LMFDB - Embedded newform 950.2.u.f.549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			549.1
Character	$\chi$	$=$	950.549
Dual form			950.2.u.f.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(-1.68231 + 2.00490i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.00490 - 1.68231i) q^{6} +(-0.840422 + 0.485218i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.668514 - 3.79133i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.68231 + 2.00490i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.00490 - 1.68231i) q^{6} +(-0.840422 + 0.485218i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.668514 - 3.79133i) q^{9} +(0.280827 - 0.486406i) q^{11} +(-2.26658 + 1.30861i) q^{12} +(-0.293901 - 0.350258i) q^{13} +(0.911911 - 0.331909i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.387080 - 0.0682527i) q^{17} +3.84982i q^{18} +(1.58943 - 4.05878i) q^{19} +(0.441039 - 2.50125i) q^{21} +(-0.361024 + 0.430251i) q^{22} +(1.79231 - 4.92432i) q^{23} +(2.45938 - 0.895141i) q^{24} +(0.228615 + 0.395972i) q^{26} +(1.92618 + 1.11208i) q^{27} +(-0.955692 + 0.168514i) q^{28} +(0.411474 + 2.33359i) q^{29} +(-5.44104 - 9.42416i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(0.502759 + 1.38132i) q^{33} +(0.369347 + 0.134431i) q^{34} +(0.668514 - 3.79133i) q^{36} +5.14885i q^{37} +(-2.27009 + 3.72112i) q^{38} +1.19667 q^{39} +(6.14611 + 5.15720i) q^{41} +(-0.868676 + 2.38667i) q^{42} +(-3.49906 - 9.61359i) q^{43} +(0.430251 - 0.361024i) q^{44} +(-2.62018 + 4.53828i) q^{46} +(12.0877 - 2.13139i) q^{47} +(-2.57745 + 0.454475i) q^{48} +(-3.02913 + 5.24660i) q^{49} +(0.788030 - 0.661236i) q^{51} +(-0.156382 - 0.429655i) q^{52} +(-1.55164 + 4.26309i) q^{53} +(-1.70381 - 1.42967i) q^{54} +0.970436 q^{56} +(5.46354 + 10.0148i) q^{57} -2.36959i q^{58} +(-0.759597 + 4.30789i) q^{59} +(4.02481 + 1.46491i) q^{61} +(3.72189 + 10.2258i) q^{62} +(2.40146 + 2.86194i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.255257 - 1.44764i) q^{66} +(12.0001 - 2.11595i) q^{67} +(-0.340392 - 0.196526i) q^{68} +(6.85757 + 11.8777i) q^{69} +(6.85757 - 2.49595i) q^{71} +(-1.31672 + 3.61765i) q^{72} +(8.96047 - 10.6787i) q^{73} +(0.894088 - 5.07062i) q^{74} +(2.88176 - 3.27039i) q^{76} +0.545048i q^{77} +(-1.17849 - 0.207799i) q^{78} +(0.730080 + 0.612610i) q^{79} +(5.38288 - 1.95921i) q^{81} +(-5.15720 - 6.14611i) q^{82} +(-9.76080 + 5.63540i) q^{83} +(1.26992 - 2.19957i) q^{84} +(1.77652 + 10.0751i) q^{86} +(-5.37084 - 3.10086i) q^{87} +(-0.486406 + 0.280827i) q^{88} +(-2.69822 + 2.26408i) q^{89} +(0.416952 + 0.151758i) q^{91} +(3.36844 - 4.01435i) q^{92} +(28.0481 + 4.94563i) q^{93} -12.2742 q^{94} +2.61722 q^{96} +(-7.10973 - 1.25364i) q^{97} +(3.89417 - 4.64089i) q^{98} +(-2.03186 - 0.739538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 24 * q + 6 * q^6 - 18 * q^9	$ 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	−1.68231	+	2.00490i	−0.971285	+	1.15753i	0.0162084	+	0.999869i	$0.494840\pi$
$3$	−1.68231	+	2.00490i	−0.971285	+	1.15753i	−0.987493	+	0.157663i	$0.949604\pi$
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	2.00490	−	1.68231i	0.818499	−	0.686802i
$7$	−0.840422	+	0.485218i	−0.317650	+	0.183395i	−0.650344	−	0.759639i	$-0.725375\pi$
$7$	−0.840422	+	0.485218i	−0.317650	+	0.183395i	0.332695	+	0.943035i	$0.392042\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−0.668514	−	3.79133i	−0.222838	−	1.26378i
$10$		0			0
$11$	0.280827	−	0.486406i	0.0846724	−	0.146657i	−0.820579	−	0.571533i	$-0.806349\pi$
$11$	0.280827	−	0.486406i	0.0846724	−	0.146657i	0.905252	+	0.424876i	$0.139682\pi$
$12$	−2.26658	+	1.30861i	−0.654304	+	0.377763i
$13$	−0.293901	−	0.350258i	−0.0815135	−	0.0971440i	0.723746	−	0.690066i	$-0.242419\pi$
$13$	−0.293901	−	0.350258i	−0.0815135	−	0.0971440i	−0.805260	+	0.592922i	$0.797974\pi$
$14$	0.911911	−	0.331909i	0.243719	−	0.0887063i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.387080	−	0.0682527i	−0.0938807	−	0.0165537i	0.126510	−	0.991965i	$-0.459622\pi$
$17$	−0.387080	−	0.0682527i	−0.0938807	−	0.0165537i	−0.220391	+	0.975412i	$0.570733\pi$
$18$			3.84982i			0.907411i
$19$	1.58943	−	4.05878i	0.364641	−	0.931148i
$19$	1.58943	−	4.05878i	0.364641	−	0.931148i
$20$		0			0
$21$	0.441039	−	2.50125i	0.0962425	−	0.545818i
$22$	−0.361024	+	0.430251i	−0.0769705	+	0.0917299i
$23$	1.79231	−	4.92432i	0.373722	−	1.02679i	−0.600188	−	0.799859i	$-0.704908\pi$
$23$	1.79231	−	4.92432i	0.373722	−	1.02679i	0.973910	−	0.226934i	$-0.0728701\pi$
$24$	2.45938	−	0.895141i	0.502019	−	0.182720i
$25$		0			0
$26$	0.228615	+	0.395972i	0.0448350	+	0.0776565i
$27$	1.92618	+	1.11208i	0.370694	+	0.214020i
$28$	−0.955692	+	0.168514i	−0.180609	+	0.0318462i
$29$	0.411474	+	2.33359i	0.0764088	+	0.433336i	0.998882	+	0.0472746i	$0.0150536\pi$
$29$	0.411474	+	2.33359i	0.0764088	+	0.433336i	−0.922473	+	0.386061i	$0.873835\pi$
$30$		0			0
$31$	−5.44104	−	9.42416i	−0.977239	−	1.69263i	−0.672338	−	0.740244i	$-0.734710\pi$
$31$	−5.44104	−	9.42416i	−0.977239	−	1.69263i	−0.304901	−	0.952384i	$-0.598624\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	0.502759	+	1.38132i	0.0875191	+	0.240457i
$34$	0.369347	+	0.134431i	0.0633426	+	0.0230548i
$35$		0			0
$36$	0.668514	−	3.79133i	0.111419	−	0.631889i
$37$			5.14885i			0.846465i	0.906021	+	0.423232i	$0.139105\pi$
$37$			5.14885i			0.846465i	−0.906021	+	0.423232i	$0.860895\pi$
$38$	−2.27009	+	3.72112i	−0.368257	+	0.603645i
$39$	1.19667			0.191620
$40$		0			0
$41$	6.14611	+	5.15720i	0.959862	+	0.805420i	0.980931	−	0.194358i	$-0.0622625\pi$
$41$	6.14611	+	5.15720i	0.959862	+	0.805420i	−0.0210689	+	0.999778i	$0.506707\pi$
$42$	−0.868676	+	2.38667i	−0.134040	+	0.368271i
$43$	−3.49906	−	9.61359i	−0.533602	−	1.46606i	−0.854755	−	0.519031i	$-0.826293\pi$
$43$	−3.49906	−	9.61359i	−0.533602	−	1.46606i	0.321154	−	0.947027i	$-0.395929\pi$
$44$	0.430251	−	0.361024i	0.0648628	−	0.0544264i
$45$		0			0
$46$	−2.62018	+	4.53828i	−0.386324	+	0.669133i
$47$	12.0877	−	2.13139i	1.76318	−	0.310896i	0.804196	−	0.594364i	$-0.202596\pi$
$47$	12.0877	−	2.13139i	1.76318	−	0.310896i	0.958982	+	0.283468i	$0.0914851\pi$
$48$	−2.57745	+	0.454475i	−0.372024	+	0.0655978i
$49$	−3.02913	+	5.24660i	−0.432732	+	0.749515i
$50$		0			0
$51$	0.788030	−	0.661236i	0.110346	−	0.0925915i
$52$	−0.156382	−	0.429655i	−0.0216862	−	0.0595824i
$53$	−1.55164	+	4.26309i	−0.213134	+	0.585581i	−0.999481	−	0.0322038i	$-0.989747\pi$
$53$	−1.55164	+	4.26309i	−0.213134	+	0.585581i	0.786347	+	0.617785i	$0.211970\pi$
$54$	−1.70381	−	1.42967i	−0.231859	−	0.194553i
$55$		0			0
$56$	0.970436			0.129680
$57$	5.46354	+	10.0148i	0.723663	+	1.32649i
$58$		−	2.36959i		−	0.311142i
$59$	−0.759597	+	4.30789i	−0.0988911	+	0.560839i	0.894594	+	0.446879i	$0.147465\pi$
$59$	−0.759597	+	4.30789i	−0.0988911	+	0.560839i	−0.993485	+	0.113960i	$0.963646\pi$
$60$		0			0
$61$	4.02481	+	1.46491i	0.515324	+	0.187562i	0.586573	−	0.809896i	$-0.300477\pi$
$61$	4.02481	+	1.46491i	0.515324	+	0.187562i	−0.0712499	+	0.997458i	$0.522699\pi$
$62$	3.72189	+	10.2258i	0.472680	+	1.29868i
$63$	2.40146	+	2.86194i	0.302555	+	0.360571i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−0.255257	−	1.44764i	−0.0314200	−	0.178192i
$67$	12.0001	−	2.11595i	1.46605	−	0.258504i	0.617061	−	0.786915i	$-0.288323\pi$
$67$	12.0001	−	2.11595i	1.46605	−	0.258504i	0.848989	+	0.528411i	$0.177212\pi$
$68$	−0.340392	−	0.196526i	−0.0412787	−	0.0238322i
$69$	6.85757	+	11.8777i	0.825555	+	1.42990i
$70$		0			0
$71$	6.85757	−	2.49595i	0.813844	−	0.296215i	0.0986333	−	0.995124i	$-0.468553\pi$
$71$	6.85757	−	2.49595i	0.813844	−	0.296215i	0.715211	+	0.698909i	$0.246331\pi$
$72$	−1.31672	+	3.61765i	−0.155177	+	0.426344i
$73$	8.96047	−	10.6787i	1.04874	−	1.24984i	0.0813181	−	0.996688i	$-0.474087\pi$
$73$	8.96047	−	10.6787i	1.04874	−	1.24984i	0.967426	−	0.253156i	$-0.0814685\pi$
$74$	0.894088	−	5.07062i	0.103936	−	0.589448i
$75$		0			0
$76$	2.88176	−	3.27039i	0.330561	−	0.375139i
$77$			0.545048i			0.0621140i
$78$	−1.17849	−	0.207799i	−0.133437	−	0.0235286i
$79$	0.730080	+	0.612610i	0.0821404	+	0.0689240i	0.682933	−	0.730481i	$-0.260704\pi$
$79$	0.730080	+	0.612610i	0.0821404	+	0.0689240i	−0.600793	+	0.799405i	$0.705148\pi$
$80$		0			0
$81$	5.38288	−	1.95921i	0.598098	−	0.217690i
$82$	−5.15720	−	6.14611i	−0.569518	−	0.678725i
$83$	−9.76080	+	5.63540i	−1.07139	+	0.618566i	−0.928560	−	0.371182i	$-0.878953\pi$
$83$	−9.76080	+	5.63540i	−1.07139	+	0.618566i	−0.142827	+	0.989748i	$0.545619\pi$
$84$	1.26992	−	2.19957i	0.138560	−	0.239992i
$85$		0			0
$86$	1.77652	+	10.0751i	0.191567	+	1.08643i
$87$	−5.37084	−	3.10086i	−0.575815	−	0.332447i
$88$	−0.486406	+	0.280827i	−0.0518511	+	0.0299362i
$89$	−2.69822	+	2.26408i	−0.286011	+	0.239992i	−0.774493	−	0.632582i	$-0.781995\pi$
$89$	−2.69822	+	2.26408i	−0.286011	+	0.239992i	0.488482	+	0.872574i	$0.337551\pi$
$90$		0			0
$91$	0.416952	+	0.151758i	0.0437085	+	0.0159086i
$92$	3.36844	−	4.01435i	0.351184	−	0.418524i
$93$	28.0481	+	4.94563i	2.90845	+	0.512838i
$94$	−12.2742			−1.26599
$95$		0			0
$96$	2.61722			0.267119
$97$	−7.10973	−	1.25364i	−0.721883	−	0.127288i	−0.199377	−	0.979923i	$-0.563892\pi$
$97$	−7.10973	−	1.25364i	−0.721883	−	0.127288i	−0.522506	+	0.852635i	$0.675003\pi$
$98$	3.89417	−	4.64089i	0.393371	−	0.468801i
$99$	−2.03186	−	0.739538i	−0.204210	−	0.0743264i
$100$		0			0
$101$	9.72875	−	8.16339i	0.968046	−	0.812287i	−0.0141968	−	0.999899i	$-0.504519\pi$
$101$	9.72875	−	8.16339i	0.968046	−	0.812287i	0.982243	+	0.187612i	$0.0600747\pi$
$102$	−0.890881	+	0.514350i	−0.0882103	+	0.0509283i
$103$	9.93425	+	5.73554i	0.978851	+	0.565140i	0.901923	−	0.431897i	$-0.142156\pi$
$103$	9.93425	+	5.73554i	0.978851	+	0.565140i	0.0769276	+	0.997037i	$0.475489\pi$
$104$	0.0793970	+	0.450283i	0.00778552	+	0.0441539i
$105$		0			0
$106$	2.26834	−	3.92889i	0.220321	−	0.381607i
$107$	10.8549	−	6.26711i	1.04939	−	0.605864i	0.126909	−	0.991914i	$-0.459494\pi$
$107$	10.8549	−	6.26711i	1.04939	−	0.605864i	0.922478	+	0.386050i	$0.126161\pi$
$108$	1.42967	+	1.70381i	0.137570	+	0.163949i
$109$	−5.34478	+	1.94534i	−0.511937	+	0.186330i	−0.585055	−	0.810993i	$-0.698927\pi$
$109$	−5.34478	+	1.94534i	−0.511937	+	0.186330i	0.0731182	+	0.997323i	$0.476705\pi$
$110$		0			0
$111$	−10.3229	−	8.66198i	−0.979810	−	0.822158i
$112$	−0.955692	−	0.168514i	−0.0903045	−	0.0159231i
$113$		−	4.13698i		−	0.389174i	−0.980885	−	0.194587i	$-0.937663\pi$
$113$		−	4.13698i		−	0.389174i	0.980885	−	0.194587i	$-0.0623367\pi$
$114$	−3.64148	−	10.8114i	−0.341056	−	1.01258i
$115$		0			0
$116$	−0.411474	+	2.33359i	−0.0382044	+	0.216668i
$117$	−1.13147	+	1.34843i	−0.104604	+	0.124662i
$118$	1.49611	−	4.11054i	0.137728	−	0.378406i
$119$	0.358428	−	0.130457i	0.0328570	−	0.0119590i
$120$		0			0
$121$	5.34227	+	9.25309i	0.485661	+	0.841190i
$122$	−3.70928	−	2.14155i	−0.335823	−	0.193887i
$123$	−20.6794	+	3.64633i	−1.86460	+	0.328779i
$124$	−1.88965	−	10.7168i	−0.169696	−	0.962393i
$125$		0			0
$126$	−1.86800	−	3.23547i	−0.166415	−	0.288239i
$127$	−1.30258	−	1.55236i	−0.115585	−	0.137749i	0.705149	−	0.709059i	$-0.250880\pi$
$127$	−1.30258	−	1.55236i	−0.115585	−	0.137749i	−0.820735	+	0.571310i	$0.806436\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	25.1608	+	9.15780i	2.21529	+	0.806299i
$130$		0			0
$131$	−1.26179	+	7.15598i	−0.110243	+	0.625221i	0.878753	+	0.477278i	$0.158376\pi$
$131$	−1.26179	+	7.15598i	−0.110243	+	0.625221i	−0.988996	+	0.147943i	$0.952735\pi$
$132$			1.46997i			0.127944i
$133$	0.633597	+	4.18231i	0.0549398	+	0.362652i
$134$	−12.1853			−1.05265
$135$		0			0
$136$	0.301095	+	0.252649i	0.0258187	+	0.0216644i
$137$	2.59205	−	7.12159i	0.221454	−	0.608439i	−0.778359	−	0.627820i	$-0.783947\pi$
$137$	2.59205	−	7.12159i	0.221454	−	0.608439i	0.999812	+	0.0193814i	$0.00616967\pi$
$138$	−4.69086	−	12.8880i	−0.399312	−	1.09710i
$139$	8.72724	−	7.32303i	0.740235	−	0.621131i	−0.192666	−	0.981264i	$-0.561713\pi$
$139$	8.72724	−	7.32303i	0.740235	−	0.621131i	0.932901	+	0.360133i	$0.117269\pi$
$140$		0			0
$141$	−16.0621	+	27.8204i	−1.35268	+	2.34290i
$142$	−7.18681	+	1.26723i	−0.603103	+	0.106343i
$143$	−0.252903	+	0.0445936i	−0.0211488	+	0.00372910i
$144$	1.92491	−	3.33404i	0.160409	−	0.277837i
$145$		0			0
$146$	−10.6787	+	8.96047i	−0.883773	+	0.741574i
$147$	−5.42299	−	14.8995i	−0.447281	−	1.22889i
$148$	−1.76101	+	4.83833i	−0.144754	+	0.397708i
$149$	0.00665635	+	0.00558534i	0.000545309	+	0.000457569i	0.643060	−	0.765816i	$-0.277664\pi$
$149$	0.00665635	+	0.00558534i	0.000545309	+	0.000457569i	−0.642515	+	0.766273i	$0.722109\pi$
$150$		0			0
$151$	−15.3824			−1.25180			−0.625901	−	0.779902i	$-0.715269\pi$
$151$	−15.3824			−1.25180			−0.625901	+	0.779902i	$0.715269\pi$
$152$	−3.40588	+	2.72029i	−0.276253	+	0.220645i
$153$			1.51318i			0.122333i
$154$	0.0946467	−	0.536768i	0.00762684	−	0.0432540i
$155$		0			0
$156$	1.12450	+	0.409284i	0.0900320	+	0.0327690i
$157$	−6.17365	−	16.9620i	−0.492711	−	1.35371i	−0.898190	−	0.439607i	$-0.855118\pi$
$157$	−6.17365	−	16.9620i	−0.492711	−	1.35371i	0.405479	−	0.914104i	$-0.367105\pi$
$158$	−0.612610	−	0.730080i	−0.0487366	−	0.0580821i
$159$	−5.93675	−	10.2827i	−0.470815	−	0.815475i
$160$		0			0
$161$	0.883075	+	5.00817i	0.0695961	+	0.394699i
$162$	−5.64132	+	0.994716i	−0.443224	+	0.0781523i
$163$	−4.25257	−	2.45522i	−0.333087	−	0.192308i	0.324124	−	0.946015i	$-0.394931\pi$
$163$	−4.25257	−	2.45522i	−0.333087	−	0.192308i	−0.657211	+	0.753707i	$0.728264\pi$
$164$	4.01159	+	6.94828i	0.313253	+	0.542569i
$165$		0			0
$166$	10.5911	−	3.85484i	0.822028	−	0.299194i
$167$	−5.69511	+	15.6472i	−0.440701	+	1.21082i	0.498331	+	0.866987i	$0.333946\pi$
$167$	−5.69511	+	15.6472i	−0.440701	+	1.21082i	−0.939032	+	0.343829i	$0.888276\pi$
$168$	−1.63258	+	1.94563i	−0.125956	+	0.150109i
$169$	2.22112	−	12.5966i	0.170856	−	0.968971i
$170$		0			0
$171$	−16.4507	−	3.31272i	−1.25802	−	0.253330i
$172$		−	10.2306i		−	0.780073i
$173$	−11.6116	−	2.04745i	−0.882817	−	0.155664i	−0.286180	−	0.958176i	$-0.592385\pi$
$173$	−11.6116	−	2.04745i	−0.882817	−	0.155664i	−0.596637	+	0.802512i	$0.703497\pi$
$174$	4.75079	+	3.98639i	0.360156	+	0.302207i
$175$		0			0
$176$	0.527781	−	0.192097i	0.0397830	−	0.0144798i
$177$	−7.35902	−	8.77014i	−0.553138	−	0.659204i
$178$	3.05038	−	1.76114i	0.228636	−	0.132003i
$179$	−7.87873	+	13.6464i	−0.588884	+	1.01998i	0.405495	+	0.914097i	$0.367099\pi$
$179$	−7.87873	+	13.6464i	−0.588884	+	1.01998i	−0.994379	+	0.105879i	$0.966234\pi$
$180$		0			0
$181$	−2.58243	−	14.6457i	−0.191951	−	1.08861i	−0.916695	−	0.399588i	$-0.869153\pi$
$181$	−2.58243	−	14.6457i	−0.191951	−	1.08861i	0.724744	−	0.689018i	$-0.241958\pi$
$182$	−0.384265	−	0.221856i	−0.0284836	−	0.0164450i
$183$	−9.70799	+	5.60491i	−0.717635	+	0.414327i
$184$	−4.01435	+	3.36844i	−0.295941	+	0.248324i
$185$		0			0
$186$	−26.7631	−	9.74099i	−1.96237	−	0.714244i
$187$	−0.141901	+	0.169111i	−0.0103768	+	0.0123666i
$188$	12.0877	+	2.13139i	0.881589	+	0.155448i
$189$	−2.15841			−0.157001
$190$		0			0
$191$	26.1567			1.89263			0.946315	−	0.323247i	$-0.104774\pi$
$191$	26.1567			1.89263			0.946315	+	0.323247i	$0.104774\pi$
$192$	−2.57745	−	0.454475i	−0.186012	−	0.0327989i
$193$	7.86704	−	9.37557i	0.566282	−	0.674868i	−0.404582	−	0.914502i	$-0.632583\pi$
$193$	7.86704	−	9.37557i	0.566282	−	0.674868i	0.970863	+	0.239634i	$0.0770273\pi$
$194$	6.78402	+	2.46918i	0.487064	+	0.177277i
$195$		0			0
$196$	−4.64089	+	3.89417i	−0.331492	+	0.278155i
$197$	−0.271540	+	0.156773i	−0.0193464	+	0.0111696i	−0.509642	−	0.860387i	$-0.670222\pi$
$197$	−0.271540	+	0.156773i	−0.0193464	+	0.0111696i	0.490296	+	0.871556i	$0.336889\pi$
$198$	1.87258	+	1.08113i	0.133078	+	0.0768327i
$199$	−3.72685	−	21.1360i	−0.264189	−	1.49829i	−0.771334	−	0.636430i	$-0.780410\pi$
$199$	−3.72685	−	21.1360i	−0.264189	−	1.49829i	0.507145	−	0.861861i	$-0.330701\pi$
$200$		0			0
$201$	−15.9457	+	27.6188i	−1.12473	+	1.94808i
$202$	−10.9985	+	6.34999i	−0.773852	+	0.446784i
$203$	−1.47811	−	1.76154i	−0.103743	−	0.123636i
$204$	0.966662	−	0.351836i	0.0676799	−	0.0246335i
$205$		0			0
$206$	−8.78736	−	7.37347i	−0.612244	−	0.513734i
$207$	−19.8679	−	3.50325i	−1.38092	−	0.243493i
$208$		−	0.457229i		−	0.0317031i
$209$	−1.52786	−	1.91292i	−0.105684	−	0.132320i
$210$		0			0
$211$	2.27645	−	12.9104i	0.156717	−	0.888788i	−0.800482	−	0.599357i	$-0.795423\pi$
$211$	2.27645	−	12.9104i	0.156717	−	0.888788i	0.957199	−	0.289431i	$-0.0934660\pi$
$212$	−2.91613	+	3.47530i	−0.200280	+	0.238685i
$213$	−6.53245	+	17.9477i	−0.447596	+	1.22976i
$214$	−11.7783	+	4.28695i	−0.805148	+	0.293050i
$215$		0			0
$216$	−1.11208	−	1.92618i	−0.0756676	−	0.131060i
$217$	9.14554	+	5.28018i	0.620839	+	0.358442i
$218$	5.60139	−	0.987675i	0.379374	−	0.0668938i
$219$	6.33539	+	35.9298i	0.428106	+	2.42791i
$220$		0			0
$221$	0.0898573	+	0.155637i	0.00604445	+	0.0104693i
$222$	8.66198	+	10.3229i	0.581354	+	0.692830i
$223$	−7.50031	−	20.6069i	−0.502258	−	1.37994i	−0.889065	−	0.457782i	$-0.848644\pi$
$223$	−7.50031	−	20.6069i	−0.502258	−	1.37994i	0.386806	−	0.922161i	$-0.373578\pi$
$224$	0.911911	+	0.331909i	0.0609296	+	0.0221766i
$225$		0			0
$226$	−0.718379	+	4.07413i	−0.0477859	+	0.271007i
$227$			3.93628i			0.261260i	0.991431	+	0.130630i	$0.0417000\pi$
$227$			3.93628i			0.261260i	−0.991431	+	0.130630i	$0.958300\pi$
$228$	1.70878	+	11.2795i	0.113167	+	0.747002i
$229$	−12.4712			−0.824122			−0.412061	−	0.911156i	$-0.635191\pi$
$229$	−12.4712			−0.824122			−0.412061	+	0.911156i	$0.635191\pi$
$230$		0			0
$231$	−1.09277	−	0.916943i	−0.0718990	−	0.0603304i
$232$	0.810446	−	2.22668i	0.0532084	−	0.146189i
$233$	−4.58978	−	12.6103i	−0.300687	−	0.826130i	−0.994381	−	0.105860i	$-0.966240\pi$
$233$	−4.58978	−	12.6103i	−0.300687	−	0.826130i	0.693694	−	0.720270i	$-0.255982\pi$
$234$	1.34843	−	1.13147i	0.0881496	−	0.0739663i
$235$		0			0
$236$	−2.18717	+	3.78829i	−0.142373	+	0.246597i
$237$	−2.45645	+	0.433138i	−0.159563	+	0.0281353i
$238$	−0.375636	+	0.0662348i	−0.0243489	+	0.00429336i
$239$	0.766043	−	1.32682i	0.0495512	−	0.0858252i	−0.840186	−	0.542298i	$-0.817554\pi$
$239$	0.766043	−	1.32682i	0.0495512	−	0.0858252i	0.889737	+	0.456473i	$0.150888\pi$
$240$		0			0
$241$	−10.7084	+	8.98543i	−0.689790	+	0.578802i	−0.918849	−	0.394610i	$-0.870880\pi$
$241$	−10.7084	+	8.98543i	−0.689790	+	0.578802i	0.229059	+	0.973413i	$0.426435\pi$
$242$	−3.65433	−	10.0402i	−0.234909	−	0.645408i
$243$	−7.40980	+	20.3583i	−0.475339	+	1.30598i
$244$	3.28105	+	2.75313i	0.210048	+	0.176251i
$245$		0			0
$246$	20.9984			1.33881
$247$	−1.88876	+	0.636169i	−0.120179	+	0.0404784i
$248$			10.8821i			0.691013i
$249$	5.12230	−	29.0500i	0.324612	−	1.84097i
$250$		0			0
$251$	−15.7226	−	5.72255i	−0.992400	−	0.361204i	−0.205751	−	0.978604i	$-0.565964\pi$
$251$	−15.7226	−	5.72255i	−0.992400	−	0.361204i	−0.786649	+	0.617400i	$0.788186\pi$
$252$	1.27779	+	3.51069i	0.0804931	+	0.221153i
$253$	−1.89189	−	2.25467i	−0.118942	−	0.141750i
$254$	1.01323	+	1.75496i	0.0635756	+	0.110116i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	5.91343	−	1.04270i	0.368870	−	0.0650417i	0.0138590	−	0.999904i	$-0.495588\pi$
$257$	5.91343	−	1.04270i	0.368870	−	0.0650417i	0.355011	+	0.934862i	$0.384477\pi$
$258$	−23.1884	−	13.3878i	−1.44364	−	0.833488i
$259$	−2.49831	−	4.32720i	−0.155238	−	0.268879i
$260$		0			0
$261$	8.57233	−	3.12007i	0.530614	−	0.193128i
$262$	2.48525	−	6.82816i	0.153539	−	0.421845i
$263$	4.05502	−	4.83259i	0.250043	−	0.297990i	−0.626393	−	0.779507i	$-0.715470\pi$
$263$	4.05502	−	4.83259i	0.250043	−	0.297990i	0.876437	+	0.481517i	$0.159914\pi$
$264$	0.255257	−	1.44764i	0.0157100	−	0.0890958i
$265$		0			0
$266$	0.102280	−	4.22879i	0.00627116	−	0.259284i
$267$		−	9.21857i		−	0.564167i
$268$	12.0001	+	2.11595i	0.733025	+	0.129252i
$269$	16.7593	+	14.0627i	1.02183	+	0.857418i	0.989856	−	0.142071i	$-0.0453762\pi$
$269$	16.7593	+	14.0627i	1.02183	+	0.857418i	0.0319740	+	0.999489i	$0.489821\pi$
$270$		0			0
$271$	−9.43077	+	3.43252i	−0.572879	+	0.208511i	−0.612182	−	0.790717i	$-0.709708\pi$
$271$	−9.43077	+	3.43252i	−0.572879	+	0.208511i	0.0393039	+	0.999227i	$0.487486\pi$
$272$	−0.252649	−	0.301095i	−0.0153191	−	0.0182566i
$273$	−1.00571	+	0.580644i	−0.0608681	+	0.0351422i
$274$	−3.78932	+	6.56329i	−0.228921	+	0.396503i
$275$		0			0
$276$	2.38161	+	13.5068i	0.143356	+	0.813013i
$277$	14.7281	+	8.50328i	0.884927	+	0.510913i	0.872280	−	0.489007i	$-0.162641\pi$
$277$	14.7281	+	8.50328i	0.884927	+	0.510913i	0.0126472	+	0.999920i	$0.495974\pi$
$278$	−9.86629	+	5.69630i	−0.591741	+	0.341642i
$279$	−32.0927	+	26.9290i	−1.92134	+	1.61220i
$280$		0			0
$281$	0.993565	+	0.361628i	0.0592711	+	0.0215729i	0.371486	−	0.928439i	$-0.378849\pi$
$281$	0.993565	+	0.361628i	0.0592711	+	0.0215729i	−0.312214	+	0.950012i	$0.601071\pi$
$282$	20.6491	−	24.6086i	1.22963	−	1.46542i
$283$	23.2379	+	4.09746i	1.38135	+	0.243569i	0.814457	−	0.580224i	$-0.197035\pi$
$283$	23.2379	+	4.09746i	1.38135	+	0.243569i	0.566891	+	0.823793i	$0.308146\pi$
$284$	7.29768			0.433037
$285$		0			0
$286$	0.256804			0.0151852
$287$	−7.66769	−	1.35202i	−0.452610	−	0.0798073i
$288$	−2.47462	+	2.94913i	−0.145818	+	0.173779i
$289$	−15.8296	−	5.76150i	−0.931153	−	0.338912i
$290$		0			0
$291$	14.4742	−	12.1453i	0.848494	−	0.711971i
$292$	12.0724	−	6.97001i	0.706484	−	0.407889i
$293$	19.2967	+	11.1409i	1.12732	+	0.650860i	0.943260	−	0.332054i	$-0.107742\pi$
$293$	19.2967	+	11.1409i	1.12732	+	0.650860i	0.184063	+	0.982915i	$0.441075\pi$
$294$	2.75332	+	15.6149i	0.160577	+	0.910678i
$295$		0			0
$296$	2.57442	−	4.45903i	0.149635	−	0.259176i
$297$	1.08185	−	0.624605i	0.0627751	−	0.0362432i
$298$	−0.00558534	−	0.00665635i	−0.000323550	−	0.000385592i
$299$	−2.25154	+	0.819495i	−0.130210	+	0.0473926i
$300$		0			0
$301$	7.60537	+	6.38166i	0.438366	+	0.367833i
$302$	15.1487	+	2.67113i	0.871710	+	0.153706i
$303$			33.2386i			1.90951i
$304$	3.82651	−	2.08754i	0.219465	−	0.119728i
$305$		0			0
$306$	0.262760	−	1.49019i	0.0150210	−	0.0851884i
$307$	−17.5713	+	20.9406i	−1.00284	+	1.19514i	−0.0221182	+	0.999755i	$0.507041\pi$
$307$	−17.5713	+	20.9406i	−1.00284	+	1.19514i	−0.980726	+	0.195388i	$0.937403\pi$
$308$	−0.186418	+	0.512178i	−0.0106221	+	0.0291840i
$309$	−28.2117	+	10.2682i	−1.60491	+	0.584139i
$310$		0			0
$311$	−15.6908	−	27.1772i	−0.889743	−	1.54108i	−0.840179	−	0.542309i	$-0.817550\pi$
$311$	−15.6908	−	27.1772i	−0.889743	−	1.54108i	−0.0495638	−	0.998771i	$-0.515783\pi$
$312$	−1.03634	−	0.598334i	−0.0586715	−	0.0338740i
$313$	1.13336	−	0.199842i	0.0640613	−	0.0112957i	−0.141526	−	0.989935i	$-0.545201\pi$
$313$	1.13336	−	0.199842i	0.0640613	−	0.0112957i	0.205587	+	0.978639i	$0.434090\pi$
$314$	3.13444	+	17.7763i	0.176887	+	1.00318i
$315$		0			0
$316$	0.476526	+	0.825367i	0.0268067	+	0.0464305i
$317$	13.2783	+	15.8245i	0.745784	+	0.888791i	0.996861	−	0.0791766i	$-0.0252291\pi$
$317$	13.2783	+	15.8245i	0.745784	+	0.888791i	−0.251077	+	0.967967i	$0.580785\pi$
$318$	4.06097	+	11.1574i	0.227728	+	0.625678i
$319$	1.25062	+	0.455190i	0.0700214	+	0.0254857i
$320$		0			0
$321$	−5.69648	+	32.3064i	−0.317947	+	1.80317i
$322$		−	5.08543i		−	0.283400i
$323$	−0.892261	+	1.46259i	−0.0496467	+	0.0813807i
$324$	5.72834			0.318241
$325$		0			0
$326$	3.76162	+	3.15637i	0.208337	+	0.174815i
$327$	5.09138	−	13.9884i	0.281554	−	0.773563i
$328$	−2.74409	−	7.53932i	−0.151517	−	0.416290i
$329$	−9.12461	+	7.65645i	−0.503056	+	0.422114i
$330$		0			0
$331$	5.97822	−	10.3546i	0.328593	−	0.569139i	−0.653640	−	0.756806i	$-0.726759\pi$
$331$	5.97822	−	10.3546i	0.328593	−	0.569139i	0.982233	+	0.187666i	$0.0600923\pi$
$332$	−11.0996	+	1.95715i	−0.609168	+	0.107413i
$333$	19.5210	−	3.44208i	1.06974	−	0.188625i
$334$	8.32569	−	14.4205i	0.455562	−	0.789056i
$335$		0			0
$336$	1.94563	−	1.63258i	0.106143	−	0.0890644i
$337$	−5.65212	−	15.5291i	−0.307891	−	0.845923i	−0.993067	−	0.117546i	$-0.962497\pi$
$337$	−5.65212	−	15.5291i	−0.307891	−	0.845923i	0.685177	−	0.728377i	$-0.259725\pi$
$338$	−4.37476	+	12.0196i	−0.237956	+	0.653778i
$339$	8.29425	+	6.95970i	0.450482	+	0.377999i
$340$		0			0
$341$	−6.11195			−0.330981
$342$	15.6256	+	6.11904i	0.844934	+	0.330880i
$343$		−	12.6722i		−	0.684234i
$344$	−1.77652	+	10.0751i	−0.0957835	+	0.543215i
$345$		0			0
$346$	11.0797	+	4.03268i	0.595648	+	0.216798i
$347$	−1.24681	−	3.42558i	−0.0669321	−	0.183895i	0.901717	−	0.432326i	$-0.142307\pi$
$347$	−1.24681	−	3.42558i	−0.0669321	−	0.183895i	−0.968649	+	0.248432i	$0.920085\pi$
$348$	−3.98639	−	4.75079i	−0.213693	−	0.254669i
$349$	−9.09715	−	15.7567i	−0.486959	−	0.843438i	0.512928	−	0.858431i	$-0.328561\pi$
$349$	−9.09715	−	15.7567i	−0.486959	−	0.843438i	−0.999888	+	0.0149933i	$0.995227\pi$
$350$		0			0
$351$	−0.176592	−	1.00150i	−0.00942579	−	0.0534563i
$352$	−0.553121	+	0.0975301i	−0.0294814	+	0.00519837i
$353$	−5.60251	−	3.23461i	−0.298191	−	0.172161i	0.343439	−	0.939175i	$-0.388408\pi$
$353$	−5.60251	−	3.23461i	−0.298191	−	0.172161i	−0.641630	+	0.767014i	$0.721742\pi$
$354$	5.72430	+	9.91478i	0.304243	+	0.526965i
$355$		0			0
$356$	−3.30986	+	1.20469i	−0.175422	+	0.0638485i
$357$	−0.341434	+	0.938083i	−0.0180706	+	0.0496486i
$358$	10.1287	−	12.0709i	0.535318	−	0.637968i
$359$	3.90895	−	22.1687i	0.206306	−	1.17002i	−0.689065	−	0.724700i	$-0.741978\pi$
$359$	3.90895	−	22.1687i	0.206306	−	1.17002i	0.895371	−	0.445321i	$-0.146910\pi$
$360$		0			0
$361$	−13.9474	−	12.9023i	−0.734073	−	0.679070i
$362$			14.8716i			0.781636i
$363$	−27.5389	−	4.85586i	−1.44542	−	0.254866i
$364$	0.339903	+	0.285212i	0.0178157	+	0.0149492i
$365$		0			0
$366$	10.5338	−	3.83398i	0.550610	−	0.200406i
$367$	1.73931	+	2.07282i	0.0907910	+	0.108200i	0.809527	−	0.587082i	$-0.199724\pi$
$367$	1.73931	+	2.07282i	0.0907910	+	0.108200i	−0.718736	+	0.695283i	$0.755279\pi$
$368$	4.53828	−	2.62018i	0.236574	−	0.136586i
$369$	15.4439	−	26.7496i	0.803978	−	1.39253i
$370$		0			0
$371$	−0.764497	−	4.33568i	−0.0396907	−	0.225097i
$372$	24.6651	+	14.2404i	1.27882	+	0.738329i
$373$	17.0106	−	9.82107i	0.880775	−	0.508516i	0.00986133	−	0.999951i	$-0.496861\pi$
$373$	17.0106	−	9.82107i	0.880775	−	0.508516i	0.870914	+	0.491436i	$0.163528\pi$
$374$	0.169111	−	0.141901i	0.00874452	−	0.00733752i
$375$		0			0
$376$	−11.5340	−	4.19803i	−0.594820	−	0.216497i
$377$	0.696424	−	0.829966i	0.0358677	−	0.0427454i
$378$	2.12562	+	0.374804i	0.109330	+	0.0192778i
$379$	29.6893			1.52504			0.762519	−	0.646966i	$-0.223962\pi$
$379$	29.6893			1.52504			0.762519	+	0.646966i	$0.223962\pi$
$380$		0			0
$381$	5.30368			0.271716
$382$	−25.7593	−	4.54206i	−1.31796	−	0.232392i
$383$	11.0417	−	13.1589i	0.564203	−	0.672391i	−0.406228	−	0.913772i	$-0.633156\pi$
$383$	11.0417	−	13.1589i	0.564203	−	0.672391i	0.970430	+	0.241381i	$0.0776005\pi$
$384$	2.45938	+	0.895141i	0.125505	+	0.0456800i
$385$		0			0
$386$	−9.37557	+	7.86704i	−0.477204	+	0.400422i
$387$	−34.1091	+	19.6929i	−1.73387	+	1.00105i
$388$	−6.25219	−	3.60970i	−0.317407	−	0.183255i
$389$	1.09317	+	6.19966i	0.0554258	+	0.314335i	0.999898	−	0.0142548i	$-0.00453759\pi$
$389$	1.09317	+	6.19966i	0.0554258	+	0.314335i	−0.944473	+	0.328590i	$0.893426\pi$
$390$		0			0
$391$	−1.02986	+	1.78378i	−0.0520825	+	0.0902095i
$392$	5.24660	−	3.02913i	0.264993	−	0.152994i
$393$	−12.2243	−	14.5684i	−0.616635	−	0.734878i
$394$	0.294638	−	0.107239i	0.0148436	−	0.00540264i
$395$		0			0
$396$	−1.65639	−	1.38988i	−0.0832368	−	0.0698439i
$397$	9.73449	+	1.71645i	0.488560	+	0.0861463i	0.412501	−	0.910957i	$-0.364655\pi$
$397$	9.73449	+	1.71645i	0.488560	+	0.0861463i	0.0760588	+	0.997103i	$0.475766\pi$
$398$			21.4620i			1.07580i
$399$	−9.45104	−	5.76566i	−0.473144	−	0.288644i
$400$		0			0
$401$	5.40131	−	30.6323i	0.269728	−	1.52971i	−0.485496	−	0.874239i	$-0.661361\pi$
$401$	5.40131	−	30.6323i	0.269728	−	1.52971i	0.755224	−	0.655467i	$-0.227528\pi$
$402$	20.4994	−	24.4303i	1.02242	−	1.21847i
$403$	−1.70176	+	4.67554i	−0.0847705	+	0.232905i
$404$	11.9341	−	4.34365i	0.593742	−	0.216105i
$405$		0			0
$406$	1.14976	+	1.99145i	0.0570619	+	0.0988341i
$407$	2.50443	+	1.44593i	0.124140	+	0.0716722i
$408$	−1.01307	+	0.178632i	−0.0501545	+	0.00884360i
$409$	−5.49089	−	31.1404i	−0.271507	−	1.53979i	−0.749843	−	0.661616i	$-0.769871\pi$
$409$	−5.49089	−	31.1404i	−0.271507	−	1.53979i	0.478336	−	0.878177i	$-0.341240\pi$
$410$		0			0
$411$	9.91747	+	17.1776i	0.489193	+	0.847306i
$412$	7.37347	+	8.78736i	0.363265	+	0.432922i
$413$	−1.45188	−	3.98901i	−0.0714424	−	0.196287i
$414$	18.9578	+	6.90006i	0.931723	+	0.339120i
$415$		0			0
$416$	−0.0793970	+	0.450283i	−0.00389276	+	0.0220769i
$417$			29.8169i			1.46014i
$418$	1.17247	+	2.14917i	0.0573475	+	0.105119i
$419$	−4.66623			−0.227960			−0.113980	−	0.993483i	$-0.536360\pi$
$419$	−4.66623			−0.227960			−0.113980	+	0.993483i	$0.536360\pi$
$420$		0			0
$421$	7.29791	+	6.12367i	0.355678	+	0.298449i	0.803065	−	0.595891i	$-0.203201\pi$
$421$	7.29791	+	6.12367i	0.355678	+	0.298449i	−0.447387	+	0.894340i	$0.647645\pi$
$422$	−4.48373	+	12.3190i	−0.218265	+	0.599677i
$423$	−16.1617	−	44.4038i	−0.785806	−	2.15899i
$424$	3.47530	−	2.91613i	0.168776	−	0.141620i
$425$		0			0
$426$	9.54980	−	16.5407i	0.462689	−	0.801401i
$427$	−4.09333	+	0.721765i	−0.198090	+	0.0349287i
$428$	12.3438	−	2.17654i	0.596659	−	0.105207i
$429$	0.336056	−	0.582066i	0.0162249	−	0.0281024i
$430$		0			0
$431$	12.6794	−	10.6393i	0.610746	−	0.512477i	−0.284133	−	0.958785i	$-0.591706\pi$
$431$	12.6794	−	10.6393i	0.610746	−	0.512477i	0.894880	+	0.446308i	$0.147261\pi$
$432$	0.760709	+	2.09003i	0.0365996	+	0.100557i
$433$	−13.2275	+	36.3423i	−0.635674	+	1.74650i	0.0292319	+	0.999573i	$0.490694\pi$
$433$	−13.2275	+	36.3423i	−0.635674	+	1.74650i	−0.664906	+	0.746927i	$0.731528\pi$
$434$	−8.08970	−	6.78807i	−0.388318	−	0.325838i
$435$		0			0
$436$	−5.68780			−0.272396
$437$	−17.1380	−	15.1015i	−0.819821	−	0.722401i
$438$		−	36.4840i		−	1.74327i
$439$	4.93804	−	28.0050i	0.235680	−	1.33661i	−0.605497	−	0.795848i	$-0.707026\pi$
$439$	4.93804	−	28.0050i	0.235680	−	1.33661i	0.841177	−	0.540760i	$-0.181863\pi$
$440$		0			0
$441$	21.9166	+	7.97700i	1.04365	+	0.379857i
$442$	−0.0614660	−	0.168876i	−0.00292364	−	0.00803263i
$443$	11.8053	+	14.0691i	0.560889	+	0.668442i	0.969734	−	0.244162i	$-0.0785129\pi$
$443$	11.8053	+	14.0691i	0.560889	+	0.668442i	−0.408845	+	0.912604i	$0.634068\pi$
$444$	−6.73782	−	11.6702i	−0.319763	−	0.553845i
$445$		0			0
$446$	3.80801	+	21.5963i	0.180314	+	1.02261i
$447$	−0.0223961	+	0.00394904i	−0.00105930	+	0.000186783i
$448$	−0.840422	−	0.485218i	−0.0397062	−	0.0229244i
$449$	1.25413	+	2.17222i	0.0591861	+	0.102513i	0.894100	−	0.447867i	$-0.147816\pi$
$449$	1.25413	+	2.17222i	0.0591861	+	0.102513i	−0.834914	+	0.550380i	$0.814483\pi$
$450$		0			0
$451$	4.23449	−	1.54123i	0.199394	−	0.0725735i
$452$	1.41493	−	3.88749i	0.0665527	−	0.182852i
$453$	25.8780	−	30.8402i	1.21586	−	1.44900i
$454$	0.683528	−	3.87648i	0.0320796	−	0.181932i
$455$		0			0
$456$	0.275843	−	11.4048i	0.0129175	−	0.534081i
$457$			32.8737i			1.53777i	0.639389	+	0.768884i	$0.279187\pi$
$457$			32.8737i			1.53777i	−0.639389	+	0.768884i	$0.720813\pi$
$458$	12.2818	+	2.16561i	0.573889	+	0.101192i
$459$	−0.669685	−	0.561932i	−0.0312582	−	0.0262287i
$460$		0			0
$461$	−1.13291	+	0.412346i	−0.0527649	+	0.0192049i	−0.368268	−	0.929720i	$-0.620049\pi$
$461$	−1.13291	+	0.412346i	−0.0527649	+	0.0192049i	0.315503	+	0.948925i	$0.397827\pi$
$462$	0.916943	+	1.09277i	0.0426600	+	0.0508402i
$463$	11.0746	−	6.39390i	0.514678	−	0.297150i	−0.220076	−	0.975483i	$-0.570631\pi$
$463$	11.0746	−	6.39390i	0.514678	−	0.297150i	0.734755	+	0.678333i	$0.237297\pi$
$464$	−1.18479	+	2.05212i	−0.0550026	+	0.0952673i
$465$		0			0
$466$	2.33029	+	13.2158i	0.107949	+	0.612208i
$467$	−28.1216	−	16.2360i	−1.30131	−	0.751313i	−0.320683	−	0.947187i	$-0.603912\pi$
$467$	−28.1216	−	16.2360i	−1.30131	−	0.751313i	−0.980629	+	0.195873i	$0.937246\pi$
$468$	−1.52442	+	0.880125i	−0.0704664	+	0.0406838i
$469$	−9.05848	+	7.60097i	−0.418282	+	0.350980i
$470$		0			0
$471$	44.3931	+	16.1578i	2.04553	+	0.744511i
$472$	2.81177	−	3.35094i	0.129422	−	0.154240i
$473$	−5.65874	−	0.997788i	−0.260189	−	0.0458783i
$474$	2.49434			0.114569
$475$		0			0
$476$	0.381431			0.0174829
$477$	17.2001	+	3.03284i	0.787538	+	0.138864i
$478$	−0.984806	+	1.17365i	−0.0450440	+	0.0536813i
$479$	16.3221	+	5.94076i	0.745775	+	0.271440i	0.686827	−	0.726821i	$-0.259003\pi$
$479$	16.3221	+	5.94076i	0.745775	+	0.271440i	0.0589485	+	0.998261i	$0.481225\pi$
$480$		0			0
$481$	1.80342	−	1.51325i	0.0822290	−	0.0689984i
$482$	12.1060	−	6.98942i	0.551415	−	0.318359i
$483$	−11.5265	−	6.65483i	−0.524474	−	0.302805i
$484$	1.85535	+	10.5222i	0.0843342	+	0.478283i
$485$		0			0
$486$	10.8324	−	18.7623i	0.491368	−	0.851074i
$487$	−6.64068	+	3.83400i	−0.300918	+	0.173735i	−0.642855	−	0.765988i	$-0.722250\pi$
$487$	−6.64068	+	3.83400i	−0.300918	+	0.173735i	0.341937	+	0.939723i	$0.388917\pi$
$488$	−2.75313	−	3.28105i	−0.124628	−	0.148526i
$489$	12.0766	−	4.39554i	0.546124	−	0.198773i
$490$		0			0
$491$	25.9882	+	21.8067i	1.17283	+	0.984124i	1.00000		0.000827334i	$-0.000263349\pi$
$491$	25.9882	+	21.8067i	1.17283	+	0.984124i	0.172833	+	0.984951i	$0.444708\pi$
$492$	−20.6794	−	3.64633i	−0.932299	−	0.164389i
$493$		−	0.931369i		−	0.0419467i
$494$	1.97053	−	0.298525i	0.0886584	−	0.0134313i
$495$		0			0
$496$	1.88965	−	10.7168i	0.0848479	−	0.481196i
$497$	−4.55217	+	5.42507i	−0.204193	+	0.243348i
$498$	−10.0890	+	27.7192i	−0.452097	+	1.24213i
$499$	−5.54507	+	2.01824i	−0.248231	+	0.0903488i	−0.463139	−	0.886285i	$-0.653277\pi$
$499$	−5.54507	+	2.01824i	−0.248231	+	0.0903488i	0.214908	+	0.976634i	$0.431055\pi$
$500$		0			0
$501$	−21.7901	−	37.7416i	−0.973512	−	1.68617i
$502$	14.4900	+	8.36580i	0.646720	+	0.373384i
$503$	−39.4651	+	6.95876i	−1.75966	+	0.310276i	−0.957843	−	0.287292i	$-0.907245\pi$
$503$	−39.4651	+	6.95876i	−1.75966	+	0.310276i	−0.801819	+	0.597567i	$0.796134\pi$
$504$	−0.648750	−	3.67924i	−0.0288976	−	0.163887i
$505$		0			0
$506$	1.47163	+	2.54894i	0.0654220	+	0.113314i
$507$	21.5184	+	25.6446i	0.955665	+	1.13892i
$508$	−0.693090	−	1.90425i	−0.0307509	−	0.0844873i
$509$	15.8140	+	5.75583i	0.700944	+	0.255123i	0.667814	−	0.744328i	$-0.267230\pi$
$509$	15.8140	+	5.75583i	0.700944	+	0.255123i	0.0331303	+	0.999451i	$0.489452\pi$
$510$		0			0
$511$	−2.34909	+	13.3224i	−0.103918	+	0.589347i
$512$		−	1.00000i		−	0.0441942i
$513$	7.57524	−	6.05037i	0.334455	−	0.267130i
$514$	−6.00465			−0.264854
$515$		0			0
$516$	20.5113	+	17.2110i	0.902960	+	0.757673i
$517$	2.35784	−	6.47810i	0.103697	−	0.284907i
$518$	1.70895	+	4.69529i	0.0750868	+	0.206299i
$519$	23.6394	−	19.8358i	1.03765	−	0.870694i
$520$		0			0
$521$	−1.40131	+	2.42714i	−0.0613926	+	0.106335i	−0.895088	−	0.445889i	$-0.852887\pi$
$521$	−1.40131	+	2.42714i	−0.0613926	+	0.106335i	0.833696	+	0.552224i	$0.186221\pi$
$522$	−8.98389	+	1.58410i	−0.393214	+	0.0693342i
$523$	−9.59389	+	1.69166i	−0.419512	+	0.0739712i	−0.379419	−	0.925225i	$-0.623876\pi$
$523$	−9.59389	+	1.69166i	−0.419512	+	0.0739712i	−0.0400921	+	0.999196i	$0.512765\pi$
$524$	−3.63319	+	6.29286i	−0.158716	+	0.274905i
$525$		0			0
$526$	−4.83259	+	4.05502i	−0.210711	+	0.176807i
$527$	1.46289	+	4.01927i	0.0637247	+	0.175082i
$528$	−0.502759	+	1.38132i	−0.0218798	+	0.0601142i
$529$	−3.41757	−	2.86768i	−0.148590	−	0.124682i
$530$		0			0
$531$	16.8404			0.730813
$532$	−0.835048	+	4.14679i	−0.0362039	+	0.179786i
$533$		−	3.66843i		−	0.158897i
$534$	−1.60079	+	9.07852i	−0.0692729	+	0.392866i
$535$		0			0
$536$	−11.4504	−	4.16760i	−0.494582	−	0.180013i
$537$	−14.1051	−	38.7536i	−0.608682	−	1.67234i
$538$	−14.0627	−	16.7593i	−0.606286	−	0.722543i
$539$	1.70132	+	2.94677i	0.0732810	+	0.126926i
$540$		0			0
$541$	4.09756	+	23.2384i	0.176168	+	0.999097i	0.936787	+	0.349899i	$0.113784\pi$
$541$	4.09756	+	23.2384i	0.176168	+	0.999097i	−0.760620	+	0.649198i	$0.775105\pi$
$542$	9.88355	−	1.74274i	0.424535	−	0.0748569i
$543$	33.7077	+	19.4611i	1.44654	+	0.835158i
$544$	0.196526	+	0.340392i	0.00842597	+	0.0145942i
$545$		0			0
$546$	1.09125	−	0.397184i	0.0467014	−	0.0169979i
$547$	1.43898	−	3.95356i	0.0615263	−	0.169042i	−0.905121	−	0.425155i	$-0.860220\pi$
$547$	1.43898	−	3.95356i	0.0615263	−	0.169042i	0.966647	+	0.256113i	$0.0824418\pi$
$548$	4.87145	−	5.80557i	0.208098	−	0.248002i
$549$	2.86332	−	16.2387i	0.122204	−	0.693050i
$550$		0			0
$551$	10.1255	+	2.03900i	0.431362	+	0.0868643i
$552$		−	13.7151i		−	0.583755i
$553$	−0.910825	−	0.160603i	−0.0387322	−	0.00682953i
$554$	−13.0278	−	10.9316i	−0.553498	−	0.464440i
$555$		0			0
$556$	10.7055	−	3.89650i	0.454016	−	0.165248i
$557$	−1.14222	−	1.36125i	−0.0483975	−	0.0576779i	0.741303	−	0.671171i	$-0.234208\pi$
$557$	−1.14222	−	1.36125i	−0.0483975	−	0.0576779i	−0.789700	+	0.613493i	$0.789764\pi$
$558$	36.2813	−	20.9470i	1.53591	−	0.886758i
$559$	−2.33886	+	4.05102i	−0.0989231	+	0.171340i
$560$		0			0
$561$	−0.100329	−	0.568995i	−0.00423590	−	0.0240230i
$562$	−0.915675	−	0.528665i	−0.0386254	−	0.0223004i
$563$	−31.5639	+	18.2234i	−1.33026	+	0.768025i	−0.985339	−	0.170607i	$-0.945427\pi$
$563$	−31.5639	+	18.2234i	−1.33026	+	0.768025i	−0.344919	+	0.938632i	$0.612094\pi$
$564$	−24.6086	+	20.6491i	−1.03621	+	0.869483i
$565$		0			0
$566$	−22.1733	−	8.07043i	−0.932014	−	0.339225i
$567$	−3.57325	+	4.25843i	−0.150062	+	0.178837i
$568$	−7.18681	−	1.26723i	−0.301552	−	0.0531717i
$569$	22.6982			0.951556			0.475778	−	0.879565i	$-0.342167\pi$
$569$	22.6982			0.951556			0.475778	+	0.879565i	$0.342167\pi$
$570$		0			0
$571$	9.60500			0.401957			0.200978	−	0.979596i	$-0.435588\pi$
$571$	9.60500			0.401957			0.200978	+	0.979596i	$0.435588\pi$
$572$	−0.252903	−	0.0445936i	−0.0105744	−	0.00186455i
$573$	−44.0037	+	52.4416i	−1.83828	+	2.19078i
$574$	7.31643	+	2.66296i	0.305382	+	0.111150i
$575$		0			0
$576$	2.94913	−	2.47462i	0.122881	−	0.103109i
$577$	1.38657	−	0.800539i	0.0577238	−	0.0333269i	−0.470860	−	0.882208i	$-0.656056\pi$
$577$	1.38657	−	0.800539i	0.0577238	−	0.0333269i	0.528584	+	0.848881i	$0.322723\pi$
$578$	14.5886	+	8.42276i	0.606807	+	0.350340i
$579$	5.56229	+	31.5453i	0.231161	+	1.31098i
$580$		0			0
$581$	5.46879	−	9.47223i	0.226884	−	0.392974i
$582$	−16.3633	+	9.44737i	−0.678282	+	0.391606i
$583$	1.63785	+	1.95192i	0.0678329	+	0.0808401i
$584$	−13.0993	+	4.76777i	−0.542054	+	0.197292i
$585$		0			0
$586$	−17.0689	−	14.3225i	−0.705110	−	0.591657i
$587$	−13.0152	−	2.29493i	−0.537196	−	0.0947221i	−0.101533	−	0.994832i	$-0.532375\pi$
$587$	−13.0152	−	2.29493i	−0.537196	−	0.0947221i	−0.435663	+	0.900110i	$0.643486\pi$
$588$		−	15.8558i		−	0.653881i
$589$	−46.8988	+	7.10490i	−1.93243	+	0.292752i
$590$		0			0
$591$	0.142499	−	0.808153i	0.00586163	−	0.0332430i
$592$	−3.30961	+	3.94424i	−0.136024	+	0.162107i
$593$	3.08987	−	8.48936i	0.126886	−	0.348616i	−0.859942	−	0.510393i	$-0.829500\pi$
$593$	3.08987	−	8.48936i	0.126886	−	0.348616i	0.986827	+	0.161776i	$0.0517223\pi$
$594$	−1.17387	+	0.427255i	−0.0481646	+	0.0175305i
$595$		0			0
$596$	0.00434462	+	0.00752511i	0.000177963	+	0.000308240i
$597$	48.6454	+	28.0854i	1.99092	+	1.14946i
$598$	2.35964	−	0.416069i	0.0964929	−	0.0170143i
$599$	−4.00135	−	22.6928i	−0.163491	−	0.927203i	−0.950607	−	0.310398i	$-0.899538\pi$
$599$	−4.00135	−	22.6928i	−0.163491	−	0.927203i	0.787116	−	0.616805i	$-0.211573\pi$
$600$		0			0
$601$	−16.0194	−	27.7465i	−0.653447	−	1.13180i	−0.982281	−	0.187415i	$-0.939989\pi$
$601$	−16.0194	−	27.7465i	−0.653447	−	1.13180i	0.328834	−	0.944388i	$-0.393344\pi$
$602$	−6.38166	−	7.60537i	−0.260097	−	0.309972i
$603$	−16.0445	−	44.0820i	−0.653384	−	1.79516i
$604$	−14.4547	−	5.26109i	−0.588155	−	0.214071i
$605$		0			0
$606$	5.77182	−	32.7336i	0.234464	−	1.32971i
$607$			7.01008i			0.284530i	0.989829	+	0.142265i	$0.0454386\pi$
$607$			7.01008i			0.284530i	−0.989829	+	0.142265i	$0.954561\pi$
$608$	−4.13088	+	1.39136i	−0.167529	+	0.0564269i
$609$	6.01837			0.243877
$610$		0			0
$611$	−4.29914	−	3.60741i	−0.173925	−	0.145940i
$612$	−0.517537	+	1.42192i	−0.0209202	+	0.0574778i
$613$	12.6172	+	34.6655i	0.509604	+	1.40013i	0.881646	+	0.471911i	$0.156436\pi$
$613$	12.6172	+	34.6655i	0.509604	+	1.40013i	−0.372042	+	0.928216i	$0.621342\pi$
$614$	20.9406	−	17.5713i	0.845094	−	0.709118i
$615$		0			0
$616$	0.272524	−	0.472026i	0.0109803	−	0.0190185i
$617$	26.6741	−	4.70336i	1.07386	−	0.189350i	0.391360	−	0.920237i	$-0.372005\pi$
$617$	26.6741	−	4.70336i	1.07386	−	0.189350i	0.682498	+	0.730887i	$0.260893\pi$
$618$	29.5662	−	5.21332i	1.18933	−	0.209710i
$619$	−11.3313	+	19.6265i	−0.455445	+	0.788855i	−0.998714	−	0.0507046i	$-0.983853\pi$
$619$	−11.3313	+	19.6265i	−0.455445	+	0.788855i	0.543268	+	0.839559i	$0.317187\pi$
$620$		0			0
$621$	8.92857	−	7.49196i	0.358291	−	0.300642i
$622$	10.7331	+	29.4890i	0.430359	+	1.18240i
$623$	1.16908	−	3.21201i	0.0468380	−	0.128686i
$624$	0.916701	+	0.769203i	0.0366974	+	0.0307928i
$625$		0			0
$626$	−1.15084			−0.0459970
$627$	6.40557	+	0.154928i	0.255814	+	0.00618723i
$628$		−	18.0505i		−	0.720295i
$629$	0.351422	−	1.99302i	0.0140121	−	0.0794667i
$630$		0			0
$631$	−12.4587	−	4.53461i	−0.495974	−	0.180520i	0.0819082	−	0.996640i	$-0.473899\pi$
$631$	−12.4587	−	4.53461i	−0.495974	−	0.180520i	−0.577882	+	0.816120i	$0.696121\pi$
$632$	−0.325963	−	0.895576i	−0.0129661	−	0.0356241i
$633$	22.0544	+	26.2834i	0.876583	+	1.04467i
$634$	−10.3287	−	17.8898i	−0.410205	−	0.710495i
$635$		0			0
$636$	−2.06181	−	11.6931i	−0.0817561	−	0.463662i
$637$	2.72793	−	0.481007i	0.108084	−	0.0190582i
$638$	−1.15258	−	0.665443i	−0.0456311	−	0.0263451i
$639$	−14.0474	−	24.3308i	−0.555705	−	0.962510i
$640$		0			0
$641$	−2.21754	+	0.807120i	−0.0875877	+	0.0318793i	−0.385442	−	0.922732i	$-0.625951\pi$
$641$	−2.21754	+	0.807120i	−0.0875877	+	0.0318793i	0.297855	+	0.954611i	$0.403729\pi$
$642$	11.2199	−	30.8264i	0.442813	−	1.21662i
$643$	−17.9758	+	21.4227i	−0.708895	+	0.844828i	−0.993502	−	0.113816i	$-0.963693\pi$
$643$	−17.9758	+	21.4227i	−0.708895	+	0.844828i	0.284607	+	0.958644i	$0.408137\pi$
$644$	−0.883075	+	5.00817i	−0.0347980	+	0.197349i
$645$		0			0
$646$	1.13268	−	1.28543i	0.0445648	−	0.0505746i
$647$			26.0773i			1.02520i	0.858626	+	0.512602i	$0.171318\pi$
$647$			26.0773i			1.02520i	−0.858626	+	0.512602i	$0.828682\pi$
$648$	−5.64132	−	0.994716i	−0.221612	−	0.0390761i
$649$	1.88207	+	1.57924i	0.0738776	+	0.0619907i
$650$		0			0
$651$	−25.9719	+	9.45300i	−1.01792	+	0.370492i
$652$	−3.15637	−	3.76162i	−0.123613	−	0.147316i
$653$	32.5381	−	18.7859i	1.27332	−	0.735149i	0.297705	−	0.954658i	$-0.403779\pi$
$653$	32.5381	−	18.7859i	1.27332	−	0.735149i	0.975611	+	0.219509i	$0.0704455\pi$
$654$	−7.44310	+	12.8918i	−0.291048	+	0.504110i
$655$		0			0
$656$	1.39321	+	7.90129i	0.0543957	+	0.308494i
$657$	−46.4766	−	26.8333i	−1.81323	−	1.04687i
$658$	10.3155	−	5.95566i	0.402141	−	0.232176i
$659$	−34.5955	+	29.0291i	−1.34765	+	1.13081i	−0.368060	+	0.929802i	$0.619978\pi$
$659$	−34.5955	+	29.0291i	−1.34765	+	1.13081i	−0.979589	+	0.201010i	$0.935578\pi$
$660$		0			0
$661$	19.6153	+	7.13939i	0.762947	+	0.277690i	0.694043	−	0.719933i	$-0.255828\pi$
$661$	19.6153	+	7.13939i	0.762947	+	0.277690i	0.0689038	+	0.997623i	$0.478050\pi$
$662$	−7.68545	+	9.15917i	−0.298704	+	0.355981i
$663$	−0.463206	−	0.0816757i	−0.0179894	−	0.00317202i
$664$	11.2708			0.437392
$665$		0			0
$666$	−19.8221			−0.768092
$667$	12.2288	+	2.15627i	0.473502	+	0.0834911i
$668$	−10.7033	+	12.7557i	−0.414123	+	0.493533i
$669$	53.9328	+	19.6299i	2.08516	+	0.758937i
$670$		0			0
$671$	1.84281	−	1.54630i	0.0711410	−	0.0596944i
$672$	−2.19957	+	1.26992i	−0.0848501	+	0.0489882i
$673$	6.59380	+	3.80693i	0.254172	+	0.146747i	0.621673	−	0.783277i	$-0.286453\pi$
$673$	6.59380	+	3.80693i	0.254172	+	0.146747i	−0.367501	+	0.930023i	$0.619786\pi$
$674$	2.86966	+	16.2746i	0.110535	+	0.626876i
$675$		0			0
$676$	6.39547	−	11.0773i	0.245980	−	0.426049i
$677$	22.0697	−	12.7420i	0.848209	−	0.489714i	−0.0118369	−	0.999930i	$-0.503768\pi$
$677$	22.0697	−	12.7420i	0.848209	−	0.489714i	0.860046	+	0.510216i	$0.170435\pi$
$678$	−6.95970	−	8.29425i	−0.267286	−	0.318539i
$679$	6.58346	−	2.39618i	0.252650	−	0.0919570i
$680$		0			0
$681$	−7.89187	−	6.62206i	−0.302417	−	0.253758i
$682$	6.01910	+	1.06133i	0.230483	+	0.0406404i
$683$			46.2882i			1.77117i	0.464478	+	0.885585i	$0.346242\pi$
$683$			46.2882i			1.77117i	−0.464478	+	0.885585i	$0.653758\pi$
$684$	−14.3256	−	8.73943i	−0.547754	−	0.334160i
$685$		0			0
$686$	−2.20050	+	12.4797i	−0.0840156	+	0.476476i
$687$	20.9805	−	25.0036i	0.800457	−	0.953948i
$688$	3.49906	−	9.61359i	0.133400	−	0.366515i
$689$	1.94921	−	0.709454i	0.0742590	−	0.0270281i
$690$		0			0
$691$	−10.4011	−	18.0153i	−0.395677	−	0.685333i	0.597510	−	0.801861i	$-0.296157\pi$
$691$	−10.4011	−	18.0153i	−0.395677	−	0.685333i	−0.993187	+	0.116528i	$0.962823\pi$
$692$	−10.2111	−	5.89538i	−0.388168	−	0.224109i
$693$	2.06646	−	0.364373i	0.0784983	−	0.0138414i
$694$	0.633021	+	3.59004i	0.0240291	+	0.136276i
$695$		0			0
$696$	3.10086	+	5.37084i	0.117538	+	0.203581i
$697$	−2.02705	−	2.41574i	−0.0767798	−	0.0915026i
$698$	6.22282	+	17.0970i	0.235537	+	0.647133i
$699$	33.0040	+	12.0125i	1.24832	+	0.454353i
$700$		0			0
$701$	−4.88207	+	27.6876i	−0.184393	+	1.04575i	0.742339	+	0.670025i	$0.233716\pi$
$701$	−4.88207	+	27.6876i	−0.184393	+	1.04575i	−0.926732	+	0.375722i	$0.877395\pi$
$702$			1.01695i			0.0383824i
$703$	20.8980	+	8.18375i	0.788184	+	0.308656i
$704$	0.561653			0.0211681
$705$		0			0
$706$	4.95571	+	4.15833i	0.186511	+	0.156501i
$707$	−4.21523	+	11.5813i	−0.158530	+	0.435558i
$708$	−3.91565	−	10.7582i	−0.147159	−	0.404317i
$709$	−3.40036	+	2.85324i	−0.127703	+	0.107156i	−0.704402	−	0.709801i	$-0.748785\pi$
$709$	−3.40036	+	2.85324i	−0.127703	+	0.107156i	0.576699	+	0.816957i	$0.304340\pi$
$710$		0			0
$711$	1.83454	−	3.17752i	0.0688006	−	0.119166i
$712$	3.46877	−	0.611638i	0.129998	−	0.0229221i
$713$	−56.1596	+	9.90245i	−2.10319	+	0.370850i
$714$	0.499144	−	0.864542i	0.0186800	−	0.0323547i
$715$		0			0
$716$	−12.0709	+	10.1287i	−0.451111	+	0.378527i
$717$	1.37143	+	3.76798i	0.0512171	+	0.140718i
$718$	−7.69912	+	21.1532i	−0.287329	+	0.789429i
$719$	14.7672	+	12.3912i	0.550725	+	0.462113i	0.875186	−	0.483786i	$-0.160739\pi$
$719$	14.7672	+	12.3912i	0.550725	+	0.462113i	−0.324461	+	0.945899i	$0.605183\pi$
$720$		0			0
$721$	−11.1319			−0.414575
$722$	11.4950	+	15.1283i	0.427801	+	0.563015i
$723$		−	36.5857i		−	1.36064i
$724$	2.58243	−	14.6457i	0.0959754	−	0.544303i
$725$		0			0
$726$	26.2773	+	9.56417i	0.975244	+	0.354960i
$727$	14.6024	+	40.1199i	0.541575	+	1.48796i	0.844819	+	0.535052i	$0.179708\pi$
$727$	14.6024	+	40.1199i	0.541575	+	1.48796i	−0.303244	+	0.952913i	$0.598070\pi$
$728$	−0.285212	−	0.339903i	−0.0105707	−	0.0125976i
$729$	−19.7582	−	34.2223i	−0.731786	−	1.26749i
$730$		0			0
$731$	0.698263	+	3.96005i	0.0258262	+	0.146468i
$732$	−11.0395	+	1.94657i	−0.408032	+	0.0719471i
$733$	5.59661	+	3.23120i	0.206715	+	0.119347i	0.599784	−	0.800162i	$-0.295253\pi$
$733$	5.59661	+	3.23120i	0.206715	+	0.119347i	−0.393069	+	0.919509i	$0.628586\pi$
$734$	−1.35294	−	2.34336i	−0.0499379	−	0.0864950i
$735$		0			0
$736$	−4.92432	+	1.79231i	−0.181513	+	0.0660653i
$737$	2.34075	−	6.43115i	0.0862226	−	0.236895i
$738$	−19.8543	+	23.6614i	−0.730847	+	0.870990i
$739$	−3.08387	+	17.4895i	−0.113442	+	0.643361i	0.874068	+	0.485804i	$0.161473\pi$
$739$	−3.08387	+	17.4895i	−0.113442	+	0.643361i	−0.987510	+	0.157557i	$0.949638\pi$
$740$		0			0
$741$	1.90203	−	4.85701i	0.0698726	−	0.178427i
$742$			4.40256i			0.161623i
$743$	13.3993	+	2.36266i	0.491572	+	0.0866774i	0.413939	−	0.910305i	$-0.364153\pi$
$743$	13.3993	+	2.36266i	0.491572	+	0.0866774i	0.0776330	+	0.996982i	$0.475264\pi$
$744$	−21.8175	−	18.3071i	−0.799869	−	0.671170i
$745$		0			0
$746$	−18.4576	+	6.71801i	−0.675780	+	0.245964i
$747$	27.8909	+	33.2391i	1.02048	+	1.21616i
$748$	−0.191183	+	0.110379i	−0.00699033	+	0.00403587i
$749$	−6.08182	+	10.5340i	−0.222225	+	0.384905i
$750$		0			0
$751$	−5.02602	−	28.5040i	−0.183402	−	1.04013i	−0.927991	−	0.372602i	$-0.878466\pi$
$751$	−5.02602	−	28.5040i	−0.183402	−	1.04013i	0.744589	−	0.667523i	$-0.232646\pi$
$752$	10.6298	+	6.13710i	0.387628	+	0.223797i
$753$	37.9235	−	21.8951i	1.38201	−	0.797902i
$754$	−0.829966	+	0.696424i	−0.0302256	+	0.0253623i
$755$		0			0
$756$	−2.02824	−	0.738219i	−0.0737664	−	0.0268488i
$757$	21.7825	−	25.9594i	0.791698	−	0.943509i	−0.207700	−	0.978193i	$-0.566598\pi$
$757$	21.7825	−	25.9594i	0.791698	−	0.943509i	0.999398	+	0.0346833i	$0.0110422\pi$
$758$	−29.2383	−	5.15550i	−1.06198	−	0.187256i
$759$	7.70316			0.279607
$760$		0			0
$761$	−45.0675			−1.63370			−0.816848	−	0.576853i	$-0.804281\pi$
$761$	−45.0675			−1.63370			−0.816848	+	0.576853i	$0.804281\pi$
$762$	−5.22310	−	0.920974i	−0.189213	−	0.0333634i
$763$	3.54796	−	4.22829i	0.128445	−	0.153074i
$764$	24.5792	+	8.94610i	0.889245	+	0.323659i
$765$		0			0
$766$	−13.1589	+	11.0417i	−0.475452	+	0.398952i
$767$	1.73212	−	1.00004i	0.0625432	−	0.0361093i
$768$	−2.26658	−	1.30861i	−0.0817880	−	0.0472203i
$769$	8.12888	+	46.1012i	0.293135	+	1.66245i	0.674687	+	0.738104i	$0.264279\pi$
$769$	8.12888	+	46.1012i	0.293135	+	1.66245i	−0.381552	+	0.924347i	$0.624610\pi$
$770$		0			0
$771$	−7.85774	+	13.6100i	−0.282990	+	0.490152i
$772$	10.5992	−	6.11947i	0.381475	−	0.220244i
$773$	−30.7840	−	36.6869i	−1.10722	−	1.31954i	−0.942880	−	0.333134i	$-0.891894\pi$
$773$	−30.7840	−	36.6869i	−1.10722	−	1.31954i	−0.164343	−	0.986403i	$-0.552550\pi$
$774$	37.0106	−	13.4708i	1.33032	−	0.484196i
$775$		0			0
$776$	5.53039	+	4.64054i	0.198529	+	0.166586i
$777$	12.8786	+	2.27084i	0.462016	+	0.0814659i
$778$		−	6.29530i		−	0.225698i
$779$	30.7008	−	16.7487i	1.09997	−	0.600084i
$780$		0			0
$781$	0.711743	−	4.03649i	0.0254682	−	0.144437i
$782$	1.32397	−	1.57784i	0.0473450	−	0.0564236i
$783$	−1.80257	+	4.95251i	−0.0644184	+	0.176988i
$784$	−5.69290	+	2.07205i	−0.203318	+	0.0740016i
$785$		0			0
$786$	9.50883	+	16.4698i	0.339169	+	0.587458i
$787$	−26.9425	−	15.5552i	−0.960396	−	0.554485i	−0.0641009	−	0.997943i	$-0.520418\pi$
$787$	−26.9425	−	15.5552i	−0.960396	−	0.554485i	−0.896295	+	0.443459i	$0.853751\pi$
$788$	−0.308783	+	0.0544469i	−0.0110000	+	0.00193959i
$789$	2.86705	+	16.2599i	0.102070	+	0.578866i
$790$		0			0
$791$	2.00734	+	3.47681i	0.0713727	+	0.123621i
$792$	1.38988	+	1.65639i	0.0493871	+	0.0588573i
$793$	−0.669799	−	1.84026i	−0.0237853	−	0.0653495i
$794$	−9.28854	−	3.38075i	−0.329638	−	0.119978i
$795$		0			0
$796$	3.72685	−	21.1360i	0.132095	−	0.749145i
$797$		−	3.73434i		−	0.132277i	−0.997810	−	0.0661385i	$-0.978932\pi$
$797$		−	3.73434i		−	0.132277i	0.997810	−	0.0661385i	$-0.0210679\pi$
$798$	8.30626	+	7.31922i	0.294038	+	0.259098i
$799$	−4.82439			−0.170675
$800$		0			0
$801$	10.3877	+	8.71630i	0.367031	+	0.307975i
$802$	−10.6385	+	29.2290i	−0.375658	+	1.03211i
$803$	−2.67783	−	7.35728i	−0.0944986	−	0.259633i
$804$	−24.4303	+	20.4994i	−0.861589	+	0.722959i
$805$		0			0
$806$	2.48780	−	4.30900i	0.0876291	−	0.151778i
$807$	−56.3887	+	9.94285i	−1.98498	+	0.350005i
$808$	−12.5070	+	2.20533i	−0.439996	+	0.0775832i
$809$	−1.59342	+	2.75989i	−0.0560217	+	0.0970325i	−0.892676	−	0.450699i	$-0.851175\pi$
$809$	−1.59342	+	2.75989i	−0.0560217	+	0.0970325i	0.836654	+	0.547731i	$0.184508\pi$
$810$		0			0
$811$	−18.9972	+	15.9405i	−0.667081	+	0.559748i	−0.912200	−	0.409745i	$-0.865618\pi$
$811$	−18.9972	+	15.9405i	−0.667081	+	0.559748i	0.245119	+	0.969493i	$0.421173\pi$
$812$	−0.786485	−	2.16085i	−0.0276002	−	0.0758310i
$813$	8.98365	−	24.6824i	0.315070	−	0.865648i
$814$	−2.21530	−	1.85886i	−0.0776462	−	0.0651529i
$815$		0			0
$816$	1.02870			0.0360117
$817$	−44.5810	−	1.07826i	−1.55969	−	0.0377234i
$818$			31.6208i			1.10559i
$819$	0.296627	−	1.68226i	0.0103650	−	0.0587829i
$820$		0			0
$821$	−29.4494	−	10.7187i	−1.02779	−	0.374085i	−0.227551	−	0.973766i	$-0.573072\pi$
$821$	−29.4494	−	10.7187i	−1.02779	−	0.374085i	−0.800239	+	0.599681i	$0.795294\pi$
$822$	−6.78395	−	18.6387i	−0.236617	−	0.650101i
$823$	13.9157	+	16.5841i	0.485071	+	0.578085i	0.951957	−	0.306233i	$-0.0990685\pi$
$823$	13.9157	+	16.5841i	0.485071	+	0.578085i	−0.466886	+	0.884318i	$0.654624\pi$
$824$	−5.73554	−	9.93425i	−0.199807	−	0.346076i
$825$		0			0
$826$	0.737140	+	4.18053i	0.0256484	+	0.145459i
$827$	−7.46717	+	1.31666i	−0.259659	+	0.0457849i	−0.301962	−	0.953320i	$-0.597642\pi$
$827$	−7.46717	+	1.31666i	−0.259659	+	0.0457849i	0.0423030	+	0.999105i	$0.486531\pi$
$828$	−17.4716	−	10.0872i	−0.607179	−	0.350555i
$829$	14.1716	+	24.5460i	0.492200	+	0.852516i	0.999960	−	0.00898284i	$-0.00285937\pi$
$829$	14.1716	+	24.5460i	0.492200	+	0.852516i	−0.507759	+	0.861499i	$0.669526\pi$
$830$		0			0
$831$	−41.8256	+	15.2233i	−1.45091	+	0.528089i
$832$	0.156382	−	0.429655i	0.00542156	−	0.0148956i
$833$	1.53061	−	1.82411i	0.0530325	−	0.0632016i
$834$	5.17765	−	29.3639i	0.179287	−	1.01679i
$835$		0			0
$836$	−0.781460	−	2.32012i	−0.0270273	−	0.0802430i
$837$		−	24.2035i		−	0.836597i
$838$	4.59534	+	0.810282i	0.158743	+	0.0279907i
$839$	−12.0688	−	10.1269i	−0.416661	−	0.349620i	0.410230	−	0.911982i	$-0.365448\pi$
$839$	−12.0688	−	10.1269i	−0.416661	−	0.349620i	−0.826891	+	0.562362i	$0.809893\pi$
$840$		0			0
$841$	21.9748	−	7.99816i	0.757751	−	0.275799i
$842$	−6.12367	−	7.29791i	−0.211036	−	0.251502i
$843$	−2.39652	+	1.38363i	−0.0825405	+	0.0476548i
$844$	6.55478	−	11.3532i	0.225625	−	0.390793i
$845$		0			0
$846$	8.20549	+	46.5356i	0.282110	+	1.59993i
$847$	−8.97953	−	5.18433i	−0.308540	−	0.178136i
$848$	−3.92889	+	2.26834i	−0.134919	+	0.0778953i
$849$	−47.3084	+	39.6965i	−1.62362	+	1.36238i
$850$		0			0
$851$	25.3546	+	9.22831i	0.869144	+	0.316342i
$852$	−12.2770	+	14.6311i	−0.420602	+	0.501255i
$853$	−7.17004	−	1.26427i	−0.245497	−	0.0432878i	0.0495453	−	0.998772i	$-0.484223\pi$
$853$	−7.17004	−	1.26427i	−0.245497	−	0.0432878i	−0.295043	+	0.955484i	$0.595334\pi$
$854$	4.15648			0.142232
$855$		0			0
$856$	−12.5342			−0.428410
$857$	−22.3205	−	3.93570i	−0.762452	−	0.134441i	−0.221117	−	0.975247i	$-0.570970\pi$
$857$	−22.3205	−	3.93570i	−0.762452	−	0.134441i	−0.541336	+	0.840806i	$0.682081\pi$
$858$	−0.432025	+	0.514868i	−0.0147491	+	0.0175773i
$859$	−13.0461	−	4.74841i	−0.445129	−	0.162014i	0.109724	−	0.993962i	$-0.465003\pi$
$859$	−13.0461	−	4.74841i	−0.445129	−	0.162014i	−0.554853	+	0.831948i	$0.687225\pi$
$860$		0			0
$861$	15.6101	−	13.0985i	0.531992	−	0.446395i
$862$	−14.3343	+	8.27591i	−0.488228	+	0.281879i
$863$	4.05238	+	2.33964i	0.137945	+	0.0796424i	0.567384	−	0.823453i	$-0.307956\pi$
$863$	4.05238	+	2.33964i	0.137945	+	0.0796424i	−0.429439	+	0.903096i	$0.641289\pi$
$864$	−0.386222	−	2.19037i	−0.0131395	−	0.0745181i
$865$		0			0
$866$	19.3373	−	33.4933i	0.657109	−	1.13815i
$867$	38.1816	−	22.0442i	1.29672	−	0.748659i
$868$	6.78807	+	8.08970i	0.230402	+	0.274582i
$869$	0.503003	−	0.183078i	0.0170632	−	0.00621050i
$870$		0			0
$871$	−4.26798	−	3.58126i	−0.144615	−	0.121346i
$872$	5.60139	+	0.987675i	0.189687	+	0.0334469i
$873$			27.7934i			0.940665i
$874$	14.2553	+	17.8480i	0.482192	+	0.603719i
$875$		0			0
$876$	−6.33539	+	35.9298i	−0.214053	+	1.21395i
$877$	0.149187	−	0.177794i	0.00503770	−	0.00600369i	−0.763520	−	0.645785i	$-0.776530\pi$
$877$	0.149187	−	0.177794i	0.00503770	−	0.00600369i	0.768557	+	0.639781i	$0.220975\pi$
$878$	−9.72605	+	26.7221i	−0.328238	+	0.901827i
$879$	−54.7995	+	19.9454i	−1.84834	+	0.672742i
$880$		0			0
$881$	13.0872	+	22.6677i	0.440920	+	0.763695i	0.997758	−	0.0669258i	$-0.0213191\pi$
$881$	13.0872	+	22.6677i	0.440920	+	0.763695i	−0.556838	+	0.830621i	$0.687986\pi$
$882$	−20.1985	−	11.6616i	−0.680118	−	0.392666i
$883$	20.5356	−	3.62098i	0.691079	−	0.121856i	0.182931	−	0.983126i	$-0.441442\pi$
$883$	20.5356	−	3.62098i	0.691079	−	0.121856i	0.508148	+	0.861270i	$0.330330\pi$
$884$	0.0312071	+	0.176984i	0.00104961	+	0.00595263i
$885$		0			0
$886$	−9.18293	−	15.9053i	−0.308507	−	0.534349i
$887$	−28.1503	−	33.5482i	−0.945195	−	1.12644i	−0.991835	−	0.127528i	$-0.959296\pi$
$887$	−28.1503	−	33.5482i	−0.945195	−	1.12644i	0.0466399	−	0.998912i	$-0.485149\pi$
$888$	4.60894	+	12.6630i	0.154666	+	0.424941i
$889$	1.84795	+	0.672599i	0.0619782	+	0.0225582i
$890$		0			0
$891$	0.558686	−	3.16846i	0.0187167	−	0.106148i
$892$		−	21.9294i		−	0.734252i
$893$	10.5618	−	52.4492i	0.353437	−	1.75514i
$894$	0.0227416			0.000760594
$895$		0			0
$896$	0.743397	+	0.623784i	0.0248351	+	0.0208392i
$897$	2.14480	−	5.89278i	0.0716126	−	0.196754i
$898$	−0.857876	−	2.35700i	−0.0286277	−	0.0786539i
$899$	19.7532	−	16.5749i	0.658807	−	0.552805i
$900$		0			0
$901$	0.891576	−	1.54425i	0.0297027	−	0.0514466i
$902$	−4.43779	+	0.782501i	−0.147762	+	0.0260544i
$903$	−25.5892	+	4.51207i	−0.851557	+	0.150152i
$904$	−2.06849	+	3.58273i	−0.0687970	+	0.119160i
$905$		0			0
$906$	−30.8402	+	25.8780i	−1.02460	+	0.859740i
$907$	−3.66995	−	10.0831i	−0.121859	−	0.334804i	0.863732	−	0.503951i	$-0.168121\pi$
$907$	−3.66995	−	10.0831i	−0.121859	−	0.334804i	−0.985591	+	0.169147i	$0.945899\pi$
$908$	−1.34629	+	3.69890i	−0.0446781	+	0.122752i
$909$	−37.4539	−	31.4276i	−1.24227	−	1.04239i
$910$		0			0
$911$	9.16696			0.303715			0.151858	−	0.988402i	$-0.451475\pi$
$911$	9.16696			0.303715			0.151858	+	0.988402i	$0.451475\pi$
$912$	−2.25208	+	11.1837i	−0.0745739	+	0.370329i
$913$			6.33028i			0.209502i
$914$	5.70846	−	32.3743i	0.188819	−	1.07085i
$915$		0			0
$916$	−11.7191	−	4.26541i	−0.387211	−	0.140933i
$917$	−2.41177	−	6.62629i	−0.0796437	−	0.218819i
$918$	0.561932	+	0.669685i	0.0185465	+	0.0221029i
$919$	−12.1439	−	21.0339i	−0.400592	−	0.693845i	0.593206	−	0.805051i	$-0.297862\pi$
$919$	−12.1439	−	21.0339i	−0.400592	−	0.693845i	−0.993797	+	0.111206i	$0.964529\pi$
$920$		0			0
$921$	−12.4235	−	70.4573i	−0.409369	−	2.32165i
$922$	1.18730	−	0.209353i	0.0391017	−	0.00689469i
$923$	−2.88968	−	1.66835i	−0.0951148	−	0.0549146i
$924$	−0.713255	−	1.23539i	−0.0234644	−	0.0406415i
$925$		0			0
$926$	−12.0166	+	4.37368i	−0.394890	+	0.143728i
$927$	15.1042	−	41.4983i	0.496086	−	1.36298i
$928$	1.52314	−	1.81521i	0.0499995	−	0.0595871i
$929$	8.78099	−	49.7995i	0.288095	−	1.63387i	−0.405921	−	0.913908i	$-0.633049\pi$
$929$	8.78099	−	49.7995i	0.288095	−	1.63387i	0.694016	−	0.719960i	$-0.255840\pi$
$930$		0			0
$931$	16.4802	+	20.6337i	0.540117	+	0.676242i
$932$		−	13.4196i		−	0.439575i
$933$	80.8846	+	14.2621i	2.64804	+	0.466921i
$934$	24.8750	+	20.8726i	0.813935	+	0.682973i
$935$		0			0
$936$	1.65409	−	0.602041i	0.0540658	−	0.0196783i
$937$	−16.5715	−	19.7492i	−0.541367	−	0.645177i	0.424126	−	0.905603i	$-0.360581\pi$
$937$	−16.5715	−	19.7492i	−0.541367	−	0.645177i	−0.965494	+	0.260426i	$0.916137\pi$
$938$	10.2408	−	5.91251i	0.334373	−	0.193050i
$939$	−1.50600	+	2.60847i	−0.0491466	+	0.0851243i
$940$		0			0
$941$	−3.67924	−	20.8660i	−0.119940	−	0.680212i	−0.984185	−	0.177142i	$-0.943315\pi$
$941$	−3.67924	−	20.8660i	−0.119940	−	0.680212i	0.864246	−	0.503070i	$-0.167796\pi$
$942$	−40.9129	−	23.6211i	−1.33301	−	0.769616i
$943$	36.4115	−	21.0222i	1.18572	−	0.684576i
$944$	−3.35094	+	2.81177i	−0.109064	+	0.0915155i
$945$		0			0
$946$	5.39950	+	1.96526i	0.175553	+	0.0638961i
$947$	16.8901	−	20.1288i	0.548855	−	0.654099i	−0.418294	−	0.908312i	$-0.637372\pi$
$947$	16.8901	−	20.1288i	0.548855	−	0.654099i	0.967148	+	0.254212i	$0.0818162\pi$
$948$	−2.45645	−	0.433138i	−0.0797817	−	0.0140677i
$949$	−6.37378			−0.206902
$950$		0			0
$951$	−54.0648			−1.75317
$952$	−0.375636	−	0.0662348i	−0.0121744	−	0.00214668i
$953$	−24.8721	+	29.6414i	−0.805686	+	0.960179i	−0.999784	−	0.0208029i	$-0.993378\pi$
$953$	−24.8721	+	29.6414i	−0.805686	+	0.960179i	0.194097	+	0.980982i	$0.437822\pi$
$954$	−16.4121	−	5.97353i	−0.531363	−	0.193400i
$955$		0			0
$956$	1.17365	−	0.984806i	0.0379584	−	0.0318509i
$957$	−3.01655	+	1.74161i	−0.0975113	+	0.0562982i
$958$	−15.0425	−	8.68480i	−0.486002	−	0.280593i
$959$	1.27711	+	7.24285i	0.0412400	+	0.233884i
$960$		0			0
$961$	−43.7098	+	75.7076i	−1.40999	+	2.44218i
$962$	−2.03880	+	1.17710i	−0.0657335	+	0.0379513i
$963$	−31.0174	−	36.9651i	−0.999521	−	1.19118i
$964$	−13.1358	+	4.78105i	−0.423076	+	0.153987i
$965$		0			0
$966$	10.1958	+	8.55529i	0.328044	+	0.275262i
$967$	−2.72211	−	0.479982i	−0.0875373	−	0.0154352i	0.129708	−	0.991552i	$-0.458596\pi$
$967$	−2.72211	−	0.479982i	−0.0875373	−	0.0154352i	−0.217245	+	0.976117i	$0.569707\pi$
$968$		−	10.6845i		−	0.343414i
$969$	−1.43129	−	4.24943i	−0.0459796	−	0.136511i
$970$		0			0
$971$	−8.07923	+	45.8196i	−0.259275	+	1.47042i	0.525582	+	0.850743i	$0.323848\pi$
$971$	−8.07923	+	45.8196i	−0.259275	+	1.47042i	−0.784857	+	0.619677i	$0.787263\pi$
$972$	−13.9259	+	16.5962i	−0.446672	+	0.532323i
$973$	−3.78130	+	10.3890i	−0.121223	+	0.333058i
$974$	7.20556	−	2.62261i	0.230881	−	0.0840338i
$975$		0			0
$976$	2.14155	+	3.70928i	0.0685495	+	0.118731i
$977$	−45.6660	−	26.3653i	−1.46099	−	0.843500i	−0.461928	−	0.886917i	$-0.652842\pi$
$977$	−45.6660	−	26.3653i	−1.46099	−	0.843500i	−0.999057	+	0.0434169i	$0.986176\pi$
$978$	−12.6564	+	2.23167i	−0.404708	+	0.0713610i
$979$	0.343528	+	1.94825i	0.0109792	+	0.0622662i
$980$		0			0
$981$	10.9485	+	18.9634i	0.349559	+	0.605453i
$982$	−21.8067	−	25.9882i	−0.695881	−	0.829318i
$983$	−8.88043	−	24.3988i	−0.283242	−	0.778200i	−0.996971	−	0.0777783i	$-0.975217\pi$
$983$	−8.88043	−	24.3988i	−0.283242	−	0.778200i	0.713729	−	0.700422i	$-0.247005\pi$
$984$	19.7320	+	7.18188i	0.629035	+	0.228950i
$985$		0			0
$986$	−0.161730	+	0.917219i	−0.00515055	+	0.0292102i
$987$		−	31.1745i		−	0.992296i
$988$	−1.99243	−	0.0481899i	−0.0633877	−	0.00153313i
$989$	−53.6118			−1.70476
$990$		0			0
$991$	−7.40666	−	6.21493i	−0.235280	−	0.197424i	0.517523	−	0.855669i	$-0.326854\pi$
$991$	−7.40666	−	6.21493i	−0.235280	−	0.197424i	−0.752803	+	0.658246i	$0.771299\pi$
$992$	−3.72189	+	10.2258i	−0.118170	+	0.324670i
$993$	10.7027	+	29.4054i	0.339640	+	0.933153i
$994$	5.42507	−	4.55217i	0.172073	−	0.144386i
$995$		0			0
$996$	14.7491	−	25.5461i	0.467342	−	0.809460i
$997$	32.2427	−	5.68526i	1.02114	−	0.180054i	0.362080	−	0.932147i	$-0.382067\pi$
$997$	32.2427	−	5.68526i	1.02114	−	0.180054i	0.659057	+	0.752093i	$0.270956\pi$
$998$	5.81129	−	1.02469i	0.183953	−	0.0324359i
$999$	−5.72594	+	9.91762i	−0.181161	+	0.313780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.f.549.1		24
5.2	odd	4		190.2.k.c.131.2	✓	12
5.3	odd	4		950.2.l.g.701.1		12
5.4	even	2	inner	950.2.u.f.549.4		24
19.9	even	9	inner	950.2.u.f.199.4		24
95.9	even	18	inner	950.2.u.f.199.1		24
95.22	even	36		3610.2.a.bd.1.1		6
95.28	odd	36		950.2.l.g.351.1		12
95.47	odd	36		190.2.k.c.161.2	yes	12
95.92	odd	36		3610.2.a.bf.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.131.2	✓	12	5.2	odd	4
190.2.k.c.161.2	yes	12	95.47	odd	36
950.2.l.g.351.1		12	95.28	odd	36
950.2.l.g.701.1		12	5.3	odd	4
950.2.u.f.199.1		24	95.9	even	18	inner
950.2.u.f.199.4		24	19.9	even	9	inner
950.2.u.f.549.1		24	1.1	even	1	trivial
950.2.u.f.549.4		24	5.4	even	2	inner
3610.2.a.bd.1.1		6	95.22	even	36
3610.2.a.bf.1.6		6	95.92	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.68231 + 2.00490i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.00490 - 1.68231i) q^{6} +(-0.840422 + 0.485218i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.668514 - 3.79133i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.68231 + 2.00490i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.00490 - 1.68231i) q^{6} +(-0.840422 + 0.485218i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.668514 - 3.79133i) q^{9} +(0.280827 - 0.486406i) q^{11} +(-2.26658 + 1.30861i) q^{12} +(-0.293901 - 0.350258i) q^{13} +(0.911911 - 0.331909i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.387080 - 0.0682527i) q^{17} +3.84982i q^{18} +(1.58943 - 4.05878i) q^{19} +(0.441039 - 2.50125i) q^{21} +(-0.361024 + 0.430251i) q^{22} +(1.79231 - 4.92432i) q^{23} +(2.45938 - 0.895141i) q^{24} +(0.228615 + 0.395972i) q^{26} +(1.92618 + 1.11208i) q^{27} +(-0.955692 + 0.168514i) q^{28} +(0.411474 + 2.33359i) q^{29} +(-5.44104 - 9.42416i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(0.502759 + 1.38132i) q^{33} +(0.369347 + 0.134431i) q^{34} +(0.668514 - 3.79133i) q^{36} +5.14885i q^{37} +(-2.27009 + 3.72112i) q^{38} +1.19667 q^{39} +(6.14611 + 5.15720i) q^{41} +(-0.868676 + 2.38667i) q^{42} +(-3.49906 - 9.61359i) q^{43} +(0.430251 - 0.361024i) q^{44} +(-2.62018 + 4.53828i) q^{46} +(12.0877 - 2.13139i) q^{47} +(-2.57745 + 0.454475i) q^{48} +(-3.02913 + 5.24660i) q^{49} +(0.788030 - 0.661236i) q^{51} +(-0.156382 - 0.429655i) q^{52} +(-1.55164 + 4.26309i) q^{53} +(-1.70381 - 1.42967i) q^{54} +0.970436 q^{56} +(5.46354 + 10.0148i) q^{57} -2.36959i q^{58} +(-0.759597 + 4.30789i) q^{59} +(4.02481 + 1.46491i) q^{61} +(3.72189 + 10.2258i) q^{62} +(2.40146 + 2.86194i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.255257 - 1.44764i) q^{66} +(12.0001 - 2.11595i) q^{67} +(-0.340392 - 0.196526i) q^{68} +(6.85757 + 11.8777i) q^{69} +(6.85757 - 2.49595i) q^{71} +(-1.31672 + 3.61765i) q^{72} +(8.96047 - 10.6787i) q^{73} +(0.894088 - 5.07062i) q^{74} +(2.88176 - 3.27039i) q^{76} +0.545048i q^{77} +(-1.17849 - 0.207799i) q^{78} +(0.730080 + 0.612610i) q^{79} +(5.38288 - 1.95921i) q^{81} +(-5.15720 - 6.14611i) q^{82} +(-9.76080 + 5.63540i) q^{83} +(1.26992 - 2.19957i) q^{84} +(1.77652 + 10.0751i) q^{86} +(-5.37084 - 3.10086i) q^{87} +(-0.486406 + 0.280827i) q^{88} +(-2.69822 + 2.26408i) q^{89} +(0.416952 + 0.151758i) q^{91} +(3.36844 - 4.01435i) q^{92} +(28.0481 + 4.94563i) q^{93} -12.2742 q^{94} +2.61722 q^{96} +(-7.10973 - 1.25364i) q^{97} +(3.89417 - 4.64089i) q^{98} +(-2.03186 - 0.739538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 24 * q + 6 * q^6 - 18 * q^9	\( 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more