LMFDB - Embedded newform 8017.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, 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("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$0$
Dimension:	$340$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72150 q^{2} +1.69330 q^{3} +5.40656 q^{4} -4.24685 q^{5} -4.60831 q^{6} -1.07458 q^{7} -9.27094 q^{8} -0.132735 q^{9} +O(q^{10})$	\(q-2.72150 q^{2} +1.69330 q^{3} +5.40656 q^{4} -4.24685 q^{5} -4.60831 q^{6} -1.07458 q^{7} -9.27094 q^{8} -0.132735 q^{9} +11.5578 q^{10} +3.77387 q^{11} +9.15492 q^{12} -3.02096 q^{13} +2.92447 q^{14} -7.19120 q^{15} +14.4178 q^{16} +1.62802 q^{17} +0.361239 q^{18} -4.57927 q^{19} -22.9609 q^{20} -1.81959 q^{21} -10.2706 q^{22} +5.92922 q^{23} -15.6985 q^{24} +13.0358 q^{25} +8.22154 q^{26} -5.30466 q^{27} -5.80979 q^{28} +4.99511 q^{29} +19.5708 q^{30} -0.611570 q^{31} -20.6960 q^{32} +6.39029 q^{33} -4.43064 q^{34} +4.56359 q^{35} -0.717641 q^{36} -8.11233 q^{37} +12.4625 q^{38} -5.11539 q^{39} +39.3723 q^{40} -11.3933 q^{41} +4.95201 q^{42} -2.97910 q^{43} +20.4036 q^{44} +0.563707 q^{45} -16.1364 q^{46} +6.48943 q^{47} +24.4136 q^{48} -5.84527 q^{49} -35.4768 q^{50} +2.75672 q^{51} -16.3330 q^{52} +9.12834 q^{53} +14.4366 q^{54} -16.0271 q^{55} +9.96239 q^{56} -7.75408 q^{57} -13.5942 q^{58} -3.23377 q^{59} -38.8796 q^{60} -7.30978 q^{61} +1.66439 q^{62} +0.142635 q^{63} +27.4887 q^{64} +12.8296 q^{65} -17.3912 q^{66} -6.49014 q^{67} +8.80196 q^{68} +10.0399 q^{69} -12.4198 q^{70} -8.51846 q^{71} +1.23058 q^{72} +11.7117 q^{73} +22.0777 q^{74} +22.0734 q^{75} -24.7581 q^{76} -4.05533 q^{77} +13.9215 q^{78} +2.64728 q^{79} -61.2301 q^{80} -8.58418 q^{81} +31.0069 q^{82} +15.5467 q^{83} -9.83772 q^{84} -6.91394 q^{85} +8.10763 q^{86} +8.45822 q^{87} -34.9873 q^{88} +5.72734 q^{89} -1.53413 q^{90} +3.24627 q^{91} +32.0567 q^{92} -1.03557 q^{93} -17.6610 q^{94} +19.4475 q^{95} -35.0446 q^{96} -12.1971 q^{97} +15.9079 q^{98} -0.500925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) $ 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * 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 $

$2$	−2.72150	−1.92439	−0.962195	−	0.272361i	$-0.912196\pi$
$2$	−2.72150	−1.92439	−0.962195	+	0.272361i	$0.912196\pi$
$3$	1.69330	0.977627	0.488814	−	0.872388i	$-0.337430\pi$
$3$	1.69330	0.977627	0.488814	+	0.872388i	$0.337430\pi$
$4$	5.40656	2.70328
$5$	−4.24685	−1.89925	−0.949625	−	0.313388i	$-0.898536\pi$
$5$	−4.24685	−1.89925	−0.949625	+	0.313388i	$0.898536\pi$
$6$	−4.60831	−1.88134
$7$	−1.07458	−0.406154	−0.203077	−	0.979163i	$-0.565094\pi$
$7$	−1.07458	−0.406154	−0.203077	+	0.979163i	$0.565094\pi$
$8$	−9.27094	−3.27777
$9$	−0.132735	−0.0442451
$10$	11.5578	3.65490
$11$	3.77387	1.13786	0.568932	−	0.822385i	$-0.307357\pi$
$11$	3.77387	1.13786	0.568932	+	0.822385i	$0.307357\pi$
$12$	9.15492	2.64280
$13$	−3.02096	−0.837864	−0.418932	−	0.908018i	$-0.637595\pi$
$13$	−3.02096	−0.837864	−0.418932	+	0.908018i	$0.637595\pi$
$14$	2.92447	0.781599
$15$	−7.19120	−1.85676
$16$	14.4178	3.60444
$17$	1.62802	0.394852	0.197426	−	0.980318i	$-0.436742\pi$
$17$	1.62802	0.394852	0.197426	+	0.980318i	$0.436742\pi$
$18$	0.361239	0.0851448
$19$	−4.57927	−1.05056	−0.525279	−	0.850930i	$-0.676039\pi$
$19$	−4.57927	−1.05056	−0.525279	+	0.850930i	$0.676039\pi$
$20$	−22.9609	−5.13420
$21$	−1.81959	−0.397067
$22$	−10.2706	−2.18970
$23$	5.92922	1.23633	0.618164	−	0.786049i	$-0.287877\pi$
$23$	5.92922	1.23633	0.618164	+	0.786049i	$0.287877\pi$
$24$	−15.6985	−3.20444
$25$	13.0358	2.60715
$26$	8.22154	1.61238
$27$	−5.30466	−1.02088
$28$	−5.80979	−1.09795
$29$	4.99511	0.927569	0.463784	−	0.885948i	$-0.346491\pi$
$29$	4.99511	0.927569	0.463784	+	0.885948i	$0.346491\pi$
$30$	19.5708	3.57313
$31$	−0.611570	−0.109841	−0.0549206	−	0.998491i	$-0.517491\pi$
$31$	−0.611570	−0.109841	−0.0549206	+	0.998491i	$0.517491\pi$
$32$	−20.6960	−3.65857
$33$	6.39029	1.11241
$34$	−4.43064	−0.759849
$35$	4.56359	0.771388
$36$	−0.717641	−0.119607
$37$	−8.11233	−1.33366	−0.666829	−	0.745211i	$-0.732349\pi$
$37$	−8.11233	−1.33366	−0.666829	+	0.745211i	$0.732349\pi$
$38$	12.4625	2.02168
$39$	−5.11539	−0.819118
$40$	39.3723	6.22531
$41$	−11.3933	−1.77934	−0.889668	−	0.456609i	$-0.849064\pi$
$41$	−11.3933	−1.77934	−0.889668	+	0.456609i	$0.849064\pi$
$42$	4.95201	0.764112
$43$	−2.97910	−0.454309	−0.227154	−	0.973859i	$-0.572942\pi$
$43$	−2.97910	−0.454309	−0.227154	+	0.973859i	$0.572942\pi$
$44$	20.4036	3.07596
$45$	0.563707	0.0840325
$46$	−16.1364	−2.37918
$47$	6.48943	0.946580	0.473290	−	0.880907i	$-0.343066\pi$
$47$	6.48943	0.946580	0.473290	+	0.880907i	$0.343066\pi$
$48$	24.4136	3.52380
$49$	−5.84527	−0.835039
$50$	−35.4768	−5.01718
$51$	2.75672	0.386018
$52$	−16.3330	−2.26498
$53$	9.12834	1.25387	0.626937	−	0.779070i	$-0.284308\pi$
$53$	9.12834	1.25387	0.626937	+	0.779070i	$0.284308\pi$
$54$	14.4366	1.96458
$55$	−16.0271	−2.16109
$56$	9.96239	1.33128
$57$	−7.75408	−1.02705
$58$	−13.5942	−1.78500
$59$	−3.23377	−0.421002	−0.210501	−	0.977594i	$-0.567509\pi$
$59$	−3.23377	−0.421002	−0.210501	+	0.977594i	$0.567509\pi$
$60$	−38.8796	−5.01934
$61$	−7.30978	−0.935922	−0.467961	−	0.883749i	$-0.655011\pi$
$61$	−7.30978	−0.935922	−0.467961	+	0.883749i	$0.655011\pi$
$62$	1.66439	0.211377
$63$	0.142635	0.0179703
$64$	27.4887	3.43608
$65$	12.8296	1.59131
$66$	−17.3912	−2.14071
$67$	−6.49014	−0.792897	−0.396449	−	0.918057i	$-0.629758\pi$
$67$	−6.49014	−0.792897	−0.396449	+	0.918057i	$0.629758\pi$
$68$	8.80196	1.06739
$69$	10.0399	1.20867
$70$	−12.4198	−1.48445
$71$	−8.51846	−1.01096	−0.505478	−	0.862840i	$-0.668684\pi$
$71$	−8.51846	−1.01096	−0.505478	+	0.862840i	$0.668684\pi$
$72$	1.23058	0.145025
$73$	11.7117	1.37075	0.685376	−	0.728189i	$-0.259638\pi$
$73$	11.7117	1.37075	0.685376	+	0.728189i	$0.259638\pi$
$74$	22.0777	2.56648
$75$	22.0734	2.54882
$76$	−24.7581	−2.83995
$77$	−4.05533	−0.462148
$78$	13.9215	1.57630
$79$	2.64728	0.297843	0.148921	−	0.988849i	$-0.452420\pi$
$79$	2.64728	0.297843	0.148921	+	0.988849i	$0.452420\pi$
$80$	−61.2301	−6.84573
$81$	−8.58418	−0.953797
$82$	31.0069	3.42414
$83$	15.5467	1.70647	0.853236	−	0.521525i	$-0.174637\pi$
$83$	15.5467	1.70647	0.853236	+	0.521525i	$0.174637\pi$
$84$	−9.83772	−1.07338
$85$	−6.91394	−0.749923
$86$	8.10763	0.874268
$87$	8.45822	0.906816
$88$	−34.9873	−3.72966
$89$	5.72734	0.607097	0.303549	−	0.952816i	$-0.401829\pi$
$89$	5.72734	0.607097	0.303549	+	0.952816i	$0.401829\pi$
$90$	−1.53413	−0.161711
$91$	3.24627	0.340302
$92$	32.0567	3.34214
$93$	−1.03557	−0.107384
$94$	−17.6610	−1.82159
$95$	19.4475	1.99527
$96$	−35.0446	−3.57672
$97$	−12.1971	−1.23843	−0.619215	−	0.785222i	$-0.712549\pi$
$97$	−12.1971	−1.23843	−0.619215	+	0.785222i	$0.712549\pi$
$98$	15.9079	1.60694
$99$	−0.500925	−0.0503449
$100$	70.4786	7.04786
$101$	0.0708563	0.00705047	0.00352523	−	0.999994i	$-0.498878\pi$
$101$	0.0708563	0.00705047	0.00352523	+	0.999994i	$0.498878\pi$
$102$	−7.50241	−0.742849
$103$	6.83415	0.673389	0.336694	−	0.941614i	$-0.390691\pi$
$103$	6.83415	0.673389	0.336694	+	0.941614i	$0.390691\pi$
$104$	28.0072	2.74633
$105$	7.72753	0.754130
$106$	−24.8428	−2.41294
$107$	−11.9791	−1.15806	−0.579029	−	0.815307i	$-0.696568\pi$
$107$	−11.9791	−1.15806	−0.579029	+	0.815307i	$0.696568\pi$
$108$	−28.6800	−2.75973
$109$	−0.449277	−0.0430330	−0.0215165	−	0.999768i	$-0.506849\pi$
$109$	−0.449277	−0.0430330	−0.0215165	+	0.999768i	$0.506849\pi$
$110$	43.6176	4.15878
$111$	−13.7366	−1.30382
$112$	−15.4931	−1.46396
$113$	−17.2485	−1.62260	−0.811302	−	0.584628i	$-0.801241\pi$
$113$	−17.2485	−1.62260	−0.811302	+	0.584628i	$0.801241\pi$
$114$	21.1027	1.97645
$115$	−25.1805	−2.34809
$116$	27.0064	2.50748
$117$	0.400988	0.0370713
$118$	8.80071	0.810171
$119$	−1.74944	−0.160371
$120$	66.6692	6.08604
$121$	3.24208	0.294735
$122$	19.8936	1.80108
$123$	−19.2923	−1.73953
$124$	−3.30649	−0.296931
$125$	−34.1267	−3.05238
$126$	−0.388181	−0.0345819
$127$	−15.5664	−1.38129	−0.690645	−	0.723194i	$-0.742673\pi$
$127$	−15.5664	−1.38129	−0.690645	+	0.723194i	$0.742673\pi$
$128$	−33.4184	−2.95380
$129$	−5.04451	−0.444145
$130$	−34.9157	−3.06231
$131$	13.1120	1.14560	0.572801	−	0.819695i	$-0.305857\pi$
$131$	13.1120	1.14560	0.572801	+	0.819695i	$0.305857\pi$
$132$	34.5495	3.00715
$133$	4.92081	0.426688
$134$	17.6629	1.52584
$135$	22.5281	1.93891
$136$	−15.0932	−1.29424
$137$	9.74808	0.832835	0.416417	−	0.909174i	$-0.363285\pi$
$137$	9.74808	0.832835	0.416417	+	0.909174i	$0.363285\pi$
$138$	−27.3237	−2.32595
$139$	11.6420	0.987465	0.493732	−	0.869614i	$-0.335632\pi$
$139$	11.6420	0.987465	0.493732	+	0.869614i	$0.335632\pi$
$140$	24.6733	2.08528
$141$	10.9885	0.925402
$142$	23.1830	1.94547
$143$	−11.4007	−0.953375
$144$	−1.91374	−0.159479
$145$	−21.2135	−1.76168
$146$	−31.8734	−2.63786
$147$	−9.89780	−0.816357
$148$	−43.8598	−3.60525
$149$	7.31866	0.599568	0.299784	−	0.954007i	$-0.403085\pi$
$149$	7.31866	0.599568	0.299784	+	0.954007i	$0.403085\pi$
$150$	−60.0729	−4.90493
$151$	−10.3491	−0.842198	−0.421099	−	0.907015i	$-0.638355\pi$
$151$	−10.3491	−0.842198	−0.421099	+	0.907015i	$0.638355\pi$
$152$	42.4542	3.44349
$153$	−0.216095	−0.0174702
$154$	11.0366	0.889353
$155$	2.59725	0.208616
$156$	−27.6567	−2.21430
$157$	12.5135	0.998682	0.499341	−	0.866405i	$-0.333575\pi$
$157$	12.5135	0.998682	0.499341	+	0.866405i	$0.333575\pi$
$158$	−7.20458	−0.573166
$159$	15.4570	1.22582
$160$	87.8929	6.94855
$161$	−6.37143	−0.502139
$162$	23.3618	1.83548
$163$	−22.9202	−1.79525	−0.897623	−	0.440763i	$-0.854708\pi$
$163$	−22.9202	−1.79525	−0.897623	+	0.440763i	$0.854708\pi$
$164$	−61.5986	−4.81004
$165$	−27.1386	−2.11274
$166$	−42.3103	−3.28392
$167$	24.9363	1.92963	0.964816	−	0.262925i	$-0.0846873\pi$
$167$	24.9363	1.92963	0.964816	+	0.262925i	$0.0846873\pi$
$168$	16.8693	1.30150
$169$	−3.87380	−0.297985
$170$	18.8163	1.44314
$171$	0.607831	0.0464820
$172$	−16.1067	−1.22812
$173$	−24.2893	−1.84668	−0.923342	−	0.383978i	$-0.874554\pi$
$173$	−24.2893	−1.84668	−0.923342	+	0.383978i	$0.874554\pi$
$174$	−23.0190	−1.74507
$175$	−14.0080	−1.05890
$176$	54.4107	4.10136
$177$	−5.47575	−0.411583
$178$	−15.5870	−1.16829
$179$	−22.6397	−1.69217	−0.846085	−	0.533047i	$-0.821047\pi$
$179$	−22.6397	−1.69217	−0.846085	+	0.533047i	$0.821047\pi$
$180$	3.04771	0.227163
$181$	−5.25171	−0.390356	−0.195178	−	0.980768i	$-0.562529\pi$
$181$	−5.25171	−0.390356	−0.195178	+	0.980768i	$0.562529\pi$
$182$	−8.83472	−0.654873
$183$	−12.3777	−0.914983
$184$	−54.9694	−4.05240
$185$	34.4519	2.53295
$186$	2.81831	0.206648
$187$	6.14392	0.449288
$188$	35.0855	2.55887
$189$	5.70029	0.414635
$190$	−52.9264	−3.83968
$191$	9.57759	0.693010	0.346505	−	0.938048i	$-0.387368\pi$
$191$	9.57759	0.693010	0.346505	+	0.938048i	$0.387368\pi$
$192$	46.5466	3.35921
$193$	6.37756	0.459067	0.229533	−	0.973301i	$-0.426280\pi$
$193$	6.37756	0.459067	0.229533	+	0.973301i	$0.426280\pi$
$194$	33.1944	2.38322
$195$	21.7243	1.55571
$196$	−31.6028	−2.25734
$197$	−18.0466	−1.28577	−0.642884	−	0.765963i	$-0.722262\pi$
$197$	−18.0466	−1.28577	−0.642884	+	0.765963i	$0.722262\pi$
$198$	1.36327	0.0968832
$199$	−15.2716	−1.08258	−0.541289	−	0.840837i	$-0.682063\pi$
$199$	−15.2716	−1.08258	−0.541289	+	0.840837i	$0.682063\pi$
$200$	−120.854	−8.54565
$201$	−10.9898	−0.775158
$202$	−0.192835	−0.0135679
$203$	−5.36766	−0.376736
$204$	14.9044	1.04351
$205$	48.3857	3.37940
$206$	−18.5991	−1.29586
$207$	−0.787016	−0.0547014
$208$	−43.5555	−3.02003
$209$	−17.2816	−1.19539
$210$	−21.0305	−1.45124
$211$	27.2033	1.87275	0.936376	−	0.350999i	$-0.114158\pi$
$211$	27.2033	1.87275	0.936376	+	0.350999i	$0.114158\pi$
$212$	49.3529	3.38957
$213$	−14.4243	−0.988338
$214$	32.6010	2.22856
$215$	12.6518	0.862846
$216$	49.1792	3.34622
$217$	0.657182	0.0446124
$218$	1.22271	0.0828122
$219$	19.8314	1.34008
$220$	−86.6512	−5.84203
$221$	−4.91817	−0.330832
$222$	37.3842	2.50906
$223$	6.83622	0.457787	0.228894	−	0.973451i	$-0.426489\pi$
$223$	6.83622	0.457787	0.228894	+	0.973451i	$0.426489\pi$
$224$	22.2396	1.48594
$225$	−1.73030	−0.115354
$226$	46.9418	3.12252
$227$	−4.20891	−0.279355	−0.139677	−	0.990197i	$-0.544607\pi$
$227$	−4.20891	−0.279355	−0.139677	+	0.990197i	$0.544607\pi$
$228$	−41.9229	−2.77641
$229$	−8.89902	−0.588064	−0.294032	−	0.955796i	$-0.594997\pi$
$229$	−8.89902	−0.588064	−0.294032	+	0.955796i	$0.594997\pi$
$230$	68.5287	4.51865
$231$	−6.86689	−0.451808
$232$	−46.3094	−3.04036
$233$	4.23563	0.277485	0.138743	−	0.990328i	$-0.455694\pi$
$233$	4.23563	0.277485	0.138743	+	0.990328i	$0.455694\pi$
$234$	−1.09129	−0.0713397
$235$	−27.5596	−1.79779
$236$	−17.4836	−1.13808
$237$	4.48265	0.291179
$238$	4.76109	0.308616
$239$	−10.1935	−0.659363	−0.329682	−	0.944092i	$-0.606941\pi$
$239$	−10.1935	−0.659363	−0.329682	+	0.944092i	$0.606941\pi$
$240$	−103.681	−6.69257
$241$	−7.99921	−0.515275	−0.257637	−	0.966242i	$-0.582944\pi$
$241$	−7.99921	−0.515275	−0.257637	+	0.966242i	$0.582944\pi$
$242$	−8.82333	−0.567185
$243$	1.37840	0.0884242
$244$	−39.5208	−2.53006
$245$	24.8240	1.58595
$246$	52.5039	3.34753
$247$	13.8338	0.880224
$248$	5.66983	0.360035
$249$	26.3252	1.66829
$250$	92.8757	5.87398
$251$	−23.6888	−1.49523	−0.747613	−	0.664135i	$-0.768800\pi$
$251$	−23.6888	−1.49523	−0.747613	+	0.664135i	$0.768800\pi$
$252$	0.771164	0.0485787
$253$	22.3761	1.40677
$254$	42.3638	2.65814
$255$	−11.7074	−0.733145
$256$	35.9708	2.24817
$257$	9.74701	0.608002	0.304001	−	0.952672i	$-0.401677\pi$
$257$	9.74701	0.608002	0.304001	+	0.952672i	$0.401677\pi$
$258$	13.7286	0.854708
$259$	8.71736	0.541671
$260$	69.3638	4.30176
$261$	−0.663027	−0.0410403
$262$	−35.6843	−2.20459
$263$	17.2501	1.06369	0.531843	−	0.846843i	$-0.321500\pi$
$263$	17.2501	1.06369	0.531843	+	0.846843i	$0.321500\pi$
$264$	−59.2440	−3.64622
$265$	−38.7667	−2.38142
$266$	−13.3920	−0.821114
$267$	9.69811	0.593515
$268$	−35.0893	−2.14342
$269$	23.1073	1.40888	0.704439	−	0.709765i	$-0.251199\pi$
$269$	23.1073	1.40888	0.704439	+	0.709765i	$0.251199\pi$
$270$	−61.3102	−3.73122
$271$	13.9376	0.846649	0.423325	−	0.905978i	$-0.360863\pi$
$271$	13.9376	0.846649	0.423325	+	0.905978i	$0.360863\pi$
$272$	23.4723	1.42322
$273$	5.49691	0.332688
$274$	−26.5294	−1.60270
$275$	49.1952	2.96658
$276$	54.2815	3.26736
$277$	18.8182	1.13068	0.565338	−	0.824860i	$-0.308746\pi$
$277$	18.8182	1.13068	0.565338	+	0.824860i	$0.308746\pi$
$278$	−31.6838	−1.90027
$279$	0.0811768	0.00485993
$280$	−42.3088	−2.52844
$281$	−9.81501	−0.585515	−0.292757	−	0.956187i	$-0.594573\pi$
$281$	−9.81501	−0.585515	−0.292757	+	0.956187i	$0.594573\pi$
$282$	−29.9053	−1.78084
$283$	25.6178	1.52282	0.761410	−	0.648270i	$-0.224507\pi$
$283$	25.6178	1.52282	0.761410	+	0.648270i	$0.224507\pi$
$284$	−46.0556	−2.73290
$285$	32.9304	1.95063
$286$	31.0270	1.83467
$287$	12.2430	0.722684
$288$	2.74709	0.161874
$289$	−14.3496	−0.844092
$290$	57.7325	3.39017
$291$	−20.6534	−1.21072
$292$	63.3201	3.70553
$293$	31.2228	1.82406	0.912028	−	0.410127i	$-0.134516\pi$
$293$	31.2228	1.82406	0.912028	+	0.410127i	$0.134516\pi$
$294$	26.9369	1.57099
$295$	13.7334	0.799587
$296$	75.2089	4.37143
$297$	−20.0191	−1.16163
$298$	−19.9177	−1.15380
$299$	−17.9119	−1.03587
$300$	119.341	6.89018
$301$	3.20129	0.184519
$302$	28.1651	1.62072
$303$	0.119981	0.00689273
$304$	−66.0228	−3.78667
$305$	31.0436	1.77755
$306$	0.588102	0.0336196
$307$	21.4160	1.22227	0.611137	−	0.791525i	$-0.290713\pi$
$307$	21.4160	1.22227	0.611137	+	0.791525i	$0.290713\pi$
$308$	−21.9254	−1.24931
$309$	11.5723	0.658323
$310$	−7.06840	−0.401458
$311$	29.6805	1.68303	0.841513	−	0.540237i	$-0.181666\pi$
$311$	29.6805	1.68303	0.841513	+	0.540237i	$0.181666\pi$
$312$	47.4245	2.68488
$313$	13.2207	0.747277	0.373638	−	0.927574i	$-0.378110\pi$
$313$	13.2207	0.747277	0.373638	+	0.927574i	$0.378110\pi$
$314$	−34.0554	−1.92185
$315$	−0.605749	−0.0341301
$316$	14.3127	0.805152
$317$	2.93772	0.164999	0.0824993	−	0.996591i	$-0.473710\pi$
$317$	2.93772	0.164999	0.0824993	+	0.996591i	$0.473710\pi$
$318$	−42.0663	−2.35896
$319$	18.8509	1.05545
$320$	−116.740	−6.52598
$321$	−20.2841	−1.13215
$322$	17.3398	0.966312
$323$	−7.45513	−0.414815
$324$	−46.4108	−2.57838
$325$	−39.3805	−2.18444
$326$	62.3772	3.45476
$327$	−0.760761	−0.0420702
$328$	105.627	5.83226
$329$	−6.97342	−0.384457
$330$	73.8578	4.06574
$331$	−27.2906	−1.50003	−0.750014	−	0.661422i	$-0.769953\pi$
$331$	−27.2906	−1.50003	−0.750014	+	0.661422i	$0.769953\pi$
$332$	84.0541	4.61307
$333$	1.07679	0.0590078
$334$	−67.8642	−3.71337
$335$	27.5627	1.50591
$336$	−26.2344	−1.43120
$337$	23.3795	1.27356	0.636780	−	0.771046i	$-0.280266\pi$
$337$	23.3795	1.27356	0.636780	+	0.771046i	$0.280266\pi$
$338$	10.5425	0.573439
$339$	−29.2069	−1.58630
$340$	−37.3806	−2.02725
$341$	−2.30798	−0.124984
$342$	−1.65421	−0.0894495
$343$	13.8033	0.745308
$344$	27.6191	1.48912
$345$	−42.6382	−2.29556
$346$	66.1034	3.55374
$347$	−13.1373	−0.705250	−0.352625	−	0.935765i	$-0.614711\pi$
$347$	−13.1373	−0.705250	−0.352625	+	0.935765i	$0.614711\pi$
$348$	45.7299	2.45138
$349$	27.2528	1.45881	0.729406	−	0.684082i	$-0.239797\pi$
$349$	27.2528	1.45881	0.729406	+	0.684082i	$0.239797\pi$
$350$	38.1227	2.03775
$351$	16.0252	0.855360
$352$	−78.1040	−4.16296
$353$	10.0534	0.535091	0.267545	−	0.963545i	$-0.413788\pi$
$353$	10.0534	0.535091	0.267545	+	0.963545i	$0.413788\pi$
$354$	14.9022	0.792046
$355$	36.1767	1.92006
$356$	30.9652	1.64115
$357$	−2.96232	−0.156783
$358$	61.6139	3.25640
$359$	36.8202	1.94329	0.971647	−	0.236435i	$-0.0759790\pi$
$359$	36.8202	1.94329	0.971647	+	0.236435i	$0.0759790\pi$
$360$	−5.22609	−0.275439
$361$	1.96974	0.103671
$362$	14.2925	0.751198
$363$	5.48982	0.288141
$364$	17.5511	0.919930
$365$	−49.7379	−2.60340
$366$	33.6858	1.76078
$367$	36.7224	1.91689	0.958446	−	0.285274i	$-0.0920845\pi$
$367$	36.7224	1.91689	0.958446	+	0.285274i	$0.0920845\pi$
$368$	85.4860	4.45626
$369$	1.51229	0.0787268
$370$	−93.7607	−4.87439
$371$	−9.80915	−0.509266
$372$	−5.59888	−0.290288
$373$	−5.65876	−0.293000	−0.146500	−	0.989211i	$-0.546801\pi$
$373$	−5.65876	−0.293000	−0.146500	+	0.989211i	$0.546801\pi$
$374$	−16.7207	−0.864605
$375$	−57.7867	−2.98409
$376$	−60.1631	−3.10268
$377$	−15.0900	−0.777176
$378$	−15.5133	−0.797920
$379$	8.28715	0.425682	0.212841	−	0.977087i	$-0.431728\pi$
$379$	8.28715	0.425682	0.212841	+	0.977087i	$0.431728\pi$
$380$	105.144	5.39377
$381$	−26.3585	−1.35039
$382$	−26.0654	−1.33362
$383$	−3.10483	−0.158649	−0.0793247	−	0.996849i	$-0.525276\pi$
$383$	−3.10483	−0.158649	−0.0793247	+	0.996849i	$0.525276\pi$
$384$	−56.5874	−2.88771
$385$	17.2224	0.877735
$386$	−17.3565	−0.883423
$387$	0.395432	0.0201009
$388$	−65.9444	−3.34782
$389$	−9.01528	−0.457093	−0.228546	−	0.973533i	$-0.573397\pi$
$389$	−9.01528	−0.457093	−0.228546	+	0.973533i	$0.573397\pi$
$390$	−59.1227	−2.99379
$391$	9.65286	0.488166
$392$	54.1912	2.73707
$393$	22.2026	1.11997
$394$	49.1139	2.47432
$395$	−11.2426	−0.565678
$396$	−2.70828	−0.136096
$397$	−3.46020	−0.173663	−0.0868313	−	0.996223i	$-0.527674\pi$
$397$	−3.46020	−0.173663	−0.0868313	+	0.996223i	$0.527674\pi$
$398$	41.5617	2.08330
$399$	8.33240	0.417142
$400$	187.946	9.39732
$401$	−16.6410	−0.831011	−0.415506	−	0.909591i	$-0.636395\pi$
$401$	−16.6410	−0.831011	−0.415506	+	0.909591i	$0.636395\pi$
$402$	29.9086	1.49171
$403$	1.84753	0.0920319
$404$	0.383089	0.0190594
$405$	36.4557	1.81150
$406$	14.6081	0.724986
$407$	−30.6149	−1.51752
$408$	−25.5574	−1.26528
$409$	−6.95127	−0.343718	−0.171859	−	0.985122i	$-0.554977\pi$
$409$	−6.95127	−0.343718	−0.171859	+	0.985122i	$0.554977\pi$
$410$	−131.682	−6.50329
$411$	16.5064	0.814202
$412$	36.9492	1.82036
$413$	3.47496	0.170991
$414$	2.14186	0.105267
$415$	−66.0246	−3.24102
$416$	62.5218	3.06538
$417$	19.7135	0.965373
$418$	47.0318	2.30040
$419$	−3.63004	−0.177339	−0.0886695	−	0.996061i	$-0.528262\pi$
$419$	−3.63004	−0.177339	−0.0886695	+	0.996061i	$0.528262\pi$
$420$	41.7793	2.03862
$421$	−12.5995	−0.614062	−0.307031	−	0.951700i	$-0.599335\pi$
$421$	−12.5995	−0.614062	−0.307031	+	0.951700i	$0.599335\pi$
$422$	−74.0337	−3.60391
$423$	−0.861375	−0.0418815
$424$	−84.6283	−4.10992
$425$	21.2224	1.02944
$426$	39.2558	1.90195
$427$	7.85496	0.380128
$428$	−64.7654	−3.13056
$429$	−19.3048	−0.932045
$430$	−34.4319	−1.66045
$431$	−14.4691	−0.696953	−0.348477	−	0.937317i	$-0.613301\pi$
$431$	−14.4691	−0.696953	−0.348477	+	0.937317i	$0.613301\pi$
$432$	−76.4813	−3.67971
$433$	−12.4410	−0.597874	−0.298937	−	0.954273i	$-0.596632\pi$
$433$	−12.4410	−0.597874	−0.298937	+	0.954273i	$0.596632\pi$
$434$	−1.78852	−0.0858517
$435$	−35.9208	−1.72227
$436$	−2.42904	−0.116330
$437$	−27.1515	−1.29883
$438$	−53.9713	−2.57885
$439$	−0.917307	−0.0437807	−0.0218903	−	0.999760i	$-0.506968\pi$
$439$	−0.917307	−0.0437807	−0.0218903	+	0.999760i	$0.506968\pi$
$440$	148.586	7.08356
$441$	0.775874	0.0369464
$442$	13.3848	0.636650
$443$	−13.5677	−0.644621	−0.322310	−	0.946634i	$-0.604459\pi$
$443$	−13.5677	−0.644621	−0.322310	+	0.946634i	$0.604459\pi$
$444$	−74.2677	−3.52459
$445$	−24.3232	−1.15303
$446$	−18.6048	−0.880961
$447$	12.3927	0.586154
$448$	−29.5388	−1.39558
$449$	−12.8066	−0.604383	−0.302192	−	0.953247i	$-0.597718\pi$
$449$	−12.8066	−0.604383	−0.302192	+	0.953247i	$0.597718\pi$
$450$	4.70902	0.221985
$451$	−42.9968	−2.02464
$452$	−93.2551	−4.38635
$453$	−17.5241	−0.823355
$454$	11.4545	0.537588
$455$	−13.7864	−0.646318
$456$	71.8877	3.36645
$457$	−19.1328	−0.894993	−0.447496	−	0.894286i	$-0.647684\pi$
$457$	−19.1328	−0.894993	−0.447496	+	0.894286i	$0.647684\pi$
$458$	24.2187	1.13166
$459$	−8.63607	−0.403097
$460$	−136.140	−6.34755
$461$	−12.4735	−0.580950	−0.290475	−	0.956883i	$-0.593813\pi$
$461$	−12.4735	−0.580950	−0.290475	+	0.956883i	$0.593813\pi$
$462$	18.6882	0.869456
$463$	23.1793	1.07723	0.538617	−	0.842551i	$-0.318947\pi$
$463$	23.1793	1.07723	0.538617	+	0.842551i	$0.318947\pi$
$464$	72.0183	3.34336
$465$	4.39792	0.203949
$466$	−11.5273	−0.533990
$467$	34.7962	1.61018	0.805089	−	0.593155i	$-0.202118\pi$
$467$	34.7962	1.61018	0.805089	+	0.593155i	$0.202118\pi$
$468$	2.16796	0.100214
$469$	6.97419	0.322038
$470$	75.0035	3.45965
$471$	21.1890	0.976339
$472$	29.9801	1.37995
$473$	−11.2427	−0.516942
$474$	−12.1995	−0.560342
$475$	−59.6943	−2.73896
$476$	−9.45843	−0.433527
$477$	−1.21165	−0.0554777
$478$	27.7416	1.26887
$479$	18.7636	0.857329	0.428665	−	0.903464i	$-0.358984\pi$
$479$	18.7636	0.857329	0.428665	+	0.903464i	$0.358984\pi$
$480$	148.829	6.79309
$481$	24.5070	1.11742
$482$	21.7699	0.991590
$483$	−10.7887	−0.490905
$484$	17.5285	0.796751
$485$	51.7993	2.35209
$486$	−3.75131	−0.170163
$487$	19.1651	0.868452	0.434226	−	0.900804i	$-0.357022\pi$
$487$	19.1651	0.868452	0.434226	+	0.900804i	$0.357022\pi$
$488$	67.7686	3.06774
$489$	−38.8107	−1.75508
$490$	−67.5585	−3.05198
$491$	11.8931	0.536727	0.268364	−	0.963318i	$-0.413517\pi$
$491$	11.8931	0.536727	0.268364	+	0.963318i	$0.413517\pi$
$492$	−104.305	−4.70243
$493$	8.13212	0.366252
$494$	−37.6487	−1.69389
$495$	2.12736	0.0956175
$496$	−8.81746	−0.395916
$497$	9.15379	0.410604
$498$	−71.6441	−3.21045
$499$	2.47939	0.110993	0.0554964	−	0.998459i	$-0.482326\pi$
$499$	2.47939	0.110993	0.0554964	+	0.998459i	$0.482326\pi$
$500$	−184.508	−8.25144
$501$	42.2247	1.88646
$502$	64.4691	2.87740
$503$	−39.9104	−1.77952	−0.889758	−	0.456432i	$-0.849127\pi$
$503$	−39.9104	−1.77952	−0.889758	+	0.456432i	$0.849127\pi$
$504$	−1.32236	−0.0589026
$505$	−0.300916	−0.0133906
$506$	−60.8965	−2.70718
$507$	−6.55951	−0.291318
$508$	−84.1604	−3.73401
$509$	−10.2739	−0.455381	−0.227691	−	0.973734i	$-0.573117\pi$
$509$	−10.2739	−0.455381	−0.227691	+	0.973734i	$0.573117\pi$
$510$	31.8616	1.41086
$511$	−12.5852	−0.556736
$512$	−31.0576	−1.37257
$513$	24.2915	1.07250
$514$	−26.5265	−1.17003
$515$	−29.0236	−1.27893
$516$	−27.2735	−1.20065
$517$	24.4902	1.07708
$518$	−23.7243	−1.04239
$519$	−41.1291	−1.80537
$520$	−118.942	−5.21596
$521$	−4.33563	−0.189947	−0.0949737	−	0.995480i	$-0.530277\pi$
$521$	−4.33563	−0.189947	−0.0949737	+	0.995480i	$0.530277\pi$
$522$	1.80443	0.0789776
$523$	3.51882	0.153867	0.0769337	−	0.997036i	$-0.475487\pi$
$523$	3.51882	0.153867	0.0769337	+	0.997036i	$0.475487\pi$
$524$	70.8909	3.09688
$525$	−23.7197	−1.03521
$526$	−46.9461	−2.04695
$527$	−0.995645	−0.0433710
$528$	92.1336	4.00960
$529$	12.1556	0.528505
$530$	105.504	4.58278
$531$	0.429236	0.0186272
$532$	26.6046	1.15346
$533$	34.4187	1.49084
$534$	−26.3934	−1.14215
$535$	50.8733	2.19944
$536$	60.1698	2.59894
$537$	−38.3358	−1.65431
$538$	−62.8865	−2.71123
$539$	−22.0593	−0.950161
$540$	121.800	5.24142
$541$	45.4558	1.95430	0.977148	−	0.212559i	$-0.0681799\pi$
$541$	45.4558	1.95430	0.977148	+	0.212559i	$0.0681799\pi$
$542$	−37.9312	−1.62928
$543$	−8.89272	−0.381623
$544$	−33.6934	−1.44459
$545$	1.90801	0.0817304
$546$	−14.9598	−0.640222
$547$	−17.4530	−0.746238	−0.373119	−	0.927783i	$-0.621712\pi$
$547$	−17.4530	−0.746238	−0.373119	+	0.927783i	$0.621712\pi$
$548$	52.7036	2.25139
$549$	0.970265	0.0414099
$550$	−133.885	−5.70887
$551$	−22.8740	−0.974464
$552$	−93.0798	−3.96174
$553$	−2.84472	−0.120970
$554$	−51.2137	−2.17586
$555$	58.3373	2.47628
$556$	62.9434	2.66939
$557$	16.2633	0.689100	0.344550	−	0.938768i	$-0.388032\pi$
$557$	16.2633	0.689100	0.344550	+	0.938768i	$0.388032\pi$
$558$	−0.220923	−0.00935240
$559$	8.99975	0.380649
$560$	65.7967	2.78042
$561$	10.4035	0.439236
$562$	26.7115	1.12676
$563$	21.0947	0.889035	0.444517	−	0.895770i	$-0.353375\pi$
$563$	21.0947	0.889035	0.444517	+	0.895770i	$0.353375\pi$
$564$	59.4102	2.50162
$565$	73.2519	3.08173
$566$	−69.7188	−2.93050
$567$	9.22440	0.387388
$568$	78.9742	3.31368
$569$	27.9844	1.17317	0.586583	−	0.809889i	$-0.300473\pi$
$569$	27.9844	1.17317	0.586583	+	0.809889i	$0.300473\pi$
$570$	−89.6202	−3.75378
$571$	−24.2397	−1.01440	−0.507199	−	0.861829i	$-0.669319\pi$
$571$	−24.2397	−1.01440	−0.507199	+	0.861829i	$0.669319\pi$
$572$	−61.6386	−2.57724
$573$	16.2177	0.677505
$574$	−33.3194	−1.39073
$575$	77.2918	3.22329
$576$	−3.64872	−0.152030
$577$	28.9872	1.20675	0.603376	−	0.797457i	$-0.293822\pi$
$577$	28.9872	1.20675	0.603376	+	0.797457i	$0.293822\pi$
$578$	39.0523	1.62436
$579$	10.7991	0.448796
$580$	−114.692	−4.76233
$581$	−16.7062	−0.693090
$582$	56.2081	2.32990
$583$	34.4492	1.42674
$584$	−108.579	−4.49302
$585$	−1.70294	−0.0704077
$586$	−84.9729	−3.51020
$587$	32.3813	1.33652	0.668260	−	0.743928i	$-0.267039\pi$
$587$	32.3813	1.33652	0.668260	+	0.743928i	$0.267039\pi$
$588$	−53.5130	−2.20684
$589$	2.80055	0.115394
$590$	−37.3753	−1.53872
$591$	−30.5584	−1.25700
$592$	−116.962	−4.80709
$593$	−7.02600	−0.288523	−0.144262	−	0.989540i	$-0.546081\pi$
$593$	−7.02600	−0.288523	−0.144262	+	0.989540i	$0.546081\pi$
$594$	54.4819	2.23542
$595$	7.42960	0.304584
$596$	39.5687	1.62080
$597$	−25.8595	−1.05836
$598$	48.7473	1.99343
$599$	25.8167	1.05484	0.527420	−	0.849605i	$-0.323159\pi$
$599$	25.8167	1.05484	0.527420	+	0.849605i	$0.323159\pi$
$600$	−204.642	−8.35446
$601$	21.3001	0.868849	0.434424	−	0.900708i	$-0.356952\pi$
$601$	21.3001	0.868849	0.434424	+	0.900708i	$0.356952\pi$
$602$	−8.71231	−0.355087
$603$	0.861471	0.0350818
$604$	−55.9530	−2.27670
$605$	−13.7687	−0.559775
$606$	−0.326528	−0.0132643
$607$	12.1455	0.492971	0.246486	−	0.969146i	$-0.420724\pi$
$607$	12.1455	0.492971	0.246486	+	0.969146i	$0.420724\pi$
$608$	94.7727	3.84354
$609$	−9.08905	−0.368307
$610$	−84.4850	−3.42070
$611$	−19.6043	−0.793105
$612$	−1.16833	−0.0472270
$613$	10.7052	0.432379	0.216190	−	0.976351i	$-0.430637\pi$
$613$	10.7052	0.432379	0.216190	+	0.976351i	$0.430637\pi$
$614$	−58.2835	−2.35213
$615$	81.9315	3.30380
$616$	37.5968	1.51482
$617$	2.36894	0.0953699	0.0476850	−	0.998862i	$-0.484816\pi$
$617$	2.36894	0.0953699	0.0476850	+	0.998862i	$0.484816\pi$
$618$	−31.4939	−1.26687
$619$	−14.2987	−0.574712	−0.287356	−	0.957824i	$-0.592776\pi$
$619$	−14.2987	−0.574712	−0.287356	+	0.957824i	$0.592776\pi$
$620$	14.0422	0.563947
$621$	−31.4525	−1.26214
$622$	−80.7754	−3.23880
$623$	−6.15450	−0.246575
$624$	−73.7524	−2.95246
$625$	79.7522	3.19009
$626$	−35.9800	−1.43805
$627$	−29.2629	−1.16865
$628$	67.6547	2.69972
$629$	−13.2070	−0.526597
$630$	1.64855	0.0656797
$631$	−30.3615	−1.20867	−0.604336	−	0.796730i	$-0.706561\pi$
$631$	−30.3615	−1.20867	−0.604336	+	0.796730i	$0.706561\pi$
$632$	−24.5428	−0.976261
$633$	46.0633	1.83085
$634$	−7.99500	−0.317522
$635$	66.1080	2.62342
$636$	83.5693	3.31374
$637$	17.6583	0.699649
$638$	−51.3027	−2.03109
$639$	1.13070	0.0447298
$640$	141.923	5.61000
$641$	13.6745	0.540112	0.270056	−	0.962845i	$-0.412958\pi$
$641$	13.6745	0.540112	0.270056	+	0.962845i	$0.412958\pi$
$642$	55.2032	2.17870
$643$	−6.23926	−0.246053	−0.123026	−	0.992403i	$-0.539260\pi$
$643$	−6.23926	−0.246053	−0.123026	+	0.992403i	$0.539260\pi$
$644$	−34.4475	−1.35742
$645$	21.4233	0.843542
$646$	20.2891	0.798265
$647$	−35.7714	−1.40632	−0.703160	−	0.711031i	$-0.748228\pi$
$647$	−35.7714	−1.40632	−0.703160	+	0.711031i	$0.748228\pi$
$648$	79.5834	3.12633
$649$	−12.2038	−0.479043
$650$	107.174	4.20371
$651$	1.11281	0.0436143
$652$	−123.919	−4.85305
$653$	2.16461	0.0847079	0.0423539	−	0.999103i	$-0.486514\pi$
$653$	2.16461	0.0847079	0.0423539	+	0.999103i	$0.486514\pi$
$654$	2.07041	0.0809595
$655$	−55.6848	−2.17578
$656$	−164.266	−6.41350
$657$	−1.55456	−0.0606490
$658$	18.9782	0.739846
$659$	−10.0287	−0.390662	−0.195331	−	0.980737i	$-0.562578\pi$
$659$	−10.0287	−0.390662	−0.195331	+	0.980737i	$0.562578\pi$
$660$	−146.727	−5.71132
$661$	16.5455	0.643546	0.321773	−	0.946817i	$-0.395721\pi$
$661$	16.5455	0.643546	0.321773	+	0.946817i	$0.395721\pi$
$662$	74.2714	2.88664
$663$	−8.32794	−0.323430
$664$	−144.133	−5.59343
$665$	−20.8979	−0.810387
$666$	−2.93049	−0.113554
$667$	29.6171	1.14678
$668$	134.820	5.21633
$669$	11.5758	0.447545
$670$	−75.0118	−2.89796
$671$	−27.5862	−1.06495
$672$	37.6583	1.45270
$673$	33.0711	1.27480	0.637398	−	0.770535i	$-0.280011\pi$
$673$	33.0711	1.27480	0.637398	+	0.770535i	$0.280011\pi$
$674$	−63.6272	−2.45083
$675$	−69.1503	−2.66160
$676$	−20.9439	−0.805536
$677$	15.4948	0.595512	0.297756	−	0.954642i	$-0.403762\pi$
$677$	15.4948	0.595512	0.297756	+	0.954642i	$0.403762\pi$
$678$	79.4865	3.05266
$679$	13.1068	0.502993
$680$	64.0988	2.45808
$681$	−7.12694	−0.273105
$682$	6.28118	0.240519
$683$	19.8347	0.758954	0.379477	−	0.925201i	$-0.376104\pi$
$683$	19.8347	0.758954	0.379477	+	0.925201i	$0.376104\pi$
$684$	3.28627	0.125654
$685$	−41.3987	−1.58176
$686$	−37.5657	−1.43426
$687$	−15.0687	−0.574907
$688$	−42.9520	−1.63753
$689$	−27.5764	−1.05058
$690$	116.040	4.41756
$691$	−23.2738	−0.885376	−0.442688	−	0.896676i	$-0.645975\pi$
$691$	−23.2738	−0.885376	−0.442688	+	0.896676i	$0.645975\pi$
$692$	−131.322	−4.99210
$693$	0.538285	0.0204478
$694$	35.7533	1.35718
$695$	−49.4420	−1.87544
$696$	−78.4157	−2.97234
$697$	−18.5485	−0.702574
$698$	−74.1686	−2.80732
$699$	7.17219	0.271277
$700$	−75.7350	−2.86251
$701$	26.0679	0.984571	0.492285	−	0.870434i	$-0.336162\pi$
$701$	26.0679	0.984571	0.492285	+	0.870434i	$0.336162\pi$
$702$	−43.6125	−1.64605
$703$	37.1486	1.40108
$704$	103.739	3.90980
$705$	−46.6667	−1.75757
$706$	−27.3604	−1.02972
$707$	−0.0761409	−0.00286357
$708$	−29.6050	−1.11262
$709$	39.3998	1.47969	0.739845	−	0.672777i	$-0.234899\pi$
$709$	39.3998	1.47969	0.739845	+	0.672777i	$0.234899\pi$
$710$	−98.4547	−3.69494
$711$	−0.351388	−0.0131781
$712$	−53.0979	−1.98993
$713$	−3.62613	−0.135800
$714$	8.06196	0.301711
$715$	48.4171	1.81070
$716$	−122.403	−4.57441
$717$	−17.2607	−0.644611
$718$	−100.206	−3.73966
$719$	32.8085	1.22355	0.611776	−	0.791031i	$-0.290456\pi$
$719$	32.8085	1.22355	0.611776	+	0.791031i	$0.290456\pi$
$720$	8.12739	0.302890
$721$	−7.34385	−0.273499
$722$	−5.36065	−0.199503
$723$	−13.5451	−0.503746
$724$	−28.3937	−1.05524
$725$	65.1150	2.41831
$726$	−14.9405	−0.554496
$727$	−6.01598	−0.223120	−0.111560	−	0.993758i	$-0.535585\pi$
$727$	−6.01598	−0.223120	−0.111560	+	0.993758i	$0.535585\pi$
$728$	−30.0960	−1.11543
$729$	28.0866	1.04024
$730$	135.362	5.00996
$731$	−4.85003	−0.179385
$732$	−66.9205	−2.47345
$733$	14.5213	0.536358	0.268179	−	0.963369i	$-0.413578\pi$
$733$	14.5213	0.536358	0.268179	+	0.963369i	$0.413578\pi$
$734$	−99.9399	−3.68885
$735$	42.0345	1.55047
$736$	−122.711	−4.52319
$737$	−24.4930	−0.902209
$738$	−4.11570	−0.151501
$739$	−13.8455	−0.509315	−0.254657	−	0.967031i	$-0.581963\pi$
$739$	−13.8455	−0.509315	−0.254657	+	0.967031i	$0.581963\pi$
$740$	186.266	6.84727
$741$	23.4248	0.860531
$742$	26.6956	0.980026
$743$	−8.62887	−0.316562	−0.158281	−	0.987394i	$-0.550595\pi$
$743$	−8.62887	−0.316562	−0.158281	+	0.987394i	$0.550595\pi$
$744$	9.60072	0.351980
$745$	−31.0813	−1.13873
$746$	15.4003	0.563846
$747$	−2.06359	−0.0755030
$748$	33.2174	1.21455
$749$	12.8725	0.470350
$750$	157.266	5.74256
$751$	−29.8980	−1.09100	−0.545498	−	0.838112i	$-0.683659\pi$
$751$	−29.8980	−1.09100	−0.545498	+	0.838112i	$0.683659\pi$
$752$	93.5629	3.41189
$753$	−40.1123	−1.46177
$754$	41.0675	1.49559
$755$	43.9511	1.59954
$756$	30.8190	1.12087
$757$	29.9860	1.08986	0.544930	−	0.838481i	$-0.316556\pi$
$757$	29.9860	1.08986	0.544930	+	0.838481i	$0.316556\pi$
$758$	−22.5535	−0.819179
$759$	37.8894	1.37530
$760$	−180.297	−6.54005
$761$	−0.545214	−0.0197640	−0.00988200	−	0.999951i	$-0.503146\pi$
$761$	−0.545214	−0.0197640	−0.00988200	+	0.999951i	$0.503146\pi$
$762$	71.7347	2.59867
$763$	0.482785	0.0174780
$764$	51.7818	1.87340
$765$	0.917724	0.0331804
$766$	8.44979	0.305303
$767$	9.76910	0.352742
$768$	60.9093	2.19787
$769$	29.3319	1.05774	0.528868	−	0.848704i	$-0.322617\pi$
$769$	29.3319	1.05774	0.528868	+	0.848704i	$0.322617\pi$
$770$	−46.8707	−1.68910
$771$	16.5046	0.594399
$772$	34.4806	1.24099
$773$	37.9331	1.36436	0.682180	−	0.731184i	$-0.261032\pi$
$773$	37.9331	1.36436	0.682180	+	0.731184i	$0.261032\pi$
$774$	−1.07617	−0.0386820
$775$	−7.97228	−0.286373
$776$	113.079	4.05929
$777$	14.7611	0.529552
$778$	24.5351	0.879625
$779$	52.1731	1.86929
$780$	117.454	4.20552
$781$	−32.1476	−1.15033
$782$	−26.2702	−0.939422
$783$	−26.4974	−0.946938
$784$	−84.2757	−3.00985
$785$	−53.1428	−1.89675
$786$	−60.4243	−2.15526
$787$	−44.9788	−1.60332	−0.801661	−	0.597780i	$-0.796050\pi$
$787$	−44.9788	−1.60332	−0.801661	+	0.597780i	$0.796050\pi$
$788$	−97.5701	−3.47579
$789$	29.2096	1.03989
$790$	30.5968	1.08859
$791$	18.5349	0.659027
$792$	4.64405	0.165019
$793$	22.0826	0.784175
$794$	9.41694	0.334195
$795$	−65.6437	−2.32814
$796$	−82.5670	−2.92651
$797$	−46.4690	−1.64602	−0.823009	−	0.568028i	$-0.807706\pi$
$797$	−46.4690	−1.64602	−0.823009	+	0.568028i	$0.807706\pi$
$798$	−22.6766	−0.802744
$799$	10.5649	0.373759
$800$	−269.788	−9.53845
$801$	−0.760220	−0.0268611
$802$	45.2884	1.59919
$803$	44.1985	1.55973
$804$	−59.4168	−2.09547
$805$	27.0585	0.953688
$806$	−5.02805	−0.177105
$807$	39.1276	1.37736
$808$	−0.656905	−0.0231098
$809$	11.7536	0.413234	0.206617	−	0.978422i	$-0.433755\pi$
$809$	11.7536	0.413234	0.206617	+	0.978422i	$0.433755\pi$
$810$	−99.2142	−3.48603
$811$	−17.5617	−0.616675	−0.308338	−	0.951277i	$-0.599773\pi$
$811$	−17.5617	−0.616675	−0.308338	+	0.951277i	$0.599773\pi$
$812$	−29.0205	−1.01842
$813$	23.6005	0.827707
$814$	83.3183	2.92031
$815$	97.3386	3.40962
$816$	39.7457	1.39138
$817$	13.6421	0.477278
$818$	18.9179	0.661448
$819$	−0.430894	−0.0150567
$820$	261.600	9.13547
$821$	30.7944	1.07473	0.537365	−	0.843350i	$-0.319420\pi$
$821$	30.7944	1.07473	0.537365	+	0.843350i	$0.319420\pi$
$822$	−44.9222	−1.56684
$823$	4.29005	0.149542	0.0747708	−	0.997201i	$-0.476177\pi$
$823$	4.29005	0.149542	0.0747708	+	0.997201i	$0.476177\pi$
$824$	−63.3590	−2.20722
$825$	83.3023	2.90021
$826$	−9.45709	−0.329054
$827$	−8.29038	−0.288285	−0.144142	−	0.989557i	$-0.546042\pi$
$827$	−8.29038	−0.288285	−0.144142	+	0.989557i	$0.546042\pi$
$828$	−4.25505	−0.147873
$829$	10.2305	0.355321	0.177660	−	0.984092i	$-0.443147\pi$
$829$	10.2305	0.355321	0.177660	+	0.984092i	$0.443147\pi$
$830$	179.686	6.23698
$831$	31.8648	1.10538
$832$	−83.0422	−2.87897
$833$	−9.51620	−0.329717
$834$	−53.6502	−1.85775
$835$	−105.901	−3.66485
$836$	−93.4338	−3.23148
$837$	3.24417	0.112135
$838$	9.87915	0.341270
$839$	32.5453	1.12359	0.561794	−	0.827277i	$-0.310112\pi$
$839$	32.5453	1.12359	0.561794	+	0.827277i	$0.310112\pi$
$840$	−71.6415	−2.47187
$841$	−4.04888	−0.139616
$842$	34.2895	1.18169
$843$	−16.6198	−0.572415
$844$	147.076	5.06257
$845$	16.4515	0.565947
$846$	2.34423	0.0805964
$847$	−3.48389	−0.119708
$848$	131.610	4.51951
$849$	43.3786	1.48875
$850$	−57.7568	−1.98104
$851$	−48.0997	−1.64884
$852$	−77.9859	−2.67175
$853$	15.3743	0.526406	0.263203	−	0.964741i	$-0.415221\pi$
$853$	15.3743	0.526406	0.263203	+	0.964741i	$0.415221\pi$
$854$	−21.3773	−0.731515
$855$	−2.58137	−0.0882809
$856$	111.057	3.79585
$857$	7.86650	0.268715	0.134357	−	0.990933i	$-0.457103\pi$
$857$	7.86650	0.268715	0.134357	+	0.990933i	$0.457103\pi$
$858$	52.5380	1.79362
$859$	−2.70326	−0.0922341	−0.0461170	−	0.998936i	$-0.514685\pi$
$859$	−2.70326	−0.0922341	−0.0461170	+	0.998936i	$0.514685\pi$
$860$	68.4027	2.33251
$861$	20.7311	0.706515
$862$	39.3777	1.34121
$863$	0.0150192	0.000511261 0	0.000255630	−	1.00000i	$-0.499919\pi$
$863$	0.0150192	0.000511261 0	0.000255630		1.00000i	$0.499919\pi$
$864$	109.785	3.73497
$865$	103.153	3.50732
$866$	33.8581	1.15054
$867$	−24.2981	−0.825207
$868$	3.55309	0.120600
$869$	9.99050	0.338905
$870$	97.7585	3.31432
$871$	19.6065	0.664340
$872$	4.16522	0.141052
$873$	1.61899	0.0547944
$874$	73.8928	2.49946
$875$	36.6719	1.23974
$876$	107.220	3.62262
$877$	−46.3300	−1.56445	−0.782227	−	0.622994i	$-0.785916\pi$
$877$	−46.3300	−1.56445	−0.782227	+	0.622994i	$0.785916\pi$
$878$	2.49645	0.0842511
$879$	52.8696	1.78325
$880$	−231.074	−7.78951
$881$	−17.4380	−0.587500	−0.293750	−	0.955882i	$-0.594903\pi$
$881$	−17.4380	−0.587500	−0.293750	+	0.955882i	$0.594903\pi$
$882$	−2.11154	−0.0710992
$883$	21.4266	0.721062	0.360531	−	0.932747i	$-0.382596\pi$
$883$	21.4266	0.721062	0.360531	+	0.932747i	$0.382596\pi$
$884$	−26.5904	−0.894331
$885$	23.2547	0.781698
$886$	36.9245	1.24050
$887$	1.39466	0.0468281	0.0234141	−	0.999726i	$-0.492546\pi$
$887$	1.39466	0.0468281	0.0234141	+	0.999726i	$0.492546\pi$
$888$	127.351	4.27363
$889$	16.7273	0.561017
$890$	66.1955	2.21888
$891$	−32.3956	−1.08529
$892$	36.9604	1.23753
$893$	−29.7169	−0.994437
$894$	−33.7267	−1.12799
$895$	96.1475	3.21386
$896$	35.9108	1.19970
$897$	−30.3303	−1.01270
$898$	34.8533	1.16307
$899$	−3.05486	−0.101885
$900$	−9.35499	−0.311833
$901$	14.8611	0.495095
$902$	117.016	3.89620
$903$	5.42075	0.180391
$904$	159.910	5.31853
$905$	22.3032	0.741385
$906$	47.6919	1.58446
$907$	0.618462	0.0205357	0.0102678	−	0.999947i	$-0.496732\pi$
$907$	0.618462	0.0205357	0.0102678	+	0.999947i	$0.496732\pi$
$908$	−22.7557	−0.755174
$909$	−0.00940513	−0.000311948 0
$910$	37.5198	1.24377
$911$	26.6949	0.884440	0.442220	−	0.896907i	$-0.354191\pi$
$911$	26.6949	0.884440	0.442220	+	0.896907i	$0.354191\pi$
$912$	−111.796	−3.70195
$913$	58.6712	1.94173
$914$	52.0698	1.72232
$915$	52.5661	1.73778
$916$	−48.1131	−1.58970
$917$	−14.0899	−0.465291
$918$	23.5031	0.775717
$919$	−29.7363	−0.980910	−0.490455	−	0.871467i	$-0.663169\pi$
$919$	−29.7363	−0.980910	−0.490455	+	0.871467i	$0.663169\pi$
$920$	233.447	7.69652
$921$	36.2636	1.19493
$922$	33.9467	1.11798
$923$	25.7339	0.847043
$924$	−37.1263	−1.22136
$925$	−105.750	−3.47705
$926$	−63.0825	−2.07302
$927$	−0.907132	−0.0297941
$928$	−103.379	−3.39358
$929$	−58.1847	−1.90898	−0.954489	−	0.298247i	$-0.903598\pi$
$929$	−58.1847	−1.90898	−0.954489	+	0.298247i	$0.903598\pi$
$930$	−11.9689	−0.392477
$931$	26.7671	0.877256
$932$	22.9002	0.750120
$933$	50.2579	1.64537
$934$	−94.6979	−3.09861
$935$	−26.0923	−0.853310
$936$	−3.71754	−0.121511
$937$	30.4410	0.994464	0.497232	−	0.867618i	$-0.334350\pi$
$937$	30.4410	0.994464	0.497232	+	0.867618i	$0.334350\pi$
$938$	−18.9803	−0.619728
$939$	22.3866	0.730558
$940$	−149.003	−4.85993
$941$	0.248625	0.00810495	0.00405247	−	0.999992i	$-0.498710\pi$
$941$	0.248625	0.00810495	0.00405247	+	0.999992i	$0.498710\pi$
$942$	−57.6659	−1.87886
$943$	−67.5534	−2.19984
$944$	−46.6238	−1.51747
$945$	−24.2083	−0.787496
$946$	30.5971	0.994798
$947$	53.3363	1.73320	0.866599	−	0.499005i	$-0.166301\pi$
$947$	53.3363	1.73320	0.866599	+	0.499005i	$0.166301\pi$
$948$	24.2357	0.787139
$949$	−35.3806	−1.14850
$950$	162.458	5.27083
$951$	4.97444	0.161307
$952$	16.2189	0.525659
$953$	25.6815	0.831907	0.415953	−	0.909386i	$-0.363448\pi$
$953$	25.6815	0.831907	0.415953	+	0.909386i	$0.363448\pi$
$954$	3.29751	0.106761
$955$	−40.6746	−1.31620
$956$	−55.1118	−1.78244
$957$	31.9202	1.03183
$958$	−51.0650	−1.64984
$959$	−10.4751	−0.338259
$960$	−197.676	−6.37998
$961$	−30.6260	−0.987935
$962$	−66.6958	−2.15036
$963$	1.59004	0.0512384
$964$	−43.2482	−1.39293
$965$	−27.0845	−0.871882
$966$	29.3616	0.944693
$967$	−26.1863	−0.842094	−0.421047	−	0.907039i	$-0.638337\pi$
$967$	−26.1863	−0.842094	−0.421047	+	0.907039i	$0.638337\pi$
$968$	−30.0572	−0.966074
$969$	−12.6238	−0.405534
$970$	−140.972	−4.52633
$971$	20.4404	0.655965	0.327983	−	0.944684i	$-0.393631\pi$
$971$	20.4404	0.655965	0.327983	+	0.944684i	$0.393631\pi$
$972$	7.45238	0.239035
$973$	−12.5103	−0.401063
$974$	−52.1577	−1.67124
$975$	−66.6830	−2.13557
$976$	−105.391	−3.37347
$977$	48.7663	1.56017	0.780087	−	0.625672i	$-0.215175\pi$
$977$	48.7663	1.56017	0.780087	+	0.625672i	$0.215175\pi$
$978$	105.623	3.37746
$979$	21.6142	0.690794
$980$	134.212	4.28726
$981$	0.0596349	0.00190400
$982$	−32.3670	−1.03287
$983$	−19.0939	−0.609000	−0.304500	−	0.952512i	$-0.598489\pi$
$983$	−19.0939	−0.609000	−0.304500	+	0.952512i	$0.598489\pi$
$984$	178.858	5.70177
$985$	76.6414	2.44200
$986$	−22.1316	−0.704812
$987$	−11.8081	−0.375856
$988$	74.7932	2.37949
$989$	−17.6637	−0.561674
$990$	−5.78960	−0.184005
$991$	17.3482	0.551085	0.275543	−	0.961289i	$-0.411143\pi$
$991$	17.3482	0.551085	0.275543	+	0.961289i	$0.411143\pi$
$992$	12.6571	0.401862
$993$	−46.2112	−1.46647
$994$	−24.9120	−0.790162
$995$	64.8564	2.05609
$996$	142.329	4.50986
$997$	−8.07898	−0.255864	−0.127932	−	0.991783i	$-0.540834\pi$
$997$	−8.07898	−0.255864	−0.127932	+	0.991783i	$0.540834\pi$
$998$	−6.74766	−0.213593
$999$	43.0331	1.36151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.5	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.5	✓	340	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72150 q^{2} +1.69330 q^{3} +5.40656 q^{4} -4.24685 q^{5} -4.60831 q^{6} -1.07458 q^{7} -9.27094 q^{8} -0.132735 q^{9} +O(q^{10})\)	\(q-2.72150 q^{2} +1.69330 q^{3} +5.40656 q^{4} -4.24685 q^{5} -4.60831 q^{6} -1.07458 q^{7} -9.27094 q^{8} -0.132735 q^{9} +11.5578 q^{10} +3.77387 q^{11} +9.15492 q^{12} -3.02096 q^{13} +2.92447 q^{14} -7.19120 q^{15} +14.4178 q^{16} +1.62802 q^{17} +0.361239 q^{18} -4.57927 q^{19} -22.9609 q^{20} -1.81959 q^{21} -10.2706 q^{22} +5.92922 q^{23} -15.6985 q^{24} +13.0358 q^{25} +8.22154 q^{26} -5.30466 q^{27} -5.80979 q^{28} +4.99511 q^{29} +19.5708 q^{30} -0.611570 q^{31} -20.6960 q^{32} +6.39029 q^{33} -4.43064 q^{34} +4.56359 q^{35} -0.717641 q^{36} -8.11233 q^{37} +12.4625 q^{38} -5.11539 q^{39} +39.3723 q^{40} -11.3933 q^{41} +4.95201 q^{42} -2.97910 q^{43} +20.4036 q^{44} +0.563707 q^{45} -16.1364 q^{46} +6.48943 q^{47} +24.4136 q^{48} -5.84527 q^{49} -35.4768 q^{50} +2.75672 q^{51} -16.3330 q^{52} +9.12834 q^{53} +14.4366 q^{54} -16.0271 q^{55} +9.96239 q^{56} -7.75408 q^{57} -13.5942 q^{58} -3.23377 q^{59} -38.8796 q^{60} -7.30978 q^{61} +1.66439 q^{62} +0.142635 q^{63} +27.4887 q^{64} +12.8296 q^{65} -17.3912 q^{66} -6.49014 q^{67} +8.80196 q^{68} +10.0399 q^{69} -12.4198 q^{70} -8.51846 q^{71} +1.23058 q^{72} +11.7117 q^{73} +22.0777 q^{74} +22.0734 q^{75} -24.7581 q^{76} -4.05533 q^{77} +13.9215 q^{78} +2.64728 q^{79} -61.2301 q^{80} -8.58418 q^{81} +31.0069 q^{82} +15.5467 q^{83} -9.83772 q^{84} -6.91394 q^{85} +8.10763 q^{86} +8.45822 q^{87} -34.9873 q^{88} +5.72734 q^{89} -1.53413 q^{90} +3.24627 q^{91} +32.0567 q^{92} -1.03557 q^{93} -17.6610 q^{94} +19.4475 q^{95} -35.0446 q^{96} -12.1971 q^{97} +15.9079 q^{98} -0.500925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more