LMFDB - Embedded newform 85.2.j.c.64.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [85,2,Mod(4,85)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("85.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 188x^{8} + 572x^{6} + 776x^{4} + 464x^{2} + 100 $ x^12 + 24x^10 + 188x^8 + 572x^6 + 776x^4 + 464*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.6
Root			$-3.38621i$ of defining polynomial
Character	$\chi$	$=$	85.64
Dual form			85.2.j.c.4.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.38621 q^{2} +(-2.23065 + 2.23065i) q^{3} +3.69399 q^{4} +(-0.518989 - 2.17501i) q^{5} +(-5.32280 + 5.32280i) q^{6} +(-0.155559 - 0.155559i) q^{7} +4.04223 q^{8} -6.95160i q^{9} +(-1.23842 - 5.19002i) q^{10} +(0.371196 - 0.371196i) q^{11} +(-8.24001 + 8.24001i) q^{12} +1.96713i q^{13} +(-0.371196 - 0.371196i) q^{14} +(6.00936 + 3.69399i) q^{15} +2.25761 q^{16} +(-3.46759 - 2.23065i) q^{17} -16.5880i q^{18} +4.00000i q^{19} +(-1.91714 - 8.03446i) q^{20} +0.693995 q^{21} +(0.885751 - 0.885751i) q^{22} +(0.263516 + 0.263516i) q^{23} +(-9.01679 + 9.01679i) q^{24} +(-4.46130 + 2.25761i) q^{25} +4.69399i q^{26} +(8.81464 + 8.81464i) q^{27} +(-0.574634 - 0.574634i) q^{28} +(4.95160 + 4.95160i) q^{29} +(14.3396 + 8.81464i) q^{30} +(2.06519 + 2.06519i) q^{31} -2.69733 q^{32} +1.65602i q^{33} +(-8.27440 - 5.32280i) q^{34} +(-0.257608 + 0.419075i) q^{35} -25.6792i q^{36} +(4.04223 - 4.04223i) q^{37} +9.54484i q^{38} +(-4.38799 - 4.38799i) q^{39} +(-2.09787 - 8.79187i) q^{40} +(0.563613 - 0.563613i) q^{41} +1.65602 q^{42} -2.49417 q^{43} +(1.37120 - 1.37120i) q^{44} +(-15.1198 + 3.60781i) q^{45} +(0.628804 + 0.628804i) q^{46} -6.73955i q^{47} +(-5.03593 + 5.03593i) q^{48} -6.95160i q^{49} +(-10.6456 + 5.38713i) q^{50} +(12.7108 - 2.75919i) q^{51} +7.26658i q^{52} +5.92169 q^{53} +(21.0336 + 21.0336i) q^{54} +(-1.00000 - 0.614707i) q^{55} +(-0.628804 - 0.628804i) q^{56} +(-8.92260 - 8.92260i) q^{57} +(11.8156 + 11.8156i) q^{58} -6.00000i q^{59} +(22.1985 + 13.6456i) q^{60} +(-4.00000 + 4.00000i) q^{61} +(4.92798 + 4.92798i) q^{62} +(-1.08138 + 1.08138i) q^{63} -10.9516 q^{64} +(4.27853 - 1.02092i) q^{65} +3.95160i q^{66} +11.5120i q^{67} +(-12.8093 - 8.24001i) q^{68} -1.17562 q^{69} +(-0.614707 + 1.00000i) q^{70} +(-5.06519 - 5.06519i) q^{71} -28.1000i q^{72} +(0.838149 - 0.838149i) q^{73} +(9.64560 - 9.64560i) q^{74} +(4.91567 - 14.9875i) q^{75} +14.7760i q^{76} -0.115486 q^{77} +(-10.4707 - 10.4707i) q^{78} +(-4.75919 + 4.75919i) q^{79} +(-1.17167 - 4.91031i) q^{80} -18.4700 q^{81} +(1.34490 - 1.34490i) q^{82} +6.11732 q^{83} +2.56361 q^{84} +(-3.05204 + 8.69972i) q^{85} -5.95160 q^{86} -22.0906 q^{87} +(1.50046 - 1.50046i) q^{88} +15.9852 q^{89} +(-36.0790 + 8.60898i) q^{90} +(0.306005 - 0.306005i) q^{91} +(0.973426 + 0.973426i) q^{92} -9.21344 q^{93} -16.0820i q^{94} +(8.70002 - 2.07596i) q^{95} +(6.01679 - 6.01679i) q^{96} +(6.51611 - 6.51611i) q^{97} -16.5880i q^{98} +(-2.58041 - 2.58041i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4} - 20 q^{6} - 4 q^{10} + 16 q^{11} - 16 q^{14} + 4 q^{16} - 32 q^{20} - 24 q^{21} - 32 q^{24} + 4 q^{29} + 52 q^{30} + 4 q^{31} + 20 q^{35} + 12 q^{39} + 24 q^{40} + 16 q^{41} + 28 q^{44}+ \cdots + 36 q^{99}+O(q^{100}) $ 12 * q + 12 * q^4 - 20 * q^6 - 4 * q^10 + 16 * q^11 - 16 * q^14 + 4 * q^16 - 32 * q^20 - 24 * q^21 - 32 * q^24 + 4 * q^29 + 52 * q^30 + 4 * q^31 + 20 * q^35 + 12 * q^39 + 24 * q^40 + 16 * q^41 + 28 * q^44 - 20 * q^45 - 4 * q^46 - 40 * q^50 + 44 * q^51 + 100 * q^54 - 12 * q^55 + 4 * q^56 - 48 * q^61 - 76 * q^64 + 8 * q^65 - 88 * q^69 - 40 * q^71 + 28 * q^74 + 64 * q^75 - 4 * q^79 + 12 * q^80 - 60 * q^81 + 40 * q^84 - 52 * q^85 - 16 * q^86 - 16 * q^89 - 84 * q^90 + 36 * q^91 - 4 * q^96 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.38621			1.68730			0.843652	−	0.536890i	$-0.180401\pi$
$2$	2.38621			1.68730			0.843652	+	0.536890i	$0.180401\pi$
$3$	−2.23065	+	2.23065i	−1.28787	+	1.28787i	−0.351786	+	0.936080i	$0.614426\pi$
$3$	−2.23065	+	2.23065i	−1.28787	+	1.28787i	−0.936080	+	0.351786i	$0.885574\pi$
$4$	3.69399			1.84700
$5$	−0.518989	−	2.17501i	−0.232099	−	0.972692i
$5$	−0.518989	−	2.17501i	−0.232099	−	0.972692i
$6$	−5.32280	+	5.32280i	−2.17302	+	2.17302i
$7$	−0.155559	−	0.155559i	−0.0587957	−	0.0587957i	0.677098	−	0.735893i	$-0.263238\pi$
$7$	−0.155559	−	0.155559i	−0.0587957	−	0.0587957i	−0.735893	+	0.677098i	$0.763238\pi$
$8$	4.04223			1.42914
$9$		−	6.95160i		−	2.31720i
$10$	−1.23842	−	5.19002i	−0.391622	−	1.64123i
$11$	0.371196	−	0.371196i	0.111920	−	0.111920i	−0.648929	−	0.760849i	$-0.724783\pi$
$11$	0.371196	−	0.371196i	0.111920	−	0.111920i	0.760849	+	0.648929i	$0.224783\pi$
$12$	−8.24001	+	8.24001i	−2.37869	+	2.37869i
$13$			1.96713i			0.545585i	0.962073	+	0.272792i	$0.0879472\pi$
$13$			1.96713i			0.545585i	−0.962073	+	0.272792i	$0.912053\pi$
$14$	−0.371196	−	0.371196i	−0.0992063	−	0.0992063i
$15$	6.00936	+	3.69399i	1.55161	+	0.953785i
$16$	2.25761			0.564402
$17$	−3.46759	−	2.23065i	−0.841015	−	0.541012i
$17$	−3.46759	−	2.23065i	−0.841015	−	0.541012i
$18$		−	16.5880i		−	3.90982i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	−1.91714	−	8.03446i	−0.428686	−	1.79656i
$21$	0.693995			0.151442
$22$	0.885751	−	0.885751i	0.188843	−	0.188843i
$23$	0.263516	+	0.263516i	0.0549469	+	0.0549469i	0.734046	−	0.679099i	$-0.237629\pi$
$23$	0.263516	+	0.263516i	0.0549469	+	0.0549469i	−0.679099	+	0.734046i	$0.737629\pi$
$24$	−9.01679	+	9.01679i	−1.84055	+	1.84055i
$25$	−4.46130	+	2.25761i	−0.892260	+	0.451522i
$26$			4.69399i			0.920568i
$27$	8.81464	+	8.81464i	1.69638	+	1.69638i
$28$	−0.574634	−	0.574634i	−0.108596	−	0.108596i
$29$	4.95160	+	4.95160i	0.919490	+	0.919490i	0.996992	−	0.0775026i	$-0.0246946\pi$
$29$	4.95160	+	4.95160i	0.919490	+	0.919490i	−0.0775026	+	0.996992i	$0.524695\pi$
$30$	14.3396	+	8.81464i	2.61804	+	1.60933i
$31$	2.06519	+	2.06519i	0.370919	+	0.370919i	0.867812	−	0.496893i	$-0.165526\pi$
$31$	2.06519	+	2.06519i	0.370919	+	0.370919i	−0.496893	+	0.867812i	$0.665526\pi$
$32$	−2.69733			−0.476825
$33$			1.65602i			0.288276i
$34$	−8.27440	−	5.32280i	−1.41905	−	0.912852i
$35$	−0.257608	+	0.419075i	−0.0435437	+	0.0708366i
$36$		−	25.6792i		−	4.27986i
$37$	4.04223	−	4.04223i	0.664538	−	0.664538i	−0.291908	−	0.956446i	$-0.594290\pi$
$37$	4.04223	−	4.04223i	0.664538	−	0.664538i	0.956446	+	0.291908i	$0.0942902\pi$
$38$			9.54484i			1.54838i
$39$	−4.38799	−	4.38799i	−0.702641	−	0.702641i
$40$	−2.09787	−	8.79187i	−0.331702	−	1.39012i
$41$	0.563613	−	0.563613i	0.0880216	−	0.0880216i	−0.661725	−	0.749747i	$-0.730175\pi$
$41$	0.563613	−	0.563613i	0.0880216	−	0.0880216i	0.749747	+	0.661725i	$0.230175\pi$
$42$	1.65602			0.255529
$43$	−2.49417			−0.380357			−0.190178	−	0.981750i	$-0.560907\pi$
$43$	−2.49417			−0.380357			−0.190178	+	0.981750i	$0.560907\pi$
$44$	1.37120	−	1.37120i	0.206716	−	0.206716i
$45$	−15.1198	+	3.60781i	−2.25392	+	0.537820i
$46$	0.628804	+	0.628804i	0.0927121	+	0.0927121i
$47$		−	6.73955i		−	0.983065i	−0.870859	−	0.491532i	$-0.836437\pi$
$47$		−	6.73955i		−	0.983065i	0.870859	−	0.491532i	$-0.163563\pi$
$48$	−5.03593	+	5.03593i	−0.726875	+	0.726875i
$49$		−	6.95160i		−	0.993086i
$50$	−10.6456	+	5.38713i	−1.50551	+	0.761855i
$51$	12.7108	−	2.75919i	1.77987	−	0.386363i
$52$			7.26658i			1.00769i
$53$	5.92169			0.813406			0.406703	−	0.913560i	$-0.366678\pi$
$53$	5.92169			0.813406			0.406703	+	0.913560i	$0.366678\pi$
$54$	21.0336	+	21.0336i	2.86231	+	2.86231i
$55$	−1.00000	−	0.614707i	−0.134840	−	0.0828870i
$56$	−0.628804	−	0.628804i	−0.0840275	−	0.0840275i
$57$	−8.92260	−	8.92260i	−1.18183	−	1.18183i
$58$	11.8156	+	11.8156i	1.55146	+	1.55146i
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$	22.1985	+	13.6456i	2.86582	+	1.76164i
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	−0.915184	−	0.403036i	$-0.867955\pi$
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	0.403036	+	0.915184i	$0.367955\pi$
$62$	4.92798	+	4.92798i	0.625854	+	0.625854i
$63$	−1.08138	+	1.08138i	−0.136241	+	0.136241i
$64$	−10.9516			−1.36895
$65$	4.27853	−	1.02092i	0.530686	−	0.126630i
$66$			3.95160i			0.486409i
$67$			11.5120i			1.40641i	0.710987	+	0.703206i	$0.248249\pi$
$67$			11.5120i			1.40641i	−0.710987	+	0.703206i	$0.751751\pi$
$68$	−12.8093	−	8.24001i	−1.55335	−	0.999248i
$69$	−1.17562			−0.141528
$70$	−0.614707	+	1.00000i	−0.0734715	+	0.119523i
$71$	−5.06519	−	5.06519i	−0.601128	−	0.601128i	0.339484	−	0.940612i	$-0.389747\pi$
$71$	−5.06519	−	5.06519i	−0.601128	−	0.601128i	−0.940612	+	0.339484i	$0.889747\pi$
$72$		−	28.1000i		−	3.31161i
$73$	0.838149	−	0.838149i	0.0980980	−	0.0980980i	−0.656355	−	0.754453i	$-0.727902\pi$
$73$	0.838149	−	0.838149i	0.0980980	−	0.0980980i	0.754453	+	0.656355i	$0.227902\pi$
$74$	9.64560	−	9.64560i	1.12128	−	1.12128i
$75$	4.91567	−	14.9875i	0.567612	−	1.73061i
$76$			14.7760i			1.69492i
$77$	−0.115486			−0.0131608
$78$	−10.4707	−	10.4707i	−1.18557	−	1.18557i
$79$	−4.75919	+	4.75919i	−0.535450	+	0.535450i	−0.922189	−	0.386739i	$-0.873601\pi$
$79$	−4.75919	+	4.75919i	−0.535450	+	0.535450i	0.386739	+	0.922189i	$0.373601\pi$
$80$	−1.17167	−	4.91031i	−0.130997	−	0.548989i
$81$	−18.4700			−2.05222
$82$	1.34490	−	1.34490i	0.148519	−	0.148519i
$83$	6.11732			0.671463			0.335731	−	0.941958i	$-0.391017\pi$
$83$	6.11732			0.671463			0.335731	+	0.941958i	$0.391017\pi$
$84$	2.56361			0.279713
$85$	−3.05204	+	8.69972i	−0.331040	+	0.943617i
$86$	−5.95160			−0.641778
$87$	−22.0906			−2.36836
$88$	1.50046	−	1.50046i	0.159949	−	0.159949i
$89$	15.9852			1.69443			0.847213	−	0.531253i	$-0.178279\pi$
$89$	15.9852			1.69443			0.847213	+	0.531253i	$0.178279\pi$
$90$	−36.0790	+	8.60898i	−3.80306	+	0.907466i
$91$	0.306005	−	0.306005i	0.0320781	−	0.0320781i
$92$	0.973426	+	0.973426i	0.101487	+	0.101487i
$93$	−9.21344			−0.955389
$94$		−	16.0820i		−	1.65873i
$95$	8.70002	−	2.07596i	0.892604	−	0.212989i
$96$	6.01679	−	6.01679i	0.614086	−	0.614086i
$97$	6.51611	−	6.51611i	0.661611	−	0.661611i	−0.294149	−	0.955760i	$-0.595036\pi$
$97$	6.51611	−	6.51611i	0.661611	−	0.661611i	0.955760	+	0.294149i	$0.0950361\pi$
$98$		−	16.5880i		−	1.67564i
$99$	−2.58041	−	2.58041i	−0.259341	−	0.259341i
$100$	−16.4800	+	8.33959i	−1.64800	+	0.833959i
$101$	−7.20921			−0.717343			−0.358672	−	0.933464i	$-0.616770\pi$
$101$	−7.20921			−0.717343			−0.358672	+	0.933464i	$0.616770\pi$
$102$	30.3306	−	6.58399i	3.00318	−	0.651913i
$103$			9.52456i			0.938482i	0.883070	+	0.469241i	$0.155472\pi$
$103$			9.52456i			0.938482i	−0.883070	+	0.469241i	$0.844528\pi$
$104$			7.95160i			0.779719i
$105$	−0.360176	−	1.50944i	−0.0351495	−	0.147307i
$106$	14.1304			1.37246
$107$	7.62530	−	7.62530i	0.737166	−	0.737166i	−0.234863	−	0.972029i	$-0.575464\pi$
$107$	7.62530	−	7.62530i	0.737166	−	0.737166i	0.972029	+	0.234863i	$0.0754640\pi$
$108$	32.5613	+	32.5613i	3.13321	+	3.13321i
$109$	−9.95160	+	9.95160i	−0.953191	+	0.953191i	−0.998952	−	0.0457617i	$-0.985429\pi$
$109$	−9.95160	+	9.95160i	−0.953191	+	0.953191i	0.0457617	+	0.998952i	$0.485429\pi$
$110$	−2.38621	−	1.46682i	−0.227516	−	0.139856i
$111$			18.0336i			1.71167i
$112$	−0.351191	−	0.351191i	−0.0331844	−	0.0331844i
$113$	−5.08354	−	5.08354i	−0.478219	−	0.478219i	0.426343	−	0.904562i	$-0.359802\pi$
$113$	−5.08354	−	5.08354i	−0.478219	−	0.478219i	−0.904562	+	0.426343i	$0.859802\pi$
$114$	−21.2912	−	21.2912i	−1.99410	−	1.99410i
$115$	0.436387	−	0.709910i	0.0406933	−	0.0661995i
$116$	18.2912	+	18.2912i	1.69829	+	1.69829i
$117$	13.6747			1.26423
$118$		−	14.3173i		−	1.31801i
$119$	0.192417	+	0.886412i	0.0176389	+	0.0812573i
$120$	24.2912	+	14.9320i	2.21747	+	1.36310i
$121$			10.7244i			0.974948i
$122$	−9.54484	+	9.54484i	−0.864149	+	0.864149i
$123$			2.51445i			0.226720i
$124$	7.62880	+	7.62880i	0.685087	+	0.685087i
$125$	7.22568	+	8.53168i	0.646284	+	0.763097i
$126$	−2.58041	+	2.58041i	−0.229881	+	0.229881i
$127$	−9.74047			−0.864327			−0.432163	−	0.901795i	$-0.642250\pi$
$127$	−9.74047			−0.864327			−0.432163	+	0.901795i	$0.642250\pi$
$128$	−20.7382			−1.83301
$129$	5.56361	−	5.56361i	0.489849	−	0.489849i
$130$	10.2095	−	2.43613i	0.895429	−	0.213663i
$131$	−13.9200	−	13.9200i	−1.21620	−	1.21620i	−0.968954	−	0.247242i	$-0.920476\pi$
$131$	−13.9200	−	13.9200i	−1.21620	−	1.21620i	−0.247242	−	0.968954i	$-0.579524\pi$
$132$			6.11732i			0.532444i
$133$	0.622235	−	0.622235i	0.0539547	−	0.0539547i
$134$			27.4700i			2.37304i
$135$	14.5972	−	23.7466i	1.25633	−	2.04378i
$136$	−14.0168	−	9.01679i	−1.20193	−	0.773184i
$137$		−	4.65693i		−	0.397869i	−0.980013	−	0.198934i	$-0.936252\pi$
$137$		−	4.65693i		−	0.397869i	0.980013	−	0.198934i	$-0.0637480\pi$
$138$	−2.80528			−0.238802
$139$	−3.71079	−	3.71079i	−0.314745	−	0.314745i	0.532000	−	0.846745i	$-0.321441\pi$
$139$	−3.71079	−	3.71079i	−0.314745	−	0.314745i	−0.846745	+	0.532000i	$0.821441\pi$
$140$	−0.951603	+	1.54806i	−0.0804251	+	0.130835i
$141$	15.0336	+	15.0336i	1.26606	+	1.26606i
$142$	−12.0866	−	12.0866i	−1.01429	−	1.01429i
$143$	0.730192	+	0.730192i	0.0610618	+	0.0610618i
$144$		−	15.6940i		−	1.30783i
$145$	8.19994	−	13.3396i	0.680968	−	1.10779i
$146$	2.00000	−	2.00000i	0.165521	−	0.165521i
$147$	15.5066	+	15.5066i	1.27896	+	1.27896i
$148$	14.9320	−	14.9320i	1.22740	−	1.22740i
$149$	8.74239			0.716205			0.358102	−	0.933682i	$-0.383424\pi$
$149$	8.74239			0.716205			0.358102	+	0.933682i	$0.383424\pi$
$150$	11.7298	−	35.7634i	0.957735	−	2.92007i
$151$		−	15.9032i		−	1.29418i	−0.762412	−	0.647092i	$-0.775985\pi$
$151$		−	15.9032i		−	1.29418i	0.762412	−	0.647092i	$-0.224015\pi$
$152$			16.1689i			1.31147i
$153$	−15.5066	+	24.1053i	−1.25363	+	1.94880i
$154$	−0.275573			−0.0222063
$155$	3.41999	−	5.56361i	0.274700	−	0.446880i
$156$	−16.2092	−	16.2092i	−1.29778	−	1.29778i
$157$		−	10.0719i		−	0.803823i	−0.915679	−	0.401911i	$-0.868346\pi$
$157$		−	10.0719i		−	0.803823i	0.915679	−	0.401911i	$-0.131654\pi$
$158$	−11.3564	+	11.3564i	−0.903468	+	0.903468i
$159$	−13.2092	+	13.2092i	−1.04756	+	1.04756i
$160$	1.39988	+	5.86670i	0.110670	+	0.463804i
$161$		−	0.0819845i		−	0.00646128i
$162$	−44.0732			−3.46272
$163$	6.77963	+	6.77963i	0.531021	+	0.531021i	0.920876	−	0.389855i	$-0.127475\pi$
$163$	6.77963	+	6.77963i	0.531021	+	0.531021i	−0.389855	+	0.920876i	$0.627475\pi$
$164$	2.08198	−	2.08198i	0.162576	−	0.162576i
$165$	3.60185	−	0.859454i	0.280403	−	0.0669084i
$166$	14.5972			1.13296
$167$	−3.77871	+	3.77871i	−0.292405	+	0.292405i	−0.838030	−	0.545624i	$-0.816293\pi$
$167$	−3.77871	+	3.77871i	−0.292405	+	0.292405i	0.545624	+	0.838030i	$0.316293\pi$
$168$	2.80528			0.216432
$169$	9.13038			0.702337
$170$	−7.28280	+	20.7593i	−0.558565	+	1.59217i
$171$	27.8064			2.12641
$172$	−9.21344			−0.702518
$173$	−12.3426	+	12.3426i	−0.938390	+	0.938390i	−0.998209	−	0.0598193i	$-0.980948\pi$
$173$	−12.3426	+	12.3426i	−0.938390	+	0.938390i	0.0598193	+	0.998209i	$0.480948\pi$
$174$	−52.7128			−3.99614
$175$	1.04519	+	0.342804i	0.0790086	+	0.0259135i
$176$	0.838015	−	0.838015i	0.0631678	−	0.0631678i
$177$	13.3839	+	13.3839i	1.00600	+	1.00600i
$178$	38.1440			2.85901
$179$			21.3248i			1.59389i	0.604052	+	0.796945i	$0.293552\pi$
$179$			21.3248i			1.59389i	−0.604052	+	0.796945i	$0.706448\pi$
$180$	−55.8524	+	13.3272i	−4.16299	+	0.993352i
$181$	10.2092	−	10.2092i	0.758845	−	0.758845i	−0.217267	−	0.976112i	$-0.569714\pi$
$181$	10.2092	−	10.2092i	0.758845	−	0.758845i	0.976112	+	0.217267i	$0.0697144\pi$
$182$	0.730192	−	0.730192i	0.0541255	−	0.0541255i
$183$		−	17.8452i		−	1.31916i
$184$	1.06519	+	1.06519i	0.0785269	+	0.0785269i
$185$	−10.8897	−	6.69399i	−0.800629	−	0.492152i
$186$	−21.9852			−1.61203
$187$	−2.11516	+	0.459148i	−0.154676	+	0.0335762i
$188$		−	24.8959i		−	1.81572i
$189$		−	2.74239i		−	0.199480i
$190$	20.7601	−	4.95367i	1.50609	−	0.359377i
$191$	−6.74239			−0.487862			−0.243931	−	0.969793i	$-0.578437\pi$
$191$	−6.74239			−0.487862			−0.243931	+	0.969793i	$0.578437\pi$
$192$	24.4292	−	24.4292i	1.76303	−	1.76303i
$193$	−10.3627	−	10.3627i	−0.745924	−	0.745924i	0.227787	−	0.973711i	$-0.426851\pi$
$193$	−10.3627	−	10.3627i	−0.745924	−	0.745924i	−0.973711	+	0.227787i	$0.926851\pi$
$194$	15.5488	−	15.5488i	1.11634	−	1.11634i
$195$	−7.26658	+	11.8212i	−0.520371	+	0.846535i
$196$		−	25.6792i		−	1.83423i
$197$	−0.614707	−	0.614707i	−0.0437960	−	0.0437960i	0.684870	−	0.728666i	$-0.259859\pi$
$197$	−0.614707	−	0.614707i	−0.0437960	−	0.0437960i	−0.728666	+	0.684870i	$0.759859\pi$
$198$	−6.15739	−	6.15739i	−0.437587	−	0.437587i
$199$	9.40478	+	9.40478i	0.666687	+	0.666687i	0.956948	−	0.290260i	$-0.0937419\pi$
$199$	9.40478	+	9.40478i	0.666687	+	0.666687i	−0.290260	+	0.956948i	$0.593742\pi$
$200$	−18.0336	+	9.12576i	−1.27517	+	0.645289i
$201$	−25.6792	−	25.6792i	−1.81127	−	1.81127i
$202$	−17.2027			−1.21038
$203$		−	1.54053i		−	0.108124i
$204$	46.9536	−	10.1924i	3.28741	−	0.713612i
$205$	−1.51837	−	0.933353i	−0.106048	−	0.0651882i
$206$			22.7276i			1.58351i
$207$	1.83186	−	1.83186i	0.127323	−	0.127323i
$208$			4.44102i			0.307929i
$209$	1.48478	+	1.48478i	0.102705	+	0.102705i
$210$	−0.859454	−	3.60185i	−0.0593080	−	0.248551i
$211$	−12.5804	+	12.5804i	−0.866071	+	0.866071i	−0.992035	−	0.125964i	$-0.959798\pi$
$211$	−12.5804	+	12.5804i	−0.866071	+	0.866071i	0.125964	+	0.992035i	$0.459798\pi$
$212$	21.8747			1.50236
$213$	22.5973			1.54834
$214$	18.1956	−	18.1956i	1.24382	−	1.24382i
$215$	1.29444	+	5.42483i	0.0882804	+	0.369970i
$216$	35.6308	+	35.6308i	2.42437	+	2.42437i
$217$		−	0.642517i		−	0.0436169i
$218$	−23.7466	+	23.7466i	−1.60832	+	1.60832i
$219$			3.73924i			0.252674i
$220$	−3.69399	−	2.27072i	−0.249049	−	0.153092i
$221$	4.38799	−	6.82122i	0.295168	−	0.458845i
$222$			43.0319i			2.88811i
$223$	−1.96713			−0.131729			−0.0658645	−	0.997829i	$-0.520981\pi$
$223$	−1.96713			−0.131729			−0.0658645	+	0.997829i	$0.520981\pi$
$224$	0.419593	+	0.419593i	0.0280352	+	0.0280352i
$225$	15.6940	+	31.0132i	1.04627	+	2.06755i
$226$	−12.1304	−	12.1304i	−0.806901	−	0.806901i
$227$	8.45593	+	8.45593i	0.561239	+	0.561239i	0.929659	−	0.368420i	$-0.120101\pi$
$227$	8.45593	+	8.45593i	0.561239	+	0.561239i	−0.368420	+	0.929659i	$0.620101\pi$
$228$	−32.9600	−	32.9600i	−2.18283	−	2.18283i
$229$		−	9.30601i		−	0.614958i	−0.951555	−	0.307479i	$-0.900515\pi$
$229$		−	9.30601i		−	0.614958i	0.951555	−	0.307479i	$-0.0994854\pi$
$230$	1.04131	−	1.69399i	0.0686620	−	0.111699i
$231$	0.257608	−	0.257608i	0.0169494	−	0.0169494i
$232$	20.0155	+	20.0155i	1.31408	+	1.31408i
$233$	18.2440	−	18.2440i	1.19520	−	1.19520i	0.219618	−	0.975586i	$-0.429519\pi$
$233$	18.2440	−	18.2440i	1.19520	−	1.19520i	0.975586	−	0.219618i	$-0.0704811\pi$
$234$	32.6308			2.13314
$235$	−14.6586	+	3.49775i	−0.956220	+	0.228168i
$236$		−	22.1640i		−	1.44275i
$237$		−	21.2322i		−	1.37918i
$238$	0.459148	+	2.11516i	0.0297621	+	0.137106i
$239$	−29.2912			−1.89469			−0.947345	−	0.320215i	$-0.896245\pi$
$239$	−29.2912			−1.89469			−0.947345	+	0.320215i	$0.896245\pi$
$240$	13.5668	+	8.33959i	0.875732	+	0.538318i
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	0.873435	−	0.486941i	$-0.161887\pi$
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	−0.486941	+	0.873435i	$0.661887\pi$
$242$			25.5907i			1.64503i
$243$	14.7561	−	14.7561i	0.946606	−	0.946606i
$244$	−14.7760	+	14.7760i	−0.945935	+	0.945935i
$245$	−15.1198	+	3.60781i	−0.965967	+	0.230494i
$246$			6.00000i			0.382546i
$247$	−7.86854			−0.500663
$248$	8.34797	+	8.34797i	0.530097	+	0.530097i
$249$	−13.6456	+	13.6456i	−0.864755	+	0.864755i
$250$	17.2420	+	20.3584i	1.09048	+	1.28758i
$251$	−1.77282			−0.111900			−0.0559498	−	0.998434i	$-0.517819\pi$
$251$	−1.77282			−0.111900			−0.0559498	+	0.998434i	$0.517819\pi$
$252$	−3.99462	+	3.99462i	−0.251638	+	0.251638i
$253$	0.195632			0.0122993
$254$	−23.2428			−1.45838
$255$	−12.5980	−	26.2141i	−0.788918	−	1.64159i
$256$	−27.5824			−1.72390
$257$	−7.40235			−0.461746			−0.230873	−	0.972984i	$-0.574158\pi$
$257$	−7.40235			−0.461746			−0.230873	+	0.972984i	$0.574158\pi$
$258$	13.2759	−	13.2759i	0.826524	−	0.826524i
$259$	−1.25761			−0.0781440
$260$	15.8049	−	3.77128i	0.980176	−	0.233885i
$261$	34.4216	−	34.4216i	2.13064	−	2.13064i
$262$	−33.2160	−	33.2160i	−2.05209	−	2.05209i
$263$	7.67291			0.473132			0.236566	−	0.971615i	$-0.423978\pi$
$263$	7.67291			0.473132			0.236566	+	0.971615i	$0.423978\pi$
$264$			6.69399i			0.411987i
$265$	−3.07329	−	12.8797i	−0.188791	−	0.791194i
$266$	1.48478	−	1.48478i	0.0910379	−	0.0910379i
$267$	−35.6574	+	35.6574i	−2.18220	+	2.18220i
$268$			42.5252i			2.59764i
$269$	−5.56677	−	5.56677i	−0.339412	−	0.339412i	0.516734	−	0.856146i	$-0.327148\pi$
$269$	−5.56677	−	5.56677i	−0.339412	−	0.339412i	−0.856146	+	0.516734i	$0.827148\pi$
$270$	34.8320	−	56.6644i	2.11981	−	3.44848i
$271$	18.0672			1.09750			0.548751	−	0.835986i	$-0.315103\pi$
$271$	18.0672			1.09750			0.548751	+	0.835986i	$0.315103\pi$
$272$	−7.82847	−	5.03593i	−0.474670	−	0.305348i
$273$			1.36518i			0.0826245i
$274$		−	11.1124i		−	0.671326i
$275$	−0.818002	+	2.49403i	−0.0493274	+	0.150396i
$276$	−4.34275			−0.261403
$277$	−18.7786	+	18.7786i	−1.12829	+	1.12829i	−0.137840	+	0.990455i	$0.544016\pi$
$277$	−18.7786	+	18.7786i	−1.12829	+	1.12829i	−0.990455	+	0.137840i	$0.955984\pi$
$278$	−8.85472	−	8.85472i	−0.531071	−	0.531071i
$279$	14.3564	−	14.3564i	0.859494	−	0.859494i
$280$	−1.04131	+	1.69399i	−0.0622302	+	0.101236i
$281$			13.7728i			0.821618i	0.911721	+	0.410809i	$0.134754\pi$
$281$			13.7728i			0.821618i	−0.911721	+	0.410809i	$0.865246\pi$
$282$	35.8733	+	35.8733i	2.13622	+	2.13622i
$283$	−9.72068	−	9.72068i	−0.577834	−	0.577834i	0.356472	−	0.934306i	$-0.383980\pi$
$283$	−9.72068	−	9.72068i	−0.577834	−	0.577834i	−0.934306	+	0.356472i	$0.883980\pi$
$284$	−18.7108	−	18.7108i	−1.11028	−	1.11028i
$285$	−14.7760	+	24.0374i	−0.875253	+	1.42386i
$286$	1.74239	+	1.74239i	0.103030	+	0.103030i
$287$	−0.175350			−0.0103506
$288$			18.7507i			1.10490i
$289$	7.04840	+	15.4700i	0.414612	+	0.909998i
$290$	19.5668	−	31.8311i	1.14900	−	1.86918i
$291$			29.0703i			1.70413i
$292$	3.09612	−	3.09612i	0.181187	−	0.181187i
$293$			19.8873i			1.16183i	0.813966	+	0.580913i	$0.197304\pi$
$293$			19.8873i			1.16183i	−0.813966	+	0.580913i	$0.802696\pi$
$294$	37.0020	+	37.0020i	2.15800	+	2.15800i
$295$	−13.0500	+	3.11393i	−0.759802	+	0.181300i
$296$	16.3396	−	16.3396i	0.949720	−	0.949720i
$297$	6.54392			0.379717
$298$	20.8612			1.20846
$299$	−0.518371	+	0.518371i	−0.0299782	+	0.0299782i
$300$	18.1585	−	55.3639i	1.04838	−	3.19644i
$301$	0.387990	+	0.387990i	0.0223634	+	0.0223634i
$302$		−	37.9484i		−	2.18368i
$303$	16.0812	−	16.0812i	0.923843	−	0.923843i
$304$			9.03043i			0.517931i
$305$	10.7760	+	6.62407i	0.617031	+	0.379293i
$306$	−37.0020	+	57.5204i	−2.11526	+	3.28822i
$307$		−	14.9598i		−	0.853799i	−0.904299	−	0.426900i	$-0.859606\pi$
$307$		−	14.9598i		−	0.853799i	0.904299	−	0.426900i	$-0.140394\pi$
$308$	−0.426603			−0.0243080
$309$	−21.2460	−	21.2460i	−1.20864	−	1.20864i
$310$	8.16081	−	13.2759i	0.463503	−	0.754023i
$311$	−20.9684	−	20.9684i	−1.18901	−	1.18901i	−0.977342	−	0.211667i	$-0.932111\pi$
$311$	−20.9684	−	20.9684i	−1.18901	−	1.18901i	−0.211667	−	0.977342i	$-0.567889\pi$
$312$	−17.7372	−	17.7372i	−1.00417	−	1.00417i
$313$	10.1671	+	10.1671i	0.574677	+	0.574677i	0.933432	−	0.358755i	$-0.116799\pi$
$313$	10.1671	+	10.1671i	0.574677	+	0.574677i	−0.358755	+	0.933432i	$0.616799\pi$
$314$		−	24.0336i		−	1.35629i
$315$	2.91324	+	1.79079i	0.164143	+	0.100900i
$316$	−17.5804	+	17.5804i	−0.988975	+	0.988975i
$317$	−9.74047	−	9.74047i	−0.547079	−	0.547079i	0.378516	−	0.925595i	$-0.376435\pi$
$317$	−9.74047	−	9.74047i	−0.547079	−	0.547079i	−0.925595	+	0.378516i	$0.876435\pi$
$318$	−31.5199	+	31.5199i	−1.76755	+	1.76755i
$319$	3.67603			0.205818
$320$	5.68376	+	23.8198i	0.317732	+	1.33157i
$321$			34.0188i			1.89874i
$322$		−	0.195632i		−	0.0109021i
$323$	8.92260	−	13.8704i	0.496467	−	0.771768i
$324$	−68.2280			−3.79044
$325$	−4.44102	−	8.77598i	−0.246343	−	0.486804i
$326$	16.1776	+	16.1776i	0.895995	+	0.895995i
$327$		−	44.3971i		−	2.45516i
$328$	2.27825	−	2.27825i	0.125795	−	0.125795i
$329$	−1.04840	+	1.04840i	−0.0578000	+	0.0578000i
$330$	8.59476	−	2.05084i	0.473126	−	0.112895i
$331$		−	20.1640i		−	1.10831i	−0.832413	−	0.554156i	$-0.813041\pi$
$331$		−	20.1640i		−	1.10831i	0.832413	−	0.554156i	$-0.186959\pi$
$332$	22.5973			1.24019
$333$	−28.1000	−	28.1000i	−1.53987	−	1.53987i
$334$	−9.01679	+	9.01679i	−0.493377	+	0.493377i
$335$	25.0386	−	5.97459i	1.36801	−	0.326427i
$336$	1.56677			0.0854742
$337$	20.2111	−	20.2111i	1.10097	−	1.10097i	0.106677	−	0.994294i	$-0.465979\pi$
$337$	20.2111	−	20.2111i	1.10097	−	1.10097i	0.994294	−	0.106677i	$-0.0340210\pi$
$338$	21.7870			1.18506
$339$	22.6792			1.23176
$340$	−11.2742	+	32.1367i	−0.611430	+	1.74286i
$341$	1.53318			0.0830264
$342$	66.3519			3.58790
$343$	−2.17030	+	2.17030i	−0.117185	+	0.117185i
$344$	−10.0820			−0.543584
$345$	0.610136	+	2.55699i	0.0328486	+	0.137664i
$346$	−29.4520	+	29.4520i	−1.58335	+	1.58335i
$347$	7.73326	+	7.73326i	0.415143	+	0.415143i	0.883526	−	0.468383i	$-0.155163\pi$
$347$	7.73326	+	7.73326i	0.415143	+	0.415143i	−0.468383	+	0.883526i	$0.655163\pi$
$348$	−81.6025			−4.37435
$349$		−	0.645598i		−	0.0345581i	−0.999851	−	0.0172790i	$-0.994500\pi$
$349$		−	0.645598i		−	0.0345581i	0.999851	−	0.0172790i	$-0.00550036\pi$
$350$	2.49403	+	0.818002i	0.133312	+	0.0437240i
$351$	−17.3396	+	17.3396i	−0.925519	+	0.925519i
$352$	−1.00124	+	1.00124i	−0.0533661	+	0.0533661i
$353$			14.3022i			0.761229i	0.924734	+	0.380615i	$0.124288\pi$
$353$			14.3022i			0.761229i	−0.924734	+	0.380615i	$0.875712\pi$
$354$	31.9368	+	31.9368i	1.69742	+	1.69742i
$355$	−8.38804	+	13.6456i	−0.445191	+	0.724233i
$356$	59.0492			3.12960
$357$	−2.40649	−	1.54806i	−0.127365	−	0.0819320i
$358$			50.8854i			2.68938i
$359$		−	15.6760i		−	0.827349i	−0.910425	−	0.413675i	$-0.864245\pi$
$359$		−	15.6760i		−	0.827349i	0.910425	−	0.413675i	$-0.135755\pi$
$360$	−61.1176	+	14.5836i	−3.22118	+	0.768621i
$361$	3.00000			0.157895
$362$	24.3613	−	24.3613i	1.28040	−	1.28040i
$363$	−23.9224	−	23.9224i	−1.25560	−	1.25560i
$364$	1.13038	−	1.13038i	0.0592481	−	0.0592481i
$365$	−2.25797	−	1.38799i	−0.118188	−	0.0726507i
$366$		−	42.5824i		−	2.22582i
$367$	15.4863	+	15.4863i	0.808379	+	0.808379i	0.984388	−	0.176009i	$-0.0563189\pi$
$367$	15.4863	+	15.4863i	0.808379	+	0.808379i	−0.176009	+	0.984388i	$0.556319\pi$
$368$	0.594916	+	0.594916i	0.0310121	+	0.0310121i
$369$	−3.91802	−	3.91802i	−0.203964	−	0.203964i
$370$	−25.9852	−	15.9733i	−1.35091	−	0.830411i
$371$	−0.921171	−	0.921171i	−0.0478248	−	0.0478248i
$372$	−34.0344			−1.76460
$373$		−	6.50858i		−	0.337002i	−0.985702	−	0.168501i	$-0.946107\pi$
$373$		−	6.50858i		−	0.337002i	0.985702	−	0.168501i	$-0.0538926\pi$
$374$	−5.04723	+	1.09562i	−0.260986	+	0.0566533i
$375$	−35.1492	−	2.91324i	−1.81509	−	0.150439i
$376$		−	27.2428i		−	1.40494i
$377$	−9.74047	+	9.74047i	−0.501660	+	0.501660i
$378$		−	6.54392i		−	0.336583i
$379$	−5.32280	−	5.32280i	−0.273414	−	0.273414i	0.557059	−	0.830473i	$-0.311930\pi$
$379$	−5.32280	−	5.32280i	−0.273414	−	0.273414i	−0.830473	+	0.557059i	$0.811930\pi$
$380$	32.1378	−	7.66857i	1.64864	−	0.393389i
$381$	21.7276	−	21.7276i	1.11314	−	1.11314i
$382$	−16.0888			−0.823172
$383$	−24.7752			−1.26595			−0.632976	−	0.774172i	$-0.718167\pi$
$383$	−24.7752			−1.26595			−0.632976	+	0.774172i	$0.718167\pi$
$384$	46.2596	−	46.2596i	2.36067	−	2.36067i
$385$	0.0599358	+	0.251182i	0.00305461	+	0.0128014i
$386$	−24.7276	−	24.7276i	−1.25860	−	1.25860i
$387$			17.3385i			0.881363i
$388$	24.0705	−	24.0705i	1.22199	−	1.22199i
$389$			23.6971i			1.20149i	0.799440	+	0.600747i	$0.205130\pi$
$389$			23.6971i			1.20149i	−0.799440	+	0.600747i	$0.794870\pi$
$390$	−17.3396	+	28.2079i	−0.878024	+	1.42836i
$391$	−0.325954	−	1.50158i	−0.0164842	−	0.0759380i
$392$		−	28.1000i		−	1.41926i
$393$	62.1013			3.13260
$394$	−1.46682	−	1.46682i	−0.0738973	−	0.0738973i
$395$	12.8212	+	7.88129i	0.645106	+	0.396551i
$396$	−9.53201	−	9.53201i	−0.479002	−	0.479002i
$397$	19.5964	+	19.5964i	0.983516	+	0.983516i	0.999866	−	0.0163500i	$-0.00520460\pi$
$397$	19.5964	+	19.5964i	0.983516	+	0.983516i	−0.0163500	+	0.999866i	$0.505205\pi$
$398$	22.4418	+	22.4418i	1.12490	+	1.12490i
$399$			2.77598i			0.138973i
$400$	−10.0719	+	5.09679i	−0.503593	+	0.254840i
$401$	−21.5972	+	21.5972i	−1.07851	+	1.07851i	−0.0818697	+	0.996643i	$0.526089\pi$
$401$	−21.5972	+	21.5972i	−1.07851	+	1.07851i	−0.996643	+	0.0818697i	$0.973911\pi$
$402$	−61.2759	−	61.2759i	−3.05616	−	3.05616i
$403$	−4.06251	+	4.06251i	−0.202368	+	0.202368i
$404$	−26.6308			−1.32493
$405$	9.58571	+	40.1723i	0.476318	+	1.99618i
$406$		−	3.67603i		−	0.182438i
$407$		−	3.00092i		−	0.148750i
$408$	51.3799	−	11.1533i	2.54368	−	0.552168i
$409$	5.90321			0.291895			0.145947	−	0.989292i	$-0.453377\pi$
$409$	5.90321			0.291895			0.145947	+	0.989292i	$0.453377\pi$
$410$	−3.62315	−	2.22718i	−0.178935	−	0.109992i
$411$	10.3880	+	10.3880i	0.512402	+	0.512402i
$412$			35.1837i			1.73337i
$413$	−0.933353	+	0.933353i	−0.0459273	+	0.0459273i
$414$	4.37120	−	4.37120i	0.214833	−	0.214833i
$415$	−3.17482	−	13.3052i	−0.155846	−	0.653127i
$416$		−	5.30601i		−	0.260148i
$417$	16.5549			0.810699
$418$	3.54301	+	3.54301i	0.173294	+	0.173294i
$419$	22.9716	−	22.9716i	1.12223	−	1.12223i	0.130829	−	0.991405i	$-0.458236\pi$
$419$	22.9716	−	22.9716i	1.12223	−	1.12223i	0.991405	−	0.130829i	$-0.0417638\pi$
$420$	−1.33049	−	5.57587i	−0.0649211	−	0.272075i
$421$	30.1156			1.46774			0.733872	−	0.679288i	$-0.237711\pi$
$421$	30.1156			1.46774			0.733872	+	0.679288i	$0.237711\pi$
$422$	−30.0195	+	30.0195i	−1.46133	+	1.46133i
$423$	−46.8507			−2.27796
$424$	23.9368			1.16247
$425$	20.5059	+	2.12314i	0.994683	+	0.102987i
$426$	53.9220			2.61253
$427$	1.24447			0.0602242
$428$	28.1678	−	28.1678i	1.36154	−	1.36154i
$429$	−3.25761			−0.157279
$430$	3.08882	+	12.9448i	0.148956	+	0.624252i
$431$	−5.88641	+	5.88641i	−0.283538	+	0.283538i	−0.834518	−	0.550980i	$-0.814254\pi$
$431$	−5.88641	+	5.88641i	−0.283538	+	0.283538i	0.550980	+	0.834518i	$0.314254\pi$
$432$	19.9000	+	19.9000i	0.957440	+	0.957440i
$433$	−13.5795			−0.652591			−0.326295	−	0.945268i	$-0.605800\pi$
$433$	−13.5795			−0.652591			−0.326295	+	0.945268i	$0.605800\pi$
$434$		−	1.53318i		−	0.0735950i
$435$	11.4648	+	48.0472i	0.549694	+	2.30369i
$436$	−36.7612	+	36.7612i	−1.76054	+	1.76054i
$437$	−1.05406	+	1.05406i	−0.0504227	+	0.0504227i
$438$			8.92260i			0.426338i
$439$	14.4048	+	14.4048i	0.687503	+	0.687503i	0.961679	−	0.274177i	$-0.0884053\pi$
$439$	14.4048	+	14.4048i	0.687503	+	0.687503i	−0.274177	+	0.961679i	$0.588405\pi$
$440$	−4.04223	−	2.48478i	−0.192706	−	0.118457i
$441$	−48.3248			−2.30118
$442$	10.4707	−	16.2769i	0.498039	−	0.774211i
$443$		−	2.45360i		−	0.116574i	−0.998300	−	0.0582871i	$-0.981436\pi$
$443$		−	2.45360i		−	0.116574i	0.998300	−	0.0582871i	$-0.0185639\pi$
$444$			66.6160i			3.16145i
$445$	−8.29614	−	34.7679i	−0.393275	−	1.64816i
$446$	−4.69399			−0.222267
$447$	−19.5012	+	19.5012i	−0.922376	+	0.922376i
$448$	1.70362	+	1.70362i	0.0804884	+	0.0804884i
$449$	2.26076	−	2.26076i	0.106692	−	0.106692i	−0.651746	−	0.758438i	$-0.725963\pi$
$449$	2.26076	−	2.26076i	0.106692	−	0.106692i	0.758438	+	0.651746i	$0.225963\pi$
$450$	37.4492	+	74.0040i	1.76537	+	3.48858i
$451$		−	0.418422i		−	0.0197027i
$452$	−18.7786	−	18.7786i	−0.883269	−	0.883269i
$453$	35.4745	+	35.4745i	1.66674	+	1.66674i
$454$	20.1776	+	20.1776i	0.946982	+	0.946982i
$455$	−0.824376	−	0.506750i	−0.0386474	−	0.0237568i
$456$	−36.0672	−	36.0672i	−1.68900	−	1.68900i
$457$	30.1803			1.41177			0.705887	−	0.708325i	$-0.250549\pi$
$457$	30.1803			1.41177			0.705887	+	0.708325i	$0.250549\pi$
$458$		−	22.2061i		−	1.03762i
$459$	−10.9032	−	50.2280i	−0.508918	−	2.34444i
$460$	1.61201	−	2.62241i	0.0751604	−	0.122270i
$461$		−	5.41527i		−	0.252214i	−0.992017	−	0.126107i	$-0.959752\pi$
$461$		−	5.41527i		−	0.252214i	0.992017	−	0.126107i	$-0.0402483\pi$
$462$	0.614707	−	0.614707i	0.0285987	−	0.0285987i
$463$		−	15.7574i		−	0.732307i	−0.930555	−	0.366153i	$-0.880675\pi$
$463$		−	15.7574i		−	0.732307i	0.930555	−	0.366153i	$-0.119325\pi$
$464$	11.1788	+	11.1788i	0.518962	+	0.518962i
$465$	4.78167	+	20.0393i	0.221745	+	0.929299i
$466$	43.5340	−	43.5340i	2.01667	−	2.01667i
$467$	−10.7690			−0.498331			−0.249166	−	0.968461i	$-0.580156\pi$
$467$	−10.7690			−0.498331			−0.249166	+	0.968461i	$0.580156\pi$
$468$	50.5144			2.33503
$469$	1.79079	−	1.79079i	0.0826910	−	0.0826910i
$470$	−34.9784	+	8.34637i	−1.61343	+	0.384989i
$471$	22.4668	+	22.4668i	1.03522	+	1.03522i
$472$		−	24.2534i		−	1.11635i
$473$	−0.925824	+	0.925824i	−0.0425695	+	0.0425695i
$474$		−	50.6644i		−	2.32709i
$475$	−9.03043	−	17.8452i	−0.414345	−	0.818794i
$476$	0.710788	+	3.27440i	0.0325789	+	0.150082i
$477$		−	41.1652i		−	1.88483i
$478$	−69.8949			−3.19692
$479$	26.0988	+	26.0988i	1.19248	+	1.19248i	0.976368	+	0.216116i	$0.0693389\pi$
$479$	26.0988	+	26.0988i	1.19248	+	1.19248i	0.216116	+	0.976368i	$0.430661\pi$
$480$	−16.2092	−	9.96391i	−0.739846	−	0.454788i
$481$	7.95160	+	7.95160i	0.362562	+	0.362562i
$482$	14.3173	+	14.3173i	0.652133	+	0.652133i
$483$	0.182879	+	0.182879i	0.00832127	+	0.00832127i
$484$			39.6160i			1.80073i
$485$	−17.5544	−	10.7908i	−0.797103	−	0.489984i
$486$	35.2112	−	35.2112i	1.59721	−	1.59721i
$487$	27.0987	+	27.0987i	1.22796	+	1.22796i	0.964734	+	0.263226i	$0.0847864\pi$
$487$	27.0987	+	27.0987i	1.22796	+	1.22796i	0.263226	+	0.964734i	$0.415214\pi$
$488$	−16.1689	+	16.1689i	−0.731932	+	0.731932i
$489$	−30.2460			−1.36777
$490$	−36.0790	+	8.60898i	−1.62988	+	0.388914i
$491$		−	38.0336i		−	1.71643i	−0.513289	−	0.858216i	$-0.671573\pi$
$491$		−	38.0336i		−	1.71643i	0.513289	−	0.858216i	$-0.328427\pi$
$492$			9.28836i			0.418752i
$493$	−6.12485	−	28.2154i	−0.275849	−	1.27076i
$494$	−18.7760			−0.844771
$495$	−4.27320	+	6.95160i	−0.192066	+	0.312451i
$496$	4.66239	+	4.66239i	0.209348	+	0.209348i
$497$			1.57587i			0.0706875i
$498$	−32.5613	+	32.5613i	−1.45910	+	1.45910i
$499$	6.58041	−	6.58041i	0.294579	−	0.294579i	−0.544307	−	0.838886i	$-0.683207\pi$
$499$	6.58041	−	6.58041i	0.294579	−	0.294579i	0.838886	+	0.544307i	$0.183207\pi$
$500$	26.6916	+	31.5160i	1.19369	+	1.40944i
$501$		−	16.8580i		−	0.753158i
$502$	−4.23033			−0.188809
$503$	−1.10919	−	1.10919i	−0.0494565	−	0.0494565i	0.681946	−	0.731403i	$-0.261134\pi$
$503$	−1.10919	−	1.10919i	−0.0494565	−	0.0494565i	−0.731403	+	0.681946i	$0.761134\pi$
$504$	−4.37120	+	4.37120i	−0.194709	+	0.194709i
$505$	3.74150	+	15.6801i	0.166495	+	0.697754i
$506$	0.466819			0.0207526
$507$	−20.3667	+	20.3667i	−0.904516	+	0.904516i
$508$	−35.9812			−1.59641
$509$	−24.4247			−1.08261			−0.541304	−	0.840827i	$-0.682069\pi$
$509$	−24.4247			−1.08261			−0.541304	+	0.840827i	$0.682069\pi$
$510$	−30.0615	−	62.5522i	−1.33114	−	2.76986i
$511$	−0.260763			−0.0115355
$512$	−24.3410			−1.07573
$513$	−35.2586	+	35.2586i	−1.55670	+	1.55670i
$514$	−17.6636			−0.779106
$515$	20.7160	−	4.94314i	0.912854	−	0.217821i
$516$	20.5520	−	20.5520i	0.904750	−	0.904750i
$517$	−2.50169	−	2.50169i	−0.110024	−	0.110024i
$518$	−3.00092			−0.131853
$519$		−	55.0640i		−	2.41704i
$520$	17.2948	−	4.12679i	0.758426	−	0.180972i
$521$	−5.30916	+	5.30916i	−0.232599	+	0.232599i	−0.813776	−	0.581178i	$-0.802592\pi$
$521$	−5.30916	+	5.30916i	−0.232599	+	0.232599i	0.581178	+	0.813776i	$0.302592\pi$
$522$	82.1371	−	82.1371i	3.59504	−	3.59504i
$523$		−	8.98247i		−	0.392776i	−0.980526	−	0.196388i	$-0.937079\pi$
$523$		−	8.98247i		−	0.392776i	0.980526	−	0.196388i	$-0.0629212\pi$
$524$	−51.4204	−	51.4204i	−2.24631	−	2.24631i
$525$	−3.09612	+	1.56677i	−0.135126	+	0.0683794i
$526$	18.3092			0.798317
$527$	−2.55452	−	11.7680i	−0.111277	−	0.512620i
$528$			3.73864i			0.162703i
$529$		−	22.8611i		−	0.993962i
$530$	−7.33351	−	30.7337i	−0.318547	−	1.33498i
$531$	−41.7096			−1.81004
$532$	2.29853	−	2.29853i	0.0996541	−	0.0996541i
$533$	1.10870	+	1.10870i	0.0480233	+	0.0480233i
$534$	−85.0860	+	85.0860i	−3.68203	+	3.68203i
$535$	−20.5425	−	12.6276i	−0.888131	−	0.545940i
$536$			46.5340i			2.00996i
$537$	−47.5681	−	47.5681i	−2.05272	−	2.05272i
$538$	−13.2835	−	13.2835i	−0.572691	−	0.572691i
$539$	−2.58041	−	2.58041i	−0.111146	−	0.111146i
$540$	53.9220	−	87.7198i	2.32043	−	3.77486i
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	43.1121			1.85182
$543$			45.5464i			1.95458i
$544$	9.35323	+	6.01679i	0.401016	+	0.257968i
$545$	26.8096	+	16.4800i	1.14840	+	0.705927i
$546$			3.25761i			0.139413i
$547$	1.81910	−	1.81910i	0.0777793	−	0.0777793i	−0.667147	−	0.744926i	$-0.732485\pi$
$547$	1.81910	−	1.81910i	0.0777793	−	0.0777793i	0.744926	+	0.667147i	$0.232485\pi$
$548$		−	17.2027i		−	0.734862i
$549$	27.8064	+	27.8064i	1.18675	+	1.18675i
$550$	−1.95192	+	5.95128i	−0.0832303	+	0.253764i
$551$	−19.8064	+	19.8064i	−0.843782	+	0.843782i
$552$	−4.75214			−0.202264
$553$	1.48067			0.0629644
$554$	−44.8096	+	44.8096i	−1.90378	+	1.90378i
$555$	39.2232	−	9.35923i	1.66493	−	0.397277i
$556$	−13.7076	−	13.7076i	−0.581333	−	0.581333i
$557$			21.0162i			0.890487i	0.895410	+	0.445243i	$0.146883\pi$
$557$			21.0162i			0.890487i	−0.895410	+	0.445243i	$0.853117\pi$
$558$	34.2573	−	34.2573i	1.45023	−	1.45023i
$559$		−	4.90636i		−	0.207517i
$560$	−0.581578	+	0.946106i	−0.0245762	+	0.0399803i
$561$	3.69399	−	5.74239i	0.155961	−	0.242444i
$562$			32.8648i			1.38632i
$563$	40.5377			1.70846			0.854231	−	0.519893i	$-0.174028\pi$
$563$	40.5377			1.70846			0.854231	+	0.519893i	$0.174028\pi$
$564$	55.5340	+	55.5340i	2.33840	+	2.33840i
$565$	−8.41842	+	13.6950i	−0.354166	+	0.576154i
$566$	−23.1956	−	23.1956i	−0.974983	−	0.974983i
$567$	2.87317	+	2.87317i	0.120662	+	0.120662i
$568$	−20.4746	−	20.4746i	−0.859097	−	0.859097i
$569$			0.612010i			0.0256568i	0.999918	+	0.0128284i	$0.00408352\pi$
$569$			0.612010i			0.0256568i	−0.999918	+	0.0128284i	$0.995916\pi$
$570$	−35.2586	+	57.3584i	−1.47682	+	2.40248i
$571$	−10.5320	+	10.5320i	−0.440751	+	0.440751i	−0.892264	−	0.451513i	$-0.850884\pi$
$571$	−10.5320	+	10.5320i	−0.440751	+	0.440751i	0.451513	+	0.892264i	$0.350884\pi$
$572$	2.69733	+	2.69733i	0.112781	+	0.112781i
$573$	15.0399	−	15.0399i	0.628302	−	0.628302i
$574$	−0.418422			−0.0174646
$575$	−1.77054	−	0.580708i	−0.0738366	−	0.0242172i
$576$			76.1312i			3.17213i
$577$			37.2107i			1.54910i	0.632513	+	0.774550i	$0.282024\pi$
$577$			37.2107i			1.54910i	−0.632513	+	0.774550i	$0.717976\pi$
$578$	16.8190	+	36.9146i	0.699576	+	1.53544i
$579$	46.2311			1.92130
$580$	30.2905	−	49.2764i	1.25775	−	2.04609i
$581$	−0.951603	−	0.951603i	−0.0394791	−	0.0394791i
$582$			69.3679i			2.87539i
$583$	2.19811	−	2.19811i	0.0910362	−	0.0910362i
$584$	3.38799	−	3.38799i	0.140196	−	0.140196i
$585$	−7.09704	−	29.7426i	−0.293426	−	1.22971i
$586$			47.4552i			1.96035i
$587$	−9.60470			−0.396428			−0.198214	−	0.980159i	$-0.563514\pi$
$587$	−9.60470			−0.396428			−0.198214	+	0.980159i	$0.563514\pi$
$588$	57.2813	+	57.2813i	2.36224	+	2.36224i
$589$	−8.26076	+	8.26076i	−0.340379	+	0.340379i
$590$	−31.1401	+	7.43050i	−1.28202	+	0.305909i
$591$	2.74239			0.112807
$592$	9.12576	−	9.12576i	0.375067	−	0.375067i
$593$	−16.5206			−0.678419			−0.339210	−	0.940711i	$-0.610160\pi$
$593$	−16.5206			−0.678419			−0.339210	+	0.940711i	$0.610160\pi$
$594$	15.6152			0.640698
$595$	1.82809	−	0.878547i	0.0749443	−	0.0360169i
$596$	32.2944			1.32283
$597$	−41.9576			−1.71721
$598$	−1.23694	+	1.23694i	−0.0505823	+	0.0505823i
$599$	34.8096			1.42228			0.711140	−	0.703050i	$-0.248179\pi$
$599$	34.8096			1.42228			0.711140	+	0.703050i	$0.248179\pi$
$600$	19.8702	−	60.5830i	0.811199	−	2.47329i
$601$	−8.26076	+	8.26076i	−0.336964	+	0.336964i	−0.855223	−	0.518260i	$-0.826580\pi$
$601$	−8.26076	+	8.26076i	−0.336964	+	0.336964i	0.518260	+	0.855223i	$0.326580\pi$
$602$	0.925824	+	0.925824i	0.0377338	+	0.0377338i
$603$	80.0267			3.25894
$604$		−	58.7464i		−	2.39036i
$605$	23.3257	−	5.56586i	0.948324	−	0.226284i
$606$	38.3732	−	38.3732i	1.55880	−	1.55880i
$607$	19.0421	−	19.0421i	0.772894	−	0.772894i	−0.205718	−	0.978611i	$-0.565953\pi$
$607$	19.0421	−	19.0421i	0.772894	−	0.772894i	0.978611	+	0.205718i	$0.0659528\pi$
$608$		−	10.7893i		−	0.437564i
$609$	3.43639	+	3.43639i	0.139249	+	0.139249i
$610$	25.7137	+	15.8064i	1.04112	+	0.639983i
$611$	13.2576			0.536345
$612$	−57.2813	+	89.0450i	−2.31546	+	3.59943i
$613$			5.43522i			0.219526i	0.993958	+	0.109763i	$0.0350092\pi$
$613$			5.43522i			0.219526i	−0.993958	+	0.109763i	$0.964991\pi$
$614$		−	35.6971i		−	1.44062i
$615$	5.46894	−	1.30497i	0.220529	−	0.0526215i
$616$	−0.466819			−0.0188087
$617$	2.47388	−	2.47388i	0.0995948	−	0.0995948i	−0.655554	−	0.755149i	$-0.727565\pi$
$617$	2.47388	−	2.47388i	0.0995948	−	0.0995948i	0.755149	+	0.655554i	$0.227565\pi$
$618$	−50.6973	−	50.6973i	−2.03934	−	2.03934i
$619$	8.57725	−	8.57725i	0.344749	−	0.344749i	−0.513400	−	0.858149i	$-0.671614\pi$
$619$	8.57725	−	8.57725i	0.344749	−	0.344749i	0.858149	+	0.513400i	$0.171614\pi$
$620$	12.6334	−	20.5520i	0.507371	−	0.825387i
$621$			4.64560i			0.186421i
$622$	−50.0350	−	50.0350i	−2.00622	−	2.00622i
$623$	−2.48664	−	2.48664i	−0.0996250	−	0.0996250i
$624$	−9.90636	−	9.90636i	−0.396572	−	0.396572i
$625$	14.8064	−	20.1437i	0.592256	−	0.805750i
$626$	24.2608	+	24.2608i	0.969655	+	0.969655i
$627$	−6.62407			−0.264540
$628$		−	37.2054i		−	1.48466i
$629$	−23.0336	+	5.00000i	−0.918409	+	0.199363i
$630$	6.95160	+	4.27320i	0.276958	+	0.170248i
$631$		−	12.6183i		−	0.502327i	−0.967945	−	0.251164i	$-0.919187\pi$
$631$		−	12.6183i		−	0.502327i	0.967945	−	0.251164i	$-0.0808132\pi$
$632$	−19.2377	+	19.2377i	−0.765235	+	0.765235i
$633$		−	56.1250i		−	2.23077i
$634$	−23.2428	−	23.2428i	−0.923089	−	0.923089i
$635$	5.05520	+	21.1856i	0.200609	+	0.840724i
$636$	−48.7948	+	48.7948i	−1.93484	+	1.93484i
$637$	13.6747			0.541813
$638$	8.77178			0.347278
$639$	−35.2112	+	35.2112i	−1.39293	+	1.39293i
$640$	10.7629	+	45.1056i	0.425440	+	1.78296i
$641$	21.3544	+	21.3544i	0.843448	+	0.843448i	0.989306	−	0.145857i	$-0.0465941\pi$
$641$	21.3544	+	21.3544i	0.843448	+	0.843448i	−0.145857	+	0.989306i	$0.546594\pi$
$642$			81.1759i			3.20376i
$643$	13.9383	−	13.9383i	0.549671	−	0.549671i	−0.376675	−	0.926346i	$-0.622932\pi$
$643$	13.9383	−	13.9383i	0.549671	−	0.549671i	0.926346	+	0.376675i	$0.122932\pi$
$644$		−	0.302850i		−	0.0119340i
$645$	−14.9883	−	9.21344i	−0.590166	−	0.362779i
$646$	21.2912	−	33.0976i	0.837691	−	1.30221i
$647$			21.0418i			0.827237i	0.910450	+	0.413618i	$0.135735\pi$
$647$			21.0418i			0.827237i	−0.910450	+	0.413618i	$0.864265\pi$
$648$	−74.6598			−2.93291
$649$	−2.22718	−	2.22718i	−0.0874243	−	0.0874243i
$650$	−10.5972	−	20.9413i	−0.415656	−	0.821386i
$651$	1.43323	+	1.43323i	0.0561728	+	0.0561728i
$652$	25.0439	+	25.0439i	0.980795	+	0.980795i
$653$	−27.3773	−	27.3773i	−1.07136	−	1.07136i	−0.997250	−	0.0741056i	$-0.976390\pi$
$653$	−27.3773	−	27.3773i	−1.07136	−	1.07136i	−0.0741056	−	0.997250i	$-0.523610\pi$
$654$		−	105.941i		−	4.14261i
$655$	−23.0518	+	37.5004i	−0.900707	+	1.46526i
$656$	1.27242	−	1.27242i	0.0496796	−	0.0496796i
$657$	−5.82648	−	5.82648i	−0.227313	−	0.227313i
$658$	−2.50169	+	2.50169i	−0.0975262	+	0.0975262i
$659$	−24.1577			−0.941049			−0.470524	−	0.882387i	$-0.655935\pi$
$659$	−24.1577			−0.941049			−0.470524	+	0.882387i	$0.655935\pi$
$660$	13.3052	−	3.17482i	0.517904	−	0.123580i
$661$			25.7432i			1.00129i	0.865651	+	0.500647i	$0.166905\pi$
$661$			25.7432i			1.00129i	−0.865651	+	0.500647i	$0.833095\pi$
$662$		−	48.1155i		−	1.87006i
$663$	5.42769	+	25.0038i	0.210794	+	0.971068i
$664$	24.7276			0.959616
$665$	−1.67630	−	1.03043i	−0.0650041	−	0.0399585i
$666$	−67.0524	−	67.0524i	−2.59823	−	2.59823i
$667$			2.60965i			0.101046i
$668$	−13.9585	+	13.9585i	−0.540072	+	0.540072i
$669$	4.38799	−	4.38799i	0.169649	−	0.169649i
$670$	59.7474	−	14.2566i	2.30824	−	0.550781i
$671$			2.96957i			0.114639i
$672$	−1.87193			−0.0722113
$673$	−7.42165	−	7.42165i	−0.286084	−	0.286084i	0.549446	−	0.835529i	$-0.314839\pi$
$673$	−7.42165	−	7.42165i	−0.286084	−	0.286084i	−0.835529	+	0.549446i	$0.814839\pi$
$674$	48.2280	−	48.2280i	1.85767	−	1.85767i
$675$	−59.2248	−	19.4248i	−2.27956	−	0.747660i
$676$	33.7276			1.29721
$677$	−6.00183	+	6.00183i	−0.230669	+	0.230669i	−0.812972	−	0.582303i	$-0.802152\pi$
$677$	−6.00183	+	6.00183i	−0.230669	+	0.230669i	0.582303	+	0.812972i	$0.302152\pi$
$678$	54.1173			2.07836
$679$	−2.02728			−0.0777998
$680$	−12.3370	+	35.1662i	−0.473103	+	1.34856i
$681$	−37.7244			−1.44560
$682$	3.65849			0.140091
$683$	10.1044	−	10.1044i	0.386635	−	0.386635i	−0.486851	−	0.873485i	$-0.661854\pi$
$683$	10.1044	−	10.1044i	0.386635	−	0.386635i	0.873485	+	0.486851i	$0.161854\pi$
$684$	102.717			3.92747
$685$	−10.1289	+	2.41690i	−0.387004	+	0.0923449i
$686$	−5.17878	+	5.17878i	−0.197727	+	0.197727i
$687$	20.7584	+	20.7584i	0.791984	+	0.791984i
$688$	−5.63085			−0.214674
$689$			11.6488i			0.443782i
$690$	1.45591	+	6.10151i	0.0554256	+	0.232280i
$691$	−6.24081	+	6.24081i	−0.237412	+	0.237412i	−0.815778	−	0.578366i	$-0.803691\pi$
$691$	−6.24081	+	6.24081i	−0.237412	+	0.237412i	0.578366	+	0.815778i	$0.303691\pi$
$692$	−45.5935	+	45.5935i	−1.73320	+	1.73320i
$693$			0.802810i			0.0304962i
$694$	18.4532	+	18.4532i	0.700473	+	0.700473i
$695$	−6.14513	+	9.99684i	−0.233098	+	0.379202i
$696$	−89.2952			−3.38472
$697$	−3.21161	+	0.697157i	−0.121648	+	0.0264067i
$698$		−	1.54053i		−	0.0583100i
$699$			81.3920i			3.07853i
$700$	3.86091	+	1.26632i	0.145929	+	0.0478622i
$701$	18.5340			0.700019			0.350010	−	0.936746i	$-0.386178\pi$
$701$	18.5340			0.700019			0.350010	+	0.936746i	$0.386178\pi$
$702$	−41.3759	+	41.3759i	−1.56163	+	1.56163i
$703$	16.1689	+	16.1689i	0.609822	+	0.609822i
$704$	−4.06519	+	4.06519i	−0.153213	+	0.153213i
$705$	24.8959	−	40.5004i	0.937633	−	1.52533i
$706$			34.1280i			1.28443i
$707$	1.12146	+	1.12146i	0.0421767	+	0.0421767i
$708$	49.4401	+	49.4401i	1.85807	+	1.85807i
$709$	−18.0304	−	18.0304i	−0.677147	−	0.677147i	0.282207	−	0.959354i	$-0.408934\pi$
$709$	−18.0304	−	18.0304i	−0.677147	−	0.677147i	−0.959354	+	0.282207i	$0.908934\pi$
$710$	−20.0156	+	32.5613i	−0.751173	+	1.22200i
$711$	33.0840	+	33.0840i	1.24075	+	1.24075i
$712$	64.6158			2.42158
$713$			1.08842i			0.0407617i
$714$	−5.74239	−	3.69399i	−0.214904	−	0.138244i
$715$	1.20921	−	1.96713i	0.0452219	−	0.0735667i
$716$			78.7736i			2.94391i
$717$	65.3384	−	65.3384i	2.44011	−	2.44011i
$718$		−	37.4063i		−	1.39599i
$719$	3.36804	+	3.36804i	0.125607	+	0.125607i	0.767116	−	0.641509i	$-0.221691\pi$
$719$	3.36804	+	3.36804i	0.125607	+	0.125607i	−0.641509	+	0.767116i	$0.721691\pi$
$720$	−34.1345	+	8.14501i	−1.27212	+	0.303547i
$721$	1.48163	−	1.48163i	0.0551787	−	0.0551787i
$722$	7.15863			0.266417
$723$	−26.7678			−0.995505
$724$	37.7128	−	37.7128i	1.40158	−	1.40158i
$725$	−33.2694	−	10.9118i	−1.23559	−	0.405255i
$726$	−57.0840	−	57.0840i	−2.11858	−	2.11858i
$727$		−	11.1858i		−	0.414858i	−0.978250	−	0.207429i	$-0.933490\pi$
$727$		−	11.1858i		−	0.414858i	0.978250	−	0.207429i	$-0.0665096\pi$
$728$	1.23694	−	1.23694i	0.0458441	−	0.0458441i
$729$			10.4216i			0.385984i
$730$	−5.38799	−	3.31203i	−0.199418	−	0.122584i
$731$	8.64875	+	5.56361i	0.319886	+	0.205778i
$732$		−	65.9201i		−	2.43648i
$733$	−26.2804			−0.970687			−0.485344	−	0.874324i	$-0.661305\pi$
$733$	−26.2804			−0.970687			−0.485344	+	0.874324i	$0.661305\pi$
$734$	36.9536	+	36.9536i	1.36398	+	1.36398i
$735$	25.6792	−	41.7747i	0.947191	−	1.54088i
$736$	−0.710788	−	0.710788i	−0.0262000	−	0.0262000i
$737$	4.27320	+	4.27320i	0.157405	+	0.157405i
$738$	−9.34921	−	9.34921i	−0.344149	−	0.344149i
$739$		−	6.00000i		−	0.220714i	−0.993892	−	0.110357i	$-0.964801\pi$
$739$		−	6.00000i		−	0.220714i	0.993892	−	0.110357i	$-0.0351994\pi$
$740$	−40.2266	−	24.7276i	−1.47876	−	0.909004i
$741$	17.5520	−	17.5520i	0.644787	−	0.644787i
$742$	−2.19811	−	2.19811i	−0.0806950	−	0.0806950i
$743$	−24.0700	+	24.0700i	−0.883042	+	0.883042i	−0.993843	−	0.110800i	$-0.964659\pi$
$743$	−24.0700	+	24.0700i	−0.883042	+	0.883042i	0.110800	+	0.993843i	$0.464659\pi$
$744$	−37.2428			−1.36539
$745$	−4.53720	−	19.0148i	−0.166230	−	0.696647i
$746$		−	15.5308i		−	0.568624i
$747$		−	42.5252i		−	1.55591i
$748$	−7.81341	+	1.69609i	−0.285686	+	0.0620152i
$749$	−2.37237			−0.0866844
$750$	−83.8733	−	6.95160i	−3.06262	−	0.253837i
$751$	−9.22285	−	9.22285i	−0.336547	−	0.336547i	0.518519	−	0.855066i	$-0.326483\pi$
$751$	−9.22285	−	9.22285i	−0.336547	−	0.336547i	−0.855066	+	0.518519i	$0.826483\pi$
$752$		−	15.2153i		−	0.554844i
$753$	3.95455	−	3.95455i	0.144112	−	0.144112i
$754$	−23.2428	+	23.2428i	−0.846453	+	0.846453i
$755$	−34.5896	+	8.25359i	−1.25884	+	0.300379i
$756$		−	10.1304i		−	0.368438i
$757$	31.8716			1.15839			0.579197	−	0.815188i	$-0.303366\pi$
$757$	31.8716			1.15839			0.579197	+	0.815188i	$0.303366\pi$
$758$	−12.7013	−	12.7013i	−0.461332	−	0.461332i
$759$	−0.436387	+	0.436387i	−0.0158398	+	0.0158398i
$760$	35.1675	−	8.39148i	1.27566	−	0.304391i
$761$	18.7549			0.679863			0.339932	−	0.940450i	$-0.389596\pi$
$761$	18.7549			0.679863			0.339932	+	0.940450i	$0.389596\pi$
$762$	51.8466	−	51.8466i	1.87820	−	1.87820i
$763$	3.09612			0.112087
$764$	−24.9064			−0.901081
$765$	60.4770	+	21.2165i	2.18655	+	0.767086i
$766$	−59.1187			−2.13605
$767$	11.8028			0.426175
$768$	61.5267	−	61.5267i	2.22015	−	2.22015i
$769$	−47.7916			−1.72341			−0.861705	−	0.507410i	$-0.830603\pi$
$769$	−47.7916			−1.72341			−0.861705	+	0.507410i	$0.830603\pi$
$770$	0.143019	+	0.599373i	0.00515406	+	0.0215999i
$771$	16.5121	−	16.5121i	0.594667	−	0.594667i
$772$	−38.2798	−	38.2798i	−1.37772	−	1.37772i
$773$	−28.3286			−1.01891			−0.509455	−	0.860497i	$-0.670153\pi$
$773$	−28.3286			−1.01891			−0.509455	+	0.860497i	$0.670153\pi$
$774$			41.3732i			1.48713i
$775$	−13.8758	−	4.55105i	−0.498434	−	0.163478i
$776$	26.3396	−	26.3396i	0.945536	−	0.945536i
$777$	2.80528	−	2.80528i	0.100639	−	0.100639i
$778$			56.5464i			2.02729i
$779$	2.25445	+	2.25445i	0.0807742	+	0.0807742i
$780$	−26.8427	+	43.6675i	−0.961124	+	1.56355i
$781$	−3.76036			−0.134556
$782$	−0.777794	−	3.58308i	−0.0278139	−	0.128131i
$783$			87.2932i			3.11961i
$784$		−	15.6940i		−	0.560500i
$785$	−21.9064	+	5.22719i	−0.781872	+	0.186566i
$786$	148.187			5.28565
$787$	−29.9191	+	29.9191i	−1.06650	+	1.06650i	−0.0688738	+	0.997625i	$0.521941\pi$
$787$	−29.9191	+	29.9191i	−1.06650	+	1.06650i	−0.997625	+	0.0688738i	$0.978059\pi$
$788$	−2.27072	−	2.27072i	−0.0808912	−	0.0808912i
$789$	−17.1156	+	17.1156i	−0.609330	+	0.609330i
$790$	30.5941	+	18.8064i	1.08849	+	0.669102i
$791$			1.58158i			0.0562344i
$792$	−10.4306	−	10.4306i	−0.370635	−	0.370635i
$793$	−7.86854	−	7.86854i	−0.279420	−	0.279420i
$794$	46.7612	+	46.7612i	1.65949	+	1.65949i
$795$	35.5855	+	21.8747i	1.26209	+	0.775815i
$796$	34.7412	+	34.7412i	1.23137	+	1.23137i
$797$	−54.1578			−1.91837			−0.959185	−	0.282780i	$-0.908743\pi$
$797$	−54.1578			−1.91837			−0.959185	+	0.282780i	$0.908743\pi$
$798$			6.62407i			0.234489i
$799$	−15.0336	+	23.3700i	−0.531850	+	0.826772i
$800$	12.0336	−	6.08951i	0.425452	−	0.215297i
$801$		−	111.123i		−	3.92633i
$802$	−51.5354	+	51.5354i	−1.81978	+	1.81978i
$803$		−	0.622235i		−	0.0219582i
$804$	−94.8588	−	94.8588i	−3.34541	−	3.34541i
$805$	−0.178317	+	0.0425490i	−0.00628484	+	0.00149966i
$806$	−9.69399	+	9.69399i	−0.341456	+	0.341456i
$807$	24.8350			0.874234
$808$	−29.1413			−1.02519
$809$	21.9064	−	21.9064i	0.770187	−	0.770187i	−0.207952	−	0.978139i	$-0.566680\pi$
$809$	21.9064	−	21.9064i	0.770187	−	0.770187i	0.978139	+	0.207952i	$0.0666799\pi$
$810$	22.8735	+	95.8595i	0.803693	+	3.36816i
$811$	−2.93481	−	2.93481i	−0.103055	−	0.103055i	0.653699	−	0.756754i	$-0.273216\pi$
$811$	−2.93481	−	2.93481i	−0.103055	−	0.103055i	−0.756754	+	0.653699i	$0.773216\pi$
$812$		−	5.69071i		−	0.199705i
$813$	−40.3016	+	40.3016i	−1.41344	+	1.41344i
$814$		−	7.16081i		−	0.250986i
$815$	11.2272	−	18.2643i	0.393271	−	0.639770i
$816$	28.6960	−	6.22916i	1.00456	−	0.218064i
$817$		−	9.97667i		−	0.349039i
$818$	14.0863			0.492515
$819$	−2.12723	−	2.12723i	−0.0743313	−	0.0743313i
$820$	−5.60886	−	3.44780i	−0.195870	−	0.120402i
$821$	−0.996845	−	0.996845i	−0.0347901	−	0.0347901i	0.689498	−	0.724288i	$-0.257831\pi$
$821$	−0.996845	−	0.996845i	−0.0347901	−	0.0347901i	−0.724288	+	0.689498i	$0.757831\pi$
$822$	24.7879	+	24.7879i	0.864578	+	0.864578i
$823$	14.2899	+	14.2899i	0.498116	+	0.498116i	0.910851	−	0.412735i	$-0.135427\pi$
$823$	14.2899	+	14.2899i	0.498116	+	0.498116i	−0.412735	+	0.910851i	$0.635427\pi$
$824$			38.5004i			1.34123i
$825$	−3.73864	−	7.38799i	−0.130163	−	0.257217i
$826$	−2.22718	+	2.22718i	−0.0774934	+	0.0774934i
$827$	−8.03163	−	8.03163i	−0.279287	−	0.279287i	0.553537	−	0.832824i	$-0.313278\pi$
$827$	−8.03163	−	8.03163i	−0.279287	−	0.279287i	−0.832824	+	0.553537i	$0.813278\pi$
$828$	6.76687	−	6.76687i	0.235165	−	0.235165i
$829$	−10.9336			−0.379741			−0.189870	−	0.981809i	$-0.560807\pi$
$829$	−10.9336			−0.379741			−0.189870	+	0.981809i	$0.560807\pi$
$830$	−7.57579	−	31.7490i	−0.262959	−	1.10202i
$831$		−	83.7768i		−	2.90618i
$832$		−	21.5433i		−	0.746879i
$833$	−15.5066	+	24.1053i	−0.537272	+	0.835200i
$834$	39.5036			1.36790
$835$	10.1798	+	6.25761i	0.352287	+	0.216553i
$836$	5.48478	+	5.48478i	0.189695	+	0.189695i
$837$			36.4078i			1.25844i
$838$	54.8149	−	54.8149i	1.89355	−	1.89355i
$839$	27.4836	−	27.4836i	0.948840	−	0.948840i	−0.0499138	−	0.998754i	$-0.515895\pi$
$839$	27.4836	−	27.4836i	0.948840	−	0.948840i	0.998754	+	0.0499138i	$0.0158947\pi$
$840$	−1.45591	−	6.10151i	−0.0502337	−	0.210522i
$841$			20.0367i			0.690922i
$842$	71.8621			2.47653
$843$	−30.7224	−	30.7224i	−1.05813	−	1.05813i
$844$	−46.4720	+	46.4720i	−1.59963	+	1.59963i
$845$	−4.73857	−	19.8586i	−0.163012	−	0.683158i
$846$	−111.796			−3.84361
$847$	1.66828	−	1.66828i	0.0573228	−	0.0573228i
$848$	13.3688			0.459088
$849$	43.3669			1.48835
$850$	48.9314	+	5.06625i	1.67833	+	0.173771i
$851$	2.13038			0.0730285
$852$	83.4745			2.85979
$853$	−22.6454	+	22.6454i	−0.775365	+	0.775365i	−0.979039	−	0.203674i	$-0.934712\pi$
$853$	−22.6454	+	22.6454i	−0.775365	+	0.775365i	0.203674	+	0.979039i	$0.434712\pi$
$854$	2.96957			0.101617
$855$	−14.4312	−	60.4791i	−0.493537	−	2.06834i
$856$	30.8232	−	30.8232i	1.05352	−	1.05352i
$857$	−18.1563	−	18.1563i	−0.620208	−	0.620208i	0.325376	−	0.945585i	$-0.394509\pi$
$857$	−18.1563	−	18.1563i	−0.620208	−	0.620208i	−0.945585	+	0.325376i	$0.894509\pi$
$858$	−7.77333			−0.265377
$859$			38.7065i			1.32065i	0.750981	+	0.660324i	$0.229581\pi$
$859$			38.7065i			1.32065i	−0.750981	+	0.660324i	$0.770419\pi$
$860$	4.78167	+	20.0393i	0.163054	+	0.683334i
$861$	0.391145	−	0.391145i	0.0133302	−	0.0133302i
$862$	−14.0462	+	14.0462i	−0.478416	+	0.478416i
$863$		−	29.5881i		−	1.00719i	−0.863939	−	0.503596i	$-0.832010\pi$
$863$		−	29.5881i		−	1.00719i	0.863939	−	0.503596i	$-0.167990\pi$
$864$	−23.7760	−	23.7760i	−0.808875	−	0.808875i
$865$	33.2509	+	20.4395i	1.13056	+	0.694965i
$866$	−32.4036			−1.10112
$867$	−50.2306	−	18.7856i	−1.70592	−	0.637992i
$868$		−	2.37346i		−	0.0805603i
$869$			3.53318i			0.119855i
$870$	27.3573	+	114.651i	0.927501	+	3.88702i
$871$	−22.6456			−0.767317
$872$	−40.2266	+	40.2266i	−1.36225	+	1.36225i
$873$	−45.2974	−	45.2974i	−1.53309	−	1.53309i
$874$	−2.51522	+	2.51522i	−0.0850785	+	0.0850785i
$875$	0.203161	−	2.45120i	0.00686808	−	0.0828656i
$876$			13.8127i			0.466689i
$877$	18.7380	+	18.7380i	0.632737	+	0.632737i	0.948754	−	0.316017i	$-0.102346\pi$
$877$	18.7380	+	18.7380i	0.632737	+	0.632737i	−0.316017	+	0.948754i	$0.602346\pi$
$878$	34.3728	+	34.3728i	1.16003	+	1.16003i
$879$	−44.3615	−	44.3615i	−1.49628	−	1.49628i
$880$	−2.25761	−	1.38777i	−0.0761040	−	0.0467816i
$881$	−7.77282	−	7.77282i	−0.261873	−	0.261873i	0.563942	−	0.825815i	$-0.309284\pi$
$881$	−7.77282	−	7.77282i	−0.261873	−	0.261873i	−0.825815	+	0.563942i	$0.809284\pi$
$882$	−115.313			−3.88279
$883$			56.2202i			1.89196i	0.324225	+	0.945980i	$0.394896\pi$
$883$			56.2202i			1.89196i	−0.324225	+	0.945980i	$0.605104\pi$
$884$	16.2092	−	25.1976i	0.545175	−	0.847486i
$885$	22.1640	−	36.0562i	0.745034	−	1.21201i
$886$		−	5.85481i		−	0.196696i
$887$	4.87988	−	4.87988i	0.163850	−	0.163850i	−0.620420	−	0.784270i	$-0.713038\pi$
$887$	4.87988	−	4.87988i	0.163850	−	0.163850i	0.784270	+	0.620420i	$0.213038\pi$
$888$			72.8958i			2.44622i
$889$	1.51522	+	1.51522i	0.0508187	+	0.0508187i
$890$	−19.7963	−	82.9634i	−0.663574	−	2.78094i
$891$	−6.85598	+	6.85598i	−0.229684	+	0.229684i
$892$	−7.26658			−0.243303
$893$	26.9582			0.902122
$894$	−46.5340	+	46.5340i	−1.55633	+	1.55633i
$895$	46.3815	−	11.0673i	1.55036	−	0.369940i
$896$	3.22600	+	3.22600i	0.107773	+	0.107773i
$897$		−	2.31261i		−	0.0772158i
$898$	5.39465	−	5.39465i	0.180022	−	0.180022i
$899$			20.4520i			0.682113i
$900$	57.9735	+	114.563i	1.93245	+	3.81875i
$901$	−20.5340	−	13.2092i	−0.684087	−	0.440063i
$902$		−	0.998442i		−	0.0332445i
$903$	−1.73094			−0.0576020
$904$	−20.5488	−	20.5488i	−0.683443	−	0.683443i
$905$	−27.5036	−	16.9066i	−0.914249	−	0.561995i
$906$	84.6496	+	84.6496i	2.81229	+	2.81229i
$907$	−22.0708	−	22.0708i	−0.732849	−	0.732849i	0.238334	−	0.971183i	$-0.423399\pi$
$907$	−22.0708	−	22.0708i	−0.732849	−	0.732849i	−0.971183	+	0.238334i	$0.923399\pi$
$908$	31.2361	+	31.2361i	1.03661	+	1.03661i
$909$			50.1156i			1.66223i
$910$	−1.96713	−	1.20921i	−0.0652099	−	0.0400850i
$911$	30.0472	−	30.0472i	0.995509	−	0.995509i	−0.00448095	−	0.999990i	$-0.501426\pi$
$911$	30.0472	−	30.0472i	0.995509	−	0.995509i	0.999990	+	0.00448095i	$0.00142634\pi$
$912$	−20.1437	−	20.1437i	−0.667026	−	0.667026i
$913$	2.27072	−	2.27072i	0.0751500	−	0.0751500i
$914$	72.0164			2.38209
$915$	−38.8134	+	9.26146i	−1.28313	+	0.306175i
$916$		−	34.3763i		−	1.13583i
$917$			4.33076i			0.143014i
$918$	−26.0173	−	119.854i	−0.858700	−	3.95579i
$919$	−29.1312			−0.960949			−0.480475	−	0.877009i	$-0.659536\pi$
$919$	−29.1312			−0.960949			−0.480475	+	0.877009i	$0.659536\pi$
$920$	1.76397	−	2.86962i	0.0581565	−	0.0946085i
$921$	33.3700	+	33.3700i	1.09958	+	1.09958i
$922$		−	12.9220i		−	0.425562i
$923$	9.96391	−	9.96391i	0.327966	−	0.327966i
$924$	0.951603	−	0.951603i	0.0313054	−	0.0313054i
$925$	−8.90782	+	27.1593i	−0.292887	+	0.892994i
$926$		−	37.6004i		−	1.23562i
$927$	66.2109			2.17465
$928$	−13.3561	−	13.3561i	−0.438435	−	0.438435i
$929$	0.921171	−	0.921171i	0.0302226	−	0.0302226i	−0.691834	−	0.722057i	$-0.743197\pi$
$929$	0.921171	−	0.921171i	0.0302226	−	0.0302226i	0.722057	+	0.691834i	$0.243197\pi$
$930$	11.4101	+	47.8179i	0.374151	+	1.56801i
$931$	27.8064			0.911318
$932$	67.3932	−	67.3932i	2.20754	−	2.20754i
$933$	93.5463			3.06257
$934$	−25.6971			−0.840836
$935$	2.09640	+	4.36220i	0.0685595	+	0.142659i
$936$	55.2764			1.80677
$937$	−9.43458			−0.308214			−0.154107	−	0.988054i	$-0.549250\pi$
$937$	−9.43458			−0.308214			−0.154107	+	0.988054i	$0.549250\pi$
$938$	4.27320	−	4.27320i	0.139525	−	0.139525i
$939$	−45.3584			−1.48021
$940$	−54.1487	+	12.9207i	−1.76613	+	0.421426i
$941$	−17.8033	+	17.8033i	−0.580370	+	0.580370i	−0.935005	−	0.354635i	$-0.884605\pi$
$941$	−17.8033	+	17.8033i	−0.580370	+	0.580370i	0.354635	+	0.935005i	$0.384605\pi$
$942$	53.6105	+	53.6105i	1.74673	+	1.74673i
$943$	0.297042			0.00967302
$944$		−	13.5456i		−	0.440873i
$945$	−5.96472	+	1.42327i	−0.194032	+	0.0462990i
$946$	−2.20921	+	2.20921i	−0.0718276	+	0.0718276i
$947$	19.5564	−	19.5564i	0.635496	−	0.635496i	−0.313945	−	0.949441i	$-0.601651\pi$
$947$	19.5564	−	19.5564i	0.635496	−	0.635496i	0.949441	+	0.313945i	$0.101651\pi$
$948$		−	78.4315i		−	2.54734i
$949$	1.64875	+	1.64875i	0.0535208	+	0.0535208i
$950$	−21.5485	−	42.5824i	−0.699126	−	1.38156i
$951$	43.4552			1.40913
$952$	0.777794	+	3.58308i	0.0252085	+	0.116128i
$953$			16.0279i			0.519195i	0.965717	+	0.259598i	$0.0835899\pi$
$953$			16.0279i			0.519195i	−0.965717	+	0.259598i	$0.916410\pi$
$954$		−	98.2288i		−	3.18027i
$955$	3.49923	+	14.6647i	0.113232	+	0.474540i
$956$	−108.202			−3.49949
$957$	−8.19994	+	8.19994i	−0.265066	+	0.265066i
$958$	62.2771	+	62.2771i	2.01208	+	2.01208i
$959$	−0.724427	+	0.724427i	−0.0233930	+	0.0233930i
$960$	−65.8121	−	40.4552i	−2.12408	−	1.30568i
$961$		−	22.4700i		−	0.724838i
$962$	18.9742	+	18.9742i	0.611752	+	0.611752i
$963$	−53.0081	−	53.0081i	−1.70816	−	1.70816i
$964$	22.1640	+	22.1640i	0.713853	+	0.713853i
$965$	−17.1608	+	27.9171i	−0.552426	+	0.898682i
$966$	0.436387	+	0.436387i	0.0140405	+	0.0140405i
$967$	10.9849			0.353252			0.176626	−	0.984278i	$-0.443482\pi$
$967$	10.9849			0.353252			0.176626	+	0.984278i	$0.443482\pi$
$968$			43.3506i			1.39334i
$969$	11.0367	+	50.8432i	0.354551	+	1.63332i
$970$	−41.8884	−	25.7491i	−1.34496	−	0.826753i
$971$		−	32.2944i		−	1.03638i	−0.855267	−	0.518188i	$-0.826607\pi$
$971$		−	32.2944i		−	1.03638i	0.855267	−	0.518188i	$-0.173393\pi$
$972$	54.5090	−	54.5090i	1.74838	−	1.74838i
$973$			1.15449i			0.0370113i
$974$	64.6632	+	64.6632i	2.07194	+	2.07194i
$975$	29.4825	+	9.66978i	0.944196	+	0.309681i
$976$	−9.03043	+	9.03043i	−0.289057	+	0.289057i
$977$	2.59459			0.0830084			0.0415042	−	0.999138i	$-0.486785\pi$
$977$	2.59459			0.0830084			0.0415042	+	0.999138i	$0.486785\pi$
$978$	−72.1732			−2.30784
$979$	5.93364	−	5.93364i	0.189640	−	0.189640i
$980$	−55.8524	+	13.3272i	−1.78414	+	0.425722i
$981$	69.1796	+	69.1796i	2.20873	+	2.20873i
$982$		−	90.7561i		−	2.89614i
$983$	−6.79991	+	6.79991i	−0.216883	+	0.216883i	−0.807184	−	0.590300i	$-0.799009\pi$
$983$	−6.79991	+	6.79991i	−0.216883	+	0.216883i	0.590300	+	0.807184i	$0.299009\pi$
$984$			10.1640i			0.324015i
$985$	−1.01796	+	1.65602i	−0.0324351	+	0.0527651i
$986$	−14.6152	−	67.3279i	−0.465442	−	2.14416i
$987$		−	4.67721i		−	0.148877i
$988$	−29.0663			−0.924723
$989$	−0.657252	−	0.657252i	−0.0208994	−	0.0208994i
$990$	−10.1967	+	16.5880i	−0.324074	+	0.527201i
$991$	19.9864	+	19.9864i	0.634888	+	0.634888i	0.949290	−	0.314402i	$-0.101804\pi$
$991$	19.9864	+	19.9864i	0.634888	+	0.634888i	−0.314402	+	0.949290i	$0.601804\pi$
$992$	−5.57049	−	5.57049i	−0.176863	−	0.176863i
$993$	44.9788	+	44.9788i	1.42736	+	1.42736i
$994$			3.76036i			0.119271i
$995$	15.5745	−	25.3364i	0.493744	−	0.803219i
$996$	−50.4068	+	50.4068i	−1.59720	+	1.59720i
$997$	−2.36593	−	2.36593i	−0.0749297	−	0.0749297i	0.668649	−	0.743578i	$-0.266873\pi$
$997$	−2.36593	−	2.36593i	−0.0749297	−	0.0749297i	−0.743578	+	0.668649i	$0.766873\pi$
$998$	15.7022	−	15.7022i	0.497045	−	0.497045i
$999$	71.2616			2.25462

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.j.c.64.6	yes	12
3.2	odd	2		765.2.t.e.64.1		12
5.2	odd	4		425.2.e.d.251.6		12
5.3	odd	4		425.2.e.d.251.1		12
5.4	even	2	inner	85.2.j.c.64.1	yes	12
15.14	odd	2		765.2.t.e.64.6		12
17.2	even	8		1445.2.b.f.579.12		12
17.4	even	4	inner	85.2.j.c.4.1	✓	12
17.15	even	8		1445.2.b.f.579.11		12
51.38	odd	4		765.2.t.e.514.6		12
85.2	odd	8		7225.2.a.bp.1.2		12
85.4	even	4	inner	85.2.j.c.4.6	yes	12
85.19	even	8		1445.2.b.f.579.1		12
85.32	odd	8		7225.2.a.bp.1.1		12
85.38	odd	4		425.2.e.d.276.6		12
85.49	even	8		1445.2.b.f.579.2		12
85.53	odd	8		7225.2.a.bp.1.11		12
85.72	odd	4		425.2.e.d.276.1		12
85.83	odd	8		7225.2.a.bp.1.12		12
255.89	odd	4		765.2.t.e.514.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.1	✓	12	17.4	even	4	inner
85.2.j.c.4.6	yes	12	85.4	even	4	inner
85.2.j.c.64.1	yes	12	5.4	even	2	inner
85.2.j.c.64.6	yes	12	1.1	even	1	trivial
425.2.e.d.251.1		12	5.3	odd	4
425.2.e.d.251.6		12	5.2	odd	4
425.2.e.d.276.1		12	85.72	odd	4
425.2.e.d.276.6		12	85.38	odd	4
765.2.t.e.64.1		12	3.2	odd	2
765.2.t.e.64.6		12	15.14	odd	2
765.2.t.e.514.1		12	255.89	odd	4
765.2.t.e.514.6		12	51.38	odd	4
1445.2.b.f.579.1		12	85.19	even	8
1445.2.b.f.579.2		12	85.49	even	8
1445.2.b.f.579.11		12	17.15	even	8
1445.2.b.f.579.12		12	17.2	even	8
7225.2.a.bp.1.1		12	85.32	odd	8
7225.2.a.bp.1.2		12	85.2	odd	8
7225.2.a.bp.1.11		12	85.53	odd	8
7225.2.a.bp.1.12		12	85.83	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.38621 q^{2} +(-2.23065 + 2.23065i) q^{3} +3.69399 q^{4} +(-0.518989 - 2.17501i) q^{5} +(-5.32280 + 5.32280i) q^{6} +(-0.155559 - 0.155559i) q^{7} +4.04223 q^{8} -6.95160i q^{9} +(-1.23842 - 5.19002i) q^{10} +(0.371196 - 0.371196i) q^{11} +(-8.24001 + 8.24001i) q^{12} +1.96713i q^{13} +(-0.371196 - 0.371196i) q^{14} +(6.00936 + 3.69399i) q^{15} +2.25761 q^{16} +(-3.46759 - 2.23065i) q^{17} -16.5880i q^{18} +4.00000i q^{19} +(-1.91714 - 8.03446i) q^{20} +0.693995 q^{21} +(0.885751 - 0.885751i) q^{22} +(0.263516 + 0.263516i) q^{23} +(-9.01679 + 9.01679i) q^{24} +(-4.46130 + 2.25761i) q^{25} +4.69399i q^{26} +(8.81464 + 8.81464i) q^{27} +(-0.574634 - 0.574634i) q^{28} +(4.95160 + 4.95160i) q^{29} +(14.3396 + 8.81464i) q^{30} +(2.06519 + 2.06519i) q^{31} -2.69733 q^{32} +1.65602i q^{33} +(-8.27440 - 5.32280i) q^{34} +(-0.257608 + 0.419075i) q^{35} -25.6792i q^{36} +(4.04223 - 4.04223i) q^{37} +9.54484i q^{38} +(-4.38799 - 4.38799i) q^{39} +(-2.09787 - 8.79187i) q^{40} +(0.563613 - 0.563613i) q^{41} +1.65602 q^{42} -2.49417 q^{43} +(1.37120 - 1.37120i) q^{44} +(-15.1198 + 3.60781i) q^{45} +(0.628804 + 0.628804i) q^{46} -6.73955i q^{47} +(-5.03593 + 5.03593i) q^{48} -6.95160i q^{49} +(-10.6456 + 5.38713i) q^{50} +(12.7108 - 2.75919i) q^{51} +7.26658i q^{52} +5.92169 q^{53} +(21.0336 + 21.0336i) q^{54} +(-1.00000 - 0.614707i) q^{55} +(-0.628804 - 0.628804i) q^{56} +(-8.92260 - 8.92260i) q^{57} +(11.8156 + 11.8156i) q^{58} -6.00000i q^{59} +(22.1985 + 13.6456i) q^{60} +(-4.00000 + 4.00000i) q^{61} +(4.92798 + 4.92798i) q^{62} +(-1.08138 + 1.08138i) q^{63} -10.9516 q^{64} +(4.27853 - 1.02092i) q^{65} +3.95160i q^{66} +11.5120i q^{67} +(-12.8093 - 8.24001i) q^{68} -1.17562 q^{69} +(-0.614707 + 1.00000i) q^{70} +(-5.06519 - 5.06519i) q^{71} -28.1000i q^{72} +(0.838149 - 0.838149i) q^{73} +(9.64560 - 9.64560i) q^{74} +(4.91567 - 14.9875i) q^{75} +14.7760i q^{76} -0.115486 q^{77} +(-10.4707 - 10.4707i) q^{78} +(-4.75919 + 4.75919i) q^{79} +(-1.17167 - 4.91031i) q^{80} -18.4700 q^{81} +(1.34490 - 1.34490i) q^{82} +6.11732 q^{83} +2.56361 q^{84} +(-3.05204 + 8.69972i) q^{85} -5.95160 q^{86} -22.0906 q^{87} +(1.50046 - 1.50046i) q^{88} +15.9852 q^{89} +(-36.0790 + 8.60898i) q^{90} +(0.306005 - 0.306005i) q^{91} +(0.973426 + 0.973426i) q^{92} -9.21344 q^{93} -16.0820i q^{94} +(8.70002 - 2.07596i) q^{95} +(6.01679 - 6.01679i) q^{96} +(6.51611 - 6.51611i) q^{97} -16.5880i q^{98} +(-2.58041 - 2.58041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} - 20 q^{6} - 4 q^{10} + 16 q^{11} - 16 q^{14} + 4 q^{16} - 32 q^{20} - 24 q^{21} - 32 q^{24} + 4 q^{29} + 52 q^{30} + 4 q^{31} + 20 q^{35} + 12 q^{39} + 24 q^{40} + 16 q^{41} + 28 q^{44}+ \cdots + 36 q^{99}+O(q^{100}) \) 12 * q + 12 * q^4 - 20 * q^6 - 4 * q^10 + 16 * q^11 - 16 * q^14 + 4 * q^16 - 32 * q^20 - 24 * q^21 - 32 * q^24 + 4 * q^29 + 52 * q^30 + 4 * q^31 + 20 * q^35 + 12 * q^39 + 24 * q^40 + 16 * q^41 + 28 * q^44 - 20 * q^45 - 4 * q^46 - 40 * q^50 + 44 * q^51 + 100 * q^54 - 12 * q^55 + 4 * q^56 - 48 * q^61 - 76 * q^64 + 8 * q^65 - 88 * q^69 - 40 * q^71 + 28 * q^74 + 64 * q^75 - 4 * q^79 + 12 * q^80 - 60 * q^81 + 40 * q^84 - 52 * q^85 - 16 * q^86 - 16 * q^89 - 84 * q^90 + 36 * q^91 - 4 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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