LMFDB - Embedded newform 4001.2.a.b.1.163

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$4001$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$0$
Dimension:	$184$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.163
Character	$\chi$	$=$	4001.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.45513 q^{2} -1.68371 q^{3} +4.02766 q^{4} -3.39190 q^{5} -4.13372 q^{6} +4.85354 q^{7} +4.97818 q^{8} -0.165134 q^{9} -8.32756 q^{10} -3.48051 q^{11} -6.78140 q^{12} -0.426081 q^{13} +11.9161 q^{14} +5.71097 q^{15} +4.16675 q^{16} -4.22969 q^{17} -0.405426 q^{18} +7.37914 q^{19} -13.6614 q^{20} -8.17194 q^{21} -8.54510 q^{22} +5.74129 q^{23} -8.38179 q^{24} +6.50500 q^{25} -1.04608 q^{26} +5.32916 q^{27} +19.5484 q^{28} -1.35939 q^{29} +14.0212 q^{30} +1.93786 q^{31} +0.273552 q^{32} +5.86015 q^{33} -10.3844 q^{34} -16.4627 q^{35} -0.665105 q^{36} +5.57311 q^{37} +18.1167 q^{38} +0.717395 q^{39} -16.8855 q^{40} -3.32289 q^{41} -20.0632 q^{42} -3.08418 q^{43} -14.0183 q^{44} +0.560119 q^{45} +14.0956 q^{46} +13.0313 q^{47} -7.01558 q^{48} +16.5569 q^{49} +15.9706 q^{50} +7.12156 q^{51} -1.71611 q^{52} +2.68870 q^{53} +13.0838 q^{54} +11.8055 q^{55} +24.1618 q^{56} -12.4243 q^{57} -3.33748 q^{58} -7.51492 q^{59} +23.0019 q^{60} +13.7021 q^{61} +4.75769 q^{62} -0.801486 q^{63} -7.66189 q^{64} +1.44522 q^{65} +14.3874 q^{66} -4.51784 q^{67} -17.0358 q^{68} -9.66665 q^{69} -40.4182 q^{70} -2.97385 q^{71} -0.822067 q^{72} +13.5805 q^{73} +13.6827 q^{74} -10.9525 q^{75} +29.7207 q^{76} -16.8928 q^{77} +1.76130 q^{78} -11.0053 q^{79} -14.1332 q^{80} -8.47733 q^{81} -8.15813 q^{82} +10.2706 q^{83} -32.9138 q^{84} +14.3467 q^{85} -7.57207 q^{86} +2.28882 q^{87} -17.3266 q^{88} +3.18827 q^{89} +1.37516 q^{90} -2.06800 q^{91} +23.1240 q^{92} -3.26278 q^{93} +31.9936 q^{94} -25.0293 q^{95} -0.460581 q^{96} +10.7849 q^{97} +40.6493 q^{98} +0.574750 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18}+ \cdots + 53 q^{99}+O(q^{100})$ 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * q^99

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

)

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

$2$	2.45513	1.73604	0.868020	−	0.496530i	$-0.165393\pi$
$2$	2.45513	1.73604	0.868020	+	0.496530i	$0.165393\pi$
$3$	−1.68371	−0.972088	−0.486044	−	0.873934i	$-0.661561\pi$
$3$	−1.68371	−0.972088	−0.486044	+	0.873934i	$0.661561\pi$
$4$	4.02766	2.01383
$5$	−3.39190	−1.51690	−0.758452	−	0.651728i	$-0.774044\pi$
$5$	−3.39190	−1.51690	−0.758452	+	0.651728i	$0.774044\pi$
$6$	−4.13372	−1.68758
$7$	4.85354	1.83447	0.917233	−	0.398350i	$-0.130417\pi$
$7$	4.85354	1.83447	0.917233	+	0.398350i	$0.130417\pi$
$8$	4.97818	1.76005
$9$	−0.165134	−0.0550447
$10$	−8.32756	−2.63341
$11$	−3.48051	−1.04941	−0.524706	−	0.851283i	$-0.675825\pi$
$11$	−3.48051	−1.04941	−0.524706	+	0.851283i	$0.675825\pi$
$12$	−6.78140	−1.95762
$13$	−0.426081	−0.118174	−0.0590868	−	0.998253i	$-0.518819\pi$
$13$	−0.426081	−0.118174	−0.0590868	+	0.998253i	$0.518819\pi$
$14$	11.9161	3.18471
$15$	5.71097	1.47457
$16$	4.16675	1.04169
$17$	−4.22969	−1.02585	−0.512926	−	0.858433i	$-0.671438\pi$
$17$	−4.22969	−1.02585	−0.512926	+	0.858433i	$0.671438\pi$
$18$	−0.405426	−0.0955598
$19$	7.37914	1.69289	0.846445	−	0.532476i	$-0.178738\pi$
$19$	7.37914	1.69289	0.846445	+	0.532476i	$0.178738\pi$
$20$	−13.6614	−3.05479
$21$	−8.17194	−1.78326
$22$	−8.54510	−1.82182
$23$	5.74129	1.19714	0.598571	−	0.801070i	$-0.295735\pi$
$23$	5.74129	1.19714	0.598571	+	0.801070i	$0.295735\pi$
$24$	−8.38179	−1.71093
$25$	6.50500	1.30100
$26$	−1.04608	−0.205154
$27$	5.32916	1.02560
$28$	19.5484	3.69431
$29$	−1.35939	−0.252433	−0.126216	−	0.992003i	$-0.540283\pi$
$29$	−1.35939	−0.252433	−0.126216	+	0.992003i	$0.540283\pi$
$30$	14.0212	2.55990
$31$	1.93786	0.348049	0.174025	−	0.984741i	$-0.444323\pi$
$31$	1.93786	0.348049	0.174025	+	0.984741i	$0.444323\pi$
$32$	0.273552	0.0483576
$33$	5.86015	1.02012
$34$	−10.3844	−1.78092
$35$	−16.4627	−2.78271
$36$	−0.665105	−0.110851
$37$	5.57311	0.916214	0.458107	−	0.888897i	$-0.348528\pi$
$37$	5.57311	0.916214	0.458107	+	0.888897i	$0.348528\pi$
$38$	18.1167	2.93892
$39$	0.717395	0.114875
$40$	−16.8855	−2.66983
$41$	−3.32289	−0.518949	−0.259474	−	0.965750i	$-0.583549\pi$
$41$	−3.32289	−0.518949	−0.259474	+	0.965750i	$0.583549\pi$
$42$	−20.0632	−3.09581
$43$	−3.08418	−0.470333	−0.235167	−	0.971955i	$-0.575564\pi$
$43$	−3.08418	−0.470333	−0.235167	+	0.971955i	$0.575564\pi$
$44$	−14.0183	−2.11334
$45$	0.560119	0.0834976
$46$	14.0956	2.07829
$47$	13.0313	1.90081	0.950406	−	0.311013i	$-0.100668\pi$
$47$	13.0313	1.90081	0.950406	+	0.311013i	$0.100668\pi$
$48$	−7.01558	−1.01261
$49$	16.5569	2.36527
$50$	15.9706	2.25859
$51$	7.12156	0.997218
$52$	−1.71611	−0.237982
$53$	2.68870	0.369321	0.184661	−	0.982802i	$-0.440881\pi$
$53$	2.68870	0.369321	0.184661	+	0.982802i	$0.440881\pi$
$54$	13.0838	1.78048
$55$	11.8055	1.59186
$56$	24.1618	3.22876
$57$	−12.4243	−1.64564
$58$	−3.33748	−0.438233
$59$	−7.51492	−0.978359	−0.489180	−	0.872183i	$-0.662704\pi$
$59$	−7.51492	−0.978359	−0.489180	+	0.872183i	$0.662704\pi$
$60$	23.0019	2.96953
$61$	13.7021	1.75437	0.877186	−	0.480150i	$-0.159418\pi$
$61$	13.7021	1.75437	0.877186	+	0.480150i	$0.159418\pi$
$62$	4.75769	0.604227
$63$	−0.801486	−0.100978
$64$	−7.66189	−0.957736
$65$	1.44522	0.179258
$66$	14.3874	1.77097
$67$	−4.51784	−0.551941	−0.275971	−	0.961166i	$-0.588999\pi$
$67$	−4.51784	−0.551941	−0.275971	+	0.961166i	$0.588999\pi$
$68$	−17.0358	−2.06589
$69$	−9.66665	−1.16373
$70$	−40.4182	−4.83090
$71$	−2.97385	−0.352931	−0.176466	−	0.984307i	$-0.556466\pi$
$71$	−2.97385	−0.352931	−0.176466	+	0.984307i	$0.556466\pi$
$72$	−0.822067	−0.0968815
$73$	13.5805	1.58948	0.794740	−	0.606950i	$-0.207607\pi$
$73$	13.5805	1.58948	0.794740	+	0.606950i	$0.207607\pi$
$74$	13.6827	1.59058
$75$	−10.9525	−1.26469
$76$	29.7207	3.40920
$77$	−16.8928	−1.92511
$78$	1.76130	0.199428
$79$	−11.0053	−1.23819	−0.619095	−	0.785316i	$-0.712500\pi$
$79$	−11.0053	−1.23819	−0.619095	+	0.785316i	$0.712500\pi$
$80$	−14.1332	−1.58014
$81$	−8.47733	−0.941925
$82$	−8.15813	−0.900915
$83$	10.2706	1.12735	0.563675	−	0.825997i	$-0.309387\pi$
$83$	10.2706	1.12735	0.563675	+	0.825997i	$0.309387\pi$
$84$	−32.9138	−3.59119
$85$	14.3467	1.55612
$86$	−7.57207	−0.816517
$87$	2.28882	0.245387
$88$	−17.3266	−1.84702
$89$	3.18827	0.337956	0.168978	−	0.985620i	$-0.445953\pi$
$89$	3.18827	0.337956	0.168978	+	0.985620i	$0.445953\pi$
$90$	1.37516	0.144955
$91$	−2.06800	−0.216785
$92$	23.1240	2.41084
$93$	−3.26278	−0.338334
$94$	31.9936	3.29988
$95$	−25.0293	−2.56795
$96$	−0.460581	−0.0470078
$97$	10.7849	1.09504	0.547519	−	0.836793i	$-0.315572\pi$
$97$	10.7849	1.09504	0.547519	+	0.836793i	$0.315572\pi$
$98$	40.6493	4.10620
$99$	0.574750	0.0577646
$100$	26.2000	2.62000
$101$	−4.99720	−0.497240	−0.248620	−	0.968601i	$-0.579977\pi$
$101$	−4.99720	−0.497240	−0.248620	+	0.968601i	$0.579977\pi$
$102$	17.4844	1.73121
$103$	17.8445	1.75827	0.879135	−	0.476572i	$-0.158121\pi$
$103$	17.8445	1.75827	0.879135	+	0.476572i	$0.158121\pi$
$104$	−2.12111	−0.207992
$105$	27.7184	2.70504
$106$	6.60110	0.641156
$107$	−3.43821	−0.332384	−0.166192	−	0.986093i	$-0.553147\pi$
$107$	−3.43821	−0.332384	−0.166192	+	0.986093i	$0.553147\pi$
$108$	21.4640	2.06538
$109$	−2.21934	−0.212574	−0.106287	−	0.994335i	$-0.533896\pi$
$109$	−2.21934	−0.212574	−0.106287	+	0.994335i	$0.533896\pi$
$110$	28.9841	2.76353
$111$	−9.38348	−0.890641
$112$	20.2235	1.91094
$113$	12.8825	1.21188	0.605940	−	0.795510i	$-0.292797\pi$
$113$	12.8825	1.21188	0.605940	+	0.795510i	$0.292797\pi$
$114$	−30.5033	−2.85689
$115$	−19.4739	−1.81595
$116$	−5.47517	−0.508357
$117$	0.0703605	0.00650483
$118$	−18.4501	−1.69847
$119$	−20.5290	−1.88189
$120$	28.4302	2.59531
$121$	1.11393	0.101266
$122$	33.6404	3.04566
$123$	5.59477	0.504464
$124$	7.80503	0.700912
$125$	−5.10481	−0.456588
$126$	−1.96775	−0.175301
$127$	−17.4405	−1.54759	−0.773796	−	0.633434i	$-0.781645\pi$
$127$	−17.4405	−1.54759	−0.773796	+	0.633434i	$0.781645\pi$
$128$	−19.3580	−1.71103
$129$	5.19286	0.457206
$130$	3.54821	0.311199
$131$	−13.9412	−1.21804	−0.609022	−	0.793153i	$-0.708438\pi$
$131$	−13.9412	−1.21804	−0.609022	+	0.793153i	$0.708438\pi$
$132$	23.6027	2.05435
$133$	35.8150	3.10555
$134$	−11.0919	−0.958192
$135$	−18.0760	−1.55573
$136$	−21.0562	−1.80555
$137$	17.4345	1.48953	0.744764	−	0.667328i	$-0.232562\pi$
$137$	17.4345	1.48953	0.744764	+	0.667328i	$0.232562\pi$
$138$	−23.7329	−2.02028
$139$	20.6453	1.75111	0.875554	−	0.483120i	$-0.160497\pi$
$139$	20.6453	1.75111	0.875554	+	0.483120i	$0.160497\pi$
$140$	−66.3064	−5.60391
$141$	−21.9409	−1.84776
$142$	−7.30120	−0.612703
$143$	1.48298	0.124013
$144$	−0.688072	−0.0573394
$145$	4.61092	0.382916
$146$	33.3419	2.75940
$147$	−27.8769	−2.29925
$148$	22.4466	1.84510
$149$	11.0111	0.902062	0.451031	−	0.892508i	$-0.351056\pi$
$149$	11.0111	0.902062	0.451031	+	0.892508i	$0.351056\pi$
$150$	−26.8898	−2.19555
$151$	21.9063	1.78271	0.891356	−	0.453304i	$-0.149755\pi$
$151$	21.9063	1.78271	0.891356	+	0.453304i	$0.149755\pi$
$152$	36.7347	2.97958
$153$	0.698467	0.0564677
$154$	−41.4740	−3.34207
$155$	−6.57302	−0.527957
$156$	2.88943	0.231339
$157$	−12.5918	−1.00494	−0.502468	−	0.864596i	$-0.667574\pi$
$157$	−12.5918	−1.00494	−0.502468	+	0.864596i	$0.667574\pi$
$158$	−27.0194	−2.14955
$159$	−4.52698	−0.359013
$160$	−0.927861	−0.0733538
$161$	27.8656	2.19612
$162$	−20.8129	−1.63522
$163$	−3.86920	−0.303059	−0.151529	−	0.988453i	$-0.548420\pi$
$163$	−3.86920	−0.303059	−0.151529	+	0.988453i	$0.548420\pi$
$164$	−13.3835	−1.04508
$165$	−19.8771	−1.54743
$166$	25.2158	1.95712
$167$	−12.6164	−0.976289	−0.488144	−	0.872763i	$-0.662326\pi$
$167$	−12.6164	−0.976289	−0.488144	+	0.872763i	$0.662326\pi$
$168$	−40.6814	−3.13864
$169$	−12.8185	−0.986035
$170$	35.2230	2.70148
$171$	−1.21855	−0.0931847
$172$	−12.4221	−0.947173
$173$	8.33232	0.633495	0.316747	−	0.948510i	$-0.397409\pi$
$173$	8.33232	0.633495	0.316747	+	0.948510i	$0.397409\pi$
$174$	5.61934	0.426001
$175$	31.5723	2.38664
$176$	−14.5024	−1.09316
$177$	12.6529	0.951052
$178$	7.82762	0.586705
$179$	−15.9978	−1.19573	−0.597866	−	0.801596i	$-0.703985\pi$
$179$	−15.9978	−1.19573	−0.597866	+	0.801596i	$0.703985\pi$
$180$	2.25597	0.168150
$181$	11.9696	0.889696	0.444848	−	0.895606i	$-0.353258\pi$
$181$	11.9696	0.889696	0.444848	+	0.895606i	$0.353258\pi$
$182$	−5.07721	−0.376348
$183$	−23.0703	−1.70540
$184$	28.5812	2.10703
$185$	−18.9034	−1.38981
$186$	−8.01055	−0.587362
$187$	14.7215	1.07654
$188$	52.4857	3.82791
$189$	25.8653	1.88142
$190$	−61.4502	−4.45807
$191$	−2.60164	−0.188248	−0.0941241	−	0.995560i	$-0.530005\pi$
$191$	−2.60164	−0.188248	−0.0941241	+	0.995560i	$0.530005\pi$
$192$	12.9004	0.931004
$193$	−7.91810	−0.569957	−0.284979	−	0.958534i	$-0.591987\pi$
$193$	−7.91810	−0.569957	−0.284979	+	0.958534i	$0.591987\pi$
$194$	26.4783	1.90103
$195$	−2.43333	−0.174255
$196$	66.6855	4.76325
$197$	4.88564	0.348087	0.174044	−	0.984738i	$-0.444317\pi$
$197$	4.88564	0.348087	0.174044	+	0.984738i	$0.444317\pi$
$198$	1.41109	0.100282
$199$	13.8846	0.984255	0.492127	−	0.870523i	$-0.336219\pi$
$199$	13.8846	0.984255	0.492127	+	0.870523i	$0.336219\pi$
$200$	32.3831	2.28983
$201$	7.60671	0.536536
$202$	−12.2688	−0.863227
$203$	−6.59787	−0.463079
$204$	28.6833	2.00823
$205$	11.2709	0.787196
$206$	43.8106	3.05243
$207$	−0.948083	−0.0658963
$208$	−1.77537	−0.123100
$209$	−25.6831	−1.77654
$210$	68.0523	4.69606
$211$	10.7942	0.743100	0.371550	−	0.928413i	$-0.378826\pi$
$211$	10.7942	0.743100	0.371550	+	0.928413i	$0.378826\pi$
$212$	10.8292	0.743751
$213$	5.00709	0.343080
$214$	−8.44126	−0.577032
$215$	10.4612	0.713451
$216$	26.5295	1.80510
$217$	9.40546	0.638484
$218$	−5.44877	−0.369037
$219$	−22.8656	−1.54511
$220$	47.5487	3.20574
$221$	1.80219	0.121229
$222$	−23.0377	−1.54619
$223$	−8.45603	−0.566258	−0.283129	−	0.959082i	$-0.591372\pi$
$223$	−8.45603	−0.566258	−0.283129	+	0.959082i	$0.591372\pi$
$224$	1.32769	0.0887103
$225$	−1.07420	−0.0716132
$226$	31.6281	2.10387
$227$	−8.41642	−0.558617	−0.279309	−	0.960201i	$-0.590105\pi$
$227$	−8.41642	−0.558617	−0.279309	+	0.960201i	$0.590105\pi$
$228$	−50.0409	−3.31404
$229$	−19.3500	−1.27869	−0.639343	−	0.768921i	$-0.720794\pi$
$229$	−19.3500	−1.27869	−0.639343	+	0.768921i	$0.720794\pi$
$230$	−47.8110	−3.15256
$231$	28.4425	1.87138
$232$	−6.76729	−0.444295
$233$	−1.72695	−0.113136	−0.0565681	−	0.998399i	$-0.518016\pi$
$233$	−1.72695	−0.113136	−0.0565681	+	0.998399i	$0.518016\pi$
$234$	0.172744	0.0112926
$235$	−44.2009	−2.88335
$236$	−30.2676	−1.97025
$237$	18.5296	1.20363
$238$	−50.4014	−3.26704
$239$	0.851466	0.0550767	0.0275384	−	0.999621i	$-0.491233\pi$
$239$	0.851466	0.0550767	0.0275384	+	0.999621i	$0.491233\pi$
$240$	23.7962	1.53604
$241$	−29.7887	−1.91886	−0.959429	−	0.281949i	$-0.909019\pi$
$241$	−29.7887	−1.91886	−0.959429	+	0.281949i	$0.909019\pi$
$242$	2.73483	0.175802
$243$	−1.71414	−0.109962
$244$	55.1874	3.53301
$245$	−56.1593	−3.58789
$246$	13.7359	0.875769
$247$	−3.14411	−0.200055
$248$	9.64699	0.612584
$249$	−17.2928	−1.09588
$250$	−12.5330	−0.792655
$251$	24.9382	1.57408	0.787042	−	0.616899i	$-0.211611\pi$
$251$	24.9382	1.57408	0.787042	+	0.616899i	$0.211611\pi$
$252$	−3.22811	−0.203352
$253$	−19.9826	−1.25630
$254$	−42.8187	−2.68668
$255$	−24.1556	−1.51268
$256$	−32.2027	−2.01267
$257$	10.6895	0.666794	0.333397	−	0.942787i	$-0.391805\pi$
$257$	10.6895	0.666794	0.333397	+	0.942787i	$0.391805\pi$
$258$	12.7491	0.793727
$259$	27.0493	1.68076
$260$	5.82088	0.360996
$261$	0.224482	0.0138951
$262$	−34.2274	−2.11457
$263$	17.7317	1.09339	0.546693	−	0.837333i	$-0.315886\pi$
$263$	17.7317	1.09339	0.546693	+	0.837333i	$0.315886\pi$
$264$	29.1729	1.79547
$265$	−9.11980	−0.560225
$266$	87.9304	5.39136
$267$	−5.36811	−0.328523
$268$	−18.1963	−1.11152
$269$	−11.0867	−0.675967	−0.337984	−	0.941152i	$-0.609745\pi$
$269$	−11.0867	−0.675967	−0.337984	+	0.941152i	$0.609745\pi$
$270$	−44.3789	−2.70081
$271$	−7.62285	−0.463055	−0.231527	−	0.972828i	$-0.574372\pi$
$271$	−7.62285	−0.463055	−0.231527	+	0.972828i	$0.574372\pi$
$272$	−17.6241	−1.06862
$273$	3.48191	0.210735
$274$	42.8039	2.58588
$275$	−22.6407	−1.36529
$276$	−38.9340	−2.34355
$277$	−10.5790	−0.635628	−0.317814	−	0.948153i	$-0.602949\pi$
$277$	−10.5790	−0.635628	−0.317814	+	0.948153i	$0.602949\pi$
$278$	50.6868	3.03999
$279$	−0.320006	−0.0191583
$280$	−81.9545	−4.89772
$281$	0.907789	0.0541542	0.0270771	−	0.999633i	$-0.491380\pi$
$281$	0.907789	0.0541542	0.0270771	+	0.999633i	$0.491380\pi$
$282$	−53.8677	−3.20778
$283$	−26.3679	−1.56741	−0.783704	−	0.621135i	$-0.786672\pi$
$283$	−26.3679	−1.56741	−0.783704	+	0.621135i	$0.786672\pi$
$284$	−11.9777	−0.710744
$285$	42.1420	2.49628
$286$	3.64090	0.215291
$287$	−16.1278	−0.951994
$288$	−0.0451727	−0.00266183
$289$	0.890314	0.0523714
$290$	11.3204	0.664758
$291$	−18.1586	−1.06447
$292$	54.6978	3.20095
$293$	−10.9282	−0.638432	−0.319216	−	0.947682i	$-0.603420\pi$
$293$	−10.9282	−0.638432	−0.319216	+	0.947682i	$0.603420\pi$
$294$	−68.4414	−3.99159
$295$	25.4899	1.48408
$296$	27.7439	1.61258
$297$	−18.5482	−1.07627
$298$	27.0336	1.56601
$299$	−2.44625	−0.141471
$300$	−44.1130	−2.54687
$301$	−14.9692	−0.862811
$302$	53.7829	3.09486
$303$	8.41381	0.483361
$304$	30.7470	1.76346
$305$	−46.4761	−2.66122
$306$	1.71483	0.0980301
$307$	17.2644	0.985330	0.492665	−	0.870219i	$-0.336023\pi$
$307$	17.2644	0.985330	0.492665	+	0.870219i	$0.336023\pi$
$308$	−68.0385	−3.87685
$309$	−30.0449	−1.70919
$310$	−16.1376	−0.916555
$311$	−5.26031	−0.298285	−0.149142	−	0.988816i	$-0.547651\pi$
$311$	−5.26031	−0.298285	−0.149142	+	0.988816i	$0.547651\pi$
$312$	3.57132	0.202186
$313$	12.2534	0.692602	0.346301	−	0.938123i	$-0.387438\pi$
$313$	12.2534	0.692602	0.346301	+	0.938123i	$0.387438\pi$
$314$	−30.9145	−1.74461
$315$	2.71856	0.153174
$316$	−44.3255	−2.49351
$317$	26.1884	1.47088	0.735442	−	0.677587i	$-0.236974\pi$
$317$	26.1884	1.47088	0.735442	+	0.677587i	$0.236974\pi$
$318$	−11.1143	−0.623260
$319$	4.73137	0.264906
$320$	25.9884	1.45279
$321$	5.78894	0.323107
$322$	68.4137	3.81255
$323$	−31.2115	−1.73665
$324$	−34.1438	−1.89688
$325$	−2.77166	−0.153744
$326$	−9.49938	−0.526122
$327$	3.73671	0.206641
$328$	−16.5420	−0.913377
$329$	63.2480	3.48698
$330$	−48.8008	−2.68639
$331$	−26.3473	−1.44818	−0.724089	−	0.689706i	$-0.757740\pi$
$331$	−26.3473	−1.44818	−0.724089	+	0.689706i	$0.757740\pi$
$332$	41.3667	2.27029
$333$	−0.920311	−0.0504327
$334$	−30.9750	−1.69488
$335$	15.3241	0.837243
$336$	−34.0504	−1.85760
$337$	17.1357	0.933442	0.466721	−	0.884405i	$-0.345435\pi$
$337$	17.1357	0.933442	0.466721	+	0.884405i	$0.345435\pi$
$338$	−31.4710	−1.71180
$339$	−21.6903	−1.17805
$340$	57.7837	3.13376
$341$	−6.74472	−0.365247
$342$	−2.99169	−0.161772
$343$	46.3847	2.50454
$344$	−15.3536	−0.827811
$345$	32.7883	1.76526
$346$	20.4569	1.09977
$347$	17.7415	0.952416	0.476208	−	0.879333i	$-0.342011\pi$
$347$	17.7415	0.952416	0.476208	+	0.879333i	$0.342011\pi$
$348$	9.21858	0.494168
$349$	−29.8296	−1.59674	−0.798372	−	0.602164i	$-0.794305\pi$
$349$	−29.8296	−1.59674	−0.798372	+	0.602164i	$0.794305\pi$
$350$	77.5141	4.14330
$351$	−2.27065	−0.121198
$352$	−0.952098	−0.0507470
$353$	3.33018	0.177248	0.0886239	−	0.996065i	$-0.471753\pi$
$353$	3.33018	0.177248	0.0886239	+	0.996065i	$0.471753\pi$
$354$	31.0646	1.65106
$355$	10.0870	0.535363
$356$	12.8413	0.680586
$357$	34.5648	1.82936
$358$	−39.2767	−2.07584
$359$	12.3715	0.652941	0.326470	−	0.945207i	$-0.394141\pi$
$359$	12.3715	0.652941	0.326470	+	0.945207i	$0.394141\pi$
$360$	2.78837	0.146960
$361$	35.4517	1.86588
$362$	29.3870	1.54455
$363$	−1.87552	−0.0984394
$364$	−8.32922	−0.436570
$365$	−46.0638	−2.41109
$366$	−56.6406	−2.96065
$367$	1.46809	0.0766338	0.0383169	−	0.999266i	$-0.487800\pi$
$367$	1.46809	0.0766338	0.0383169	+	0.999266i	$0.487800\pi$
$368$	23.9225	1.24705
$369$	0.548723	0.0285654
$370$	−46.4104	−2.41276
$371$	13.0497	0.677507
$372$	−13.1414	−0.681349
$373$	2.17868	0.112808	0.0564040	−	0.998408i	$-0.482037\pi$
$373$	2.17868	0.112808	0.0564040	+	0.998408i	$0.482037\pi$
$374$	36.1431	1.86892
$375$	8.59500	0.443844
$376$	64.8722	3.34553
$377$	0.579211	0.0298309
$378$	63.5026	3.26622
$379$	−33.9374	−1.74325	−0.871623	−	0.490178i	$-0.836932\pi$
$379$	−33.9374	−1.74325	−0.871623	+	0.490178i	$0.836932\pi$
$380$	−100.810	−5.17143
$381$	29.3646	1.50440
$382$	−6.38737	−0.326806
$383$	14.0581	0.718337	0.359169	−	0.933273i	$-0.383060\pi$
$383$	14.0581	0.718337	0.359169	+	0.933273i	$0.383060\pi$
$384$	32.5933	1.66327
$385$	57.2987	2.92021
$386$	−19.4400	−0.989468
$387$	0.509304	0.0258894
$388$	43.4378	2.20522
$389$	−22.7645	−1.15420	−0.577102	−	0.816672i	$-0.695817\pi$
$389$	−22.7645	−1.15420	−0.577102	+	0.816672i	$0.695817\pi$
$390$	−5.97415	−0.302513
$391$	−24.2839	−1.22809
$392$	82.4231	4.16299
$393$	23.4728	1.18405
$394$	11.9949	0.604293
$395$	37.3288	1.87822
$396$	2.31490	0.116328
$397$	−21.7040	−1.08929	−0.544646	−	0.838666i	$-0.683336\pi$
$397$	−21.7040	−1.08929	−0.544646	+	0.838666i	$0.683336\pi$
$398$	34.0886	1.70870
$399$	−60.3019	−3.01887
$400$	27.1047	1.35523
$401$	21.6302	1.08016	0.540080	−	0.841614i	$-0.318394\pi$
$401$	21.6302	1.08016	0.540080	+	0.841614i	$0.318394\pi$
$402$	18.6755	0.931447
$403$	−0.825683	−0.0411302
$404$	−20.1270	−1.00136
$405$	28.7543	1.42881
$406$	−16.1986	−0.803924
$407$	−19.3973	−0.961486
$408$	35.4524	1.75516
$409$	16.2837	0.805177	0.402588	−	0.915381i	$-0.368111\pi$
$409$	16.2837	0.805177	0.402588	+	0.915381i	$0.368111\pi$
$410$	27.6716	1.36660
$411$	−29.3545	−1.44795
$412$	71.8716	3.54086
$413$	−36.4740	−1.79477
$414$	−2.32767	−0.114399
$415$	−34.8370	−1.71008
$416$	−0.116555	−0.00571459
$417$	−34.7605	−1.70223
$418$	−63.0555	−3.08414
$419$	−22.5997	−1.10407	−0.552034	−	0.833821i	$-0.686148\pi$
$419$	−22.5997	−1.10407	−0.552034	+	0.833821i	$0.686148\pi$
$420$	111.640	5.44750
$421$	−10.7229	−0.522601	−0.261301	−	0.965257i	$-0.584151\pi$
$421$	−10.7229	−0.522601	−0.261301	+	0.965257i	$0.584151\pi$
$422$	26.5010	1.29005
$423$	−2.15191	−0.104630
$424$	13.3848	0.650024
$425$	−27.5142	−1.33463
$426$	12.2931	0.595601
$427$	66.5037	3.21834
$428$	−13.8480	−0.669366
$429$	−2.49690	−0.120551
$430$	25.6837	1.23858
$431$	10.5556	0.508448	0.254224	−	0.967145i	$-0.418180\pi$
$431$	10.5556	0.508448	0.254224	+	0.967145i	$0.418180\pi$
$432$	22.2052	1.06835
$433$	−9.28043	−0.445989	−0.222994	−	0.974820i	$-0.571583\pi$
$433$	−9.28043	−0.445989	−0.222994	+	0.974820i	$0.571583\pi$
$434$	23.0916	1.10843
$435$	−7.76344	−0.372228
$436$	−8.93875	−0.428089
$437$	42.3658	2.02663
$438$	−56.1380	−2.68238
$439$	−2.40958	−0.115003	−0.0575014	−	0.998345i	$-0.518313\pi$
$439$	−2.40958	−0.115003	−0.0575014	+	0.998345i	$0.518313\pi$
$440$	58.7701	2.80175
$441$	−2.73411	−0.130195
$442$	4.42462	0.210458
$443$	4.00274	0.190176	0.0950879	−	0.995469i	$-0.469687\pi$
$443$	4.00274	0.190176	0.0950879	+	0.995469i	$0.469687\pi$
$444$	−37.7935	−1.79360
$445$	−10.8143	−0.512647
$446$	−20.7607	−0.983046
$447$	−18.5394	−0.876883
$448$	−37.1873	−1.75694
$449$	22.6782	1.07025	0.535125	−	0.844773i	$-0.320265\pi$
$449$	22.6782	1.07025	0.535125	+	0.844773i	$0.320265\pi$
$450$	−2.63729	−0.124323
$451$	11.5653	0.544591
$452$	51.8862	2.44052
$453$	−36.8838	−1.73295
$454$	−20.6634	−0.969781
$455$	7.01446	0.328843
$456$	−61.8504	−2.89641
$457$	4.48023	0.209576	0.104788	−	0.994495i	$-0.466584\pi$
$457$	4.48023	0.209576	0.104788	+	0.994495i	$0.466584\pi$
$458$	−47.5069	−2.21985
$459$	−22.5407	−1.05211
$460$	−78.4343	−3.65702
$461$	−13.5759	−0.632292	−0.316146	−	0.948710i	$-0.602389\pi$
$461$	−13.5759	−0.632292	−0.316146	+	0.948710i	$0.602389\pi$
$462$	69.8300	3.24879
$463$	−39.1044	−1.81734	−0.908668	−	0.417520i	$-0.862899\pi$
$463$	−39.1044	−1.81734	−0.908668	+	0.417520i	$0.862899\pi$
$464$	−5.66424	−0.262956
$465$	11.0670	0.513221
$466$	−4.23989	−0.196409
$467$	36.9311	1.70897	0.854483	−	0.519479i	$-0.173874\pi$
$467$	36.9311	1.70897	0.854483	+	0.519479i	$0.173874\pi$
$468$	0.283388	0.0130996
$469$	−21.9275	−1.01252
$470$	−108.519	−5.00561
$471$	21.2009	0.976885
$472$	−37.4106	−1.72196
$473$	10.7345	0.493574
$474$	45.4927	2.08955
$475$	48.0013	2.20245
$476$	−82.6839	−3.78981
$477$	−0.443996	−0.0203292
$478$	2.09046	0.0956154
$479$	−9.60238	−0.438744	−0.219372	−	0.975641i	$-0.570401\pi$
$479$	−9.60238	−0.438744	−0.219372	+	0.975641i	$0.570401\pi$
$480$	1.56224	0.0713064
$481$	−2.37460	−0.108272
$482$	−73.1351	−3.33121
$483$	−46.9175	−2.13482
$484$	4.48652	0.203933
$485$	−36.5812	−1.66107
$486$	−4.20843	−0.190898
$487$	−7.82233	−0.354464	−0.177232	−	0.984169i	$-0.556714\pi$
$487$	−7.82233	−0.354464	−0.177232	+	0.984169i	$0.556714\pi$
$488$	68.2114	3.08779
$489$	6.51459	0.294600
$490$	−137.878	−6.22871
$491$	−31.0270	−1.40023	−0.700114	−	0.714031i	$-0.746867\pi$
$491$	−31.0270	−1.40023	−0.700114	+	0.714031i	$0.746867\pi$
$492$	22.5339	1.01591
$493$	5.74981	0.258958
$494$	−7.71920	−0.347303
$495$	−1.94950	−0.0876234
$496$	8.07456	0.362558
$497$	−14.4337	−0.647441
$498$	−42.4560	−1.90250
$499$	−38.2468	−1.71216	−0.856080	−	0.516843i	$-0.827107\pi$
$499$	−38.2468	−1.71216	−0.856080	+	0.516843i	$0.827107\pi$
$500$	−20.5605	−0.919492
$501$	21.2424	0.949039
$502$	61.2265	2.73267
$503$	4.97067	0.221631	0.110816	−	0.993841i	$-0.464654\pi$
$503$	4.97067	0.221631	0.110816	+	0.993841i	$0.464654\pi$
$504$	−3.98994	−0.177726
$505$	16.9500	0.754265
$506$	−49.0599	−2.18098
$507$	21.5825	0.958513
$508$	−70.2444	−3.11659
$509$	−18.1195	−0.803134	−0.401567	−	0.915830i	$-0.631534\pi$
$509$	−18.1195	−0.803134	−0.401567	+	0.915830i	$0.631534\pi$
$510$	−59.3052	−2.62608
$511$	65.9136	2.91585
$512$	−40.3458	−1.78305
$513$	39.3246	1.73622
$514$	26.2442	1.15758
$515$	−60.5268	−2.66713
$516$	20.9151	0.920735
$517$	−45.3555	−1.99473
$518$	66.4096	2.91787
$519$	−14.0292	−0.615813
$520$	7.19459	0.315503
$521$	−41.9498	−1.83786	−0.918928	−	0.394426i	$-0.870943\pi$
$521$	−41.9498	−1.83786	−0.918928	+	0.394426i	$0.870943\pi$
$522$	0.551132	0.0241224
$523$	25.5330	1.11648	0.558239	−	0.829680i	$-0.311477\pi$
$523$	25.5330	1.11648	0.558239	+	0.829680i	$0.311477\pi$
$524$	−56.1503	−2.45294
$525$	−53.1585	−2.32003
$526$	43.5337	1.89816
$527$	−8.19654	−0.357047
$528$	24.4178	1.06265
$529$	9.96243	0.433149
$530$	−22.3903	−0.972573
$531$	1.24097	0.0538535
$532$	144.251	6.25406
$533$	1.41582	0.0613260
$534$	−13.1794	−0.570329
$535$	11.6621	0.504195
$536$	−22.4906	−0.971446
$537$	26.9356	1.16236
$538$	−27.2193	−1.17351
$539$	−57.6263	−2.48214
$540$	−72.8039	−3.13298
$541$	39.2494	1.68746	0.843732	−	0.536764i	$-0.180354\pi$
$541$	39.2494	1.68746	0.843732	+	0.536764i	$0.180354\pi$
$542$	−18.7151	−0.803881
$543$	−20.1533	−0.864863
$544$	−1.15704	−0.0496077
$545$	7.52778	0.322455
$546$	8.54853	0.365844
$547$	9.71122	0.415222	0.207611	−	0.978211i	$-0.433431\pi$
$547$	9.71122	0.415222	0.207611	+	0.978211i	$0.433431\pi$
$548$	70.2202	2.99966
$549$	−2.26268	−0.0965689
$550$	−55.5859	−2.37019
$551$	−10.0311	−0.427341
$552$	−48.1223	−2.04822
$553$	−53.4146	−2.27142
$554$	−25.9727	−1.10347
$555$	31.8278	1.35102
$556$	83.1522	3.52644
$557$	−21.9292	−0.929169	−0.464584	−	0.885529i	$-0.653796\pi$
$557$	−21.9292	−0.929169	−0.464584	+	0.885529i	$0.653796\pi$
$558$	−0.785657	−0.0332595
$559$	1.31411	0.0555810
$560$	−68.5961	−2.89871
$561$	−24.7866	−1.04649
$562$	2.22874	0.0940138
$563$	−20.3681	−0.858413	−0.429207	−	0.903206i	$-0.641207\pi$
$563$	−20.3681	−0.858413	−0.429207	+	0.903206i	$0.641207\pi$
$564$	−88.3705	−3.72107
$565$	−43.6961	−1.83831
$566$	−64.7366	−2.72108
$567$	−41.1451	−1.72793
$568$	−14.8044	−0.621178
$569$	10.1505	0.425530	0.212765	−	0.977103i	$-0.431753\pi$
$569$	10.1505	0.425530	0.212765	+	0.977103i	$0.431753\pi$
$570$	103.464	4.33364
$571$	−22.4729	−0.940462	−0.470231	−	0.882543i	$-0.655829\pi$
$571$	−22.4729	−0.940462	−0.470231	+	0.882543i	$0.655829\pi$
$572$	5.97293	0.249741
$573$	4.38040	0.182994
$574$	−39.5959	−1.65270
$575$	37.3471	1.55748
$576$	1.26524	0.0527183
$577$	4.10618	0.170943	0.0854713	−	0.996341i	$-0.472760\pi$
$577$	4.10618	0.170943	0.0854713	+	0.996341i	$0.472760\pi$
$578$	2.18584	0.0909188
$579$	13.3318	0.554049
$580$	18.5713	0.771129
$581$	49.8490	2.06809
$582$	−44.5816	−1.84797
$583$	−9.35803	−0.387570
$584$	67.6063	2.79757
$585$	−0.238656	−0.00986721
$586$	−26.8301	−1.10834
$587$	22.9876	0.948798	0.474399	−	0.880310i	$-0.342665\pi$
$587$	22.9876	0.948798	0.474399	+	0.880310i	$0.342665\pi$
$588$	−112.279	−4.63030
$589$	14.2997	0.589209
$590$	62.5810	2.57642
$591$	−8.22598	−0.338371
$592$	23.2218	0.954408
$593$	1.78019	0.0731037	0.0365518	−	0.999332i	$-0.488363\pi$
$593$	1.78019	0.0731037	0.0365518	+	0.999332i	$0.488363\pi$
$594$	−45.5381	−1.86845
$595$	69.6324	2.85465
$596$	44.3489	1.81660
$597$	−23.3776	−0.956782
$598$	−6.00587	−0.245598
$599$	−9.79284	−0.400124	−0.200062	−	0.979783i	$-0.564114\pi$
$599$	−9.79284	−0.400124	−0.200062	+	0.979783i	$0.564114\pi$
$600$	−54.5235	−2.22591
$601$	38.0291	1.55124	0.775619	−	0.631201i	$-0.217438\pi$
$601$	38.0291	1.55124	0.775619	+	0.631201i	$0.217438\pi$
$602$	−36.7514	−1.49787
$603$	0.746049	0.0303815
$604$	88.2313	3.59008
$605$	−3.77833	−0.153611
$606$	20.6570	0.839133
$607$	−8.30354	−0.337030	−0.168515	−	0.985699i	$-0.553897\pi$
$607$	−8.30354	−0.337030	−0.168515	+	0.985699i	$0.553897\pi$
$608$	2.01858	0.0818641
$609$	11.1089	0.450154
$610$	−114.105	−4.61998
$611$	−5.55239	−0.224626
$612$	2.81319	0.113716
$613$	−25.6858	−1.03744	−0.518720	−	0.854944i	$-0.673591\pi$
$613$	−25.6858	−1.03744	−0.518720	+	0.854944i	$0.673591\pi$
$614$	42.3863	1.71057
$615$	−18.9769	−0.765224
$616$	−84.0953	−3.38830
$617$	5.44989	0.219404	0.109702	−	0.993964i	$-0.465010\pi$
$617$	5.44989	0.219404	0.109702	+	0.993964i	$0.465010\pi$
$618$	−73.7641	−2.96723
$619$	−3.76621	−0.151377	−0.0756885	−	0.997132i	$-0.524115\pi$
$619$	−3.76621	−0.151377	−0.0756885	+	0.997132i	$0.524115\pi$
$620$	−26.4739	−1.06322
$621$	30.5962	1.22778
$622$	−12.9147	−0.517834
$623$	15.4744	0.619969
$624$	2.98920	0.119664
$625$	−15.2100	−0.608399
$626$	30.0837	1.20238
$627$	43.2429	1.72695
$628$	−50.7155	−2.02377
$629$	−23.5726	−0.939899
$630$	6.67442	0.265915
$631$	−42.3230	−1.68485	−0.842427	−	0.538810i	$-0.818874\pi$
$631$	−42.3230	−1.68485	−0.842427	+	0.538810i	$0.818874\pi$
$632$	−54.7862	−2.17928
$633$	−18.1742	−0.722359
$634$	64.2958	2.55351
$635$	59.1564	2.34755
$636$	−18.2331	−0.722991
$637$	−7.05457	−0.279512
$638$	11.6161	0.459887
$639$	0.491085	0.0194270
$640$	65.6606	2.59546
$641$	−14.9924	−0.592163	−0.296082	−	0.955163i	$-0.595680\pi$
$641$	−14.9924	−0.592163	−0.296082	+	0.955163i	$0.595680\pi$
$642$	14.2126	0.560926
$643$	−2.76592	−0.109077	−0.0545386	−	0.998512i	$-0.517369\pi$
$643$	−2.76592	−0.109077	−0.0545386	+	0.998512i	$0.517369\pi$
$644$	112.233	4.42261
$645$	−17.6137	−0.693537
$646$	−76.6283	−3.01490
$647$	−23.5620	−0.926319	−0.463159	−	0.886275i	$-0.653284\pi$
$647$	−23.5620	−0.926319	−0.463159	+	0.886275i	$0.653284\pi$
$648$	−42.2017	−1.65784
$649$	26.1557	1.02670
$650$	−6.80478	−0.266905
$651$	−15.8360	−0.620663
$652$	−15.5838	−0.610309
$653$	−11.5492	−0.451957	−0.225978	−	0.974132i	$-0.572558\pi$
$653$	−11.5492	−0.451957	−0.225978	+	0.974132i	$0.572558\pi$
$654$	9.17412	0.358737
$655$	47.2871	1.84766
$656$	−13.8457	−0.540582
$657$	−2.24261	−0.0874925
$658$	155.282	6.05353
$659$	−23.0029	−0.896065	−0.448033	−	0.894017i	$-0.647875\pi$
$659$	−23.0029	−0.896065	−0.448033	+	0.894017i	$0.647875\pi$
$660$	−80.0581	−3.11626
$661$	−38.7427	−1.50692	−0.753459	−	0.657495i	$-0.771616\pi$
$661$	−38.7427	−1.50692	−0.753459	+	0.657495i	$0.771616\pi$
$662$	−64.6861	−2.51410
$663$	−3.03436	−0.117845
$664$	51.1291	1.98419
$665$	−121.481	−4.71083
$666$	−2.25948	−0.0875532
$667$	−7.80466	−0.302198
$668$	−50.8147	−1.96608
$669$	14.2375	0.550453
$670$	37.6225	1.45349
$671$	−47.6902	−1.84106
$672$	−2.23545	−0.0862343
$673$	1.09656	0.0422692	0.0211346	−	0.999777i	$-0.493272\pi$
$673$	1.09656	0.0422692	0.0211346	+	0.999777i	$0.493272\pi$
$674$	42.0704	1.62049
$675$	34.6662	1.33430
$676$	−51.6284	−1.98571
$677$	14.8640	0.571269	0.285634	−	0.958339i	$-0.407796\pi$
$677$	14.8640	0.571269	0.285634	+	0.958339i	$0.407796\pi$
$678$	−53.2525	−2.04515
$679$	52.3448	2.00881
$680$	71.4205	2.73885
$681$	14.1708	0.543025
$682$	−16.5592	−0.634083
$683$	7.91661	0.302921	0.151460	−	0.988463i	$-0.451602\pi$
$683$	7.91661	0.302921	0.151460	+	0.988463i	$0.451602\pi$
$684$	−4.90790	−0.187658
$685$	−59.1360	−2.25947
$686$	113.880	4.34798
$687$	32.5798	1.24300
$688$	−12.8510	−0.489940
$689$	−1.14560	−0.0436440
$690$	80.4996	3.06457
$691$	17.8706	0.679829	0.339914	−	0.940456i	$-0.389602\pi$
$691$	17.8706	0.679829	0.339914	+	0.940456i	$0.389602\pi$
$692$	33.5598	1.27575
$693$	2.78958	0.105967
$694$	43.5578	1.65343
$695$	−70.0267	−2.65626
$696$	11.3941	0.431894
$697$	14.0548	0.532364
$698$	−73.2357	−2.77201
$699$	2.90768	0.109978
$700$	127.163	4.80629
$701$	42.3565	1.59978	0.799892	−	0.600144i	$-0.204890\pi$
$701$	42.3565	1.59978	0.799892	+	0.600144i	$0.204890\pi$
$702$	−5.57474	−0.210405
$703$	41.1248	1.55105
$704$	26.6673	1.00506
$705$	74.4214	2.80287
$706$	8.17604	0.307709
$707$	−24.2541	−0.912169
$708$	50.9617	1.91526
$709$	24.1365	0.906467	0.453233	−	0.891392i	$-0.350270\pi$
$709$	24.1365	0.906467	0.453233	+	0.891392i	$0.350270\pi$
$710$	24.7649	0.929412
$711$	1.81735	0.0681558
$712$	15.8718	0.594820
$713$	11.1258	0.416664
$714$	84.8611	3.17585
$715$	−5.03011	−0.188116
$716$	−64.4338	−2.40800
$717$	−1.43362	−0.0535394
$718$	30.3736	1.13353
$719$	−21.3950	−0.797901	−0.398950	−	0.916973i	$-0.630625\pi$
$719$	−21.3950	−0.797901	−0.398950	+	0.916973i	$0.630625\pi$
$720$	2.33387	0.0869784
$721$	86.6090	3.22549
$722$	87.0385	3.23924
$723$	50.1554	1.86530
$724$	48.2097	1.79170
$725$	−8.84284	−0.328415
$726$	−4.60465	−0.170895
$727$	−3.36788	−0.124908	−0.0624538	−	0.998048i	$-0.519893\pi$
$727$	−3.36788	−0.124908	−0.0624538	+	0.998048i	$0.519893\pi$
$728$	−10.2949	−0.381554
$729$	28.3181	1.04882
$730$	−113.093	−4.18575
$731$	13.0452	0.482492
$732$	−92.9194	−3.43440
$733$	3.98604	0.147228	0.0736139	−	0.997287i	$-0.476547\pi$
$733$	3.98604	0.147228	0.0736139	+	0.997287i	$0.476547\pi$
$734$	3.60436	0.133039
$735$	94.5557	3.48774
$736$	1.57054	0.0578909
$737$	15.7244	0.579214
$738$	1.34719	0.0495906
$739$	49.4424	1.81877	0.909385	−	0.415956i	$-0.136553\pi$
$739$	49.4424	1.81877	0.909385	+	0.415956i	$0.136553\pi$
$740$	−76.1367	−2.79884
$741$	5.29376	0.194471
$742$	32.0387	1.17618
$743$	−18.2597	−0.669884	−0.334942	−	0.942239i	$-0.608717\pi$
$743$	−18.2597	−0.669884	−0.334942	+	0.942239i	$0.608717\pi$
$744$	−16.2427	−0.595486
$745$	−37.3485	−1.36834
$746$	5.34895	0.195839
$747$	−1.69603	−0.0620547
$748$	59.2932	2.16797
$749$	−16.6875	−0.609748
$750$	21.1019	0.770531
$751$	49.9351	1.82216	0.911079	−	0.412231i	$-0.135250\pi$
$751$	49.9351	1.82216	0.911079	+	0.412231i	$0.135250\pi$
$752$	54.2982	1.98005
$753$	−41.9886	−1.53015
$754$	1.42204	0.0517876
$755$	−74.3041	−2.70420
$756$	104.177	3.78887
$757$	−27.7753	−1.00951	−0.504755	−	0.863263i	$-0.668417\pi$
$757$	−27.7753	−1.00951	−0.504755	+	0.863263i	$0.668417\pi$
$758$	−83.3206	−3.02634
$759$	33.6448	1.22123
$760$	−124.600	−4.51973
$761$	8.08376	0.293036	0.146518	−	0.989208i	$-0.453193\pi$
$761$	8.08376	0.293036	0.146518	+	0.989208i	$0.453193\pi$
$762$	72.0940	2.61169
$763$	−10.7717	−0.389960
$764$	−10.4785	−0.379100
$765$	−2.36913	−0.0856561
$766$	34.5146	1.24706
$767$	3.20196	0.115616
$768$	54.2199	1.95649
$769$	8.00443	0.288647	0.144324	−	0.989531i	$-0.453899\pi$
$769$	8.00443	0.288647	0.144324	+	0.989531i	$0.453899\pi$
$770$	140.676	5.06960
$771$	−17.9980	−0.648183
$772$	−31.8915	−1.14780
$773$	51.7562	1.86154	0.930771	−	0.365603i	$-0.119137\pi$
$773$	51.7562	1.86154	0.930771	+	0.365603i	$0.119137\pi$
$774$	1.25041	0.0449450
$775$	12.6058	0.452812
$776$	53.6890	1.92732
$777$	−45.5431	−1.63385
$778$	−55.8897	−2.00374
$779$	−24.5201	−0.878523
$780$	−9.80065	−0.350920
$781$	10.3505	0.370371
$782$	−59.6202	−2.13201
$783$	−7.24441	−0.258894
$784$	68.9883	2.46387
$785$	42.7102	1.52439
$786$	57.6288	2.05555
$787$	38.6301	1.37702	0.688508	−	0.725229i	$-0.258266\pi$
$787$	38.6301	1.37702	0.688508	+	0.725229i	$0.258266\pi$
$788$	19.6777	0.700989
$789$	−29.8550	−1.06287
$790$	91.6471	3.26066
$791$	62.5256	2.22315
$792$	2.86121	0.101669
$793$	−5.83820	−0.207321
$794$	−53.2861	−1.89105
$795$	15.3551	0.544588
$796$	55.9226	1.98212
$797$	−46.6619	−1.65285	−0.826424	−	0.563048i	$-0.809629\pi$
$797$	−46.6619	−1.65285	−0.826424	+	0.563048i	$0.809629\pi$
$798$	−148.049	−5.24088
$799$	−55.1184	−1.94995
$800$	1.77945	0.0629132
$801$	−0.526492	−0.0186027
$802$	53.1049	1.87520
$803$	−47.2671	−1.66802
$804$	30.6373	1.08049
$805$	−94.5174	−3.33130
$806$	−2.02716	−0.0714037
$807$	18.6667	0.657100
$808$	−24.8769	−0.875167
$809$	26.5733	0.934267	0.467133	−	0.884187i	$-0.345287\pi$
$809$	26.5733	0.934267	0.467133	+	0.884187i	$0.345287\pi$
$810$	70.5955	2.48047
$811$	32.5016	1.14129	0.570644	−	0.821198i	$-0.306694\pi$
$811$	32.5016	1.14129	0.570644	+	0.821198i	$0.306694\pi$
$812$	−26.5740	−0.932564
$813$	12.8346	0.450130
$814$	−47.6228	−1.66918
$815$	13.1239	0.459711
$816$	29.6738	1.03879
$817$	−22.7586	−0.796223
$818$	39.9786	1.39782
$819$	0.341498	0.0119329
$820$	45.3955	1.58528
$821$	−43.7002	−1.52515	−0.762573	−	0.646902i	$-0.776064\pi$
$821$	−43.7002	−1.52515	−0.762573	+	0.646902i	$0.776064\pi$
$822$	−72.0692	−2.51370
$823$	32.0137	1.11593	0.557964	−	0.829865i	$-0.311583\pi$
$823$	32.0137	1.11593	0.557964	+	0.829865i	$0.311583\pi$
$824$	88.8331	3.09465
$825$	38.1203	1.32718
$826$	−89.5484	−3.11579
$827$	−24.0050	−0.834735	−0.417368	−	0.908738i	$-0.637047\pi$
$827$	−24.0050	−0.834735	−0.417368	+	0.908738i	$0.637047\pi$
$828$	−3.81856	−0.132704
$829$	−46.8935	−1.62868	−0.814339	−	0.580390i	$-0.802900\pi$
$829$	−46.8935	−1.62868	−0.814339	+	0.580390i	$0.802900\pi$
$830$	−85.5295	−2.96877
$831$	17.8118	0.617886
$832$	3.26459	0.113179
$833$	−70.0305	−2.42641
$834$	−85.3417	−2.95514
$835$	42.7937	1.48094
$836$	−103.443	−3.57765
$837$	10.3271	0.356958
$838$	−55.4853	−1.91671
$839$	23.7493	0.819917	0.409958	−	0.912104i	$-0.365543\pi$
$839$	23.7493	0.819917	0.409958	+	0.912104i	$0.365543\pi$
$840$	137.987	4.76101
$841$	−27.1521	−0.936278
$842$	−26.3261	−0.907257
$843$	−1.52845	−0.0526426
$844$	43.4752	1.49648
$845$	43.4789	1.49572
$846$	−5.28323	−0.181641
$847$	5.40648	0.185769
$848$	11.2031	0.384717
$849$	44.3958	1.52366
$850$	−67.5508	−2.31697
$851$	31.9969	1.09684
$852$	20.1669	0.690906
$853$	42.5399	1.45654	0.728269	−	0.685292i	$-0.240325\pi$
$853$	42.5399	1.45654	0.728269	+	0.685292i	$0.240325\pi$
$854$	163.275	5.58716
$855$	4.13319	0.141352
$856$	−17.1160	−0.585014
$857$	−3.36702	−0.115015	−0.0575076	−	0.998345i	$-0.518315\pi$
$857$	−3.36702	−0.115015	−0.0575076	+	0.998345i	$0.518315\pi$
$858$	−6.13021	−0.209282
$859$	−15.4734	−0.527945	−0.263972	−	0.964530i	$-0.585033\pi$
$859$	−15.4734	−0.527945	−0.263972	+	0.964530i	$0.585033\pi$
$860$	42.1344	1.43677
$861$	27.1545	0.925422
$862$	25.9155	0.882685
$863$	41.0989	1.39902	0.699511	−	0.714622i	$-0.253401\pi$
$863$	41.0989	1.39902	0.699511	+	0.714622i	$0.253401\pi$
$864$	1.45780	0.0495953
$865$	−28.2624	−0.960951
$866$	−22.7847	−0.774254
$867$	−1.49903	−0.0509096
$868$	37.8820	1.28580
$869$	38.3039	1.29937
$870$	−19.0603	−0.646203
$871$	1.92496	0.0652249
$872$	−11.0483	−0.374142
$873$	−1.78095	−0.0602760
$874$	104.014	3.51831
$875$	−24.7764	−0.837596
$876$	−92.0950	−3.11160
$877$	42.0576	1.42018	0.710092	−	0.704109i	$-0.248653\pi$
$877$	42.0576	1.42018	0.710092	+	0.704109i	$0.248653\pi$
$878$	−5.91582	−0.199649
$879$	18.3999	0.620612
$880$	49.1907	1.65822
$881$	21.8530	0.736246	0.368123	−	0.929777i	$-0.380001\pi$
$881$	21.8530	0.736246	0.368123	+	0.929777i	$0.380001\pi$
$882$	−6.71258	−0.226024
$883$	−4.84112	−0.162917	−0.0814583	−	0.996677i	$-0.525958\pi$
$883$	−4.84112	−0.162917	−0.0814583	+	0.996677i	$0.525958\pi$
$884$	7.25862	0.244134
$885$	−42.9175	−1.44265
$886$	9.82725	0.330153
$887$	−7.88437	−0.264731	−0.132366	−	0.991201i	$-0.542257\pi$
$887$	−7.88437	−0.264731	−0.132366	+	0.991201i	$0.542257\pi$
$888$	−46.7126	−1.56757
$889$	−84.6481	−2.83901
$890$	−26.5505	−0.889975
$891$	29.5054	0.988468
$892$	−34.0581	−1.14035
$893$	96.1598	3.21787
$894$	−45.5166	−1.52230
$895$	54.2630	1.81381
$896$	−93.9551	−3.13882
$897$	4.11877	0.137522
$898$	55.6779	1.85800
$899$	−2.63430	−0.0878590
$900$	−4.32651	−0.144217
$901$	−11.3724	−0.378869
$902$	28.3944	0.945431
$903$	25.2038	0.838728
$904$	64.1312	2.13297
$905$	−40.5998	−1.34958
$906$	−90.5546	−3.00847
$907$	37.8701	1.25746	0.628728	−	0.777626i	$-0.283576\pi$
$907$	37.8701	1.25746	0.628728	+	0.777626i	$0.283576\pi$
$908$	−33.8985	−1.12496
$909$	0.825208	0.0273704
$910$	17.2214	0.570884
$911$	13.0667	0.432920	0.216460	−	0.976292i	$-0.430549\pi$
$911$	13.0667	0.432920	0.216460	+	0.976292i	$0.430549\pi$
$912$	−51.7689	−1.71424
$913$	−35.7471	−1.18306
$914$	10.9995	0.363833
$915$	78.2522	2.58694
$916$	−77.9355	−2.57506
$917$	−67.6640	−2.23446
$918$	−55.3403	−1.82650
$919$	−31.9778	−1.05485	−0.527425	−	0.849601i	$-0.676843\pi$
$919$	−31.9778	−1.05485	−0.527425	+	0.849601i	$0.676843\pi$
$920$	−96.9445	−3.19617
$921$	−29.0681	−0.957827
$922$	−33.3306	−1.09768
$923$	1.26710	0.0417072
$924$	114.557	3.76864
$925$	36.2531	1.19199
$926$	−96.0064	−3.15497
$927$	−2.94674	−0.0967835
$928$	−0.371864	−0.0122070
$929$	33.6309	1.10340	0.551698	−	0.834044i	$-0.313980\pi$
$929$	33.6309	1.10340	0.551698	+	0.834044i	$0.313980\pi$
$930$	27.1710	0.890972
$931$	122.175	4.00414
$932$	−6.95557	−0.227837
$933$	8.85681	0.289959
$934$	90.6706	2.96683
$935$	−49.9338	−1.63301
$936$	0.350267	0.0114488
$937$	−11.2217	−0.366598	−0.183299	−	0.983057i	$-0.558678\pi$
$937$	−11.2217	−0.366598	−0.183299	+	0.983057i	$0.558678\pi$
$938$	−53.8349	−1.75777
$939$	−20.6311	−0.673270
$940$	−178.026	−5.80658
$941$	−40.1158	−1.30774	−0.653869	−	0.756608i	$-0.726855\pi$
$941$	−40.1158	−1.30774	−0.653869	+	0.756608i	$0.726855\pi$
$942$	52.0509	1.69591
$943$	−19.0777	−0.621255
$944$	−31.3128	−1.01914
$945$	−87.7325	−2.85394
$946$	26.3546	0.856863
$947$	−22.4602	−0.729857	−0.364929	−	0.931035i	$-0.618907\pi$
$947$	−22.4602	−0.729857	−0.364929	+	0.931035i	$0.618907\pi$
$948$	74.6312	2.42391
$949$	−5.78640	−0.187835
$950$	117.849	3.82354
$951$	−44.0935	−1.42983
$952$	−102.197	−3.31222
$953$	−13.5722	−0.439648	−0.219824	−	0.975540i	$-0.570548\pi$
$953$	−13.5722	−0.439648	−0.219824	+	0.975540i	$0.570548\pi$
$954$	−1.09007	−0.0352922
$955$	8.82451	0.285555
$956$	3.42942	0.110915
$957$	−7.96624	−0.257512
$958$	−23.5751	−0.761676
$959$	84.6189	2.73249
$960$	−43.7568	−1.41224
$961$	−27.2447	−0.878862
$962$	−5.82994	−0.187965
$963$	0.567766	0.0182960
$964$	−119.979	−3.86426
$965$	26.8574	0.864571
$966$	−115.189	−3.70613
$967$	7.77861	0.250143	0.125072	−	0.992148i	$-0.460084\pi$
$967$	7.77861	0.250143	0.125072	+	0.992148i	$0.460084\pi$
$968$	5.54532	0.178233
$969$	52.5510	1.68818
$970$	−89.8117	−2.88368
$971$	16.7610	0.537886	0.268943	−	0.963156i	$-0.413326\pi$
$971$	16.7610	0.537886	0.268943	+	0.963156i	$0.413326\pi$
$972$	−6.90397	−0.221445
$973$	100.203	3.21235
$974$	−19.2048	−0.615363
$975$	4.66665	0.149453
$976$	57.0932	1.82751
$977$	23.5536	0.753546	0.376773	−	0.926306i	$-0.377034\pi$
$977$	23.5536	0.753546	0.376773	+	0.926306i	$0.377034\pi$
$978$	15.9942	0.511437
$979$	−11.0968	−0.354655
$980$	−226.191	−7.22540
$981$	0.366489	0.0117011
$982$	−76.1752	−2.43085
$983$	47.0503	1.50067	0.750336	−	0.661057i	$-0.229892\pi$
$983$	47.0503	1.50067	0.750336	+	0.661057i	$0.229892\pi$
$984$	27.8518	0.887882
$985$	−16.5716	−0.528015
$986$	14.1165	0.449562
$987$	−106.491	−3.38965
$988$	−12.6634	−0.402877
$989$	−17.7072	−0.563056
$990$	−4.78627	−0.152118
$991$	30.7486	0.976761	0.488380	−	0.872631i	$-0.337588\pi$
$991$	30.7486	0.976761	0.488380	+	0.872631i	$0.337588\pi$
$992$	0.530104	0.0168308
$993$	44.3611	1.40776
$994$	−35.4367	−1.12398
$995$	−47.0953	−1.49302
$996$	−69.6494	−2.20693
$997$	42.3465	1.34113	0.670563	−	0.741852i	$-0.266052\pi$
$997$	42.3465	1.34113	0.670563	+	0.741852i	$0.266052\pi$
$998$	−93.9008	−2.97238
$999$	29.7000	0.939666

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.163	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.163	✓	184	1.1	even	1	trivial

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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 $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	4001.2.a.b.1.163

Level	$4001$
Weight	$2$
Character	4001.1
Self dual	yes
Analytic conductor	$31.948$
Analytic rank	$0$
Dimension	$184$
CM	no
Inner twists	$1$