LMFDB - Embedded newform 867.2.h.g.712.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(688,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("867.688");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			712.2
Root			$-0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	867.712
Dual form			867.2.h.g.688.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.541196 + 0.541196i) q^{2} +(-0.382683 - 0.923880i) q^{3} -1.41421i q^{4} +(1.92388 - 0.796897i) q^{5} +(0.292893 - 0.707107i) q^{6} +(1.14065 + 0.472474i) q^{7} +(1.84776 - 1.84776i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(1.47247 + 0.609919i) q^{10} +(0.572726 - 1.38268i) q^{11} +(-1.30656 + 0.541196i) q^{12} -4.10973i q^{13} +(0.361616 + 0.873017i) q^{14} +(-1.47247 - 1.47247i) q^{15} -0.828427 q^{16} -0.765367 q^{18} +(4.81684 + 4.81684i) q^{19} +(-1.12698 - 2.72078i) q^{20} -1.23463i q^{21} +(1.05826 - 0.438346i) q^{22} +(-1.26616 + 3.05679i) q^{23} +(-2.41421 - 1.00000i) q^{24} +(-0.469266 + 0.469266i) q^{25} +(2.22417 - 2.22417i) q^{26} +(0.923880 + 0.382683i) q^{27} +(0.668179 - 1.61313i) q^{28} +(-5.76745 + 2.38896i) q^{29} -1.59379i q^{30} +(-3.93015 - 9.48822i) q^{31} +(-4.14386 - 4.14386i) q^{32} -1.49661 q^{33} +2.57099 q^{35} +(1.00000 + 1.00000i) q^{36} +(1.50660 + 3.63726i) q^{37} +5.21371i q^{38} +(-3.79690 + 1.57273i) q^{39} +(2.08239 - 5.02734i) q^{40} +(11.2132 + 4.64466i) q^{41} +(0.668179 - 0.668179i) q^{42} +(2.43675 - 2.43675i) q^{43} +(-1.95541 - 0.809957i) q^{44} +(-0.796897 + 1.92388i) q^{45} +(-2.33956 + 0.969079i) q^{46} -1.56940i q^{47} +(0.317025 + 0.765367i) q^{48} +(-3.87189 - 3.87189i) q^{49} -0.507930 q^{50} -5.81204 q^{52} +(-2.80109 - 2.80109i) q^{53} +(0.292893 + 0.707107i) q^{54} -3.11652i q^{55} +(2.98067 - 1.23463i) q^{56} +(2.60685 - 6.29350i) q^{57} +(-4.41421 - 1.82843i) q^{58} +(5.70144 - 5.70144i) q^{59} +(-2.08239 + 2.08239i) q^{60} +(-3.02413 - 1.25264i) q^{61} +(3.00801 - 7.26197i) q^{62} +(-1.14065 + 0.472474i) q^{63} -2.82843i q^{64} +(-3.27503 - 7.90663i) q^{65} +(-0.809957 - 0.809957i) q^{66} -2.11652 q^{67} +3.30864 q^{69} +(1.39141 + 1.39141i) q^{70} +(-0.0867259 - 0.209375i) q^{71} +2.61313i q^{72} +(-0.340203 + 0.140917i) q^{73} +(-1.15310 + 2.78384i) q^{74} +(0.613126 + 0.253965i) q^{75} +(6.81204 - 6.81204i) q^{76} +(1.30656 - 1.30656i) q^{77} +(-2.90602 - 1.20371i) q^{78} +(-1.03893 + 2.50819i) q^{79} +(-1.59379 + 0.660171i) q^{80} -1.00000i q^{81} +(3.55487 + 8.58221i) q^{82} +(10.1921 + 10.1921i) q^{83} -1.74603 q^{84} +2.63752 q^{86} +(4.41421 + 4.41421i) q^{87} +(-1.49661 - 3.61313i) q^{88} +13.6694i q^{89} +(-1.47247 + 0.609919i) q^{90} +(1.94174 - 4.68777i) q^{91} +(4.32295 + 1.79063i) q^{92} +(-7.26197 + 7.26197i) q^{93} +(0.849352 - 0.849352i) q^{94} +(13.1055 + 5.42849i) q^{95} +(-2.24264 + 5.41421i) q^{96} +(2.48022 - 1.02734i) q^{97} -4.19090i q^{98} +(0.572726 + 1.38268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{5} + 8 q^{6} - 8 q^{11} + 16 q^{14} + 16 q^{16} - 8 q^{19} - 16 q^{20} + 8 q^{22} - 8 q^{23} - 8 q^{24} - 16 q^{25} + 16 q^{26} + 8 q^{28} - 8 q^{31} + 8 q^{33} + 32 q^{35} + 8 q^{36} + 8 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^5 + 8 * q^6 - 8 * q^11 + 16 * q^14 + 16 * q^16 - 8 * q^19 - 16 * q^20 + 8 * q^22 - 8 * q^23 - 8 * q^24 - 16 * q^25 + 16 * q^26 + 8 * q^28 - 8 * q^31 + 8 * q^33 + 32 * q^35 + 8 * q^36 + 8 * q^37 - 16 * q^39 + 8 * q^40 + 24 * q^41 + 8 * q^42 - 8 * q^43 + 8 * q^45 - 8 * q^49 - 32 * q^50 - 16 * q^52 - 32 * q^53 + 8 * q^54 + 16 * q^56 + 16 * q^57 - 24 * q^58 + 16 * q^59 - 8 * q^60 - 16 * q^61 - 16 * q^62 - 24 * q^65 - 16 * q^66 - 16 * q^67 - 24 * q^69 + 40 * q^70 + 16 * q^71 - 48 * q^73 - 64 * q^74 - 16 * q^75 + 24 * q^76 - 8 * q^78 + 16 * q^80 + 8 * q^82 + 32 * q^83 - 32 * q^86 + 24 * q^87 + 8 * q^88 + 16 * q^91 + 32 * q^92 - 32 * q^93 + 40 * q^95 + 16 * q^96 - 8 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.541196	+	0.541196i	0.382683	+	0.382683i	0.872068	−	0.489385i	$-0.162779\pi$
$2$	0.541196	+	0.541196i	0.382683	+	0.382683i	−0.489385	+	0.872068i	$0.662779\pi$
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$		−	1.41421i		−	0.707107i
$5$	1.92388	−	0.796897i	0.860385	−	0.356383i	0.0915270	−	0.995803i	$-0.470825\pi$
$5$	1.92388	−	0.796897i	0.860385	−	0.356383i	0.768858	+	0.639419i	$0.220825\pi$
$6$	0.292893	−	0.707107i	0.119573	−	0.288675i
$7$	1.14065	+	0.472474i	0.431126	+	0.178578i	0.587684	−	0.809091i	$-0.300040\pi$
$7$	1.14065	+	0.472474i	0.431126	+	0.178578i	−0.156558	+	0.987669i	$0.550040\pi$
$8$	1.84776	−	1.84776i	0.653281	−	0.653281i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	1.47247	+	0.609919i	0.465637	+	0.192873i
$11$	0.572726	−	1.38268i	0.172683	−	0.416895i	−0.813716	−	0.581263i	$-0.802559\pi$
$11$	0.572726	−	1.38268i	0.172683	−	0.416895i	0.986399	+	0.164369i	$0.0525586\pi$
$12$	−1.30656	+	0.541196i	−0.377172	+	0.156230i
$13$		−	4.10973i		−	1.13983i	−0.821702	−	0.569917i	$-0.806975\pi$
$13$		−	4.10973i		−	1.13983i	0.821702	−	0.569917i	$-0.193025\pi$
$14$	0.361616	+	0.873017i	0.0966459	+	0.233324i
$15$	−1.47247	−	1.47247i	−0.380191	−	0.380191i
$16$	−0.828427			−0.207107
$17$		0			0
$17$		0			0
$18$	−0.765367			−0.180399
$19$	4.81684	+	4.81684i	1.10506	+	1.10506i	0.993790	+	0.111268i	$0.0354912\pi$
$19$	4.81684	+	4.81684i	1.10506	+	1.10506i	0.111268	+	0.993790i	$0.464509\pi$
$20$	−1.12698	−	2.72078i	−0.252001	−	0.608384i
$21$		−	1.23463i		−	0.269419i
$22$	1.05826	−	0.438346i	0.225622	−	0.0934556i
$23$	−1.26616	+	3.05679i	−0.264013	+	0.637384i	−0.999179	−	0.0405025i	$-0.987104\pi$
$23$	−1.26616	+	3.05679i	−0.264013	+	0.637384i	0.735166	+	0.677887i	$0.237104\pi$
$24$	−2.41421	−	1.00000i	−0.492799	−	0.204124i
$25$	−0.469266	+	0.469266i	−0.0938533	+	0.0938533i
$26$	2.22417	−	2.22417i	0.436196	−	0.436196i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	0.668179	−	1.61313i	0.126274	−	0.304852i
$29$	−5.76745	+	2.38896i	−1.07099	+	0.443618i	−0.847339	−	0.531052i	$-0.821797\pi$
$29$	−5.76745	+	2.38896i	−1.07099	+	0.443618i	−0.223649	+	0.974670i	$0.571797\pi$
$30$		−	1.59379i		−	0.290986i
$31$	−3.93015	−	9.48822i	−0.705876	−	1.70414i	−0.710057	−	0.704144i	$-0.751331\pi$
$31$	−3.93015	−	9.48822i	−0.705876	−	1.70414i	0.00418103	−	0.999991i	$-0.498669\pi$
$32$	−4.14386	−	4.14386i	−0.732538	−	0.732538i
$33$	−1.49661			−0.260526
$34$		0			0
$35$	2.57099			0.434577
$36$	1.00000	+	1.00000i	0.166667	+	0.166667i
$37$	1.50660	+	3.63726i	0.247684	+	0.597962i	0.998007	−	0.0631101i	$-0.0201019\pi$
$37$	1.50660	+	3.63726i	0.247684	+	0.597962i	−0.750323	+	0.661072i	$0.770102\pi$
$38$			5.21371i			0.845775i
$39$	−3.79690	+	1.57273i	−0.607990	+	0.251838i
$40$	2.08239	−	5.02734i	0.329255	−	0.794892i
$41$	11.2132	+	4.64466i	1.75121	+	0.725373i	0.997689	+	0.0679453i	$0.0216443\pi$
$41$	11.2132	+	4.64466i	1.75121	+	0.725373i	0.753517	+	0.657428i	$0.228356\pi$
$42$	0.668179	−	0.668179i	0.103102	−	0.103102i
$43$	2.43675	−	2.43675i	0.371601	−	0.371601i	−0.496459	−	0.868060i	$-0.665367\pi$
$43$	2.43675	−	2.43675i	0.371601	−	0.371601i	0.868060	+	0.496459i	$0.165367\pi$
$44$	−1.95541	−	0.809957i	−0.294789	−	0.122106i
$45$	−0.796897	+	1.92388i	−0.118794	+	0.286795i
$46$	−2.33956	+	0.969079i	−0.344950	+	0.142883i
$47$		−	1.56940i		−	0.228920i	−0.993428	−	0.114460i	$-0.963486\pi$
$47$		−	1.56940i		−	0.228920i	0.993428	−	0.114460i	$-0.0365138\pi$
$48$	0.317025	+	0.765367i	0.0457587	+	0.110471i
$49$	−3.87189	−	3.87189i	−0.553127	−	0.553127i
$50$	−0.507930			−0.0718322
$51$		0			0
$52$	−5.81204			−0.805985
$53$	−2.80109	−	2.80109i	−0.384759	−	0.384759i	0.488054	−	0.872813i	$-0.337707\pi$
$53$	−2.80109	−	2.80109i	−0.384759	−	0.384759i	−0.872813	+	0.488054i	$0.837707\pi$
$54$	0.292893	+	0.707107i	0.0398577	+	0.0962250i
$55$		−	3.11652i		−	0.420231i
$56$	2.98067	−	1.23463i	0.398309	−	0.164985i
$57$	2.60685	−	6.29350i	0.345286	−	0.833595i
$58$	−4.41421	−	1.82843i	−0.579615	−	0.240084i
$59$	5.70144	−	5.70144i	0.742265	−	0.742265i	−0.230749	−	0.973013i	$-0.574117\pi$
$59$	5.70144	−	5.70144i	0.742265	−	0.742265i	0.973013	+	0.230749i	$0.0741175\pi$
$60$	−2.08239	+	2.08239i	−0.268836	+	0.268836i
$61$	−3.02413	−	1.25264i	−0.387200	−	0.160384i	0.180587	−	0.983559i	$-0.442200\pi$
$61$	−3.02413	−	1.25264i	−0.387200	−	0.160384i	−0.567787	+	0.823175i	$0.692200\pi$
$62$	3.00801	−	7.26197i	0.382017	−	0.922271i
$63$	−1.14065	+	0.472474i	−0.143709	+	0.0595261i
$64$		−	2.82843i		−	0.353553i
$65$	−3.27503	−	7.90663i	−0.406218	−	0.980697i
$66$	−0.809957	−	0.809957i	−0.0996988	−	0.0996988i
$67$	−2.11652			−0.258574			−0.129287	−	0.991607i	$-0.541269\pi$
$67$	−2.11652			−0.258574			−0.129287	+	0.991607i	$0.541269\pi$
$68$		0			0
$69$	3.30864			0.398314
$70$	1.39141	+	1.39141i	0.166305	+	0.166305i
$71$	−0.0867259	−	0.209375i	−0.0102925	−	0.0248482i	0.918650	−	0.395073i	$-0.129281\pi$
$71$	−0.0867259	−	0.209375i	−0.0102925	−	0.0248482i	−0.928942	+	0.370225i	$0.879281\pi$
$72$			2.61313i			0.307960i
$73$	−0.340203	+	0.140917i	−0.0398177	+	0.0164930i	−0.402503	−	0.915418i	$-0.631860\pi$
$73$	−0.340203	+	0.140917i	−0.0398177	+	0.0164930i	0.362686	+	0.931912i	$0.381860\pi$
$74$	−1.15310	+	2.78384i	−0.134045	+	0.323614i
$75$	0.613126	+	0.253965i	0.0707977	+	0.0293254i
$76$	6.81204	−	6.81204i	0.781394	−	0.781394i
$77$	1.30656	−	1.30656i	0.148897	−	0.148897i
$78$	−2.90602	−	1.20371i	−0.329042	−	0.136294i
$79$	−1.03893	+	2.50819i	−0.116889	+	0.282194i	−0.971486	−	0.237097i	$-0.923804\pi$
$79$	−1.03893	+	2.50819i	−0.116889	+	0.282194i	0.854597	+	0.519291i	$0.173804\pi$
$80$	−1.59379	+	0.660171i	−0.178192	+	0.0738094i
$81$		−	1.00000i		−	0.111111i
$82$	3.55487	+	8.58221i	0.392569	+	0.947746i
$83$	10.1921	+	10.1921i	1.11873	+	1.11873i	0.991928	+	0.126803i	$0.0404716\pi$
$83$	10.1921	+	10.1921i	1.11873	+	1.11873i	0.126803	+	0.991928i	$0.459528\pi$
$84$	−1.74603			−0.190508
$85$		0			0
$86$	2.63752			0.284411
$87$	4.41421	+	4.41421i	0.473253	+	0.473253i
$88$	−1.49661	−	3.61313i	−0.159539	−	0.385161i
$89$			13.6694i			1.44895i	0.689299	+	0.724477i	$0.257918\pi$
$89$			13.6694i			1.44895i	−0.689299	+	0.724477i	$0.742082\pi$
$90$	−1.47247	+	0.609919i	−0.155212	+	0.0642911i
$91$	1.94174	−	4.68777i	0.203550	−	0.491412i
$92$	4.32295	+	1.79063i	0.450699	+	0.186686i
$93$	−7.26197	+	7.26197i	−0.753031	+	0.753031i
$94$	0.849352	−	0.849352i	0.0876040	−	0.0876040i
$95$	13.1055	+	5.42849i	1.34460	+	0.556952i
$96$	−2.24264	+	5.41421i	−0.228889	+	0.552586i
$97$	2.48022	−	1.02734i	0.251828	−	0.104311i	−0.253199	−	0.967414i	$-0.581483\pi$
$97$	2.48022	−	1.02734i	0.251828	−	0.104311i	0.505027	+	0.863104i	$0.331483\pi$
$98$		−	4.19090i		−	0.423345i
$99$	0.572726	+	1.38268i	0.0575612	+	0.138965i
$100$	0.663643	+	0.663643i	0.0663643	+	0.0663643i
$101$	2.38009			0.236827			0.118414	−	0.992964i	$-0.462219\pi$
$101$	2.38009			0.236827			0.118414	+	0.992964i	$0.462219\pi$
$102$		0			0
$103$	−13.2909			−1.30959			−0.654796	−	0.755806i	$-0.727245\pi$
$103$	−13.2909			−1.30959			−0.654796	+	0.755806i	$0.727245\pi$
$104$	−7.59379	−	7.59379i	−0.744633	−	0.744633i
$105$	−0.983875	−	2.37529i	−0.0960164	−	0.231804i
$106$		−	3.03188i		−	0.294482i
$107$	12.0773	−	5.00260i	1.16756	−	0.483619i	0.287175	−	0.957878i	$-0.407284\pi$
$107$	12.0773	−	5.00260i	1.16756	−	0.483619i	0.880386	+	0.474259i	$0.157284\pi$
$108$	0.541196	−	1.30656i	0.0520766	−	0.125724i
$109$	0.883480	+	0.365949i	0.0846220	+	0.0350516i	0.424593	−	0.905384i	$-0.360417\pi$
$109$	0.883480	+	0.365949i	0.0846220	+	0.0350516i	−0.339971	+	0.940436i	$0.610417\pi$
$110$	1.68665	−	1.68665i	0.160816	−	0.160816i
$111$	2.78384	−	2.78384i	0.264230	−	0.264230i
$112$	−0.944947	−	0.391410i	−0.0892891	−	0.0369848i
$113$	−3.30237	+	7.97263i	−0.310661	+	0.750002i	0.689020	+	0.724742i	$0.258041\pi$
$113$	−3.30237	+	7.97263i	−0.310661	+	0.750002i	−0.999681	+	0.0252597i	$0.991959\pi$
$114$	4.81684	−	1.99520i	0.451138	−	0.186868i
$115$			6.88989i			0.642486i
$116$	3.37849	+	8.15640i	0.313685	+	0.757303i
$117$	2.90602	+	2.90602i	0.268662	+	0.268662i
$118$	6.17120			0.568105
$119$		0			0
$120$	−5.44155			−0.496744
$121$	6.19438	+	6.19438i	0.563125	+	0.563125i
$122$	−0.958726	−	2.31457i	−0.0867990	−	0.209551i
$123$		−	12.1371i		−	1.09436i
$124$	−13.4184	+	5.55807i	−1.20501	+	0.499130i
$125$	−4.51334	+	10.8962i	−0.403685	+	0.974583i
$126$	−0.873017	−	0.361616i	−0.0777746	−	0.0322153i
$127$	−10.0044	+	10.0044i	−0.887749	+	0.887749i	−0.994307	−	0.106557i	$-0.966017\pi$
$127$	−10.0044	+	10.0044i	−0.887749	+	0.887749i	0.106557	+	0.994307i	$0.466017\pi$
$128$	−6.75699	+	6.75699i	−0.597239	+	0.597239i
$129$	−3.18377	−	1.31876i	−0.280315	−	0.116110i
$130$	2.50660	−	6.05147i	0.219844	−	0.530749i
$131$	2.39363	−	0.991476i	0.209133	−	0.0866256i	−0.275658	−	0.961256i	$-0.588896\pi$
$131$	2.39363	−	0.991476i	0.209133	−	0.0866256i	0.484791	+	0.874630i	$0.338896\pi$
$132$			2.11652i			0.184219i
$133$	3.21851	+	7.77017i	0.279080	+	0.673759i
$134$	−1.14545	−	1.14545i	−0.0989520	−	0.0989520i
$135$	2.08239			0.179224
$136$		0			0
$137$	15.2684			1.30447			0.652233	−	0.758018i	$-0.273832\pi$
$137$	15.2684			1.30447			0.652233	+	0.758018i	$0.273832\pi$
$138$	1.79063	+	1.79063i	0.152428	+	0.152428i
$139$	1.54686	+	3.73445i	0.131203	+	0.316752i	0.975805	−	0.218643i	$-0.0701630\pi$
$139$	1.54686	+	3.73445i	0.131203	+	0.316752i	−0.844602	+	0.535394i	$0.820163\pi$
$140$		−	3.63593i		−	0.307292i
$141$	−1.44993	+	0.600582i	−0.122106	+	0.0505782i
$142$	0.0663771	−	0.160248i	0.00557024	−	0.0134478i
$143$	−5.68246	−	2.35375i	−0.475191	−	0.196831i
$144$	0.585786	−	0.585786i	0.0488155	−	0.0488155i
$145$	−9.19212	+	9.19212i	−0.763364	+	0.763364i
$146$	−0.260380	−	0.107853i	−0.0215492	−	0.00892597i
$147$	−2.09545	+	5.05887i	−0.172830	+	0.417249i
$148$	5.14386	−	2.13066i	0.422823	−	0.175139i
$149$			18.1219i			1.48460i	0.670065	+	0.742302i	$0.266266\pi$
$149$			18.1219i			1.48460i	−0.670065	+	0.742302i	$0.733734\pi$
$150$	0.194376	+	0.469266i	0.0158708	+	0.0383154i
$151$	3.72739	+	3.72739i	0.303331	+	0.303331i	0.842316	−	0.538985i	$-0.181192\pi$
$151$	3.72739	+	3.72739i	0.303331	+	0.303331i	−0.538985	+	0.842316i	$0.681192\pi$
$152$	17.8007			1.44383
$153$		0			0
$154$	1.41421			0.113961
$155$	−15.1223	−	15.1223i	−1.21465	−	1.21465i
$156$	2.22417	+	5.36962i	0.178076	+	0.429914i
$157$		−	3.80334i		−	0.303540i	−0.988416	−	0.151770i	$-0.951503\pi$
$157$		−	3.80334i		−	0.303540i	0.988416	−	0.151770i	$-0.0484972\pi$
$158$	−1.91969	+	0.795161i	−0.152722	+	0.0632596i
$159$	−1.51594	+	3.65980i	−0.120222	+	0.290241i
$160$	−11.2745	−	4.67006i	−0.891329	−	0.369200i
$161$	−2.88850	+	2.88850i	−0.227646	+	0.227646i
$162$	0.541196	−	0.541196i	0.0425204	−	0.0425204i
$163$	−8.37849	−	3.47049i	−0.656254	−	0.271829i	0.0296072	−	0.999562i	$-0.490574\pi$
$163$	−8.37849	−	3.47049i	−0.656254	−	0.271829i	−0.685861	+	0.727732i	$0.740574\pi$
$164$	6.56854	−	15.8578i	0.512916	−	1.23829i
$165$	−2.87929	+	1.19264i	−0.224152	+	0.0928469i
$166$			11.0319i			0.856240i
$167$	−3.40115	−	8.21111i	−0.263189	−	0.635395i	0.735943	−	0.677043i	$-0.236739\pi$
$167$	−3.40115	−	8.21111i	−0.263189	−	0.635395i	−0.999132	+	0.0416485i	$0.986739\pi$
$168$	−2.28130	−	2.28130i	−0.176006	−	0.176006i
$169$	−3.88989			−0.299223
$170$		0			0
$171$	−6.81204			−0.520930
$172$	−3.44609	−	3.44609i	−0.262762	−	0.262762i
$173$	4.68679	+	11.3149i	0.356330	+	0.860257i	0.995810	+	0.0914490i	$0.0291499\pi$
$173$	4.68679	+	11.3149i	0.356330	+	0.860257i	−0.639480	+	0.768808i	$0.720850\pi$
$174$			4.77791i			0.362212i
$175$	−0.756986	+	0.313554i	−0.0572227	+	0.0237024i
$176$	−0.474462	+	1.14545i	−0.0357639	+	0.0863417i
$177$	−7.44930	−	3.08560i	−0.559923	−	0.231928i
$178$	−7.39782	+	7.39782i	−0.554490	+	0.554490i
$179$	7.50756	−	7.50756i	0.561141	−	0.561141i	−0.368490	−	0.929632i	$-0.620125\pi$
$179$	7.50756	−	7.50756i	0.561141	−	0.561141i	0.929632	+	0.368490i	$0.120125\pi$
$180$	2.72078	+	1.12698i	0.202795	+	0.0840003i
$181$	−6.32477	+	15.2693i	−0.470116	+	1.13496i	0.493995	+	0.869465i	$0.335536\pi$
$181$	−6.32477	+	15.2693i	−0.470116	+	1.13496i	−0.964112	+	0.265497i	$0.914464\pi$
$182$	3.58787	−	1.48614i	0.265950	−	0.110160i
$183$			3.27330i			0.241969i
$184$	3.30864	+	7.98777i	0.243916	+	0.588866i
$185$	5.79704	+	5.79704i	0.426207	+	0.426207i
$186$	−7.86030			−0.576345
$187$		0			0
$188$	−2.21946			−0.161871
$189$	0.873017	+	0.873017i	0.0635027	+	0.0635027i
$190$	4.15479	+	10.0305i	0.301420	+	0.727692i
$191$		−	12.0167i		−	0.869498i	−0.900552	−	0.434749i	$-0.856837\pi$
$191$		−	12.0167i		−	0.869498i	0.900552	−	0.434749i	$-0.143163\pi$
$192$	−2.61313	+	1.08239i	−0.188586	+	0.0781149i
$193$	−4.10172	+	9.90244i	−0.295249	+	0.712793i	0.704746	+	0.709460i	$0.251061\pi$
$193$	−4.10172	+	9.90244i	−0.295249	+	0.712793i	−0.999994	+	0.00333326i	$0.998939\pi$
$194$	1.89828	+	0.786292i	0.136288	+	0.0564524i
$195$	−6.05147	+	6.05147i	−0.433355	+	0.433355i
$196$	−5.47568	+	5.47568i	−0.391120	+	0.391120i
$197$	2.92772	+	1.21270i	0.208592	+	0.0864015i	0.484533	−	0.874773i	$-0.338990\pi$
$197$	2.92772	+	1.21270i	0.208592	+	0.0864015i	−0.275941	+	0.961174i	$0.588990\pi$
$198$	−0.438346	+	1.05826i	−0.0311519	+	0.0752073i
$199$	12.6337	−	5.23304i	0.895578	−	0.370960i	0.113060	−	0.993588i	$-0.463935\pi$
$199$	12.6337	−	5.23304i	0.895578	−	0.370960i	0.782518	+	0.622628i	$0.213935\pi$
$200$			1.73418i			0.122625i
$201$	0.809957	+	1.95541i	0.0571300	+	0.137924i
$202$	1.28809	+	1.28809i	0.0906299	+	0.0906299i
$203$	−7.70737			−0.540951
$204$		0			0
$205$	25.2741			1.76522
$206$	−7.19299	−	7.19299i	−0.501159	−	0.501159i
$207$	−1.26616	−	3.05679i	−0.0880044	−	0.212461i
$208$			3.40461i			0.236067i
$209$	9.41889	−	3.90143i	0.651518	−	0.269868i
$210$	0.753026	−	1.81796i	0.0519637	−	0.125451i
$211$	−5.47727	−	2.26876i	−0.377071	−	0.156188i	0.186095	−	0.982532i	$-0.440417\pi$
$211$	−5.47727	−	2.26876i	−0.377071	−	0.156188i	−0.563166	+	0.826344i	$0.690417\pi$
$212$	−3.96134	+	3.96134i	−0.272066	+	0.272066i
$213$	−0.160248	+	0.160248i	−0.0109800	+	0.0109800i
$214$	9.24360	+	3.82882i	0.631879	+	0.261733i
$215$	2.74618	−	6.62986i	0.187288	−	0.452153i
$216$	2.41421	−	1.00000i	0.164266	−	0.0680414i
$217$		−	12.6797i		−	0.860751i
$218$	0.280085	+	0.676186i	0.0189698	+	0.0457971i
$219$	0.260380	+	0.260380i	0.0175948	+	0.0175948i
$220$	−4.40743			−0.297149
$221$		0			0
$222$	3.01320			0.202233
$223$	−18.4892	−	18.4892i	−1.23813	−	1.23813i	−0.960766	−	0.277361i	$-0.910540\pi$
$223$	−18.4892	−	18.4892i	−1.23813	−	1.23813i	−0.277361	−	0.960766i	$-0.589460\pi$
$224$	−2.76884	−	6.68457i	−0.185001	−	0.446631i
$225$		−	0.663643i		−	0.0442428i
$226$	−6.10199	+	2.52753i	−0.405898	+	0.168129i
$227$	−4.19979	+	10.1392i	−0.278750	+	0.672961i	−0.999802	−	0.0199199i	$-0.993659\pi$
$227$	−4.19979	+	10.1392i	−0.278750	+	0.672961i	0.721052	+	0.692881i	$0.243659\pi$
$228$	−8.90036	−	3.68665i	−0.589441	−	0.244154i
$229$	−10.2440	+	10.2440i	−0.676942	+	0.676942i	−0.959307	−	0.282365i	$-0.908881\pi$
$229$	−10.2440	+	10.2440i	−0.676942	+	0.676942i	0.282365	+	0.959307i	$0.408881\pi$
$230$	−3.72878	+	3.72878i	−0.245869	+	0.245869i
$231$	−1.70711	−	0.707107i	−0.112319	−	0.0465242i
$232$	−6.24264	+	15.0711i	−0.409849	+	0.989464i
$233$	17.6443	−	7.30850i	1.15592	−	0.478796i	0.279402	−	0.960174i	$-0.409864\pi$
$233$	17.6443	−	7.30850i	1.15592	−	0.478796i	0.876513	+	0.481378i	$0.159864\pi$
$234$			3.14545i			0.205625i
$235$	−1.25065	−	3.01933i	−0.0815833	−	0.196959i
$236$	−8.06306	−	8.06306i	−0.524861	−	0.524861i
$237$	2.71485			0.176348
$238$		0			0
$239$	0.740970			0.0479294			0.0239647	−	0.999713i	$-0.492371\pi$
$239$	0.740970			0.0479294			0.0239647	+	0.999713i	$0.492371\pi$
$240$	1.21984	+	1.21984i	0.0787401	+	0.0787401i
$241$	−8.17478	−	19.7357i	−0.526584	−	1.27129i	−0.933748	−	0.357931i	$-0.883482\pi$
$241$	−8.17478	−	19.7357i	−0.526584	−	1.27129i	0.407164	−	0.913355i	$-0.366518\pi$
$242$			6.70474i			0.430997i
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$	−1.77150	+	4.27677i	−0.113408	+	0.273792i
$245$	−10.5346	−	4.36355i	−0.673028	−	0.278777i
$246$	6.56854	−	6.56854i	0.418795	−	0.418795i
$247$	19.7959	−	19.7959i	1.25958	−	1.25958i
$248$	−24.7939	−	10.2700i	−1.57442	−	0.652144i
$249$	5.51594	−	13.3167i	0.349558	−	0.843909i
$250$	−8.33956	+	3.45436i	−0.527440	+	0.218473i
$251$			0.938819i			0.0592577i	0.999561	+	0.0296289i	$0.00943254\pi$
$251$			0.938819i			0.0592577i	−0.999561	+	0.0296289i	$0.990567\pi$
$252$	0.668179	+	1.61313i	0.0420913	+	0.101617i
$253$	3.50141	+	3.50141i	0.220132	+	0.220132i
$254$	−10.8287			−0.679454
$255$		0			0
$256$	−12.9706			−0.810660
$257$	11.1930	+	11.1930i	0.698199	+	0.698199i	0.964022	−	0.265823i	$-0.0856436\pi$
$257$	11.1930	+	11.1930i	0.698199	+	0.698199i	−0.265823	+	0.964022i	$0.585644\pi$
$258$	−1.00934	−	2.43675i	−0.0628385	−	0.151706i
$259$			4.86068i			0.302028i
$260$	−11.1817	+	4.63160i	−0.693457	+	0.287239i
$261$	2.38896	−	5.76745i	0.147873	−	0.356996i
$262$	1.83201	+	0.758843i	0.113182	+	0.0468815i
$263$	8.10152	−	8.10152i	0.499561	−	0.499561i	−0.411740	−	0.911301i	$-0.635079\pi$
$263$	8.10152	−	8.10152i	0.499561	−	0.499561i	0.911301	+	0.411740i	$0.135079\pi$
$264$	−2.76537	+	2.76537i	−0.170197	+	0.170197i
$265$	−7.62113	−	3.15678i	−0.468163	−	0.193919i
$266$	−2.46334	+	5.94703i	−0.151037	+	0.364636i
$267$	12.6289	−	5.23105i	0.772875	−	0.320135i
$268$			2.99321i			0.182839i
$269$	7.33564	+	17.7098i	0.447262	+	1.07979i	0.973344	+	0.229351i	$0.0736605\pi$
$269$	7.33564	+	17.7098i	0.447262	+	1.07979i	−0.526082	+	0.850434i	$0.676339\pi$
$270$	1.12698	+	1.12698i	0.0685860	+	0.0685860i
$271$	−6.82805			−0.414775			−0.207387	−	0.978259i	$-0.566496\pi$
$271$	−6.82805			−0.414775			−0.207387	+	0.978259i	$0.566496\pi$
$272$		0			0
$273$	−5.07401			−0.307093
$274$	8.26319	+	8.26319i	0.499198	+	0.499198i
$275$	0.380086	+	0.917608i	0.0229200	+	0.0553338i
$276$		−	4.67913i		−	0.281650i
$277$	7.50915	−	3.11039i	0.451181	−	0.186885i	−0.145509	−	0.989357i	$-0.546482\pi$
$277$	7.50915	−	3.11039i	0.451181	−	0.186885i	0.596690	+	0.802472i	$0.296482\pi$
$278$	−1.18391	+	2.85822i	−0.0710064	+	0.171425i
$279$	9.48822	+	3.93015i	0.568045	+	0.235292i
$280$	4.75057	−	4.75057i	0.283901	−	0.283901i
$281$	−8.20741	+	8.20741i	−0.489613	+	0.489613i	−0.908184	−	0.418571i	$-0.862531\pi$
$281$	−8.20741	+	8.20741i	−0.489613	+	0.489613i	0.418571	+	0.908184i	$0.362531\pi$
$282$	−1.10973	−	0.459666i	−0.0660836	−	0.0273727i
$283$	2.32061	−	5.60244i	0.137946	−	0.333030i	−0.839777	−	0.542932i	$-0.817314\pi$
$283$	2.32061	−	5.60244i	0.137946	−	0.333030i	0.977723	+	0.209901i	$0.0673142\pi$
$284$	−0.296101	+	0.122649i	−0.0175703	+	0.00727787i
$285$		−	14.1853i		−	0.840267i
$286$	−1.80148	−	4.34917i	−0.106524	−	0.257172i
$287$	10.5959	+	10.5959i	0.625455	+	0.625455i
$288$	5.86030			0.345322
$289$		0			0
$290$	−9.94948			−0.584254
$291$	−1.89828	−	1.89828i	−0.111279	−	0.111279i
$292$	0.199286	+	0.481119i	0.0116623	+	0.0281554i
$293$			6.87547i			0.401669i	0.979625	+	0.200835i	$0.0643654\pi$
$293$			6.87547i			0.401669i	−0.979625	+	0.200835i	$0.935635\pi$
$294$	−3.87189	+	1.60379i	−0.225813	+	0.0935349i
$295$	6.42543	−	15.5124i	0.374103	−	0.903164i
$296$	9.50461	+	3.93694i	0.552444	+	0.228830i
$297$	1.05826	−	1.05826i	0.0614065	−	0.0614065i
$298$	−9.80750	+	9.80750i	−0.568133	+	0.568133i
$299$	12.5626	+	5.20359i	0.726513	+	0.300931i
$300$	0.359161	−	0.867091i	0.0207362	−	0.0500615i
$301$	3.93079	−	1.62819i	0.226567	−	0.0938471i
$302$			4.03450i			0.232159i
$303$	−0.910819	−	2.19891i	−0.0523252	−	0.126324i
$304$	−3.99040	−	3.99040i	−0.228865	−	0.228865i
$305$	−6.81629			−0.390300
$306$		0			0
$307$	22.2451			1.26959			0.634797	−	0.772679i	$-0.281084\pi$
$307$	22.2451			1.26959			0.634797	+	0.772679i	$0.281084\pi$
$308$	−1.84776	−	1.84776i	−0.105286	−	0.105286i
$309$	5.08621	+	12.2792i	0.289344	+	0.698539i
$310$		−	16.3682i		−	0.929653i
$311$	−5.00208	+	2.07193i	−0.283642	+	0.117488i	−0.519969	−	0.854185i	$-0.674056\pi$
$311$	−5.00208	+	2.07193i	−0.283642	+	0.117488i	0.236327	+	0.971674i	$0.424056\pi$
$312$	−4.10973	+	9.92177i	−0.232668	+	0.561710i
$313$	10.4348	+	4.32222i	0.589808	+	0.244306i	0.657568	−	0.753395i	$-0.271585\pi$
$313$	10.4348	+	4.32222i	0.589808	+	0.244306i	−0.0677602	+	0.997702i	$0.521585\pi$
$314$	2.05835	−	2.05835i	0.116160	−	0.116160i
$315$	−1.81796	+	1.81796i	−0.102431	+	0.102431i
$316$	3.54712	+	1.46927i	0.199541	+	0.0826527i
$317$	−7.06127	+	17.0474i	−0.396600	+	0.957477i	0.591866	+	0.806036i	$0.298391\pi$
$317$	−7.06127	+	17.0474i	−0.396600	+	0.957477i	−0.988466	+	0.151441i	$0.951609\pi$
$318$	−2.80109	+	1.16025i	−0.157077	+	0.0650635i
$319$			9.34277i			0.523095i
$320$	−2.25397	−	5.44155i	−0.126000	−	0.304192i
$321$	−9.24360	−	9.24360i	−0.515927	−	0.515927i
$322$	−3.12649			−0.174233
$323$		0			0
$324$	−1.41421			−0.0785674
$325$	1.92856	+	1.92856i	0.106977	+	0.106977i
$326$	−2.65619	−	6.41262i	−0.147113	−	0.355162i
$327$		−	0.956272i		−	0.0528819i
$328$	29.3015	−	12.1371i	1.61790	−	0.670158i
$329$	0.741499	−	1.79014i	0.0408802	−	0.0986934i
$330$	−2.20371	−	0.912808i	−0.121310	−	0.0502484i
$331$	4.07722	−	4.07722i	0.224104	−	0.224104i	−0.586120	−	0.810224i	$-0.699345\pi$
$331$	4.07722	−	4.07722i	0.224104	−	0.224104i	0.810224	+	0.586120i	$0.199345\pi$
$332$	14.4138	−	14.4138i	0.791062	−	0.791062i
$333$	−3.63726	−	1.50660i	−0.199321	−	0.0825613i
$334$	2.60313	−	6.28451i	0.142437	−	0.343873i
$335$	−4.07193	+	1.68665i	−0.222473	+	0.0921515i
$336$			1.02280i			0.0557985i
$337$	−6.22652	−	15.0321i	−0.339180	−	0.818853i	−0.997795	−	0.0663727i	$-0.978857\pi$
$337$	−6.22652	−	15.0321i	−0.339180	−	0.818853i	0.658615	−	0.752480i	$-0.271143\pi$
$338$	−2.10520	−	2.10520i	−0.114508	−	0.114508i
$339$	8.62951			0.468691
$340$		0			0
$341$	−15.3701			−0.832338
$342$	−3.68665	−	3.68665i	−0.199351	−	0.199351i
$343$	−5.89443	−	14.2304i	−0.318269	−	0.768370i
$344$		−	9.00506i		−	0.485521i
$345$	6.36543	−	2.63665i	0.342703	−	0.141952i
$346$	−3.58711	+	8.66006i	−0.192844	+	0.465568i
$347$	−3.96379	−	1.64186i	−0.212787	−	0.0881394i	0.273744	−	0.961803i	$-0.411738\pi$
$347$	−3.96379	−	1.64186i	−0.212787	−	0.0881394i	−0.486531	+	0.873663i	$0.661738\pi$
$348$	6.24264	−	6.24264i	0.334641	−	0.334641i
$349$	−10.0093	+	10.0093i	−0.535787	+	0.535787i	−0.922289	−	0.386501i	$-0.873683\pi$
$349$	−10.0093	+	10.0093i	−0.535787	+	0.535787i	0.386501	+	0.922289i	$0.373683\pi$
$350$	−0.579372	−	0.239984i	−0.0309687	−	0.0128277i
$351$	1.57273	−	3.79690i	0.0839459	−	0.202663i
$352$	−8.10294	+	3.35635i	−0.431888	+	0.178894i
$353$		−	23.8142i		−	1.26750i	−0.773536	−	0.633752i	$-0.781514\pi$
$353$		−	23.8142i		−	1.26750i	0.773536	−	0.633752i	$-0.218486\pi$
$354$	−2.36162	−	5.70144i	−0.125518	−	0.303028i
$355$	−0.333700	−	0.333700i	−0.0177110	−	0.0177110i
$356$	19.3314			1.02456
$357$		0			0
$358$	8.12612			0.429479
$359$	24.9380	+	24.9380i	1.31618	+	1.31618i	0.916777	+	0.399400i	$0.130781\pi$
$359$	24.9380	+	24.9380i	1.31618	+	1.31618i	0.399400	+	0.916777i	$0.369219\pi$
$360$	2.08239	+	5.02734i	0.109752	+	0.264964i
$361$			27.4039i			1.44231i
$362$	−11.6866	+	4.84077i	−0.614237	+	0.254425i
$363$	3.35237	−	8.09334i	0.175954	−	0.424790i
$364$	−6.62951	−	2.74603i	−0.347481	−	0.143931i
$365$	−0.542213	+	0.542213i	−0.0283807	+	0.0283807i
$366$	−1.77150	+	1.77150i	−0.0925976	+	0.0925976i
$367$	15.0788	+	6.24585i	0.787108	+	0.326031i	0.739780	−	0.672849i	$-0.234930\pi$
$367$	15.0788	+	6.24585i	0.787108	+	0.326031i	0.0473275	+	0.998879i	$0.484930\pi$
$368$	1.04892	−	2.53233i	0.0546789	−	0.132007i
$369$	−11.2132	+	4.64466i	−0.583735	+	0.241791i
$370$			6.27467i			0.326205i
$371$	−1.87163	−	4.51851i	−0.0971700	−	0.234589i
$372$	10.2700	+	10.2700i	0.532474	+	0.532474i
$373$	25.0156			1.29526			0.647630	−	0.761955i	$-0.275760\pi$
$373$	25.0156			1.29526			0.647630	+	0.761955i	$0.275760\pi$
$374$		0			0
$375$	11.7939			0.609036
$376$	−2.89987	−	2.89987i	−0.149549	−	0.149549i
$377$	9.81796	+	23.7027i	0.505651	+	1.22075i
$378$			0.944947i			0.0486028i
$379$	−30.1444	+	12.4862i	−1.54842	+	0.641375i	−0.983029	−	0.183451i	$-0.941273\pi$
$379$	−30.1444	+	12.4862i	−1.54842	+	0.641375i	−0.565387	+	0.824826i	$0.691273\pi$
$380$	7.67705	−	18.5340i	0.393824	−	0.950776i
$381$	13.0714	+	5.41436i	0.669669	+	0.277386i
$382$	6.50339	−	6.50339i	0.332743	−	0.332743i
$383$	0.413840	−	0.413840i	0.0211462	−	0.0211462i	−0.696455	−	0.717601i	$-0.745240\pi$
$383$	0.413840	−	0.413840i	0.0211462	−	0.0211462i	0.717601	+	0.696455i	$0.245240\pi$
$384$	8.82843	+	3.65685i	0.450524	+	0.186613i
$385$	1.47247	−	3.55487i	0.0750442	−	0.181173i
$386$	−7.57900	+	3.13932i	−0.385761	+	0.159787i
$387$			3.44609i			0.175175i
$388$	−1.45288	−	3.50756i	−0.0737587	−	0.178069i
$389$	−15.6455	−	15.6455i	−0.793258	−	0.793258i	0.188765	−	0.982022i	$-0.439552\pi$
$389$	−15.6455	−	15.6455i	−0.793258	−	0.793258i	−0.982022	+	0.188765i	$0.939552\pi$
$390$	−6.55007			−0.331675
$391$		0			0
$392$	−14.3086			−0.722696
$393$	−1.83201	−	1.83201i	−0.0924126	−	0.0924126i
$394$	0.928163	+	2.24078i	0.0467602	+	0.112889i
$395$			5.65338i			0.284453i
$396$	1.95541	−	0.809957i	0.0982630	−	0.0407019i
$397$	2.23116	−	5.38650i	0.111979	−	0.270341i	−0.857948	−	0.513736i	$-0.828261\pi$
$397$	2.23116	−	5.38650i	0.111979	−	0.270341i	0.969927	+	0.243395i	$0.0782612\pi$
$398$	9.66940	+	4.00520i	0.484683	+	0.200762i
$399$	5.94703	−	5.94703i	0.297724	−	0.297724i
$400$	0.388753	−	0.388753i	0.0194376	−	0.0194376i
$401$	−4.79513	−	1.98621i	−0.239458	−	0.0991865i	0.259728	−	0.965682i	$-0.416367\pi$
$401$	−4.79513	−	1.98621i	−0.239458	−	0.0991865i	−0.499185	+	0.866495i	$0.666367\pi$
$402$	−0.619914	+	1.49661i	−0.0309185	+	0.0746439i
$403$	−38.9941	+	16.1519i	−1.94243	+	0.804582i
$404$		−	3.36595i		−	0.167462i
$405$	−0.796897	−	1.92388i	−0.0395981	−	0.0955983i
$406$	−4.17120	−	4.17120i	−0.207013	−	0.207013i
$407$	5.89205			0.292058
$408$		0			0
$409$	−27.2400			−1.34693			−0.673465	−	0.739219i	$-0.735195\pi$
$409$	−27.2400			−1.34693			−0.673465	+	0.739219i	$0.735195\pi$
$410$	13.6783	+	13.6783i	0.675521	+	0.675521i
$411$	−5.84296	−	14.1062i	−0.288212	−	0.695805i
$412$			18.7962i			0.926021i
$413$	9.19715	−	3.80958i	0.452562	−	0.187457i
$414$	0.969079	−	2.33956i	0.0476277	−	0.114983i
$415$	27.7305	+	11.4863i	1.36124	+	0.563843i
$416$	−17.0302	+	17.0302i	−0.834972	+	0.834972i
$417$	2.85822	−	2.85822i	0.139968	−	0.139968i
$418$	7.20891	+	2.98603i	0.352599	+	0.146051i
$419$	5.36909	−	12.9621i	0.262297	−	0.633242i	−0.736782	−	0.676130i	$-0.763656\pi$
$419$	5.36909	−	12.9621i	0.262297	−	0.633242i	0.999080	+	0.0428878i	$0.0136558\pi$
$420$	−3.35916	+	1.39141i	−0.163910	+	0.0678939i
$421$		−	15.3811i		−	0.749627i	−0.927100	−	0.374814i	$-0.877707\pi$
$421$		−	15.3811i		−	0.749627i	0.927100	−	0.374814i	$-0.122293\pi$
$422$	−1.73643	−	4.19212i	−0.0845283	−	0.204069i
$423$	1.10973	+	1.10973i	0.0539570	+	0.0539570i
$424$	−10.3515			−0.502712
$425$		0			0
$426$	−0.173452			−0.00840376
$427$	−2.85765	−	2.85765i	−0.138291	−	0.138291i
$428$	−7.07474	−	17.0799i	−0.341971	−	0.825590i
$429$			6.15065i			0.296956i
$430$	5.07428	−	2.10183i	0.244703	−	0.101359i
$431$	6.27243	−	15.1430i	0.302133	−	0.729413i	−0.697782	−	0.716311i	$-0.745829\pi$
$431$	6.27243	−	15.1430i	0.302133	−	0.729413i	0.999914	−	0.0131020i	$-0.00417060\pi$
$432$	−0.765367	−	0.317025i	−0.0368237	−	0.0152529i
$433$	15.3517	−	15.3517i	0.737757	−	0.737757i	−0.234386	−	0.972144i	$-0.575308\pi$
$433$	15.3517	−	15.3517i	0.737757	−	0.737757i	0.972144	+	0.234386i	$0.0753080\pi$
$434$	6.86218	−	6.86218i	0.329395	−	0.329395i
$435$	12.0101	+	4.97474i	0.575840	+	0.238521i
$436$	0.517531	−	1.24943i	0.0247852	−	0.0598368i
$437$	−20.8230	+	8.62515i	−0.996097	+	0.412597i
$438$			0.281833i			0.0134665i
$439$	9.00469	+	21.7392i	0.429770	+	1.03756i	0.979360	+	0.202123i	$0.0647841\pi$
$439$	9.00469	+	21.7392i	0.429770	+	1.03756i	−0.549590	+	0.835435i	$0.685216\pi$
$440$	−5.75858	−	5.75858i	−0.274529	−	0.274529i
$441$	5.47568			0.260747
$442$		0			0
$443$	−15.4238			−0.732808			−0.366404	−	0.930456i	$-0.619411\pi$
$443$	−15.4238			−0.732808			−0.366404	+	0.930456i	$0.619411\pi$
$444$	−3.93694	−	3.93694i	−0.186839	−	0.186839i
$445$	10.8931	+	26.2983i	0.516383	+	1.24666i
$446$		−	20.0125i		−	0.947621i
$447$	16.7425	−	6.93495i	0.791891	−	0.328012i
$448$	1.33636	−	3.22625i	0.0631369	−	0.152426i
$449$	−12.5181	−	5.18515i	−0.590764	−	0.244702i	0.0672154	−	0.997738i	$-0.478589\pi$
$449$	−12.5181	−	5.18515i	−0.590764	−	0.244702i	−0.657979	+	0.753036i	$0.728589\pi$
$450$	0.359161	−	0.359161i	0.0169310	−	0.0169310i
$451$	12.8442	−	12.8442i	0.604809	−	0.604809i
$452$	11.2750	+	4.67026i	0.530332	+	0.219671i
$453$	2.01725	−	4.87007i	0.0947787	−	0.228816i
$454$	−7.76019	+	3.21438i	−0.364204	+	0.150858i
$455$		−	10.5661i		−	0.495346i
$456$	−6.81204	−	16.4457i	−0.319003	−	0.770141i
$457$	−10.8806	−	10.8806i	−0.508972	−	0.508972i	0.405239	−	0.914211i	$-0.367188\pi$
$457$	−10.8806	−	10.8806i	−0.508972	−	0.508972i	−0.914211	+	0.405239i	$0.867188\pi$
$458$	−11.0880			−0.518109
$459$		0			0
$460$	9.74378			0.454306
$461$	14.7082	+	14.7082i	0.685031	+	0.685031i	0.961129	−	0.276099i	$-0.0890416\pi$
$461$	14.7082	+	14.7082i	0.685031	+	0.685031i	−0.276099	+	0.961129i	$0.589042\pi$
$462$	−0.541196	−	1.30656i	−0.0251787	−	0.0607868i
$463$		−	26.4325i		−	1.22842i	−0.789141	−	0.614212i	$-0.789474\pi$
$463$		−	26.4325i		−	1.22842i	0.789141	−	0.614212i	$-0.210526\pi$
$464$	4.77791	−	1.97908i	0.221809	−	0.0918763i
$465$	−8.18412	+	19.7582i	−0.379529	+	0.916265i
$466$	13.5043	+	5.59368i	0.625577	+	0.259122i
$467$	−5.07058	+	5.07058i	−0.234638	+	0.234638i	−0.814626	−	0.579987i	$-0.803058\pi$
$467$	−5.07058	+	5.07058i	−0.234638	+	0.234638i	0.579987	+	0.814626i	$0.303058\pi$
$468$	4.10973	−	4.10973i	0.189972	−	0.189972i
$469$	−2.41421	−	1.00000i	−0.111478	−	0.0461757i
$470$	0.957205	−	2.31090i	0.0441526	−	0.106594i
$471$	−3.51383	+	1.45548i	−0.161909	+	0.0670648i
$472$		−	21.0698i		−	0.969816i
$473$	−1.97367	−	4.76485i	−0.0907492	−	0.219088i
$474$	1.46927	+	1.46927i	0.0674856	+	0.0674856i
$475$	−4.52076			−0.207427
$476$		0			0
$477$	3.96134			0.181377
$478$	0.401010	+	0.401010i	0.0183418	+	0.0183418i
$479$	−1.12279	−	2.71066i	−0.0513017	−	0.123853i	0.896151	−	0.443749i	$-0.146352\pi$
$479$	−1.12279	−	2.71066i	−0.0513017	−	0.123853i	−0.947453	+	0.319896i	$0.896352\pi$
$480$			12.2034i			0.557009i
$481$	14.9482	−	6.19173i	0.681577	−	0.282319i
$482$	6.25671	−	15.1050i	0.284985	−	0.688015i
$483$	3.77401	+	1.56325i	0.171724	+	0.0711302i
$484$	8.76017	−	8.76017i	0.398190	−	0.398190i
$485$	3.95295	−	3.95295i	0.179494	−	0.179494i
$486$	−0.707107	−	0.292893i	−0.0320750	−	0.0132859i
$487$	8.89432	−	21.4728i	0.403040	−	0.973025i	−0.583884	−	0.811837i	$-0.698468\pi$
$487$	8.89432	−	21.4728i	0.403040	−	0.973025i	0.986924	−	0.161188i	$-0.0515324\pi$
$488$	−7.90244	+	3.27330i	−0.357727	+	0.148175i
$489$			9.06882i			0.410106i
$490$	−3.33972	−	8.06280i	−0.150873	−	0.364240i
$491$	9.65807	+	9.65807i	0.435863	+	0.435863i	0.890617	−	0.454754i	$-0.150273\pi$
$491$	9.65807	+	9.65807i	0.435863	+	0.435863i	−0.454754	+	0.890617i	$0.650273\pi$
$492$	−17.1644			−0.773831
$493$		0			0
$494$	21.4269			0.964044
$495$	2.20371	+	2.20371i	0.0990495	+	0.0990495i
$496$	3.25584	+	7.86030i	0.146192	+	0.352938i
$497$		−	0.279799i		−	0.0125507i
$498$	10.1921	−	4.22172i	0.456720	−	0.189180i
$499$	2.88245	−	6.95884i	0.129036	−	0.311521i	−0.846137	−	0.532966i	$-0.821077\pi$
$499$	2.88245	−	6.95884i	0.129036	−	0.311521i	0.975173	+	0.221445i	$0.0710774\pi$
$500$	15.4095	+	6.38283i	0.689134	+	0.285449i
$501$	−6.28451	+	6.28451i	−0.280771	+	0.280771i
$502$	−0.508085	+	0.508085i	−0.0226769	+	0.0226769i
$503$	−23.7585	−	9.84111i	−1.05934	−	0.438794i	−0.216124	−	0.976366i	$-0.569341\pi$
$503$	−23.7585	−	9.84111i	−1.05934	−	0.438794i	−0.843218	+	0.537572i	$0.819341\pi$
$504$	−1.23463	+	2.98067i	−0.0549949	+	0.132770i
$505$	4.57900	−	1.89668i	0.203763	−	0.0844013i
$506$			3.78989i			0.168481i
$507$	1.48860	+	3.59379i	0.0661110	+	0.159606i
$508$	14.1484	+	14.1484i	0.627734	+	0.627734i
$509$	−34.7796			−1.54158			−0.770789	−	0.637090i	$-0.780138\pi$
$509$	−34.7796			−1.54158			−0.770789	+	0.637090i	$0.780138\pi$
$510$		0			0
$511$	−0.454632			−0.0201117
$512$	6.49435	+	6.49435i	0.287013	+	0.287013i
$513$	2.60685	+	6.29350i	0.115095	+	0.277865i
$514$			12.1152i			0.534379i
$515$	−25.5701	+	10.5915i	−1.12675	+	0.466716i
$516$	−1.86501	+	4.50253i	−0.0821025	+	0.198213i
$517$	−2.16998	−	0.898835i	−0.0954356	−	0.0395307i
$518$	−2.63058	+	2.63058i	−0.115581	+	0.115581i
$519$	8.66006	−	8.66006i	0.380135	−	0.380135i
$520$	−20.6610	−	8.55807i	−0.906046	−	0.375296i
$521$	−17.0594	+	41.1851i	−0.747387	+	1.80435i	−0.174617	+	0.984637i	$0.555869\pi$
$521$	−17.0594	+	41.1851i	−0.747387	+	1.80435i	−0.572771	+	0.819716i	$0.694131\pi$
$522$	4.41421	−	1.82843i	0.193205	−	0.0800281i
$523$		−	19.8918i		−	0.869808i	−0.900477	−	0.434904i	$-0.856782\pi$
$523$		−	19.8918i		−	0.869808i	0.900477	−	0.434904i	$-0.143218\pi$
$524$	−1.40216	−	3.38511i	−0.0612536	−	0.147879i
$525$	0.579372	+	0.579372i	0.0252859	+	0.0252859i
$526$	8.76902			0.382348
$527$		0			0
$528$	1.23983			0.0539566
$529$	8.52267	+	8.52267i	0.370551	+	0.370551i
$530$	−2.41609	−	5.83296i	−0.104948	−	0.253368i
$531$			8.06306i			0.349907i
$532$	10.9887	−	4.55166i	0.476420	−	0.197339i
$533$	19.0883	−	46.0832i	0.826806	−	1.99609i
$534$	9.66572	+	4.00367i	0.418277	+	0.173256i
$535$	19.2488	−	19.2488i	0.832198	−	0.832198i
$536$	−3.91082	+	3.91082i	−0.168922	+	0.168922i
$537$	−9.80910	−	4.06306i	−0.423294	−	0.175334i
$538$	−5.61445	+	13.5545i	−0.242056	+	0.584376i
$539$	−7.57113	+	3.13607i	−0.326112	+	0.135080i
$540$		−	2.94495i		−	0.126730i
$541$	0.299022	+	0.721903i	0.0128560	+	0.0310370i	0.930177	−	0.367111i	$-0.119653\pi$
$541$	0.299022	+	0.721903i	0.0128560	+	0.0310370i	−0.917321	+	0.398148i	$0.869653\pi$
$542$	−3.69532	−	3.69532i	−0.158727	−	0.158727i
$543$	16.5274			0.709259
$544$		0			0
$545$	1.99133			0.0852993
$546$	−2.74603	−	2.74603i	−0.117519	−	0.117519i
$547$	−14.9463	−	36.0835i	−0.639057	−	1.54282i	−0.827938	−	0.560819i	$-0.810486\pi$
$547$	−14.9463	−	36.0835i	−0.639057	−	1.54282i	0.188882	−	0.982000i	$-0.439514\pi$
$548$		−	21.5928i		−	0.922397i
$549$	3.02413	−	1.25264i	0.129067	−	0.0534612i
$550$	−0.290905	+	0.702307i	−0.0124042	+	0.0299465i
$551$	−39.2881	−	16.2737i	−1.67373	−	0.693281i
$552$	6.11358	−	6.11358i	0.260211	−	0.260211i
$553$	−2.37011	+	2.37011i	−0.100787	+	0.100787i
$554$	5.74725	+	2.38059i	0.244177	+	0.101142i
$555$	3.13734	−	7.57420i	0.133172	−	0.321507i
$556$	5.28130	−	2.18759i	0.223977	−	0.0927744i
$557$			13.0371i			0.552398i	0.961100	+	0.276199i	$0.0890750\pi$
$557$			13.0371i			0.552398i	−0.961100	+	0.276199i	$0.910925\pi$
$558$	3.00801	+	7.26197i	0.127339	+	0.307424i
$559$	−10.0144	−	10.0144i	−0.423564	−	0.423564i
$560$	−2.12988			−0.0900038
$561$		0			0
$562$	−8.88363			−0.374734
$563$	−7.93150	−	7.93150i	−0.334273	−	0.334273i	0.519934	−	0.854207i	$-0.325957\pi$
$563$	−7.93150	−	7.93150i	−0.334273	−	0.334273i	−0.854207	+	0.519934i	$0.825957\pi$
$564$	0.849352	+	2.05052i	0.0357642	+	0.0863423i
$565$			17.9700i			0.756005i
$566$	4.28792	−	1.77612i	0.180235	−	0.0746557i
$567$	0.472474	−	1.14065i	0.0198420	−	0.0479029i
$568$	−0.547123	−	0.226626i	−0.0229568	−	0.00950900i
$569$	25.7878	−	25.7878i	1.08108	−	1.08108i	0.0846732	−	0.996409i	$-0.473015\pi$
$569$	25.7878	−	25.7878i	1.08108	−	1.08108i	0.996409	−	0.0846732i	$-0.0269846\pi$
$570$	7.67705	−	7.67705i	0.321556	−	0.321556i
$571$	12.5140	+	5.18346i	0.523693	+	0.216921i	0.628838	−	0.777536i	$-0.283531\pi$
$571$	12.5140	+	5.18346i	0.523693	+	0.216921i	−0.105145	+	0.994457i	$0.533531\pi$
$572$	−3.32871	+	8.03621i	−0.139180	+	0.336011i
$573$	−11.1020	+	4.59859i	−0.463792	+	0.192109i
$574$			11.4689i			0.478702i
$575$	−0.840280	−	2.02862i	−0.0350421	−	0.0845991i
$576$	2.00000	+	2.00000i	0.0833333	+	0.0833333i
$577$	7.10617			0.295834			0.147917	−	0.989000i	$-0.452743\pi$
$577$	7.10617			0.295834			0.147917	+	0.989000i	$0.452743\pi$
$578$		0			0
$579$	10.7183			0.445438
$580$	12.9996	+	12.9996i	0.539780	+	0.539780i
$581$	6.81016	+	16.4412i	0.282533	+	0.682095i
$582$		−	2.05468i		−	0.0851692i
$583$	−5.47727	+	2.26876i	−0.226846	+	0.0939625i
$584$	−0.368233	+	0.888992i	−0.0152376	+	0.0367868i
$585$	7.90663	+	3.27503i	0.326899	+	0.135406i
$586$	−3.72098	+	3.72098i	−0.153712	+	0.153712i
$587$	−28.4929	+	28.4929i	−1.17603	+	1.17603i	−0.195281	+	0.980747i	$0.562562\pi$
$587$	−28.4929	+	28.4929i	−1.17603	+	1.17603i	−0.980747	+	0.195281i	$0.937438\pi$
$588$	7.15432	+	2.96342i	0.295039	+	0.122209i
$589$	26.7723	−	64.6341i	1.10314	−	2.66320i
$590$	11.8726	−	4.91781i	0.488789	−	0.202463i
$591$		−	3.16895i		−	0.130353i
$592$	−1.24811	−	3.01320i	−0.0512970	−	0.123842i
$593$	−26.7582	−	26.7582i	−1.09883	−	1.09883i	−0.994548	−	0.104280i	$-0.966746\pi$
$593$	−26.7582	−	26.7582i	−1.09883	−	1.09883i	−0.104280	−	0.994548i	$-0.533254\pi$
$594$	1.14545			0.0469985
$595$		0			0
$596$	25.6282			1.04977
$597$	−9.66940	−	9.66940i	−0.395742	−	0.395742i
$598$	3.98266	+	9.61498i	0.162863	+	0.393186i
$599$		−	10.1505i		−	0.414739i	−0.978263	−	0.207369i	$-0.933510\pi$
$599$		−	10.1505i		−	0.414739i	0.978263	−	0.207369i	$-0.0664902\pi$
$600$	1.60218	−	0.663643i	0.0654085	−	0.0270931i
$601$	−13.4910	+	32.5702i	−0.550311	+	1.32857i	0.366935	+	0.930247i	$0.380407\pi$
$601$	−13.4910	+	32.5702i	−0.550311	+	1.32857i	−0.917246	+	0.398321i	$0.869593\pi$
$602$	3.00850	+	1.24616i	0.122617	+	0.0507897i
$603$	1.49661	−	1.49661i	0.0609465	−	0.0609465i
$604$	5.27133	−	5.27133i	0.214487	−	0.214487i
$605$	16.8535	+	6.98095i	0.685193	+	0.283816i
$606$	0.697111	−	1.68297i	0.0283182	−	0.0683662i
$607$	43.9654	−	18.2111i	1.78450	−	0.739164i	0.792974	−	0.609255i	$-0.208532\pi$
$607$	43.9654	−	18.2111i	1.78450	−	0.739164i	0.991526	−	0.129909i	$-0.0414685\pi$
$608$		−	39.9206i		−	1.61899i
$609$	2.94948	+	7.12068i	0.119519	+	0.288545i
$610$	−3.68895	−	3.68895i	−0.149361	−	0.149361i
$611$	−6.44980			−0.260931
$612$		0			0
$613$	−26.9812			−1.08976			−0.544880	−	0.838514i	$-0.683425\pi$
$613$	−26.9812			−1.08976			−0.544880	+	0.838514i	$0.683425\pi$
$614$	12.0389	+	12.0389i	0.485852	+	0.485852i
$615$	−9.67200	−	23.3503i	−0.390013	−	0.941573i
$616$		−	4.82843i		−	0.194543i
$617$	−13.8507	+	5.73717i	−0.557610	+	0.230970i	−0.643647	−	0.765322i	$-0.722580\pi$
$617$	−13.8507	+	5.73717i	−0.557610	+	0.230970i	0.0860373	+	0.996292i	$0.472580\pi$
$618$	−3.89282	+	9.39809i	−0.156592	+	0.378047i
$619$	2.03477	+	0.842828i	0.0817841	+	0.0338761i	0.423200	−	0.906036i	$-0.360907\pi$
$619$	2.03477	+	0.842828i	0.0817841	+	0.0338761i	−0.341416	+	0.939912i	$0.610907\pi$
$620$	−21.3861	+	21.3861i	−0.858888	+	0.858888i
$621$	−2.33956	+	2.33956i	−0.0938835	+	0.0938835i
$622$	−3.82843	−	1.58579i	−0.153506	−	0.0635842i
$623$	−6.45843	+	15.5920i	−0.258752	+	0.624681i
$624$	3.14545	−	1.30289i	0.125919	−	0.0521573i
$625$			21.2414i			0.849655i
$626$	3.30808	+	7.98642i	0.132218	+	0.319202i
$627$	−7.20891	−	7.20891i	−0.287896	−	0.287896i
$628$	−5.37874			−0.214635
$629$		0			0
$630$	−1.96775			−0.0783971
$631$	−24.5529	−	24.5529i	−0.977435	−	0.977435i	0.0223155	−	0.999751i	$-0.492896\pi$
$631$	−24.5529	−	24.5529i	−0.977435	−	0.977435i	−0.999751	+	0.0223155i	$0.992896\pi$
$632$	2.71485	+	6.55423i	0.107991	+	0.260713i
$633$			5.92856i			0.235639i
$634$	−13.0475	+	5.40446i	−0.518183	+	0.214638i
$635$	−11.2748	+	27.2198i	−0.447427	+	1.08019i
$636$	5.17574	+	2.14386i	0.205231	+	0.0850096i
$637$	−15.9124	+	15.9124i	−0.630474	+	0.630474i
$638$	−5.05627	+	5.05627i	−0.200180	+	0.200180i
$639$	0.209375	+	0.0867259i	0.00828274	+	0.00343082i
$640$	−7.61500	+	18.3842i	−0.301009	+	0.726701i
$641$	23.0324	−	9.54032i	0.909724	−	0.376820i	0.121773	−	0.992558i	$-0.461142\pi$
$641$	23.0324	−	9.54032i	0.909724	−	0.376820i	0.787951	+	0.615738i	$0.211142\pi$
$642$		−	10.0052i		−	0.394874i
$643$	−13.4557	−	32.4849i	−0.530641	−	1.28108i	−0.931100	−	0.364765i	$-0.881149\pi$
$643$	−13.4557	−	32.4849i	−0.530641	−	1.28108i	0.400459	−	0.916315i	$-0.368851\pi$
$644$	4.08496	+	4.08496i	0.160970	+	0.160970i
$645$	−7.17611			−0.282559
$646$		0			0
$647$	−28.0142			−1.10135			−0.550677	−	0.834719i	$-0.685630\pi$
$647$	−28.0142			−1.10135			−0.550677	+	0.834719i	$0.685630\pi$
$648$	−1.84776	−	1.84776i	−0.0725868	−	0.0725868i
$649$	−4.61793	−	11.1487i	−0.181269	−	0.437623i
$650$			2.08746i			0.0818768i
$651$	−11.7145	+	4.85229i	−0.459127	+	0.190176i
$652$	−4.90801	+	11.8490i	−0.192212	+	0.464042i
$653$	−34.8057	−	14.4170i	−1.36205	−	0.564181i	−0.422432	−	0.906395i	$-0.638823\pi$
$653$	−34.8057	−	14.4170i	−1.36205	−	0.564181i	−0.939622	+	0.342213i	$0.888823\pi$
$654$	0.517531	−	0.517531i	0.0202370	−	0.0202370i
$655$	3.81496	−	3.81496i	0.149063	−	0.149063i
$656$	−9.28931	−	3.84776i	−0.362687	−	0.150230i
$657$	0.140917	−	0.340203i	0.00549768	−	0.0132726i
$658$	1.37011	−	0.567519i	0.0534125	−	0.0221242i
$659$			13.5356i			0.527272i	0.964622	+	0.263636i	$0.0849217\pi$
$659$			13.5356i			0.527272i	−0.964622	+	0.263636i	$0.915078\pi$
$660$	1.68665	+	4.07193i	0.0656527	+	0.158500i
$661$	−1.41864	−	1.41864i	−0.0551787	−	0.0551787i	0.678979	−	0.734158i	$-0.262423\pi$
$661$	−1.41864	−	1.41864i	−0.0551787	−	0.0551787i	−0.734158	+	0.678979i	$0.762423\pi$
$662$	4.41315			0.171522
$663$		0			0
$664$	37.6652			1.46169
$665$	12.3840	+	12.3840i	0.480233	+	0.480233i
$666$	−1.15310	−	2.78384i	−0.0446818	−	0.107871i
$667$		−	20.6547i		−	0.799752i
$668$	−11.6123	+	4.80996i	−0.449292	+	0.186103i
$669$	−10.0063	+	24.1573i	−0.386865	+	0.933974i
$670$	−3.11652	−	1.29090i	−0.120402	−	0.0498720i
$671$	−3.46400	+	3.46400i	−0.133726	+	0.133726i
$672$	−5.11615	+	5.11615i	−0.197360	+	0.197360i
$673$	−15.4873	−	6.41506i	−0.596992	−	0.247282i	0.0636633	−	0.997971i	$-0.479722\pi$
$673$	−15.4873	−	6.41506i	−0.596992	−	0.247282i	−0.660656	+	0.750689i	$0.729722\pi$
$674$	4.76557	−	11.5051i	0.183563	−	0.443160i
$675$	−0.613126	+	0.253965i	−0.0235992	+	0.00977512i
$676$			5.50114i			0.211582i
$677$	−8.82649	−	21.3090i	−0.339230	−	0.818973i	−0.997790	−	0.0664448i	$-0.978834\pi$
$677$	−8.82649	−	21.3090i	−0.339230	−	0.818973i	0.658561	−	0.752528i	$-0.271166\pi$
$678$	4.67026	+	4.67026i	0.179360	+	0.179360i
$679$	3.31446			0.127197
$680$		0			0
$681$	10.9746			0.420546
$682$	−8.31824	−	8.31824i	−0.318522	−	0.318522i
$683$	−10.7220	−	25.8852i	−0.410265	−	0.990468i	−0.985066	−	0.172175i	$-0.944921\pi$
$683$	−10.7220	−	25.8852i	−0.410265	−	0.990468i	0.574801	−	0.818293i	$-0.305079\pi$
$684$			9.63368i			0.368353i
$685$	29.3745	−	12.1673i	1.12234	−	0.464890i
$686$	4.51140	−	10.8915i	0.172246	−	0.415839i
$687$	13.3844	+	5.54401i	0.510647	+	0.211517i
$688$	−2.01867	+	2.01867i	−0.0769612	+	0.0769612i
$689$	−11.5117	+	11.5117i	−0.438562	+	0.438562i
$690$	4.87189	+	2.01800i	0.185470	+	0.0768241i
$691$	−10.2085	+	24.6455i	−0.388350	+	0.937560i	0.601940	+	0.798542i	$0.294395\pi$
$691$	−10.2085	+	24.6455i	−0.388350	+	0.937560i	−0.990290	+	0.139019i	$0.955605\pi$
$692$	16.0017	−	6.62812i	0.608294	−	0.251963i
$693$			1.84776i			0.0701906i
$694$	−1.25662	−	3.03375i	−0.0477007	−	0.115160i
$695$	5.95194	+	5.95194i	0.225770	+	0.225770i
$696$	16.3128			0.618335
$697$		0			0
$698$	−10.8340			−0.410074
$699$	−13.5043	−	13.5043i	−0.510781	−	0.510781i
$700$	0.443432	+	1.07054i	0.0167602	+	0.0404626i
$701$		−	9.75054i		−	0.368273i	−0.982901	−	0.184136i	$-0.941051\pi$
$701$		−	9.75054i		−	0.368273i	0.982901	−	0.184136i	$-0.0589488\pi$
$702$	2.90602	−	1.20371i	0.109681	−	0.0454312i
$703$	−10.2630	+	24.7771i	−0.387077	+	0.934488i
$704$	−3.91082	−	1.61991i	−0.147395	−	0.0610528i
$705$	−2.31090	+	2.31090i	−0.0870334	+	0.0870334i
$706$	12.8882	−	12.8882i	0.485053	−	0.485053i
$707$	2.71485	+	1.12453i	0.102102	+	0.0422922i
$708$	−4.36370	+	10.5349i	−0.163998	+	0.395926i
$709$	−26.5647	+	11.0035i	−0.997659	+	0.413244i	−0.820938	−	0.571017i	$-0.806549\pi$
$709$	−26.5647	+	11.0035i	−0.997659	+	0.413244i	−0.176721	+	0.984261i	$0.556549\pi$
$710$		−	0.361194i		−	0.0135554i
$711$	−1.03893	−	2.50819i	−0.0389628	−	0.0940646i
$712$	25.2578	+	25.2578i	0.946574	+	0.946574i
$713$	33.9797			1.27255
$714$		0			0
$715$	−12.8081			−0.478994
$716$	−10.6173	−	10.6173i	−0.396787	−	0.396787i
$717$	−0.283557	−	0.684567i	−0.0105896	−	0.0255656i
$718$			26.9927i			1.00736i
$719$	−43.6299	+	18.0721i	−1.62712	+	0.673976i	−0.994905	−	0.100816i	$-0.967855\pi$
$719$	−43.6299	+	18.0721i	−1.62712	+	0.673976i	−0.632216	+	0.774792i	$0.717855\pi$
$720$	0.660171	−	1.59379i	0.0246031	−	0.0593972i
$721$	−15.1603	−	6.27960i	−0.564599	−	0.233865i
$722$	−14.8309	+	14.8309i	−0.551948	+	0.551948i
$723$	−15.1050	+	15.1050i	−0.561762	+	0.561762i
$724$	21.5941	+	8.94457i	0.802539	+	0.332422i
$725$	1.58541	−	3.82752i	0.0588808	−	0.142151i
$726$	6.19438	−	2.56579i	0.229895	−	0.0952256i
$727$			27.7790i			1.03027i	0.857110	+	0.515134i	$0.172258\pi$
$727$			27.7790i			1.03027i	−0.857110	+	0.515134i	$0.827742\pi$
$728$	−5.07401	−	12.2497i	−0.188055	−	0.454006i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−0.586887			−0.0217217
$731$		0			0
$732$	4.62914			0.171098
$733$	3.81122	+	3.81122i	0.140770	+	0.140770i	0.773980	−	0.633210i	$-0.218263\pi$
$733$	3.81122	+	3.81122i	0.140770	+	0.140770i	−0.633210	+	0.773980i	$0.718263\pi$
$734$	4.78037	+	11.5408i	0.176446	+	0.425980i
$735$			11.4025i			0.420588i
$736$	17.9137	−	7.42010i	0.660308	−	0.273509i
$737$	−1.21219	+	2.92648i	−0.0446515	+	0.107798i
$738$	−8.58221	−	3.55487i	−0.315915	−	0.130856i
$739$	−2.55818	+	2.55818i	−0.0941043	+	0.0941043i	−0.752592	−	0.658487i	$-0.771197\pi$
$739$	−2.55818	+	2.55818i	−0.0941043	+	0.0941043i	0.658487	+	0.752592i	$0.271197\pi$
$740$	8.19825	−	8.19825i	0.301374	−	0.301374i
$741$	−25.8646	−	10.7135i	−0.950160	−	0.393569i
$742$	1.43248	−	3.45832i	0.0525880	−	0.126959i
$743$	5.71326	−	2.36651i	0.209599	−	0.0868188i	−0.275414	−	0.961326i	$-0.588815\pi$
$743$	5.71326	−	2.36651i	0.209599	−	0.0868188i	0.485013	+	0.874507i	$0.338815\pi$
$744$			26.8368i			0.983883i
$745$	14.4413	+	34.8644i	0.529088	+	1.27733i
$746$	13.5384	+	13.5384i	0.495675	+	0.495675i
$747$	−14.4138			−0.527375
$748$		0			0
$749$	16.1396			0.589730
$750$	6.38283	+	6.38283i	0.233068	+	0.233068i
$751$	19.6438	+	47.4243i	0.716812	+	1.73054i	0.682233	+	0.731135i	$0.261009\pi$
$751$	19.6438	+	47.4243i	0.716812	+	1.73054i	0.0345787	+	0.999402i	$0.488991\pi$
$752$			1.30013i			0.0474109i
$753$	0.867355	−	0.359270i	0.0316082	−	0.0130925i
$754$	−7.51434	+	18.1412i	−0.273656	+	0.660665i
$755$	10.1414	+	4.20071i	0.369084	+	0.152879i
$756$	1.23463	−	1.23463i	0.0449032	−	0.0449032i
$757$	−2.71352	+	2.71352i	−0.0986246	+	0.0986246i	−0.754698	−	0.656073i	$-0.772216\pi$
$757$	−2.71352	+	2.71352i	−0.0986246	+	0.0986246i	0.656073	+	0.754698i	$0.272216\pi$
$758$	−23.0716	−	9.55655i	−0.837997	−	0.347110i
$759$	1.89495	−	4.57481i	0.0687822	−	0.166055i
$760$	34.2464	−	14.1853i	1.24225	−	0.514556i
$761$			16.5850i			0.601206i	0.953749	+	0.300603i	$0.0971878\pi$
$761$			16.5850i			0.601206i	−0.953749	+	0.300603i	$0.902812\pi$
$762$	4.14397	+	10.0044i	0.150120	+	0.362422i
$763$	0.834842	+	0.834842i	0.0302233	+	0.0302233i
$764$	−16.9942			−0.614828
$765$		0			0
$766$	0.447937			0.0161846
$767$	−23.4314	−	23.4314i	−0.846059	−	0.846059i
$768$	4.96362	+	11.9832i	0.179109	+	0.432408i
$769$		−	27.7826i		−	1.00187i	−0.865486	−	0.500933i	$-0.832990\pi$
$769$		−	27.7826i		−	1.00187i	0.865486	−	0.500933i	$-0.167010\pi$
$770$	2.72078	−	1.12698i	0.0980500	−	0.0406136i
$771$	6.05760	−	14.6243i	0.218159	−	0.526683i
$772$	14.0042	+	5.80071i	0.504021	+	0.208772i
$773$	−9.86475	+	9.86475i	−0.354810	+	0.354810i	−0.861896	−	0.507085i	$-0.830723\pi$
$773$	−9.86475	+	9.86475i	−0.354810	+	0.354810i	0.507085	+	0.861896i	$0.330723\pi$
$774$	−1.86501	+	1.86501i	−0.0670364	+	0.0670364i
$775$	6.29679	+	2.60822i	0.226187	+	0.0936899i
$776$	2.68457	−	6.48112i	0.0963704	−	0.232659i
$777$	4.49068	−	1.86010i	0.161102	−	0.0667307i
$778$		−	16.9346i		−	0.607133i
$779$	31.6396	+	76.3847i	1.13361	+	2.73677i
$780$	8.55807	+	8.55807i	0.306428	+	0.306428i
$781$	−0.339169			−0.0121364
$782$		0			0
$783$	−6.24264			−0.223094
$784$	3.20758	+	3.20758i	0.114556	+	0.114556i
$785$	−3.03087	−	7.31717i	−0.108176	−	0.261161i
$786$		−	1.98295i		−	0.0707295i
$787$	−3.90992	+	1.61954i	−0.139373	+	0.0577304i	−0.451280	−	0.892382i	$-0.649032\pi$
$787$	−3.90992	+	1.61954i	−0.139373	+	0.0577304i	0.311907	+	0.950113i	$0.399032\pi$
$788$	1.71502	−	4.14043i	0.0610951	−	0.147497i
$789$	−10.5851	−	4.38451i	−0.376841	−	0.156093i
$790$	−3.05959	+	3.05959i	−0.108855	+	0.108855i
$791$	−7.53372	+	7.53372i	−0.267868	+	0.267868i
$792$	3.61313	+	1.49661i	0.128387	+	0.0531796i
$793$	−5.14800	+	12.4284i	−0.182811	+	0.441344i
$794$	4.12265	−	1.70766i	0.146307	−	0.0606025i
$795$			8.24906i			0.292564i
$796$	−7.40064	−	17.8667i	−0.262309	−	0.633269i
$797$	−19.6224	−	19.6224i	−0.695059	−	0.695059i	0.268281	−	0.963341i	$-0.413544\pi$
$797$	−19.6224	−	19.6224i	−0.695059	−	0.695059i	−0.963341	+	0.268281i	$0.913544\pi$
$798$	6.43702			0.227868
$799$		0			0
$800$	3.88915			0.137502
$801$	−9.66572	−	9.66572i	−0.341522	−	0.341522i
$802$	−1.52018	−	3.67004i	−0.0536794	−	0.129593i
$803$			0.551099i			0.0194479i
$804$	2.76537	−	1.14545i	0.0975270	−	0.0403970i
$805$	−3.25529	+	7.85897i	−0.114734	+	0.276992i
$806$	−29.8448	−	12.3621i	−1.05124	−	0.435437i
$807$	13.5545	−	13.5545i	0.477141	−	0.477141i
$808$	4.39782	−	4.39782i	0.154715	−	0.154715i
$809$	3.76277	+	1.55859i	0.132292	+	0.0547971i	0.447847	−	0.894110i	$-0.352191\pi$
$809$	3.76277	+	1.55859i	0.132292	+	0.0547971i	−0.315555	+	0.948907i	$0.602191\pi$
$810$	0.609919	−	1.47247i	0.0214304	−	0.0517375i
$811$	5.80819	−	2.40583i	0.203953	−	0.0844802i	−0.278368	−	0.960474i	$-0.589794\pi$
$811$	5.80819	−	2.40583i	0.203953	−	0.0844802i	0.482322	+	0.875994i	$0.339794\pi$
$812$			10.8999i			0.382510i
$813$	2.61298	+	6.30830i	0.0916413	+	0.221242i
$814$	3.18875	+	3.18875i	0.111766	+	0.111766i
$815$	−18.8848			−0.661507
$816$		0			0
$817$	23.4749			0.821282
$818$	−14.7422	−	14.7422i	−0.515448	−	0.515448i
$819$	1.94174	+	4.68777i	0.0678499	+	0.163804i
$820$		−	35.7430i		−	1.24820i
$821$	18.2926	−	7.57706i	0.638418	−	0.264441i	−0.0399072	−	0.999203i	$-0.512706\pi$
$821$	18.2926	−	7.57706i	0.638418	−	0.264441i	0.678325	+	0.734762i	$0.262706\pi$
$822$	4.47201	−	10.7964i	0.155979	−	0.376567i
$823$	−10.7853	−	4.46741i	−0.375951	−	0.155724i	0.186703	−	0.982416i	$-0.440220\pi$
$823$	−10.7853	−	4.46741i	−0.375951	−	0.155724i	−0.562654	+	0.826692i	$0.690220\pi$
$824$	−24.5584	+	24.5584i	−0.855532	+	0.855532i
$825$	0.702307	−	0.702307i	0.0244512	−	0.0244512i
$826$	7.03919	+	2.91573i	0.244925	+	0.101451i
$827$	−5.31585	+	12.8336i	−0.184850	+	0.446268i	−0.988954	−	0.148221i	$-0.952645\pi$
$827$	−5.31585	+	12.8336i	−0.184850	+	0.446268i	0.804104	+	0.594488i	$0.202645\pi$
$828$	−4.32295	+	1.79063i	−0.150233	+	0.0622285i
$829$			34.2670i			1.19014i	0.803673	+	0.595071i	$0.202876\pi$
$829$			34.2670i			1.19014i	−0.803673	+	0.595071i	$0.797124\pi$
$830$	8.79127	+	21.2240i	0.305149	+	0.736696i
$831$	−5.74725	−	5.74725i	−0.199370	−	0.199370i
$832$	−11.6241			−0.402992
$833$		0			0
$834$	3.09372			0.107127
$835$	−13.0868	−	13.0868i	−0.452888	−	0.452888i
$836$	−5.51746	−	13.3203i	−0.190825	−	0.460693i
$837$		−	10.2700i		−	0.354982i
$838$	9.92079	−	4.10933i	0.342708	−	0.141954i
$839$	9.27891	−	22.4013i	0.320344	−	0.773378i	−0.678890	−	0.734240i	$-0.737539\pi$
$839$	9.27891	−	22.4013i	0.320344	−	0.773378i	0.999234	−	0.0391379i	$-0.0124612\pi$
$840$	−6.20692	−	2.57099i	−0.214159	−	0.0887076i
$841$	7.05025	−	7.05025i	0.243112	−	0.243112i
$842$	8.32417	−	8.32417i	0.286870	−	0.286870i
$843$	10.7235	+	4.44182i	0.369337	+	0.152984i
$844$	−3.20851	+	7.74603i	−0.110442	+	0.266630i
$845$	−7.48369	+	3.09985i	−0.257447	+	0.106638i
$846$			1.20116i			0.0412969i
$847$	4.13895	+	9.99231i	0.142216	+	0.343340i
$848$	2.32050	+	2.32050i	0.0796862	+	0.0796862i
$849$	−6.06404			−0.208117
$850$		0			0
$851$	−13.0259			−0.446523
$852$	0.226626	+	0.226626i	0.00776406	+	0.00776406i
$853$	2.82779	+	6.82689i	0.0968217	+	0.233748i	0.964868	−	0.262735i	$-0.0846245\pi$
$853$	2.82779	+	6.82689i	0.0968217	+	0.233748i	−0.868046	+	0.496483i	$0.834624\pi$
$854$		−	3.09309i		−	0.105843i
$855$	−13.1055	+	5.42849i	−0.448200	+	0.185651i
$856$	13.0724	−	31.5596i	0.446806	−	1.07869i
$857$	−7.42181	−	3.07421i	−0.253524	−	0.105013i	0.252302	−	0.967649i	$-0.418812\pi$
$857$	−7.42181	−	3.07421i	−0.253524	−	0.105013i	−0.505826	+	0.862635i	$0.668812\pi$
$858$	−3.32871	+	3.32871i	−0.113640	+	0.113640i
$859$	5.42119	−	5.42119i	0.184969	−	0.184969i	−0.608548	−	0.793517i	$-0.708248\pi$
$859$	5.42119	−	5.42119i	0.184969	−	0.184969i	0.793517	+	0.608548i	$0.208248\pi$
$860$	−9.37604	−	3.88368i	−0.319720	−	0.132432i
$861$	5.73445	−	13.8442i	0.195429	−	0.471808i
$862$	11.5899	−	4.80071i	0.394755	−	0.163513i
$863$			14.4183i			0.490804i	0.969421	+	0.245402i	$0.0789200\pi$
$863$			14.4183i			0.490804i	−0.969421	+	0.245402i	$0.921080\pi$
$864$	−2.24264	−	5.41421i	−0.0762962	−	0.184195i
$865$	18.0336	+	18.0336i	0.613162	+	0.613162i
$866$	16.6166			0.564655
$867$		0			0
$868$	−17.9317			−0.608643
$869$	2.87302	+	2.87302i	0.0974604	+	0.0974604i
$870$	3.80750	+	9.19212i	0.129086	+	0.311642i
$871$			8.69833i			0.294732i
$872$	2.30864	−	0.956272i	0.0781806	−	0.0323834i
$873$	−1.02734	+	2.48022i	−0.0347702	+	0.0839426i
$874$	−15.9372	−	6.60141i	−0.539084	−	0.223296i
$875$	−10.2963	+	10.2963i	−0.348079	+	0.348079i
$876$	0.368233	−	0.368233i	0.0124414	−	0.0124414i
$877$	−49.7256	−	20.5970i	−1.67912	−	0.695512i	−0.679832	−	0.733368i	$-0.737947\pi$
$877$	−49.7256	−	20.5970i	−1.67912	−	0.695512i	−0.999283	+	0.0378554i	$0.987947\pi$
$878$	−6.89189	+	16.6385i	−0.232590	+	0.561522i
$879$	6.35211	−	2.63113i	0.214251	−	0.0887458i
$880$			2.58181i			0.0870328i
$881$	11.4019	+	27.5265i	0.384138	+	0.927392i	0.991156	+	0.132703i	$0.0423658\pi$
$881$	11.4019	+	27.5265i	0.384138	+	0.927392i	−0.607018	+	0.794688i	$0.707634\pi$
$882$	2.96342	+	2.96342i	0.0997834	+	0.0997834i
$883$	28.2666			0.951247			0.475624	−	0.879649i	$-0.342222\pi$
$883$	28.2666			0.951247			0.475624	+	0.879649i	$0.342222\pi$
$884$		0			0
$885$	−16.7905			−0.564405
$886$	−8.34731	−	8.34731i	−0.280433	−	0.280433i
$887$	9.61176	+	23.2049i	0.322731	+	0.779143i	0.999093	+	0.0425732i	$0.0135556\pi$
$887$	9.61176	+	23.2049i	0.322731	+	0.779143i	−0.676362	+	0.736569i	$0.736444\pi$
$888$		−	10.2877i		−	0.345233i
$889$	−16.1384	+	6.68474i	−0.541265	+	0.224199i
$890$	−8.33722	+	20.1278i	−0.279464	+	0.674686i
$891$	−1.38268	−	0.572726i	−0.0463216	−	0.0191871i
$892$	−26.1476	+	26.1476i	−0.875488	+	0.875488i
$893$	7.55953	−	7.55953i	0.252970	−	0.252970i
$894$	12.8141	+	5.30778i	0.428568	+	0.177519i
$895$	8.46088	−	20.4264i	0.282816	−	0.682779i
$896$	−10.8999	+	4.51487i	−0.364139	+	0.150831i
$897$		−	13.5976i		−	0.454012i
$898$	−3.96854	−	9.58091i	−0.132432	−	0.319719i
$899$	45.3339	+	45.3339i	1.51197	+	1.51197i
$900$	−0.938533			−0.0312844
$901$		0			0
$902$	13.9024			0.462901
$903$	−3.00850	−	3.00850i	−0.100116	−	0.100116i
$904$	8.62951	+	20.8335i	0.287013	+	0.692912i
$905$			34.4166i			1.14405i
$906$	3.72739	−	1.54394i	0.123834	−	0.0512939i
$907$	18.7895	−	45.3619i	0.623895	−	1.50622i	−0.223199	−	0.974773i	$-0.571650\pi$
$907$	18.7895	−	45.3619i	0.623895	−	1.50622i	0.847094	−	0.531443i	$-0.178350\pi$
$908$	14.3390	+	5.93939i	0.475855	+	0.197106i
$909$	−1.68297	+	1.68297i	−0.0558207	+	0.0558207i
$910$	5.71832	−	5.71832i	0.189561	−	0.189561i
$911$	7.36911	+	3.05238i	0.244149	+	0.101130i	0.501403	−	0.865214i	$-0.332817\pi$
$911$	7.36911	+	3.05238i	0.244149	+	0.101130i	−0.257253	+	0.966344i	$0.582817\pi$
$912$	−2.15959	+	5.21371i	−0.0715111	+	0.172643i
$913$	19.9298	−	8.25518i	0.659579	−	0.273207i
$914$		−	11.7771i		−	0.389551i
$915$	2.60848	+	6.29743i	0.0862337	+	0.208187i
$916$	14.4872	+	14.4872i	0.478670	+	0.478670i
$917$	3.19875			0.105632
$918$		0			0
$919$	19.8027			0.653229			0.326615	−	0.945158i	$-0.394092\pi$
$919$	19.8027			0.653229			0.326615	+	0.945158i	$0.394092\pi$
$920$	12.7309	+	12.7309i	0.419724	+	0.419724i
$921$	−8.51282	−	20.5518i	−0.280507	−	0.677204i
$922$			15.9201i			0.524300i
$923$	−0.860474	+	0.356420i	−0.0283228	+	0.0117317i
$924$	−1.00000	+	2.41421i	−0.0328976	+	0.0794218i
$925$	−2.41384	−	0.999845i	−0.0793666	−	0.0328747i
$926$	14.3052	−	14.3052i	0.470097	−	0.470097i
$927$	9.39809	−	9.39809i	0.308674	−	0.308674i
$928$	33.7990	+	14.0000i	1.10951	+	0.459573i
$929$	−2.13327	+	5.15017i	−0.0699903	+	0.168972i	−0.955004	−	0.296594i	$-0.904149\pi$
$929$	−2.13327	+	5.15017i	−0.0699903	+	0.168972i	0.885013	+	0.465566i	$0.154149\pi$
$930$	−15.1223	+	6.26385i	−0.495879	+	0.205400i
$931$		−	37.3005i		−	1.22248i
$932$	−10.3358	−	24.9528i	−0.338560	−	0.817356i
$933$	3.82843	+	3.82843i	0.125337	+	0.125337i
$934$	−5.48836			−0.179584
$935$		0			0
$936$	10.7392			0.351023
$937$	−0.281833	−	0.281833i	−0.00920709	−	0.00920709i	0.702488	−	0.711695i	$-0.252072\pi$
$937$	−0.281833	−	0.281833i	−0.00920709	−	0.00920709i	−0.711695	+	0.702488i	$0.752072\pi$
$938$	−0.765367	−	1.84776i	−0.0249901	−	0.0603315i
$939$		−	11.2945i		−	0.368582i
$940$	−4.26998	+	1.76868i	−0.139271	+	0.0576881i
$941$	−1.64878	+	3.98050i	−0.0537486	+	0.129760i	−0.948473	−	0.316858i	$-0.897372\pi$
$941$	−1.64878	+	3.98050i	−0.0537486	+	0.129760i	0.894724	+	0.446619i	$0.147372\pi$
$942$	−2.68937	−	1.11397i	−0.0876243	−	0.0362952i
$943$	−28.3955	+	28.3955i	−0.924683	+	0.924683i
$944$	−4.72323	+	4.72323i	−0.153728	+	0.153728i
$945$	2.37529	+	0.983875i	0.0772680	+	0.0320055i
$946$	1.51058	−	3.64686i	0.0491131	−	0.118570i
$947$	−10.5466	+	4.36856i	−0.342720	+	0.141959i	−0.547403	−	0.836869i	$-0.684384\pi$
$947$	−10.5466	+	4.36856i	−0.342720	+	0.141959i	0.204683	+	0.978828i	$0.434384\pi$
$948$		−	3.83938i		−	0.124697i
$949$	0.579129	+	1.39814i	0.0187993	+	0.0453856i
$950$	−2.44662	−	2.44662i	−0.0793788	−	0.0793788i
$951$	18.4520			0.598346
$952$		0			0
$953$	−40.8932			−1.32466			−0.662330	−	0.749213i	$-0.730432\pi$
$953$	−40.8932			−1.32466			−0.662330	+	0.749213i	$0.730432\pi$
$954$	2.14386	+	2.14386i	0.0694100	+	0.0694100i
$955$	−9.57608	−	23.1187i	−0.309875	−	0.748103i
$956$		−	1.04789i		−	0.0338912i
$957$	8.63160	−	3.57532i	0.279020	−	0.115574i
$958$	0.859348	−	2.07465i	0.0277643	−	0.0670289i
$959$	17.4159	+	7.21391i	0.562389	+	0.232949i
$960$	−4.16478	+	4.16478i	−0.134418	+	0.134418i
$961$	−52.6600	+	52.6600i	−1.69871	+	1.69871i
$962$	11.4408	+	4.73894i	0.368867	+	0.152790i
$963$	−5.00260	+	12.0773i	−0.161206	+	0.389187i
$964$	−27.9104	+	11.5609i	−0.898935	+	0.372351i
$965$			22.3197i			0.718498i
$966$	1.19646	+	2.88850i	0.0384954	+	0.0929361i
$967$	16.6407	+	16.6407i	0.535130	+	0.535130i	0.922095	−	0.386965i	$-0.126476\pi$
$967$	16.6407	+	16.6407i	0.535130	+	0.535130i	−0.386965	+	0.922095i	$0.626476\pi$
$968$	22.8914			0.735758
$969$		0			0
$970$	4.27865			0.137379
$971$	−4.55476	−	4.55476i	−0.146169	−	0.146169i	0.630235	−	0.776404i	$-0.282958\pi$
$971$	−4.55476	−	4.55476i	−0.146169	−	0.146169i	−0.776404	+	0.630235i	$0.782958\pi$
$972$	0.541196	+	1.30656i	0.0173589	+	0.0419080i
$973$			4.99055i			0.159990i
$974$	16.4346	−	6.80742i	0.526597	−	0.218124i
$975$	1.04373	−	2.51978i	0.0334261	−	0.0806976i
$976$	2.50527	+	1.03772i	0.0801918	+	0.0332165i
$977$	12.6200	−	12.6200i	0.403750	−	0.403750i	−0.475802	−	0.879552i	$-0.657842\pi$
$977$	12.6200	−	12.6200i	0.403750	−	0.403750i	0.879552	+	0.475802i	$0.157842\pi$
$978$	−4.90801	+	4.90801i	−0.156941	+	0.156941i
$979$	18.9004	+	7.82882i	0.604061	+	0.250210i
$980$	−6.17100	+	14.8981i	−0.197125	+	0.475902i
$981$	−0.883480	+	0.365949i	−0.0282073	+	0.0116839i
$982$			10.4538i			0.333595i
$983$	−9.22941	−	22.2818i	−0.294372	−	0.710678i	−0.999998	−	0.00209283i	$-0.999334\pi$
$983$	−9.22941	−	22.2818i	−0.294372	−	0.710678i	0.705625	−	0.708585i	$-0.250666\pi$
$984$	−22.4264	−	22.4264i	−0.714927	−	0.714927i
$985$	6.59899			0.210261
$986$		0			0
$987$	−1.93763			−0.0616755
$988$	−27.9956	−	27.9956i	−0.890660	−	0.890660i
$989$	4.36331	+	10.5340i	0.138745	+	0.334961i
$990$			2.38528i			0.0758092i
$991$	−22.3633	+	9.26319i	−0.710394	+	0.294255i	−0.708468	−	0.705743i	$-0.750613\pi$
$991$	−22.3633	+	9.26319i	−0.710394	+	0.294255i	−0.00192659	+	0.999998i	$0.500613\pi$
$992$	−23.0319	+	55.6039i	−0.731263	+	1.76542i
$993$	−5.32714	−	2.20657i	−0.169052	−	0.0700235i
$994$	0.151426	−	0.151426i	0.00480295	−	0.00480295i
$995$	20.1355	−	20.1355i	0.638338	−	0.638338i
$996$	−18.8326	−	7.80071i	−0.596733	−	0.247175i
$997$	−14.1268	+	34.1051i	−0.447400	+	1.08012i	0.525892	+	0.850551i	$0.323732\pi$
$997$	−14.1268	+	34.1051i	−0.447400	+	1.08012i	−0.973292	+	0.229569i	$0.926268\pi$
$998$	5.32607	−	2.20613i	0.168594	−	0.0698338i
$999$			3.93694i			0.124559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.g.712.2		8
17.2	even	8		867.2.h.f.757.1		8
17.3	odd	16		867.2.d.e.577.5		8
17.4	even	4		867.2.h.f.733.1		8
17.5	odd	16		867.2.a.n.1.2		4
17.6	odd	16		867.2.e.i.829.3		8
17.7	odd	16		867.2.e.i.616.2		8
17.8	even	8	inner	867.2.h.g.688.2		8
17.9	even	8		51.2.h.a.25.2	✓	8
17.10	odd	16		867.2.e.h.616.2		8
17.11	odd	16		867.2.e.h.829.3		8
17.12	odd	16		867.2.a.m.1.2		4
17.13	even	4		867.2.h.b.733.1		8
17.14	odd	16		867.2.d.e.577.6		8
17.15	even	8		867.2.h.b.757.1		8
17.16	even	2		51.2.h.a.49.2	yes	8
51.5	even	16		2601.2.a.bd.1.3		4
51.26	odd	8		153.2.l.e.127.1		8
51.29	even	16		2601.2.a.bc.1.3		4
51.50	odd	2		153.2.l.e.100.1		8
68.43	odd	8		816.2.bq.a.433.1		8
68.67	odd	2		816.2.bq.a.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.25.2	✓	8	17.9	even	8
51.2.h.a.49.2	yes	8	17.16	even	2
153.2.l.e.100.1		8	51.50	odd	2
153.2.l.e.127.1		8	51.26	odd	8
816.2.bq.a.49.1		8	68.67	odd	2
816.2.bq.a.433.1		8	68.43	odd	8
867.2.a.m.1.2		4	17.12	odd	16
867.2.a.n.1.2		4	17.5	odd	16
867.2.d.e.577.5		8	17.3	odd	16
867.2.d.e.577.6		8	17.14	odd	16
867.2.e.h.616.2		8	17.10	odd	16
867.2.e.h.829.3		8	17.11	odd	16
867.2.e.i.616.2		8	17.7	odd	16
867.2.e.i.829.3		8	17.6	odd	16
867.2.h.b.733.1		8	17.13	even	4
867.2.h.b.757.1		8	17.15	even	8
867.2.h.f.733.1		8	17.4	even	4
867.2.h.f.757.1		8	17.2	even	8
867.2.h.g.688.2		8	17.8	even	8	inner
867.2.h.g.712.2		8	1.1	even	1	trivial
2601.2.a.bc.1.3		4	51.29	even	16
2601.2.a.bd.1.3		4	51.5	even	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.541196 + 0.541196i) q^{2} +(-0.382683 - 0.923880i) q^{3} -1.41421i q^{4} +(1.92388 - 0.796897i) q^{5} +(0.292893 - 0.707107i) q^{6} +(1.14065 + 0.472474i) q^{7} +(1.84776 - 1.84776i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(1.47247 + 0.609919i) q^{10} +(0.572726 - 1.38268i) q^{11} +(-1.30656 + 0.541196i) q^{12} -4.10973i q^{13} +(0.361616 + 0.873017i) q^{14} +(-1.47247 - 1.47247i) q^{15} -0.828427 q^{16} -0.765367 q^{18} +(4.81684 + 4.81684i) q^{19} +(-1.12698 - 2.72078i) q^{20} -1.23463i q^{21} +(1.05826 - 0.438346i) q^{22} +(-1.26616 + 3.05679i) q^{23} +(-2.41421 - 1.00000i) q^{24} +(-0.469266 + 0.469266i) q^{25} +(2.22417 - 2.22417i) q^{26} +(0.923880 + 0.382683i) q^{27} +(0.668179 - 1.61313i) q^{28} +(-5.76745 + 2.38896i) q^{29} -1.59379i q^{30} +(-3.93015 - 9.48822i) q^{31} +(-4.14386 - 4.14386i) q^{32} -1.49661 q^{33} +2.57099 q^{35} +(1.00000 + 1.00000i) q^{36} +(1.50660 + 3.63726i) q^{37} +5.21371i q^{38} +(-3.79690 + 1.57273i) q^{39} +(2.08239 - 5.02734i) q^{40} +(11.2132 + 4.64466i) q^{41} +(0.668179 - 0.668179i) q^{42} +(2.43675 - 2.43675i) q^{43} +(-1.95541 - 0.809957i) q^{44} +(-0.796897 + 1.92388i) q^{45} +(-2.33956 + 0.969079i) q^{46} -1.56940i q^{47} +(0.317025 + 0.765367i) q^{48} +(-3.87189 - 3.87189i) q^{49} -0.507930 q^{50} -5.81204 q^{52} +(-2.80109 - 2.80109i) q^{53} +(0.292893 + 0.707107i) q^{54} -3.11652i q^{55} +(2.98067 - 1.23463i) q^{56} +(2.60685 - 6.29350i) q^{57} +(-4.41421 - 1.82843i) q^{58} +(5.70144 - 5.70144i) q^{59} +(-2.08239 + 2.08239i) q^{60} +(-3.02413 - 1.25264i) q^{61} +(3.00801 - 7.26197i) q^{62} +(-1.14065 + 0.472474i) q^{63} -2.82843i q^{64} +(-3.27503 - 7.90663i) q^{65} +(-0.809957 - 0.809957i) q^{66} -2.11652 q^{67} +3.30864 q^{69} +(1.39141 + 1.39141i) q^{70} +(-0.0867259 - 0.209375i) q^{71} +2.61313i q^{72} +(-0.340203 + 0.140917i) q^{73} +(-1.15310 + 2.78384i) q^{74} +(0.613126 + 0.253965i) q^{75} +(6.81204 - 6.81204i) q^{76} +(1.30656 - 1.30656i) q^{77} +(-2.90602 - 1.20371i) q^{78} +(-1.03893 + 2.50819i) q^{79} +(-1.59379 + 0.660171i) q^{80} -1.00000i q^{81} +(3.55487 + 8.58221i) q^{82} +(10.1921 + 10.1921i) q^{83} -1.74603 q^{84} +2.63752 q^{86} +(4.41421 + 4.41421i) q^{87} +(-1.49661 - 3.61313i) q^{88} +13.6694i q^{89} +(-1.47247 + 0.609919i) q^{90} +(1.94174 - 4.68777i) q^{91} +(4.32295 + 1.79063i) q^{92} +(-7.26197 + 7.26197i) q^{93} +(0.849352 - 0.849352i) q^{94} +(13.1055 + 5.42849i) q^{95} +(-2.24264 + 5.41421i) q^{96} +(2.48022 - 1.02734i) q^{97} -4.19090i q^{98} +(0.572726 + 1.38268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{5} + 8 q^{6} - 8 q^{11} + 16 q^{14} + 16 q^{16} - 8 q^{19} - 16 q^{20} + 8 q^{22} - 8 q^{23} - 8 q^{24} - 16 q^{25} + 16 q^{26} + 8 q^{28} - 8 q^{31} + 8 q^{33} + 32 q^{35} + 8 q^{36} + 8 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^5 + 8 * q^6 - 8 * q^11 + 16 * q^14 + 16 * q^16 - 8 * q^19 - 16 * q^20 + 8 * q^22 - 8 * q^23 - 8 * q^24 - 16 * q^25 + 16 * q^26 + 8 * q^28 - 8 * q^31 + 8 * q^33 + 32 * q^35 + 8 * q^36 + 8 * q^37 - 16 * q^39 + 8 * q^40 + 24 * q^41 + 8 * q^42 - 8 * q^43 + 8 * q^45 - 8 * q^49 - 32 * q^50 - 16 * q^52 - 32 * q^53 + 8 * q^54 + 16 * q^56 + 16 * q^57 - 24 * q^58 + 16 * q^59 - 8 * q^60 - 16 * q^61 - 16 * q^62 - 24 * q^65 - 16 * q^66 - 16 * q^67 - 24 * q^69 + 40 * q^70 + 16 * q^71 - 48 * q^73 - 64 * q^74 - 16 * q^75 + 24 * q^76 - 8 * q^78 + 16 * q^80 + 8 * q^82 + 32 * q^83 - 32 * q^86 + 24 * q^87 + 8 * q^88 + 16 * q^91 + 32 * q^92 - 32 * q^93 + 40 * q^95 + 16 * q^96 - 8 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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