LMFDB - Embedded newform 169.4.c.b.146.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(22,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			146.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	169.146
Dual form			169.4.c.b.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(1.50000 - 2.59808i) q^{6} +(-7.50000 + 12.9904i) q^{7} -21.0000 q^{8} +(13.0000 - 22.5167i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(1.50000 - 2.59808i) q^{6} +(-7.50000 + 12.9904i) q^{7} -21.0000 q^{8} +(13.0000 - 22.5167i) q^{9} +(13.5000 + 23.3827i) q^{10} +(24.0000 + 41.5692i) q^{11} -1.00000 q^{12} +45.0000 q^{14} +(-4.50000 - 7.79423i) q^{15} +(35.5000 + 61.4878i) q^{16} +(-22.5000 + 38.9711i) q^{17} -78.0000 q^{18} +(-3.00000 + 5.19615i) q^{19} +(4.50000 - 7.79423i) q^{20} -15.0000 q^{21} +(72.0000 - 124.708i) q^{22} +(81.0000 + 140.296i) q^{23} +(-10.5000 - 18.1865i) q^{24} -44.0000 q^{25} +53.0000 q^{27} +(-7.50000 - 12.9904i) q^{28} +(72.0000 + 124.708i) q^{29} +(-13.5000 + 23.3827i) q^{30} +264.000 q^{31} +(22.5000 - 38.9711i) q^{32} +(-24.0000 + 41.5692i) q^{33} +135.000 q^{34} +(67.5000 - 116.913i) q^{35} +(13.0000 + 22.5167i) q^{36} +(-151.500 - 262.406i) q^{37} +18.0000 q^{38} +189.000 q^{40} +(96.0000 + 166.277i) q^{41} +(22.5000 + 38.9711i) q^{42} +(-48.5000 + 84.0045i) q^{43} -48.0000 q^{44} +(-117.000 + 202.650i) q^{45} +(243.000 - 420.888i) q^{46} +111.000 q^{47} +(-35.5000 + 61.4878i) q^{48} +(59.0000 + 102.191i) q^{49} +(66.0000 + 114.315i) q^{50} -45.0000 q^{51} -414.000 q^{53} +(-79.5000 - 137.698i) q^{54} +(-216.000 - 374.123i) q^{55} +(157.500 - 272.798i) q^{56} -6.00000 q^{57} +(216.000 - 374.123i) q^{58} +(-261.000 + 452.065i) q^{59} +9.00000 q^{60} +(-188.000 + 325.626i) q^{61} +(-396.000 - 685.892i) q^{62} +(195.000 + 337.750i) q^{63} +433.000 q^{64} +144.000 q^{66} +(18.0000 + 31.1769i) q^{67} +(-22.5000 - 38.9711i) q^{68} +(-81.0000 + 140.296i) q^{69} -405.000 q^{70} +(-178.500 + 309.171i) q^{71} +(-273.000 + 472.850i) q^{72} -1098.00 q^{73} +(-454.500 + 787.217i) q^{74} +(-22.0000 - 38.1051i) q^{75} +(-3.00000 - 5.19615i) q^{76} -720.000 q^{77} -830.000 q^{79} +(-319.500 - 553.390i) q^{80} +(-324.500 - 562.050i) q^{81} +(288.000 - 498.831i) q^{82} -438.000 q^{83} +(7.50000 - 12.9904i) q^{84} +(202.500 - 350.740i) q^{85} +291.000 q^{86} +(-72.0000 + 124.708i) q^{87} +(-504.000 - 872.954i) q^{88} +(219.000 + 379.319i) q^{89} +702.000 q^{90} -162.000 q^{92} +(132.000 + 228.631i) q^{93} +(-166.500 - 288.386i) q^{94} +(27.0000 - 46.7654i) q^{95} +45.0000 q^{96} +(426.000 - 737.854i) q^{97} +(177.000 - 306.573i) q^{98} +1248.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + q^{3} - q^{4} - 18 q^{5} + 3 q^{6} - 15 q^{7} - 42 q^{8} + 26 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + q^3 - q^4 - 18 * q^5 + 3 * q^6 - 15 * q^7 - 42 * q^8 + 26 * q^9	\( 2 q - 3 q^{2} + q^{3} - q^{4} - 18 q^{5} + 3 q^{6} - 15 q^{7} - 42 q^{8} + 26 q^{9} + 27 q^{10} + 48 q^{11} - 2 q^{12} + 90 q^{14} - 9 q^{15} + 71 q^{16} - 45 q^{17} - 156 q^{18} - 6 q^{19} + 9 q^{20} - 30 q^{21} + 144 q^{22} + 162 q^{23} - 21 q^{24} - 88 q^{25} + 106 q^{27} - 15 q^{28} + 144 q^{29} - 27 q^{30} + 528 q^{31} + 45 q^{32} - 48 q^{33} + 270 q^{34} + 135 q^{35} + 26 q^{36} - 303 q^{37} + 36 q^{38} + 378 q^{40} + 192 q^{41} + 45 q^{42} - 97 q^{43} - 96 q^{44} - 234 q^{45} + 486 q^{46} + 222 q^{47} - 71 q^{48} + 118 q^{49} + 132 q^{50} - 90 q^{51} - 828 q^{53} - 159 q^{54} - 432 q^{55} + 315 q^{56} - 12 q^{57} + 432 q^{58} - 522 q^{59} + 18 q^{60} - 376 q^{61} - 792 q^{62} + 390 q^{63} + 866 q^{64} + 288 q^{66} + 36 q^{67} - 45 q^{68} - 162 q^{69} - 810 q^{70} - 357 q^{71} - 546 q^{72} - 2196 q^{73} - 909 q^{74} - 44 q^{75} - 6 q^{76} - 1440 q^{77} - 1660 q^{79} - 639 q^{80} - 649 q^{81} + 576 q^{82} - 876 q^{83} + 15 q^{84} + 405 q^{85} + 582 q^{86} - 144 q^{87} - 1008 q^{88} + 438 q^{89} + 1404 q^{90} - 324 q^{92} + 264 q^{93} - 333 q^{94} + 54 q^{95} + 90 q^{96} + 852 q^{97} + 354 q^{98} + 2496 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + q^3 - q^4 - 18 * q^5 + 3 * q^6 - 15 * q^7 - 42 * q^8 + 26 * q^9 + 27 * q^10 + 48 * q^11 - 2 * q^12 + 90 * q^14 - 9 * q^15 + 71 * q^16 - 45 * q^17 - 156 * q^18 - 6 * q^19 + 9 * q^20 - 30 * q^21 + 144 * q^22 + 162 * q^23 - 21 * q^24 - 88 * q^25 + 106 * q^27 - 15 * q^28 + 144 * q^29 - 27 * q^30 + 528 * q^31 + 45 * q^32 - 48 * q^33 + 270 * q^34 + 135 * q^35 + 26 * q^36 - 303 * q^37 + 36 * q^38 + 378 * q^40 + 192 * q^41 + 45 * q^42 - 97 * q^43 - 96 * q^44 - 234 * q^45 + 486 * q^46 + 222 * q^47 - 71 * q^48 + 118 * q^49 + 132 * q^50 - 90 * q^51 - 828 * q^53 - 159 * q^54 - 432 * q^55 + 315 * q^56 - 12 * q^57 + 432 * q^58 - 522 * q^59 + 18 * q^60 - 376 * q^61 - 792 * q^62 + 390 * q^63 + 866 * q^64 + 288 * q^66 + 36 * q^67 - 45 * q^68 - 162 * q^69 - 810 * q^70 - 357 * q^71 - 546 * q^72 - 2196 * q^73 - 909 * q^74 - 44 * q^75 - 6 * q^76 - 1440 * q^77 - 1660 * q^79 - 639 * q^80 - 649 * q^81 + 576 * q^82 - 876 * q^83 + 15 * q^84 + 405 * q^85 + 582 * q^86 - 144 * q^87 - 1008 * q^88 + 438 * q^89 + 1404 * q^90 - 324 * q^92 + 264 * q^93 - 333 * q^94 + 54 * q^95 + 90 * q^96 + 852 * q^97 + 354 * q^98 + 2496 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.50000	−	2.59808i	−0.530330	−	0.918559i	−0.999374	−	0.0353837i	$-0.988735\pi$
$2$	−1.50000	−	2.59808i	−0.530330	−	0.918559i	0.469044	−	0.883175i	$-0.344599\pi$
$3$	0.500000	+	0.866025i	0.0962250	+	0.166667i	0.910119	−	0.414346i	$-0.135990\pi$
$3$	0.500000	+	0.866025i	0.0962250	+	0.166667i	−0.813894	+	0.581013i	$0.802656\pi$
$4$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$5$	−9.00000			−0.804984			−0.402492	−	0.915423i	$-0.631856\pi$
$5$	−9.00000			−0.804984			−0.402492	+	0.915423i	$0.631856\pi$
$6$	1.50000	−	2.59808i	0.102062	−	0.176777i
$7$	−7.50000	+	12.9904i	−0.404962	+	0.701415i	−0.994317	−	0.106459i	$-0.966049\pi$
$7$	−7.50000	+	12.9904i	−0.404962	+	0.701415i	0.589355	+	0.807874i	$0.299382\pi$
$8$	−21.0000			−0.928078
$9$	13.0000	−	22.5167i	0.481481	−	0.833950i
$10$	13.5000	+	23.3827i	0.426907	+	0.739425i
$11$	24.0000	+	41.5692i	0.657843	+	1.13942i	0.981173	+	0.193131i	$0.0618643\pi$
$11$	24.0000	+	41.5692i	0.657843	+	1.13942i	−0.323330	+	0.946286i	$0.604802\pi$
$12$	−1.00000			−0.0240563
$13$		0			0
$13$		0			0
$14$	45.0000			0.859054
$15$	−4.50000	−	7.79423i	−0.0774597	−	0.134164i
$16$	35.5000	+	61.4878i	0.554688	+	0.960747i
$17$	−22.5000	+	38.9711i	−0.321003	+	0.555994i	−0.980695	−	0.195542i	$-0.937353\pi$
$17$	−22.5000	+	38.9711i	−0.321003	+	0.555994i	0.659692	+	0.751536i	$0.270687\pi$
$18$	−78.0000			−1.02138
$19$	−3.00000	+	5.19615i	−0.0362235	+	0.0627410i	−0.883569	−	0.468301i	$-0.844866\pi$
$19$	−3.00000	+	5.19615i	−0.0362235	+	0.0627410i	0.847345	+	0.531042i	$0.178199\pi$
$20$	4.50000	−	7.79423i	0.0503115	−	0.0871421i
$21$	−15.0000			−0.155870
$22$	72.0000	−	124.708i	0.697748	−	1.20853i
$23$	81.0000	+	140.296i	0.734333	+	1.27190i	0.955015	+	0.296557i	$0.0958384\pi$
$23$	81.0000	+	140.296i	0.734333	+	1.27190i	−0.220682	+	0.975346i	$0.570828\pi$
$24$	−10.5000	−	18.1865i	−0.0893043	−	0.154680i
$25$	−44.0000			−0.352000
$26$		0			0
$27$	53.0000			0.377772
$28$	−7.50000	−	12.9904i	−0.0506202	−	0.0876768i
$29$	72.0000	+	124.708i	0.461037	+	0.798539i	0.999013	−	0.0444210i	$-0.0141443\pi$
$29$	72.0000	+	124.708i	0.461037	+	0.798539i	−0.537976	+	0.842960i	$0.680811\pi$
$30$	−13.5000	+	23.3827i	−0.0821584	+	0.142302i
$31$	264.000			1.52954			0.764771	−	0.644302i	$-0.222852\pi$
$31$	264.000			1.52954			0.764771	+	0.644302i	$0.222852\pi$
$32$	22.5000	−	38.9711i	0.124296	−	0.215287i
$33$	−24.0000	+	41.5692i	−0.126602	+	0.219281i
$34$	135.000			0.680950
$35$	67.5000	−	116.913i	0.325988	−	0.564628i
$36$	13.0000	+	22.5167i	0.0601852	+	0.104244i
$37$	−151.500	−	262.406i	−0.673147	−	1.16593i	−0.977007	−	0.213208i	$-0.931609\pi$
$37$	−151.500	−	262.406i	−0.673147	−	1.16593i	0.303860	−	0.952717i	$-0.401725\pi$
$38$	18.0000			0.0768417
$39$		0			0
$40$	189.000			0.747088
$41$	96.0000	+	166.277i	0.365675	+	0.633368i	0.988884	−	0.148687i	$-0.0475048\pi$
$41$	96.0000	+	166.277i	0.365675	+	0.633368i	−0.623209	+	0.782055i	$0.714171\pi$
$42$	22.5000	+	38.9711i	0.0826625	+	0.143176i
$43$	−48.5000	+	84.0045i	−0.172004	+	0.297920i	−0.939120	−	0.343588i	$-0.888358\pi$
$43$	−48.5000	+	84.0045i	−0.172004	+	0.297920i	0.767116	+	0.641508i	$0.221691\pi$
$44$	−48.0000			−0.164461
$45$	−117.000	+	202.650i	−0.387585	+	0.671317i
$46$	243.000	−	420.888i	0.778878	−	1.34906i
$47$	111.000			0.344490			0.172245	−	0.985054i	$-0.444898\pi$
$47$	111.000			0.344490			0.172245	+	0.985054i	$0.444898\pi$
$48$	−35.5000	+	61.4878i	−0.106750	+	0.184896i
$49$	59.0000	+	102.191i	0.172012	+	0.297933i
$50$	66.0000	+	114.315i	0.186676	+	0.323333i
$51$	−45.0000			−0.123554
$52$		0			0
$53$	−414.000			−1.07297			−0.536484	−	0.843911i	$-0.680248\pi$
$53$	−414.000			−1.07297			−0.536484	+	0.843911i	$0.680248\pi$
$54$	−79.5000	−	137.698i	−0.200344	−	0.347006i
$55$	−216.000	−	374.123i	−0.529553	−	0.917213i
$56$	157.500	−	272.798i	0.375836	−	0.650967i
$57$	−6.00000			−0.0139424
$58$	216.000	−	374.123i	0.489003	−	0.846979i
$59$	−261.000	+	452.065i	−0.575920	+	0.997523i	0.420021	+	0.907515i	$0.362023\pi$
$59$	−261.000	+	452.065i	−0.575920	+	0.997523i	−0.995941	+	0.0900089i	$0.971310\pi$
$60$	9.00000			0.0193649
$61$	−188.000	+	325.626i	−0.394605	+	0.683477i	−0.993051	−	0.117687i	$-0.962452\pi$
$61$	−188.000	+	325.626i	−0.394605	+	0.683477i	0.598445	+	0.801164i	$0.295785\pi$
$62$	−396.000	−	685.892i	−0.811162	−	1.40497i
$63$	195.000	+	337.750i	0.389963	+	0.675436i
$64$	433.000			0.845703
$65$		0			0
$66$	144.000			0.268563
$67$	18.0000	+	31.1769i	0.0328216	+	0.0568488i	0.881970	−	0.471306i	$-0.156217\pi$
$67$	18.0000	+	31.1769i	0.0328216	+	0.0568488i	−0.849148	+	0.528155i	$0.822884\pi$
$68$	−22.5000	−	38.9711i	−0.0401254	−	0.0694992i
$69$	−81.0000	+	140.296i	−0.141323	+	0.244778i
$70$	−405.000			−0.691525
$71$	−178.500	+	309.171i	−0.298367	+	0.516787i	−0.975762	−	0.218832i	$-0.929775\pi$
$71$	−178.500	+	309.171i	−0.298367	+	0.516787i	0.677396	+	0.735619i	$0.263109\pi$
$72$	−273.000	+	472.850i	−0.446852	+	0.773971i
$73$	−1098.00			−1.76043			−0.880214	−	0.474578i	$-0.842601\pi$
$73$	−1098.00			−1.76043			−0.880214	+	0.474578i	$0.842601\pi$
$74$	−454.500	+	787.217i	−0.713980	+	1.23665i
$75$	−22.0000	−	38.1051i	−0.0338712	−	0.0586667i
$76$	−3.00000	−	5.19615i	−0.00452794	−	0.00784263i
$77$	−720.000			−1.06561
$78$		0			0
$79$	−830.000			−1.18205			−0.591027	−	0.806652i	$-0.701277\pi$
$79$	−830.000			−1.18205			−0.591027	+	0.806652i	$0.701277\pi$
$80$	−319.500	−	553.390i	−0.446515	−	0.773386i
$81$	−324.500	−	562.050i	−0.445130	−	0.770988i
$82$	288.000	−	498.831i	0.387857	−	0.671788i
$83$	−438.000			−0.579238			−0.289619	−	0.957142i	$-0.593529\pi$
$83$	−438.000			−0.579238			−0.289619	+	0.957142i	$0.593529\pi$
$84$	7.50000	−	12.9904i	0.00974187	−	0.0168734i
$85$	202.500	−	350.740i	0.258402	−	0.447566i
$86$	291.000			0.364876
$87$	−72.0000	+	124.708i	−0.0887266	+	0.153679i
$88$	−504.000	−	872.954i	−0.610529	−	1.05747i
$89$	219.000	+	379.319i	0.260831	+	0.451772i	0.966463	−	0.256806i	$-0.0826702\pi$
$89$	219.000	+	379.319i	0.260831	+	0.451772i	−0.705632	+	0.708578i	$0.749337\pi$
$90$	702.000			0.822192
$91$		0			0
$92$	−162.000			−0.183583
$93$	132.000	+	228.631i	0.147180	+	0.254924i
$94$	−166.500	−	288.386i	−0.182693	−	0.316434i
$95$	27.0000	−	46.7654i	0.0291594	−	0.0505055i
$96$	45.0000			0.0478416
$97$	426.000	−	737.854i	0.445915	−	0.772347i	−0.552201	−	0.833711i	$-0.686212\pi$
$97$	426.000	−	737.854i	0.445915	−	0.772347i	0.998115	+	0.0613640i	$0.0195451\pi$
$98$	177.000	−	306.573i	0.182446	−	0.316006i
$99$	1248.00			1.26696
$100$	22.0000	−	38.1051i	0.0220000	−	0.0381051i
$101$	198.000	+	342.946i	0.195067	+	0.337865i	0.946922	−	0.321462i	$-0.104174\pi$
$101$	198.000	+	342.946i	0.195067	+	0.337865i	−0.751856	+	0.659328i	$0.770841\pi$
$102$	67.5000	+	116.913i	0.0655245	+	0.113492i
$103$	−182.000			−0.174107			−0.0870534	−	0.996204i	$-0.527745\pi$
$103$	−182.000			−0.174107			−0.0870534	+	0.996204i	$0.527745\pi$
$104$		0			0
$105$	135.000			0.125473
$106$	621.000	+	1075.60i	0.569027	+	0.985584i
$107$	306.000	+	530.008i	0.276469	+	0.478858i	0.970505	−	0.241083i	$-0.0775025\pi$
$107$	306.000	+	530.008i	0.276469	+	0.478858i	−0.694036	+	0.719940i	$0.744169\pi$
$108$	−26.5000	+	45.8993i	−0.0236108	+	0.0408951i
$109$	1083.00			0.951675			0.475838	−	0.879533i	$-0.342145\pi$
$109$	1083.00			0.951675			0.475838	+	0.879533i	$0.342145\pi$
$110$	−648.000	+	1122.37i	−0.561676	+	0.972852i
$111$	151.500	−	262.406i	0.129547	−	0.224382i
$112$	−1065.00			−0.898509
$113$	−45.0000	+	77.9423i	−0.0374623	+	0.0648867i	−0.884149	−	0.467206i	$-0.845261\pi$
$113$	−45.0000	+	77.9423i	−0.0374623	+	0.0648867i	0.846686	+	0.532092i	$0.178594\pi$
$114$	9.00000	+	15.5885i	0.00739410	+	0.0128070i
$115$	−729.000	−	1262.67i	−0.591127	−	1.02386i
$116$	−144.000			−0.115259
$117$		0			0
$118$	1566.00			1.22171
$119$	−337.500	−	584.567i	−0.259988	−	0.450312i
$120$	94.5000	+	163.679i	0.0718886	+	0.124515i
$121$	−486.500	+	842.643i	−0.365515	+	0.633090i
$122$	1128.00			0.837085
$123$	−96.0000	+	166.277i	−0.0703742	+	0.121892i
$124$	−132.000	+	228.631i	−0.0955964	+	0.165578i
$125$	1521.00			1.08834
$126$	585.000	−	1013.25i	0.413619	−	0.716408i
$127$	1043.00	+	1806.53i	0.728750	+	1.26223i	0.957412	+	0.288726i	$0.0932318\pi$
$127$	1043.00	+	1806.53i	0.728750	+	1.26223i	−0.228661	+	0.973506i	$0.573435\pi$
$128$	−829.500	−	1436.74i	−0.572798	−	0.992115i
$129$	−97.0000			−0.0662044
$130$		0			0
$131$	−1467.00			−0.978415			−0.489208	−	0.872167i	$-0.662714\pi$
$131$	−1467.00			−0.978415			−0.489208	+	0.872167i	$0.662714\pi$
$132$	−24.0000	−	41.5692i	−0.0158252	−	0.0274101i
$133$	−45.0000	−	77.9423i	−0.0293383	−	0.0508154i
$134$	54.0000	−	93.5307i	0.0348126	−	0.0602972i
$135$	−477.000			−0.304101
$136$	472.500	−	818.394i	0.297916	−	0.516005i
$137$	207.000	−	358.535i	0.129089	−	0.223589i	−0.794235	−	0.607611i	$-0.792128\pi$
$137$	207.000	−	358.535i	0.129089	−	0.223589i	0.923324	+	0.384022i	$0.125461\pi$
$138$	486.000			0.299790
$139$	1209.50	−	2094.92i	0.738046	−	1.27833i	−0.215327	−	0.976542i	$-0.569082\pi$
$139$	1209.50	−	2094.92i	0.738046	−	1.27833i	0.953374	−	0.301792i	$-0.0975848\pi$
$140$	67.5000	+	116.913i	0.0407485	+	0.0705785i
$141$	55.5000	+	96.1288i	0.0331485	+	0.0574149i
$142$	1071.00			0.632932
$143$		0			0
$144$	1846.00			1.06829
$145$	−648.000	−	1122.37i	−0.371127	−	0.642811i
$146$	1647.00	+	2852.69i	0.933607	+	1.61706i
$147$	−59.0000	+	102.191i	−0.0331037	+	0.0573372i
$148$	303.000			0.168287
$149$	465.000	−	805.404i	0.255666	−	0.442827i	−0.709410	−	0.704796i	$-0.751038\pi$
$149$	465.000	−	805.404i	0.255666	−	0.442827i	0.965076	+	0.261969i	$0.0843718\pi$
$150$	−66.0000	+	114.315i	−0.0359258	+	0.0622254i
$151$	−1683.00			−0.907024			−0.453512	−	0.891250i	$-0.649829\pi$
$151$	−1683.00			−0.907024			−0.453512	+	0.891250i	$0.649829\pi$
$152$	63.0000	−	109.119i	0.0336183	−	0.0582285i
$153$	585.000	+	1013.25i	0.309114	+	0.535401i
$154$	1080.00	+	1870.61i	0.565123	+	0.978821i
$155$	−2376.00			−1.23126
$156$		0			0
$157$	1874.00			0.952621			0.476310	−	0.879277i	$-0.341974\pi$
$157$	1874.00			0.952621			0.476310	+	0.879277i	$0.341974\pi$
$158$	1245.00	+	2156.40i	0.626879	+	1.08579i
$159$	−207.000	−	358.535i	−0.103246	−	0.178828i
$160$	−202.500	+	350.740i	−0.100056	+	0.173303i
$161$	−2430.00			−1.18951
$162$	−973.500	+	1686.15i	−0.472132	+	0.817757i
$163$	597.000	−	1034.03i	0.286875	−	0.496882i	−0.686187	−	0.727425i	$-0.740717\pi$
$163$	597.000	−	1034.03i	0.286875	−	0.496882i	0.973062	+	0.230543i	$0.0740502\pi$
$164$	−192.000			−0.0914188
$165$	216.000	−	374.123i	0.101913	−	0.176518i
$166$	657.000	+	1137.96i	0.307187	+	0.532064i
$167$	1194.00	+	2068.07i	0.553260	+	0.958275i	0.998037	+	0.0626334i	$0.0199499\pi$
$167$	1194.00	+	2068.07i	0.553260	+	0.958275i	−0.444776	+	0.895642i	$0.646717\pi$
$168$	315.000			0.144659
$169$		0			0
$170$	−1215.00			−0.548154
$171$	78.0000	+	135.100i	0.0348819	+	0.0604173i
$172$	−48.5000	−	84.0045i	−0.0215005	−	0.0372400i
$173$	−783.000	+	1356.20i	−0.344106	+	0.596010i	−0.985191	−	0.171461i	$-0.945151\pi$
$173$	−783.000	+	1356.20i	−0.344106	+	0.596010i	0.641085	+	0.767470i	$0.278485\pi$
$174$	432.000			0.188217
$175$	330.000	−	571.577i	0.142547	−	0.246898i
$176$	−1704.00	+	2951.41i	−0.729795	+	1.26404i
$177$	−522.000			−0.221672
$178$	657.000	−	1137.96i	0.276653	−	0.479177i
$179$	−328.500	−	568.979i	−0.137169	−	0.237584i	0.789255	−	0.614066i	$-0.210467\pi$
$179$	−328.500	−	568.979i	−0.137169	−	0.237584i	−0.926424	+	0.376482i	$0.877134\pi$
$180$	−117.000	−	202.650i	−0.0484481	−	0.0839146i
$181$	1222.00			0.501826			0.250913	−	0.968010i	$-0.419269\pi$
$181$	1222.00			0.501826			0.250913	+	0.968010i	$0.419269\pi$
$182$		0			0
$183$	−376.000			−0.151884
$184$	−1701.00	−	2946.22i	−0.681518	−	1.18042i
$185$	1363.50	+	2361.65i	0.541873	+	0.938552i
$186$	396.000	−	685.892i	0.156108	−	0.270387i
$187$	−2160.00			−0.844678
$188$	−55.5000	+	96.1288i	−0.0215306	+	0.0372921i
$189$	−397.500	+	688.490i	−0.152983	+	0.264975i
$190$	−162.000			−0.0618564
$191$	−630.000	+	1091.19i	−0.238666	+	0.413382i	−0.960332	−	0.278860i	$-0.910043\pi$
$191$	−630.000	+	1091.19i	−0.238666	+	0.413382i	0.721666	+	0.692242i	$0.243377\pi$
$192$	216.500	+	374.989i	0.0813778	+	0.140951i
$193$	−171.000	−	296.181i	−0.0637764	−	0.110464i	0.832374	−	0.554214i	$-0.186981\pi$
$193$	−171.000	−	296.181i	−0.0637764	−	0.110464i	−0.896151	+	0.443750i	$0.853648\pi$
$194$	−2556.00			−0.945928
$195$		0			0
$196$	−118.000			−0.0430029
$197$	−40.5000	−	70.1481i	−0.0146472	−	0.0253698i	0.858609	−	0.512631i	$-0.171329\pi$
$197$	−40.5000	−	70.1481i	−0.0146472	−	0.0253698i	−0.873256	+	0.487261i	$0.837996\pi$
$198$	−1872.00	−	3242.40i	−0.671905	−	1.16377i
$199$	998.000	−	1728.59i	0.355509	−	0.615760i	−0.631696	−	0.775216i	$-0.717641\pi$
$199$	998.000	−	1728.59i	0.355509	−	0.615760i	0.987205	+	0.159456i	$0.0509741\pi$
$200$	924.000			0.326683
$201$	−18.0000	+	31.1769i	−0.00631653	+	0.0109405i
$202$	594.000	−	1028.84i	0.206899	−	0.358360i
$203$	−2160.00			−0.746809
$204$	22.5000	−	38.9711i	0.00772213	−	0.0133751i
$205$	−864.000	−	1496.49i	−0.294363	−	0.509851i
$206$	273.000	+	472.850i	0.0923340	+	0.159927i
$207$	4212.00			1.41427
$208$		0			0
$209$	−288.000			−0.0953176
$210$	−202.500	−	350.740i	−0.0665420	−	0.115254i
$211$	−1416.50	−	2453.45i	−0.462161	−	0.800486i	0.536908	−	0.843641i	$-0.319592\pi$
$211$	−1416.50	−	2453.45i	−0.462161	−	0.800486i	−0.999068	+	0.0431553i	$0.986259\pi$
$212$	207.000	−	358.535i	0.0670605	−	0.116152i
$213$	−357.000			−0.114841
$214$	918.000	−	1590.02i	0.293239	−	0.507905i
$215$	436.500	−	756.040i	0.138461	−	0.239821i
$216$	−1113.00			−0.350602
$217$	−1980.00	+	3429.46i	−0.619406	+	1.07284i
$218$	−1624.50	−	2813.72i	−0.504702	−	0.874169i
$219$	−549.000	−	950.896i	−0.169397	−	0.293405i
$220$	432.000			0.132388
$221$		0			0
$222$	−909.000			−0.274811
$223$	1753.50	+	3037.15i	0.526561	+	0.912030i	0.999521	+	0.0309462i	$0.00985206\pi$
$223$	1753.50	+	3037.15i	0.526561	+	0.912030i	−0.472960	+	0.881084i	$0.656815\pi$
$224$	337.500	+	584.567i	0.100670	+	0.174366i
$225$	−572.000	+	990.733i	−0.169481	+	0.293551i
$226$	270.000			0.0794696
$227$	114.000	−	197.454i	0.0333324	−	0.0577333i	−0.848878	−	0.528589i	$-0.822721\pi$
$227$	114.000	−	197.454i	0.0333324	−	0.0577333i	0.882210	+	0.470855i	$0.156055\pi$
$228$	3.00000	−	5.19615i	0.000871403	−	0.00150931i
$229$	5493.00			1.58510			0.792549	−	0.609808i	$-0.208753\pi$
$229$	5493.00			1.58510			0.792549	+	0.609808i	$0.208753\pi$
$230$	−2187.00	+	3788.00i	−0.626985	+	1.08597i
$231$	−360.000	−	623.538i	−0.102538	−	0.177601i
$232$	−1512.00	−	2618.86i	−0.427878	−	0.741106i
$233$	−3627.00			−1.01980			−0.509898	−	0.860235i	$-0.670317\pi$
$233$	−3627.00			−1.01980			−0.509898	+	0.860235i	$0.670317\pi$
$234$		0			0
$235$	−999.000			−0.277309
$236$	−261.000	−	452.065i	−0.0719901	−	0.124690i
$237$	−415.000	−	718.801i	−0.113743	−	0.197009i
$238$	−1012.50	+	1753.70i	−0.275759	+	0.477628i
$239$	6075.00			1.64418			0.822090	−	0.569357i	$-0.192808\pi$
$239$	6075.00			1.64418			0.822090	+	0.569357i	$0.192808\pi$
$240$	319.500	−	553.390i	0.0859318	−	0.148838i
$241$	−105.000	+	181.865i	−0.0280649	+	0.0486099i	−0.879717	−	0.475498i	$-0.842268\pi$
$241$	−105.000	+	181.865i	−0.0280649	+	0.0486099i	0.851652	+	0.524108i	$0.175601\pi$
$242$	2919.00			0.775374
$243$	1040.00	−	1801.33i	0.274552	−	0.475537i
$244$	−188.000	−	325.626i	−0.0493257	−	0.0854346i
$245$	−531.000	−	919.719i	−0.138467	−	0.239831i
$246$	576.000			0.149286
$247$		0			0
$248$	−5544.00			−1.41953
$249$	−219.000	−	379.319i	−0.0557372	−	0.0965397i
$250$	−2281.50	−	3951.67i	−0.577179	−	0.999703i
$251$	3546.00	−	6141.85i	0.891719	−	1.54450i	0.0539061	−	0.998546i	$-0.482833\pi$
$251$	3546.00	−	6141.85i	0.891719	−	1.54450i	0.837813	−	0.545957i	$-0.183834\pi$
$252$	−390.000			−0.0974908
$253$	−3888.00	+	6734.21i	−0.966152	+	1.67342i
$254$	3129.00	−	5419.59i	0.772956	−	1.33880i
$255$	405.000			0.0994592
$256$	−756.500	+	1310.30i	−0.184692	+	0.319897i
$257$	−2902.50	−	5027.28i	−0.704486	−	1.22021i	−0.966877	−	0.255244i	$-0.917844\pi$
$257$	−2902.50	−	5027.28i	−0.704486	−	1.22021i	0.262390	−	0.964962i	$-0.415489\pi$
$258$	145.500	+	252.013i	0.0351102	+	0.0608127i
$259$	4545.00			1.09040
$260$		0			0
$261$	3744.00			0.887923
$262$	2200.50	+	3811.38i	0.518883	+	0.898732i
$263$	−396.000	−	685.892i	−0.0928457	−	0.160813i	0.815862	−	0.578247i	$-0.196263\pi$
$263$	−396.000	−	685.892i	−0.0928457	−	0.160813i	−0.908707	+	0.417434i	$0.862930\pi$
$264$	504.000	−	872.954i	0.117496	−	0.203510i
$265$	3726.00			0.863722
$266$	−135.000	+	233.827i	−0.0311180	+	0.0538979i
$267$	−219.000	+	379.319i	−0.0501969	+	0.0869436i
$268$	−36.0000			−0.00820541
$269$	−2736.00	+	4738.89i	−0.620137	+	1.07411i	0.369323	+	0.929301i	$0.379590\pi$
$269$	−2736.00	+	4738.89i	−0.620137	+	1.07411i	−0.989460	+	0.144808i	$0.953744\pi$
$270$	715.500	+	1239.28i	0.161274	+	0.279335i
$271$	−1165.50	−	2018.71i	−0.261251	−	0.452500i	0.705323	−	0.708886i	$-0.250802\pi$
$271$	−1165.50	−	2018.71i	−0.261251	−	0.452500i	−0.966575	+	0.256385i	$0.917468\pi$
$272$	−3195.00			−0.712225
$273$		0			0
$274$	−1242.00			−0.273839
$275$	−1056.00	−	1829.05i	−0.231561	−	0.401075i
$276$	−81.0000	−	140.296i	−0.0176653	−	0.0305972i
$277$	−692.000	+	1198.58i	−0.150102	+	0.259984i	−0.931265	−	0.364343i	$-0.881294\pi$
$277$	−692.000	+	1198.58i	−0.150102	+	0.259984i	0.781163	+	0.624327i	$0.214627\pi$
$278$	−7257.00			−1.56563
$279$	3432.00	−	5944.40i	0.736446	−	1.27556i
$280$	−1417.50	+	2455.18i	−0.302542	+	0.524019i
$281$	−4062.00			−0.862344			−0.431172	−	0.902270i	$-0.641900\pi$
$281$	−4062.00			−0.862344			−0.431172	+	0.902270i	$0.641900\pi$
$282$	166.500	−	288.386i	0.0351593	−	0.0608977i
$283$	−1882.00	−	3259.72i	−0.395312	−	0.684700i	0.597829	−	0.801624i	$-0.296030\pi$
$283$	−1882.00	−	3259.72i	−0.395312	−	0.684700i	−0.993141	+	0.116923i	$0.962697\pi$
$284$	−178.500	−	309.171i	−0.0372959	−	0.0645983i
$285$	54.0000			0.0112235
$286$		0			0
$287$	−2880.00			−0.592338
$288$	−585.000	−	1013.25i	−0.119693	−	0.207314i
$289$	1444.00	+	2501.08i	0.293914	+	0.509074i
$290$	−1944.00	+	3367.11i	−0.393640	+	0.681805i
$291$	852.000			0.171633
$292$	549.000	−	950.896i	0.110027	−	0.190572i
$293$	−2113.50	+	3660.69i	−0.421406	+	0.729897i	−0.996077	−	0.0884876i	$-0.971797\pi$
$293$	−2113.50	+	3660.69i	−0.421406	+	0.729897i	0.574671	+	0.818384i	$0.305130\pi$
$294$	354.000			0.0702235
$295$	2349.00	−	4068.59i	0.463607	−	0.802991i
$296$	3181.50	+	5510.52i	0.624733	+	1.08207i
$297$	1272.00	+	2203.17i	0.248515	+	0.430440i
$298$	−2790.00			−0.542350
$299$		0			0
$300$	44.0000			0.00846780
$301$	−727.500	−	1260.07i	−0.139310	−	0.241293i
$302$	2524.50	+	4372.56i	0.481022	+	0.833155i
$303$	−198.000	+	342.946i	−0.0375406	+	0.0650222i
$304$	−426.000			−0.0803710
$305$	1692.00	−	2930.63i	0.317651	−	0.550188i
$306$	1755.00	−	3039.75i	0.327865	−	0.567879i
$307$	306.000			0.0568871			0.0284436	−	0.999595i	$-0.490945\pi$
$307$	306.000			0.0568871			0.0284436	+	0.999595i	$0.490945\pi$
$308$	360.000	−	623.538i	0.0666003	−	0.115355i
$309$	−91.0000	−	157.617i	−0.0167534	−	0.0290178i
$310$	3564.00	+	6173.03i	0.652973	+	1.13098i
$311$	2106.00			0.383988			0.191994	−	0.981396i	$-0.438505\pi$
$311$	2106.00			0.383988			0.191994	+	0.981396i	$0.438505\pi$
$312$		0			0
$313$	10051.0			1.81507			0.907534	−	0.419979i	$-0.137963\pi$
$313$	10051.0			1.81507			0.907534	+	0.419979i	$0.137963\pi$
$314$	−2811.00	−	4868.79i	−0.505204	−	0.875038i
$315$	−1755.00	−	3039.75i	−0.313914	−	0.543716i
$316$	415.000	−	718.801i	0.0738784	−	0.127961i
$317$	−2154.00			−0.381643			−0.190821	−	0.981625i	$-0.561115\pi$
$317$	−2154.00			−0.381643			−0.190821	+	0.981625i	$0.561115\pi$
$318$	−621.000	+	1075.60i	−0.109509	+	0.189676i
$319$	−3456.00	+	5985.97i	−0.606579	+	1.05063i
$320$	−3897.00			−0.680778
$321$	−306.000	+	530.008i	−0.0532064	+	0.0921562i
$322$	3645.00	+	6313.33i	0.630832	+	1.09263i
$323$	−135.000	−	233.827i	−0.0232557	−	0.0402801i
$324$	649.000			0.111283
$325$		0			0
$326$	−3582.00			−0.608554
$327$	541.500	+	937.906i	0.0915750	+	0.158613i
$328$	−2016.00	−	3491.81i	−0.339375	−	0.587815i
$329$	−832.500	+	1441.93i	−0.139505	+	0.241630i
$330$	−1296.00			−0.216189
$331$	−5385.00	+	9327.09i	−0.894219	+	1.54883i	−0.0594500	+	0.998231i	$0.518935\pi$
$331$	−5385.00	+	9327.09i	−0.894219	+	1.54883i	−0.834769	+	0.550601i	$0.814399\pi$
$332$	219.000	−	379.319i	0.0362024	−	0.0627043i
$333$	−7878.00			−1.29643
$334$	3582.00	−	6204.21i	0.586821	−	1.01640i
$335$	−162.000	−	280.592i	−0.0264209	−	0.0457624i
$336$	−532.500	−	922.317i	−0.0864591	−	0.149752i
$337$	2171.00			0.350926			0.175463	−	0.984486i	$-0.443858\pi$
$337$	2171.00			0.350926			0.175463	+	0.984486i	$0.443858\pi$
$338$		0			0
$339$	−90.0000			−0.0144193
$340$	202.500	+	350.740i	0.0323003	+	0.0559458i
$341$	6336.00	+	10974.3i	1.00620	+	1.74279i
$342$	234.000	−	405.300i	0.0369979	−	0.0640822i
$343$	−6915.00			−1.08856
$344$	1018.50	−	1764.09i	0.159633	−	0.276493i
$345$	729.000	−	1262.67i	0.113762	−	0.197042i
$346$	4698.00			0.729960
$347$	3523.50	−	6102.88i	0.545105	−	0.944149i	−0.453495	−	0.891259i	$-0.649823\pi$
$347$	3523.50	−	6102.88i	0.545105	−	0.944149i	0.998600	−	0.0528907i	$-0.0168435\pi$
$348$	−72.0000	−	124.708i	−0.0110908	−	0.0192099i
$349$	3436.50	+	5952.19i	0.527082	+	0.912933i	0.999502	+	0.0315592i	$0.0100473\pi$
$349$	3436.50	+	5952.19i	0.527082	+	0.912933i	−0.472420	+	0.881374i	$0.656619\pi$
$350$	−1980.00			−0.302387
$351$		0			0
$352$	2160.00			0.327069
$353$	4659.00	+	8069.62i	0.702475	+	1.21672i	0.967595	+	0.252507i	$0.0812549\pi$
$353$	4659.00	+	8069.62i	0.702475	+	1.21672i	−0.265121	+	0.964215i	$0.585412\pi$
$354$	783.000	+	1356.20i	0.117559	+	0.203619i
$355$	1606.50	−	2782.54i	0.240181	−	0.416005i
$356$	−438.000			−0.0652077
$357$	337.500	−	584.567i	0.0500347	−	0.0866627i
$358$	−985.500	+	1706.94i	−0.145490	+	0.251995i
$359$	4128.00			0.606873			0.303437	−	0.952852i	$-0.401866\pi$
$359$	4128.00			0.606873			0.303437	+	0.952852i	$0.401866\pi$
$360$	2457.00	−	4255.65i	0.359709	−	0.623034i
$361$	3411.50	+	5908.89i	0.497376	+	0.861480i
$362$	−1833.00	−	3174.85i	−0.266134	−	0.460957i
$363$	−973.000			−0.140687
$364$		0			0
$365$	9882.00			1.41712
$366$	564.000	+	976.877i	0.0805485	+	0.139514i
$367$	1268.00	+	2196.24i	0.180352	+	0.312378i	0.942000	−	0.335612i	$-0.108943\pi$
$367$	1268.00	+	2196.24i	0.180352	+	0.312378i	−0.761649	+	0.647990i	$0.775610\pi$
$368$	−5751.00	+	9961.02i	−0.814651	+	1.41102i
$369$	4992.00			0.704263
$370$	4090.50	−	7084.95i	0.574743	−	0.995484i
$371$	3105.00	−	5378.02i	0.434511	−	0.752595i
$372$	−264.000			−0.0367951
$373$	46.0000	−	79.6743i	0.00638550	−	0.0110600i	−0.862815	−	0.505520i	$-0.831301\pi$
$373$	46.0000	−	79.6743i	0.00638550	−	0.0110600i	0.869200	+	0.494460i	$0.164634\pi$
$374$	3240.00	+	5611.84i	0.447958	+	0.775887i
$375$	760.500	+	1317.22i	0.104725	+	0.181390i
$376$	−2331.00			−0.319713
$377$		0			0
$378$	2385.00			0.324527
$379$	−5091.00	−	8817.87i	−0.689992	−	1.19510i	−0.971840	−	0.235643i	$-0.924281\pi$
$379$	−5091.00	−	8817.87i	−0.689992	−	1.19510i	0.281847	−	0.959459i	$-0.409053\pi$
$380$	27.0000	+	46.7654i	0.00364492	+	0.00631319i
$381$	−1043.00	+	1806.53i	−0.140248	+	0.242917i
$382$	3780.00			0.506287
$383$	289.500	−	501.429i	0.0386234	−	0.0668977i	−0.846068	−	0.533076i	$-0.821036\pi$
$383$	289.500	−	501.429i	0.0386234	−	0.0668977i	0.884691	+	0.466178i	$0.154369\pi$
$384$	829.500	−	1436.74i	0.110235	−	0.190933i
$385$	6480.00			0.857796
$386$	−513.000	+	888.542i	−0.0676451	+	0.117165i
$387$	1261.00	+	2184.12i	0.165634	+	0.286886i
$388$	426.000	+	737.854i	0.0557394	+	0.0965434i
$389$	−2106.00			−0.274495			−0.137247	−	0.990537i	$-0.543826\pi$
$389$	−2106.00			−0.274495			−0.137247	+	0.990537i	$0.543826\pi$
$390$		0			0
$391$	−7290.00			−0.942893
$392$	−1239.00	−	2146.01i	−0.159640	−	0.276505i
$393$	−733.500	−	1270.46i	−0.0941480	−	0.163069i
$394$	−121.500	+	210.444i	−0.0155357	+	0.0269087i
$395$	7470.00			0.951535
$396$	−624.000	+	1080.80i	−0.0791848	+	0.137152i
$397$	987.000	−	1709.53i	0.124776	−	0.216119i	−0.796869	−	0.604152i	$-0.793512\pi$
$397$	987.000	−	1709.53i	0.124776	−	0.216119i	0.921645	+	0.388033i	$0.126845\pi$
$398$	−5988.00			−0.754149
$399$	45.0000	−	77.9423i	0.00564616	−	0.00977944i
$400$	−1562.00	−	2705.46i	−0.195250	−	0.338183i
$401$	−5943.00	−	10293.6i	−0.740098	−	1.28189i	−0.952450	−	0.304694i	$-0.901446\pi$
$401$	−5943.00	−	10293.6i	−0.740098	−	1.28189i	0.212352	−	0.977193i	$-0.431888\pi$
$402$	108.000			0.0133994
$403$		0			0
$404$	−396.000			−0.0487667
$405$	2920.50	+	5058.45i	0.358323	+	0.620634i
$406$	3240.00	+	5611.84i	0.396055	+	0.685988i
$407$	7272.00	−	12595.5i	0.885650	−	1.53399i
$408$	945.000			0.114668
$409$	−627.000	+	1086.00i	−0.0758023	+	0.131293i	−0.901435	−	0.432915i	$-0.857485\pi$
$409$	−627.000	+	1086.00i	−0.0758023	+	0.131293i	0.825633	+	0.564208i	$0.190818\pi$
$410$	−2592.00	+	4489.48i	−0.312219	+	0.540779i
$411$	414.000			0.0496864
$412$	91.0000	−	157.617i	0.0108817	−	0.0188476i
$413$	−3915.00	−	6780.98i	−0.466452	−	0.807918i
$414$	−6318.00	−	10943.1i	−0.750031	−	1.29909i
$415$	3942.00			0.466278
$416$		0			0
$417$	2419.00			0.284074
$418$	432.000	+	748.246i	0.0505498	+	0.0875548i
$419$	−2911.50	−	5042.87i	−0.339466	−	0.587972i	0.644867	−	0.764295i	$-0.276913\pi$
$419$	−2911.50	−	5042.87i	−0.339466	−	0.587972i	−0.984332	+	0.176323i	$0.943580\pi$
$420$	−67.5000	+	116.913i	−0.00784205	+	0.0135828i
$421$	−7341.00			−0.849830			−0.424915	−	0.905233i	$-0.639696\pi$
$421$	−7341.00			−0.849830			−0.424915	+	0.905233i	$0.639696\pi$
$422$	−4249.50	+	7360.35i	−0.490195	+	0.849043i
$423$	1443.00	−	2499.35i	0.165865	−	0.287287i
$424$	8694.00			0.995797
$425$	990.000	−	1714.73i	0.112993	−	0.195710i
$426$	535.500	+	927.513i	0.0609039	+	0.105489i
$427$	−2820.00	−	4884.38i	−0.319600	−	0.553564i
$428$	−612.000			−0.0691171
$429$		0			0
$430$	−2619.00			−0.293720
$431$	3742.50	+	6482.20i	0.418260	+	0.724447i	0.995765	−	0.0919403i	$-0.0293069\pi$
$431$	3742.50	+	6482.20i	0.418260	+	0.724447i	−0.577505	+	0.816387i	$0.695974\pi$
$432$	1881.50	+	3258.85i	0.209546	+	0.362944i
$433$	−7601.50	+	13166.2i	−0.843660	+	1.46126i	0.0431199	+	0.999070i	$0.486270\pi$
$433$	−7601.50	+	13166.2i	−0.843660	+	1.46126i	−0.886780	+	0.462192i	$0.847063\pi$
$434$	11880.0			1.31396
$435$	648.000	−	1122.37i	0.0714235	−	0.123709i
$436$	−541.500	+	937.906i	−0.0594797	+	0.103022i
$437$	−972.000			−0.106401
$438$	−1647.00	+	2852.69i	−0.179673	+	0.311202i
$439$	−881.000	−	1525.94i	−0.0957809	−	0.165897i	0.814153	−	0.580650i	$-0.197201\pi$
$439$	−881.000	−	1525.94i	−0.0957809	−	0.165897i	−0.909934	+	0.414752i	$0.863868\pi$
$440$	4536.00	+	7856.58i	0.491467	+	0.851245i
$441$	3068.00			0.331282
$442$		0			0
$443$	−7317.00			−0.784743			−0.392372	−	0.919807i	$-0.628345\pi$
$443$	−7317.00			−0.784743			−0.392372	+	0.919807i	$0.628345\pi$
$444$	151.500	+	262.406i	0.0161934	+	0.0280478i
$445$	−1971.00	−	3413.87i	−0.209965	−	0.363670i
$446$	5260.50	−	9111.45i	0.558502	−	0.967354i
$447$	930.000			0.0984060
$448$	−3247.50	+	5624.83i	−0.342478	+	0.593189i
$449$	2508.00	−	4343.98i	0.263608	−	0.456582i	−0.703590	−	0.710606i	$-0.748421\pi$
$449$	2508.00	−	4343.98i	0.263608	−	0.456582i	0.967198	+	0.254024i	$0.0817542\pi$
$450$	3432.00			0.359525
$451$	−4608.00	+	7981.29i	−0.481114	+	0.833313i
$452$	−45.0000	−	77.9423i	−0.00468279	−	0.00811083i
$453$	−841.500	−	1457.52i	−0.0872784	−	0.151171i
$454$	−684.000			−0.0707086
$455$		0			0
$456$	126.000			0.0129397
$457$	−4935.00	−	8547.67i	−0.505141	−	0.874930i	−0.999982	−	0.00594684i	$-0.998107\pi$
$457$	−4935.00	−	8547.67i	−0.505141	−	0.874930i	0.494841	−	0.868984i	$-0.335226\pi$
$458$	−8239.50	−	14271.2i	−0.840626	−	1.45601i
$459$	−1192.50	+	2065.47i	−0.121266	+	0.210039i
$460$	1458.00			0.147782
$461$	7270.50	−	12592.9i	0.734536	−	1.27225i	−0.220391	−	0.975412i	$-0.570733\pi$
$461$	7270.50	−	12592.9i	0.734536	−	1.27225i	0.954927	−	0.296842i	$-0.0959333\pi$
$462$	−1080.00	+	1870.61i	−0.108758	+	0.188374i
$463$	−2112.00			−0.211993			−0.105997	−	0.994366i	$-0.533803\pi$
$463$	−2112.00			−0.211993			−0.105997	+	0.994366i	$0.533803\pi$
$464$	−5112.00	+	8854.24i	−0.511463	+	0.885879i
$465$	−1188.00	−	2057.68i	−0.118478	−	0.205210i
$466$	5440.50	+	9423.22i	0.540829	+	0.936743i
$467$	−3276.00			−0.324615			−0.162307	−	0.986740i	$-0.551894\pi$
$467$	−3276.00			−0.324615			−0.162307	+	0.986740i	$0.551894\pi$
$468$		0			0
$469$	−540.000			−0.0531661
$470$	1498.50	+	2595.48i	0.147065	+	0.254724i
$471$	937.000	+	1622.93i	0.0916660	+	0.158770i
$472$	5481.00	−	9493.37i	0.534499	−	0.925779i
$473$	−4656.00			−0.452607
$474$	−1245.00	+	2156.40i	−0.120643	+	0.208960i
$475$	132.000	−	228.631i	0.0127507	−	0.0220848i
$476$	675.000			0.0649970
$477$	−5382.00	+	9321.90i	−0.516614	+	0.894802i
$478$	−9112.50	−	15783.3i	−0.871958	−	1.51028i
$479$	7726.50	+	13382.7i	0.737020	+	1.27656i	0.953831	+	0.300343i	$0.0971012\pi$
$479$	7726.50	+	13382.7i	0.737020	+	1.27656i	−0.216811	+	0.976214i	$0.569565\pi$
$480$	−405.000			−0.0385117
$481$		0			0
$482$	630.000			0.0595347
$483$	−1215.00	−	2104.44i	−0.114460	−	0.198251i
$484$	−486.500	−	842.643i	−0.0456893	−	0.0791362i
$485$	−3834.00	+	6640.68i	−0.358955	+	0.621728i
$486$	−6240.00			−0.582412
$487$	1830.00	−	3169.65i	0.170278	−	0.294930i	−0.768239	−	0.640163i	$-0.778867\pi$
$487$	1830.00	−	3169.65i	0.170278	−	0.294930i	0.938517	+	0.345233i	$0.112200\pi$
$488$	3948.00	−	6838.14i	0.366225	−	0.634319i
$489$	1194.00			0.110418
$490$	−1593.00	+	2759.16i	−0.146866	+	0.254380i
$491$	373.500	+	646.921i	0.0343296	+	0.0594606i	0.882680	−	0.469975i	$-0.155737\pi$
$491$	373.500	+	646.921i	0.0343296	+	0.0594606i	−0.848350	+	0.529436i	$0.822404\pi$
$492$	−96.0000	−	166.277i	−0.00879678	−	0.0152365i
$493$	−6480.00			−0.591977
$494$		0			0
$495$	−11232.0			−1.01988
$496$	9372.00	+	16232.8i	0.848418	+	1.46950i
$497$	−2677.50	−	4637.57i	−0.241655	−	0.418558i
$498$	−657.000	+	1137.96i	−0.0591182	+	0.102396i
$499$	−15804.0			−1.41780			−0.708902	−	0.705307i	$-0.750809\pi$
$499$	−15804.0			−1.41780			−0.708902	+	0.705307i	$0.750809\pi$
$500$	−760.500	+	1317.22i	−0.0680212	+	0.117816i
$501$	−1194.00	+	2068.07i	−0.106475	+	0.184420i
$502$	−21276.0			−1.89162
$503$	6039.00	−	10459.9i	0.535319	−	0.927201i	−0.463828	−	0.885925i	$-0.653525\pi$
$503$	6039.00	−	10459.9i	0.535319	−	0.927201i	0.999148	−	0.0412754i	$-0.0131421\pi$
$504$	−4095.00	−	7092.75i	−0.361916	−	0.626857i
$505$	−1782.00	−	3086.51i	−0.157026	−	0.271976i
$506$	23328.0			2.04952
$507$		0			0
$508$	−2086.00			−0.182188
$509$	−8055.00	−	13951.7i	−0.701437	−	1.21493i	−0.967962	−	0.251097i	$-0.919209\pi$
$509$	−8055.00	−	13951.7i	−0.701437	−	1.21493i	0.266525	−	0.963828i	$-0.414125\pi$
$510$	−607.500	−	1052.22i	−0.0527462	−	0.0913591i
$511$	8235.00	−	14263.4i	0.712906	−	1.23479i
$512$	−8733.00			−0.753804
$513$	−159.000	+	275.396i	−0.0136843	+	0.0237018i
$514$	−8707.50	+	15081.8i	−0.747221	+	1.29422i
$515$	1638.00			0.140153
$516$	48.5000	−	84.0045i	0.00413778	−	0.00716684i
$517$	2664.00	+	4614.18i	0.226620	+	0.392518i
$518$	−6817.50	−	11808.3i	−0.578270	−	1.00159i
$519$	−1566.00			−0.132447
$520$		0			0
$521$	3915.00			0.329212			0.164606	−	0.986359i	$-0.447365\pi$
$521$	3915.00			0.329212			0.164606	+	0.986359i	$0.447365\pi$
$522$	−5616.00	−	9727.20i	−0.470892	−	0.815609i
$523$	−8092.00	−	14015.8i	−0.676555	−	1.17183i	−0.976012	−	0.217718i	$-0.930139\pi$
$523$	−8092.00	−	14015.8i	−0.676555	−	1.17183i	0.299456	−	0.954110i	$-0.403195\pi$
$524$	733.500	−	1270.46i	0.0611509	−	0.105917i
$525$	660.000			0.0548662
$526$	−1188.00	+	2057.68i	−0.0984777	+	0.170568i
$527$	−5940.00	+	10288.4i	−0.490988	+	0.850415i
$528$	−3408.00			−0.280898
$529$	−7038.50	+	12191.0i	−0.578491	+	1.00198i
$530$	−5589.00	−	9680.43i	−0.458058	−	0.793379i
$531$	6786.00	+	11753.7i	0.554590	+	0.960578i
$532$	90.0000			0.00733458
$533$		0			0
$534$	1314.00			0.106484
$535$	−2754.00	−	4770.07i	−0.222553	−	0.385473i
$536$	−378.000	−	654.715i	−0.0304610	−	0.0527601i
$537$	328.500	−	568.979i	0.0263982	−	0.0457230i
$538$	16416.0			1.31551
$539$	−2832.00	+	4905.17i	−0.226313	+	0.391986i
$540$	238.500	−	413.094i	0.0190063	−	0.0329199i
$541$	−7923.00			−0.629642			−0.314821	−	0.949151i	$-0.601945\pi$
$541$	−7923.00			−0.629642			−0.314821	+	0.949151i	$0.601945\pi$
$542$	−3496.50	+	6056.12i	−0.277099	+	0.479949i
$543$	611.000	+	1058.28i	0.0482882	+	0.0836377i
$544$	1012.50	+	1753.70i	0.0797989	+	0.138216i
$545$	−9747.00			−0.766084
$546$		0			0
$547$	−14389.0			−1.12473			−0.562367	−	0.826888i	$-0.690109\pi$
$547$	−14389.0			−1.12473			−0.562367	+	0.826888i	$0.690109\pi$
$548$	207.000	+	358.535i	0.0161361	+	0.0279486i
$549$	4888.00	+	8466.26i	0.379990	+	0.658163i
$550$	−3168.00	+	5487.14i	−0.245607	+	0.425404i
$551$	−864.000			−0.0668015
$552$	1701.00	−	2946.22i	0.131158	−	0.227173i
$553$	6225.00	−	10782.0i	0.478687	−	0.829110i
$554$	4152.00			0.318414
$555$	−1363.50	+	2361.65i	−0.104284	+	0.180624i
$556$	1209.50	+	2094.92i	0.0922558	+	0.159792i
$557$	5191.50	+	8991.94i	0.394921	+	0.684023i	0.993091	−	0.117346i	$-0.0374387\pi$
$557$	5191.50	+	8991.94i	0.394921	+	0.684023i	−0.598170	+	0.801369i	$0.704105\pi$
$558$	−20592.0			−1.56224
$559$		0			0
$560$	9585.00			0.723286
$561$	−1080.00	−	1870.61i	−0.0812792	−	0.140780i
$562$	6093.00	+	10553.4i	0.457327	+	0.792113i
$563$	−8212.50	+	14224.5i	−0.614770	+	1.06481i	0.375655	+	0.926760i	$0.377418\pi$
$563$	−8212.50	+	14224.5i	−0.614770	+	1.06481i	−0.990425	+	0.138053i	$0.955915\pi$
$564$	−111.000			−0.00828713
$565$	405.000	−	701.481i	0.0301566	−	0.0522328i
$566$	−5646.00	+	9779.16i	−0.419292	+	0.726234i
$567$	9735.00			0.721043
$568$	3748.50	−	6492.59i	0.276908	−	0.479618i
$569$	6106.50	+	10576.8i	0.449908	+	0.779264i	0.998380	−	0.0569054i	$-0.0181233\pi$
$569$	6106.50	+	10576.8i	0.449908	+	0.779264i	−0.548471	+	0.836169i	$0.684790\pi$
$570$	−81.0000	−	140.296i	−0.00595213	−	0.0103094i
$571$	6383.00			0.467811			0.233906	−	0.972259i	$-0.424849\pi$
$571$	6383.00			0.467811			0.233906	+	0.972259i	$0.424849\pi$
$572$		0			0
$573$	−1260.00			−0.0918626
$574$	4320.00	+	7482.46i	0.314135	+	0.544097i
$575$	−3564.00	−	6173.03i	−0.258485	−	0.447710i
$576$	5629.00	−	9749.71i	0.407190	−	0.705274i
$577$	6426.00			0.463636			0.231818	−	0.972759i	$-0.425533\pi$
$577$	6426.00			0.463636			0.231818	+	0.972759i	$0.425533\pi$
$578$	4332.00	−	7503.24i	0.311743	−	0.539955i
$579$	171.000	−	296.181i	0.0122738	−	0.0212588i
$580$	1296.00			0.0927818
$581$	3285.00	−	5689.79i	0.234569	−	0.406286i
$582$	−1278.00	−	2213.56i	−0.0910220	−	0.157655i
$583$	−9936.00	−	17209.7i	−0.705844	−	1.22256i
$584$	23058.0			1.63381
$585$		0			0
$586$	12681.0			0.893937
$587$	10665.0	+	18472.3i	0.749901	+	1.29887i	0.947870	+	0.318658i	$0.103232\pi$
$587$	10665.0	+	18472.3i	0.749901	+	1.29887i	−0.197969	+	0.980208i	$0.563435\pi$
$588$	−59.0000	−	102.191i	−0.00413796	−	0.00716715i
$589$	−792.000	+	1371.78i	−0.0554054	+	0.0959650i
$590$	−14094.0			−0.983459
$591$	40.5000	−	70.1481i	0.00281886	−	0.00488241i
$592$	10756.5	−	18630.8i	0.746773	−	1.29345i
$593$	12084.0			0.836813			0.418407	−	0.908260i	$-0.362589\pi$
$593$	12084.0			0.836813			0.418407	+	0.908260i	$0.362589\pi$
$594$	3816.00	−	6609.51i	0.263590	−	0.456551i
$595$	3037.50	+	5261.10i	0.209286	+	0.362495i
$596$	465.000	+	805.404i	0.0319583	+	0.0553534i
$597$	1996.00			0.136836
$598$		0			0
$599$	2394.00			0.163299			0.0816496	−	0.996661i	$-0.473981\pi$
$599$	2394.00			0.163299			0.0816496	+	0.996661i	$0.473981\pi$
$600$	462.000	+	800.207i	0.0314351	+	0.0544472i
$601$	10985.5	+	19027.4i	0.745604	+	1.29142i	0.949912	+	0.312517i	$0.101172\pi$
$601$	10985.5	+	19027.4i	0.745604	+	1.29142i	−0.204308	+	0.978907i	$0.565495\pi$
$602$	−2182.50	+	3780.20i	−0.147761	+	0.255929i
$603$	936.000			0.0632121
$604$	841.500	−	1457.52i	0.0566890	−	0.0981882i
$605$	4378.50	−	7583.78i	0.294234	−	0.509628i
$606$	1188.00			0.0796356
$607$	7703.00	−	13342.0i	0.515083	−	0.892149i	−0.484764	−	0.874645i	$-0.661095\pi$
$607$	7703.00	−	13342.0i	0.515083	−	0.892149i	0.999847	−	0.0175043i	$-0.00557208\pi$
$608$	135.000	+	233.827i	0.00900489	+	0.0155969i
$609$	−1080.00	−	1870.61i	−0.0718618	−	0.124468i
$610$	−10152.0			−0.673840
$611$		0			0
$612$	−1170.00			−0.0772785
$613$	4815.00	+	8339.82i	0.317253	+	0.549498i	0.979914	−	0.199421i	$-0.0639063\pi$
$613$	4815.00	+	8339.82i	0.317253	+	0.549498i	−0.662661	+	0.748920i	$0.730573\pi$
$614$	−459.000	−	795.011i	−0.0301689	−	0.0522541i
$615$	864.000	−	1496.49i	0.0566502	−	0.0981209i
$616$	15120.0			0.988965
$617$	−7374.00	+	12772.1i	−0.481144	+	0.833366i	−0.999766	−	0.0216375i	$-0.993112\pi$
$617$	−7374.00	+	12772.1i	−0.481144	+	0.833366i	0.518622	+	0.855004i	$0.326445\pi$
$618$	−273.000	+	472.850i	−0.0177697	+	0.0307780i
$619$	−3672.00			−0.238433			−0.119217	−	0.992868i	$-0.538038\pi$
$619$	−3672.00			−0.238433			−0.119217	+	0.992868i	$0.538038\pi$
$620$	1188.00	−	2057.68i	0.0769536	−	0.133288i
$621$	4293.00	+	7435.69i	0.277411	+	0.480490i
$622$	−3159.00	−	5471.55i	−0.203640	−	0.352716i
$623$	−6570.00			−0.422506
$624$		0			0
$625$	−8189.00			−0.524096
$626$	−15076.5	−	26113.3i	−0.962585	−	1.66725i
$627$	−144.000	−	249.415i	−0.00917194	−	0.0158863i
$628$	−937.000	+	1622.93i	−0.0595388	+	0.103124i
$629$	13635.0			0.864329
$630$	−5265.00	+	9119.25i	−0.332957	+	0.576698i
$631$	9937.50	−	17212.3i	0.626950	−	1.08591i	−0.361210	−	0.932485i	$-0.617636\pi$
$631$	9937.50	−	17212.3i	0.626950	−	1.08591i	0.988160	−	0.153425i	$-0.0490304\pi$
$632$	17430.0			1.09704
$633$	1416.50	−	2453.45i	0.0889428	−	0.154054i
$634$	3231.00	+	5596.26i	0.202397	+	0.350561i
$635$	−9387.00	−	16258.8i	−0.586633	−	1.01608i
$636$	414.000			0.0258116
$637$		0			0
$638$	20736.0			1.28675
$639$	4641.00	+	8038.45i	0.287316	+	0.497646i
$640$	7465.50	+	12930.6i	0.461093	+	0.798637i
$641$	855.000	−	1480.90i	0.0526840	−	0.0912514i	−0.838481	−	0.544931i	$-0.816556\pi$
$641$	855.000	−	1480.90i	0.0526840	−	0.0912514i	0.891165	+	0.453680i	$0.149889\pi$
$642$	1836.00			0.112868
$643$	8226.00	−	14247.8i	0.504513	−	0.873842i	−0.495474	−	0.868623i	$-0.665005\pi$
$643$	8226.00	−	14247.8i	0.504513	−	0.873842i	0.999986	−	0.00521887i	$-0.00166123\pi$
$644$	1215.00	−	2104.44i	0.0743443	−	0.128768i
$645$	873.000			0.0532936
$646$	−405.000	+	701.481i	−0.0246664	+	0.0427235i
$647$	12951.0	+	22431.8i	0.786950	+	1.36304i	0.927827	+	0.373010i	$0.121674\pi$
$647$	12951.0	+	22431.8i	0.786950	+	1.36304i	−0.140878	+	0.990027i	$0.544993\pi$
$648$	6814.50	+	11803.1i	0.413115	+	0.715537i
$649$	−25056.0			−1.51546
$650$		0			0
$651$	−3960.00			−0.238410
$652$	597.000	+	1034.03i	0.0358594	+	0.0621103i
$653$	−9054.00	−	15682.0i	−0.542589	−	0.939791i	−0.998754	−	0.0498963i	$-0.984111\pi$
$653$	−9054.00	−	15682.0i	−0.542589	−	0.939791i	0.456166	−	0.889895i	$-0.349222\pi$
$654$	1624.50	−	2813.72i	0.0971299	−	0.168234i
$655$	13203.0			0.787609
$656$	−6816.00	+	11805.7i	−0.405671	+	0.702643i
$657$	−14274.0	+	24723.3i	−0.847613	+	1.46811i
$658$	4995.00			0.295935
$659$	16452.0	−	28495.7i	0.972502	−	1.68442i	0.284559	−	0.958658i	$-0.408153\pi$
$659$	16452.0	−	28495.7i	0.972502	−	1.68442i	0.687943	−	0.725765i	$-0.258514\pi$
$660$	216.000	+	374.123i	0.0127391	+	0.0220647i
$661$	−7659.00	−	13265.8i	−0.450682	−	0.780604i	0.547747	−	0.836644i	$-0.315486\pi$
$661$	−7659.00	−	13265.8i	−0.450682	−	0.780604i	−0.998428	+	0.0560406i	$0.982152\pi$
$662$	32310.0			1.89692
$663$		0			0
$664$	9198.00			0.537578
$665$	405.000	+	701.481i	0.0236169	+	0.0409056i
$666$	11817.0	+	20467.6i	0.687537	+	1.19085i
$667$	−11664.0	+	20202.6i	−0.677109	+	1.17279i
$668$	−2388.00			−0.138315
$669$	−1753.50	+	3037.15i	−0.101337	+	0.175520i
$670$	−486.000	+	841.777i	−0.0280236	+	0.0485383i
$671$	−18048.0			−1.03835
$672$	−337.500	+	584.567i	−0.0193740	+	0.0335568i
$673$	−3864.50	−	6693.51i	−0.221346	−	0.383382i	0.733871	−	0.679289i	$-0.237712\pi$
$673$	−3864.50	−	6693.51i	−0.221346	−	0.383382i	−0.955217	+	0.295907i	$0.904378\pi$
$674$	−3256.50	−	5640.42i	−0.186106	−	0.322346i
$675$	−2332.00			−0.132976
$676$		0			0
$677$	19242.0			1.09236			0.546182	−	0.837667i	$-0.316081\pi$
$677$	19242.0			1.09236			0.546182	+	0.837667i	$0.316081\pi$
$678$	135.000	+	233.827i	0.00764697	+	0.0132449i
$679$	6390.00	+	11067.8i	0.361157	+	0.625543i
$680$	−4252.50	+	7365.55i	−0.239818	+	0.415376i
$681$	228.000			0.0128296
$682$	19008.0	−	32922.8i	1.06723	−	1.84850i
$683$	−11259.0	+	19501.2i	−0.630767	+	1.09252i	0.356629	+	0.934246i	$0.383926\pi$
$683$	−11259.0	+	19501.2i	−0.630767	+	1.09252i	−0.987395	+	0.158274i	$0.949407\pi$
$684$	−156.000			−0.00872048
$685$	−1863.00	+	3226.81i	−0.103915	+	0.179986i
$686$	10372.5	+	17965.7i	0.577294	+	0.999903i
$687$	2746.50	+	4757.08i	0.152526	+	0.264183i
$688$	−6887.00			−0.381634
$689$		0			0
$690$	−4374.00			−0.241327
$691$	−4584.00	−	7939.72i	−0.252364	−	0.437107i	0.711812	−	0.702370i	$-0.247875\pi$
$691$	−4584.00	−	7939.72i	−0.252364	−	0.437107i	−0.964176	+	0.265262i	$0.914541\pi$
$692$	−783.000	−	1356.20i	−0.0430133	−	0.0745012i
$693$	−9360.00	+	16212.0i	−0.513069	+	0.888662i
$694$	−21141.0			−1.15634
$695$	−10885.5	+	18854.2i	−0.594116	+	1.02904i
$696$	1512.00	−	2618.86i	0.0823451	−	0.142626i
$697$	−8640.00			−0.469531
$698$	10309.5	−	17856.6i	0.559055	−	0.968312i
$699$	−1813.50	−	3141.07i	−0.0981300	−	0.169966i
$700$	330.000	+	571.577i	0.0178183	+	0.0308622i
$701$	−1170.00			−0.0630389			−0.0315195	−	0.999503i	$-0.510035\pi$
$701$	−1170.00			−0.0630389			−0.0315195	+	0.999503i	$0.510035\pi$
$702$		0			0
$703$	1818.00			0.0975351
$704$	10392.0	+	17999.5i	0.556340	+	0.963609i
$705$	−499.500	−	865.159i	−0.0266841	−	0.0462181i
$706$	13977.0	−	24208.9i	0.745087	−	1.29053i
$707$	−5940.00			−0.315978
$708$	261.000	−	452.065i	0.0138545	−	0.0239967i
$709$	831.000	−	1439.33i	0.0440181	−	0.0762417i	−0.843177	−	0.537636i	$-0.819317\pi$
$709$	831.000	−	1439.33i	0.0440181	−	0.0762417i	0.887195	+	0.461395i	$0.152651\pi$
$710$	−9639.00			−0.509500
$711$	−10790.0	+	18688.8i	−0.569137	+	0.985775i
$712$	−4599.00	−	7965.70i	−0.242071	−	0.419280i
$713$	21384.0	+	37038.2i	1.12319	+	1.94543i
$714$	−2025.00			−0.106140
$715$		0			0
$716$	657.000			0.0342922
$717$	3037.50	+	5261.10i	0.158211	+	0.274030i
$718$	−6192.00	−	10724.9i	−0.321843	−	0.557449i
$719$	15480.0	−	26812.1i	0.802930	−	1.39072i	−0.114750	−	0.993394i	$-0.536607\pi$
$719$	15480.0	−	26812.1i	0.802930	−	1.39072i	0.917680	−	0.397321i	$-0.130060\pi$
$720$	−16614.0			−0.859954
$721$	1365.00	−	2364.25i	0.0705066	−	0.122121i
$722$	10234.5	−	17726.7i	0.527547	−	0.913738i
$723$	−210.000			−0.0108022
$724$	−611.000	+	1058.28i	−0.0313641	+	0.0543243i
$725$	−3168.00	−	5487.14i	−0.162285	−	0.281086i
$726$	1459.50	+	2527.93i	0.0746104	+	0.129229i
$727$	8372.00			0.427098			0.213549	−	0.976932i	$-0.431498\pi$
$727$	8372.00			0.427098			0.213549	+	0.976932i	$0.431498\pi$
$728$		0			0
$729$	−15443.0			−0.784586
$730$	−14823.0	−	25674.2i	−0.751540	−	1.30170i
$731$	−2182.50	−	3780.20i	−0.110428	−	0.191266i
$732$	188.000	−	325.626i	0.00949273	−	0.0164419i
$733$	−2739.00			−0.138018			−0.0690091	−	0.997616i	$-0.521984\pi$
$733$	−2739.00			−0.138018			−0.0690091	+	0.997616i	$0.521984\pi$
$734$	3804.00	−	6588.72i	0.191292	−	0.331327i
$735$	531.000	−	919.719i	0.0266479	−	0.0461556i
$736$	7290.00			0.365099
$737$	−864.000	+	1496.49i	−0.0431830	+	0.0747951i
$738$	−7488.00	−	12969.6i	−0.373492	−	0.646907i
$739$	3378.00	+	5850.87i	0.168148	+	0.291242i	0.937769	−	0.347260i	$-0.112888\pi$
$739$	3378.00	+	5850.87i	0.168148	+	0.291242i	−0.769620	+	0.638502i	$0.779555\pi$
$740$	−2727.00			−0.135468
$741$		0			0
$742$	−18630.0			−0.921737
$743$	−14821.5	−	25671.6i	−0.731828	−	1.26756i	−0.956101	−	0.293037i	$-0.905334\pi$
$743$	−14821.5	−	25671.6i	−0.731828	−	1.26756i	0.224273	−	0.974526i	$-0.427999\pi$
$744$	−2772.00	−	4801.24i	−0.136595	−	0.236589i
$745$	−4185.00	+	7248.63i	−0.205807	+	0.356469i
$746$	−276.000			−0.0135457
$747$	−5694.00	+	9862.30i	−0.278892	+	0.483056i
$748$	1080.00	−	1870.61i	0.0527924	−	0.0914391i
$749$	−9180.00			−0.447837
$750$	2281.50	−	3951.67i	0.111078	−	0.192393i
$751$	9064.00	+	15699.3i	0.440413	+	0.762817i	0.997720	−	0.0674890i	$-0.0214987\pi$
$751$	9064.00	+	15699.3i	0.440413	+	0.762817i	−0.557307	+	0.830306i	$0.688165\pi$
$752$	3940.50	+	6825.15i	0.191084	+	0.330967i
$753$	7092.00			0.343223
$754$		0			0
$755$	15147.0			0.730140
$756$	−397.500	−	688.490i	−0.0191229	−	0.0331219i
$757$	3205.00	+	5551.22i	0.153881	+	0.266529i	0.932651	−	0.360780i	$-0.117490\pi$
$757$	3205.00	+	5551.22i	0.153881	+	0.266529i	−0.778770	+	0.627309i	$0.784156\pi$
$758$	−15273.0	+	26453.6i	−0.731847	+	1.26760i
$759$	−7776.00			−0.371872
$760$	−567.000	+	982.073i	−0.0270622	+	0.0468731i
$761$	−14145.0	+	24499.9i	−0.673792	+	1.16704i	0.303028	+	0.952982i	$0.402002\pi$
$761$	−14145.0	+	24499.9i	−0.673792	+	1.16704i	−0.976820	+	0.214061i	$0.931331\pi$
$762$	6258.00			0.297511
$763$	−8122.50	+	14068.6i	−0.385392	+	0.667519i
$764$	−630.000	−	1091.19i	−0.0298332	−	0.0516727i
$765$	−5265.00	−	9119.25i	−0.248832	−	0.430990i
$766$	−1737.00			−0.0819326
$767$		0			0
$768$	−1513.00			−0.0710881
$769$	13980.0	+	24214.1i	0.655568	+	1.13548i	0.981751	+	0.190170i	$0.0609040\pi$
$769$	13980.0	+	24214.1i	0.655568	+	1.13548i	−0.326183	+	0.945307i	$0.605763\pi$
$770$	−9720.00	−	16835.5i	−0.454915	−	0.787936i
$771$	2902.50	−	5027.28i	0.135578	−	0.234829i
$772$	342.000			0.0159441
$773$	2824.50	−	4892.18i	0.131423	−	0.227632i	−0.792802	−	0.609479i	$-0.791379\pi$
$773$	2824.50	−	4892.18i	0.131423	−	0.227632i	0.924225	+	0.381847i	$0.124712\pi$
$774$	3783.00	−	6552.35i	0.175681	−	0.304288i
$775$	−11616.0			−0.538399
$776$	−8946.00	+	15494.9i	−0.413844	+	0.716798i
$777$	2272.50	+	3936.09i	0.104923	+	0.181733i
$778$	3159.00	+	5471.55i	0.145573	+	0.252139i
$779$	−1152.00			−0.0529842
$780$		0			0
$781$	−17136.0			−0.785114
$782$	10935.0	+	18940.0i	0.500045	+	0.866102i
$783$	3816.00	+	6609.51i	0.174167	+	0.301666i
$784$	−4189.00	+	7255.56i	−0.190825	+	0.330519i
$785$	−16866.0			−0.766845
$786$	−2200.50	+	3811.38i	−0.0998591	+	0.172961i
$787$	−378.000	+	654.715i	−0.0171210	+	0.0296545i	−0.874459	−	0.485099i	$-0.838783\pi$
$787$	−378.000	+	654.715i	−0.0171210	+	0.0296545i	0.857338	+	0.514754i	$0.172117\pi$
$788$	81.0000			0.00366181
$789$	396.000	−	685.892i	0.0178682	−	0.0309486i
$790$	−11205.0	−	19407.6i	−0.504628	−	0.874041i
$791$	−675.000	−	1169.13i	−0.0303416	−	0.0525533i
$792$	−26208.0			−1.17583
$793$		0			0
$794$	−5922.00			−0.264690
$795$	1863.00	+	3226.81i	0.0831117	+	0.143954i
$796$	998.000	+	1728.59i	0.0444387	+	0.0769700i
$797$	15597.0	−	27014.8i	0.693192	−	1.20064i	−0.277594	−	0.960698i	$-0.589537\pi$
$797$	15597.0	−	27014.8i	0.693192	−	1.20064i	0.970786	−	0.239945i	$-0.0771296\pi$
$798$	−270.000			−0.0119773
$799$	−2497.50	+	4325.80i	−0.110582	+	0.191534i
$800$	−990.000	+	1714.73i	−0.0437522	+	0.0757811i
$801$	11388.0			0.502341
$802$	−17829.0	+	30880.7i	−0.784992	+	1.35965i
$803$	−26352.0	−	45643.0i	−1.15808	−	2.00586i
$804$	−18.0000	−	31.1769i	−0.000789566	−	0.00136757i
$805$	21870.0			0.957536
$806$		0			0
$807$	−5472.00			−0.238691
$808$	−4158.00	−	7201.87i	−0.181037	−	0.313565i
$809$	−8527.50	−	14770.1i	−0.370594	−	0.641888i	0.619063	−	0.785342i	$-0.287513\pi$
$809$	−8527.50	−	14770.1i	−0.370594	−	0.641888i	−0.989657	+	0.143453i	$0.954179\pi$
$810$	8761.50	−	15175.4i	0.380059	−	0.658281i
$811$	35520.0			1.53795			0.768974	−	0.639280i	$-0.220768\pi$
$811$	35520.0			1.53795			0.768974	+	0.639280i	$0.220768\pi$
$812$	1080.00	−	1870.61i	0.0466756	−	0.0808445i
$813$	1165.50	−	2018.71i	0.0502778	−	0.0870837i
$814$	−43632.0			−1.87875
$815$	−5373.00	+	9306.31i	−0.230930	+	0.399983i
$816$	−1597.50	−	2766.95i	−0.0685339	−	0.118704i
$817$	−291.000	−	504.027i	−0.0124612	−	0.0215834i
$818$	3762.00			0.160801
$819$		0			0
$820$	1728.00			0.0735907
$821$	−547.500	−	948.298i	−0.0232739	−	0.0403116i	0.854154	−	0.520020i	$-0.174076\pi$
$821$	−547.500	−	948.298i	−0.0232739	−	0.0403116i	−0.877428	+	0.479709i	$0.840742\pi$
$822$	−621.000	−	1075.60i	−0.0263502	−	0.0456399i
$823$	−1277.00	+	2211.83i	−0.0540868	+	0.0936811i	−0.891801	−	0.452428i	$-0.850558\pi$
$823$	−1277.00	+	2211.83i	−0.0540868	+	0.0936811i	0.837714	+	0.546109i	$0.183891\pi$
$824$	3822.00			0.161585
$825$	1056.00	−	1829.05i	0.0445639	−	0.0771869i
$826$	−11745.0	+	20342.9i	−0.494747	+	0.856927i
$827$	21522.0			0.904950			0.452475	−	0.891777i	$-0.350541\pi$
$827$	21522.0			0.904950			0.452475	+	0.891777i	$0.350541\pi$
$828$	−2106.00	+	3647.70i	−0.0883920	+	0.153099i
$829$	−6562.00	−	11365.7i	−0.274919	−	0.476173i	0.695196	−	0.718820i	$-0.255318\pi$
$829$	−6562.00	−	11365.7i	−0.274919	−	0.476173i	−0.970115	+	0.242647i	$0.921984\pi$
$830$	−5913.00	−	10241.6i	−0.247281	−	0.428303i
$831$	−1384.00			−0.0577743
$832$		0			0
$833$	−5310.00			−0.220865
$834$	−3628.50	−	6284.75i	−0.150653	−	0.260939i
$835$	−10746.0	−	18612.6i	−0.445366	−	0.771397i
$836$	144.000	−	249.415i	0.00595735	−	0.0103184i
$837$	13992.0			0.577819
$838$	−8734.50	+	15128.6i	−0.360058	+	0.623638i
$839$	11712.0	−	20285.8i	0.481935	−	0.834735i	−0.517850	−	0.855471i	$-0.673268\pi$
$839$	11712.0	−	20285.8i	0.481935	−	0.834735i	0.999785	+	0.0207360i	$0.00660094\pi$
$840$	−2835.00			−0.116449
$841$	1826.50	−	3163.59i	0.0748903	−	0.129714i
$842$	11011.5	+	19072.5i	0.450690	+	0.780619i
$843$	−2031.00	−	3517.80i	−0.0829791	−	0.143724i
$844$	2833.00			0.115540
$845$		0			0
$846$	−8658.00			−0.351854
$847$	−7297.50	−	12639.6i	−0.296039	−	0.512755i
$848$	−14697.0	−	25456.0i	−0.595162	−	1.03085i
$849$	1882.00	−	3259.72i	0.0760778	−	0.131771i
$850$	−5940.00			−0.239694
$851$	24543.0	−	42509.7i	0.988629	−	1.71236i
$852$	178.500	−	309.171i	0.00717759	−	0.0124320i
$853$	31077.0			1.24743			0.623714	−	0.781653i	$-0.285623\pi$
$853$	31077.0			1.24743			0.623714	+	0.781653i	$0.285623\pi$
$854$	−8460.00	+	14653.1i	−0.338987	+	0.587143i
$855$	−702.000	−	1215.90i	−0.0280794	−	0.0486350i
$856$	−6426.00	−	11130.2i	−0.256584	−	0.444417i
$857$	19422.0			0.774146			0.387073	−	0.922049i	$-0.373486\pi$
$857$	19422.0			0.774146			0.387073	+	0.922049i	$0.373486\pi$
$858$		0			0
$859$	1744.00			0.0692718			0.0346359	−	0.999400i	$-0.488973\pi$
$859$	1744.00			0.0692718			0.0346359	+	0.999400i	$0.488973\pi$
$860$	436.500	+	756.040i	0.0173076	+	0.0299776i
$861$	−1440.00	−	2494.15i	−0.0569978	−	0.0987230i
$862$	11227.5	−	19446.6i	0.443631	−	0.768392i
$863$	19179.0			0.756501			0.378251	−	0.925703i	$-0.376526\pi$
$863$	19179.0			0.756501			0.378251	+	0.925703i	$0.376526\pi$
$864$	1192.50	−	2065.47i	0.0469556	−	0.0813296i
$865$	7047.00	−	12205.8i	0.277000	−	0.479778i
$866$	45609.0			1.78967
$867$	−1444.00	+	2501.08i	−0.0565638	+	0.0979714i
$868$	−1980.00	−	3429.46i	−0.0774258	−	0.134105i
$869$	−19920.0	−	34502.5i	−0.777606	−	1.34685i
$870$	−3888.00			−0.151512
$871$		0			0
$872$	−22743.0			−0.883228
$873$	−11076.0	−	19184.2i	−0.429400	−	0.743742i
$874$	1458.00	+	2525.33i	0.0564274	+	0.0977352i
$875$	−11407.5	+	19758.4i	−0.440736	+	0.763377i
$876$	1098.00			0.0423493
$877$	−14608.5	+	25302.7i	−0.562479	+	0.974242i	0.434800	+	0.900527i	$0.356819\pi$
$877$	−14608.5	+	25302.7i	−0.562479	+	0.974242i	−0.997279	+	0.0737152i	$0.976514\pi$
$878$	−2643.00	+	4577.81i	−0.101591	+	0.175961i
$879$	−4227.00			−0.162199
$880$	15336.0	−	26562.7i	0.587473	−	1.01753i
$881$	−7816.50	−	13538.6i	−0.298916	−	0.517737i	0.676973	−	0.736008i	$-0.263292\pi$
$881$	−7816.50	−	13538.6i	−0.298916	−	0.517737i	−0.975888	+	0.218271i	$0.929958\pi$
$882$	−4602.00	−	7970.90i	−0.175689	−	0.304302i
$883$	−30589.0			−1.16580			−0.582900	−	0.812544i	$-0.698082\pi$
$883$	−30589.0			−1.16580			−0.582900	+	0.812544i	$0.698082\pi$
$884$		0			0
$885$	4698.00			0.178442
$886$	10975.5	+	19010.1i	0.416173	+	0.720832i
$887$	12942.0	+	22416.2i	0.489910	+	0.848548i	0.999933	−	0.0116124i	$-0.00369644\pi$
$887$	12942.0	+	22416.2i	0.489910	+	0.848548i	−0.510023	+	0.860161i	$0.670363\pi$
$888$	−3181.50	+	5510.52i	−0.120230	+	0.208244i
$889$	−31290.0			−1.18046
$890$	−5913.00	+	10241.6i	−0.222701	+	0.385730i
$891$	15576.0	−	26978.4i	0.585652	−	1.01438i
$892$	−3507.00			−0.131640
$893$	−333.000	+	576.773i	−0.0124786	+	0.0216136i
$894$	−1395.00	−	2416.21i	−0.0521877	−	0.0903917i
$895$	2956.50	+	5120.81i	0.110419	+	0.191251i
$896$	24885.0			0.927845
$897$		0			0
$898$	−15048.0			−0.559196
$899$	19008.0	+	32922.8i	0.705175	+	1.22140i
$900$	−572.000	−	990.733i	−0.0211852	−	0.0366938i
$901$	9315.00	−	16134.1i	0.344426	−	0.596563i
$902$	27648.0			1.02060
$903$	727.500	−	1260.07i	0.0268103	−	0.0464368i
$904$	945.000	−	1636.79i	0.0347680	−	0.0602199i
$905$	−10998.0			−0.403962
$906$	−2524.50	+	4372.56i	−0.0925727	+	0.160341i
$907$	−6152.50	−	10656.4i	−0.225237	−	0.390123i	0.731153	−	0.682213i	$-0.238982\pi$
$907$	−6152.50	−	10656.4i	−0.225237	−	0.390123i	−0.956391	+	0.292091i	$0.905649\pi$
$908$	114.000	+	197.454i	0.00416655	+	0.00721667i
$909$	10296.0			0.375684
$910$		0			0
$911$	29772.0			1.08276			0.541378	−	0.840779i	$-0.317903\pi$
$911$	29772.0			1.08276			0.541378	+	0.840779i	$0.317903\pi$
$912$	−213.000	−	368.927i	−0.00773370	−	0.0133952i
$913$	−10512.0	−	18207.3i	−0.381048	−	0.659994i
$914$	−14805.0	+	25643.0i	−0.535783	+	0.928004i
$915$	3384.00			0.122264
$916$	−2746.50	+	4757.08i	−0.0990687	+	0.171592i
$917$	11002.5	−	19056.9i	0.396221	−	0.686275i
$918$	7155.00			0.257244
$919$	−23822.0	+	41260.9i	−0.855076	+	1.48104i	0.0214976	+	0.999769i	$0.493157\pi$
$919$	−23822.0	+	41260.9i	−0.855076	+	1.48104i	−0.876574	+	0.481267i	$0.840177\pi$
$920$	15309.0	+	26516.0i	0.548612	+	0.950223i
$921$	153.000	+	265.004i	0.00547396	+	0.00948118i
$922$	−43623.0			−1.55819
$923$		0			0
$924$	720.000			0.0256345
$925$	6666.00	+	11545.9i	0.236948	+	0.410406i
$926$	3168.00	+	5487.14i	0.112427	+	0.194728i
$927$	−2366.00	+	4098.03i	−0.0838292	+	0.145196i
$928$	6480.00			0.229220
$929$	−10962.0	+	18986.7i	−0.387138	+	0.670543i	−0.992063	−	0.125739i	$-0.959870\pi$
$929$	−10962.0	+	18986.7i	−0.387138	+	0.670543i	0.604925	+	0.796282i	$0.293203\pi$
$930$	−3564.00	+	6173.03i	−0.125665	+	0.217658i
$931$	−708.000			−0.0249235
$932$	1813.50	−	3141.07i	0.0637373	−	0.110396i
$933$	1053.00	+	1823.85i	0.0369493	+	0.0639980i
$934$	4914.00	+	8511.30i	0.172153	+	0.298178i
$935$	19440.0			0.679953
$936$		0			0
$937$	32398.0			1.12956			0.564779	−	0.825242i	$-0.308961\pi$
$937$	32398.0			1.12956			0.564779	+	0.825242i	$0.308961\pi$
$938$	810.000	+	1402.96i	0.0281956	+	0.0488361i
$939$	5025.50	+	8704.42i	0.174655	+	0.302511i
$940$	499.500	−	865.159i	0.0173318	−	0.0300196i
$941$	2097.00			0.0726464			0.0363232	−	0.999340i	$-0.488435\pi$
$941$	2097.00			0.0726464			0.0363232	+	0.999340i	$0.488435\pi$
$942$	2811.00	−	4868.79i	0.0972265	−	0.168401i
$943$	−15552.0	+	26936.9i	−0.537055	+	0.930206i
$944$	−37062.0			−1.27782
$945$	3577.50	−	6196.41i	0.123149	−	0.213301i
$946$	6984.00	+	12096.6i	0.240031	+	0.415746i
$947$	10008.0	+	17334.4i	0.343417	+	0.594816i	0.985065	−	0.172183i	$-0.0550821\pi$
$947$	10008.0	+	17334.4i	0.343417	+	0.594816i	−0.641648	+	0.767000i	$0.721749\pi$
$948$	830.000			0.0284358
$949$		0			0
$950$	−792.000			−0.0270483
$951$	−1077.00	−	1865.42i	−0.0367236	−	0.0636071i
$952$	7087.50	+	12275.9i	0.241289	+	0.417925i
$953$	12496.5	−	21644.6i	0.424765	−	0.735715i	−0.571633	−	0.820509i	$-0.693690\pi$
$953$	12496.5	−	21644.6i	0.424765	−	0.735715i	0.996398	+	0.0847942i	$0.0270233\pi$
$954$	32292.0			1.09590
$955$	5670.00	−	9820.73i	0.192122	−	0.332766i
$956$	−3037.50	+	5261.10i	−0.102761	+	0.177988i
$957$	−6912.00			−0.233473
$958$	23179.5	−	40148.1i	0.781728	−	1.35399i
$959$	3105.00	+	5378.02i	0.104552	+	0.181090i
$960$	−1948.50	−	3374.90i	−0.0655079	−	0.113463i
$961$	39905.0			1.33950
$962$		0			0
$963$	15912.0			0.532458
$964$	−105.000	−	181.865i	−0.00350811	−	0.00607623i
$965$	1539.00	+	2665.63i	0.0513390	+	0.0889218i
$966$	−3645.00	+	6313.33i	−0.121404	+	0.210277i
$967$	−40959.0			−1.36210			−0.681051	−	0.732236i	$-0.738477\pi$
$967$	−40959.0			−1.36210			−0.681051	+	0.732236i	$0.738477\pi$
$968$	10216.5	−	17695.5i	0.339226	−	0.587557i
$969$	135.000	−	233.827i	0.00447557	−	0.00775191i
$970$	23004.0			0.761458
$971$	24466.5	−	42377.2i	0.808617	−	1.40057i	−0.105204	−	0.994451i	$-0.533550\pi$
$971$	24466.5	−	42377.2i	0.808617	−	1.40057i	0.913822	−	0.406116i	$-0.133117\pi$
$972$	1040.00	+	1801.33i	0.0343189	+	0.0594422i
$973$	18142.5	+	31423.7i	0.597761	+	1.03535i
$974$	−10980.0			−0.361213
$975$		0			0
$976$	−26696.0			−0.875531
$977$	−23694.0	−	41039.2i	−0.775884	−	1.34387i	−0.934297	−	0.356497i	$-0.883971\pi$
$977$	−23694.0	−	41039.2i	−0.775884	−	1.34387i	0.158413	−	0.987373i	$-0.449362\pi$
$978$	−1791.00	−	3102.10i	−0.0585581	−	0.101426i
$979$	−10512.0	+	18207.3i	−0.343172	+	0.594391i
$980$	1062.00			0.0346167
$981$	14079.0	−	24385.5i	0.458214	−	0.793650i
$982$	1120.50	−	1940.76i	0.0364120	−	0.0630674i
$983$	16803.0			0.545201			0.272600	−	0.962127i	$-0.412116\pi$
$983$	16803.0			0.545201			0.272600	+	0.962127i	$0.412116\pi$
$984$	2016.00	−	3491.81i	0.0653127	−	0.113125i
$985$	364.500	+	631.333i	0.0117908	+	0.0204223i
$986$	9720.00	+	16835.5i	0.313943	+	0.543765i
$987$	−1665.00			−0.0536956
$988$		0			0
$989$	−15714.0			−0.505234
$990$	16848.0	+	29181.6i	0.540873	+	0.936820i
$991$	28763.0	+	49819.0i	0.921985	+	1.59692i	0.796340	+	0.604849i	$0.206767\pi$
$991$	28763.0	+	49819.0i	0.921985	+	1.59692i	0.125644	+	0.992075i	$0.459900\pi$
$992$	5940.00	−	10288.4i	0.190116	−	0.329291i
$993$	−10770.0			−0.344185
$994$	−8032.50	+	13912.7i	−0.256313	+	0.443948i
$995$	−8982.00	+	15557.3i	−0.286179	+	0.495677i
$996$	438.000			0.0139343
$997$	12500.0	−	21650.6i	0.397070	−	0.687746i	−0.596293	−	0.802767i	$-0.703360\pi$
$997$	12500.0	−	21650.6i	0.397070	−	0.687746i	0.993363	+	0.115021i	$0.0366936\pi$
$998$	23706.0	+	41060.0i	0.751904	+	1.30234i
$999$	−8029.50	−	13907.5i	−0.254296	−	0.440454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.b.146.1		2
13.2	odd	12		13.4.b.a.12.1	✓	2
13.3	even	3		169.4.a.c.1.1		1
13.4	even	6		169.4.c.c.22.1		2
13.5	odd	4		169.4.e.d.23.1		4
13.6	odd	12		169.4.e.d.147.2		4
13.7	odd	12		169.4.e.d.147.1		4
13.8	odd	4		169.4.e.d.23.2		4
13.9	even	3	inner	169.4.c.b.22.1		2
13.10	even	6		169.4.a.b.1.1		1
13.11	odd	12		13.4.b.a.12.2	yes	2
13.12	even	2		169.4.c.c.146.1		2
39.2	even	12		117.4.b.a.64.2		2
39.11	even	12		117.4.b.a.64.1		2
39.23	odd	6		1521.4.a.i.1.1		1
39.29	odd	6		1521.4.a.d.1.1		1
52.11	even	12		208.4.f.b.129.1		2
52.15	even	12		208.4.f.b.129.2		2
65.2	even	12		325.4.d.b.324.2		2
65.24	odd	12		325.4.c.b.51.1		2
65.28	even	12		325.4.d.a.324.1		2
65.37	even	12		325.4.d.a.324.2		2
65.54	odd	12		325.4.c.b.51.2		2
65.63	even	12		325.4.d.b.324.1		2
104.11	even	12		832.4.f.c.129.2		2
104.37	odd	12		832.4.f.e.129.2		2
104.67	even	12		832.4.f.c.129.1		2
104.93	odd	12		832.4.f.e.129.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.b.a.12.1	✓	2	13.2	odd	12
13.4.b.a.12.2	yes	2	13.11	odd	12
117.4.b.a.64.1		2	39.11	even	12
117.4.b.a.64.2		2	39.2	even	12
169.4.a.b.1.1		1	13.10	even	6
169.4.a.c.1.1		1	13.3	even	3
169.4.c.b.22.1		2	13.9	even	3	inner
169.4.c.b.146.1		2	1.1	even	1	trivial
169.4.c.c.22.1		2	13.4	even	6
169.4.c.c.146.1		2	13.12	even	2
169.4.e.d.23.1		4	13.5	odd	4
169.4.e.d.23.2		4	13.8	odd	4
169.4.e.d.147.1		4	13.7	odd	12
169.4.e.d.147.2		4	13.6	odd	12
208.4.f.b.129.1		2	52.11	even	12
208.4.f.b.129.2		2	52.15	even	12
325.4.c.b.51.1		2	65.24	odd	12
325.4.c.b.51.2		2	65.54	odd	12
325.4.d.a.324.1		2	65.28	even	12
325.4.d.a.324.2		2	65.37	even	12
325.4.d.b.324.1		2	65.63	even	12
325.4.d.b.324.2		2	65.2	even	12
832.4.f.c.129.1		2	104.67	even	12
832.4.f.c.129.2		2	104.11	even	12
832.4.f.e.129.1		2	104.93	odd	12
832.4.f.e.129.2		2	104.37	odd	12
1521.4.a.d.1.1		1	39.29	odd	6
1521.4.a.i.1.1		1	39.23	odd	6

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(1.50000 - 2.59808i) q^{6} +(-7.50000 + 12.9904i) q^{7} -21.0000 q^{8} +(13.0000 - 22.5167i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -9.00000 q^{5} +(1.50000 - 2.59808i) q^{6} +(-7.50000 + 12.9904i) q^{7} -21.0000 q^{8} +(13.0000 - 22.5167i) q^{9} +(13.5000 + 23.3827i) q^{10} +(24.0000 + 41.5692i) q^{11} -1.00000 q^{12} +45.0000 q^{14} +(-4.50000 - 7.79423i) q^{15} +(35.5000 + 61.4878i) q^{16} +(-22.5000 + 38.9711i) q^{17} -78.0000 q^{18} +(-3.00000 + 5.19615i) q^{19} +(4.50000 - 7.79423i) q^{20} -15.0000 q^{21} +(72.0000 - 124.708i) q^{22} +(81.0000 + 140.296i) q^{23} +(-10.5000 - 18.1865i) q^{24} -44.0000 q^{25} +53.0000 q^{27} +(-7.50000 - 12.9904i) q^{28} +(72.0000 + 124.708i) q^{29} +(-13.5000 + 23.3827i) q^{30} +264.000 q^{31} +(22.5000 - 38.9711i) q^{32} +(-24.0000 + 41.5692i) q^{33} +135.000 q^{34} +(67.5000 - 116.913i) q^{35} +(13.0000 + 22.5167i) q^{36} +(-151.500 - 262.406i) q^{37} +18.0000 q^{38} +189.000 q^{40} +(96.0000 + 166.277i) q^{41} +(22.5000 + 38.9711i) q^{42} +(-48.5000 + 84.0045i) q^{43} -48.0000 q^{44} +(-117.000 + 202.650i) q^{45} +(243.000 - 420.888i) q^{46} +111.000 q^{47} +(-35.5000 + 61.4878i) q^{48} +(59.0000 + 102.191i) q^{49} +(66.0000 + 114.315i) q^{50} -45.0000 q^{51} -414.000 q^{53} +(-79.5000 - 137.698i) q^{54} +(-216.000 - 374.123i) q^{55} +(157.500 - 272.798i) q^{56} -6.00000 q^{57} +(216.000 - 374.123i) q^{58} +(-261.000 + 452.065i) q^{59} +9.00000 q^{60} +(-188.000 + 325.626i) q^{61} +(-396.000 - 685.892i) q^{62} +(195.000 + 337.750i) q^{63} +433.000 q^{64} +144.000 q^{66} +(18.0000 + 31.1769i) q^{67} +(-22.5000 - 38.9711i) q^{68} +(-81.0000 + 140.296i) q^{69} -405.000 q^{70} +(-178.500 + 309.171i) q^{71} +(-273.000 + 472.850i) q^{72} -1098.00 q^{73} +(-454.500 + 787.217i) q^{74} +(-22.0000 - 38.1051i) q^{75} +(-3.00000 - 5.19615i) q^{76} -720.000 q^{77} -830.000 q^{79} +(-319.500 - 553.390i) q^{80} +(-324.500 - 562.050i) q^{81} +(288.000 - 498.831i) q^{82} -438.000 q^{83} +(7.50000 - 12.9904i) q^{84} +(202.500 - 350.740i) q^{85} +291.000 q^{86} +(-72.0000 + 124.708i) q^{87} +(-504.000 - 872.954i) q^{88} +(219.000 + 379.319i) q^{89} +702.000 q^{90} -162.000 q^{92} +(132.000 + 228.631i) q^{93} +(-166.500 - 288.386i) q^{94} +(27.0000 - 46.7654i) q^{95} +45.0000 q^{96} +(426.000 - 737.854i) q^{97} +(177.000 - 306.573i) q^{98} +1248.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + q^{3} - q^{4} - 18 q^{5} + 3 q^{6} - 15 q^{7} - 42 q^{8} + 26 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + q^3 - q^4 - 18 * q^5 + 3 * q^6 - 15 * q^7 - 42 * q^8 + 26 * q^9	\( 2 q - 3 q^{2} + q^{3} - q^{4} - 18 q^{5} + 3 q^{6} - 15 q^{7} - 42 q^{8} + 26 q^{9} + 27 q^{10} + 48 q^{11} - 2 q^{12} + 90 q^{14} - 9 q^{15} + 71 q^{16} - 45 q^{17} - 156 q^{18} - 6 q^{19} + 9 q^{20} - 30 q^{21} + 144 q^{22} + 162 q^{23} - 21 q^{24} - 88 q^{25} + 106 q^{27} - 15 q^{28} + 144 q^{29} - 27 q^{30} + 528 q^{31} + 45 q^{32} - 48 q^{33} + 270 q^{34} + 135 q^{35} + 26 q^{36} - 303 q^{37} + 36 q^{38} + 378 q^{40} + 192 q^{41} + 45 q^{42} - 97 q^{43} - 96 q^{44} - 234 q^{45} + 486 q^{46} + 222 q^{47} - 71 q^{48} + 118 q^{49} + 132 q^{50} - 90 q^{51} - 828 q^{53} - 159 q^{54} - 432 q^{55} + 315 q^{56} - 12 q^{57} + 432 q^{58} - 522 q^{59} + 18 q^{60} - 376 q^{61} - 792 q^{62} + 390 q^{63} + 866 q^{64} + 288 q^{66} + 36 q^{67} - 45 q^{68} - 162 q^{69} - 810 q^{70} - 357 q^{71} - 546 q^{72} - 2196 q^{73} - 909 q^{74} - 44 q^{75} - 6 q^{76} - 1440 q^{77} - 1660 q^{79} - 639 q^{80} - 649 q^{81} + 576 q^{82} - 876 q^{83} + 15 q^{84} + 405 q^{85} + 582 q^{86} - 144 q^{87} - 1008 q^{88} + 438 q^{89} + 1404 q^{90} - 324 q^{92} + 264 q^{93} - 333 q^{94} + 54 q^{95} + 90 q^{96} + 852 q^{97} + 354 q^{98} + 2496 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + q^3 - q^4 - 18 * q^5 + 3 * q^6 - 15 * q^7 - 42 * q^8 + 26 * q^9 + 27 * q^10 + 48 * q^11 - 2 * q^12 + 90 * q^14 - 9 * q^15 + 71 * q^16 - 45 * q^17 - 156 * q^18 - 6 * q^19 + 9 * q^20 - 30 * q^21 + 144 * q^22 + 162 * q^23 - 21 * q^24 - 88 * q^25 + 106 * q^27 - 15 * q^28 + 144 * q^29 - 27 * q^30 + 528 * q^31 + 45 * q^32 - 48 * q^33 + 270 * q^34 + 135 * q^35 + 26 * q^36 - 303 * q^37 + 36 * q^38 + 378 * q^40 + 192 * q^41 + 45 * q^42 - 97 * q^43 - 96 * q^44 - 234 * q^45 + 486 * q^46 + 222 * q^47 - 71 * q^48 + 118 * q^49 + 132 * q^50 - 90 * q^51 - 828 * q^53 - 159 * q^54 - 432 * q^55 + 315 * q^56 - 12 * q^57 + 432 * q^58 - 522 * q^59 + 18 * q^60 - 376 * q^61 - 792 * q^62 + 390 * q^63 + 866 * q^64 + 288 * q^66 + 36 * q^67 - 45 * q^68 - 162 * q^69 - 810 * q^70 - 357 * q^71 - 546 * q^72 - 2196 * q^73 - 909 * q^74 - 44 * q^75 - 6 * q^76 - 1440 * q^77 - 1660 * q^79 - 639 * q^80 - 649 * q^81 + 576 * q^82 - 876 * q^83 + 15 * q^84 + 405 * q^85 + 582 * q^86 - 144 * q^87 - 1008 * q^88 + 438 * q^89 + 1404 * q^90 - 324 * q^92 + 264 * q^93 - 333 * q^94 + 54 * q^95 + 90 * q^96 + 852 * q^97 + 354 * q^98 + 2496 * q^99

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