LMFDB - Embedded newform 170.3.e.b.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,3,Mod(13,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("170.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	170.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.63216449413$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 80 x^{14} + 2532 x^{12} + 40532 x^{10} + 346464 x^{8} + 1518752 x^{6} + 2895224 x^{4} + \cdots + 148996 $ x^16 + 80x^14 + 2532x^12 + 40532x^10 + 346464x^8 + 1518752x^6 + 2895224x^4 + 1253728*x^2 + 148996
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.6
Root			$-2.41271i$ of defining polynomial
Character	$\chi$	$=$	170.13
Dual form			170.3.e.b.157.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +2.41271i q^{3} +2.00000i q^{4} +(3.70308 - 3.35964i) q^{5} +(-2.41271 + 2.41271i) q^{6} +8.30225i q^{7} +(-2.00000 + 2.00000i) q^{8} +3.17881 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +2.41271i q^{3} +2.00000i q^{4} +(3.70308 - 3.35964i) q^{5} +(-2.41271 + 2.41271i) q^{6} +8.30225i q^{7} +(-2.00000 + 2.00000i) q^{8} +3.17881 q^{9} +(7.06272 + 0.343440i) q^{10} +(-5.03999 + 5.03999i) q^{11} -4.82543 q^{12} +(-3.86948 - 3.86948i) q^{13} +(-8.30225 + 8.30225i) q^{14} +(8.10586 + 8.93448i) q^{15} -4.00000 q^{16} +(16.8592 + 2.18308i) q^{17} +(3.17881 + 3.17881i) q^{18} -18.8139 q^{19} +(6.71928 + 7.40616i) q^{20} -20.0309 q^{21} -10.0800 q^{22} -1.97550 q^{23} +(-4.82543 - 4.82543i) q^{24} +(2.42562 - 24.8820i) q^{25} -7.73895i q^{26} +29.3840i q^{27} -16.6045 q^{28} +(12.7036 - 12.7036i) q^{29} +(-0.828624 + 17.0403i) q^{30} +(-18.1118 - 18.1118i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-12.1601 - 12.1601i) q^{33} +(14.6762 + 19.0423i) q^{34} +(27.8926 + 30.7439i) q^{35} +6.35762i q^{36} +41.9260 q^{37} +(-18.8139 - 18.8139i) q^{38} +(9.33594 - 9.33594i) q^{39} +(-0.686881 + 14.1254i) q^{40} +(41.1714 - 41.1714i) q^{41} +(-20.0309 - 20.0309i) q^{42} +(28.4243 - 28.4243i) q^{43} +(-10.0800 - 10.0800i) q^{44} +(11.7714 - 10.6797i) q^{45} +(-1.97550 - 1.97550i) q^{46} +(55.5354 - 55.5354i) q^{47} -9.65086i q^{48} -19.9273 q^{49} +(27.3077 - 22.4564i) q^{50} +(-5.26715 + 40.6766i) q^{51} +(7.73895 - 7.73895i) q^{52} +(-44.3219 + 44.3219i) q^{53} +(-29.3840 + 29.3840i) q^{54} +(-1.73094 + 35.5961i) q^{55} +(-16.6045 - 16.6045i) q^{56} -45.3925i q^{57} +25.4072 q^{58} -51.9453 q^{59} +(-17.8690 + 16.2117i) q^{60} +(-26.2200 + 26.2200i) q^{61} -36.2236i q^{62} +26.3912i q^{63} -8.00000i q^{64} +(-27.3290 - 1.32893i) q^{65} -24.3201i q^{66} +(56.6967 - 56.6967i) q^{67} +(-4.36616 + 33.7185i) q^{68} -4.76633i q^{69} +(-2.85133 + 58.6365i) q^{70} +(-37.1298 - 37.1298i) q^{71} +(-6.35762 + 6.35762i) q^{72} -64.7741i q^{73} +(41.9260 + 41.9260i) q^{74} +(60.0333 + 5.85234i) q^{75} -37.6277i q^{76} +(-41.8433 - 41.8433i) q^{77} +18.6719 q^{78} +(-17.3775 - 17.3775i) q^{79} +(-14.8123 + 13.4386i) q^{80} -42.2859 q^{81} +82.3428 q^{82} +(-60.2128 + 60.2128i) q^{83} -40.0619i q^{84} +(69.7655 - 48.5569i) q^{85} +56.8486 q^{86} +(30.6501 + 30.6501i) q^{87} -20.1600i q^{88} +122.541i q^{89} +(22.4510 + 1.09173i) q^{90} +(32.1253 - 32.1253i) q^{91} -3.95101i q^{92} +(43.6986 - 43.6986i) q^{93} +111.071 q^{94} +(-69.6692 + 63.2078i) q^{95} +(9.65086 - 9.65086i) q^{96} -28.2565 q^{97} +(-19.9273 - 19.9273i) q^{98} +(-16.0212 + 16.0212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	$ 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 q^{45} + 16 q^{46} + 112 q^{47} + 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} + 48 q^{53} + 108 q^{54} + 40 q^{55} - 24 q^{56} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * q^45 + 16 * q^46 + 112 * q^47 + 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 + 48 * q^53 + 108 * q^54 + 40 * q^55 - 24 * q^56 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$			2.41271i			0.804238i	0.915587	+	0.402119i	$0.131726\pi$
$3$			2.41271i			0.804238i	−0.915587	+	0.402119i	$0.868274\pi$
$4$			2.00000i			0.500000i
$5$	3.70308	−	3.35964i	0.740616	−	0.671928i
$5$	3.70308	−	3.35964i	0.740616	−	0.671928i
$6$	−2.41271	+	2.41271i	−0.402119	+	0.402119i
$7$			8.30225i			1.18604i	0.805190	+	0.593018i	$0.202064\pi$
$7$			8.30225i			1.18604i	−0.805190	+	0.593018i	$0.797936\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	3.17881			0.353201
$10$	7.06272	+	0.343440i	0.706272	+	0.0343440i
$11$	−5.03999	+	5.03999i	−0.458181	+	0.458181i	−0.898058	−	0.439877i	$-0.855022\pi$
$11$	−5.03999	+	5.03999i	−0.458181	+	0.458181i	0.439877	+	0.898058i	$0.355022\pi$
$12$	−4.82543			−0.402119
$13$	−3.86948	−	3.86948i	−0.297652	−	0.297652i	0.542442	−	0.840094i	$-0.317500\pi$
$13$	−3.86948	−	3.86948i	−0.297652	−	0.297652i	−0.840094	+	0.542442i	$0.817500\pi$
$14$	−8.30225	+	8.30225i	−0.593018	+	0.593018i
$15$	8.10586	+	8.93448i	0.540390	+	0.595632i
$16$	−4.00000			−0.250000
$17$	16.8592	+	2.18308i	0.991720	+	0.128416i
$17$	16.8592	+	2.18308i	0.991720	+	0.128416i
$18$	3.17881	+	3.17881i	0.176600	+	0.176600i
$19$	−18.8139			−0.990203			−0.495101	−	0.868835i	$-0.664869\pi$
$19$	−18.8139			−0.990203			−0.495101	+	0.868835i	$0.664869\pi$
$20$	6.71928	+	7.40616i	0.335964	+	0.370308i
$21$	−20.0309			−0.953855
$22$	−10.0800			−0.458181
$23$	−1.97550			−0.0858915			−0.0429457	−	0.999077i	$-0.513674\pi$
$23$	−1.97550			−0.0858915			−0.0429457	+	0.999077i	$0.513674\pi$
$24$	−4.82543	−	4.82543i	−0.201060	−	0.201060i
$25$	2.42562	−	24.8820i	0.0970250	−	0.995282i
$26$		−	7.73895i		−	0.297652i
$27$			29.3840i			1.08830i
$28$	−16.6045			−0.593018
$29$	12.7036	−	12.7036i	0.438055	−	0.438055i	−0.453302	−	0.891357i	$-0.649754\pi$
$29$	12.7036	−	12.7036i	0.438055	−	0.438055i	0.891357	+	0.453302i	$0.149754\pi$
$30$	−0.828624	+	17.0403i	−0.0276208	+	0.568011i
$31$	−18.1118	−	18.1118i	−0.584251	−	0.584251i	0.351818	−	0.936069i	$-0.385564\pi$
$31$	−18.1118	−	18.1118i	−0.584251	−	0.584251i	−0.936069	+	0.351818i	$0.885564\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−12.1601	−	12.1601i	−0.368487	−	0.368487i
$34$	14.6762	+	19.0423i	0.431652	+	0.560068i
$35$	27.8926	+	30.7439i	0.796930	+	0.878397i
$36$			6.35762i			0.176600i
$37$	41.9260			1.13314			0.566568	−	0.824015i	$-0.308271\pi$
$37$	41.9260			1.13314			0.566568	+	0.824015i	$0.308271\pi$
$38$	−18.8139	−	18.8139i	−0.495101	−	0.495101i
$39$	9.33594	−	9.33594i	0.239383	−	0.239383i
$40$	−0.686881	+	14.1254i	−0.0171720	+	0.353136i
$41$	41.1714	−	41.1714i	1.00418	−	1.00418i	0.00418968	−	0.999991i	$-0.498666\pi$
$41$	41.1714	−	41.1714i	1.00418	−	1.00418i	0.999991	−	0.00418968i	$-0.00133362\pi$
$42$	−20.0309	−	20.0309i	−0.476927	−	0.476927i
$43$	28.4243	−	28.4243i	0.661030	−	0.661030i	−0.294593	−	0.955623i	$-0.595184\pi$
$43$	28.4243	−	28.4243i	0.661030	−	0.661030i	0.955623	+	0.294593i	$0.0951840\pi$
$44$	−10.0800	−	10.0800i	−0.229091	−	0.229091i
$45$	11.7714	−	10.6797i	0.261586	−	0.237326i
$46$	−1.97550	−	1.97550i	−0.0429457	−	0.0429457i
$47$	55.5354	−	55.5354i	1.18160	−	1.18160i	0.202276	−	0.979328i	$-0.435166\pi$
$47$	55.5354	−	55.5354i	1.18160	−	1.18160i	0.979328	−	0.202276i	$-0.0648339\pi$
$48$		−	9.65086i		−	0.201060i
$49$	−19.9273			−0.406679
$50$	27.3077	−	22.4564i	0.546153	−	0.449128i
$51$	−5.26715	+	40.6766i	−0.103277	+	0.797579i
$52$	7.73895	−	7.73895i	0.148826	−	0.148826i
$53$	−44.3219	+	44.3219i	−0.836262	+	0.836262i	−0.988365	−	0.152103i	$-0.951396\pi$
$53$	−44.3219	+	44.3219i	−0.836262	+	0.836262i	0.152103	+	0.988365i	$0.451396\pi$
$54$	−29.3840	+	29.3840i	−0.544148	+	0.544148i
$55$	−1.73094	+	35.5961i	−0.0314716	+	0.647202i
$56$	−16.6045	−	16.6045i	−0.296509	−	0.296509i
$57$		−	45.3925i		−	0.796359i
$58$	25.4072			0.438055
$59$	−51.9453			−0.880428			−0.440214	−	0.897893i	$-0.645097\pi$
$59$	−51.9453			−0.880428			−0.440214	+	0.897893i	$0.645097\pi$
$60$	−17.8690	+	16.2117i	−0.297816	+	0.270195i
$61$	−26.2200	+	26.2200i	−0.429836	+	0.429836i	−0.888573	−	0.458736i	$-0.848302\pi$
$61$	−26.2200	+	26.2200i	−0.429836	+	0.429836i	0.458736	+	0.888573i	$0.348302\pi$
$62$		−	36.2236i		−	0.584251i
$63$			26.3912i			0.418909i
$64$		−	8.00000i		−	0.125000i
$65$	−27.3290	−	1.32893i	−0.420447	−	0.0204451i
$66$		−	24.3201i		−	0.368487i
$67$	56.6967	−	56.6967i	0.846220	−	0.846220i	−0.143439	−	0.989659i	$-0.545816\pi$
$67$	56.6967	−	56.6967i	0.846220	−	0.846220i	0.989659	+	0.143439i	$0.0458161\pi$
$68$	−4.36616	+	33.7185i	−0.0642082	+	0.495860i
$69$		−	4.76633i		−	0.0690772i
$70$	−2.85133	+	58.6365i	−0.0407332	+	0.837664i
$71$	−37.1298	−	37.1298i	−0.522956	−	0.522956i	0.395507	−	0.918463i	$-0.370569\pi$
$71$	−37.1298	−	37.1298i	−0.522956	−	0.522956i	−0.918463	+	0.395507i	$0.870569\pi$
$72$	−6.35762	+	6.35762i	−0.0883002	+	0.0883002i
$73$		−	64.7741i		−	0.887316i	−0.896196	−	0.443658i	$-0.853680\pi$
$73$		−	64.7741i		−	0.887316i	0.896196	−	0.443658i	$-0.146320\pi$
$74$	41.9260	+	41.9260i	0.566568	+	0.566568i
$75$	60.0333	+	5.85234i	0.800444	+	0.0780312i
$76$		−	37.6277i		−	0.495101i
$77$	−41.8433	−	41.8433i	−0.543419	−	0.543419i
$78$	18.6719			0.239383
$79$	−17.3775	−	17.3775i	−0.219968	−	0.219968i	0.588517	−	0.808485i	$-0.299712\pi$
$79$	−17.3775	−	17.3775i	−0.219968	−	0.219968i	−0.808485	+	0.588517i	$0.799712\pi$
$80$	−14.8123	+	13.4386i	−0.185154	+	0.167982i
$81$	−42.2859			−0.522048
$82$	82.3428			1.00418
$83$	−60.2128	+	60.2128i	−0.725455	+	0.725455i	−0.969711	−	0.244255i	$-0.921456\pi$
$83$	−60.2128	+	60.2128i	−0.725455	+	0.725455i	0.244255	+	0.969711i	$0.421456\pi$
$84$		−	40.0619i		−	0.476927i
$85$	69.7655	−	48.5569i	0.820771	−	0.571258i
$86$	56.8486			0.661030
$87$	30.6501	+	30.6501i	0.352300	+	0.352300i
$88$		−	20.1600i		−	0.229091i
$89$			122.541i			1.37686i	0.725301	+	0.688432i	$0.241701\pi$
$89$			122.541i			1.37686i	−0.725301	+	0.688432i	$0.758299\pi$
$90$	22.4510	+	1.09173i	0.249456	+	0.0121303i
$91$	32.1253	−	32.1253i	0.353026	−	0.353026i
$92$		−	3.95101i		−	0.0429457i
$93$	43.6986	−	43.6986i	0.469877	−	0.469877i
$94$	111.071			1.18160
$95$	−69.6692	+	63.2078i	−0.733360	+	0.665345i
$96$	9.65086	−	9.65086i	0.100530	−	0.100530i
$97$	−28.2565			−0.291304			−0.145652	−	0.989336i	$-0.546528\pi$
$97$	−28.2565			−0.291304			−0.145652	+	0.989336i	$0.546528\pi$
$98$	−19.9273	−	19.9273i	−0.203340	−	0.203340i
$99$	−16.0212	+	16.0212i	−0.161830	+	0.161830i
$100$	49.7641	+	4.85125i	0.497641	+	0.0485125i
$101$	−199.497			−1.97522			−0.987609	−	0.156932i	$-0.949840\pi$
$101$	−199.497			−1.97522			−0.987609	+	0.156932i	$0.949840\pi$
$102$	−45.9437	+	35.4094i	−0.450428	+	0.347151i
$103$	−75.2216	−	75.2216i	−0.730307	−	0.730307i	0.240373	−	0.970681i	$-0.422730\pi$
$103$	−75.2216	−	75.2216i	−0.730307	−	0.730307i	−0.970681	+	0.240373i	$0.922730\pi$
$104$	15.4779			0.148826
$105$	−74.1762	+	67.2968i	−0.706440	+	0.640922i
$106$	−88.6438			−0.836262
$107$	123.185			1.15127			0.575633	−	0.817708i	$-0.304756\pi$
$107$	123.185			1.15127			0.575633	+	0.817708i	$0.304756\pi$
$108$	−58.7680			−0.544148
$109$	56.2917	+	56.2917i	0.516437	+	0.516437i	0.916491	−	0.400054i	$-0.131009\pi$
$109$	56.2917	+	56.2917i	0.516437	+	0.516437i	−0.400054	+	0.916491i	$0.631009\pi$
$110$	−37.3270	+	33.8651i	−0.339337	+	0.307865i
$111$			101.156i			0.911311i
$112$		−	33.2090i		−	0.296509i
$113$	−38.5272			−0.340949			−0.170474	−	0.985362i	$-0.554530\pi$
$113$	−38.5272			−0.340949			−0.170474	+	0.985362i	$0.554530\pi$
$114$	45.3925	−	45.3925i	0.398179	−	0.398179i
$115$	−7.31545	+	6.63698i	−0.0636126	+	0.0577129i
$116$	25.4072	+	25.4072i	0.219027	+	0.219027i
$117$	−12.3003	−	12.3003i	−0.105131	−	0.105131i
$118$	−51.9453	−	51.9453i	−0.440214	−	0.440214i
$119$	−18.1245	+	139.970i	−0.152306	+	1.17622i
$120$	−34.0807	−	1.65725i	−0.284006	−	0.0138104i
$121$			70.1969i			0.580140i
$122$	−52.4400			−0.429836
$123$	99.3349	+	99.3349i	0.807601	+	0.807601i
$124$	36.2236	−	36.2236i	0.292125	−	0.292125i
$125$	−74.6125	−	100.289i	−0.596900	−	0.802316i
$126$	−26.3912	+	26.3912i	−0.209454	+	0.209454i
$127$	−17.8750	−	17.8750i	−0.140748	−	0.140748i	0.633222	−	0.773970i	$-0.281732\pi$
$127$	−17.8750	−	17.8750i	−0.140748	−	0.140748i	−0.773970	+	0.633222i	$0.781732\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	68.5797	+	68.5797i	0.531626	+	0.531626i
$130$	−26.0001	−	28.6580i	−0.200001	−	0.220446i
$131$	99.3420	+	99.3420i	0.758336	+	0.758336i	0.976019	−	0.217683i	$-0.0698500\pi$
$131$	99.3420	+	99.3420i	0.758336	+	0.758336i	−0.217683	+	0.976019i	$0.569850\pi$
$132$	24.3201	−	24.3201i	0.184243	−	0.184243i
$133$		−	156.197i		−	1.17442i
$134$	113.393			0.846220
$135$	98.7197	+	108.811i	0.731257	+	0.806010i
$136$	−38.0846	+	29.3523i	−0.280034	+	0.215826i
$137$	−173.979	+	173.979i	−1.26992	+	1.26992i	−0.323796	+	0.946127i	$0.604959\pi$
$137$	−173.979	+	173.979i	−1.26992	+	1.26992i	−0.946127	+	0.323796i	$0.895041\pi$
$138$	4.76633	−	4.76633i	0.0345386	−	0.0345386i
$139$	−58.1000	+	58.1000i	−0.417985	+	0.417985i	−0.884509	−	0.466524i	$-0.845506\pi$
$139$	−58.1000	+	58.1000i	−0.417985	+	0.417985i	0.466524	+	0.884509i	$0.345506\pi$
$140$	−61.4878	+	55.7851i	−0.439198	+	0.398465i
$141$	133.991	+	133.991i	0.950292	+	0.950292i
$142$		−	74.2597i		−	0.522956i
$143$	39.0043			0.272757
$144$	−12.7152			−0.0883002
$145$	4.36293	−	89.7219i	0.0300891	−	0.618772i
$146$	64.7741	−	64.7741i	0.443658	−	0.443658i
$147$		−	48.0788i		−	0.327067i
$148$			83.8521i			0.566568i
$149$		−	123.242i		−	0.827129i	−0.910475	−	0.413564i	$-0.864284\pi$
$149$		−	123.242i		−	0.827129i	0.910475	−	0.413564i	$-0.135716\pi$
$150$	54.1809	+	65.8856i	0.361206	+	0.439238i
$151$			12.5308i			0.0829856i	0.999139	+	0.0414928i	$0.0132114\pi$
$151$			12.5308i			0.0829856i	−0.999139	+	0.0414928i	$0.986789\pi$
$152$	37.6277	−	37.6277i	0.247551	−	0.247551i
$153$	53.5923	+	6.93959i	0.350276	+	0.0453568i
$154$		−	83.6865i		−	0.543419i
$155$	−127.918	−	6.22032i	−0.825280	−	0.0401311i
$156$	18.6719	+	18.6719i	0.119692	+	0.119692i
$157$	−114.494	+	114.494i	−0.729260	+	0.729260i	−0.970472	−	0.241213i	$-0.922455\pi$
$157$	−114.494	+	114.494i	−0.729260	+	0.729260i	0.241213	+	0.970472i	$0.422455\pi$
$158$		−	34.7550i		−	0.219968i
$159$	−106.936	−	106.936i	−0.672554	−	0.672554i
$160$	−28.2509	−	1.37376i	−0.176568	−	0.00858601i
$161$		−	16.4011i		−	0.101870i
$162$	−42.2859	−	42.2859i	−0.261024	−	0.261024i
$163$	75.8608			0.465404			0.232702	−	0.972548i	$-0.425243\pi$
$163$	75.8608			0.465404			0.232702	+	0.972548i	$0.425243\pi$
$164$	82.3428	+	82.3428i	0.502090	+	0.502090i
$165$	−85.8832	−	4.17626i	−0.520504	−	0.0253107i
$166$	−120.426			−0.725455
$167$	256.618			1.53663			0.768316	−	0.640070i	$-0.221095\pi$
$167$	256.618			1.53663			0.768316	+	0.640070i	$0.221095\pi$
$168$	40.0619	−	40.0619i	0.238464	−	0.238464i
$169$		−	139.054i		−	0.822807i
$170$	118.322	+	21.2086i	0.696014	+	0.124757i
$171$	−59.8056			−0.349740
$172$	56.8486	+	56.8486i	0.330515	+	0.330515i
$173$		−	199.417i		−	1.15270i	−0.817203	−	0.576350i	$-0.804477\pi$
$173$		−	199.417i		−	1.15270i	0.817203	−	0.576350i	$-0.195523\pi$
$174$			61.3002i			0.352300i
$175$	206.577	+	20.1381i	1.18044	+	0.115075i
$176$	20.1600	−	20.1600i	0.114545	−	0.114545i
$177$		−	125.329i		−	0.708074i
$178$	−122.541	+	122.541i	−0.688432	+	0.688432i
$179$	−290.286			−1.62171			−0.810854	−	0.585249i	$-0.800997\pi$
$179$	−290.286			−1.62171			−0.810854	+	0.585249i	$0.800997\pi$
$180$	21.3593	+	23.5428i	0.118663	+	0.130793i
$181$	89.4771	−	89.4771i	0.494349	−	0.494349i	−0.415324	−	0.909673i	$-0.636332\pi$
$181$	89.4771	−	89.4771i	0.494349	−	0.494349i	0.909673	+	0.415324i	$0.136332\pi$
$182$	64.2507			0.353026
$183$	−63.2614	−	63.2614i	−0.345691	−	0.345691i
$184$	3.95101	−	3.95101i	0.0214729	−	0.0214729i
$185$	155.256	−	140.856i	0.839219	−	0.761386i
$186$	87.3971			0.469877
$187$	−95.9732	+	73.9678i	−0.513226	+	0.395550i
$188$	111.071	+	111.071i	0.590802	+	0.590802i
$189$	−243.953			−1.29076
$190$	−132.877	−	6.46144i	−0.699353	−	0.0340076i
$191$	−67.7994			−0.354971			−0.177485	−	0.984123i	$-0.556796\pi$
$191$	−67.7994			−0.354971			−0.177485	+	0.984123i	$0.556796\pi$
$192$	19.3017			0.100530
$193$	−3.93341			−0.0203804			−0.0101902	−	0.999948i	$-0.503244\pi$
$193$	−3.93341			−0.0203804			−0.0101902	+	0.999948i	$0.503244\pi$
$194$	−28.2565	−	28.2565i	−0.145652	−	0.145652i
$195$	3.20634	−	65.9372i	0.0164428	−	0.338139i
$196$		−	39.8545i		−	0.203340i
$197$			290.490i			1.47457i	0.675583	+	0.737284i	$0.263892\pi$
$197$			290.490i			1.47457i	−0.675583	+	0.737284i	$0.736108\pi$
$198$	−32.0423			−0.161830
$199$	117.520	−	117.520i	0.590551	−	0.590551i	−0.347229	−	0.937780i	$-0.612877\pi$
$199$	117.520	−	117.520i	0.590551	−	0.590551i	0.937780	+	0.347229i	$0.112877\pi$
$200$	44.9128	+	54.6153i	0.224564	+	0.273077i
$201$	136.793	+	136.793i	0.680562	+	0.680562i
$202$	−199.497	−	199.497i	−0.987609	−	0.987609i
$203$	105.468	+	105.468i	0.519548	+	0.519548i
$204$	−81.3531	−	10.5343i	−0.398790	−	0.0516387i
$205$	14.1399	−	290.782i	0.0689753	−	1.41845i
$206$		−	150.443i		−	0.730307i
$207$	−6.27975			−0.0303369
$208$	15.4779	+	15.4779i	0.0744130	+	0.0744130i
$209$	94.8217	−	94.8217i	0.453692	−	0.453692i
$210$	−141.473	−	6.87944i	−0.673681	−	0.0327592i
$211$	26.2629	−	26.2629i	0.124469	−	0.124469i	−0.642128	−	0.766597i	$-0.721948\pi$
$211$	26.2629	−	26.2629i	0.124469	−	0.124469i	0.766597	+	0.642128i	$0.221948\pi$
$212$	−88.6438	−	88.6438i	−0.418131	−	0.418131i
$213$	89.5837	−	89.5837i	0.420581	−	0.420581i
$214$	123.185	+	123.185i	0.575633	+	0.575633i
$215$	9.76206	−	200.753i	0.0454049	−	0.933735i
$216$	−58.7680	−	58.7680i	−0.272074	−	0.272074i
$217$	150.368	−	150.368i	0.692942	−	0.692942i
$218$			112.583i			0.516437i
$219$	156.281			0.713614
$220$	−71.1922	−	3.46188i	−0.323601	−	0.0157358i
$221$	−56.7891	−	73.6838i	−0.256964	−	0.333411i
$222$	−101.156	+	101.156i	−0.455656	+	0.455656i
$223$	282.086	−	282.086i	1.26496	−	1.26496i	0.316301	−	0.948659i	$-0.397559\pi$
$223$	282.086	−	282.086i	1.26496	−	1.26496i	0.948659	−	0.316301i	$-0.102441\pi$
$224$	33.2090	−	33.2090i	0.148254	−	0.148254i
$225$	7.71060	−	79.0952i	0.0342693	−	0.351534i
$226$	−38.5272	−	38.5272i	−0.170474	−	0.170474i
$227$			157.026i			0.691745i	0.938281	+	0.345873i	$0.112417\pi$
$227$			157.026i			0.691745i	−0.938281	+	0.345873i	$0.887583\pi$
$228$	90.7849			0.398179
$229$	−264.566			−1.15531			−0.577655	−	0.816281i	$-0.696032\pi$
$229$	−264.566			−1.15531			−0.577655	+	0.816281i	$0.696032\pi$
$230$	−13.9524	−	0.678468i	−0.0606628	−	0.00294986i
$231$	100.956	−	100.956i	0.437038	−	0.437038i
$232$			50.8143i			0.219027i
$233$			312.623i			1.34173i	0.741579	+	0.670865i	$0.234077\pi$
$233$			312.623i			1.34173i	−0.741579	+	0.670865i	$0.765923\pi$
$234$		−	24.6006i		−	0.105131i
$235$	19.0731	−	392.231i	0.0811622	−	1.66907i
$236$		−	103.891i		−	0.440214i
$237$	41.9269	−	41.9269i	0.176907	−	0.176907i
$238$	−158.094	+	121.845i	−0.664261	+	0.511954i
$239$		−	176.726i		−	0.739439i	−0.929143	−	0.369719i	$-0.879454\pi$
$239$		−	176.726i		−	0.739439i	0.929143	−	0.369719i	$-0.120546\pi$
$240$	−32.4234	−	35.7379i	−0.135098	−	0.148908i
$241$	−65.6582	−	65.6582i	−0.272440	−	0.272440i	0.557641	−	0.830082i	$-0.311706\pi$
$241$	−65.6582	−	65.6582i	−0.272440	−	0.272440i	−0.830082	+	0.557641i	$0.811706\pi$
$242$	−70.1969	+	70.1969i	−0.290070	+	0.290070i
$243$			162.432i			0.668445i
$244$	−52.4400	−	52.4400i	−0.214918	−	0.214918i
$245$	−73.7923	+	66.9485i	−0.301193	+	0.273259i
$246$			198.670i			0.807601i
$247$	72.7997	+	72.7997i	0.294736	+	0.294736i
$248$	72.4471			0.292125
$249$	−145.276	−	145.276i	−0.583439	−	0.583439i
$250$	25.6770	−	174.902i	0.102708	−	0.699608i
$251$	−38.5890			−0.153741			−0.0768704	−	0.997041i	$-0.524493\pi$
$251$	−38.5890			−0.153741			−0.0768704	+	0.997041i	$0.524493\pi$
$252$	−52.7825			−0.209454
$253$	9.95653	−	9.95653i	0.0393539	−	0.0393539i
$254$		−	35.7500i		−	0.140748i
$255$	117.154	+	168.324i	0.459427	+	0.660095i
$256$	16.0000			0.0625000
$257$	−153.441	−	153.441i	−0.597048	−	0.597048i	0.342478	−	0.939526i	$-0.388734\pi$
$257$	−153.441	−	153.441i	−0.597048	−	0.597048i	−0.939526	+	0.342478i	$0.888734\pi$
$258$			137.159i			0.531626i
$259$			348.080i			1.34394i
$260$	2.65787	−	54.6581i	0.0102226	−	0.210223i
$261$	40.3823	−	40.3823i	0.154721	−	0.154721i
$262$			198.684i			0.758336i
$263$	−303.177	+	303.177i	−1.15277	+	1.15277i	−0.166769	+	0.985996i	$0.553333\pi$
$263$	−303.177	+	303.177i	−1.15277	+	1.15277i	−0.985996	+	0.166769i	$0.946667\pi$
$264$	48.6403			0.184243
$265$	−15.2219	+	313.033i	−0.0574413	+	1.18126i
$266$	156.197	−	156.197i	0.587208	−	0.587208i
$267$	−295.656			−1.10733
$268$	113.393	+	113.393i	0.423110	+	0.423110i
$269$	230.980	−	230.980i	0.858662	−	0.858662i	−0.132518	−	0.991181i	$-0.542306\pi$
$269$	230.980	−	230.980i	0.858662	−	0.858662i	0.991181	+	0.132518i	$0.0423063\pi$
$270$	−10.0917	+	207.531i	−0.0373765	+	0.768633i
$271$	349.991			1.29148			0.645740	−	0.763558i	$-0.276549\pi$
$271$	349.991			1.29148			0.645740	+	0.763558i	$0.276549\pi$
$272$	−67.4370	−	8.73231i	−0.247930	−	0.0321041i
$273$	77.5093	+	77.5093i	0.283917	+	0.283917i
$274$	−347.959			−1.26992
$275$	113.180	+	137.631i	0.411565	+	0.500475i
$276$	9.53265			0.0345386
$277$	−186.999			−0.675088			−0.337544	−	0.941310i	$-0.609596\pi$
$277$	−186.999			−0.675088			−0.337544	+	0.941310i	$0.609596\pi$
$278$	−116.200			−0.417985
$279$	−57.5739	−	57.5739i	−0.206358	−	0.206358i
$280$	−117.273	−	5.70265i	−0.418832	−	0.0203666i
$281$			333.798i			1.18789i	0.804504	+	0.593947i	$0.202431\pi$
$281$			333.798i			1.18789i	−0.804504	+	0.593947i	$0.797569\pi$
$282$			267.982i			0.950292i
$283$	−394.052			−1.39241			−0.696204	−	0.717844i	$-0.745129\pi$
$283$	−394.052			−1.39241			−0.696204	+	0.717844i	$0.745129\pi$
$284$	74.2597	−	74.2597i	0.261478	−	0.261478i
$285$	−152.502	−	168.092i	−0.535096	−	0.589796i
$286$	39.0043	+	39.0043i	0.136379	+	0.136379i
$287$	341.815	+	341.815i	1.19099	+	1.19099i
$288$	−12.7152	−	12.7152i	−0.0441501	−	0.0441501i
$289$	279.468	+	73.6101i	0.967018	+	0.254706i
$290$	94.0848	−	85.3590i	0.324430	−	0.294341i
$291$		−	68.1748i		−	0.234278i
$292$	129.548			0.443658
$293$	348.953	+	348.953i	1.19097	+	1.19097i	0.976797	+	0.214169i	$0.0687044\pi$
$293$	348.953	+	348.953i	1.19097	+	1.19097i	0.214169	+	0.976797i	$0.431296\pi$
$294$	48.0788	−	48.0788i	0.163533	−	0.163533i
$295$	−192.358	+	174.517i	−0.652059	+	0.591585i
$296$	−83.8521	+	83.8521i	−0.283284	+	0.283284i
$297$	−148.095	−	148.095i	−0.498637	−	0.498637i
$298$	123.242	−	123.242i	0.413564	−	0.413564i
$299$	7.64416	+	7.64416i	0.0255658	+	0.0255658i
$300$	−11.7047	+	120.067i	−0.0390156	+	0.400222i
$301$	235.986	+	235.986i	0.784005	+	0.784005i
$302$	−12.5308	+	12.5308i	−0.0414928	+	0.0414928i
$303$		−	481.330i		−	1.58855i
$304$	75.2554			0.247551
$305$	−9.00502	+	185.185i	−0.0295246	+	0.607163i
$306$	46.6527	+	60.5319i	0.152460	+	0.197817i
$307$	−129.862	+	129.862i	−0.423004	+	0.423004i	−0.886237	−	0.463233i	$-0.846689\pi$
$307$	−129.862	+	129.862i	−0.423004	+	0.423004i	0.463233	+	0.886237i	$0.346689\pi$
$308$	83.6865	−	83.6865i	0.271710	−	0.271710i
$309$	181.488	−	181.488i	0.587341	−	0.587341i
$310$	−121.698	−	134.139i	−0.392575	−	0.432706i
$311$	−227.463	−	227.463i	−0.731391	−	0.731391i	0.239505	−	0.970895i	$-0.423015\pi$
$311$	−227.463	−	227.463i	−0.731391	−	0.731391i	−0.970895	+	0.239505i	$0.923015\pi$
$312$			37.3438i			0.119692i
$313$	102.582			0.327737			0.163868	−	0.986482i	$-0.447603\pi$
$313$	102.582			0.327737			0.163868	+	0.986482i	$0.447603\pi$
$314$	−228.988			−0.729260
$315$	88.6651	+	97.7289i	0.281476	+	0.310251i
$316$	34.7550	−	34.7550i	0.109984	−	0.109984i
$317$			322.734i			1.01809i	0.860740	+	0.509045i	$0.170001\pi$
$317$			322.734i			1.01809i	−0.860740	+	0.509045i	$0.829999\pi$
$318$		−	213.872i		−	0.672554i
$319$			128.052i			0.401417i
$320$	−26.8771	−	29.6247i	−0.0839910	−	0.0925770i
$321$			297.211i			0.925892i
$322$	16.4011	−	16.4011i	0.0509351	−	0.0509351i
$323$	−317.187	−	41.0721i	−0.982004	−	0.127158i
$324$		−	84.5718i		−	0.261024i
$325$	−105.666	+	86.8946i	−0.325127	+	0.267368i
$326$	75.8608	+	75.8608i	0.232702	+	0.232702i
$327$	−135.816	+	135.816i	−0.415339	+	0.415339i
$328$			164.686i			0.502090i
$329$	461.069	+	461.069i	1.40142	+	1.40142i
$330$	−81.7069	−	90.0595i	−0.247597	−	0.272907i
$331$		−	456.048i		−	1.37779i	−0.724862	−	0.688894i	$-0.758096\pi$
$331$		−	456.048i		−	1.37779i	0.724862	−	0.688894i	$-0.241904\pi$
$332$	−120.426	−	120.426i	−0.362728	−	0.362728i
$333$	133.275			0.400225
$334$	256.618	+	256.618i	0.768316	+	0.768316i
$335$	19.4720	−	400.433i	0.0581252	−	1.19532i
$336$	80.1238			0.238464
$337$	471.246			1.39836			0.699179	−	0.714947i	$-0.253549\pi$
$337$	471.246			1.39836			0.699179	+	0.714947i	$0.253549\pi$
$338$	139.054	−	139.054i	0.411403	−	0.411403i
$339$		−	92.9552i		−	0.274204i
$340$	97.1138	+	139.531i	0.285629	+	0.410385i
$341$	182.567			0.535386
$342$	−59.8056	−	59.8056i	−0.174870	−	0.174870i
$343$			241.369i			0.703699i
$344$			113.697i			0.330515i
$345$	−16.0131	−	17.6501i	−0.0464149	−	0.0511597i
$346$	199.417	−	199.417i	0.576350	−	0.576350i
$347$			410.274i			1.18235i	0.806545	+	0.591173i	$0.201335\pi$
$347$			410.274i			1.18235i	−0.806545	+	0.591173i	$0.798665\pi$
$348$	−61.3002	+	61.3002i	−0.176150	+	0.176150i
$349$	−506.479			−1.45123			−0.725614	−	0.688102i	$-0.758444\pi$
$349$	−506.479			−1.45123			−0.725614	+	0.688102i	$0.758444\pi$
$350$	186.439	+	226.715i	0.532682	+	0.647757i
$351$	113.701	−	113.701i	0.323933	−	0.323933i
$352$	40.3200			0.114545
$353$	−52.0421	−	52.0421i	−0.147428	−	0.147428i	0.629540	−	0.776968i	$-0.283243\pi$
$353$	−52.0421	−	52.0421i	−0.147428	−	0.147428i	−0.776968	+	0.629540i	$0.783243\pi$
$354$	125.329	−	125.329i	0.354037	−	0.354037i
$355$	−262.238	−	12.7519i	−0.738698	−	0.0359208i
$356$	−245.082			−0.688432
$357$	−337.707	−	43.7291i	−0.945957	−	0.122491i
$358$	−290.286	−	290.286i	−0.810854	−	0.810854i
$359$	−140.638			−0.391750			−0.195875	−	0.980629i	$-0.562755\pi$
$359$	−140.638			−0.391750			−0.195875	+	0.980629i	$0.562755\pi$
$360$	−2.18346	+	44.9021i	−0.00606517	+	0.124728i
$361$	−7.03894			−0.0194984
$362$	178.954			0.494349
$363$	−169.365			−0.466571
$364$	64.2507	+	64.2507i	0.176513	+	0.176513i
$365$	−217.618	−	239.864i	−0.596213	−	0.657161i
$366$		−	126.523i		−	0.345691i
$367$		−	577.909i		−	1.57468i	−0.616517	−	0.787342i	$-0.711457\pi$
$367$		−	577.909i		−	1.57468i	0.616517	−	0.787342i	$-0.288543\pi$
$368$	7.90201			0.0214729
$369$	130.876	−	130.876i	0.354678	−	0.354678i
$370$	296.112	+	14.3991i	0.800303	+	0.0389165i
$371$	−367.971	−	367.971i	−0.991836	−	0.991836i
$372$	87.3971	+	87.3971i	0.234938	+	0.234938i
$373$	283.410	+	283.410i	0.759814	+	0.759814i	0.976288	−	0.216475i	$-0.0694559\pi$
$373$	283.410	+	283.410i	0.759814	+	0.759814i	−0.216475	+	0.976288i	$0.569456\pi$
$374$	−169.941	−	22.0054i	−0.454388	−	0.0588380i
$375$	241.970	−	180.019i	0.645253	−	0.480050i
$376$			222.142i			0.590802i
$377$	−98.3124			−0.260776
$378$	−243.953	−	243.953i	−0.645379	−	0.645379i
$379$	−491.221	+	491.221i	−1.29610	+	1.29610i	−0.365150	+	0.930949i	$0.618982\pi$
$379$	−491.221	+	491.221i	−1.29610	+	1.29610i	−0.930949	+	0.365150i	$0.881018\pi$
$380$	−126.416	−	139.338i	−0.332673	−	0.366680i
$381$	43.1273	−	43.1273i	0.113195	−	0.113195i
$382$	−67.7994	−	67.7994i	−0.177485	−	0.177485i
$383$	−125.274	+	125.274i	−0.327086	+	0.327086i	−0.851477	−	0.524391i	$-0.824293\pi$
$383$	−125.274	+	125.274i	−0.327086	+	0.327086i	0.524391	+	0.851477i	$0.324293\pi$
$384$	19.3017	+	19.3017i	0.0502649	+	0.0502649i
$385$	−295.527	−	14.3707i	−0.767604	−	0.0373264i
$386$	−3.93341	−	3.93341i	−0.0101902	−	0.0101902i
$387$	90.3554	−	90.3554i	0.233476	−	0.233476i
$388$		−	56.5130i		−	0.145652i
$389$	81.0769			0.208424			0.104212	−	0.994555i	$-0.466768\pi$
$389$	81.0769			0.208424			0.104212	+	0.994555i	$0.466768\pi$
$390$	69.1435	−	62.7308i	0.177291	−	0.160848i
$391$	−33.3055	−	4.31268i	−0.0851803	−	0.0110299i
$392$	39.8545	−	39.8545i	0.101670	−	0.101670i
$393$	−239.684	+	239.684i	−0.609883	+	0.609883i
$394$	−290.490	+	290.490i	−0.737284	+	0.737284i
$395$	−122.732	−	5.96813i	−0.310715	−	0.0151092i
$396$	−32.0423	−	32.0423i	−0.0809150	−	0.0809150i
$397$		−	516.365i		−	1.30067i	−0.759649	−	0.650334i	$-0.774629\pi$
$397$		−	516.365i		−	1.30067i	0.759649	−	0.650334i	$-0.225371\pi$
$398$	235.039			0.590551
$399$	376.859			0.944510
$400$	−9.70250	+	99.5282i	−0.0242562	+	0.248820i
$401$	−70.1150	+	70.1150i	−0.174850	+	0.174850i	−0.789107	−	0.614256i	$-0.789456\pi$
$401$	−70.1150	+	70.1150i	−0.174850	+	0.174850i	0.614256	+	0.789107i	$0.289456\pi$
$402$			273.586i			0.680562i
$403$			140.166i			0.347807i
$404$		−	398.994i		−	0.987609i
$405$	−156.588	+	142.065i	−0.386637	+	0.350779i
$406$			210.937i			0.519548i
$407$	−211.307	+	211.307i	−0.519182	+	0.519182i
$408$	−70.8188	−	91.8874i	−0.173576	−	0.225214i
$409$		−	256.957i		−	0.628257i	−0.949380	−	0.314129i	$-0.898288\pi$
$409$		−	256.957i		−	0.628257i	0.949380	−	0.314129i	$-0.101712\pi$
$410$	304.922	−	276.642i	0.743713	−	0.674737i
$411$	−419.763	−	419.763i	−1.02132	−	1.02132i
$412$	150.443	−	150.443i	0.365154	−	0.365154i
$413$		−	431.262i		−	1.04422i
$414$	−6.27975	−	6.27975i	−0.0151685	−	0.0151685i
$415$	−20.6795	+	425.266i	−0.0498302	+	1.02474i
$416$			30.9558i			0.0744130i
$417$	−140.179	−	140.179i	−0.336160	−	0.336160i
$418$	189.643			0.453692
$419$	−482.674	−	482.674i	−1.15197	−	1.15197i	−0.986158	−	0.165809i	$-0.946976\pi$
$419$	−482.674	−	482.674i	−1.15197	−	1.15197i	−0.165809	−	0.986158i	$-0.553024\pi$
$420$	−134.594	−	148.352i	−0.320461	−	0.353220i
$421$	318.706			0.757020			0.378510	−	0.925597i	$-0.376437\pi$
$421$	318.706			0.757020			0.378510	+	0.925597i	$0.376437\pi$
$422$	52.5259			0.124469
$423$	176.536	−	176.536i	0.417344	−	0.417344i
$424$		−	177.288i		−	0.418131i
$425$	95.2137	−	414.197i	0.224032	−	0.974582i
$426$	179.167			0.420581
$427$	−217.685	−	217.685i	−0.509801	−	0.509801i
$428$			246.371i			0.575633i
$429$			94.1062i			0.219362i
$430$	210.515	−	190.991i	0.489570	−	0.444165i
$431$	457.844	−	457.844i	1.06228	−	1.06228i	0.0643567	−	0.997927i	$-0.479500\pi$
$431$	457.844	−	457.844i	1.06228	−	1.06228i	0.997927	−	0.0643567i	$-0.0204995\pi$
$432$		−	117.536i		−	0.272074i
$433$	41.4850	−	41.4850i	0.0958082	−	0.0958082i	−0.657578	−	0.753386i	$-0.728419\pi$
$433$	41.4850	−	41.4850i	0.0958082	−	0.0958082i	0.753386	+	0.657578i	$0.228419\pi$
$434$	300.737			0.692942
$435$	216.473	+	10.5265i	0.497640	+	0.0241988i
$436$	−112.583	+	112.583i	−0.258219	+	0.258219i
$437$	37.1668			0.0850500
$438$	156.281	+	156.281i	0.356807	+	0.356807i
$439$	251.929	−	251.929i	0.573871	−	0.573871i	−0.359337	−	0.933208i	$-0.616997\pi$
$439$	251.929	−	251.929i	0.573871	−	0.573871i	0.933208	+	0.359337i	$0.116997\pi$
$440$	−67.7303	−	74.6540i	−0.153932	−	0.169668i
$441$	−63.3450			−0.143639
$442$	16.8947	−	130.473i	0.0382234	−	0.295188i
$443$	247.891	+	247.891i	0.559574	+	0.559574i	0.929186	−	0.369612i	$-0.120509\pi$
$443$	247.891	+	247.891i	0.559574	+	0.559574i	−0.369612	+	0.929186i	$0.620509\pi$
$444$	−202.311			−0.455656
$445$	411.693	+	453.779i	0.925153	+	1.01973i
$446$	564.172			1.26496
$447$	297.348			0.665208
$448$	66.4180			0.148254
$449$	−54.6100	−	54.6100i	−0.121626	−	0.121626i	0.643674	−	0.765300i	$-0.277409\pi$
$449$	−54.6100	−	54.6100i	−0.121626	−	0.121626i	−0.765300	+	0.643674i	$0.777409\pi$
$450$	86.8058	−	71.3847i	0.192902	−	0.158633i
$451$			415.007i			0.920194i
$452$		−	77.0544i		−	0.170474i
$453$	−30.2333			−0.0667402
$454$	−157.026	+	157.026i	−0.345873	+	0.345873i
$455$	11.0331	−	226.892i	0.0242487	−	0.498664i
$456$	90.7849	+	90.7849i	0.199090	+	0.199090i
$457$	−41.2370	−	41.2370i	−0.0902341	−	0.0902341i	0.660549	−	0.750783i	$-0.270324\pi$
$457$	−41.2370	−	41.2370i	−0.0902341	−	0.0902341i	−0.750783	+	0.660549i	$0.770324\pi$
$458$	−264.566	−	264.566i	−0.577655	−	0.577655i
$459$	−64.1476	+	495.392i	−0.139755	+	1.07929i
$460$	−13.2740	−	14.6309i	−0.0288564	−	0.0318063i
$461$			676.449i			1.46735i	0.679500	+	0.733676i	$0.262197\pi$
$461$			676.449i			1.46735i	−0.679500	+	0.733676i	$0.737803\pi$
$462$	201.912			0.437038
$463$	321.990	+	321.990i	0.695442	+	0.695442i	0.963424	−	0.267982i	$-0.0863566\pi$
$463$	321.990	+	321.990i	0.695442	+	0.695442i	−0.267982	+	0.963424i	$0.586357\pi$
$464$	−50.8143	+	50.8143i	−0.109514	+	0.109514i
$465$	15.0079	−	308.631i	0.0322750	−	0.663722i
$466$	−312.623	+	312.623i	−0.670865	+	0.670865i
$467$	−56.3480	−	56.3480i	−0.120659	−	0.120659i	0.644199	−	0.764858i	$-0.277191\pi$
$467$	−56.3480	−	56.3480i	−0.120659	−	0.120659i	−0.764858	+	0.644199i	$0.777191\pi$
$468$	24.6006	−	24.6006i	0.0525655	−	0.0525655i
$469$	470.710	+	470.710i	1.00365	+	1.00365i
$470$	411.304	−	373.158i	0.875116	−	0.793954i
$471$	−276.241	−	276.241i	−0.586499	−	0.586499i
$472$	103.891	−	103.891i	0.220107	−	0.220107i
$473$			286.517i			0.605743i
$474$	83.8538			0.176907
$475$	−45.6354	+	468.127i	−0.0960744	+	0.985531i
$476$	−279.939	−	36.2489i	−0.588108	−	0.0761532i
$477$	−140.891	+	140.891i	−0.295368	+	0.295368i
$478$	176.726	−	176.726i	0.369719	−	0.369719i
$479$	566.948	−	566.948i	1.18361	−	1.18361i	0.204805	−	0.978803i	$-0.434344\pi$
$479$	566.948	−	566.948i	1.18361	−	1.18361i	0.978803	−	0.204805i	$-0.0656559\pi$
$480$	3.31450	−	68.1613i	0.00690520	−	0.142003i
$481$	−162.232	−	162.232i	−0.337280	−	0.337280i
$482$		−	131.316i		−	0.272440i
$483$	39.5712			0.0819280
$484$	−140.394			−0.290070
$485$	−104.636	+	94.9317i	−0.215744	+	0.195735i
$486$	−162.432	+	162.432i	−0.334222	+	0.334222i
$487$			146.169i			0.300141i	0.988675	+	0.150070i	$0.0479501\pi$
$487$			146.169i			0.300141i	−0.988675	+	0.150070i	$0.952050\pi$
$488$		−	104.880i		−	0.214918i
$489$			183.030i			0.374295i
$490$	−140.741	−	6.84383i	−0.287226	−	0.0139670i
$491$		−	431.126i		−	0.878057i	−0.898473	−	0.439028i	$-0.855323\pi$
$491$		−	431.126i		−	0.878057i	0.898473	−	0.439028i	$-0.144677\pi$
$492$	−198.670	+	198.670i	−0.403800	+	0.403800i
$493$	241.906	−	186.440i	0.490681	−	0.378174i
$494$			145.599i			0.294736i
$495$	−5.50232	+	113.153i	−0.0111158	+	0.228592i
$496$	72.4471	+	72.4471i	0.146063	+	0.146063i
$497$	308.261	−	308.261i	0.620244	−	0.620244i
$498$		−	290.553i		−	0.583439i
$499$	−47.5683	−	47.5683i	−0.0953273	−	0.0953273i	0.657835	−	0.753162i	$-0.271472\pi$
$499$	−47.5683	−	47.5683i	−0.0953273	−	0.0953273i	−0.753162	+	0.657835i	$0.771472\pi$
$500$	200.579	−	149.225i	0.401158	−	0.298450i
$501$			619.145i			1.23582i
$502$	−38.5890	−	38.5890i	−0.0768704	−	0.0768704i
$503$	−794.434			−1.57939			−0.789696	−	0.613498i	$-0.789762\pi$
$503$	−794.434			−1.57939			−0.789696	+	0.613498i	$0.789762\pi$
$504$	−52.7825	−	52.7825i	−0.104727	−	0.104727i
$505$	−738.754	+	670.239i	−1.46288	+	1.32721i
$506$	19.9131			0.0393539
$507$	335.498			0.661733
$508$	35.7500	−	35.7500i	0.0703740	−	0.0703740i
$509$		−	249.834i		−	0.490832i	−0.969418	−	0.245416i	$-0.921075\pi$
$509$		−	249.834i		−	0.490832i	0.969418	−	0.245416i	$-0.0789246\pi$
$510$	−51.1704	+	285.478i	−0.100334	+	0.559761i
$511$	537.770			1.05239
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		−	552.826i		−	1.07763i
$514$		−	306.883i		−	0.597048i
$515$	−531.270	−	25.8342i	−1.03159	−	0.0501634i
$516$	−137.159	+	137.159i	−0.265813	+	0.265813i
$517$			559.797i			1.08278i
$518$	−348.080	+	348.080i	−0.671970	+	0.671970i
$519$	481.136			0.927045
$520$	57.3159	−	52.0002i	0.110223	−	0.100000i
$521$	−342.003	+	342.003i	−0.656435	+	0.656435i	−0.954535	−	0.298100i	$-0.903647\pi$
$521$	−342.003	+	342.003i	−0.656435	+	0.656435i	0.298100	+	0.954535i	$0.403647\pi$
$522$	80.7645			0.154721
$523$	−284.938	−	284.938i	−0.544815	−	0.544815i	0.380122	−	0.924936i	$-0.375882\pi$
$523$	−284.938	−	284.938i	−0.544815	−	0.544815i	−0.924936	+	0.380122i	$0.875882\pi$
$524$	−198.684	+	198.684i	−0.379168	+	0.379168i
$525$	−48.5876	+	498.411i	−0.0925478	+	0.949354i
$526$	−606.354			−1.15277
$527$	−265.811	−	344.890i	−0.504386	−	0.654441i
$528$	48.6403	+	48.6403i	0.0921217	+	0.0921217i
$529$	−525.097			−0.992623
$530$	−328.255	+	297.811i	−0.619349	+	0.561908i
$531$	−165.124			−0.310968
$532$	312.394			0.587208
$533$	−318.624			−0.597793
$534$	−295.656	−	295.656i	−0.553663	−	0.553663i
$535$	456.166	−	413.859i	0.852646	−	0.773568i
$536$			226.787i			0.423110i
$537$		−	700.376i		−	1.30424i
$538$	461.960			0.858662
$539$	100.433	−	100.433i	0.186333	−	0.186333i
$540$	−217.623	+	197.439i	−0.403005	+	0.365628i
$541$	449.791	+	449.791i	0.831406	+	0.831406i	0.987709	−	0.156303i	$-0.0499577\pi$
$541$	449.791	+	449.791i	0.831406	+	0.831406i	−0.156303	+	0.987709i	$0.549958\pi$
$542$	349.991	+	349.991i	0.645740	+	0.645740i
$543$	215.883	+	215.883i	0.397574	+	0.397574i
$544$	−58.7047	−	76.1693i	−0.107913	−	0.140017i
$545$	397.572	+	19.3328i	0.729491	+	0.0354731i
$546$			155.019i			0.283917i
$547$	−423.025			−0.773355			−0.386678	−	0.922215i	$-0.626377\pi$
$547$	−423.025			−0.773355			−0.386678	+	0.922215i	$0.626377\pi$
$548$	−347.959	−	347.959i	−0.634962	−	0.634962i
$549$	−83.3484	+	83.3484i	−0.151819	+	0.151819i
$550$	−24.4503	+	250.811i	−0.0444550	+	0.456020i
$551$	−239.003	+	239.003i	−0.433763	+	0.433763i
$552$	9.53265	+	9.53265i	0.0172693	+	0.0172693i
$553$	144.272	−	144.272i	0.260890	−	0.260890i
$554$	−186.999	−	186.999i	−0.337544	−	0.337544i
$555$	339.846	+	374.587i	0.612336	+	0.674932i
$556$	−116.200	−	116.200i	−0.208993	−	0.208993i
$557$	410.023	−	410.023i	0.736128	−	0.736128i	−0.235699	−	0.971826i	$-0.575738\pi$
$557$	410.023	−	410.023i	0.736128	−	0.736128i	0.971826	+	0.235699i	$0.0757378\pi$
$558$		−	115.148i		−	0.206358i
$559$	−219.974			−0.393514
$560$	−111.570	−	122.976i	−0.199233	−	0.219599i
$561$	−178.463	−	231.556i	−0.318116	−	0.412756i
$562$	−333.798	+	333.798i	−0.593947	+	0.593947i
$563$	472.554	−	472.554i	0.839351	−	0.839351i	−0.149423	−	0.988773i	$-0.547742\pi$
$563$	472.554	−	472.554i	0.839351	−	0.839351i	0.988773	+	0.149423i	$0.0477415\pi$
$564$	−267.982	+	267.982i	−0.475146	+	0.475146i
$565$	−142.669	+	129.438i	−0.252512	+	0.229093i
$566$	−394.052	−	394.052i	−0.696204	−	0.696204i
$567$		−	351.068i		−	0.619168i
$568$	148.519			0.261478
$569$	1074.05			1.88760			0.943802	−	0.330511i	$-0.107221\pi$
$569$	1074.05			1.88760			0.943802	+	0.330511i	$0.107221\pi$
$570$	15.5896	−	320.594i	0.0273502	−	0.562446i
$571$	−281.349	+	281.349i	−0.492730	+	0.492730i	−0.909165	−	0.416435i	$-0.863279\pi$
$571$	−281.349	+	281.349i	−0.492730	+	0.492730i	0.416435	+	0.909165i	$0.363279\pi$
$572$			78.0086i			0.136379i
$573$		−	163.581i		−	0.285481i
$574$			683.630i			1.19099i
$575$	−4.79183	+	49.1546i	−0.00833362	+	0.0854862i
$576$		−	25.4305i		−	0.0441501i
$577$	−164.787	+	164.787i	−0.285593	+	0.285593i	−0.835335	−	0.549742i	$-0.814726\pi$
$577$	−164.787	+	164.787i	−0.285593	+	0.285593i	0.549742	+	0.835335i	$0.314726\pi$
$578$	205.858	+	353.078i	0.356156	+	0.610862i
$579$		−	9.49020i		−	0.0163907i
$580$	179.444	+	8.72585i	0.309386	+	0.0150446i
$581$	−499.901	−	499.901i	−0.860416	−	0.860416i
$582$	68.1748	−	68.1748i	0.117139	−	0.117139i
$583$		−	446.764i		−	0.766319i
$584$	129.548	+	129.548i	0.221829	+	0.221829i
$585$	−86.8737	−	4.22443i	−0.148502	−	0.00722124i
$586$			697.906i			1.19097i
$587$	−122.695	−	122.695i	−0.209020	−	0.209020i	0.594831	−	0.803851i	$-0.297219\pi$
$587$	−122.695	−	122.695i	−0.209020	−	0.209020i	−0.803851	+	0.594831i	$0.797219\pi$
$588$	96.1577			0.163533
$589$	340.752	+	340.752i	0.578527	+	0.578527i
$590$	−366.875	−	17.8401i	−0.621822	−	0.0302375i
$591$	−700.869			−1.18590
$592$	−167.704			−0.283284
$593$	−49.4137	+	49.4137i	−0.0833284	+	0.0833284i	−0.747542	−	0.664214i	$-0.768766\pi$
$593$	−49.4137	+	49.4137i	−0.0833284	+	0.0833284i	0.664214	+	0.747542i	$0.268766\pi$
$594$		−	296.190i		−	0.498637i
$595$	403.131	+	579.210i	0.677532	+	0.973463i
$596$	246.484			0.413564
$597$	283.542	+	283.542i	0.474944	+	0.474944i
$598$			15.2883i			0.0255658i
$599$			52.8169i			0.0881752i	0.999028	+	0.0440876i	$0.0140381\pi$
$599$			52.8169i			0.0881752i	−0.999028	+	0.0440876i	$0.985962\pi$
$600$	−131.771	+	108.362i	−0.219619	+	0.180603i
$601$	−547.219	+	547.219i	−0.910513	+	0.910513i	−0.996312	−	0.0857991i	$-0.972656\pi$
$601$	−547.219	+	547.219i	−0.910513	+	0.910513i	0.0857991	+	0.996312i	$0.472656\pi$
$602$			471.971i			0.784005i
$603$	180.228	−	180.228i	0.298886	−	0.298886i
$604$	−25.0616			−0.0414928
$605$	235.836	+	259.945i	0.389812	+	0.429661i
$606$	481.330	−	481.330i	0.794273	−	0.794273i
$607$	557.074			0.917749			0.458875	−	0.888501i	$-0.348253\pi$
$607$	557.074			0.917749			0.458875	+	0.888501i	$0.348253\pi$
$608$	75.2554	+	75.2554i	0.123775	+	0.123775i
$609$	−254.465	+	254.465i	−0.417840	+	0.417840i
$610$	−194.190	+	176.180i	−0.318344	+	0.288819i
$611$	−429.786			−0.703414
$612$	−13.8792	+	107.185i	−0.0226784	+	0.175138i
$613$	−382.541	−	382.541i	−0.624048	−	0.624048i	0.322516	−	0.946564i	$-0.395471\pi$
$613$	−382.541	−	382.541i	−0.624048	−	0.624048i	−0.946564	+	0.322516i	$0.895471\pi$
$614$	−259.724			−0.423004
$615$	701.575	+	34.1156i	1.14077	+	0.0554726i
$616$	167.373			0.271710
$617$	654.079			1.06009			0.530047	−	0.847968i	$-0.322174\pi$
$617$	654.079			1.06009			0.530047	+	0.847968i	$0.322174\pi$
$618$	362.977			0.587341
$619$	0.999497	+	0.999497i	0.00161470	+	0.00161470i	0.707914	−	0.706299i	$-0.249637\pi$
$619$	0.999497	+	0.999497i	0.00161470	+	0.00161470i	−0.706299	+	0.707914i	$0.749637\pi$
$620$	12.4406	−	255.837i	0.0200655	−	0.412640i
$621$		−	58.0482i		−	0.0934753i
$622$		−	454.925i		−	0.731391i
$623$	−1017.36			−1.63301
$624$	−37.3438	+	37.3438i	−0.0598458	+	0.0598458i
$625$	−613.233	−	120.709i	−0.981172	−	0.193134i
$626$	102.582	+	102.582i	0.163868	+	0.163868i
$627$	228.778	+	228.778i	0.364877	+	0.364877i
$628$	−228.988	−	228.988i	−0.364630	−	0.364630i
$629$	706.841	+	91.5278i	1.12375	+	0.145513i
$630$	−9.06382	+	186.394i	−0.0143870	+	0.295864i
$631$			73.6868i			0.116778i	0.998294	+	0.0583889i	$0.0185963\pi$
$631$			73.6868i			0.116778i	−0.998294	+	0.0583889i	$0.981404\pi$
$632$	69.5099			0.109984
$633$	63.3650	+	63.3650i	0.100103	+	0.100103i
$634$	−322.734	+	322.734i	−0.509045	+	0.509045i
$635$	−126.246	−	6.13900i	−0.198813	−	0.00966771i
$636$	213.872	−	213.872i	0.336277	−	0.336277i
$637$	77.1081	+	77.1081i	0.121049	+	0.121049i
$638$	−128.052	+	128.052i	−0.200708	+	0.200708i
$639$	−118.029	−	118.029i	−0.184708	−	0.184708i
$640$	2.74752	−	56.5018i	0.00429301	−	0.0882840i
$641$	−275.738	−	275.738i	−0.430169	−	0.430169i	0.458517	−	0.888686i	$-0.348381\pi$
$641$	−275.738	−	275.738i	−0.430169	−	0.430169i	−0.888686	+	0.458517i	$0.848381\pi$
$642$	−297.211	+	297.211i	−0.462946	+	0.462946i
$643$			649.175i			1.00960i	0.863235	+	0.504802i	$0.168435\pi$
$643$			649.175i			1.00960i	−0.863235	+	0.504802i	$0.831565\pi$
$644$	32.8022			0.0509351
$645$	484.360	+	23.5531i	0.750945	+	0.0365164i
$646$	−276.115	−	358.259i	−0.427423	−	0.554581i
$647$	126.919	−	126.919i	0.196166	−	0.196166i	−0.602188	−	0.798354i	$-0.705704\pi$
$647$	126.919	−	126.919i	0.196166	−	0.196166i	0.798354	+	0.602188i	$0.205704\pi$
$648$	84.5718	−	84.5718i	0.130512	−	0.130512i
$649$	261.804	−	261.804i	0.403396	−	0.403396i
$650$	−192.561	−	18.7718i	−0.296248	−	0.0288797i
$651$	362.796	+	362.796i	0.557290	+	0.557290i
$652$			151.722i			0.232702i
$653$	−388.422			−0.594827			−0.297413	−	0.954749i	$-0.596124\pi$
$653$	−388.422			−0.594827			−0.297413	+	0.954749i	$0.596124\pi$
$654$	−271.631			−0.415339
$655$	701.625	+	34.1181i	1.07118	+	0.0520887i
$656$	−164.686	+	164.686i	−0.251045	+	0.251045i
$657$		−	205.904i		−	0.313401i
$658$			922.137i			1.40142i
$659$			322.721i			0.489714i	0.969559	+	0.244857i	$0.0787410\pi$
$659$			322.721i			0.489714i	−0.969559	+	0.244857i	$0.921259\pi$
$660$	8.35252	−	171.766i	0.0126553	−	0.260252i
$661$		−	1101.79i		−	1.66685i	−0.552635	−	0.833424i	$-0.686377\pi$
$661$		−	1101.79i		−	1.66685i	0.552635	−	0.833424i	$-0.313623\pi$
$662$	456.048	−	456.048i	0.688894	−	0.688894i
$663$	177.778	−	137.016i	0.268142	−	0.206660i
$664$		−	240.851i		−	0.362728i
$665$	−524.767	−	578.411i	−0.789123	−	0.869791i
$666$	133.275	+	133.275i	0.200112	+	0.200112i
$667$	−25.0960	+	25.0960i	−0.0376252	+	0.0376252i
$668$			513.235i			0.768316i
$669$	680.593	+	680.593i	1.01733	+	1.01733i
$670$	419.905	−	380.961i	0.626724	−	0.568599i
$671$		−	264.297i		−	0.393886i
$672$	80.1238	+	80.1238i	0.119232	+	0.119232i
$673$	−702.785			−1.04426			−0.522129	−	0.852867i	$-0.674862\pi$
$673$	−702.785			−1.04426			−0.522129	+	0.852867i	$0.674862\pi$
$674$	471.246	+	471.246i	0.699179	+	0.699179i
$675$	731.134	+	71.2745i	1.08316	+	0.105592i
$676$	278.109			0.411403
$677$	−460.083			−0.679591			−0.339795	−	0.940499i	$-0.610358\pi$
$677$	−460.083			−0.679591			−0.339795	+	0.940499i	$0.610358\pi$
$678$	92.9552	−	92.9552i	0.137102	−	0.137102i
$679$		−	234.592i		−	0.345497i
$680$	−42.4173	+	236.645i	−0.0623783	+	0.348007i
$681$	−378.859			−0.556328
$682$	182.567	+	182.567i	0.267693	+	0.267693i
$683$			342.928i			0.502091i	0.967975	+	0.251046i	$0.0807745\pi$
$683$			342.928i			0.502091i	−0.967975	+	0.251046i	$0.919226\pi$
$684$		−	119.611i		−	0.174870i
$685$	−59.7516	+	1228.77i	−0.0872286	+	1.79382i
$686$	−241.369	+	241.369i	−0.351850	+	0.351850i
$687$		−	638.322i		−	0.929144i
$688$	−113.697	+	113.697i	−0.165258	+	0.165258i
$689$	343.005			0.497830
$690$	1.63695	−	33.6632i	0.00237239	−	0.0487873i
$691$	385.226	−	385.226i	0.557491	−	0.557491i	−0.371101	−	0.928592i	$-0.621020\pi$
$691$	385.226	−	385.226i	0.557491	−	0.557491i	0.928592	+	0.371101i	$0.121020\pi$
$692$	398.834			0.576350
$693$	−133.012	−	133.012i	−0.191936	−	0.191936i
$694$	−410.274	+	410.274i	−0.591173	+	0.591173i
$695$	−19.9539	+	410.344i	−0.0287106	+	0.590423i
$696$	−122.600			−0.176150
$697$	783.999	−	604.239i	1.12482	−	0.866913i
$698$	−506.479	−	506.479i	−0.725614	−	0.725614i
$699$	−754.270			−1.07907
$700$	−40.2763	+	413.154i	−0.0575375	+	0.590220i
$701$	670.617			0.956658			0.478329	−	0.878181i	$-0.341243\pi$
$701$	670.617			0.956658			0.478329	+	0.878181i	$0.341243\pi$
$702$	227.401			0.323933
$703$	−788.790			−1.12203
$704$	40.3200	+	40.3200i	0.0572727	+	0.0572727i
$705$	946.342	+	46.0180i	1.34233	+	0.0652737i
$706$		−	104.084i		−	0.147428i
$707$		−	1656.27i		−	2.34268i
$708$	250.658			0.354037
$709$	−559.927	+	559.927i	−0.789742	+	0.789742i	−0.981452	−	0.191710i	$-0.938597\pi$
$709$	−559.927	+	559.927i	−0.789742	+	0.789742i	0.191710	+	0.981452i	$0.438597\pi$
$710$	−249.486	−	274.990i	−0.351389	−	0.387309i
$711$	−55.2397	−	55.2397i	−0.0776929	−	0.0776929i
$712$	−245.082	−	245.082i	−0.344216	−	0.344216i
$713$	35.7799	+	35.7799i	0.0501822	+	0.0501822i
$714$	−293.978	−	381.436i	−0.411733	−	0.534224i
$715$	144.436	−	131.040i	0.202008	−	0.183273i
$716$		−	580.571i		−	0.810854i
$717$	426.389			0.594685
$718$	−140.638	−	140.638i	−0.195875	−	0.195875i
$719$	75.2945	−	75.2945i	0.104721	−	0.104721i	−0.652805	−	0.757526i	$-0.726408\pi$
$719$	75.2945	−	75.2945i	0.104721	−	0.104721i	0.757526	+	0.652805i	$0.226408\pi$
$720$	−47.0855	+	42.7186i	−0.0653966	+	0.0593314i
$721$	624.508	−	624.508i	0.866170	−	0.866170i
$722$	−7.03894	−	7.03894i	−0.00974922	−	0.00974922i
$723$	158.414	−	158.414i	0.219107	−	0.219107i
$724$	178.954	+	178.954i	0.247174	+	0.247174i
$725$	−285.277	−	346.905i	−0.393486	−	0.478490i
$726$	−169.365	−	169.365i	−0.233285	−	0.233285i
$727$	−771.411	+	771.411i	−1.06109	+	1.06109i	−0.0630792	+	0.998009i	$0.520092\pi$
$727$	−771.411	+	771.411i	−1.06109	+	1.06109i	−0.998009	+	0.0630792i	$0.979908\pi$
$728$			128.501i			0.176513i
$729$	−772.475			−1.05964
$730$	22.2460	−	457.481i	0.0304740	−	0.626687i
$731$	541.265	−	417.160i	0.740444	−	0.570670i
$732$	126.523	−	126.523i	0.172845	−	0.172845i
$733$	720.383	−	720.383i	0.982788	−	0.982788i	−0.0170665	−	0.999854i	$-0.505433\pi$
$733$	720.383	−	720.383i	0.982788	−	0.982788i	0.999854	+	0.0170665i	$0.00543270\pi$
$734$	577.909	−	577.909i	0.787342	−	0.787342i
$735$	−161.528	−	178.040i	−0.219765	−	0.242231i
$736$	7.90201	+	7.90201i	0.0107364	+	0.0107364i
$737$			571.503i			0.775444i
$738$	261.752			0.354678
$739$	−713.604			−0.965635			−0.482817	−	0.875721i	$-0.660387\pi$
$739$	−713.604			−0.965635			−0.482817	+	0.875721i	$0.660387\pi$
$740$	281.713	+	310.511i	0.380693	+	0.419610i
$741$	−175.645	+	175.645i	−0.237038	+	0.237038i
$742$		−	735.942i		−	0.991836i
$743$			283.513i			0.381579i	0.981631	+	0.190790i	$0.0611048\pi$
$743$			283.513i			0.381579i	−0.981631	+	0.190790i	$0.938895\pi$
$744$			174.794i			0.234938i
$745$	−414.049	−	456.376i	−0.555771	−	0.612585i
$746$			566.821i			0.759814i
$747$	−191.405	+	191.405i	−0.256231	+	0.256231i
$748$	−147.936	−	191.946i	−0.197775	−	0.256613i
$749$			1022.72i			1.36544i
$750$	421.988	+	61.9513i	0.562651	+	0.0826018i
$751$	−403.130	−	403.130i	−0.536791	−	0.536791i	0.385794	−	0.922585i	$-0.373928\pi$
$751$	−403.130	−	403.130i	−0.536791	−	0.536791i	−0.922585	+	0.385794i	$0.873928\pi$
$752$	−222.142	+	222.142i	−0.295401	+	0.295401i
$753$		−	93.1041i		−	0.123644i
$754$	−98.3124	−	98.3124i	−0.130388	−	0.130388i
$755$	42.0991	+	46.4026i	0.0557603	+	0.0614605i
$756$		−	487.906i		−	0.645379i
$757$	−769.323	−	769.323i	−1.01628	−	1.01628i	−0.999865	−	0.0164137i	$-0.994775\pi$
$757$	−769.323	−	769.323i	−1.01628	−	1.01628i	−0.0164137	−	0.999865i	$-0.505225\pi$
$758$	−982.443			−1.29610
$759$	24.0223	+	24.0223i	0.0316499	+	0.0316499i
$760$	12.9229	−	265.754i	0.0170038	−	0.349676i
$761$	961.545			1.26353			0.631764	−	0.775160i	$-0.282331\pi$
$761$	961.545			1.26353			0.631764	+	0.775160i	$0.282331\pi$
$762$	86.2545			0.113195
$763$	−467.347	+	467.347i	−0.612513	+	0.612513i
$764$		−	135.599i		−	0.177485i
$765$	221.771	−	154.353i	0.289897	−	0.201769i
$766$	−250.548			−0.327086
$767$	201.001	+	201.001i	0.262061	+	0.262061i
$768$			38.6034i			0.0502649i
$769$		−	1185.00i		−	1.54096i	−0.637466	−	0.770479i	$-0.720017\pi$
$769$		−	1185.00i		−	1.54096i	0.637466	−	0.770479i	$-0.279983\pi$
$770$	−281.157	−	309.898i	−0.365139	−	0.402465i
$771$	370.210	−	370.210i	0.480169	−	0.480169i
$772$		−	7.86682i		−	0.0101902i
$773$	547.098	−	547.098i	0.707759	−	0.707759i	−0.258305	−	0.966064i	$-0.583164\pi$
$773$	547.098	−	547.098i	0.707759	−	0.707759i	0.966064	+	0.258305i	$0.0831638\pi$
$774$	180.711			0.233476
$775$	−494.591	+	406.726i	−0.638181	+	0.524807i
$776$	56.5130	−	56.5130i	0.0728260	−	0.0728260i
$777$	−839.818			−1.08085
$778$	81.0769	+	81.0769i	0.104212	+	0.104212i
$779$	−774.593	+	774.593i	−0.994343	+	0.994343i
$780$	131.874	+	6.41268i	0.169070	+	0.00822139i
$781$	374.268			0.479217
$782$	−28.9928	−	37.6182i	−0.0370752	−	0.0481051i
$783$	373.282	+	373.282i	0.476733	+	0.476733i
$784$	79.7091			0.101670
$785$	−39.3218	+	808.638i	−0.0500915	+	1.03011i
$786$	−479.368			−0.609883
$787$	−127.928			−0.162551			−0.0812757	−	0.996692i	$-0.525899\pi$
$787$	−127.928			−0.162551			−0.0812757	+	0.996692i	$0.525899\pi$
$788$	−580.979			−0.737284
$789$	−731.480	−	731.480i	−0.927098	−	0.927098i
$790$	−116.764	−	128.700i	−0.147803	−	0.162912i
$791$		−	319.862i		−	0.404377i
$792$		−	64.0847i		−	0.0809150i
$793$	202.915			0.255883
$794$	516.365	−	516.365i	0.650334	−	0.650334i
$795$	−755.260	−	36.7262i	−0.950012	−	0.0461965i
$796$	235.039	+	235.039i	0.295276	+	0.295276i
$797$	−500.226	−	500.226i	−0.627636	−	0.627636i	0.319837	−	0.947473i	$-0.396372\pi$
$797$	−500.226	−	500.226i	−0.627636	−	0.627636i	−0.947473	+	0.319837i	$0.896372\pi$
$798$	376.859	+	376.859i	0.472255	+	0.472255i
$799$	1057.52	−	815.047i	1.32356	−	1.02008i
$800$	−109.231	+	89.8257i	−0.136538	+	0.112282i
$801$			389.534i			0.486309i
$802$	−140.230			−0.174850
$803$	326.461	+	326.461i	0.406552	+	0.406552i
$804$	−273.586	+	273.586i	−0.340281	+	0.340281i
$805$	−55.1019	−	60.7347i	−0.0684495	−	0.0754468i
$806$	−140.166	+	140.166i	−0.173903	+	0.173903i
$807$	557.289	+	557.289i	0.690569	+	0.690569i
$808$	398.994	−	398.994i	0.493805	−	0.493805i
$809$	595.819	+	595.819i	0.736488	+	0.736488i	0.971896	−	0.235409i	$-0.0756429\pi$
$809$	595.819	+	595.819i	0.736488	+	0.736488i	−0.235409	+	0.971896i	$0.575643\pi$
$810$	−298.654	−	14.5227i	−0.368708	−	0.0179293i
$811$	911.537	+	911.537i	1.12397	+	1.12397i	0.991139	+	0.132827i	$0.0424054\pi$
$811$	911.537	+	911.537i	1.12397	+	1.12397i	0.132827	+	0.991139i	$0.457595\pi$
$812$	−210.937	+	210.937i	−0.259774	+	0.259774i
$813$			844.428i			1.03866i
$814$	−422.614			−0.519182
$815$	280.919	−	254.865i	0.344686	−	0.312718i
$816$	21.0686	−	162.706i	0.0258193	−	0.199395i
$817$	−534.771	+	534.771i	−0.654554	+	0.654554i
$818$	256.957	−	256.957i	0.314129	−	0.314129i
$819$	102.120	−	102.120i	0.124689	−	0.124689i
$820$	581.565	+	28.2799i	0.709225	+	0.0344876i
$821$	−280.121	−	280.121i	−0.341194	−	0.341194i	0.515622	−	0.856816i	$-0.327561\pi$
$821$	−280.121	−	280.121i	−0.341194	−	0.341194i	−0.856816	+	0.515622i	$0.827561\pi$
$822$		−	839.526i		−	1.02132i
$823$	708.959			0.861433			0.430716	−	0.902487i	$-0.358261\pi$
$823$	708.959			0.861433			0.430716	+	0.902487i	$0.358261\pi$
$824$	300.887			0.365154
$825$	−332.063	+	273.072i	−0.402501	+	0.330996i
$826$	431.262	−	431.262i	0.522109	−	0.522109i
$827$			573.260i			0.693181i	0.938017	+	0.346590i	$0.112661\pi$
$827$			573.260i			0.693181i	−0.938017	+	0.346590i	$0.887339\pi$
$828$		−	12.5595i		−	0.0151685i
$829$		−	674.526i		−	0.813662i	−0.913503	−	0.406831i	$-0.866634\pi$
$829$		−	674.526i		−	0.813662i	0.913503	−	0.406831i	$-0.133366\pi$
$830$	−445.946	+	404.587i	−0.537284	+	0.487454i
$831$		−	451.176i		−	0.542932i
$832$	−30.9558	+	30.9558i	−0.0372065	+	0.0372065i
$833$	−335.959	−	43.5028i	−0.403312	−	0.0522243i
$834$		−	280.357i		−	0.336160i
$835$	950.276	−	862.143i	1.13806	−	1.03251i
$836$	189.643	+	189.643i	0.226846	+	0.226846i
$837$	532.196	−	532.196i	0.635838	−	0.635838i
$838$		−	965.349i		−	1.15197i
$839$	986.140	+	986.140i	1.17538	+	1.17538i	0.980909	+	0.194466i	$0.0622973\pi$
$839$	986.140	+	986.140i	1.17538	+	1.17538i	0.194466	+	0.980909i	$0.437703\pi$
$840$	13.7589	−	282.946i	0.0163796	−	0.336841i
$841$			518.238i			0.616216i
$842$	318.706	+	318.706i	0.378510	+	0.378510i
$843$	−805.360			−0.955350
$844$	52.5259	+	52.5259i	0.0622345	+	0.0622345i
$845$	−467.173	−	514.929i	−0.552867	−	0.609384i
$846$	353.073			0.417344
$847$	−582.792			−0.688066
$848$	177.288	−	177.288i	0.209066	−	0.209066i
$849$		−	950.734i		−	1.11983i
$850$	509.411	−	318.984i	0.599307	−	0.375275i
$851$	−82.8250			−0.0973267
$852$	179.167	+	179.167i	0.210290	+	0.210290i
$853$		−	1327.22i		−	1.55594i	−0.628302	−	0.777969i	$-0.716250\pi$
$853$		−	1327.22i		−	1.55594i	0.628302	−	0.777969i	$-0.283750\pi$
$854$		−	435.370i		−	0.509801i
$855$	−221.465	+	200.925i	−0.259023	+	0.235000i
$856$	−246.371	+	246.371i	−0.287816	+	0.287816i
$857$			1356.18i			1.58247i	0.611509	+	0.791237i	$0.290563\pi$
$857$			1356.18i			1.58247i	−0.611509	+	0.791237i	$0.709437\pi$
$858$	−94.1062	+	94.1062i	−0.109681	+	0.109681i
$859$	−145.243			−0.169084			−0.0845419	−	0.996420i	$-0.526943\pi$
$859$	−145.243			−0.169084			−0.0845419	+	0.996420i	$0.526943\pi$
$860$	401.506	+	19.5241i	0.466867	+	0.0227025i
$861$	−824.703	+	824.703i	−0.957843	+	0.957843i
$862$	915.689			1.06228
$863$	349.259	+	349.259i	0.404703	+	0.404703i	0.879887	−	0.475184i	$-0.157618\pi$
$863$	349.259	+	349.259i	0.404703	+	0.404703i	−0.475184	+	0.879887i	$0.657618\pi$
$864$	117.536	−	117.536i	0.136037	−	0.136037i
$865$	−669.970	−	738.458i	−0.774531	−	0.853708i
$866$	82.9699			0.0958082
$867$	−177.600	+	674.277i	−0.204845	+	0.777713i
$868$	300.737	+	300.737i	0.346471	+	0.346471i
$869$	175.165			0.201571
$870$	205.947	+	227.000i	0.236720	+	0.260919i
$871$	−438.773			−0.503758
$872$	−225.167			−0.258219
$873$	−89.8219			−0.102889
$874$	37.1668	+	37.1668i	0.0425250	+	0.0425250i
$875$	832.628	−	619.451i	0.951575	−	0.707944i
$876$			312.563i			0.356807i
$877$		−	410.419i		−	0.467981i	−0.972239	−	0.233990i	$-0.924822\pi$
$877$		−	410.419i		−	0.467981i	0.972239	−	0.233990i	$-0.0751784\pi$
$878$	503.859			0.573871
$879$	−841.924	+	841.924i	−0.957820	+	0.957820i
$880$	6.92375	−	142.384i	0.00786790	−	0.161800i
$881$	−343.973	−	343.973i	−0.390435	−	0.390435i	0.484407	−	0.874843i	$-0.339035\pi$
$881$	−343.973	−	343.973i	−0.390435	−	0.390435i	−0.874843	+	0.484407i	$0.839035\pi$
$882$	−63.3450	−	63.3450i	−0.0718197	−	0.0718197i
$883$	1019.22	+	1019.22i	1.15427	+	1.15427i	0.985688	+	0.168580i	$0.0539182\pi$
$883$	1019.22	+	1019.22i	1.15427	+	1.15427i	0.168580	+	0.985688i	$0.446082\pi$
$884$	147.368	−	113.578i	0.166705	−	0.128482i
$885$	−421.061	−	464.104i	−0.475775	−	0.524411i
$886$			495.783i			0.559574i
$887$	−531.060			−0.598714			−0.299357	−	0.954141i	$-0.596772\pi$
$887$	−531.060			−0.598714			−0.299357	+	0.954141i	$0.596772\pi$
$888$	−202.311	−	202.311i	−0.227828	−	0.227828i
$889$	148.403	−	148.403i	0.166932	−	0.166932i
$890$	−42.0855	+	865.472i	−0.0472871	+	0.972440i
$891$	213.121	−	213.121i	0.239193	−	0.239193i
$892$	564.172	+	564.172i	0.632480	+	0.632480i
$893$	−1044.84	+	1044.84i	−1.17003	+	1.17003i
$894$	297.348	+	297.348i	0.332604	+	0.332604i
$895$	−1074.95	+	975.255i	−1.20106	+	1.08967i
$896$	66.4180	+	66.4180i	0.0741272	+	0.0741272i
$897$	−18.4432	+	18.4432i	−0.0205610	+	0.0205610i
$898$		−	109.220i		−	0.121626i
$899$	−460.169			−0.511868
$900$	158.190	+	15.4212i	0.175767	+	0.0171347i
$901$	−843.992	+	650.475i	−0.936728	+	0.721948i
$902$	−415.007	+	415.007i	−0.460097	+	0.460097i
$903$	−569.366	+	569.366i	−0.630527	+	0.630527i
$904$	77.0544	−	77.0544i	0.0852372	−	0.0852372i
$905$	30.7301	−	631.952i	0.0339559	−	0.698290i
$906$	−30.2333	−	30.2333i	−0.0333701	−	0.0333701i
$907$			1061.47i			1.17031i	0.810921	+	0.585156i	$0.198967\pi$
$907$			1061.47i			1.17031i	−0.810921	+	0.585156i	$0.801033\pi$
$908$	−314.052			−0.345873
$909$	−634.163			−0.697649
$910$	237.925	−	215.859i	0.261457	−	0.237208i
$911$	458.938	−	458.938i	0.503773	−	0.503773i	−0.408835	−	0.912608i	$-0.634065\pi$
$911$	458.938	−	458.938i	0.503773	−	0.503773i	0.912608	+	0.408835i	$0.134065\pi$
$912$			181.570i			0.199090i
$913$		−	606.944i		−	0.664780i
$914$		−	82.4740i		−	0.0902341i
$915$	−446.798	−	21.7265i	−0.488304	−	0.0237448i
$916$		−	529.132i		−	0.577655i
$917$	−824.762	+	824.762i	−0.899413	+	0.899413i
$918$	−559.539	+	431.244i	−0.609520	+	0.469765i
$919$		−	642.211i		−	0.698815i	−0.936971	−	0.349408i	$-0.886383\pi$
$919$		−	642.211i		−	0.698815i	0.936971	−	0.349408i	$-0.113617\pi$
$920$	1.35694	−	27.9049i	0.00147493	−	0.0303314i
$921$	−313.320	−	313.320i	−0.340196	−	0.340196i
$922$	−676.449	+	676.449i	−0.733676	+	0.733676i
$923$			287.346i			0.311318i
$924$	201.912	+	201.912i	0.218519	+	0.218519i
$925$	101.697	−	1043.21i	0.109943	−	1.12779i
$926$			643.980i			0.695442i
$927$	−239.115	−	239.115i	−0.257945	−	0.257945i
$928$	−101.629			−0.109514
$929$	278.802	+	278.802i	0.300110	+	0.300110i	0.841057	−	0.540947i	$-0.181934\pi$
$929$	278.802	+	278.802i	0.300110	+	0.300110i	−0.540947	+	0.841057i	$0.681934\pi$
$930$	323.639	−	293.623i	0.347999	−	0.315724i
$931$	374.909			0.402695
$932$	−625.246			−0.670865
$933$	548.802	−	548.802i	0.588212	−	0.588212i
$934$		−	112.696i		−	0.120659i
$935$	−106.891	+	596.344i	−0.114322	+	0.637801i
$936$	49.2013			0.0525655
$937$	1035.12	+	1035.12i	1.10472	+	1.10472i	0.993833	+	0.110886i	$0.0353688\pi$
$937$	1035.12	+	1035.12i	1.10472	+	1.10472i	0.110886	+	0.993833i	$0.464631\pi$
$938$			941.420i			1.00365i
$939$			247.500i			0.263579i
$940$	784.463	+	38.1462i	0.834535	+	0.0405811i
$941$	852.254	−	852.254i	0.905690	−	0.905690i	−0.0902311	−	0.995921i	$-0.528761\pi$
$941$	852.254	−	852.254i	0.905690	−	0.905690i	0.995921	+	0.0902311i	$0.0287606\pi$
$942$		−	552.482i		−	0.586499i
$943$	−81.3343	+	81.3343i	−0.0862506	+	0.0862506i
$944$	207.781			0.220107
$945$	−903.378	+	819.595i	−0.955956	+	0.867296i
$946$	−286.517	+	286.517i	−0.302872	+	0.302872i
$947$	1243.23			1.31281			0.656404	−	0.754410i	$-0.272077\pi$
$947$	1243.23			1.31281			0.656404	+	0.754410i	$0.272077\pi$
$948$	83.8538	+	83.8538i	0.0884534	+	0.0884534i
$949$	−250.642	+	250.642i	−0.264111	+	0.264111i
$950$	−513.763	+	422.492i	−0.540803	+	0.444728i
$951$	−778.666			−0.818787
$952$	−243.690	−	316.188i	−0.255977	−	0.332130i
$953$	1221.36	+	1221.36i	1.28159	+	1.28159i	0.939760	+	0.341835i	$0.111048\pi$
$953$	1221.36	+	1221.36i	1.28159	+	1.28159i	0.341835	+	0.939760i	$0.388952\pi$
$954$	−281.782			−0.295368
$955$	−251.067	+	227.782i	−0.262897	+	0.238515i
$956$	353.452			0.369719
$957$	−308.953			−0.322835
$958$	1133.90			1.18361
$959$	−1444.42	−	1444.42i	−1.50617	−	1.50617i
$960$	71.4758	−	64.8468i	0.0744540	−	0.0675488i
$961$		−	304.927i		−	0.317302i
$962$		−	324.464i		−	0.337280i
$963$	391.583			0.406628
$964$	131.316	−	131.316i	0.136220	−	0.136220i
$965$	−14.5657	+	13.2149i	−0.0150940	+	0.0136941i
$966$	39.5712	+	39.5712i	0.0409640	+	0.0409640i
$967$	895.371	+	895.371i	0.925926	+	0.925926i	0.997440	−	0.0715133i	$-0.0227828\pi$
$967$	895.371	+	895.371i	0.925926	+	0.925926i	−0.0715133	+	0.997440i	$0.522783\pi$
$968$	−140.394	−	140.394i	−0.145035	−	0.145035i
$969$	99.0953	−	765.283i	0.102266	−	0.789765i
$970$	−199.568	−	9.70442i	−0.205740	−	0.0100046i
$971$			1592.15i			1.63970i	0.572575	+	0.819852i	$0.305944\pi$
$971$			1592.15i			1.63970i	−0.572575	+	0.819852i	$0.694056\pi$
$972$	−324.864			−0.334222
$973$	−482.360	−	482.360i	−0.495745	−	0.495745i
$974$	−146.169	+	146.169i	−0.150070	+	0.150070i
$975$	−209.652	−	254.943i	−0.215028	−	0.261480i
$976$	104.880	−	104.880i	0.107459	−	0.107459i
$977$	292.802	+	292.802i	0.299695	+	0.299695i	0.840894	−	0.541199i	$-0.182029\pi$
$977$	292.802	+	292.802i	0.299695	+	0.299695i	−0.541199	+	0.840894i	$0.682029\pi$
$978$	−183.030	+	183.030i	−0.187148	+	0.187148i
$979$	−617.605	−	617.605i	−0.630853	−	0.630853i
$980$	−133.897	−	147.585i	−0.136630	−	0.150597i
$981$	178.940	+	178.940i	0.182406	+	0.182406i
$982$	431.126	−	431.126i	0.439028	−	0.439028i
$983$			220.429i			0.224241i	0.993695	+	0.112121i	$0.0357643\pi$
$983$			220.429i			0.224241i	−0.993695	+	0.112121i	$0.964236\pi$
$984$	−397.340			−0.403800
$985$	975.941	+	1075.71i	0.990803	+	1.09209i
$986$	428.346	+	55.4658i	0.434428	+	0.0562534i
$987$	−1112.43	+	1112.43i	−1.12708	+	1.12708i
$988$	−145.599	+	145.599i	−0.147368	+	0.147368i
$989$	−56.1523	+	56.1523i	−0.0567769	+	0.0567769i
$990$	−118.655	+	107.651i	−0.119854	+	0.108738i
$991$	1227.11	+	1227.11i	1.23825	+	1.23825i	0.960715	+	0.277535i	$0.0895176\pi$
$991$	1227.11	+	1227.11i	1.23825	+	1.23825i	0.277535	+	0.960715i	$0.410482\pi$
$992$			144.894i			0.146063i
$993$	1100.31			1.10807
$994$	616.522			0.620244
$995$	40.3610	−	830.009i	0.0405639	−	0.834180i
$996$	290.553	−	290.553i	0.291720	−	0.291720i
$997$		−	897.167i		−	0.899867i	−0.893062	−	0.449933i	$-0.851448\pi$
$997$		−	897.167i		−	0.899867i	0.893062	−	0.449933i	$-0.148552\pi$
$998$		−	95.1367i		−	0.0953273i
$999$			1231.95i			1.23319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.3.e.b.13.6	✓	16
5.2	odd	4		170.3.j.b.47.6	yes	16
17.4	even	4		170.3.j.b.123.6	yes	16
85.72	odd	4	inner	170.3.e.b.157.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.3.e.b.13.6	✓	16	1.1	even	1	trivial
170.3.e.b.157.3	yes	16	85.72	odd	4	inner
170.3.j.b.47.6	yes	16	5.2	odd	4
170.3.j.b.123.6	yes	16	17.4	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	170.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +2.41271i q^{3} +2.00000i q^{4} +(3.70308 - 3.35964i) q^{5} +(-2.41271 + 2.41271i) q^{6} +8.30225i q^{7} +(-2.00000 + 2.00000i) q^{8} +3.17881 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +2.41271i q^{3} +2.00000i q^{4} +(3.70308 - 3.35964i) q^{5} +(-2.41271 + 2.41271i) q^{6} +8.30225i q^{7} +(-2.00000 + 2.00000i) q^{8} +3.17881 q^{9} +(7.06272 + 0.343440i) q^{10} +(-5.03999 + 5.03999i) q^{11} -4.82543 q^{12} +(-3.86948 - 3.86948i) q^{13} +(-8.30225 + 8.30225i) q^{14} +(8.10586 + 8.93448i) q^{15} -4.00000 q^{16} +(16.8592 + 2.18308i) q^{17} +(3.17881 + 3.17881i) q^{18} -18.8139 q^{19} +(6.71928 + 7.40616i) q^{20} -20.0309 q^{21} -10.0800 q^{22} -1.97550 q^{23} +(-4.82543 - 4.82543i) q^{24} +(2.42562 - 24.8820i) q^{25} -7.73895i q^{26} +29.3840i q^{27} -16.6045 q^{28} +(12.7036 - 12.7036i) q^{29} +(-0.828624 + 17.0403i) q^{30} +(-18.1118 - 18.1118i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-12.1601 - 12.1601i) q^{33} +(14.6762 + 19.0423i) q^{34} +(27.8926 + 30.7439i) q^{35} +6.35762i q^{36} +41.9260 q^{37} +(-18.8139 - 18.8139i) q^{38} +(9.33594 - 9.33594i) q^{39} +(-0.686881 + 14.1254i) q^{40} +(41.1714 - 41.1714i) q^{41} +(-20.0309 - 20.0309i) q^{42} +(28.4243 - 28.4243i) q^{43} +(-10.0800 - 10.0800i) q^{44} +(11.7714 - 10.6797i) q^{45} +(-1.97550 - 1.97550i) q^{46} +(55.5354 - 55.5354i) q^{47} -9.65086i q^{48} -19.9273 q^{49} +(27.3077 - 22.4564i) q^{50} +(-5.26715 + 40.6766i) q^{51} +(7.73895 - 7.73895i) q^{52} +(-44.3219 + 44.3219i) q^{53} +(-29.3840 + 29.3840i) q^{54} +(-1.73094 + 35.5961i) q^{55} +(-16.6045 - 16.6045i) q^{56} -45.3925i q^{57} +25.4072 q^{58} -51.9453 q^{59} +(-17.8690 + 16.2117i) q^{60} +(-26.2200 + 26.2200i) q^{61} -36.2236i q^{62} +26.3912i q^{63} -8.00000i q^{64} +(-27.3290 - 1.32893i) q^{65} -24.3201i q^{66} +(56.6967 - 56.6967i) q^{67} +(-4.36616 + 33.7185i) q^{68} -4.76633i q^{69} +(-2.85133 + 58.6365i) q^{70} +(-37.1298 - 37.1298i) q^{71} +(-6.35762 + 6.35762i) q^{72} -64.7741i q^{73} +(41.9260 + 41.9260i) q^{74} +(60.0333 + 5.85234i) q^{75} -37.6277i q^{76} +(-41.8433 - 41.8433i) q^{77} +18.6719 q^{78} +(-17.3775 - 17.3775i) q^{79} +(-14.8123 + 13.4386i) q^{80} -42.2859 q^{81} +82.3428 q^{82} +(-60.2128 + 60.2128i) q^{83} -40.0619i q^{84} +(69.7655 - 48.5569i) q^{85} +56.8486 q^{86} +(30.6501 + 30.6501i) q^{87} -20.1600i q^{88} +122.541i q^{89} +(22.4510 + 1.09173i) q^{90} +(32.1253 - 32.1253i) q^{91} -3.95101i q^{92} +(43.6986 - 43.6986i) q^{93} +111.071 q^{94} +(-69.6692 + 63.2078i) q^{95} +(9.65086 - 9.65086i) q^{96} -28.2565 q^{97} +(-19.9273 - 19.9273i) q^{98} +(-16.0212 + 16.0212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 q^{45} + 16 q^{46} + 112 q^{47} + 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} + 48 q^{53} + 108 q^{54} + 40 q^{55} - 24 q^{56} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * q^45 + 16 * q^46 + 112 * q^47 + 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 + 48 * q^53 + 108 * q^54 + 40 * q^55 - 24 * q^56 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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