LMFDB - Embedded newform 112.3.k.a.43.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,3,Mod(43,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("112.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.k (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:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.24
Character	$\chi$	$=$	112.43
Dual form			112.3.k.a.99.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99944 - 0.0471243i) q^{2} +(-2.60485 - 2.60485i) q^{3} +(3.99556 - 0.188445i) q^{4} +(-5.26925 - 5.26925i) q^{5} +(-5.33100 - 5.08550i) q^{6} -2.64575 q^{7} +(7.98002 - 0.565073i) q^{8} +4.57046i q^{9} +O(q^{10})$	\(q+(1.99944 - 0.0471243i) q^{2} +(-2.60485 - 2.60485i) q^{3} +(3.99556 - 0.188445i) q^{4} +(-5.26925 - 5.26925i) q^{5} +(-5.33100 - 5.08550i) q^{6} -2.64575 q^{7} +(7.98002 - 0.565073i) q^{8} +4.57046i q^{9} +(-10.7839 - 10.2873i) q^{10} +(-0.0342750 + 0.0342750i) q^{11} +(-10.8987 - 9.91695i) q^{12} +(5.31088 - 5.31088i) q^{13} +(-5.29003 + 0.124679i) q^{14} +27.4512i q^{15} +(15.9290 - 1.50589i) q^{16} +27.5699 q^{17} +(0.215380 + 9.13839i) q^{18} +(-1.06310 - 1.06310i) q^{19} +(-22.0465 - 20.0606i) q^{20} +(6.89178 + 6.89178i) q^{21} +(-0.0669158 + 0.0701461i) q^{22} -8.59472 q^{23} +(-22.2587 - 19.3148i) q^{24} +30.5299i q^{25} +(10.3685 - 10.8691i) q^{26} +(-11.5383 + 11.5383i) q^{27} +(-10.5713 + 0.498578i) q^{28} +(35.6808 - 35.6808i) q^{29} +(1.29362 + 54.8871i) q^{30} +49.7626i q^{31} +(31.7781 - 3.76158i) q^{32} +0.178562 q^{33} +(55.1245 - 1.29921i) q^{34} +(13.9411 + 13.9411i) q^{35} +(0.861281 + 18.2616i) q^{36} +(-28.9728 - 28.9728i) q^{37} +(-2.17571 - 2.07552i) q^{38} -27.6681 q^{39} +(-45.0262 - 39.0712i) q^{40} +47.8460i q^{41} +(14.1045 + 13.4550i) q^{42} +(-8.62924 + 8.62924i) q^{43} +(-0.130489 + 0.143407i) q^{44} +(24.0829 - 24.0829i) q^{45} +(-17.1847 + 0.405020i) q^{46} -79.5643i q^{47} +(-45.4152 - 37.5700i) q^{48} +7.00000 q^{49} +(1.43870 + 61.0429i) q^{50} +(-71.8154 - 71.8154i) q^{51} +(20.2191 - 22.2207i) q^{52} +(26.1653 + 26.1653i) q^{53} +(-22.5264 + 23.6139i) q^{54} +0.361207 q^{55} +(-21.1131 + 1.49504i) q^{56} +5.53844i q^{57} +(69.6604 - 73.0233i) q^{58} +(28.4333 - 28.4333i) q^{59} +(5.17303 + 109.683i) q^{60} +(-39.9332 + 39.9332i) q^{61} +(2.34503 + 99.4976i) q^{62} -12.0923i q^{63} +(63.3614 - 9.01859i) q^{64} -55.9687 q^{65} +(0.357025 - 0.00841462i) q^{66} +(59.3574 + 59.3574i) q^{67} +(110.157 - 5.19541i) q^{68} +(22.3879 + 22.3879i) q^{69} +(28.5315 + 27.2175i) q^{70} -76.2561 q^{71} +(2.58265 + 36.4724i) q^{72} -103.027i q^{73} +(-59.2947 - 56.5641i) q^{74} +(79.5258 - 79.5258i) q^{75} +(-4.44803 - 4.04735i) q^{76} +(0.0906831 - 0.0906831i) q^{77} +(-55.3208 + 1.30384i) q^{78} -45.1896i q^{79} +(-91.8686 - 75.9988i) q^{80} +101.245 q^{81} +(2.25471 + 95.6654i) q^{82} +(55.5063 + 55.5063i) q^{83} +(28.8352 + 26.2378i) q^{84} +(-145.273 - 145.273i) q^{85} +(-16.8470 + 17.6603i) q^{86} -185.886 q^{87} +(-0.254147 + 0.292883i) q^{88} +51.0768i q^{89} +(47.0175 - 49.2873i) q^{90} +(-14.0513 + 14.0513i) q^{91} +(-34.3407 + 1.61963i) q^{92} +(129.624 - 129.624i) q^{93} +(-3.74941 - 159.084i) q^{94} +11.2035i q^{95} +(-92.5756 - 72.9789i) q^{96} -27.5785 q^{97} +(13.9961 - 0.329870i) q^{98} +(-0.156653 - 0.156653i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} + 12 q^{6}+O(q^{10}) $ 48 * q + 6 * q^4 + 12 * q^6	$ 48 q + 6 q^{4} + 12 q^{6} - 40 q^{10} + 16 q^{11} - 108 q^{12} - 14 q^{14} + 66 q^{16} + 30 q^{18} - 64 q^{19} + 84 q^{20} + 94 q^{22} - 64 q^{23} + 40 q^{24} - 196 q^{26} - 96 q^{27} + 16 q^{29} - 72 q^{30} + 160 q^{32} - 28 q^{34} + 64 q^{36} - 48 q^{37} - 224 q^{38} + 384 q^{39} + 180 q^{40} + 176 q^{43} - 114 q^{44} - 256 q^{46} + 52 q^{48} + 336 q^{49} + 6 q^{50} - 192 q^{51} - 48 q^{52} - 80 q^{53} - 288 q^{54} - 512 q^{55} - 98 q^{56} - 50 q^{58} - 288 q^{59} + 512 q^{60} - 64 q^{61} + 156 q^{62} + 126 q^{64} - 32 q^{65} - 116 q^{66} + 80 q^{67} - 32 q^{68} + 192 q^{69} + 168 q^{70} + 26 q^{72} + 330 q^{74} + 608 q^{75} + 672 q^{76} + 112 q^{77} - 352 q^{78} - 980 q^{80} - 432 q^{81} - 76 q^{82} - 160 q^{83} + 320 q^{85} - 542 q^{86} - 896 q^{87} - 214 q^{88} + 1144 q^{90} - 12 q^{92} + 96 q^{93} + 660 q^{94} + 184 q^{96} + 496 q^{99}+O(q^{100}) $ 48 * q + 6 * q^4 + 12 * q^6 - 40 * q^10 + 16 * q^11 - 108 * q^12 - 14 * q^14 + 66 * q^16 + 30 * q^18 - 64 * q^19 + 84 * q^20 + 94 * q^22 - 64 * q^23 + 40 * q^24 - 196 * q^26 - 96 * q^27 + 16 * q^29 - 72 * q^30 + 160 * q^32 - 28 * q^34 + 64 * q^36 - 48 * q^37 - 224 * q^38 + 384 * q^39 + 180 * q^40 + 176 * q^43 - 114 * q^44 - 256 * q^46 + 52 * q^48 + 336 * q^49 + 6 * q^50 - 192 * q^51 - 48 * q^52 - 80 * q^53 - 288 * q^54 - 512 * q^55 - 98 * q^56 - 50 * q^58 - 288 * q^59 + 512 * q^60 - 64 * q^61 + 156 * q^62 + 126 * q^64 - 32 * q^65 - 116 * q^66 + 80 * q^67 - 32 * q^68 + 192 * q^69 + 168 * q^70 + 26 * q^72 + 330 * q^74 + 608 * q^75 + 672 * q^76 + 112 * q^77 - 352 * q^78 - 980 * q^80 - 432 * q^81 - 76 * q^82 - 160 * q^83 + 320 * q^85 - 542 * q^86 - 896 * q^87 - 214 * q^88 + 1144 * q^90 - 12 * q^92 + 96 * q^93 + 660 * q^94 + 184 * q^96 + 496 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.99944	−	0.0471243i	0.999722	−	0.0235622i
$2$	1.99944	−	0.0471243i	0.999722	−	0.0235622i
$3$	−2.60485	−	2.60485i	−0.868283	−	0.868283i	0.124000	−	0.992282i	$-0.460428\pi$
$3$	−2.60485	−	2.60485i	−0.868283	−	0.868283i	−0.992282	+	0.124000i	$0.960428\pi$
$4$	3.99556	−	0.188445i	0.998890	−	0.0471112i
$5$	−5.26925	−	5.26925i	−1.05385	−	1.05385i	−0.998465	−	0.0553843i	$-0.982362\pi$
$5$	−5.26925	−	5.26925i	−1.05385	−	1.05385i	−0.0553843	−	0.998465i	$-0.517638\pi$
$6$	−5.33100	−	5.08550i	−0.888500	−	0.847583i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$	7.98002	−	0.565073i	0.997502	−	0.0706341i
$9$			4.57046i			0.507829i
$10$	−10.7839	−	10.2873i	−1.07839	−	1.02873i
$11$	−0.0342750	+	0.0342750i	−0.00311591	+	0.00311591i	−0.708663	−	0.705547i	$-0.750701\pi$
$11$	−0.0342750	+	0.0342750i	−0.00311591	+	0.00311591i	0.705547	+	0.708663i	$0.250701\pi$
$12$	−10.8987	−	9.91695i	−0.908224	−	0.826413i
$13$	5.31088	−	5.31088i	0.408529	−	0.408529i	−0.472696	−	0.881225i	$-0.656719\pi$
$13$	5.31088	−	5.31088i	0.408529	−	0.408529i	0.881225	+	0.472696i	$0.156719\pi$
$14$	−5.29003	+	0.124679i	−0.377860	+	0.00890566i
$15$			27.4512i			1.83008i
$16$	15.9290	−	1.50589i	0.995561	−	0.0941178i
$17$	27.5699			1.62176			0.810880	−	0.585213i	$-0.198989\pi$
$17$	27.5699			1.62176			0.810880	+	0.585213i	$0.198989\pi$
$18$	0.215380	+	9.13839i	0.0119656	+	0.507688i
$19$	−1.06310	−	1.06310i	−0.0559528	−	0.0559528i	0.678577	−	0.734530i	$-0.262597\pi$
$19$	−1.06310	−	1.06310i	−0.0559528	−	0.0559528i	−0.734530	+	0.678577i	$0.762597\pi$
$20$	−22.0465	−	20.0606i	−1.10233	−	1.00303i
$21$	6.89178	+	6.89178i	0.328180	+	0.328180i
$22$	−0.0669158	+	0.0701461i	−0.00304163	+	0.00318846i
$23$	−8.59472			−0.373684			−0.186842	−	0.982390i	$-0.559825\pi$
$23$	−8.59472			−0.373684			−0.186842	+	0.982390i	$0.559825\pi$
$24$	−22.2587	−	19.3148i	−0.927444	−	0.804783i
$25$			30.5299i			1.22120i
$26$	10.3685	−	10.8691i	0.398790	−	0.418042i
$27$	−11.5383	+	11.5383i	−0.427343	+	0.427343i
$28$	−10.5713	+	0.498578i	−0.377545	+	0.0178064i
$29$	35.6808	−	35.6808i	1.23037	−	1.23037i	0.266553	−	0.963820i	$-0.414115\pi$
$29$	35.6808	−	35.6808i	1.23037	−	1.23037i	0.963820	−	0.266553i	$-0.0858848\pi$
$30$	1.29362	+	54.8871i	0.0431206	+	1.82957i
$31$			49.7626i			1.60525i	0.596487	+	0.802623i	$0.296563\pi$
$31$			49.7626i			1.60525i	−0.596487	+	0.802623i	$0.703437\pi$
$32$	31.7781	−	3.76158i	0.993067	−	0.117549i
$33$	0.178562			0.00541098
$34$	55.1245	−	1.29921i	1.62131	−	0.0382121i
$35$	13.9411	+	13.9411i	0.398318	+	0.398318i
$36$	0.861281	+	18.2616i	0.0239245	+	0.507265i
$37$	−28.9728	−	28.9728i	−0.783047	−	0.783047i	0.197296	−	0.980344i	$-0.436784\pi$
$37$	−28.9728	−	28.9728i	−0.783047	−	0.783047i	−0.980344	+	0.197296i	$0.936784\pi$
$38$	−2.17571	−	2.07552i	−0.0572556	−	0.0546189i
$39$	−27.6681			−0.709437
$40$	−45.0262	−	39.0712i	−1.12565	−	0.976779i
$41$			47.8460i			1.16698i	0.812122	+	0.583488i	$0.198312\pi$
$41$			47.8460i			1.16698i	−0.812122	+	0.583488i	$0.801688\pi$
$42$	14.1045	+	13.4550i	0.335821	+	0.320356i
$43$	−8.62924	+	8.62924i	−0.200680	+	0.200680i	−0.800291	−	0.599611i	$-0.795322\pi$
$43$	−8.62924	+	8.62924i	−0.200680	+	0.200680i	0.599611	+	0.800291i	$0.295322\pi$
$44$	−0.130489	+	0.143407i	−0.00296565	+	0.00325924i
$45$	24.0829	−	24.0829i	0.535176	−	0.535176i
$46$	−17.1847	+	0.405020i	−0.373580	+	0.00880479i
$47$		−	79.5643i		−	1.69286i	−0.532503	−	0.846428i	$-0.678748\pi$
$47$		−	79.5643i		−	1.69286i	0.532503	−	0.846428i	$-0.321252\pi$
$48$	−45.4152	−	37.5700i	−0.946149	−	0.782707i
$49$	7.00000			0.142857
$50$	1.43870	+	61.0429i	0.0287740	+	1.22086i
$51$	−71.8154	−	71.8154i	−1.40815	−	1.40815i
$52$	20.2191	−	22.2207i	0.388829	−	0.427322i
$53$	26.1653	+	26.1653i	0.493686	+	0.493686i	0.909465	−	0.415780i	$-0.136491\pi$
$53$	26.1653	+	26.1653i	0.493686	+	0.493686i	−0.415780	+	0.909465i	$0.636491\pi$
$54$	−22.5264	+	23.6139i	−0.417155	+	0.437294i
$55$	0.361207			0.00656740
$56$	−21.1131	+	1.49504i	−0.377020	+	0.0266972i
$57$			5.53844i			0.0971656i
$58$	69.6604	−	73.0233i	1.20104	−	1.25902i
$59$	28.4333	−	28.4333i	0.481921	−	0.481921i	−0.423824	−	0.905745i	$-0.639312\pi$
$59$	28.4333	−	28.4333i	0.481921	−	0.481921i	0.905745	+	0.423824i	$0.139312\pi$
$60$	5.17303	+	109.683i	0.0862172	+	1.82805i
$61$	−39.9332	+	39.9332i	−0.654642	+	0.654642i	−0.954107	−	0.299465i	$-0.903192\pi$
$61$	−39.9332	+	39.9332i	−0.654642	+	0.654642i	0.299465	+	0.954107i	$0.403192\pi$
$62$	2.34503	+	99.4976i	0.0378230	+	1.60480i
$63$		−	12.0923i		−	0.191941i
$64$	63.3614	−	9.01859i	0.990022	−	0.140915i
$65$	−55.9687			−0.861056
$66$	0.357025	−	0.00841462i	0.00540948	−	0.000127494i
$67$	59.3574	+	59.3574i	0.885932	+	0.885932i	0.994129	−	0.108197i	$-0.0345079\pi$
$67$	59.3574	+	59.3574i	0.885932	+	0.885932i	−0.108197	+	0.994129i	$0.534508\pi$
$68$	110.157	−	5.19541i	1.61996	−	0.0764031i
$69$	22.3879	+	22.3879i	0.324463	+	0.324463i
$70$	28.5315	+	27.2175i	0.407592	+	0.388822i
$71$	−76.2561			−1.07403			−0.537015	−	0.843573i	$-0.680448\pi$
$71$	−76.2561			−1.07403			−0.537015	+	0.843573i	$0.680448\pi$
$72$	2.58265	+	36.4724i	0.0358701	+	0.506561i
$73$		−	103.027i		−	1.41133i	−0.708546	−	0.705664i	$-0.750649\pi$
$73$		−	103.027i		−	1.41133i	0.708546	−	0.705664i	$-0.249351\pi$
$74$	−59.2947	−	56.5641i	−0.801280	−	0.764380i
$75$	79.5258	−	79.5258i	1.06034	−	1.06034i
$76$	−4.44803	−	4.04735i	−0.0585267	−	0.0532546i
$77$	0.0906831	−	0.0906831i	0.00117770	−	0.00117770i
$78$	−55.3208	+	1.30384i	−0.709240	+	0.0167159i
$79$		−	45.1896i		−	0.572020i	−0.958227	−	0.286010i	$-0.907671\pi$
$79$		−	45.1896i		−	0.572020i	0.958227	−	0.286010i	$-0.0923291\pi$
$80$	−91.8686	−	75.9988i	−1.14836	−	0.949985i
$81$	101.245			1.24994
$82$	2.25471	+	95.6654i	0.0274964	+	1.16665i
$83$	55.5063	+	55.5063i	0.668750	+	0.668750i	0.957427	−	0.288676i	$-0.0932152\pi$
$83$	55.5063	+	55.5063i	0.668750	+	0.668750i	−0.288676	+	0.957427i	$0.593215\pi$
$84$	28.8352	+	26.2378i	0.343277	+	0.312355i
$85$	−145.273	−	145.273i	−1.70909	−	1.70909i
$86$	−16.8470	+	17.6603i	−0.195896	+	0.205353i
$87$	−185.886			−2.13662
$88$	−0.254147	+	0.292883i	−0.00288804	+	0.00332822i
$89$			51.0768i			0.573896i	0.957946	+	0.286948i	$0.0926408\pi$
$89$			51.0768i			0.573896i	−0.957946	+	0.286948i	$0.907359\pi$
$90$	47.0175	−	49.2873i	0.522417	−	0.547637i
$91$	−14.0513	+	14.0513i	−0.154409	+	0.154409i
$92$	−34.3407	+	1.61963i	−0.373269	+	0.0176047i
$93$	129.624	−	129.624i	1.39381	−	1.39381i
$94$	−3.74941	−	159.084i	−0.0398873	−	1.69239i
$95$			11.2035i			0.117932i
$96$	−92.5756	−	72.9789i	−0.964329	−	0.760197i
$97$	−27.5785			−0.284315			−0.142157	−	0.989844i	$-0.545404\pi$
$97$	−27.5785			−0.284315			−0.142157	+	0.989844i	$0.545404\pi$
$98$	13.9961	−	0.329870i	0.142817	−	0.00336602i
$99$	−0.156653	−	0.156653i	−0.00158235	−	0.00158235i
$100$	5.75321	+	121.984i	0.0575321	+	1.21984i
$101$	−63.1521	−	63.1521i	−0.625269	−	0.625269i	0.321605	−	0.946874i	$-0.395778\pi$
$101$	−63.1521	−	63.1521i	−0.625269	−	0.625269i	−0.946874	+	0.321605i	$0.895778\pi$
$102$	−146.975	−	140.207i	−1.44093	−	1.37458i
$103$	57.5674			0.558907			0.279454	−	0.960159i	$-0.409847\pi$
$103$	57.5674			0.558907			0.279454	+	0.960159i	$0.409847\pi$
$104$	39.3799	−	45.3819i	0.378653	−	0.436365i
$105$		−	72.6290i		−	0.691705i
$106$	53.5492	+	51.0831i	0.505181	+	0.481916i
$107$	17.4928	−	17.4928i	0.163485	−	0.163485i	−0.620624	−	0.784108i	$-0.713121\pi$
$107$	17.4928	−	17.4928i	0.163485	−	0.163485i	0.784108	+	0.620624i	$0.213121\pi$
$108$	−43.9275	+	48.2762i	−0.406736	+	0.447001i
$109$	−136.211	+	136.211i	−1.24964	+	1.24964i	−0.293767	+	0.955877i	$0.594909\pi$
$109$	−136.211	+	136.211i	−1.24964	+	1.24964i	−0.955877	+	0.293767i	$0.905091\pi$
$110$	0.722213	−	0.0170216i	0.00656557	−	0.000154742i
$111$			150.939i			1.35981i
$112$	−42.1441	+	3.98420i	−0.376287	+	0.0355732i
$113$	198.803			1.75932			0.879660	−	0.475603i	$-0.157770\pi$
$113$	198.803			1.75932			0.879660	+	0.475603i	$0.157770\pi$
$114$	0.260995	+	11.0738i	0.00228943	+	0.0971387i
$115$	45.2877	+	45.2877i	0.393806	+	0.393806i
$116$	135.841	−	149.289i	1.17104	−	1.28697i
$117$	24.2732	+	24.2732i	0.207463	+	0.207463i
$118$	55.5110	−	58.1908i	0.470432	−	0.493142i
$119$	−72.9431			−0.612968
$120$	15.5119	+	219.061i	0.129266	+	1.82551i
$121$			120.998i			0.999981i
$122$	−77.9623	+	81.7260i	−0.639035	+	0.669885i
$123$	124.631	−	124.631i	1.01326	−	1.01326i
$124$	9.37751	+	198.829i	0.0756251	+	1.60346i
$125$	29.1386	−	29.1386i	0.233108	−	0.233108i
$126$	−0.569842	−	24.1779i	−0.00452255	−	0.191888i
$127$			115.874i			0.912397i	0.889878	+	0.456198i	$0.150789\pi$
$127$			115.874i			0.912397i	−0.889878	+	0.456198i	$0.849211\pi$
$128$	126.263	−	21.0180i	0.986427	−	0.164203i
$129$	44.9557			0.348494
$130$	−111.906	+	2.63748i	−0.860817	+	0.0202883i
$131$	116.621	+	116.621i	0.890234	+	0.890234i	0.994545	−	0.104311i	$-0.0332637\pi$
$131$	116.621	+	116.621i	0.890234	+	0.890234i	−0.104311	+	0.994545i	$0.533264\pi$
$132$	0.713456	−	0.0336491i	0.00540497	−	0.000254918i
$133$	2.81271	+	2.81271i	0.0211482	+	0.0211482i
$134$	121.479	+	115.885i	0.906560	+	0.864812i
$135$	121.596			0.900711
$136$	220.008	−	15.5790i	1.61771	−	0.114552i
$137$			79.6980i			0.581737i	0.956763	+	0.290869i	$0.0939443\pi$
$137$			79.6980i			0.581737i	−0.956763	+	0.290869i	$0.906056\pi$
$138$	45.8185	+	43.7085i	0.332018	+	0.316728i
$139$	−122.108	+	122.108i	−0.878472	+	0.878472i	−0.993377	−	0.114905i	$-0.963344\pi$
$139$	−122.108	+	122.108i	−0.878472	+	0.878472i	0.114905	+	0.993377i	$0.463344\pi$
$140$	58.3297	+	53.0754i	0.416641	+	0.379110i
$141$	−207.253	+	207.253i	−1.46988	+	1.46988i
$142$	−152.470	+	3.59352i	−1.07373	+	0.0253065i
$143$			0.364061i			0.00254588i
$144$	6.88259	+	72.8028i	0.0477958	+	0.505575i
$145$	−376.022			−2.59326
$146$	−4.85507	−	205.997i	−0.0332539	−	1.41094i
$147$	−18.2339	−	18.2339i	−0.124040	−	0.124040i
$148$	−121.222	−	110.303i	−0.819068	−	0.745288i
$149$	32.1547	+	32.1547i	0.215803	+	0.215803i	0.806727	−	0.590924i	$-0.201237\pi$
$149$	32.1547	+	32.1547i	0.215803	+	0.215803i	−0.590924	+	0.806727i	$0.701237\pi$
$150$	155.260	−	162.755i	1.03507	−	1.08503i
$151$	−115.195			−0.762878			−0.381439	−	0.924394i	$-0.624571\pi$
$151$	−115.195			−0.762878			−0.381439	+	0.924394i	$0.624571\pi$
$152$	−9.08431	−	7.88285i	−0.0597652	−	0.0518608i
$153$			126.007i			0.823577i
$154$	0.177042	−	0.185589i	0.00114963	−	0.00120512i
$155$	262.211	−	262.211i	1.69169	−	1.69169i
$156$	−110.549	+	5.21390i	−0.708650	+	0.0334225i
$157$	16.5196	−	16.5196i	0.105220	−	0.105220i	−0.652537	−	0.757757i	$-0.726295\pi$
$157$	16.5196	−	16.5196i	0.105220	−	0.105220i	0.757757	+	0.652537i	$0.226295\pi$
$158$	−2.12953	−	90.3541i	−0.0134780	−	0.571862i
$159$		−	136.313i		−	0.857317i
$160$	−187.268	−	147.626i	−1.17042	−	0.922664i
$161$	22.7395			0.141239
$162$	202.434	−	4.77110i	1.24959	−	0.0294512i
$163$	−95.7869	−	95.7869i	−0.587650	−	0.587650i	0.349345	−	0.936994i	$-0.386404\pi$
$163$	−95.7869	−	95.7869i	−0.587650	−	0.587650i	−0.936994	+	0.349345i	$0.886404\pi$
$164$	9.01633	+	191.171i	0.0549776	+	1.16568i
$165$	−0.940889	−	0.940889i	−0.00570236	−	0.00570236i
$166$	113.597	+	108.366i	0.684322	+	0.652807i
$167$	290.923			1.74205			0.871027	−	0.491235i	$-0.163455\pi$
$167$	290.923			1.74205			0.871027	+	0.491235i	$0.163455\pi$
$168$	58.8909	+	51.1022i	0.350541	+	0.304180i
$169$			112.589i			0.666208i
$170$	−297.311	−	283.619i	−1.74889	−	1.66835i
$171$	4.85887	−	4.85887i	0.0284145	−	0.0284145i
$172$	−32.8525	+	36.1048i	−0.191003	+	0.209911i
$173$	−84.4773	+	84.4773i	−0.488308	+	0.488308i	−0.907772	−	0.419464i	$-0.862218\pi$
$173$	−84.4773	+	84.4773i	−0.488308	+	0.488308i	0.419464	+	0.907772i	$0.362218\pi$
$174$	−371.669	+	8.75976i	−2.13603	+	0.0503435i
$175$		−	80.7746i		−	0.461569i
$176$	−0.494351	+	0.597580i	−0.00280881	+	0.00339534i
$177$	−148.129			−0.836887
$178$	2.40696	+	102.125i	0.0135222	+	0.573737i
$179$	−83.2957	−	83.2957i	−0.465339	−	0.465339i	0.435062	−	0.900401i	$-0.356727\pi$
$179$	−83.2957	−	83.2957i	−0.465339	−	0.465339i	−0.900401	+	0.435062i	$0.856727\pi$
$180$	91.6864	−	100.763i	0.509369	−	0.559794i
$181$	66.8607	+	66.8607i	0.369396	+	0.369396i	0.867257	−	0.497861i	$-0.165881\pi$
$181$	66.8607	+	66.8607i	0.369396	+	0.369396i	−0.497861	+	0.867257i	$0.665881\pi$
$182$	−27.4326	+	28.7569i	−0.150728	+	0.158005i
$183$	208.040			1.13683
$184$	−68.5861	+	4.85665i	−0.372750	+	0.0263948i
$185$			305.329i			1.65043i
$186$	253.068	−	265.284i	1.36058	−	1.42626i
$187$	−0.944959	+	0.944959i	−0.00505325	+	0.00505325i
$188$	−14.9935	−	317.904i	−0.0797525	−	1.69098i
$189$	30.5274	−	30.5274i	0.161521	−	0.161521i
$190$	0.527957	+	22.4008i	0.00277872	+	0.117899i
$191$			78.8368i			0.412758i	0.978472	+	0.206379i	$0.0661680\pi$
$191$			78.8368i			0.412758i	−0.978472	+	0.206379i	$0.933832\pi$
$192$	−188.539	−	141.555i	−0.981973	−	0.737264i
$193$	99.3044			0.514531			0.257265	−	0.966341i	$-0.417179\pi$
$193$	99.3044			0.514531			0.257265	+	0.966341i	$0.417179\pi$
$194$	−55.1418	+	1.29962i	−0.284236	+	0.00669907i
$195$	145.790	+	145.790i	0.747640	+	0.747640i
$196$	27.9689	−	1.31911i	0.142699	−	0.00673017i
$197$	−108.838	−	108.838i	−0.552478	−	0.552478i	0.374678	−	0.927155i	$-0.377753\pi$
$197$	−108.838	−	108.838i	−0.552478	−	0.552478i	−0.927155	+	0.374678i	$0.877753\pi$
$198$	−0.320600	−	0.305836i	−0.00161919	−	0.00154463i
$199$	183.004			0.919618			0.459809	−	0.888018i	$-0.347918\pi$
$199$	183.004			0.919618			0.459809	+	0.888018i	$0.347918\pi$
$200$	17.2516	+	243.629i	0.0862582	+	1.21815i
$201$		−	309.234i		−	1.53848i
$202$	−129.245	−	123.293i	−0.639828	−	0.610363i
$203$	−94.4026	+	94.4026i	−0.465037	+	0.465037i
$204$	−300.476	−	273.410i	−1.47292	−	1.34024i
$205$	252.112	−	252.112i	1.22982	−	1.22982i
$206$	115.103	−	2.71283i	0.558752	−	0.0131691i
$207$		−	39.2819i		−	0.189768i
$208$	76.5993	−	92.5944i	0.368266	−	0.445166i
$209$	0.0728757			0.000348687
$210$	−3.42259	−	145.218i	−0.0162980	−	0.691513i
$211$	−67.3257	−	67.3257i	−0.319079	−	0.319079i	0.529334	−	0.848413i	$-0.322442\pi$
$211$	−67.3257	−	67.3257i	−0.319079	−	0.319079i	−0.848413	+	0.529334i	$0.822442\pi$
$212$	109.476	+	99.6144i	0.516396	+	0.469879i
$213$	198.636	+	198.636i	0.932561	+	0.932561i
$214$	34.1516	−	35.8003i	0.159587	−	0.167291i
$215$	90.9391			0.422973
$216$	−85.5556	+	98.5955i	−0.396091	+	0.456461i
$217$		−	131.659i		−	0.606726i
$218$	−265.928	+	278.766i	−1.21985	+	1.27874i
$219$	−268.370	+	268.370i	−1.22543	+	1.22543i
$220$	1.44322	−	0.0680676i	0.00656010	−	0.000309398i
$221$	146.420	−	146.420i	0.662536	−	0.662536i
$222$	7.11291	+	301.795i	0.0320401	+	1.35944i
$223$		−	261.480i		−	1.17256i	−0.810110	−	0.586278i	$-0.800593\pi$
$223$		−	261.480i		−	1.17256i	0.810110	−	0.586278i	$-0.199407\pi$
$224$	−84.0771	+	9.95219i	−0.375344	+	0.0444294i
$225$	−139.536			−0.620160
$226$	397.496	−	9.36846i	1.75883	−	0.0414534i
$227$	−232.278	−	232.278i	−1.02325	−	1.02325i	−0.999723	−	0.0235289i	$-0.992510\pi$
$227$	−232.278	−	232.278i	−1.02325	−	1.02325i	−0.0235289	−	0.999723i	$-0.507490\pi$
$228$	1.04369	+	22.1292i	0.00457759	+	0.0970578i
$229$	4.69312	+	4.69312i	0.0204940	+	0.0204940i	0.717280	−	0.696786i	$-0.245387\pi$
$229$	4.69312	+	4.69312i	0.0204940	+	0.0204940i	−0.696786	+	0.717280i	$0.745387\pi$
$230$	92.6845	+	88.4162i	0.402976	+	0.384418i
$231$	−0.472431			−0.00204516
$232$	264.571	−	304.896i	1.14039	−	1.31421i
$233$		−	262.715i		−	1.12753i	−0.825934	−	0.563766i	$-0.809352\pi$
$233$		−	262.715i		−	1.12753i	0.825934	−	0.563766i	$-0.190648\pi$
$234$	49.6767	+	47.3890i	0.212294	+	0.202517i
$235$	−419.244	+	419.244i	−1.78402	+	1.78402i
$236$	108.249	−	118.965i	0.458682	−	0.504090i
$237$	−117.712	+	117.712i	−0.496675	+	0.496675i
$238$	−145.846	+	3.43739i	−0.612797	+	0.0144428i
$239$		−	451.256i		−	1.88810i	−0.329801	−	0.944051i	$-0.606982\pi$
$239$		−	451.256i		−	1.88810i	0.329801	−	0.944051i	$-0.393018\pi$
$240$	41.3383	+	437.269i	0.172243	+	1.82195i
$241$	−186.818			−0.775180			−0.387590	−	0.921832i	$-0.626692\pi$
$241$	−186.818			−0.775180			−0.387590	+	0.921832i	$0.626692\pi$
$242$	5.70193	+	241.928i	0.0235617	+	0.999703i
$243$	−159.883	−	159.883i	−0.657957	−	0.657957i
$244$	−152.030	+	167.080i	−0.623074	+	0.684756i
$245$	−36.8847	−	36.8847i	−0.150550	−	0.150550i
$246$	243.321	−	255.067i	0.989108	−	1.03686i
$247$	−11.2920			−0.0457167
$248$	28.1195	+	397.106i	0.113385	+	1.60124i
$249$		−	289.171i		−	1.16133i
$250$	56.8878	−	59.6341i	0.227551	−	0.238536i
$251$	−91.8783	+	91.8783i	−0.366049	+	0.366049i	−0.866034	−	0.499985i	$-0.833339\pi$
$251$	−91.8783	+	91.8783i	−0.366049	+	0.366049i	0.499985	+	0.866034i	$0.333339\pi$
$252$	−2.27873	−	48.3155i	−0.00904260	−	0.191728i
$253$	0.294584	−	0.294584i	0.00116436	−	0.00116436i
$254$	5.46050	+	231.684i	0.0214980	+	0.912143i
$255$			756.826i			2.96795i
$256$	251.465	−	47.9744i	0.982284	−	0.187400i
$257$	−151.189			−0.588284			−0.294142	−	0.955762i	$-0.595034\pi$
$257$	−151.189			−0.588284			−0.294142	+	0.955762i	$0.595034\pi$
$258$	89.8864	−	2.11851i	0.348397	−	0.00821126i
$259$	76.6547	+	76.6547i	0.295964	+	0.295964i
$260$	−223.626	+	10.5470i	−0.860100	+	0.0405654i
$261$	163.078	+	163.078i	0.624820	+	0.624820i
$262$	238.672	+	227.681i	0.910963	+	0.869011i
$263$	−144.762			−0.550427			−0.275214	−	0.961383i	$-0.588749\pi$
$263$	−144.762			−0.550427			−0.275214	+	0.961383i	$0.588749\pi$
$264$	1.42493	−	0.100901i	0.00539746	−	0.000382200i
$265$		−	275.743i		−	1.04054i
$266$	5.75640	+	5.49130i	0.0216406	+	0.0206440i
$267$	133.047	−	133.047i	0.498304	−	0.498304i
$268$	248.352	+	225.981i	0.926686	+	0.843211i
$269$	107.045	−	107.045i	0.397936	−	0.397936i	−0.479569	−	0.877504i	$-0.659207\pi$
$269$	107.045	−	107.045i	0.397936	−	0.397936i	0.877504	+	0.479569i	$0.159207\pi$
$270$	243.124	−	5.73013i	0.900461	−	0.0212227i
$271$		−	85.1410i		−	0.314173i	−0.987585	−	0.157087i	$-0.949790\pi$
$271$		−	85.1410i		−	0.314173i	0.987585	−	0.157087i	$-0.0502102\pi$
$272$	439.161	−	41.5171i	1.61456	−	0.152636i
$273$	73.2028			0.268142
$274$	3.75571	+	159.352i	0.0137070	+	0.581576i
$275$	−1.04641	−	1.04641i	−0.00380514	−	0.00380514i
$276$	93.6713	+	85.2335i	0.339389	+	0.308817i
$277$	−116.995	−	116.995i	−0.422365	−	0.422365i	0.463652	−	0.886017i	$-0.346539\pi$
$277$	−116.995	−	116.995i	−0.422365	−	0.422365i	−0.886017	+	0.463652i	$0.846539\pi$
$278$	−238.393	+	249.902i	−0.857529	+	0.898927i
$279$	−227.438			−0.815191
$280$	119.128	+	103.373i	0.425458	+	0.369188i
$281$		−	40.2996i		−	0.143415i	−0.997426	−	0.0717075i	$-0.977155\pi$
$281$		−	40.2996i		−	0.143415i	0.997426	−	0.0717075i	$-0.0228448\pi$
$282$	−404.624	+	424.157i	−1.43484	+	1.50410i
$283$	150.943	−	150.943i	0.533366	−	0.533366i	−0.388207	−	0.921572i	$-0.626905\pi$
$283$	150.943	−	150.943i	0.533366	−	0.533366i	0.921572	+	0.388207i	$0.126905\pi$
$284$	−304.686	+	14.3701i	−1.07284	+	0.0505989i
$285$	29.1834	−	29.1834i	0.102398	−	0.102398i
$286$	0.0171561	+	0.727919i	5.99864e−5	+	0.00254517i
$287$		−	126.589i		−	0.441075i
$288$	17.1921	+	145.241i	0.0596950	+	0.504309i
$289$	471.100			1.63010
$290$	−751.836	+	17.7198i	−2.59254	+	0.0611027i
$291$	71.8379	+	71.8379i	0.246866	+	0.246866i
$292$	−19.4149	−	411.650i	−0.0664894	−	1.40976i
$293$	237.816	+	237.816i	0.811659	+	0.811659i	0.984883	−	0.173224i	$-0.0554184\pi$
$293$	237.816	+	237.816i	0.811659	+	0.811659i	−0.173224	+	0.984883i	$0.555418\pi$
$294$	−37.3170	−	35.5985i	−0.126929	−	0.121083i
$295$	−299.644			−1.01574
$296$	−247.575	−	214.831i	−0.836401	−	0.725782i
$297$		−	0.790948i		−	0.00266312i
$298$	65.8067	+	62.7762i	0.220828	+	0.210658i
$299$	−45.6455	+	45.6455i	−0.152661	+	0.152661i
$300$	302.764	−	332.736i	1.00921	−	1.10912i
$301$	22.8308	−	22.8308i	0.0758499	−	0.0758499i
$302$	−230.325	+	5.42846i	−0.762666	+	0.0179750i
$303$			329.003i			1.08582i
$304$	−18.5351	−	15.3332i	−0.0609706	−	0.0504383i
$305$	420.835			1.37979
$306$	5.93801	+	251.945i	0.0194052	+	0.823348i
$307$	20.6127	+	20.6127i	0.0671424	+	0.0671424i	0.739881	−	0.672738i	$-0.234882\pi$
$307$	20.6127	+	20.6127i	0.0671424	+	0.0671424i	−0.672738	+	0.739881i	$0.734882\pi$
$308$	0.345241	−	0.379418i	0.00112091	−	0.00123188i
$309$	−149.954	−	149.954i	−0.485289	−	0.485289i
$310$	511.921	−	536.634i	1.65136	−	1.73108i
$311$	153.723			0.494286			0.247143	−	0.968979i	$-0.420508\pi$
$311$	153.723			0.494286			0.247143	+	0.968979i	$0.420508\pi$
$312$	−220.792	+	15.6345i	−0.707665	+	0.0501105i
$313$			119.591i			0.382081i	0.981582	+	0.191040i	$0.0611862\pi$
$313$			119.591i			0.382081i	−0.981582	+	0.191040i	$0.938814\pi$
$314$	32.2515	−	33.8084i	0.102712	−	0.107670i
$315$	−63.7174	+	63.7174i	−0.202277	+	0.202277i
$316$	−8.51575	−	180.558i	−0.0269486	−	0.571385i
$317$	−250.641	+	250.641i	−0.790665	+	0.790665i	−0.981602	−	0.190937i	$-0.938847\pi$
$317$	−250.641	+	250.641i	−0.790665	+	0.790665i	0.190937	+	0.981602i	$0.438847\pi$
$318$	−6.42368	−	272.551i	−0.0202002	−	0.857079i
$319$			2.44592i			0.00766746i
$320$	−381.388	−	286.346i	−1.19184	−	0.894830i
$321$	−91.1324			−0.283902
$322$	45.4664	−	1.07158i	0.141200	−	0.00332790i
$323$	−29.3097	−	29.3097i	−0.0907420	−	0.0907420i
$324$	404.530	−	19.0791i	1.24855	−	0.0588861i
$325$	162.141	+	162.141i	0.498895	+	0.498895i
$326$	−196.034	−	187.007i	−0.601333	−	0.573640i
$327$	709.619			2.17009
$328$	27.0365	+	381.812i	0.0824283	+	1.16406i
$329$			210.507i			0.639840i
$330$	−1.92559	−	1.83692i	−0.00583513	−	0.00556641i
$331$	−67.5747	+	67.5747i	−0.204153	+	0.204153i	−0.801777	−	0.597624i	$-0.796112\pi$
$331$	−67.5747	+	67.5747i	−0.204153	+	0.204153i	0.597624	+	0.801777i	$0.296112\pi$
$332$	232.238	+	211.319i	0.699513	+	0.636502i
$333$	132.419	−	132.419i	0.397654	−	0.397654i
$334$	581.684	−	13.7095i	1.74157	−	0.0410465i
$335$		−	625.538i		−	1.86728i
$336$	120.157	+	99.4008i	0.357611	+	0.295836i
$337$	149.179			0.442668			0.221334	−	0.975198i	$-0.428959\pi$
$337$	149.179			0.442668			0.221334	+	0.975198i	$0.428959\pi$
$338$	5.30568	+	225.116i	0.0156973	+	0.666023i
$339$	−517.852	−	517.852i	−1.52759	−	1.52759i
$340$	−607.821	−	553.070i	−1.78771	−	1.62668i
$341$	−1.70561	−	1.70561i	−0.00500180	−	0.00500180i
$342$	9.48608	−	9.94402i	0.0277371	−	0.0290761i
$343$	−18.5203			−0.0539949
$344$	−63.9853	+	73.7376i	−0.186004	+	0.214354i
$345$		−	235.935i		−	0.683870i
$346$	−164.927	+	172.889i	−0.476667	+	0.499678i
$347$	−151.702	+	151.702i	−0.437182	+	0.437182i	−0.891062	−	0.453881i	$-0.850039\pi$
$347$	−151.702	+	151.702i	−0.437182	+	0.437182i	0.453881	+	0.891062i	$0.350039\pi$
$348$	−742.719	+	35.0293i	−2.13425	+	0.100659i
$349$	−232.328	+	232.328i	−0.665698	+	0.665698i	−0.956717	−	0.291020i	$-0.906006\pi$
$349$	−232.328	+	232.328i	−0.665698	+	0.665698i	0.291020	+	0.956717i	$0.406006\pi$
$350$	−3.80645	−	161.504i	−0.0108756	−	0.461441i
$351$			122.557i			0.349164i
$352$	−0.960268	+	1.21812i	−0.00272803	+	0.00346058i
$353$	205.431			0.581956			0.290978	−	0.956730i	$-0.406019\pi$
$353$	205.431			0.581956			0.290978	+	0.956730i	$0.406019\pi$
$354$	−296.176	+	6.98047i	−0.836654	+	0.0197189i
$355$	401.812	+	401.812i	1.13187	+	1.13187i
$356$	9.62516	+	204.080i	0.0270370	+	0.573259i
$357$	190.006	+	190.006i	0.532229	+	0.532229i
$358$	−170.470	−	162.620i	−0.476174	−	0.454245i
$359$	−607.058			−1.69097			−0.845485	−	0.534000i	$-0.820688\pi$
$359$	−607.058			−1.69097			−0.845485	+	0.534000i	$0.820688\pi$
$360$	178.573	−	205.791i	0.496037	−	0.571641i
$361$		−	358.740i		−	0.993739i
$362$	136.835	+	130.533i	0.377997	+	0.360590i
$363$	315.180	−	315.180i	0.868266	−	0.868266i
$364$	−53.4948	+	58.7905i	−0.146964	+	0.161512i
$365$	−542.875	+	542.875i	−1.48733	+	1.48733i
$366$	415.964	−	9.80372i	1.13651	−	0.0267861i
$367$			103.467i			0.281927i	0.990015	+	0.140964i	$0.0450201\pi$
$367$			103.467i			0.281927i	−0.990015	+	0.140964i	$0.954980\pi$
$368$	−136.905	+	12.9427i	−0.372025	+	0.0351703i
$369$	−218.678			−0.592624
$370$	14.3884	+	610.489i	0.0388876	+	1.64997i
$371$	−69.2270	−	69.2270i	−0.186596	−	0.186596i
$372$	493.493	−	542.347i	1.32659	−	1.45792i
$373$	247.603	+	247.603i	0.663816	+	0.663816i	0.956277	−	0.292461i	$-0.0944743\pi$
$373$	247.603	+	247.603i	0.663816	+	0.663816i	−0.292461	+	0.956277i	$0.594474\pi$
$374$	−1.84486	+	1.93392i	−0.00493279	+	0.00517092i
$375$	−151.803			−0.404808
$376$	−44.9596	−	634.924i	−0.119573	−	1.68863i
$377$		−	378.993i		−	1.00529i
$378$	59.5992	−	62.4764i	0.157670	−	0.165281i
$379$	−262.881	+	262.881i	−0.693618	+	0.693618i	−0.963026	−	0.269408i	$-0.913172\pi$
$379$	−262.881	+	262.881i	−0.693618	+	0.693618i	0.269408	+	0.963026i	$0.413172\pi$
$380$	2.11124	+	44.7643i	0.00555590	+	0.117801i
$381$	301.835	−	301.835i	0.792218	−	0.792218i
$382$	3.71513	+	157.630i	0.00972547	+	0.412644i
$383$			468.920i			1.22434i	0.790728	+	0.612168i	$0.209702\pi$
$383$			468.920i			1.22434i	−0.790728	+	0.612168i	$0.790298\pi$
$384$	−383.644	−	274.146i	−0.999072	−	0.713922i
$385$	−0.955663			−0.00248224
$386$	198.554	−	4.67965i	0.514388	−	0.0121235i
$387$	−39.4396	−	39.4396i	−0.101911	−	0.101911i
$388$	−110.192	+	5.19704i	−0.283999	+	0.0133944i
$389$	278.401	+	278.401i	0.715685	+	0.715685i	0.967718	−	0.252034i	$-0.0810993\pi$
$389$	278.401	+	278.401i	0.715685	+	0.715685i	−0.252034	+	0.967718i	$0.581099\pi$
$390$	298.369	+	284.628i	0.765049	+	0.729817i
$391$	−236.956			−0.606025
$392$	55.8601	−	3.95551i	0.142500	−	0.0100906i
$393$		−	607.558i		−	1.54595i
$394$	−222.745	−	212.487i	−0.565342	−	0.539307i
$395$	−238.115	+	238.115i	−0.602823	+	0.602823i
$396$	−0.655435	−	0.596394i	−0.00165514	−	0.00150605i
$397$	29.5239	−	29.5239i	0.0743676	−	0.0743676i	−0.668945	−	0.743312i	$-0.733254\pi$
$397$	29.5239	−	29.5239i	0.0743676	−	0.0743676i	0.743312	+	0.668945i	$0.233254\pi$
$398$	365.906	−	8.62394i	0.919363	−	0.0216682i
$399$		−	14.6533i		−	0.0367252i
$400$	45.9746	+	486.311i	0.114936	+	1.21578i
$401$	−569.183			−1.41941			−0.709705	−	0.704499i	$-0.751172\pi$
$401$	−569.183			−1.41941			−0.709705	+	0.704499i	$0.751172\pi$
$402$	−14.5724	−	618.297i	−0.0362499	−	1.53805i
$403$	264.283	+	264.283i	0.655789	+	0.655789i
$404$	−264.229	−	240.427i	−0.654032	−	0.595117i
$405$	−533.485	−	533.485i	−1.31725	−	1.31725i
$406$	−184.304	+	193.201i	−0.453951	+	0.475866i
$407$	1.98608			0.00487981
$408$	−613.669	−	532.507i	−1.50409	−	1.30517i
$409$			442.593i			1.08214i	0.840979	+	0.541068i	$0.181980\pi$
$409$			442.593i			1.08214i	−0.840979	+	0.541068i	$0.818020\pi$
$410$	492.204	−	515.965i	1.20050	−	1.25845i
$411$	207.601	−	207.601i	0.505112	−	0.505112i
$412$	230.014	−	10.8483i	0.558287	−	0.0263308i
$413$	−75.2275	+	75.2275i	−0.182149	+	0.182149i
$414$	−1.85113	−	78.5419i	−0.00447133	−	0.189715i
$415$		−	584.953i		−	1.40952i
$416$	148.793	−	188.747i	0.357675	−	0.453719i
$417$	636.143			1.52552
$418$	0.145711	−	0.00343422i	0.000348591	−	8.21583e-6i
$419$	−154.181	−	154.181i	−0.367974	−	0.367974i	0.498764	−	0.866738i	$-0.333787\pi$
$419$	−154.181	−	154.181i	−0.367974	−	0.367974i	−0.866738	+	0.498764i	$0.833787\pi$
$420$	−13.6866	−	290.193i	−0.0325870	−	0.690937i
$421$	174.166	+	174.166i	0.413696	+	0.413696i	0.883024	−	0.469328i	$-0.155504\pi$
$421$	174.166	+	174.166i	0.413696	+	0.413696i	−0.469328	+	0.883024i	$0.655504\pi$
$422$	−137.787	−	131.441i	−0.326509	−	0.311473i
$423$	363.646			0.859682
$424$	223.585	+	194.015i	0.527324	+	0.457581i
$425$			841.708i			1.98049i
$426$	406.521	+	387.800i	0.954276	+	0.910329i
$427$	105.653	−	105.653i	0.247431	−	0.247431i
$428$	66.5973	−	73.1901i	0.155601	−	0.171005i
$429$	0.948323	−	0.948323i	0.00221054	−	0.00221054i
$430$	181.828	−	4.28544i	0.422855	−	0.00996615i
$431$			108.471i			0.251673i	0.992051	+	0.125837i	$0.0401615\pi$
$431$			108.471i			0.251673i	−0.992051	+	0.125837i	$0.959838\pi$
$432$	−166.417	+	201.168i	−0.385226	+	0.465667i
$433$	−457.359			−1.05626			−0.528128	−	0.849165i	$-0.677106\pi$
$433$	−457.359			−1.05626			−0.528128	+	0.849165i	$0.677106\pi$
$434$	−6.20436	−	263.246i	−0.0142958	−	0.606557i
$435$	979.481	+	979.481i	2.25168	+	2.25168i
$436$	−518.571	+	569.908i	−1.18938	+	1.30713i
$437$	9.13708	+	9.13708i	0.0209086	+	0.0209086i
$438$	−523.943	+	549.237i	−1.19622	+	1.25397i
$439$	287.953			0.655930			0.327965	−	0.944690i	$-0.393637\pi$
$439$	287.953			0.655930			0.327965	+	0.944690i	$0.393637\pi$
$440$	2.88244	−	0.204108i	0.00655099	−	0.000463882i
$441$			31.9932i			0.0725470i
$442$	285.860	−	299.660i	0.646741	−	0.677963i
$443$	175.112	−	175.112i	0.395286	−	0.395286i	−0.481281	−	0.876567i	$-0.659828\pi$
$443$	175.112	−	175.112i	0.395286	−	0.395286i	0.876567	+	0.481281i	$0.159828\pi$
$444$	28.4437	+	603.087i	0.0640624	+	1.35830i
$445$	269.136	−	269.136i	0.604800	−	0.604800i
$446$	−12.3221	−	522.815i	−0.0276280	−	1.17223i
$447$		−	167.516i		−	0.374756i
$448$	−167.638	+	23.8609i	−0.374193	+	0.0532610i
$449$	628.471			1.39971			0.699856	−	0.714284i	$-0.253247\pi$
$449$	628.471			1.39971			0.699856	+	0.714284i	$0.253247\pi$
$450$	−278.994	+	6.57553i	−0.619988	+	0.0146123i
$451$	−1.63992	−	1.63992i	−0.00363619	−	0.00363619i
$452$	794.330	−	37.4635i	1.75737	−	0.0828837i
$453$	300.064	+	300.064i	0.662394	+	0.662394i
$454$	−475.373	−	453.481i	−1.04708	−	0.998858i
$455$	148.079			0.325449
$456$	3.12962	+	44.1969i	0.00686321	+	0.0969230i
$457$		−	89.4733i		−	0.195784i	−0.995197	−	0.0978920i	$-0.968790\pi$
$457$		−	89.4733i		−	0.195784i	0.995197	−	0.0978920i	$-0.0312100\pi$
$458$	9.60480	+	9.16248i	0.0209712	+	0.0200054i
$459$	−318.109	+	318.109i	−0.693048	+	0.693048i
$460$	189.484	+	172.416i	0.411922	+	0.374816i
$461$	−452.303	+	452.303i	−0.981134	+	0.981134i	−0.999825	−	0.0186911i	$-0.994050\pi$
$461$	−452.303	+	452.303i	−0.981134	+	0.981134i	0.0186911	+	0.999825i	$0.494050\pi$
$462$	−0.944600	+	0.0222630i	−0.00204459	+	4.81883e-5i
$463$		−	306.653i		−	0.662317i	−0.943575	−	0.331159i	$-0.892560\pi$
$463$		−	306.653i		−	0.662317i	0.943575	−	0.331159i	$-0.107440\pi$
$464$	514.628	−	622.090i	1.10911	−	1.34071i
$465$	−1366.04			−2.93772
$466$	−12.3803	−	525.284i	−0.0265671	−	1.12722i
$467$	−630.902	−	630.902i	−1.35097	−	1.35097i	−0.884580	−	0.466389i	$-0.845555\pi$
$467$	−630.902	−	630.902i	−1.35097	−	1.35097i	−0.466389	−	0.884580i	$-0.654445\pi$
$468$	101.559	+	92.4107i	0.217007	+	0.197459i
$469$	−157.045	−	157.045i	−0.334851	−	0.334851i
$470$	−818.498	+	858.011i	−1.74149	+	1.82556i
$471$	−86.0618			−0.182722
$472$	210.832	−	242.965i	0.446677	−	0.514757i
$473$		−	0.591534i		−	0.00125060i
$474$	−229.812	+	240.906i	−0.484835	+	0.508240i
$475$	32.4565	−	32.4565i	0.0683294	−	0.0683294i
$476$	−291.449	+	13.7458i	−0.612287	+	0.0288776i
$477$	−119.588	+	119.588i	−0.250708	+	0.250708i
$478$	−21.2651	−	902.262i	−0.0444877	−	1.88758i
$479$		−	235.666i		−	0.491996i	−0.969270	−	0.245998i	$-0.920884\pi$
$479$		−	235.666i		−	0.491996i	0.969270	−	0.245998i	$-0.0791157\pi$
$480$	103.260	+	872.347i	0.215124	+	1.81739i
$481$	−307.742			−0.639795
$482$	−373.533	+	8.80369i	−0.774965	+	0.0182649i
$483$	−59.2329	−	59.2329i	−0.122636	−	0.122636i
$484$	22.8014	+	483.453i	0.0471103	+	0.998870i
$485$	145.318	+	145.318i	0.299625	+	0.299625i
$486$	−327.213	−	312.144i	−0.673277	−	0.642271i
$487$	20.2420			0.0415646			0.0207823	−	0.999784i	$-0.493384\pi$
$487$	20.2420			0.0415646			0.0207823	+	0.999784i	$0.493384\pi$
$488$	−296.102	+	341.232i	−0.606767	+	0.699247i
$489$			499.021i			1.02049i
$490$	−75.4871	−	72.0108i	−0.154055	−	0.146961i
$491$	−375.295	+	375.295i	−0.764349	+	0.764349i	−0.977105	−	0.212756i	$-0.931756\pi$
$491$	−375.295	+	375.295i	−0.764349	+	0.764349i	0.212756	+	0.977105i	$0.431756\pi$
$492$	474.486	−	521.459i	0.964403	−	1.05988i
$493$	983.717	−	983.717i	1.99537	−	1.99537i
$494$	−22.5778	+	0.532129i	−0.0457040	+	0.00107718i
$495$			1.65088i			0.00333512i
$496$	74.9368	+	792.667i	0.151082	+	1.59812i
$497$	201.755			0.405945
$498$	−13.6270	−	578.181i	−0.0273634	−	1.16101i
$499$	318.122	+	318.122i	0.637518	+	0.637518i	0.949943	−	0.312424i	$-0.101141\pi$
$499$	318.122	+	318.122i	0.637518	+	0.637518i	−0.312424	+	0.949943i	$0.601141\pi$
$500$	110.934	−	121.916i	0.221868	−	0.243832i
$501$	−757.810	−	757.810i	−1.51259	−	1.51259i
$502$	−179.376	+	188.035i	−0.357323	+	0.374572i
$503$	645.420			1.28314			0.641571	−	0.767064i	$-0.278283\pi$
$503$	645.420			1.28314			0.641571	+	0.767064i	$0.278283\pi$
$504$	−6.83304	−	96.4969i	−0.0135576	−	0.191462i
$505$			665.529i			1.31788i
$506$	0.575123	−	0.602887i	0.00113661	−	0.00119148i
$507$	293.278	−	293.278i	0.578457	−	0.578457i
$508$	21.8359	+	462.983i	0.0429841	+	0.911384i
$509$	−27.0881	+	27.0881i	−0.0532183	+	0.0532183i	−0.733215	−	0.679997i	$-0.761981\pi$
$509$	−27.0881	+	27.0881i	−0.0532183	+	0.0532183i	0.679997	+	0.733215i	$0.261981\pi$
$510$	35.6649	+	1513.23i	0.0699312	+	2.96712i
$511$			272.584i			0.533432i
$512$	500.529	−	107.772i	0.977595	−	0.210493i
$513$	24.5327			0.0478221
$514$	−302.294	+	7.12468i	−0.588121	+	0.0138612i
$515$	−303.337	−	303.337i	−0.589004	−	0.589004i
$516$	179.623	−	8.47167i	0.348107	−	0.0164180i
$517$	2.72706	+	2.72706i	0.00527479	+	0.00527479i
$518$	156.879	+	149.655i	0.302855	+	0.288908i
$519$	440.101			0.847979
$520$	−446.631	+	31.6264i	−0.858906	+	0.0608200i
$521$		−	414.463i		−	0.795513i	−0.917491	−	0.397757i	$-0.869789\pi$
$521$		−	414.463i		−	0.795513i	0.917491	−	0.397757i	$-0.130211\pi$
$522$	333.750	+	318.380i	0.639368	+	0.609924i
$523$	121.736	−	121.736i	0.232764	−	0.232764i	−0.581082	−	0.813845i	$-0.697370\pi$
$523$	121.736	−	121.736i	0.232764	−	0.232764i	0.813845	+	0.581082i	$0.197370\pi$
$524$	487.941	+	443.988i	0.931186	+	0.847306i
$525$	−210.406	+	210.406i	−0.400772	+	0.400772i
$526$	−289.444	+	6.82182i	−0.550274	+	0.0129692i
$527$			1371.95i			2.60332i
$528$	2.84431	−	0.268894i	0.00538696	−	0.000509270i
$529$	−455.131			−0.860361
$530$	−12.9942	−	551.333i	−0.0245174	−	1.04025i
$531$	129.953	+	129.953i	0.244733	+	0.244733i
$532$	11.7684	+	10.7083i	0.0221210	+	0.0201284i
$533$	254.104	+	254.104i	0.476743	+	0.476743i
$534$	259.751	−	272.290i	0.486425	−	0.509907i
$535$	−184.348			−0.344576
$536$	507.215	+	440.132i	0.946296	+	0.821142i
$537$			433.945i			0.808091i
$538$	208.985	−	219.074i	0.388449	−	0.407201i
$539$	−0.239925	+	0.239925i	−0.000445130	+	0.000445130i
$540$	485.844	−	22.9141i	0.899711	−	0.0424336i
$541$	315.972	−	315.972i	0.584052	−	0.584052i	−0.351962	−	0.936014i	$-0.614485\pi$
$541$	315.972	−	315.972i	0.584052	−	0.584052i	0.936014	+	0.351962i	$0.114485\pi$
$542$	−4.01221	−	170.235i	−0.00740260	−	0.314086i
$543$		−	348.324i		−	0.641480i
$544$	876.121	−	103.706i	1.61052	−	0.190637i
$545$	1435.46			2.63387
$546$	146.365	−	3.44963i	0.268068	−	0.00631801i
$547$	194.242	+	194.242i	0.355104	+	0.355104i	0.862005	−	0.506900i	$-0.169209\pi$
$547$	194.242	+	194.242i	0.355104	+	0.355104i	−0.506900	+	0.862005i	$0.669209\pi$
$548$	15.0187	+	318.438i	0.0274064	+	0.581091i
$549$	−182.513	−	182.513i	−0.332446	−	0.332446i
$550$	−2.14156	−	2.04293i	−0.00389374	−	0.00371442i
$551$	−75.8648			−0.137686
$552$	191.307	+	166.005i	0.346571	+	0.300734i
$553$			119.560i			0.216203i
$554$	−239.439	−	228.412i	−0.432200	−	0.412296i
$555$	795.336	−	795.336i	1.43304	−	1.43304i
$556$	−464.877	+	510.899i	−0.836110	+	0.918882i
$557$	−611.421	+	611.421i	−1.09770	+	1.09770i	−0.103025	+	0.994679i	$0.532852\pi$
$557$	−611.421	+	611.421i	−1.09770	+	1.09770i	−0.994679	+	0.103025i	$0.967148\pi$
$558$	−454.750	+	10.7179i	−0.814964	+	0.0192076i
$559$			91.6576i			0.163967i
$560$	243.061	+	201.074i	0.434038	+	0.359061i
$561$	4.92295			0.00877531
$562$	−1.89909	−	80.5768i	−0.00337916	−	0.143375i
$563$	−587.190	−	587.190i	−1.04297	−	1.04297i	−0.999035	−	0.0439324i	$-0.986011\pi$
$563$	−587.190	−	587.190i	−1.04297	−	1.04297i	−0.0439324	−	0.999035i	$-0.513989\pi$
$564$	−789.035	+	867.146i	−1.39900	+	1.53749i
$565$	−1047.54	−	1047.54i	−1.85406	−	1.85406i
$566$	294.688	−	308.914i	0.520651	−	0.545785i
$567$	−267.869			−0.472432
$568$	−608.525	+	43.0903i	−1.07135	+	0.0758632i
$569$			462.064i			0.812063i	0.913859	+	0.406031i	$0.133088\pi$
$569$			462.064i			0.812063i	−0.913859	+	0.406031i	$0.866912\pi$
$570$	56.9754	−	59.7259i	0.0999568	−	0.104782i
$571$	397.152	−	397.152i	0.695538	−	0.695538i	−0.267907	−	0.963445i	$-0.586332\pi$
$571$	397.152	−	397.152i	0.695538	−	0.695538i	0.963445	+	0.267907i	$0.0863319\pi$
$572$	0.0686054	+	1.45463i	0.000119939	+	0.00254305i
$573$	205.358	−	205.358i	0.358391	−	0.358391i
$574$	−5.96540	−	253.107i	−0.0103927	−	0.440953i
$575$		−	262.396i		−	0.456341i
$576$	41.2191	+	289.591i	0.0715610	+	0.502762i
$577$	−871.434			−1.51028			−0.755142	−	0.655561i	$-0.772432\pi$
$577$	−871.434			−1.51028			−0.755142	+	0.655561i	$0.772432\pi$
$578$	941.939	−	22.2003i	1.62965	−	0.0384088i
$579$	−258.673	−	258.673i	−0.446758	−	0.446758i
$580$	−1502.42	+	70.8595i	−2.59038	+	0.122171i
$581$	−146.856	−	146.856i	−0.252764	−	0.252764i
$582$	147.021	+	140.251i	0.252614	+	0.240980i
$583$	−1.79363			−0.00307656
$584$	−58.2178	−	822.157i	−0.0996880	−	1.40780i
$585$		−	255.803i		−	0.437270i
$586$	486.707	+	464.293i	0.830558	+	0.792309i
$587$	628.244	−	628.244i	1.07026	−	1.07026i	0.0729252	−	0.997337i	$-0.476767\pi$
$587$	628.244	−	628.244i	1.07026	−	1.07026i	0.997337	−	0.0729252i	$-0.0232334\pi$
$588$	−76.2908	−	69.4187i	−0.129746	−	0.118059i
$589$	52.9028	−	52.9028i	0.0898179	−	0.0898179i
$590$	−599.122	+	14.1205i	−1.01546	+	0.0239331i
$591$			567.013i			0.959414i
$592$	−505.136	−	417.877i	−0.853270	−	0.705873i
$593$	−400.187			−0.674852			−0.337426	−	0.941352i	$-0.609556\pi$
$593$	−400.187			−0.674852			−0.337426	+	0.941352i	$0.609556\pi$
$594$	−0.0372729	−	1.58146i	−6.27490e−5	−	0.00266239i
$595$	384.355	+	384.355i	0.645975	+	0.645975i
$596$	134.535	+	122.416i	0.225730	+	0.205397i
$597$	−476.698	−	476.698i	−0.798488	−	0.798488i
$598$	−89.1147	+	93.4167i	−0.149021	+	0.156215i
$599$	−437.482			−0.730355			−0.365177	−	0.930938i	$-0.618992\pi$
$599$	−437.482			−0.730355			−0.365177	+	0.930938i	$0.618992\pi$
$600$	589.680	−	679.555i	0.982799	−	1.13259i
$601$		−	374.850i		−	0.623710i	−0.950130	−	0.311855i	$-0.899050\pi$
$601$		−	374.850i		−	0.623710i	0.950130	−	0.311855i	$-0.100950\pi$
$602$	44.5731	−	46.7248i	0.0740416	−	0.0776160i
$603$	−271.291	+	271.291i	−0.449902	+	0.449902i
$604$	−460.267	+	21.7078i	−0.762031	+	0.0359401i
$605$	637.567	−	637.567i	1.05383	−	1.05383i
$606$	15.5041	+	657.824i	0.0255843	+	1.08552i
$607$			326.106i			0.537242i	0.963246	+	0.268621i	$0.0865679\pi$
$607$			326.106i			0.537242i	−0.963246	+	0.268621i	$0.913432\pi$
$608$	−37.7824	−	29.7845i	−0.0621421	−	0.0489877i
$609$	491.809			0.807568
$610$	841.437	−	19.8316i	1.37940	−	0.0325108i
$611$	−422.556	−	422.556i	−0.691581	−	0.691581i
$612$	23.7454	+	503.470i	0.0387997	+	0.822663i
$613$	−17.5228	−	17.5228i	−0.0285853	−	0.0285853i	0.692670	−	0.721255i	$-0.256434\pi$
$613$	−17.5228	−	17.5228i	−0.0285853	−	0.0285853i	−0.721255	+	0.692670i	$0.756434\pi$
$614$	42.1854	+	40.2426i	0.0687058	+	0.0655418i
$615$	−1313.43			−2.13566
$616$	0.672410	−	0.774895i	0.00109158	−	0.00125795i
$617$			51.8009i			0.0839562i	0.999119	+	0.0419781i	$0.0133660\pi$
$617$			51.8009i			0.0839562i	−0.999119	+	0.0419781i	$0.986634\pi$
$618$	−306.892	−	292.759i	−0.496589	−	0.473720i
$619$	360.793	−	360.793i	0.582864	−	0.582864i	−0.352825	−	0.935689i	$-0.614779\pi$
$619$	360.793	−	360.793i	0.582864	−	0.582864i	0.935689	+	0.352825i	$0.114779\pi$
$620$	998.269	−	1097.09i	1.61011	−	1.76951i
$621$	99.1682	−	99.1682i	0.159691	−	0.159691i
$622$	307.360	−	7.24409i	0.494149	−	0.0116464i
$623$		−	135.136i		−	0.216912i
$624$	−440.724	+	41.6649i	−0.706288	+	0.0667707i
$625$	456.172			0.729875
$626$	5.63566	+	239.116i	0.00900265	+	0.381975i
$627$	−0.189830	−	0.189830i	−0.000302759	−	0.000302759i
$628$	62.8918	−	69.1179i	0.100146	−	0.110060i
$629$	−798.776	−	798.776i	−1.26991	−	1.26991i
$630$	−124.397	+	130.402i	−0.197455	+	0.206987i
$631$	−7.85965			−0.0124559			−0.00622793	−	0.999981i	$-0.501982\pi$
$631$	−7.85965			−0.0124559			−0.00622793	+	0.999981i	$0.501982\pi$
$632$	−25.5354	−	360.614i	−0.0404042	−	0.570592i
$633$			350.747i			0.554102i
$634$	−489.331	+	512.954i	−0.771815	+	0.809075i
$635$	610.571	−	610.571i	0.961529	−	0.961529i
$636$	−25.6876	−	544.648i	−0.0403893	−	0.856365i
$637$	37.1761	−	37.1761i	0.0583613	−	0.0583613i
$638$	0.115262	+	4.89048i	0.000180662	+	0.00766533i
$639$		−	348.526i		−	0.545424i
$640$	−776.058	−	554.560i	−1.21259	−	0.866499i
$641$	−655.356			−1.02240			−0.511198	−	0.859463i	$-0.670798\pi$
$641$	−655.356			−1.02240			−0.511198	+	0.859463i	$0.670798\pi$
$642$	−182.214	+	4.29455i	−0.283823	+	0.00668933i
$643$	115.057	+	115.057i	0.178938	+	0.178938i	0.790893	−	0.611955i	$-0.209617\pi$
$643$	115.057	+	115.057i	0.178938	+	0.178938i	−0.611955	+	0.790893i	$0.709617\pi$
$644$	90.8570	−	4.28514i	0.141082	−	0.00665395i
$645$	−236.883	−	236.883i	−0.367260	−	0.367260i
$646$	−59.9842	−	57.2218i	−0.0928548	−	0.0885787i
$647$	51.9916			0.0803580			0.0401790	−	0.999192i	$-0.487207\pi$
$647$	51.9916			0.0803580			0.0401790	+	0.999192i	$0.487207\pi$
$648$	807.937	−	57.2108i	1.24682	−	0.0882883i
$649$			1.94910i			0.00300324i
$650$	331.832	+	316.551i	0.510511	+	0.487001i
$651$	−342.953	+	342.953i	−0.526809	+	0.526809i
$652$	−400.773	−	364.672i	−0.614682	−	0.559312i
$653$	−286.170	+	286.170i	−0.438238	+	0.438238i	−0.891419	−	0.453180i	$-0.850289\pi$
$653$	−286.170	+	286.170i	−0.438238	+	0.438238i	0.453180	+	0.891419i	$0.350289\pi$
$654$	1418.84	−	33.4403i	2.16949	−	0.0511319i
$655$		−	1229.01i		−	1.87635i
$656$	72.0505	+	762.137i	0.109833	+	1.16179i
$657$	470.881			0.716714
$658$	9.92001	+	420.898i	0.0150760	+	0.639662i
$659$	−64.6005	−	64.6005i	−0.0980281	−	0.0980281i	0.656392	−	0.754420i	$-0.272082\pi$
$659$	−64.6005	−	64.6005i	−0.0980281	−	0.0980281i	−0.754420	+	0.656392i	$0.772082\pi$
$660$	−3.93668	−	3.58207i	−0.00596467	−	0.00542738i
$661$	120.408	+	120.408i	0.182160	+	0.182160i	0.792297	−	0.610136i	$-0.208885\pi$
$661$	120.408	+	120.408i	0.182160	+	0.182160i	−0.610136	+	0.792297i	$0.708885\pi$
$662$	−131.927	+	138.296i	−0.199286	+	0.208907i
$663$	−762.806			−1.15054
$664$	474.306	+	411.576i	0.714317	+	0.619843i
$665$		−	29.6417i		−	0.0445740i
$666$	258.524	−	271.004i	0.388174	−	0.406914i
$667$	−306.667	+	306.667i	−0.459770	+	0.459770i
$668$	1162.40	−	54.8229i	1.74012	−	0.0820703i
$669$	−681.116	+	681.116i	−1.01811	+	1.01811i
$670$	−29.4780	−	1250.73i	−0.0439971	−	1.86676i
$671$		−	2.73742i		−	0.00407961i
$672$	244.932	+	193.084i	0.364482	+	0.287327i
$673$	−772.248			−1.14747			−0.573736	−	0.819041i	$-0.694506\pi$
$673$	−772.248			−1.14747			−0.573736	+	0.819041i	$0.694506\pi$
$674$	298.275	−	7.02996i	0.442545	−	0.0104302i
$675$	−352.262	−	352.262i	−0.521870	−	0.521870i
$676$	21.2168	+	449.857i	0.0313859	+	0.665468i
$677$	143.226	+	143.226i	0.211560	+	0.211560i	0.804930	−	0.593370i	$-0.202203\pi$
$677$	143.226	+	143.226i	0.211560	+	0.211560i	−0.593370	+	0.804930i	$0.702203\pi$
$678$	−1059.82	−	1011.01i	−1.56316	−	1.49117i
$679$	72.9660			0.107461
$680$	−1241.37	−	1077.19i	−1.82554	−	1.58410i
$681$			1210.10i			1.77694i
$682$	−3.49065	−	3.32990i	−0.00511826	−	0.00488256i
$683$	855.173	−	855.173i	1.25208	−	1.25208i	0.297299	−	0.954784i	$-0.403914\pi$
$683$	855.173	−	855.173i	1.25208	−	1.25208i	0.954784	−	0.297299i	$-0.0960859\pi$
$684$	18.4983	−	20.3295i	0.0270443	−	0.0297216i
$685$	419.948	−	419.948i	0.613063	−	0.613063i
$686$	−37.0302	+	0.872754i	−0.0539799	+	0.00127224i
$687$		−	24.4497i		−	0.0355891i
$688$	−124.460	+	150.450i	−0.180902	+	0.218677i
$689$	277.922			0.403370
$690$	−11.1183	−	471.740i	−0.0161135	−	0.683680i
$691$	579.764	+	579.764i	0.839022	+	0.839022i	0.988730	−	0.149709i	$-0.0478335\pi$
$691$	579.764	+	579.764i	0.839022	+	0.839022i	−0.149709	+	0.988730i	$0.547834\pi$
$692$	−321.615	+	353.454i	−0.464761	+	0.510771i
$693$	0.414464	+	0.414464i	0.000598072	+	0.000598072i
$694$	−296.171	+	310.469i	−0.426759	+	0.447361i
$695$	1286.83			1.85155
$696$	−1483.38	+	105.039i	−2.13129	+	0.150919i
$697$			1319.11i			1.89255i
$698$	−453.580	+	475.476i	−0.649827	+	0.681198i
$699$	−684.333	+	684.333i	−0.979017	+	0.979017i
$700$	−15.2216	−	322.740i	−0.0217451	−	0.461057i
$701$	339.029	−	339.029i	0.483637	−	0.483637i	−0.422654	−	0.906291i	$-0.638902\pi$
$701$	339.029	−	339.029i	0.483637	−	0.483637i	0.906291	+	0.422654i	$0.138902\pi$
$702$	5.77540	+	245.045i	0.00822706	+	0.349067i
$703$			61.6020i			0.0876274i
$704$	−1.86260	+	2.48082i	−0.00264574	+	0.00352390i
$705$	2184.13			3.09806
$706$	410.747	−	9.68077i	0.581795	−	0.0137121i
$707$	167.085	+	167.085i	0.236329	+	0.236329i
$708$	−591.858	+	27.9141i	−0.835958	+	0.0394268i
$709$	650.641	+	650.641i	0.917688	+	0.917688i	0.996861	−	0.0791726i	$-0.0252278\pi$
$709$	650.641	+	650.641i	0.917688	+	0.917688i	−0.0791726	+	0.996861i	$0.525228\pi$
$710$	822.337	+	784.466i	1.15822	+	1.10488i
$711$	206.537			0.290489
$712$	28.8621	+	407.594i	0.0405367	+	0.572463i
$713$		−	427.696i		−	0.599854i
$714$	388.860	+	370.952i	0.544622	+	0.519541i
$715$	1.91833	−	1.91833i	0.00268297	−	0.00268297i
$716$	−348.509	−	317.116i	−0.486745	−	0.442900i
$717$	−1175.45	+	1175.45i	−1.63941	+	1.63941i
$718$	−1213.78	+	28.6072i	−1.69050	+	0.0398429i
$719$			498.150i			0.692838i	0.938080	+	0.346419i	$0.112602\pi$
$719$			498.150i			0.692838i	−0.938080	+	0.346419i	$0.887398\pi$
$720$	347.350	−	419.882i	0.482430	−	0.583170i
$721$	−152.309			−0.211247
$722$	−16.9054	−	717.280i	−0.0234146	−	0.993463i
$723$	486.634	+	486.634i	0.673076	+	0.673076i
$724$	279.745	+	254.546i	0.386389	+	0.351583i
$725$	1089.33	+	1089.33i	1.50253	+	1.50253i
$726$	615.333	−	645.039i	0.847566	−	0.888483i
$727$	−481.762			−0.662671			−0.331335	−	0.943513i	$-0.607499\pi$
$727$	−481.762			−0.662671			−0.331335	+	0.943513i	$0.607499\pi$
$728$	−104.189	+	120.069i	−0.143117	+	0.164930i
$729$		−	78.2610i		−	0.107354i
$730$	−1059.87	+	1111.03i	−1.45187	+	1.52196i
$731$	−237.907	+	237.907i	−0.325455	+	0.325455i
$732$	831.234	−	39.2040i	1.13557	−	0.0535574i
$733$	−152.972	+	152.972i	−0.208693	+	0.208693i	−0.803712	−	0.595019i	$-0.797145\pi$
$733$	−152.972	+	152.972i	−0.208693	+	0.208693i	0.595019	+	0.803712i	$0.297145\pi$
$734$	4.87582	+	206.877i	0.00664281	+	0.281849i
$735$			192.158i			0.261440i
$736$	−273.124	+	32.3297i	−0.371093	+	0.0439262i
$737$	−4.06895			−0.00552097
$738$	−437.235	+	10.3051i	−0.592460	+	0.0139635i
$739$	1028.07	+	1028.07i	1.39117	+	1.39117i	0.822716	+	0.568452i	$0.192458\pi$
$739$	1028.07	+	1028.07i	1.39117	+	1.39117i	0.568452	+	0.822716i	$0.307542\pi$
$740$	57.5377	+	1219.96i	0.0777537	+	1.64860i
$741$	29.4140	+	29.4140i	0.0396950	+	0.0396950i
$742$	−141.678	−	135.153i	−0.190940	−	0.182147i
$743$	−701.518			−0.944169			−0.472085	−	0.881553i	$-0.656498\pi$
$743$	−701.518			−0.944169			−0.472085	+	0.881553i	$0.656498\pi$
$744$	961.155	−	1107.65i	1.29187	−	1.48878i
$745$		−	338.862i		−	0.454848i
$746$	506.737	+	483.401i	0.679273	+	0.647991i
$747$	−253.689	+	253.689i	−0.339611	+	0.339611i
$748$	−3.59757	+	3.95371i	−0.00480958	+	0.00528571i
$749$	−46.2817	+	46.2817i	−0.0617914	+	0.0617914i
$750$	−303.522	+	7.15361i	−0.404696	+	0.00953815i
$751$			1256.03i			1.67248i	0.548367	+	0.836238i	$0.315250\pi$
$751$			1256.03i			1.67248i	−0.548367	+	0.836238i	$0.684750\pi$
$752$	−119.815	−	1267.38i	−0.159328	−	1.68534i
$753$	478.658			0.635668
$754$	−17.8598	−	757.776i	−0.0236867	−	1.00501i
$755$	606.989	+	606.989i	0.803958	+	0.803958i
$756$	116.221	−	127.727i	0.153732	−	0.168951i
$757$	1001.27	+	1001.27i	1.32268	+	1.32268i	0.911600	+	0.411078i	$0.134848\pi$
$757$	1001.27	+	1001.27i	1.32268	+	1.32268i	0.411078	+	0.911600i	$0.365152\pi$
$758$	−513.228	+	538.005i	−0.677082	+	0.709769i
$759$	−1.53469			−0.00202199
$760$	6.33080	+	89.4042i	0.00833000	+	0.117637i
$761$		−	1399.88i		−	1.83952i	−0.392481	−	0.919760i	$-0.628383\pi$
$761$		−	1399.88i		−	1.83952i	0.392481	−	0.919760i	$-0.371617\pi$
$762$	589.279	−	617.726i	0.773332	−	0.810665i
$763$	360.381	−	360.381i	0.472321	−	0.472321i
$764$	14.8564	+	314.997i	0.0194455	+	0.412300i
$765$	663.964	−	663.964i	0.867926	−	0.867926i
$766$	22.0976	+	937.581i	0.0288480	+	1.22400i
$767$		−	302.012i		−	0.393757i
$768$	−779.993	−	530.061i	−1.01562	−	0.690184i
$769$	−160.348			−0.208515			−0.104257	−	0.994550i	$-0.533247\pi$
$769$	−160.348			−0.208515			−0.104257	+	0.994550i	$0.533247\pi$
$770$	−1.91080	+	0.0450350i	−0.00248155	+	5.84870e-5i
$771$	393.825	+	393.825i	0.510797	+	0.510797i
$772$	396.777	−	18.7134i	0.513959	−	0.0242402i
$773$	228.104	+	228.104i	0.295089	+	0.295089i	0.839087	−	0.543998i	$-0.183090\pi$
$773$	228.104	+	228.104i	0.295089	+	0.295089i	−0.543998	+	0.839087i	$0.683090\pi$
$774$	−80.7159	−	76.9988i	−0.104284	−	0.0994816i
$775$	−1519.25			−1.96032
$776$	−220.077	+	15.5839i	−0.283605	+	0.0200823i
$777$		−	399.348i		−	0.513961i
$778$	569.768	+	543.529i	0.732349	+	0.698623i
$779$	50.8652	−	50.8652i	0.0652955	−	0.0652955i
$780$	609.985	+	555.039i	0.782032	+	0.711588i
$781$	2.61368	−	2.61368i	0.00334658	−	0.00334658i
$782$	−473.780	+	11.1664i	−0.605857	+	0.0142793i
$783$			823.390i			1.05158i
$784$	111.503	−	10.5412i	0.142223	−	0.0134454i
$785$	−174.091			−0.221772
$786$	−28.6308	−	1214.78i	−0.0364259	−	1.54552i
$787$	−249.697	−	249.697i	−0.317278	−	0.317278i	0.530443	−	0.847721i	$-0.322026\pi$
$787$	−249.697	−	249.697i	−0.317278	−	0.317278i	−0.847721	+	0.530443i	$0.822026\pi$
$788$	−455.379	−	414.359i	−0.577892	−	0.525836i
$789$	377.084	+	377.084i	0.477926	+	0.477926i
$790$	−464.877	+	487.319i	−0.588452	+	0.616860i
$791$	−525.984			−0.664961
$792$	−1.33861	−	1.16157i	−0.00169017	−	0.00146663i
$793$			424.160i			0.534881i
$794$	57.6402	−	60.4228i	0.0725947	−	0.0760992i
$795$	−718.269	+	718.269i	−0.903483	+	0.903483i
$796$	731.203	−	34.4862i	0.918597	−	0.0433243i
$797$	252.225	−	252.225i	0.316468	−	0.316468i	−0.530941	−	0.847409i	$-0.678161\pi$
$797$	252.225	−	252.225i	0.316468	−	0.316468i	0.847409	+	0.530941i	$0.178161\pi$
$798$	−0.690528	−	29.2985i	−0.000865324	−	0.0367150i
$799$		−	2193.58i		−	2.74541i
$800$	114.841	+	970.185i	0.143551	+	1.21273i
$801$	−233.445			−0.291441
$802$	−1138.05	+	26.8224i	−1.41902	+	0.0334443i
$803$	3.53125	+	3.53125i	0.00439757	+	0.00439757i
$804$	−58.2736	−	1235.56i	−0.0724796	−	1.53677i
$805$	−119.820	−	119.820i	−0.148845	−	0.148845i
$806$	540.874	+	515.965i	0.671059	+	0.640155i
$807$	−557.670			−0.691041
$808$	−539.641	−	468.270i	−0.667872	−	0.579542i
$809$		−	264.570i		−	0.327033i	−0.986541	−	0.163517i	$-0.947716\pi$
$809$		−	264.570i		−	0.327033i	0.986541	−	0.163517i	$-0.0522837\pi$
$810$	−1091.81	−	1041.53i	−1.34792	−	1.28584i
$811$	−342.030	+	342.030i	−0.421739	+	0.421739i	−0.885802	−	0.464063i	$-0.846391\pi$
$811$	−342.030	+	342.030i	−0.421739	+	0.421739i	0.464063	+	0.885802i	$0.346391\pi$
$812$	−359.401	+	394.981i	−0.442613	+	0.486430i
$813$	−221.779	+	221.779i	−0.272791	+	0.272791i
$814$	3.97106	−	0.0935927i	0.00487845	−	0.000114979i
$815$			1009.45i			1.23859i
$816$	−1252.09	−	1035.80i	−1.53443	−	1.26936i
$817$	18.3475			0.0224572
$818$	20.8569	+	884.941i	0.0254974	+	1.08184i
$819$	−64.2208	−	64.2208i	−0.0784137	−	0.0784137i
$820$	959.820	−	1054.84i	1.17051	−	1.28639i
$821$	−1063.31	−	1063.31i	−1.29514	−	1.29514i	−0.931563	−	0.363580i	$-0.881554\pi$
$821$	−1063.31	−	1063.31i	−1.29514	−	1.29514i	−0.363580	−	0.931563i	$-0.618446\pi$
$822$	405.304	−	424.870i	0.493071	−	0.516874i
$823$	604.202			0.734145			0.367073	−	0.930192i	$-0.380360\pi$
$823$	604.202			0.734145			0.367073	+	0.930192i	$0.380360\pi$
$824$	459.389	−	32.5298i	0.557511	−	0.0394779i
$825$			5.45149i			0.00660787i
$826$	−146.868	+	153.958i	−0.177807	+	0.186390i
$827$	−908.534	+	908.534i	−1.09859	+	1.09859i	−0.104014	+	0.994576i	$0.533169\pi$
$827$	−908.534	+	908.534i	−1.09859	+	1.09859i	−0.994576	+	0.104014i	$0.966831\pi$
$828$	−7.40247	−	156.953i	−0.00894018	−	0.189557i
$829$	608.698	−	608.698i	0.734255	−	0.734255i	−0.237205	−	0.971460i	$-0.576231\pi$
$829$	608.698	−	608.698i	0.734255	−	0.734255i	0.971460	+	0.237205i	$0.0762311\pi$
$830$	−27.5655	−	1169.58i	−0.0332114	−	1.40913i
$831$			609.509i			0.733464i
$832$	288.608	−	384.401i	0.346885	−	0.462021i
$833$	192.989			0.231680
$834$	1271.93	−	29.9778i	1.52510	−	0.0359446i
$835$	−1532.94	−	1532.94i	−1.83586	−	1.83586i
$836$	0.291179	−	0.0137330i	0.000348300	−	1.64271e-5i
$837$	−574.174	−	574.174i	−0.685991	−	0.685991i
$838$	−315.542	−	301.011i	−0.376542	−	0.359202i
$839$	70.3128			0.0838055			0.0419027	−	0.999122i	$-0.486658\pi$
$839$	70.3128			0.0838055			0.0419027	+	0.999122i	$0.486658\pi$
$840$	−41.0407	−	579.581i	−0.0488579	−	0.689977i
$841$		−	1705.24i		−	2.02764i
$842$	356.442	+	340.027i	0.423328	+	0.403833i
$843$	−104.974	+	104.974i	−0.124525	+	0.124525i
$844$	−281.691	−	256.317i	−0.333757	−	0.303693i
$845$	593.260	−	593.260i	0.702083	−	0.702083i
$846$	727.089	−	17.1365i	0.859444	−	0.0202560i
$847$		−	320.130i		−	0.377957i
$848$	456.189	+	377.385i	0.537959	+	0.445030i
$849$	−786.365			−0.926225
$850$	39.6649	+	1682.95i	0.0466646	+	1.97994i
$851$	249.013	+	249.013i	0.292612	+	0.292612i
$852$	831.092	+	756.228i	0.975460	+	0.887592i
$853$	105.286	+	105.286i	0.123430	+	0.123430i	0.766124	−	0.642693i	$-0.222183\pi$
$853$	105.286	+	105.286i	0.123430	+	0.123430i	−0.642693	+	0.766124i	$0.722183\pi$
$854$	206.269	−	216.227i	0.241533	−	0.253193i
$855$	−51.2052			−0.0598891
$856$	129.709	−	149.478i	0.151529	−	0.174624i
$857$		−	42.0246i		−	0.0490369i	−0.999699	−	0.0245184i	$-0.992195\pi$
$857$		−	42.0246i		−	0.0490369i	0.999699	−	0.0245184i	$-0.00780524\pi$
$858$	1.85143	−	1.94081i	0.00215784	−	0.00226201i
$859$	−551.162	+	551.162i	−0.641632	+	0.641632i	−0.950956	−	0.309325i	$-0.899897\pi$
$859$	−551.162	+	551.162i	−0.641632	+	0.641632i	0.309325	+	0.950956i	$0.399897\pi$
$860$	363.353	−	17.1370i	0.422503	−	0.0199268i
$861$	−329.744	+	329.744i	−0.382978	+	0.382978i
$862$	5.11163	+	216.882i	0.00592996	+	0.251603i
$863$			332.787i			0.385617i	0.981236	+	0.192809i	$0.0617596\pi$
$863$			332.787i			0.385617i	−0.981236	+	0.192809i	$0.938240\pi$
$864$	−323.263	+	410.067i	−0.374147	+	0.474614i
$865$	890.264			1.02921
$866$	−914.464	+	21.5527i	−1.05596	+	0.0248877i
$867$	−1227.14	−	1227.14i	−1.41539	−	1.41539i
$868$	−24.8106	−	526.053i	−0.0285836	−	0.606052i
$869$	1.54887	+	1.54887i	0.00178236	+	0.00178236i
$870$	2004.57	+	1912.26i	2.30411	+	2.19800i
$871$	630.480			0.723858
$872$	−1010.00	+	1163.94i	−1.15826	+	1.33479i
$873$		−	126.047i		−	0.144383i
$874$	18.6997	+	17.8385i	0.0213955	+	0.0204102i
$875$	−77.0934	+	77.0934i	−0.0881067	+	0.0881067i
$876$	−1021.71	+	1122.86i	−1.16634	+	1.28180i
$877$	112.953	−	112.953i	0.128795	−	0.128795i	−0.639771	−	0.768566i	$-0.720971\pi$
$877$	112.953	−	112.953i	0.128795	−	0.128795i	0.768566	+	0.639771i	$0.220971\pi$
$878$	575.746	−	13.5696i	0.655748	−	0.0154551i
$879$		−	1238.95i		−	1.40950i
$880$	5.75366	−	0.543936i	0.00653824	−	0.000618109i
$881$	232.822			0.264270			0.132135	−	0.991232i	$-0.457817\pi$
$881$	232.822			0.264270			0.132135	+	0.991232i	$0.457817\pi$
$882$	1.50766	+	63.9687i	0.00170936	+	0.0725269i
$883$	−12.0542	−	12.0542i	−0.0136514	−	0.0136514i	0.700248	−	0.713900i	$-0.253073\pi$
$883$	−12.0542	−	12.0542i	−0.0136514	−	0.0136514i	−0.713900	+	0.700248i	$0.753073\pi$
$884$	557.439	−	612.624i	0.630587	−	0.693013i
$885$	780.528	+	780.528i	0.881953	+	0.881953i
$886$	341.874	−	358.378i	0.385863	−	0.404490i
$887$	−405.899			−0.457608			−0.228804	−	0.973472i	$-0.573482\pi$
$887$	−405.899			−0.457608			−0.228804	+	0.973472i	$0.573482\pi$
$888$	85.2917	+	1204.50i	0.0960492	+	1.35642i
$889$		−	306.575i		−	0.344854i
$890$	525.440	−	550.806i	0.590382	−	0.618883i
$891$	−3.47017	+	3.47017i	−0.00389469	+	0.00389469i
$892$	−49.2746	−	1044.76i	−0.0552406	−	1.17125i
$893$	−84.5850	+	84.5850i	−0.0947200	+	0.0947200i
$894$	−7.89407	−	334.939i	−0.00883006	−	0.374652i
$895$			877.811i			0.980794i
$896$	−334.059	+	55.6085i	−0.372834	+	0.0620630i
$897$	237.799			0.265105
$898$	1256.59	−	29.6162i	1.39932	−	0.0329802i
$899$	1775.57	+	1775.57i	1.97505	+	1.97505i
$900$	−557.524	+	26.2948i	−0.619471	+	0.0292165i
$901$	721.376	+	721.376i	0.800639	+	0.800639i
$902$	−3.35621	−	3.20165i	−0.00372085	−	0.00354950i
$903$	−118.942			−0.131718
$904$	1586.45	−	112.338i	1.75493	−	0.124268i
$905$		−	704.611i		−	0.778576i
$906$	614.102	+	585.822i	0.677817	+	0.646602i
$907$	−269.543	+	269.543i	−0.297181	+	0.297181i	−0.839909	−	0.542728i	$-0.817391\pi$
$907$	−269.543	+	269.543i	−0.297181	+	0.297181i	0.542728	+	0.839909i	$0.317391\pi$
$908$	−971.853	−	884.310i	−1.07032	−	0.973909i
$909$	288.635	−	288.635i	0.317530	−	0.317530i
$910$	296.076	−	6.97813i	0.325358	−	0.00766827i
$911$		−	107.577i		−	0.118087i	−0.998255	−	0.0590434i	$-0.981195\pi$
$911$		−	107.577i		−	0.118087i	0.998255	−	0.0590434i	$-0.0188050\pi$
$912$	8.34026	+	88.2217i	0.00914502	+	0.0967343i
$913$	−3.80495			−0.00416753
$914$	−4.21637	−	178.897i	−0.00461309	−	0.195730i
$915$	−1096.21	−	1096.21i	−1.19805	−	1.19805i
$916$	19.6360	+	17.8673i	0.0214367	+	0.0195057i
$917$	−308.549	−	308.549i	−0.336477	−	0.336477i
$918$	−621.051	+	651.032i	−0.676526	+	0.709185i
$919$	1479.46			1.60986			0.804930	−	0.593370i	$-0.202203\pi$
$919$	1479.46			1.60986			0.804930	+	0.593370i	$0.202203\pi$
$920$	386.988	+	335.806i	0.420639	+	0.365007i
$921$		−	107.386i		−	0.116597i
$922$	−883.040	+	925.669i	−0.957744	+	1.00398i
$923$	−404.987	+	404.987i	−0.438772	+	0.438772i
$924$	−1.88763	+	0.0890273i	−0.00204289	+	9.63499e-5i
$925$	884.536	−	884.536i	0.956255	−	0.956255i
$926$	−14.4508	−	613.136i	−0.0156056	−	0.662134i
$927$			263.110i			0.283829i
$928$	999.654	−	1268.09i	1.07721	−	1.36647i
$929$	256.867			0.276498			0.138249	−	0.990397i	$-0.455853\pi$
$929$	256.867			0.276498			0.138249	+	0.990397i	$0.455853\pi$
$930$	−2731.32	+	64.3738i	−2.93691	+	0.0692191i
$931$	−7.44172	−	7.44172i	−0.00799325	−	0.00799325i
$932$	−49.5073	−	1049.69i	−0.0531195	−	1.12628i
$933$	−400.425	−	400.425i	−0.429180	−	0.429180i
$934$	−1291.19	−	1231.72i	−1.38243	−	1.31876i
$935$	9.95844			0.0106507
$936$	207.417	+	179.984i	0.221599	+	0.192291i
$937$			183.878i			0.196241i	0.995175	+	0.0981203i	$0.0312830\pi$
$937$			183.878i			0.196241i	−0.995175	+	0.0981203i	$0.968717\pi$
$938$	−321.403	−	306.602i	−0.342648	−	0.326868i
$939$	311.517	−	311.517i	0.331754	−	0.331754i
$940$	−1596.11	+	1754.12i	−1.69799	+	1.86608i
$941$	−359.757	+	359.757i	−0.382313	+	0.382313i	−0.871935	−	0.489622i	$-0.837135\pi$
$941$	−359.757	+	359.757i	−0.382313	+	0.382313i	0.489622	+	0.871935i	$0.337135\pi$
$942$	−172.076	+	4.05560i	−0.182671	+	0.00430531i
$943$		−	411.223i		−	0.436080i
$944$	410.096	−	495.731i	0.434424	−	0.525139i
$945$	−321.713			−0.340437
$946$	−0.0278756	−	1.18274i	−2.94668e−5	−	0.00125025i
$947$	−636.682	−	636.682i	−0.672315	−	0.672315i	0.285934	−	0.958249i	$-0.407696\pi$
$947$	−636.682	−	636.682i	−0.672315	−	0.672315i	−0.958249	+	0.285934i	$0.907696\pi$
$948$	−448.143	+	492.508i	−0.472725	+	0.519523i
$949$	−547.164	−	547.164i	−0.576569	−	0.576569i
$950$	63.3654	−	66.4244i	0.0667004	−	0.0699204i
$951$	1305.76			1.37304
$952$	−582.088	+	41.2182i	−0.611437	+	0.0432964i
$953$			1086.51i			1.14010i	0.821612	+	0.570048i	$0.193075\pi$
$953$			1086.51i			1.14010i	−0.821612	+	0.570048i	$0.806925\pi$
$954$	−233.474	+	244.745i	−0.244731	+	0.256546i
$955$	415.411	−	415.411i	0.434985	−	0.434985i
$956$	−85.0369	−	1803.02i	−0.0889507	−	1.88600i
$957$	6.37125	−	6.37125i	0.00665752	−	0.00665752i
$958$	−11.1056	−	471.202i	−0.0115925	−	0.491860i
$959$		−	210.861i		−	0.219876i
$960$	247.571	+	1739.34i	0.257886	+	1.81182i
$961$	−1515.32			−1.57681
$962$	−615.312	+	14.5021i	−0.639618	+	0.0150750i
$963$	79.9504	+	79.9504i	0.0830223	+	0.0830223i
$964$	−746.444	+	35.2050i	−0.774320	+	0.0365197i
$965$	−523.260	−	523.260i	−0.542238	−	0.542238i
$966$	−121.224	−	115.642i	−0.125491	−	0.119712i
$967$	−341.586			−0.353243			−0.176622	−	0.984279i	$-0.556517\pi$
$967$	−341.586			−0.353243			−0.176622	+	0.984279i	$0.556517\pi$
$968$	68.3725	+	965.563i	0.0706328	+	0.997483i
$969$			152.694i			0.157579i
$970$	297.404	+	283.708i	0.306602	+	0.292482i
$971$	622.601	−	622.601i	0.641196	−	0.641196i	−0.309653	−	0.950849i	$-0.600213\pi$
$971$	622.601	−	622.601i	0.641196	−	0.641196i	0.950849	+	0.309653i	$0.100213\pi$
$972$	−668.953	−	608.695i	−0.688223	−	0.626229i
$973$	323.066	−	323.066i	0.332031	−	0.332031i
$974$	40.4727	−	0.953889i	0.0415531	−	0.000979352i
$975$		−	844.704i		−	0.866363i
$976$	−575.960	+	696.229i	−0.590123	+	0.713350i
$977$	−1065.93			−1.09103			−0.545514	−	0.838102i	$-0.683666\pi$
$977$	−1065.93			−1.09103			−0.545514	+	0.838102i	$0.683666\pi$
$978$	23.5160	+	997.764i	0.0240450	+	1.02021i
$979$	−1.75066	−	1.75066i	−0.00178821	−	0.00178821i
$980$	−154.326	−	140.424i	−0.157475	−	0.143290i
$981$	−622.548	−	622.548i	−0.634606	−	0.634606i
$982$	−732.697	+	768.068i	−0.746127	+	0.782146i
$983$	−612.836			−0.623434			−0.311717	−	0.950175i	$-0.600904\pi$
$983$	−612.836			−0.623434			−0.311717	+	0.950175i	$0.600904\pi$
$984$	924.136	−	1064.99i	0.939162	−	1.08230i
$985$			1146.99i			1.16446i
$986$	1920.53	−	2013.25i	1.94780	−	2.04183i
$987$	548.339	−	548.339i	0.555562	−	0.555562i
$988$	−45.1179	+	2.12792i	−0.0456659	+	0.00215377i
$989$	74.1659	−	74.1659i	0.0749908	−	0.0749908i
$990$	0.0777967	+	3.30085i	7.85825e−5	+	0.00333419i
$991$			49.8899i			0.0503430i	0.999683	+	0.0251715i	$0.00801319\pi$
$991$			49.8899i			0.0503430i	−0.999683	+	0.0251715i	$0.991987\pi$
$992$	187.186	+	1581.36i	0.188695	+	1.59412i
$993$	352.044			0.354525
$994$	403.397	−	9.50755i	0.405832	−	0.00956494i
$995$	−964.293	−	964.293i	−0.969139	−	0.969139i
$996$	−54.4928	−	1155.40i	−0.0547116	−	1.16004i
$997$	1288.31	+	1288.31i	1.29218	+	1.29218i	0.933435	+	0.358747i	$0.116796\pi$
$997$	1288.31	+	1288.31i	1.29218	+	1.29218i	0.358747	+	0.933435i	$0.383204\pi$
$998$	651.058	+	621.075i	0.652363	+	0.622320i
$999$	668.591			0.669260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.k.a.43.24	✓	48
4.3	odd	2		448.3.k.a.15.20		48
8.3	odd	2		896.3.k.b.799.5		48
8.5	even	2		896.3.k.a.799.20		48
16.3	odd	4	inner	112.3.k.a.99.24	yes	48
16.5	even	4		896.3.k.b.351.5		48
16.11	odd	4		896.3.k.a.351.20		48
16.13	even	4		448.3.k.a.239.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.k.a.43.24	✓	48	1.1	even	1	trivial
112.3.k.a.99.24	yes	48	16.3	odd	4	inner
448.3.k.a.15.20		48	4.3	odd	2
448.3.k.a.239.20		48	16.13	even	4
896.3.k.a.351.20		48	16.11	odd	4
896.3.k.a.799.20		48	8.5	even	2
896.3.k.b.351.5		48	16.5	even	4
896.3.k.b.799.5		48	8.3	odd	2

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99944 - 0.0471243i) q^{2} +(-2.60485 - 2.60485i) q^{3} +(3.99556 - 0.188445i) q^{4} +(-5.26925 - 5.26925i) q^{5} +(-5.33100 - 5.08550i) q^{6} -2.64575 q^{7} +(7.98002 - 0.565073i) q^{8} +4.57046i q^{9} +O(q^{10})\)	\(q+(1.99944 - 0.0471243i) q^{2} +(-2.60485 - 2.60485i) q^{3} +(3.99556 - 0.188445i) q^{4} +(-5.26925 - 5.26925i) q^{5} +(-5.33100 - 5.08550i) q^{6} -2.64575 q^{7} +(7.98002 - 0.565073i) q^{8} +4.57046i q^{9} +(-10.7839 - 10.2873i) q^{10} +(-0.0342750 + 0.0342750i) q^{11} +(-10.8987 - 9.91695i) q^{12} +(5.31088 - 5.31088i) q^{13} +(-5.29003 + 0.124679i) q^{14} +27.4512i q^{15} +(15.9290 - 1.50589i) q^{16} +27.5699 q^{17} +(0.215380 + 9.13839i) q^{18} +(-1.06310 - 1.06310i) q^{19} +(-22.0465 - 20.0606i) q^{20} +(6.89178 + 6.89178i) q^{21} +(-0.0669158 + 0.0701461i) q^{22} -8.59472 q^{23} +(-22.2587 - 19.3148i) q^{24} +30.5299i q^{25} +(10.3685 - 10.8691i) q^{26} +(-11.5383 + 11.5383i) q^{27} +(-10.5713 + 0.498578i) q^{28} +(35.6808 - 35.6808i) q^{29} +(1.29362 + 54.8871i) q^{30} +49.7626i q^{31} +(31.7781 - 3.76158i) q^{32} +0.178562 q^{33} +(55.1245 - 1.29921i) q^{34} +(13.9411 + 13.9411i) q^{35} +(0.861281 + 18.2616i) q^{36} +(-28.9728 - 28.9728i) q^{37} +(-2.17571 - 2.07552i) q^{38} -27.6681 q^{39} +(-45.0262 - 39.0712i) q^{40} +47.8460i q^{41} +(14.1045 + 13.4550i) q^{42} +(-8.62924 + 8.62924i) q^{43} +(-0.130489 + 0.143407i) q^{44} +(24.0829 - 24.0829i) q^{45} +(-17.1847 + 0.405020i) q^{46} -79.5643i q^{47} +(-45.4152 - 37.5700i) q^{48} +7.00000 q^{49} +(1.43870 + 61.0429i) q^{50} +(-71.8154 - 71.8154i) q^{51} +(20.2191 - 22.2207i) q^{52} +(26.1653 + 26.1653i) q^{53} +(-22.5264 + 23.6139i) q^{54} +0.361207 q^{55} +(-21.1131 + 1.49504i) q^{56} +5.53844i q^{57} +(69.6604 - 73.0233i) q^{58} +(28.4333 - 28.4333i) q^{59} +(5.17303 + 109.683i) q^{60} +(-39.9332 + 39.9332i) q^{61} +(2.34503 + 99.4976i) q^{62} -12.0923i q^{63} +(63.3614 - 9.01859i) q^{64} -55.9687 q^{65} +(0.357025 - 0.00841462i) q^{66} +(59.3574 + 59.3574i) q^{67} +(110.157 - 5.19541i) q^{68} +(22.3879 + 22.3879i) q^{69} +(28.5315 + 27.2175i) q^{70} -76.2561 q^{71} +(2.58265 + 36.4724i) q^{72} -103.027i q^{73} +(-59.2947 - 56.5641i) q^{74} +(79.5258 - 79.5258i) q^{75} +(-4.44803 - 4.04735i) q^{76} +(0.0906831 - 0.0906831i) q^{77} +(-55.3208 + 1.30384i) q^{78} -45.1896i q^{79} +(-91.8686 - 75.9988i) q^{80} +101.245 q^{81} +(2.25471 + 95.6654i) q^{82} +(55.5063 + 55.5063i) q^{83} +(28.8352 + 26.2378i) q^{84} +(-145.273 - 145.273i) q^{85} +(-16.8470 + 17.6603i) q^{86} -185.886 q^{87} +(-0.254147 + 0.292883i) q^{88} +51.0768i q^{89} +(47.0175 - 49.2873i) q^{90} +(-14.0513 + 14.0513i) q^{91} +(-34.3407 + 1.61963i) q^{92} +(129.624 - 129.624i) q^{93} +(-3.74941 - 159.084i) q^{94} +11.2035i q^{95} +(-92.5756 - 72.9789i) q^{96} -27.5785 q^{97} +(13.9961 - 0.329870i) q^{98} +(-0.156653 - 0.156653i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} + 12 q^{6}+O(q^{10}) \) 48 * q + 6 * q^4 + 12 * q^6	\( 48 q + 6 q^{4} + 12 q^{6} - 40 q^{10} + 16 q^{11} - 108 q^{12} - 14 q^{14} + 66 q^{16} + 30 q^{18} - 64 q^{19} + 84 q^{20} + 94 q^{22} - 64 q^{23} + 40 q^{24} - 196 q^{26} - 96 q^{27} + 16 q^{29} - 72 q^{30} + 160 q^{32} - 28 q^{34} + 64 q^{36} - 48 q^{37} - 224 q^{38} + 384 q^{39} + 180 q^{40} + 176 q^{43} - 114 q^{44} - 256 q^{46} + 52 q^{48} + 336 q^{49} + 6 q^{50} - 192 q^{51} - 48 q^{52} - 80 q^{53} - 288 q^{54} - 512 q^{55} - 98 q^{56} - 50 q^{58} - 288 q^{59} + 512 q^{60} - 64 q^{61} + 156 q^{62} + 126 q^{64} - 32 q^{65} - 116 q^{66} + 80 q^{67} - 32 q^{68} + 192 q^{69} + 168 q^{70} + 26 q^{72} + 330 q^{74} + 608 q^{75} + 672 q^{76} + 112 q^{77} - 352 q^{78} - 980 q^{80} - 432 q^{81} - 76 q^{82} - 160 q^{83} + 320 q^{85} - 542 q^{86} - 896 q^{87} - 214 q^{88} + 1144 q^{90} - 12 q^{92} + 96 q^{93} + 660 q^{94} + 184 q^{96} + 496 q^{99}+O(q^{100}) \) 48 * q + 6 * q^4 + 12 * q^6 - 40 * q^10 + 16 * q^11 - 108 * q^12 - 14 * q^14 + 66 * q^16 + 30 * q^18 - 64 * q^19 + 84 * q^20 + 94 * q^22 - 64 * q^23 + 40 * q^24 - 196 * q^26 - 96 * q^27 + 16 * q^29 - 72 * q^30 + 160 * q^32 - 28 * q^34 + 64 * q^36 - 48 * q^37 - 224 * q^38 + 384 * q^39 + 180 * q^40 + 176 * q^43 - 114 * q^44 - 256 * q^46 + 52 * q^48 + 336 * q^49 + 6 * q^50 - 192 * q^51 - 48 * q^52 - 80 * q^53 - 288 * q^54 - 512 * q^55 - 98 * q^56 - 50 * q^58 - 288 * q^59 + 512 * q^60 - 64 * q^61 + 156 * q^62 + 126 * q^64 - 32 * q^65 - 116 * q^66 + 80 * q^67 - 32 * q^68 + 192 * q^69 + 168 * q^70 + 26 * q^72 + 330 * q^74 + 608 * q^75 + 672 * q^76 + 112 * q^77 - 352 * q^78 - 980 * q^80 - 432 * q^81 - 76 * q^82 - 160 * q^83 + 320 * q^85 - 542 * q^86 - 896 * q^87 - 214 * q^88 + 1144 * q^90 - 12 * q^92 + 96 * q^93 + 660 * q^94 + 184 * q^96 + 496 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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