LMFDB - Embedded newform 867.2.h.f.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			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	867.712
Dual form			867.2.h.f.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+(1.30656 + 1.30656i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.41421i q^{4} +(1.49033 - 0.617317i) q^{5} +(-0.707107 + 1.70711i) q^{6} +(-0.140652 - 0.0582601i) q^{7} +(0.765367 - 0.765367i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(2.75378 + 1.14065i) q^{10} +(1.92388 - 4.64466i) q^{11} +(-1.30656 + 0.541196i) q^{12} +3.94495i q^{13} +(-0.107651 - 0.259892i) q^{14} +(1.14065 + 1.14065i) q^{15} +4.82843 q^{16} -1.84776 q^{18} +(4.65205 + 4.65205i) q^{19} +(0.873017 + 2.10765i) q^{20} -0.152241i q^{21} +(8.58221 - 3.55487i) q^{22} +(-1.31962 + 3.18585i) q^{23} +(1.00000 + 0.414214i) q^{24} +(-1.69552 + 1.69552i) q^{25} +(-5.15432 + 5.15432i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(0.0823922 - 0.198912i) q^{28} +(-2.07193 + 0.858221i) q^{29} +2.98067i q^{30} +(-0.985204 - 2.37849i) q^{31} +(4.77791 + 4.77791i) q^{32} +5.02734 q^{33} -0.245584 q^{35} +(-1.00000 - 1.00000i) q^{36} +(-4.08560 - 9.86351i) q^{37} +12.1564i q^{38} +(-3.64466 + 1.50967i) q^{39} +(0.668179 - 1.61313i) q^{40} +(0.255701 + 0.105915i) q^{41} +(0.198912 - 0.198912i) q^{42} +(-4.48502 + 4.48502i) q^{43} +(6.56854 + 2.72078i) q^{44} +(-0.617317 + 1.49033i) q^{45} +(-5.88669 + 2.43835i) q^{46} -9.82164i q^{47} +(1.84776 + 4.46088i) q^{48} +(-4.93336 - 4.93336i) q^{49} -4.43060 q^{50} -5.57900 q^{52} +(1.50339 + 1.50339i) q^{53} +(-0.707107 - 1.70711i) q^{54} -8.10973i q^{55} +(-0.152241 + 0.0630603i) q^{56} +(-2.51767 + 6.07820i) q^{57} +(-3.82843 - 1.58579i) q^{58} +(0.936078 - 0.936078i) q^{59} +(-1.61313 + 1.61313i) q^{60} +(7.64821 + 3.16799i) q^{61} +(1.82042 - 4.39488i) q^{62} +(0.140652 - 0.0582601i) q^{63} +2.82843i q^{64} +(2.43528 + 5.87929i) q^{65} +(6.56854 + 6.56854i) q^{66} -7.10973 q^{67} -3.44834 q^{69} +(-0.320871 - 0.320871i) q^{70} +(2.50548 + 6.04875i) q^{71} +1.08239i q^{72} +(-7.69258 + 3.18637i) q^{73} +(7.54920 - 18.2254i) q^{74} +(-2.21530 - 0.917608i) q^{75} +(-6.57900 + 6.57900i) q^{76} +(-0.541196 + 0.541196i) q^{77} +(-6.73445 - 2.78950i) q^{78} +(0.203713 - 0.491806i) q^{79} +(7.19597 - 2.98067i) q^{80} -1.00000i q^{81} +(0.195705 + 0.472474i) q^{82} +(1.55807 + 1.55807i) q^{83} +0.215301 q^{84} -11.7199 q^{86} +(-1.58579 - 1.58579i) q^{87} +(-2.08239 - 5.02734i) q^{88} -7.64847i q^{89} +(-2.75378 + 1.14065i) q^{90} +(0.229833 - 0.554866i) q^{91} +(-4.50548 - 1.86623i) q^{92} +(1.82042 - 1.82042i) q^{93} +(12.8326 - 12.8326i) q^{94} +(9.80490 + 4.06132i) q^{95} +(-2.58579 + 6.24264i) q^{96} +(3.33182 - 1.38009i) q^{97} -12.8915i q^{98} +(1.92388 + 4.64466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{5} + 8 q^{7} - 8 q^{10} + 8 q^{11} + 16 q^{16} + 8 q^{19} + 16 q^{22} - 24 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^{40} - 8 q^{41}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^5 + 8 * q^7 - 8 * q^10 + 8 * q^11 + 16 * q^16 + 8 * q^19 + 16 * q^22 - 24 * 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^40 - 8 * q^41 - 8 * q^42 + 8 * q^43 + 16 * q^44 - 8 * q^45 - 24 * q^46 + 8 * q^49 - 32 * q^50 - 16 * q^52 + 32 * q^53 - 16 * q^56 + 16 * q^57 - 8 * q^58 - 16 * q^59 + 8 * q^60 - 8 * q^61 + 32 * q^62 - 8 * q^63 - 8 * q^65 + 16 * q^66 - 16 * q^67 - 24 * q^69 - 40 * q^70 - 32 * q^73 + 16 * q^74 - 16 * q^75 - 24 * q^76 - 16 * q^78 - 24 * q^79 + 48 * q^80 + 16 * q^82 - 32 * q^83 - 32 * q^86 - 24 * q^87 - 8 * q^88 + 8 * q^90 + 24 * q^91 - 16 * q^92 + 32 * q^93 + 24 * q^95 - 32 * q^96 + 24 * 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 $

$2$	1.30656	+	1.30656i	0.923880	+	0.923880i	0.997301	−	0.0734215i	$-0.0233918\pi$
$2$	1.30656	+	1.30656i	0.923880	+	0.923880i	−0.0734215	+	0.997301i	$0.523392\pi$
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$4$			1.41421i			0.707107i
$5$	1.49033	−	0.617317i	0.666498	−	0.276072i	−0.0236722	−	0.999720i	$-0.507536\pi$
$5$	1.49033	−	0.617317i	0.666498	−	0.276072i	0.690170	+	0.723647i	$0.257536\pi$
$6$	−0.707107	+	1.70711i	−0.288675	+	0.696923i
$7$	−0.140652	−	0.0582601i	−0.0531616	−	0.0220202i	0.355944	−	0.934507i	$-0.384159\pi$
$7$	−0.140652	−	0.0582601i	−0.0531616	−	0.0220202i	−0.409106	+	0.912487i	$0.634159\pi$
$8$	0.765367	−	0.765367i	0.270598	−	0.270598i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	2.75378	+	1.14065i	0.870821	+	0.360706i
$11$	1.92388	−	4.64466i	0.580072	−	1.40042i	−0.312676	−	0.949860i	$-0.601226\pi$
$11$	1.92388	−	4.64466i	0.580072	−	1.40042i	0.892748	−	0.450557i	$-0.148774\pi$
$12$	−1.30656	+	0.541196i	−0.377172	+	0.156230i
$13$			3.94495i			1.09413i	0.837090	+	0.547066i	$0.184255\pi$
$13$			3.94495i			1.09413i	−0.837090	+	0.547066i	$0.815745\pi$
$14$	−0.107651	−	0.259892i	−0.0287708	−	0.0694589i
$15$	1.14065	+	1.14065i	0.294515	+	0.294515i
$16$	4.82843			1.20711
$17$		0			0
$17$		0			0
$18$	−1.84776			−0.435521
$19$	4.65205	+	4.65205i	1.06725	+	1.06725i	0.997569	+	0.0696854i	$0.0221995\pi$
$19$	4.65205	+	4.65205i	1.06725	+	1.06725i	0.0696854	+	0.997569i	$0.477800\pi$
$20$	0.873017	+	2.10765i	0.195213	+	0.471285i
$21$		−	0.152241i		−	0.0332217i
$22$	8.58221	−	3.55487i	1.82973	−	0.757900i
$23$	−1.31962	+	3.18585i	−0.275160	+	0.664296i	−0.999689	−	0.0249490i	$-0.992058\pi$
$23$	−1.31962	+	3.18585i	−0.275160	+	0.664296i	0.724528	+	0.689245i	$0.242058\pi$
$24$	1.00000	+	0.414214i	0.204124	+	0.0845510i
$25$	−1.69552	+	1.69552i	−0.339104	+	0.339104i
$26$	−5.15432	+	5.15432i	−1.01085	+	1.01085i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	0.0823922	−	0.198912i	0.0155707	−	0.0375909i
$29$	−2.07193	+	0.858221i	−0.384748	+	0.159368i	−0.566669	−	0.823945i	$-0.691768\pi$
$29$	−2.07193	+	0.858221i	−0.384748	+	0.159368i	0.181922	+	0.983313i	$0.441768\pi$
$30$			2.98067i			0.544193i
$31$	−0.985204	−	2.37849i	−0.176948	−	0.427190i	0.810376	−	0.585911i	$-0.199263\pi$
$31$	−0.985204	−	2.37849i	−0.176948	−	0.427190i	−0.987324	+	0.158721i	$0.949263\pi$
$32$	4.77791	+	4.77791i	0.844623	+	0.844623i
$33$	5.02734			0.875147
$34$		0			0
$35$	−0.245584			−0.0415112
$36$	−1.00000	−	1.00000i	−0.166667	−	0.166667i
$37$	−4.08560	−	9.86351i	−0.671668	−	1.62155i	−0.778775	−	0.627303i	$-0.784159\pi$
$37$	−4.08560	−	9.86351i	−0.671668	−	1.62155i	0.107106	−	0.994248i	$-0.465841\pi$
$38$			12.1564i			1.97203i
$39$	−3.64466	+	1.50967i	−0.583612	+	0.241740i
$40$	0.668179	−	1.61313i	0.105648	−	0.255058i
$41$	0.255701	+	0.105915i	0.0399338	+	0.0165411i	0.402561	−	0.915393i	$-0.368120\pi$
$41$	0.255701	+	0.105915i	0.0399338	+	0.0165411i	−0.362627	+	0.931934i	$0.618120\pi$
$42$	0.198912	−	0.198912i	0.0306928	−	0.0306928i
$43$	−4.48502	+	4.48502i	−0.683959	+	0.683959i	−0.960890	−	0.276931i	$-0.910683\pi$
$43$	−4.48502	+	4.48502i	−0.683959	+	0.683959i	0.276931	+	0.960890i	$0.410683\pi$
$44$	6.56854	+	2.72078i	0.990244	+	0.410172i
$45$	−0.617317	+	1.49033i	−0.0920241	+	0.222166i
$46$	−5.88669	+	2.43835i	−0.867945	+	0.359514i
$47$		−	9.82164i		−	1.43263i	−0.697775	−	0.716317i	$-0.745827\pi$
$47$		−	9.82164i		−	1.43263i	0.697775	−	0.716317i	$-0.254173\pi$
$48$	1.84776	+	4.46088i	0.266701	+	0.643873i
$49$	−4.93336	−	4.93336i	−0.704766	−	0.704766i
$50$	−4.43060			−0.626582
$51$		0			0
$52$	−5.57900			−0.773668
$53$	1.50339	+	1.50339i	0.206507	+	0.206507i	0.802781	−	0.596274i	$-0.203353\pi$
$53$	1.50339	+	1.50339i	0.206507	+	0.206507i	−0.596274	+	0.802781i	$0.703353\pi$
$54$	−0.707107	−	1.70711i	−0.0962250	−	0.232308i
$55$		−	8.10973i		−	1.09352i
$56$	−0.152241	+	0.0630603i	−0.0203441	+	0.00842678i
$57$	−2.51767	+	6.07820i	−0.333474	+	0.805077i
$58$	−3.82843	−	1.58579i	−0.502697	−	0.208224i
$59$	0.936078	−	0.936078i	0.121867	−	0.121867i	−0.643543	−	0.765410i	$-0.722536\pi$
$59$	0.936078	−	0.936078i	0.121867	−	0.121867i	0.765410	+	0.643543i	$0.222536\pi$
$60$	−1.61313	+	1.61313i	−0.208254	+	0.208254i
$61$	7.64821	+	3.16799i	0.979253	+	0.405620i	0.814149	−	0.580656i	$-0.197204\pi$
$61$	7.64821	+	3.16799i	0.979253	+	0.405620i	0.165104	+	0.986276i	$0.447204\pi$
$62$	1.82042	−	4.39488i	0.231194	−	0.558151i
$63$	0.140652	−	0.0582601i	0.0177205	−	0.00734008i
$64$			2.82843i			0.353553i
$65$	2.43528	+	5.87929i	0.302059	+	0.729236i
$66$	6.56854	+	6.56854i	0.808531	+	0.808531i
$67$	−7.10973			−0.868592			−0.434296	−	0.900770i	$-0.643003\pi$
$67$	−7.10973			−0.868592			−0.434296	+	0.900770i	$0.643003\pi$
$68$		0			0
$69$	−3.44834			−0.415132
$70$	−0.320871	−	0.320871i	−0.0383514	−	0.0383514i
$71$	2.50548	+	6.04875i	0.297345	+	0.717855i	0.999980	+	0.00630431i	$0.00200674\pi$
$71$	2.50548	+	6.04875i	0.297345	+	0.717855i	−0.702635	+	0.711551i	$0.747993\pi$
$72$			1.08239i			0.127561i
$73$	−7.69258	+	3.18637i	−0.900348	+	0.372936i	−0.784354	−	0.620314i	$-0.787005\pi$
$73$	−7.69258	+	3.18637i	−0.900348	+	0.372936i	−0.115994	+	0.993250i	$0.537005\pi$
$74$	7.54920	−	18.2254i	0.877577	−	2.11866i
$75$	−2.21530	−	0.917608i	−0.255801	−	0.105956i
$76$	−6.57900	+	6.57900i	−0.754663	+	0.754663i
$77$	−0.541196	+	0.541196i	−0.0616750	+	0.0616750i
$78$	−6.73445	−	2.78950i	−0.762526	−	0.315849i
$79$	0.203713	−	0.491806i	0.0229195	−	0.0553325i	−0.912005	−	0.410178i	$-0.865467\pi$
$79$	0.203713	−	0.491806i	0.0229195	−	0.0553325i	0.934925	+	0.354846i	$0.115467\pi$
$80$	7.19597	−	2.98067i	0.804534	−	0.333249i
$81$		−	1.00000i		−	0.111111i
$82$	0.195705	+	0.472474i	0.0216120	+	0.0521760i
$83$	1.55807	+	1.55807i	0.171021	+	0.171021i	0.787428	−	0.616407i	$-0.211412\pi$
$83$	1.55807	+	1.55807i	0.171021	+	0.171021i	−0.616407	+	0.787428i	$0.711412\pi$
$84$	0.215301			0.0234913
$85$		0			0
$86$	−11.7199			−1.26379
$87$	−1.58579	−	1.58579i	−0.170014	−	0.170014i
$88$	−2.08239	−	5.02734i	−0.221984	−	0.535916i
$89$		−	7.64847i		−	0.810737i	−0.914153	−	0.405368i	$-0.867143\pi$
$89$		−	7.64847i		−	0.810737i	0.914153	−	0.405368i	$-0.132857\pi$
$90$	−2.75378	+	1.14065i	−0.290274	+	0.120235i
$91$	0.229833	−	0.554866i	0.0240930	−	0.0581657i
$92$	−4.50548	−	1.86623i	−0.469728	−	0.194568i
$93$	1.82042	−	1.82042i	0.188769	−	0.188769i
$94$	12.8326	−	12.8326i	1.32358	−	1.32358i
$95$	9.80490	+	4.06132i	1.00596	+	0.416683i
$96$	−2.58579	+	6.24264i	−0.263911	+	0.637137i
$97$	3.33182	−	1.38009i	0.338295	−	0.140126i	−0.207067	−	0.978327i	$-0.566392\pi$
$97$	3.33182	−	1.38009i	0.338295	−	0.140126i	0.545363	+	0.838200i	$0.316392\pi$
$98$		−	12.8915i		−	1.30224i
$99$	1.92388	+	4.64466i	0.193357	+	0.466805i
$100$	−2.39782	−	2.39782i	−0.239782	−	0.239782i
$101$	−9.13707			−0.909173			−0.454586	−	0.890703i	$-0.650213\pi$
$101$	−9.13707			−0.909173			−0.454586	+	0.890703i	$0.650213\pi$
$102$		0			0
$103$	7.57862			0.746744			0.373372	−	0.927682i	$-0.378202\pi$
$103$	7.57862			0.746744			0.373372	+	0.927682i	$0.378202\pi$
$104$	3.01933	+	3.01933i	0.296070	+	0.296070i
$105$	−0.0939809	−	0.226890i	−0.00917159	−	0.0221422i
$106$			3.92856i			0.381575i
$107$	−17.0610	+	7.06688i	−1.64934	+	0.683181i	−0.997191	−	0.0749059i	$-0.976134\pi$
$107$	−17.0610	+	7.06688i	−1.64934	+	0.683181i	−0.652154	+	0.758087i	$0.726134\pi$
$108$	0.541196	−	1.30656i	0.0520766	−	0.125724i
$109$	−9.92177	−	4.10973i	−0.950333	−	0.393641i	−0.146977	−	0.989140i	$-0.546954\pi$
$109$	−9.92177	−	4.10973i	−0.950333	−	0.393641i	−0.803356	+	0.595499i	$0.796954\pi$
$110$	10.5959	−	10.5959i	1.01028	−	1.01028i
$111$	7.54920	−	7.54920i	0.716539	−	0.716539i
$112$	−0.679129	−	0.281305i	−0.0641717	−	0.0265808i
$113$	0.640982	−	1.54747i	0.0602985	−	0.145574i	−0.890859	−	0.454281i	$-0.849896\pi$
$113$	0.640982	−	1.54747i	0.0602985	−	0.145574i	0.951157	+	0.308707i	$0.0998963\pi$
$114$	−11.2311	+	4.65205i	−1.05188	+	0.435705i
$115$			5.56261i			0.518716i
$116$	−1.21371	−	2.93015i	−0.112690	−	0.272058i
$117$	−2.78950	−	2.78950i	−0.257889	−	0.257889i
$118$	2.44609			0.225181
$119$		0			0
$120$	1.74603			0.159390
$121$	−10.0933	−	10.0933i	−0.917577	−	0.917577i
$122$	5.85369	+	14.1320i	0.529968	+	1.27946i
$123$			0.276769i			0.0249554i
$124$	3.36370	−	1.39329i	0.302069	−	0.125121i
$125$	−4.56680	+	11.0252i	−0.408467	+	0.986127i
$126$	0.259892	+	0.107651i	0.0231530	+	0.00959028i
$127$	−8.61339	+	8.61339i	−0.764315	+	0.764315i	−0.977099	−	0.212784i	$-0.931747\pi$
$127$	−8.61339	+	8.61339i	−0.764315	+	0.764315i	0.212784	+	0.977099i	$0.431747\pi$
$128$	5.86030	−	5.86030i	0.517982	−	0.517982i
$129$	−5.85996	−	2.42727i	−0.515940	−	0.213710i
$130$	−4.49981	+	10.8635i	−0.394660	+	0.952793i
$131$	9.65561	−	3.99948i	0.843614	−	0.349436i	0.0813367	−	0.996687i	$-0.474081\pi$
$131$	9.65561	−	3.99948i	0.843614	−	0.349436i	0.762278	+	0.647250i	$0.224081\pi$
$132$			7.10973i			0.618823i
$133$	−0.383293	−	0.925351i	−0.0332357	−	0.0802381i
$134$	−9.28931	−	9.28931i	−0.802474	−	0.802474i
$135$	−1.61313			−0.138836
$136$		0			0
$137$	13.4928			1.15276			0.576382	−	0.817180i	$-0.304464\pi$
$137$	13.4928			1.15276			0.576382	+	0.817180i	$0.304464\pi$
$138$	−4.50548	−	4.50548i	−0.383532	−	0.383532i
$139$	−2.03893	−	4.92241i	−0.172940	−	0.417513i	0.813516	−	0.581543i	$-0.197551\pi$
$139$	−2.03893	−	4.92241i	−0.172940	−	0.417513i	−0.986455	+	0.164030i	$0.947551\pi$
$140$		−	0.347308i		−	0.0293529i
$141$	9.07401	−	3.75858i	0.764170	−	0.316529i
$142$	−4.62951	+	11.1766i	−0.388500	+	0.937923i
$143$	18.3229	+	7.58960i	1.53224	+	0.634675i
$144$	−3.41421	+	3.41421i	−0.284518	+	0.284518i
$145$	−2.55807	+	2.55807i	−0.212436	+	0.212436i
$146$	−14.2140	−	5.88764i	−1.17636	−	0.487265i
$147$	2.66991	−	6.44574i	0.220211	−	0.531636i
$148$	13.9491	−	5.77791i	1.14661	−	0.474941i
$149$		−	9.31890i		−	0.763434i	−0.924279	−	0.381717i	$-0.875333\pi$
$149$		−	9.31890i		−	0.763434i	0.924279	−	0.381717i	$-0.124667\pi$
$150$	−1.69552	−	4.09334i	−0.138438	−	0.334220i
$151$	8.45929	+	8.45929i	0.688407	+	0.688407i	0.961880	−	0.273472i	$-0.0881722\pi$
$151$	8.45929	+	8.45929i	0.688407	+	0.688407i	−0.273472	+	0.961880i	$0.588172\pi$
$152$	7.12106			0.577594
$153$		0			0
$154$	−1.41421			−0.113961
$155$	−2.93657	−	2.93657i	−0.235871	−	0.235871i
$156$	−2.13499	−	5.15432i	−0.170936	−	0.412676i
$157$		−	18.1548i		−	1.44891i	−0.689321	−	0.724456i	$-0.742091\pi$
$157$		−	18.1548i		−	1.44891i	0.689321	−	0.724456i	$-0.257909\pi$
$158$	0.908738	−	0.376412i	0.0722953	−	0.0299457i
$159$	−0.813631	+	1.96428i	−0.0645251	+	0.155777i
$160$	10.0702	+	4.17120i	0.796116	+	0.329762i
$161$	0.371216	−	0.371216i	0.0292559	−	0.0292559i
$162$	1.30656	−	1.30656i	0.102653	−	0.102653i
$163$	−19.1451	−	7.93015i	−1.49956	−	0.621137i	−0.526186	−	0.850369i	$-0.676379\pi$
$163$	−19.1451	−	7.93015i	−1.49956	−	0.621137i	−0.973372	+	0.229232i	$0.926379\pi$
$164$	−0.149786	+	0.361616i	−0.0116963	+	0.0282374i
$165$	7.49242	−	3.10346i	0.583284	−	0.241604i
$166$			4.07144i			0.316005i
$167$	−3.09545	−	7.47308i	−0.239533	−	0.578285i	0.757701	−	0.652601i	$-0.226322\pi$
$167$	−3.09545	−	7.47308i	−0.239533	−	0.578285i	−0.997235	+	0.0743169i	$0.976322\pi$
$168$	−0.116520	−	0.116520i	−0.00898973	−	0.00898973i
$169$	−2.56261			−0.197124
$170$		0			0
$171$	−6.57900			−0.503109
$172$	−6.34277	−	6.34277i	−0.483632	−	0.483632i
$173$	−0.444151	−	1.07228i	−0.0337682	−	0.0815236i	0.906096	−	0.423073i	$-0.139048\pi$
$173$	−0.444151	−	1.07228i	−0.0337682	−	0.0815236i	−0.939864	+	0.341549i	$0.889048\pi$
$174$		−	4.14386i		−	0.314145i
$175$	0.337260	−	0.139697i	0.0254944	−	0.0105601i
$176$	9.28931	−	22.4264i	0.700208	−	1.69045i
$177$	1.22304	+	0.506602i	0.0919297	+	0.0380785i
$178$	9.99321	−	9.99321i	0.749023	−	0.749023i
$179$	−2.04826	+	2.04826i	−0.153094	+	0.153094i	−0.779499	−	0.626404i	$-0.784526\pi$
$179$	−2.04826	+	2.04826i	−0.153094	+	0.153094i	0.626404	+	0.779499i	$0.284526\pi$
$180$	−2.10765	−	0.873017i	−0.157095	−	0.0650709i
$181$	0.322485	−	0.778548i	0.0239701	−	0.0578690i	−0.911441	−	0.411430i	$-0.865029\pi$
$181$	0.322485	−	0.778548i	0.0239701	−	0.0578690i	0.935411	+	0.353561i	$0.115029\pi$
$182$	1.02526	−	0.424676i	0.0759972	−	0.0314791i
$183$			8.27836i			0.611954i
$184$	1.42835	+	3.44834i	0.105299	+	0.254215i
$185$	−12.1778	−	12.1778i	−0.895331	−	0.895331i
$186$	4.75699			0.348799
$187$		0			0
$188$	13.8899			1.01302
$189$	0.107651	+	0.107651i	0.00783043	+	0.00783043i
$190$	7.50435	+	18.1171i	0.544423	+	1.31435i
$191$			9.97069i			0.721454i	0.932671	+	0.360727i	$0.117471\pi$
$191$			9.97069i			0.721454i	−0.932671	+	0.360727i	$0.882529\pi$
$192$	−2.61313	+	1.08239i	−0.188586	+	0.0781149i
$193$	1.42901	−	3.44993i	0.102862	−	0.248332i	−0.864067	−	0.503377i	$-0.832091\pi$
$193$	1.42901	−	3.44993i	0.102862	−	0.248332i	0.966929	+	0.255046i	$0.0820905\pi$
$194$	6.15640	+	2.55007i	0.442004	+	0.183084i
$195$	−4.49981	+	4.49981i	−0.322238	+	0.322238i
$196$	6.97682	−	6.97682i	0.498344	−	0.498344i
$197$	14.9718	+	6.20151i	1.06669	+	0.441839i	0.845823	−	0.533464i	$-0.179110\pi$
$197$	14.9718	+	6.20151i	1.06669	+	0.441839i	0.220871	+	0.975303i	$0.429110\pi$
$198$	−3.55487	+	8.58221i	−0.252633	+	0.609911i
$199$	−15.2195	+	6.30411i	−1.07888	+	0.446886i	−0.850116	−	0.526596i	$-0.823468\pi$
$199$	−15.2195	+	6.30411i	−1.07888	+	0.446886i	−0.228763	+	0.973482i	$0.573468\pi$
$200$			2.59539i			0.183522i
$201$	−2.72078	−	6.56854i	−0.191909	−	0.463309i
$202$	−11.9382	−	11.9382i	−0.839966	−	0.839966i
$203$	0.341422			0.0239631
$204$		0			0
$205$	0.446463			0.0311823
$206$	9.90195	+	9.90195i	0.689902	+	0.689902i
$207$	−1.31962	−	3.18585i	−0.0917202	−	0.221432i
$208$			19.0479i			1.32073i
$209$	30.5572	−	12.6572i	2.11368	−	0.875517i
$210$	0.173654	−	0.419238i	0.0119833	−	0.0289302i
$211$	9.87510	+	4.09040i	0.679830	+	0.281595i	0.695756	−	0.718278i	$-0.255070\pi$
$211$	9.87510	+	4.09040i	0.679830	+	0.281595i	−0.0159259	+	0.999873i	$0.505070\pi$
$212$	−2.12612	+	2.12612i	−0.146023	+	0.146023i
$213$	−4.62951	+	4.62951i	−0.317209	+	0.317209i
$214$	−31.5245	−	13.0579i	−2.15497	−	0.892619i
$215$	−3.91550	+	9.45285i	−0.267035	+	0.644679i
$216$	−1.00000	+	0.414214i	−0.0680414	+	0.0281837i
$217$			0.391939i			0.0266065i
$218$	−7.59379	−	18.3330i	−0.514317	−	1.24167i
$219$	−5.88764	−	5.88764i	−0.397850	−	0.397850i
$220$	11.4689			0.773233
$221$		0			0
$222$	19.7270			1.32399
$223$	−3.83004	−	3.83004i	−0.256479	−	0.256479i	0.567142	−	0.823620i	$-0.308049\pi$
$223$	−3.83004	−	3.83004i	−0.256479	−	0.256479i	−0.823620	+	0.567142i	$0.808049\pi$
$224$	−0.393663	−	0.950385i	−0.0263027	−	0.0635003i
$225$		−	2.39782i		−	0.159855i
$226$	2.85935	−	1.18438i	0.190201	−	0.0787838i
$227$	−4.70650	+	11.3625i	−0.312381	+	0.754155i	0.687235	+	0.726436i	$0.258824\pi$
$227$	−4.70650	+	11.3625i	−0.312381	+	0.754155i	−0.999616	+	0.0277193i	$0.991176\pi$
$228$	−8.59588	−	3.56053i	−0.569276	−	0.235802i
$229$	21.2951	−	21.2951i	1.40722	−	1.40722i	0.633362	−	0.773856i	$-0.281674\pi$
$229$	21.2951	−	21.2951i	1.40722	−	1.40722i	0.773856	−	0.633362i	$-0.218326\pi$
$230$	−7.26790	+	7.26790i	−0.479231	+	0.479231i
$231$	−0.707107	−	0.292893i	−0.0465242	−	0.0192710i
$232$	−0.928932	+	2.24264i	−0.0609874	+	0.147237i
$233$	8.11649	−	3.36196i	0.531729	−	0.220249i	−0.100631	−	0.994924i	$-0.532086\pi$
$233$	8.11649	−	3.36196i	0.531729	−	0.220249i	0.632360	+	0.774674i	$0.282086\pi$
$234$		−	7.28931i		−	0.476517i
$235$	−6.06306	−	14.6375i	−0.395510	−	0.954847i
$236$	1.32381	+	1.32381i	0.0861729	+	0.0861729i
$237$	0.532327			0.0345783
$238$		0			0
$239$	14.6501			0.947634			0.473817	−	0.880623i	$-0.342876\pi$
$239$	14.6501			0.947634			0.473817	+	0.880623i	$0.342876\pi$
$240$	5.50756	+	5.50756i	0.355511	+	0.355511i
$241$	6.48849	+	15.6646i	0.417960	+	1.00905i	0.982938	+	0.183939i	$0.0588849\pi$
$241$	6.48849	+	15.6646i	0.417960	+	1.00905i	−0.564977	+	0.825106i	$0.691115\pi$
$242$		−	26.3752i		−	1.69546i
$243$	0.923880	−	0.382683i	0.0592669	−	0.0245492i
$244$	−4.48022	+	10.8162i	−0.286816	+	0.692436i
$245$	−10.3978	−	4.30691i	−0.664291	−	0.275158i
$246$	−0.361616	+	0.361616i	−0.0230558	+	0.0230558i
$247$	−18.3521	+	18.3521i	−1.16772	+	1.16772i
$248$	−2.57446	−	1.06638i	−0.163479	−	0.0677150i
$249$	−0.843223	+	2.03572i	−0.0534371	+	0.129009i
$250$	−20.3720	+	8.43835i	−1.28844	+	0.533688i
$251$			13.9453i			0.880217i	0.897945	+	0.440109i	$0.145060\pi$
$251$			13.9453i			0.880217i	−0.897945	+	0.440109i	$0.854940\pi$
$252$	0.0823922	+	0.198912i	0.00519022	+	0.0125303i
$253$	12.2584	+	12.2584i	0.770678	+	0.770678i
$254$	−22.5079			−1.41227
$255$		0			0
$256$	20.9706			1.31066
$257$	−13.9019	−	13.9019i	−0.867180	−	0.867180i	0.124980	−	0.992159i	$-0.460113\pi$
$257$	−13.9019	−	13.9019i	−0.867180	−	0.867180i	−0.992159	+	0.124980i	$0.960113\pi$
$258$	−4.48502	−	10.8278i	−0.279225	−	0.674109i
$259$			1.62535i			0.100994i
$260$	−8.31457	+	3.44401i	−0.515648	+	0.213588i
$261$	0.858221	−	2.07193i	0.0531226	−	0.128249i
$262$	17.8412	+	7.39008i	1.10224	+	0.456561i
$263$	−19.7085	+	19.7085i	−1.21528	+	1.21528i	−0.246015	+	0.969266i	$0.579121\pi$
$263$	−19.7085	+	19.7085i	−1.21528	+	1.21528i	−0.969266	+	0.246015i	$0.920879\pi$
$264$	3.84776	−	3.84776i	0.236813	−	0.236813i
$265$	3.16863	+	1.31249i	0.194647	+	0.0806256i
$266$	0.708233	−	1.70983i	0.0434246	−	0.104836i
$267$	7.06627	−	2.92694i	0.432449	−	0.179126i
$268$		−	10.0547i		−	0.614187i
$269$	0.0785753	+	0.189698i	0.00479082	+	0.0115661i	0.926257	−	0.376893i	$-0.123008\pi$
$269$	0.0785753	+	0.189698i	0.00479082	+	0.0115661i	−0.921466	+	0.388459i	$0.873008\pi$
$270$	−2.10765	−	2.10765i	−0.128268	−	0.128268i
$271$	8.21077			0.498768			0.249384	−	0.968405i	$-0.419772\pi$
$271$	8.21077			0.498768			0.249384	+	0.968405i	$0.419772\pi$
$272$		0			0
$273$	0.600582			0.0363489
$274$	17.6291	+	17.6291i	1.06502	+	1.06502i
$275$	4.61313	+	11.1371i	0.278182	+	0.671591i
$276$		−	4.87669i		−	0.293542i
$277$	−21.7737	+	9.01896i	−1.30825	+	0.541897i	−0.924374	−	0.381486i	$-0.875412\pi$
$277$	−21.7737	+	9.01896i	−1.30825	+	0.541897i	−0.383880	+	0.923383i	$0.625412\pi$
$278$	3.76745	−	9.09542i	0.225957	−	0.545507i
$279$	2.37849	+	0.985204i	0.142397	+	0.0589826i
$280$	−0.187962	+	0.187962i	−0.0112329	+	0.0112329i
$281$	7.17941	−	7.17941i	0.428288	−	0.428288i	−0.459757	−	0.888045i	$-0.652064\pi$
$281$	7.17941	−	7.17941i	0.428288	−	0.428288i	0.888045	+	0.459757i	$0.152064\pi$
$282$	16.7666	+	6.94495i	0.998436	+	0.413566i
$283$	−3.62753	+	8.75762i	−0.215634	+	0.520587i	−0.994271	−	0.106888i	$-0.965911\pi$
$283$	−3.62753	+	8.75762i	−0.215634	+	0.520587i	0.778637	+	0.627475i	$0.215911\pi$
$284$	−8.55423	+	3.54328i	−0.507600	+	0.210255i
$285$			10.6128i			0.628645i
$286$	14.0238	+	33.8563i	0.829242	+	2.00197i
$287$	−0.0297943	−	0.0297943i	−0.00175870	−	0.00175870i
$288$	−6.75699			−0.398159
$289$		0			0
$290$	−6.68457			−0.392531
$291$	2.55007	+	2.55007i	0.149487	+	0.149487i
$292$	−4.50621	−	10.8789i	−0.263706	−	0.636642i
$293$			9.28515i			0.542444i	0.962517	+	0.271222i	$0.0874278\pi$
$293$			9.28515i			0.542444i	−0.962517	+	0.271222i	$0.912572\pi$
$294$	11.9102	−	4.93336i	0.694616	−	0.287719i
$295$	0.817212	−	1.97292i	0.0475799	−	0.114868i
$296$	−10.6762	−	4.42222i	−0.620541	−	0.257036i
$297$	−3.55487	+	3.55487i	−0.206274	+	0.206274i
$298$	12.1757	−	12.1757i	0.705321	−	0.705321i
$299$	−12.5680	−	5.20584i	−0.726827	−	0.301062i
$300$	1.29769	−	3.13291i	0.0749224	−	0.180879i
$301$	0.892125	−	0.369530i	0.0514213	−	0.0212994i
$302$			22.1052i			1.27201i
$303$	−3.49661	−	8.44155i	−0.200875	−	0.484955i
$304$	22.4621	+	22.4621i	1.28829	+	1.28829i
$305$	13.3540			0.764650
$306$		0			0
$307$	−27.1418			−1.54906			−0.774531	−	0.632536i	$-0.782014\pi$
$307$	−27.1418			−1.54906			−0.774531	+	0.632536i	$0.782014\pi$
$308$	−0.765367	−	0.765367i	−0.0436108	−	0.0436108i
$309$	2.90021	+	7.00174i	0.164987	+	0.398315i
$310$		−	7.67362i		−	0.435832i
$311$	2.38896	−	0.989538i	0.135465	−	0.0561115i	−0.313921	−	0.949449i	$-0.601643\pi$
$311$	2.38896	−	0.989538i	0.135465	−	0.0561115i	0.449386	+	0.893338i	$0.351643\pi$
$312$	−1.63405	+	3.94495i	−0.0925099	+	0.223339i
$313$	−23.6610	−	9.80071i	−1.33740	−	0.553969i	−0.404643	−	0.914475i	$-0.632604\pi$
$313$	−23.6610	−	9.80071i	−1.33740	−	0.553969i	−0.932757	+	0.360506i	$0.882604\pi$
$314$	23.7204	−	23.7204i	1.33862	−	1.33862i
$315$	0.173654	−	0.173654i	0.00978429	−	0.00978429i
$316$	0.695518	+	0.288093i	0.0391260	+	0.0162065i
$317$	9.79601	−	23.6497i	0.550199	−	1.32830i	−0.367131	−	0.930169i	$-0.619660\pi$
$317$	9.79601	−	23.6497i	0.550199	−	1.32830i	0.917330	−	0.398128i	$-0.130340\pi$
$318$	−3.62951	+	1.50339i	−0.203533	+	0.0843062i
$319$			11.2745i			0.631252i
$320$	1.74603	+	4.21530i	0.0976063	+	0.235643i
$321$	−13.0579	−	13.0579i	−0.728820	−	0.728820i
$322$	0.970034			0.0540579
$323$		0			0
$324$	1.41421			0.0785674
$325$	−6.68873	−	6.68873i	−0.371024	−	0.371024i
$326$	−14.6530	−	35.3755i	−0.811555	−	1.95927i
$327$		−	10.7392i		−	0.593882i
$328$	0.276769	−	0.114641i	0.0152820	−	0.00633001i
$329$	−0.572209	+	1.38144i	−0.0315469	+	0.0761610i
$330$	13.8442	+	5.73445i	0.762097	+	0.315671i
$331$	−0.235588	+	0.235588i	−0.0129491	+	0.0129491i	−0.713552	−	0.700603i	$-0.752915\pi$
$331$	−0.235588	+	0.235588i	−0.0129491	+	0.0129491i	0.700603	+	0.713552i	$0.252915\pi$
$332$	−2.20345	+	2.20345i	−0.120930	+	0.120930i
$333$	9.86351	+	4.08560i	0.540517	+	0.223889i
$334$	5.71965	−	13.8085i	0.312965	−	0.755565i
$335$	−10.5959	+	4.38896i	−0.578914	+	0.239794i
$336$		−	0.735084i		−	0.0401021i
$337$	−1.43713	−	3.46953i	−0.0782853	−	0.188997i	0.879891	−	0.475175i	$-0.157615\pi$
$337$	−1.43713	−	3.46953i	−0.0782853	−	0.188997i	−0.958177	+	0.286178i	$0.907615\pi$
$338$	−3.34821	−	3.34821i	−0.182119	−	0.182119i
$339$	1.67497			0.0909717
$340$		0			0
$341$	−12.9427			−0.700886
$342$	−8.59588	−	8.59588i	−0.464812	−	0.464812i
$343$	0.814291	+	1.96587i	0.0439676	+	0.106147i
$344$			6.86537i			0.370156i
$345$	−5.13918	+	2.12872i	−0.276684	+	0.114606i
$346$	0.820684	−	1.98131i	0.0441202	−	0.106516i
$347$	−3.05804	−	1.26668i	−0.164164	−	0.0679989i	0.299088	−	0.954225i	$-0.403318\pi$
$347$	−3.05804	−	1.26668i	−0.164164	−	0.0679989i	−0.463252	+	0.886227i	$0.653318\pi$
$348$	2.24264	−	2.24264i	0.120218	−	0.120218i
$349$	−1.82779	+	1.82779i	−0.0978393	+	0.0978393i	−0.754332	−	0.656493i	$-0.772039\pi$
$349$	−1.82779	+	1.82779i	−0.0978393	+	0.0978393i	0.656493	+	0.754332i	$0.272039\pi$
$350$	0.623174	+	0.258127i	0.0333101	+	0.0137975i
$351$	1.50967	−	3.64466i	0.0805800	−	0.194537i
$352$	31.3839	−	12.9996i	1.67277	−	0.692882i
$353$		−	13.2848i		−	0.707079i	−0.935420	−	0.353539i	$-0.884978\pi$
$353$		−	13.2848i		−	0.707079i	0.935420	−	0.353539i	$-0.115022\pi$
$354$	0.936078	+	2.25989i	0.0497520	+	0.120112i
$355$	7.46799	+	7.46799i	0.396360	+	0.396360i
$356$	10.8166			0.573277
$357$		0			0
$358$	−5.35237			−0.282882
$359$	10.4143	+	10.4143i	0.549647	+	0.549647i	0.926339	−	0.376692i	$-0.122938\pi$
$359$	10.4143	+	10.4143i	0.549647	+	0.549647i	−0.376692	+	0.926339i	$0.622938\pi$
$360$	0.668179	+	1.61313i	0.0352161	+	0.0850192i
$361$			24.2832i			1.27806i
$362$	1.43857	−	0.595875i	0.0756095	−	0.0313185i
$363$	5.46248	−	13.1876i	0.286706	−	0.692169i
$364$	0.784699	+	0.325033i	0.0411294	+	0.0170364i
$365$	−9.49751	+	9.49751i	−0.497122	+	0.497122i
$366$	−10.8162	+	10.8162i	−0.565372	+	0.565372i
$367$	0.406470	+	0.168365i	0.0212176	+	0.00878861i	0.393267	−	0.919424i	$-0.371345\pi$
$367$	0.406470	+	0.168365i	0.0212176	+	0.00878861i	−0.372049	+	0.928213i	$0.621345\pi$
$368$	−6.37170	+	15.3827i	−0.332148	+	0.801876i
$369$	−0.255701	+	0.105915i	−0.0133113	+	0.00551370i
$370$		−	31.8222i		−	1.65436i
$371$	−0.123868	−	0.299044i	−0.00643090	−	0.0155256i
$372$	2.57446	+	2.57446i	0.133480	+	0.133480i
$373$	0.827899			0.0428670			0.0214335	−	0.999770i	$-0.493177\pi$
$373$	0.827899			0.0428670			0.0214335	+	0.999770i	$0.493177\pi$
$374$		0			0
$375$	−11.9336			−0.616250
$376$	−7.51716	−	7.51716i	−0.387668	−	0.387668i
$377$	−3.38564	−	8.17365i	−0.174369	−	0.420965i
$378$			0.281305i			0.0144687i
$379$	−18.3005	+	7.58033i	−0.940035	+	0.389375i	−0.799477	−	0.600697i	$-0.794890\pi$
$379$	−18.3005	+	7.58033i	−0.940035	+	0.389375i	−0.140558	+	0.990072i	$0.544890\pi$
$380$	−5.74358	+	13.8662i	−0.294639	+	0.711323i
$381$	−11.2539	−	4.66153i	−0.576557	−	0.238818i
$382$	−13.0273	+	13.0273i	−0.666537	+	0.666537i
$383$	11.7966	−	11.7966i	0.602776	−	0.602776i	−0.338273	−	0.941048i	$-0.609843\pi$
$383$	11.7966	−	11.7966i	0.602776	−	0.602776i	0.941048	+	0.338273i	$0.109843\pi$
$384$	7.65685	+	3.17157i	0.390737	+	0.161849i
$385$	−0.472474	+	1.14065i	−0.0240795	+	0.0581330i
$386$	6.37465	−	2.64047i	0.324461	−	0.134396i
$387$		−	6.34277i		−	0.322421i
$388$	1.95174	+	4.71191i	0.0990844	+	0.239211i
$389$	12.2315	+	12.2315i	0.620163	+	0.620163i	0.945573	−	0.325410i	$-0.105502\pi$
$389$	12.2315	+	12.2315i	0.620163	+	0.620163i	−0.325410	+	0.945573i	$0.605502\pi$
$390$	−11.7586			−0.595419
$391$		0			0
$392$	−7.55166			−0.381416
$393$	7.39008	+	7.39008i	0.372780	+	0.372780i
$394$	11.4589	+	27.6642i	0.577291	+	1.39370i
$395$		−	0.858710i		−	0.0432064i
$396$	−6.56854	+	2.72078i	−0.330081	+	0.136724i
$397$	−2.46473	+	5.95039i	−0.123701	+	0.298641i	−0.973583	−	0.228331i	$-0.926673\pi$
$397$	−2.46473	+	5.95039i	−0.123701	+	0.298641i	0.849882	+	0.526973i	$0.176673\pi$
$398$	−28.1219	−	11.6485i	−1.40962	−	0.583885i
$399$	0.708233	−	0.708233i	0.0354560	−	0.0354560i
$400$	−8.18669	+	8.18669i	−0.409334	+	0.409334i
$401$	19.4684	+	8.06407i	0.972204	+	0.402700i	0.811532	−	0.584308i	$-0.198634\pi$
$401$	19.4684	+	8.06407i	0.972204	+	0.402700i	0.160672	+	0.987008i	$0.448634\pi$
$402$	5.02734	−	12.1371i	0.250741	−	0.605342i
$403$	9.38303	−	3.88658i	0.467402	−	0.193604i
$404$		−	12.9218i		−	0.642882i
$405$	−0.617317	−	1.49033i	−0.0306747	−	0.0740553i
$406$	0.446089	+	0.446089i	0.0221390	+	0.0221390i
$407$	−53.6728			−2.66046
$408$		0			0
$409$	−27.6232			−1.36588			−0.682939	−	0.730475i	$-0.739299\pi$
$409$	−27.6232			−1.36588			−0.682939	+	0.730475i	$0.739299\pi$
$410$	0.583332	+	0.583332i	0.0288087	+	0.0288087i
$411$	5.16346	+	12.4657i	0.254694	+	0.614887i
$412$			10.7178i			0.528028i
$413$	−0.186197	+	0.0771255i	−0.00916218	+	0.00379510i
$414$	2.43835	−	5.88669i	0.119838	−	0.289315i
$415$	3.28387	+	1.36023i	0.161199	+	0.0667708i
$416$	−18.8486	+	18.8486i	−0.924129	+	0.924129i
$417$	3.76745	−	3.76745i	0.184493	−	0.184493i
$418$	56.4623	+	23.3875i	2.76166	+	1.14392i
$419$	−4.61170	+	11.1336i	−0.225297	+	0.543914i	−0.995594	−	0.0937711i	$-0.970108\pi$
$419$	−4.61170	+	11.1336i	−0.225297	+	0.543914i	0.770297	+	0.637685i	$0.220108\pi$
$420$	0.320871	−	0.132909i	0.0156569	−	0.00648529i
$421$		−	14.0183i		−	0.683210i	−0.939844	−	0.341605i	$-0.889029\pi$
$421$		−	14.0183i		−	0.683210i	0.939844	−	0.341605i	$-0.110971\pi$
$422$	7.55807	+	18.2468i	0.367921	+	0.888240i
$423$	6.94495	+	6.94495i	0.337675	+	0.337675i
$424$	2.30130			0.111761
$425$		0			0
$426$	−12.0975			−0.586126
$427$	−0.891171	−	0.891171i	−0.0431268	−	0.0431268i
$428$	−9.99407	−	24.1278i	−0.483082	−	1.16626i
$429$			19.8326i			0.957526i
$430$	−17.4666	+	7.23490i	−0.842314	+	0.348898i
$431$	1.31789	−	3.18166i	0.0634804	−	0.153255i	−0.888956	−	0.457992i	$-0.848569\pi$
$431$	1.31789	−	3.18166i	0.0634804	−	0.153255i	0.952436	+	0.304737i	$0.0985687\pi$
$432$	−4.46088	−	1.84776i	−0.214624	−	0.0889003i
$433$	3.93561	−	3.93561i	0.189133	−	0.189133i	−0.606188	−	0.795321i	$-0.707302\pi$
$433$	3.93561	−	3.93561i	0.189133	−	0.189133i	0.795321	+	0.606188i	$0.207302\pi$
$434$	−0.512092	+	0.512092i	−0.0245812	+	0.0245812i
$435$	−3.34228	−	1.38442i	−0.160250	−	0.0663778i
$436$	5.81204	−	14.0315i	0.278346	−	0.671987i
$437$	−20.9597	+	8.68180i	−1.00264	+	0.415307i
$438$		−	15.3852i		−	0.735131i
$439$	6.73002	+	16.2477i	0.321206	+	0.775461i	0.999184	+	0.0403786i	$0.0128564\pi$
$439$	6.73002	+	16.2477i	0.321206	+	0.775461i	−0.677978	+	0.735082i	$0.737144\pi$
$440$	−6.20692	−	6.20692i	−0.295903	−	0.295903i
$441$	6.97682			0.332230
$442$		0			0
$443$	5.87632			0.279192			0.139596	−	0.990209i	$-0.455420\pi$
$443$	5.87632			0.279192			0.139596	+	0.990209i	$0.455420\pi$
$444$	10.6762	+	10.6762i	0.506669	+	0.506669i
$445$	−4.72153	−	11.3988i	−0.223822	−	0.540354i
$446$		−	10.0084i		−	0.473911i
$447$	8.60954	−	3.56619i	0.407217	−	0.168675i
$448$	0.164784	−	0.397825i	0.00778533	−	0.0187955i
$449$	36.9378	+	15.3001i	1.74320	+	0.722058i	0.998505	+	0.0546546i	$0.0174058\pi$
$449$	36.9378	+	15.3001i	1.74320	+	0.722058i	0.744697	+	0.667403i	$0.232594\pi$
$450$	3.13291	−	3.13291i	0.147687	−	0.147687i
$451$	0.983875	−	0.983875i	0.0463289	−	0.0463289i
$452$	2.18845	+	0.906486i	0.102936	+	0.0426375i
$453$	−4.57814	+	11.0526i	−0.215100	+	0.519296i
$454$	−20.9951	+	8.69647i	−0.985351	+	0.408146i
$455$		−	0.968815i		−	0.0454188i
$456$	2.72511	+	6.57900i	0.127615	+	0.308090i
$457$	−12.5092	−	12.5092i	−0.585154	−	0.585154i	0.351161	−	0.936315i	$-0.385787\pi$
$457$	−12.5092	−	12.5092i	−0.585154	−	0.585154i	−0.936315	+	0.351161i	$0.885787\pi$
$458$	55.6467			2.60020
$459$		0			0
$460$	−7.86672			−0.366788
$461$	−21.1186	−	21.1186i	−0.983591	−	0.983591i	0.0162762	−	0.999868i	$-0.494819\pi$
$461$	−21.1186	−	21.1186i	−0.983591	−	0.983591i	−0.999868	+	0.0162762i	$0.994819\pi$
$462$	−0.541196	−	1.30656i	−0.0251787	−	0.0607868i
$463$			9.45213i			0.439278i	0.975581	+	0.219639i	$0.0704879\pi$
$463$			9.45213i			0.439278i	−0.975581	+	0.219639i	$0.929512\pi$
$464$	−10.0042	+	4.14386i	−0.464432	+	0.192374i
$465$	1.58926	−	3.83681i	0.0737001	−	0.177928i
$466$	14.9973	+	6.21209i	0.694737	+	0.287770i
$467$	−14.1488	+	14.1488i	−0.654726	+	0.654726i	−0.954127	−	0.299401i	$-0.903213\pi$
$467$	−14.1488	+	14.1488i	−0.654726	+	0.654726i	0.299401	+	0.954127i	$0.403213\pi$
$468$	3.94495	−	3.94495i	0.182355	−	0.182355i
$469$	1.00000	+	0.414214i	0.0461757	+	0.0191266i
$470$	11.2031	−	27.0466i	0.516759	−	1.24757i
$471$	16.7729	−	6.94755i	0.772852	−	0.320126i
$472$		−	1.43289i		−	0.0659539i
$473$	12.2027	+	29.4600i	0.561082	+	1.35457i
$474$	0.695518	+	0.695518i	0.0319462	+	0.0319462i
$475$	−15.7753			−0.723820
$476$		0			0
$477$	−2.12612			−0.0973484
$478$	19.1412	+	19.1412i	0.875500	+	0.875500i
$479$	0.461402	+	1.11392i	0.0210820	+	0.0508964i	0.934070	−	0.357090i	$-0.116231\pi$
$479$	0.461402	+	1.11392i	0.0210820	+	0.0508964i	−0.912988	+	0.407986i	$0.866231\pi$
$480$			10.8999i			0.497509i
$481$	38.9110	−	16.1175i	1.77419	−	0.734894i
$482$	−11.9892	+	28.9444i	−0.546091	+	1.31838i
$483$	0.485017	+	0.200901i	0.0220690	+	0.00914130i
$484$	14.2741	−	14.2741i	0.648825	−	0.648825i
$485$	4.11358	−	4.11358i	0.186788	−	0.186788i
$486$	1.70711	+	0.707107i	0.0774359	+	0.0320750i
$487$	4.57738	−	11.0508i	0.207421	−	0.500759i	−0.785595	−	0.618742i	$-0.787643\pi$
$487$	4.57738	−	11.0508i	0.207421	−	0.500759i	0.993016	+	0.117983i	$0.0376428\pi$
$488$	8.27836	−	3.42901i	0.374744	−	0.155224i
$489$		−	20.7225i		−	0.937103i
$490$	−7.95813	−	19.2126i	−0.359512	−	0.867938i
$491$	22.1064	+	22.1064i	0.997649	+	0.997649i	0.999997	−	0.00234871i	$-0.000747617\pi$
$491$	22.1064	+	22.1064i	0.997649	+	0.997649i	−0.00234871	+	0.999997i	$0.500748\pi$
$492$	−0.391410			−0.0176461
$493$		0			0
$494$	−47.9564			−2.15766
$495$	5.73445	+	5.73445i	0.257744	+	0.257744i
$496$	−4.75699	−	11.4844i	−0.213595	−	0.515664i
$497$		−	0.996740i		−	0.0447099i
$498$	−3.76152	+	1.55807i	−0.168558	+	0.0698189i
$499$	15.8274	−	38.2107i	0.708531	−	1.71055i	0.00489302	−	0.999988i	$-0.498442\pi$
$499$	15.8274	−	38.2107i	0.708531	−	1.71055i	0.703638	−	0.710558i	$-0.251558\pi$
$500$	−15.5920	−	6.45843i	−0.697297	−	0.288830i
$501$	5.71965	−	5.71965i	0.255535	−	0.255535i
$502$	−18.2204	+	18.2204i	−0.813215	+	0.813215i
$503$	2.84810	+	1.17972i	0.126991	+	0.0526013i	0.445274	−	0.895394i	$-0.353106\pi$
$503$	2.84810	+	1.17972i	0.126991	+	0.0526013i	−0.318283	+	0.947996i	$0.603106\pi$
$504$	0.0630603	−	0.152241i	0.00280893	−	0.00678135i
$505$	−13.6173	+	5.64047i	−0.605961	+	0.250997i
$506$			32.0327i			1.42403i
$507$	−0.980668	−	2.36754i	−0.0435530	−	0.105146i
$508$	−12.1812	−	12.1812i	−0.540452	−	0.540452i
$509$	33.8077			1.49850			0.749249	−	0.662288i	$-0.230415\pi$
$509$	33.8077			1.49850			0.749249	+	0.662288i	$0.230415\pi$
$510$		0			0
$511$	1.26762			0.0560760
$512$	15.6788	+	15.6788i	0.692910	+	0.692910i
$513$	−2.51767	−	6.07820i	−0.111158	−	0.268359i
$514$		−	36.3275i		−	1.60234i
$515$	11.2947	−	4.67841i	0.497703	−	0.206155i
$516$	3.43268	−	8.28723i	0.151115	−	0.364825i
$517$	−45.6181	−	18.8956i	−2.00628	−	0.831030i
$518$	−2.12363	+	2.12363i	−0.0933067	+	0.0933067i
$519$	0.820684	−	0.820684i	0.0360240	−	0.0360240i
$520$	6.36370	+	2.63593i	0.279067	+	0.115593i
$521$	−15.6731	+	37.8381i	−0.686649	+	1.65772i	0.0647762	+	0.997900i	$0.479367\pi$
$521$	−15.6731	+	37.8381i	−0.686649	+	1.65772i	−0.751425	+	0.659818i	$0.770633\pi$
$522$	3.82843	−	1.58579i	0.167566	−	0.0694080i
$523$			9.06788i			0.396511i	0.980150	+	0.198255i	$0.0635275\pi$
$523$			9.06788i			0.396511i	−0.980150	+	0.198255i	$0.936472\pi$
$524$	5.65612	+	13.6551i	0.247089	+	0.596525i
$525$	0.258127	+	0.258127i	0.0112656	+	0.0112656i
$526$	−51.5009			−2.24555
$527$		0			0
$528$	24.2741			1.05640
$529$	7.85521	+	7.85521i	0.341531	+	0.341531i
$530$	2.42516	+	5.85486i	0.105342	+	0.254319i
$531$			1.32381i			0.0574486i
$532$	1.30864	−	0.542058i	0.0567369	−	0.0235012i
$533$	−0.417828	+	1.00873i	−0.0180981	+	0.0436928i
$534$	13.0568	+	5.40829i	0.565021	+	0.234039i
$535$	−21.0640	+	21.0640i	−0.910677	+	0.910677i
$536$	−5.44155	+	5.44155i	−0.235039	+	0.235039i
$537$	−2.67619	−	1.10851i	−0.115486	−	0.0478359i
$538$	−0.145188	+	0.350515i	−0.00625951	+	0.0151118i
$539$	−32.4049	+	13.4226i	−1.39578	+	0.578151i
$540$		−	2.28130i		−	0.0981717i
$541$	4.95269	+	11.9569i	0.212933	+	0.514065i	0.993871	−	0.110543i	$-0.0352588\pi$
$541$	4.95269	+	11.9569i	0.212933	+	0.514065i	−0.780939	+	0.624608i	$0.785259\pi$
$542$	10.7279	+	10.7279i	0.460802	+	0.460802i
$543$	0.842695			0.0361635
$544$		0			0
$545$	−17.3238			−0.742068
$546$	0.784699	+	0.784699i	0.0335820	+	0.0335820i
$547$	4.07934	+	9.84840i	0.174420	+	0.421087i	0.986779	−	0.162070i	$-0.0518171\pi$
$547$	4.07934	+	9.84840i	0.174420	+	0.421087i	−0.812359	+	0.583157i	$0.801817\pi$
$548$			19.0816i			0.815127i
$549$	−7.64821	+	3.16799i	−0.326418	+	0.135207i
$550$	−8.52395	+	20.5786i	−0.363462	+	0.877475i
$551$	−13.6312	−	5.64624i	−0.580710	−	0.240538i
$552$	−2.63925	+	2.63925i	−0.112334	+	0.112334i
$553$	−0.0573053	+	0.0573053i	−0.00243687	+	0.00243687i
$554$	−40.2325	−	16.6649i	−1.70932	−	0.708022i
$555$	6.59059	−	15.9111i	0.279755	−	0.675388i
$556$	6.96134	−	2.88348i	0.295226	−	0.122287i
$557$			30.1933i			1.27933i	0.768653	+	0.639667i	$0.220928\pi$
$557$			30.1933i			1.27933i	−0.768653	+	0.639667i	$0.779072\pi$
$558$	1.82042	+	4.39488i	0.0770645	+	0.186050i
$559$	−17.6932	−	17.6932i	−0.748341	−	0.748341i
$560$	−1.18578			−0.0501085
$561$		0			0
$562$	18.7607			0.791372
$563$	21.1592	+	21.1592i	0.891755	+	0.891755i	0.994688	−	0.102934i	$-0.0328229\pi$
$563$	21.1592	+	21.1592i	0.891755	+	0.891755i	−0.102934	+	0.994688i	$0.532823\pi$
$564$	5.31543	+	12.8326i	0.223820	+	0.540349i
$565$		−	2.70193i		−	0.113671i
$566$	−16.1820	+	6.70279i	−0.680179	+	0.281739i
$567$	−0.0582601	+	0.140652i	−0.00244669	+	0.00590684i
$568$	6.54712	+	2.71191i	0.274711	+	0.113789i
$569$	18.1692	−	18.1692i	0.761694	−	0.761694i	−0.214935	−	0.976628i	$-0.568954\pi$
$569$	18.1692	−	18.1692i	0.761694	−	0.761694i	0.976628	+	0.214935i	$0.0689538\pi$
$570$	−13.8662	+	13.8662i	−0.580792	+	0.580792i
$571$	25.8818	+	10.7206i	1.08312	+	0.448643i	0.851603	−	0.524187i	$-0.175631\pi$
$571$	25.8818	+	10.7206i	1.08312	+	0.448643i	0.231518	+	0.972831i	$0.425631\pi$
$572$	−10.7333	+	25.9125i	−0.448783	+	1.08346i
$573$	−9.21172	+	3.81562i	−0.384825	+	0.159400i
$574$		−	0.0778563i		−	0.00324966i
$575$	−3.16423	−	7.63912i	−0.131957	−	0.318573i
$576$	−2.00000	−	2.00000i	−0.0833333	−	0.0833333i
$577$	11.8072			0.491538			0.245769	−	0.969328i	$-0.420959\pi$
$577$	11.8072			0.491538			0.245769	+	0.969328i	$0.420959\pi$
$578$		0			0
$579$	3.73418			0.155187
$580$	−3.61766	−	3.61766i	−0.150215	−	0.150215i
$581$	−0.128373	−	0.309920i	−0.00532581	−	0.0128576i
$582$			6.66364i			0.276217i
$583$	9.87510	−	4.09040i	0.408985	−	0.169407i
$584$	−3.44890	+	8.32638i	−0.142717	+	0.344548i
$585$	−5.87929	−	2.43528i	−0.243079	−	0.100686i
$586$	−12.1316	+	12.1316i	−0.501153	+	0.501153i
$587$	−5.26250	+	5.26250i	−0.217207	+	0.217207i	−0.807320	−	0.590114i	$-0.799083\pi$
$587$	−5.26250	+	5.26250i	−0.217207	+	0.217207i	0.590114	+	0.807320i	$0.299083\pi$
$588$	9.11566	+	3.77583i	0.375923	+	0.155713i
$589$	6.48165	−	15.6481i	0.267072	−	0.644769i
$590$	3.64549	−	1.51001i	0.150082	−	0.0621662i
$591$			16.2053i			0.666598i
$592$	−19.7270	−	47.6252i	−0.810776	−	1.95739i
$593$	5.41074	+	5.41074i	0.222193	+	0.222193i	0.809421	−	0.587229i	$-0.199781\pi$
$593$	5.41074	+	5.41074i	0.222193	+	0.222193i	−0.587229	+	0.809421i	$0.699781\pi$
$594$	−9.28931			−0.381145
$595$		0			0
$596$	13.1789			0.539830
$597$	−11.6485	−	11.6485i	−0.476740	−	0.476740i
$598$	−9.61915	−	23.2227i	−0.393356	−	0.949646i
$599$			16.1547i			0.660062i	0.943970	+	0.330031i	$0.107059\pi$
$599$			16.1547i			0.660062i	−0.943970	+	0.330031i	$0.892941\pi$
$600$	−2.39782	+	0.993212i	−0.0978908	+	0.0405477i
$601$	−10.9897	+	26.5316i	−0.448281	+	1.08225i	0.524685	+	0.851296i	$0.324183\pi$
$601$	−10.9897	+	26.5316i	−0.448281	+	1.08225i	−0.972966	+	0.230949i	$0.925817\pi$
$602$	1.64843	+	0.682803i	0.0671851	+	0.0278290i
$603$	5.02734	−	5.02734i	0.204729	−	0.204729i
$604$	−11.9632	+	11.9632i	−0.486778	+	0.486778i
$605$	−21.2732	−	8.81166i	−0.864880	−	0.358245i
$606$	6.46088	−	15.5980i	0.262456	−	0.633624i
$607$	23.8480	−	9.87815i	0.967959	−	0.400942i	0.158007	−	0.987438i	$-0.449493\pi$
$607$	23.8480	−	9.87815i	0.967959	−	0.400942i	0.809952	+	0.586496i	$0.199493\pi$
$608$			44.4542i			1.80286i
$609$	0.130656	+	0.315433i	0.00529447	+	0.0127820i
$610$	17.4479	+	17.4479i	0.706445	+	0.706445i
$611$	38.7458			1.56749
$612$		0			0
$613$	49.1769			1.98623			0.993117	−	0.117123i	$-0.0373670\pi$
$613$	49.1769			1.98623			0.993117	+	0.117123i	$0.0373670\pi$
$614$	−35.4624	−	35.4624i	−1.43115	−	1.43115i
$615$	0.170854	+	0.412478i	0.00688949	+	0.0166327i
$616$			0.828427i			0.0333783i
$617$	−3.28044	+	1.35880i	−0.132066	+	0.0547034i	−0.447738	−	0.894165i	$-0.647770\pi$
$617$	−3.28044	+	1.35880i	−0.132066	+	0.0547034i	0.315672	+	0.948868i	$0.397770\pi$
$618$	−5.35890	+	12.9375i	−0.215566	+	0.520423i
$619$	32.5216	+	13.4709i	1.30715	+	0.541440i	0.924052	−	0.382266i	$-0.124856\pi$
$619$	32.5216	+	13.4709i	1.30715	+	0.541440i	0.383101	+	0.923707i	$0.374856\pi$
$620$	4.15293	−	4.15293i	0.166786	−	0.166786i
$621$	2.43835	−	2.43835i	0.0978474	−	0.0978474i
$622$	4.41421	+	1.82843i	0.176994	+	0.0733132i
$623$	−0.445601	+	1.07578i	−0.0178526	+	0.0431000i
$624$	−17.5980	+	7.28931i	−0.704482	+	0.291806i
$625$			7.26131i			0.290453i
$626$	−18.1094	−	43.7199i	−0.723796	−	1.74740i
$627$	23.3875	+	23.3875i	0.934005	+	0.934005i
$628$	25.6748			1.02454
$629$		0			0
$630$	0.453780			0.0180790
$631$	22.2124	+	22.2124i	0.884262	+	0.884262i	0.993964	−	0.109702i	$-0.0349898\pi$
$631$	22.2124	+	22.2124i	0.884262	+	0.884262i	−0.109702	+	0.993964i	$0.534990\pi$
$632$	−0.220497	−	0.532327i	−0.00877089	−	0.0211748i
$633$			10.6887i			0.424839i
$634$	43.6989	−	18.1007i	1.73550	−	0.718869i
$635$	−7.51964	+	18.1540i	−0.298408	+	0.720420i
$636$	−2.77791	−	1.15065i	−0.110151	−	0.0456262i
$637$	19.4618	−	19.4618i	0.771106	−	0.771106i
$638$	−14.7309	+	14.7309i	−0.583201	+	0.583201i
$639$	−6.04875	−	2.50548i	−0.239285	−	0.0991151i
$640$	5.11615	−	12.3515i	0.202233	−	0.488235i
$641$	−24.5525	+	10.1700i	−0.969767	+	0.401691i	−0.810625	−	0.585565i	$-0.800873\pi$
$641$	−24.5525	+	10.1700i	−0.969767	+	0.401691i	−0.159141	+	0.987256i	$0.550873\pi$
$642$		−	34.1219i		−	1.34668i
$643$	−6.13238	−	14.8049i	−0.241837	−	0.583847i	0.755628	−	0.655001i	$-0.227332\pi$
$643$	−6.13238	−	14.8049i	−0.241837	−	0.583847i	−0.997465	+	0.0711538i	$0.977332\pi$
$644$	0.524979	+	0.524979i	0.0206871	+	0.0206871i
$645$	−10.2317			−0.402872
$646$		0			0
$647$	41.6554			1.63764			0.818822	−	0.574048i	$-0.194628\pi$
$647$	41.6554			1.63764			0.818822	+	0.574048i	$0.194628\pi$
$648$	−0.765367	−	0.765367i	−0.0300665	−	0.0300665i
$649$	−2.54686	−	6.14866i	−0.0999729	−	0.241356i
$650$		−	17.4785i		−	0.685563i
$651$	−0.362104	+	0.149988i	−0.0141920	+	0.00587851i
$652$	11.2149	−	27.0752i	0.439210	−	1.06035i
$653$	11.3881	+	4.71711i	0.445652	+	0.184595i	0.594212	−	0.804308i	$-0.297464\pi$
$653$	11.3881	+	4.71711i	0.445652	+	0.184595i	−0.148560	+	0.988903i	$0.547464\pi$
$654$	14.0315	−	14.0315i	0.548675	−	0.548675i
$655$	11.9211	−	11.9211i	0.465797	−	0.465797i
$656$	1.23463	+	0.511402i	0.0482043	+	0.0199669i
$657$	3.18637	−	7.69258i	0.124312	−	0.300116i
$658$	−2.55256	+	1.05731i	−0.0995092	+	0.0412181i
$659$		−	3.46449i		−	0.134957i	−0.997721	−	0.0674786i	$-0.978505\pi$
$659$		−	3.46449i		−	0.134957i	0.997721	−	0.0674786i	$-0.0214955\pi$
$660$	4.38896	+	10.5959i	0.170840	+	0.412444i
$661$	−20.0276	−	20.0276i	−0.778984	−	0.778984i	0.200674	−	0.979658i	$-0.435687\pi$
$661$	−20.0276	−	20.0276i	−0.778984	−	0.778984i	−0.979658	+	0.200674i	$0.935687\pi$
$662$	−0.615621			−0.0239268
$663$		0			0
$664$	2.38500			0.0925558
$665$	−1.14247	−	1.14247i	−0.0443031	−	0.0443031i
$666$	7.54920	+	18.2254i	0.292526	+	0.706220i
$667$		−	7.73339i		−	0.299438i
$668$	10.5685	−	4.37763i	0.408909	−	0.169376i
$669$	2.07280	−	5.00419i	0.0801392	−	0.193473i
$670$	−19.5786	−	8.10973i	−0.756388	−	0.313306i
$671$	29.4285	−	29.4285i	1.13607	−	1.13607i
$672$	0.727394	−	0.727394i	0.0280598	−	0.0280598i
$673$	−26.2461	−	10.8715i	−1.01171	−	0.419065i	−0.185634	−	0.982619i	$-0.559434\pi$
$673$	−26.2461	−	10.8715i	−1.01171	−	0.419065i	−0.826079	+	0.563554i	$0.809434\pi$
$674$	2.65546	−	6.41086i	0.102285	−	0.246937i
$675$	2.21530	−	0.917608i	0.0852670	−	0.0353187i
$676$		−	3.62408i		−	0.139388i
$677$	7.38512	+	17.8293i	0.283833	+	0.685234i	0.999918	−	0.0127789i	$-0.00406775\pi$
$677$	7.38512	+	17.8293i	0.283833	+	0.685234i	−0.716085	+	0.698013i	$0.754068\pi$
$678$	2.18845	+	2.18845i	0.0840469	+	0.0840469i
$679$	−0.549032			−0.0210699
$680$		0			0
$681$	−12.2987			−0.471286
$682$	−16.9104	−	16.9104i	−0.647534	−	0.647534i
$683$	7.45441	+	17.9965i	0.285235	+	0.688618i	0.999942	−	0.0108060i	$-0.00343973\pi$
$683$	7.45441	+	17.9965i	0.285235	+	0.688618i	−0.714707	+	0.699424i	$0.753440\pi$
$684$		−	9.30411i		−	0.355751i
$685$	20.1087	−	8.32930i	0.768315	−	0.318246i
$686$	−1.50461	+	3.63246i	−0.0574464	+	0.138688i
$687$	27.8233	+	11.5248i	1.06153	+	0.439699i
$688$	−21.6556	+	21.6556i	−0.825611	+	0.825611i
$689$	−5.93081	+	5.93081i	−0.225946	+	0.225946i
$690$	−9.49597	−	3.93336i	−0.361505	−	0.149740i
$691$	−2.88520	+	6.96550i	−0.109758	+	0.264980i	−0.969209	−	0.246238i	$-0.920806\pi$
$691$	−2.88520	+	6.96550i	−0.109758	+	0.264980i	0.859451	+	0.511218i	$0.170806\pi$
$692$	1.51643	−	0.628124i	0.0576459	−	0.0238777i
$693$		−	0.765367i		−	0.0290739i
$694$	−2.34052	−	5.65051i	−0.0888449	−	0.214491i
$695$	−6.07737	−	6.07737i	−0.230528	−	0.230528i
$696$	−2.42742			−0.0920110
$697$		0			0
$698$	−4.77624			−0.180783
$699$	6.21209	+	6.21209i	0.234963	+	0.234963i
$700$	0.197562	+	0.476957i	0.00746714	+	0.0180273i
$701$		−	39.0875i		−	1.47632i	−0.674628	−	0.738158i	$-0.735696\pi$
$701$		−	39.0875i		−	1.47632i	0.674628	−	0.738158i	$-0.264304\pi$
$702$	6.73445	−	2.78950i	0.254175	−	0.105283i
$703$	26.8792	−	64.8920i	1.01377	−	2.44745i
$704$	13.1371	+	5.44155i	0.495122	+	0.205086i
$705$	11.2031	−	11.2031i	0.421932	−	0.421932i
$706$	17.3574	−	17.3574i	0.653256	−	0.653256i
$707$	1.28515	+	0.532327i	0.0483330	+	0.0200202i
$708$	−0.716443	+	1.72965i	−0.0269256	+	0.0650041i
$709$	6.20186	−	2.56889i	0.232916	−	0.0964768i	−0.263173	−	0.964749i	$-0.584769\pi$
$709$	6.20186	−	2.56889i	0.232916	−	0.0964768i	0.496089	+	0.868272i	$0.334769\pi$
$710$			19.5148i			0.732377i
$711$	0.203713	+	0.491806i	0.00763982	+	0.0184442i
$712$	−5.85389	−	5.85389i	−0.219384	−	0.219384i
$713$	8.87762			0.332470
$714$		0			0
$715$	31.9925			1.19645
$716$	−2.89668	−	2.89668i	−0.108254	−	0.108254i
$717$	5.60634	+	13.5349i	0.209373	+	0.505470i
$718$			27.2140i			1.01562i
$719$	−6.84246	+	2.83424i	−0.255181	+	0.105699i	−0.506607	−	0.862177i	$-0.669100\pi$
$719$	−6.84246	+	2.83424i	−0.255181	+	0.105699i	0.251426	+	0.967876i	$0.419100\pi$
$720$	−2.98067	+	7.19597i	−0.111083	+	0.268178i
$721$	−1.06595	−	0.441531i	−0.0396981	−	0.0164435i
$722$	−31.7275	+	31.7275i	−1.18078	+	1.18078i
$723$	−11.9892	+	11.9892i	−0.445882	+	0.445882i
$724$	1.10103	+	0.456063i	0.0409196	+	0.0169494i
$725$	2.05786	−	4.96812i	0.0764272	−	0.184512i
$726$	24.3675	−	10.0933i	0.904362	−	0.374599i
$727$			6.36054i			0.235899i	0.993020	+	0.117950i	$0.0376322\pi$
$727$			6.36054i			0.235899i	−0.993020	+	0.117950i	$0.962368\pi$
$728$	−0.248769	−	0.600582i	−0.00922001	−	0.0222591i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	−24.8182			−0.918562
$731$		0			0
$732$	−11.7074			−0.432717
$733$	29.2273	+	29.2273i	1.07954	+	1.07954i	0.996551	+	0.0829857i	$0.0264456\pi$
$733$	29.2273	+	29.2273i	1.07954	+	1.07954i	0.0829857	+	0.996551i	$0.473554\pi$
$734$	0.311099	+	0.751059i	0.0114829	+	0.0277221i
$735$		−	11.2545i		−	0.415128i
$736$	−21.5268	+	8.91667i	−0.793487	+	0.328673i
$737$	−13.6783	+	33.0223i	−0.503845	+	1.21639i
$738$	−0.472474	−	0.195705i	−0.0173920	−	0.00720400i
$739$	16.3803	−	16.3803i	0.602561	−	0.602561i	−0.338430	−	0.940991i	$-0.609896\pi$
$739$	16.3803	−	16.3803i	0.602561	−	0.602561i	0.940991	+	0.338430i	$0.109896\pi$
$740$	17.2220	−	17.2220i	0.633095	−	0.633095i
$741$	−23.9782	−	9.93209i	−0.880861	−	0.364864i
$742$	0.228878	−	0.552561i	0.00840238	−	0.0202851i
$743$	35.2464	−	14.5995i	1.29307	−	0.535606i	0.373168	−	0.927764i	$-0.378271\pi$
$743$	35.2464	−	14.5995i	1.29307	−	0.535606i	0.919898	+	0.392158i	$0.128271\pi$
$744$		−	2.78658i		−	0.102161i
$745$	−5.75271	−	13.8883i	−0.210763	−	0.508827i
$746$	1.08170	+	1.08170i	0.0396039	+	0.0396039i
$747$	−2.20345			−0.0806200
$748$		0			0
$749$	2.81138			0.102726
$750$	−15.5920	−	15.5920i	−0.569340	−	0.569340i
$751$	−13.0906	−	31.6034i	−0.477681	−	1.15322i	−0.960694	−	0.277611i	$-0.910457\pi$
$751$	−13.0906	−	31.6034i	−0.477681	−	1.15322i	0.483013	−	0.875613i	$-0.339543\pi$
$752$		−	47.4231i		−	1.72934i
$753$	−12.8837	+	5.33662i	−0.469510	+	0.194477i
$754$	6.25584	−	15.1029i	0.227824	−	0.550017i
$755$	17.8292	+	7.38511i	0.648872	+	0.268772i
$756$	−0.152241	+	0.152241i	−0.00553695	+	0.00553695i
$757$	4.96523	−	4.96523i	0.180465	−	0.180465i	−0.611094	−	0.791558i	$-0.709270\pi$
$757$	4.96523	−	4.96523i	0.180465	−	0.180465i	0.791558	+	0.611094i	$0.209270\pi$
$758$	−33.8150	−	14.0066i	−1.22821	−	0.508743i
$759$	−6.63419	+	16.0164i	−0.240806	+	0.581357i
$760$	10.6128	−	4.39595i	0.384965	−	0.159458i
$761$		−	47.2917i		−	1.71432i	−0.515048	−	0.857161i	$-0.672226\pi$
$761$		−	47.2917i		−	1.71432i	0.515048	−	0.857161i	$-0.327774\pi$
$762$	−8.61339	−	20.7946i	−0.312030	−	0.753308i
$763$	1.15609	+	1.15609i	0.0418531	+	0.0418531i
$764$	−14.1007			−0.510145
$765$		0			0
$766$	30.8259			1.11378
$767$	3.69278	+	3.69278i	0.133338	+	0.133338i
$768$	8.02509	+	19.3743i	0.289580	+	0.699109i
$769$			6.39156i			0.230486i	0.993337	+	0.115243i	$0.0367646\pi$
$769$			6.39156i			0.230486i	−0.993337	+	0.115243i	$0.963235\pi$
$770$	−2.10765	+	0.873017i	−0.0759545	+	0.0314614i
$771$	7.52368	−	18.1638i	0.270959	−	0.654152i
$772$	4.87894	+	2.02092i	0.175597	+	0.0727347i
$773$	2.60024	−	2.60024i	0.0935241	−	0.0935241i	−0.658797	−	0.752321i	$-0.728934\pi$
$773$	2.60024	−	2.60024i	0.0935241	−	0.0935241i	0.752321	+	0.658797i	$0.228934\pi$
$774$	8.28723	−	8.28723i	0.297878	−	0.297878i
$775$	5.70321	+	2.36235i	0.204865	+	0.0848580i
$776$	1.49379	−	3.60634i	0.0536241	−	0.129460i
$777$	−1.50163	+	0.621995i	−0.0538707	+	0.0223140i
$778$			31.9625i			1.14591i
$779$	0.696813	+	1.68226i	0.0249659	+	0.0602731i
$780$	−6.36370	−	6.36370i	−0.227857	−	0.227857i
$781$	32.9146			1.17778
$782$		0			0
$783$	2.24264			0.0801454
$784$	−23.8204	−	23.8204i	−0.850727	−	0.850727i
$785$	−11.2073	−	27.0567i	−0.400004	−	0.965696i
$786$			19.3112i			0.688808i
$787$	3.75473	−	1.55526i	0.133842	−	0.0554391i	−0.314757	−	0.949172i	$-0.601923\pi$
$787$	3.75473	−	1.55526i	0.133842	−	0.0554391i	0.448599	+	0.893733i	$0.351923\pi$
$788$	−8.77026	+	21.1733i	−0.312428	+	0.754267i
$789$	−25.7505	−	10.6662i	−0.916741	−	0.379726i
$790$	1.12196	−	1.12196i	0.0399175	−	0.0399175i
$791$	−0.180311	+	0.180311i	−0.00641113	+	0.00641113i
$792$	5.02734	+	2.08239i	0.178639	+	0.0739946i
$793$	−12.4976	+	30.1718i	−0.443801	+	1.07143i
$794$	−10.9949	+	4.55423i	−0.390194	+	0.161623i
$795$			3.42970i			0.121639i
$796$	−8.91536	−	21.5236i	−0.315996	−	0.762883i
$797$	−9.76205	−	9.76205i	−0.345790	−	0.345790i	0.512749	−	0.858539i	$-0.328627\pi$
$797$	−9.76205	−	9.76205i	−0.345790	−	0.345790i	−0.858539	+	0.512749i	$0.828627\pi$
$798$	1.85070			0.0655141
$799$		0			0
$800$	−16.2021			−0.572830
$801$	5.40829	+	5.40829i	0.191092	+	0.191092i
$802$	14.9004	+	35.9729i	0.526153	+	1.27025i
$803$			41.8596i			1.47719i
$804$	9.28931	−	3.84776i	0.327609	−	0.135700i
$805$	0.324078	−	0.782394i	0.0114223	−	0.0275758i
$806$	17.3376	+	7.18146i	0.610690	+	0.252956i
$807$	−0.145188	+	0.145188i	−0.00511087	+	0.00511087i
$808$	−6.99321	+	6.99321i	−0.246020	+	0.246020i
$809$	−17.4142	−	7.21319i	−0.612250	−	0.253602i	0.0549401	−	0.998490i	$-0.482503\pi$
$809$	−17.4142	−	7.21319i	−0.612250	−	0.253602i	−0.667190	+	0.744887i	$0.732503\pi$
$810$	1.14065	−	2.75378i	0.0400784	−	0.0967579i
$811$	2.40167	−	0.994804i	0.0843340	−	0.0349323i	−0.340118	−	0.940383i	$-0.610467\pi$
$811$	2.40167	−	0.994804i	0.0843340	−	0.0349323i	0.424452	+	0.905451i	$0.360467\pi$
$812$			0.482843i			0.0169445i
$813$	3.14212	+	7.58576i	0.110199	+	0.266044i
$814$	−70.1269	−	70.1269i	−2.45795	−	2.45795i
$815$	−33.4280			−1.17093
$816$		0			0
$817$	−41.7291			−1.45992
$818$	−36.0914	−	36.0914i	−1.26191	−	1.26191i
$819$	0.229833	+	0.554866i	0.00803101	+	0.0193886i
$820$			0.631394i			0.0220492i
$821$	−12.0172	+	4.97770i	−0.419404	+	0.173723i	−0.582397	−	0.812904i	$-0.697885\pi$
$821$	−12.0172	+	4.97770i	−0.419404	+	0.173723i	0.162993	+	0.986627i	$0.447885\pi$
$822$	−9.54082	+	23.0336i	−0.332774	+	0.803388i
$823$	20.0060	+	8.28676i	0.697366	+	0.288858i	0.703065	−	0.711125i	$-0.251814\pi$
$823$	20.0060	+	8.28676i	0.697366	+	0.288858i	−0.00569929	+	0.999984i	$0.501814\pi$
$824$	5.80043	−	5.80043i	0.202067	−	0.202067i
$825$	−8.52395	+	8.52395i	−0.296766	+	0.296766i
$826$	−0.344048	−	0.142509i	−0.0119710	−	0.00495853i
$827$	−18.3207	+	44.2300i	−0.637072	+	1.53803i	0.193490	+	0.981102i	$0.438019\pi$
$827$	−18.3207	+	44.2300i	−0.637072	+	1.53803i	−0.830562	+	0.556926i	$0.811981\pi$
$828$	4.50548	−	1.86623i	0.156576	−	0.0648559i
$829$		−	12.9906i		−	0.451181i	−0.974222	−	0.225590i	$-0.927569\pi$
$829$		−	12.9906i		−	0.451181i	0.974222	−	0.225590i	$-0.0724311\pi$
$830$	2.51337	+	6.06781i	0.0872403	+	0.210617i
$831$	−16.6649	−	16.6649i	−0.578098	−	0.578098i
$832$	−11.1580			−0.386834
$833$		0			0
$834$	9.84482			0.340898
$835$	−9.22652	−	9.22652i	−0.319297	−	0.319297i
$836$	17.9000	+	43.2144i	0.619084	+	1.49460i
$837$			2.57446i			0.0889864i
$838$	−20.5723	+	8.52132i	−0.710658	+	0.294364i
$839$	7.22226	−	17.4361i	0.249340	−	0.601961i	−0.748808	−	0.662787i	$-0.769374\pi$
$839$	7.22226	−	17.4361i	0.249340	−	0.601961i	0.998148	+	0.0608263i	$0.0193736\pi$
$840$	−0.245584	−	0.101724i	−0.00847345	−	0.00350982i
$841$	−16.9497	+	16.9497i	−0.584474	+	0.584474i
$842$	18.3158	−	18.3158i	0.631204	−	0.631204i
$843$	9.38035	+	3.88547i	0.323076	+	0.133823i
$844$	−5.78470	+	13.9655i	−0.199118	+	0.480712i
$845$	−3.81914	+	1.58194i	−0.131383	+	0.0544204i
$846$			18.1480i			0.623942i
$847$	0.831613	+	2.00769i	0.0285746	+	0.0689851i
$848$	7.25903	+	7.25903i	0.249276	+	0.249276i
$849$	−9.47918			−0.325325
$850$		0			0
$851$	36.8151			1.26201
$852$	−6.54712	−	6.54712i	−0.224301	−	0.224301i
$853$	2.30984	+	5.57645i	0.0790875	+	0.190934i	0.958478	−	0.285168i	$-0.0920493\pi$
$853$	2.30984	+	5.57645i	0.0790875	+	0.190934i	−0.879390	+	0.476102i	$0.842049\pi$
$854$		−	2.32874i		−	0.0796879i
$855$	−9.80490	+	4.06132i	−0.335321	+	0.138894i
$856$	−7.64913	+	18.4666i	−0.261442	+	0.631177i
$857$	−14.8592	−	6.15488i	−0.507581	−	0.210247i	0.114171	−	0.993461i	$-0.463579\pi$
$857$	−14.8592	−	6.15488i	−0.507581	−	0.210247i	−0.621752	+	0.783214i	$0.713579\pi$
$858$	−25.9125	+	25.9125i	−0.884639	+	0.884639i
$859$	40.9101	−	40.9101i	1.39583	−	1.39583i	0.584285	−	0.811548i	$-0.301375\pi$
$859$	40.9101	−	40.9101i	1.39583	−	1.39583i	0.811548	−	0.584285i	$-0.198625\pi$
$860$	−13.3683	−	5.53735i	−0.455857	−	0.188822i
$861$	0.0161246	−	0.0389281i	0.000549524	−	0.00132667i
$862$	5.87894	−	2.43514i	0.200238	−	0.0829411i
$863$			7.56067i			0.257368i	0.991686	+	0.128684i	$0.0410753\pi$
$863$			7.56067i			0.257368i	−0.991686	+	0.128684i	$0.958925\pi$
$864$	−2.58579	−	6.24264i	−0.0879702	−	0.212379i
$865$	−1.32387	−	1.32387i	−0.0450128	−	0.0450128i
$866$	10.2842			0.349473
$867$		0			0
$868$	−0.554285			−0.0188137
$869$	−1.89235	−	1.89235i	−0.0641936	−	0.0641936i
$870$	−2.55807	−	6.17574i	−0.0867268	−	0.209377i
$871$		−	28.0475i		−	0.950354i
$872$	−10.7392	+	4.44834i	−0.363677	+	0.150640i
$873$	−1.38009	+	3.33182i	−0.0467088	+	0.112765i
$874$	−38.7285	−	16.0419i	−1.31001	−	0.542624i
$875$	1.28466	−	1.28466i	0.0434295	−	0.0434295i
$876$	8.32638	−	8.32638i	0.281322	−	0.281322i
$877$	−16.0441	−	6.64567i	−0.541770	−	0.224408i	0.0949797	−	0.995479i	$-0.469721\pi$
$877$	−16.0441	−	6.64567i	−0.541770	−	0.224408i	−0.636749	+	0.771071i	$0.719721\pi$
$878$	−12.4355	+	30.0218i	−0.419676	+	1.01319i
$879$	−8.57836	+	3.55327i	−0.289341	+	0.119849i
$880$		−	39.1572i		−	1.31999i
$881$	15.7290	+	37.9731i	0.529923	+	1.27935i	0.931573	+	0.363554i	$0.118437\pi$
$881$	15.7290	+	37.9731i	0.529923	+	1.27935i	−0.401650	+	0.915793i	$0.631563\pi$
$882$	9.11566	+	9.11566i	0.306940	+	0.306940i
$883$	−28.3729			−0.954824			−0.477412	−	0.878680i	$-0.658425\pi$
$883$	−28.3729			−0.954824			−0.477412	+	0.878680i	$0.658425\pi$
$884$		0			0
$885$	2.13548			0.0717833
$886$	7.67778	+	7.67778i	0.257940	+	0.257940i
$887$	−8.22786	−	19.8638i	−0.276264	−	0.666961i	0.723462	−	0.690364i	$-0.242550\pi$
$887$	−8.22786	−	19.8638i	−0.276264	−	0.666961i	−0.999726	+	0.0234033i	$0.992550\pi$
$888$		−	11.5558i		−	0.387788i
$889$	1.71331	−	0.709676i	0.0574626	−	0.0238018i
$890$	8.72425	−	21.0622i	0.292437	−	0.706006i
$891$	−4.64466	−	1.92388i	−0.155602	−	0.0644524i
$892$	5.41650	−	5.41650i	0.181358	−	0.181358i
$893$	45.6908	−	45.6908i	1.52898	−	1.52898i
$894$	15.9084	+	6.58946i	0.532055	+	0.220385i
$895$	−1.78817	+	4.31703i	−0.0597719	+	0.144302i
$896$	−1.16569	+	0.482843i	−0.0389429	+	0.0161307i
$897$		−	13.6035i		−	0.454208i
$898$	28.2710	+	68.2521i	0.943414	+	2.27760i
$899$	4.08255	+	4.08255i	0.136161	+	0.136161i
$900$	3.39104			0.113035
$901$		0			0
$902$	2.57099			0.0856046
$903$	0.682803	+	0.682803i	0.0227223	+	0.0227223i
$904$	−0.693794	−	1.67497i	−0.0230752	−	0.0557086i
$905$		−	1.35937i		−	0.0451871i
$906$	−20.4225	+	8.45929i	−0.678493	+	0.281041i
$907$	−5.66635	+	13.6798i	−0.188148	+	0.454229i	−0.989603	−	0.143826i	$-0.954060\pi$
$907$	−5.66635	+	13.6798i	−0.188148	+	0.454229i	0.801455	+	0.598055i	$0.204060\pi$
$908$	−16.0690	−	6.65599i	−0.533268	−	0.220887i
$909$	6.46088	−	6.46088i	0.214294	−	0.214294i
$910$	1.26582	−	1.26582i	0.0419615	−	0.0419615i
$911$	−43.9036	−	18.1855i	−1.45459	−	0.602512i	−0.491306	−	0.870987i	$-0.663480\pi$
$911$	−43.9036	−	18.1855i	−1.45459	−	0.602512i	−0.963287	+	0.268475i	$0.913480\pi$
$912$	−12.1564	+	29.3482i	−0.402539	+	0.971814i
$913$	10.2343	−	4.23917i	0.338705	−	0.140296i
$914$		−	32.6880i		−	1.08122i
$915$	5.11037	+	12.3375i	0.168944	+	0.407866i
$916$	30.1158	+	30.1158i	0.995053	+	0.995053i
$917$	−1.59109			−0.0525425
$918$		0			0
$919$	−52.4090			−1.72881			−0.864407	−	0.502793i	$-0.832306\pi$
$919$	−52.4090			−1.72881			−0.864407	+	0.502793i	$0.832306\pi$
$920$	4.25744	+	4.25744i	0.140364	+	0.140364i
$921$	−10.3867	−	25.0757i	−0.342253	−	0.826273i
$922$		−	55.1856i		−	1.81744i
$923$	−23.8620	+	9.88397i	−0.785428	+	0.325335i
$924$	0.414214	−	1.00000i	0.0136266	−	0.0328976i
$925$	23.6510	+	9.79655i	0.777639	+	0.322109i
$926$	−12.3498	+	12.3498i	−0.405840	+	0.405840i
$927$	−5.35890	+	5.35890i	−0.176009	+	0.176009i
$928$	−14.0000	−	5.79899i	−0.459573	−	0.190361i
$929$	17.5642	−	42.4038i	0.576263	−	1.39122i	−0.319880	−	0.947458i	$-0.603643\pi$
$929$	17.5642	−	42.4038i	0.576263	−	1.39122i	0.896143	−	0.443764i	$-0.146357\pi$
$930$	7.08950	−	2.93657i	0.232474	−	0.0962938i
$931$		−	45.9005i		−	1.50433i
$932$	4.75453	+	11.4785i	0.155740	+	0.375989i
$933$	1.82843	+	1.82843i	0.0598600	+	0.0598600i
$934$	−36.9725			−1.20978
$935$		0			0
$936$	−4.26998			−0.139569
$937$	−15.3852	−	15.3852i	−0.502611	−	0.502611i	0.409637	−	0.912248i	$-0.365655\pi$
$937$	−15.3852	−	15.3852i	−0.502611	−	0.502611i	−0.912248	+	0.409637i	$0.865655\pi$
$938$	0.765367	+	1.84776i	0.0249901	+	0.0603315i
$939$		−	25.6105i		−	0.835767i
$940$	20.7006	−	8.57446i	0.675179	−	0.279668i
$941$	20.7040	−	49.9839i	0.674932	−	1.62943i	−0.0981874	−	0.995168i	$-0.531304\pi$
$941$	20.7040	−	49.9839i	0.674932	−	1.62943i	0.773119	−	0.634261i	$-0.218696\pi$
$942$	30.9922	+	12.8374i	1.00978	+	0.418265i
$943$	−0.674858	+	0.674858i	−0.0219764	+	0.0219764i
$944$	4.51978	−	4.51978i	0.147106	−	0.147106i
$945$	0.226890	+	0.0939809i	0.00738073	+	0.00305720i
$946$	−22.5477	+	54.4350i	−0.733089	+	1.76983i
$947$	−5.33640	+	2.21041i	−0.173410	+	0.0718286i	−0.467699	−	0.883888i	$-0.654917\pi$
$947$	−5.33640	+	2.21041i	−0.173410	+	0.0718286i	0.294290	+	0.955716i	$0.404917\pi$
$948$			0.752823i			0.0244506i
$949$	−12.5701	−	30.3468i	−0.408041	−	0.985099i
$950$	−20.6114	−	20.6114i	−0.668722	−	0.668722i
$951$	25.5982			0.830078
$952$		0			0
$953$	−31.4698			−1.01941			−0.509704	−	0.860350i	$-0.670245\pi$
$953$	−31.4698			−1.01941			−0.509704	+	0.860350i	$0.670245\pi$
$954$	−2.77791	−	2.77791i	−0.0899382	−	0.0899382i
$955$	6.15507	+	14.8597i	0.199174	+	0.480847i
$956$			20.7183i			0.670078i
$957$	−10.4163	+	4.31457i	−0.336711	+	0.139470i
$958$	−0.852559	+	2.05826i	−0.0275449	+	0.0664994i
$959$	−1.89779	−	0.786089i	−0.0612828	−	0.0253841i
$960$	−3.22625	+	3.22625i	−0.104127	+	0.104127i
$961$	17.2337	−	17.2337i	0.555926	−	0.555926i
$962$	71.8982	+	29.7812i	2.31809	+	0.960185i
$963$	7.06688	−	17.0610i	0.227727	−	0.549781i
$964$	−22.1531	+	9.17611i	−0.713503	+	0.295543i
$965$		−	6.02371i		−	0.193910i
$966$	0.371216	+	0.896195i	0.0119437	+	0.0288346i
$967$	−4.11626	−	4.11626i	−0.132370	−	0.132370i	0.637818	−	0.770187i	$-0.279837\pi$
$967$	−4.11626	−	4.11626i	−0.132370	−	0.132370i	−0.770187	+	0.637818i	$0.779837\pi$
$968$	−15.4502			−0.496589
$969$		0			0
$970$	10.7493			0.345139
$971$	−15.4891	−	15.4891i	−0.497070	−	0.497070i	0.413455	−	0.910525i	$-0.364322\pi$
$971$	−15.4891	−	15.4891i	−0.497070	−	0.497070i	−0.910525	+	0.413455i	$0.864322\pi$
$972$	0.541196	+	1.30656i	0.0173589	+	0.0419080i
$973$			0.811136i			0.0260038i
$974$	20.4192	−	8.45790i	0.654273	−	0.271009i
$975$	3.61991	−	8.73925i	0.115930	−	0.279880i
$976$	36.9288	+	15.2964i	1.18206	+	0.489626i
$977$	−19.8324	+	19.8324i	−0.634495	+	0.634495i	−0.949192	−	0.314697i	$-0.898097\pi$
$977$	−19.8324	+	19.8324i	−0.634495	+	0.634495i	0.314697	+	0.949192i	$0.398097\pi$
$978$	27.0752	−	27.0752i	0.865770	−	0.865770i
$979$	−35.5245	−	14.7147i	−1.13537	−	0.470285i
$980$	6.09089	−	14.7047i	0.194566	−	0.469725i
$981$	9.92177	−	4.10973i	0.316778	−	0.131214i
$982$			57.7668i			1.84341i
$983$	−11.9884	−	28.9425i	−0.382369	−	0.923121i	−0.991507	−	0.130056i	$-0.958484\pi$
$983$	−11.9884	−	28.9425i	−0.382369	−	0.923121i	0.609137	−	0.793065i	$-0.291516\pi$
$984$	0.211830	+	0.211830i	0.00675288	+	0.00675288i
$985$	26.1412			0.832929
$986$		0			0
$987$	−1.49526			−0.0475945
$988$	−25.9538	−	25.9538i	−0.825700	−	0.825700i
$989$	−8.37007	−	20.2071i	−0.266153	−	0.642549i
$990$			14.9848i			0.476249i
$991$	−16.6291	+	6.88802i	−0.528242	+	0.218805i	−0.630833	−	0.775919i	$-0.717287\pi$
$991$	−16.6291	+	6.88802i	−0.528242	+	0.218805i	0.102591	+	0.994724i	$0.467287\pi$
$992$	6.65701	−	16.0714i	0.211360	−	0.510269i
$993$	−0.307810	−	0.127499i	−0.00976807	−	0.00404607i
$994$	1.30230	−	1.30230i	0.0413066	−	0.0413066i
$995$	−18.7905	+	18.7905i	−0.595697	+	0.595697i
$996$	−2.87894	−	1.19250i	−0.0912228	−	0.0377857i
$997$	21.2644	−	51.3369i	0.673451	−	1.62586i	−0.102253	−	0.994758i	$-0.532605\pi$
$997$	21.2644	−	51.3369i	0.673451	−	1.62586i	0.775704	−	0.631097i	$-0.217395\pi$
$998$	70.6042	−	29.2452i	2.23494	−	0.925741i
$999$			10.6762i			0.337780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.f.712.2		8
17.2	even	8		51.2.h.a.43.1	yes	8
17.3	odd	16		867.2.d.e.577.8		8
17.4	even	4		51.2.h.a.19.1	✓	8
17.5	odd	16		867.2.a.m.1.1		4
17.6	odd	16		867.2.e.i.829.4		8
17.7	odd	16		867.2.e.i.616.1		8
17.8	even	8	inner	867.2.h.f.688.2		8
17.9	even	8		867.2.h.b.688.2		8
17.10	odd	16		867.2.e.h.616.1		8
17.11	odd	16		867.2.e.h.829.4		8
17.12	odd	16		867.2.a.n.1.1		4
17.13	even	4		867.2.h.g.733.1		8
17.14	odd	16		867.2.d.e.577.7		8
17.15	even	8		867.2.h.g.757.1		8
17.16	even	2		867.2.h.b.712.2		8
51.2	odd	8		153.2.l.e.145.2		8
51.5	even	16		2601.2.a.bc.1.4		4
51.29	even	16		2601.2.a.bd.1.4		4
51.38	odd	4		153.2.l.e.19.2		8
68.19	odd	8		816.2.bq.a.145.1		8
68.55	odd	4		816.2.bq.a.529.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.19.1	✓	8	17.4	even	4
51.2.h.a.43.1	yes	8	17.2	even	8
153.2.l.e.19.2		8	51.38	odd	4
153.2.l.e.145.2		8	51.2	odd	8
816.2.bq.a.145.1		8	68.19	odd	8
816.2.bq.a.529.1		8	68.55	odd	4
867.2.a.m.1.1		4	17.5	odd	16
867.2.a.n.1.1		4	17.12	odd	16
867.2.d.e.577.7		8	17.14	odd	16
867.2.d.e.577.8		8	17.3	odd	16
867.2.e.h.616.1		8	17.10	odd	16
867.2.e.h.829.4		8	17.11	odd	16
867.2.e.i.616.1		8	17.7	odd	16
867.2.e.i.829.4		8	17.6	odd	16
867.2.h.b.688.2		8	17.9	even	8
867.2.h.b.712.2		8	17.16	even	2
867.2.h.f.688.2		8	17.8	even	8	inner
867.2.h.f.712.2		8	1.1	even	1	trivial
867.2.h.g.733.1		8	17.13	even	4
867.2.h.g.757.1		8	17.15	even	8
2601.2.a.bc.1.4		4	51.5	even	16
2601.2.a.bd.1.4		4	51.29	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+(1.30656 + 1.30656i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.41421i q^{4} +(1.49033 - 0.617317i) q^{5} +(-0.707107 + 1.70711i) q^{6} +(-0.140652 - 0.0582601i) q^{7} +(0.765367 - 0.765367i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(2.75378 + 1.14065i) q^{10} +(1.92388 - 4.64466i) q^{11} +(-1.30656 + 0.541196i) q^{12} +3.94495i q^{13} +(-0.107651 - 0.259892i) q^{14} +(1.14065 + 1.14065i) q^{15} +4.82843 q^{16} -1.84776 q^{18} +(4.65205 + 4.65205i) q^{19} +(0.873017 + 2.10765i) q^{20} -0.152241i q^{21} +(8.58221 - 3.55487i) q^{22} +(-1.31962 + 3.18585i) q^{23} +(1.00000 + 0.414214i) q^{24} +(-1.69552 + 1.69552i) q^{25} +(-5.15432 + 5.15432i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(0.0823922 - 0.198912i) q^{28} +(-2.07193 + 0.858221i) q^{29} +2.98067i q^{30} +(-0.985204 - 2.37849i) q^{31} +(4.77791 + 4.77791i) q^{32} +5.02734 q^{33} -0.245584 q^{35} +(-1.00000 - 1.00000i) q^{36} +(-4.08560 - 9.86351i) q^{37} +12.1564i q^{38} +(-3.64466 + 1.50967i) q^{39} +(0.668179 - 1.61313i) q^{40} +(0.255701 + 0.105915i) q^{41} +(0.198912 - 0.198912i) q^{42} +(-4.48502 + 4.48502i) q^{43} +(6.56854 + 2.72078i) q^{44} +(-0.617317 + 1.49033i) q^{45} +(-5.88669 + 2.43835i) q^{46} -9.82164i q^{47} +(1.84776 + 4.46088i) q^{48} +(-4.93336 - 4.93336i) q^{49} -4.43060 q^{50} -5.57900 q^{52} +(1.50339 + 1.50339i) q^{53} +(-0.707107 - 1.70711i) q^{54} -8.10973i q^{55} +(-0.152241 + 0.0630603i) q^{56} +(-2.51767 + 6.07820i) q^{57} +(-3.82843 - 1.58579i) q^{58} +(0.936078 - 0.936078i) q^{59} +(-1.61313 + 1.61313i) q^{60} +(7.64821 + 3.16799i) q^{61} +(1.82042 - 4.39488i) q^{62} +(0.140652 - 0.0582601i) q^{63} +2.82843i q^{64} +(2.43528 + 5.87929i) q^{65} +(6.56854 + 6.56854i) q^{66} -7.10973 q^{67} -3.44834 q^{69} +(-0.320871 - 0.320871i) q^{70} +(2.50548 + 6.04875i) q^{71} +1.08239i q^{72} +(-7.69258 + 3.18637i) q^{73} +(7.54920 - 18.2254i) q^{74} +(-2.21530 - 0.917608i) q^{75} +(-6.57900 + 6.57900i) q^{76} +(-0.541196 + 0.541196i) q^{77} +(-6.73445 - 2.78950i) q^{78} +(0.203713 - 0.491806i) q^{79} +(7.19597 - 2.98067i) q^{80} -1.00000i q^{81} +(0.195705 + 0.472474i) q^{82} +(1.55807 + 1.55807i) q^{83} +0.215301 q^{84} -11.7199 q^{86} +(-1.58579 - 1.58579i) q^{87} +(-2.08239 - 5.02734i) q^{88} -7.64847i q^{89} +(-2.75378 + 1.14065i) q^{90} +(0.229833 - 0.554866i) q^{91} +(-4.50548 - 1.86623i) q^{92} +(1.82042 - 1.82042i) q^{93} +(12.8326 - 12.8326i) q^{94} +(9.80490 + 4.06132i) q^{95} +(-2.58579 + 6.24264i) q^{96} +(3.33182 - 1.38009i) q^{97} -12.8915i q^{98} +(1.92388 + 4.64466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{5} + 8 q^{7} - 8 q^{10} + 8 q^{11} + 16 q^{16} + 8 q^{19} + 16 q^{22} - 24 q^{23} + 8 q^{24} + 16 q^{25} - 16 q^{26} - 8 q^{28} - 8 q^{31} + 8 q^{33} + 32 q^{35} - 8 q^{36} + 8 q^{40} - 8 q^{41}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^5 + 8 * q^7 - 8 * q^10 + 8 * q^11 + 16 * q^16 + 8 * q^19 + 16 * q^22 - 24 * 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^40 - 8 * q^41 - 8 * q^42 + 8 * q^43 + 16 * q^44 - 8 * q^45 - 24 * q^46 + 8 * q^49 - 32 * q^50 - 16 * q^52 + 32 * q^53 - 16 * q^56 + 16 * q^57 - 8 * q^58 - 16 * q^59 + 8 * q^60 - 8 * q^61 + 32 * q^62 - 8 * q^63 - 8 * q^65 + 16 * q^66 - 16 * q^67 - 24 * q^69 - 40 * q^70 - 32 * q^73 + 16 * q^74 - 16 * q^75 - 24 * q^76 - 16 * q^78 - 24 * q^79 + 48 * q^80 + 16 * q^82 - 32 * q^83 - 32 * q^86 - 24 * q^87 - 8 * q^88 + 8 * q^90 + 24 * q^91 - 16 * q^92 + 32 * q^93 + 24 * q^95 - 32 * q^96 + 24 * q^97 + 8 * q^99

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