LMFDB - Embedded newform 6022.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.92893 q^{3} +1.00000 q^{4} +1.84484 q^{5} +1.92893 q^{6} +2.06972 q^{7} -1.00000 q^{8} +0.720763 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.92893 q^{3} +1.00000 q^{4} +1.84484 q^{5} +1.92893 q^{6} +2.06972 q^{7} -1.00000 q^{8} +0.720763 q^{9} -1.84484 q^{10} -1.96017 q^{11} -1.92893 q^{12} +4.15799 q^{13} -2.06972 q^{14} -3.55856 q^{15} +1.00000 q^{16} +3.62247 q^{17} -0.720763 q^{18} -4.96714 q^{19} +1.84484 q^{20} -3.99235 q^{21} +1.96017 q^{22} +3.26159 q^{23} +1.92893 q^{24} -1.59658 q^{25} -4.15799 q^{26} +4.39648 q^{27} +2.06972 q^{28} -6.33193 q^{29} +3.55856 q^{30} -0.153700 q^{31} -1.00000 q^{32} +3.78103 q^{33} -3.62247 q^{34} +3.81830 q^{35} +0.720763 q^{36} -3.71755 q^{37} +4.96714 q^{38} -8.02047 q^{39} -1.84484 q^{40} -4.06522 q^{41} +3.99235 q^{42} -9.51798 q^{43} -1.96017 q^{44} +1.32969 q^{45} -3.26159 q^{46} +10.6669 q^{47} -1.92893 q^{48} -2.71624 q^{49} +1.59658 q^{50} -6.98749 q^{51} +4.15799 q^{52} -4.00881 q^{53} -4.39648 q^{54} -3.61620 q^{55} -2.06972 q^{56} +9.58127 q^{57} +6.33193 q^{58} +0.927683 q^{59} -3.55856 q^{60} -2.23317 q^{61} +0.153700 q^{62} +1.49178 q^{63} +1.00000 q^{64} +7.67082 q^{65} -3.78103 q^{66} +10.2966 q^{67} +3.62247 q^{68} -6.29137 q^{69} -3.81830 q^{70} -5.27837 q^{71} -0.720763 q^{72} -11.4150 q^{73} +3.71755 q^{74} +3.07968 q^{75} -4.96714 q^{76} -4.05701 q^{77} +8.02047 q^{78} +0.462430 q^{79} +1.84484 q^{80} -10.6428 q^{81} +4.06522 q^{82} +2.41784 q^{83} -3.99235 q^{84} +6.68287 q^{85} +9.51798 q^{86} +12.2138 q^{87} +1.96017 q^{88} -10.3998 q^{89} -1.32969 q^{90} +8.60589 q^{91} +3.26159 q^{92} +0.296477 q^{93} -10.6669 q^{94} -9.16357 q^{95} +1.92893 q^{96} +7.64119 q^{97} +2.71624 q^{98} -1.41282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * 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
$3$	−1.92893	−1.11367	−0.556834	−	0.830624i	$-0.687984\pi$
$3$	−1.92893	−1.11367	−0.556834	+	0.830624i	$0.687984\pi$
$4$	1.00000	0.500000
$5$	1.84484	0.825036	0.412518	−	0.910949i	$-0.364649\pi$
$5$	1.84484	0.825036	0.412518	+	0.910949i	$0.364649\pi$
$6$	1.92893	0.787482
$7$	2.06972	0.782282	0.391141	−	0.920331i	$-0.372080\pi$
$7$	2.06972	0.782282	0.391141	+	0.920331i	$0.372080\pi$
$8$	−1.00000	−0.353553
$9$	0.720763	0.240254
$10$	−1.84484	−0.583389
$11$	−1.96017	−0.591014	−0.295507	−	0.955341i	$-0.595489\pi$
$11$	−1.96017	−0.591014	−0.295507	+	0.955341i	$0.595489\pi$
$12$	−1.92893	−0.556834
$13$	4.15799	1.15322	0.576610	−	0.817020i	$-0.304375\pi$
$13$	4.15799	1.15322	0.576610	+	0.817020i	$0.304375\pi$
$14$	−2.06972	−0.553157
$15$	−3.55856	−0.918816
$16$	1.00000	0.250000
$17$	3.62247	0.878579	0.439289	−	0.898346i	$-0.355230\pi$
$17$	3.62247	0.878579	0.439289	+	0.898346i	$0.355230\pi$
$18$	−0.720763	−0.169886
$19$	−4.96714	−1.13954	−0.569771	−	0.821804i	$-0.692968\pi$
$19$	−4.96714	−1.13954	−0.569771	+	0.821804i	$0.692968\pi$
$20$	1.84484	0.412518
$21$	−3.99235	−0.871202
$22$	1.96017	0.417910
$23$	3.26159	0.680089	0.340044	−	0.940409i	$-0.389558\pi$
$23$	3.26159	0.680089	0.340044	+	0.940409i	$0.389558\pi$
$24$	1.92893	0.393741
$25$	−1.59658	−0.319315
$26$	−4.15799	−0.815449
$27$	4.39648	0.846104
$28$	2.06972	0.391141
$29$	−6.33193	−1.17581	−0.587904	−	0.808930i	$-0.700047\pi$
$29$	−6.33193	−1.17581	−0.587904	+	0.808930i	$0.700047\pi$
$30$	3.55856	0.649701
$31$	−0.153700	−0.0276054	−0.0138027	−	0.999905i	$-0.504394\pi$
$31$	−0.153700	−0.0276054	−0.0138027	+	0.999905i	$0.504394\pi$
$32$	−1.00000	−0.176777
$33$	3.78103	0.658193
$34$	−3.62247	−0.621249
$35$	3.81830	0.645411
$36$	0.720763	0.120127
$37$	−3.71755	−0.611161	−0.305580	−	0.952166i	$-0.598850\pi$
$37$	−3.71755	−0.611161	−0.305580	+	0.952166i	$0.598850\pi$
$38$	4.96714	0.805777
$39$	−8.02047	−1.28430
$40$	−1.84484	−0.291694
$41$	−4.06522	−0.634881	−0.317440	−	0.948278i	$-0.602823\pi$
$41$	−4.06522	−0.634881	−0.317440	+	0.948278i	$0.602823\pi$
$42$	3.99235	0.616033
$43$	−9.51798	−1.45148	−0.725739	−	0.687970i	$-0.758502\pi$
$43$	−9.51798	−1.45148	−0.725739	+	0.687970i	$0.758502\pi$
$44$	−1.96017	−0.295507
$45$	1.32969	0.198219
$46$	−3.26159	−0.480895
$47$	10.6669	1.55593	0.777966	−	0.628307i	$-0.216252\pi$
$47$	10.6669	1.55593	0.777966	+	0.628307i	$0.216252\pi$
$48$	−1.92893	−0.278417
$49$	−2.71624	−0.388035
$50$	1.59658	0.225790
$51$	−6.98749	−0.978444
$52$	4.15799	0.576610
$53$	−4.00881	−0.550653	−0.275326	−	0.961351i	$-0.588786\pi$
$53$	−4.00881	−0.550653	−0.275326	+	0.961351i	$0.588786\pi$
$54$	−4.39648	−0.598286
$55$	−3.61620	−0.487608
$56$	−2.06972	−0.276578
$57$	9.58127	1.26907
$58$	6.33193	0.831423
$59$	0.927683	0.120774	0.0603870	−	0.998175i	$-0.480767\pi$
$59$	0.927683	0.120774	0.0603870	+	0.998175i	$0.480767\pi$
$60$	−3.55856	−0.459408
$61$	−2.23317	−0.285928	−0.142964	−	0.989728i	$-0.545663\pi$
$61$	−2.23317	−0.285928	−0.142964	+	0.989728i	$0.545663\pi$
$62$	0.153700	0.0195200
$63$	1.49178	0.187947
$64$	1.00000	0.125000
$65$	7.67082	0.951448
$66$	−3.78103	−0.465412
$67$	10.2966	1.25793	0.628963	−	0.777435i	$-0.283480\pi$
$67$	10.2966	1.25793	0.628963	+	0.777435i	$0.283480\pi$
$68$	3.62247	0.439289
$69$	−6.29137	−0.757392
$70$	−3.81830	−0.456374
$71$	−5.27837	−0.626427	−0.313213	−	0.949683i	$-0.601405\pi$
$71$	−5.27837	−0.626427	−0.313213	+	0.949683i	$0.601405\pi$
$72$	−0.720763	−0.0849428
$73$	−11.4150	−1.33603	−0.668014	−	0.744149i	$-0.732855\pi$
$73$	−11.4150	−1.33603	−0.668014	+	0.744149i	$0.732855\pi$
$74$	3.71755	0.432156
$75$	3.07968	0.355611
$76$	−4.96714	−0.569771
$77$	−4.05701	−0.462339
$78$	8.02047	0.908139
$79$	0.462430	0.0520274	0.0260137	−	0.999662i	$-0.491719\pi$
$79$	0.462430	0.0520274	0.0260137	+	0.999662i	$0.491719\pi$
$80$	1.84484	0.206259
$81$	−10.6428	−1.18253
$82$	4.06522	0.448928
$83$	2.41784	0.265392	0.132696	−	0.991157i	$-0.457637\pi$
$83$	2.41784	0.265392	0.132696	+	0.991157i	$0.457637\pi$
$84$	−3.99235	−0.435601
$85$	6.68287	0.724859
$86$	9.51798	1.02635
$87$	12.2138	1.30946
$88$	1.96017	0.208955
$89$	−10.3998	−1.10237	−0.551187	−	0.834382i	$-0.685825\pi$
$89$	−10.3998	−1.10237	−0.551187	+	0.834382i	$0.685825\pi$
$90$	−1.32969	−0.140162
$91$	8.60589	0.902143
$92$	3.26159	0.340044
$93$	0.296477	0.0307432
$94$	−10.6669	−1.10021
$95$	−9.16357	−0.940163
$96$	1.92893	0.196870
$97$	7.64119	0.775845	0.387923	−	0.921692i	$-0.373193\pi$
$97$	7.64119	0.775845	0.387923	+	0.921692i	$0.373193\pi$
$98$	2.71624	0.274382
$99$	−1.41282	−0.141994
$100$	−1.59658	−0.159658
$101$	−13.5928	−1.35254	−0.676268	−	0.736655i	$-0.736404\pi$
$101$	−13.5928	−1.35254	−0.676268	+	0.736655i	$0.736404\pi$
$102$	6.98749	0.691865
$103$	−13.4844	−1.32866	−0.664328	−	0.747441i	$-0.731282\pi$
$103$	−13.4844	−1.32866	−0.664328	+	0.747441i	$0.731282\pi$
$104$	−4.15799	−0.407725
$105$	−7.36523	−0.718773
$106$	4.00881	0.389370
$107$	6.06662	0.586483	0.293241	−	0.956038i	$-0.405266\pi$
$107$	6.06662	0.586483	0.293241	+	0.956038i	$0.405266\pi$
$108$	4.39648	0.423052
$109$	−7.66739	−0.734403	−0.367201	−	0.930141i	$-0.619684\pi$
$109$	−7.66739	−0.734403	−0.367201	+	0.930141i	$0.619684\pi$
$110$	3.61620	0.344791
$111$	7.17088	0.680630
$112$	2.06972	0.195570
$113$	−15.4698	−1.45527	−0.727637	−	0.685963i	$-0.759381\pi$
$113$	−15.4698	−1.45527	−0.727637	+	0.685963i	$0.759381\pi$
$114$	−9.58127	−0.897368
$115$	6.01710	0.561098
$116$	−6.33193	−0.587904
$117$	2.99693	0.277066
$118$	−0.927683	−0.0854002
$119$	7.49752	0.687296
$120$	3.55856	0.324850
$121$	−7.15773	−0.650703
$122$	2.23317	0.202182
$123$	7.84152	0.707046
$124$	−0.153700	−0.0138027
$125$	−12.1696	−1.08848
$126$	−1.49178	−0.132898
$127$	−6.56529	−0.582575	−0.291288	−	0.956636i	$-0.594084\pi$
$127$	−6.56529	−0.582575	−0.291288	+	0.956636i	$0.594084\pi$
$128$	−1.00000	−0.0883883
$129$	18.3595	1.61646
$130$	−7.67082	−0.672775
$131$	−12.7235	−1.11166	−0.555830	−	0.831296i	$-0.687599\pi$
$131$	−12.7235	−1.11166	−0.555830	+	0.831296i	$0.687599\pi$
$132$	3.78103	0.329096
$133$	−10.2806	−0.891443
$134$	−10.2966	−0.889489
$135$	8.11080	0.698066
$136$	−3.62247	−0.310625
$137$	18.7852	1.60493	0.802465	−	0.596700i	$-0.203522\pi$
$137$	18.7852	1.60493	0.802465	+	0.596700i	$0.203522\pi$
$138$	6.29137	0.535557
$139$	15.6033	1.32346	0.661729	−	0.749743i	$-0.269823\pi$
$139$	15.6033	1.32346	0.661729	+	0.749743i	$0.269823\pi$
$140$	3.81830	0.322705
$141$	−20.5757	−1.73279
$142$	5.27837	0.442951
$143$	−8.15037	−0.681569
$144$	0.720763	0.0600636
$145$	−11.6814	−0.970085
$146$	11.4150	0.944714
$147$	5.23944	0.432142
$148$	−3.71755	−0.305580
$149$	−21.3749	−1.75110	−0.875551	−	0.483126i	$-0.839501\pi$
$149$	−21.3749	−1.75110	−0.875551	+	0.483126i	$0.839501\pi$
$150$	−3.07968	−0.251455
$151$	14.6495	1.19216	0.596080	−	0.802925i	$-0.296724\pi$
$151$	14.6495	1.19216	0.596080	+	0.802925i	$0.296724\pi$
$152$	4.96714	0.402889
$153$	2.61095	0.211082
$154$	4.05701	0.326923
$155$	−0.283552	−0.0227754
$156$	−8.02047	−0.642151
$157$	10.3340	0.824744	0.412372	−	0.911015i	$-0.364700\pi$
$157$	10.3340	0.824744	0.412372	+	0.911015i	$0.364700\pi$
$158$	−0.462430	−0.0367890
$159$	7.73271	0.613244
$160$	−1.84484	−0.145847
$161$	6.75059	0.532021
$162$	10.6428	0.836177
$163$	12.4946	0.978649	0.489325	−	0.872102i	$-0.337243\pi$
$163$	12.4946	0.978649	0.489325	+	0.872102i	$0.337243\pi$
$164$	−4.06522	−0.317440
$165$	6.97538	0.543033
$166$	−2.41784	−0.187661
$167$	9.18523	0.710774	0.355387	−	0.934719i	$-0.384349\pi$
$167$	9.18523	0.710774	0.355387	+	0.934719i	$0.384349\pi$
$168$	3.99235	0.308016
$169$	4.28889	0.329915
$170$	−6.68287	−0.512553
$171$	−3.58014	−0.273780
$172$	−9.51798	−0.725739
$173$	12.9952	0.988008	0.494004	−	0.869460i	$-0.335533\pi$
$173$	12.9952	0.988008	0.494004	+	0.869460i	$0.335533\pi$
$174$	−12.2138	−0.925928
$175$	−3.30447	−0.249795
$176$	−1.96017	−0.147753
$177$	−1.78943	−0.134502
$178$	10.3998	0.779496
$179$	−17.1008	−1.27818	−0.639088	−	0.769134i	$-0.720688\pi$
$179$	−17.1008	−1.27818	−0.639088	+	0.769134i	$0.720688\pi$
$180$	1.32969	0.0991093
$181$	13.5848	1.00975	0.504873	−	0.863193i	$-0.331539\pi$
$181$	13.5848	1.00975	0.504873	+	0.863193i	$0.331539\pi$
$182$	−8.60589	−0.637911
$183$	4.30763	0.318429
$184$	−3.26159	−0.240448
$185$	−6.85827	−0.504230
$186$	−0.296477	−0.0217387
$187$	−7.10067	−0.519252
$188$	10.6669	0.777966
$189$	9.09950	0.661892
$190$	9.16357	0.664795
$191$	15.6729	1.13405	0.567027	−	0.823699i	$-0.308093\pi$
$191$	15.6729	1.13405	0.567027	+	0.823699i	$0.308093\pi$
$192$	−1.92893	−0.139208
$193$	15.8463	1.14064	0.570321	−	0.821422i	$-0.306819\pi$
$193$	15.8463	1.14064	0.570321	+	0.821422i	$0.306819\pi$
$194$	−7.64119	−0.548605
$195$	−14.7965	−1.05960
$196$	−2.71624	−0.194017
$197$	−18.2576	−1.30080	−0.650398	−	0.759593i	$-0.725398\pi$
$197$	−18.2576	−1.30080	−0.650398	+	0.759593i	$0.725398\pi$
$198$	1.41282	0.100405
$199$	20.5073	1.45372	0.726861	−	0.686784i	$-0.240978\pi$
$199$	20.5073	1.45372	0.726861	+	0.686784i	$0.240978\pi$
$200$	1.59658	0.112895
$201$	−19.8614	−1.40091
$202$	13.5928	0.956388
$203$	−13.1053	−0.919814
$204$	−6.98749	−0.489222
$205$	−7.49967	−0.523800
$206$	13.4844	0.939501
$207$	2.35084	0.163394
$208$	4.15799	0.288305
$209$	9.73645	0.673485
$210$	7.36523	0.508249
$211$	−3.66650	−0.252412	−0.126206	−	0.992004i	$-0.540280\pi$
$211$	−3.66650	−0.252412	−0.126206	+	0.992004i	$0.540280\pi$
$212$	−4.00881	−0.275326
$213$	10.1816	0.697631
$214$	−6.06662	−0.414706
$215$	−17.5591	−1.19752
$216$	−4.39648	−0.299143
$217$	−0.318117	−0.0215952
$218$	7.66739	0.519301
$219$	22.0188	1.48789
$220$	−3.61620	−0.243804
$221$	15.0622	1.01319
$222$	−7.17088	−0.481278
$223$	22.1709	1.48467	0.742337	−	0.670026i	$-0.233717\pi$
$223$	22.1709	1.48467	0.742337	+	0.670026i	$0.233717\pi$
$224$	−2.06972	−0.138289
$225$	−1.15075	−0.0767169
$226$	15.4698	1.02903
$227$	−20.4420	−1.35678	−0.678392	−	0.734700i	$-0.737323\pi$
$227$	−20.4420	−1.35678	−0.678392	+	0.734700i	$0.737323\pi$
$228$	9.58127	0.634535
$229$	1.01912	0.0673454	0.0336727	−	0.999433i	$-0.489280\pi$
$229$	1.01912	0.0673454	0.0336727	+	0.999433i	$0.489280\pi$
$230$	−6.01710	−0.396756
$231$	7.82568	0.514892
$232$	6.33193	0.415711
$233$	−3.48573	−0.228358	−0.114179	−	0.993460i	$-0.536424\pi$
$233$	−3.48573	−0.228358	−0.114179	+	0.993460i	$0.536424\pi$
$234$	−2.99693	−0.195915
$235$	19.6787	1.28370
$236$	0.927683	0.0603870
$237$	−0.891994	−0.0579413
$238$	−7.49752	−0.485992
$239$	−3.05390	−0.197541	−0.0987703	−	0.995110i	$-0.531491\pi$
$239$	−3.05390	−0.197541	−0.0987703	+	0.995110i	$0.531491\pi$
$240$	−3.55856	−0.229704
$241$	14.1364	0.910605	0.455302	−	0.890337i	$-0.349531\pi$
$241$	14.1364	0.910605	0.455302	+	0.890337i	$0.349531\pi$
$242$	7.15773	0.460116
$243$	7.33973	0.470844
$244$	−2.23317	−0.142964
$245$	−5.01103	−0.320143
$246$	−7.84152	−0.499957
$247$	−20.6533	−1.31414
$248$	0.153700	0.00975998
$249$	−4.66383	−0.295558
$250$	12.1696	0.769674
$251$	7.58042	0.478472	0.239236	−	0.970961i	$-0.423103\pi$
$251$	7.58042	0.478472	0.239236	+	0.970961i	$0.423103\pi$
$252$	1.49178	0.0939734
$253$	−6.39328	−0.401942
$254$	6.56529	0.411943
$255$	−12.8908	−0.807252
$256$	1.00000	0.0625000
$257$	30.8555	1.92472	0.962358	−	0.271786i	$-0.0876144\pi$
$257$	30.8555	1.92472	0.962358	+	0.271786i	$0.0876144\pi$
$258$	−18.3595	−1.14301
$259$	−7.69429	−0.478100
$260$	7.67082	0.475724
$261$	−4.56382	−0.282493
$262$	12.7235	0.786062
$263$	−8.39921	−0.517917	−0.258959	−	0.965888i	$-0.583379\pi$
$263$	−8.39921	−0.517917	−0.258959	+	0.965888i	$0.583379\pi$
$264$	−3.78103	−0.232706
$265$	−7.39561	−0.454308
$266$	10.2806	0.630345
$267$	20.0604	1.22768
$268$	10.2966	0.628963
$269$	−3.15627	−0.192441	−0.0962205	−	0.995360i	$-0.530675\pi$
$269$	−3.15627	−0.192441	−0.0962205	+	0.995360i	$0.530675\pi$
$270$	−8.11080	−0.493607
$271$	5.04628	0.306540	0.153270	−	0.988184i	$-0.451020\pi$
$271$	5.04628	0.306540	0.153270	+	0.988184i	$0.451020\pi$
$272$	3.62247	0.219645
$273$	−16.6001	−1.00469
$274$	−18.7852	−1.13486
$275$	3.12956	0.188720
$276$	−6.29137	−0.378696
$277$	−15.6119	−0.938027	−0.469013	−	0.883191i	$-0.655390\pi$
$277$	−15.6119	−0.938027	−0.469013	+	0.883191i	$0.655390\pi$
$278$	−15.6033	−0.935826
$279$	−0.110782	−0.00663232
$280$	−3.81830	−0.228187
$281$	−14.4963	−0.864778	−0.432389	−	0.901687i	$-0.642329\pi$
$281$	−14.4963	−0.864778	−0.432389	+	0.901687i	$0.642329\pi$
$282$	20.5757	1.22527
$283$	9.02685	0.536591	0.268295	−	0.963337i	$-0.413540\pi$
$283$	9.02685	0.536591	0.268295	+	0.963337i	$0.413540\pi$
$284$	−5.27837	−0.313213
$285$	17.6759	1.04703
$286$	8.15037	0.481942
$287$	−8.41388	−0.496656
$288$	−0.720763	−0.0424714
$289$	−3.87769	−0.228099
$290$	11.6814	0.685954
$291$	−14.7393	−0.864033
$292$	−11.4150	−0.668014
$293$	−11.7657	−0.687359	−0.343679	−	0.939087i	$-0.611673\pi$
$293$	−11.7657	−0.687359	−0.343679	+	0.939087i	$0.611673\pi$
$294$	−5.23944	−0.305570
$295$	1.71142	0.0996430
$296$	3.71755	0.216078
$297$	−8.61786	−0.500059
$298$	21.3749	1.23822
$299$	13.5617	0.784291
$300$	3.07968	0.177805
$301$	−19.6996	−1.13547
$302$	−14.6495	−0.842985
$303$	26.2196	1.50628
$304$	−4.96714	−0.284885
$305$	−4.11984	−0.235901
$306$	−2.61095	−0.149258
$307$	6.74904	0.385188	0.192594	−	0.981279i	$-0.438310\pi$
$307$	6.74904	0.385188	0.192594	+	0.981279i	$0.438310\pi$
$308$	−4.05701	−0.231170
$309$	26.0104	1.47968
$310$	0.283552	0.0161047
$311$	−18.4183	−1.04441	−0.522204	−	0.852821i	$-0.674890\pi$
$311$	−18.4183	−1.04441	−0.522204	+	0.852821i	$0.674890\pi$
$312$	8.02047	0.454069
$313$	−9.98811	−0.564561	−0.282281	−	0.959332i	$-0.591091\pi$
$313$	−9.98811	−0.564561	−0.282281	+	0.959332i	$0.591091\pi$
$314$	−10.3340	−0.583182
$315$	2.75209	0.155063
$316$	0.462430	0.0260137
$317$	−18.9662	−1.06525	−0.532624	−	0.846352i	$-0.678794\pi$
$317$	−18.9662	−1.06525	−0.532624	+	0.846352i	$0.678794\pi$
$318$	−7.73271	−0.433629
$319$	12.4117	0.694919
$320$	1.84484	0.103130
$321$	−11.7021	−0.653146
$322$	−6.75059	−0.376196
$323$	−17.9933	−1.00118
$324$	−10.6428	−0.591266
$325$	−6.63855	−0.368241
$326$	−12.4946	−0.692009
$327$	14.7898	0.817880
$328$	4.06522	0.224464
$329$	22.0776	1.21718
$330$	−6.97538	−0.383982
$331$	−15.0493	−0.827183	−0.413592	−	0.910462i	$-0.635726\pi$
$331$	−15.0493	−0.827183	−0.413592	+	0.910462i	$0.635726\pi$
$332$	2.41784	0.132696
$333$	−2.67947	−0.146834
$334$	−9.18523	−0.502593
$335$	18.9955	1.03784
$336$	−3.99235	−0.217800
$337$	−9.40521	−0.512335	−0.256167	−	0.966632i	$-0.582460\pi$
$337$	−9.40521	−0.512335	−0.256167	+	0.966632i	$0.582460\pi$
$338$	−4.28889	−0.233285
$339$	29.8401	1.62069
$340$	6.68287	0.362430
$341$	0.301279	0.0163152
$342$	3.58014	0.193592
$343$	−20.1099	−1.08583
$344$	9.51798	0.513175
$345$	−11.6066	−0.624876
$346$	−12.9952	−0.698627
$347$	−14.2735	−0.766242	−0.383121	−	0.923698i	$-0.625151\pi$
$347$	−14.2735	−0.766242	−0.383121	+	0.923698i	$0.625151\pi$
$348$	12.2138	0.654730
$349$	25.6507	1.37305	0.686526	−	0.727105i	$-0.259135\pi$
$349$	25.6507	1.37305	0.686526	+	0.727105i	$0.259135\pi$
$350$	3.30447	0.176631
$351$	18.2805	0.975743
$352$	1.96017	0.104477
$353$	−28.5456	−1.51933	−0.759664	−	0.650316i	$-0.774637\pi$
$353$	−28.5456	−1.51933	−0.759664	+	0.650316i	$0.774637\pi$
$354$	1.78943	0.0951074
$355$	−9.73772	−0.516825
$356$	−10.3998	−0.551187
$357$	−14.4622	−0.765419
$358$	17.1008	0.903807
$359$	−33.3297	−1.75907	−0.879536	−	0.475832i	$-0.842147\pi$
$359$	−33.3297	−1.75907	−0.879536	+	0.475832i	$0.842147\pi$
$360$	−1.32969	−0.0700809
$361$	5.67253	0.298554
$362$	−13.5848	−0.713999
$363$	13.8067	0.724666
$364$	8.60589	0.451071
$365$	−21.0589	−1.10227
$366$	−4.30763	−0.225163
$367$	2.56798	0.134048	0.0670238	−	0.997751i	$-0.478650\pi$
$367$	2.56798	0.134048	0.0670238	+	0.997751i	$0.478650\pi$
$368$	3.26159	0.170022
$369$	−2.93006	−0.152533
$370$	6.85827	0.356544
$371$	−8.29713	−0.430766
$372$	0.296477	0.0153716
$373$	−18.5566	−0.960823	−0.480412	−	0.877043i	$-0.659513\pi$
$373$	−18.5566	−0.960823	−0.480412	+	0.877043i	$0.659513\pi$
$374$	7.10067	0.367167
$375$	23.4743	1.21221
$376$	−10.6669	−0.550105
$377$	−26.3281	−1.35597
$378$	−9.09950	−0.468028
$379$	−12.4055	−0.637230	−0.318615	−	0.947884i	$-0.603218\pi$
$379$	−12.4055	−0.637230	−0.318615	+	0.947884i	$0.603218\pi$
$380$	−9.16357	−0.470081
$381$	12.6640	0.648795
$382$	−15.6729	−0.801898
$383$	−10.5151	−0.537298	−0.268649	−	0.963238i	$-0.586577\pi$
$383$	−10.5151	−0.537298	−0.268649	+	0.963238i	$0.586577\pi$
$384$	1.92893	0.0984352
$385$	−7.48453	−0.381447
$386$	−15.8463	−0.806556
$387$	−6.86021	−0.348724
$388$	7.64119	0.387923
$389$	20.7136	1.05022	0.525111	−	0.851034i	$-0.324024\pi$
$389$	20.7136	1.05022	0.525111	+	0.851034i	$0.324024\pi$
$390$	14.7965	0.749248
$391$	11.8150	0.597511
$392$	2.71624	0.137191
$393$	24.5428	1.23802
$394$	18.2576	0.919802
$395$	0.853108	0.0429245
$396$	−1.41282	−0.0709969
$397$	0.775858	0.0389392	0.0194696	−	0.999810i	$-0.493802\pi$
$397$	0.775858	0.0389392	0.0194696	+	0.999810i	$0.493802\pi$
$398$	−20.5073	−1.02794
$399$	19.8306	0.992770
$400$	−1.59658	−0.0798288
$401$	10.8927	0.543953	0.271977	−	0.962304i	$-0.412323\pi$
$401$	10.8927	0.543953	0.271977	+	0.962304i	$0.412323\pi$
$402$	19.8614	0.990594
$403$	−0.639084	−0.0318351
$404$	−13.5928	−0.676268
$405$	−19.6342	−0.975632
$406$	13.1053	0.650407
$407$	7.28703	0.361204
$408$	6.98749	0.345932
$409$	−23.6448	−1.16916	−0.584579	−	0.811336i	$-0.698740\pi$
$409$	−23.6448	−1.16916	−0.584579	+	0.811336i	$0.698740\pi$
$410$	7.49967	0.370382
$411$	−36.2353	−1.78736
$412$	−13.4844	−0.664328
$413$	1.92005	0.0944794
$414$	−2.35084	−0.115537
$415$	4.46052	0.218958
$416$	−4.15799	−0.203862
$417$	−30.0977	−1.47389
$418$	−9.73645	−0.476226
$419$	17.6033	0.859980	0.429990	−	0.902834i	$-0.358517\pi$
$419$	17.6033	0.859980	0.429990	+	0.902834i	$0.358517\pi$
$420$	−7.36523	−0.359386
$421$	−11.7714	−0.573702	−0.286851	−	0.957975i	$-0.592609\pi$
$421$	−11.7714	−0.573702	−0.286851	+	0.957975i	$0.592609\pi$
$422$	3.66650	0.178482
$423$	7.68833	0.373820
$424$	4.00881	0.194685
$425$	−5.78355	−0.280544
$426$	−10.1816	−0.493300
$427$	−4.62205	−0.223677
$428$	6.06662	0.293241
$429$	15.7215	0.759040
$430$	17.5591	0.846776
$431$	6.08475	0.293092	0.146546	−	0.989204i	$-0.453184\pi$
$431$	6.08475	0.293092	0.146546	+	0.989204i	$0.453184\pi$
$432$	4.39648	0.211526
$433$	32.3284	1.55361	0.776803	−	0.629744i	$-0.216840\pi$
$433$	32.3284	1.55361	0.776803	+	0.629744i	$0.216840\pi$
$434$	0.318117	0.0152701
$435$	22.5325	1.08035
$436$	−7.66739	−0.367201
$437$	−16.2008	−0.774989
$438$	−22.0188	−1.05210
$439$	−8.27340	−0.394868	−0.197434	−	0.980316i	$-0.563261\pi$
$439$	−8.27340	−0.394868	−0.197434	+	0.980316i	$0.563261\pi$
$440$	3.61620	0.172395
$441$	−1.95777	−0.0932271
$442$	−15.0622	−0.716436
$443$	−11.0430	−0.524667	−0.262334	−	0.964977i	$-0.584492\pi$
$443$	−11.0430	−0.524667	−0.262334	+	0.964977i	$0.584492\pi$
$444$	7.17088	0.340315
$445$	−19.1859	−0.909499
$446$	−22.1709	−1.04982
$447$	41.2307	1.95014
$448$	2.06972	0.0977852
$449$	−30.1371	−1.42226	−0.711129	−	0.703062i	$-0.751816\pi$
$449$	−30.1371	−1.42226	−0.711129	+	0.703062i	$0.751816\pi$
$450$	1.15075	0.0542471
$451$	7.96853	0.375223
$452$	−15.4698	−0.727637
$453$	−28.2579	−1.32767
$454$	20.4420	0.959391
$455$	15.8765	0.744300
$456$	−9.58127	−0.448684
$457$	−14.0842	−0.658833	−0.329416	−	0.944185i	$-0.606852\pi$
$457$	−14.0842	−0.658833	−0.329416	+	0.944185i	$0.606852\pi$
$458$	−1.01912	−0.0476204
$459$	15.9261	0.743369
$460$	6.01710	0.280549
$461$	−10.3788	−0.483391	−0.241695	−	0.970352i	$-0.577704\pi$
$461$	−10.3788	−0.483391	−0.241695	+	0.970352i	$0.577704\pi$
$462$	−7.82568	−0.364084
$463$	20.8875	0.970724	0.485362	−	0.874313i	$-0.338688\pi$
$463$	20.8875	0.970724	0.485362	+	0.874313i	$0.338688\pi$
$464$	−6.33193	−0.293952
$465$	0.546951	0.0253643
$466$	3.48573	0.161473
$467$	−25.7178	−1.19008	−0.595040	−	0.803696i	$-0.702864\pi$
$467$	−25.7178	−1.19008	−0.595040	+	0.803696i	$0.702864\pi$
$468$	2.99693	0.138533
$469$	21.3111	0.984053
$470$	−19.6787	−0.907713
$471$	−19.9336	−0.918491
$472$	−0.927683	−0.0427001
$473$	18.6569	0.857844
$474$	0.891994	0.0409707
$475$	7.93043	0.363873
$476$	7.49752	0.343648
$477$	−2.88941	−0.132297
$478$	3.05390	0.139682
$479$	−18.2231	−0.832636	−0.416318	−	0.909219i	$-0.636680\pi$
$479$	−18.2231	−0.832636	−0.416318	+	0.909219i	$0.636680\pi$
$480$	3.55856	0.162425
$481$	−15.4575	−0.704802
$482$	−14.1364	−0.643895
$483$	−13.0214	−0.592494
$484$	−7.15773	−0.325351
$485$	14.0967	0.640100
$486$	−7.33973	−0.332937
$487$	18.8008	0.851944	0.425972	−	0.904736i	$-0.359932\pi$
$487$	18.8008	0.851944	0.425972	+	0.904736i	$0.359932\pi$
$488$	2.23317	0.101091
$489$	−24.1011	−1.08989
$490$	5.01103	0.226375
$491$	−36.7814	−1.65992	−0.829960	−	0.557823i	$-0.811637\pi$
$491$	−36.7814	−1.65992	−0.829960	+	0.557823i	$0.811637\pi$
$492$	7.84152	0.353523
$493$	−22.9372	−1.03304
$494$	20.6533	0.929238
$495$	−2.60642	−0.117150
$496$	−0.153700	−0.00690135
$497$	−10.9248	−0.490042
$498$	4.66383	0.208991
$499$	−30.7719	−1.37754	−0.688769	−	0.724981i	$-0.741849\pi$
$499$	−30.7719	−1.37754	−0.688769	+	0.724981i	$0.741849\pi$
$500$	−12.1696	−0.544241
$501$	−17.7176	−0.791566
$502$	−7.58042	−0.338331
$503$	−16.1152	−0.718541	−0.359271	−	0.933233i	$-0.616975\pi$
$503$	−16.1152	−0.718541	−0.359271	+	0.933233i	$0.616975\pi$
$504$	−1.49178	−0.0664492
$505$	−25.0766	−1.11589
$506$	6.39328	0.284216
$507$	−8.27297	−0.367415
$508$	−6.56529	−0.291288
$509$	25.3412	1.12323	0.561614	−	0.827400i	$-0.310181\pi$
$509$	25.3412	1.12323	0.561614	+	0.827400i	$0.310181\pi$
$510$	12.8908	0.570813
$511$	−23.6259	−1.04515
$512$	−1.00000	−0.0441942
$513$	−21.8380	−0.964170
$514$	−30.8555	−1.36098
$515$	−24.8765	−1.09619
$516$	18.3595	0.808232
$517$	−20.9090	−0.919577
$518$	7.69429	0.338068
$519$	−25.0668	−1.10031
$520$	−7.67082	−0.336388
$521$	42.8044	1.87529	0.937647	−	0.347588i	$-0.112999\pi$
$521$	42.8044	1.87529	0.937647	+	0.347588i	$0.112999\pi$
$522$	4.56382	0.199753
$523$	1.61286	0.0705255	0.0352628	−	0.999378i	$-0.488773\pi$
$523$	1.61286	0.0705255	0.0352628	+	0.999378i	$0.488773\pi$
$524$	−12.7235	−0.555830
$525$	6.37409	0.278188
$526$	8.39921	0.366223
$527$	−0.556775	−0.0242535
$528$	3.78103	0.164548
$529$	−12.3620	−0.537479
$530$	7.39561	0.321245
$531$	0.668640	0.0290165
$532$	−10.2806	−0.445721
$533$	−16.9031	−0.732157
$534$	−20.0604	−0.868099
$535$	11.1919	0.483869
$536$	−10.2966	−0.444744
$537$	32.9863	1.42346
$538$	3.15627	0.136076
$539$	5.32430	0.229334
$540$	8.11080	0.349033
$541$	−26.0424	−1.11965	−0.559826	−	0.828610i	$-0.689132\pi$
$541$	−26.0424	−1.11965	−0.559826	+	0.828610i	$0.689132\pi$
$542$	−5.04628	−0.216756
$543$	−26.2040	−1.12452
$544$	−3.62247	−0.155312
$545$	−14.1451	−0.605909
$546$	16.6001	0.710421
$547$	6.85551	0.293120	0.146560	−	0.989202i	$-0.453180\pi$
$547$	6.85551	0.293120	0.146560	+	0.989202i	$0.453180\pi$
$548$	18.7852	0.802465
$549$	−1.60959	−0.0686956
$550$	−3.12956	−0.133445
$551$	31.4516	1.33988
$552$	6.29137	0.267779
$553$	0.957102	0.0407001
$554$	15.6119	0.663285
$555$	13.2291	0.561544
$556$	15.6033	0.661729
$557$	−32.0068	−1.35617	−0.678086	−	0.734983i	$-0.737190\pi$
$557$	−32.0068	−1.35617	−0.678086	+	0.734983i	$0.737190\pi$
$558$	0.110782	0.00468976
$559$	−39.5757	−1.67387
$560$	3.81830	0.161353
$561$	13.6967	0.578274
$562$	14.4963	0.611491
$563$	−5.70246	−0.240330	−0.120165	−	0.992754i	$-0.538342\pi$
$563$	−5.70246	−0.240330	−0.120165	+	0.992754i	$0.538342\pi$
$564$	−20.5757	−0.866395
$565$	−28.5392	−1.20065
$566$	−9.02685	−0.379427
$567$	−22.0276	−0.925074
$568$	5.27837	0.221475
$569$	19.5339	0.818902	0.409451	−	0.912332i	$-0.365720\pi$
$569$	19.5339	0.818902	0.409451	+	0.912332i	$0.365720\pi$
$570$	−17.6759	−0.740361
$571$	−34.3549	−1.43771	−0.718854	−	0.695162i	$-0.755333\pi$
$571$	−34.3549	−1.43771	−0.718854	+	0.695162i	$0.755333\pi$
$572$	−8.15037	−0.340784
$573$	−30.2320	−1.26296
$574$	8.41388	0.351189
$575$	−5.20738	−0.217163
$576$	0.720763	0.0300318
$577$	8.61934	0.358828	0.179414	−	0.983774i	$-0.442580\pi$
$577$	8.61934	0.358828	0.179414	+	0.983774i	$0.442580\pi$
$578$	3.87769	0.161291
$579$	−30.5664	−1.27030
$580$	−11.6814	−0.485043
$581$	5.00425	0.207611
$582$	14.7393	0.610964
$583$	7.85796	0.325443
$584$	11.4150	0.472357
$585$	5.52884	0.228590
$586$	11.7657	0.486036
$587$	−29.9493	−1.23614	−0.618070	−	0.786123i	$-0.712085\pi$
$587$	−29.9493	−1.23614	−0.618070	+	0.786123i	$0.712085\pi$
$588$	5.23944	0.216071
$589$	0.763452	0.0314575
$590$	−1.71142	−0.0704582
$591$	35.2175	1.44865
$592$	−3.71755	−0.152790
$593$	18.0069	0.739455	0.369727	−	0.929140i	$-0.379451\pi$
$593$	18.0069	0.739455	0.369727	+	0.929140i	$0.379451\pi$
$594$	8.61786	0.353595
$595$	13.8317	0.567044
$596$	−21.3749	−0.875551
$597$	−39.5571	−1.61896
$598$	−13.5617	−0.554578
$599$	−2.40718	−0.0983549	−0.0491774	−	0.998790i	$-0.515660\pi$
$599$	−2.40718	−0.0983549	−0.0491774	+	0.998790i	$0.515660\pi$
$600$	−3.07968	−0.125727
$601$	22.0604	0.899863	0.449932	−	0.893063i	$-0.351448\pi$
$601$	22.0604	0.899863	0.449932	+	0.893063i	$0.351448\pi$
$602$	19.6996	0.802896
$603$	7.42139	0.302223
$604$	14.6495	0.596080
$605$	−13.2048	−0.536853
$606$	−26.2196	−1.06510
$607$	0.879569	0.0357006	0.0178503	−	0.999841i	$-0.494318\pi$
$607$	0.879569	0.0357006	0.0178503	+	0.999841i	$0.494318\pi$
$608$	4.96714	0.201444
$609$	25.2792	1.02437
$610$	4.11984	0.166807
$611$	44.3530	1.79433
$612$	2.61095	0.105541
$613$	4.93266	0.199228	0.0996141	−	0.995026i	$-0.468239\pi$
$613$	4.93266	0.199228	0.0996141	+	0.995026i	$0.468239\pi$
$614$	−6.74904	−0.272369
$615$	14.4663	0.583338
$616$	4.05701	0.163462
$617$	−47.1946	−1.89998	−0.949992	−	0.312273i	$-0.898910\pi$
$617$	−47.1946	−1.89998	−0.949992	+	0.312273i	$0.898910\pi$
$618$	−26.0104	−1.04629
$619$	−2.22131	−0.0892821	−0.0446410	−	0.999003i	$-0.514214\pi$
$619$	−2.22131	−0.0892821	−0.0446410	+	0.999003i	$0.514214\pi$
$620$	−0.283552	−0.0113877
$621$	14.3395	0.575425
$622$	18.4183	0.738508
$623$	−21.5247	−0.862367
$624$	−8.02047	−0.321076
$625$	−14.4681	−0.578723
$626$	9.98811	0.399205
$627$	−18.7809	−0.750038
$628$	10.3340	0.412372
$629$	−13.4667	−0.536953
$630$	−2.75209	−0.109646
$631$	27.2558	1.08504	0.542519	−	0.840044i	$-0.317471\pi$
$631$	27.2558	1.08504	0.542519	+	0.840044i	$0.317471\pi$
$632$	−0.462430	−0.0183945
$633$	7.07241	0.281103
$634$	18.9662	0.753244
$635$	−12.1119	−0.480646
$636$	7.73271	0.306622
$637$	−11.2941	−0.447489
$638$	−12.4117	−0.491382
$639$	−3.80445	−0.150502
$640$	−1.84484	−0.0729236
$641$	15.3372	0.605781	0.302891	−	0.953025i	$-0.402048\pi$
$641$	15.3372	0.605781	0.302891	+	0.953025i	$0.402048\pi$
$642$	11.7021	0.461844
$643$	10.6541	0.420158	0.210079	−	0.977684i	$-0.432628\pi$
$643$	10.6541	0.420158	0.210079	+	0.977684i	$0.432628\pi$
$644$	6.75059	0.266011
$645$	33.8703	1.33364
$646$	17.9933	0.707939
$647$	34.9017	1.37213	0.686065	−	0.727541i	$-0.259337\pi$
$647$	34.9017	1.37213	0.686065	+	0.727541i	$0.259337\pi$
$648$	10.6428	0.418088
$649$	−1.81842	−0.0713791
$650$	6.63855	0.260385
$651$	0.613625	0.0240499
$652$	12.4946	0.489325
$653$	−22.7002	−0.888326	−0.444163	−	0.895946i	$-0.646499\pi$
$653$	−22.7002	−0.888326	−0.444163	+	0.895946i	$0.646499\pi$
$654$	−14.7898	−0.578329
$655$	−23.4728	−0.917160
$656$	−4.06522	−0.158720
$657$	−8.22753	−0.320987
$658$	−22.0776	−0.860674
$659$	−12.6042	−0.490992	−0.245496	−	0.969398i	$-0.578951\pi$
$659$	−12.6042	−0.490992	−0.245496	+	0.969398i	$0.578951\pi$
$660$	6.97538	0.271516
$661$	−27.0788	−1.05324	−0.526622	−	0.850099i	$-0.676542\pi$
$661$	−27.0788	−1.05324	−0.526622	+	0.850099i	$0.676542\pi$
$662$	15.0493	0.584907
$663$	−29.0539	−1.12836
$664$	−2.41784	−0.0938303
$665$	−18.9661	−0.735472
$666$	2.67947	0.103827
$667$	−20.6521	−0.799654
$668$	9.18523	0.355387
$669$	−42.7661	−1.65343
$670$	−18.9955	−0.733860
$671$	4.37740	0.168988
$672$	3.99235	0.154008
$673$	−48.3478	−1.86367	−0.931836	−	0.362880i	$-0.881793\pi$
$673$	−48.3478	−1.86367	−0.931836	+	0.362880i	$0.881793\pi$
$674$	9.40521	0.362275
$675$	−7.01932	−0.270174
$676$	4.28889	0.164957
$677$	−5.43765	−0.208986	−0.104493	−	0.994526i	$-0.533322\pi$
$677$	−5.43765	−0.208986	−0.104493	+	0.994526i	$0.533322\pi$
$678$	−29.8401	−1.14600
$679$	15.8151	0.606930
$680$	−6.68287	−0.256276
$681$	39.4312	1.51101
$682$	−0.301279	−0.0115366
$683$	17.9656	0.687436	0.343718	−	0.939073i	$-0.388314\pi$
$683$	17.9656	0.687436	0.343718	+	0.939073i	$0.388314\pi$
$684$	−3.58014	−0.136890
$685$	34.6557	1.32412
$686$	20.1099	0.767801
$687$	−1.96581	−0.0750004
$688$	−9.51798	−0.362870
$689$	−16.6686	−0.635023
$690$	11.6066	0.441854
$691$	−25.2529	−0.960664	−0.480332	−	0.877087i	$-0.659484\pi$
$691$	−25.2529	−0.960664	−0.480332	+	0.877087i	$0.659484\pi$
$692$	12.9952	0.494004
$693$	−2.92415	−0.111079
$694$	14.2735	0.541815
$695$	28.7856	1.09190
$696$	−12.2138	−0.462964
$697$	−14.7262	−0.557793
$698$	−25.6507	−0.970894
$699$	6.72372	0.254315
$700$	−3.30447	−0.124897
$701$	18.1573	0.685791	0.342895	−	0.939374i	$-0.388592\pi$
$701$	18.1573	0.685791	0.342895	+	0.939374i	$0.388592\pi$
$702$	−18.2805	−0.689955
$703$	18.4656	0.696443
$704$	−1.96017	−0.0738767
$705$	−37.9589	−1.42961
$706$	28.5456	1.07433
$707$	−28.1334	−1.05807
$708$	−1.78943	−0.0672511
$709$	20.1454	0.756575	0.378288	−	0.925688i	$-0.376513\pi$
$709$	20.1454	0.756575	0.378288	+	0.925688i	$0.376513\pi$
$710$	9.73772	0.365450
$711$	0.333303	0.0124998
$712$	10.3998	0.389748
$713$	−0.501307	−0.0187741
$714$	14.4622	0.541233
$715$	−15.0361	−0.562319
$716$	−17.1008	−0.639088
$717$	5.89076	0.219995
$718$	33.3297	1.24385
$719$	−18.6676	−0.696183	−0.348092	−	0.937461i	$-0.613170\pi$
$719$	−18.6676	−0.696183	−0.348092	+	0.937461i	$0.613170\pi$
$720$	1.32969	0.0495547
$721$	−27.9089	−1.03938
$722$	−5.67253	−0.211110
$723$	−27.2681	−1.01411
$724$	13.5848	0.504873
$725$	10.1094	0.375454
$726$	−13.8067	−0.512416
$727$	5.05691	0.187550	0.0937751	−	0.995593i	$-0.470107\pi$
$727$	5.05691	0.187550	0.0937751	+	0.995593i	$0.470107\pi$
$728$	−8.60589	−0.318956
$729$	17.7706	0.658169
$730$	21.0589	0.779424
$731$	−34.4786	−1.27524
$732$	4.30763	0.159215
$733$	6.76243	0.249776	0.124888	−	0.992171i	$-0.460143\pi$
$733$	6.76243	0.249776	0.124888	+	0.992171i	$0.460143\pi$
$734$	−2.56798	−0.0947859
$735$	9.66591	0.356533
$736$	−3.26159	−0.120224
$737$	−20.1830	−0.743452
$738$	2.93006	0.107857
$739$	−25.5652	−0.940430	−0.470215	−	0.882552i	$-0.655824\pi$
$739$	−25.5652	−0.940430	−0.470215	+	0.882552i	$0.655824\pi$
$740$	−6.85827	−0.252115
$741$	39.8388	1.46352
$742$	8.29713	0.304597
$743$	28.3644	1.04059	0.520294	−	0.853987i	$-0.325822\pi$
$743$	28.3644	1.04059	0.520294	+	0.853987i	$0.325822\pi$
$744$	−0.296477	−0.0108694
$745$	−39.4332	−1.44472
$746$	18.5566	0.679405
$747$	1.74269	0.0637616
$748$	−7.10067	−0.259626
$749$	12.5562	0.458795
$750$	−23.4743	−0.857160
$751$	−8.55285	−0.312098	−0.156049	−	0.987749i	$-0.549876\pi$
$751$	−8.55285	−0.312098	−0.156049	+	0.987749i	$0.549876\pi$
$752$	10.6669	0.388983
$753$	−14.6221	−0.532859
$754$	26.3281	0.958813
$755$	27.0260	0.983576
$756$	9.09950	0.330946
$757$	34.9027	1.26856	0.634280	−	0.773103i	$-0.281296\pi$
$757$	34.9027	1.26856	0.634280	+	0.773103i	$0.281296\pi$
$758$	12.4055	0.450590
$759$	12.3322	0.447629
$760$	9.16357	0.332398
$761$	−15.4425	−0.559789	−0.279895	−	0.960031i	$-0.590300\pi$
$761$	−15.4425	−0.559789	−0.279895	+	0.960031i	$0.590300\pi$
$762$	−12.6640	−0.458767
$763$	−15.8694	−0.574510
$764$	15.6729	0.567027
$765$	4.81677	0.174151
$766$	10.5151	0.379927
$767$	3.85730	0.139279
$768$	−1.92893	−0.0696042
$769$	−4.74552	−0.171128	−0.0855640	−	0.996333i	$-0.527269\pi$
$769$	−4.74552	−0.171128	−0.0855640	+	0.996333i	$0.527269\pi$
$770$	7.48453	0.269724
$771$	−59.5181	−2.14349
$772$	15.8463	0.570321
$773$	3.96378	0.142567	0.0712837	−	0.997456i	$-0.477290\pi$
$773$	3.96378	0.142567	0.0712837	+	0.997456i	$0.477290\pi$
$774$	6.86021	0.246585
$775$	0.245394	0.00881482
$776$	−7.64119	−0.274303
$777$	14.8417	0.532444
$778$	−20.7136	−0.742619
$779$	20.1925	0.723473
$780$	−14.7965	−0.529798
$781$	10.3465	0.370227
$782$	−11.8150	−0.422504
$783$	−27.8382	−0.994856
$784$	−2.71624	−0.0970087
$785$	19.0646	0.680444
$786$	−24.5428	−0.875412
$787$	30.2421	1.07802	0.539008	−	0.842301i	$-0.318799\pi$
$787$	30.2421	1.07802	0.539008	+	0.842301i	$0.318799\pi$
$788$	−18.2576	−0.650398
$789$	16.2015	0.576787
$790$	−0.853108	−0.0303522
$791$	−32.0181	−1.13843
$792$	1.41282	0.0502024
$793$	−9.28551	−0.329738
$794$	−0.775858	−0.0275342
$795$	14.2656	0.505948
$796$	20.5073	0.726861
$797$	21.2555	0.752909	0.376454	−	0.926435i	$-0.377143\pi$
$797$	21.2555	0.752909	0.376454	+	0.926435i	$0.377143\pi$
$798$	−19.8306	−0.701995
$799$	38.6407	1.36701
$800$	1.59658	0.0564475
$801$	−7.49578	−0.264850
$802$	−10.8927	−0.384633
$803$	22.3754	0.789611
$804$	−19.8614	−0.700456
$805$	12.4537	0.438937
$806$	0.639084	0.0225108
$807$	6.08821	0.214315
$808$	13.5928	0.478194
$809$	4.80609	0.168973	0.0844865	−	0.996425i	$-0.473075\pi$
$809$	4.80609	0.168973	0.0844865	+	0.996425i	$0.473075\pi$
$810$	19.6342	0.689876
$811$	33.1854	1.16530	0.582648	−	0.812725i	$-0.302017\pi$
$811$	33.1854	1.16530	0.582648	+	0.812725i	$0.302017\pi$
$812$	−13.1053	−0.459907
$813$	−9.73391	−0.341383
$814$	−7.28703	−0.255410
$815$	23.0504	0.807421
$816$	−6.98749	−0.244611
$817$	47.2772	1.65402
$818$	23.6448	0.826720
$819$	6.20281	0.216744
$820$	−7.49967	−0.261900
$821$	28.8817	1.00798	0.503989	−	0.863710i	$-0.331865\pi$
$821$	28.8817	1.00798	0.503989	+	0.863710i	$0.331865\pi$
$822$	36.2353	1.26385
$823$	−43.4541	−1.51472	−0.757358	−	0.653000i	$-0.773510\pi$
$823$	−43.4541	−1.51472	−0.757358	+	0.653000i	$0.773510\pi$
$824$	13.4844	0.469751
$825$	−6.03670	−0.210171
$826$	−1.92005	−0.0668070
$827$	−32.7898	−1.14021	−0.570106	−	0.821571i	$-0.693098\pi$
$827$	−32.7898	−1.14021	−0.570106	+	0.821571i	$0.693098\pi$
$828$	2.35084	0.0816972
$829$	30.7910	1.06941	0.534707	−	0.845037i	$-0.320422\pi$
$829$	30.7910	1.06941	0.534707	+	0.845037i	$0.320422\pi$
$830$	−4.46052	−0.154827
$831$	30.1142	1.04465
$832$	4.15799	0.144152
$833$	−9.83952	−0.340919
$834$	30.0977	1.04220
$835$	16.9452	0.586414
$836$	9.73645	0.336742
$837$	−0.675741	−0.0233570
$838$	−17.6033	−0.608097
$839$	−29.5652	−1.02071	−0.510353	−	0.859965i	$-0.670485\pi$
$839$	−29.5652	−1.02071	−0.510353	+	0.859965i	$0.670485\pi$
$840$	7.36523	0.254125
$841$	11.0933	0.382527
$842$	11.7714	0.405669
$843$	27.9624	0.963075
$844$	−3.66650	−0.126206
$845$	7.91231	0.272192
$846$	−7.68833	−0.264330
$847$	−14.8145	−0.509033
$848$	−4.00881	−0.137663
$849$	−17.4121	−0.597583
$850$	5.78355	0.198374
$851$	−12.1251	−0.415644
$852$	10.1816	0.348815
$853$	−11.2141	−0.383965	−0.191982	−	0.981398i	$-0.561492\pi$
$853$	−11.2141	−0.383965	−0.191982	+	0.981398i	$0.561492\pi$
$854$	4.62205	0.158163
$855$	−6.60477	−0.225878
$856$	−6.06662	−0.207353
$857$	26.1439	0.893058	0.446529	−	0.894769i	$-0.352660\pi$
$857$	26.1439	0.893058	0.446529	+	0.894769i	$0.352660\pi$
$858$	−15.7215	−0.536723
$859$	7.07221	0.241301	0.120650	−	0.992695i	$-0.461502\pi$
$859$	7.07221	0.241301	0.120650	+	0.992695i	$0.461502\pi$
$860$	−17.5591	−0.598761
$861$	16.2298	0.553109
$862$	−6.08475	−0.207247
$863$	−18.3357	−0.624154	−0.312077	−	0.950057i	$-0.601025\pi$
$863$	−18.3357	−0.624154	−0.312077	+	0.950057i	$0.601025\pi$
$864$	−4.39648	−0.149571
$865$	23.9741	0.815142
$866$	−32.3284	−1.09856
$867$	7.47978	0.254027
$868$	−0.318117	−0.0107976
$869$	−0.906442	−0.0307489
$870$	−22.5325	−0.763924
$871$	42.8131	1.45067
$872$	7.66739	0.259651
$873$	5.50749	0.186400
$874$	16.2008	0.548000
$875$	−25.1877	−0.851501
$876$	22.0188	0.743945
$877$	45.5840	1.53926	0.769630	−	0.638490i	$-0.220440\pi$
$877$	45.5840	1.53926	0.769630	+	0.638490i	$0.220440\pi$
$878$	8.27340	0.279214
$879$	22.6952	0.765489
$880$	−3.61620	−0.121902
$881$	52.9851	1.78511	0.892557	−	0.450935i	$-0.148909\pi$
$881$	52.9851	1.78511	0.892557	+	0.450935i	$0.148909\pi$
$882$	1.95777	0.0659215
$883$	35.9302	1.20915	0.604573	−	0.796550i	$-0.293344\pi$
$883$	35.9302	1.20915	0.604573	+	0.796550i	$0.293344\pi$
$884$	15.0622	0.506597
$885$	−3.30121	−0.110969
$886$	11.0430	0.370996
$887$	3.75693	0.126145	0.0630727	−	0.998009i	$-0.479910\pi$
$887$	3.75693	0.126145	0.0630727	+	0.998009i	$0.479910\pi$
$888$	−7.17088	−0.240639
$889$	−13.5883	−0.455738
$890$	19.1859	0.643113
$891$	20.8617	0.698893
$892$	22.1709	0.742337
$893$	−52.9842	−1.77305
$894$	−41.2307	−1.37896
$895$	−31.5482	−1.05454
$896$	−2.06972	−0.0691446
$897$	−26.1595	−0.873440
$898$	30.1371	1.00569
$899$	0.973219	0.0324587
$900$	−1.15075	−0.0383585
$901$	−14.5218	−0.483792
$902$	−7.96853	−0.265323
$903$	37.9991	1.26453
$904$	15.4698	0.514517
$905$	25.0617	0.833078
$906$	28.2579	0.938805
$907$	−4.63027	−0.153746	−0.0768728	−	0.997041i	$-0.524494\pi$
$907$	−4.63027	−0.153746	−0.0768728	+	0.997041i	$0.524494\pi$
$908$	−20.4420	−0.678392
$909$	−9.79721	−0.324953
$910$	−15.8765	−0.526300
$911$	−3.05544	−0.101231	−0.0506157	−	0.998718i	$-0.516118\pi$
$911$	−3.05544	−0.101231	−0.0506157	+	0.998718i	$0.516118\pi$
$912$	9.58127	0.317267
$913$	−4.73937	−0.156850
$914$	14.0842	0.465865
$915$	7.94687	0.262715
$916$	1.01912	0.0336727
$917$	−26.3342	−0.869632
$918$	−15.9261	−0.525641
$919$	−39.1153	−1.29029	−0.645147	−	0.764059i	$-0.723204\pi$
$919$	−39.1153	−1.29029	−0.645147	+	0.764059i	$0.723204\pi$
$920$	−6.01710	−0.198378
$921$	−13.0184	−0.428971
$922$	10.3788	0.341809
$923$	−21.9474	−0.722407
$924$	7.82568	0.257446
$925$	5.93535	0.195153
$926$	−20.8875	−0.686406
$927$	−9.71905	−0.319215
$928$	6.33193	0.207856
$929$	52.9677	1.73781	0.868907	−	0.494976i	$-0.164823\pi$
$929$	52.9677	1.73781	0.868907	+	0.494976i	$0.164823\pi$
$930$	−0.546951	−0.0179352
$931$	13.4920	0.442182
$932$	−3.48573	−0.114179
$933$	35.5276	1.16312
$934$	25.7178	0.841513
$935$	−13.0996	−0.428402
$936$	−2.99693	−0.0979577
$937$	15.0363	0.491215	0.245607	−	0.969369i	$-0.421013\pi$
$937$	15.0363	0.491215	0.245607	+	0.969369i	$0.421013\pi$
$938$	−21.3111	−0.695831
$939$	19.2663	0.628733
$940$	19.6787	0.641850
$941$	−47.3482	−1.54351	−0.771754	−	0.635922i	$-0.780620\pi$
$941$	−47.3482	−1.54351	−0.771754	+	0.635922i	$0.780620\pi$
$942$	19.9336	0.649471
$943$	−13.2591	−0.431775
$944$	0.927683	0.0301935
$945$	16.7871	0.546085
$946$	−18.6569	−0.606587
$947$	−38.3923	−1.24758	−0.623792	−	0.781591i	$-0.714409\pi$
$947$	−38.3923	−1.24758	−0.623792	+	0.781591i	$0.714409\pi$
$948$	−0.891994	−0.0289706
$949$	−47.4636	−1.54073
$950$	−7.93043	−0.257297
$951$	36.5844	1.18633
$952$	−7.49752	−0.242996
$953$	59.1140	1.91489	0.957446	−	0.288613i	$-0.0931941\pi$
$953$	59.1140	1.91489	0.957446	+	0.288613i	$0.0931941\pi$
$954$	2.88941	0.0935480
$955$	28.9140	0.935636
$956$	−3.05390	−0.0987703
$957$	−23.9412	−0.773909
$958$	18.2231	0.588763
$959$	38.8802	1.25551
$960$	−3.55856	−0.114852
$961$	−30.9764	−0.999238
$962$	15.4575	0.498371
$963$	4.37260	0.140905
$964$	14.1364	0.455302
$965$	29.2339	0.941071
$966$	13.0214	0.418957
$967$	−16.3802	−0.526751	−0.263376	−	0.964693i	$-0.584836\pi$
$967$	−16.3802	−0.526751	−0.263376	+	0.964693i	$0.584836\pi$
$968$	7.15773	0.230058
$969$	34.7079	1.11498
$970$	−14.0967	−0.452619
$971$	44.0056	1.41221	0.706104	−	0.708108i	$-0.250451\pi$
$971$	44.0056	1.41221	0.706104	+	0.708108i	$0.250451\pi$
$972$	7.33973	0.235422
$973$	32.2946	1.03532
$974$	−18.8008	−0.602415
$975$	12.8053	0.410097
$976$	−2.23317	−0.0714821
$977$	−34.8428	−1.11472	−0.557361	−	0.830271i	$-0.688186\pi$
$977$	−34.8428	−1.11472	−0.557361	+	0.830271i	$0.688186\pi$
$978$	24.1011	0.770668
$979$	20.3853	0.651518
$980$	−5.01103	−0.160071
$981$	−5.52637	−0.176444
$982$	36.7814	1.17374
$983$	−34.6480	−1.10510	−0.552549	−	0.833480i	$-0.686345\pi$
$983$	−34.6480	−1.10510	−0.552549	+	0.833480i	$0.686345\pi$
$984$	−7.84152	−0.249978
$985$	−33.6822	−1.07320
$986$	22.9372	0.730470
$987$	−42.5861	−1.35553
$988$	−20.6533	−0.657070
$989$	−31.0438	−0.987134
$990$	2.60642	0.0828375
$991$	−52.6212	−1.67157	−0.835783	−	0.549060i	$-0.814986\pi$
$991$	−52.6212	−1.67157	−0.835783	+	0.549060i	$0.814986\pi$
$992$	0.153700	0.00487999
$993$	29.0290	0.921207
$994$	10.9248	0.346512
$995$	37.8326	1.19937
$996$	−4.66383	−0.147779
$997$	28.1033	0.890040	0.445020	−	0.895521i	$-0.353197\pi$
$997$	28.1033	0.890040	0.445020	+	0.895521i	$0.353197\pi$
$998$	30.7719	0.974067
$999$	−16.3441	−0.517105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.d.1.18	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.d.1.18	✓	64	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.92893 q^{3} +1.00000 q^{4} +1.84484 q^{5} +1.92893 q^{6} +2.06972 q^{7} -1.00000 q^{8} +0.720763 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.92893 q^{3} +1.00000 q^{4} +1.84484 q^{5} +1.92893 q^{6} +2.06972 q^{7} -1.00000 q^{8} +0.720763 q^{9} -1.84484 q^{10} -1.96017 q^{11} -1.92893 q^{12} +4.15799 q^{13} -2.06972 q^{14} -3.55856 q^{15} +1.00000 q^{16} +3.62247 q^{17} -0.720763 q^{18} -4.96714 q^{19} +1.84484 q^{20} -3.99235 q^{21} +1.96017 q^{22} +3.26159 q^{23} +1.92893 q^{24} -1.59658 q^{25} -4.15799 q^{26} +4.39648 q^{27} +2.06972 q^{28} -6.33193 q^{29} +3.55856 q^{30} -0.153700 q^{31} -1.00000 q^{32} +3.78103 q^{33} -3.62247 q^{34} +3.81830 q^{35} +0.720763 q^{36} -3.71755 q^{37} +4.96714 q^{38} -8.02047 q^{39} -1.84484 q^{40} -4.06522 q^{41} +3.99235 q^{42} -9.51798 q^{43} -1.96017 q^{44} +1.32969 q^{45} -3.26159 q^{46} +10.6669 q^{47} -1.92893 q^{48} -2.71624 q^{49} +1.59658 q^{50} -6.98749 q^{51} +4.15799 q^{52} -4.00881 q^{53} -4.39648 q^{54} -3.61620 q^{55} -2.06972 q^{56} +9.58127 q^{57} +6.33193 q^{58} +0.927683 q^{59} -3.55856 q^{60} -2.23317 q^{61} +0.153700 q^{62} +1.49178 q^{63} +1.00000 q^{64} +7.67082 q^{65} -3.78103 q^{66} +10.2966 q^{67} +3.62247 q^{68} -6.29137 q^{69} -3.81830 q^{70} -5.27837 q^{71} -0.720763 q^{72} -11.4150 q^{73} +3.71755 q^{74} +3.07968 q^{75} -4.96714 q^{76} -4.05701 q^{77} +8.02047 q^{78} +0.462430 q^{79} +1.84484 q^{80} -10.6428 q^{81} +4.06522 q^{82} +2.41784 q^{83} -3.99235 q^{84} +6.68287 q^{85} +9.51798 q^{86} +12.2138 q^{87} +1.96017 q^{88} -10.3998 q^{89} -1.32969 q^{90} +8.60589 q^{91} +3.26159 q^{92} +0.296477 q^{93} -10.6669 q^{94} -9.16357 q^{95} +1.92893 q^{96} +7.64119 q^{97} +2.71624 q^{98} -1.41282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more