LMFDB - Embedded newform 456.2.e.a.379.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(379,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

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

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

chi := DirichletCharacter("456.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.e (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.36
Character	$\chi$	$=$	456.379
Dual form			456.2.e.a.379.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33983 + 0.452615i) q^{2} +1.00000i q^{3} +(1.59028 + 1.21285i) q^{4} +0.393257i q^{5} +(-0.452615 + 1.33983i) q^{6} +1.35370i q^{7} +(1.58175 + 2.34480i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.33983 + 0.452615i) q^{2} +1.00000i q^{3} +(1.59028 + 1.21285i) q^{4} +0.393257i q^{5} +(-0.452615 + 1.33983i) q^{6} +1.35370i q^{7} +(1.58175 + 2.34480i) q^{8} -1.00000 q^{9} +(-0.177994 + 0.526897i) q^{10} +1.21598 q^{11} +(-1.21285 + 1.59028i) q^{12} -3.30636 q^{13} +(-0.612703 + 1.81372i) q^{14} -0.393257 q^{15} +(1.05798 + 3.85755i) q^{16} -0.00555711 q^{17} +(-1.33983 - 0.452615i) q^{18} +(2.48659 - 3.58007i) q^{19} +(-0.476963 + 0.625388i) q^{20} -1.35370 q^{21} +(1.62920 + 0.550370i) q^{22} -0.677182i q^{23} +(-2.34480 + 1.58175i) q^{24} +4.84535 q^{25} +(-4.42996 - 1.49651i) q^{26} -1.00000i q^{27} +(-1.64183 + 2.15275i) q^{28} -5.04174 q^{29} +(-0.526897 - 0.177994i) q^{30} +4.84195 q^{31} +(-0.328479 + 5.64731i) q^{32} +1.21598i q^{33} +(-0.00744557 - 0.00251523i) q^{34} -0.532350 q^{35} +(-1.59028 - 1.21285i) q^{36} -4.23826 q^{37} +(4.95199 - 3.67121i) q^{38} -3.30636i q^{39} +(-0.922108 + 0.622032i) q^{40} +1.96739i q^{41} +(-1.81372 - 0.612703i) q^{42} +4.59845 q^{43} +(1.93374 + 1.47480i) q^{44} -0.393257i q^{45} +(0.306503 - 0.907308i) q^{46} -10.9421i q^{47} +(-3.85755 + 1.05798i) q^{48} +5.16751 q^{49} +(6.49194 + 2.19308i) q^{50} -0.00555711i q^{51} +(-5.25804 - 4.01013i) q^{52} -4.67945 q^{53} +(0.452615 - 1.33983i) q^{54} +0.478192i q^{55} +(-3.17414 + 2.14120i) q^{56} +(3.58007 + 2.48659i) q^{57} +(-6.75507 - 2.28197i) q^{58} -9.88941i q^{59} +(-0.625388 - 0.476963i) q^{60} -4.99390i q^{61} +(6.48738 + 2.19154i) q^{62} -1.35370i q^{63} +(-2.99616 + 7.41775i) q^{64} -1.30025i q^{65} +(-0.550370 + 1.62920i) q^{66} +2.46296i q^{67} +(-0.00883735 - 0.00673995i) q^{68} +0.677182 q^{69} +(-0.713258 - 0.240950i) q^{70} +0.424001 q^{71} +(-1.58175 - 2.34480i) q^{72} -1.23201 q^{73} +(-5.67855 - 1.91830i) q^{74} +4.84535i q^{75} +(8.29646 - 2.67744i) q^{76} +1.64606i q^{77} +(1.49651 - 4.42996i) q^{78} +11.1012 q^{79} +(-1.51701 + 0.416056i) q^{80} +1.00000 q^{81} +(-0.890470 + 2.63596i) q^{82} -7.42465 q^{83} +(-2.15275 - 1.64183i) q^{84} -0.00218537i q^{85} +(6.16114 + 2.08133i) q^{86} -5.04174i q^{87} +(1.92337 + 2.85122i) q^{88} -11.9802i q^{89} +(0.177994 - 0.526897i) q^{90} -4.47581i q^{91} +(0.821323 - 1.07691i) q^{92} +4.84195i q^{93} +(4.95256 - 14.6605i) q^{94} +(1.40789 + 0.977868i) q^{95} +(-5.64731 - 0.328479i) q^{96} +2.05436i q^{97} +(6.92357 + 2.33889i) q^{98} -1.21598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4} + 4 q^{6} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^4 + 4 * q^6 - 40 * q^9	$ 40 q - 4 q^{4} + 4 q^{6} - 40 q^{9} + 4 q^{16} + 8 q^{19} + 32 q^{20} - 4 q^{24} - 40 q^{25} + 40 q^{26} - 8 q^{28} - 48 q^{35} + 4 q^{36} - 8 q^{44} - 56 q^{49} - 4 q^{54} - 8 q^{57} + 16 q^{58} + 40 q^{62} + 68 q^{64} + 8 q^{66} - 88 q^{68} - 16 q^{73} - 40 q^{74} - 12 q^{76} - 32 q^{80} + 40 q^{81} - 64 q^{82} + 80 q^{83} - 48 q^{92} + 44 q^{96}+O(q^{100}) $ 40 * q - 4 * q^4 + 4 * q^6 - 40 * q^9 + 4 * q^16 + 8 * q^19 + 32 * q^20 - 4 * q^24 - 40 * q^25 + 40 * q^26 - 8 * q^28 - 48 * q^35 + 4 * q^36 - 8 * q^44 - 56 * q^49 - 4 * q^54 - 8 * q^57 + 16 * q^58 + 40 * q^62 + 68 * q^64 + 8 * q^66 - 88 * q^68 - 16 * q^73 - 40 * q^74 - 12 * q^76 - 32 * q^80 + 40 * q^81 - 64 * q^82 + 80 * q^83 - 48 * q^92 + 44 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	1.33983	+	0.452615i	0.947402	+	0.320047i
$2$	1.33983	+	0.452615i	0.947402	+	0.320047i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.59028	+	1.21285i	0.795140	+	0.606426i
$5$			0.393257i			0.175870i	0.996126	+	0.0879349i	$0.0280268\pi$
$5$			0.393257i			0.175870i	−0.996126	+	0.0879349i	$0.971973\pi$
$6$	−0.452615	+	1.33983i	−0.184779	+	0.546983i
$7$			1.35370i			0.511649i	0.966723	+	0.255824i	$0.0823469\pi$
$7$			1.35370i			0.511649i	−0.966723	+	0.255824i	$0.917653\pi$
$8$	1.58175	+	2.34480i	0.559231	+	0.829012i
$9$	−1.00000			−0.333333
$10$	−0.177994	+	0.526897i	−0.0562866	+	0.166619i
$11$	1.21598			0.366631			0.183316	−	0.983054i	$-0.441317\pi$
$11$	1.21598			0.366631			0.183316	+	0.983054i	$0.441317\pi$
$12$	−1.21285	+	1.59028i	−0.350120	+	0.459074i
$13$	−3.30636			−0.917020			−0.458510	−	0.888689i	$-0.651617\pi$
$13$	−3.30636			−0.917020			−0.458510	+	0.888689i	$0.651617\pi$
$14$	−0.612703	+	1.81372i	−0.163752	+	0.484737i
$15$	−0.393257			−0.101538
$16$	1.05798	+	3.85755i	0.264494	+	0.964387i
$17$	−0.00555711			−0.00134780			−0.000673898	−	1.00000i	$-0.500215\pi$
$17$	−0.00555711			−0.00134780			−0.000673898		1.00000i	$0.500215\pi$
$18$	−1.33983	−	0.452615i	−0.315801	−	0.106682i
$19$	2.48659	−	3.58007i	0.570462	−	0.821324i
$19$	2.48659	−	3.58007i	0.570462	−	0.821324i
$20$	−0.476963	+	0.625388i	−0.106652	+	0.139841i
$21$	−1.35370			−0.295401
$22$	1.62920	+	0.550370i	0.347347	+	0.117339i
$23$		−	0.677182i		−	0.141202i	−0.997505	−	0.0706011i	$-0.977508\pi$
$23$		−	0.677182i		−	0.141202i	0.997505	−	0.0706011i	$-0.0224918\pi$
$24$	−2.34480	+	1.58175i	−0.478630	+	0.322872i
$25$	4.84535			0.969070
$26$	−4.42996	−	1.49651i	−0.868786	−	0.293490i
$27$		−	1.00000i		−	0.192450i
$28$	−1.64183	+	2.15275i	−0.310277	+	0.406832i
$29$	−5.04174			−0.936228			−0.468114	−	0.883668i	$-0.655066\pi$
$29$	−5.04174			−0.936228			−0.468114	+	0.883668i	$0.655066\pi$
$30$	−0.526897	−	0.177994i	−0.0961977	−	0.0324971i
$31$	4.84195			0.869639			0.434820	−	0.900518i	$-0.356812\pi$
$31$	4.84195			0.869639			0.434820	+	0.900518i	$0.356812\pi$
$32$	−0.328479	+	5.64731i	−0.0580674	+	0.998313i
$33$			1.21598i			0.211675i
$34$	−0.00744557	−	0.00251523i	−0.00127690	−	0.000431358i
$35$	−0.532350			−0.0899836
$36$	−1.59028	−	1.21285i	−0.265047	−	0.202142i
$37$	−4.23826			−0.696766			−0.348383	−	0.937352i	$-0.613269\pi$
$37$	−4.23826			−0.696766			−0.348383	+	0.937352i	$0.613269\pi$
$38$	4.95199	−	3.67121i	0.803319	−	0.595549i
$39$		−	3.30636i		−	0.529442i
$40$	−0.922108	+	0.622032i	−0.145798	+	0.0983519i
$41$			1.96739i			0.307254i	0.988129	+	0.153627i	$0.0490955\pi$
$41$			1.96739i			0.307254i	−0.988129	+	0.153627i	$0.950905\pi$
$42$	−1.81372	−	0.612703i	−0.279863	−	0.0945421i
$43$	4.59845			0.701257			0.350629	−	0.936515i	$-0.385968\pi$
$43$	4.59845			0.701257			0.350629	+	0.936515i	$0.385968\pi$
$44$	1.93374	+	1.47480i	0.291523	+	0.222335i
$45$		−	0.393257i		−	0.0586233i
$46$	0.306503	−	0.907308i	0.0451914	−	0.133775i
$47$		−	10.9421i		−	1.59607i	−0.602612	−	0.798034i	$-0.705873\pi$
$47$		−	10.9421i		−	1.59607i	0.602612	−	0.798034i	$-0.294127\pi$
$48$	−3.85755	+	1.05798i	−0.556789	+	0.152706i
$49$	5.16751			0.738215
$50$	6.49194	+	2.19308i	0.918098	+	0.310148i
$51$		−	0.00555711i		−	0.000778151i
$52$	−5.25804	−	4.01013i	−0.729159	−	0.556105i
$53$	−4.67945			−0.642772			−0.321386	−	0.946948i	$-0.604149\pi$
$53$	−4.67945			−0.642772			−0.321386	+	0.946948i	$0.604149\pi$
$54$	0.452615	−	1.33983i	0.0615931	−	0.182328i
$55$			0.478192i			0.0644793i
$56$	−3.17414	+	2.14120i	−0.424163	+	0.286130i
$57$	3.58007	+	2.48659i	0.474191	+	0.329357i
$58$	−6.75507	−	2.28197i	−0.886984	−	0.299637i
$59$		−	9.88941i		−	1.28749i	−0.765240	−	0.643745i	$-0.777380\pi$
$59$		−	9.88941i		−	1.28749i	0.765240	−	0.643745i	$-0.222620\pi$
$60$	−0.625388	−	0.476963i	−0.0807373	−	0.0615756i
$61$		−	4.99390i		−	0.639403i	−0.947518	−	0.319701i	$-0.896417\pi$
$61$		−	4.99390i		−	0.639403i	0.947518	−	0.319701i	$-0.103583\pi$
$62$	6.48738	+	2.19154i	0.823897	+	0.278326i
$63$		−	1.35370i		−	0.170550i
$64$	−2.99616	+	7.41775i	−0.374520	+	0.927219i
$65$		−	1.30025i		−	0.161276i
$66$	−0.550370	+	1.62920i	−0.0677458	+	0.200541i
$67$			2.46296i			0.300899i	0.988618	+	0.150450i	$0.0480721\pi$
$67$			2.46296i			0.300899i	−0.988618	+	0.150450i	$0.951928\pi$
$68$	−0.00883735	−	0.00673995i	−0.00107169	−	0.000817339i
$69$	0.677182			0.0815232
$70$	−0.713258	−	0.240950i	−0.0852506	−	0.0287990i
$71$	0.424001			0.0503197			0.0251598	−	0.999683i	$-0.491991\pi$
$71$	0.424001			0.0503197			0.0251598	+	0.999683i	$0.491991\pi$
$72$	−1.58175	−	2.34480i	−0.186410	−	0.276337i
$73$	−1.23201			−0.144196			−0.0720978	−	0.997398i	$-0.522969\pi$
$73$	−1.23201			−0.144196			−0.0720978	+	0.997398i	$0.522969\pi$
$74$	−5.67855	−	1.91830i	−0.660118	−	0.222998i
$75$			4.84535i			0.559493i
$76$	8.29646	−	2.67744i	0.951670	−	0.307124i
$77$			1.64606i			0.187586i
$78$	1.49651	−	4.42996i	0.169446	−	0.501594i
$79$	11.1012			1.24899			0.624494	−	0.781030i	$-0.285305\pi$
$79$	11.1012			1.24899			0.624494	+	0.781030i	$0.285305\pi$
$80$	−1.51701	+	0.416056i	−0.169607	+	0.0465165i
$81$	1.00000			0.111111
$82$	−0.890470	+	2.63596i	−0.0983359	+	0.291093i
$83$	−7.42465			−0.814961			−0.407481	−	0.913214i	$-0.633593\pi$
$83$	−7.42465			−0.814961			−0.407481	+	0.913214i	$0.633593\pi$
$84$	−2.15275	−	1.64183i	−0.234885	−	0.179139i
$85$		−	0.00218537i		−	0.000237037i
$86$	6.16114	+	2.08133i	0.664372	+	0.224435i
$87$		−	5.04174i		−	0.540532i
$88$	1.92337	+	2.85122i	0.205032	+	0.303941i
$89$		−	11.9802i		−	1.26990i	−0.772552	−	0.634952i	$-0.781020\pi$
$89$		−	11.9802i		−	1.26990i	0.772552	−	0.634952i	$-0.218980\pi$
$90$	0.177994	−	0.526897i	0.0187622	−	0.0555398i
$91$		−	4.47581i		−	0.469192i
$92$	0.821323	−	1.07691i	0.0856288	−	0.112276i
$93$			4.84195i			0.502086i
$94$	4.95256	−	14.6605i	0.510817	−	1.51212i
$95$	1.40789	+	0.977868i	0.144446	+	0.100327i
$96$	−5.64731	−	0.328479i	−0.576376	−	0.0335253i
$97$			2.05436i			0.208589i	0.994546	+	0.104295i	$0.0332585\pi$
$97$			2.05436i			0.208589i	−0.994546	+	0.104295i	$0.966742\pi$
$98$	6.92357	+	2.33889i	0.699386	+	0.236264i
$99$	−1.21598			−0.122210
$100$	7.70546	+	5.87670i	0.770546	+	0.587670i
$101$			8.75636i			0.871291i	0.900118	+	0.435645i	$0.143480\pi$
$101$			8.75636i			0.871291i	−0.900118	+	0.435645i	$0.856520\pi$
$102$	0.00251523	−	0.00744557i	0.000249045	−	0.000737221i
$103$	9.60437			0.946346			0.473173	−	0.880969i	$-0.343108\pi$
$103$	9.60437			0.946346			0.473173	+	0.880969i	$0.343108\pi$
$104$	−5.22982	−	7.75275i	−0.512826	−	0.760220i
$105$		−	0.532350i		−	0.0519521i
$106$	−6.26966	−	2.11799i	−0.608964	−	0.205718i
$107$		−	7.32145i		−	0.707791i	−0.935285	−	0.353896i	$-0.884857\pi$
$107$		−	7.32145i		−	0.707791i	0.935285	−	0.353896i	$-0.115143\pi$
$108$	1.21285	−	1.59028i	0.116707	−	0.153025i
$109$	−6.70281			−0.642013			−0.321006	−	0.947077i	$-0.604021\pi$
$109$	−6.70281			−0.642013			−0.321006	+	0.947077i	$0.604021\pi$
$110$	−0.216437	+	0.640695i	−0.0206364	+	0.0610878i
$111$		−	4.23826i		−	0.402278i
$112$	−5.22195	+	1.43218i	−0.493428	+	0.135328i
$113$			2.04224i			0.192118i	0.995376	+	0.0960588i	$0.0306237\pi$
$113$			2.04224i			0.192118i	−0.995376	+	0.0960588i	$0.969376\pi$
$114$	3.67121	+	4.95199i	0.343840	+	0.463797i
$115$	0.266307			0.0248332
$116$	−8.01778	−	6.11489i	−0.744432	−	0.567753i
$117$	3.30636			0.305673
$118$	4.47609	−	13.2501i	0.412058	−	1.21977i
$119$		−	0.00752263i		−	0.000689598i
$120$	−0.622032	−	0.922108i	−0.0567835	−	0.0841766i
$121$	−9.52140			−0.865582
$122$	2.26031	−	6.69096i	0.204639	−	0.605771i
$123$	−1.96739			−0.177393
$124$	7.70005	+	5.87257i	0.691484	+	0.527372i
$125$			3.87175i			0.346300i
$126$	0.612703	−	1.81372i	0.0545839	−	0.161579i
$127$	−5.00649			−0.444254			−0.222127	−	0.975018i	$-0.571300\pi$
$127$	−5.00649			−0.444254			−0.222127	+	0.975018i	$0.571300\pi$
$128$	−7.37173	+	8.58240i	−0.651575	+	0.758584i
$129$			4.59845i			0.404871i
$130$	0.588513	−	1.74211i	0.0516160	−	0.152793i
$131$	−16.6424			−1.45406			−0.727028	−	0.686608i	$-0.759099\pi$
$131$	−16.6424			−1.45406			−0.727028	+	0.686608i	$0.759099\pi$
$132$	−1.47480	+	1.93374i	−0.128365	+	0.168311i
$133$	4.84632	+	3.36608i	0.420229	+	0.291876i
$134$	−1.11477	+	3.29995i	−0.0963019	+	0.285072i
$135$	0.393257			0.0338462
$136$	−0.00878993	−	0.0130303i	−0.000753730	−	0.00111734i
$137$	−13.3028			−1.13653			−0.568267	−	0.822844i	$-0.692386\pi$
$137$	−13.3028			−1.13653			−0.568267	+	0.822844i	$0.692386\pi$
$138$	0.907308	+	0.306503i	0.0772352	+	0.0260913i
$139$	14.9252			1.26594			0.632968	−	0.774178i	$-0.281836\pi$
$139$	14.9252			1.26594			0.632968	+	0.774178i	$0.281836\pi$
$140$	−0.846585	−	0.645662i	−0.0715495	−	0.0545684i
$141$	10.9421			0.921491
$142$	0.568089	+	0.191909i	0.0476729	+	0.0161047i
$143$	−4.02046			−0.336208
$144$	−1.05798	−	3.85755i	−0.0881647	−	0.321462i
$145$		−	1.98270i		−	0.164654i
$146$	−1.65068	−	0.557625i	−0.136611	−	0.0461494i
$147$			5.16751i			0.426209i
$148$	−6.74002	−	5.14039i	−0.554027	−	0.422538i
$149$			19.2617i			1.57798i	0.614408	+	0.788989i	$0.289395\pi$
$149$			19.2617i			1.57798i	−0.614408	+	0.788989i	$0.710605\pi$
$150$	−2.19308	+	6.49194i	−0.179064	+	0.530064i
$151$	19.3294			1.57300			0.786501	−	0.617589i	$-0.211890\pi$
$151$	19.3294			1.57300			0.786501	+	0.617589i	$0.211890\pi$
$152$	12.3277	+	0.167793i	0.999907	+	0.0136098i
$153$	0.00555711			0.000449265
$154$	−0.745033	+	2.20544i	−0.0600365	+	0.177720i
$155$			1.90413i			0.152943i
$156$	4.01013	−	5.25804i	0.321067	−	0.420980i
$157$		−	2.56382i		−	0.204615i	−0.994753	−	0.102307i	$-0.967377\pi$
$157$		−	2.56382i		−	0.204615i	0.994753	−	0.102307i	$-0.0326226\pi$
$158$	14.8738	+	5.02459i	1.18329	+	0.399735i
$159$		−	4.67945i		−	0.371105i
$160$	−2.22084	−	0.129177i	−0.175573	−	0.0102123i
$161$	0.916699			0.0722460
$162$	1.33983	+	0.452615i	0.105267	+	0.0355608i
$163$	−16.0963			−1.26076			−0.630378	−	0.776288i	$-0.717100\pi$
$163$	−16.0963			−1.26076			−0.630378	+	0.776288i	$0.717100\pi$
$164$	−2.38615	+	3.12870i	−0.186327	+	0.244310i
$165$	−0.478192			−0.0372272
$166$	−9.94775	−	3.36051i	−0.772096	−	0.260826i
$167$	−16.5107			−1.27764			−0.638818	−	0.769358i	$-0.720576\pi$
$167$	−16.5107			−1.27764			−0.638818	+	0.769358i	$0.720576\pi$
$168$	−2.14120	−	3.17414i	−0.165197	−	0.244891i
$169$	−2.06797			−0.159075
$170$	0.000989132	−	0.00292802i	7.58629e−5	−	0.000224569i
$171$	−2.48659	+	3.58007i	−0.190154	+	0.273775i
$172$	7.31282	+	5.57725i	0.557598	+	0.425261i
$173$	−13.8251			−1.05110			−0.525550	−	0.850763i	$-0.676140\pi$
$173$	−13.8251			−1.05110			−0.525550	+	0.850763i	$0.676140\pi$
$174$	2.28197	−	6.75507i	0.172996	−	0.512100i
$175$			6.55913i			0.495823i
$176$	1.28648	+	4.69069i	0.0969717	+	0.353574i
$177$	9.88941			0.743333
$178$	5.42244	−	16.0515i	0.406429	−	1.20311i
$179$			9.07865i			0.678570i	0.940684	+	0.339285i	$0.110185\pi$
$179$			9.07865i			0.678570i	−0.940684	+	0.339285i	$0.889815\pi$
$180$	0.476963	−	0.625388i	0.0355507	−	0.0466137i
$181$	−4.43828			−0.329895			−0.164947	−	0.986302i	$-0.552745\pi$
$181$	−4.43828			−0.329895			−0.164947	+	0.986302i	$0.552745\pi$
$182$	2.02582	−	5.99681i	0.150164	−	0.444513i
$183$	4.99390			0.369159
$184$	1.58786	−	1.07113i	0.117058	−	0.0789648i
$185$		−	1.66673i		−	0.122540i
$186$	−2.19154	+	6.48738i	−0.160691	+	0.475677i
$187$	−0.00675732			−0.000494144
$188$	13.2712	−	17.4010i	0.967898	−	1.26910i
$189$	1.35370			0.0984669
$190$	1.44373	+	1.94741i	0.104739	+	0.141280i
$191$			10.7380i			0.776976i	0.921454	+	0.388488i	$0.127003\pi$
$191$			10.7380i			0.776976i	−0.921454	+	0.388488i	$0.872997\pi$
$192$	−7.41775	−	2.99616i	−0.535330	−	0.216229i
$193$			24.4529i			1.76016i	0.474826	+	0.880080i	$0.342511\pi$
$193$			24.4529i			1.76016i	−0.474826	+	0.880080i	$0.657489\pi$
$194$	−0.929836	+	2.75250i	−0.0667584	+	0.197618i
$195$	1.30025			0.0931128
$196$	8.21778	+	6.26743i	0.586984	+	0.447673i
$197$			0.602544i			0.0429295i	0.999770	+	0.0214647i	$0.00683297\pi$
$197$			0.602544i			0.0429295i	−0.999770	+	0.0214647i	$0.993167\pi$
$198$	−1.62920	−	0.550370i	−0.115782	−	0.0391131i
$199$		−	1.82192i		−	0.129152i	−0.997913	−	0.0645761i	$-0.979430\pi$
$199$		−	1.82192i		−	0.129152i	0.997913	−	0.0645761i	$-0.0205695\pi$
$200$	7.66411	+	11.3614i	0.541934	+	0.803370i
$201$	−2.46296			−0.173724
$202$	−3.96326	+	11.7320i	−0.278854	+	0.825462i
$203$		−	6.82498i		−	0.479020i
$204$	0.00673995	−	0.00883735i	0.000471891	−	0.000618738i
$205$	−0.773689			−0.0540368
$206$	12.8682	+	4.34708i	0.896570	+	0.302875i
$207$			0.677182i			0.0470674i
$208$	−3.49805	−	12.7545i	−0.242546	−	0.884362i
$209$	3.02364	−	4.35328i	0.209149	−	0.301123i
$210$	0.240950	−	0.713258i	0.0166271	−	0.0492195i
$211$			5.00976i			0.344886i	0.985020	+	0.172443i	$0.0551660\pi$
$211$			5.00976i			0.344886i	−0.985020	+	0.172443i	$0.944834\pi$
$212$	−7.44164	−	5.67549i	−0.511094	−	0.389794i
$213$			0.424001i			0.0290521i
$214$	3.31380	−	9.80948i	0.226527	−	0.670563i
$215$			1.80837i			0.123330i
$216$	2.34480	−	1.58175i	0.159543	−	0.107624i
$217$			6.55452i			0.444950i
$218$	−8.98061	−	3.03379i	−0.608244	−	0.205474i
$219$		−	1.23201i		−	0.0832513i
$220$	−0.579976	+	0.760458i	−0.0391020	+	0.0512701i
$221$	0.0183738			0.00123596
$222$	1.91830	−	5.67855i	0.128748	−	0.381119i
$223$	−6.38809			−0.427778			−0.213889	−	0.976858i	$-0.568613\pi$
$223$	−6.38809			−0.427778			−0.213889	+	0.976858i	$0.568613\pi$
$224$	−7.64474	−	0.444661i	−0.510786	−	0.0297101i
$225$	−4.84535			−0.323023
$226$	−0.924347	+	2.73625i	−0.0614867	+	0.182012i
$227$			12.2227i			0.811248i	0.914040	+	0.405624i	$0.132946\pi$
$227$			12.2227i			0.811248i	−0.914040	+	0.405624i	$0.867054\pi$
$228$	2.67744	+	8.29646i	0.177318	+	0.549447i
$229$		−	22.2874i		−	1.47280i	−0.676549	−	0.736398i	$-0.736525\pi$
$229$		−	22.2874i		−	1.47280i	0.676549	−	0.736398i	$-0.263475\pi$
$230$	0.356805	+	0.120534i	0.0235270	+	0.00794780i
$231$	−1.64606			−0.108303
$232$	−7.97475	−	11.8219i	−0.523568	−	0.776144i
$233$	6.96654			0.456393			0.228197	−	0.973615i	$-0.426717\pi$
$233$	6.96654			0.456393			0.228197	+	0.973615i	$0.426717\pi$
$234$	4.42996	+	1.49651i	0.289595	+	0.0978299i
$235$	4.30306			0.280700
$236$	11.9944	−	15.7269i	0.780769	−	1.02374i
$237$			11.1012i			0.721103i
$238$	0.00340486	−	0.0100790i	0.000220704	−	0.000653327i
$239$		−	9.25488i		−	0.598648i	−0.954151	−	0.299324i	$-0.903239\pi$
$239$		−	9.25488i		−	0.598648i	0.954151	−	0.299324i	$-0.0967612\pi$
$240$	−0.416056	−	1.51701i	−0.0268563	−	0.0979224i
$241$			7.83870i			0.504935i	0.967605	+	0.252468i	$0.0812421\pi$
$241$			7.83870i			0.504935i	−0.967605	+	0.252468i	$0.918758\pi$
$242$	−12.7570	−	4.30953i	−0.820053	−	0.277027i
$243$			1.00000i			0.0641500i
$244$	6.05686	−	7.94169i	0.387751	−	0.508414i
$245$			2.03216i			0.129830i
$246$	−2.63596	−	0.890470i	−0.168063	−	0.0567743i
$247$	−8.22156	+	11.8370i	−0.523125	+	0.753170i
$248$	7.65873	+	11.3534i	0.486330	+	0.720941i
$249$		−	7.42465i		−	0.470518i
$250$	−1.75241	+	5.18748i	−0.110832	+	0.328085i
$251$	−8.09717			−0.511089			−0.255544	−	0.966797i	$-0.582255\pi$
$251$	−8.09717			−0.511089			−0.255544	+	0.966797i	$0.582255\pi$
$252$	1.64183	−	2.15275i	0.103426	−	0.135611i
$253$		−	0.823439i		−	0.0517691i
$254$	−6.70784	−	2.26601i	−0.420887	−	0.142182i
$255$	0.00218537			0.000136853
$256$	−13.7614	+	8.16239i	−0.860086	+	0.510149i
$257$		−	4.42157i		−	0.275810i	−0.990445	−	0.137905i	$-0.955963\pi$
$257$		−	4.42157i		−	0.275810i	0.990445	−	0.137905i	$-0.0440369\pi$
$258$	−2.08133	+	6.16114i	−0.129578	+	0.383576i
$259$		−	5.73732i		−	0.356500i
$260$	1.57701	−	2.06776i	0.0978021	−	0.128237i
$261$	5.04174			0.312076
$262$	−22.2980	−	7.53262i	−1.37758	−	0.465367i
$263$		−	0.798438i		−	0.0492338i	−0.999697	−	0.0246169i	$-0.992163\pi$
$263$		−	0.798438i		−	0.0492338i	0.999697	−	0.0246169i	$-0.00783660\pi$
$264$	−2.85122	+	1.92337i	−0.175481	+	0.118375i
$265$		−	1.84023i		−	0.113044i
$266$	4.96970	+	6.70349i	0.304712	+	0.411017i
$267$	11.9802			0.733179
$268$	−2.98721	+	3.91680i	−0.182473	+	0.239257i
$269$	14.3823			0.876903			0.438451	−	0.898755i	$-0.355527\pi$
$269$	14.3823			0.876903			0.438451	+	0.898755i	$0.355527\pi$
$270$	0.526897	+	0.177994i	0.0320659	+	0.0108324i
$271$			29.7531i			1.80737i	0.428197	+	0.903686i	$0.359149\pi$
$271$			29.7531i			1.80737i	−0.428197	+	0.903686i	$0.640851\pi$
$272$	−0.00587928	−	0.0214368i	−0.000356484	−	0.00129980i
$273$	4.47581			0.270888
$274$	−17.8235	−	6.02105i	−1.07675	−	0.363745i
$275$	5.89184			0.355291
$276$	1.07691	+	0.821323i	0.0648223	+	0.0494378i
$277$		−	26.7252i		−	1.60576i	−0.596138	−	0.802882i	$-0.703299\pi$
$277$		−	26.7252i		−	1.60576i	0.596138	−	0.802882i	$-0.296701\pi$
$278$	19.9972	+	6.75536i	1.19935	+	0.405159i
$279$	−4.84195			−0.289880
$280$	−0.842042	−	1.24825i	−0.0503217	−	0.0745974i
$281$			9.71220i			0.579381i	0.957120	+	0.289690i	$0.0935524\pi$
$281$			9.71220i			0.579381i	−0.957120	+	0.289690i	$0.906448\pi$
$282$	14.6605	+	4.95256i	0.873022	+	0.294921i
$283$	−0.279927			−0.0166399			−0.00831995	−	0.999965i	$-0.502648\pi$
$283$	−0.279927			−0.0166399			−0.00831995	+	0.999965i	$0.502648\pi$
$284$	0.674280	+	0.514251i	0.0400112	+	0.0305152i
$285$	−0.977868	+	1.40789i	−0.0579239	+	0.0833960i
$286$	−5.38673	−	1.81972i	−0.318524	−	0.107602i
$287$	−2.66325			−0.157206
$288$	0.328479	−	5.64731i	0.0193558	−	0.332771i
$289$	−17.0000			−0.999998
$290$	0.897400	−	2.65648i	0.0526971	−	0.155994i
$291$	−2.05436			−0.120429
$292$	−1.95923	−	1.49424i	−0.114656	−	0.0874440i
$293$	26.6739			1.55831			0.779154	−	0.626833i	$-0.215649\pi$
$293$	26.6739			1.55831			0.779154	+	0.626833i	$0.215649\pi$
$294$	−2.33889	+	6.92357i	−0.136407	+	0.403791i
$295$	3.88908			0.226431
$296$	−6.70386	−	9.93788i	−0.389654	−	0.577627i
$297$		−	1.21598i		−	0.0705582i
$298$	−8.71812	+	25.8073i	−0.505027	+	1.49498i
$299$			2.23901i			0.129485i
$300$	−5.87670	+	7.70546i	−0.339291	+	0.444875i
$301$			6.22491i			0.358798i
$302$	25.8980	+	8.74877i	1.49026	+	0.503435i
$303$	−8.75636			−0.503040
$304$	16.4410	+	5.80451i	0.942958	+	0.332911i
$305$	1.96388			0.112452
$306$	0.00744557	+	0.00251523i	0.000425635	+	0.000143786i
$307$			18.0033i			1.02750i	0.857939	+	0.513751i	$0.171744\pi$
$307$			18.0033i			1.02750i	−0.857939	+	0.513751i	$0.828256\pi$
$308$	−1.99643	+	2.61770i	−0.113757	+	0.149157i
$309$			9.60437i			0.546373i
$310$	−0.861837	+	2.55121i	−0.0489491	+	0.144899i
$311$			19.2359i			1.09077i	0.838186	+	0.545385i	$0.183616\pi$
$311$			19.2359i			1.09077i	−0.838186	+	0.545385i	$0.816384\pi$
$312$	7.75275	−	5.22982i	0.438913	−	0.296080i
$313$	−20.0287			−1.13209			−0.566044	−	0.824375i	$-0.691527\pi$
$313$	−20.0287			−1.13209			−0.566044	+	0.824375i	$0.691527\pi$
$314$	1.16042	−	3.43507i	0.0654864	−	0.193852i
$315$	0.532350			0.0299945
$316$	17.6541	+	13.4642i	0.993119	+	0.757419i
$317$	11.0972			0.623283			0.311642	−	0.950200i	$-0.399121\pi$
$317$	11.0972			0.623283			0.311642	+	0.950200i	$0.399121\pi$
$318$	2.11799	−	6.26966i	0.118771	−	0.351585i
$319$	−6.13065			−0.343250
$320$	−2.91708	−	1.17826i	−0.163070	−	0.0658668i
$321$	7.32145			0.408643
$322$	1.22822	+	0.414912i	0.0684460	+	0.0231221i
$323$	−0.0138182	+	0.0198948i	−0.000768867	+	0.00110698i
$324$	1.59028	+	1.21285i	0.0883488	+	0.0673807i
$325$	−16.0205			−0.888656
$326$	−21.5662	−	7.28541i	−1.19444	−	0.403502i
$327$		−	6.70281i		−	0.370666i
$328$	−4.61313	+	3.11191i	−0.254718	+	0.171826i
$329$	14.8123			0.816627
$330$	−0.640695	−	0.216437i	−0.0352691	−	0.0119145i
$331$			23.0048i			1.26446i	0.774781	+	0.632230i	$0.217860\pi$
$331$			23.0048i			1.26446i	−0.774781	+	0.632230i	$0.782140\pi$
$332$	−11.8073	−	9.00501i	−0.648008	−	0.494214i
$333$	4.23826			0.232255
$334$	−22.1215	−	7.47299i	−1.21044	−	0.408904i
$335$	−0.968578			−0.0529191
$336$	−1.43218	−	5.22195i	−0.0781317	−	0.284881i
$337$			14.7725i			0.804710i	0.915484	+	0.402355i	$0.131808\pi$
$337$			14.7725i			0.804710i	−0.915484	+	0.402355i	$0.868192\pi$
$338$	−2.77073	−	0.935995i	−0.150708	−	0.0509114i
$339$	−2.04224			−0.110919
$340$	0.00265053	−	0.00347535i	0.000143745	−	0.000188477i
$341$	5.88770			0.318837
$342$	−4.95199	+	3.67121i	−0.267773	+	0.198516i
$343$			16.4711i			0.889356i
$344$	7.27358	+	10.7824i	0.392165	+	0.581351i
$345$			0.266307i			0.0143375i
$346$	−18.5232	−	6.25743i	−0.995813	−	0.336401i
$347$	32.3507			1.73668			0.868338	−	0.495973i	$-0.165189\pi$
$347$	32.3507			1.73668			0.868338	+	0.495973i	$0.165189\pi$
$348$	6.11489	−	8.01778i	0.327793	−	0.429798i
$349$		−	28.8848i		−	1.54617i	−0.634303	−	0.773084i	$-0.718713\pi$
$349$		−	28.8848i		−	1.54617i	0.634303	−	0.773084i	$-0.281287\pi$
$350$	−2.96876	+	8.78810i	−0.158687	+	0.469744i
$351$			3.30636i			0.176481i
$352$	−0.399423	+	6.86700i	−0.0212893	+	0.366012i
$353$	−22.1629			−1.17961			−0.589806	−	0.807545i	$-0.700796\pi$
$353$	−22.1629			−1.17961			−0.589806	+	0.807545i	$0.700796\pi$
$354$	13.2501	+	4.47609i	0.704235	+	0.237902i
$355$			0.166741i			0.00884971i
$356$	14.5303	−	19.0519i	0.770103	−	1.00975i
$357$	0.00752263			0.000398140
$358$	−4.10913	+	12.1638i	−0.217174	+	0.642878i
$359$		−	21.0084i		−	1.10878i	−0.832256	−	0.554391i	$-0.812951\pi$
$359$		−	21.0084i		−	1.10878i	0.832256	−	0.554391i	$-0.187049\pi$
$360$	0.922108	−	0.622032i	0.0485994	−	0.0327840i
$361$	−6.63376	−	17.8043i	−0.349145	−	0.937069i
$362$	−5.94653	−	2.00883i	−0.312543	−	0.105582i
$363$		−	9.52140i		−	0.499744i
$364$	5.42850	−	7.11778i	0.284531	−	0.373073i
$365$		−	0.484495i		−	0.0253596i
$366$	6.69096	+	2.26031i	0.349742	+	0.118148i
$367$		−	4.90961i		−	0.256280i	−0.991756	−	0.128140i	$-0.959099\pi$
$367$		−	4.90961i		−	0.256280i	0.991756	−	0.128140i	$-0.0409007\pi$
$368$	2.61226	−	0.716443i	0.136174	−	0.0373472i
$369$		−	1.96739i		−	0.102418i
$370$	0.754386	−	2.23313i	0.0392186	−	0.116095i
$371$		−	6.33456i		−	0.328874i
$372$	−5.87257	+	7.70005i	−0.304478	+	0.399229i
$373$	−16.5859			−0.858784			−0.429392	−	0.903118i	$-0.641272\pi$
$373$	−16.5859			−0.858784			−0.429392	+	0.903118i	$0.641272\pi$
$374$	−0.00905365	−	0.00305846i	−0.000468153	−	0.000158149i
$375$	−3.87175			−0.199936
$376$	25.6570	−	17.3076i	1.32316	−	0.892572i
$377$	16.6698			0.858540
$378$	1.81372	+	0.612703i	0.0932877	+	0.0315140i
$379$		−	25.6241i		−	1.31622i	−0.752920	−	0.658112i	$-0.771356\pi$
$379$		−	25.6241i		−	1.31622i	0.752920	−	0.658112i	$-0.228644\pi$
$380$	1.05292	+	3.26264i	0.0540138	+	0.167370i
$381$		−	5.00649i		−	0.256490i
$382$	−4.86019	+	14.3871i	−0.248669	+	0.736108i
$383$	24.1194			1.23245			0.616223	−	0.787572i	$-0.288662\pi$
$383$	24.1194			1.23245			0.616223	+	0.787572i	$0.288662\pi$
$384$	−8.58240	−	7.37173i	−0.437969	−	0.376187i
$385$	−0.647326			−0.0329908
$386$	−11.0678	+	32.7627i	−0.563334	+	1.66758i
$387$	−4.59845			−0.233752
$388$	−2.49164	+	3.26701i	−0.126494	+	0.165857i
$389$		−	26.1872i		−	1.32774i	−0.747847	−	0.663871i	$-0.768913\pi$
$389$		−	26.1872i		−	1.32774i	0.747847	−	0.663871i	$-0.231087\pi$
$390$	1.74211	+	0.588513i	0.0882152	+	0.0298005i
$391$			0.00376317i			0.000190312i
$392$	8.17368	+	12.1168i	0.412833	+	0.611989i
$393$		−	16.6424i		−	0.839500i
$394$	−0.272721	+	0.807306i	−0.0137395	+	0.0406715i
$395$			4.36564i			0.219659i
$396$	−1.93374	−	1.47480i	−0.0971743	−	0.0741116i
$397$			5.83861i			0.293032i	0.989208	+	0.146516i	$0.0468059\pi$
$397$			5.83861i			0.293032i	−0.989208	+	0.146516i	$0.953194\pi$
$398$	0.824627	−	2.44106i	0.0413348	−	0.122359i
$399$	−3.36608	+	4.84632i	−0.168515	+	0.242620i
$400$	5.12626	+	18.6912i	0.256313	+	0.934559i
$401$		−	10.8439i		−	0.541519i	−0.962647	−	0.270759i	$-0.912725\pi$
$401$		−	10.8439i		−	0.541519i	0.962647	−	0.270759i	$-0.0872748\pi$
$402$	−3.29995	−	1.11477i	−0.164587	−	0.0555999i
$403$	−16.0092			−0.797476
$404$	−10.6202	+	13.9251i	−0.528374	+	0.692798i
$405$			0.393257i			0.0195411i
$406$	3.08909	−	9.14431i	0.153309	−	0.453824i
$407$	−5.15364			−0.255456
$408$	0.0130303	−	0.00878993i	0.000645096	−	0.000435166i
$409$		−	23.8663i		−	1.18011i	−0.807363	−	0.590055i	$-0.799106\pi$
$409$		−	23.8663i		−	1.18011i	0.807363	−	0.590055i	$-0.200894\pi$
$410$	−1.03661	−	0.350183i	−0.0511945	−	0.0172943i
$411$		−	13.3028i		−	0.656179i
$412$	15.2736	+	11.6487i	0.752477	+	0.573889i
$413$	13.3872			0.658743
$414$	−0.306503	+	0.907308i	−0.0150638	+	0.0445918i
$415$		−	2.91979i		−	0.143327i
$416$	1.08607	−	18.6720i	0.0532490	−	0.915472i
$417$			14.9252i			0.730889i
$418$	6.02151	−	4.46411i	0.294522	−	0.218347i
$419$	10.0928			0.493064			0.246532	−	0.969135i	$-0.420709\pi$
$419$	10.0928			0.493064			0.246532	+	0.969135i	$0.420709\pi$
$420$	0.645662	−	0.846585i	0.0315051	−	0.0413091i
$421$	21.2013			1.03329			0.516645	−	0.856200i	$-0.327181\pi$
$421$	21.2013			1.03329			0.516645	+	0.856200i	$0.327181\pi$
$422$	−2.26749	+	6.71221i	−0.110380	+	0.326745i
$423$			10.9421i			0.532023i
$424$	−7.40171	−	10.9724i	−0.359459	−	0.532866i
$425$	−0.0269261			−0.00130611
$426$	−0.191909	+	0.568089i	−0.00929804	+	0.0275240i
$427$	6.76021			0.327150
$428$	8.87984	−	11.6431i	0.429223	−	0.562793i
$429$		−	4.02046i		−	0.194110i
$430$	−0.818497	+	2.42291i	−0.0394714	+	0.116843i
$431$	−29.6252			−1.42700			−0.713498	−	0.700657i	$-0.752890\pi$
$431$	−29.6252			−1.42700			−0.713498	+	0.700657i	$0.752890\pi$
$432$	3.85755	−	1.05798i	0.185596	−	0.0509019i
$433$		−	37.6370i		−	1.80872i	−0.426770	−	0.904360i	$-0.640349\pi$
$433$		−	37.6370i		−	1.80872i	0.426770	−	0.904360i	$-0.359651\pi$
$434$	−2.96667	+	8.78193i	−0.142405	+	0.421546i
$435$	1.98270			0.0950632
$436$	−10.6593	−	8.12952i	−0.510490	−	0.389333i
$437$	−2.42436	−	1.68387i	−0.115973	−	0.0805506i
$438$	0.557625	−	1.65068i	0.0266443	−	0.0788724i
$439$	−4.58779			−0.218963			−0.109482	−	0.993989i	$-0.534919\pi$
$439$	−4.58779			−0.218963			−0.109482	+	0.993989i	$0.534919\pi$
$440$	−1.12126	+	0.756377i	−0.0534541	+	0.0360589i
$441$	−5.16751			−0.246072
$442$	0.0246177	+	0.00831626i	0.00117095	+	0.000395564i
$443$	−2.78642			−0.132387			−0.0661935	−	0.997807i	$-0.521085\pi$
$443$	−2.78642			−0.132387			−0.0661935	+	0.997807i	$0.521085\pi$
$444$	5.14039	−	6.74002i	0.243952	−	0.319867i
$445$	4.71131			0.223338
$446$	−8.55894	−	2.89135i	−0.405278	−	0.136909i
$447$	−19.2617			−0.911045
$448$	−10.0414	−	4.05589i	−0.474410	−	0.191623i
$449$		−	25.9258i		−	1.22352i	−0.791045	−	0.611758i	$-0.790463\pi$
$449$		−	25.9258i		−	1.22352i	0.791045	−	0.611758i	$-0.209537\pi$
$450$	−6.49194	−	2.19308i	−0.306033	−	0.103383i
$451$			2.39230i			0.112649i
$452$	−2.47693	+	3.24773i	−0.116505	+	0.152760i
$453$			19.3294i			0.908173i
$454$	−5.53217	+	16.3763i	−0.259638	+	0.768577i
$455$	1.76014			0.0825167
$456$	−0.167793	+	12.3277i	−0.00785761	+	0.577297i
$457$	11.1120			0.519798			0.259899	−	0.965636i	$-0.416311\pi$
$457$	11.1120			0.519798			0.259899	+	0.965636i	$0.416311\pi$
$458$	10.0876	−	29.8613i	0.471364	−	1.39533i
$459$			0.00555711i			0.000259384i
$460$	0.423502	+	0.322991i	0.0197459	+	0.0150595i
$461$		−	40.3495i		−	1.87927i	−0.342185	−	0.939633i	$-0.611167\pi$
$461$		−	40.3495i		−	1.87927i	0.342185	−	0.939633i	$-0.388833\pi$
$462$	−2.20544	−	0.745033i	−0.102606	−	0.0346621i
$463$		−	3.44187i		−	0.159957i	−0.996797	−	0.0799787i	$-0.974515\pi$
$463$		−	3.44187i		−	0.159957i	0.996797	−	0.0799787i	$-0.0254852\pi$
$464$	−5.33404	−	19.4488i	−0.247627	−	0.902886i
$465$	−1.90413			−0.0883018
$466$	9.33397	+	3.15316i	0.432388	+	0.146067i
$467$	−31.1938			−1.44348			−0.721738	−	0.692166i	$-0.756656\pi$
$467$	−31.1938			−1.44348			−0.721738	+	0.692166i	$0.756656\pi$
$468$	5.25804	+	4.01013i	0.243053	+	0.185368i
$469$	−3.33410			−0.153955
$470$	5.76535	+	1.94763i	0.265936	+	0.0898374i
$471$	2.56382			0.118134
$472$	23.1887	−	15.6425i	1.06734	−	0.720005i
$473$	5.59162			0.257103
$474$	−5.02459	+	14.8738i	−0.230787	+	0.683174i
$475$	12.0484	−	17.3467i	0.552818	−	0.795920i
$476$	0.00912384	−	0.0119631i	0.000418191	−	0.000548327i
$477$	4.67945			0.214257
$478$	4.18890	−	12.3999i	0.191596	−	0.567160i
$479$			0.844102i			0.0385680i	0.999814	+	0.0192840i	$0.00613867\pi$
$479$			0.844102i			0.0385680i	−0.999814	+	0.0192840i	$0.993861\pi$
$480$	0.129177	−	2.22084i	0.00589608	−	0.101367i
$481$	14.0132			0.638949
$482$	−3.54791	+	10.5025i	−0.161603	+	0.478376i
$483$			0.916699i			0.0417112i
$484$	−15.1417	−	11.5481i	−0.688258	−	0.524912i
$485$	−0.807893			−0.0366845
$486$	−0.452615	+	1.33983i	−0.0205310	+	0.0607758i
$487$	−31.4332			−1.42437			−0.712186	−	0.701990i	$-0.752295\pi$
$487$	−31.4332			−1.42437			−0.712186	+	0.701990i	$0.752295\pi$
$488$	11.7097	−	7.89907i	0.530072	−	0.357574i
$489$		−	16.0963i		−	0.727898i
$490$	−0.919785	+	2.72274i	−0.0415517	+	0.123001i
$491$	33.2319			1.49974			0.749868	−	0.661588i	$-0.230117\pi$
$491$	33.2319			1.49974			0.749868	+	0.661588i	$0.230117\pi$
$492$	−3.12870	−	2.38615i	−0.141053	−	0.107576i
$493$	0.0280175			0.00126184
$494$	−16.3731	+	12.1383i	−0.736660	+	0.546130i
$495$		−	0.478192i		−	0.0214931i
$496$	5.12266	+	18.6780i	0.230014	+	0.838669i
$497$			0.573969i			0.0257460i
$498$	3.36051	−	9.94775i	0.150588	−	0.445770i
$499$	−1.07956			−0.0483275			−0.0241638	−	0.999708i	$-0.507692\pi$
$499$	−1.07956			−0.0483275			−0.0241638	+	0.999708i	$0.507692\pi$
$500$	−4.69586	+	6.15717i	−0.210005	+	0.275357i
$501$		−	16.5107i		−	0.737644i
$502$	−10.8488	−	3.66490i	−0.484206	−	0.163573i
$503$		−	34.2767i		−	1.52832i	−0.645025	−	0.764162i	$-0.723153\pi$
$503$		−	34.2767i		−	1.52832i	0.645025	−	0.764162i	$-0.276847\pi$
$504$	3.17414	−	2.14120i	0.141388	−	0.0953767i
$505$	−3.44350			−0.153234
$506$	0.372701	−	1.10327i	0.0165686	−	0.0490462i
$507$		−	2.06797i		−	0.0918418i
$508$	−7.96172	−	6.07214i	−0.353244	−	0.269407i
$509$	15.7347			0.697429			0.348715	−	0.937229i	$-0.386618\pi$
$509$	15.7347			0.697429			0.348715	+	0.937229i	$0.386618\pi$
$510$	0.00292802		0.000989132i	0.000129655		4.37995e-5i
$511$		−	1.66776i		−	0.0737775i
$512$	−22.1323	+	4.70759i	−0.978119	+	0.208048i
$513$	−3.58007	−	2.48659i	−0.158064	−	0.109786i
$514$	2.00127	−	5.92415i	0.0882722	−	0.261303i
$515$			3.77698i			0.166434i
$516$	−5.57725	+	7.31282i	−0.245525	+	0.321929i
$517$		−	13.3053i		−	0.585169i
$518$	2.59680	−	7.68702i	0.114097	−	0.337748i
$519$		−	13.8251i		−	0.606852i
$520$	3.04882	−	2.05666i	0.133700	−	0.0901907i
$521$			31.7648i			1.39164i	0.718215	+	0.695822i	$0.244960\pi$
$521$			31.7648i			1.39164i	−0.718215	+	0.695822i	$0.755040\pi$
$522$	6.75507	+	2.28197i	0.295661	+	0.0998791i
$523$		−	36.2049i		−	1.58313i	−0.611086	−	0.791564i	$-0.709267\pi$
$523$		−	36.2049i		−	1.58313i	0.611086	−	0.791564i	$-0.290733\pi$
$524$	−26.4661	−	20.1848i	−1.15618	−	0.881778i
$525$	−6.55913			−0.286264
$526$	0.361385	−	1.06977i	0.0157571	−	0.0466442i
$527$	−0.0269072			−0.00117210
$528$	−4.69069	+	1.28648i	−0.204136	+	0.0559866i
$529$	22.5414			0.980062
$530$	0.832915	−	2.46559i	0.0361795	−	0.107098i
$531$			9.88941i			0.429164i
$532$	3.62444	+	11.2309i	0.157139	+	0.486921i
$533$		−	6.50490i		−	0.281758i
$534$	16.0515	+	5.42244i	0.694615	+	0.234652i
$535$	2.87921			0.124479
$536$	−5.77516	+	3.89578i	−0.249449	+	0.168272i
$537$	−9.07865			−0.391773
$538$	19.2698	+	6.50964i	0.830779	+	0.280650i
$539$	6.28358			0.270653
$540$	0.625388	+	0.476963i	0.0269124	+	0.0205252i
$541$			13.8419i			0.595108i	0.954705	+	0.297554i	$0.0961708\pi$
$541$			13.8419i			0.595108i	−0.954705	+	0.297554i	$0.903829\pi$
$542$	−13.4667	+	39.8640i	−0.578444	+	1.71231i
$543$		−	4.43828i		−	0.190465i
$544$	0.00182539	−	0.0313827i	7.82631e−5	−	0.00134552i
$545$		−	2.63593i		−	0.112911i
$546$	5.99681	+	2.02582i	0.256640	+	0.0866970i
$547$			12.2681i			0.524545i	0.964994	+	0.262272i	$0.0844719\pi$
$547$			12.2681i			0.524545i	−0.964994	+	0.262272i	$0.915528\pi$
$548$	−21.1552	−	16.1343i	−0.903704	−	0.689225i
$549$			4.99390i			0.213134i
$550$	7.89405	+	2.66673i	0.336603	+	0.113710i
$551$	−12.5367	+	18.0498i	−0.534083	+	0.768946i
$552$	1.07113	+	1.58786i	0.0455903	+	0.0675837i
$553$			15.0277i			0.639043i
$554$	12.0962	−	35.8072i	0.513920	−	1.52130i
$555$	1.66673			0.0707486
$556$	23.7352	+	18.1020i	1.00660	+	0.767697i
$557$			41.7859i			1.77053i	0.465090	+	0.885263i	$0.346022\pi$
$557$			41.7859i			1.77053i	−0.465090	+	0.885263i	$0.653978\pi$
$558$	−6.48738	−	2.19154i	−0.274632	−	0.0927752i
$559$	−15.2041			−0.643067
$560$	−0.563214	−	2.05357i	−0.0238001	−	0.0867790i
$561$		−	0.00675732i		−	0.000285294i
$562$	−4.39589	+	13.0127i	−0.185429	+	0.548906i
$563$		−	5.24786i		−	0.221171i	−0.993867	−	0.110585i	$-0.964727\pi$
$563$		−	5.24786i		−	0.221171i	0.993867	−	0.110585i	$-0.0352726\pi$
$564$	17.4010	+	13.2712i	0.732714	+	0.558816i
$565$	−0.803124			−0.0337877
$566$	−0.375054	−	0.126699i	−0.0157647	−	0.00532556i
$567$			1.35370i			0.0568499i
$568$	0.670662	+	0.994197i	0.0281403	+	0.0417156i
$569$			32.6133i			1.36722i	0.729846	+	0.683611i	$0.239592\pi$
$569$			32.6133i			1.36722i	−0.729846	+	0.683611i	$0.760408\pi$
$570$	−1.94741	+	1.44373i	−0.0815678	+	0.0604711i
$571$	27.2472			1.14026			0.570129	−	0.821555i	$-0.306893\pi$
$571$	27.2472			1.14026			0.570129	+	0.821555i	$0.306893\pi$
$572$	−6.39366	−	4.87623i	−0.267332	−	0.203885i
$573$	−10.7380			−0.448587
$574$	−3.56829	−	1.20542i	−0.148938	−	0.0503135i
$575$		−	3.28118i		−	0.136835i
$576$	2.99616	−	7.41775i	0.124840	−	0.309073i
$577$	−13.9778			−0.581902			−0.290951	−	0.956738i	$-0.593972\pi$
$577$	−13.9778			−0.581902			−0.290951	+	0.956738i	$0.593972\pi$
$578$	−22.7770	−	7.69444i	−0.947400	−	0.320047i
$579$	−24.4529			−1.01623
$580$	2.40472	−	3.15305i	0.0998507	−	0.130923i
$581$		−	10.0507i		−	0.416974i
$582$	−2.75250	−	0.929836i	−0.114095	−	0.0385430i
$583$	−5.69011			−0.235660
$584$	−1.94872	−	2.88881i	−0.0806387	−	0.119540i
$585$			1.30025i			0.0537587i
$586$	35.7385	+	12.0730i	1.47634	+	0.498732i
$587$	7.74807			0.319797			0.159899	−	0.987133i	$-0.448883\pi$
$587$	7.74807			0.319797			0.159899	+	0.987133i	$0.448883\pi$
$588$	−6.26743	+	8.21778i	−0.258464	+	0.338896i
$589$	12.0399	−	17.3345i	0.496096	−	0.714255i
$590$	5.21070	+	1.76025i	0.214521	+	0.0724685i
$591$	−0.602544			−0.0247854
$592$	−4.48398	−	16.3493i	−0.184291	−	0.671953i
$593$	−10.7668			−0.442140			−0.221070	−	0.975258i	$-0.570955\pi$
$593$	−10.7668			−0.442140			−0.221070	+	0.975258i	$0.570955\pi$
$594$	0.550370	−	1.62920i	0.0225819	−	0.0668469i
$595$	0.00295833			0.000121280
$596$	−23.3616	+	30.6314i	−0.956927	+	1.25471i
$597$	1.82192			0.0745661
$598$	−1.01341	+	2.99989i	−0.0414414	+	0.122675i
$599$	−17.5934			−0.718845			−0.359422	−	0.933175i	$-0.617026\pi$
$599$	−17.5934			−0.718845			−0.359422	+	0.933175i	$0.617026\pi$
$600$	−11.3614	+	7.66411i	−0.463826	+	0.312886i
$601$		−	12.6891i		−	0.517599i	−0.965931	−	0.258799i	$-0.916673\pi$
$601$		−	12.6891i		−	0.517599i	0.965931	−	0.258799i	$-0.0833269\pi$
$602$	−2.81749	+	8.34030i	−0.114832	+	0.339925i
$603$		−	2.46296i		−	0.100300i
$604$	30.7391	+	23.4437i	1.25076	+	0.953910i
$605$		−	3.74436i		−	0.152230i
$606$	−11.7320	−	3.96326i	−0.476581	−	0.160997i
$607$	28.0538			1.13867			0.569334	−	0.822106i	$-0.307201\pi$
$607$	28.0538			1.13867			0.569334	+	0.822106i	$0.307201\pi$
$608$	19.4010	+	15.2185i	0.786813	+	0.617192i
$609$	6.82498			0.276562
$610$	2.63127	+	0.888883i	0.106537	+	0.0359898i
$611$			36.1785i			1.46363i
$612$	0.00883735	+	0.00673995i	0.000357229	+	0.000272446i
$613$		−	0.510517i		−	0.0206196i	−0.999947	−	0.0103098i	$-0.996718\pi$
$613$		−	0.510517i		−	0.0206196i	0.999947	−	0.0103098i	$-0.00328177\pi$
$614$	−8.14856	+	24.1213i	−0.328849	+	0.973457i
$615$		−	0.773689i		−	0.0311982i
$616$	−3.85969	+	2.60365i	−0.155511	+	0.104904i
$617$	31.9714			1.28712			0.643560	−	0.765396i	$-0.277457\pi$
$617$	31.9714			1.28712			0.643560	+	0.765396i	$0.277457\pi$
$618$	−4.34708	+	12.8682i	−0.174865	+	0.517635i
$619$	8.53505			0.343053			0.171526	−	0.985180i	$-0.445130\pi$
$619$	8.53505			0.343053			0.171526	+	0.985180i	$0.445130\pi$
$620$	−2.30943	+	3.02810i	−0.0927488	+	0.121611i
$621$	−0.677182			−0.0271744
$622$	−8.70647	+	25.7728i	−0.349098	+	1.03340i
$623$	16.2176			0.649745
$624$	12.7545	−	3.49805i	0.510587	−	0.140034i
$625$	22.7042			0.908166
$626$	−26.8350	−	9.06529i	−1.07254	−	0.362322i
$627$	4.35328	+	3.02364i	0.173853	+	0.120752i
$628$	3.10953	−	4.07719i	0.124084	−	0.162697i
$629$	0.0235525			0.000939099
$630$	0.713258	+	0.240950i	0.0284169	+	0.00959967i
$631$		−	4.94467i		−	0.196844i	−0.995145	−	0.0984221i	$-0.968620\pi$
$631$		−	4.94467i		−	0.196844i	0.995145	−	0.0984221i	$-0.0313795\pi$
$632$	17.5593	+	26.0302i	0.698473	+	1.03543i
$633$	−5.00976			−0.199120
$634$	14.8684	+	5.02278i	0.590499	+	0.199480i
$635$		−	1.96884i		−	0.0781309i
$636$	5.67549	−	7.44164i	0.225048	−	0.295080i
$637$	−17.0857			−0.676958
$638$	−8.21401	−	2.77482i	−0.325196	−	0.109856i
$639$	−0.424001			−0.0167732
$640$	−3.37509	−	2.89898i	−0.133412	−	0.114592i
$641$			9.73828i			0.384639i	0.981332	+	0.192320i	$0.0616010\pi$
$641$			9.73828i			0.384639i	−0.981332	+	0.192320i	$0.938399\pi$
$642$	9.80948	+	3.31380i	0.387149	+	0.130785i
$643$	−34.7059			−1.36867			−0.684334	−	0.729168i	$-0.739907\pi$
$643$	−34.7059			−1.36867			−0.684334	+	0.729168i	$0.739907\pi$
$644$	1.45781	+	1.11182i	0.0574456	+	0.0438119i
$645$	−1.80837			−0.0712046
$646$	−0.0275188	+	0.0204013i	−0.00108271	+	0.000802678i
$647$			15.7832i			0.620502i	0.950655	+	0.310251i	$0.100413\pi$
$647$			15.7832i			0.620502i	−0.950655	+	0.310251i	$0.899587\pi$
$648$	1.58175	+	2.34480i	0.0621368	+	0.0921124i
$649$		−	12.0253i		−	0.472034i
$650$	−21.4647	−	7.25111i	−0.841914	−	0.284412i
$651$	−6.55452			−0.256892
$652$	−25.5975	−	19.5224i	−1.00248	−	0.764556i
$653$			18.6709i			0.730650i	0.930880	+	0.365325i	$0.119042\pi$
$653$			18.6709i			0.730650i	−0.930880	+	0.365325i	$0.880958\pi$
$654$	3.03379	−	8.98061i	0.118631	−	0.351170i
$655$		−	6.54475i		−	0.255725i
$656$	−7.58930	+	2.08145i	−0.296312	+	0.0812670i
$657$	1.23201			0.0480652
$658$	19.8459	+	6.70426i	0.773674	+	0.261359i
$659$			5.70895i			0.222389i	0.993799	+	0.111195i	$0.0354677\pi$
$659$			5.70895i			0.222389i	−0.993799	+	0.111195i	$0.964532\pi$
$660$	−0.760458	−	0.579976i	−0.0296008	−	0.0225755i
$661$	37.3664			1.45338			0.726692	−	0.686963i	$-0.241057\pi$
$661$	37.3664			1.45338			0.726692	+	0.686963i	$0.241057\pi$
$662$	−10.4123	+	30.8225i	−0.404687	+	1.19795i
$663$			0.0183738i			0.000713579i
$664$	−11.7439	−	17.4093i	−0.455752	−	0.675612i
$665$	−1.32374	+	1.90585i	−0.0513323	+	0.0739057i
$666$	5.67855	+	1.91830i	0.220039	+	0.0743327i
$667$			3.41418i			0.132198i
$668$	−26.2566	−	20.0251i	−1.01590	−	0.774793i
$669$		−	6.38809i		−	0.246978i
$670$	−1.29773	−	0.438393i	−0.0501356	−	0.0169366i
$671$		−	6.07247i		−	0.234425i
$672$	0.444661	−	7.64474i	0.0171532	−	0.294902i
$673$			23.1675i			0.893040i	0.894774	+	0.446520i	$0.147337\pi$
$673$			23.1675i			0.893040i	−0.894774	+	0.446520i	$0.852663\pi$
$674$	−6.68626	+	19.7926i	−0.257545	+	0.762384i
$675$		−	4.84535i		−	0.186498i
$676$	−3.28865	−	2.50814i	−0.126487	−	0.0964671i
$677$	−28.2705			−1.08652			−0.543262	−	0.839564i	$-0.682811\pi$
$677$	−28.2705			−1.08652			−0.543262	+	0.839564i	$0.682811\pi$
$678$	−2.73625	−	0.924347i	−0.105085	−	0.0354994i
$679$	−2.78098			−0.106724
$680$	0.00512425	−	0.00345670i	0.000196506	−	0.000132558i
$681$	−12.2227			−0.468374
$682$	7.88850	+	2.66486i	0.302066	+	0.102043i
$683$			26.5216i			1.01482i	0.861704	+	0.507411i	$0.169397\pi$
$683$			26.5216i			1.01482i	−0.861704	+	0.507411i	$0.830603\pi$
$684$	−8.29646	+	2.67744i	−0.317223	+	0.102375i
$685$		−	5.23142i		−	0.199882i
$686$	−7.45507	+	22.0684i	−0.284636	+	0.842577i
$687$	22.2874			0.850319
$688$	4.86505	+	17.7388i	0.185478	+	0.676284i
$689$	15.4720			0.589435
$690$	−0.120534	+	0.356805i	−0.00458867	+	0.0135833i
$691$	8.53640			0.324740			0.162370	−	0.986730i	$-0.448086\pi$
$691$	8.53640			0.324740			0.162370	+	0.986730i	$0.448086\pi$
$692$	−21.9857	−	16.7678i	−0.835771	−	0.637414i
$693$		−	1.64606i		−	0.0625288i
$694$	43.3444	+	14.6424i	1.64533	+	0.555818i
$695$			5.86942i			0.222640i
$696$	11.8219	−	7.97475i	0.448107	−	0.302282i
$697$		−	0.0109330i		−	0.000414116i
$698$	13.0737	−	38.7007i	0.494847	−	1.46484i
$699$			6.96654i			0.263499i
$700$	−7.95526	+	10.4308i	−0.300680	+	0.394249i
$701$			14.2487i			0.538166i	0.963117	+	0.269083i	$0.0867207\pi$
$701$			14.2487i			0.538166i	−0.963117	+	0.269083i	$0.913279\pi$
$702$	−1.49651	+	4.42996i	−0.0564821	+	0.167198i
$703$	−10.5388	+	15.1733i	−0.397479	+	0.572271i
$704$	−3.64327	+	9.01982i	−0.137311	+	0.339947i
$705$			4.30306i			0.162062i
$706$	−29.6945	−	10.0313i	−1.11757	−	0.377531i
$707$	−11.8535			−0.445795
$708$	15.7269	+	11.9944i	0.591054	+	0.450777i
$709$			51.2166i			1.92348i	0.273963	+	0.961740i	$0.411665\pi$
$709$			51.2166i			1.92348i	−0.273963	+	0.961740i	$0.588335\pi$
$710$	−0.0754697	+	0.223405i	−0.00283233	+	0.00838423i
$711$	−11.1012			−0.416329
$712$	28.0913	−	18.9497i	1.05276	−	0.710170i
$713$		−	3.27888i		−	0.122795i
$714$	0.0100790	+	0.00340486i	0.000377198	+	0.000127424i
$715$		−	1.58107i		−	0.0591288i
$716$	−11.0111	+	14.4376i	−0.411503	+	0.539558i
$717$	9.25488			0.345630
$718$	9.50872	−	28.1477i	0.354862	−	1.05046i
$719$		−	39.4189i		−	1.47008i	−0.678026	−	0.735038i	$-0.737164\pi$
$719$		−	39.4189i		−	1.47008i	0.678026	−	0.735038i	$-0.262836\pi$
$720$	1.51701	−	0.416056i	0.0565355	−	0.0155055i
$721$			13.0014i			0.484197i
$722$	−0.829608	−	26.8572i	−0.0308748	−	0.999523i
$723$	−7.83870			−0.291524
$724$	−7.05810	−	5.38298i	−0.262312	−	0.200057i
$725$	−24.4290			−0.907270
$726$	4.30953	−	12.7570i	0.159942	−	0.473458i
$727$			32.9620i			1.22249i	0.791440	+	0.611246i	$0.209332\pi$
$727$			32.9620i			1.22249i	−0.791440	+	0.611246i	$0.790668\pi$
$728$	10.4949	−	7.07959i	0.388966	−	0.262387i
$729$	−1.00000			−0.0370370
$730$	0.219290	−	0.649140i	0.00811628	−	0.0240258i
$731$	−0.0255541			−0.000945152
$732$	7.94169	+	6.05686i	0.293533	+	0.223868i
$733$			39.5261i			1.45993i	0.683485	+	0.729965i	$0.260464\pi$
$733$			39.5261i			1.45993i	−0.683485	+	0.729965i	$0.739536\pi$
$734$	2.22217	−	6.57804i	0.0820216	−	0.242800i
$735$	−2.03216			−0.0749573
$736$	3.82426	+	0.222440i	0.140964	+	0.00819925i
$737$			2.99491i			0.110319i
$738$	0.890470	−	2.63596i	0.0327786	−	0.0970311i
$739$	−2.89967			−0.106666			−0.0533330	−	0.998577i	$-0.516984\pi$
$739$	−2.89967			−0.106666			−0.0533330	+	0.998577i	$0.516984\pi$
$740$	2.02149	−	2.65056i	0.0743116	−	0.0974366i
$741$	−11.8370	−	8.22156i	−0.434843	−	0.302027i
$742$	2.86712	−	8.48722i	0.105255	−	0.311576i
$743$	44.8357			1.64486			0.822431	−	0.568865i	$-0.192617\pi$
$743$	44.8357			1.64486			0.822431	+	0.568865i	$0.192617\pi$
$744$	−11.3534	+	7.65873i	−0.416235	+	0.280782i
$745$	−7.57478			−0.277519
$746$	−22.2222	−	7.50702i	−0.813614	−	0.274851i
$747$	7.42465			0.271654
$748$	−0.0107460	−	0.00819563i	−0.000392914	−	0.000299662i
$749$	9.91101			0.362141
$750$	−5.18748	−	1.75241i	−0.189420	−	0.0639891i
$751$	19.9481			0.727918			0.363959	−	0.931415i	$-0.381425\pi$
$751$	19.9481			0.727918			0.363959	+	0.931415i	$0.381425\pi$
$752$	42.2097	−	11.5765i	1.53923	−	0.422151i
$753$		−	8.09717i		−	0.295077i
$754$	22.3347	+	7.54501i	0.813382	+	0.274773i
$755$			7.60141i			0.276644i
$756$	2.15275	+	1.64183i	0.0782949	+	0.0597129i
$757$			24.8537i			0.903322i	0.892190	+	0.451661i	$0.149168\pi$
$757$			24.8537i			0.903322i	−0.892190	+	0.451661i	$0.850832\pi$
$758$	11.5979	−	34.3319i	0.421253	−	1.24699i
$759$	0.823439			0.0298889
$760$	−0.0659856	+	4.84795i	−0.00239355	+	0.175854i
$761$	−29.7493			−1.07841			−0.539206	−	0.842174i	$-0.681275\pi$
$761$	−29.7493			−1.07841			−0.539206	+	0.842174i	$0.681275\pi$
$762$	2.26601	−	6.70784i	0.0820890	−	0.242999i
$763$		−	9.07356i		−	0.328485i
$764$	−13.0236	+	17.0765i	−0.471179	+	0.617804i
$765$			0.00218537i			7.90122e-5i
$766$	32.3159	+	10.9168i	1.16762	+	0.394441i
$767$			32.6980i			1.18065i
$768$	−8.16239	−	13.7614i	−0.294535	−	0.496571i
$769$	−17.7979			−0.641809			−0.320905	−	0.947112i	$-0.603987\pi$
$769$	−17.7979			−0.641809			−0.320905	+	0.947112i	$0.603987\pi$
$770$	−0.867306	−	0.292989i	−0.0312555	−	0.0105586i
$771$	4.42157			0.159239
$772$	−29.6578	+	38.8870i	−1.06741	+	1.39957i
$773$	2.50404			0.0900641			0.0450320	−	0.998986i	$-0.485661\pi$
$773$	2.50404			0.0900641			0.0450320	+	0.998986i	$0.485661\pi$
$774$	−6.16114	−	2.08133i	−0.221457	−	0.0748118i
$775$	23.4609			0.842741
$776$	−4.81707	+	3.24948i	−0.172923	+	0.116650i
$777$	5.73732			0.205825
$778$	11.8527	−	35.0863i	0.424940	−	1.25790i
$779$	7.04338	+	4.89208i	0.252355	+	0.175277i
$780$	2.06776	+	1.57701i	0.0740377	+	0.0564661i
$781$	0.515576			0.0184488
$782$	−0.00170327	+	0.00504201i	−6.09088e−5	+	0.000180302i
$783$			5.04174i			0.180177i
$784$	5.46710	+	19.9339i	0.195254	+	0.711926i
$785$	1.00824			0.0359856
$786$	7.53262	−	22.2980i	0.268680	−	0.795343i
$787$			48.3385i			1.72308i	0.507689	+	0.861540i	$0.330500\pi$
$787$			48.3385i			1.72308i	−0.507689	+	0.861540i	$0.669500\pi$
$788$	−0.730797	+	0.958213i	−0.0260336	+	0.0341349i
$789$	0.798438			0.0284252
$790$	−1.97595	+	5.84921i	−0.0703013	+	0.208105i
$791$	−2.76457			−0.0982967
$792$	−1.92337	−	2.85122i	−0.0683439	−	0.101314i
$793$			16.5116i			0.586345i
$794$	−2.64264	+	7.82274i	−0.0937839	+	0.277619i
$795$	1.84023			0.0652661
$796$	2.20972	−	2.89736i	0.0783214	−	0.102694i
$797$	4.38865			0.155454			0.0777271	−	0.996975i	$-0.475234\pi$
$797$	4.38865			0.155454			0.0777271	+	0.996975i	$0.475234\pi$
$798$	−6.70349	+	4.96970i	−0.237301	+	0.175925i
$799$			0.0608064i			0.00215118i
$800$	−1.59160	+	27.3632i	−0.0562714	+	0.967435i
$801$			11.9802i			0.423301i
$802$	4.90811	−	14.5290i	0.173312	−	0.513036i
$803$	−1.49809			−0.0528666
$804$	−3.91680	−	2.98721i	−0.138135	−	0.105351i
$805$			0.360498i			0.0127059i
$806$	−21.4496	−	7.24602i	−0.755530	−	0.255230i
$807$			14.3823i			0.506280i
$808$	−20.5319	+	13.8503i	−0.722310	+	0.487253i
$809$	−1.71674			−0.0603574			−0.0301787	−	0.999545i	$-0.509608\pi$
$809$	−1.71674			−0.0603574			−0.0301787	+	0.999545i	$0.509608\pi$
$810$	−0.177994	+	0.526897i	−0.00625407	+	0.0185133i
$811$		−	39.8836i		−	1.40050i	−0.713897	−	0.700251i	$-0.753072\pi$
$811$		−	39.8836i		−	1.40050i	0.713897	−	0.700251i	$-0.246928\pi$
$812$	8.27770	−	10.8536i	0.290490	−	0.380888i
$813$	−29.7531			−1.04349
$814$	−6.90499	−	2.33261i	−0.242020	−	0.0817580i
$815$		−	6.32997i		−	0.221729i
$816$	0.0214368	−	0.00587928i	0.000750439	−	0.000205816i
$817$	11.4345	−	16.4628i	0.400041	−	0.575959i
$818$	10.8022	−	31.9767i	0.377691	−	1.11804i
$819$			4.47581i			0.156397i
$820$	−1.23038	−	0.938371i	−0.0429668	−	0.0327693i
$821$		−	21.5429i		−	0.751853i	−0.926650	−	0.375926i	$-0.877325\pi$
$821$		−	21.5429i		−	0.751853i	0.926650	−	0.375926i	$-0.122675\pi$
$822$	6.02105	−	17.8235i	0.210008	−	0.621665i
$823$		−	51.4146i		−	1.79220i	−0.443852	−	0.896100i	$-0.646388\pi$
$823$		−	51.4146i		−	1.79220i	0.443852	−	0.896100i	$-0.353612\pi$
$824$	15.1917	+	22.5203i	0.529227	+	0.784532i
$825$			5.89184i			0.205127i
$826$	17.9366	+	6.05927i	0.624094	+	0.210829i
$827$		−	28.1995i		−	0.980592i	−0.871556	−	0.490296i	$-0.836889\pi$
$827$		−	28.1995i		−	0.980592i	0.871556	−	0.490296i	$-0.163111\pi$
$828$	−0.821323	+	1.07691i	−0.0285429	+	0.0374252i
$829$	−56.6258			−1.96670			−0.983348	−	0.181734i	$-0.941829\pi$
$829$	−56.6258			−1.96670			−0.983348	+	0.181734i	$0.941829\pi$
$830$	1.32154	−	3.91202i	0.0458714	−	0.135788i
$831$	26.7252			0.927088
$832$	9.90640	−	24.5258i	0.343443	−	0.850278i
$833$	−0.0287164			−0.000994964
$834$	−6.75536	+	19.9972i	−0.233919	+	0.692445i
$835$		−	6.49295i		−	0.224698i
$836$	10.0883	−	3.25571i	0.348912	−	0.112601i
$837$		−	4.84195i		−	0.167362i
$838$	13.5226	+	4.56814i	0.467130	+	0.157804i
$839$	12.4990			0.431513			0.215756	−	0.976447i	$-0.430778\pi$
$839$	12.4990			0.431513			0.215756	+	0.976447i	$0.430778\pi$
$840$	1.24825	−	0.842042i	0.0430689	−	0.0290532i
$841$	−3.58083			−0.123477
$842$	28.4061	+	9.59604i	0.978940	+	0.330701i
$843$	−9.71220			−0.334506
$844$	−6.07610	+	7.96691i	−0.209148	+	0.274232i
$845$		−	0.813244i		−	0.0279764i
$846$	−4.95256	+	14.6605i	−0.170272	+	0.504039i
$847$		−	12.8891i		−	0.442874i
$848$	−4.95075	−	18.0512i	−0.170009	−	0.619882i
$849$		−	0.279927i		−	0.00960706i
$850$	−0.0360764	−	0.0121872i	−0.00123741	−	0.000418016i
$851$			2.87008i			0.0983850i
$852$	−0.514251	+	0.674280i	−0.0176179	+	0.0231005i
$853$			32.9738i			1.12900i	0.825433	+	0.564500i	$0.190931\pi$
$853$			32.9738i			1.12900i	−0.825433	+	0.564500i	$0.809069\pi$
$854$	9.05753	+	3.05977i	0.309942	+	0.104703i
$855$	−1.40789	−	0.977868i	−0.0481487	−	0.0334424i
$856$	17.1673	−	11.5807i	0.586767	−	0.395819i
$857$			32.4358i			1.10799i	0.832521	+	0.553993i	$0.186897\pi$
$857$			32.4358i			1.10799i	−0.832521	+	0.553993i	$0.813103\pi$
$858$	1.81972	−	5.38673i	0.0621243	−	0.183900i
$859$	18.7433			0.639514			0.319757	−	0.947500i	$-0.396399\pi$
$859$	18.7433			0.639514			0.319757	+	0.947500i	$0.396399\pi$
$860$	−2.19329	+	2.87582i	−0.0747906	+	0.0980646i
$861$		−	2.66325i		−	0.0907632i
$862$	−39.6927	−	13.4088i	−1.35194	−	0.456706i
$863$	29.2455			0.995529			0.497765	−	0.867312i	$-0.334154\pi$
$863$	29.2455			0.995529			0.497765	+	0.867312i	$0.334154\pi$
$864$	5.64731	+	0.328479i	0.192125	+	0.0111751i
$865$		−	5.43680i		−	0.184857i
$866$	17.0351	−	50.4271i	0.578876	−	1.71358i
$867$		−	17.0000i		−	0.577349i
$868$	−7.94967	+	10.4235i	−0.269829	+	0.353797i
$869$	13.4989			0.457918
$870$	2.65648	+	0.897400i	0.0900630	+	0.0304247i
$871$		−	8.14345i		−	0.275930i
$872$	−10.6021	−	15.7167i	−0.359034	−	0.532236i
$873$		−	2.05436i		−	0.0695297i
$874$	−2.48608	−	3.35340i	−0.0840928	−	0.113431i
$875$	−5.24117			−0.177184
$876$	1.49424	−	1.95923i	0.0504858	−	0.0661964i
$877$	29.1471			0.984229			0.492114	−	0.870531i	$-0.336224\pi$
$877$	29.1471			0.984229			0.492114	+	0.870531i	$0.336224\pi$
$878$	−6.14685	−	2.07650i	−0.207446	−	0.0700786i
$879$			26.6739i			0.899689i
$880$	−1.84465	+	0.505915i	−0.0621831	+	0.0170544i
$881$	−9.86763			−0.332449			−0.166224	−	0.986088i	$-0.553158\pi$
$881$	−9.86763			−0.332449			−0.166224	+	0.986088i	$0.553158\pi$
$882$	−6.92357	−	2.33889i	−0.233129	−	0.0787546i
$883$	−45.5997			−1.53455			−0.767276	−	0.641317i	$-0.778388\pi$
$883$	−45.5997			−1.53455			−0.767276	+	0.641317i	$0.778388\pi$
$884$	0.0292195	+	0.0222847i	0.000982758	+	0.000749516i
$885$			3.88908i			0.130730i
$886$	−3.73333	−	1.26118i	−0.125424	−	0.0423701i
$887$	−5.88747			−0.197682			−0.0988410	−	0.995103i	$-0.531514\pi$
$887$	−5.88747			−0.197682			−0.0988410	+	0.995103i	$0.531514\pi$
$888$	9.93788	−	6.70386i	0.333493	−	0.224967i
$889$		−	6.77726i		−	0.227302i
$890$	6.31235	+	2.13241i	0.211591	+	0.0714786i
$891$	1.21598			0.0407368
$892$	−10.1588	−	7.74781i	−0.340143	−	0.259416i
$893$	−39.1734	−	27.2085i	−1.31089	−	0.910497i
$894$	−25.8073	−	8.71812i	−0.863126	−	0.291578i
$895$	−3.57024			−0.119340
$896$	−11.6180	−	9.97908i	−0.388129	−	0.333378i
$897$	−2.23901			−0.0747584
$898$	11.7344	−	34.7362i	0.391583	−	1.15916i
$899$	−24.4118			−0.814181
$900$	−7.70546	−	5.87670i	−0.256849	−	0.195890i
$901$	0.0260042			0.000866326
$902$	−1.08279	+	3.20527i	−0.0360530	+	0.106724i
$903$	−6.22491			−0.207152
$904$	−4.78864	+	3.23030i	−0.159268	+	0.107438i
$905$		−	1.74538i		−	0.0580185i
$906$	−8.74877	+	25.8980i	−0.290658	+	0.860405i
$907$			32.4697i			1.07814i	0.842261	+	0.539069i	$0.181224\pi$
$907$			32.4697i			1.07814i	−0.842261	+	0.539069i	$0.818776\pi$
$908$	−14.8243	+	19.4375i	−0.491962	+	0.645055i
$909$		−	8.75636i		−	0.290430i
$910$	2.35829	+	0.796667i	0.0781765	+	0.0264092i
$911$	22.2375			0.736760			0.368380	−	0.929675i	$-0.379913\pi$
$911$	22.2375			0.736760			0.368380	+	0.929675i	$0.379913\pi$
$912$	−5.80451	+	16.4410i	−0.192207	+	0.544417i
$913$	−9.02821			−0.298790
$914$	14.8882	+	5.02947i	0.492458	+	0.166360i
$915$			1.96388i			0.0649240i
$916$	27.0314	−	35.4433i	0.893142	−	1.17108i
$917$		−	22.5288i		−	0.743966i
$918$	−0.00251523	+	0.00744557i	−8.30150e−5	+	0.000245740i
$919$			1.82361i			0.0601553i	0.999548	+	0.0300776i	$0.00957546\pi$
$919$			1.82361i			0.0601553i	−0.999548	+	0.0300776i	$0.990425\pi$
$920$	0.421229	+	0.624435i	0.0138875	+	0.0205870i
$921$	−18.0033			−0.593229
$922$	18.2628	−	54.0614i	0.601453	−	1.78042i
$923$	−1.40190			−0.0461441
$924$	−2.61770	−	1.99643i	−0.0861160	−	0.0656778i
$925$	−20.5359			−0.675215
$926$	1.55784	−	4.61152i	0.0511939	−	0.151544i
$927$	−9.60437			−0.315449
$928$	1.65611	−	28.4723i	0.0543644	−	0.934648i
$929$	−48.0824			−1.57753			−0.788767	−	0.614693i	$-0.789280\pi$
$929$	−48.0824			−1.57753			−0.788767	+	0.614693i	$0.789280\pi$
$930$	−2.55121	−	0.861837i	−0.0836573	−	0.0282608i
$931$	12.8495	−	18.5000i	0.421124	−	0.606314i
$932$	11.0787	+	8.44939i	0.362896	+	0.276769i
$933$	−19.2359			−0.629756
$934$	−41.7943	−	14.1188i	−1.36755	−	0.461980i
$935$		−	0.00265736i		−	8.69050e-5i
$936$	5.22982	+	7.75275i	0.170942	+	0.253407i
$937$	12.8423			0.419540			0.209770	−	0.977751i	$-0.432728\pi$
$937$	12.8423			0.419540			0.209770	+	0.977751i	$0.432728\pi$
$938$	−4.46713	−	1.50907i	−0.145857	−	0.0492727i
$939$		−	20.0287i		−	0.653612i
$940$	6.84306	+	5.21897i	0.223196	+	0.170224i
$941$	−4.78698			−0.156051			−0.0780256	−	0.996951i	$-0.524862\pi$
$941$	−4.78698			−0.156051			−0.0780256	+	0.996951i	$0.524862\pi$
$942$	3.43507	+	1.16042i	0.111921	+	0.0378086i
$943$	1.33228			0.0433850
$944$	38.1489	−	10.4628i	1.24164	−	0.340534i
$945$			0.532350i			0.0173174i
$946$	7.49181	+	2.53085i	0.243580	+	0.0822850i
$947$	−26.3364			−0.855817			−0.427908	−	0.903822i	$-0.640749\pi$
$947$	−26.3364			−0.855817			−0.427908	+	0.903822i	$0.640749\pi$
$948$	−13.4642	+	17.6541i	−0.437296	+	0.573378i
$949$	4.07346			0.132230
$950$	23.9941	−	17.7883i	0.778472	−	0.577128i
$951$			11.0972i			0.359853i
$952$	0.0176391	−	0.0118989i	0.000571685	−	0.000385645i
$953$			50.7687i			1.64456i	0.569084	+	0.822279i	$0.307298\pi$
$953$			50.7687i			1.64456i	−0.569084	+	0.822279i	$0.692702\pi$
$954$	6.26966	+	2.11799i	0.202988	+	0.0685725i
$955$	−4.22280			−0.136647
$956$	11.2248	−	14.7178i	0.363036	−	0.476009i
$957$		−	6.13065i		−	0.198176i
$958$	−0.382053	+	1.13095i	−0.0123436	+	0.0365394i
$959$		−	18.0079i		−	0.581507i
$960$	1.17826	−	2.91708i	0.0380282	−	0.0941484i
$961$	−7.55556			−0.243728
$962$	18.7753	+	6.34260i	0.605341	+	0.204494i
$963$			7.32145i			0.235930i
$964$	−9.50719	+	12.4657i	−0.306206	+	0.401494i
$965$	−9.61628			−0.309559
$966$	−0.414912	+	1.22822i	−0.0133496	+	0.0395173i
$967$		−	49.0390i		−	1.57699i	−0.615042	−	0.788494i	$-0.710861\pi$
$967$		−	49.0390i		−	1.57699i	0.615042	−	0.788494i	$-0.289139\pi$
$968$	−15.0604	−	22.3258i	−0.484060	−	0.717577i
$969$	−0.0198948	−	0.0138182i	−0.000639114	−	0.000443906i
$970$	−1.08244	−	0.365665i	−0.0347550	−	0.0117408i
$971$		−	22.1251i		−	0.710027i	−0.934861	−	0.355013i	$-0.884476\pi$
$971$		−	22.1251i		−	0.710027i	0.934861	−	0.355013i	$-0.115524\pi$
$972$	−1.21285	+	1.59028i	−0.0389023	+	0.0510082i
$973$			20.2041i			0.647715i
$974$	−42.1150	−	14.2271i	−1.34945	−	0.455866i
$975$		−	16.0205i		−	0.513066i
$976$	19.2642	−	5.28342i	0.616632	−	0.169118i
$977$		−	45.0576i		−	1.44152i	−0.693184	−	0.720761i	$-0.743793\pi$
$977$		−	45.0576i		−	1.44152i	0.693184	−	0.720761i	$-0.256207\pi$
$978$	7.28541	−	21.5662i	0.232962	−	0.689612i
$979$		−	14.5677i		−	0.465586i
$980$	−2.46471	+	3.23170i	−0.0787322	+	0.103233i
$981$	6.70281			0.214004
$982$	44.5251	+	15.0413i	1.42085	+	0.479986i
$983$	58.9765			1.88106			0.940529	−	0.339713i	$-0.110330\pi$
$983$	58.9765			1.88106			0.940529	+	0.339713i	$0.110330\pi$
$984$	−3.11191	−	4.61313i	−0.0992040	−	0.147061i
$985$	−0.236955			−0.00755000
$986$	0.0375386	+	0.0126811i	0.00119547	+	0.000403850i
$987$			14.8123i			0.471480i
$988$	−27.4311	+	8.85259i	−0.872700	+	0.281638i
$989$		−	3.11399i		−	0.0990192i
$990$	0.216437	−	0.640695i	0.00687881	−	0.0203626i
$991$	−36.9320			−1.17318			−0.586592	−	0.809882i	$-0.699531\pi$
$991$	−36.9320			−1.17318			−0.586592	+	0.809882i	$0.699531\pi$
$992$	−1.59048	+	27.3440i	−0.0504977	+	0.868172i
$993$	−23.0048			−0.730036
$994$	−0.259787	+	0.769019i	−0.00823994	+	0.0243918i
$995$	0.716481			0.0227140
$996$	9.00501	−	11.8073i	0.285335	−	0.374128i
$997$			34.0903i			1.07965i	0.841777	+	0.539825i	$0.181510\pi$
$997$			34.0903i			1.07965i	−0.841777	+	0.539825i	$0.818490\pi$
$998$	−1.44642	−	0.488623i	−0.0457856	−	0.0154671i
$999$			4.23826i			0.134093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.e.a.379.36	yes	40
3.2	odd	2		1368.2.e.g.379.5		40
4.3	odd	2		1824.2.e.a.1519.25		40
8.3	odd	2	inner	456.2.e.a.379.6	yes	40
8.5	even	2		1824.2.e.a.1519.9		40
12.11	even	2		5472.2.e.g.5167.31		40
19.18	odd	2	inner	456.2.e.a.379.5	✓	40
24.5	odd	2		5472.2.e.g.5167.16		40
24.11	even	2		1368.2.e.g.379.35		40
57.56	even	2		1368.2.e.g.379.36		40
76.75	even	2		1824.2.e.a.1519.10		40
152.37	odd	2		1824.2.e.a.1519.26		40
152.75	even	2	inner	456.2.e.a.379.35	yes	40
228.227	odd	2		5472.2.e.g.5167.15		40
456.227	odd	2		1368.2.e.g.379.6		40
456.341	even	2		5472.2.e.g.5167.32		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.e.a.379.5	✓	40	19.18	odd	2	inner
456.2.e.a.379.6	yes	40	8.3	odd	2	inner
456.2.e.a.379.35	yes	40	152.75	even	2	inner
456.2.e.a.379.36	yes	40	1.1	even	1	trivial
1368.2.e.g.379.5		40	3.2	odd	2
1368.2.e.g.379.6		40	456.227	odd	2
1368.2.e.g.379.35		40	24.11	even	2
1368.2.e.g.379.36		40	57.56	even	2
1824.2.e.a.1519.9		40	8.5	even	2
1824.2.e.a.1519.10		40	76.75	even	2
1824.2.e.a.1519.25		40	4.3	odd	2
1824.2.e.a.1519.26		40	152.37	odd	2
5472.2.e.g.5167.15		40	228.227	odd	2
5472.2.e.g.5167.16		40	24.5	odd	2
5472.2.e.g.5167.31		40	12.11	even	2
5472.2.e.g.5167.32		40	456.341	even	2

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.33983 + 0.452615i) q^{2} +1.00000i q^{3} +(1.59028 + 1.21285i) q^{4} +0.393257i q^{5} +(-0.452615 + 1.33983i) q^{6} +1.35370i q^{7} +(1.58175 + 2.34480i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.33983 + 0.452615i) q^{2} +1.00000i q^{3} +(1.59028 + 1.21285i) q^{4} +0.393257i q^{5} +(-0.452615 + 1.33983i) q^{6} +1.35370i q^{7} +(1.58175 + 2.34480i) q^{8} -1.00000 q^{9} +(-0.177994 + 0.526897i) q^{10} +1.21598 q^{11} +(-1.21285 + 1.59028i) q^{12} -3.30636 q^{13} +(-0.612703 + 1.81372i) q^{14} -0.393257 q^{15} +(1.05798 + 3.85755i) q^{16} -0.00555711 q^{17} +(-1.33983 - 0.452615i) q^{18} +(2.48659 - 3.58007i) q^{19} +(-0.476963 + 0.625388i) q^{20} -1.35370 q^{21} +(1.62920 + 0.550370i) q^{22} -0.677182i q^{23} +(-2.34480 + 1.58175i) q^{24} +4.84535 q^{25} +(-4.42996 - 1.49651i) q^{26} -1.00000i q^{27} +(-1.64183 + 2.15275i) q^{28} -5.04174 q^{29} +(-0.526897 - 0.177994i) q^{30} +4.84195 q^{31} +(-0.328479 + 5.64731i) q^{32} +1.21598i q^{33} +(-0.00744557 - 0.00251523i) q^{34} -0.532350 q^{35} +(-1.59028 - 1.21285i) q^{36} -4.23826 q^{37} +(4.95199 - 3.67121i) q^{38} -3.30636i q^{39} +(-0.922108 + 0.622032i) q^{40} +1.96739i q^{41} +(-1.81372 - 0.612703i) q^{42} +4.59845 q^{43} +(1.93374 + 1.47480i) q^{44} -0.393257i q^{45} +(0.306503 - 0.907308i) q^{46} -10.9421i q^{47} +(-3.85755 + 1.05798i) q^{48} +5.16751 q^{49} +(6.49194 + 2.19308i) q^{50} -0.00555711i q^{51} +(-5.25804 - 4.01013i) q^{52} -4.67945 q^{53} +(0.452615 - 1.33983i) q^{54} +0.478192i q^{55} +(-3.17414 + 2.14120i) q^{56} +(3.58007 + 2.48659i) q^{57} +(-6.75507 - 2.28197i) q^{58} -9.88941i q^{59} +(-0.625388 - 0.476963i) q^{60} -4.99390i q^{61} +(6.48738 + 2.19154i) q^{62} -1.35370i q^{63} +(-2.99616 + 7.41775i) q^{64} -1.30025i q^{65} +(-0.550370 + 1.62920i) q^{66} +2.46296i q^{67} +(-0.00883735 - 0.00673995i) q^{68} +0.677182 q^{69} +(-0.713258 - 0.240950i) q^{70} +0.424001 q^{71} +(-1.58175 - 2.34480i) q^{72} -1.23201 q^{73} +(-5.67855 - 1.91830i) q^{74} +4.84535i q^{75} +(8.29646 - 2.67744i) q^{76} +1.64606i q^{77} +(1.49651 - 4.42996i) q^{78} +11.1012 q^{79} +(-1.51701 + 0.416056i) q^{80} +1.00000 q^{81} +(-0.890470 + 2.63596i) q^{82} -7.42465 q^{83} +(-2.15275 - 1.64183i) q^{84} -0.00218537i q^{85} +(6.16114 + 2.08133i) q^{86} -5.04174i q^{87} +(1.92337 + 2.85122i) q^{88} -11.9802i q^{89} +(0.177994 - 0.526897i) q^{90} -4.47581i q^{91} +(0.821323 - 1.07691i) q^{92} +4.84195i q^{93} +(4.95256 - 14.6605i) q^{94} +(1.40789 + 0.977868i) q^{95} +(-5.64731 - 0.328479i) q^{96} +2.05436i q^{97} +(6.92357 + 2.33889i) q^{98} -1.21598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4} + 4 q^{6} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^4 + 4 * q^6 - 40 * q^9	\( 40 q - 4 q^{4} + 4 q^{6} - 40 q^{9} + 4 q^{16} + 8 q^{19} + 32 q^{20} - 4 q^{24} - 40 q^{25} + 40 q^{26} - 8 q^{28} - 48 q^{35} + 4 q^{36} - 8 q^{44} - 56 q^{49} - 4 q^{54} - 8 q^{57} + 16 q^{58} + 40 q^{62} + 68 q^{64} + 8 q^{66} - 88 q^{68} - 16 q^{73} - 40 q^{74} - 12 q^{76} - 32 q^{80} + 40 q^{81} - 64 q^{82} + 80 q^{83} - 48 q^{92} + 44 q^{96}+O(q^{100}) \) 40 * q - 4 * q^4 + 4 * q^6 - 40 * q^9 + 4 * q^16 + 8 * q^19 + 32 * q^20 - 4 * q^24 - 40 * q^25 + 40 * q^26 - 8 * q^28 - 48 * q^35 + 4 * q^36 - 8 * q^44 - 56 * q^49 - 4 * q^54 - 8 * q^57 + 16 * q^58 + 40 * q^62 + 68 * q^64 + 8 * q^66 - 88 * q^68 - 16 * q^73 - 40 * q^74 - 12 * q^76 - 32 * q^80 + 40 * q^81 - 64 * q^82 + 80 * q^83 - 48 * q^92 + 44 * q^96

Introduction

L-functions

Modular forms

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