	+	0.586697i	$0.800428\pi$
$678$	−59.0958	−2.26956
$679$	0.338044	0.0129730
$680$	0	0
$681$	12.9511	0.496288
$682$	9.15165	0.350435
$683$	−1.21611	−0.0465333	−0.0232666	−	0.999729i	$-0.507407\pi$
$683$	−1.21611	−0.0465333	−0.0232666	+	0.999729i	$0.507407\pi$
$684$	6.33804	0.242341
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	−15.2544	−0.581993
$688$	−2.62721	−0.100162
$689$	47.9305	1.82601
$690$	0	0
$691$	−21.4514	−0.816049	−0.408025	−	0.912971i	$-0.633782\pi$
$691$	−21.4514	−0.816049	−0.408025	+	0.912971i	$0.633782\pi$
$692$	3.08362	0.117222
$693$	−4.91638	−0.186758
$694$	6.28917	0.238734
$695$	0	0
$696$	−5.25443	−0.199169
$697$	−59.7422	−2.26290
$698$	−23.2283	−0.879203
$699$	−7.25443	−0.274388
$700$	0	0
$701$	−37.3275	−1.40984	−0.704920	−	0.709287i	$-0.749017\pi$
$701$	−37.3275	−1.40984	−0.704920	+	0.709287i	$0.749017\pi$
$702$	−26.5089	−1.00051
$703$	8.71440	0.328670
$704$	1.00000	0.0376889
$705$	0	0
$706$	−9.21968	−0.346987
$707$	−16.5139	−0.621068
$708$	3.91638	0.147187
$709$	24.1602	0.907357	0.453679	−	0.891165i	$-0.350111\pi$
$709$	24.1602	0.907357	0.453679	+	0.891165i	$0.350111\pi$
$710$	0	0
$711$	−30.9200	−1.15959
$712$	−6.71083	−0.251499
$713$	68.5890	2.56868
$714$	−13.5436	−0.506856
$715$	0	0
$716$	−17.0489	−0.637146
$717$	−59.2630	−2.21322
$718$	28.0766	1.04781
$719$	20.8816	0.778754	0.389377	−	0.921079i	$-0.372690\pi$
$719$	20.8816	0.778754	0.389377	+	0.921079i	$0.372690\pi$
$720$	0	0
$721$	−5.83779	−0.217411
$722$	−17.3380	−0.645255
$723$	59.1396	2.19943
$724$	−11.0872	−0.412052
$725$	0	0
$726$	2.81361	0.104423
$727$	48.8172	1.81053	0.905264	−	0.424849i	$-0.139673\pi$
$727$	48.8172	1.81053	0.905264	+	0.424849i	$0.139673\pi$
$728$	4.91638	0.182213
$729$	−43.4394	−1.60887
$730$	0	0
$731$	−12.6464	−0.467743
$732$	18.5089	0.684107
$733$	20.6600	0.763094	0.381547	−	0.924349i	$-0.375391\pi$
$733$	20.6600	0.763094	0.381547	+	0.924349i	$0.375391\pi$
$734$	6.87807	0.253874
$735$	0	0
$736$	7.49472	0.276259
$737$	3.62721	0.133610
$738$	−61.0177	−2.24609
$739$	−8.46355	−0.311337	−0.155668	−	0.987809i	$-0.549753\pi$
$739$	−8.46355	−0.311337	−0.155668	+	0.987809i	$0.549753\pi$
$740$	0	0
$741$	−17.8328	−0.655103
$742$	9.74914	0.357902
$743$	−9.27861	−0.340399	−0.170200	−	0.985410i	$-0.554441\pi$
$743$	−9.27861	−0.340399	−0.170200	+	0.985410i	$0.554441\pi$
$744$	25.7491	0.944009
$745$	0	0
$746$	10.3627	0.379407
$747$	47.9824	1.75559
$748$	4.81361	0.176003
$749$	0.0488759	0.00178589
$750$	0	0
$751$	14.9164	0.544306	0.272153	−	0.962254i	$-0.412264\pi$
$751$	14.9164	0.544306	0.272153	+	0.962254i	$0.412264\pi$
$752$	11.0192	0.401827
$753$	−77.3452	−2.81862
$754$	9.18137	0.334366
$755$	0	0
$756$	−5.39194	−0.196103
$757$	−22.4736	−0.816817	−0.408408	−	0.912799i	$-0.633916\pi$
$757$	−22.4736	−0.816817	−0.408408	+	0.912799i	$0.633916\pi$
$758$	−32.4494	−1.17862
$759$	21.0872	0.765416
$760$	0	0
$761$	16.2836	0.590281	0.295141	−	0.955454i	$-0.404634\pi$
$761$	16.2836	0.590281	0.295141	+	0.955454i	$0.404634\pi$
$762$	13.9703	0.506090
$763$	−0.240293	−0.00869918
$764$	−1.55416	−0.0562274
$765$	0	0
$766$	30.7194	1.10994
$767$	−6.84333	−0.247098
$768$	2.81361	0.101527
$769$	10.5783	0.381465	0.190732	−	0.981642i	$-0.438914\pi$
$769$	10.5783	0.381465	0.190732	+	0.981642i	$0.438914\pi$
$770$	0	0
$771$	−23.1567	−0.833967
$772$	12.9894	0.467500
$773$	6.90276	0.248275	0.124138	−	0.992265i	$-0.460384\pi$
$773$	6.90276	0.248275	0.124138	+	0.992265i	$0.460384\pi$
$774$	−12.9164	−0.464270
$775$	0	0
$776$	−0.338044	−0.0121351
$777$	−19.0192	−0.682308
$778$	−29.3169	−1.05106
$779$	−16.0000	−0.573259
$780$	0	0
$781$	−0.338044	−0.0120962
$782$	36.0766	1.29010
$783$	−10.0695	−0.359854
$784$	1.00000	0.0357143
$785$	0	0
$786$	34.1361	1.21759
$787$	7.25443	0.258592	0.129296	−	0.991606i	$-0.458728\pi$
$787$	7.25443	0.258592	0.129296	+	0.991606i	$0.458728\pi$
$788$	−0.710831	−0.0253223
$789$	25.2247	0.898023
$790$	0	0
$791$	21.0036	0.746801
$792$	4.91638	0.174696
$793$	−32.3416	−1.14848
$794$	22.1955	0.787689
$795$	0	0
$796$	15.2197	0.539447
$797$	−35.7733	−1.26716	−0.633578	−	0.773679i	$-0.718414\pi$
$797$	−35.7733	−1.26716	−0.633578	+	0.773679i	$0.718414\pi$
$798$	−3.62721	−0.128402
$799$	53.0419	1.87649
$800$	0	0
$801$	−32.9930	−1.16575
$802$	−20.2544	−0.715209
$803$	−13.6952	−0.483295
$804$	10.2056	0.359922
$805$	0	0
$806$	−44.9930	−1.58481
$807$	21.2927	0.749540
$808$	16.5139	0.580956
$809$	−32.8122	−1.15361	−0.576807	−	0.816880i	$-0.695702\pi$
$809$	−32.8122	−1.15361	−0.576807	+	0.816880i	$0.695702\pi$
$810$	0	0
$811$	6.31335	0.221692	0.110846	−	0.993838i	$-0.464644\pi$
$811$	6.31335	0.221692	0.110846	+	0.993838i	$0.464644\pi$
$812$	1.86751	0.0655366
$813$	58.0071	2.03440
$814$	6.75971	0.236928
$815$	0	0
$816$	13.5436	0.474121
$817$	−3.38692	−0.118493
$818$	−22.1658	−0.775008
$819$	24.1708	0.844596
$820$	0	0
$821$	−30.5225	−1.06524	−0.532621	−	0.846354i	$-0.678793\pi$
$821$	−30.5225	−1.06524	−0.532621	+	0.846354i	$0.678793\pi$
$822$	−47.1255	−1.64369
$823$	−9.57885	−0.333898	−0.166949	−	0.985966i	$-0.553391\pi$
$823$	−9.57885	−0.333898	−0.166949	+	0.985966i	$0.553391\pi$
$824$	5.83779	0.203369
$825$	0	0
$826$	−1.39194	−0.0484319
$827$	−44.7250	−1.55524	−0.777620	−	0.628735i	$-0.783573\pi$
$827$	−44.7250	−1.55524	−0.777620	+	0.628735i	$0.783573\pi$
$828$	36.8469	1.28052
$829$	−38.7910	−1.34727	−0.673634	−	0.739065i	$-0.735268\pi$
$829$	−38.7910	−1.34727	−0.673634	+	0.739065i	$0.735268\pi$
$830$	0	0
$831$	62.8888	2.18159
$832$	−4.91638	−0.170445
$833$	4.81361	0.166782
$834$	−63.5366	−2.20009
$835$	0	0
$836$	1.28917	0.0445868
$837$	49.3452	1.70562
$838$	36.5769	1.26353
$839$	24.6861	0.852260	0.426130	−	0.904662i	$-0.359877\pi$
$839$	24.6861	0.852260	0.426130	+	0.904662i	$0.359877\pi$
$840$	0	0
$841$	−25.5124	−0.879739
$842$	−2.94108	−0.101356
$843$	−17.4600	−0.601354
$844$	−12.0242	−0.413889
$845$	0	0
$846$	54.1744	1.86255
$847$	−1.00000	−0.0343604
$848$	−9.74914	−0.334787
$849$	−30.0383	−1.03091
$850$	0	0
$851$	50.6621	1.73667
$852$	−0.951124	−0.0325850
$853$	4.68468	0.160400	0.0802002	−	0.996779i	$-0.474444\pi$
$853$	4.68468	0.160400	0.0802002	+	0.996779i	$0.474444\pi$
$854$	−6.57834	−0.225106
$855$	0	0
$856$	−0.0488759	−0.00167054
$857$	13.9022	0.474892	0.237446	−	0.971401i	$-0.423690\pi$
$857$	13.9022	0.474892	0.237446	+	0.971401i	$0.423690\pi$
$858$	−13.8328	−0.472243
$859$	25.4585	0.868634	0.434317	−	0.900760i	$-0.356990\pi$
$859$	25.4585	0.868634	0.434317	+	0.900760i	$0.356990\pi$
$860$	0	0
$861$	34.9200	1.19007
$862$	6.53303	0.222516
$863$	11.1814	0.380618	0.190309	−	0.981724i	$-0.439051\pi$
$863$	11.1814	0.380618	0.190309	+	0.981724i	$0.439051\pi$
$864$	5.39194	0.183438
$865$	0	0
$866$	−16.0347	−0.544883
$867$	17.3622	0.589652
$868$	−9.15165	−0.310627
$869$	−6.28917	−0.213345
$870$	0	0
$871$	−17.8328	−0.604240
$872$	0.240293	0.00813734
$873$	−1.66196	−0.0562487
$874$	9.66196	0.326821
$875$	0	0
$876$	−38.5330	−1.30191
$877$	9.11189	0.307687	0.153843	−	0.988095i	$-0.450835\pi$
$877$	9.11189	0.307687	0.153843	+	0.988095i	$0.450835\pi$
$878$	−14.2650	−0.481420
$879$	−34.5330	−1.16477
$880$	0	0
$881$	28.2786	0.952730	0.476365	−	0.879248i	$-0.341954\pi$
$881$	28.2786	0.952730	0.476365	+	0.879248i	$0.341954\pi$
$882$	4.91638	0.165543
$883$	−43.6061	−1.46746	−0.733731	−	0.679440i	$-0.762223\pi$
$883$	−43.6061	−1.46746	−0.733731	+	0.679440i	$0.762223\pi$
$884$	−23.6655	−0.795958
$885$	0	0
$886$	13.9022	0.467055
$887$	22.8505	0.767244	0.383622	−	0.923490i	$-0.374677\pi$
$887$	22.8505	0.767244	0.383622	+	0.923490i	$0.374677\pi$
$888$	19.0192	0.638241
$889$	−4.96526	−0.166529
$890$	0	0
$891$	0.421663	0.0141262
$892$	6.03831	0.202178
$893$	14.2056	0.475371
$894$	−37.7633	−1.26299
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	−103.673	−3.46153
$898$	11.5089	0.384055
$899$	−17.0908	−0.570009
$900$	0	0
$901$	−46.9285	−1.56342
$902$	−12.4111	−0.413244
$903$	7.39194	0.245988
$904$	−21.0036	−0.698568
$905$	0	0
$906$	−42.9200	−1.42592
$907$	1.78440	0.0592501	0.0296251	−	0.999561i	$-0.490569\pi$
$907$	1.78440	0.0592501	0.0296251	+	0.999561i	$0.490569\pi$
$908$	4.60303	0.152757
$909$	81.1885	2.69285
$910$	0	0
$911$	−13.8539	−0.459000	−0.229500	−	0.973309i	$-0.573709\pi$
$911$	−13.8539	−0.459000	−0.229500	+	0.973309i	$0.573709\pi$
$912$	3.62721	0.120109
$913$	9.75971	0.322999
$914$	17.4600	0.577525
$915$	0	0
$916$	−5.42166	−0.179137
$917$	−12.1325	−0.400650
$918$	25.9547	0.856633
$919$	−31.4741	−1.03824	−0.519118	−	0.854703i	$-0.673739\pi$
$919$	−31.4741	−1.03824	−0.519118	+	0.854703i	$0.673739\pi$
$920$	0	0
$921$	54.1744	1.78511
$922$	9.35363	0.308045
$923$	1.66196	0.0547039
$924$	−2.81361	−0.0925609
$925$	0	0
$926$	−16.3380	−0.536901
$927$	28.7008	0.942657
$928$	−1.86751	−0.0613039
$929$	−45.9341	−1.50705	−0.753524	−	0.657420i	$-0.771648\pi$
$929$	−45.9341	−1.50705	−0.753524	+	0.657420i	$0.771648\pi$
$930$	0	0
$931$	1.28917	0.0422508
$932$	−2.57834	−0.0844562
$933$	−3.84690	−0.125942
$934$	−3.55918	−0.116460
$935$	0	0
$936$	−24.1708	−0.790048
$937$	20.2141	0.660367	0.330184	−	0.943917i	$-0.392889\pi$
$937$	20.2141	0.660367	0.330184	+	0.943917i	$0.392889\pi$
$938$	−3.62721	−0.118433
$939$	−90.8293	−2.96410
$940$	0	0
$941$	26.3713	0.859681	0.429840	−	0.902905i	$-0.358570\pi$
$941$	26.3713	0.859681	0.429840	+	0.902905i	$0.358570\pi$
$942$	−23.9406	−0.780026
$943$	−93.0177	−3.02907
$944$	1.39194	0.0453039
$945$	0	0
$946$	−2.62721	−0.0854181
$947$	−24.1149	−0.783630	−0.391815	−	0.920044i	$-0.628153\pi$
$947$	−24.1149	−0.783630	−0.391815	+	0.920044i	$0.628153\pi$
$948$	−17.6952	−0.574715
$949$	67.3311	2.18566
$950$	0	0
$951$	31.9008	1.03445
$952$	−4.81361	−0.156010
$953$	50.1361	1.62407	0.812033	−	0.583611i	$-0.198361\pi$
$953$	50.1361	1.62407	0.812033	+	0.583611i	$0.198361\pi$
$954$	−47.9305	−1.55181
$955$	0	0
$956$	−21.0630	−0.681226
$957$	−5.25443	−0.169851
$958$	−38.7144	−1.25081
$959$	16.7491	0.540858
$960$	0	0
$961$	52.7527	1.70170
$962$	−33.2333	−1.07148
$963$	−0.240293	−0.00774332
$964$	21.0192	0.676981
$965$	0	0
$966$	−21.0872	−0.678469
$967$	−39.9305	−1.28408	−0.642039	−	0.766672i	$-0.721911\pi$
$967$	−39.9305	−1.28408	−0.642039	+	0.766672i	$0.721911\pi$
$968$	1.00000	0.0321412
$969$	17.4600	0.560895
$970$	0	0
$971$	7.38335	0.236943	0.118471	−	0.992957i	$-0.462201\pi$
$971$	7.38335	0.236943	0.118471	+	0.992957i	$0.462201\pi$
$972$	−14.9894	−0.480786
$973$	22.5819	0.723943
$974$	14.8781	0.476724
$975$	0	0
$976$	6.57834	0.210567
$977$	10.4111	0.333081	0.166540	−	0.986035i	$-0.446740\pi$
$977$	10.4111	0.333081	0.166540	+	0.986035i	$0.446740\pi$
$978$	44.2439	1.41476
$979$	−6.71083	−0.214479
$980$	0	0
$981$	1.18137	0.0377183
$982$	12.2927	0.392277
$983$	6.10278	0.194648	0.0973241	−	0.995253i	$-0.468972\pi$
$983$	6.10278	0.194648	0.0973241	+	0.995253i	$0.468972\pi$
$984$	−34.9200	−1.11321
$985$	0	0
$986$	−8.98944	−0.286282
$987$	−31.0036	−0.986855
$988$	−6.33804	−0.201640
$989$	−19.6902	−0.626113
$990$	0	0
$991$	−40.6550	−1.29145	−0.645724	−	0.763571i	$-0.723444\pi$
$991$	−40.6550	−1.29145	−0.645724	+	0.763571i	$0.723444\pi$
$992$	9.15165	0.290565
$993$	−92.0455	−2.92097
$994$	0.338044	0.0107221
$995$	0	0
$996$	27.4600	0.870103
$997$	−51.0575	−1.61701	−0.808503	−	0.588492i	$-0.799722\pi$
$997$	−51.0575	−1.61701	−0.808503	+	0.588492i	$0.799722\pi$
$998$	20.0383	0.634302
$999$	36.4480	1.15316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.bv.1.3	yes	3
5.2	odd	4		3850.2.c.bb.1849.4		6
5.3	odd	4		3850.2.c.bb.1849.3		6
5.4	even	2		3850.2.a.bs.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3850.2.a.bs.1.1	✓	3	5.4	even	2
3850.2.a.bv.1.3	yes	3	1.1	even	1	trivial
3850.2.c.bb.1849.3		6	5.3	odd	4
3850.2.c.bb.1849.4		6	5.2	odd	4

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.81361 q^{3} +1.00000 q^{4} +2.81361 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.91638 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.81361 q^{3} +1.00000 q^{4} +2.81361 q^{6} -1.00000 q^{7} +1.00000 q^{8} +4.91638 q^{9} +1.00000 q^{11} +2.81361 q^{12} -4.91638 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.81361 q^{17} +4.91638 q^{18} +1.28917 q^{19} -2.81361 q^{21} +1.00000 q^{22} +7.49472 q^{23} +2.81361 q^{24} -4.91638 q^{26} +5.39194 q^{27} -1.00000 q^{28} -1.86751 q^{29} +9.15165 q^{31} +1.00000 q^{32} +2.81361 q^{33} +4.81361 q^{34} +4.91638 q^{36} +6.75971 q^{37} +1.28917 q^{38} -13.8328 q^{39} -12.4111 q^{41} -2.81361 q^{42} -2.62721 q^{43} +1.00000 q^{44} +7.49472 q^{46} +11.0192 q^{47} +2.81361 q^{48} +1.00000 q^{49} +13.5436 q^{51} -4.91638 q^{52} -9.74914 q^{53} +5.39194 q^{54} -1.00000 q^{56} +3.62721 q^{57} -1.86751 q^{58} +1.39194 q^{59} +6.57834 q^{61} +9.15165 q^{62} -4.91638 q^{63} +1.00000 q^{64} +2.81361 q^{66} +3.62721 q^{67} +4.81361 q^{68} +21.0872 q^{69} -0.338044 q^{71} +4.91638 q^{72} -13.6952 q^{73} +6.75971 q^{74} +1.28917 q^{76} -1.00000 q^{77} -13.8328 q^{78} -6.28917 q^{79} +0.421663 q^{81} -12.4111 q^{82} +9.75971 q^{83} -2.81361 q^{84} -2.62721 q^{86} -5.25443 q^{87} +1.00000 q^{88} -6.71083 q^{89} +4.91638 q^{91} +7.49472 q^{92} +25.7491 q^{93} +11.0192 q^{94} +2.81361 q^{96} -0.338044 q^{97} +1.00000 q^{98} +4.91638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} - 3 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 - 3 * q^7 + 3 * q^8 + q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} - 3 q^{7} + 3 q^{8} + q^{9} + 3 q^{11} + 2 q^{12} - q^{13} - 3 q^{14} + 3 q^{16} + 8 q^{17} + q^{18} + 3 q^{19} - 2 q^{21} + 3 q^{22} + 7 q^{23} + 2 q^{24} - q^{26} + 8 q^{27} - 3 q^{28} - 3 q^{29} + 9 q^{31} + 3 q^{32} + 2 q^{33} + 8 q^{34} + q^{36} + 10 q^{37} + 3 q^{38} - 14 q^{39} - 8 q^{41} - 2 q^{42} + 5 q^{43} + 3 q^{44} + 7 q^{46} + 12 q^{47} + 2 q^{48} + 3 q^{49} + 14 q^{51} - q^{52} + 12 q^{53} + 8 q^{54} - 3 q^{56} - 2 q^{57} - 3 q^{58} - 4 q^{59} + 18 q^{61} + 9 q^{62} - q^{63} + 3 q^{64} + 2 q^{66} - 2 q^{67} + 8 q^{68} + 10 q^{69} + 11 q^{71} + q^{72} + 4 q^{73} + 10 q^{74} + 3 q^{76} - 3 q^{77} - 14 q^{78} - 18 q^{79} + 3 q^{81} - 8 q^{82} + 19 q^{83} - 2 q^{84} + 5 q^{86} + 10 q^{87} + 3 q^{88} - 21 q^{89} + q^{91} + 7 q^{92} + 36 q^{93} + 12 q^{94} + 2 q^{96} + 11 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 - 3 * q^7 + 3 * q^8 + q^9 + 3 * q^11 + 2 * q^12 - q^13 - 3 * q^14 + 3 * q^16 + 8 * q^17 + q^18 + 3 * q^19 - 2 * q^21 + 3 * q^22 + 7 * q^23 + 2 * q^24 - q^26 + 8 * q^27 - 3 * q^28 - 3 * q^29 + 9 * q^31 + 3 * q^32 + 2 * q^33 + 8 * q^34 + q^36 + 10 * q^37 + 3 * q^38 - 14 * q^39 - 8 * q^41 - 2 * q^42 + 5 * q^43 + 3 * q^44 + 7 * q^46 + 12 * q^47 + 2 * q^48 + 3 * q^49 + 14 * q^51 - q^52 + 12 * q^53 + 8 * q^54 - 3 * q^56 - 2 * q^57 - 3 * q^58 - 4 * q^59 + 18 * q^61 + 9 * q^62 - q^63 + 3 * q^64 + 2 * q^66 - 2 * q^67 + 8 * q^68 + 10 * q^69 + 11 * q^71 + q^72 + 4 * q^73 + 10 * q^74 + 3 * q^76 - 3 * q^77 - 14 * q^78 - 18 * q^79 + 3 * q^81 - 8 * q^82 + 19 * q^83 - 2 * q^84 + 5 * q^86 + 10 * q^87 + 3 * q^88 - 21 * q^89 + q^91 + 7 * q^92 + 36 * q^93 + 12 * q^94 + 2 * q^96 + 11 * q^97 + 3 * q^98 + q^99

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