LMFDB - Embedded newform 325.2.k.d.268.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(57,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("325.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.k (of order $4$, degree $2$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 111x^{12} + 329x^{8} + 168x^{4} + 16 $ x^16 + 111x^12 + 329x^8 + 168*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			268.8
Root			$0.419746 - 0.419746i$ of defining polynomial
Character	$\chi$	$=$	325.268
Dual form			325.2.k.d.57.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38239 q^{2} +(0.648130 + 0.648130i) q^{3} +3.67579 q^{4} +(1.54410 + 1.54410i) q^{6} -2.38239i q^{7} +3.99239 q^{8} -2.15985i q^{9} +O(q^{10})$	\(q+2.38239 q^{2} +(0.648130 + 0.648130i) q^{3} +3.67579 q^{4} +(1.54410 + 1.54410i) q^{6} -2.38239i q^{7} +3.99239 q^{8} -2.15985i q^{9} +(-3.88966 + 3.88966i) q^{11} +(2.38239 + 2.38239i) q^{12} +(-2.31088 + 2.76764i) q^{13} -5.67579i q^{14} +2.15985 q^{16} +(-0.262878 - 0.262878i) q^{17} -5.14562i q^{18} +(-0.587589 + 0.587589i) q^{19} +(1.54410 - 1.54410i) q^{21} +(-9.26669 + 9.26669i) q^{22} +(1.98090 - 1.98090i) q^{23} +(2.58759 + 2.58759i) q^{24} +(-5.50541 + 6.59361i) q^{26} +(3.34426 - 3.34426i) q^{27} -8.75717i q^{28} +7.92385i q^{29} +(6.59361 + 6.59361i) q^{31} -2.83916 q^{32} -5.04201 q^{33} +(-0.626279 - 0.626279i) q^{34} -7.93917i q^{36} -10.3366i q^{37} +(-1.39987 + 1.39987i) q^{38} +(-3.29154 + 0.296046i) q^{39} +(-6.37974 - 6.37974i) q^{41} +(3.67865 - 3.67865i) q^{42} +(3.09762 - 3.09762i) q^{43} +(-14.2976 + 14.2976i) q^{44} +(4.71928 - 4.71928i) q^{46} -5.67137i q^{47} +(1.39987 + 1.39987i) q^{48} +1.32421 q^{49} -0.340759i q^{51} +(-8.49429 + 10.1733i) q^{52} +(-1.54732 - 1.54732i) q^{53} +(7.96733 - 7.96733i) q^{54} -9.51143i q^{56} -0.761669 q^{57} +18.8777i q^{58} +(5.49009 + 5.49009i) q^{59} +4.11885 q^{61} +(15.7086 + 15.7086i) q^{62} -5.14562 q^{63} -11.0837 q^{64} -12.0120 q^{66} -3.74764 q^{67} +(-0.966285 - 0.966285i) q^{68} +2.56776 q^{69} +(-2.04349 - 2.04349i) q^{71} -8.62298i q^{72} +7.56049 q^{73} -24.6258i q^{74} +(-2.15985 + 2.15985i) q^{76} +(9.26669 + 9.26669i) q^{77} +(-7.84175 + 0.705296i) q^{78} -6.07165i q^{79} -2.14453 q^{81} +(-15.1991 - 15.1991i) q^{82} +13.0415i q^{83} +(5.67579 - 5.67579i) q^{84} +(7.37974 - 7.37974i) q^{86} +(-5.13569 + 5.13569i) q^{87} +(-15.5290 + 15.5290i) q^{88} +(-2.23522 - 2.23522i) q^{89} +(6.59361 + 5.50541i) q^{91} +(7.28137 - 7.28137i) q^{92} +8.54704i q^{93} -13.5114i q^{94} +(-1.84015 - 1.84015i) q^{96} +1.88723 q^{97} +3.15479 q^{98} +(8.40109 + 8.40109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{6}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^6	$ 16 q + 8 q^{4} + 12 q^{6} - 20 q^{11} - 8 q^{16} + 16 q^{19} + 12 q^{21} + 16 q^{24} - 16 q^{26} + 8 q^{31} - 44 q^{34} + 28 q^{39} + 4 q^{41} - 76 q^{44} + 12 q^{46} + 72 q^{49} - 4 q^{54} + 24 q^{59} + 24 q^{61} - 16 q^{64} - 48 q^{66} - 112 q^{69} - 20 q^{71} + 8 q^{76} + 40 q^{84} + 12 q^{86} + 36 q^{89} + 8 q^{91} - 72 q^{96} - 52 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^6 - 20 * q^11 - 8 * q^16 + 16 * q^19 + 12 * q^21 + 16 * q^24 - 16 * q^26 + 8 * q^31 - 44 * q^34 + 28 * q^39 + 4 * q^41 - 76 * q^44 + 12 * q^46 + 72 * q^49 - 4 * q^54 + 24 * q^59 + 24 * q^61 - 16 * q^64 - 48 * q^66 - 112 * q^69 - 20 * q^71 + 8 * q^76 + 40 * q^84 + 12 * q^86 + 36 * q^89 + 8 * q^91 - 72 * q^96 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.38239			1.68461			0.842303	−	0.539005i	$-0.181200\pi$
$2$	2.38239			1.68461			0.842303	+	0.539005i	$0.181200\pi$
$3$	0.648130	+	0.648130i	0.374198	+	0.374198i	0.869004	−	0.494805i	$-0.164761\pi$
$3$	0.648130	+	0.648130i	0.374198	+	0.374198i	−0.494805	+	0.869004i	$0.664761\pi$
$4$	3.67579			1.83790
$5$		0			0
$5$		0			0
$6$	1.54410	+	1.54410i	0.630376	+	0.630376i
$7$		−	2.38239i		−	0.900459i	−0.892913	−	0.450230i	$-0.851342\pi$
$7$		−	2.38239i		−	0.900459i	0.892913	−	0.450230i	$-0.148658\pi$
$8$	3.99239			1.41152
$9$		−	2.15985i		−	0.719951i
$10$		0			0
$11$	−3.88966	+	3.88966i	−1.17278	+	1.17278i	−0.191231	+	0.981545i	$0.561248\pi$
$11$	−3.88966	+	3.88966i	−1.17278	+	1.17278i	−0.981545	+	0.191231i	$0.938752\pi$
$12$	2.38239	+	2.38239i	0.687737	+	0.687737i
$13$	−2.31088	+	2.76764i	−0.640922	+	0.767606i
$13$	−2.31088	+	2.76764i	−0.640922	+	0.767606i
$14$		−	5.67579i		−	1.51692i
$15$		0			0
$16$	2.15985			0.539963
$17$	−0.262878	−	0.262878i	−0.0637573	−	0.0637573i	0.674509	−	0.738266i	$-0.264355\pi$
$17$	−0.262878	−	0.262878i	−0.0637573	−	0.0637573i	−0.738266	+	0.674509i	$0.764355\pi$
$18$		−	5.14562i		−	1.21283i
$19$	−0.587589	+	0.587589i	−0.134802	+	0.134802i	−0.771288	−	0.636486i	$-0.780387\pi$
$19$	−0.587589	+	0.587589i	−0.134802	+	0.134802i	0.636486	+	0.771288i	$0.280387\pi$
$20$		0			0
$21$	1.54410	−	1.54410i	0.336950	−	0.336950i
$22$	−9.26669	+	9.26669i	−1.97566	+	1.97566i
$23$	1.98090	−	1.98090i	0.413046	−	0.413046i	−0.469752	−	0.882798i	$-0.655657\pi$
$23$	1.98090	−	1.98090i	0.413046	−	0.413046i	0.882798	+	0.469752i	$0.155657\pi$
$24$	2.58759	+	2.58759i	0.528189	+	0.528189i
$25$		0			0
$26$	−5.50541	+	6.59361i	−1.07970	+	1.29311i
$27$	3.34426	−	3.34426i	0.643603	−	0.643603i
$28$		−	8.75717i		−	1.65495i
$29$			7.92385i			1.47142i	0.677296	+	0.735711i	$0.263152\pi$
$29$			7.92385i			1.47142i	−0.677296	+	0.735711i	$0.736848\pi$
$30$		0			0
$31$	6.59361	+	6.59361i	1.18425	+	1.18425i	0.978633	+	0.205615i	$0.0659194\pi$
$31$	6.59361	+	6.59361i	1.18425	+	1.18425i	0.205615	+	0.978633i	$0.434081\pi$
$32$	−2.83916			−0.501897
$33$	−5.04201			−0.877702
$34$	−0.626279	−	0.626279i	−0.107406	−	0.107406i
$35$		0			0
$36$		−	7.93917i		−	1.32319i
$37$		−	10.3366i		−	1.69932i	−0.527328	−	0.849662i	$-0.676806\pi$
$37$		−	10.3366i		−	1.69932i	0.527328	−	0.849662i	$-0.323194\pi$
$38$	−1.39987	+	1.39987i	−0.227088	+	0.227088i
$39$	−3.29154	+	0.296046i	−0.527069	+	0.0474052i
$40$		0			0
$41$	−6.37974	−	6.37974i	−0.996349	−	0.996349i	0.00364462	−	0.999993i	$-0.498840\pi$
$41$	−6.37974	−	6.37974i	−0.996349	−	0.996349i	−0.999993	+	0.00364462i	$0.998840\pi$
$42$	3.67865	−	3.67865i	0.567628	−	0.567628i
$43$	3.09762	−	3.09762i	0.472383	−	0.472383i	−0.430302	−	0.902685i	$-0.641593\pi$
$43$	3.09762	−	3.09762i	0.472383	−	0.472383i	0.902685	+	0.430302i	$0.141593\pi$
$44$	−14.2976	+	14.2976i	−2.15544	+	2.15544i
$45$		0			0
$46$	4.71928	−	4.71928i	0.695820	−	0.695820i
$47$		−	5.67137i		−	0.827255i	−0.910446	−	0.413627i	$-0.864262\pi$
$47$		−	5.67137i		−	0.827255i	0.910446	−	0.413627i	$-0.135738\pi$
$48$	1.39987	+	1.39987i	0.202053	+	0.202053i
$49$	1.32421			0.189173
$50$		0			0
$51$		−	0.340759i		−	0.0477158i
$52$	−8.49429	+	10.1733i	−1.17795	+	1.41078i
$53$	−1.54732	−	1.54732i	−0.212540	−	0.212540i	0.592805	−	0.805346i	$-0.298020\pi$
$53$	−1.54732	−	1.54732i	−0.212540	−	0.212540i	−0.805346	+	0.592805i	$0.798020\pi$
$54$	7.96733	−	7.96733i	1.08422	−	1.08422i
$55$		0			0
$56$		−	9.51143i		−	1.27102i
$57$	−0.761669			−0.100885
$58$			18.8777i			2.47876i
$59$	5.49009	+	5.49009i	0.714748	+	0.714748i	0.967525	−	0.252776i	$-0.0813437\pi$
$59$	5.49009	+	5.49009i	0.714748	+	0.714748i	−0.252776	+	0.967525i	$0.581344\pi$
$60$		0			0
$61$	4.11885			0.527365			0.263682	−	0.964610i	$-0.415063\pi$
$61$	4.11885			0.527365			0.263682	+	0.964610i	$0.415063\pi$
$62$	15.7086	+	15.7086i	1.99499	+	1.99499i
$63$	−5.14562			−0.648287
$64$	−11.0837			−1.38546
$65$		0			0
$66$	−12.0120			−1.47858
$67$	−3.74764			−0.457847			−0.228924	−	0.973444i	$-0.573521\pi$
$67$	−3.74764			−0.457847			−0.228924	+	0.973444i	$0.573521\pi$
$68$	−0.966285	−	0.966285i	−0.117179	−	0.117179i
$69$	2.56776			0.309122
$70$		0			0
$71$	−2.04349	−	2.04349i	−0.242517	−	0.242517i	0.575373	−	0.817891i	$-0.304857\pi$
$71$	−2.04349	−	2.04349i	−0.242517	−	0.242517i	−0.817891	+	0.575373i	$0.804857\pi$
$72$		−	8.62298i		−	1.01623i
$73$	7.56049			0.884888			0.442444	−	0.896796i	$-0.354111\pi$
$73$	7.56049			0.884888			0.442444	+	0.896796i	$0.354111\pi$
$74$		−	24.6258i		−	2.86269i
$75$		0			0
$76$	−2.15985	+	2.15985i	−0.247752	+	0.247752i
$77$	9.26669	+	9.26669i	1.05604	+	1.05604i
$78$	−7.84175	+	0.705296i	−0.887903	+	0.0798591i
$79$		−	6.07165i		−	0.683114i	−0.939861	−	0.341557i	$-0.889046\pi$
$79$		−	6.07165i		−	0.683114i	0.939861	−	0.341557i	$-0.110954\pi$
$80$		0			0
$81$	−2.14453			−0.238281
$82$	−15.1991	−	15.1991i	−1.67845	−	1.67845i
$83$			13.0415i			1.43150i	0.698359	+	0.715748i	$0.253914\pi$
$83$			13.0415i			1.43150i	−0.698359	+	0.715748i	$0.746086\pi$
$84$	5.67579	−	5.67579i	0.619279	−	0.619279i
$85$		0			0
$86$	7.37974	−	7.37974i	0.795778	−	0.795778i
$87$	−5.13569	+	5.13569i	−0.550603	+	0.550603i
$88$	−15.5290	+	15.5290i	−1.65540	+	1.65540i
$89$	−2.23522	−	2.23522i	−0.236932	−	0.236932i	0.578646	−	0.815579i	$-0.303581\pi$
$89$	−2.23522	−	2.23522i	−0.236932	−	0.236932i	−0.815579	+	0.578646i	$0.803581\pi$
$90$		0			0
$91$	6.59361	+	5.50541i	0.691198	+	0.577124i
$92$	7.28137	−	7.28137i	0.759135	−	0.759135i
$93$			8.54704i			0.886287i
$94$		−	13.5114i		−	1.39360i
$95$		0			0
$96$	−1.84015	−	1.84015i	−0.187809	−	0.187809i
$97$	1.88723			0.191619			0.0958094	−	0.995400i	$-0.469456\pi$
$97$	1.88723			0.191619			0.0958094	+	0.995400i	$0.469456\pi$
$98$	3.15479			0.318682
$99$	8.40109	+	8.40109i	0.844342	+	0.844342i
$100$		0			0
$101$			6.40791i			0.637611i	0.947820	+	0.318805i	$0.103282\pi$
$101$			6.40791i			0.637611i	−0.947820	+	0.318805i	$0.896718\pi$
$102$		−	0.811821i		−	0.0803822i
$103$	6.56425	−	6.56425i	0.646795	−	0.646795i	−0.305422	−	0.952217i	$-0.598798\pi$
$103$	6.56425	−	6.56425i	0.646795	−	0.646795i	0.952217	+	0.305422i	$0.0987975\pi$
$104$	−9.22591	+	11.0495i	−0.904675	+	1.08349i
$105$		0			0
$106$	−3.68632	−	3.68632i	−0.358047	−	0.358047i
$107$	1.34459	−	1.34459i	0.129987	−	0.129987i	−0.639120	−	0.769107i	$-0.720701\pi$
$107$	1.34459	−	1.34459i	0.129987	−	0.129987i	0.769107	+	0.639120i	$0.220701\pi$
$108$	12.2928	−	12.2928i	1.18287	−	1.18287i
$109$	−11.7474	+	11.7474i	−1.12520	+	1.12520i	−0.134254	+	0.990947i	$0.542864\pi$
$109$	−11.7474	+	11.7474i	−1.12520	+	1.12520i	−0.990947	+	0.134254i	$0.957136\pi$
$110$		0			0
$111$	6.69945	−	6.69945i	0.635884	−	0.635884i
$112$		−	5.14562i		−	0.486215i
$113$	−0.581032	−	0.581032i	−0.0546589	−	0.0546589i	0.679249	−	0.733908i	$-0.262306\pi$
$113$	−0.581032	−	0.581032i	−0.0546589	−	0.0546589i	−0.733908	+	0.679249i	$0.762306\pi$
$114$	−1.81459			−0.169952
$115$		0			0
$116$			29.1264i			2.70432i
$117$	5.97771	+	4.99115i	0.552639	+	0.461432i
$118$	13.0795	+	13.0795i	1.20407	+	1.20407i
$119$	−0.626279	+	0.626279i	−0.0574109	+	0.0574109i
$120$		0			0
$121$		−	19.2589i		−	1.75081i
$122$	9.81271			0.888401
$123$		−	8.26981i		−	0.745664i
$124$	24.2367	+	24.2367i	2.17652	+	2.17652i
$125$		0			0
$126$	−12.2589			−1.09211
$127$	4.56648	+	4.56648i	0.405209	+	0.405209i	0.880064	−	0.474855i	$-0.157499\pi$
$127$	4.56648	+	4.56648i	0.405209	+	0.405209i	−0.474855	+	0.880064i	$0.657499\pi$
$128$	−20.7274			−1.83206
$129$	4.01532			0.353530
$130$		0			0
$131$	14.9085			1.30256			0.651282	−	0.758836i	$-0.274232\pi$
$131$	14.9085			1.30256			0.651282	+	0.758836i	$0.274232\pi$
$132$	−18.5334			−1.61312
$133$	1.39987	+	1.39987i	0.121384	+	0.121384i
$134$	−8.92835			−0.771292
$135$		0			0
$136$	−1.04951	−	1.04951i	−0.0899949	−	0.0899949i
$137$		−	9.21583i		−	0.787362i	−0.919247	−	0.393681i	$-0.871202\pi$
$137$		−	9.21583i		−	0.787362i	0.919247	−	0.393681i	$-0.128798\pi$
$138$	6.11742			0.520749
$139$		−	5.87665i		−	0.498451i	−0.968446	−	0.249225i	$-0.919824\pi$
$139$		−	5.87665i		−	0.498451i	0.968446	−	0.249225i	$-0.0801760\pi$
$140$		0			0
$141$	3.67579	−	3.67579i	0.309557	−	0.309557i
$142$	−4.86839	−	4.86839i	−0.408546	−	0.408546i
$143$	−1.77667	−	19.7537i	−0.148573	−	1.65189i
$144$		−	4.66497i		−	0.388747i
$145$		0			0
$146$	18.0120			1.49069
$147$	0.858261	+	0.858261i	0.0707881	+	0.0707881i
$148$		−	37.9951i		−	3.12318i
$149$	−5.89568	+	5.89568i	−0.482993	+	0.482993i	−0.906086	−	0.423093i	$-0.860944\pi$
$149$	−5.89568	+	5.89568i	−0.482993	+	0.482993i	0.423093	+	0.906086i	$0.360944\pi$
$150$		0			0
$151$	−12.9452	+	12.9452i	−1.05346	+	1.05346i	−0.0549773	+	0.998488i	$0.517509\pi$
$151$	−12.9452	+	12.9452i	−1.05346	+	1.05346i	−0.998488	+	0.0549773i	$0.982491\pi$
$152$	−2.34588	+	2.34588i	−0.190276	+	0.190276i
$153$	−0.567778	+	0.567778i	−0.0459022	+	0.0459022i
$154$	22.0769	+	22.0769i	1.77901	+	1.77901i
$155$		0			0
$156$	−12.0990	+	1.08820i	−0.968697	+	0.0871258i
$157$	−13.8195	+	13.8195i	−1.10291	+	1.10291i	−0.108855	+	0.994058i	$0.534718\pi$
$157$	−13.8195	+	13.8195i	−1.10291	+	1.10291i	−0.994058	+	0.108855i	$0.965282\pi$
$158$		−	14.4651i		−	1.15078i
$159$		−	2.00573i		−	0.159064i
$160$		0			0
$161$	−4.71928	−	4.71928i	−0.371931	−	0.371931i
$162$	−5.10911			−0.401410
$163$	−3.80590			−0.298101			−0.149051	−	0.988830i	$-0.547622\pi$
$163$	−3.80590			−0.298101			−0.149051	+	0.988830i	$0.547622\pi$
$164$	−23.4506	−	23.4506i	−1.83118	−	1.83118i
$165$		0			0
$166$			31.0701i			2.41150i
$167$			18.2483i			1.41210i	0.708162	+	0.706050i	$0.249524\pi$
$167$			18.2483i			1.41210i	−0.708162	+	0.706050i	$0.750476\pi$
$168$	6.16465	−	6.16465i	0.475613	−	0.475613i
$169$	−2.31971	−	12.7914i	−0.178439	−	0.983951i
$170$		0			0
$171$	1.26911	+	1.26911i	0.0970510	+	0.0970510i
$172$	11.3862	−	11.3862i	0.868190	−	0.868190i
$173$	0.00740374	−	0.00740374i	0.000562896	−	0.000562896i	−0.706825	−	0.707388i	$-0.749873\pi$
$173$	0.00740374	−	0.00740374i	0.000562896	−	0.000562896i	0.707388	+	0.706825i	$0.249873\pi$
$174$	−12.2352	+	12.2352i	−0.927549	+	0.927549i
$175$		0			0
$176$	−8.40109	+	8.40109i	−0.633256	+	0.633256i
$177$			7.11659i			0.534915i
$178$	−5.32516	−	5.32516i	−0.399137	−	0.399137i
$179$	12.0717			0.902278			0.451139	−	0.892454i	$-0.351018\pi$
$179$	12.0717			0.902278			0.451139	+	0.892454i	$0.351018\pi$
$180$		0			0
$181$		−	18.2589i		−	1.35717i	−0.734521	−	0.678586i	$-0.762593\pi$
$181$		−	18.2589i		−	1.35717i	0.734521	−	0.678586i	$-0.237407\pi$
$182$	15.7086	+	13.1160i	1.16440	+	0.972226i
$183$	2.66955	+	2.66955i	0.197339	+	0.197339i
$184$	7.90852	−	7.90852i	0.583024	−	0.583024i
$185$		0			0
$186$			20.3624i			1.49304i
$187$	2.04501			0.149546
$188$		−	20.8468i		−	1.52041i
$189$	−7.96733	−	7.96733i	−0.579538	−	0.579538i
$190$		0			0
$191$	−6.39878			−0.462999			−0.231500	−	0.972835i	$-0.574363\pi$
$191$	−6.39878			−0.462999			−0.231500	+	0.972835i	$0.574363\pi$
$192$	−7.18368	−	7.18368i	−0.518438	−	0.518438i
$193$	12.4812			0.898414			0.449207	−	0.893428i	$-0.351707\pi$
$193$	12.4812			0.898414			0.449207	+	0.893428i	$0.351707\pi$
$194$	4.49611			0.322802
$195$		0			0
$196$	4.86752			0.347680
$197$	−19.8948			−1.41745			−0.708725	−	0.705485i	$-0.750729\pi$
$197$	−19.8948			−1.41745			−0.708725	+	0.705485i	$0.750729\pi$
$198$	20.0147	+	20.0147i	1.42238	+	1.42238i
$199$	13.5740			0.962232			0.481116	−	0.876657i	$-0.340232\pi$
$199$	13.5740			0.962232			0.481116	+	0.876657i	$0.340232\pi$
$200$		0			0
$201$	−2.42896	−	2.42896i	−0.171326	−	0.171326i
$202$			15.2661i			1.07412i
$203$	18.8777			1.32496
$204$		−	1.25256i		−	0.0876966i
$205$		0			0
$206$	15.6386	−	15.6386i	1.08959	−	1.08959i
$207$	−4.27845	−	4.27845i	−0.297373	−	0.297373i
$208$	−4.99115	+	5.97771i	−0.346074	+	0.414479i
$209$		−	4.57104i		−	0.316185i
$210$		0			0
$211$	−10.6348			−0.732129			−0.366064	−	0.930590i	$-0.619295\pi$
$211$	−10.6348			−0.732129			−0.366064	+	0.930590i	$0.619295\pi$
$212$	−5.68761	−	5.68761i	−0.390627	−	0.390627i
$213$		−	2.64889i		−	0.181499i
$214$	3.20334	−	3.20334i	0.218976	−	0.218976i
$215$		0			0
$216$	13.3516	−	13.3516i	0.908460	−	0.908460i
$217$	15.7086	−	15.7086i	1.06637	−	1.06637i
$218$	−27.9870	+	27.9870i	−1.89552	+	1.89552i
$219$	4.90018	+	4.90018i	0.331124	+	0.331124i
$220$		0			0
$221$	1.33503	−	0.120074i	0.0898039	−	0.00807708i
$222$	15.9607	−	15.9607i	1.07121	−	1.07121i
$223$			10.1659i			0.680757i	0.940288	+	0.340379i	$0.110555\pi$
$223$			10.1659i			0.680757i	−0.940288	+	0.340379i	$0.889445\pi$
$224$			6.76399i			0.451938i
$225$		0			0
$226$	−1.38425	−	1.38425i	−0.0920787	−	0.0920787i
$227$	18.5876			1.23370			0.616852	−	0.787080i	$-0.288408\pi$
$227$	18.5876			1.23370			0.616852	+	0.787080i	$0.288408\pi$
$228$	−2.79973			−0.185417
$229$	−6.29605	−	6.29605i	−0.416054	−	0.416054i	0.467787	−	0.883841i	$-0.345051\pi$
$229$	−6.29605	−	6.29605i	−0.416054	−	0.416054i	−0.883841	+	0.467787i	$0.845051\pi$
$230$		0			0
$231$			12.0120i			0.790335i
$232$			31.6351i			2.07694i
$233$	−19.7706	+	19.7706i	−1.29521	+	1.29521i	−0.363696	+	0.931518i	$0.618485\pi$
$233$	−19.7706	+	19.7706i	−1.29521	+	1.29521i	−0.931518	+	0.363696i	$0.881515\pi$
$234$	14.2412	+	11.8909i	0.930979	+	0.777331i
$235$		0			0
$236$	20.1804	+	20.1804i	1.31363	+	1.31363i
$237$	3.93522	−	3.93522i	0.255620	−	0.255620i
$238$	−1.49204	+	1.49204i	−0.0967147	+	0.0967147i
$239$	10.0206	−	10.0206i	0.648176	−	0.648176i	−0.304376	−	0.952552i	$-0.598448\pi$
$239$	10.0206	−	10.0206i	0.648176	−	0.648176i	0.952552	+	0.304376i	$0.0984480\pi$
$240$		0			0
$241$	2.79586	−	2.79586i	0.180097	−	0.180097i	−0.611301	−	0.791398i	$-0.709353\pi$
$241$	2.79586	−	2.79586i	0.180097	−	0.180097i	0.791398	+	0.611301i	$0.209353\pi$
$242$		−	45.8822i		−	2.94942i
$243$	−11.4227	−	11.4227i	−0.732767	−	0.732767i
$244$	15.1400			0.969241
$245$		0			0
$246$		−	19.7019i		−	1.25615i
$247$	−0.268392	−	2.98408i	−0.0170774	−	0.189873i
$248$	26.3243	+	26.3243i	1.67159	+	1.67159i
$249$	−8.45262	+	8.45262i	−0.535663	+	0.535663i
$250$		0			0
$251$			22.3744i			1.41226i	0.708081	+	0.706131i	$0.249561\pi$
$251$			22.3744i			1.41226i	−0.708081	+	0.706131i	$0.750439\pi$
$252$	−18.9142			−1.19148
$253$			15.4100i			0.968821i
$254$	10.8791	+	10.8791i	0.682617	+	0.682617i
$255$		0			0
$256$	−27.2134			−1.70084
$257$	−1.41312	−	1.41312i	−0.0881481	−	0.0881481i	0.661658	−	0.749806i	$-0.269853\pi$
$257$	−1.41312	−	1.41312i	−0.0881481	−	0.0881481i	−0.749806	+	0.661658i	$0.769853\pi$
$258$	9.56607			0.595558
$259$	−24.6258			−1.53017
$260$		0			0
$261$	17.1143			1.05935
$262$	35.5179			2.19431
$263$	3.71113	+	3.71113i	0.228838	+	0.228838i	0.812207	−	0.583369i	$-0.198266\pi$
$263$	3.71113	+	3.71113i	0.228838	+	0.228838i	−0.583369	+	0.812207i	$0.698266\pi$
$264$	−20.1297			−1.23890
$265$		0			0
$266$	3.33503	+	3.33503i	0.204484	+	0.204484i
$267$		−	2.89742i		−	0.177319i
$268$	−13.7755			−0.841475
$269$		−	0.372632i		−	0.0227198i	−0.999935	−	0.0113599i	$-0.996384\pi$
$269$		−	0.372632i		−	0.0227198i	0.999935	−	0.0113599i	$-0.00361604\pi$
$270$		0			0
$271$	−3.10584	+	3.10584i	−0.188666	+	0.188666i	−0.795119	−	0.606453i	$-0.792592\pi$
$271$	−3.10584	+	3.10584i	−0.188666	+	0.188666i	0.606453	+	0.795119i	$0.292592\pi$
$272$	−0.567778	−	0.567778i	−0.0344266	−	0.0344266i
$273$	0.705296	+	7.84175i	0.0426865	+	0.474604i
$274$		−	21.9557i		−	1.32639i
$275$		0			0
$276$	9.43856			0.568134
$277$	−12.4546	−	12.4546i	−0.748324	−	0.748324i	0.225840	−	0.974164i	$-0.427487\pi$
$277$	−12.4546	−	12.4546i	−0.748324	−	0.748324i	−0.974164	+	0.225840i	$0.927487\pi$
$278$		−	14.0005i		−	0.839693i
$279$	14.2412	−	14.2412i	0.852601	−	0.852601i
$280$		0			0
$281$	−7.18924	+	7.18924i	−0.428874	+	0.428874i	−0.888245	−	0.459370i	$-0.848075\pi$
$281$	−7.18924	+	7.18924i	−0.428874	+	0.428874i	0.459370	+	0.888245i	$0.348075\pi$
$282$	8.75717	−	8.75717i	0.521482	−	0.521482i
$283$	21.6211	−	21.6211i	1.28524	−	1.28524i	0.347594	−	0.937645i	$-0.386999\pi$
$283$	21.6211	−	21.6211i	1.28524	−	1.28524i	0.937645	−	0.347594i	$-0.113001\pi$
$284$	−7.51143	−	7.51143i	−0.445722	−	0.445722i
$285$		0			0
$286$	−4.23273	−	47.0611i	−0.250287	−	2.78278i
$287$	−15.1991	+	15.1991i	−0.897172	+	0.897172i
$288$			6.13217i			0.361342i
$289$		−	16.8618i		−	0.991870i
$290$		0			0
$291$	1.22317	+	1.22317i	0.0717034	+	0.0717034i
$292$	27.7908			1.62633
$293$	−25.7477			−1.50419			−0.752097	−	0.659053i	$-0.770957\pi$
$293$	−25.7477			−1.50419			−0.752097	+	0.659053i	$0.770957\pi$
$294$	2.04471	+	2.04471i	0.119250	+	0.119250i
$295$		0			0
$296$		−	41.2676i		−	2.39863i
$297$			26.0160i			1.50960i
$298$	−14.0458	+	14.0458i	−0.813653	+	0.813653i
$299$	0.904812	+	10.0600i	0.0523267	+	0.581787i
$300$		0			0
$301$	−7.37974	−	7.37974i	−0.425361	−	0.425361i
$302$	−30.8405	+	30.8405i	−1.77467	+	1.77467i
$303$	−4.15316	+	4.15316i	−0.238593	+	0.238593i
$304$	−1.26911	+	1.26911i	−0.0727882	+	0.0727882i
$305$		0			0
$306$	−1.35267	+	1.35267i	−0.0773270	+	0.0773270i
$307$		−	1.82202i		−	0.103988i	−0.998647	−	0.0519940i	$-0.983442\pi$
$307$		−	1.82202i		−	0.103988i	0.998647	−	0.0519940i	$-0.0165577\pi$
$308$	34.0624	+	34.0624i	1.94089	+	1.94089i
$309$	8.50898			0.484059
$310$		0			0
$311$			7.73334i			0.438518i	0.975667	+	0.219259i	$0.0703639\pi$
$311$			7.73334i			0.438518i	−0.975667	+	0.219259i	$0.929636\pi$
$312$	−13.1411	+	1.18193i	−0.743970	+	0.0669136i
$313$	−13.6675	−	13.6675i	−0.772534	−	0.772534i	0.206015	−	0.978549i	$-0.433950\pi$
$313$	−13.6675	−	13.6675i	−0.772534	−	0.772534i	−0.978549	+	0.206015i	$0.933950\pi$
$314$	−32.9233	+	32.9233i	−1.85797	+	1.85797i
$315$		0			0
$316$		−	22.3181i		−	1.25549i
$317$	−14.3180			−0.804179			−0.402089	−	0.915600i	$-0.631716\pi$
$317$	−14.3180			−0.804179			−0.402089	+	0.915600i	$0.631716\pi$
$318$		−	4.77843i		−	0.267961i
$319$	−30.8210	−	30.8210i	−1.72565	−	1.72565i
$320$		0			0
$321$	1.74294			0.0972815
$322$	−11.2432	−	11.2432i	−0.626557	−	0.626557i
$323$	0.308929			0.0171892
$324$	−7.88284			−0.437936
$325$		0			0
$326$	−9.06715			−0.502183
$327$	−15.2278			−0.842097
$328$	−25.4704	−	25.4704i	−1.40637	−	1.40637i
$329$	−13.5114			−0.744909
$330$		0			0
$331$	−10.8440	−	10.8440i	−0.596039	−	0.596039i	0.343217	−	0.939256i	$-0.388483\pi$
$331$	−10.8440	−	10.8440i	−0.596039	−	0.596039i	−0.939256	+	0.343217i	$0.888483\pi$
$332$			47.9380i			2.63094i
$333$	−22.3255			−1.22343
$334$			43.4747i			2.37883i
$335$		0			0
$336$	3.33503	−	3.33503i	0.181941	−	0.181941i
$337$	−5.26248	−	5.26248i	−0.286665	−	0.286665i	0.549095	−	0.835760i	$-0.314973\pi$
$337$	−5.26248	−	5.26248i	−0.286665	−	0.286665i	−0.835760	+	0.549095i	$0.814973\pi$
$338$	−5.52645	−	30.4740i	−0.300599	−	1.65757i
$339$		−	0.753170i		−	0.0409066i
$340$		0			0
$341$	−51.2938			−2.77771
$342$	3.02351	+	3.02351i	0.163493	+	0.163493i
$343$		−	19.8315i		−	1.07080i
$344$	12.3669	−	12.3669i	0.666779	−	0.666779i
$345$		0			0
$346$	0.0176386	−	0.0176386i	0.000948257	−	0.000948257i
$347$	7.90775	−	7.90775i	0.424510	−	0.424510i	−0.462243	−	0.886753i	$-0.652955\pi$
$347$	7.90775	−	7.90775i	0.424510	−	0.424510i	0.886753	+	0.462243i	$0.152955\pi$
$348$	−18.8777	+	18.8777i	−1.01195	+	1.01195i
$349$	−1.59130	−	1.59130i	−0.0851802	−	0.0851802i	0.663233	−	0.748413i	$-0.269184\pi$
$349$	−1.59130	−	1.59130i	−0.0851802	−	0.0851802i	−0.748413	+	0.663233i	$0.769184\pi$
$350$		0			0
$351$	1.52755	+	16.9839i	0.0815347	+	0.906533i
$352$	11.0434	−	11.0434i	0.588613	−	0.588613i
$353$			19.3600i			1.03043i	0.857061	+	0.515215i	$0.172288\pi$
$353$			19.3600i			1.03043i	−0.857061	+	0.515215i	$0.827712\pi$
$354$			16.9545i			0.901121i
$355$		0			0
$356$	−8.21618	−	8.21618i	−0.435457	−	0.435457i
$357$	−0.811821			−0.0429661
$358$	28.7594			1.51998
$359$	3.46070	+	3.46070i	0.182649	+	0.182649i	0.792509	−	0.609860i	$-0.208774\pi$
$359$	3.46070	+	3.46070i	0.182649	+	0.182649i	−0.609860	+	0.792509i	$0.708774\pi$
$360$		0			0
$361$			18.3095i			0.963657i
$362$		−	43.4998i		−	2.28630i
$363$	12.4823	−	12.4823i	0.655149	−	0.655149i
$364$	24.2367	+	20.2367i	1.27035	+	1.06069i
$365$		0			0
$366$	6.35992	+	6.35992i	0.332438	+	0.332438i
$367$	7.68286	−	7.68286i	0.401042	−	0.401042i	−0.477558	−	0.878600i	$-0.658478\pi$
$367$	7.68286	−	7.68286i	0.401042	−	0.401042i	0.878600	+	0.477558i	$0.158478\pi$
$368$	4.27845	−	4.27845i	0.223030	−	0.223030i
$369$	−13.7793	+	13.7793i	−0.717323	+	0.717323i
$370$		0			0
$371$	−3.68632	+	3.68632i	−0.191384	+	0.191384i
$372$			31.4171i			1.62890i
$373$	−6.30515	−	6.30515i	−0.326469	−	0.326469i	0.524773	−	0.851242i	$-0.324150\pi$
$373$	−6.30515	−	6.30515i	−0.326469	−	0.326469i	−0.851242	+	0.524773i	$0.824150\pi$
$374$	4.87202			0.251926
$375$		0			0
$376$		−	22.6423i		−	1.16769i
$377$	−21.9304	−	18.3110i	−1.12947	−	0.943066i
$378$	−18.9813	−	18.9813i	−0.976293	−	0.976293i
$379$	0.333942	−	0.333942i	0.0171534	−	0.0171534i	−0.698478	−	0.715631i	$-0.746139\pi$
$379$	0.333942	−	0.333942i	0.0171534	−	0.0171534i	0.715631	+	0.698478i	$0.246139\pi$
$380$		0			0
$381$			5.91934i			0.303257i
$382$	−15.2444			−0.779971
$383$			5.09138i			0.260158i	0.991504	+	0.130079i	$0.0415230\pi$
$383$			5.09138i			0.260158i	−0.991504	+	0.130079i	$0.958477\pi$
$384$	−13.4341	−	13.4341i	−0.685554	−	0.685554i
$385$		0			0
$386$	29.7350			1.51347
$387$	−6.69041	−	6.69041i	−0.340092	−	0.340092i
$388$	6.93704			0.352175
$389$	33.6544			1.70634			0.853172	−	0.521629i	$-0.174676\pi$
$389$	33.6544			1.70634			0.853172	+	0.521629i	$0.174676\pi$
$390$		0			0
$391$	−1.04147			−0.0526694
$392$	5.28676			0.267022
$393$	9.66267	+	9.66267i	0.487417	+	0.487417i
$394$	−47.3973			−2.38784
$395$		0			0
$396$	30.8807	+	30.8807i	1.55181	+	1.55181i
$397$		−	11.6763i		−	0.586019i	−0.956110	−	0.293010i	$-0.905343\pi$
$397$		−	11.6763i		−	0.586019i	0.956110	−	0.293010i	$-0.0946568\pi$
$398$	32.3385			1.62098
$399$			1.81459i			0.0908433i
$400$		0			0
$401$	6.30809	−	6.30809i	0.315011	−	0.315011i	−0.531836	−	0.846847i	$-0.678498\pi$
$401$	6.30809	−	6.30809i	0.315011	−	0.315011i	0.846847	+	0.531836i	$0.178498\pi$
$402$	−5.78673	−	5.78673i	−0.288616	−	0.288616i
$403$	−33.4858	+	3.01175i	−1.66805	+	0.150026i
$404$			23.5541i			1.17186i
$405$		0			0
$406$	44.9741			2.23203
$407$	40.2058	+	40.2058i	1.99293	+	1.99293i
$408$		−	1.36044i		−	0.0673519i
$409$	−12.8746	+	12.8746i	−0.636609	+	0.636609i	−0.949718	−	0.313108i	$-0.898630\pi$
$409$	−12.8746	+	12.8746i	−0.636609	+	0.636609i	0.313108	+	0.949718i	$0.398630\pi$
$410$		0			0
$411$	5.97306	−	5.97306i	0.294629	−	0.294629i
$412$	24.1288	−	24.1288i	1.18874	−	1.18874i
$413$	13.0795	−	13.0795i	0.643602	−	0.643602i
$414$	−10.1930	−	10.1930i	−0.500956	−	0.500956i
$415$		0			0
$416$	6.56095	−	7.85778i	0.321677	−	0.385260i
$417$	3.80883	−	3.80883i	0.186519	−	0.186519i
$418$		−	10.8900i		−	0.532648i
$419$			31.0270i			1.51577i	0.652389	+	0.757884i	$0.273767\pi$
$419$			31.0270i			1.51577i	−0.652389	+	0.757884i	$0.726233\pi$
$420$		0			0
$421$	−6.82280	−	6.82280i	−0.332523	−	0.332523i	0.521021	−	0.853544i	$-0.325551\pi$
$421$	−6.82280	−	6.82280i	−0.332523	−	0.332523i	−0.853544	+	0.521021i	$0.825551\pi$
$422$	−25.3362			−1.23335
$423$	−12.2493			−0.595583
$424$	−6.17749	−	6.17749i	−0.300006	−	0.300006i
$425$		0			0
$426$		−	6.31070i		−	0.305755i
$427$		−	9.81271i		−	0.474870i
$428$	4.94243	−	4.94243i	0.238902	−	0.238902i
$429$	11.6515	−	13.9545i	0.562538	−	0.673729i
$430$		0			0
$431$	−8.95943	−	8.95943i	−0.431560	−	0.431560i	0.457599	−	0.889159i	$-0.348710\pi$
$431$	−8.95943	−	8.95943i	−0.431560	−	0.431560i	−0.889159	+	0.457599i	$0.848710\pi$
$432$	7.22311	−	7.22311i	0.347522	−	0.347522i
$433$	15.4575	−	15.4575i	0.742841	−	0.742841i	−0.230283	−	0.973124i	$-0.573965\pi$
$433$	15.4575	−	15.4575i	0.742841	−	0.742841i	0.973124	+	0.230283i	$0.0739652\pi$
$434$	37.4240	−	37.4240i	1.79641	−	1.79641i
$435$		0			0
$436$	−43.1811	+	43.1811i	−2.06800	+	2.06800i
$437$			2.32791i			0.111359i
$438$	11.6742	+	11.6742i	0.557813	+	0.557813i
$439$	24.6942			1.17859			0.589294	−	0.807919i	$-0.299406\pi$
$439$	24.6942			1.17859			0.589294	+	0.807919i	$0.299406\pi$
$440$		0			0
$441$		−	2.86010i		−	0.136195i
$442$	3.18057	−	0.286064i	0.151284	−	0.0136067i
$443$	22.0612	+	22.0612i	1.04816	+	1.04816i	0.998780	+	0.0493786i	$0.0157241\pi$
$443$	22.0612	+	22.0612i	1.04816	+	1.04816i	0.0493786	+	0.998780i	$0.484276\pi$
$444$	24.6258	−	24.6258i	1.16869	−	1.16869i
$445$		0			0
$446$			24.2191i			1.14681i
$447$	−7.64234			−0.361470
$448$			26.4057i			1.24755i
$449$	0.902668	+	0.902668i	0.0425995	+	0.0425995i	0.728086	−	0.685486i	$-0.240410\pi$
$449$	0.902668	+	0.902668i	0.0425995	+	0.0425995i	−0.685486	+	0.728086i	$0.740410\pi$
$450$		0			0
$451$	49.6300			2.33699
$452$	−2.13575	−	2.13575i	−0.100457	−	0.100457i
$453$	−16.7803			−0.788410
$454$	44.2830			2.07830
$455$		0			0
$456$	−3.04088			−0.142402
$457$	31.9104			1.49271			0.746353	−	0.665550i	$-0.231803\pi$
$457$	31.9104			1.49271			0.746353	+	0.665550i	$0.231803\pi$
$458$	−14.9996	−	14.9996i	−0.700887	−	0.700887i
$459$	−1.75826			−0.0820688
$460$		0			0
$461$	−1.65292	−	1.65292i	−0.0769842	−	0.0769842i	0.667566	−	0.744550i	$-0.267336\pi$
$461$	−1.65292	−	1.65292i	−0.0769842	−	0.0769842i	−0.744550	+	0.667566i	$0.767336\pi$
$462$			28.6174i			1.33140i
$463$	−3.04132			−0.141342			−0.0706710	−	0.997500i	$-0.522514\pi$
$463$	−3.04132			−0.141342			−0.0706710	+	0.997500i	$0.522514\pi$
$464$			17.1143i			0.794514i
$465$		0			0
$466$	−47.1013	+	47.1013i	−2.18192	+	2.18192i
$467$	−14.5459	−	14.5459i	−0.673102	−	0.673102i	0.285328	−	0.958430i	$-0.407898\pi$
$467$	−14.5459	−	14.5459i	−0.673102	−	0.673102i	−0.958430	+	0.285328i	$0.907898\pi$
$468$	21.9728	+	18.3464i	1.01569	+	0.848064i
$469$			8.92835i			0.412273i
$470$		0			0
$471$	−17.9136			−0.825416
$472$	21.9186	+	21.9186i	1.00888	+	1.00888i
$473$			24.0974i			1.10800i
$474$	9.37524	−	9.37524i	0.430619	−	0.430619i
$475$		0			0
$476$	−2.30207	+	2.30207i	−0.105515	+	0.105515i
$477$	−3.34198	+	3.34198i	−0.153019	+	0.153019i
$478$	23.8729	−	23.8729i	1.09192	−	1.09192i
$479$	−25.2765	−	25.2765i	−1.15491	−	1.15491i	−0.985554	−	0.169359i	$-0.945830\pi$
$479$	−25.2765	−	25.2765i	−1.15491	−	1.15491i	−0.169359	−	0.985554i	$-0.554170\pi$
$480$		0			0
$481$	28.6080	+	23.8866i	1.30441	+	1.08913i
$482$	6.66084	−	6.66084i	0.303393	−	0.303393i
$483$		−	6.11742i		−	0.278352i
$484$		−	70.7916i		−	3.21780i
$485$		0			0
$486$	−27.2134	−	27.2134i	−1.23442	−	1.23442i
$487$	−20.4552			−0.926915			−0.463457	−	0.886119i	$-0.653391\pi$
$487$	−20.4552			−0.926915			−0.463457	+	0.886119i	$0.653391\pi$
$488$	16.4440			0.744387
$489$	−2.46672	−	2.46672i	−0.111549	−	0.111549i
$490$		0			0
$491$		−	7.81787i		−	0.352816i	−0.984317	−	0.176408i	$-0.943552\pi$
$491$		−	7.81787i		−	0.352816i	0.984317	−	0.176408i	$-0.0564477\pi$
$492$		−	30.3981i		−	1.37045i
$493$	2.08301	−	2.08301i	0.0938139	−	0.0938139i
$494$	−0.639415	−	7.10925i	−0.0287686	−	0.319860i
$495$		0			0
$496$	14.2412	+	14.2412i	0.639450	+	0.639450i
$497$	−4.86839	+	4.86839i	−0.218377	+	0.218377i
$498$	−20.1375	+	20.1375i	−0.902381	+	0.902381i
$499$	19.1295	−	19.1295i	0.856354	−	0.856354i	−0.134552	−	0.990906i	$-0.542960\pi$
$499$	19.1295	−	19.1295i	0.856354	−	0.856354i	0.990906	+	0.134552i	$0.0429596\pi$
$500$		0			0
$501$	−11.8273	+	11.8273i	−0.528405	+	0.528405i
$502$			53.3047i			2.37911i
$503$	1.20851	+	1.20851i	0.0538846	+	0.0538846i	0.733536	−	0.679651i	$-0.237869\pi$
$503$	1.20851	+	1.20851i	0.0538846	+	0.0538846i	−0.679651	+	0.733536i	$0.737869\pi$
$504$	−20.5433			−0.915072
$505$		0			0
$506$			36.7128i			1.63208i
$507$	6.78700	−	9.79395i	0.301421	−	0.434964i
$508$	16.7854	+	16.7854i	0.744732	+	0.744732i
$509$	−10.5094	+	10.5094i	−0.465822	+	0.465822i	−0.900558	−	0.434736i	$-0.856842\pi$
$509$	−10.5094	+	10.5094i	−0.465822	+	0.465822i	0.434736	+	0.900558i	$0.356842\pi$
$510$		0			0
$511$		−	18.0120i		−	0.796806i
$512$	−23.3781			−1.03318
$513$			3.93010i			0.173518i
$514$	−3.36661	−	3.36661i	−0.148495	−	0.148495i
$515$		0			0
$516$	14.7595			0.649750
$517$	22.0597	+	22.0597i	0.970185	+	0.970185i
$518$	−58.6683			−2.57774
$519$	0.00959718			0.000421269
$520$		0			0
$521$	−8.86424			−0.388349			−0.194175	−	0.980967i	$-0.562203\pi$
$521$	−8.86424			−0.388349			−0.194175	+	0.980967i	$0.562203\pi$
$522$	40.7731			1.78459
$523$	2.10327	+	2.10327i	0.0919697	+	0.0919697i	0.751595	−	0.659625i	$-0.229285\pi$
$523$	2.10327	+	2.10327i	0.0919697	+	0.0919697i	−0.659625	+	0.751595i	$0.729285\pi$
$524$	54.8006			2.39398
$525$		0			0
$526$	8.84137	+	8.84137i	0.385502	+	0.385502i
$527$		−	3.46663i		−	0.151009i
$528$	−10.8900			−0.473927
$529$			15.1521i			0.658786i
$530$		0			0
$531$	11.8578	−	11.8578i	0.514584	−	0.514584i
$532$	5.14562	+	5.14562i	0.223091	+	0.223091i
$533$	32.3997	−	2.91407i	1.40339	−	0.126222i
$534$		−	6.90279i		−	0.298713i
$535$		0			0
$536$	−14.9620			−0.646262
$537$	7.82401	+	7.82401i	0.337631	+	0.337631i
$538$		−	0.887755i		−	0.0382738i
$539$	−5.15072	+	5.15072i	−0.221857	+	0.221857i
$540$		0			0
$541$	4.31137	−	4.31137i	0.185360	−	0.185360i	−0.608327	−	0.793687i	$-0.708159\pi$
$541$	4.31137	−	4.31137i	0.185360	−	0.185360i	0.793687	+	0.608327i	$0.208159\pi$
$542$	−7.39933	+	7.39933i	−0.317828	+	0.317828i
$543$	11.8341	−	11.8341i	0.507851	−	0.507851i
$544$	0.746353	+	0.746353i	0.0319996	+	0.0319996i
$545$		0			0
$546$	1.68029	+	18.6821i	0.0719099	+	0.799521i
$547$	12.6865	−	12.6865i	0.542435	−	0.542435i	−0.381807	−	0.924242i	$-0.624698\pi$
$547$	12.6865	−	12.6865i	0.542435	−	0.542435i	0.924242	+	0.381807i	$0.124698\pi$
$548$		−	33.8755i		−	1.44709i
$549$		−	8.89611i		−	0.379677i
$550$		0			0
$551$	−4.65596	−	4.65596i	−0.198351	−	0.198351i
$552$	10.2515			0.436333
$553$	−14.4651			−0.615117
$554$	−29.6717	−	29.6717i	−1.26063	−	1.26063i
$555$		0			0
$556$		−	21.6013i		−	0.916100i
$557$			1.92751i			0.0816713i	0.999166	+	0.0408357i	$0.0130020\pi$
$557$			1.92751i			0.0816713i	−0.999166	+	0.0408357i	$0.986998\pi$
$558$	33.9282	−	33.9282i	1.43630	−	1.43630i
$559$	1.41490	+	15.7313i	0.0598437	+	0.665364i
$560$		0			0
$561$	1.32543	+	1.32543i	0.0559599	+	0.0559599i
$562$	−17.1276	+	17.1276i	−0.722484	+	0.722484i
$563$	10.3956	−	10.3956i	0.438124	−	0.438124i	−0.453256	−	0.891380i	$-0.649738\pi$
$563$	10.3956	−	10.3956i	0.438124	−	0.438124i	0.891380	+	0.453256i	$0.149738\pi$
$564$	13.5114	−	13.5114i	0.568934	−	0.568934i
$565$		0			0
$566$	51.5098	−	51.5098i	2.16512	−	2.16512i
$567$			5.10911i			0.214562i
$568$	−8.15840	−	8.15840i	−0.342319	−	0.342319i
$569$	25.2005			1.05646			0.528230	−	0.849101i	$-0.322856\pi$
$569$	25.2005			1.05646			0.528230	+	0.849101i	$0.322856\pi$
$570$		0			0
$571$		−	21.7839i		−	0.911630i	−0.890075	−	0.455815i	$-0.849348\pi$
$571$		−	21.7839i		−	0.911630i	0.890075	−	0.455815i	$-0.150652\pi$
$572$	−6.53068	−	72.6105i	−0.273061	−	3.03600i
$573$	−4.14724	−	4.14724i	−0.173254	−	0.173254i
$574$	−36.2101	+	36.2101i	−1.51138	+	1.51138i
$575$		0			0
$576$			23.9392i			0.997465i
$577$	−36.6110			−1.52414			−0.762068	−	0.647497i	$-0.775816\pi$
$577$	−36.6110			−1.52414			−0.762068	+	0.647497i	$0.775816\pi$
$578$		−	40.1714i		−	1.67091i
$579$	8.08943	+	8.08943i	0.336185	+	0.336185i
$580$		0			0
$581$	31.0701			1.28900
$582$	2.91407	+	2.91407i	0.120792	+	0.120792i
$583$	12.0371			0.498524
$584$	30.1844			1.24904
$585$		0			0
$586$	−61.3410			−2.53397
$587$	5.27384			0.217675			0.108837	−	0.994060i	$-0.465287\pi$
$587$	5.27384			0.217675			0.108837	+	0.994060i	$0.465287\pi$
$588$	3.15479	+	3.15479i	0.130101	+	0.130101i
$589$	−7.74867			−0.319278
$590$		0			0
$591$	−12.8945	−	12.8945i	−0.530407	−	0.530407i
$592$		−	22.3255i		−	0.917572i
$593$	22.9283			0.941552			0.470776	−	0.882253i	$-0.343974\pi$
$593$	22.9283			0.941552			0.470776	+	0.882253i	$0.343974\pi$
$594$			61.9804i			2.54309i
$595$		0			0
$596$	−21.6713	+	21.6713i	−0.887691	+	0.887691i
$597$	8.79769	+	8.79769i	0.360066	+	0.360066i
$598$	2.15562	+	23.9669i	0.0881498	+	0.980081i
$599$		−	2.73954i		−	0.111934i	−0.998433	−	0.0559672i	$-0.982176\pi$
$599$		−	2.73954i		−	0.111934i	0.998433	−	0.0559672i	$-0.0178242\pi$
$600$		0			0
$601$	42.4400			1.73116			0.865582	−	0.500767i	$-0.166949\pi$
$601$	42.4400			1.73116			0.865582	+	0.500767i	$0.166949\pi$
$602$	−17.5814	−	17.5814i	−0.716566	−	0.716566i
$603$			8.09436i			0.329628i
$604$	−47.5838	+	47.5838i	−1.93616	+	1.93616i
$605$		0			0
$606$	−9.89446	+	9.89446i	−0.401935	+	0.401935i
$607$	−17.7698	+	17.7698i	−0.721255	+	0.721255i	−0.968861	−	0.247606i	$-0.920356\pi$
$607$	−17.7698	+	17.7698i	−0.721255	+	0.721255i	0.247606	+	0.968861i	$0.420356\pi$
$608$	1.66826	−	1.66826i	0.0676568	−	0.0676568i
$609$	12.2352	+	12.2352i	0.495796	+	0.495796i
$610$		0			0
$611$	15.6963	+	13.1058i	0.635006	+	0.530206i
$612$	−2.08703	+	2.08703i	−0.0843633	+	0.0843633i
$613$			25.4815i			1.02919i	0.857435	+	0.514593i	$0.172057\pi$
$613$			25.4815i			1.02919i	−0.857435	+	0.514593i	$0.827943\pi$
$614$		−	4.34076i		−	0.175179i
$615$		0			0
$616$	36.9962	+	36.9962i	1.49062	+	1.49062i
$617$	17.0369			0.685880			0.342940	−	0.939357i	$-0.388577\pi$
$617$	17.0369			0.685880			0.342940	+	0.939357i	$0.388577\pi$
$618$	20.2717			0.815449
$619$	26.5396	+	26.5396i	1.06672	+	1.06672i	0.997609	+	0.0691073i	$0.0220151\pi$
$619$	26.5396	+	26.5396i	1.06672	+	1.06672i	0.0691073	+	0.997609i	$0.477985\pi$
$620$		0			0
$621$		−	13.2493i		−	0.531675i
$622$			18.4239i			0.738729i
$623$	−5.32516	+	5.32516i	−0.213348	+	0.213348i
$624$	−7.10925	+	0.639415i	−0.284598	+	0.0255971i
$625$		0			0
$626$	−32.5614	−	32.5614i	−1.30141	−	1.30141i
$627$	2.96263	−	2.96263i	0.118316	−	0.118316i
$628$	−50.7974	+	50.7974i	−2.02704	+	2.02704i
$629$	−2.71726	+	2.71726i	−0.108344	+	0.108344i
$630$		0			0
$631$	−8.89770	+	8.89770i	−0.354212	+	0.354212i	−0.861674	−	0.507462i	$-0.830584\pi$
$631$	−8.89770	+	8.89770i	−0.354212	+	0.354212i	0.507462	+	0.861674i	$0.330584\pi$
$632$		−	24.2404i		−	0.964231i
$633$	−6.89273	−	6.89273i	−0.273961	−	0.273961i
$634$	−34.1111			−1.35472
$635$		0			0
$636$		−	7.37263i		−	0.292344i
$637$	−3.06008	+	3.66494i	−0.121245	+	0.145210i
$638$	−73.4278	−	73.4278i	−2.90703	−	2.90703i
$639$	−4.41364	+	4.41364i	−0.174601	+	0.174601i
$640$		0			0
$641$		−	39.6332i		−	1.56542i	−0.622388	−	0.782709i	$-0.713838\pi$
$641$		−	39.6332i		−	1.56542i	0.622388	−	0.782709i	$-0.286162\pi$
$642$	4.15237			0.163881
$643$		−	2.08560i		−	0.0822481i	−0.999154	−	0.0411240i	$-0.986906\pi$
$643$		−	2.08560i		−	0.0822481i	0.999154	−	0.0411240i	$-0.0130939\pi$
$644$	−17.3471	−	17.3471i	−0.683571	−	0.683571i
$645$		0			0
$646$	0.735989			0.0289571
$647$	9.45363	+	9.45363i	0.371661	+	0.371661i	0.868082	−	0.496421i	$-0.165353\pi$
$647$	9.45363	+	9.45363i	0.371661	+	0.371661i	−0.496421	+	0.868082i	$0.665353\pi$
$648$	−8.56180			−0.336339
$649$	−42.7091			−1.67648
$650$		0			0
$651$	20.3624			0.798065
$652$	−13.9897			−0.547879
$653$	−7.46934	−	7.46934i	−0.292298	−	0.292298i	0.545689	−	0.837987i	$-0.316268\pi$
$653$	−7.46934	−	7.46934i	−0.292298	−	0.292298i	−0.837987	+	0.545689i	$0.816268\pi$
$654$	−36.2785			−1.41860
$655$		0			0
$656$	−13.7793	−	13.7793i	−0.537992	−	0.537992i
$657$		−	16.3296i		−	0.637076i
$658$	−32.1895			−1.25488
$659$			13.0165i			0.507053i	0.967328	+	0.253526i	$0.0815905\pi$
$659$			13.0165i			0.507053i	−0.967328	+	0.253526i	$0.918410\pi$
$660$		0			0
$661$	−10.1615	+	10.1615i	−0.395238	+	0.395238i	−0.876550	−	0.481311i	$-0.840161\pi$
$661$	−10.1615	+	10.1615i	−0.395238	+	0.395238i	0.481311	+	0.876550i	$0.340161\pi$
$662$	−25.8346	−	25.8346i	−1.00409	−	1.00409i
$663$	0.943099	+	0.787451i	0.0366269	+	0.0305821i
$664$			52.0669i			2.02059i
$665$		0			0
$666$	−53.1881			−2.06100
$667$	15.6963	+	15.6963i	0.607765	+	0.607765i
$668$			67.0771i			2.59529i
$669$	−6.58881	+	6.58881i	−0.254738	+	0.254738i
$670$		0			0
$671$	−16.0209	+	16.0209i	−0.618481	+	0.618481i
$672$	−4.38395	+	4.38395i	−0.169115	+	0.169115i
$673$	21.0987	−	21.0987i	0.813295	−	0.813295i	−0.171832	−	0.985126i	$-0.554969\pi$
$673$	21.0987	−	21.0987i	0.813295	−	0.813295i	0.985126	+	0.171832i	$0.0549686\pi$
$674$	−12.5373	−	12.5373i	−0.482918	−	0.482918i
$675$		0			0
$676$	−8.52676	−	47.0184i	−0.327952	−	1.80840i
$677$	2.76719	−	2.76719i	0.106352	−	0.106352i	−0.651929	−	0.758280i	$-0.726040\pi$
$677$	2.76719	−	2.76719i	0.106352	−	0.106352i	0.758280	+	0.651929i	$0.226040\pi$
$678$		−	1.79435i		−	0.0689114i
$679$		−	4.49611i		−	0.172545i
$680$		0			0
$681$	12.0472	+	12.0472i	0.461650	+	0.461650i
$682$	−122.202			−4.67935
$683$	−43.9664			−1.68233			−0.841164	−	0.540780i	$-0.818129\pi$
$683$	−43.9664			−1.68233			−0.841164	+	0.540780i	$0.818129\pi$
$684$	4.66497	+	4.66497i	0.178370	+	0.178370i
$685$		0			0
$686$		−	47.2465i		−	1.80388i
$687$		−	8.16132i		−	0.311374i
$688$	6.69041	−	6.69041i	0.255069	−	0.255069i
$689$	7.85808	−	0.706766i	0.299369	−	0.0269256i
$690$		0			0
$691$	3.17085	+	3.17085i	0.120625	+	0.120625i	0.764842	−	0.644218i	$-0.222817\pi$
$691$	3.17085	+	3.17085i	0.120625	+	0.120625i	−0.644218	+	0.764842i	$0.722817\pi$
$692$	0.0272146	−	0.0272146i	0.00103454	−	0.00103454i
$693$	20.0147	−	20.0147i	0.760295	−	0.760295i
$694$	18.8394	−	18.8394i	0.715132	−	0.715132i
$695$		0			0
$696$	−20.5037	+	20.5037i	−0.777189	+	0.777189i
$697$			3.35419i			0.127049i
$698$	−3.79109	−	3.79109i	−0.143495	−	0.143495i
$699$	−25.6278			−0.969334
$700$		0			0
$701$		−	28.6817i		−	1.08329i	−0.840606	−	0.541647i	$-0.817801\pi$
$701$		−	28.6817i		−	1.08329i	0.840606	−	0.541647i	$-0.182199\pi$
$702$	3.63923	+	40.4623i	0.137354	+	1.52715i
$703$	6.07366	+	6.07366i	0.229072	+	0.229072i
$704$	43.1118	−	43.1118i	1.62484	−	1.62484i
$705$		0			0
$706$			46.1231i			1.73587i
$707$	15.2661			0.574143
$708$			26.1591i			0.983118i
$709$	−10.9424	−	10.9424i	−0.410952	−	0.410952i	0.471118	−	0.882070i	$-0.343851\pi$
$709$	−10.9424	−	10.9424i	−0.410952	−	0.410952i	−0.882070	+	0.471118i	$0.843851\pi$
$710$		0			0
$711$	−13.1139			−0.491809
$712$	−8.92385	−	8.92385i	−0.334435	−	0.334435i
$713$	26.1226			0.978298
$714$	−1.93407			−0.0723809
$715$		0			0
$716$	44.3729			1.65829
$717$	12.9893			0.485093
$718$	8.24474	+	8.24474i	0.307691	+	0.307691i
$719$	1.67615			0.0625099			0.0312550	−	0.999511i	$-0.490050\pi$
$719$	1.67615			0.0625099			0.0312550	+	0.999511i	$0.490050\pi$
$720$		0			0
$721$	−15.6386	−	15.6386i	−0.582413	−	0.582413i
$722$			43.6203i			1.62338i
$723$	3.62417			0.134784
$724$		−	67.1158i		−	2.49434i
$725$		0			0
$726$	29.7376	−	29.7376i	1.10367	−	1.10367i
$727$	9.40127	+	9.40127i	0.348674	+	0.348674i	0.859615	−	0.510942i	$-0.170703\pi$
$727$	9.40127	+	9.40127i	0.348674	+	0.348674i	−0.510942	+	0.859615i	$0.670703\pi$
$728$	26.3243	+	21.9797i	0.975642	+	0.814623i
$729$		−	8.37322i		−	0.310119i
$730$		0			0
$731$	−1.62859			−0.0602357
$732$	9.81271	+	9.81271i	0.362688	+	0.362688i
$733$			17.2489i			0.637104i	0.947905	+	0.318552i	$0.103196\pi$
$733$			17.2489i			0.637104i	−0.947905	+	0.318552i	$0.896804\pi$
$734$	18.3036	−	18.3036i	0.675598	−	0.675598i
$735$		0			0
$736$	−5.62409	+	5.62409i	−0.207307	+	0.207307i
$737$	14.5770	−	14.5770i	0.536952	−	0.536952i
$738$	−32.8277	+	32.8277i	−1.20841	+	1.20841i
$739$	17.3014	+	17.3014i	0.636442	+	0.636442i	0.949676	−	0.313234i	$-0.101412\pi$
$739$	17.3014	+	17.3014i	0.636442	+	0.636442i	−0.313234	+	0.949676i	$0.601412\pi$
$740$		0			0
$741$	1.76012	−	2.10803i	0.0646597	−	0.0774403i
$742$	−8.78225	+	8.78225i	−0.322406	+	0.322406i
$743$		−	19.0572i		−	0.699142i	−0.936910	−	0.349571i	$-0.886327\pi$
$743$		−	19.0572i		−	0.699142i	0.936910	−	0.349571i	$-0.113673\pi$
$744$			34.1231i			1.25101i
$745$		0			0
$746$	−15.0213	−	15.0213i	−0.549971	−	0.549971i
$747$	28.1678			1.03061
$748$	7.51703			0.274850
$749$	−3.20334	−	3.20334i	−0.117048	−	0.117048i
$750$		0			0
$751$			6.28578i			0.229371i	0.993402	+	0.114686i	$0.0365861\pi$
$751$			6.28578i			0.229371i	−0.993402	+	0.114686i	$0.963414\pi$
$752$		−	12.2493i		−	0.446687i
$753$	−14.5016	+	14.5016i	−0.528466	+	0.528466i
$754$	−52.2468	−	43.6240i	−1.90271	−	1.58869i
$755$		0			0
$756$	−29.2862	−	29.2862i	−1.06513	−	1.06513i
$757$	1.17728	−	1.17728i	0.0427888	−	0.0427888i	−0.685389	−	0.728177i	$-0.740368\pi$
$757$	1.17728	−	1.17728i	0.0427888	−	0.0427888i	0.728177	+	0.685389i	$0.240368\pi$
$758$	0.795581	−	0.795581i	0.0288968	−	0.0288968i
$759$	−9.98772	+	9.98772i	−0.362531	+	0.362531i
$760$		0			0
$761$	8.23399	−	8.23399i	0.298482	−	0.298482i	−0.541937	−	0.840419i	$-0.682309\pi$
$761$	8.23399	−	8.23399i	0.298482	−	0.298482i	0.840419	+	0.541937i	$0.182309\pi$
$762$			14.1022i			0.510869i
$763$	27.9870	+	27.9870i	1.01320	+	1.01320i
$764$	−23.5206			−0.850944
$765$		0			0
$766$			12.1297i			0.438263i
$767$	−27.8815	+	2.50770i	−1.00674	+	0.0905477i
$768$	−17.6378	−	17.6378i	−0.636450	−	0.636450i
$769$	33.1546	−	33.1546i	1.19558	−	1.19558i	0.220109	−	0.975475i	$-0.429359\pi$
$769$	33.1546	−	33.1546i	1.19558	−	1.19558i	0.975475	−	0.220109i	$-0.0706412\pi$
$770$		0			0
$771$		−	1.83177i		−	0.0659697i
$772$	45.8782			1.65119
$773$		−	53.2581i		−	1.91556i	−0.287502	−	0.957780i	$-0.592825\pi$
$773$		−	53.2581i		−	1.91556i	0.287502	−	0.957780i	$-0.407175\pi$
$774$	−15.9392	−	15.9392i	−0.572922	−	0.572922i
$775$		0			0
$776$	7.53454			0.270474
$777$	−15.9607	−	15.9607i	−0.572588	−	0.572588i
$778$	80.1779			2.87452
$779$	7.49734			0.268620
$780$		0			0
$781$	15.8969			0.568837
$782$	−2.48119			−0.0887272
$783$	26.4994	+	26.4994i	0.947011	+	0.947011i
$784$	2.86010			0.102146
$785$		0			0
$786$	23.0203	+	23.0203i	0.821105	+	0.821105i
$787$		−	39.5579i		−	1.41009i	−0.709165	−	0.705043i	$-0.750928\pi$
$787$		−	39.5579i		−	1.41009i	0.709165	−	0.705043i	$-0.249072\pi$
$788$	−73.1293			−2.60512
$789$			4.81060i			0.171262i
$790$		0			0
$791$	−1.38425	+	1.38425i	−0.0492182	+	0.0492182i
$792$	33.5404	+	33.5404i	1.19181	+	1.19181i
$793$	−9.51815	+	11.3995i	−0.337999	+	0.404808i
$794$		−	27.8176i		−	0.987211i
$795$		0			0
$796$	49.8950			1.76848
$797$	−17.6570	−	17.6570i	−0.625443	−	0.625443i	0.321475	−	0.946918i	$-0.395821\pi$
$797$	−17.6570	−	17.6570i	−0.625443	−	0.625443i	−0.946918	+	0.321475i	$0.895821\pi$
$798$			4.32307i			0.153035i
$799$	−1.49088	+	1.49088i	−0.0527435	+	0.0527435i
$800$		0			0
$801$	−4.82774	+	4.82774i	−0.170580	+	0.170580i
$802$	15.0283	−	15.0283i	0.530669	−	0.530669i
$803$	−29.4077	+	29.4077i	−1.03778	+	1.03778i
$804$	−8.92835	−	8.92835i	−0.314879	−	0.314879i
$805$		0			0
$806$	−79.7763	+	7.17518i	−2.81000	+	0.252735i
$807$	0.241514	−	0.241514i	0.00850169	−	0.00850169i
$808$			25.5829i			0.900002i
$809$			26.8465i			0.943871i	0.881633	+	0.471936i	$0.156445\pi$
$809$			26.8465i			0.943871i	−0.881633	+	0.471936i	$0.843555\pi$
$810$		0			0
$811$	22.1320	+	22.1320i	0.777159	+	0.777159i	0.979347	−	0.202188i	$-0.0648051\pi$
$811$	22.1320	+	22.1320i	0.777159	+	0.777159i	−0.202188	+	0.979347i	$0.564805\pi$
$812$	69.3905			2.43513
$813$	−4.02598			−0.141197
$814$	95.7859	+	95.7859i	3.35729	+	3.35729i
$815$		0			0
$816$		−	0.735989i		−	0.0257648i
$817$			3.64025i			0.127356i
$818$	−30.6724	+	30.6724i	−1.07244	+	1.07244i
$819$	11.8909	−	14.2412i	0.415501	−	0.497629i
$820$		0			0
$821$	32.5151	+	32.5151i	1.13479	+	1.13479i	0.989371	+	0.145416i	$0.0464519\pi$
$821$	32.5151	+	32.5151i	1.13479	+	1.13479i	0.145416	+	0.989371i	$0.453548\pi$
$822$	14.2302	−	14.2302i	0.496334	−	0.496334i
$823$	−14.6543	+	14.6543i	−0.510816	+	0.510816i	−0.914776	−	0.403960i	$-0.867633\pi$
$823$	−14.6543	+	14.6543i	−0.510816	+	0.510816i	0.403960	+	0.914776i	$0.367633\pi$
$824$	26.2071	−	26.2071i	0.912966	−	0.912966i
$825$		0			0
$826$	31.1606	−	31.1606i	1.08422	−	1.08422i
$827$		−	2.99000i		−	0.103972i	−0.998648	−	0.0519862i	$-0.983445\pi$
$827$		−	2.99000i		−	0.103972i	0.998648	−	0.0519862i	$-0.0165552\pi$
$828$	−15.7267	−	15.7267i	−0.546541	−	0.546541i
$829$	−1.29806			−0.0450836			−0.0225418	−	0.999746i	$-0.507176\pi$
$829$	−1.29806			−0.0450836			−0.0225418	+	0.999746i	$0.507176\pi$
$830$		0			0
$831$		−	16.1444i		−	0.560043i
$832$	25.6131	−	30.6757i	0.887973	−	1.06349i
$833$	−0.348106	−	0.348106i	−0.0120611	−	0.0120611i
$834$	9.07414	−	9.07414i	0.314212	−	0.314212i
$835$		0			0
$836$		−	16.8022i		−	0.581116i
$837$	44.1015			1.52437
$838$			73.9185i			2.55347i
$839$	3.30809	+	3.30809i	0.114208	+	0.114208i	0.761901	−	0.647693i	$-0.224266\pi$
$839$	3.30809	+	3.30809i	0.114208	+	0.114208i	−0.647693	+	0.761901i	$0.724266\pi$
$840$		0			0
$841$	−33.7873			−1.16508
$842$	−16.2546	−	16.2546i	−0.560170	−	0.560170i
$843$	−9.31913			−0.320968
$844$	−39.0912			−1.34558
$845$		0			0
$846$	−29.1827			−1.00332
$847$	−45.8822			−1.57653
$848$	−3.34198	−	3.34198i	−0.114764	−	0.114764i
$849$	28.0265			0.961868
$850$		0			0
$851$	−20.4757	−	20.4757i	−0.701899	−	0.701899i
$852$		−	9.73678i		−	0.333577i
$853$	23.1640			0.793119			0.396560	−	0.918009i	$-0.370204\pi$
$853$	23.1640			0.793119			0.396560	+	0.918009i	$0.370204\pi$
$854$		−	23.3777i		−	0.799969i
$855$		0			0
$856$	5.36813	−	5.36813i	0.183479	−	0.183479i
$857$	−0.287160	−	0.287160i	−0.00980921	−	0.00980921i	0.702185	−	0.711994i	$-0.252208\pi$
$857$	−0.287160	−	0.287160i	−0.00980921	−	0.00980921i	−0.711994	+	0.702185i	$0.752208\pi$
$858$	27.7583	−	33.2451i	0.947654	−	1.13497i
$859$			34.3061i			1.17051i	0.810850	+	0.585254i	$0.199005\pi$
$859$			34.3061i			1.17051i	−0.810850	+	0.585254i	$0.800995\pi$
$860$		0			0
$861$	−19.7019			−0.671440
$862$	−21.3449	−	21.3449i	−0.727009	−	0.727009i
$863$			13.0838i			0.445377i	0.974890	+	0.222688i	$0.0714833\pi$
$863$			13.0838i			0.445377i	−0.974890	+	0.222688i	$0.928517\pi$
$864$	−9.49489	+	9.49489i	−0.323023	+	0.323023i
$865$		0			0
$866$	36.8258	−	36.8258i	1.25139	−	1.25139i
$867$	10.9286	−	10.9286i	0.371156	−	0.371156i
$868$	57.7414	−	57.7414i	1.95987	−	1.95987i
$869$	23.6167	+	23.6167i	0.801140	+	0.801140i
$870$		0			0
$871$	8.66033	−	10.3721i	0.293444	−	0.351446i
$872$	−46.9004	+	46.9004i	−1.58825	+	1.58825i
$873$		−	4.07613i		−	0.137956i
$874$			5.54599i			0.187596i
$875$		0			0
$876$	18.0120	+	18.0120i	0.608571	+	0.608571i
$877$	43.5876			1.47185			0.735924	−	0.677064i	$-0.236748\pi$
$877$	43.5876			1.47185			0.735924	+	0.677064i	$0.236748\pi$
$878$	58.8312			1.98546
$879$	−16.6878	−	16.6878i	−0.562867	−	0.562867i
$880$		0			0
$881$			53.6106i			1.80619i	0.429445	+	0.903093i	$0.358709\pi$
$881$			53.6106i			1.80619i	−0.429445	+	0.903093i	$0.641291\pi$
$882$		−	6.81388i		−	0.229435i
$883$	−13.4449	+	13.4449i	−0.452458	+	0.452458i	−0.896170	−	0.443712i	$-0.853661\pi$
$883$	−13.4449	+	13.4449i	−0.452458	+	0.452458i	0.443712	+	0.896170i	$0.353661\pi$
$884$	4.90730	−	0.441368i	0.165050	−	0.0148448i
$885$		0			0
$886$	52.5584	+	52.5584i	1.76573	+	1.76573i
$887$	−16.8456	+	16.8456i	−0.565618	+	0.565618i	−0.930898	−	0.365279i	$-0.880973\pi$
$887$	−16.8456	+	16.8456i	−0.565618	+	0.565618i	0.365279	+	0.930898i	$0.380973\pi$
$888$	26.7468	−	26.7468i	0.897564	−	0.897564i
$889$	10.8791	−	10.8791i	0.364874	−	0.364874i
$890$		0			0
$891$	8.34149	−	8.34149i	0.279450	−	0.279450i
$892$			37.3676i			1.25116i
$893$	3.33244	+	3.33244i	0.111516	+	0.111516i
$894$	−18.2071			−0.608935
$895$		0			0
$896$			49.3808i			1.64970i
$897$	−5.93378	+	7.10665i	−0.198123	+	0.237284i
$898$	2.15051	+	2.15051i	0.0717634	+	0.0717634i
$899$	−52.2468	+	52.2468i	−1.74253	+	1.74253i
$900$		0			0
$901$			0.813512i			0.0271020i
$902$	118.238			3.93690
$903$		−	9.56607i		−	0.318339i
$904$	−2.31971	−	2.31971i	−0.0771523	−	0.0771523i
$905$		0			0
$906$	−39.9774			−1.32816
$907$	−18.6035	−	18.6035i	−0.617718	−	0.617718i	0.327228	−	0.944946i	$-0.393886\pi$
$907$	−18.6035	−	18.6035i	−0.617718	−	0.617718i	−0.944946	+	0.327228i	$0.893886\pi$
$908$	68.3242			2.26742
$909$	13.8401			0.459049
$910$		0			0
$911$	17.7993			0.589716			0.294858	−	0.955541i	$-0.404728\pi$
$911$	17.7993			0.589716			0.294858	+	0.955541i	$0.404728\pi$
$912$	−1.64509			−0.0544745
$913$	−50.7271	−	50.7271i	−1.67882	−	1.67882i
$914$	76.0231			2.51462
$915$		0			0
$916$	−23.1429	−	23.1429i	−0.764664	−	0.764664i
$917$		−	35.5179i		−	1.17291i
$918$	−4.18888			−0.138253
$919$		−	55.5174i		−	1.83135i	−0.401920	−	0.915675i	$-0.631657\pi$
$919$		−	55.5174i		−	1.83135i	0.401920	−	0.915675i	$-0.368343\pi$
$920$		0			0
$921$	1.18090	−	1.18090i	0.0389121	−	0.0389121i
$922$	−3.93791	−	3.93791i	−0.129688	−	0.129688i
$923$	10.3779	−	0.933401i	0.341593	−	0.0307233i
$924$			44.1538i			1.45255i
$925$		0			0
$926$	−7.24561			−0.238105
$927$	−14.1778	−	14.1778i	−0.465661	−	0.465661i
$928$		−	22.4971i		−	0.738502i
$929$	26.7318	−	26.7318i	0.877040	−	0.877040i	−0.116187	−	0.993227i	$-0.537067\pi$
$929$	26.7318	−	26.7318i	0.877040	−	0.877040i	0.993227	+	0.116187i	$0.0370671\pi$
$930$		0			0
$931$	−0.778091	+	0.778091i	−0.0255009	+	0.0255009i
$932$	−72.6725	+	72.6725i	−2.38047	+	2.38047i
$933$	−5.01222	+	5.01222i	−0.164093	+	0.164093i
$934$	−34.6539	−	34.6539i	−1.13391	−	1.13391i
$935$		0			0
$936$	23.8653	+	19.9266i	0.780063	+	0.651322i
$937$	−43.2141	+	43.2141i	−1.41174	+	1.41174i	−0.664101	+	0.747643i	$0.731185\pi$
$937$	−43.2141	+	43.2141i	−1.41174	+	1.41174i	−0.747643	+	0.664101i	$0.768815\pi$
$938$			21.2708i			0.694517i
$939$		−	17.7167i		−	0.578162i
$940$		0			0
$941$	−16.7446	−	16.7446i	−0.545859	−	0.545859i	0.379381	−	0.925240i	$-0.376137\pi$
$941$	−16.7446	−	16.7446i	−0.545859	−	0.545859i	−0.925240	+	0.379381i	$0.876137\pi$
$942$	−42.6773			−1.39050
$943$	−25.2753			−0.823076
$944$	11.8578	+	11.8578i	0.385938	+	0.385938i
$945$		0			0
$946$			57.4094i			1.86654i
$947$		−	5.66954i		−	0.184235i	−0.995748	−	0.0921176i	$-0.970636\pi$
$947$		−	5.66954i		−	0.184235i	0.995748	−	0.0921176i	$-0.0293636\pi$
$948$	14.4651	−	14.4651i	0.469803	−	0.469803i
$949$	−17.4714	+	20.9247i	−0.567144	+	0.679246i
$950$		0			0
$951$	−9.27993	−	9.27993i	−0.300922	−	0.300922i
$952$	−2.50035	+	2.50035i	−0.0810367	+	0.0810367i
$953$	8.52197	−	8.52197i	0.276054	−	0.276054i	−0.555478	−	0.831531i	$-0.687465\pi$
$953$	8.52197	−	8.52197i	0.276054	−	0.276054i	0.831531	+	0.555478i	$0.187465\pi$
$954$	−7.96190	+	7.96190i	−0.257776	+	0.257776i
$955$		0			0
$956$	36.8335	−	36.8335i	1.19128	−	1.19128i
$957$		−	39.9521i		−	1.29147i
$958$	−60.2186	−	60.2186i	−1.94557	−	1.94557i
$959$	−21.9557			−0.708987
$960$		0			0
$961$			55.9514i			1.80489i
$962$	68.1554	+	56.9071i	2.19742	+	1.83476i
$963$	−2.90412	−	2.90412i	−0.0935839	−	0.0935839i
$964$	10.2770	−	10.2770i	0.331000	−	0.331000i
$965$		0			0
$966$		−	14.5741i		−	0.468913i
$967$	−14.0855			−0.452959			−0.226480	−	0.974016i	$-0.572722\pi$
$967$	−14.0855			−0.452959			−0.226480	+	0.974016i	$0.572722\pi$
$968$		−	76.8889i		−	2.47130i
$969$	0.200226	+	0.200226i	0.00643219	+	0.00643219i
$970$		0			0
$971$	−41.4963			−1.33168			−0.665840	−	0.746094i	$-0.731927\pi$
$971$	−41.4963			−1.33168			−0.665840	+	0.746094i	$0.731927\pi$
$972$	−41.9875	−	41.9875i	−1.34675	−	1.34675i
$973$	−14.0005			−0.448835
$974$	−48.7323			−1.56149
$975$		0			0
$976$	8.89611			0.284758
$977$	−7.91854			−0.253337			−0.126668	−	0.991945i	$-0.540428\pi$
$977$	−7.91854			−0.253337			−0.126668	+	0.991945i	$0.540428\pi$
$978$	−5.87670	−	5.87670i	−0.187916	−	0.187916i
$979$	17.3884			0.555737
$980$		0			0
$981$	25.3728	+	25.3728i	0.810090	+	0.810090i
$982$		−	18.6252i		−	0.594355i
$983$	−55.0656			−1.75632			−0.878160	−	0.478367i	$-0.841229\pi$
$983$	−55.0656			−1.75632			−0.878160	+	0.478367i	$0.841229\pi$
$984$		−	33.0163i		−	1.05252i
$985$		0			0
$986$	4.96254	−	4.96254i	0.158039	−	0.158039i
$987$	−8.75717	−	8.75717i	−0.278744	−	0.278744i
$988$	−0.986553	−	10.9689i	−0.0313864	−	0.348966i
$989$		−	12.2721i		−	0.390232i
$990$		0			0
$991$	7.92894			0.251871			0.125936	−	0.992038i	$-0.459807\pi$
$991$	7.92894			0.251871			0.125936	+	0.992038i	$0.459807\pi$
$992$	−18.7203	−	18.7203i	−0.594371	−	0.594371i
$993$		−	14.0566i		−	0.446074i
$994$	−11.5984	+	11.5984i	−0.367879	+	0.367879i
$995$		0			0
$996$	−31.0701	+	31.0701i	−0.984493	+	0.984493i
$997$	−20.5699	+	20.5699i	−0.651457	+	0.651457i	−0.953344	−	0.301887i	$-0.902383\pi$
$997$	−20.5699	+	20.5699i	−0.651457	+	0.651457i	0.301887	+	0.953344i	$0.402383\pi$
$998$	45.5740	−	45.5740i	1.44262	−	1.44262i
$999$	−34.5682	−	34.5682i	−1.09369	−	1.09369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.k.d.268.8	yes	16
5.2	odd	4		325.2.f.d.307.8	yes	16
5.3	odd	4		325.2.f.d.307.1	yes	16
5.4	even	2	inner	325.2.k.d.268.1	yes	16
13.5	odd	4		325.2.f.d.18.1	✓	16
65.18	even	4	inner	325.2.k.d.57.1	yes	16
65.44	odd	4		325.2.f.d.18.8	yes	16
65.57	even	4	inner	325.2.k.d.57.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.f.d.18.1	✓	16	13.5	odd	4
325.2.f.d.18.8	yes	16	65.44	odd	4
325.2.f.d.307.1	yes	16	5.3	odd	4
325.2.f.d.307.8	yes	16	5.2	odd	4
325.2.k.d.57.1	yes	16	65.18	even	4	inner
325.2.k.d.57.8	yes	16	65.57	even	4	inner
325.2.k.d.268.1	yes	16	5.4	even	2	inner
325.2.k.d.268.8	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.38239 q^{2} +(0.648130 + 0.648130i) q^{3} +3.67579 q^{4} +(1.54410 + 1.54410i) q^{6} -2.38239i q^{7} +3.99239 q^{8} -2.15985i q^{9} +O(q^{10})\)	\(q+2.38239 q^{2} +(0.648130 + 0.648130i) q^{3} +3.67579 q^{4} +(1.54410 + 1.54410i) q^{6} -2.38239i q^{7} +3.99239 q^{8} -2.15985i q^{9} +(-3.88966 + 3.88966i) q^{11} +(2.38239 + 2.38239i) q^{12} +(-2.31088 + 2.76764i) q^{13} -5.67579i q^{14} +2.15985 q^{16} +(-0.262878 - 0.262878i) q^{17} -5.14562i q^{18} +(-0.587589 + 0.587589i) q^{19} +(1.54410 - 1.54410i) q^{21} +(-9.26669 + 9.26669i) q^{22} +(1.98090 - 1.98090i) q^{23} +(2.58759 + 2.58759i) q^{24} +(-5.50541 + 6.59361i) q^{26} +(3.34426 - 3.34426i) q^{27} -8.75717i q^{28} +7.92385i q^{29} +(6.59361 + 6.59361i) q^{31} -2.83916 q^{32} -5.04201 q^{33} +(-0.626279 - 0.626279i) q^{34} -7.93917i q^{36} -10.3366i q^{37} +(-1.39987 + 1.39987i) q^{38} +(-3.29154 + 0.296046i) q^{39} +(-6.37974 - 6.37974i) q^{41} +(3.67865 - 3.67865i) q^{42} +(3.09762 - 3.09762i) q^{43} +(-14.2976 + 14.2976i) q^{44} +(4.71928 - 4.71928i) q^{46} -5.67137i q^{47} +(1.39987 + 1.39987i) q^{48} +1.32421 q^{49} -0.340759i q^{51} +(-8.49429 + 10.1733i) q^{52} +(-1.54732 - 1.54732i) q^{53} +(7.96733 - 7.96733i) q^{54} -9.51143i q^{56} -0.761669 q^{57} +18.8777i q^{58} +(5.49009 + 5.49009i) q^{59} +4.11885 q^{61} +(15.7086 + 15.7086i) q^{62} -5.14562 q^{63} -11.0837 q^{64} -12.0120 q^{66} -3.74764 q^{67} +(-0.966285 - 0.966285i) q^{68} +2.56776 q^{69} +(-2.04349 - 2.04349i) q^{71} -8.62298i q^{72} +7.56049 q^{73} -24.6258i q^{74} +(-2.15985 + 2.15985i) q^{76} +(9.26669 + 9.26669i) q^{77} +(-7.84175 + 0.705296i) q^{78} -6.07165i q^{79} -2.14453 q^{81} +(-15.1991 - 15.1991i) q^{82} +13.0415i q^{83} +(5.67579 - 5.67579i) q^{84} +(7.37974 - 7.37974i) q^{86} +(-5.13569 + 5.13569i) q^{87} +(-15.5290 + 15.5290i) q^{88} +(-2.23522 - 2.23522i) q^{89} +(6.59361 + 5.50541i) q^{91} +(7.28137 - 7.28137i) q^{92} +8.54704i q^{93} -13.5114i q^{94} +(-1.84015 - 1.84015i) q^{96} +1.88723 q^{97} +3.15479 q^{98} +(8.40109 + 8.40109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{6}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^6	\( 16 q + 8 q^{4} + 12 q^{6} - 20 q^{11} - 8 q^{16} + 16 q^{19} + 12 q^{21} + 16 q^{24} - 16 q^{26} + 8 q^{31} - 44 q^{34} + 28 q^{39} + 4 q^{41} - 76 q^{44} + 12 q^{46} + 72 q^{49} - 4 q^{54} + 24 q^{59} + 24 q^{61} - 16 q^{64} - 48 q^{66} - 112 q^{69} - 20 q^{71} + 8 q^{76} + 40 q^{84} + 12 q^{86} + 36 q^{89} + 8 q^{91} - 72 q^{96} - 52 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^6 - 20 * q^11 - 8 * q^16 + 16 * q^19 + 12 * q^21 + 16 * q^24 - 16 * q^26 + 8 * q^31 - 44 * q^34 + 28 * q^39 + 4 * q^41 - 76 * q^44 + 12 * q^46 + 72 * q^49 - 4 * q^54 + 24 * q^59 + 24 * q^61 - 16 * q^64 - 48 * q^66 - 112 * q^69 - 20 * q^71 + 8 * q^76 + 40 * q^84 + 12 * q^86 + 36 * q^89 + 8 * q^91 - 72 * q^96 - 52 * q^99

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