LMFDB - Embedded newform 325.2.f.d.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(18,325)]

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([3, 3]))

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

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

chi := DirichletCharacter("325.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.f (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			307.1
Root			$-0.419746 - 0.419746i$ of defining polynomial
Character	$\chi$	$=$	325.307
Dual form			325.2.f.d.18.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38239i q^{2} +(-0.648130 + 0.648130i) q^{3} -3.67579 q^{4} +(1.54410 + 1.54410i) q^{6} -2.38239 q^{7} +3.99239i q^{8} +2.15985i q^{9} +O(q^{10})$	\(q-2.38239i q^{2} +(-0.648130 + 0.648130i) q^{3} -3.67579 q^{4} +(1.54410 + 1.54410i) q^{6} -2.38239 q^{7} +3.99239i q^{8} +2.15985i q^{9} +(-3.88966 + 3.88966i) q^{11} +(2.38239 - 2.38239i) q^{12} +(-2.76764 - 2.31088i) q^{13} +5.67579i q^{14} +2.15985 q^{16} +(-0.262878 + 0.262878i) q^{17} +5.14562 q^{18} +(0.587589 - 0.587589i) q^{19} +(1.54410 - 1.54410i) q^{21} +(9.26669 + 9.26669i) q^{22} +(1.98090 + 1.98090i) q^{23} +(-2.58759 - 2.58759i) q^{24} +(-5.50541 + 6.59361i) q^{26} +(-3.34426 - 3.34426i) q^{27} +8.75717 q^{28} -7.92385i q^{29} +(6.59361 + 6.59361i) q^{31} +2.83916i q^{32} -5.04201i q^{33} +(0.626279 + 0.626279i) q^{34} -7.93917i q^{36} -10.3366 q^{37} +(-1.39987 - 1.39987i) q^{38} +(3.29154 - 0.296046i) q^{39} +(-6.37974 - 6.37974i) q^{41} +(-3.67865 - 3.67865i) q^{42} +(3.09762 + 3.09762i) q^{43} +(14.2976 - 14.2976i) q^{44} +(4.71928 - 4.71928i) q^{46} -5.67137 q^{47} +(-1.39987 + 1.39987i) q^{48} -1.32421 q^{49} -0.340759i q^{51} +(10.1733 + 8.49429i) q^{52} +(1.54732 - 1.54732i) q^{53} +(-7.96733 + 7.96733i) q^{54} -9.51143i q^{56} +0.761669i q^{57} -18.8777 q^{58} +(-5.49009 - 5.49009i) q^{59} +4.11885 q^{61} +(15.7086 - 15.7086i) q^{62} -5.14562i q^{63} +11.0837 q^{64} -12.0120 q^{66} +3.74764i q^{67} +(0.966285 - 0.966285i) q^{68} -2.56776 q^{69} +(-2.04349 - 2.04349i) q^{71} -8.62298 q^{72} +7.56049i q^{73} +24.6258i q^{74} +(-2.15985 + 2.15985i) q^{76} +(9.26669 - 9.26669i) q^{77} +(-0.705296 - 7.84175i) q^{78} +6.07165i q^{79} -2.14453 q^{81} +(-15.1991 + 15.1991i) q^{82} -13.0415 q^{83} +(-5.67579 + 5.67579i) q^{84} +(7.37974 - 7.37974i) q^{86} +(5.13569 + 5.13569i) q^{87} +(-15.5290 - 15.5290i) q^{88} +(2.23522 + 2.23522i) q^{89} +(6.59361 + 5.50541i) q^{91} +(-7.28137 - 7.28137i) q^{92} -8.54704 q^{93} +13.5114i q^{94} +(-1.84015 - 1.84015i) q^{96} -1.88723i q^{97} +3.15479i q^{98} +(-8.40109 - 8.40109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	2.38239i		−	1.68461i	−0.539005	−	0.842303i	$-0.681200\pi$
$2$		−	2.38239i		−	1.68461i	0.539005	−	0.842303i	$-0.318800\pi$
$3$	−0.648130	+	0.648130i	−0.374198	+	0.374198i	−0.869004	−	0.494805i	$-0.835239\pi$
$3$	−0.648130	+	0.648130i	−0.374198	+	0.374198i	0.494805	+	0.869004i	$0.335239\pi$
$4$	−3.67579			−1.83790
$5$		0			0
$5$		0			0
$6$	1.54410	+	1.54410i	0.630376	+	0.630376i
$7$	−2.38239			−0.900459			−0.450230	−	0.892913i	$-0.648658\pi$
$7$	−2.38239			−0.900459			−0.450230	+	0.892913i	$0.648658\pi$
$8$			3.99239i			1.41152i
$9$			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
$13$	−2.76764	−	2.31088i	−0.767606	−	0.640922i
$13$	−2.76764	−	2.31088i	−0.767606	−	0.640922i
$14$			5.67579i			1.51692i
$15$		0			0
$16$	2.15985			0.539963
$17$	−0.262878	+	0.262878i	−0.0637573	+	0.0637573i	−0.738266	−	0.674509i	$-0.764355\pi$
$17$	−0.262878	+	0.262878i	−0.0637573	+	0.0637573i	0.674509	+	0.738266i	$0.264355\pi$
$18$	5.14562			1.21283
$19$	0.587589	−	0.587589i	0.134802	−	0.134802i	−0.636486	−	0.771288i	$-0.719613\pi$
$19$	0.587589	−	0.587589i	0.134802	−	0.134802i	0.771288	+	0.636486i	$0.219613\pi$
$20$		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	0.882798	−	0.469752i	$-0.155657\pi$
$23$	1.98090	+	1.98090i	0.413046	+	0.413046i	−0.469752	+	0.882798i	$0.655657\pi$
$24$	−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
$28$	8.75717			1.65495
$29$		−	7.92385i		−	1.47142i	−0.677296	−	0.735711i	$-0.736848\pi$
$29$		−	7.92385i		−	1.47142i	0.677296	−	0.735711i	$-0.263152\pi$
$30$		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	$0.434081\pi$
$32$			2.83916i			0.501897i
$33$		−	5.04201i		−	0.877702i
$34$	0.626279	+	0.626279i	0.107406	+	0.107406i
$35$		0			0
$36$		−	7.93917i		−	1.32319i
$37$	−10.3366			−1.69932			−0.849662	−	0.527328i	$-0.823194\pi$
$37$	−10.3366			−1.69932			−0.849662	+	0.527328i	$0.823194\pi$
$38$	−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	0.902685	−	0.430302i	$-0.141593\pi$
$43$	3.09762	+	3.09762i	0.472383	+	0.472383i	−0.430302	+	0.902685i	$0.641593\pi$
$44$	14.2976	−	14.2976i	2.15544	−	2.15544i
$45$		0			0
$46$	4.71928	−	4.71928i	0.695820	−	0.695820i
$47$	−5.67137			−0.827255			−0.413627	−	0.910446i	$-0.635738\pi$
$47$	−5.67137			−0.827255			−0.413627	+	0.910446i	$0.635738\pi$
$48$	−1.39987	+	1.39987i	−0.202053	+	0.202053i
$49$	−1.32421			−0.189173
$50$		0			0
$51$		−	0.340759i		−	0.0477158i
$52$	10.1733	+	8.49429i	1.41078	+	1.17795i
$53$	1.54732	−	1.54732i	0.212540	−	0.212540i	−0.592805	−	0.805346i	$-0.701980\pi$
$53$	1.54732	−	1.54732i	0.212540	−	0.212540i	0.805346	+	0.592805i	$0.201980\pi$
$54$	−7.96733	+	7.96733i	−1.08422	+	1.08422i
$55$		0			0
$56$		−	9.51143i		−	1.27102i
$57$			0.761669i			0.100885i
$58$	−18.8777			−2.47876
$59$	−5.49009	−	5.49009i	−0.714748	−	0.714748i	0.252776	−	0.967525i	$-0.418656\pi$
$59$	−5.49009	−	5.49009i	−0.714748	−	0.714748i	−0.967525	+	0.252776i	$0.918656\pi$
$60$		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
$63$		−	5.14562i		−	0.648287i
$64$	11.0837			1.38546
$65$		0			0
$66$	−12.0120			−1.47858
$67$			3.74764i			0.457847i	0.973444	+	0.228924i	$0.0735206\pi$
$67$			3.74764i			0.457847i	−0.973444	+	0.228924i	$0.926479\pi$
$68$	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	$0.804857\pi$
$72$	−8.62298			−1.01623
$73$			7.56049i			0.884888i	0.896796	+	0.442444i	$0.145889\pi$
$73$			7.56049i			0.884888i	−0.896796	+	0.442444i	$0.854111\pi$
$74$			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
$78$	−0.705296	−	7.84175i	−0.0798591	−	0.887903i
$79$			6.07165i			0.683114i	0.939861	+	0.341557i	$0.110954\pi$
$79$			6.07165i			0.683114i	−0.939861	+	0.341557i	$0.889046\pi$
$80$		0			0
$81$	−2.14453			−0.238281
$82$	−15.1991	+	15.1991i	−1.67845	+	1.67845i
$83$	−13.0415			−1.43150			−0.715748	−	0.698359i	$-0.753914\pi$
$83$	−13.0415			−1.43150			−0.715748	+	0.698359i	$0.753914\pi$
$84$	−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	0.815579	−	0.578646i	$-0.196419\pi$
$89$	2.23522	+	2.23522i	0.236932	+	0.236932i	−0.578646	+	0.815579i	$0.696419\pi$
$90$		0			0
$91$	6.59361	+	5.50541i	0.691198	+	0.577124i
$92$	−7.28137	−	7.28137i	−0.759135	−	0.759135i
$93$	−8.54704			−0.886287
$94$			13.5114i			1.39360i
$95$		0			0
$96$	−1.84015	−	1.84015i	−0.187809	−	0.187809i
$97$		−	1.88723i		−	0.191619i	−0.995400	−	0.0958094i	$-0.969456\pi$
$97$		−	1.88723i		−	0.191619i	0.995400	−	0.0958094i	$-0.0305439\pi$
$98$			3.15479i			0.318682i
$99$	−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	$0.896718\pi$
$102$	−0.811821			−0.0803822
$103$	6.56425	+	6.56425i	0.646795	+	0.646795i	0.952217	−	0.305422i	$-0.0987975\pi$
$103$	6.56425	+	6.56425i	0.646795	+	0.646795i	−0.305422	+	0.952217i	$0.598798\pi$
$104$	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	$-0.279299\pi$
$107$	−1.34459	−	1.34459i	−0.129987	−	0.129987i	−0.769107	+	0.639120i	$0.779299\pi$
$108$	12.2928	+	12.2928i	1.18287	+	1.18287i
$109$	11.7474	−	11.7474i	1.12520	−	1.12520i	0.134254	−	0.990947i	$-0.457136\pi$
$109$	11.7474	−	11.7474i	1.12520	−	1.12520i	0.990947	−	0.134254i	$-0.0428638\pi$
$110$		0			0
$111$	6.69945	−	6.69945i	0.635884	−	0.635884i
$112$	−5.14562			−0.486215
$113$	0.581032	−	0.581032i	0.0546589	−	0.0546589i	−0.679249	−	0.733908i	$-0.737694\pi$
$113$	0.581032	−	0.581032i	0.0546589	−	0.0546589i	0.733908	+	0.679249i	$0.237694\pi$
$114$	1.81459			0.169952
$115$		0			0
$116$			29.1264i			2.70432i
$117$	4.99115	−	5.97771i	0.461432	−	0.552639i
$118$	−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
$122$		−	9.81271i		−	0.888401i
$123$	8.26981			0.745664
$124$	−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	−0.474855	−	0.880064i	$-0.657499\pi$
$127$	4.56648	−	4.56648i	0.405209	−	0.405209i	0.880064	+	0.474855i	$0.157499\pi$
$128$		−	20.7274i		−	1.83206i
$129$	−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	$0.274232\pi$
$132$			18.5334i			1.61312i
$133$	−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
$137$	−9.21583			−0.787362			−0.393681	−	0.919247i	$-0.628798\pi$
$137$	−9.21583			−0.787362			−0.393681	+	0.919247i	$0.628798\pi$
$138$			6.11742i			0.520749i
$139$			5.87665i			0.498451i	0.968446	+	0.249225i	$0.0801760\pi$
$139$			5.87665i			0.498451i	−0.968446	+	0.249225i	$0.919824\pi$
$140$		0			0
$141$	3.67579	−	3.67579i	0.309557	−	0.309557i
$142$	−4.86839	+	4.86839i	−0.408546	+	0.408546i
$143$	19.7537	−	1.77667i	1.65189	−	0.148573i
$144$			4.66497i			0.388747i
$145$		0			0
$146$	18.0120			1.49069
$147$	0.858261	−	0.858261i	0.0707881	−	0.0707881i
$148$	37.9951			3.12318
$149$	5.89568	−	5.89568i	0.482993	−	0.482993i	−0.423093	−	0.906086i	$-0.639056\pi$
$149$	5.89568	−	5.89568i	0.482993	−	0.482993i	0.906086	+	0.423093i	$0.139056\pi$
$150$		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	0.994058	+	0.108855i	$0.0347183\pi$
$157$	13.8195	+	13.8195i	1.10291	+	1.10291i	0.108855	+	0.994058i	$0.465282\pi$
$158$	14.4651			1.15078
$159$			2.00573i			0.159064i
$160$		0			0
$161$	−4.71928	−	4.71928i	−0.371931	−	0.371931i
$162$			5.10911i			0.401410i
$163$		−	3.80590i		−	0.298101i	−0.988830	−	0.149051i	$-0.952378\pi$
$163$		−	3.80590i		−	0.298101i	0.988830	−	0.149051i	$-0.0476217\pi$
$164$	23.4506	+	23.4506i	1.83118	+	1.83118i
$165$		0			0
$166$			31.0701i			2.41150i
$167$	18.2483			1.41210			0.706050	−	0.708162i	$-0.250476\pi$
$167$	18.2483			1.41210			0.706050	+	0.708162i	$0.250476\pi$
$168$	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	0.707388	−	0.706825i	$-0.249873\pi$
$173$	0.00740374	+	0.00740374i	0.000562896	+	0.000562896i	−0.706825	+	0.707388i	$0.749873\pi$
$174$	12.2352	−	12.2352i	0.927549	−	0.927549i
$175$		0			0
$176$	−8.40109	+	8.40109i	−0.633256	+	0.633256i
$177$	7.11659			0.534915
$178$	5.32516	−	5.32516i	0.399137	−	0.399137i
$179$	−12.0717			−0.902278			−0.451139	−	0.892454i	$-0.648982\pi$
$179$	−12.0717			−0.902278			−0.451139	+	0.892454i	$0.648982\pi$
$180$		0			0
$181$		−	18.2589i		−	1.35717i	−0.734521	−	0.678586i	$-0.762593\pi$
$181$		−	18.2589i		−	1.35717i	0.734521	−	0.678586i	$-0.237407\pi$
$182$	13.1160	−	15.7086i	0.972226	−	1.16440i
$183$	−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
$187$		−	2.04501i		−	0.149546i
$188$	20.8468			1.52041
$189$	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
$193$			12.4812i			0.898414i	0.893428	+	0.449207i	$0.148293\pi$
$193$			12.4812i			0.898414i	−0.893428	+	0.449207i	$0.851707\pi$
$194$	−4.49611			−0.322802
$195$		0			0
$196$	4.86752			0.347680
$197$			19.8948i			1.41745i	0.705485	+	0.708725i	$0.250729\pi$
$197$			19.8948i			1.41745i	−0.705485	+	0.708725i	$0.749271\pi$
$198$	−20.0147	+	20.0147i	−1.42238	+	1.42238i
$199$	−13.5740			−0.962232			−0.481116	−	0.876657i	$-0.659768\pi$
$199$	−13.5740			−0.962232			−0.481116	+	0.876657i	$0.659768\pi$
$200$		0			0
$201$	−2.42896	−	2.42896i	−0.171326	−	0.171326i
$202$	15.2661			1.07412
$203$			18.8777i			1.32496i
$204$			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
$208$	−5.97771	−	4.99115i	−0.414479	−	0.346074i
$209$			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
$213$	2.64889			0.181499
$214$	−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
$223$	−10.1659			−0.680757			−0.340379	−	0.940288i	$-0.610555\pi$
$223$	−10.1659			−0.680757			−0.340379	+	0.940288i	$0.610555\pi$
$224$		−	6.76399i		−	0.451938i
$225$		0			0
$226$	−1.38425	−	1.38425i	−0.0920787	−	0.0920787i
$227$		−	18.5876i		−	1.23370i	−0.787080	−	0.616852i	$-0.788408\pi$
$227$		−	18.5876i		−	1.23370i	0.787080	−	0.616852i	$-0.211592\pi$
$228$		−	2.79973i		−	0.185417i
$229$	6.29605	+	6.29605i	0.416054	+	0.416054i	0.883841	−	0.467787i	$-0.154949\pi$
$229$	6.29605	+	6.29605i	0.416054	+	0.416054i	−0.467787	+	0.883841i	$0.654949\pi$
$230$		0			0
$231$			12.0120i			0.790335i
$232$	31.6351			2.07694
$233$	−19.7706	−	19.7706i	−1.29521	−	1.29521i	−0.931518	−	0.363696i	$-0.881515\pi$
$233$	−19.7706	−	19.7706i	−1.29521	−	1.29521i	−0.363696	−	0.931518i	$-0.618485\pi$
$234$	−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	−0.952552	−	0.304376i	$-0.901552\pi$
$239$	−10.0206	+	10.0206i	−0.648176	+	0.648176i	0.304376	+	0.952552i	$0.401552\pi$
$240$		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	$0.209353\pi$
$242$	−45.8822			−2.94942
$243$	11.4227	−	11.4227i	0.732767	−	0.732767i
$244$	−15.1400			−0.969241
$245$		0			0
$246$		−	19.7019i		−	1.25615i
$247$	−2.98408	+	0.268392i	−0.189873	+	0.0170774i
$248$	−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	$0.750439\pi$
$252$			18.9142i			1.19148i
$253$	−15.4100			−0.968821
$254$	−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	−0.749806	−	0.661658i	$-0.769853\pi$
$257$	−1.41312	+	1.41312i	−0.0881481	+	0.0881481i	0.661658	+	0.749806i	$0.269853\pi$
$258$			9.56607i			0.595558i
$259$	24.6258			1.53017
$260$		0			0
$261$	17.1143			1.05935
$262$		−	35.5179i		−	2.19431i
$263$	−3.71113	+	3.71113i	−0.228838	+	0.228838i	−0.812207	−	0.583369i	$-0.801734\pi$
$263$	−3.71113	+	3.71113i	−0.228838	+	0.228838i	0.583369	+	0.812207i	$0.301734\pi$
$264$	20.1297			1.23890
$265$		0			0
$266$	3.33503	+	3.33503i	0.204484	+	0.204484i
$267$	−2.89742			−0.177319
$268$		−	13.7755i		−	0.841475i
$269$			0.372632i			0.0227198i	0.999935	+	0.0113599i	$0.00361604\pi$
$269$			0.372632i			0.0227198i	−0.999935	+	0.0113599i	$0.996384\pi$
$270$		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
$273$	−7.84175	+	0.705296i	−0.474604	+	0.0426865i
$274$			21.9557i			1.32639i
$275$		0			0
$276$	9.43856			0.568134
$277$	−12.4546	+	12.4546i	−0.748324	+	0.748324i	−0.974164	−	0.225840i	$-0.927487\pi$
$277$	−12.4546	+	12.4546i	−0.748324	+	0.748324i	0.225840	+	0.974164i	$0.427487\pi$
$278$	14.0005			0.839693
$279$	−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	0.937645	+	0.347594i	$0.113001\pi$
$283$	21.6211	+	21.6211i	1.28524	+	1.28524i	0.347594	+	0.937645i	$0.386999\pi$
$284$	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
$288$	−6.13217			−0.361342
$289$			16.8618i			0.991870i
$290$		0			0
$291$	1.22317	+	1.22317i	0.0717034	+	0.0717034i
$292$		−	27.7908i		−	1.62633i
$293$		−	25.7477i		−	1.50419i	−0.659053	−	0.752097i	$-0.729043\pi$
$293$		−	25.7477i		−	1.50419i	0.659053	−	0.752097i	$-0.270957\pi$
$294$	−2.04471	−	2.04471i	−0.119250	−	0.119250i
$295$		0			0
$296$		−	41.2676i		−	2.39863i
$297$	26.0160			1.50960
$298$	−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
$307$	−1.82202			−0.103988			−0.0519940	−	0.998647i	$-0.516558\pi$
$307$	−1.82202			−0.103988			−0.0519940	+	0.998647i	$0.516558\pi$
$308$	−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	$0.929636\pi$
$312$	1.18193	+	13.1411i	0.0669136	+	0.743970i
$313$	13.6675	−	13.6675i	0.772534	−	0.772534i	−0.206015	−	0.978549i	$-0.566050\pi$
$313$	13.6675	−	13.6675i	0.772534	−	0.772534i	0.978549	+	0.206015i	$0.0660496\pi$
$314$	32.9233	−	32.9233i	1.85797	−	1.85797i
$315$		0			0
$316$		−	22.3181i		−	1.25549i
$317$			14.3180i			0.804179i	0.915600	+	0.402089i	$0.131716\pi$
$317$			14.3180i			0.804179i	−0.915600	+	0.402089i	$0.868284\pi$
$318$	4.77843			0.267961
$319$	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
$323$			0.308929i			0.0171892i
$324$	7.88284			0.437936
$325$		0			0
$326$	−9.06715			−0.502183
$327$			15.2278i			0.842097i
$328$	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	$0.888483\pi$
$332$	47.9380			2.63094
$333$		−	22.3255i		−	1.22343i
$334$		−	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	−0.835760	−	0.549095i	$-0.814973\pi$
$337$	−5.26248	+	5.26248i	−0.286665	+	0.286665i	0.549095	+	0.835760i	$0.314973\pi$
$338$	30.4740	−	5.52645i	1.65757	−	0.300599i
$339$			0.753170i			0.0409066i
$340$		0			0
$341$	−51.2938			−2.77771
$342$	3.02351	−	3.02351i	0.163493	−	0.163493i
$343$	19.8315			1.07080
$344$	−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	$-0.347045\pi$
$347$	−7.90775	−	7.90775i	−0.424510	−	0.424510i	−0.886753	+	0.462243i	$0.847045\pi$
$348$	−18.8777	−	18.8777i	−1.01195	−	1.01195i
$349$	1.59130	+	1.59130i	0.0851802	+	0.0851802i	0.748413	−	0.663233i	$-0.230816\pi$
$349$	1.59130	+	1.59130i	0.0851802	+	0.0851802i	−0.663233	+	0.748413i	$0.730816\pi$
$350$		0			0
$351$	1.52755	+	16.9839i	0.0815347	+	0.906533i
$352$	−11.0434	−	11.0434i	−0.588613	−	0.588613i
$353$	−19.3600			−1.03043			−0.515215	−	0.857061i	$-0.672288\pi$
$353$	−19.3600			−1.03043			−0.515215	+	0.857061i	$0.672288\pi$
$354$		−	16.9545i		−	0.901121i
$355$		0			0
$356$	−8.21618	−	8.21618i	−0.435457	−	0.435457i
$357$			0.811821i			0.0429661i
$358$			28.7594i			1.51998i
$359$	−3.46070	−	3.46070i	−0.182649	−	0.182649i	0.609860	−	0.792509i	$-0.291226\pi$
$359$	−3.46070	−	3.46070i	−0.182649	−	0.182649i	−0.792509	+	0.609860i	$0.791226\pi$
$360$		0			0
$361$			18.3095i			0.963657i
$362$	−43.4998			−2.28630
$363$	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	$-0.341522\pi$
$367$	−7.68286	−	7.68286i	−0.401042	−	0.401042i	−0.878600	+	0.477558i	$0.841522\pi$
$368$	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
$372$	31.4171			1.62890
$373$	6.30515	−	6.30515i	0.326469	−	0.326469i	−0.524773	−	0.851242i	$-0.675850\pi$
$373$	6.30515	−	6.30515i	0.326469	−	0.326469i	0.851242	+	0.524773i	$0.175850\pi$
$374$	−4.87202			−0.251926
$375$		0			0
$376$		−	22.6423i		−	1.16769i
$377$	−18.3110	+	21.9304i	−0.943066	+	1.12947i
$378$	18.9813	−	18.9813i	0.976293	−	0.976293i
$379$	−0.333942	+	0.333942i	−0.0171534	+	0.0171534i	−0.715631	−	0.698478i	$-0.753861\pi$
$379$	−0.333942	+	0.333942i	−0.0171534	+	0.0171534i	0.698478	+	0.715631i	$0.253861\pi$
$380$		0			0
$381$			5.91934i			0.303257i
$382$			15.2444i			0.779971i
$383$	−5.09138			−0.260158			−0.130079	−	0.991504i	$-0.541523\pi$
$383$	−5.09138			−0.260158			−0.130079	+	0.991504i	$0.541523\pi$
$384$	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
$388$			6.93704i			0.352175i
$389$	−33.6544			−1.70634			−0.853172	−	0.521629i	$-0.825324\pi$
$389$	−33.6544			−1.70634			−0.853172	+	0.521629i	$0.825324\pi$
$390$		0			0
$391$	−1.04147			−0.0526694
$392$		−	5.28676i		−	0.267022i
$393$	−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
$397$	−11.6763			−0.586019			−0.293010	−	0.956110i	$-0.594657\pi$
$397$	−11.6763			−0.586019			−0.293010	+	0.956110i	$0.594657\pi$
$398$			32.3385i			1.62098i
$399$		−	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
$403$	−3.01175	−	33.4858i	−0.150026	−	1.66805i
$404$		−	23.5541i		−	1.17186i
$405$		0			0
$406$	44.9741			2.23203
$407$	40.2058	−	40.2058i	1.99293	−	1.99293i
$408$	1.36044			0.0673519
$409$	12.8746	−	12.8746i	0.636609	−	0.636609i	−0.313108	−	0.949718i	$-0.601370\pi$
$409$	12.8746	−	12.8746i	0.636609	−	0.636609i	0.949718	+	0.313108i	$0.101370\pi$
$410$		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
$418$	10.8900			0.532648
$419$		−	31.0270i		−	1.51577i	−0.652389	−	0.757884i	$-0.726233\pi$
$419$		−	31.0270i		−	1.51577i	0.652389	−	0.757884i	$-0.273767\pi$
$420$		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	$0.825551\pi$
$422$			25.3362i			1.23335i
$423$		−	12.2493i		−	0.595583i
$424$	6.17749	+	6.17749i	0.300006	+	0.300006i
$425$		0			0
$426$		−	6.31070i		−	0.305755i
$427$	−9.81271			−0.474870
$428$	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	0.973124	−	0.230283i	$-0.0739652\pi$
$433$	15.4575	+	15.4575i	0.742841	+	0.742841i	−0.230283	+	0.973124i	$0.573965\pi$
$434$	−37.4240	+	37.4240i	−1.79641	+	1.79641i
$435$		0			0
$436$	−43.1811	+	43.1811i	−2.06800	+	2.06800i
$437$	2.32791			0.111359
$438$	−11.6742	+	11.6742i	−0.557813	+	0.557813i
$439$	−24.6942			−1.17859			−0.589294	−	0.807919i	$-0.700594\pi$
$439$	−24.6942			−1.17859			−0.589294	+	0.807919i	$0.700594\pi$
$440$		0			0
$441$		−	2.86010i		−	0.136195i
$442$	−0.286064	−	3.18057i	−0.0136067	−	0.151284i
$443$	−22.0612	+	22.0612i	−1.04816	+	1.04816i	−0.0493786	+	0.998780i	$0.515724\pi$
$443$	−22.0612	+	22.0612i	−1.04816	+	1.04816i	−0.998780	+	0.0493786i	$0.984276\pi$
$444$	−24.6258	+	24.6258i	−1.16869	+	1.16869i
$445$		0			0
$446$			24.2191i			1.14681i
$447$			7.64234i			0.361470i
$448$	−26.4057			−1.24755
$449$	−0.902668	−	0.902668i	−0.0425995	−	0.0425995i	0.685486	−	0.728086i	$-0.259590\pi$
$449$	−0.902668	−	0.902668i	−0.0425995	−	0.0425995i	−0.728086	+	0.685486i	$0.759590\pi$
$450$		0			0
$451$	49.6300			2.33699
$452$	−2.13575	+	2.13575i	−0.100457	+	0.100457i
$453$		−	16.7803i		−	0.788410i
$454$	−44.2830			−2.07830
$455$		0			0
$456$	−3.04088			−0.142402
$457$		−	31.9104i		−	1.49271i	−0.665550	−	0.746353i	$-0.731803\pi$
$457$		−	31.9104i		−	1.49271i	0.665550	−	0.746353i	$-0.268197\pi$
$458$	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	$0.767336\pi$
$462$	28.6174			1.33140
$463$		−	3.04132i		−	0.141342i	−0.997500	−	0.0706710i	$-0.977486\pi$
$463$		−	3.04132i		−	0.141342i	0.997500	−	0.0706710i	$-0.0225140\pi$
$464$		−	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	−0.958430	−	0.285328i	$-0.907898\pi$
$467$	−14.5459	+	14.5459i	−0.673102	+	0.673102i	0.285328	+	0.958430i	$0.407898\pi$
$468$	−18.3464	+	21.9728i	−0.848064	+	1.01569i
$469$		−	8.92835i		−	0.412273i
$470$		0			0
$471$	−17.9136			−0.825416
$472$	21.9186	−	21.9186i	1.00888	−	1.00888i
$473$	−24.0974			−1.10800
$474$	−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	$0.0541698\pi$
$479$	25.2765	+	25.2765i	1.15491	+	1.15491i	0.169359	+	0.985554i	$0.445830\pi$
$480$		0			0
$481$	28.6080	+	23.8866i	1.30441	+	1.08913i
$482$	−6.66084	−	6.66084i	−0.303393	−	0.303393i
$483$	6.11742			0.278352
$484$			70.7916i			3.21780i
$485$		0			0
$486$	−27.2134	−	27.2134i	−1.23442	−	1.23442i
$487$			20.4552i			0.926915i	0.886119	+	0.463457i	$0.153391\pi$
$487$			20.4552i			0.926915i	−0.886119	+	0.463457i	$0.846609\pi$
$488$			16.4440i			0.744387i
$489$	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	$-0.0564477\pi$
$492$	−30.3981			−1.37045
$493$	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	−0.990906	−	0.134552i	$-0.957040\pi$
$499$	−19.1295	+	19.1295i	−0.856354	+	0.856354i	0.134552	+	0.990906i	$0.457040\pi$
$500$		0			0
$501$	−11.8273	+	11.8273i	−0.528405	+	0.528405i
$502$	53.3047			2.37911
$503$	−1.20851	+	1.20851i	−0.0538846	+	0.0538846i	−0.733536	−	0.679651i	$-0.762131\pi$
$503$	−1.20851	+	1.20851i	−0.0538846	+	0.0538846i	0.679651	+	0.733536i	$0.262131\pi$
$504$	20.5433			0.915072
$505$		0			0
$506$			36.7128i			1.63208i
$507$	−9.79395	−	6.78700i	−0.434964	−	0.301421i
$508$	−16.7854	+	16.7854i	−0.744732	+	0.744732i
$509$	10.5094	−	10.5094i	0.465822	−	0.465822i	−0.434736	−	0.900558i	$-0.643158\pi$
$509$	10.5094	−	10.5094i	0.465822	−	0.465822i	0.900558	+	0.434736i	$0.143158\pi$
$510$		0			0
$511$		−	18.0120i		−	0.796806i
$512$			23.3781i			1.03318i
$513$	−3.93010			−0.173518
$514$	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
$518$		−	58.6683i		−	2.57774i
$519$	−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	$0.562203\pi$
$522$		−	40.7731i		−	1.78459i
$523$	−2.10327	+	2.10327i	−0.0919697	+	0.0919697i	−0.751595	−	0.659625i	$-0.770715\pi$
$523$	−2.10327	+	2.10327i	−0.0919697	+	0.0919697i	0.659625	+	0.751595i	$0.270715\pi$
$524$	−54.8006			−2.39398
$525$		0			0
$526$	8.84137	+	8.84137i	0.385502	+	0.385502i
$527$	−3.46663			−0.151009
$528$		−	10.8900i		−	0.473927i
$529$		−	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
$533$	2.91407	+	32.3997i	0.126222	+	1.40339i
$534$			6.90279i			0.298713i
$535$		0			0
$536$	−14.9620			−0.646262
$537$	7.82401	−	7.82401i	0.337631	−	0.337631i
$538$	0.887755			0.0382738
$539$	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	$-0.375302\pi$
$547$	−12.6865	−	12.6865i	−0.542435	−	0.542435i	−0.924242	+	0.381807i	$0.875302\pi$
$548$	33.8755			1.44709
$549$			8.89611i			0.379677i
$550$		0			0
$551$	−4.65596	−	4.65596i	−0.198351	−	0.198351i
$552$		−	10.2515i		−	0.436333i
$553$		−	14.4651i		−	0.615117i
$554$	29.6717	+	29.6717i	1.26063	+	1.26063i
$555$		0			0
$556$		−	21.6013i		−	0.916100i
$557$	1.92751			0.0816713			0.0408357	−	0.999166i	$-0.486998\pi$
$557$	1.92751			0.0816713			0.0408357	+	0.999166i	$0.486998\pi$
$558$	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	0.891380	−	0.453256i	$-0.149738\pi$
$563$	10.3956	+	10.3956i	0.438124	+	0.438124i	−0.453256	+	0.891380i	$0.649738\pi$
$564$	−13.5114	+	13.5114i	−0.568934	+	0.568934i
$565$		0			0
$566$	51.5098	−	51.5098i	2.16512	−	2.16512i
$567$	5.10911			0.214562
$568$	8.15840	−	8.15840i	0.342319	−	0.342319i
$569$	−25.2005			−1.05646			−0.528230	−	0.849101i	$-0.677144\pi$
$569$	−25.2005			−1.05646			−0.528230	+	0.849101i	$0.677144\pi$
$570$		0			0
$571$		−	21.7839i		−	0.911630i	−0.890075	−	0.455815i	$-0.849348\pi$
$571$		−	21.7839i		−	0.911630i	0.890075	−	0.455815i	$-0.150652\pi$
$572$	−72.6105	+	6.53068i	−3.03600	+	0.273061i
$573$	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
$577$			36.6110i			1.52414i	0.647497	+	0.762068i	$0.275816\pi$
$577$			36.6110i			1.52414i	−0.647497	+	0.762068i	$0.724184\pi$
$578$	40.1714			1.67091
$579$	−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
$583$			12.0371i			0.498524i
$584$	−30.1844			−1.24904
$585$		0			0
$586$	−61.3410			−2.53397
$587$		−	5.27384i		−	0.217675i	−0.994060	−	0.108837i	$-0.965287\pi$
$587$		−	5.27384i		−	0.217675i	0.994060	−	0.108837i	$-0.0347128\pi$
$588$	−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
$592$	−22.3255			−0.917572
$593$			22.9283i			0.941552i	0.882253	+	0.470776i	$0.156026\pi$
$593$			22.9283i			0.941552i	−0.882253	+	0.470776i	$0.843974\pi$
$594$		−	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
$598$	−23.9669	+	2.15562i	−0.980081	+	0.0881498i
$599$			2.73954i			0.111934i	0.998433	+	0.0559672i	$0.0178242\pi$
$599$			2.73954i			0.111934i	−0.998433	+	0.0559672i	$0.982176\pi$
$600$		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
$603$	−8.09436			−0.329628
$604$	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	$-0.0796439\pi$
$607$	17.7698	+	17.7698i	0.721255	+	0.721255i	−0.247606	+	0.968861i	$0.579644\pi$
$608$	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
$613$	−25.4815			−1.02919			−0.514593	−	0.857435i	$-0.672057\pi$
$613$	−25.4815			−1.02919			−0.514593	+	0.857435i	$0.672057\pi$
$614$			4.34076i			0.175179i
$615$		0			0
$616$	36.9962	+	36.9962i	1.49062	+	1.49062i
$617$		−	17.0369i		−	0.685880i	−0.939357	−	0.342940i	$-0.888577\pi$
$617$		−	17.0369i		−	0.685880i	0.939357	−	0.342940i	$-0.111423\pi$
$618$			20.2717i			0.815449i
$619$	−26.5396	−	26.5396i	−1.06672	−	1.06672i	−0.997609	−	0.0691073i	$-0.977985\pi$
$619$	−26.5396	−	26.5396i	−1.06672	−	1.06672i	−0.0691073	−	0.997609i	$-0.522015\pi$
$620$		0			0
$621$		−	13.2493i		−	0.531675i
$622$	18.4239			0.738729
$623$	−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	$0.330584\pi$
$632$	−24.2404			−0.964231
$633$	6.89273	−	6.89273i	0.273961	−	0.273961i
$634$	34.1111			1.35472
$635$		0			0
$636$		−	7.37263i		−	0.292344i
$637$	3.66494	+	3.06008i	0.145210	+	0.121245i
$638$	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	$-0.286162\pi$
$642$		−	4.15237i		−	0.163881i
$643$	2.08560			0.0822481			0.0411240	−	0.999154i	$-0.486906\pi$
$643$	2.08560			0.0822481			0.0411240	+	0.999154i	$0.486906\pi$
$644$	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	−0.496421	−	0.868082i	$-0.665353\pi$
$647$	9.45363	−	9.45363i	0.371661	−	0.371661i	0.868082	+	0.496421i	$0.165353\pi$
$648$		−	8.56180i		−	0.336339i
$649$	42.7091			1.67648
$650$		0			0
$651$	20.3624			0.798065
$652$			13.9897i			0.547879i
$653$	7.46934	−	7.46934i	0.292298	−	0.292298i	−0.545689	−	0.837987i	$-0.683732\pi$
$653$	7.46934	−	7.46934i	0.292298	−	0.292298i	0.837987	+	0.545689i	$0.183732\pi$
$654$	36.2785			1.41860
$655$		0			0
$656$	−13.7793	−	13.7793i	−0.537992	−	0.537992i
$657$	−16.3296			−0.637076
$658$		−	32.1895i		−	1.25488i
$659$		−	13.0165i		−	0.507053i	−0.967328	−	0.253526i	$-0.918410\pi$
$659$		−	13.0165i		−	0.507053i	0.967328	−	0.253526i	$-0.0815905\pi$
$660$		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
$663$	−0.787451	+	0.943099i	−0.0305821	+	0.0366269i
$664$		−	52.0669i		−	2.02059i
$665$		0			0
$666$	−53.1881			−2.06100
$667$	15.6963	−	15.6963i	0.607765	−	0.607765i
$668$	−67.0771			−2.59529
$669$	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	0.985126	−	0.171832i	$-0.0549686\pi$
$673$	21.0987	+	21.0987i	0.813295	+	0.813295i	−0.171832	+	0.985126i	$0.554969\pi$
$674$	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	$-0.273960\pi$
$677$	−2.76719	−	2.76719i	−0.106352	−	0.106352i	−0.758280	+	0.651929i	$0.773960\pi$
$678$	1.79435			0.0689114
$679$			4.49611i			0.172545i
$680$		0			0
$681$	12.0472	+	12.0472i	0.461650	+	0.461650i
$682$			122.202i			4.67935i
$683$		−	43.9664i		−	1.68233i	−0.540780	−	0.841164i	$-0.681871\pi$
$683$		−	43.9664i		−	1.68233i	0.540780	−	0.841164i	$-0.318129\pi$
$684$	−4.66497	−	4.66497i	−0.178370	−	0.178370i
$685$		0			0
$686$		−	47.2465i		−	1.80388i
$687$	−8.16132			−0.311374
$688$	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
$697$	3.35419			0.127049
$698$	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	$-0.182199\pi$
$702$	40.4623	−	3.63923i	1.52715	−	0.137354i
$703$	−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
$707$		−	15.2661i		−	0.574143i
$708$	−26.1591			−0.983118
$709$	10.9424	+	10.9424i	0.410952	+	0.410952i	0.882070	−	0.471118i	$-0.156149\pi$
$709$	10.9424	+	10.9424i	0.410952	+	0.410952i	−0.471118	+	0.882070i	$0.656149\pi$
$710$		0			0
$711$	−13.1139			−0.491809
$712$	−8.92385	+	8.92385i	−0.334435	+	0.334435i
$713$			26.1226i			0.978298i
$714$	1.93407			0.0723809
$715$		0			0
$716$	44.3729			1.65829
$717$		−	12.9893i		−	0.485093i
$718$	−8.24474	+	8.24474i	−0.307691	+	0.307691i
$719$	−1.67615			−0.0625099			−0.0312550	−	0.999511i	$-0.509950\pi$
$719$	−1.67615			−0.0625099			−0.0312550	+	0.999511i	$0.509950\pi$
$720$		0			0
$721$	−15.6386	−	15.6386i	−0.582413	−	0.582413i
$722$	43.6203			1.62338
$723$			3.62417i			0.134784i
$724$			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	−0.510942	−	0.859615i	$-0.670703\pi$
$727$	9.40127	−	9.40127i	0.348674	−	0.348674i	0.859615	+	0.510942i	$0.170703\pi$
$728$	−21.9797	+	26.3243i	−0.814623	+	0.975642i
$729$			8.37322i			0.310119i
$730$		0			0
$731$	−1.62859			−0.0602357
$732$	9.81271	−	9.81271i	0.362688	−	0.362688i
$733$	−17.2489			−0.637104			−0.318552	−	0.947905i	$-0.603196\pi$
$733$	−17.2489			−0.637104			−0.318552	+	0.947905i	$0.603196\pi$
$734$	−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	0.313234	−	0.949676i	$-0.398588\pi$
$739$	−17.3014	−	17.3014i	−0.636442	−	0.636442i	−0.949676	+	0.313234i	$0.898588\pi$
$740$		0			0
$741$	1.76012	−	2.10803i	0.0646597	−	0.0774403i
$742$	8.78225	+	8.78225i	0.322406	+	0.322406i
$743$	19.0572			0.699142			0.349571	−	0.936910i	$-0.386327\pi$
$743$	19.0572			0.699142			0.349571	+	0.936910i	$0.386327\pi$
$744$		−	34.1231i		−	1.25101i
$745$		0			0
$746$	−15.0213	−	15.0213i	−0.549971	−	0.549971i
$747$		−	28.1678i		−	1.03061i
$748$			7.51703i			0.274850i
$749$	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	$0.963414\pi$
$752$	−12.2493			−0.446687
$753$	−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	$-0.259632\pi$
$757$	−1.17728	−	1.17728i	−0.0427888	−	0.0427888i	−0.728177	+	0.685389i	$0.759632\pi$
$758$	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	$0.182309\pi$
$762$	14.1022			0.510869
$763$	−27.9870	+	27.9870i	−1.01320	+	1.01320i
$764$	23.5206			0.850944
$765$		0			0
$766$			12.1297i			0.438263i
$767$	2.50770	+	27.8815i	0.0905477	+	1.00674i
$768$	17.6378	−	17.6378i	0.636450	−	0.636450i
$769$	−33.1546	+	33.1546i	−1.19558	+	1.19558i	−0.220109	+	0.975475i	$0.570641\pi$
$769$	−33.1546	+	33.1546i	−1.19558	+	1.19558i	−0.975475	+	0.220109i	$0.929359\pi$
$770$		0			0
$771$		−	1.83177i		−	0.0659697i
$772$		−	45.8782i		−	1.65119i
$773$	53.2581			1.91556			0.957780	−	0.287502i	$-0.0928248\pi$
$773$	53.2581			1.91556			0.957780	+	0.287502i	$0.0928248\pi$
$774$	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
$778$			80.1779i			2.87452i
$779$	−7.49734			−0.268620
$780$		0			0
$781$	15.8969			0.568837
$782$			2.48119i			0.0887272i
$783$	−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
$787$	−39.5579			−1.41009			−0.705043	−	0.709165i	$-0.749072\pi$
$787$	−39.5579			−1.41009			−0.705043	+	0.709165i	$0.749072\pi$
$788$		−	73.1293i		−	2.60512i
$789$		−	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
$793$	−11.3995	−	9.51815i	−0.404808	−	0.337999i
$794$			27.8176i			0.987211i
$795$		0			0
$796$	49.8950			1.76848
$797$	−17.6570	+	17.6570i	−0.625443	+	0.625443i	−0.946918	−	0.321475i	$-0.895821\pi$
$797$	−17.6570	+	17.6570i	−0.625443	+	0.625443i	0.321475	+	0.946918i	$0.395821\pi$
$798$	−4.32307			−0.153035
$799$	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
$808$	−25.5829			−0.900002
$809$		−	26.8465i		−	0.943871i	−0.881633	−	0.471936i	$-0.843555\pi$
$809$		−	26.8465i		−	0.943871i	0.881633	−	0.471936i	$-0.156445\pi$
$810$		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	$0.564805\pi$
$812$		−	69.3905i		−	2.43513i
$813$		−	4.02598i		−	0.141197i
$814$	−95.7859	−	95.7859i	−3.35729	−	3.35729i
$815$		0			0
$816$		−	0.735989i		−	0.0257648i
$817$	3.64025			0.127356
$818$	−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	0.403960	−	0.914776i	$-0.367633\pi$
$823$	−14.6543	−	14.6543i	−0.510816	−	0.510816i	−0.914776	+	0.403960i	$0.867633\pi$
$824$	−26.2071	+	26.2071i	−0.912966	+	0.912966i
$825$		0			0
$826$	31.1606	−	31.1606i	1.08422	−	1.08422i
$827$	−2.99000			−0.103972			−0.0519862	−	0.998648i	$-0.516555\pi$
$827$	−2.99000			−0.103972			−0.0519862	+	0.998648i	$0.516555\pi$
$828$	15.7267	−	15.7267i	0.546541	−	0.546541i
$829$	1.29806			0.0450836			0.0225418	−	0.999746i	$-0.492824\pi$
$829$	1.29806			0.0450836			0.0225418	+	0.999746i	$0.492824\pi$
$830$		0			0
$831$		−	16.1444i		−	0.560043i
$832$	−30.6757	−	25.6131i	−1.06349	−	0.887973i
$833$	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
$837$		−	44.1015i		−	1.52437i
$838$	−73.9185			−2.55347
$839$	−3.30809	−	3.30809i	−0.114208	−	0.114208i	0.647693	−	0.761901i	$-0.275734\pi$
$839$	−3.30809	−	3.30809i	−0.114208	−	0.114208i	−0.761901	+	0.647693i	$0.775734\pi$
$840$		0			0
$841$	−33.7873			−1.16508
$842$	−16.2546	+	16.2546i	−0.560170	+	0.560170i
$843$		−	9.31913i		−	0.320968i
$844$	39.0912			1.34558
$845$		0			0
$846$	−29.1827			−1.00332
$847$			45.8822i			1.57653i
$848$	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
$852$	−9.73678			−0.333577
$853$			23.1640i			0.793119i	0.918009	+	0.396560i	$0.129796\pi$
$853$			23.1640i			0.793119i	−0.918009	+	0.396560i	$0.870204\pi$
$854$			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	−0.711994	−	0.702185i	$-0.752208\pi$
$857$	−0.287160	+	0.287160i	−0.00980921	+	0.00980921i	0.702185	+	0.711994i	$0.252208\pi$
$858$	33.2451	+	27.7583i	1.13497	+	0.947654i
$859$		−	34.3061i		−	1.17051i	−0.810850	−	0.585254i	$-0.800995\pi$
$859$		−	34.3061i		−	1.17051i	0.810850	−	0.585254i	$-0.199005\pi$
$860$		0			0
$861$	−19.7019			−0.671440
$862$	−21.3449	+	21.3449i	−0.727009	+	0.727009i
$863$	−13.0838			−0.445377			−0.222688	−	0.974890i	$-0.571483\pi$
$863$	−13.0838			−0.445377			−0.222688	+	0.974890i	$0.571483\pi$
$864$	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
$873$	4.07613			0.137956
$874$		−	5.54599i		−	0.187596i
$875$		0			0
$876$	18.0120	+	18.0120i	0.608571	+	0.608571i
$877$		−	43.5876i		−	1.47185i	−0.677064	−	0.735924i	$-0.736748\pi$
$877$		−	43.5876i		−	1.47185i	0.677064	−	0.735924i	$-0.263252\pi$
$878$			58.8312i			1.98546i
$879$	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	$0.641291\pi$
$882$	−6.81388			−0.229435
$883$	−13.4449	−	13.4449i	−0.452458	−	0.452458i	0.443712	−	0.896170i	$-0.353661\pi$
$883$	−13.4449	−	13.4449i	−0.452458	−	0.452458i	−0.896170	+	0.443712i	$0.853661\pi$
$884$	−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	$-0.119027\pi$
$887$	16.8456	+	16.8456i	0.565618	+	0.565618i	−0.365279	+	0.930898i	$0.619027\pi$
$888$	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
$892$	37.3676			1.25116
$893$	−3.33244	+	3.33244i	−0.111516	+	0.111516i
$894$	18.2071			0.608935
$895$		0			0
$896$			49.3808i			1.64970i
$897$	7.10665	+	5.93378i	0.237284	+	0.198123i
$898$	−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
$902$		−	118.238i		−	3.93690i
$903$	9.56607			0.318339
$904$	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	−0.944946	−	0.327228i	$-0.893886\pi$
$907$	−18.6035	+	18.6035i	−0.617718	+	0.617718i	0.327228	+	0.944946i	$0.393886\pi$
$908$			68.3242i			2.26742i
$909$	−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	$0.404728\pi$
$912$			1.64509i			0.0544745i
$913$	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
$917$	−35.5179			−1.17291
$918$		−	4.18888i		−	0.138253i
$919$			55.5174i			1.83135i	0.401920	+	0.915675i	$0.368343\pi$
$919$			55.5174i			1.83135i	−0.401920	+	0.915675i	$0.631657\pi$
$920$		0			0
$921$	1.18090	−	1.18090i	0.0389121	−	0.0389121i
$922$	−3.93791	+	3.93791i	−0.129688	+	0.129688i
$923$	0.933401	+	10.3779i	0.0307233	+	0.341593i
$924$		−	44.1538i		−	1.45255i
$925$		0			0
$926$	−7.24561			−0.238105
$927$	−14.1778	+	14.1778i	−0.465661	+	0.465661i
$928$	22.4971			0.738502
$929$	−26.7318	+	26.7318i	−0.877040	+	0.877040i	−0.993227	−	0.116187i	$-0.962933\pi$
$929$	−26.7318	+	26.7318i	−0.877040	+	0.877040i	0.116187	+	0.993227i	$0.462933\pi$
$930$		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	0.747643	+	0.664101i	$0.231185\pi$
$937$	43.2141	+	43.2141i	1.41174	+	1.41174i	0.664101	+	0.747643i	$0.268815\pi$
$938$	−21.2708			−0.694517
$939$			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	$0.876137\pi$
$942$			42.6773i			1.39050i
$943$		−	25.2753i		−	0.823076i
$944$	−11.8578	−	11.8578i	−0.385938	−	0.385938i
$945$		0			0
$946$			57.4094i			1.86654i
$947$	−5.66954			−0.184235			−0.0921176	−	0.995748i	$-0.529364\pi$
$947$	−5.66954			−0.184235			−0.0921176	+	0.995748i	$0.529364\pi$
$948$	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	0.831531	−	0.555478i	$-0.187465\pi$
$953$	8.52197	+	8.52197i	0.276054	+	0.276054i	−0.555478	+	0.831531i	$0.687465\pi$
$954$	7.96190	−	7.96190i	0.257776	−	0.257776i
$955$		0			0
$956$	36.8335	−	36.8335i	1.19128	−	1.19128i
$957$	−39.9521			−1.29147
$958$	60.2186	−	60.2186i	1.94557	−	1.94557i
$959$	21.9557			0.708987
$960$		0			0
$961$			55.9514i			1.80489i
$962$	56.9071	−	68.1554i	1.83476	−	2.19742i
$963$	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
$967$			14.0855i			0.452959i	0.974016	+	0.226480i	$0.0727216\pi$
$967$			14.0855i			0.452959i	−0.974016	+	0.226480i	$0.927278\pi$
$968$	76.8889			2.47130
$969$	−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
$973$		−	14.0005i		−	0.448835i
$974$	48.7323			1.56149
$975$		0			0
$976$	8.89611			0.284758
$977$			7.91854i			0.253337i	0.991945	+	0.126668i	$0.0404284\pi$
$977$			7.91854i			0.253337i	−0.991945	+	0.126668i	$0.959572\pi$
$978$	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
$982$	−18.6252			−0.594355
$983$		−	55.0656i		−	1.75632i	−0.478367	−	0.878160i	$-0.658771\pi$
$983$		−	55.0656i		−	1.75632i	0.478367	−	0.878160i	$-0.341229\pi$
$984$			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
$988$	10.9689	−	0.986553i	0.348966	−	0.0313864i
$989$			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
$993$	14.0566			0.446074
$994$	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	$-0.0976166\pi$
$997$	20.5699	+	20.5699i	0.651457	+	0.651457i	−0.301887	+	0.953344i	$0.597617\pi$
$998$	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.f.d.307.1	yes	16
5.2	odd	4		325.2.k.d.268.8	yes	16
5.3	odd	4		325.2.k.d.268.1	yes	16
5.4	even	2	inner	325.2.f.d.307.8	yes	16
13.5	odd	4		325.2.k.d.57.1	yes	16
65.18	even	4	inner	325.2.f.d.18.8	yes	16
65.44	odd	4		325.2.k.d.57.8	yes	16
65.57	even	4	inner	325.2.f.d.18.1	✓	16

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

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.f (of order \(4\), degree \(2\), minimal)

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