LMFDB - Embedded newform 8023.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60713 q^{2} -0.132138 q^{3} +4.79710 q^{4} -1.04101 q^{5} +0.344501 q^{6} +4.69646 q^{7} -7.29239 q^{8} -2.98254 q^{9} +O(q^{10})$	\(q-2.60713 q^{2} -0.132138 q^{3} +4.79710 q^{4} -1.04101 q^{5} +0.344501 q^{6} +4.69646 q^{7} -7.29239 q^{8} -2.98254 q^{9} +2.71405 q^{10} +4.69565 q^{11} -0.633881 q^{12} -0.770799 q^{13} -12.2443 q^{14} +0.137558 q^{15} +9.41798 q^{16} +2.52012 q^{17} +7.77585 q^{18} -0.742339 q^{19} -4.99384 q^{20} -0.620582 q^{21} -12.2422 q^{22} +2.34793 q^{23} +0.963604 q^{24} -3.91629 q^{25} +2.00957 q^{26} +0.790522 q^{27} +22.5294 q^{28} +9.05133 q^{29} -0.358630 q^{30} -6.01808 q^{31} -9.96907 q^{32} -0.620476 q^{33} -6.57026 q^{34} -4.88907 q^{35} -14.3075 q^{36} +0.990473 q^{37} +1.93537 q^{38} +0.101852 q^{39} +7.59147 q^{40} +2.46733 q^{41} +1.61794 q^{42} -4.95908 q^{43} +22.5255 q^{44} +3.10486 q^{45} -6.12134 q^{46} -1.31549 q^{47} -1.24448 q^{48} +15.0567 q^{49} +10.2103 q^{50} -0.333004 q^{51} -3.69760 q^{52} +7.66011 q^{53} -2.06099 q^{54} -4.88823 q^{55} -34.2484 q^{56} +0.0980914 q^{57} -23.5979 q^{58} -1.77387 q^{59} +0.659878 q^{60} -5.27936 q^{61} +15.6899 q^{62} -14.0074 q^{63} +7.15464 q^{64} +0.802411 q^{65} +1.61766 q^{66} -1.78634 q^{67} +12.0892 q^{68} -0.310251 q^{69} +12.7464 q^{70} +1.00000 q^{71} +21.7499 q^{72} +0.555267 q^{73} -2.58229 q^{74} +0.517492 q^{75} -3.56108 q^{76} +22.0530 q^{77} -0.265541 q^{78} +7.22184 q^{79} -9.80423 q^{80} +8.84316 q^{81} -6.43264 q^{82} +5.79165 q^{83} -2.97700 q^{84} -2.62347 q^{85} +12.9289 q^{86} -1.19603 q^{87} -34.2426 q^{88} -5.40418 q^{89} -8.09476 q^{90} -3.62003 q^{91} +11.2632 q^{92} +0.795218 q^{93} +3.42965 q^{94} +0.772785 q^{95} +1.31729 q^{96} +13.6023 q^{97} -39.2548 q^{98} -14.0050 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	−2.60713	−1.84352	−0.921758	−	0.387766i	$-0.873247\pi$
$2$	−2.60713	−1.84352	−0.921758	+	0.387766i	$0.873247\pi$
$3$	−0.132138	−0.0762901	−0.0381450	−	0.999272i	$-0.512145\pi$
$3$	−0.132138	−0.0762901	−0.0381450	+	0.999272i	$0.512145\pi$
$4$	4.79710	2.39855
$5$	−1.04101	−0.465555	−0.232777	−	0.972530i	$-0.574781\pi$
$5$	−1.04101	−0.465555	−0.232777	+	0.972530i	$0.574781\pi$
$6$	0.344501	0.140642
$7$	4.69646	1.77510	0.887548	−	0.460716i	$-0.152407\pi$
$7$	4.69646	1.77510	0.887548	+	0.460716i	$0.152407\pi$
$8$	−7.29239	−2.57825
$9$	−2.98254	−0.994180
$10$	2.71405	0.858258
$11$	4.69565	1.41579	0.707897	−	0.706316i	$-0.249644\pi$
$11$	4.69565	1.41579	0.707897	+	0.706316i	$0.249644\pi$
$12$	−0.633881	−0.182986
$13$	−0.770799	−0.213781	−0.106891	−	0.994271i	$-0.534089\pi$
$13$	−0.770799	−0.213781	−0.106891	+	0.994271i	$0.534089\pi$
$14$	−12.2443	−3.27242
$15$	0.137558	0.0355172
$16$	9.41798	2.35450
$17$	2.52012	0.611218	0.305609	−	0.952157i	$-0.401140\pi$
$17$	2.52012	0.611218	0.305609	+	0.952157i	$0.401140\pi$
$18$	7.77585	1.83279
$19$	−0.742339	−0.170304	−0.0851522	−	0.996368i	$-0.527138\pi$
$19$	−0.742339	−0.170304	−0.0851522	+	0.996368i	$0.527138\pi$
$20$	−4.99384	−1.11666
$21$	−0.620582	−0.135422
$22$	−12.2422	−2.61004
$23$	2.34793	0.489577	0.244788	−	0.969577i	$-0.421282\pi$
$23$	2.34793	0.489577	0.244788	+	0.969577i	$0.421282\pi$
$24$	0.963604	0.196695
$25$	−3.91629	−0.783259
$26$	2.00957	0.394109
$27$	0.790522	0.152136
$28$	22.5294	4.25766
$29$	9.05133	1.68079	0.840395	−	0.541975i	$-0.182323\pi$
$29$	9.05133	1.68079	0.840395	+	0.541975i	$0.182323\pi$
$30$	−0.358630	−0.0654765
$31$	−6.01808	−1.08088	−0.540439	−	0.841383i	$-0.681742\pi$
$31$	−6.01808	−1.08088	−0.540439	+	0.841383i	$0.681742\pi$
$32$	−9.96907	−1.76230
$33$	−0.620476	−0.108011
$34$	−6.57026	−1.12679
$35$	−4.88907	−0.826404
$36$	−14.3075	−2.38459
$37$	0.990473	0.162833	0.0814163	−	0.996680i	$-0.474056\pi$
$37$	0.990473	0.162833	0.0814163	+	0.996680i	$0.474056\pi$
$38$	1.93537	0.313959
$39$	0.101852	0.0163094
$40$	7.59147	1.20032
$41$	2.46733	0.385332	0.192666	−	0.981264i	$-0.438287\pi$
$41$	2.46733	0.385332	0.192666	+	0.981264i	$0.438287\pi$
$42$	1.61794	0.249653
$43$	−4.95908	−0.756253	−0.378126	−	0.925754i	$-0.623431\pi$
$43$	−4.95908	−0.756253	−0.378126	+	0.925754i	$0.623431\pi$
$44$	22.5255	3.39585
$45$	3.10486	0.462845
$46$	−6.12134	−0.902543
$47$	−1.31549	−0.191884	−0.0959419	−	0.995387i	$-0.530586\pi$
$47$	−1.31549	−0.191884	−0.0959419	+	0.995387i	$0.530586\pi$
$48$	−1.24448	−0.179625
$49$	15.0567	2.15096
$50$	10.2103	1.44395
$51$	−0.333004	−0.0466298
$52$	−3.69760	−0.512765
$53$	7.66011	1.05220	0.526099	−	0.850424i	$-0.323654\pi$
$53$	7.66011	1.05220	0.526099	+	0.850424i	$0.323654\pi$
$54$	−2.06099	−0.280465
$55$	−4.88823	−0.659129
$56$	−34.2484	−4.57664
$57$	0.0980914	0.0129925
$58$	−23.5979	−3.09856
$59$	−1.77387	−0.230938	−0.115469	−	0.993311i	$-0.536837\pi$
$59$	−1.77387	−0.230938	−0.115469	+	0.993311i	$0.536837\pi$
$60$	0.659878	0.0851898
$61$	−5.27936	−0.675953	−0.337976	−	0.941155i	$-0.609742\pi$
$61$	−5.27936	−0.675953	−0.337976	+	0.941155i	$0.609742\pi$
$62$	15.6899	1.99262
$63$	−14.0074	−1.76476
$64$	7.15464	0.894330
$65$	0.802411	0.0995269
$66$	1.61766	0.199120
$67$	−1.78634	−0.218236	−0.109118	−	0.994029i	$-0.534803\pi$
$67$	−1.78634	−0.218236	−0.109118	+	0.994029i	$0.534803\pi$
$68$	12.0892	1.46604
$69$	−0.310251	−0.0373498
$70$	12.7464	1.52349
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	21.7499	2.56324
$73$	0.555267	0.0649891	0.0324946	−	0.999472i	$-0.489655\pi$
$73$	0.555267	0.0649891	0.0324946	+	0.999472i	$0.489655\pi$
$74$	−2.58229	−0.300185
$75$	0.517492	0.0597548
$76$	−3.56108	−0.408484
$77$	22.0530	2.51317
$78$	−0.265541	−0.0300666
$79$	7.22184	0.812520	0.406260	−	0.913757i	$-0.366833\pi$
$79$	7.22184	0.812520	0.406260	+	0.913757i	$0.366833\pi$
$80$	−9.80423	−1.09615
$81$	8.84316	0.982573
$82$	−6.43264	−0.710366
$83$	5.79165	0.635716	0.317858	−	0.948138i	$-0.397036\pi$
$83$	5.79165	0.635716	0.317858	+	0.948138i	$0.397036\pi$
$84$	−2.97700	−0.324817
$85$	−2.62347	−0.284555
$86$	12.9289	1.39416
$87$	−1.19603	−0.128227
$88$	−34.2426	−3.65027
$89$	−5.40418	−0.572842	−0.286421	−	0.958104i	$-0.592466\pi$
$89$	−5.40418	−0.572842	−0.286421	+	0.958104i	$0.592466\pi$
$90$	−8.09476	−0.853263
$91$	−3.62003	−0.379482
$92$	11.2632	1.17427
$93$	0.795218	0.0824603
$94$	3.42965	0.353741
$95$	0.772785	0.0792860
$96$	1.31729	0.134446
$97$	13.6023	1.38111	0.690554	−	0.723281i	$-0.257367\pi$
$97$	13.6023	1.38111	0.690554	+	0.723281i	$0.257367\pi$
$98$	−39.2548	−3.96533
$99$	−14.0050	−1.40755
$100$	−18.7869	−1.87869
$101$	−0.644013	−0.0640817	−0.0320408	−	0.999487i	$-0.510201\pi$
$101$	−0.644013	−0.0640817	−0.0320408	+	0.999487i	$0.510201\pi$
$102$	0.868182	0.0859628
$103$	−10.5847	−1.04294	−0.521468	−	0.853271i	$-0.674616\pi$
$103$	−10.5847	−1.04294	−0.521468	+	0.853271i	$0.674616\pi$
$104$	5.62097	0.551181
$105$	0.646034	0.0630464
$106$	−19.9709	−1.93974
$107$	−16.4738	−1.59258	−0.796289	−	0.604916i	$-0.793207\pi$
$107$	−16.4738	−1.59258	−0.796289	+	0.604916i	$0.793207\pi$
$108$	3.79222	0.364906
$109$	13.9572	1.33686	0.668428	−	0.743777i	$-0.266967\pi$
$109$	13.9572	1.33686	0.668428	+	0.743777i	$0.266967\pi$
$110$	12.7442	1.21512
$111$	−0.130879	−0.0124225
$112$	44.2312	4.17945
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−0.255737	−0.0239519
$115$	−2.44422	−0.227925
$116$	43.4201	4.03146
$117$	2.29894	0.212537
$118$	4.62469	0.425737
$119$	11.8356	1.08497
$120$	−1.00312	−0.0915723
$121$	11.0492	1.00447
$122$	13.7640	1.24613
$123$	−0.326029	−0.0293970
$124$	−28.8693	−2.59254
$125$	9.28197	0.830205
$126$	36.5190	3.25337
$127$	6.76083	0.599927	0.299963	−	0.953951i	$-0.403026\pi$
$127$	6.76083	0.599927	0.299963	+	0.953951i	$0.403026\pi$
$128$	1.28508	0.113586
$129$	0.655284	0.0576945
$130$	−2.09199	−0.183479
$131$	11.2932	0.986691	0.493346	−	0.869833i	$-0.335774\pi$
$131$	11.2932	0.986691	0.493346	+	0.869833i	$0.335774\pi$
$132$	−2.97648	−0.259070
$133$	−3.48637	−0.302306
$134$	4.65722	0.402322
$135$	−0.822943	−0.0708277
$136$	−18.3777	−1.57587
$137$	9.54655	0.815617	0.407808	−	0.913068i	$-0.366293\pi$
$137$	9.54655	0.815617	0.407808	+	0.913068i	$0.366293\pi$
$138$	0.808863	0.0688550
$139$	−0.387695	−0.0328838	−0.0164419	−	0.999865i	$-0.505234\pi$
$139$	−0.387695	−0.0328838	−0.0164419	+	0.999865i	$0.505234\pi$
$140$	−23.4534	−1.98217
$141$	0.173826	0.0146388
$142$	−2.60713	−0.218785
$143$	−3.61941	−0.302670
$144$	−28.0895	−2.34079
$145$	−9.42254	−0.782500
$146$	−1.44765	−0.119808
$147$	−1.98957	−0.164097
$148$	4.75140	0.390562
$149$	−8.34883	−0.683963	−0.341981	−	0.939707i	$-0.611098\pi$
$149$	−8.34883	−0.683963	−0.341981	+	0.939707i	$0.611098\pi$
$150$	−1.34917	−0.110159
$151$	5.25746	0.427846	0.213923	−	0.976850i	$-0.431376\pi$
$151$	5.25746	0.427846	0.213923	+	0.976850i	$0.431376\pi$
$152$	5.41343	0.439087
$153$	−7.51634	−0.607660
$154$	−57.4948	−4.63306
$155$	6.26489	0.503208
$156$	0.488594	0.0391189
$157$	−0.927304	−0.0740069	−0.0370035	−	0.999315i	$-0.511781\pi$
$157$	−0.927304	−0.0740069	−0.0370035	+	0.999315i	$0.511781\pi$
$158$	−18.8282	−1.49789
$159$	−1.01219	−0.0802722
$160$	10.3779	0.820447
$161$	11.0269	0.869045
$162$	−23.0552	−1.81139
$163$	−1.40021	−0.109673	−0.0548366	−	0.998495i	$-0.517464\pi$
$163$	−1.40021	−0.109673	−0.0548366	+	0.998495i	$0.517464\pi$
$164$	11.8360	0.924238
$165$	0.645923	0.0502850
$166$	−15.0996	−1.17195
$167$	0.134470	0.0104056	0.00520282	−	0.999986i	$-0.498344\pi$
$167$	0.134470	0.0104056	0.00520282	+	0.999986i	$0.498344\pi$
$168$	4.52553	0.349152
$169$	−12.4059	−0.954298
$170$	6.83972	0.524582
$171$	2.21406	0.169313
$172$	−23.7892	−1.81391
$173$	6.18178	0.469992	0.234996	−	0.971996i	$-0.424492\pi$
$173$	6.18178	0.469992	0.234996	+	0.971996i	$0.424492\pi$
$174$	3.11819	0.236389
$175$	−18.3927	−1.39036
$176$	44.2236	3.33348
$177$	0.234396	0.0176183
$178$	14.0894	1.05604
$179$	16.5305	1.23555	0.617773	−	0.786356i	$-0.288035\pi$
$179$	16.5305	1.23555	0.617773	+	0.786356i	$0.288035\pi$
$180$	14.8943	1.11016
$181$	6.55887	0.487517	0.243759	−	0.969836i	$-0.421620\pi$
$181$	6.55887	0.487517	0.243759	+	0.969836i	$0.421620\pi$
$182$	9.43786	0.699581
$183$	0.697605	0.0515685
$184$	−17.1220	−1.26225
$185$	−1.03109	−0.0758076
$186$	−2.07323	−0.152017
$187$	11.8336	0.865358
$188$	−6.31054	−0.460243
$189$	3.71266	0.270056
$190$	−2.01475	−0.146165
$191$	−0.703232	−0.0508841	−0.0254420	−	0.999676i	$-0.508099\pi$
$191$	−0.703232	−0.0508841	−0.0254420	+	0.999676i	$0.508099\pi$
$192$	−0.945402	−0.0682285
$193$	−0.787864	−0.0567117	−0.0283558	−	0.999598i	$-0.509027\pi$
$193$	−0.787864	−0.0567117	−0.0283558	+	0.999598i	$0.509027\pi$
$194$	−35.4630	−2.54609
$195$	−0.106029	−0.00759291
$196$	72.2287	5.15919
$197$	20.8152	1.48302	0.741510	−	0.670942i	$-0.234110\pi$
$197$	20.8152	1.48302	0.741510	+	0.670942i	$0.234110\pi$
$198$	36.5127	2.59485
$199$	2.85265	0.202219	0.101109	−	0.994875i	$-0.467761\pi$
$199$	2.85265	0.202219	0.101109	+	0.994875i	$0.467761\pi$
$200$	28.5592	2.01944
$201$	0.236044	0.0166493
$202$	1.67902	0.118136
$203$	42.5092	2.98356
$204$	−1.59745	−0.111844
$205$	−2.56852	−0.179393
$206$	27.5955	1.92267
$207$	−7.00279	−0.486727
$208$	−7.25937	−0.503347
$209$	−3.48577	−0.241116
$210$	−1.68429	−0.116227
$211$	−8.51134	−0.585945	−0.292972	−	0.956121i	$-0.594644\pi$
$211$	−8.51134	−0.585945	−0.292972	+	0.956121i	$0.594644\pi$
$212$	36.7463	2.52375
$213$	−0.132138	−0.00905396
$214$	42.9492	2.93594
$215$	5.16246	0.352077
$216$	−5.76480	−0.392245
$217$	−28.2637	−1.91866
$218$	−36.3881	−2.46452
$219$	−0.0733720	−0.00495802
$220$	−23.4494	−1.58096
$221$	−1.94250	−0.130667
$222$	0.341219	0.0229011
$223$	14.8410	0.993826	0.496913	−	0.867800i	$-0.334467\pi$
$223$	14.8410	0.993826	0.496913	+	0.867800i	$0.334467\pi$
$224$	−46.8193	−3.12825
$225$	11.6805	0.778700
$226$	2.60713	0.173423
$227$	−9.90733	−0.657573	−0.328786	−	0.944404i	$-0.606640\pi$
$227$	−9.90733	−0.657573	−0.328786	+	0.944404i	$0.606640\pi$
$228$	0.470555	0.0311632
$229$	3.98989	0.263659	0.131830	−	0.991272i	$-0.457915\pi$
$229$	3.98989	0.263659	0.131830	+	0.991272i	$0.457915\pi$
$230$	6.37239	0.420183
$231$	−2.91404	−0.191730
$232$	−66.0058	−4.33350
$233$	−15.2858	−1.00141	−0.500704	−	0.865619i	$-0.666925\pi$
$233$	−15.2858	−1.00141	−0.500704	+	0.865619i	$0.666925\pi$
$234$	−5.99362	−0.391815
$235$	1.36944	0.0893325
$236$	−8.50942	−0.553916
$237$	−0.954281	−0.0619872
$238$	−30.8569	−2.00016
$239$	3.84856	0.248943	0.124471	−	0.992223i	$-0.460276\pi$
$239$	3.84856	0.248943	0.124471	+	0.992223i	$0.460276\pi$
$240$	1.29551	0.0836251
$241$	−8.03816	−0.517784	−0.258892	−	0.965906i	$-0.583357\pi$
$241$	−8.03816	−0.517784	−0.258892	+	0.965906i	$0.583357\pi$
$242$	−28.8066	−1.85176
$243$	−3.54009	−0.227097
$244$	−25.3256	−1.62131
$245$	−15.6743	−1.00139
$246$	0.849997	0.0541938
$247$	0.572194	0.0364079
$248$	43.8862	2.78678
$249$	−0.765298	−0.0484988
$250$	−24.1993	−1.53050
$251$	23.7932	1.50181	0.750907	−	0.660408i	$-0.229617\pi$
$251$	23.7932	1.50181	0.750907	+	0.660408i	$0.229617\pi$
$252$	−67.1948	−4.23288
$253$	11.0251	0.693139
$254$	−17.6263	−1.10597
$255$	0.346661	0.0217087
$256$	−17.6597	−1.10373
$257$	−4.64130	−0.289516	−0.144758	−	0.989467i	$-0.546240\pi$
$257$	−4.64130	−0.289516	−0.144758	+	0.989467i	$0.546240\pi$
$258$	−1.70841	−0.106361
$259$	4.65172	0.289044
$260$	3.84925	0.238720
$261$	−26.9959	−1.67101
$262$	−29.4428	−1.81898
$263$	17.8606	1.10133	0.550665	−	0.834726i	$-0.314374\pi$
$263$	17.8606	1.10133	0.550665	+	0.834726i	$0.314374\pi$
$264$	4.52475	0.278479
$265$	−7.97427	−0.489856
$266$	9.08940	0.557307
$267$	0.714099	0.0437021
$268$	−8.56926	−0.523451
$269$	15.2193	0.927939	0.463970	−	0.885851i	$-0.346425\pi$
$269$	15.2193	0.927939	0.463970	+	0.885851i	$0.346425\pi$
$270$	2.14552	0.130572
$271$	−18.3813	−1.11658	−0.558292	−	0.829644i	$-0.688543\pi$
$271$	−18.3813	−1.11658	−0.558292	+	0.829644i	$0.688543\pi$
$272$	23.7344	1.43911
$273$	0.478344	0.0289507
$274$	−24.8890	−1.50360
$275$	−18.3896	−1.10893
$276$	−1.48831	−0.0895855
$277$	−2.60697	−0.156637	−0.0783187	−	0.996928i	$-0.524955\pi$
$277$	−2.60697	−0.156637	−0.0783187	+	0.996928i	$0.524955\pi$
$278$	1.01077	0.0606219
$279$	17.9492	1.07459
$280$	35.6530	2.13068
$281$	−8.26660	−0.493144	−0.246572	−	0.969124i	$-0.579304\pi$
$281$	−8.26660	−0.493144	−0.246572	+	0.969124i	$0.579304\pi$
$282$	−0.453187	−0.0269869
$283$	24.0114	1.42733	0.713665	−	0.700487i	$-0.247034\pi$
$283$	24.0114	1.42733	0.713665	+	0.700487i	$0.247034\pi$
$284$	4.79710	0.284656
$285$	−0.102114	−0.00604874
$286$	9.43624	0.557977
$287$	11.5877	0.684001
$288$	29.7331	1.75204
$289$	−10.6490	−0.626413
$290$	24.5657	1.44255
$291$	−1.79739	−0.105365
$292$	2.66367	0.155880
$293$	−11.2049	−0.654596	−0.327298	−	0.944921i	$-0.606138\pi$
$293$	−11.2049	−0.654596	−0.327298	+	0.944921i	$0.606138\pi$
$294$	5.18706	0.302516
$295$	1.84662	0.107514
$296$	−7.22292	−0.419823
$297$	3.71202	0.215393
$298$	21.7664	1.26090
$299$	−1.80978	−0.104662
$300$	2.48246	0.143325
$301$	−23.2901	−1.34242
$302$	−13.7069	−0.788742
$303$	0.0850987	0.00488879
$304$	−6.99134	−0.400981
$305$	5.49588	0.314693
$306$	19.5960	1.12023
$307$	16.7655	0.956857	0.478428	−	0.878127i	$-0.341207\pi$
$307$	16.7655	0.956857	0.478428	+	0.878127i	$0.341207\pi$
$308$	105.790	6.02796
$309$	1.39864	0.0795657
$310$	−16.3334	−0.927673
$311$	−7.61318	−0.431704	−0.215852	−	0.976426i	$-0.569253\pi$
$311$	−7.61318	−0.431704	−0.215852	+	0.976426i	$0.569253\pi$
$312$	−0.742745	−0.0420497
$313$	18.7176	1.05798	0.528991	−	0.848627i	$-0.322570\pi$
$313$	18.7176	1.05798	0.528991	+	0.848627i	$0.322570\pi$
$314$	2.41760	0.136433
$315$	14.5819	0.821594
$316$	34.6439	1.94887
$317$	−7.45534	−0.418733	−0.209367	−	0.977837i	$-0.567140\pi$
$317$	−7.45534	−0.418733	−0.209367	+	0.977837i	$0.567140\pi$
$318$	2.63892	0.147983
$319$	42.5019	2.37965
$320$	−7.44807	−0.416360
$321$	2.17681	0.121498
$322$	−28.7486	−1.60210
$323$	−1.87078	−0.104093
$324$	42.4215	2.35675
$325$	3.01867	0.167446
$326$	3.65053	0.202184
$327$	−1.84428	−0.101989
$328$	−17.9927	−0.993483
$329$	−6.17814	−0.340612
$330$	−1.68400	−0.0927012
$331$	−26.8364	−1.47506	−0.737531	−	0.675314i	$-0.764008\pi$
$331$	−26.8364	−1.47506	−0.737531	+	0.675314i	$0.764008\pi$
$332$	27.7831	1.52480
$333$	−2.95412	−0.161885
$334$	−0.350581	−0.0191830
$335$	1.85960	0.101601
$336$	−5.84463	−0.318851
$337$	−3.45024	−0.187946	−0.0939732	−	0.995575i	$-0.529957\pi$
$337$	−3.45024	−0.187946	−0.0939732	+	0.995575i	$0.529957\pi$
$338$	32.3437	1.75926
$339$	0.132138	0.00717676
$340$	−12.5851	−0.682521
$341$	−28.2588	−1.53030
$342$	−5.77232	−0.312131
$343$	37.8381	2.04307
$344$	36.1636	1.94981
$345$	0.322975	0.0173884
$346$	−16.1167	−0.866438
$347$	−30.4789	−1.63619	−0.818096	−	0.575082i	$-0.804970\pi$
$347$	−30.4789	−1.63619	−0.818096	+	0.575082i	$0.804970\pi$
$348$	−5.73746	−0.307560
$349$	−27.2428	−1.45828	−0.729138	−	0.684367i	$-0.760079\pi$
$349$	−27.2428	−1.45828	−0.729138	+	0.684367i	$0.760079\pi$
$350$	47.9521	2.56315
$351$	−0.609334	−0.0325238
$352$	−46.8113	−2.49505
$353$	1.68565	0.0897180	0.0448590	−	0.998993i	$-0.485716\pi$
$353$	1.68565	0.0897180	0.0448590	+	0.998993i	$0.485716\pi$
$354$	−0.611099	−0.0324795
$355$	−1.04101	−0.0552512
$356$	−25.9244	−1.37399
$357$	−1.56394	−0.0827724
$358$	−43.0971	−2.27775
$359$	3.30392	0.174374	0.0871870	−	0.996192i	$-0.472212\pi$
$359$	3.30392	0.174374	0.0871870	+	0.996192i	$0.472212\pi$
$360$	−22.6419	−1.19333
$361$	−18.4489	−0.970996
$362$	−17.0998	−0.898746
$363$	−1.46002	−0.0766311
$364$	−17.3656	−0.910207
$365$	−0.578040	−0.0302560
$366$	−1.81874	−0.0950673
$367$	−33.7225	−1.76030	−0.880151	−	0.474694i	$-0.842559\pi$
$367$	−33.7225	−1.76030	−0.880151	+	0.474694i	$0.842559\pi$
$368$	22.1127	1.15271
$369$	−7.35891	−0.383089
$370$	2.68819	0.139752
$371$	35.9754	1.86775
$372$	3.81474	0.197785
$373$	−6.62181	−0.342865	−0.171432	−	0.985196i	$-0.554839\pi$
$373$	−6.62181	−0.342865	−0.171432	+	0.985196i	$0.554839\pi$
$374$	−30.8517	−1.59530
$375$	−1.22650	−0.0633364
$376$	9.59307	0.494725
$377$	−6.97675	−0.359321
$378$	−9.67936	−0.497853
$379$	12.4508	0.639553	0.319777	−	0.947493i	$-0.396392\pi$
$379$	12.4508	0.639553	0.319777	+	0.947493i	$0.396392\pi$
$380$	3.70713	0.190172
$381$	−0.893365	−0.0457685
$382$	1.83341	0.0938056
$383$	28.6779	1.46537	0.732687	−	0.680566i	$-0.238266\pi$
$383$	28.6779	1.46537	0.732687	+	0.680566i	$0.238266\pi$
$384$	−0.169809	−0.00866552
$385$	−22.9574	−1.17002
$386$	2.05406	0.104549
$387$	14.7907	0.751851
$388$	65.2518	3.31266
$389$	19.1396	0.970416	0.485208	−	0.874399i	$-0.338744\pi$
$389$	19.1396	0.970416	0.485208	+	0.874399i	$0.338744\pi$
$390$	0.276431	0.0139976
$391$	5.91705	0.299238
$392$	−109.800	−5.54572
$393$	−1.49226	−0.0752747
$394$	−54.2678	−2.73397
$395$	−7.51802	−0.378273
$396$	−67.1833	−3.37609
$397$	8.27109	0.415114	0.207557	−	0.978223i	$-0.433449\pi$
$397$	8.27109	0.415114	0.207557	+	0.978223i	$0.433449\pi$
$398$	−7.43721	−0.372794
$399$	0.460683	0.0230630
$400$	−36.8836	−1.84418
$401$	20.1378	1.00563	0.502817	−	0.864393i	$-0.332297\pi$
$401$	20.1378	1.00563	0.502817	+	0.864393i	$0.332297\pi$
$402$	−0.615396	−0.0306932
$403$	4.63873	0.231072
$404$	−3.08939	−0.153703
$405$	−9.20584	−0.457442
$406$	−110.827	−5.50024
$407$	4.65092	0.230537
$408$	2.42839	0.120223
$409$	6.91059	0.341706	0.170853	−	0.985296i	$-0.445348\pi$
$409$	6.91059	0.341706	0.170853	+	0.985296i	$0.445348\pi$
$410$	6.69645	0.330714
$411$	−1.26146	−0.0622234
$412$	−50.7756	−2.50154
$413$	−8.33090	−0.409937
$414$	18.2571	0.897290
$415$	−6.02918	−0.295961
$416$	7.68415	0.376746
$417$	0.0512293	0.00250871
$418$	9.08784	0.444501
$419$	21.7740	1.06373	0.531864	−	0.846830i	$-0.321492\pi$
$419$	21.7740	1.06373	0.531864	+	0.846830i	$0.321492\pi$
$420$	3.09909	0.151220
$421$	−8.44393	−0.411532	−0.205766	−	0.978601i	$-0.565969\pi$
$421$	−8.44393	−0.411532	−0.205766	+	0.978601i	$0.565969\pi$
$422$	22.1901	1.08020
$423$	3.92350	0.190767
$424$	−55.8605	−2.71283
$425$	−9.86951	−0.478742
$426$	0.344501	0.0166911
$427$	−24.7943	−1.19988
$428$	−79.0263	−3.81988
$429$	0.478262	0.0230907
$430$	−13.4592	−0.649060
$431$	−1.90788	−0.0918995	−0.0459497	−	0.998944i	$-0.514631\pi$
$431$	−1.90788	−0.0918995	−0.0459497	+	0.998944i	$0.514631\pi$
$432$	7.44512	0.358204
$433$	4.07882	0.196016	0.0980079	−	0.995186i	$-0.468753\pi$
$433$	4.07882	0.196016	0.0980079	+	0.995186i	$0.468753\pi$
$434$	73.6869	3.53708
$435$	1.24508	0.0596969
$436$	66.9541	3.20652
$437$	−1.74296	−0.0833771
$438$	0.191290	0.00914019
$439$	−28.0182	−1.33723	−0.668617	−	0.743607i	$-0.733114\pi$
$439$	−28.0182	−1.33723	−0.668617	+	0.743607i	$0.733114\pi$
$440$	35.6469	1.69940
$441$	−44.9073	−2.13844
$442$	5.06435	0.240886
$443$	−32.7397	−1.55551	−0.777755	−	0.628567i	$-0.783642\pi$
$443$	−32.7397	−1.55551	−0.777755	+	0.628567i	$0.783642\pi$
$444$	−0.627841	−0.0297960
$445$	5.62582	0.266689
$446$	−38.6923	−1.83213
$447$	1.10320	0.0521796
$448$	33.6015	1.58752
$449$	29.3206	1.38372	0.691861	−	0.722030i	$-0.256791\pi$
$449$	29.3206	1.38372	0.691861	+	0.722030i	$0.256791\pi$
$450$	−30.4525	−1.43555
$451$	11.5857	0.545550
$452$	−4.79710	−0.225637
$453$	−0.694712	−0.0326404
$454$	25.8296	1.21225
$455$	3.76849	0.176670
$456$	−0.715321	−0.0334980
$457$	−11.9502	−0.559005	−0.279502	−	0.960145i	$-0.590169\pi$
$457$	−11.9502	−0.559005	−0.279502	+	0.960145i	$0.590169\pi$
$458$	−10.4021	−0.486060
$459$	1.99221	0.0929883
$460$	−11.7252	−0.546689
$461$	0.635106	0.0295798	0.0147899	−	0.999891i	$-0.495292\pi$
$461$	0.635106	0.0295798	0.0147899	+	0.999891i	$0.495292\pi$
$462$	7.59726	0.353457
$463$	−34.8744	−1.62075	−0.810376	−	0.585910i	$-0.800737\pi$
$463$	−34.8744	−1.62075	−0.810376	+	0.585910i	$0.800737\pi$
$464$	85.2452	3.95741
$465$	−0.827832	−0.0383898
$466$	39.8520	1.84611
$467$	−16.6350	−0.769776	−0.384888	−	0.922963i	$-0.625760\pi$
$467$	−16.6350	−0.769776	−0.384888	+	0.922963i	$0.625760\pi$
$468$	11.0282	0.509781
$469$	−8.38948	−0.387390
$470$	−3.57030	−0.164686
$471$	0.122532	0.00564599
$472$	12.9357	0.595416
$473$	−23.2861	−1.07070
$474$	2.48793	0.114274
$475$	2.90722	0.133392
$476$	56.7767	2.60235
$477$	−22.8466	−1.04607
$478$	−10.0337	−0.458930
$479$	−20.9974	−0.959397	−0.479699	−	0.877433i	$-0.659254\pi$
$479$	−20.9974	−0.959397	−0.479699	+	0.877433i	$0.659254\pi$
$480$	−1.37132	−0.0625919
$481$	−0.763455	−0.0348106
$482$	20.9565	0.954542
$483$	−1.45708	−0.0662995
$484$	53.0040	2.40927
$485$	−14.1602	−0.642981
$486$	9.22945	0.418656
$487$	21.2359	0.962289	0.481145	−	0.876641i	$-0.340221\pi$
$487$	21.2359	0.962289	0.481145	+	0.876641i	$0.340221\pi$
$488$	38.4992	1.74278
$489$	0.185022	0.00836697
$490$	40.8647	1.84608
$491$	−34.1587	−1.54156	−0.770780	−	0.637101i	$-0.780133\pi$
$491$	−34.1587	−1.54156	−0.770780	+	0.637101i	$0.780133\pi$
$492$	−1.56399	−0.0705102
$493$	22.8104	1.02733
$494$	−1.49178	−0.0671185
$495$	14.5794	0.655293
$496$	−56.6781	−2.54492
$497$	4.69646	0.210665
$498$	1.99523	0.0894083
$499$	−15.2360	−0.682056	−0.341028	−	0.940053i	$-0.610775\pi$
$499$	−15.2360	−0.682056	−0.341028	+	0.940053i	$0.610775\pi$
$500$	44.5266	1.99129
$501$	−0.0177687	−0.000793846 0
$502$	−62.0319	−2.76862
$503$	41.7571	1.86186	0.930929	−	0.365201i	$-0.119000\pi$
$503$	41.7571	1.86186	0.930929	+	0.365201i	$0.119000\pi$
$504$	102.147	4.55000
$505$	0.670425	0.0298335
$506$	−28.7437	−1.27781
$507$	1.63929	0.0728034
$508$	32.4324	1.43896
$509$	−7.22555	−0.320267	−0.160133	−	0.987095i	$-0.551192\pi$
$509$	−7.22555	−0.320267	−0.160133	+	0.987095i	$0.551192\pi$
$510$	−0.903788	−0.0400204
$511$	2.60779	0.115362
$512$	43.4708	1.92116
$513$	−0.586836	−0.0259094
$514$	12.1004	0.533728
$515$	11.0188	0.485544
$516$	3.14346	0.138383
$517$	−6.17708	−0.271668
$518$	−12.1276	−0.532856
$519$	−0.816850	−0.0358557
$520$	−5.85150	−0.256605
$521$	20.9147	0.916289	0.458145	−	0.888878i	$-0.348514\pi$
$521$	20.9147	0.916289	0.458145	+	0.888878i	$0.348514\pi$
$522$	70.3818	3.08053
$523$	30.7877	1.34625	0.673127	−	0.739527i	$-0.264951\pi$
$523$	30.7877	1.34625	0.673127	+	0.739527i	$0.264951\pi$
$524$	54.1746	2.36663
$525$	2.43038	0.106071
$526$	−46.5648	−2.03032
$527$	−15.1663	−0.660652
$528$	−5.84363	−0.254311
$529$	−17.4872	−0.760315
$530$	20.7899	0.903056
$531$	5.29063	0.229594
$532$	−16.7245	−0.725097
$533$	−1.90181	−0.0823767
$534$	−1.86175	−0.0805656
$535$	17.1494	0.741433
$536$	13.0267	0.562668
$537$	−2.18431	−0.0942599
$538$	−39.6787	−1.71067
$539$	70.7012	3.04532
$540$	−3.94774	−0.169884
$541$	−32.3340	−1.39015	−0.695073	−	0.718940i	$-0.744628\pi$
$541$	−32.3340	−1.39015	−0.695073	+	0.718940i	$0.744628\pi$
$542$	47.9224	2.05844
$543$	−0.866678	−0.0371927
$544$	−25.1232	−1.07715
$545$	−14.5296	−0.622380
$546$	−1.24710	−0.0533711
$547$	35.2950	1.50910	0.754552	−	0.656240i	$-0.227854\pi$
$547$	35.2950	1.50910	0.754552	+	0.656240i	$0.227854\pi$
$548$	45.7958	1.95630
$549$	15.7459	0.672019
$550$	47.9439	2.04433
$551$	−6.71916	−0.286246
$552$	2.26247	0.0962972
$553$	33.9171	1.44230
$554$	6.79669	0.288764
$555$	0.136247	0.00578336
$556$	−1.85981	−0.0788736
$557$	8.28684	0.351125	0.175562	−	0.984468i	$-0.443826\pi$
$557$	8.28684	0.351125	0.175562	+	0.984468i	$0.443826\pi$
$558$	−46.7957	−1.98102
$559$	3.82245	0.161673
$560$	−46.0452	−1.94576
$561$	−1.56367	−0.0660182
$562$	21.5521	0.909119
$563$	23.6432	0.996441	0.498220	−	0.867050i	$-0.333987\pi$
$563$	23.6432	0.996441	0.498220	+	0.867050i	$0.333987\pi$
$564$	0.833863	0.0351120
$565$	1.04101	0.0437957
$566$	−62.6008	−2.63131
$567$	41.5315	1.74416
$568$	−7.29239	−0.305982
$569$	−5.80611	−0.243405	−0.121702	−	0.992567i	$-0.538835\pi$
$569$	−5.80611	−0.243405	−0.121702	+	0.992567i	$0.538835\pi$
$570$	0.266225	0.0111509
$571$	−14.5049	−0.607012	−0.303506	−	0.952830i	$-0.598157\pi$
$571$	−14.5049	−0.607012	−0.303506	+	0.952830i	$0.598157\pi$
$572$	−17.3627	−0.725969
$573$	0.0929238	0.00388195
$574$	−30.2106	−1.26097
$575$	−9.19517	−0.383465
$576$	−21.3390	−0.889125
$577$	−16.2470	−0.676370	−0.338185	−	0.941080i	$-0.609813\pi$
$577$	−16.2470	−0.676370	−0.338185	+	0.941080i	$0.609813\pi$
$578$	27.7633	1.15480
$579$	0.104107	0.00432654
$580$	−45.2009	−1.87687
$581$	27.2002	1.12846
$582$	4.68602	0.194242
$583$	35.9692	1.48969
$584$	−4.04923	−0.167558
$585$	−2.39322	−0.0989476
$586$	29.2125	1.20676
$587$	−0.566541	−0.0233836	−0.0116918	−	0.999932i	$-0.503722\pi$
$587$	−0.566541	−0.0233836	−0.0116918	+	0.999932i	$0.503722\pi$
$588$	−9.54417	−0.393595
$589$	4.46746	0.184078
$590$	−4.81436	−0.198204
$591$	−2.75048	−0.113140
$592$	9.32825	0.383389
$593$	−29.9157	−1.22849	−0.614246	−	0.789114i	$-0.710540\pi$
$593$	−29.9157	−1.22849	−0.614246	+	0.789114i	$0.710540\pi$
$594$	−9.67770	−0.397081
$595$	−12.3210	−0.505113
$596$	−40.0502	−1.64052
$597$	−0.376944	−0.0154273
$598$	4.71832	0.192947
$599$	41.6216	1.70061	0.850306	−	0.526289i	$-0.176417\pi$
$599$	41.6216	1.70061	0.850306	+	0.526289i	$0.176417\pi$
$600$	−3.77376	−0.154063
$601$	9.57766	0.390681	0.195340	−	0.980736i	$-0.437419\pi$
$601$	9.57766	0.390681	0.195340	+	0.980736i	$0.437419\pi$
$602$	60.7203	2.47477
$603$	5.32783	0.216966
$604$	25.2206	1.02621
$605$	−11.5023	−0.467636
$606$	−0.221863	−0.00901257
$607$	21.6093	0.877093	0.438547	−	0.898708i	$-0.355493\pi$
$607$	21.6093	0.877093	0.438547	+	0.898708i	$0.355493\pi$
$608$	7.40043	0.300127
$609$	−5.61709	−0.227616
$610$	−14.3284	−0.580142
$611$	1.01398	0.0410212
$612$	−36.0567	−1.45750
$613$	−4.23077	−0.170879	−0.0854396	−	0.996343i	$-0.527229\pi$
$613$	−4.23077	−0.170879	−0.0854396	+	0.996343i	$0.527229\pi$
$614$	−43.7097	−1.76398
$615$	0.339400	0.0136859
$616$	−160.819	−6.47958
$617$	9.99800	0.402504	0.201252	−	0.979539i	$-0.435499\pi$
$617$	9.99800	0.402504	0.201252	+	0.979539i	$0.435499\pi$
$618$	−3.64642	−0.146681
$619$	−40.9271	−1.64500	−0.822499	−	0.568767i	$-0.807421\pi$
$619$	−40.9271	−1.64500	−0.822499	+	0.568767i	$0.807421\pi$
$620$	30.0533	1.20697
$621$	1.85609	0.0744823
$622$	19.8485	0.795853
$623$	−25.3805	−1.01685
$624$	0.959240	0.0384003
$625$	9.91882	0.396753
$626$	−48.7992	−1.95041
$627$	0.460604	0.0183947
$628$	−4.44837	−0.177509
$629$	2.49611	0.0995262
$630$	−38.0167	−1.51462
$631$	22.6218	0.900561	0.450280	−	0.892887i	$-0.351324\pi$
$631$	22.6218	0.900561	0.450280	+	0.892887i	$0.351324\pi$
$632$	−52.6645	−2.09488
$633$	1.12467	0.0447018
$634$	19.4370	0.771942
$635$	−7.03811	−0.279299
$636$	−4.85560	−0.192537
$637$	−11.6057	−0.459835
$638$	−110.808	−4.38692
$639$	−2.98254	−0.117987
$640$	−1.33779	−0.0528807
$641$	−4.35109	−0.171858	−0.0859288	−	0.996301i	$-0.527386\pi$
$641$	−4.35109	−0.171858	−0.0859288	+	0.996301i	$0.527386\pi$
$642$	−5.67523	−0.223983
$643$	−0.0499750	−0.00197082	−0.000985411	−	1.00000i	$-0.500314\pi$
$643$	−0.0499750	−0.00197082	−0.000985411		1.00000i	$0.500314\pi$
$644$	52.8974	2.08445
$645$	−0.682159	−0.0268600
$646$	4.87736	0.191897
$647$	25.7153	1.01097	0.505486	−	0.862835i	$-0.331313\pi$
$647$	25.7153	1.01097	0.505486	+	0.862835i	$0.331313\pi$
$648$	−64.4878	−2.53332
$649$	−8.32947	−0.326960
$650$	−7.87006	−0.308689
$651$	3.73471	0.146375
$652$	−6.71697	−0.263057
$653$	−15.3431	−0.600421	−0.300210	−	0.953873i	$-0.597057\pi$
$653$	−15.3431	−0.600421	−0.300210	+	0.953873i	$0.597057\pi$
$654$	4.80827	0.188018
$655$	−11.7564	−0.459359
$656$	23.2373	0.907262
$657$	−1.65611	−0.0646109
$658$	16.1072	0.627924
$659$	−47.0097	−1.83124	−0.915619	−	0.402048i	$-0.868299\pi$
$659$	−47.0097	−1.83124	−0.915619	+	0.402048i	$0.868299\pi$
$660$	3.09856	0.120611
$661$	23.5418	0.915668	0.457834	−	0.889038i	$-0.348625\pi$
$661$	23.5418	0.915668	0.457834	+	0.889038i	$0.348625\pi$
$662$	69.9658	2.71930
$663$	0.256679	0.00996858
$664$	−42.2350	−1.63904
$665$	3.62935	0.140740
$666$	7.70177	0.298438
$667$	21.2519	0.822875
$668$	0.645068	0.0249584
$669$	−1.96106	−0.0758191
$670$	−4.84822	−0.187303
$671$	−24.7901	−0.957009
$672$	6.18662	0.238654
$673$	−2.08689	−0.0804438	−0.0402219	−	0.999191i	$-0.512806\pi$
$673$	−2.08689	−0.0804438	−0.0402219	+	0.999191i	$0.512806\pi$
$674$	8.99520	0.346482
$675$	−3.09592	−0.119162
$676$	−59.5122	−2.28893
$677$	33.5707	1.29023	0.645114	−	0.764087i	$-0.276810\pi$
$677$	33.5707	1.29023	0.645114	+	0.764087i	$0.276810\pi$
$678$	−0.344501	−0.0132305
$679$	63.8828	2.45160
$680$	19.1314	0.733655
$681$	1.30914	0.0501662
$682$	73.6743	2.82113
$683$	24.1408	0.923721	0.461860	−	0.886953i	$-0.347182\pi$
$683$	24.1408	0.923721	0.461860	+	0.886953i	$0.347182\pi$
$684$	10.6211	0.406106
$685$	−9.93807	−0.379714
$686$	−98.6488	−3.76643
$687$	−0.527217	−0.0201146
$688$	−46.7045	−1.78059
$689$	−5.90440	−0.224940
$690$	−0.842037	−0.0320558
$691$	13.9804	0.531839	0.265920	−	0.963995i	$-0.414324\pi$
$691$	13.9804	0.531839	0.265920	+	0.963995i	$0.414324\pi$
$692$	29.6546	1.12730
$693$	−65.7738	−2.49854
$694$	79.4622	3.01635
$695$	0.403595	0.0153092
$696$	8.72190	0.330603
$697$	6.21795	0.235522
$698$	71.0255	2.68835
$699$	2.01984	0.0763974
$700$	−88.2317	−3.33485
$701$	4.29291	0.162141	0.0810704	−	0.996708i	$-0.474166\pi$
$701$	4.29291	0.162141	0.0810704	+	0.996708i	$0.474166\pi$
$702$	1.58861	0.0599582
$703$	−0.735267	−0.0277311
$704$	33.5957	1.26619
$705$	−0.180956	−0.00681518
$706$	−4.39470	−0.165397
$707$	−3.02458	−0.113751
$708$	1.12442	0.0422583
$709$	30.6910	1.15262	0.576312	−	0.817230i	$-0.304491\pi$
$709$	30.6910	1.15262	0.576312	+	0.817230i	$0.304491\pi$
$710$	2.71405	0.101856
$711$	−21.5394	−0.807791
$712$	39.4094	1.47693
$713$	−14.1300	−0.529173
$714$	4.07738	0.152592
$715$	3.76785	0.140909
$716$	79.2984	2.96352
$717$	−0.508543	−0.0189919
$718$	−8.61373	−0.321461
$719$	−29.0994	−1.08522	−0.542611	−	0.839984i	$-0.682564\pi$
$719$	−29.0994	−1.08522	−0.542611	+	0.839984i	$0.682564\pi$
$720$	29.2415	1.08977
$721$	−49.7104	−1.85131
$722$	48.0987	1.79005
$723$	1.06215	0.0395017
$724$	31.4636	1.16934
$725$	−35.4477	−1.31649
$726$	3.80645	0.141271
$727$	15.2956	0.567282	0.283641	−	0.958931i	$-0.408458\pi$
$727$	15.2956	0.567282	0.283641	+	0.958931i	$0.408458\pi$
$728$	26.3987	0.978399
$729$	−26.0617	−0.965248
$730$	1.50702	0.0557774
$731$	−12.4975	−0.462235
$732$	3.34648	0.123690
$733$	46.1677	1.70524	0.852622	−	0.522529i	$-0.175011\pi$
$733$	46.1677	1.70524	0.852622	+	0.522529i	$0.175011\pi$
$734$	87.9189	3.24514
$735$	2.07117	0.0763962
$736$	−23.4066	−0.862780
$737$	−8.38804	−0.308978
$738$	19.1856	0.706231
$739$	−6.40973	−0.235786	−0.117893	−	0.993026i	$-0.537614\pi$
$739$	−6.40973	−0.235786	−0.117893	+	0.993026i	$0.537614\pi$
$740$	−4.94626	−0.181828
$741$	−0.0756088	−0.00277756
$742$	−93.7924	−3.44323
$743$	17.5947	0.645487	0.322744	−	0.946486i	$-0.395395\pi$
$743$	17.5947	0.645487	0.322744	+	0.946486i	$0.395395\pi$
$744$	−5.79905	−0.212603
$745$	8.69124	0.318422
$746$	17.2639	0.632076
$747$	−17.2738	−0.632016
$748$	56.7669	2.07560
$749$	−77.3684	−2.82698
$750$	3.19765	0.116762
$751$	−51.3869	−1.87513	−0.937567	−	0.347805i	$-0.886927\pi$
$751$	−51.3869	−1.87513	−0.937567	+	0.347805i	$0.886927\pi$
$752$	−12.3893	−0.451790
$753$	−3.14399	−0.114573
$754$	18.1893	0.662414
$755$	−5.47309	−0.199186
$756$	17.8100	0.647743
$757$	−2.48839	−0.0904419	−0.0452210	−	0.998977i	$-0.514399\pi$
$757$	−2.48839	−0.0904419	−0.0452210	+	0.998977i	$0.514399\pi$
$758$	−32.4607	−1.17903
$759$	−1.45683	−0.0528796
$760$	−5.63545	−0.204419
$761$	−12.8385	−0.465395	−0.232697	−	0.972549i	$-0.574755\pi$
$761$	−12.8385	−0.465395	−0.232697	+	0.972549i	$0.574755\pi$
$762$	2.32911	0.0843749
$763$	65.5494	2.37305
$764$	−3.37347	−0.122048
$765$	7.82461	0.282899
$766$	−74.7670	−2.70144
$767$	1.36729	0.0493701
$768$	2.33352	0.0842035
$769$	28.8715	1.04113	0.520566	−	0.853821i	$-0.325721\pi$
$769$	28.8715	1.04113	0.520566	+	0.853821i	$0.325721\pi$
$770$	59.8528	2.15695
$771$	0.613293	0.0220872
$772$	−3.77946	−0.136026
$773$	32.1343	1.15579	0.577896	−	0.816111i	$-0.303874\pi$
$773$	32.1343	1.15579	0.577896	+	0.816111i	$0.303874\pi$
$774$	−38.5611	−1.38605
$775$	23.5686	0.846608
$776$	−99.1936	−3.56084
$777$	−0.614669	−0.0220511
$778$	−49.8993	−1.78898
$779$	−1.83160	−0.0656237
$780$	−0.508633	−0.0182120
$781$	4.69565	0.168024
$782$	−15.4265	−0.551650
$783$	7.15528	0.255709
$784$	141.804	5.06443
$785$	0.965335	0.0344543
$786$	3.89052	0.138770
$787$	23.6738	0.843880	0.421940	−	0.906624i	$-0.361349\pi$
$787$	23.6738	0.843880	0.421940	+	0.906624i	$0.361349\pi$
$788$	99.8525	3.55710
$789$	−2.36007	−0.0840206
$790$	19.6004	0.697352
$791$	−4.69646	−0.166987
$792$	102.130	3.62902
$793$	4.06933	0.144506
$794$	−21.5638	−0.765269
$795$	1.05371	0.0373711
$796$	13.6844	0.485032
$797$	−53.0770	−1.88008	−0.940042	−	0.341058i	$-0.889215\pi$
$797$	−53.0770	−1.88008	−0.940042	+	0.341058i	$0.889215\pi$
$798$	−1.20106	−0.0425170
$799$	−3.31519	−0.117283
$800$	39.0418	1.38034
$801$	16.1182	0.569508
$802$	−52.5017	−1.85390
$803$	2.60734	0.0920111
$804$	1.13233	0.0399341
$805$	−11.4792	−0.404588
$806$	−12.0937	−0.425984
$807$	−2.01106	−0.0707925
$808$	4.69639	0.165219
$809$	13.4018	0.471184	0.235592	−	0.971852i	$-0.424297\pi$
$809$	13.4018	0.471184	0.235592	+	0.971852i	$0.424297\pi$
$810$	24.0008	0.843301
$811$	−18.8438	−0.661696	−0.330848	−	0.943684i	$-0.607335\pi$
$811$	−18.8438	−0.661696	−0.330848	+	0.943684i	$0.607335\pi$
$812$	203.921	7.15622
$813$	2.42887	0.0851843
$814$	−12.1255	−0.424999
$815$	1.45764	0.0510589
$816$	−3.13622	−0.109790
$817$	3.68132	0.128793
$818$	−18.0168	−0.629941
$819$	10.7969	0.377273
$820$	−12.3215	−0.430284
$821$	−13.2902	−0.463830	−0.231915	−	0.972736i	$-0.574499\pi$
$821$	−13.2902	−0.463830	−0.231915	+	0.972736i	$0.574499\pi$
$822$	3.28879	0.114710
$823$	−5.88166	−0.205022	−0.102511	−	0.994732i	$-0.532688\pi$
$823$	−5.88166	−0.205022	−0.102511	+	0.994732i	$0.532688\pi$
$824$	77.1874	2.68895
$825$	2.42996	0.0846005
$826$	21.7197	0.755725
$827$	−3.58793	−0.124765	−0.0623823	−	0.998052i	$-0.519870\pi$
$827$	−3.58793	−0.124765	−0.0623823	+	0.998052i	$0.519870\pi$
$828$	−33.5931	−1.16744
$829$	41.8577	1.45378	0.726889	−	0.686755i	$-0.240965\pi$
$829$	41.8577	1.45378	0.726889	+	0.686755i	$0.240965\pi$
$830$	15.7188	0.545608
$831$	0.344480	0.0119499
$832$	−5.51479	−0.191191
$833$	37.9447	1.31471
$834$	−0.133561	−0.00462485
$835$	−0.139985	−0.00484439
$836$	−16.7216	−0.578328
$837$	−4.75742	−0.164441
$838$	−56.7674	−1.96100
$839$	22.1277	0.763932	0.381966	−	0.924176i	$-0.375247\pi$
$839$	22.1277	0.763932	0.381966	+	0.924176i	$0.375247\pi$
$840$	−4.71113	−0.162549
$841$	52.9265	1.82505
$842$	22.0144	0.758665
$843$	1.09233	0.0376220
$844$	−40.8298	−1.40542
$845$	12.9147	0.444278
$846$	−10.2291	−0.351682
$847$	51.8920	1.78303
$848$	72.1428	2.47739
$849$	−3.17283	−0.108891
$850$	25.7310	0.882568
$851$	2.32556	0.0797191
$852$	−0.633881	−0.0217164
$853$	−22.5005	−0.770402	−0.385201	−	0.922833i	$-0.625868\pi$
$853$	−22.5005	−0.770402	−0.385201	+	0.922833i	$0.625868\pi$
$854$	64.6419	2.21200
$855$	−2.30486	−0.0788246
$856$	120.133	4.10607
$857$	50.4417	1.72306	0.861529	−	0.507709i	$-0.169507\pi$
$857$	50.4417	1.72306	0.861529	+	0.507709i	$0.169507\pi$
$858$	−1.24689	−0.0425681
$859$	27.0357	0.922446	0.461223	−	0.887284i	$-0.347411\pi$
$859$	27.0357	0.922446	0.461223	+	0.887284i	$0.347411\pi$
$860$	24.7649	0.844475
$861$	−1.53118	−0.0521825
$862$	4.97409	0.169418
$863$	23.9927	0.816721	0.408360	−	0.912821i	$-0.366101\pi$
$863$	23.9927	0.816721	0.408360	+	0.912821i	$0.366101\pi$
$864$	−7.88077	−0.268109
$865$	−6.43531	−0.218807
$866$	−10.6340	−0.361358
$867$	1.40714	0.0477891
$868$	−135.584	−4.60201
$869$	33.9113	1.15036
$870$	−3.24608	−0.110052
$871$	1.37691	0.0466548
$872$	−101.781	−3.44675
$873$	−40.5695	−1.37307
$874$	4.54411	0.153707
$875$	43.5924	1.47369
$876$	−0.351973	−0.0118921
$877$	7.97100	0.269162	0.134581	−	0.990903i	$-0.457031\pi$
$877$	7.97100	0.269162	0.134581	+	0.990903i	$0.457031\pi$
$878$	73.0469	2.46521
$879$	1.48059	0.0499392
$880$	−46.0373	−1.55192
$881$	47.0967	1.58673	0.793363	−	0.608748i	$-0.208328\pi$
$881$	47.0967	1.58673	0.793363	+	0.608748i	$0.208328\pi$
$882$	117.079	3.94225
$883$	9.65683	0.324978	0.162489	−	0.986710i	$-0.448048\pi$
$883$	9.65683	0.324978	0.162489	+	0.986710i	$0.448048\pi$
$884$	−9.31838	−0.313411
$885$	−0.244009	−0.00820227
$886$	85.3565	2.86761
$887$	−7.86757	−0.264167	−0.132084	−	0.991239i	$-0.542167\pi$
$887$	−7.86757	−0.264167	−0.132084	+	0.991239i	$0.542167\pi$
$888$	0.954424	0.0320284
$889$	31.7520	1.06493
$890$	−14.6672	−0.491646
$891$	41.5244	1.39112
$892$	71.1937	2.38374
$893$	0.976540	0.0326787
$894$	−2.87618	−0.0961939
$895$	−17.2084	−0.575215
$896$	6.03535	0.201627
$897$	0.239141	0.00798469
$898$	−76.4424	−2.55091
$899$	−54.4716	−1.81673
$900$	56.0325	1.86775
$901$	19.3044	0.643122
$902$	−30.2054	−1.00573
$903$	3.07752	0.102413
$904$	7.29239	0.242541
$905$	−6.82787	−0.226966
$906$	1.81120	0.0601731
$907$	47.8827	1.58992	0.794959	−	0.606663i	$-0.207492\pi$
$907$	47.8827	1.58992	0.794959	+	0.606663i	$0.207492\pi$
$908$	−47.5265	−1.57722
$909$	1.92079	0.0637087
$910$	−9.82493	−0.325693
$911$	−29.0498	−0.962463	−0.481231	−	0.876594i	$-0.659810\pi$
$911$	−29.0498	−0.962463	−0.481231	+	0.876594i	$0.659810\pi$
$912$	0.923823	0.0305908
$913$	27.1956	0.900042
$914$	31.1555	1.03053
$915$	−0.726216	−0.0240080
$916$	19.1399	0.632400
$917$	53.0381	1.75147
$918$	−5.19393	−0.171425
$919$	23.0614	0.760727	0.380363	−	0.924837i	$-0.375799\pi$
$919$	23.0614	0.760727	0.380363	+	0.924837i	$0.375799\pi$
$920$	17.8242	0.587647
$921$	−2.21536	−0.0729987
$922$	−1.65580	−0.0545309
$923$	−0.770799	−0.0253712
$924$	−13.9789	−0.459873
$925$	−3.87898	−0.127540
$926$	90.9220	2.98788
$927$	31.5691	1.03687
$928$	−90.2333	−2.96205
$929$	3.13545	0.102871	0.0514354	−	0.998676i	$-0.483620\pi$
$929$	3.13545	0.102871	0.0514354	+	0.998676i	$0.483620\pi$
$930$	2.15826	0.0707722
$931$	−11.1772	−0.366318
$932$	−73.3276	−2.40193
$933$	1.00599	0.0329347
$934$	43.3696	1.41910
$935$	−12.3189	−0.402872
$936$	−16.7648	−0.547973
$937$	59.3774	1.93977	0.969887	−	0.243554i	$-0.0783132\pi$
$937$	59.3774	1.93977	0.969887	+	0.243554i	$0.0783132\pi$
$938$	21.8724	0.714160
$939$	−2.47331	−0.0807136
$940$	6.56935	0.214268
$941$	2.14709	0.0699930	0.0349965	−	0.999387i	$-0.488858\pi$
$941$	2.14709	0.0699930	0.0349965	+	0.999387i	$0.488858\pi$
$942$	−0.319457	−0.0104085
$943$	5.79311	0.188650
$944$	−16.7062	−0.543742
$945$	−3.86492	−0.125726
$946$	60.7098	1.97385
$947$	18.9680	0.616378	0.308189	−	0.951325i	$-0.400277\pi$
$947$	18.9680	0.616378	0.308189	+	0.951325i	$0.400277\pi$
$948$	−4.57778	−0.148679
$949$	−0.427999	−0.0138934
$950$	−7.57948	−0.245911
$951$	0.985135	0.0319452
$952$	−86.3100	−2.79732
$953$	−7.17607	−0.232456	−0.116228	−	0.993223i	$-0.537080\pi$
$953$	−7.17607	−0.232456	−0.116228	+	0.993223i	$0.537080\pi$
$954$	59.5639	1.92845
$955$	0.732073	0.0236893
$956$	18.4620	0.597102
$957$	−5.61613	−0.181544
$958$	54.7430	1.76866
$959$	44.8350	1.44780
$960$	0.984175	0.0317641
$961$	5.21726	0.168299
$962$	1.99042	0.0641738
$963$	49.1336	1.58331
$964$	−38.5599	−1.24193
$965$	0.820176	0.0264024
$966$	3.79879	0.122224
$967$	2.49758	0.0803167	0.0401583	−	0.999193i	$-0.487214\pi$
$967$	2.49758	0.0803167	0.0401583	+	0.999193i	$0.487214\pi$
$968$	−80.5749	−2.58978
$969$	0.247202	0.00794126
$970$	36.9174	1.18535
$971$	27.1305	0.870660	0.435330	−	0.900271i	$-0.356632\pi$
$971$	27.1305	0.870660	0.435330	+	0.900271i	$0.356632\pi$
$972$	−16.9822	−0.544703
$973$	−1.82079	−0.0583720
$974$	−55.3646	−1.77400
$975$	−0.398882	−0.0127745
$976$	−49.7209	−1.59153
$977$	−11.6925	−0.374075	−0.187037	−	0.982353i	$-0.559889\pi$
$977$	−11.6925	−0.374075	−0.187037	+	0.982353i	$0.559889\pi$
$978$	−0.482375	−0.0154246
$979$	−25.3762	−0.811026
$980$	−75.1910	−2.40189
$981$	−41.6279	−1.32908
$982$	89.0560	2.84189
$983$	−5.39586	−0.172101	−0.0860506	−	0.996291i	$-0.527425\pi$
$983$	−5.39586	−0.172101	−0.0860506	+	0.996291i	$0.527425\pi$
$984$	2.37753	0.0757928
$985$	−21.6688	−0.690427
$986$	−59.4695	−1.89390
$987$	0.816369	0.0259853
$988$	2.74487	0.0873261
$989$	−11.6436	−0.370244
$990$	−38.0102	−1.20804
$991$	59.9054	1.90296	0.951479	−	0.307713i	$-0.0995636\pi$
$991$	59.9054	1.90296	0.951479	+	0.307713i	$0.0995636\pi$
$992$	59.9946	1.90483
$993$	3.54611	0.112532
$994$	−12.2443	−0.388364
$995$	−2.96964	−0.0941440
$996$	−3.67121	−0.116327
$997$	3.72545	0.117986	0.0589931	−	0.998258i	$-0.481211\pi$
$997$	3.72545	0.117986	0.0589931	+	0.998258i	$0.481211\pi$
$998$	39.7221	1.25738
$999$	0.782991	0.0247727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.6	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.6	✓	165	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60713 q^{2} -0.132138 q^{3} +4.79710 q^{4} -1.04101 q^{5} +0.344501 q^{6} +4.69646 q^{7} -7.29239 q^{8} -2.98254 q^{9} +O(q^{10})\)	\(q-2.60713 q^{2} -0.132138 q^{3} +4.79710 q^{4} -1.04101 q^{5} +0.344501 q^{6} +4.69646 q^{7} -7.29239 q^{8} -2.98254 q^{9} +2.71405 q^{10} +4.69565 q^{11} -0.633881 q^{12} -0.770799 q^{13} -12.2443 q^{14} +0.137558 q^{15} +9.41798 q^{16} +2.52012 q^{17} +7.77585 q^{18} -0.742339 q^{19} -4.99384 q^{20} -0.620582 q^{21} -12.2422 q^{22} +2.34793 q^{23} +0.963604 q^{24} -3.91629 q^{25} +2.00957 q^{26} +0.790522 q^{27} +22.5294 q^{28} +9.05133 q^{29} -0.358630 q^{30} -6.01808 q^{31} -9.96907 q^{32} -0.620476 q^{33} -6.57026 q^{34} -4.88907 q^{35} -14.3075 q^{36} +0.990473 q^{37} +1.93537 q^{38} +0.101852 q^{39} +7.59147 q^{40} +2.46733 q^{41} +1.61794 q^{42} -4.95908 q^{43} +22.5255 q^{44} +3.10486 q^{45} -6.12134 q^{46} -1.31549 q^{47} -1.24448 q^{48} +15.0567 q^{49} +10.2103 q^{50} -0.333004 q^{51} -3.69760 q^{52} +7.66011 q^{53} -2.06099 q^{54} -4.88823 q^{55} -34.2484 q^{56} +0.0980914 q^{57} -23.5979 q^{58} -1.77387 q^{59} +0.659878 q^{60} -5.27936 q^{61} +15.6899 q^{62} -14.0074 q^{63} +7.15464 q^{64} +0.802411 q^{65} +1.61766 q^{66} -1.78634 q^{67} +12.0892 q^{68} -0.310251 q^{69} +12.7464 q^{70} +1.00000 q^{71} +21.7499 q^{72} +0.555267 q^{73} -2.58229 q^{74} +0.517492 q^{75} -3.56108 q^{76} +22.0530 q^{77} -0.265541 q^{78} +7.22184 q^{79} -9.80423 q^{80} +8.84316 q^{81} -6.43264 q^{82} +5.79165 q^{83} -2.97700 q^{84} -2.62347 q^{85} +12.9289 q^{86} -1.19603 q^{87} -34.2426 q^{88} -5.40418 q^{89} -8.09476 q^{90} -3.62003 q^{91} +11.2632 q^{92} +0.795218 q^{93} +3.42965 q^{94} +0.772785 q^{95} +1.31729 q^{96} +13.6023 q^{97} -39.2548 q^{98} -14.0050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more