LMFDB - Embedded newform 460.2.g.c.459.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(459,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("460.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.g (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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			459.10
Character	$\chi$	$=$	460.459
Dual form			460.2.g.c.459.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20833 - 0.734800i) q^{2} -1.77158 q^{3} +(0.920137 + 1.77577i) q^{4} +(1.90499 + 1.17090i) q^{5} +(2.14066 + 1.30176i) q^{6} -1.27817i q^{7} +(0.193001 - 2.82183i) q^{8} +0.138505 q^{9} +O(q^{10})$	\(q+(-1.20833 - 0.734800i) q^{2} -1.77158 q^{3} +(0.920137 + 1.77577i) q^{4} +(1.90499 + 1.17090i) q^{5} +(2.14066 + 1.30176i) q^{6} -1.27817i q^{7} +(0.193001 - 2.82183i) q^{8} +0.138505 q^{9} +(-1.44148 - 2.81463i) q^{10} +2.00757 q^{11} +(-1.63010 - 3.14592i) q^{12} +2.02460i q^{13} +(-0.939197 + 1.54445i) q^{14} +(-3.37485 - 2.07435i) q^{15} +(-2.30669 + 3.26790i) q^{16} -3.14239 q^{17} +(-0.167360 - 0.101774i) q^{18} +1.66004 q^{19} +(-0.326397 + 4.46021i) q^{20} +2.26438i q^{21} +(-2.42581 - 1.47516i) q^{22} +(1.99168 + 4.36271i) q^{23} +(-0.341917 + 4.99911i) q^{24} +(2.25797 + 4.46112i) q^{25} +(1.48768 - 2.44639i) q^{26} +5.06937 q^{27} +(2.26973 - 1.17609i) q^{28} +3.92182 q^{29} +(2.55371 + 4.98634i) q^{30} -0.284658i q^{31} +(5.18851 - 2.25375i) q^{32} -3.55658 q^{33} +(3.79706 + 2.30903i) q^{34} +(1.49661 - 2.43490i) q^{35} +(0.127444 + 0.245953i) q^{36} -4.55939 q^{37} +(-2.00588 - 1.21979i) q^{38} -3.58675i q^{39} +(3.67176 - 5.14958i) q^{40} +6.34849 q^{41} +(1.66387 - 2.73612i) q^{42} +10.3623i q^{43} +(1.84724 + 3.56498i) q^{44} +(0.263851 + 0.162176i) q^{45} +(0.799107 - 6.73509i) q^{46} +7.17707 q^{47} +(4.08650 - 5.78935i) q^{48} +5.36629 q^{49} +(0.549644 - 7.04967i) q^{50} +5.56701 q^{51} +(-3.59522 + 1.86291i) q^{52} +9.11216 q^{53} +(-6.12549 - 3.72498i) q^{54} +(3.82440 + 2.35067i) q^{55} +(-3.60678 - 0.246688i) q^{56} -2.94089 q^{57} +(-4.73886 - 2.88175i) q^{58} -0.407679i q^{59} +(0.578239 - 7.90163i) q^{60} +1.31896i q^{61} +(-0.209167 + 0.343961i) q^{62} -0.177033i q^{63} +(-7.92550 - 1.08923i) q^{64} +(-2.37061 + 3.85685i) q^{65} +(4.29753 + 2.61337i) q^{66} -3.80009i q^{67} +(-2.89144 - 5.58016i) q^{68} +(-3.52842 - 7.72890i) q^{69} +(-3.59756 + 1.84246i) q^{70} +7.51415i q^{71} +(0.0267316 - 0.390839i) q^{72} +13.3491i q^{73} +(5.50926 + 3.35024i) q^{74} +(-4.00019 - 7.90324i) q^{75} +(1.52746 + 2.94784i) q^{76} -2.56601i q^{77} +(-2.63554 + 4.33399i) q^{78} -14.7610 q^{79} +(-8.22062 + 3.52440i) q^{80} -9.39633 q^{81} +(-7.67108 - 4.66487i) q^{82} -1.17696i q^{83} +(-4.02101 + 2.08354i) q^{84} +(-5.98623 - 3.67944i) q^{85} +(7.61420 - 12.5211i) q^{86} -6.94782 q^{87} +(0.387463 - 5.66503i) q^{88} +12.7290i q^{89} +(-0.199653 - 0.389840i) q^{90} +2.58778 q^{91} +(-5.91453 + 7.55105i) q^{92} +0.504295i q^{93} +(-8.67229 - 5.27371i) q^{94} +(3.16235 + 1.94374i) q^{95} +(-9.19187 + 3.99271i) q^{96} -7.31027 q^{97} +(-6.48426 - 3.94315i) q^{98} +0.278059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) $ 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	$ 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 8 q^{16} - 100 q^{24} - 24 q^{25} - 24 q^{26} - 16 q^{29} + 104 q^{41} - 8 q^{46} + 32 q^{49} - 32 q^{50} + 52 q^{54} - 92 q^{64} + 32 q^{69} - 44 q^{70} + 24 q^{81} + 56 q^{85} + 28 q^{94} + 88 q^{96}+O(q^{100}) $ 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 8 * q^16 - 100 * q^24 - 24 * q^25 - 24 * q^26 - 16 * q^29 + 104 * q^41 - 8 * q^46 + 32 * q^49 - 32 * q^50 + 52 * q^54 - 92 * q^64 + 32 * q^69 - 44 * q^70 + 24 * q^81 + 56 * q^85 + 28 * q^94 + 88 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.20833	−	0.734800i	−0.854420	−	0.519582i
$2$	−1.20833	−	0.734800i	−0.854420	−	0.519582i
$3$	−1.77158			−1.02282			−0.511412	−	0.859336i	$-0.670877\pi$
$3$	−1.77158			−1.02282			−0.511412	+	0.859336i	$0.670877\pi$
$4$	0.920137	+	1.77577i	0.460069	+	0.887883i
$5$	1.90499	+	1.17090i	0.851937	+	0.523644i
$5$	1.90499	+	1.17090i	0.851937	+	0.523644i
$6$	2.14066	+	1.30176i	0.873922	+	0.531441i
$7$		−	1.27817i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$7$		−	1.27817i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$8$	0.193001	−	2.82183i	0.0682362	−	0.997669i
$9$	0.138505			0.0461684
$10$	−1.44148	−	2.81463i	−0.455837	−	0.890063i
$11$	2.00757			0.605305			0.302653	−	0.953101i	$-0.402128\pi$
$11$	2.00757			0.605305			0.302653	+	0.953101i	$0.402128\pi$
$12$	−1.63010	−	3.14592i	−0.470569	−	0.908148i
$13$			2.02460i			0.561524i	0.959777	+	0.280762i	$0.0905871\pi$
$13$			2.02460i			0.561524i	−0.959777	+	0.280762i	$0.909413\pi$
$14$	−0.939197	+	1.54445i	−0.251011	+	0.412772i
$15$	−3.37485	−	2.07435i	−0.871382	−	0.535595i
$16$	−2.30669	+	3.26790i	−0.576674	+	0.816975i
$17$	−3.14239			−0.762143			−0.381071	−	0.924546i	$-0.624445\pi$
$17$	−3.14239			−0.762143			−0.381071	+	0.924546i	$0.624445\pi$
$18$	−0.167360	−	0.101774i	−0.0394472	−	0.0239883i
$19$	1.66004			0.380838			0.190419	−	0.981703i	$-0.439015\pi$
$19$	1.66004			0.380838			0.190419	+	0.981703i	$0.439015\pi$
$20$	−0.326397	+	4.46021i	−0.0729846	+	0.997333i
$21$			2.26438i			0.494128i
$22$	−2.42581	−	1.47516i	−0.517185	−	0.314506i
$23$	1.99168	+	4.36271i	0.415294	+	0.909687i
$23$	1.99168	+	4.36271i	0.415294	+	0.909687i
$24$	−0.341917	+	4.99911i	−0.0697936	+	1.02044i
$25$	2.25797	+	4.46112i	0.451595	+	0.892223i
$26$	1.48768	−	2.44639i	0.291758	−	0.479777i
$27$	5.06937			0.975602
$28$	2.26973	−	1.17609i	0.428938	−	0.222260i
$29$	3.92182			0.728263			0.364131	−	0.931348i	$-0.381366\pi$
$29$	3.92182			0.728263			0.364131	+	0.931348i	$0.381366\pi$
$30$	2.55371	+	4.98634i	0.466241	+	0.910378i
$31$		−	0.284658i		−	0.0511261i	−0.999673	−	0.0255630i	$-0.991862\pi$
$31$		−	0.284658i		−	0.0511261i	0.999673	−	0.0255630i	$-0.00813785\pi$
$32$	5.18851	−	2.25375i	0.917207	−	0.398411i
$33$	−3.55658			−0.619121
$34$	3.79706	+	2.30903i	0.651190	+	0.395996i
$35$	1.49661	−	2.43490i	0.252973	−	0.411572i
$36$	0.127444	+	0.245953i	0.0212406	+	0.0409921i
$37$	−4.55939			−0.749559			−0.374780	−	0.927114i	$-0.622282\pi$
$37$	−4.55939			−0.749559			−0.374780	+	0.927114i	$0.622282\pi$
$38$	−2.00588	−	1.21979i	−0.325396	−	0.197877i
$39$		−	3.58675i		−	0.574340i
$40$	3.67176	−	5.14958i	0.580556	−	0.814220i
$41$	6.34849			0.991467			0.495733	−	0.868475i	$-0.334899\pi$
$41$	6.34849			0.991467			0.495733	+	0.868475i	$0.334899\pi$
$42$	1.66387	−	2.73612i	0.256740	−	0.422193i
$43$			10.3623i			1.58023i	0.612957	+	0.790116i	$0.289980\pi$
$43$			10.3623i			1.58023i	−0.612957	+	0.790116i	$0.710020\pi$
$44$	1.84724	+	3.56498i	0.278482	+	0.537440i
$45$	0.263851	+	0.162176i	0.0393326	+	0.0241758i
$46$	0.799107	−	6.73509i	0.117822	−	0.993035i
$47$	7.17707			1.04688			0.523442	−	0.852061i	$-0.324648\pi$
$47$	7.17707			1.04688			0.523442	+	0.852061i	$0.324648\pi$
$48$	4.08650	−	5.78935i	0.589835	−	0.835621i
$49$	5.36629			0.766613
$50$	0.549644	−	7.04967i	0.0777314	−	0.996974i
$51$	5.56701			0.779538
$52$	−3.59522	+	1.86291i	−0.498567	+	0.258339i
$53$	9.11216			1.25165			0.625826	−	0.779963i	$-0.284762\pi$
$53$	9.11216			1.25165			0.625826	+	0.779963i	$0.284762\pi$
$54$	−6.12549	−	3.72498i	−0.833574	−	0.506905i
$55$	3.82440	+	2.35067i	0.515682	+	0.316964i
$56$	−3.60678	−	0.246688i	−0.481976	−	0.0329650i
$57$	−2.94089			−0.389530
$58$	−4.73886	−	2.88175i	−0.622243	−	0.378392i
$59$		−	0.407679i		−	0.0530753i	−0.999648	−	0.0265377i	$-0.991552\pi$
$59$		−	0.407679i		−	0.0530753i	0.999648	−	0.0265377i	$-0.00844819\pi$
$60$	0.578239	−	7.90163i	0.0746504	−	1.02010i
$61$			1.31896i			0.168875i	0.996429	+	0.0844377i	$0.0269094\pi$
$61$			1.31896i			0.168875i	−0.996429	+	0.0844377i	$0.973091\pi$
$62$	−0.209167	+	0.343961i	−0.0265642	+	0.0436831i
$63$		−	0.177033i		−	0.0223040i
$64$	−7.92550	−	1.08923i	−0.990688	−	0.136154i
$65$	−2.37061	+	3.85685i	−0.294038	+	0.478383i
$66$	4.29753	+	2.61337i	0.528989	+	0.321684i
$67$		−	3.80009i		−	0.464255i	−0.972685	−	0.232127i	$-0.925431\pi$
$67$		−	3.80009i		−	0.464255i	0.972685	−	0.232127i	$-0.0745686\pi$
$68$	−2.89144	−	5.58016i	−0.350638	−	0.676694i
$69$	−3.52842	−	7.72890i	−0.424772	−	0.930450i
$70$	−3.59756	+	1.84246i	−0.429991	+	0.220216i
$71$			7.51415i			0.891766i	0.895091	+	0.445883i	$0.147110\pi$
$71$			7.51415i			0.891766i	−0.895091	+	0.445883i	$0.852890\pi$
$72$	0.0267316	−	0.390839i	0.00315035	−	0.0460608i
$73$			13.3491i			1.56239i	0.624288	+	0.781194i	$0.285389\pi$
$73$			13.3491i			1.56239i	−0.624288	+	0.781194i	$0.714611\pi$
$74$	5.50926	+	3.35024i	0.640439	+	0.389457i
$75$	−4.00019	−	7.90324i	−0.461902	−	0.912587i
$76$	1.52746	+	2.94784i	0.175212	+	0.338140i
$77$		−	2.56601i		−	0.292424i
$78$	−2.63554	+	4.33399i	−0.298417	+	0.490728i
$79$	−14.7610			−1.66074			−0.830369	−	0.557214i	$-0.811870\pi$
$79$	−14.7610			−1.66074			−0.830369	+	0.557214i	$0.811870\pi$
$80$	−8.22062	+	3.52440i	−0.919093	+	0.394040i
$81$	−9.39633			−1.04404
$82$	−7.67108	−	4.66487i	−0.847130	−	0.515149i
$83$		−	1.17696i		−	0.129188i	−0.997912	−	0.0645938i	$-0.979425\pi$
$83$		−	1.17696i		−	0.129188i	0.997912	−	0.0645938i	$-0.0205752\pi$
$84$	−4.02101	+	2.08354i	−0.438728	+	0.227333i
$85$	−5.98623	−	3.67944i	−0.649298	−	0.399091i
$86$	7.61420	−	12.5211i	0.821060	−	1.35018i
$87$	−6.94782			−0.744885
$88$	0.387463	−	5.66503i	0.0413037	−	0.603894i
$89$			12.7290i			1.34927i	0.738151	+	0.674636i	$0.235699\pi$
$89$			12.7290i			1.34927i	−0.738151	+	0.674636i	$0.764301\pi$
$90$	−0.199653	−	0.389840i	−0.0210453	−	0.0410928i
$91$	2.58778			0.271273
$92$	−5.91453	+	7.55105i	−0.616633	+	0.787251i
$93$			0.504295i			0.0522929i
$94$	−8.67229	−	5.27371i	−0.894479	−	0.543942i
$95$	3.16235	+	1.94374i	0.324450	+	0.199423i
$96$	−9.19187	+	3.99271i	−0.938141	+	0.407504i
$97$	−7.31027			−0.742245			−0.371123	−	0.928584i	$-0.621027\pi$
$97$	−7.31027			−0.742245			−0.371123	+	0.928584i	$0.621027\pi$
$98$	−6.48426	−	3.94315i	−0.655010	−	0.398318i
$99$	0.278059			0.0279460
$100$	−5.84425	+	8.11447i	−0.584425	+	0.811447i
$101$	2.90934			0.289490			0.144745	−	0.989469i	$-0.453764\pi$
$101$	2.90934			0.289490			0.144745	+	0.989469i	$0.453764\pi$
$102$	−6.72680	−	4.09064i	−0.666053	−	0.405034i
$103$		−	4.11531i		−	0.405493i	−0.979231	−	0.202747i	$-0.935013\pi$
$103$		−	4.11531i		−	0.405493i	0.979231	−	0.202747i	$-0.0649868\pi$
$104$	5.71309	+	0.390750i	0.560215	+	0.0383162i
$105$	−2.65137	+	4.31362i	−0.258747	+	0.420966i
$106$	−11.0105	−	6.69562i	−1.06944	−	0.650336i
$107$		−	13.8494i		−	1.33888i	−0.742868	−	0.669438i	$-0.766535\pi$
$107$		−	13.8494i		−	1.33888i	0.742868	−	0.669438i	$-0.233465\pi$
$108$	4.66452	+	9.00203i	0.448844	+	0.866220i
$109$		−	12.2651i		−	1.17478i	−0.809303	−	0.587392i	$-0.800155\pi$
$109$		−	12.2651i		−	1.17478i	0.809303	−	0.587392i	$-0.199845\pi$
$110$	−2.89388	−	5.65056i	−0.275920	−	0.538760i
$111$	8.07734			0.766667
$112$	4.17692	+	2.94834i	0.394682	+	0.278592i
$113$	15.1939			1.42932			0.714660	−	0.699472i	$-0.246581\pi$
$113$	15.1939			1.42932			0.714660	+	0.699472i	$0.246581\pi$
$114$	3.55357	+	2.16097i	0.332823	+	0.202393i
$115$	−1.31418	+	10.6430i	−0.122548	+	0.992463i
$116$	3.60861	+	6.96423i	0.335051	+	0.646612i
$117$			0.280418i			0.0259246i
$118$	−0.299563	+	0.492612i	−0.0275770	+	0.0453486i
$119$			4.01651i			0.368192i
$120$	−6.50482	+	9.12291i	−0.593806	+	0.832804i
$121$	−6.96966			−0.633606
$122$	0.969171	−	1.59374i	0.0877447	−	0.144291i
$123$	−11.2469			−1.01410
$124$	0.505486	−	0.261924i	0.0453940	−	0.0235215i
$125$	−0.922114	+	11.1422i	−0.0824764	+	0.996593i
$126$	−0.130084	+	0.213915i	−0.0115888	+	0.0190570i
$127$	0.743250			0.0659528			0.0329764	−	0.999456i	$-0.489501\pi$
$127$	0.743250			0.0659528			0.0329764	+	0.999456i	$0.489501\pi$
$128$	8.77628	+	7.13982i	0.775720	+	0.631077i
$129$		−	18.3576i		−	1.61630i
$130$	5.69850	−	2.91843i	0.499792	−	0.255963i
$131$		−	3.64274i		−	0.318268i	−0.987257	−	0.159134i	$-0.949130\pi$
$131$		−	3.64274i		−	0.318268i	0.987257	−	0.159134i	$-0.0508702\pi$
$132$	−3.27254	−	6.31565i	−0.284838	−	0.549707i
$133$		−	2.12180i		−	0.183984i
$134$	−2.79231	+	4.59177i	−0.241218	+	0.396669i
$135$	9.65711	+	5.93574i	0.831152	+	0.510868i
$136$	−0.606485	+	8.86732i	−0.0520057	+	0.760366i
$137$	−0.996193			−0.0851105			−0.0425553	−	0.999094i	$-0.513550\pi$
$137$	−0.996193			−0.0851105			−0.0425553	+	0.999094i	$0.513550\pi$
$138$	−1.41568	+	11.9318i	−0.120511	+	1.01570i
$139$		−	11.4907i		−	0.974631i	−0.873226	−	0.487316i	$-0.837976\pi$
$139$		−	11.4907i		−	0.974631i	0.873226	−	0.487316i	$-0.162024\pi$
$140$	5.70089	+	0.417190i	0.481813	+	0.0352590i
$141$	−12.7148			−1.07078
$142$	5.52140	−	9.07960i	0.463346	−	0.761943i
$143$			4.06453i			0.339893i
$144$	−0.319489	+	0.452621i	−0.0266241	+	0.0377184i
$145$	7.47102	+	4.59206i	0.620434	+	0.381350i
$146$	9.80889	−	16.1301i	0.811789	−	1.33494i
$147$	−9.50682			−0.784110
$148$	−4.19527	−	8.09641i	−0.344849	−	0.665521i
$149$		−	21.5503i		−	1.76547i	−0.469870	−	0.882735i	$-0.655699\pi$
$149$		−	21.5503i		−	1.76547i	0.469870	−	0.882735i	$-0.344301\pi$
$150$	−0.973739	+	12.4891i	−0.0795055	+	1.01973i
$151$		−	7.10647i		−	0.578317i	−0.957281	−	0.289158i	$-0.906625\pi$
$151$		−	7.10647i		−	0.578317i	0.957281	−	0.289158i	$-0.0933754\pi$
$152$	0.320389	−	4.68435i	0.0259869	−	0.379951i
$153$	−0.435238			−0.0351869
$154$	−1.88550	+	3.10059i	−0.151938	+	0.249853i
$155$	0.333307	−	0.542270i	0.0267718	−	0.0435562i
$156$	6.36923	−	3.30030i	0.509947	−	0.264236i
$157$	−19.0039			−1.51667			−0.758337	−	0.651863i	$-0.773988\pi$
$157$	−19.0039			−1.51667			−0.758337	+	0.651863i	$0.773988\pi$
$158$	17.8362	+	10.8464i	1.41897	+	0.862890i
$159$	−16.1429			−1.28022
$160$	12.5230	+	1.78186i	0.990028	+	0.140869i
$161$	5.57627	−	2.54570i	0.439472	−	0.200629i
$162$	11.3539	+	6.90443i	0.892046	+	0.542463i
$163$	−3.65003			−0.285892			−0.142946	−	0.989730i	$-0.545658\pi$
$163$	−3.65003			−0.285892			−0.142946	+	0.989730i	$0.545658\pi$
$164$	5.84148	+	11.2734i	0.456143	+	0.880307i
$165$	−6.77524	−	4.16440i	−0.527452	−	0.324198i
$166$	−0.864827	+	1.42215i	−0.0671236	+	0.110381i
$167$	4.78902			0.370586			0.185293	−	0.982683i	$-0.440677\pi$
$167$	4.78902			0.370586			0.185293	+	0.982683i	$0.440677\pi$
$168$	6.38970	+	0.437027i	0.492976	+	0.0337174i
$169$	8.90099			0.684691
$170$	4.52971	+	8.84467i	0.347413	+	0.678355i
$171$	0.229923			0.0175827
$172$	−18.4010	+	9.53472i	−1.40306	+	0.727015i
$173$		−	9.16554i		−	0.696843i	−0.937338	−	0.348421i	$-0.886718\pi$
$173$		−	9.16554i		−	0.696843i	0.937338	−	0.348421i	$-0.113282\pi$
$174$	8.39528	+	5.10526i	0.636445	+	0.387029i
$175$	5.70205	−	2.88607i	0.431035	−	0.218166i
$176$	−4.63085	+	6.56054i	−0.349063	+	0.494519i
$177$			0.722238i			0.0542867i
$178$	9.35327	−	15.3809i	0.701058	−	1.15285i
$179$		−	3.74110i		−	0.279623i	−0.990178	−	0.139812i	$-0.955350\pi$
$179$		−	3.74110i		−	0.279623i	0.990178	−	0.139812i	$-0.0446497\pi$
$180$	−0.0452077	+	0.617762i	−0.00336958	+	0.0460453i
$181$			24.0543i			1.78794i	0.448127	+	0.893970i	$0.352091\pi$
$181$			24.0543i			1.78794i	−0.448127	+	0.893970i	$0.647909\pi$
$182$	−3.12690	−	1.90150i	−0.231781	−	0.140949i
$183$		−	2.33665i		−	0.172730i
$184$	12.6952	−	4.77818i	0.935905	−	0.352252i
$185$	−8.68559	−	5.33860i	−0.638577	−	0.392502i
$186$	0.370556	−	0.609356i	0.0271705	−	0.0446802i
$187$	−6.30858			−0.461329
$188$	6.60389	+	12.7448i	0.481638	+	0.929510i
$189$		−	6.47951i		−	0.471315i
$190$	−2.39291	−	4.67238i	−0.173600	−	0.338970i
$191$	−12.2497			−0.886355			−0.443177	−	0.896434i	$-0.646149\pi$
$191$	−12.2497			−0.886355			−0.443177	+	0.896434i	$0.646149\pi$
$192$	14.0407	+	1.92967i	1.01330	+	0.139262i
$193$		−	2.06172i		−	0.148406i	−0.997243	−	0.0742028i	$-0.976359\pi$
$193$		−	2.06172i		−	0.148406i	0.997243	−	0.0742028i	$-0.0236412\pi$
$194$	8.83324	+	5.37159i	0.634190	+	0.385657i
$195$	4.19973	−	6.83272i	0.300749	−	0.489301i
$196$	4.93772	+	9.52928i	0.352695	+	0.680663i
$197$		−	23.9037i		−	1.70307i	−0.524300	−	0.851534i	$-0.675673\pi$
$197$		−	23.9037i		−	1.70307i	0.524300	−	0.851534i	$-0.324327\pi$
$198$	−0.335988	−	0.204318i	−0.0238776	−	0.0145202i
$199$	−4.81160			−0.341085			−0.170543	−	0.985350i	$-0.554552\pi$
$199$	−4.81160			−0.341085			−0.170543	+	0.985350i	$0.554552\pi$
$200$	13.0243	−	5.51063i	0.920959	−	0.389660i
$201$			6.73217i			0.474851i
$202$	−3.51545	−	2.13778i	−0.247346	−	0.150414i
$203$		−	5.01274i		−	0.351825i
$204$	5.12242	+	9.88571i	0.358641	+	0.692138i
$205$	12.0938	+	7.43346i	0.844668	+	0.519175i
$206$	−3.02393	+	4.97266i	−0.210687	+	0.346462i
$207$	0.275858	+	0.604258i	0.0191734	+	0.0419988i
$208$	−6.61619	−	4.67014i	−0.458751	−	0.323816i
$209$	3.33264			0.230523
$210$	6.37338	−	3.26406i	0.439805	−	0.225242i
$211$			3.78230i			0.260385i	0.991489	+	0.130192i	$0.0415595\pi$
$211$			3.78230i			0.260385i	−0.991489	+	0.130192i	$0.958441\pi$
$212$	8.38444	+	16.1811i	0.575846	+	1.11132i
$213$		−	13.3119i		−	0.912119i
$214$	−10.1766	+	16.7347i	−0.695656	+	1.14396i
$215$	−12.1332	+	19.7400i	−0.827478	+	1.34626i
$216$	0.978395	−	14.3049i	0.0665713	−	0.973328i
$217$	−0.363840			−0.0246991
$218$	−9.01240	+	14.8203i	−0.610397	+	1.00376i
$219$		−	23.6490i		−	1.59805i
$220$	−0.655265	+	8.95418i	−0.0441780	+	0.603691i
$221$		−	6.36210i		−	0.427961i
$222$	−9.76011	−	5.93523i	−0.655056	−	0.398346i
$223$	14.8969			0.997570			0.498785	−	0.866726i	$-0.333780\pi$
$223$	14.8969			0.997570			0.498785	+	0.866726i	$0.333780\pi$
$224$	−2.88067	−	6.63178i	−0.192473	−	0.443104i
$225$	0.312741	+	0.617888i	0.0208494	+	0.0411925i
$226$	−18.3593	−	11.1645i	−1.22124	−	0.742650i
$227$			16.3331i			1.08407i	0.840357	+	0.542033i	$0.182345\pi$
$227$			16.3331i			1.08407i	−0.840357	+	0.542033i	$0.817655\pi$
$228$	−2.70602	−	5.22233i	−0.179211	−	0.345858i
$229$		−	2.40444i		−	0.158890i	−0.996839	−	0.0794449i	$-0.974685\pi$
$229$		−	2.40444i		−	0.158890i	0.996839	−	0.0794449i	$-0.0253148\pi$
$230$	9.40843	−	11.8946i	0.620373	−	0.784307i
$231$			4.54590i			0.299098i
$232$	0.756915	−	11.0667i	0.0496939	−	0.726565i
$233$		−	13.7561i		−	0.901195i	−0.892727	−	0.450598i	$-0.851211\pi$
$233$		−	13.7561i		−	0.901195i	0.892727	−	0.450598i	$-0.148789\pi$
$234$	0.206051	−	0.338838i	0.0134700	−	0.0221505i
$235$	13.6722	+	8.40365i	0.891879	+	0.548194i
$236$	0.723943	−	0.375121i	0.0471247	−	0.0244183i
$237$	26.1503			1.69864
$238$	2.95133	−	4.85328i	0.191306	−	0.314591i
$239$			27.4657i			1.77661i	0.459258	+	0.888303i	$0.348115\pi$
$239$			27.4657i			1.77661i	−0.459258	+	0.888303i	$0.651885\pi$
$240$	14.5635	−	6.24377i	0.940070	−	0.403033i
$241$		−	13.2834i		−	0.855657i	−0.903860	−	0.427829i	$-0.859279\pi$
$241$		−	13.2834i		−	0.855657i	0.903860	−	0.427829i	$-0.140721\pi$
$242$	8.42167	+	5.12131i	0.541366	+	0.329210i
$243$	1.43825			0.0922641
$244$	−2.34216	+	1.21362i	−0.149942	+	0.0776943i
$245$	10.2227	+	6.28340i	0.653106	+	0.401432i
$246$	13.5900	+	8.26420i	0.866464	+	0.526906i
$247$			3.36091i			0.213850i
$248$	−0.803257	−	0.0549393i	−0.0510069	−	0.00348865i
$249$			2.08507i			0.132136i
$250$	9.30155	−	12.7860i	0.588281	−	0.808656i
$251$	−24.6282			−1.55452			−0.777259	−	0.629181i	$-0.783390\pi$
$251$	−24.6282			−1.55452			−0.777259	+	0.629181i	$0.783390\pi$
$252$	0.314369	−	0.162894i	0.0198034	−	0.0102614i
$253$	3.99843	+	8.75844i	0.251379	+	0.550638i
$254$	−0.898093	−	0.546140i	−0.0563514	−	0.0342679i
$255$	10.6051	+	6.51843i	0.664117	+	0.408200i
$256$	−5.35833	−	15.0761i	−0.334895	−	0.942255i
$257$		−	19.9497i		−	1.24443i	−0.782847	−	0.622214i	$-0.786233\pi$
$257$		−	19.9497i		−	1.24443i	0.782847	−	0.622214i	$-0.213767\pi$
$258$	−13.4892	+	22.1821i	−0.839800	+	1.38100i
$259$			5.82766i			0.362113i
$260$	−9.03015	−	0.660824i	−0.560026	−	0.0409826i
$261$	0.543192			0.0336227
$262$	−2.67669	+	4.40165i	−0.165366	+	0.271935i
$263$			11.6844i			0.720490i	0.932858	+	0.360245i	$0.117307\pi$
$263$			11.6844i			0.720490i	−0.932858	+	0.360245i	$0.882693\pi$
$264$	−0.686423	+	10.0361i	−0.0422464	+	0.617677i
$265$	17.3586	+	10.6695i	1.06633	+	0.655419i
$266$	−1.55910	+	2.56384i	−0.0955946	+	0.157199i
$267$		−	22.5505i		−	1.38007i
$268$	6.74807	−	3.49660i	0.412204	−	0.213589i
$269$	6.07560			0.370436			0.185218	−	0.982697i	$-0.440701\pi$
$269$	6.07560			0.370436			0.185218	+	0.982697i	$0.440701\pi$
$270$	−7.30742	−	14.2684i	−0.444715	−	0.868347i
$271$			18.4847i			1.12287i	0.827521	+	0.561434i	$0.189750\pi$
$271$			18.4847i			1.12287i	−0.827521	+	0.561434i	$0.810250\pi$
$272$	7.24854	−	10.2690i	0.439507	−	0.622651i
$273$	−4.58447			−0.277464
$274$	1.20373	+	0.732003i	0.0727202	+	0.0442219i
$275$	4.53304	+	8.95600i	0.273353	+	0.540067i
$276$	10.4781	−	13.3773i	0.630706	−	0.805219i
$277$			5.09369i			0.306050i	0.988222	+	0.153025i	$0.0489015\pi$
$277$			5.09369i			0.306050i	−0.988222	+	0.153025i	$0.951098\pi$
$278$	−8.44339	+	13.8846i	−0.506401	+	0.832745i
$279$		−	0.0394266i		−	0.00236041i
$280$	−6.58203	−	4.69312i	−0.393351	−	0.280468i
$281$		−	2.02480i		−	0.120789i	−0.998175	−	0.0603947i	$-0.980764\pi$
$281$		−	2.02480i		−	0.120789i	0.998175	−	0.0603947i	$-0.0192359\pi$
$282$	15.3637	+	9.34282i	0.914894	+	0.556357i
$283$		−	25.5315i		−	1.51769i	−0.651270	−	0.758846i	$-0.725764\pi$
$283$		−	25.5315i		−	1.51769i	0.651270	−	0.758846i	$-0.274236\pi$
$284$	−13.3434	+	6.91405i	−0.791784	+	0.410274i
$285$	−5.60237	−	3.44350i	−0.331856	−	0.203975i
$286$	2.98662	−	4.91131i	0.176602	−	0.290412i
$287$		−	8.11443i		−	0.478979i
$288$	0.718635	−	0.312156i	0.0423460	−	0.0183940i
$289$	−7.12536			−0.419139
$290$	−5.65323	−	11.0384i	−0.331969	−	0.648200i
$291$	12.9507			0.759186
$292$	−23.7048	+	12.2830i	−1.38722	+	0.718806i
$293$	−7.43188			−0.434175			−0.217087	−	0.976152i	$-0.569656\pi$
$293$	−7.43188			−0.434175			−0.217087	+	0.976152i	$0.569656\pi$
$294$	11.4874	+	6.98562i	0.669959	+	0.407409i
$295$	0.477353	−	0.776625i	0.0277925	−	0.0452169i
$296$	−0.879967	+	12.8658i	−0.0511470	+	0.747812i
$297$	10.1771			0.590537
$298$	−15.8352	+	26.0400i	−0.917307	+	1.50845i
$299$	−8.83275	+	4.03236i	−0.510811	+	0.233197i
$300$	10.3536	−	14.3755i	0.597764	−	0.829968i
$301$	13.2447			0.763413
$302$	−5.22184	+	8.58699i	−0.300483	+	0.494125i
$303$	−5.15414			−0.296098
$304$	−3.82919	+	5.42483i	−0.219619	+	0.311135i
$305$	−1.54437	+	2.51260i	−0.0884305	+	0.143871i
$306$	0.525912	+	0.319813i	0.0300644	+	0.0182825i
$307$	20.7426			1.18384			0.591921	−	0.805996i	$-0.298370\pi$
$307$	20.7426			1.18384			0.591921	+	0.805996i	$0.298370\pi$
$308$	4.55664	−	2.36108i	0.259638	−	0.134535i
$309$			7.29061i			0.414748i
$310$	−0.801206	+	0.410329i	−0.0455054	+	0.0233051i
$311$			14.0598i			0.797256i	0.917113	+	0.398628i	$0.130513\pi$
$311$			14.0598i			0.797256i	−0.917113	+	0.398628i	$0.869487\pi$
$312$	−10.1212	−	0.692247i	−0.573001	−	0.0391907i
$313$	−21.8115			−1.23286			−0.616429	−	0.787410i	$-0.711421\pi$
$313$	−21.8115			−1.23286			−0.616429	+	0.787410i	$0.711421\pi$
$314$	22.9630	+	13.9640i	1.29588	+	0.788037i
$315$	0.207288	−	0.337246i	0.0116794	−	0.0190016i
$316$	−13.5821	−	26.2120i	−0.764054	−	1.47454i
$317$			20.9689i			1.17773i	0.808231	+	0.588866i	$0.200425\pi$
$317$			20.9689i			1.17773i	−0.808231	+	0.588866i	$0.799575\pi$
$318$	19.5061	+	11.8618i	1.09385	+	0.665179i
$319$	7.87332			0.440821
$320$	−13.8226	−	11.3550i	−0.772708	−	0.634762i
$321$			24.5354i			1.36943i
$322$	−8.60857	−	1.02139i	−0.479737	−	0.0569200i
$323$	−5.21649			−0.290253
$324$	−8.64592	−	16.6857i	−0.480329	−	0.926983i
$325$	−9.03198	+	4.57150i	−0.501004	+	0.253581i
$326$	4.41045	+	2.68204i	0.244272	+	0.148545i
$327$			21.7286i			1.20160i
$328$	1.22526	−	17.9144i	0.0676539	−	0.989156i
$329$		−	9.17350i		−	0.505751i
$330$	5.12674	+	10.0104i	0.282218	+	0.551056i
$331$		−	32.7363i		−	1.79935i	−0.436560	−	0.899675i	$-0.643803\pi$
$331$		−	32.7363i		−	1.79935i	0.436560	−	0.899675i	$-0.356197\pi$
$332$	2.09000	−	1.08296i	0.114704	−	0.0594352i
$333$	−0.631499			−0.0346059
$334$	−5.78673	−	3.51897i	−0.316636	−	0.192550i
$335$	4.44953	−	7.23913i	0.243104	−	0.395516i
$336$	−7.39976	−	5.22323i	−0.403690	−	0.284950i
$337$	28.2019			1.53625			0.768127	−	0.640298i	$-0.221189\pi$
$337$	28.2019			1.53625			0.768127	+	0.640298i	$0.221189\pi$
$338$	−10.7554	−	6.54045i	−0.585014	−	0.355753i
$339$	−26.9172			−1.46194
$340$	1.02567	−	14.0157i	0.0556247	−	0.760110i
$341$		−	0.571471i		−	0.0309469i
$342$	−0.277824	−	0.168948i	−0.0150230	−	0.00913565i
$343$		−	15.8062i		−	0.853454i
$344$	29.2406	+	1.99993i	1.57655	+	0.107829i
$345$	2.32818	−	18.8549i	0.125345	−	1.01511i
$346$	−6.73484	+	11.0750i	−0.362067	+	0.595397i
$347$	−19.8612			−1.06620			−0.533102	−	0.846051i	$-0.678974\pi$
$347$	−19.8612			−1.06620			−0.533102	+	0.846051i	$0.678974\pi$
$348$	−6.39295	−	12.3377i	−0.342698	−	0.661371i
$349$	26.5042			1.41874			0.709369	−	0.704838i	$-0.248980\pi$
$349$	26.5042			1.41874			0.709369	+	0.704838i	$0.248980\pi$
$350$	−9.01066	−	0.702536i	−0.481640	−	0.0375522i
$351$			10.2635i			0.547823i
$352$	10.4163	−	4.52456i	0.555190	−	0.241160i
$353$		−	8.81853i		−	0.469363i	−0.972072	−	0.234681i	$-0.924595\pi$
$353$		−	8.81853i		−	0.469363i	0.972072	−	0.234681i	$-0.0754047\pi$
$354$	0.530700	−	0.872703i	0.0282064	−	0.0463837i
$355$	−8.79834	+	14.3144i	−0.466967	+	0.759729i
$356$	−22.6037	+	11.7124i	−1.19800	+	0.620758i
$357$		−	7.11557i		−	0.376596i
$358$	−2.74896	+	4.52050i	−0.145287	+	0.238916i
$359$	16.6623			0.879401			0.439700	−	0.898145i	$-0.355085\pi$
$359$	16.6623			0.879401			0.439700	+	0.898145i	$0.355085\pi$
$360$	0.508558	−	0.713244i	0.0268033	−	0.0375912i
$361$	−16.2443			−0.854962
$362$	17.6751	−	29.0656i	0.928982	−	1.52765i
$363$	12.3473			0.648067
$364$	2.38111	+	4.59529i	0.124804	+	0.240859i
$365$	−15.6304	+	25.4298i	−0.818135	+	1.33106i
$366$	−1.71697	+	2.82345i	−0.0897473	+	0.147584i
$367$			31.1423i			1.62562i	0.582531	+	0.812808i	$0.302062\pi$
$367$			31.1423i			1.62562i	−0.582531	+	0.812808i	$0.697938\pi$
$368$	−18.8511	−	3.55483i	−0.982680	−	0.185308i
$369$	0.879298			0.0457744
$370$	6.57228	+	12.8330i	0.341677	+	0.667155i
$371$		−	11.6469i		−	0.604675i
$372$	−0.895510	+	0.464021i	−0.0464300	+	0.0240583i
$373$	−24.0915			−1.24741			−0.623705	−	0.781660i	$-0.714373\pi$
$373$	−24.0915			−1.24741			−0.623705	+	0.781660i	$0.714373\pi$
$374$	7.62286	+	4.63554i	0.394169	+	0.239698i
$375$	1.63360	−	19.7394i	0.0843588	−	1.01934i
$376$	1.38518	−	20.2525i	0.0714353	−	1.04444i
$377$			7.94012i			0.408937i
$378$	−4.76114	+	7.82940i	−0.244887	+	0.402701i
$379$	12.3451			0.634127			0.317063	−	0.948404i	$-0.397303\pi$
$379$	12.3451			0.634127			0.317063	+	0.948404i	$0.397303\pi$
$380$	−0.541831	+	7.40410i	−0.0277953	+	0.379823i
$381$	−1.31673			−0.0674580
$382$	14.8017	+	9.00106i	0.757320	+	0.460534i
$383$		−	10.4177i		−	0.532320i	−0.963929	−	0.266160i	$-0.914245\pi$
$383$		−	10.4177i		−	0.532320i	0.963929	−	0.266160i	$-0.0857550\pi$
$384$	−15.5479	−	12.6488i	−0.793425	−	0.645480i
$385$	3.00455	−	4.88822i	0.153126	−	0.249127i
$386$	−1.51495	+	2.49124i	−0.0771089	+	0.126801i
$387$			1.43523i			0.0729568i
$388$	−6.72645	−	12.9813i	−0.341484	−	0.659027i
$389$		−	10.5916i		−	0.537015i	−0.963278	−	0.268508i	$-0.913470\pi$
$389$		−	10.5916i		−	0.537015i	0.963278	−	0.268508i	$-0.0865305\pi$
$390$	−10.0954	+	5.17024i	−0.511199	+	0.261805i
$391$	−6.25864	−	13.7093i	−0.316513	−	0.693312i
$392$	1.03570	−	15.1428i	0.0523107	−	0.764826i
$393$			6.45342i			0.325532i
$394$	−17.5644	+	28.8836i	−0.884884	+	1.45514i
$395$	−28.1195	−	17.2837i	−1.41485	−	0.869635i
$396$	0.255852	+	0.493768i	0.0128571	+	0.0248128i
$397$			37.4766i			1.88090i	0.339935	+	0.940449i	$0.389595\pi$
$397$			37.4766i			1.88090i	−0.339935	+	0.940449i	$0.610405\pi$
$398$	5.81402	+	3.53556i	0.291430	+	0.177222i
$399$			3.75895i			0.188183i
$400$	−19.7869	−	2.91160i	−0.989346	−	0.145580i
$401$		−	8.87101i		−	0.442997i	−0.975161	−	0.221499i	$-0.928905\pi$
$401$		−	8.87101i		−	0.442997i	0.975161	−	0.221499i	$-0.0710948\pi$
$402$	4.94680	−	8.13470i	0.246724	−	0.405722i
$403$	0.576319			0.0287085
$404$	2.67699	+	5.16631i	0.133185	+	0.257034i
$405$	−17.8999	−	11.0022i	−0.889454	−	0.546703i
$406$	−3.68336	+	6.05705i	−0.182802	+	0.300607i
$407$	−9.15329			−0.453712
$408$	1.07444	−	15.7092i	0.0531927	−	0.777721i
$409$	−2.79046			−0.137979			−0.0689896	−	0.997617i	$-0.521978\pi$
$409$	−2.79046			−0.137979			−0.0689896	+	0.997617i	$0.521978\pi$
$410$	−9.15123	−	17.8686i	−0.451947	−	0.882468i
$411$	1.76484			0.0870531
$412$	7.30782	−	3.78665i	0.360031	−	0.186555i
$413$	−0.521082			−0.0256408
$414$	0.110680	−	0.932845i	0.00543965	−	0.0458468i
$415$	1.37810	−	2.24209i	0.0676483	−	0.110060i
$416$	4.56295	+	10.5047i	0.223717	+	0.515033i
$417$			20.3568i			0.996876i
$418$	−4.02694	−	2.44882i	−0.196964	−	0.119776i
$419$	37.8916			1.85113			0.925563	−	0.378593i	$-0.123592\pi$
$419$	37.8916			1.85113			0.925563	+	0.378593i	$0.123592\pi$
$420$	−10.0996	−	0.739086i	−0.492810	−	0.0360637i
$421$		−	4.54929i		−	0.221719i	−0.993836	−	0.110859i	$-0.964640\pi$
$421$		−	4.54929i		−	0.221719i	0.993836	−	0.110859i	$-0.0353603\pi$
$422$	2.77924	−	4.57028i	0.135291	−	0.222478i
$423$	0.994061			0.0483329
$424$	1.75866	−	25.7130i	0.0854079	−	1.24873i
$425$	−7.09545	−	14.0186i	−0.344180	−	0.680001i
$426$	−9.78162	+	16.0853i	−0.473921	+	0.779333i
$427$	1.68585			0.0815840
$428$	24.5934	−	12.7434i	1.18877	−	0.615975i
$429$		−	7.20065i		−	0.347651i
$430$	29.1659	−	14.9370i	1.40651	−	0.720328i
$431$	−30.1685			−1.45316			−0.726582	−	0.687079i	$-0.758892\pi$
$431$	−30.1685			−1.45316			−0.726582	+	0.687079i	$0.758892\pi$
$432$	−11.6935	+	16.5662i	−0.562604	+	0.797042i
$433$	−8.39490			−0.403433			−0.201717	−	0.979444i	$-0.564652\pi$
$433$	−8.39490			−0.403433			−0.201717	+	0.979444i	$0.564652\pi$
$434$	0.439640	+	0.267350i	0.0211034	+	0.0128332i
$435$	−13.2355	−	8.13522i	−0.634595	−	0.390054i
$436$	21.7800	−	11.2856i	1.04307	−	0.540481i
$437$	3.30626	+	7.24225i	0.158160	+	0.346444i
$438$	−17.3773	+	28.5758i	−0.830317	+	1.36541i
$439$		−	13.8344i		−	0.660278i	−0.943932	−	0.330139i	$-0.892904\pi$
$439$		−	13.8344i		−	0.660278i	0.943932	−	0.330139i	$-0.107096\pi$
$440$	7.37131	−	10.3381i	0.351414	−	0.492852i
$441$	0.743259			0.0353933
$442$	−4.67487	+	7.68753i	−0.222361	+	0.365659i
$443$	4.14183			0.196784			0.0983922	−	0.995148i	$-0.468630\pi$
$443$	4.14183			0.196784			0.0983922	+	0.995148i	$0.468630\pi$
$444$	7.43226	+	14.3435i	0.352719	+	0.680711i
$445$	−14.9044	+	24.2486i	−0.706537	+	1.14950i
$446$	−18.0004	−	10.9462i	−0.852344	−	0.518320i
$447$			38.1782i			1.80577i
$448$	−1.39222	+	10.1301i	−0.0657764	+	0.478603i
$449$	−37.8144			−1.78457			−0.892286	−	0.451470i	$-0.850900\pi$
$449$	−37.8144			−1.78457			−0.892286	+	0.451470i	$0.850900\pi$
$450$	0.0761285	−	0.976416i	0.00358873	−	0.0460287i
$451$	12.7450			0.600140
$452$	13.9805	+	26.9808i	0.657586	+	1.26907i
$453$			12.5897i			0.591516i
$454$	12.0016	−	19.7358i	0.563262	−	0.926249i
$455$	4.92969	+	3.03004i	0.231108	+	0.142050i
$456$	−0.567595	+	8.29870i	−0.0265801	+	0.388622i
$457$	−12.8189			−0.599642			−0.299821	−	0.953996i	$-0.596927\pi$
$457$	−12.8189			−0.599642			−0.299821	+	0.953996i	$0.596927\pi$
$458$	−1.76678	+	2.90536i	−0.0825563	+	0.135759i
$459$	−15.9300			−0.743548
$460$	−20.1087	+	7.45933i	−0.937571	+	0.347793i
$461$	−8.34863			−0.388834			−0.194417	−	0.980919i	$-0.562282\pi$
$461$	−8.34863			−0.388834			−0.194417	+	0.980919i	$0.562282\pi$
$462$	3.34033	−	5.49296i	0.155406	−	0.255556i
$463$	20.8027			0.966786			0.483393	−	0.875404i	$-0.339404\pi$
$463$	20.8027			0.966786			0.483393	+	0.875404i	$0.339404\pi$
$464$	−9.04643	+	12.8161i	−0.419970	+	0.594972i
$465$	−0.590480	+	0.960677i	−0.0273829	+	0.0445503i
$466$	−10.1080	+	16.6220i	−0.468245	+	0.770000i
$467$		−	38.7967i		−	1.79530i	−0.440713	−	0.897648i	$-0.645274\pi$
$467$		−	38.7967i		−	1.79530i	0.440713	−	0.897648i	$-0.354726\pi$
$468$	−0.497957	+	0.258023i	−0.0230181	+	0.0119271i
$469$	−4.85715			−0.224282
$470$	−10.3456	−	20.2008i	−0.477208	−	0.931792i
$471$	33.6669			1.55129
$472$	−1.15040	−	0.0786825i	−0.0529516	−	0.00362166i
$473$			20.8030i			0.956523i
$474$	−31.5982	−	19.2152i	−1.45136	−	0.882584i
$475$	3.74832	+	7.40561i	0.171985	+	0.339793i
$476$	−7.13238	+	3.69574i	−0.326912	+	0.169394i
$477$	1.26208			0.0577867
$478$	20.1818	−	33.1877i	0.923093	−	1.51797i
$479$	4.32999			0.197842			0.0989212	−	0.995095i	$-0.468461\pi$
$479$	4.32999			0.197842			0.0989212	+	0.995095i	$0.468461\pi$
$480$	−22.1855	−	3.15672i	−1.01262	−	0.144084i
$481$		−	9.23095i		−	0.420895i
$482$	−9.76062	+	16.0507i	−0.444584	+	0.731091i
$483$	−9.87882	+	4.50991i	−0.449502	+	0.205208i
$484$	−6.41305	−	12.3765i	−0.291502	−	0.562568i
$485$	−13.9260	−	8.55961i	−0.632347	−	0.388672i
$486$	−1.73789	−	1.05683i	−0.0788323	−	0.0479388i
$487$	24.4278			1.10693			0.553465	−	0.832872i	$-0.313305\pi$
$487$	24.4278			1.10693			0.553465	+	0.832872i	$0.313305\pi$
$488$	3.72188	+	0.254560i	0.168482	+	0.0115234i
$489$	6.46633			0.292417
$490$	−7.73541	−	15.1041i	−0.349450	−	0.682334i
$491$		−	27.9260i		−	1.26028i	−0.776480	−	0.630142i	$-0.782997\pi$
$491$		−	27.9260i		−	1.26028i	0.776480	−	0.630142i	$-0.217003\pi$
$492$	−10.3487	−	19.9718i	−0.466554	−	0.900399i
$493$	−12.3239			−0.555040
$494$	2.46960	−	4.06110i	0.111112	−	0.182718i
$495$	0.529699	+	0.325580i	0.0238082	+	0.0146337i
$496$	0.930233	+	0.656619i	0.0417687	+	0.0294830i
$497$	9.60434			0.430814
$498$	1.53211	−	2.51946i	0.0686556	−	0.112900i
$499$		−	31.1413i		−	1.39408i	−0.717034	−	0.697038i	$-0.754501\pi$
$499$		−	31.1413i		−	1.39408i	0.717034	−	0.697038i	$-0.245499\pi$
$500$	−20.6345	+	8.61494i	−0.922803	+	0.385272i
$501$	−8.48415			−0.379044
$502$	29.7590	+	18.0968i	1.32821	+	0.807699i
$503$			22.8311i			1.01799i	0.860771	+	0.508993i	$0.169982\pi$
$503$			22.8311i			1.01799i	−0.860771	+	0.508993i	$0.830018\pi$
$504$	−0.499557	−	0.0341675i	−0.0222520	−	0.00152194i
$505$	5.54227	+	3.40656i	0.246628	+	0.151590i
$506$	1.60426	−	13.5212i	0.0713182	−	0.601089i
$507$	−15.7688			−0.700318
$508$	0.683892	+	1.31984i	0.0303428	+	0.0585584i
$509$	35.6570			1.58047			0.790235	−	0.612804i	$-0.209958\pi$
$509$	35.6570			1.58047			0.790235	+	0.612804i	$0.209958\pi$
$510$	−8.02475	−	15.6691i	−0.355342	−	0.693838i
$511$	17.0623			0.754793
$512$	−4.60327	+	22.1542i	−0.203438	+	0.979088i
$513$	8.41534			0.371546
$514$	−14.6590	+	24.1059i	−0.646582	+	1.06326i
$515$	4.81862	−	7.83962i	0.212334	−	0.345455i
$516$	32.5989	−	16.8915i	1.43508	−	0.743609i
$517$	14.4085			0.633684
$518$	4.28217	−	7.04176i	0.188148	−	0.309397i
$519$			16.2375i			0.712747i
$520$	10.4259	+	7.43385i	0.457204	+	0.325996i
$521$			5.01032i			0.219506i	0.993959	+	0.109753i	$0.0350060\pi$
$521$			5.01032i			0.219506i	−0.993959	+	0.109753i	$0.964994\pi$
$522$	−0.656357	−	0.399137i	−0.0287279	−	0.0174698i
$523$		−	1.23284i		−	0.0539085i	−0.999637	−	0.0269542i	$-0.991419\pi$
$523$		−	1.23284i		−	0.0539085i	0.999637	−	0.0269542i	$-0.00858084\pi$
$524$	6.46866	−	3.35182i	0.282585	−	0.146425i
$525$	−10.1017	+	5.11291i	−0.440872	+	0.223146i
$526$	8.58568	−	14.1186i	0.374354	−	0.615601i
$527$			0.894507i			0.0389653i
$528$	8.20393	−	11.6225i	0.357030	−	0.505806i
$529$	−15.0664	+	17.3782i	−0.655062	+	0.755575i
$530$	−13.1350	−	25.6473i	−0.570549	−	1.11405i
$531$		−	0.0564657i		−	0.00245040i
$532$	3.76783	−	1.95235i	0.163356	−	0.0846451i
$533$			12.8532i			0.556732i
$534$	−16.5701	+	27.2485i	−0.717058	+	1.17916i
$535$	16.2163	−	26.3830i	0.701094	−	1.14064i
$536$	−10.7232	−	0.733421i	−0.463173	−	0.0316790i
$537$			6.62767i			0.286005i
$538$	−7.34134	−	4.46435i	−0.316508	−	0.192472i
$539$	10.7732			0.464035
$540$	−1.65463	+	22.6105i	−0.0712039	+	0.973000i
$541$	23.8421			1.02505			0.512526	−	0.858672i	$-0.328710\pi$
$541$	23.8421			1.02505			0.512526	+	0.858672i	$0.328710\pi$
$542$	13.5826	−	22.3357i	0.583422	−	0.959402i
$543$		−	42.6141i		−	1.82875i
$544$	−16.3043	+	7.08218i	−0.699043	+	0.303646i
$545$	14.3612	−	23.3649i	0.615168	−	1.00084i
$546$	5.53956	+	3.36867i	0.237071	+	0.144166i
$547$	4.14950			0.177420			0.0887099	−	0.996058i	$-0.471726\pi$
$547$	4.14950			0.177420			0.0887099	+	0.996058i	$0.471726\pi$
$548$	−0.916635	−	1.76901i	−0.0391567	−	0.0755682i
$549$			0.182683i			0.00779671i
$550$	1.10345	−	14.1527i	0.0470512	−	0.603474i
$551$	6.51035			0.277350
$552$	−22.4907	+	8.46494i	−0.957266	+	0.360292i
$553$			18.8670i			0.802306i
$554$	3.74284	−	6.15487i	0.159018	−	0.261495i
$555$	15.3872	+	9.45777i	0.653152	+	0.401460i
$556$	20.4049	−	10.5731i	0.865359	−	0.448397i
$557$	−25.9135			−1.09799			−0.548996	−	0.835825i	$-0.684990\pi$
$557$	−25.9135			−1.09799			−0.548996	+	0.835825i	$0.684990\pi$
$558$	−0.0289707	+	0.0476404i	−0.00122643	+	0.00201678i
$559$	−20.9795			−0.887338
$560$	4.50477	+	10.5073i	0.190361	+	0.444016i
$561$	11.1762			0.471858
$562$	−1.48782	+	2.44663i	−0.0627600	+	0.103205i
$563$		−	2.41729i		−	0.101877i	−0.998702	−	0.0509384i	$-0.983779\pi$
$563$		−	2.41729i		−	0.101877i	0.998702	−	0.0509384i	$-0.0162212\pi$
$564$	−11.6993	−	22.5785i	−0.492631	−	0.950725i
$565$	28.9442	+	17.7906i	1.21769	+	0.748455i
$566$	−18.7606	+	30.8506i	−0.788565	+	1.29675i
$567$			12.0101i			0.504376i
$568$	21.2037	+	1.45024i	0.889687	+	0.0608507i
$569$			34.2149i			1.43436i	0.696886	+	0.717182i	$0.254568\pi$
$569$			34.2149i			1.43436i	−0.696886	+	0.717182i	$0.745432\pi$
$570$	4.23924	+	8.27751i	0.177562	+	0.346707i
$571$	45.1587			1.88983			0.944917	−	0.327309i	$-0.106142\pi$
$571$	45.1587			1.88983			0.944917	+	0.327309i	$0.106142\pi$
$572$	−7.21766	+	3.73993i	−0.301785	+	0.156374i
$573$	21.7013			0.906585
$574$	−5.96248	+	9.80493i	−0.248869	+	0.409250i
$575$	−14.9654	+	18.7360i	−0.624100	+	0.781345i
$576$	−1.09772	−	0.150865i	−0.0457385	−	0.00628602i
$577$		−	10.7803i		−	0.448791i	−0.974498	−	0.224395i	$-0.927959\pi$
$577$		−	10.7803i		−	0.448791i	0.974498	−	0.224395i	$-0.0720407\pi$
$578$	8.60980	+	5.23571i	0.358121	+	0.217777i
$579$			3.65250i			0.151793i
$580$	−1.28007	+	17.4921i	−0.0531520	+	0.726321i
$581$	−1.50435			−0.0624108
$582$	−15.6488	−	9.51621i	−0.648664	−	0.394460i
$583$	18.2933			0.757631
$584$	37.6688	+	2.57638i	1.55875	+	0.106611i
$585$	−0.328342	+	0.534193i	−0.0135753	+	0.0220862i
$586$	8.98018	+	5.46094i	0.370968	+	0.225589i
$587$	20.1830			0.833040			0.416520	−	0.909127i	$-0.363250\pi$
$587$	20.1830			0.833040			0.416520	+	0.909127i	$0.363250\pi$
$588$	−8.74759	−	16.8819i	−0.360744	−	0.696198i
$589$		−	0.472542i		−	0.0194708i
$590$	−1.14747	+	0.587663i	−0.0472404	+	0.0241937i
$591$			42.3474i			1.74194i
$592$	10.5171	−	14.8996i	0.432251	−	0.612371i
$593$		−	27.1614i		−	1.11538i	−0.830048	−	0.557692i	$-0.811687\pi$
$593$		−	27.1614i		−	1.11538i	0.830048	−	0.557692i	$-0.188313\pi$
$594$	−12.2974	−	7.47815i	−0.504567	−	0.306832i
$595$	−4.70294	+	7.65140i	−0.192802	+	0.313677i
$596$	38.2683	−	19.8293i	1.56753	−	0.812238i
$597$	8.52415			0.348870
$598$	13.6359	+	1.61787i	0.557612	+	0.0661598i
$599$		−	29.2766i		−	1.19621i	−0.801418	−	0.598105i	$-0.795921\pi$
$599$		−	29.2766i		−	1.19621i	0.801418	−	0.598105i	$-0.204079\pi$
$600$	−23.0737	+	9.76254i	−0.941978	+	0.398554i
$601$	17.8309			0.727338			0.363669	−	0.931528i	$-0.381524\pi$
$601$	17.8309			0.727338			0.363669	+	0.931528i	$0.381524\pi$
$602$	−16.0040	−	9.73222i	−0.652276	−	0.396656i
$603$		−	0.526332i		−	0.0214339i
$604$	12.6194	−	6.53893i	0.513478	−	0.266065i
$605$	−13.2771	−	8.16080i	−0.539792	−	0.331784i
$606$	6.22792	+	3.78726i	0.252992	+	0.153847i
$607$	−8.00797			−0.325033			−0.162517	−	0.986706i	$-0.551961\pi$
$607$	−8.00797			−0.325033			−0.162517	+	0.986706i	$0.551961\pi$
$608$	8.61310	−	3.74131i	0.349308	−	0.151730i
$609$			8.88048i			0.359855i
$610$	3.71238	−	1.90126i	0.150310	−	0.0769797i
$611$			14.5307i			0.587850i
$612$	−0.400479	−	0.772881i	−0.0161884	−	0.0312419i
$613$	13.3191			0.537952			0.268976	−	0.963147i	$-0.413315\pi$
$613$	13.3191			0.537952			0.268976	+	0.963147i	$0.413315\pi$
$614$	−25.0639	−	15.2416i	−1.01150	−	0.615103i
$615$	−21.4252	−	13.1690i	−0.863946	−	0.531025i
$616$	−7.24086	−	0.495243i	−0.291742	−	0.0199539i
$617$	12.7250			0.512290			0.256145	−	0.966638i	$-0.417548\pi$
$617$	12.7250			0.512290			0.256145	+	0.966638i	$0.417548\pi$
$618$	5.35714	−	8.80948i	0.215496	−	0.354369i
$619$	−12.1732			−0.489283			−0.244641	−	0.969614i	$-0.578670\pi$
$619$	−12.1732			−0.489283			−0.244641	+	0.969614i	$0.578670\pi$
$620$	1.26963	+	0.0929115i	0.0509897	+	0.00373141i
$621$	10.0966	+	22.1162i	0.405161	+	0.887492i
$622$	10.3311	−	16.9889i	0.414240	−	0.681192i
$623$	16.2698			0.651836
$624$	11.7211	+	8.27353i	0.469221	+	0.331206i
$625$	−14.8031	+	20.1462i	−0.592124	+	0.805847i
$626$	26.3555	+	16.0271i	1.05338	+	0.640571i
$627$	−5.90404			−0.235785
$628$	−17.4862	−	33.7464i	−0.697774	−	1.34663i
$629$	14.3274			0.571271
$630$	−0.498281	+	0.255190i	−0.0198520	+	0.0101670i
$631$	−35.3099			−1.40566			−0.702832	−	0.711356i	$-0.748081\pi$
$631$	−35.3099			−1.40566			−0.702832	+	0.711356i	$0.748081\pi$
$632$	−2.84888	+	41.6530i	−0.113322	+	1.65687i
$633$		−	6.70066i		−	0.266327i
$634$	15.4080	−	25.3374i	0.611928	−	1.00628i
$635$	1.41588	+	0.870273i	0.0561876	+	0.0345357i
$636$	−14.8537	−	28.6661i	−0.588989	−	1.13668i
$637$			10.8646i			0.430471i
$638$	−9.51359	−	5.78532i	−0.376647	−	0.229043i
$639$			1.04075i			0.0411714i
$640$	8.35869	+	23.8774i	0.330406	+	0.943839i
$641$		−	18.1190i		−	0.715656i	−0.933788	−	0.357828i	$-0.883517\pi$
$641$		−	18.1190i		−	0.715656i	0.933788	−	0.357828i	$-0.116483\pi$
$642$	18.0286	−	29.6470i	0.711534	−	1.17007i
$643$			40.3890i			1.59279i	0.604778	+	0.796394i	$0.293262\pi$
$643$			40.3890i			1.59279i	−0.604778	+	0.796394i	$0.706738\pi$
$644$	9.65150	+	7.55976i	0.380322	+	0.297896i
$645$	21.4950	−	34.9711i	0.846364	−	1.37699i
$646$	6.30325	+	3.83307i	0.247998	+	0.150810i
$647$	−39.1470			−1.53903			−0.769514	−	0.638630i	$-0.779502\pi$
$647$	−39.1470			−1.53903			−0.769514	+	0.638630i	$0.779502\pi$
$648$	−1.81350	+	26.5149i	−0.0712411	+	1.04160i
$649$		−	0.818445i		−	0.0321268i
$650$	14.2728	+	1.11281i	0.559825	+	0.0436480i
$651$	0.644573			0.0252628
$652$	−3.35853	−	6.48160i	−0.131530	−	0.253839i
$653$			30.4895i			1.19315i	0.802558	+	0.596574i	$0.203472\pi$
$653$			30.4895i			1.19315i	−0.802558	+	0.596574i	$0.796528\pi$
$654$	15.9662	−	26.2554i	0.624328	−	1.02667i
$655$	4.26530	−	6.93939i	0.166659	−	0.271144i
$656$	−14.6440	+	20.7462i	−0.571753	+	0.810003i
$657$			1.84891i			0.0721330i
$658$	−6.74069	+	11.0846i	−0.262779	+	0.432124i
$659$	−17.9308			−0.698487			−0.349243	−	0.937032i	$-0.613561\pi$
$659$	−17.9308			−0.698487			−0.349243	+	0.937032i	$0.613561\pi$
$660$	1.16086	−	15.8631i	0.0451863	−	0.617469i
$661$			35.5572i			1.38301i	0.722370	+	0.691507i	$0.243053\pi$
$661$			35.5572i			1.38301i	−0.722370	+	0.691507i	$0.756947\pi$
$662$	−24.0546	+	39.5564i	−0.934910	+	1.53740i
$663$			11.2710i			0.437729i
$664$	−3.32117	−	0.227154i	−0.128886	−	0.00881527i
$665$	2.48442	−	4.04201i	0.0963418	−	0.156743i
$666$	0.763061	+	0.464026i	0.0295680	+	0.0179806i
$667$	7.81100	+	17.1097i	0.302443	+	0.662492i
$668$	4.40656	+	8.50419i	0.170495	+	0.329037i
$669$	−26.3911			−1.02034
$670$	−10.6958	+	5.47776i	−0.413216	+	0.211624i
$671$			2.64790i			0.102221i
$672$	5.10335	+	11.7487i	0.196866	+	0.453218i
$673$		−	49.8311i		−	1.92085i	−0.278543	−	0.960424i	$-0.589852\pi$
$673$		−	49.8311i		−	1.92085i	0.278543	−	0.960424i	$-0.410148\pi$
$674$	−34.0773	−	20.7227i	−1.31261	−	0.798210i
$675$	11.4465	+	22.6151i	0.440577	+	0.870454i
$676$	8.19013	+	15.8061i	0.315005	+	0.607926i
$677$	24.1638			0.928688			0.464344	−	0.885655i	$-0.346290\pi$
$677$	24.1638			0.928688			0.464344	+	0.885655i	$0.346290\pi$
$678$	32.5250	+	19.7788i	1.24911	+	0.759600i
$679$			9.34374i			0.358580i
$680$	−11.5381	+	16.1820i	−0.442467	+	0.620552i
$681$		−	28.9355i		−	1.10881i
$682$	−0.419917	+	0.690527i	−0.0160794	+	0.0264416i
$683$	−33.5547			−1.28394			−0.641968	−	0.766732i	$-0.721882\pi$
$683$	−33.5547			−1.28394			−0.641968	+	0.766732i	$0.721882\pi$
$684$	0.211561	+	0.408290i	0.00808924	+	0.0156114i
$685$	−1.89774	−	1.16645i	−0.0725088	−	0.0445676i
$686$	−11.6144	+	19.0991i	−0.443439	+	0.729208i
$687$			4.25966i			0.162516i
$688$	−33.8629	−	23.9026i	−1.29101	−	0.911278i
$689$			18.4485i			0.702832i
$690$	−16.6678	+	21.0723i	−0.634532	+	0.802208i
$691$			51.0577i			1.94233i	0.238415	+	0.971163i	$0.423372\pi$
$691$			51.0577i			1.94233i	−0.238415	+	0.971163i	$0.576628\pi$
$692$	16.2759	−	8.43355i	0.618715	−	0.320596i
$693$		−	0.355406i		−	0.0135007i
$694$	23.9989	+	14.5940i	0.910986	+	0.553980i
$695$	13.4545	−	21.8897i	0.510359	−	0.830325i
$696$	−1.34094	+	19.6056i	−0.0508281	+	0.743148i
$697$	−19.9494			−0.755639
$698$	−32.0259	−	19.4753i	−1.21220	−	0.737151i
$699$			24.3702i			0.921764i
$700$	10.3717	+	7.46993i	0.392012	+	0.282337i
$701$		−	27.2145i		−	1.02788i	−0.857827	−	0.513939i	$-0.828186\pi$
$701$		−	27.2145i		−	1.02788i	0.857827	−	0.513939i	$-0.171814\pi$
$702$	7.54160	−	12.4017i	0.284639	−	0.468071i
$703$	−7.56875			−0.285461
$704$	−15.9110	−	2.18671i	−0.599668	−	0.0824149i
$705$	−24.2215	−	14.8878i	−0.912235	−	0.560706i
$706$	−6.47986	+	10.6557i	−0.243873	+	0.401033i
$707$		−	3.71862i		−	0.139853i
$708$	−1.28253	+	0.664558i	−0.0482003	+	0.0249756i
$709$		−	16.0965i		−	0.604518i	−0.953226	−	0.302259i	$-0.902259\pi$
$709$		−	16.0965i		−	0.604518i	0.953226	−	0.302259i	$-0.0977407\pi$
$710$	21.1495	−	10.8315i	0.793728	−	0.406500i
$711$	−2.04447			−0.0766736
$712$	35.9191	+	2.45671i	1.34613	+	0.0920691i
$713$	1.24188	−	0.566947i	0.0465087	−	0.0212323i
$714$	−5.22852	+	8.59798i	−0.195673	+	0.321771i
$715$	−4.75917	+	7.74289i	−0.177983	+	0.289568i
$716$	6.64333	−	3.44233i	0.248273	−	0.128646i
$717$		−	48.6577i		−	1.81715i
$718$	−20.1336	−	12.2434i	−0.751378	−	0.456921i
$719$			39.4635i			1.47174i	0.677122	+	0.735870i	$0.263227\pi$
$719$			39.4635i			1.47174i	−0.677122	+	0.735870i	$0.736773\pi$
$720$	−1.13860	+	0.488148i	−0.0424331	+	0.0181922i
$721$	−5.26005			−0.195894
$722$	19.6285	+	11.9363i	0.730497	+	0.444223i
$723$			23.5326i			0.875186i
$724$	−42.7148	+	22.1332i	−1.58748	+	0.822575i
$725$	8.85536	+	17.4957i	0.328880	+	0.649773i
$726$	−14.9197	−	9.07282i	−0.553722	−	0.336724i
$727$		−	12.8559i		−	0.476798i	−0.971167	−	0.238399i	$-0.923377\pi$
$727$		−	12.8559i		−	0.476798i	0.971167	−	0.238399i	$-0.0766226\pi$
$728$	0.499444	−	7.30229i	0.0185106	−	0.270641i
$729$	25.6410			0.949667
$730$	37.5726	−	19.2424i	1.39062	−	0.712194i
$731$		−	32.5624i		−	1.20436i
$732$	4.14934	−	2.15003i	0.153364	−	0.0794676i
$733$	−31.2706			−1.15501			−0.577503	−	0.816388i	$-0.695973\pi$
$733$	−31.2706			−1.15501			−0.577503	+	0.816388i	$0.695973\pi$
$734$	22.8834	−	37.6303i	0.844642	−	1.38896i
$735$	−18.1104	−	11.1316i	−0.668012	−	0.410594i
$736$	20.1663	+	18.1472i	0.743339	+	0.668914i
$737$		−	7.62894i		−	0.281016i
$738$	−1.06248	−	0.646108i	−0.0391106	−	0.0237836i
$739$			14.1135i			0.519174i	0.965720	+	0.259587i	$0.0835864\pi$
$739$			14.1135i			0.519174i	−0.965720	+	0.259587i	$0.916414\pi$
$740$	1.48817	−	20.3358i	0.0547063	−	0.747560i
$741$		−	5.95413i		−	0.218730i
$742$	−8.55812	+	14.0733i	−0.314178	+	0.516647i
$743$		−	15.2288i		−	0.558691i	−0.960191	−	0.279345i	$-0.909883\pi$
$743$		−	15.2288i		−	0.558691i	0.960191	−	0.279345i	$-0.0901175\pi$
$744$	1.42304	+	0.0973294i	0.0521711	+	0.00356827i
$745$	25.2333	−	41.0531i	0.924477	−	1.50407i
$746$	29.1105	+	17.7024i	1.06581	+	0.648132i
$747$		−	0.163014i		−	0.00596438i
$748$	−5.80476	−	11.2026i	−0.212243	−	0.409606i
$749$	−17.7019			−0.646813
$750$	−16.4785	+	22.6514i	−0.601708	+	0.827113i
$751$	−19.8242			−0.723396			−0.361698	−	0.932295i	$-0.617803\pi$
$751$	−19.8242			−0.723396			−0.361698	+	0.932295i	$0.617803\pi$
$752$	−16.5553	+	23.4539i	−0.603710	+	0.855277i
$753$	43.6309			1.59000
$754$	5.83440	−	9.59431i	0.212476	−	0.349404i
$755$	8.32099	−	13.5378i	0.302832	−	0.492689i
$756$	11.5061	−	5.96204i	0.418473	−	0.216837i
$757$	5.98547			0.217545			0.108773	−	0.994067i	$-0.465308\pi$
$757$	5.98547			0.217545			0.108773	+	0.994067i	$0.465308\pi$
$758$	−14.9170	−	9.07121i	−0.541811	−	0.329481i
$759$	−7.08356	−	15.5163i	−0.257117	−	0.563206i
$760$	6.09525	−	8.54849i	0.221098	−	0.310086i
$761$	6.47102			0.234574			0.117287	−	0.993098i	$-0.462580\pi$
$761$	6.47102			0.234574			0.117287	+	0.993098i	$0.462580\pi$
$762$	1.59105	+	0.967532i	0.0576375	+	0.0350500i
$763$	−15.6768			−0.567540
$764$	−11.2714	−	21.7526i	−0.407784	−	0.786980i
$765$	−0.829124	−	0.509621i	−0.0299770	−	0.0184254i
$766$	−7.65494	+	12.5881i	−0.276584	+	0.454825i
$767$	0.825388			0.0298030
$768$	9.49272	+	26.7085i	0.342539	+	0.963761i
$769$			22.1852i			0.800017i	0.916511	+	0.400009i	$0.130993\pi$
$769$			22.1852i			0.800017i	−0.916511	+	0.400009i	$0.869007\pi$
$770$	−7.22236	+	3.69886i	−0.260276	+	0.133298i
$771$			35.3425i			1.27283i
$772$	3.66113	−	1.89706i	0.131767	−	0.0682767i
$773$	20.9231			0.752551			0.376276	−	0.926508i	$-0.377205\pi$
$773$	20.9231			0.752551			0.376276	+	0.926508i	$0.377205\pi$
$774$	1.05461	−	1.73423i	0.0379070	−	0.0623358i
$775$	1.26989	−	0.642750i	0.0456158	−	0.0230883i
$776$	−1.41089	+	20.6284i	−0.0506480	+	0.740515i
$777$		−	10.3242i		−	0.370378i
$778$	−7.78271	+	12.7982i	−0.279024	+	0.458837i
$779$	10.5387			0.377588
$780$	15.9977	+	1.17070i	0.572808	+	0.0419179i
$781$			15.0852i			0.539790i
$782$	−2.51111	+	21.1643i	−0.0897971	+	0.756834i
$783$	19.8812			0.710494
$784$	−12.3784	+	17.5365i	−0.442085	+	0.626303i
$785$	−36.2022	−	22.2517i	−1.29211	−	0.794196i
$786$	4.74198	−	7.79788i	0.169141	−	0.278141i
$787$		−	38.9650i		−	1.38895i	−0.719515	−	0.694476i	$-0.755636\pi$
$787$		−	38.9650i		−	1.38895i	0.719515	−	0.694476i	$-0.244364\pi$
$788$	42.4474	−	21.9947i	1.51213	−	0.783528i
$789$		−	20.6998i		−	0.736934i
$790$	21.2777	+	41.5466i	0.757026	+	1.47816i
$791$		−	19.4203i		−	0.690507i
$792$	0.0536657	−	0.784636i	0.00190693	−	0.0278808i
$793$	−2.67037			−0.0948275
$794$	27.5378	−	45.2842i	0.977281	−	1.60708i
$795$	−30.7521	−	18.9018i	−1.09067	−	0.670378i
$796$	−4.42733	−	8.54428i	−0.156923	−	0.302844i
$797$	0.230952			0.00818073			0.00409036	−	0.999992i	$-0.498698\pi$
$797$	0.230952			0.00818073			0.00409036	+	0.999992i	$0.498698\pi$
$798$	2.76208	−	4.54206i	0.0977764	−	0.160787i
$799$	−22.5532			−0.797875
$800$	21.7698	+	18.0576i	0.769677	+	0.638433i
$801$			1.76303i			0.0622937i
$802$	−6.51842	+	10.7191i	−0.230173	+	0.378506i
$803$			26.7992i			0.945722i
$804$	−11.9548	+	6.19452i	−0.421612	+	0.218464i
$805$	13.6035	+	1.67974i	0.479460	+	0.0592030i
$806$	−0.696385	−	0.423479i	−0.0245291	−	0.0149164i
$807$	−10.7634			−0.378890
$808$	0.561506	−	8.20968i	0.0197537	−	0.288816i
$809$	−18.7034			−0.657576			−0.328788	−	0.944404i	$-0.606640\pi$
$809$	−18.7034			−0.657576			−0.328788	+	0.944404i	$0.606640\pi$
$810$	13.5447	+	26.4472i	0.475911	+	0.929259i
$811$		−	7.83804i		−	0.275231i	−0.990486	−	0.137615i	$-0.956056\pi$
$811$		−	7.83804i		−	0.275231i	0.990486	−	0.137615i	$-0.0439438\pi$
$812$	8.90145	−	4.61241i	0.312380	−	0.161864i
$813$		−	32.7473i		−	1.14850i
$814$	11.0602	+	6.72584i	0.387661	+	0.235741i
$815$	−6.95327	−	4.27383i	−0.243562	−	0.149706i
$816$	−12.8414	+	18.1924i	−0.449539	+	0.636863i
$817$			17.2017i			0.601813i
$818$	3.37180	+	2.05043i	0.117892	+	0.0716915i
$819$	0.358421			0.0125242
$820$	−2.07213	+	28.3156i	−0.0723618	+	0.988823i
$821$	−10.5077			−0.366720			−0.183360	−	0.983046i	$-0.558697\pi$
$821$	−10.5077			−0.366720			−0.183360	+	0.983046i	$0.558697\pi$
$822$	−2.13251	−	1.29680i	−0.0743799	−	0.0452312i
$823$	−46.7259			−1.62876			−0.814381	−	0.580330i	$-0.802924\pi$
$823$	−46.7259			−1.62876			−0.814381	+	0.580330i	$0.802924\pi$
$824$	−11.6127	−	0.794258i	−0.404548	−	0.0276693i
$825$	−8.03066	−	15.8663i	−0.279592	−	0.552394i
$826$	0.629641	+	0.382891i	0.0219080	+	0.0133225i
$827$		−	12.6771i		−	0.440826i	−0.975407	−	0.220413i	$-0.929259\pi$
$827$		−	12.6771i		−	0.440826i	0.975407	−	0.220413i	$-0.0707405\pi$
$828$	−0.819193	+	1.04586i	−0.0284689	+	0.0363461i
$829$	27.8620			0.967686			0.483843	−	0.875155i	$-0.339241\pi$
$829$	27.8620			0.967686			0.483843	+	0.875155i	$0.339241\pi$
$830$	−3.31269	+	1.69656i	−0.114985	+	0.0588885i
$831$		−	9.02389i		−	0.313035i
$832$	2.20527	−	16.0460i	0.0764538	−	0.556294i
$833$	−16.8630			−0.584268
$834$	14.9582	−	24.5978i	0.517959	−	0.851751i
$835$	9.12304	+	5.60748i	0.315716	+	0.194055i
$836$	3.06648	+	5.91799i	0.106057	+	0.204678i
$837$		−	1.44304i		−	0.0498787i
$838$	−45.7857	−	27.8428i	−1.58164	−	0.961812i
$839$	41.6414			1.43762			0.718810	−	0.695206i	$-0.244687\pi$
$839$	41.6414			1.43762			0.718810	+	0.695206i	$0.244687\pi$
$840$	11.6606	+	8.31425i	0.402329	+	0.286869i
$841$	−13.6194			−0.469633
$842$	−3.34282	+	5.49706i	−0.115201	+	0.189441i
$843$			3.58710i			0.123546i
$844$	−6.71649	+	3.48024i	−0.231191	+	0.119795i
$845$	16.9563	+	10.4222i	0.583314	+	0.358534i
$846$	−1.20116	−	0.730437i	−0.0412966	−	0.0251129i
$847$			8.90839i			0.306096i
$848$	−21.0190	+	29.7776i	−0.721794	+	1.02257i
$849$			45.2312i			1.55233i
$850$	−1.72720	+	22.1529i	−0.0592424	+	0.759837i
$851$	−9.08084	−	19.8913i	−0.311287	−	0.681864i
$852$	23.6389	−	12.2488i	0.809855	−	0.419638i
$853$			1.29526i			0.0443489i	0.999754	+	0.0221744i	$0.00705892\pi$
$853$			1.29526i			0.0443489i	−0.999754	+	0.0221744i	$0.992941\pi$
$854$	−2.03707	−	1.23876i	−0.0697070	−	0.0423896i
$855$	0.438002	+	0.269218i	0.0149793	+	0.00920706i
$856$	−39.0808	−	2.67296i	−1.33576	−	0.0913598i
$857$			3.79939i			0.129785i	0.997892	+	0.0648924i	$0.0206704\pi$
$857$			3.79939i			0.129785i	−0.997892	+	0.0648924i	$0.979330\pi$
$858$	−5.29104	+	8.70079i	−0.180633	+	0.297040i
$859$		−	33.2447i		−	1.13430i	−0.823616	−	0.567148i	$-0.808047\pi$
$859$		−	33.2447i		−	1.13430i	0.823616	−	0.567148i	$-0.191953\pi$
$860$	−46.2179	−	3.38222i	−1.57602	−	0.115333i
$861$			14.3754i			0.489911i
$862$	36.4536	+	22.1678i	1.24161	+	0.755038i
$863$	−14.8617			−0.505898			−0.252949	−	0.967480i	$-0.581400\pi$
$863$	−14.8617			−0.505898			−0.252949	+	0.967480i	$0.581400\pi$
$864$	26.3025	−	11.4251i	0.894829	−	0.388690i
$865$	10.7319	−	17.4603i	0.364897	−	0.593666i
$866$	10.1438	+	6.16858i	0.344702	+	0.209617i
$867$	12.6232			0.428705
$868$	−0.334783	−	0.646095i	−0.0113633	−	0.0219299i
$869$	−29.6337			−1.00525
$870$	10.0152	+	19.5555i	0.339546	+	0.662994i
$871$	7.69367			0.260690
$872$	−34.6101	−	2.36718i	−1.17205	−	0.0801627i
$873$	−1.01251			−0.0342683
$874$	1.32655	−	11.1805i	0.0448711	−	0.378186i
$875$	14.2417	+	1.17862i	0.481456	+	0.0398445i
$876$	41.9950	−	21.7603i	1.41888	−	0.735212i
$877$			11.1811i			0.377558i	0.982020	+	0.188779i	$0.0604529\pi$
$877$			11.1811i			0.377558i	−0.982020	+	0.188779i	$0.939547\pi$
$878$	−10.1655	+	16.7165i	−0.343069	+	0.564155i
$879$	13.1662			0.444084
$880$	−16.5035	+	7.07548i	−0.556332	+	0.238514i
$881$		−	46.4474i		−	1.56485i	−0.622743	−	0.782426i	$-0.713982\pi$
$881$		−	46.4474i		−	1.56485i	0.622743	−	0.782426i	$-0.286018\pi$
$882$	−0.898104	−	0.546147i	−0.0302407	−	0.0183897i
$883$	16.7375			0.563262			0.281631	−	0.959523i	$-0.409125\pi$
$883$	16.7375			0.563262			0.281631	+	0.959523i	$0.409125\pi$
$884$	11.2976	−	5.85401i	0.379980	−	0.196892i
$885$	−0.845670	+	1.37586i	−0.0284269	+	0.0462489i
$886$	−5.00471	−	3.04342i	−0.168137	−	0.102246i
$887$	42.1114			1.41396			0.706981	−	0.707232i	$-0.250056\pi$
$887$	42.1114			1.41396			0.706981	+	0.707232i	$0.250056\pi$
$888$	1.55893	−	22.7929i	0.0523144	−	0.764880i
$889$		−	0.949997i		−	0.0318619i
$890$	35.8274	−	18.3486i	1.20094	−	0.615048i
$891$	−18.8638			−0.631961
$892$	13.7072	+	26.4534i	0.458951	+	0.885726i
$893$	11.9142			0.398693
$894$	28.0533	−	46.1319i	0.938244	−	1.54288i
$895$	4.38047	−	7.12676i	0.146423	−	0.238221i
$896$	9.12588	−	11.2175i	0.304874	−	0.374752i
$897$	15.6479	−	7.14365i	0.522470	−	0.238520i
$898$	45.6924	+	27.7860i	1.52478	+	0.927232i
$899$		−	1.11638i		−	0.0372332i
$900$	−0.809459	+	1.12390i	−0.0269820	+	0.0374632i
$901$	−28.6340			−0.953937
$902$	−15.4002	−	9.36505i	−0.512772	−	0.311822i
$903$	−23.4641			−0.780837
$904$	2.93244	−	42.8746i	0.0975314	−	1.42599i
$905$	−28.1652	+	45.8232i	−0.936243	+	1.52321i
$906$	9.25092	−	15.2126i	0.307341	−	0.505403i
$907$		−	34.7744i		−	1.15466i	−0.816509	−	0.577332i	$-0.804094\pi$
$907$		−	34.7744i		−	1.15466i	0.816509	−	0.577332i	$-0.195906\pi$
$908$	−29.0038	+	15.0287i	−0.962525	+	0.498745i
$909$	0.402959			0.0133653
$910$	−3.73024	−	7.28364i	−0.123656	−	0.241450i
$911$	25.7678			0.853724			0.426862	−	0.904317i	$-0.359619\pi$
$911$	25.7678			0.853724			0.426862	+	0.904317i	$0.359619\pi$
$912$	6.78373	−	9.61053i	0.224632	−	0.318236i
$913$		−	2.36282i		−	0.0781979i
$914$	15.4895	+	9.41931i	0.512346	+	0.311563i
$915$	2.73598	−	4.45129i	0.0904488	−	0.147155i
$916$	4.26972	−	2.21241i	0.141076	−	0.0731002i
$917$	−4.65604			−0.153756
$918$	19.2487	+	11.7053i	0.635302	+	0.386334i
$919$	22.1371			0.730237			0.365119	−	0.930961i	$-0.381028\pi$
$919$	22.1371			0.730237			0.365119	+	0.930961i	$0.381028\pi$
$920$	29.7791	+	5.76250i	0.981787	+	0.189984i
$921$	−36.7472			−1.21086
$922$	10.0879	+	6.13457i	0.332228	+	0.202031i
$923$	−15.2132			−0.500747
$924$	−8.07246	+	4.18285i	−0.265564	+	0.137606i
$925$	−10.2950	−	20.3400i	−0.338497	−	0.668774i
$926$	−25.1366	−	15.2859i	−0.826041	−	0.502325i
$927$		−	0.569991i		−	0.0187210i
$928$	20.3484	−	8.83880i	0.667968	−	0.290148i
$929$	−39.8417			−1.30717			−0.653583	−	0.756855i	$-0.726735\pi$
$929$	−39.8417			−1.30717			−0.653583	+	0.756855i	$0.726735\pi$
$930$	1.41940	−	0.726932i	0.0465440	−	0.0238371i
$931$	8.90823			0.291955
$932$	24.4277	−	12.6575i	0.800156	−	0.414612i
$933$		−	24.9080i		−	0.815452i
$934$	−28.5078	+	46.8793i	−0.932804	+	1.53394i
$935$	−12.0178	−	7.38673i	−0.393023	−	0.241572i
$936$	0.791293	+	0.0541209i	0.0258642	+	0.00176900i
$937$	34.8765			1.13937			0.569683	−	0.821865i	$-0.307066\pi$
$937$	34.8765			1.13937			0.569683	+	0.821865i	$0.307066\pi$
$938$	5.86905	+	3.56903i	0.191631	+	0.116533i
$939$	38.6409			1.26100
$940$	−2.34257	+	32.0112i	−0.0764064	+	1.04409i
$941$		−	35.7740i		−	1.16620i	−0.812400	−	0.583100i	$-0.801840\pi$
$941$		−	35.7740i		−	1.16620i	0.812400	−	0.583100i	$-0.198160\pi$
$942$	−40.6809	−	24.7385i	−1.32545	−	0.806023i
$943$	12.6441	+	27.6966i	0.411750	+	0.901925i
$944$	1.33225	+	0.940391i	0.0433612	+	0.0306071i
$945$	7.58687	−	12.3434i	0.246801	−	0.401531i
$946$	15.2860	−	25.1369i	0.496992	−	0.817272i
$947$	39.1911			1.27354			0.636770	−	0.771054i	$-0.280270\pi$
$947$	39.1911			1.27354			0.636770	+	0.771054i	$0.280270\pi$
$948$	24.0618	+	46.4368i	0.781492	+	1.50820i
$949$	−27.0265			−0.877318
$950$	0.912428	−	11.7027i	0.0296031	−	0.379686i
$951$		−	37.1482i		−	1.20461i
$952$	11.3339	+	0.775190i	0.367334	+	0.0251240i
$953$	45.4643			1.47273			0.736366	−	0.676583i	$-0.236540\pi$
$953$	45.4643			1.47273			0.736366	+	0.676583i	$0.236540\pi$
$954$	−1.52501	−	0.927377i	−0.0493742	−	0.0300250i
$955$	−23.3355	−	14.3432i	−0.755119	−	0.464134i
$956$	−48.7726	+	25.2722i	−1.57742	+	0.817361i
$957$	−13.9482			−0.450882
$958$	−5.23207	−	3.18168i	−0.169041	−	0.102795i
$959$			1.27330i			0.0411170i
$960$	24.4879	+	20.1163i	0.790344	+	0.649250i
$961$	30.9190			0.997386
$962$	−6.78290	+	11.1541i	−0.218690	+	0.359621i
$963$		−	1.91822i		−	0.0618138i
$964$	23.5882	−	12.2225i	0.759724	−	0.393661i
$965$	2.41407	−	3.92755i	0.0777116	−	0.126432i
$966$	15.2508	+	1.80948i	0.490686	+	0.0582191i
$967$	−48.2956			−1.55308			−0.776541	−	0.630067i	$-0.783028\pi$
$967$	−48.2956			−1.55308			−0.776541	+	0.630067i	$0.783028\pi$
$968$	−1.34515	+	19.6672i	−0.0432348	+	0.632129i
$969$	9.24144			0.296878
$970$	10.5376	+	20.5757i	0.338343	+	0.660645i
$971$	15.4880			0.497032			0.248516	−	0.968628i	$-0.420057\pi$
$971$	15.4880			0.497032			0.248516	+	0.968628i	$0.420057\pi$
$972$	1.32339	+	2.55400i	0.0424478	+	0.0819197i
$973$	−14.6871			−0.470846
$974$	−29.5170	−	17.9496i	−0.945784	−	0.575142i
$975$	16.0009	−	8.09879i	0.512439	−	0.259369i
$976$	−4.31022	−	3.04244i	−0.137967	−	0.0973860i
$977$	−53.6843			−1.71751			−0.858756	−	0.512385i	$-0.828762\pi$
$977$	−53.6843			−1.71751			−0.858756	+	0.512385i	$0.828762\pi$
$978$	−7.81348	−	4.75146i	−0.249847	−	0.151935i
$979$			25.5544i			0.816721i
$980$	−1.75154	+	23.9348i	−0.0559509	+	0.764568i
$981$		−	1.69878i		−	0.0542379i
$982$	−20.5201	+	33.7440i	−0.654821	+	1.07681i
$983$			10.7086i			0.341550i	0.985310	+	0.170775i	$0.0546271\pi$
$983$			10.7086i			0.341550i	−0.985310	+	0.170775i	$0.945373\pi$
$984$	−2.17066	+	31.7368i	−0.0691980	+	1.01173i
$985$	27.9889	−	45.5363i	0.891800	−	1.45091i
$986$	14.8914	+	9.05560i	0.474238	+	0.288389i
$987$			16.2516i			0.517294i
$988$	−5.96819	+	3.09250i	−0.189874	+	0.0983855i
$989$	−45.2076	+	20.6383i	−1.43752	+	0.656260i
$990$	−0.400817	−	0.782632i	−0.0127388	−	0.0248737i
$991$		−	51.1415i		−	1.62456i	−0.583266	−	0.812282i	$-0.698225\pi$
$991$		−	51.1415i		−	1.62456i	0.583266	−	0.812282i	$-0.301775\pi$
$992$	−0.641548	−	1.47695i	−0.0203692	−	0.0468932i
$993$			57.9951i			1.84042i
$994$	−11.6052	−	7.05727i	−0.368096	−	0.223843i
$995$	−9.16605	−	5.63392i	−0.290583	−	0.178607i
$996$	−3.70260	+	1.91855i	−0.117321	+	0.0607917i
$997$		−	44.5820i		−	1.41193i	−0.708249	−	0.705963i	$-0.750514\pi$
$997$		−	44.5820i		−	1.41193i	0.708249	−	0.705963i	$-0.249486\pi$
$998$	−22.8826	+	37.6291i	−0.724337	+	1.19113i
$999$	−23.1133			−0.731271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.g.c.459.10	yes	56
4.3	odd	2	inner	460.2.g.c.459.46	yes	56
5.4	even	2	inner	460.2.g.c.459.47	yes	56
20.19	odd	2	inner	460.2.g.c.459.11	yes	56
23.22	odd	2	inner	460.2.g.c.459.9	✓	56
92.91	even	2	inner	460.2.g.c.459.45	yes	56
115.114	odd	2	inner	460.2.g.c.459.48	yes	56
460.459	even	2	inner	460.2.g.c.459.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.g.c.459.9	✓	56	23.22	odd	2	inner
460.2.g.c.459.10	yes	56	1.1	even	1	trivial
460.2.g.c.459.11	yes	56	20.19	odd	2	inner
460.2.g.c.459.12	yes	56	460.459	even	2	inner
460.2.g.c.459.45	yes	56	92.91	even	2	inner
460.2.g.c.459.46	yes	56	4.3	odd	2	inner
460.2.g.c.459.47	yes	56	5.4	even	2	inner
460.2.g.c.459.48	yes	56	115.114	odd	2	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20833 - 0.734800i) q^{2} -1.77158 q^{3} +(0.920137 + 1.77577i) q^{4} +(1.90499 + 1.17090i) q^{5} +(2.14066 + 1.30176i) q^{6} -1.27817i q^{7} +(0.193001 - 2.82183i) q^{8} +0.138505 q^{9} +O(q^{10})\)	\(q+(-1.20833 - 0.734800i) q^{2} -1.77158 q^{3} +(0.920137 + 1.77577i) q^{4} +(1.90499 + 1.17090i) q^{5} +(2.14066 + 1.30176i) q^{6} -1.27817i q^{7} +(0.193001 - 2.82183i) q^{8} +0.138505 q^{9} +(-1.44148 - 2.81463i) q^{10} +2.00757 q^{11} +(-1.63010 - 3.14592i) q^{12} +2.02460i q^{13} +(-0.939197 + 1.54445i) q^{14} +(-3.37485 - 2.07435i) q^{15} +(-2.30669 + 3.26790i) q^{16} -3.14239 q^{17} +(-0.167360 - 0.101774i) q^{18} +1.66004 q^{19} +(-0.326397 + 4.46021i) q^{20} +2.26438i q^{21} +(-2.42581 - 1.47516i) q^{22} +(1.99168 + 4.36271i) q^{23} +(-0.341917 + 4.99911i) q^{24} +(2.25797 + 4.46112i) q^{25} +(1.48768 - 2.44639i) q^{26} +5.06937 q^{27} +(2.26973 - 1.17609i) q^{28} +3.92182 q^{29} +(2.55371 + 4.98634i) q^{30} -0.284658i q^{31} +(5.18851 - 2.25375i) q^{32} -3.55658 q^{33} +(3.79706 + 2.30903i) q^{34} +(1.49661 - 2.43490i) q^{35} +(0.127444 + 0.245953i) q^{36} -4.55939 q^{37} +(-2.00588 - 1.21979i) q^{38} -3.58675i q^{39} +(3.67176 - 5.14958i) q^{40} +6.34849 q^{41} +(1.66387 - 2.73612i) q^{42} +10.3623i q^{43} +(1.84724 + 3.56498i) q^{44} +(0.263851 + 0.162176i) q^{45} +(0.799107 - 6.73509i) q^{46} +7.17707 q^{47} +(4.08650 - 5.78935i) q^{48} +5.36629 q^{49} +(0.549644 - 7.04967i) q^{50} +5.56701 q^{51} +(-3.59522 + 1.86291i) q^{52} +9.11216 q^{53} +(-6.12549 - 3.72498i) q^{54} +(3.82440 + 2.35067i) q^{55} +(-3.60678 - 0.246688i) q^{56} -2.94089 q^{57} +(-4.73886 - 2.88175i) q^{58} -0.407679i q^{59} +(0.578239 - 7.90163i) q^{60} +1.31896i q^{61} +(-0.209167 + 0.343961i) q^{62} -0.177033i q^{63} +(-7.92550 - 1.08923i) q^{64} +(-2.37061 + 3.85685i) q^{65} +(4.29753 + 2.61337i) q^{66} -3.80009i q^{67} +(-2.89144 - 5.58016i) q^{68} +(-3.52842 - 7.72890i) q^{69} +(-3.59756 + 1.84246i) q^{70} +7.51415i q^{71} +(0.0267316 - 0.390839i) q^{72} +13.3491i q^{73} +(5.50926 + 3.35024i) q^{74} +(-4.00019 - 7.90324i) q^{75} +(1.52746 + 2.94784i) q^{76} -2.56601i q^{77} +(-2.63554 + 4.33399i) q^{78} -14.7610 q^{79} +(-8.22062 + 3.52440i) q^{80} -9.39633 q^{81} +(-7.67108 - 4.66487i) q^{82} -1.17696i q^{83} +(-4.02101 + 2.08354i) q^{84} +(-5.98623 - 3.67944i) q^{85} +(7.61420 - 12.5211i) q^{86} -6.94782 q^{87} +(0.387463 - 5.66503i) q^{88} +12.7290i q^{89} +(-0.199653 - 0.389840i) q^{90} +2.58778 q^{91} +(-5.91453 + 7.55105i) q^{92} +0.504295i q^{93} +(-8.67229 - 5.27371i) q^{94} +(3.16235 + 1.94374i) q^{95} +(-9.19187 + 3.99271i) q^{96} -7.31027 q^{97} +(-6.48426 - 3.94315i) q^{98} +0.278059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \) 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9	\( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 8 q^{16} - 100 q^{24} - 24 q^{25} - 24 q^{26} - 16 q^{29} + 104 q^{41} - 8 q^{46} + 32 q^{49} - 32 q^{50} + 52 q^{54} - 92 q^{64} + 32 q^{69} - 44 q^{70} + 24 q^{81} + 56 q^{85} + 28 q^{94} + 88 q^{96}+O(q^{100}) \) 56 * q - 8 * q^4 - 8 * q^6 + 16 * q^9 - 8 * q^16 - 100 * q^24 - 24 * q^25 - 24 * q^26 - 16 * q^29 + 104 * q^41 - 8 * q^46 + 32 * q^49 - 32 * q^50 + 52 * q^54 - 92 * q^64 + 32 * q^69 - 44 * q^70 + 24 * q^81 + 56 * q^85 + 28 * q^94 + 88 * q^96

Introduction

L-functions

Modular forms

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