LMFDB - Embedded newform 8018.2.a.f.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.916646 q^{3} +1.00000 q^{4} -1.80395 q^{5} +0.916646 q^{6} -2.30047 q^{7} -1.00000 q^{8} -2.15976 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.916646 q^{3} +1.00000 q^{4} -1.80395 q^{5} +0.916646 q^{6} -2.30047 q^{7} -1.00000 q^{8} -2.15976 q^{9} +1.80395 q^{10} +5.03734 q^{11} -0.916646 q^{12} +3.75894 q^{13} +2.30047 q^{14} +1.65359 q^{15} +1.00000 q^{16} -1.14389 q^{17} +2.15976 q^{18} -1.00000 q^{19} -1.80395 q^{20} +2.10872 q^{21} -5.03734 q^{22} -3.89553 q^{23} +0.916646 q^{24} -1.74576 q^{25} -3.75894 q^{26} +4.72967 q^{27} -2.30047 q^{28} -6.08127 q^{29} -1.65359 q^{30} +2.27780 q^{31} -1.00000 q^{32} -4.61746 q^{33} +1.14389 q^{34} +4.14994 q^{35} -2.15976 q^{36} +6.22253 q^{37} +1.00000 q^{38} -3.44562 q^{39} +1.80395 q^{40} +11.2605 q^{41} -2.10872 q^{42} -10.5371 q^{43} +5.03734 q^{44} +3.89610 q^{45} +3.89553 q^{46} -7.77272 q^{47} -0.916646 q^{48} -1.70784 q^{49} +1.74576 q^{50} +1.04855 q^{51} +3.75894 q^{52} +4.91807 q^{53} -4.72967 q^{54} -9.08712 q^{55} +2.30047 q^{56} +0.916646 q^{57} +6.08127 q^{58} +0.349209 q^{59} +1.65359 q^{60} +1.02372 q^{61} -2.27780 q^{62} +4.96846 q^{63} +1.00000 q^{64} -6.78096 q^{65} +4.61746 q^{66} +2.71873 q^{67} -1.14389 q^{68} +3.57082 q^{69} -4.14994 q^{70} +7.52431 q^{71} +2.15976 q^{72} -5.77390 q^{73} -6.22253 q^{74} +1.60024 q^{75} -1.00000 q^{76} -11.5882 q^{77} +3.44562 q^{78} +1.97978 q^{79} -1.80395 q^{80} +2.14384 q^{81} -11.2605 q^{82} -7.97117 q^{83} +2.10872 q^{84} +2.06353 q^{85} +10.5371 q^{86} +5.57437 q^{87} -5.03734 q^{88} +8.56375 q^{89} -3.89610 q^{90} -8.64734 q^{91} -3.89553 q^{92} -2.08793 q^{93} +7.77272 q^{94} +1.80395 q^{95} +0.916646 q^{96} -8.80542 q^{97} +1.70784 q^{98} -10.8794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.916646	−0.529226	−0.264613	−	0.964355i	$-0.585244\pi$
$3$	−0.916646	−0.529226	−0.264613	+	0.964355i	$0.585244\pi$
$4$	1.00000	0.500000
$5$	−1.80395	−0.806752	−0.403376	−	0.915034i	$-0.632163\pi$
$5$	−1.80395	−0.806752	−0.403376	+	0.915034i	$0.632163\pi$
$6$	0.916646	0.374219
$7$	−2.30047	−0.869496	−0.434748	−	0.900552i	$-0.643163\pi$
$7$	−2.30047	−0.869496	−0.434748	+	0.900552i	$0.643163\pi$
$8$	−1.00000	−0.353553
$9$	−2.15976	−0.719920
$10$	1.80395	0.570460
$11$	5.03734	1.51882	0.759408	−	0.650615i	$-0.225489\pi$
$11$	5.03734	1.51882	0.759408	+	0.650615i	$0.225489\pi$
$12$	−0.916646	−0.264613
$13$	3.75894	1.04254	0.521272	−	0.853391i	$-0.325458\pi$
$13$	3.75894	1.04254	0.521272	+	0.853391i	$0.325458\pi$
$14$	2.30047	0.614826
$15$	1.65359	0.426954
$16$	1.00000	0.250000
$17$	−1.14389	−0.277435	−0.138718	−	0.990332i	$-0.544298\pi$
$17$	−1.14389	−0.277435	−0.138718	+	0.990332i	$0.544298\pi$
$18$	2.15976	0.509060
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.80395	−0.403376
$21$	2.10872	0.460160
$22$	−5.03734	−1.07396
$23$	−3.89553	−0.812273	−0.406137	−	0.913812i	$-0.633124\pi$
$23$	−3.89553	−0.812273	−0.406137	+	0.913812i	$0.633124\pi$
$24$	0.916646	0.187110
$25$	−1.74576	−0.349151
$26$	−3.75894	−0.737190
$27$	4.72967	0.910226
$28$	−2.30047	−0.434748
$29$	−6.08127	−1.12926	−0.564632	−	0.825343i	$-0.690982\pi$
$29$	−6.08127	−1.12926	−0.564632	+	0.825343i	$0.690982\pi$
$30$	−1.65359	−0.301902
$31$	2.27780	0.409104	0.204552	−	0.978856i	$-0.434426\pi$
$31$	2.27780	0.409104	0.204552	+	0.978856i	$0.434426\pi$
$32$	−1.00000	−0.176777
$33$	−4.61746	−0.803796
$34$	1.14389	0.196176
$35$	4.14994	0.701467
$36$	−2.15976	−0.359960
$37$	6.22253	1.02298	0.511489	−	0.859290i	$-0.329094\pi$
$37$	6.22253	1.02298	0.511489	+	0.859290i	$0.329094\pi$
$38$	1.00000	0.162221
$39$	−3.44562	−0.551741
$40$	1.80395	0.285230
$41$	11.2605	1.75859	0.879294	−	0.476280i	$-0.158015\pi$
$41$	11.2605	1.75859	0.879294	+	0.476280i	$0.158015\pi$
$42$	−2.10872	−0.325382
$43$	−10.5371	−1.60689	−0.803444	−	0.595381i	$-0.797001\pi$
$43$	−10.5371	−1.60689	−0.803444	+	0.595381i	$0.797001\pi$
$44$	5.03734	0.759408
$45$	3.89610	0.580797
$46$	3.89553	0.574364
$47$	−7.77272	−1.13377	−0.566884	−	0.823798i	$-0.691851\pi$
$47$	−7.77272	−1.13377	−0.566884	+	0.823798i	$0.691851\pi$
$48$	−0.916646	−0.132306
$49$	−1.70784	−0.243977
$50$	1.74576	0.246887
$51$	1.04855	0.146826
$52$	3.75894	0.521272
$53$	4.91807	0.675548	0.337774	−	0.941227i	$-0.390326\pi$
$53$	4.91807	0.675548	0.337774	+	0.941227i	$0.390326\pi$
$54$	−4.72967	−0.643627
$55$	−9.08712	−1.22531
$56$	2.30047	0.307413
$57$	0.916646	0.121413
$58$	6.08127	0.798510
$59$	0.349209	0.0454631	0.0227316	−	0.999742i	$-0.492764\pi$
$59$	0.349209	0.0454631	0.0227316	+	0.999742i	$0.492764\pi$
$60$	1.65359	0.213477
$61$	1.02372	0.131073	0.0655367	−	0.997850i	$-0.479124\pi$
$61$	1.02372	0.131073	0.0655367	+	0.997850i	$0.479124\pi$
$62$	−2.27780	−0.289280
$63$	4.96846	0.625967
$64$	1.00000	0.125000
$65$	−6.78096	−0.841074
$66$	4.61746	0.568370
$67$	2.71873	0.332146	0.166073	−	0.986113i	$-0.446891\pi$
$67$	2.71873	0.332146	0.166073	+	0.986113i	$0.446891\pi$
$68$	−1.14389	−0.138718
$69$	3.57082	0.429876
$70$	−4.14994	−0.496012
$71$	7.52431	0.892972	0.446486	−	0.894791i	$-0.352675\pi$
$71$	7.52431	0.892972	0.446486	+	0.894791i	$0.352675\pi$
$72$	2.15976	0.254530
$73$	−5.77390	−0.675784	−0.337892	−	0.941185i	$-0.609714\pi$
$73$	−5.77390	−0.675784	−0.337892	+	0.941185i	$0.609714\pi$
$74$	−6.22253	−0.723354
$75$	1.60024	0.184780
$76$	−1.00000	−0.114708
$77$	−11.5882	−1.32060
$78$	3.44562	0.390140
$79$	1.97978	0.222743	0.111372	−	0.993779i	$-0.464476\pi$
$79$	1.97978	0.222743	0.111372	+	0.993779i	$0.464476\pi$
$80$	−1.80395	−0.201688
$81$	2.14384	0.238205
$82$	−11.2605	−1.24351
$83$	−7.97117	−0.874949	−0.437475	−	0.899231i	$-0.644127\pi$
$83$	−7.97117	−0.874949	−0.437475	+	0.899231i	$0.644127\pi$
$84$	2.10872	0.230080
$85$	2.06353	0.223821
$86$	10.5371	1.13624
$87$	5.57437	0.597635
$88$	−5.03734	−0.536982
$89$	8.56375	0.907755	0.453878	−	0.891064i	$-0.350040\pi$
$89$	8.56375	0.907755	0.453878	+	0.891064i	$0.350040\pi$
$90$	−3.89610	−0.410685
$91$	−8.64734	−0.906487
$92$	−3.89553	−0.406137
$93$	−2.08793	−0.216508
$94$	7.77272	0.801695
$95$	1.80395	0.185082
$96$	0.916646	0.0935548
$97$	−8.80542	−0.894055	−0.447028	−	0.894520i	$-0.647517\pi$
$97$	−8.80542	−0.894055	−0.447028	+	0.894520i	$0.647517\pi$
$98$	1.70784	0.172518
$99$	−10.8794	−1.09343
$100$	−1.74576	−0.174576
$101$	−0.929275	−0.0924663	−0.0462332	−	0.998931i	$-0.514722\pi$
$101$	−0.929275	−0.0924663	−0.0462332	+	0.998931i	$0.514722\pi$
$102$	−1.04855	−0.103822
$103$	6.26961	0.617763	0.308881	−	0.951101i	$-0.400045\pi$
$103$	6.26961	0.617763	0.308881	+	0.951101i	$0.400045\pi$
$104$	−3.75894	−0.368595
$105$	−3.80402	−0.371235
$106$	−4.91807	−0.477685
$107$	9.91391	0.958413	0.479207	−	0.877702i	$-0.340924\pi$
$107$	9.91391	0.958413	0.479207	+	0.877702i	$0.340924\pi$
$108$	4.72967	0.455113
$109$	13.5714	1.29991	0.649954	−	0.759974i	$-0.274788\pi$
$109$	13.5714	1.29991	0.649954	+	0.759974i	$0.274788\pi$
$110$	9.08712	0.866423
$111$	−5.70386	−0.541386
$112$	−2.30047	−0.217374
$113$	1.30944	0.123182	0.0615910	−	0.998101i	$-0.480383\pi$
$113$	1.30944	0.123182	0.0615910	+	0.998101i	$0.480383\pi$
$114$	−0.916646	−0.0858518
$115$	7.02734	0.655303
$116$	−6.08127	−0.564632
$117$	−8.11842	−0.750548
$118$	−0.349209	−0.0321473
$119$	2.63149	0.241229
$120$	−1.65359	−0.150951
$121$	14.3748	1.30680
$122$	−1.02372	−0.0926829
$123$	−10.3218	−0.930690
$124$	2.27780	0.204552
$125$	12.1690	1.08843
$126$	−4.96846	−0.442626
$127$	19.3759	1.71933	0.859666	−	0.510856i	$-0.170671\pi$
$127$	19.3759	1.71933	0.859666	+	0.510856i	$0.170671\pi$
$128$	−1.00000	−0.0883883
$129$	9.65876	0.850406
$130$	6.78096	0.594729
$131$	19.6343	1.71546	0.857729	−	0.514102i	$-0.171875\pi$
$131$	19.6343	1.71546	0.857729	+	0.514102i	$0.171875\pi$
$132$	−4.61746	−0.401898
$133$	2.30047	0.199476
$134$	−2.71873	−0.234863
$135$	−8.53210	−0.734327
$136$	1.14389	0.0980881
$137$	11.8902	1.01585	0.507926	−	0.861401i	$-0.330412\pi$
$137$	11.8902	1.01585	0.507926	+	0.861401i	$0.330412\pi$
$138$	−3.57082	−0.303968
$139$	7.08368	0.600830	0.300415	−	0.953809i	$-0.402875\pi$
$139$	7.08368	0.600830	0.300415	+	0.953809i	$0.402875\pi$
$140$	4.14994	0.350734
$141$	7.12483	0.600019
$142$	−7.52431	−0.631426
$143$	18.9351	1.58343
$144$	−2.15976	−0.179980
$145$	10.9703	0.911036
$146$	5.77390	0.477852
$147$	1.56548	0.129119
$148$	6.22253	0.511489
$149$	−19.2546	−1.57740	−0.788699	−	0.614780i	$-0.789245\pi$
$149$	−19.2546	−1.57740	−0.788699	+	0.614780i	$0.789245\pi$
$150$	−1.60024	−0.130659
$151$	8.28752	0.674429	0.337215	−	0.941428i	$-0.390515\pi$
$151$	8.28752	0.674429	0.337215	+	0.941428i	$0.390515\pi$
$152$	1.00000	0.0811107
$153$	2.47054	0.199731
$154$	11.5882	0.933808
$155$	−4.10903	−0.330046
$156$	−3.44562	−0.275870
$157$	−9.56476	−0.763351	−0.381676	−	0.924296i	$-0.624653\pi$
$157$	−9.56476	−0.763351	−0.381676	+	0.924296i	$0.624653\pi$
$158$	−1.97978	−0.157503
$159$	−4.50813	−0.357518
$160$	1.80395	0.142615
$161$	8.96154	0.706268
$162$	−2.14384	−0.168436
$163$	−8.95337	−0.701282	−0.350641	−	0.936510i	$-0.614036\pi$
$163$	−8.95337	−0.701282	−0.350641	+	0.936510i	$0.614036\pi$
$164$	11.2605	0.879294
$165$	8.32967	0.648464
$166$	7.97117	0.618682
$167$	−13.8531	−1.07198	−0.535992	−	0.844223i	$-0.680062\pi$
$167$	−13.8531	−1.07198	−0.535992	+	0.844223i	$0.680062\pi$
$168$	−2.10872	−0.162691
$169$	1.12966	0.0868970
$170$	−2.06353	−0.158266
$171$	2.15976	0.165161
$172$	−10.5371	−0.803444
$173$	−6.26054	−0.475980	−0.237990	−	0.971268i	$-0.576488\pi$
$173$	−6.26054	−0.475980	−0.237990	+	0.971268i	$0.576488\pi$
$174$	−5.57437	−0.422592
$175$	4.01606	0.303586
$176$	5.03734	0.379704
$177$	−0.320101	−0.0240603
$178$	−8.56375	−0.641880
$179$	−10.0094	−0.748139	−0.374069	−	0.927401i	$-0.622038\pi$
$179$	−10.0094	−0.748139	−0.374069	+	0.927401i	$0.622038\pi$
$180$	3.89610	0.290398
$181$	3.46958	0.257892	0.128946	−	0.991652i	$-0.458841\pi$
$181$	3.46958	0.257892	0.128946	+	0.991652i	$0.458841\pi$
$182$	8.64734	0.640983
$183$	−0.938385	−0.0693674
$184$	3.89553	0.287182
$185$	−11.2251	−0.825289
$186$	2.08793	0.153095
$187$	−5.76218	−0.421373
$188$	−7.77272	−0.566884
$189$	−10.8805	−0.791438
$190$	−1.80395	−0.130872
$191$	−10.8516	−0.785197	−0.392599	−	0.919710i	$-0.628424\pi$
$191$	−10.8516	−0.785197	−0.392599	+	0.919710i	$0.628424\pi$
$192$	−0.916646	−0.0661532
$193$	−21.2725	−1.53123	−0.765614	−	0.643300i	$-0.777565\pi$
$193$	−21.2725	−1.53123	−0.765614	+	0.643300i	$0.777565\pi$
$194$	8.80542	0.632192
$195$	6.21574	0.445118
$196$	−1.70784	−0.121989
$197$	13.9011	0.990416	0.495208	−	0.868775i	$-0.335092\pi$
$197$	13.9011	0.990416	0.495208	+	0.868775i	$0.335092\pi$
$198$	10.8794	0.773169
$199$	−4.74177	−0.336135	−0.168067	−	0.985775i	$-0.553753\pi$
$199$	−4.74177	−0.336135	−0.168067	+	0.985775i	$0.553753\pi$
$200$	1.74576	0.123444
$201$	−2.49211	−0.175780
$202$	0.929275	0.0653836
$203$	13.9898	0.981890
$204$	1.04855	0.0734129
$205$	−20.3133	−1.41874
$206$	−6.26961	−0.436824
$207$	8.41340	0.584772
$208$	3.75894	0.260636
$209$	−5.03734	−0.348440
$210$	3.80402	0.262503
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	4.91807	0.337774
$213$	−6.89713	−0.472584
$214$	−9.91391	−0.677701
$215$	19.0084	1.29636
$216$	−4.72967	−0.321814
$217$	−5.24000	−0.355714
$218$	−13.5714	−0.919173
$219$	5.29263	0.357642
$220$	−9.08712	−0.612654
$221$	−4.29983	−0.289238
$222$	5.70386	0.382818
$223$	19.4130	1.29999	0.649996	−	0.759937i	$-0.274770\pi$
$223$	19.4130	1.29999	0.649996	+	0.759937i	$0.274770\pi$
$224$	2.30047	0.153707
$225$	3.77041	0.251361
$226$	−1.30944	−0.0871028
$227$	0.405414	0.0269083	0.0134541	−	0.999909i	$-0.495717\pi$
$227$	0.405414	0.0269083	0.0134541	+	0.999909i	$0.495717\pi$
$228$	0.916646	0.0607064
$229$	−11.0518	−0.730321	−0.365160	−	0.930945i	$-0.618986\pi$
$229$	−11.0518	−0.730321	−0.365160	+	0.930945i	$0.618986\pi$
$230$	−7.02734	−0.463369
$231$	10.6223	0.698898
$232$	6.08127	0.399255
$233$	26.9676	1.76670	0.883352	−	0.468711i	$-0.155281\pi$
$233$	26.9676	1.76670	0.883352	+	0.468711i	$0.155281\pi$
$234$	8.11842	0.530718
$235$	14.0216	0.914669
$236$	0.349209	0.0227316
$237$	−1.81476	−0.117881
$238$	−2.63149	−0.170574
$239$	−5.99193	−0.387586	−0.193793	−	0.981042i	$-0.562079\pi$
$239$	−5.99193	−0.387586	−0.193793	+	0.981042i	$0.562079\pi$
$240$	1.65359	0.106738
$241$	−13.9854	−0.900880	−0.450440	−	0.892807i	$-0.648733\pi$
$241$	−13.9854	−0.900880	−0.450440	+	0.892807i	$0.648733\pi$
$242$	−14.3748	−0.924047
$243$	−16.1542	−1.03629
$244$	1.02372	0.0655367
$245$	3.08086	0.196829
$246$	10.3218	0.658097
$247$	−3.75894	−0.239176
$248$	−2.27780	−0.144640
$249$	7.30674	0.463046
$250$	−12.1690	−0.769637
$251$	−3.43023	−0.216514	−0.108257	−	0.994123i	$-0.534527\pi$
$251$	−3.43023	−0.216514	−0.108257	+	0.994123i	$0.534527\pi$
$252$	4.96846	0.312984
$253$	−19.6231	−1.23369
$254$	−19.3759	−1.21575
$255$	−1.89153	−0.118452
$256$	1.00000	0.0625000
$257$	−29.4124	−1.83469	−0.917347	−	0.398090i	$-0.869673\pi$
$257$	−29.4124	−1.83469	−0.917347	+	0.398090i	$0.869673\pi$
$258$	−9.65876	−0.601328
$259$	−14.3147	−0.889475
$260$	−6.78096	−0.420537
$261$	13.1341	0.812979
$262$	−19.6343	−1.21301
$263$	3.88200	0.239374	0.119687	−	0.992812i	$-0.461811\pi$
$263$	3.88200	0.239374	0.119687	+	0.992812i	$0.461811\pi$
$264$	4.61746	0.284185
$265$	−8.87196	−0.545000
$266$	−2.30047	−0.141051
$267$	−7.84993	−0.480408
$268$	2.71873	0.166073
$269$	29.0181	1.76926	0.884631	−	0.466292i	$-0.154410\pi$
$269$	29.0181	1.76926	0.884631	+	0.466292i	$0.154410\pi$
$270$	8.53210	0.519247
$271$	−18.6560	−1.13327	−0.566635	−	0.823969i	$-0.691755\pi$
$271$	−18.6560	−1.13327	−0.566635	+	0.823969i	$0.691755\pi$
$272$	−1.14389	−0.0693588
$273$	7.92655	0.479736
$274$	−11.8902	−0.718316
$275$	−8.79397	−0.530296
$276$	3.57082	0.214938
$277$	−10.7555	−0.646235	−0.323118	−	0.946359i	$-0.604731\pi$
$277$	−10.7555	−0.646235	−0.323118	+	0.946359i	$0.604731\pi$
$278$	−7.08368	−0.424851
$279$	−4.91949	−0.294522
$280$	−4.14994	−0.248006
$281$	3.44052	0.205244	0.102622	−	0.994720i	$-0.467277\pi$
$281$	3.44052	0.205244	0.102622	+	0.994720i	$0.467277\pi$
$282$	−7.12483	−0.424278
$283$	12.3736	0.735532	0.367766	−	0.929918i	$-0.380123\pi$
$283$	12.3736	0.735532	0.367766	+	0.929918i	$0.380123\pi$
$284$	7.52431	0.446486
$285$	−1.65359	−0.0979500
$286$	−18.9351	−1.11965
$287$	−25.9043	−1.52908
$288$	2.15976	0.127265
$289$	−15.6915	−0.923030
$290$	−10.9703	−0.644199
$291$	8.07145	0.473157
$292$	−5.77390	−0.337892
$293$	−26.9137	−1.57232	−0.786159	−	0.618024i	$-0.787933\pi$
$293$	−26.9137	−1.57232	−0.786159	+	0.618024i	$0.787933\pi$
$294$	−1.56548	−0.0913009
$295$	−0.629956	−0.0366775
$296$	−6.22253	−0.361677
$297$	23.8250	1.38247
$298$	19.2546	1.11539
$299$	−14.6431	−0.846830
$300$	1.60024	0.0923899
$301$	24.2402	1.39718
$302$	−8.28752	−0.476893
$303$	0.851816	0.0489356
$304$	−1.00000	−0.0573539
$305$	−1.84673	−0.105744
$306$	−2.47054	−0.141231
$307$	−6.75633	−0.385604	−0.192802	−	0.981238i	$-0.561758\pi$
$307$	−6.75633	−0.385604	−0.192802	+	0.981238i	$0.561758\pi$
$308$	−11.5882	−0.660302
$309$	−5.74701	−0.326936
$310$	4.10903	0.233377
$311$	12.3349	0.699447	0.349723	−	0.936853i	$-0.386276\pi$
$311$	12.3349	0.699447	0.349723	+	0.936853i	$0.386276\pi$
$312$	3.44562	0.195070
$313$	−24.5621	−1.38833	−0.694165	−	0.719816i	$-0.744226\pi$
$313$	−24.5621	−1.38833	−0.694165	+	0.719816i	$0.744226\pi$
$314$	9.56476	0.539771
$315$	−8.96287	−0.505000
$316$	1.97978	0.111372
$317$	−0.769189	−0.0432020	−0.0216010	−	0.999767i	$-0.506876\pi$
$317$	−0.769189	−0.0432020	−0.0216010	+	0.999767i	$0.506876\pi$
$318$	4.50813	0.252803
$319$	−30.6334	−1.71514
$320$	−1.80395	−0.100844
$321$	−9.08754	−0.507217
$322$	−8.96154	−0.499407
$323$	1.14389	0.0636480
$324$	2.14384	0.119102
$325$	−6.56220	−0.364005
$326$	8.95337	0.495882
$327$	−12.4402	−0.687945
$328$	−11.2605	−0.621755
$329$	17.8809	0.985806
$330$	−8.32967	−0.458533
$331$	−12.0282	−0.661129	−0.330565	−	0.943783i	$-0.607239\pi$
$331$	−12.0282	−0.661129	−0.330565	+	0.943783i	$0.607239\pi$
$332$	−7.97117	−0.437475
$333$	−13.4392	−0.736462
$334$	13.8531	0.758007
$335$	−4.90446	−0.267959
$336$	2.10872	0.115040
$337$	1.51714	0.0826441	0.0413220	−	0.999146i	$-0.486843\pi$
$337$	1.51714	0.0826441	0.0413220	+	0.999146i	$0.486843\pi$
$338$	−1.12966	−0.0614455
$339$	−1.20029	−0.0651911
$340$	2.06353	0.111911
$341$	11.4740	0.621354
$342$	−2.15976	−0.116786
$343$	20.0321	1.08163
$344$	10.5371	0.568120
$345$	−6.44159	−0.346803
$346$	6.26054	0.336568
$347$	−8.02304	−0.430699	−0.215350	−	0.976537i	$-0.569089\pi$
$347$	−8.02304	−0.430699	−0.215350	+	0.976537i	$0.569089\pi$
$348$	5.57437	0.298818
$349$	−32.8943	−1.76079	−0.880394	−	0.474242i	$-0.842722\pi$
$349$	−32.8943	−1.76079	−0.880394	+	0.474242i	$0.842722\pi$
$350$	−4.01606	−0.214667
$351$	17.7786	0.948950
$352$	−5.03734	−0.268491
$353$	−2.29128	−0.121952	−0.0609761	−	0.998139i	$-0.519421\pi$
$353$	−2.29128	−0.121952	−0.0609761	+	0.998139i	$0.519421\pi$
$354$	0.320101	0.0170132
$355$	−13.5735	−0.720407
$356$	8.56375	0.453878
$357$	−2.41215	−0.127664
$358$	10.0094	0.529014
$359$	−14.9524	−0.789157	−0.394579	−	0.918862i	$-0.629109\pi$
$359$	−14.9524	−0.789157	−0.394579	+	0.918862i	$0.629109\pi$
$360$	−3.89610	−0.205343
$361$	1.00000	0.0526316
$362$	−3.46958	−0.182357
$363$	−13.1766	−0.691593
$364$	−8.64734	−0.453244
$365$	10.4158	0.545190
$366$	0.938385	0.0490502
$367$	7.59164	0.396281	0.198140	−	0.980174i	$-0.436510\pi$
$367$	7.59164	0.396281	0.198140	+	0.980174i	$0.436510\pi$
$368$	−3.89553	−0.203068
$369$	−24.3199	−1.26604
$370$	11.2251	0.583568
$371$	−11.3139	−0.587386
$372$	−2.08793	−0.108254
$373$	−15.0313	−0.778292	−0.389146	−	0.921176i	$-0.627230\pi$
$373$	−15.0313	−0.778292	−0.389146	+	0.921176i	$0.627230\pi$
$374$	5.76218	0.297955
$375$	−11.1547	−0.576025
$376$	7.77272	0.400847
$377$	−22.8592	−1.17731
$378$	10.8805	0.559631
$379$	−16.5727	−0.851282	−0.425641	−	0.904892i	$-0.639951\pi$
$379$	−16.5727	−0.851282	−0.425641	+	0.904892i	$0.639951\pi$
$380$	1.80395	0.0925408
$381$	−17.7608	−0.909915
$382$	10.8516	0.555218
$383$	−12.1259	−0.619603	−0.309801	−	0.950801i	$-0.600263\pi$
$383$	−12.1259	−0.619603	−0.309801	+	0.950801i	$0.600263\pi$
$384$	0.916646	0.0467774
$385$	20.9046	1.06540
$386$	21.2725	1.08274
$387$	22.7575	1.15683
$388$	−8.80542	−0.447028
$389$	−0.291108	−0.0147597	−0.00737987	−	0.999973i	$-0.502349\pi$
$389$	−0.291108	−0.0147597	−0.00737987	+	0.999973i	$0.502349\pi$
$390$	−6.21574	−0.314746
$391$	4.45607	0.225353
$392$	1.70784	0.0862589
$393$	−17.9977	−0.907864
$394$	−13.9011	−0.700330
$395$	−3.57144	−0.179698
$396$	−10.8794	−0.546713
$397$	−32.4759	−1.62992	−0.814960	−	0.579518i	$-0.803241\pi$
$397$	−32.4759	−1.62992	−0.814960	+	0.579518i	$0.803241\pi$
$398$	4.74177	0.237683
$399$	−2.10872	−0.105568
$400$	−1.74576	−0.0872878
$401$	17.3177	0.864804	0.432402	−	0.901681i	$-0.357666\pi$
$401$	17.3177	0.864804	0.432402	+	0.901681i	$0.357666\pi$
$402$	2.49211	0.124295
$403$	8.56211	0.426509
$404$	−0.929275	−0.0462332
$405$	−3.86739	−0.192172
$406$	−13.9898	−0.694301
$407$	31.3450	1.55371
$408$	−1.04855	−0.0519108
$409$	19.0537	0.942143	0.471071	−	0.882095i	$-0.343867\pi$
$409$	19.0537	0.942143	0.471071	+	0.882095i	$0.343867\pi$
$410$	20.3133	1.00320
$411$	−10.8991	−0.537615
$412$	6.26961	0.308881
$413$	−0.803345	−0.0395300
$414$	−8.41340	−0.413496
$415$	14.3796	0.705867
$416$	−3.75894	−0.184297
$417$	−6.49322	−0.317975
$418$	5.03734	0.246384
$419$	8.34101	0.407485	0.203743	−	0.979024i	$-0.434689\pi$
$419$	8.34101	0.407485	0.203743	+	0.979024i	$0.434689\pi$
$420$	−3.80402	−0.185617
$421$	−11.4766	−0.559336	−0.279668	−	0.960097i	$-0.590224\pi$
$421$	−11.4766	−0.559336	−0.279668	+	0.960097i	$0.590224\pi$
$422$	1.00000	0.0486792
$423$	16.7872	0.816222
$424$	−4.91807	−0.238842
$425$	1.99696	0.0968668
$426$	6.89713	0.334167
$427$	−2.35503	−0.113968
$428$	9.91391	0.479207
$429$	−17.3568	−0.837993
$430$	−19.0084	−0.916664
$431$	−8.54311	−0.411507	−0.205754	−	0.978604i	$-0.565965\pi$
$431$	−8.54311	−0.411507	−0.205754	+	0.978604i	$0.565965\pi$
$432$	4.72967	0.227557
$433$	28.9936	1.39334	0.696671	−	0.717391i	$-0.254664\pi$
$433$	28.9936	1.39334	0.696671	+	0.717391i	$0.254664\pi$
$434$	5.24000	0.251528
$435$	−10.0559	−0.482144
$436$	13.5714	0.649954
$437$	3.89553	0.186348
$438$	−5.29263	−0.252891
$439$	−29.5292	−1.40935	−0.704676	−	0.709530i	$-0.748907\pi$
$439$	−29.5292	−1.40935	−0.704676	+	0.709530i	$0.748907\pi$
$440$	9.08712	0.433212
$441$	3.68852	0.175644
$442$	4.29983	0.204522
$443$	−25.1195	−1.19346	−0.596732	−	0.802440i	$-0.703535\pi$
$443$	−25.1195	−1.19346	−0.596732	+	0.802440i	$0.703535\pi$
$444$	−5.70386	−0.270693
$445$	−15.4486	−0.732334
$446$	−19.4130	−0.919234
$447$	17.6496	0.834800
$448$	−2.30047	−0.108687
$449$	22.6595	1.06937	0.534683	−	0.845053i	$-0.320431\pi$
$449$	22.6595	1.06937	0.534683	+	0.845053i	$0.320431\pi$
$450$	−3.77041	−0.177739
$451$	56.7227	2.67097
$452$	1.30944	0.0615910
$453$	−7.59673	−0.356925
$454$	−0.405414	−0.0190270
$455$	15.5994	0.731310
$456$	−0.916646	−0.0429259
$457$	29.8646	1.39701	0.698503	−	0.715607i	$-0.253850\pi$
$457$	29.8646	1.39701	0.698503	+	0.715607i	$0.253850\pi$
$458$	11.0518	0.516415
$459$	−5.41024	−0.252529
$460$	7.02734	0.327652
$461$	−19.8220	−0.923204	−0.461602	−	0.887087i	$-0.652725\pi$
$461$	−19.8220	−0.923204	−0.461602	+	0.887087i	$0.652725\pi$
$462$	−10.6223	−0.494195
$463$	19.5899	0.910418	0.455209	−	0.890385i	$-0.349565\pi$
$463$	19.5899	0.910418	0.455209	+	0.890385i	$0.349565\pi$
$464$	−6.08127	−0.282316
$465$	3.76653	0.174669
$466$	−26.9676	−1.24925
$467$	31.7186	1.46776	0.733881	−	0.679278i	$-0.237707\pi$
$467$	31.7186	1.46776	0.733881	+	0.679278i	$0.237707\pi$
$468$	−8.11842	−0.375274
$469$	−6.25436	−0.288799
$470$	−14.0216	−0.646769
$471$	8.76750	0.403985
$472$	−0.349209	−0.0160736
$473$	−53.0788	−2.44056
$474$	1.81476	0.0833547
$475$	1.74576	0.0801008
$476$	2.63149	0.120614
$477$	−10.6218	−0.486341
$478$	5.99193	0.274064
$479$	22.0025	1.00532	0.502661	−	0.864484i	$-0.332354\pi$
$479$	22.0025	1.00532	0.502661	+	0.864484i	$0.332354\pi$
$480$	−1.65359	−0.0754755
$481$	23.3901	1.06650
$482$	13.9854	0.637018
$483$	−8.21456	−0.373775
$484$	14.3748	0.653400
$485$	15.8846	0.721281
$486$	16.1542	0.732768
$487$	−13.3471	−0.604814	−0.302407	−	0.953179i	$-0.597790\pi$
$487$	−13.3471	−0.604814	−0.302407	+	0.953179i	$0.597790\pi$
$488$	−1.02372	−0.0463415
$489$	8.20707	0.371137
$490$	−3.08086	−0.139179
$491$	−31.5431	−1.42352	−0.711759	−	0.702424i	$-0.752101\pi$
$491$	−31.5431	−1.42352	−0.711759	+	0.702424i	$0.752101\pi$
$492$	−10.3218	−0.465345
$493$	6.95633	0.313297
$494$	3.75894	0.169123
$495$	19.6260	0.882123
$496$	2.27780	0.102276
$497$	−17.3095	−0.776435
$498$	−7.30674	−0.327423
$499$	14.3523	0.642497	0.321248	−	0.946995i	$-0.395898\pi$
$499$	14.3523	0.642497	0.321248	+	0.946995i	$0.395898\pi$
$500$	12.1690	0.544215
$501$	12.6984	0.567322
$502$	3.43023	0.153099
$503$	−33.9717	−1.51472	−0.757362	−	0.652996i	$-0.773512\pi$
$503$	−33.9717	−1.51472	−0.757362	+	0.652996i	$0.773512\pi$
$504$	−4.96846	−0.221313
$505$	1.67637	0.0745974
$506$	19.6231	0.872353
$507$	−1.03550	−0.0459881
$508$	19.3759	0.859666
$509$	−12.1682	−0.539348	−0.269674	−	0.962952i	$-0.586916\pi$
$509$	−12.1682	−0.539348	−0.269674	+	0.962952i	$0.586916\pi$
$510$	1.89153	0.0837582
$511$	13.2827	0.587592
$512$	−1.00000	−0.0441942
$513$	−4.72967	−0.208820
$514$	29.4124	1.29732
$515$	−11.3101	−0.498381
$516$	9.65876	0.425203
$517$	−39.1538	−1.72198
$518$	14.3147	0.628954
$519$	5.73869	0.251901
$520$	6.78096	0.297365
$521$	30.0526	1.31663	0.658314	−	0.752744i	$-0.271270\pi$
$521$	30.0526	1.31663	0.658314	+	0.752744i	$0.271270\pi$
$522$	−13.1341	−0.574863
$523$	11.1640	0.488169	0.244084	−	0.969754i	$-0.421513\pi$
$523$	11.1640	0.488169	0.244084	+	0.969754i	$0.421513\pi$
$524$	19.6343	0.857729
$525$	−3.68130	−0.160665
$526$	−3.88200	−0.169263
$527$	−2.60556	−0.113500
$528$	−4.61746	−0.200949
$529$	−7.82487	−0.340212
$530$	8.87196	0.385373
$531$	−0.754208	−0.0327298
$532$	2.30047	0.0997380
$533$	42.3274	1.83340
$534$	7.84993	0.339699
$535$	−17.8842	−0.773202
$536$	−2.71873	−0.117431
$537$	9.17509	0.395934
$538$	−29.0181	−1.25106
$539$	−8.60297	−0.370556
$540$	−8.53210	−0.367163
$541$	−25.0047	−1.07504	−0.537519	−	0.843252i	$-0.680638\pi$
$541$	−25.0047	−1.07504	−0.537519	+	0.843252i	$0.680638\pi$
$542$	18.6560	0.801343
$543$	−3.18038	−0.136483
$544$	1.14389	0.0490440
$545$	−24.4822	−1.04870
$546$	−7.92655	−0.339225
$547$	−27.0033	−1.15458	−0.577289	−	0.816540i	$-0.695889\pi$
$547$	−27.0033	−1.15458	−0.577289	+	0.816540i	$0.695889\pi$
$548$	11.8902	0.507926
$549$	−2.21098	−0.0943624
$550$	8.79397	0.374976
$551$	6.08127	0.259071
$552$	−3.57082	−0.151984
$553$	−4.55443	−0.193674
$554$	10.7555	0.456957
$555$	10.2895	0.436764
$556$	7.08368	0.300415
$557$	29.5619	1.25258	0.626290	−	0.779590i	$-0.284573\pi$
$557$	29.5619	1.25258	0.626290	+	0.779590i	$0.284573\pi$
$558$	4.91949	0.208259
$559$	−39.6082	−1.67525
$560$	4.14994	0.175367
$561$	5.28188	0.223001
$562$	−3.44052	−0.145130
$563$	−31.8337	−1.34163	−0.670816	−	0.741624i	$-0.734056\pi$
$563$	−31.8337	−1.34163	−0.670816	+	0.741624i	$0.734056\pi$
$564$	7.12483	0.300010
$565$	−2.36217	−0.0993773
$566$	−12.3736	−0.520099
$567$	−4.93185	−0.207118
$568$	−7.52431	−0.315713
$569$	38.0016	1.59311	0.796555	−	0.604566i	$-0.206654\pi$
$569$	38.0016	1.59311	0.796555	+	0.604566i	$0.206654\pi$
$570$	1.65359	0.0692611
$571$	−23.6507	−0.989752	−0.494876	−	0.868964i	$-0.664786\pi$
$571$	−23.6507	−0.989752	−0.494876	+	0.868964i	$0.664786\pi$
$572$	18.9351	0.791716
$573$	9.94711	0.415547
$574$	25.9043	1.08123
$575$	6.80064	0.283606
$576$	−2.15976	−0.0899900
$577$	39.7472	1.65470	0.827349	−	0.561689i	$-0.189848\pi$
$577$	39.7472	1.65470	0.827349	+	0.561689i	$0.189848\pi$
$578$	15.6915	0.652681
$579$	19.4994	0.810366
$580$	10.9703	0.455518
$581$	18.3374	0.760765
$582$	−8.07145	−0.334573
$583$	24.7740	1.02603
$584$	5.77390	0.238926
$585$	14.6452	0.605506
$586$	26.9137	1.11180
$587$	−34.1703	−1.41036	−0.705179	−	0.709029i	$-0.749133\pi$
$587$	−34.1703	−1.41036	−0.705179	+	0.709029i	$0.749133\pi$
$588$	1.56548	0.0645595
$589$	−2.27780	−0.0938549
$590$	0.629956	0.0259349
$591$	−12.7424	−0.524153
$592$	6.22253	0.255744
$593$	5.27597	0.216658	0.108329	−	0.994115i	$-0.465450\pi$
$593$	5.27597	0.216658	0.108329	+	0.994115i	$0.465450\pi$
$594$	−23.8250	−0.977551
$595$	−4.74709	−0.194612
$596$	−19.2546	−0.788699
$597$	4.34652	0.177891
$598$	14.6431	0.598800
$599$	−30.3111	−1.23848	−0.619239	−	0.785203i	$-0.712559\pi$
$599$	−30.3111	−1.23848	−0.619239	+	0.785203i	$0.712559\pi$
$600$	−1.60024	−0.0653295
$601$	−1.51024	−0.0616038	−0.0308019	−	0.999526i	$-0.509806\pi$
$601$	−1.51024	−0.0616038	−0.0308019	+	0.999526i	$0.509806\pi$
$602$	−24.2402	−0.987957
$603$	−5.87181	−0.239118
$604$	8.28752	0.337215
$605$	−25.9315	−1.05426
$606$	−0.851816	−0.0346027
$607$	14.9361	0.606238	0.303119	−	0.952953i	$-0.401972\pi$
$607$	14.9361	0.606238	0.303119	+	0.952953i	$0.401972\pi$
$608$	1.00000	0.0405554
$609$	−12.8237	−0.519641
$610$	1.84673	0.0747721
$611$	−29.2172	−1.18200
$612$	2.47054	0.0998655
$613$	−4.57905	−0.184946	−0.0924730	−	0.995715i	$-0.529477\pi$
$613$	−4.57905	−0.184946	−0.0924730	+	0.995715i	$0.529477\pi$
$614$	6.75633	0.272663
$615$	18.6201	0.750836
$616$	11.5882	0.466904
$617$	−41.9578	−1.68916	−0.844579	−	0.535430i	$-0.820149\pi$
$617$	−41.9578	−1.68916	−0.844579	+	0.535430i	$0.820149\pi$
$618$	5.74701	0.231179
$619$	−11.7878	−0.473793	−0.236896	−	0.971535i	$-0.576130\pi$
$619$	−11.7878	−0.473793	−0.236896	+	0.971535i	$0.576130\pi$
$620$	−4.10903	−0.165023
$621$	−18.4246	−0.739352
$622$	−12.3349	−0.494584
$623$	−19.7006	−0.789290
$624$	−3.44562	−0.137935
$625$	−13.2236	−0.528942
$626$	24.5621	0.981698
$627$	4.61746	0.184404
$628$	−9.56476	−0.381676
$629$	−7.11791	−0.283810
$630$	8.96287	0.357089
$631$	−31.5924	−1.25767	−0.628837	−	0.777537i	$-0.716469\pi$
$631$	−31.5924	−1.25767	−0.628837	+	0.777537i	$0.716469\pi$
$632$	−1.97978	−0.0787516
$633$	0.916646	0.0364334
$634$	0.769189	0.0305484
$635$	−34.9532	−1.38708
$636$	−4.50813	−0.178759
$637$	−6.41967	−0.254357
$638$	30.6334	1.21279
$639$	−16.2507	−0.642868
$640$	1.80395	0.0713075
$641$	12.2690	0.484597	0.242298	−	0.970202i	$-0.422099\pi$
$641$	12.2690	0.484597	0.242298	+	0.970202i	$0.422099\pi$
$642$	9.08754	0.358657
$643$	−33.0276	−1.30248	−0.651241	−	0.758871i	$-0.725751\pi$
$643$	−33.0276	−1.30248	−0.651241	+	0.758871i	$0.725751\pi$
$644$	8.96154	0.353134
$645$	−17.4239	−0.686067
$646$	−1.14389	−0.0450059
$647$	−10.2503	−0.402982	−0.201491	−	0.979490i	$-0.564579\pi$
$647$	−10.2503	−0.402982	−0.201491	+	0.979490i	$0.564579\pi$
$648$	−2.14384	−0.0842182
$649$	1.75908	0.0690501
$650$	6.56220	0.257391
$651$	4.80322	0.188253
$652$	−8.95337	−0.350641
$653$	36.6172	1.43294	0.716471	−	0.697617i	$-0.245756\pi$
$653$	36.6172	1.43294	0.716471	+	0.697617i	$0.245756\pi$
$654$	12.4402	0.486450
$655$	−35.4194	−1.38395
$656$	11.2605	0.439647
$657$	12.4702	0.486511
$658$	−17.8809	−0.697070
$659$	−9.86508	−0.384289	−0.192145	−	0.981367i	$-0.561544\pi$
$659$	−9.86508	−0.384289	−0.192145	+	0.981367i	$0.561544\pi$
$660$	8.32967	0.324232
$661$	31.3352	1.21880	0.609398	−	0.792864i	$-0.291411\pi$
$661$	31.3352	1.21880	0.609398	+	0.792864i	$0.291411\pi$
$662$	12.0282	0.467489
$663$	3.94143	0.153072
$664$	7.97117	0.309341
$665$	−4.14994	−0.160928
$666$	13.4392	0.520757
$667$	23.6897	0.917271
$668$	−13.8531	−0.535992
$669$	−17.7949	−0.687990
$670$	4.90446	0.189476
$671$	5.15681	0.199076
$672$	−2.10872	−0.0813455
$673$	−3.11963	−0.120253	−0.0601264	−	0.998191i	$-0.519150\pi$
$673$	−3.11963	−0.120253	−0.0601264	+	0.998191i	$0.519150\pi$
$674$	−1.51714	−0.0584382
$675$	−8.25686	−0.317807
$676$	1.12966	0.0434485
$677$	28.6072	1.09946	0.549732	−	0.835341i	$-0.314730\pi$
$677$	28.6072	1.09946	0.549732	+	0.835341i	$0.314730\pi$
$678$	1.20029	0.0460971
$679$	20.2566	0.777377
$680$	−2.06353	−0.0791328
$681$	−0.371621	−0.0142406
$682$	−11.4740	−0.439363
$683$	−3.83116	−0.146595	−0.0732976	−	0.997310i	$-0.523352\pi$
$683$	−3.83116	−0.146595	−0.0732976	+	0.997310i	$0.523352\pi$
$684$	2.15976	0.0825805
$685$	−21.4494	−0.819541
$686$	−20.0321	−0.764830
$687$	10.1305	0.386504
$688$	−10.5371	−0.401722
$689$	18.4867	0.704289
$690$	6.44159	0.245227
$691$	13.4824	0.512893	0.256447	−	0.966558i	$-0.417448\pi$
$691$	13.4824	0.512893	0.256447	+	0.966558i	$0.417448\pi$
$692$	−6.26054	−0.237990
$693$	25.0278	0.950729
$694$	8.02304	0.304550
$695$	−12.7786	−0.484721
$696$	−5.57437	−0.211296
$697$	−12.8808	−0.487894
$698$	32.8943	1.24507
$699$	−24.7197	−0.934985
$700$	4.01606	0.151793
$701$	1.49666	0.0565281	0.0282640	−	0.999600i	$-0.491002\pi$
$701$	1.49666	0.0565281	0.0282640	+	0.999600i	$0.491002\pi$
$702$	−17.7786	−0.671009
$703$	−6.22253	−0.234687
$704$	5.03734	0.189852
$705$	−12.8529	−0.484067
$706$	2.29128	0.0862333
$707$	2.13777	0.0803991
$708$	−0.320101	−0.0120301
$709$	−12.8767	−0.483595	−0.241797	−	0.970327i	$-0.577737\pi$
$709$	−12.8767	−0.483595	−0.241797	+	0.970327i	$0.577737\pi$
$710$	13.5735	0.509404
$711$	−4.27586	−0.160357
$712$	−8.56375	−0.320940
$713$	−8.87321	−0.332304
$714$	2.41215	0.0902724
$715$	−34.1580	−1.27744
$716$	−10.0094	−0.374069
$717$	5.49248	0.205120
$718$	14.9524	0.558018
$719$	8.83064	0.329327	0.164664	−	0.986350i	$-0.447346\pi$
$719$	8.83064	0.329327	0.164664	+	0.986350i	$0.447346\pi$
$720$	3.89610	0.145199
$721$	−14.4230	−0.537142
$722$	−1.00000	−0.0372161
$723$	12.8197	0.476769
$724$	3.46958	0.128946
$725$	10.6164	0.394284
$726$	13.1766	0.489030
$727$	−48.4962	−1.79862	−0.899312	−	0.437308i	$-0.855932\pi$
$727$	−48.4962	−1.79862	−0.899312	+	0.437308i	$0.855932\pi$
$728$	8.64734	0.320492
$729$	8.37612	0.310227
$730$	−10.4158	−0.385508
$731$	12.0533	0.445807
$732$	−0.938385	−0.0346837
$733$	−8.35967	−0.308771	−0.154386	−	0.988011i	$-0.549340\pi$
$733$	−8.35967	−0.308771	−0.154386	+	0.988011i	$0.549340\pi$
$734$	−7.59164	−0.280213
$735$	−2.82406	−0.104167
$736$	3.89553	0.143591
$737$	13.6952	0.504468
$738$	24.3199	0.895227
$739$	−15.1413	−0.556983	−0.278491	−	0.960439i	$-0.589834\pi$
$739$	−15.1413	−0.556983	−0.278491	+	0.960439i	$0.589834\pi$
$740$	−11.2251	−0.412645
$741$	3.44562	0.126578
$742$	11.3139	0.415345
$743$	−27.4040	−1.00536	−0.502678	−	0.864474i	$-0.667652\pi$
$743$	−27.4040	−1.00536	−0.502678	+	0.864474i	$0.667652\pi$
$744$	2.08793	0.0765473
$745$	34.7344	1.27257
$746$	15.0313	0.550335
$747$	17.2158	0.629893
$748$	−5.76218	−0.210686
$749$	−22.8066	−0.833336
$750$	11.1547	0.407312
$751$	−3.93228	−0.143491	−0.0717454	−	0.997423i	$-0.522857\pi$
$751$	−3.93228	−0.143491	−0.0717454	+	0.997423i	$0.522857\pi$
$752$	−7.77272	−0.283442
$753$	3.14431	0.114585
$754$	22.8592	0.832481
$755$	−14.9503	−0.544097
$756$	−10.8805	−0.395719
$757$	−22.4832	−0.817166	−0.408583	−	0.912721i	$-0.633977\pi$
$757$	−22.4832	−0.817166	−0.408583	+	0.912721i	$0.633977\pi$
$758$	16.5727	0.601947
$759$	17.9874	0.652902
$760$	−1.80395	−0.0654362
$761$	16.6118	0.602178	0.301089	−	0.953596i	$-0.402650\pi$
$761$	16.6118	0.602178	0.301089	+	0.953596i	$0.402650\pi$
$762$	17.7608	0.643407
$763$	−31.2207	−1.13026
$764$	−10.8516	−0.392599
$765$	−4.45673	−0.161133
$766$	12.1259	0.438125
$767$	1.31266	0.0473973
$768$	−0.916646	−0.0330766
$769$	−40.5577	−1.46255	−0.731274	−	0.682084i	$-0.761074\pi$
$769$	−40.5577	−1.46255	−0.731274	+	0.682084i	$0.761074\pi$
$770$	−20.9046	−0.753351
$771$	26.9607	0.970967
$772$	−21.2725	−0.765614
$773$	−28.5300	−1.02615	−0.513077	−	0.858343i	$-0.671495\pi$
$773$	−28.5300	−1.02615	−0.513077	+	0.858343i	$0.671495\pi$
$774$	−22.7575	−0.818002
$775$	−3.97648	−0.142839
$776$	8.80542	0.316096
$777$	13.1215	0.470733
$778$	0.291108	0.0104367
$779$	−11.2605	−0.403448
$780$	6.21574	0.222559
$781$	37.9025	1.35626
$782$	−4.45607	−0.159349
$783$	−28.7624	−1.02789
$784$	−1.70784	−0.0609943
$785$	17.2544	0.615835
$786$	17.9977	0.641957
$787$	−21.7389	−0.774908	−0.387454	−	0.921889i	$-0.626645\pi$
$787$	−21.7389	−0.774908	−0.387454	+	0.921889i	$0.626645\pi$
$788$	13.9011	0.495208
$789$	−3.55842	−0.126683
$790$	3.57144	0.127066
$791$	−3.01233	−0.107106
$792$	10.8794	0.386584
$793$	3.84809	0.136650
$794$	32.4759	1.15253
$795$	8.13244	0.288428
$796$	−4.74177	−0.168067
$797$	−8.16785	−0.289320	−0.144660	−	0.989481i	$-0.546209\pi$
$797$	−8.16785	−0.289320	−0.144660	+	0.989481i	$0.546209\pi$
$798$	2.10872	0.0746477
$799$	8.89117	0.314547
$800$	1.74576	0.0617218
$801$	−18.4956	−0.653511
$802$	−17.3177	−0.611509
$803$	−29.0851	−1.02639
$804$	−2.49211	−0.0878901
$805$	−16.1662	−0.569783
$806$	−8.56211	−0.301587
$807$	−26.5993	−0.936339
$808$	0.929275	0.0326918
$809$	56.0399	1.97026	0.985129	−	0.171814i	$-0.0549628\pi$
$809$	56.0399	1.97026	0.985129	+	0.171814i	$0.0549628\pi$
$810$	3.86739	0.135886
$811$	24.5101	0.860665	0.430332	−	0.902671i	$-0.358396\pi$
$811$	24.5101	0.860665	0.430332	+	0.902671i	$0.358396\pi$
$812$	13.9898	0.490945
$813$	17.1009	0.599756
$814$	−31.3450	−1.09864
$815$	16.1515	0.565761
$816$	1.04855	0.0367064
$817$	10.5371	0.368645
$818$	−19.0537	−0.666196
$819$	18.6762	0.652598
$820$	−20.3133	−0.709372
$821$	−37.7694	−1.31816	−0.659081	−	0.752072i	$-0.729055\pi$
$821$	−37.7694	−1.31816	−0.659081	+	0.752072i	$0.729055\pi$
$822$	10.8991	0.380151
$823$	−40.6626	−1.41741	−0.708704	−	0.705506i	$-0.750720\pi$
$823$	−40.6626	−1.41741	−0.708704	+	0.705506i	$0.750720\pi$
$824$	−6.26961	−0.218412
$825$	8.06096	0.280647
$826$	0.803345	0.0279519
$827$	15.1717	0.527573	0.263786	−	0.964581i	$-0.415029\pi$
$827$	15.1717	0.527573	0.263786	+	0.964581i	$0.415029\pi$
$828$	8.41340	0.292386
$829$	−13.2935	−0.461702	−0.230851	−	0.972989i	$-0.574151\pi$
$829$	−13.2935	−0.461702	−0.230851	+	0.972989i	$0.574151\pi$
$830$	−14.3796	−0.499123
$831$	9.85898	0.342004
$832$	3.75894	0.130318
$833$	1.95359	0.0676878
$834$	6.49322	0.224842
$835$	24.9903	0.864825
$836$	−5.03734	−0.174220
$837$	10.7732	0.372377
$838$	−8.34101	−0.288136
$839$	−42.0679	−1.45235	−0.726173	−	0.687512i	$-0.758703\pi$
$839$	−42.0679	−1.45235	−0.726173	+	0.687512i	$0.758703\pi$
$840$	3.80402	0.131251
$841$	7.98185	0.275236
$842$	11.4766	0.395510
$843$	−3.15374	−0.108621
$844$	−1.00000	−0.0344214
$845$	−2.03785	−0.0701043
$846$	−16.7872	−0.577156
$847$	−33.0688	−1.13626
$848$	4.91807	0.168887
$849$	−11.3422	−0.389262
$850$	−1.99696	−0.0684952
$851$	−24.2400	−0.830937
$852$	−6.89713	−0.236292
$853$	−38.7786	−1.32775	−0.663877	−	0.747842i	$-0.731090\pi$
$853$	−38.7786	−1.32775	−0.663877	+	0.747842i	$0.731090\pi$
$854$	2.35503	0.0805874
$855$	−3.89610	−0.133244
$856$	−9.91391	−0.338850
$857$	41.5158	1.41815	0.709077	−	0.705131i	$-0.249112\pi$
$857$	41.5158	1.41815	0.709077	+	0.705131i	$0.249112\pi$
$858$	17.3568	0.592550
$859$	17.4319	0.594770	0.297385	−	0.954758i	$-0.403885\pi$
$859$	17.4319	0.594770	0.297385	+	0.954758i	$0.403885\pi$
$860$	19.0084	0.648180
$861$	23.7451	0.809231
$862$	8.54311	0.290979
$863$	1.79213	0.0610048	0.0305024	−	0.999535i	$-0.490289\pi$
$863$	1.79213	0.0610048	0.0305024	+	0.999535i	$0.490289\pi$
$864$	−4.72967	−0.160907
$865$	11.2937	0.383998
$866$	−28.9936	−0.985241
$867$	14.3836	0.488491
$868$	−5.24000	−0.177857
$869$	9.97285	0.338306
$870$	10.0559	0.340927
$871$	10.2196	0.346276
$872$	−13.5714	−0.459587
$873$	19.0176	0.643648
$874$	−3.89553	−0.131768
$875$	−27.9945	−0.946386
$876$	5.29263	0.178821
$877$	−8.55332	−0.288825	−0.144413	−	0.989518i	$-0.546129\pi$
$877$	−8.55332	−0.288825	−0.144413	+	0.989518i	$0.546129\pi$
$878$	29.5292	0.996562
$879$	24.6704	0.832111
$880$	−9.08712	−0.306327
$881$	−3.67238	−0.123726	−0.0618628	−	0.998085i	$-0.519704\pi$
$881$	−3.67238	−0.123726	−0.0618628	+	0.998085i	$0.519704\pi$
$882$	−3.68852	−0.124199
$883$	8.32051	0.280007	0.140004	−	0.990151i	$-0.455289\pi$
$883$	8.32051	0.280007	0.140004	+	0.990151i	$0.455289\pi$
$884$	−4.29983	−0.144619
$885$	0.577447	0.0194107
$886$	25.1195	0.843907
$887$	20.9799	0.704437	0.352218	−	0.935918i	$-0.385427\pi$
$887$	20.9799	0.704437	0.352218	+	0.935918i	$0.385427\pi$
$888$	5.70386	0.191409
$889$	−44.5737	−1.49495
$890$	15.4486	0.517838
$891$	10.7993	0.361789
$892$	19.4130	0.649996
$893$	7.77272	0.260104
$894$	−17.6496	−0.590292
$895$	18.0565	0.603562
$896$	2.30047	0.0768533
$897$	13.4225	0.448165
$898$	−22.6595	−0.756156
$899$	−13.8519	−0.461986
$900$	3.77041	0.125680
$901$	−5.62575	−0.187421
$902$	−56.7227	−1.88866
$903$	−22.2197	−0.739425
$904$	−1.30944	−0.0435514
$905$	−6.25896	−0.208055
$906$	7.59673	0.252384
$907$	−27.8852	−0.925913	−0.462957	−	0.886381i	$-0.653211\pi$
$907$	−27.8852	−0.925913	−0.462957	+	0.886381i	$0.653211\pi$
$908$	0.405414	0.0134541
$909$	2.00701	0.0665684
$910$	−15.5994	−0.517114
$911$	−15.8265	−0.524356	−0.262178	−	0.965020i	$-0.584441\pi$
$911$	−15.8265	−0.524356	−0.262178	+	0.965020i	$0.584441\pi$
$912$	0.916646	0.0303532
$913$	−40.1535	−1.32889
$914$	−29.8646	−0.987833
$915$	1.69280	0.0559623
$916$	−11.0518	−0.365160
$917$	−45.1681	−1.49158
$918$	5.41024	0.178565
$919$	−48.3342	−1.59440	−0.797199	−	0.603717i	$-0.793686\pi$
$919$	−48.3342	−1.59440	−0.797199	+	0.603717i	$0.793686\pi$
$920$	−7.02734	−0.231685
$921$	6.19316	0.204072
$922$	19.8220	0.652804
$923$	28.2835	0.930962
$924$	10.6223	0.349449
$925$	−10.8630	−0.357174
$926$	−19.5899	−0.643763
$927$	−13.5408	−0.444740
$928$	6.08127	0.199627
$929$	3.54595	0.116339	0.0581694	−	0.998307i	$-0.481474\pi$
$929$	3.54595	0.116339	0.0581694	+	0.998307i	$0.481474\pi$
$930$	−3.76653	−0.123509
$931$	1.70784	0.0559722
$932$	26.9676	0.883352
$933$	−11.3067	−0.370165
$934$	−31.7186	−1.03787
$935$	10.3947	0.339943
$936$	8.11842	0.265359
$937$	15.1613	0.495299	0.247649	−	0.968850i	$-0.420342\pi$
$937$	15.1613	0.495299	0.247649	+	0.968850i	$0.420342\pi$
$938$	6.25436	0.204212
$939$	22.5147	0.734740
$940$	14.0216	0.457335
$941$	4.94062	0.161060	0.0805299	−	0.996752i	$-0.474339\pi$
$941$	4.94062	0.161060	0.0805299	+	0.996752i	$0.474339\pi$
$942$	−8.76750	−0.285661
$943$	−43.8654	−1.42845
$944$	0.349209	0.0113658
$945$	19.6278	0.638494
$946$	53.0788	1.72574
$947$	−26.7617	−0.869639	−0.434819	−	0.900518i	$-0.643188\pi$
$947$	−26.7617	−0.869639	−0.434819	+	0.900518i	$0.643188\pi$
$948$	−1.81476	−0.0589407
$949$	−21.7038	−0.704535
$950$	−1.74576	−0.0566398
$951$	0.705074	0.0228636
$952$	−2.63149	−0.0852872
$953$	−52.7036	−1.70724	−0.853619	−	0.520898i	$-0.825597\pi$
$953$	−52.7036	−1.70724	−0.853619	+	0.520898i	$0.825597\pi$
$954$	10.6218	0.343895
$955$	19.5758	0.633459
$956$	−5.99193	−0.193793
$957$	28.0800	0.907698
$958$	−22.0025	−0.710870
$959$	−27.3531	−0.883279
$960$	1.65359	0.0533692
$961$	−25.8116	−0.832634
$962$	−23.3901	−0.754128
$963$	−21.4117	−0.689981
$964$	−13.9854	−0.450440
$965$	38.3746	1.23532
$966$	8.21456	0.264299
$967$	3.40608	0.109532	0.0547661	−	0.998499i	$-0.482559\pi$
$967$	3.40608	0.109532	0.0547661	+	0.998499i	$0.482559\pi$
$968$	−14.3748	−0.462024
$969$	−1.04855	−0.0336841
$970$	−15.8846	−0.510022
$971$	15.8162	0.507566	0.253783	−	0.967261i	$-0.418325\pi$
$971$	15.8162	0.507566	0.253783	+	0.967261i	$0.418325\pi$
$972$	−16.1542	−0.518145
$973$	−16.2958	−0.522419
$974$	13.3471	0.427668
$975$	6.01521	0.192641
$976$	1.02372	0.0327684
$977$	6.22552	0.199172	0.0995860	−	0.995029i	$-0.468248\pi$
$977$	6.22552	0.199172	0.0995860	+	0.995029i	$0.468248\pi$
$978$	−8.20707	−0.262433
$979$	43.1385	1.37871
$980$	3.08086	0.0984145
$981$	−29.3110	−0.935829
$982$	31.5431	1.00658
$983$	−9.10856	−0.290518	−0.145259	−	0.989394i	$-0.546402\pi$
$983$	−9.10856	−0.290518	−0.145259	+	0.989394i	$0.546402\pi$
$984$	10.3218	0.329049
$985$	−25.0770	−0.799020
$986$	−6.95633	−0.221535
$987$	−16.3905	−0.521714
$988$	−3.75894	−0.119588
$989$	41.0474	1.30523
$990$	−19.6260	−0.623755
$991$	34.9823	1.11125	0.555625	−	0.831433i	$-0.312479\pi$
$991$	34.9823	1.11125	0.555625	+	0.831433i	$0.312479\pi$
$992$	−2.27780	−0.0723201
$993$	11.0256	0.349887
$994$	17.3095	0.549022
$995$	8.55392	0.271178
$996$	7.30674	0.231523
$997$	46.6233	1.47657	0.738287	−	0.674487i	$-0.235635\pi$
$997$	46.6233	1.47657	0.738287	+	0.674487i	$0.235635\pi$
$998$	−14.3523	−0.454314
$999$	29.4305	0.931141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.15	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.15	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.916646 q^{3} +1.00000 q^{4} -1.80395 q^{5} +0.916646 q^{6} -2.30047 q^{7} -1.00000 q^{8} -2.15976 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.916646 q^{3} +1.00000 q^{4} -1.80395 q^{5} +0.916646 q^{6} -2.30047 q^{7} -1.00000 q^{8} -2.15976 q^{9} +1.80395 q^{10} +5.03734 q^{11} -0.916646 q^{12} +3.75894 q^{13} +2.30047 q^{14} +1.65359 q^{15} +1.00000 q^{16} -1.14389 q^{17} +2.15976 q^{18} -1.00000 q^{19} -1.80395 q^{20} +2.10872 q^{21} -5.03734 q^{22} -3.89553 q^{23} +0.916646 q^{24} -1.74576 q^{25} -3.75894 q^{26} +4.72967 q^{27} -2.30047 q^{28} -6.08127 q^{29} -1.65359 q^{30} +2.27780 q^{31} -1.00000 q^{32} -4.61746 q^{33} +1.14389 q^{34} +4.14994 q^{35} -2.15976 q^{36} +6.22253 q^{37} +1.00000 q^{38} -3.44562 q^{39} +1.80395 q^{40} +11.2605 q^{41} -2.10872 q^{42} -10.5371 q^{43} +5.03734 q^{44} +3.89610 q^{45} +3.89553 q^{46} -7.77272 q^{47} -0.916646 q^{48} -1.70784 q^{49} +1.74576 q^{50} +1.04855 q^{51} +3.75894 q^{52} +4.91807 q^{53} -4.72967 q^{54} -9.08712 q^{55} +2.30047 q^{56} +0.916646 q^{57} +6.08127 q^{58} +0.349209 q^{59} +1.65359 q^{60} +1.02372 q^{61} -2.27780 q^{62} +4.96846 q^{63} +1.00000 q^{64} -6.78096 q^{65} +4.61746 q^{66} +2.71873 q^{67} -1.14389 q^{68} +3.57082 q^{69} -4.14994 q^{70} +7.52431 q^{71} +2.15976 q^{72} -5.77390 q^{73} -6.22253 q^{74} +1.60024 q^{75} -1.00000 q^{76} -11.5882 q^{77} +3.44562 q^{78} +1.97978 q^{79} -1.80395 q^{80} +2.14384 q^{81} -11.2605 q^{82} -7.97117 q^{83} +2.10872 q^{84} +2.06353 q^{85} +10.5371 q^{86} +5.57437 q^{87} -5.03734 q^{88} +8.56375 q^{89} -3.89610 q^{90} -8.64734 q^{91} -3.89553 q^{92} -2.08793 q^{93} +7.77272 q^{94} +1.80395 q^{95} +0.916646 q^{96} -8.80542 q^{97} +1.70784 q^{98} -10.8794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more