LMFDB - Embedded newform 97.3.l.a.5.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,3,Mod(5,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(96)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.5"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	97.l (of order $96$, degree $32$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.64305856429$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$15$ over $\Q(\zeta_{96})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{96}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	97.5
Dual form			97.3.l.a.39.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40167 - 2.84231i) q^{2} +(2.77755 - 3.16719i) q^{3} +(-3.67900 + 4.79457i) q^{4} +(-0.883234 - 0.0289141i) q^{5} +(-12.8954 - 3.45530i) q^{6} +(-2.96741 - 4.77199i) q^{7} +(6.35145 + 1.26338i) q^{8} +(-1.14157 - 8.67110i) q^{9} +(1.15582 + 2.55096i) q^{10} +(4.61358 - 1.56610i) q^{11} +(4.96670 + 24.9693i) q^{12} +(1.68695 + 1.80114i) q^{13} +(-9.40414 + 15.1231i) q^{14} +(-2.54481 + 2.71706i) q^{15} +(0.944879 + 3.52634i) q^{16} +(12.7664 - 2.97671i) q^{17} +(-23.0458 + 15.3987i) q^{18} +(-13.7911 + 7.37152i) q^{19} +(3.38805 - 4.12835i) q^{20} +(-23.3560 - 3.85609i) q^{21} +(-10.9181 - 10.9181i) q^{22} +(32.9069 - 23.5807i) q^{23} +(21.6429 - 16.6072i) q^{24} +(-24.1672 - 1.58400i) q^{25} +(2.75484 - 7.31944i) q^{26} +(0.889957 + 0.594650i) q^{27} +(33.7968 + 3.32869i) q^{28} +(29.1626 + 13.2134i) q^{29} +(11.2897 + 3.42470i) q^{30} +(-3.09455 - 47.2138i) q^{31} +(28.1738 - 24.7078i) q^{32} +(7.85432 - 18.9620i) q^{33} +(-26.3550 - 32.1137i) q^{34} +(2.48294 + 4.30059i) q^{35} +(45.7740 + 26.4276i) q^{36} +(-24.4281 + 4.03309i) q^{37} +(40.2828 + 28.8663i) q^{38} +(10.3901 - 0.340138i) q^{39} +(-5.57329 - 1.29951i) q^{40} +(-19.6050 + 7.37878i) q^{41} +(21.7772 + 71.7899i) q^{42} +(59.0383 + 7.77254i) q^{43} +(-9.46460 + 27.8818i) q^{44} +(0.757558 + 7.69162i) q^{45} +(-113.148 - 60.4791i) q^{46} +(-33.6147 + 13.9237i) q^{47} +(13.7930 + 6.80198i) q^{48} +(7.70580 - 15.6258i) q^{49} +(29.3723 + 70.9110i) q^{50} +(26.0316 - 48.7016i) q^{51} +(-14.8420 + 1.46181i) q^{52} +(-9.77212 - 3.31719i) q^{53} +(0.442752 - 3.36304i) q^{54} +(-4.12015 + 1.24983i) q^{55} +(-12.8185 - 34.0580i) q^{56} +(-14.9586 + 64.1540i) q^{57} +(-3.31982 - 101.410i) q^{58} +(23.5077 - 32.8050i) q^{59} +(-3.66480 - 22.1973i) q^{60} +(-32.9991 + 57.1561i) q^{61} +(-129.859 + 74.9739i) q^{62} +(-37.9909 + 31.1783i) q^{63} +(-96.2264 - 39.8583i) q^{64} +(-1.43789 - 1.63960i) q^{65} +(-64.9052 + 4.25411i) q^{66} +(-28.0650 + 92.5178i) q^{67} +(-32.6956 + 72.1607i) q^{68} +(16.7159 - 169.719i) q^{69} +(8.74333 - 13.0853i) q^{70} +(27.1959 + 10.2358i) q^{71} +(3.70427 - 56.5163i) q^{72} +(64.4618 + 84.0083i) q^{73} +(45.7035 + 63.7791i) q^{74} +(-72.1426 + 72.1426i) q^{75} +(15.3944 - 93.2424i) q^{76} +(-21.1638 - 17.3687i) q^{77} +(-15.5304 - 29.0553i) q^{78} +(33.3573 + 49.9228i) q^{79} +(-0.732589 - 3.14190i) q^{80} +(80.3864 - 21.5395i) q^{81} +(48.4525 + 45.3807i) q^{82} +(113.681 + 70.6911i) q^{83} +(104.415 - 97.7953i) q^{84} +(-11.3618 + 2.26000i) q^{85} +(-60.6604 - 178.700i) q^{86} +(122.850 - 55.6626i) q^{87} +(31.2815 - 4.11829i) q^{88} +(-12.5007 + 62.8450i) q^{89} +(20.8001 - 12.9343i) q^{90} +(3.58913 - 13.3948i) q^{91} +(-8.00501 + 244.528i) q^{92} +(-158.130 - 121.338i) q^{93} +(86.6922 + 76.0270i) q^{94} +(12.3940 - 6.11202i) q^{95} -157.859i q^{96} +(96.4087 + 10.6938i) q^{97} -55.2144 q^{98} +(-18.8465 - 38.2170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) $ 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{96}\right)$

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 $

$2$	−1.40167	−	2.84231i	−0.700836	−	1.42116i	−0.897647	−	0.440714i	$-0.854725\pi$
$2$	−1.40167	−	2.84231i	−0.700836	−	1.42116i	0.196811	−	0.980441i	$-0.436941\pi$
$3$	2.77755	−	3.16719i	0.925851	−	1.05573i	−0.0724444	−	0.997372i	$-0.523080\pi$
$3$	2.77755	−	3.16719i	0.925851	−	1.05573i	0.998296	−	0.0583586i	$-0.0185867\pi$
$4$	−3.67900	+	4.79457i	−0.919751	+	1.19864i
$5$	−0.883234	−	0.0289141i	−0.176647	−	0.00578282i	−0.0557324	−	0.998446i	$-0.517749\pi$
$5$	−0.883234	−	0.0289141i	−0.176647	−	0.00578282i	−0.120915	+	0.992663i	$0.538583\pi$
$6$	−12.8954	−	3.45530i	−2.14923	−	0.575884i
$7$	−2.96741	−	4.77199i	−0.423916	−	0.681713i	0.565834	−	0.824519i	$-0.308554\pi$
$7$	−2.96741	−	4.77199i	−0.423916	−	0.681713i	−0.989751	+	0.142806i	$0.954388\pi$
$8$	6.35145	+	1.26338i	0.793931	+	0.157923i
$9$	−1.14157	−	8.67110i	−0.126841	−	0.963455i
$10$	1.15582	+	2.55096i	0.115582	+	0.255096i
$11$	4.61358	−	1.56610i	0.419416	−	0.142373i	−0.103750	−	0.994603i	$-0.533084\pi$
$11$	4.61358	−	1.56610i	0.419416	−	0.142373i	0.523166	+	0.852231i	$0.324751\pi$
$12$	4.96670	+	24.9693i	0.413892	+	2.08077i
$13$	1.68695	+	1.80114i	0.129765	+	0.138549i	0.791452	−	0.611232i	$-0.209326\pi$
$13$	1.68695	+	1.80114i	0.129765	+	0.138549i	−0.661686	+	0.749781i	$0.730159\pi$
$14$	−9.40414	+	15.1231i	−0.671724	+	1.08022i
$15$	−2.54481	+	2.71706i	−0.169654	+	0.181138i
$16$	0.944879	+	3.52634i	0.0590550	+	0.220396i
$17$	12.7664	−	2.97671i	0.750965	−	0.175100i	0.165962	−	0.986132i	$-0.446927\pi$
$17$	12.7664	−	2.97671i	0.750965	−	0.175100i	0.585002	+	0.811032i	$0.301094\pi$
$18$	−23.0458	+	15.3987i	−1.28032	+	0.855486i
$19$	−13.7911	+	7.37152i	−0.725850	+	0.387975i	−0.792557	−	0.609798i	$-0.791251\pi$
$19$	−13.7911	+	7.37152i	−0.725850	+	0.387975i	0.0667073	+	0.997773i	$0.478751\pi$
$20$	3.38805	−	4.12835i	0.169403	−	0.206418i
$21$	−23.3560	−	3.85609i	−1.11219	−	0.183623i
$22$	−10.9181	−	10.9181i	−0.496276	−	0.496276i
$23$	32.9069	−	23.5807i	1.43073	−	1.02525i	0.438787	−	0.898591i	$-0.355408\pi$
$23$	32.9069	−	23.5807i	1.43073	−	1.02525i	0.991946	−	0.126658i	$-0.0404251\pi$
$24$	21.6429	−	16.6072i	0.901786	−	0.691965i
$25$	−24.1672	−	1.58400i	−0.966688	−	0.0633601i
$26$	2.75484	−	7.31944i	0.105955	−	0.281517i
$27$	0.889957	+	0.594650i	0.0329614	+	0.0220241i
$28$	33.7968	+	3.32869i	1.20703	+	0.118882i
$29$	29.1626	+	13.2134i	1.00561	+	0.455634i	0.846934	−	0.531697i	$-0.178446\pi$
$29$	29.1626	+	13.2134i	1.00561	+	0.455634i	0.158671	+	0.987331i	$0.449279\pi$
$30$	11.2897	+	3.42470i	0.376324	+	0.114157i
$31$	−3.09455	−	47.2138i	−0.0998243	−	1.52302i	−0.694755	−	0.719247i	$-0.744487\pi$
$31$	−3.09455	−	47.2138i	−0.0998243	−	1.52302i	0.594930	−	0.803777i	$-0.297180\pi$
$32$	28.1738	−	24.7078i	0.880433	−	0.772119i
$33$	7.85432	−	18.9620i	0.238010	−	0.574607i
$34$	−26.3550	−	32.1137i	−0.775148	−	0.944521i
$35$	2.48294	+	4.30059i	0.0709413	+	0.122874i
$36$	45.7740	+	26.4276i	1.27150	+	0.734101i
$37$	−24.4281	+	4.03309i	−0.660218	+	0.109002i	−0.483617	−	0.875280i	$-0.660677\pi$
$37$	−24.4281	+	4.03309i	−0.660218	+	0.109002i	−0.176602	+	0.984282i	$0.556510\pi$
$38$	40.2828	+	28.8663i	1.06007	+	0.759639i
$39$	10.3901	−	0.340138i	0.266414	−	0.00872149i
$40$	−5.57329	−	1.29951i	−0.139332	−	0.0324877i
$41$	−19.6050	+	7.37878i	−0.478170	+	0.179970i	−0.579647	−	0.814868i	$-0.696810\pi$
$41$	−19.6050	+	7.37878i	−0.478170	+	0.179970i	0.101478	+	0.994838i	$0.467643\pi$
$42$	21.7772	+	71.7899i	0.518506	+	1.70928i
$43$	59.0383	+	7.77254i	1.37298	+	0.180757i	0.780667	−	0.624948i	$-0.214880\pi$
$43$	59.0383	+	7.77254i	1.37298	+	0.180757i	0.592318	+	0.805704i	$0.298213\pi$
$44$	−9.46460	+	27.8818i	−0.215104	+	0.633677i
$45$	0.757558	+	7.69162i	0.0168346	+	0.170925i
$46$	−113.148	−	60.4791i	−2.45975	−	1.31476i
$47$	−33.6147	+	13.9237i	−0.715206	+	0.296248i	−0.710457	−	0.703741i	$-0.751512\pi$
$47$	−33.6147	+	13.9237i	−0.715206	+	0.296248i	−0.00474903	+	0.999989i	$0.501512\pi$
$48$	13.7930	+	6.80198i	0.287355	+	0.141708i
$49$	7.70580	−	15.6258i	0.157261	−	0.318894i
$50$	29.3723	+	70.9110i	0.587446	+	1.41822i
$51$	26.0316	−	48.7016i	0.510423	−	0.954934i
$52$	−14.8420	+	1.46181i	−0.285422	+	0.0281117i
$53$	−9.77212	−	3.31719i	−0.184380	−	0.0625884i	0.227723	−	0.973726i	$-0.426872\pi$
$53$	−9.77212	−	3.31719i	−0.184380	−	0.0625884i	−0.412102	+	0.911138i	$0.635205\pi$
$54$	0.442752	−	3.36304i	0.00819912	−	0.0622785i
$55$	−4.12015	+	1.24983i	−0.0749119	+	0.0227243i
$56$	−12.8185	−	34.0580i	−0.228903	−	0.608179i
$57$	−14.9586	+	64.1540i	−0.262432	+	1.12551i
$58$	−3.31982	−	101.410i	−0.0572383	−	1.74845i
$59$	23.5077	−	32.8050i	0.398436	−	0.556017i	−0.564609	−	0.825359i	$-0.690973\pi$
$59$	23.5077	−	32.8050i	0.398436	−	0.556017i	0.963045	+	0.269342i	$0.0868063\pi$
$60$	−3.66480	−	22.1973i	−0.0610799	−	0.369956i
$61$	−32.9991	+	57.1561i	−0.540968	+	0.936984i	0.457881	+	0.889014i	$0.348609\pi$
$61$	−32.9991	+	57.1561i	−0.540968	+	0.936984i	−0.998849	+	0.0479707i	$0.984725\pi$
$62$	−129.859	+	74.9739i	−2.09449	+	1.20926i
$63$	−37.9909	+	31.1783i	−0.603030	+	0.494894i
$64$	−96.2264	−	39.8583i	−1.50354	−	0.622786i
$65$	−1.43789	−	1.63960i	−0.0221214	−	0.0252247i
$66$	−64.9052	+	4.25411i	−0.983412	+	0.0644562i
$67$	−28.0650	+	92.5178i	−0.418880	+	1.38086i	0.453160	+	0.891429i	$0.350296\pi$
$67$	−28.0650	+	92.5178i	−0.418880	+	1.38086i	−0.872041	+	0.489434i	$0.837204\pi$
$68$	−32.6956	+	72.1607i	−0.480817	+	1.06119i
$69$	16.7159	−	169.719i	0.242259	−	2.45970i
$70$	8.74333	−	13.0853i	0.124905	−	0.186933i
$71$	27.1959	+	10.2358i	0.383041	+	0.144167i	0.536316	−	0.844017i	$-0.319815\pi$
$71$	27.1959	+	10.2358i	0.383041	+	0.144167i	−0.153275	+	0.988184i	$0.548982\pi$
$72$	3.70427	−	56.5163i	0.0514482	−	0.784948i
$73$	64.4618	+	84.0083i	0.883038	+	1.15080i	0.987711	+	0.156291i	$0.0499539\pi$
$73$	64.4618	+	84.0083i	0.883038	+	1.15080i	−0.104672	+	0.994507i	$0.533379\pi$
$74$	45.7035	+	63.7791i	0.617615	+	0.861880i
$75$	−72.1426	+	72.1426i	−0.961901	+	0.961901i
$76$	15.3944	−	93.2424i	0.202558	−	1.22687i
$77$	−21.1638	−	17.3687i	−0.274855	−	0.225567i
$78$	−15.5304	−	29.0553i	−0.199107	−	0.372503i
$79$	33.3573	+	49.9228i	0.422245	+	0.631934i	0.980217	−	0.197926i	$-0.0634205\pi$
$79$	33.3573	+	49.9228i	0.422245	+	0.631934i	−0.557972	+	0.829859i	$0.688421\pi$
$80$	−0.732589	−	3.14190i	−0.00915736	−	0.0392738i
$81$	80.3864	−	21.5395i	0.992425	−	0.265920i
$82$	48.4525	+	45.3807i	0.590885	+	0.553424i
$83$	113.681	+	70.6911i	1.36964	+	0.851700i	0.997084	−	0.0763080i	$-0.0243132\pi$
$83$	113.681	+	70.6911i	1.36964	+	0.851700i	0.372561	+	0.928008i	$0.378480\pi$
$84$	104.415	−	97.7953i	1.24304	−	1.16423i
$85$	−11.3618	+	2.26000i	−0.133668	+	0.0265882i
$86$	−60.6604	−	178.700i	−0.705354	−	2.07791i
$87$	122.850	−	55.6626i	1.41207	−	0.639800i
$88$	31.2815	−	4.11829i	0.355472	−	0.0467987i
$89$	−12.5007	+	62.8450i	−0.140457	+	0.706124i	0.844805	+	0.535074i	$0.179716\pi$
$89$	−12.5007	+	62.8450i	−0.140457	+	0.706124i	−0.985262	+	0.171050i	$0.945284\pi$
$90$	20.8001	−	12.9343i	0.231112	−	0.143715i
$91$	3.58913	−	13.3948i	0.0394410	−	0.147196i
$92$	−8.00501	+	244.528i	−0.0870110	+	2.65791i
$93$	−158.130	−	121.338i	−1.70033	−	1.30471i
$94$	86.6922	+	76.0270i	0.922257	+	0.808798i
$95$	12.3940	−	6.11202i	0.130463	−	0.0643371i
$96$		−	157.859i		−	1.64437i
$97$	96.4087	+	10.6938i	0.993904	+	0.110245i
$97$	96.4087	+	10.6938i	0.993904	+	0.110245i
$98$	−55.2144			−0.563413
$99$	−18.8465	−	38.2170i	−0.190369	−	0.386030i
$100$	96.5058	−	110.044i	0.965058	−	1.10044i
$101$	−46.4517	+	60.5371i	−0.459918	+	0.599377i	−0.964531	−	0.263969i	$-0.914968\pi$
$101$	−46.4517	+	60.5371i	−0.459918	+	0.599377i	0.504613	+	0.863345i	$0.331635\pi$
$102$	−174.913	−	5.72606i	−1.71483	−	0.0561378i
$103$	−77.5406	−	20.7769i	−0.752821	−	0.201718i	−0.138052	−	0.990425i	$-0.544084\pi$
$103$	−77.5406	−	20.7769i	−0.752821	−	0.201718i	−0.614769	+	0.788707i	$0.710751\pi$
$104$	8.43905	+	13.5711i	0.0811447	+	0.130491i
$105$	20.5173	+	4.08114i	0.195403	+	0.0388680i
$106$	4.26883	+	32.4250i	0.0402720	+	0.305896i
$107$	−1.80444	−	3.98248i	−0.0168639	−	0.0372194i	0.902242	−	0.431231i	$-0.141920\pi$
$107$	−1.80444	−	3.98248i	−0.0168639	−	0.0372194i	−0.919106	+	0.394011i	$0.871087\pi$
$108$	−6.12524	+	2.07924i	−0.0567152	+	0.0192522i
$109$	−33.6473	−	169.156i	−0.308690	−	1.55189i	−0.754218	−	0.656624i	$-0.771984\pi$
$109$	−33.6473	−	169.156i	−0.308690	−	1.55189i	0.445528	−	0.895268i	$-0.353016\pi$
$110$	9.32753	+	9.95890i	0.0847957	+	0.0905354i
$111$	−55.0767	+	88.5706i	−0.496187	+	0.797933i
$112$	14.0238	−	14.9731i	0.125213	−	0.133688i
$113$	−0.946659	−	3.53298i	−0.00837752	−	0.0312653i	0.961611	−	0.274418i	$-0.0884851\pi$
$113$	−0.946659	−	3.53298i	−0.00837752	−	0.0312653i	−0.969988	+	0.243152i	$0.921818\pi$
$114$	203.313	−	47.4059i	1.78345	−	0.415841i
$115$	−29.7463	+	19.8758i	−0.258663	+	0.172833i
$116$	−170.642	+	91.2099i	−1.47105	+	0.786292i
$117$	13.6921	−	16.6838i	0.117026	−	0.142597i
$118$	−126.192	−	20.8344i	−1.06942	−	0.176563i
$119$	−52.0880	−	52.0880i	−0.437714	−	0.437714i
$120$	−19.5959	+	14.0422i	−0.163299	+	0.117019i
$121$	−77.1633	+	59.2095i	−0.637713	+	0.489335i
$122$	208.709	+	13.6795i	1.71073	+	0.112127i
$123$	−31.0838	+	82.5876i	−0.252714	+	0.671444i
$124$	237.754	+	158.862i	1.91737	+	1.28115i
$125$	43.2858	+	4.26328i	0.346286	+	0.0341062i
$126$	141.869	+	64.2801i	1.12595	+	0.510160i
$127$	−48.0297	−	14.5697i	−0.378187	−	0.114722i	0.0954676	−	0.995433i	$-0.469565\pi$
$127$	−48.0297	−	14.5697i	−0.378187	−	0.114722i	−0.473654	+	0.880711i	$0.657065\pi$
$128$	11.7848	+	179.802i	0.0920691	+	1.40470i
$129$	188.599	−	165.397i	1.46201	−	1.28215i
$130$	−2.64481	+	6.38513i	−0.0203447	+	0.0491164i
$131$	−60.7608	−	74.0373i	−0.463823	−	0.565170i	0.487596	−	0.873069i	$-0.337874\pi$
$131$	−60.7608	−	74.0373i	−0.463823	−	0.565170i	−0.951419	+	0.307899i	$0.900374\pi$
$132$	62.0186	+	107.419i	0.469838	+	0.813783i
$133$	76.1009	+	43.9369i	0.572187	+	0.330352i
$134$	302.302	−	49.9103i	2.25599	−	0.372465i
$135$	−0.768846	−	0.550948i	−0.00569516	−	0.00408109i
$136$	84.8459	−	2.77757i	0.623867	−	0.0204233i
$137$	−155.664	−	36.2958i	−1.13623	−	0.264933i	−0.383682	−	0.923465i	$-0.625344\pi$
$137$	−155.664	−	36.2958i	−1.13623	−	0.264933i	−0.752552	+	0.658533i	$0.771177\pi$
$138$	−505.825	+	190.379i	−3.66540	+	1.37956i
$139$	65.3460	+	215.417i	0.470115	+	1.54976i	0.796568	+	0.604548i	$0.206646\pi$
$139$	65.3460	+	215.417i	0.470115	+	1.54976i	−0.326453	+	0.945213i	$0.605854\pi$
$140$	−29.7542	−	3.91722i	−0.212530	−	0.0279801i
$141$	−49.2677	+	145.138i	−0.349416	+	1.02935i
$142$	−9.02640	−	91.6466i	−0.0635662	−	0.645399i
$143$	10.6036	+	5.66776i	0.0741513	+	0.0396347i
$144$	29.4986	−	12.2187i	0.204851	−	0.0848521i
$145$	−25.3753	−	12.5137i	−0.175002	−	0.0863016i
$146$	148.423	−	300.973i	1.01660	−	2.06146i
$147$	−28.0867	−	67.8073i	−0.191066	−	0.461274i
$148$	70.5340	−	131.960i	0.476581	−	0.891621i
$149$	−108.543	+	10.6906i	−0.728480	+	0.0717490i	−0.455456	−	0.890258i	$-0.650524\pi$
$149$	−108.543	+	10.6906i	−0.728480	+	0.0717490i	−0.273024	+	0.962007i	$0.588024\pi$
$150$	306.172	+	103.931i	2.04115	+	0.692876i
$151$	−35.0565	+	266.281i	−0.232162	+	1.76345i	0.337268	+	0.941409i	$0.390497\pi$
$151$	−35.0565	+	266.281i	−0.232162	+	1.76345i	−0.569430	+	0.822040i	$0.692836\pi$
$152$	−96.9068	+	29.3964i	−0.637545	+	0.193397i
$153$	−40.3851	−	107.301i	−0.263955	−	0.701311i
$154$	−19.7025	+	84.4994i	−0.127938	+	0.548697i
$155$	1.36807	+	41.7903i	0.00882627	+	0.269615i
$156$	−36.5945	+	51.0676i	−0.234580	+	0.327357i
$157$	−38.5193	−	233.308i	−0.245346	−	1.48604i	−0.771816	−	0.635846i	$-0.780651\pi$
$157$	−38.5193	−	233.308i	−0.245346	−	1.48604i	0.526470	−	0.850194i	$-0.323515\pi$
$158$	95.1400	−	164.787i	0.602152	−	1.04296i
$159$	−37.6487	+	21.7365i	−0.236785	+	0.136708i
$160$	−25.5985	+	21.0082i	−0.159991	+	0.131301i
$161$	−210.175	−	87.0575i	−1.30544	−	0.540730i
$162$	−173.897	−	198.292i	−1.07344	−	1.22402i
$163$	−151.463	+	9.92739i	−0.929219	+	0.0609042i	−0.522491	−	0.852645i	$-0.674997\pi$
$163$	−151.463	+	9.92739i	−0.929219	+	0.0609042i	−0.406728	+	0.913549i	$0.633330\pi$
$164$	36.7486	−	121.144i	0.224077	−	0.738682i
$165$	−7.48548	+	16.5208i	−0.0453665	+	0.100126i
$166$	41.5832	−	422.201i	0.250501	−	2.54338i
$167$	−63.4765	+	94.9992i	−0.380099	+	0.568858i	−0.971357	−	0.237624i	$-0.923631\pi$
$167$	−63.4765	+	94.9992i	−0.380099	+	0.568858i	0.591259	+	0.806482i	$0.298631\pi$
$168$	−143.473	−	53.9993i	−0.854004	−	0.321424i
$169$	10.6548	−	162.561i	0.0630463	−	0.961901i
$170$	22.3491	+	29.1260i	0.131466	+	0.171329i
$171$	79.6627	+	111.169i	0.465864	+	0.650112i
$172$	−254.468	+	254.468i	−1.47947	+	1.47947i
$173$	49.7400	−	301.271i	0.287515	−	1.74145i	−0.320250	−	0.947333i	$-0.603767\pi$
$173$	49.7400	−	301.271i	0.287515	−	1.74145i	0.607765	−	0.794117i	$-0.292066\pi$
$174$	−330.406	−	271.157i	−1.89888	−	1.55837i
$175$	64.1553	+	120.026i	0.366602	+	0.685863i
$176$	9.88187	+	14.7893i	0.0561470	+	0.0840299i
$177$	−38.6058	−	165.571i	−0.218112	−	0.935430i
$178$	196.147	−	52.5574i	1.10195	−	0.295266i
$179$	184.927	+	173.203i	1.03311	+	0.967613i	0.999494	−	0.0318220i	$-0.0101310\pi$
$179$	184.927	+	173.203i	1.03311	+	0.967613i	0.0336161	+	0.999435i	$0.489298\pi$
$180$	−39.6650	−	24.6653i	−0.220361	−	0.137030i
$181$	−38.9048	+	36.4383i	−0.214943	+	0.201316i	−0.783612	−	0.621250i	$-0.786625\pi$
$181$	−38.9048	+	36.4383i	−0.214943	+	0.201316i	0.568669	+	0.822566i	$0.307459\pi$
$182$	−43.1031	+	8.57373i	−0.236830	+	0.0471084i
$183$	89.3676	+	263.268i	0.488347	+	1.43863i
$184$	238.798	−	108.198i	1.29781	−	0.588032i
$185$	21.6923	−	2.85585i	0.117256	−	0.0154370i
$186$	−123.232	+	619.532i	−0.662540	+	3.33081i
$187$	54.2370	−	33.7267i	0.290037	−	0.180357i
$188$	56.9106	−	212.393i	0.302716	−	1.12975i
$189$	0.196794	−	6.01144i	0.00104124	−	0.0318065i
$190$	−34.7445	−	26.6604i	−0.182866	−	0.140318i
$191$	−31.5958	−	27.7088i	−0.165423	−	0.145072i	0.572632	−	0.819812i	$-0.305922\pi$
$191$	−31.5958	−	27.7088i	−0.165423	−	0.145072i	−0.738055	+	0.674740i	$0.764256\pi$
$192$	−393.513	+	194.059i	−2.04955	+	1.01072i
$193$			153.058i			0.793046i	0.918025	+	0.396523i	$0.129783\pi$
$193$			153.058i			0.793046i	−0.918025	+	0.396523i	$0.870217\pi$
$194$	−104.739	−	289.013i	−0.539889	−	1.48976i
$195$	−9.18676			−0.0471116
$196$	46.5694	+	94.4334i	0.237599	+	0.481803i
$197$	99.1400	−	113.047i	0.503249	−	0.573845i	−0.443314	−	0.896367i	$-0.646197\pi$
$197$	99.1400	−	113.047i	0.503249	−	0.573845i	0.946562	+	0.322522i	$0.104531\pi$
$198$	−82.2079	+	107.135i	−0.415191	+	0.541088i
$199$	−23.2323	−	0.760545i	−0.116745	−	0.00382184i	−0.0257093	−	0.999669i	$-0.508184\pi$
$199$	−23.2323	−	0.760545i	−0.116745	−	0.00382184i	−0.0910357	+	0.995848i	$0.529018\pi$
$200$	−151.496	−	40.5931i	−0.757478	−	0.202966i
$201$	215.070	+	345.860i	1.07000	+	1.72070i
$202$	237.175	+	47.1771i	1.17414	+	0.233550i
$203$	−23.4833	−	178.373i	−0.115681	−	0.878685i
$204$	137.733	+	303.983i	0.675162	+	1.49012i
$205$	17.5291	−	5.95033i	0.0855079	−	0.0290260i
$206$	49.6320	+	249.517i	0.240932	+	1.21125i
$207$	−242.036	−	258.420i	−1.16926	−	1.24840i
$208$	−4.75746	+	7.65061i	−0.0228724	+	0.0367818i
$209$	−52.0820	+	55.6074i	−0.249196	+	0.266064i
$210$	−17.1587	−	64.0370i	−0.0817079	−	0.304938i
$211$	186.147	−	43.4034i	0.882213	−	0.205703i	0.238659	−	0.971104i	$-0.423292\pi$
$211$	186.147	−	43.4034i	0.882213	−	0.205703i	0.643555	+	0.765400i	$0.277459\pi$
$212$	51.8561	−	34.6491i	0.244604	−	0.163439i
$213$	107.957	−	57.7042i	0.506840	−	0.270912i
$214$	−8.79021	+	10.7109i	−0.0410758	+	0.0500510i
$215$	−51.9199	−	8.57202i	−0.241488	−	0.0398698i
$216$	4.90125	+	4.90125i	0.0226910	+	0.0226910i
$217$	−216.121	+	154.870i	−0.995948	+	0.713686i
$218$	−433.632	+	332.738i	−1.98914	+	1.52632i
$219$	445.117	+	29.1745i	2.03250	+	0.133217i
$220$	9.16563	−	24.3525i	0.0416620	−	0.110693i
$221$	26.8977	+	17.9725i	0.121709	+	0.0813235i
$222$	328.945	+	32.3982i	1.48173	+	0.145938i
$223$	130.285	+	59.0316i	0.584240	+	0.264715i	0.683027	−	0.730393i	$-0.260663\pi$
$223$	130.285	+	59.0316i	0.584240	+	0.264715i	−0.0987876	+	0.995109i	$0.531496\pi$
$224$	−201.509	−	61.1271i	−0.899593	−	0.272889i
$225$	13.8536	+	211.364i	0.0615714	+	0.939397i
$226$	−8.71493	+	7.64279i	−0.0385616	+	0.0338176i
$227$	−86.4778	+	208.776i	−0.380960	+	0.919718i	0.610821	+	0.791769i	$0.290839\pi$
$227$	−86.4778	+	208.776i	−0.380960	+	0.919718i	−0.991781	+	0.127949i	$0.959161\pi$
$228$	−252.558	−	307.743i	−1.10771	−	1.34975i
$229$	−85.8729	−	148.736i	−0.374991	−	0.649503i	0.615335	−	0.788266i	$-0.289021\pi$
$229$	−85.8729	−	148.736i	−0.374991	−	0.649503i	−0.990326	+	0.138763i	$0.955687\pi$
$230$	98.1879	+	56.6888i	0.426904	+	0.246473i
$231$	−113.794	+	18.7874i	−0.492613	+	0.0813307i
$232$	168.531	+	120.768i	0.726427	+	0.520550i
$233$	196.657	−	6.43789i	0.844022	−	0.0276304i	0.392351	−	0.919815i	$-0.371662\pi$
$233$	196.657	−	6.43789i	0.844022	−	0.0276304i	0.451670	+	0.892185i	$0.350828\pi$
$234$	−66.6124	−	15.5318i	−0.284668	−	0.0663754i
$235$	30.0922	−	11.3259i	0.128052	−	0.0481954i
$236$	70.8008	+	233.399i	0.300003	+	0.988979i
$237$	250.767	+	33.0141i	1.05809	+	0.139300i
$238$	−75.0400	+	221.061i	−0.315294	+	0.928827i
$239$	−33.0836	−	335.903i	−0.138425	−	1.40545i	−0.773888	−	0.633322i	$-0.781691\pi$
$239$	−33.0836	−	335.903i	−0.138425	−	1.40545i	0.635463	−	0.772131i	$-0.280809\pi$
$240$	−11.9858	−	6.40655i	−0.0499409	−	0.0266940i
$241$	−49.2331	+	20.3930i	−0.204287	+	0.0846183i	−0.482481	−	0.875907i	$-0.660264\pi$
$241$	−49.2331	+	20.3930i	−0.204287	+	0.0846183i	0.278194	+	0.960525i	$0.410264\pi$
$242$	276.450	+	136.330i	1.14235	+	0.563346i
$243$	150.797	−	305.787i	0.620565	−	1.25838i
$244$	−152.635	−	368.494i	−0.625553	−	1.51022i
$245$	−7.25783	+	13.5784i	−0.0296238	+	0.0554222i
$246$	278.309	−	27.4111i	1.13134	−	0.111427i
$247$	−36.5421	−	12.4044i	−0.147944	−	0.0502201i
$248$	39.9941	−	303.785i	0.161267	−	1.22494i
$249$	539.646	−	163.700i	2.16725	−	0.657429i
$250$	−48.5550	−	129.007i	−0.194220	−	0.516030i
$251$	50.2128	−	215.351i	0.200051	−	0.857972i	−0.774278	−	0.632845i	$-0.781887\pi$
$251$	50.2128	−	215.351i	0.200051	−	0.857972i	0.974329	−	0.225127i	$-0.0722797\pi$
$252$	−9.71802	−	296.855i	−0.0385636	−	1.17800i
$253$	114.889	−	160.327i	0.454105	−	0.633703i
$254$	25.9105	+	156.937i	0.102010	+	0.617863i
$255$	−24.4001	+	42.2623i	−0.0956868	+	0.165734i
$256$	133.732	−	77.2102i	0.522391	−	0.301602i
$257$	−59.0110	+	48.4291i	−0.229615	+	0.188440i	−0.742165	−	0.670217i	$-0.766201\pi$
$257$	−59.0110	+	48.4291i	−0.229615	+	0.188440i	0.512550	+	0.858657i	$0.328701\pi$
$258$	−734.465	−	304.225i	−2.84676	−	1.17917i
$259$	91.7341	+	104.603i	0.354186	+	0.403871i
$260$	13.1512	−	0.861975i	0.0505815	−	0.00331529i
$261$	81.2834	−	267.955i	0.311431	−	1.02665i
$262$	−125.270	+	276.477i	−0.478131	+	1.05526i
$263$	−7.10208	+	72.1086i	−0.0270041	+	0.274177i	0.972195	+	0.234171i	$0.0752377\pi$
$263$	−7.10208	+	72.1086i	−0.0270041	+	0.274177i	−0.999199	+	0.0400059i	$0.987262\pi$
$264$	73.8426	−	110.513i	0.279707	−	0.418611i
$265$	8.53515	+	3.21240i	0.0322081	+	0.0121223i
$266$	18.2137	−	277.887i	0.0684726	−	1.04469i
$267$	164.321	+	214.147i	0.615435	+	0.802050i
$268$	−340.332	−	474.933i	−1.26990	−	1.77214i
$269$	−218.106	+	218.106i	−0.810803	+	0.810803i	−0.984754	−	0.173951i	$-0.944347\pi$
$269$	−218.106	+	218.106i	−0.810803	+	0.810803i	0.173951	+	0.984754i	$0.444347\pi$
$270$	−0.488293	+	2.95755i	−0.00180849	+	0.0109539i
$271$	−188.853	−	154.987i	−0.696873	−	0.571909i	0.217854	−	0.975981i	$-0.430094\pi$
$271$	−188.853	−	154.987i	−0.696873	−	0.571909i	−0.914727	+	0.404073i	$0.867594\pi$
$272$	22.5596	+	42.2060i	0.0829396	+	0.155169i
$273$	−32.4550	−	48.5723i	−0.118883	−	0.177921i
$274$	115.026	+	493.321i	0.419804	+	1.80044i
$275$	−113.978	+	30.5403i	−0.414465	+	0.111056i
$276$	752.233	+	704.543i	2.72548	+	2.55269i
$277$	54.0033	+	33.5814i	0.194958	+	0.121232i	0.622056	−	0.782973i	$-0.286298\pi$
$277$	54.0033	+	33.5814i	0.194958	+	0.121232i	−0.427098	+	0.904205i	$0.640464\pi$
$278$	520.688	−	487.678i	1.87298	−	1.75424i
$279$	−405.862	+	80.7310i	−1.45470	+	0.289359i
$280$	10.3370	+	30.4519i	0.0369179	+	0.108757i
$281$	−302.064	+	136.863i	−1.07496	+	0.487058i	−0.870678	−	0.491854i	$-0.836319\pi$
$281$	−302.064	+	136.863i	−1.07496	+	0.487058i	−0.204282	+	0.978912i	$0.565486\pi$
$282$	481.584	−	63.4018i	1.70775	−	0.224829i
$283$	−83.2224	+	418.387i	−0.294072	+	1.47840i	0.497575	+	0.867421i	$0.334224\pi$
$283$	−83.2224	+	418.387i	−0.294072	+	1.47840i	−0.791647	+	0.610979i	$0.790776\pi$
$284$	−149.130	+	92.7352i	−0.525107	+	0.326532i
$285$	15.0669	−	56.2305i	0.0528664	−	0.197300i
$286$	1.24671	−	38.0832i	0.00435914	−	0.133158i
$287$	93.3875	+	71.6588i	0.325392	+	0.249682i
$288$	−246.406	−	216.092i	−0.855577	−	0.750321i
$289$	−105.076	+	51.8178i	−0.363585	+	0.179300i
$290$			89.6647i			0.309189i
$291$	301.650	−	275.643i	1.03660	−	0.947225i
$292$	−639.939			−2.19157
$293$	31.0258	+	62.9140i	0.105890	+	0.214724i	0.943369	−	0.331746i	$-0.107638\pi$
$293$	31.0258	+	62.9140i	0.105890	+	0.214724i	−0.837479	+	0.546470i	$0.815971\pi$
$294$	−153.361	+	174.875i	−0.521636	+	0.594812i
$295$	−21.7113	+	28.2948i	−0.0735978	+	0.0959145i
$296$	−160.249	−	5.24601i	−0.541382	−	0.0177230i
$297$	5.03716	+	1.34970i	0.0169602	+	0.00454446i
$298$	182.528	+	293.530i	0.612512	+	0.984999i
$299$	97.9843	+	19.4903i	0.327707	+	0.0651849i
$300$	−80.4799	−	611.305i	−0.268266	−	2.03768i
$301$	−138.101	−	304.795i	−0.458806	−	1.01261i
$302$	805.991	−	273.597i	2.66884	−	0.905950i
$303$	62.7104	+	315.266i	0.206965	+	1.04048i
$304$	−39.0254	−	41.6670i	−0.128373	−	0.137063i
$305$	30.7985	−	49.5280i	0.100979	−	0.162387i
$306$	−248.375	+	265.187i	−0.811683	+	0.866625i
$307$	−146.031	−	544.994i	−0.475670	−	1.77522i	−0.618830	−	0.785525i	$-0.712393\pi$
$307$	−146.031	−	544.994i	−0.475670	−	1.77522i	0.143160	−	0.989700i	$-0.454274\pi$
$308$	161.137	−	37.5719i	0.523172	−	0.121987i
$309$	−281.178	+	187.877i	−0.909960	+	0.608016i
$310$	116.863	−	62.4648i	0.376979	−	0.201499i
$311$	186.992	−	227.850i	0.601261	−	0.732638i	−0.380072	−	0.924957i	$-0.624101\pi$
$311$	186.992	−	227.850i	0.601261	−	0.732638i	0.981332	+	0.192319i	$0.0616008\pi$
$312$	66.4222	+	10.9664i	0.212892	+	0.0351486i
$313$	181.995	+	181.995i	0.581454	+	0.581454i	0.935303	−	0.353849i	$-0.115127\pi$
$313$	181.995	+	181.995i	0.581454	+	0.581454i	−0.353849	+	0.935303i	$0.615127\pi$
$314$	−609.143	+	436.506i	−1.93995	+	1.39015i
$315$	34.4563	−	26.4393i	0.109385	−	0.0839342i
$316$	−362.080	−	23.7320i	−1.14582	−	0.0751011i
$317$	86.9844	−	231.112i	0.274399	−	0.729060i	−0.724797	−	0.688962i	$-0.758066\pi$
$317$	86.9844	−	231.112i	0.274399	−	0.729060i	0.999196	−	0.0400975i	$-0.0127668\pi$
$318$	114.553	+	76.5420i	0.360230	+	0.240698i
$319$	155.237	+	15.2895i	0.486637	+	0.0479296i
$320$	83.8380	+	37.9865i	0.261994	+	0.118708i
$321$	−17.6252	−	5.34655i	−0.0549072	−	0.0166559i
$322$	47.1526	+	719.410i	0.146437	+	2.23419i
$323$	−154.120	+	135.160i	−0.477153	+	0.418452i
$324$	−192.469	+	464.662i	−0.594041	+	1.43414i
$325$	−37.9158	−	46.2006i	−0.116664	−	0.142156i
$326$	240.518	+	416.589i	0.737785	+	1.27788i
$327$	−629.207	−	363.273i	−1.92418	−	1.11093i
$328$	−133.842	+	22.0974i	−0.408055	+	0.0673702i
$329$	166.192	+	119.092i	0.505144	+	0.361981i
$330$	57.4495	−	1.88070i	0.174089	−	0.00569909i
$331$	−48.3246	−	11.2677i	−0.145996	−	0.0340414i	0.153440	−	0.988158i	$-0.450965\pi$
$331$	−48.3246	−	11.2677i	−0.145996	−	0.0340414i	−0.299435	+	0.954117i	$0.596798\pi$
$332$	−757.164	+	284.976i	−2.28062	+	0.858363i
$333$	62.8577	+	207.214i	0.188762	+	0.622265i
$334$	358.991	+	47.2620i	1.07482	+	0.141503i
$335$	27.4630	−	80.9034i	0.0819791	−	0.241503i
$336$	−8.47071	−	86.0046i	−0.0252105	−	0.255966i
$337$	−67.8029	−	36.2414i	−0.201196	−	0.107541i	0.367722	−	0.929936i	$-0.380138\pi$
$337$	−67.8029	−	36.2414i	−0.201196	−	0.107541i	−0.568918	+	0.822394i	$0.692638\pi$
$338$	−476.984	+	197.573i	−1.41120	+	0.584537i
$339$	−13.8190	−	6.81479i	−0.0407641	−	0.0201026i
$340$	30.9643	−	62.7894i	0.0910715	−	0.184675i
$341$	−88.2184	−	212.978i	−0.258705	−	0.624569i
$342$	204.316	−	382.249i	0.597416	−	1.11769i
$343$	−371.456	+	36.5853i	−1.08296	+	0.106663i
$344$	365.159	+	123.955i	1.06151	+	0.360334i
$345$	−19.6713	+	149.418i	−0.0570183	+	0.433097i
$346$	−926.025	+	280.907i	−2.67637	+	0.811869i
$347$	−109.824	−	291.796i	−0.316496	−	0.840910i	−0.994392	−	0.105753i	$-0.966275\pi$
$347$	−109.824	−	291.796i	−0.316496	−	0.840910i	0.677896	−	0.735158i	$-0.262892\pi$
$348$	−185.087	+	793.796i	−0.531860	+	2.28102i
$349$	1.59392	+	48.6893i	0.00456711	+	0.139511i	0.999311	+	0.0371161i	$0.0118171\pi$
$349$	1.59392	+	48.6893i	0.00456711	+	0.139511i	−0.994744	+	0.102395i	$0.967350\pi$
$350$	251.227	−	350.587i	0.717791	−	1.00168i
$351$	0.430265	+	2.60608i	0.00122583	+	0.00742472i
$352$	91.2874	−	158.114i	0.259339	−	0.449189i
$353$	−154.753	+	89.3467i	−0.438394	+	0.253107i	−0.702916	−	0.711273i	$-0.748119\pi$
$353$	−154.753	+	89.3467i	−0.438394	+	0.253107i	0.264522	+	0.964380i	$0.414786\pi$
$354$	−416.492	+	341.806i	−1.17653	+	0.965554i
$355$	−23.7244	−	9.82698i	−0.0668294	−	0.0276816i
$356$	−255.325	−	291.142i	−0.717205	−	0.817815i
$357$	−309.650	+	20.2955i	−0.867367	+	0.0568502i
$358$	233.089	−	768.393i	0.651088	−	2.14635i
$359$	190.521	−	420.490i	0.530700	−	1.17128i	−0.432288	−	0.901736i	$-0.642294\pi$
$359$	190.521	−	420.490i	0.530700	−	1.17128i	0.962988	−	0.269544i	$-0.0868731\pi$
$360$	−4.90586	+	49.8100i	−0.0136274	+	0.138361i
$361$	−64.7045	+	96.8372i	−0.179237	+	0.268247i
$362$	158.101	+	59.5049i	0.436742	+	0.164378i
$363$	−26.7974	+	408.849i	−0.0738219	+	1.12630i
$364$	51.0180	+	66.4879i	0.140159	+	0.182659i
$365$	−54.5059	−	76.0628i	−0.149331	−	0.208391i
$366$	623.027	−	623.027i	1.70226	−	1.70226i
$367$	9.70901	−	58.8066i	0.0264551	−	0.160236i	−0.970158	−	0.242476i	$-0.922041\pi$
$367$	9.70901	−	58.8066i	0.0264551	−	0.160236i	0.996613	+	0.0822396i	$0.0262073\pi$
$368$	114.247	+	93.7598i	0.310453	+	0.254782i
$369$	86.3626	+	161.573i	0.234045	+	0.437867i
$370$	−38.5228	−	57.6534i	−0.104116	−	0.155820i
$371$	13.1683	+	56.4759i	0.0354942	+	0.152226i
$372$	1163.52	−	311.765i	3.12775	−	0.838079i
$373$	103.290	+	96.7419i	0.276918	+	0.259362i	0.809638	−	0.586930i	$-0.199664\pi$
$373$	103.290	+	96.7419i	0.276918	+	0.259362i	−0.532720	+	0.846291i	$0.678830\pi$
$374$	−171.884	−	106.885i	−0.459584	−	0.285788i
$375$	133.731	−	125.253i	0.356617	−	0.334008i
$376$	−231.093	+	45.9672i	−0.614609	+	0.122253i
$377$	25.3966	+	74.8161i	0.0673651	+	0.198451i
$378$	−17.3622	+	7.86672i	−0.0459318	+	0.0208114i
$379$	415.766	−	54.7366i	1.09701	−	0.144424i	0.439772	−	0.898109i	$-0.355059\pi$
$379$	415.766	−	54.7366i	1.09701	−	0.144424i	0.657235	+	0.753686i	$0.271726\pi$
$380$	−16.2929	+	81.9098i	−0.0428760	+	0.215552i
$381$	−179.550	+	111.651i	−0.471260	+	0.293048i
$382$	−34.4700	+	128.644i	−0.0902355	+	0.336764i
$383$	23.7777	−	726.334i	0.0620828	−	1.89643i	−0.284891	−	0.958560i	$-0.591957\pi$
$383$	23.7777	−	726.334i	0.0620828	−	1.89643i	0.346974	−	0.937875i	$-0.387209\pi$
$384$	602.201	+	462.085i	1.56823	+	1.20335i
$385$	18.1904	+	15.9526i	0.0472478	+	0.0414352i
$386$	435.038	−	214.537i	1.12704	−	0.555795i
$387$		−	520.800i		−	1.34574i
$388$	−405.960	+	422.896i	−1.04629	+	1.08994i
$389$	192.225			0.494151			0.247075	−	0.968996i	$-0.420530\pi$
$389$	192.225			0.494151			0.247075	+	0.968996i	$0.420530\pi$
$390$	12.8768	+	26.1116i	0.0330175	+	0.0669529i
$391$	349.909	−	398.995i	0.894909	−	1.02045i
$392$	68.6844	−	89.5112i	0.175215	−	0.228345i
$393$	−403.257	−	13.2013i	−1.02610	−	0.0335910i
$394$	−460.278	−	123.331i	−1.16822	−	0.313023i
$395$	−28.0189	−	45.0580i	−0.0709338	−	0.114071i
$396$	252.570	+	50.2394i	0.637804	+	0.126867i
$397$	22.0924	+	167.808i	0.0556483	+	0.422691i	0.996481	+	0.0838195i	$0.0267119\pi$
$397$	22.0924	+	167.808i	0.0556483	+	0.422691i	−0.940833	+	0.338872i	$0.889955\pi$
$398$	30.4023	+	67.0993i	0.0763877	+	0.168591i
$399$	350.531	−	118.989i	0.878523	−	0.298218i
$400$	−17.2494	−	86.7184i	−0.0431234	−	0.216796i
$401$	−352.877	−	376.763i	−0.879993	−	0.939559i	0.118581	−	0.992944i	$-0.462166\pi$
$401$	−352.877	−	376.763i	−0.879993	−	0.939559i	−0.998574	+	0.0533852i	$0.982999\pi$
$402$	681.585	−	1096.08i	1.69549	−	2.72656i
$403$	79.8181	−	85.2209i	0.198060	−	0.211466i
$404$	−119.353	−	445.432i	−0.295429	−	1.10255i
$405$	−71.6229	+	16.7001i	−0.176847	+	0.0412348i
$406$	−474.076	+	316.768i	−1.16768	+	0.780216i
$407$	−106.385	+	56.8638i	−0.261387	+	0.139714i
$408$	226.867	−	276.438i	0.556046	−	0.677545i
$409$	114.584	+	18.9179i	0.280157	+	0.0462541i	0.301324	−	0.953522i	$-0.402571\pi$
$409$	114.584	+	18.9179i	0.280157	+	0.0462541i	−0.0211669	+	0.999776i	$0.506738\pi$
$410$	−41.4828	−	41.4828i	−0.101178	−	0.101178i
$411$	−547.321	+	392.205i	−1.33168	+	0.954269i
$412$	384.889	−	295.335i	0.934196	−	0.716833i
$413$	−226.302	−	14.8326i	−0.547947	−	0.0359144i
$414$	−395.253	+	1050.16i	−0.954718	+	2.53662i
$415$	−98.3626	−	65.7238i	−0.237018	−	0.158371i
$416$	92.0300	+	9.06416i	0.221226	+	0.0217889i
$417$	863.769	+	391.369i	2.07139	+	0.938534i
$418$	231.055	+	70.0899i	0.552764	+	0.167679i
$419$	−6.54964	−	99.9282i	−0.0156316	−	0.238492i	−0.998524	−	0.0543116i	$-0.982704\pi$
$419$	−6.54964	−	99.9282i	−0.0156316	−	0.238492i	0.982892	−	0.184181i	$-0.0589631\pi$
$420$	−95.0505	+	83.3571i	−0.226311	+	0.198469i
$421$	−165.194	+	398.815i	−0.392386	+	0.947304i	0.597033	+	0.802217i	$0.296346\pi$
$421$	−165.194	+	398.815i	−0.392386	+	0.947304i	−0.989419	+	0.145087i	$0.953654\pi$
$422$	−384.283	−	468.250i	−0.910624	−	1.10960i
$423$	159.107	+	275.581i	0.376139	+	0.651492i
$424$	−57.8762	−	33.4149i	−0.136501	−	0.0788086i
$425$	−313.243	+	51.7167i	−0.737043	+	0.121686i
$426$	−315.334	−	225.965i	−0.740220	−	0.530434i
$427$	370.670	−	12.1345i	0.868080	−	0.0284180i
$428$	25.7328	+	6.00005i	0.0601234	+	0.0140188i
$429$	47.4030	−	17.8412i	0.110497	−	0.0415880i
$430$	48.4104	+	159.588i	0.112582	+	0.371134i
$431$	747.821	+	98.4525i	1.73508	+	0.228428i	0.930726	−	0.365717i	$-0.119176\pi$
$431$	747.821	+	98.4525i	1.73508	+	0.228428i	0.804358	+	0.594145i	$0.202510\pi$
$432$	−1.25604	+	3.70016i	−0.00290749	+	0.00856519i
$433$	50.1224	+	508.901i	0.115756	+	1.17529i	0.861038	+	0.508541i	$0.169815\pi$
$433$	50.1224	+	508.901i	0.115756	+	1.17529i	−0.745281	+	0.666750i	$0.767685\pi$
$434$	743.119	+	397.206i	1.71226	+	0.915220i
$435$	−110.115	+	45.6110i	−0.253137	+	0.104853i
$436$	934.820	+	461.002i	2.14408	+	1.05734i
$437$	−279.998	+	567.779i	−0.640727	+	1.29927i
$438$	−540.985	−	1306.05i	−1.23513	−	2.98186i
$439$	−397.678	+	744.003i	−0.905872	+	1.69477i	−0.208548	+	0.978012i	$0.566874\pi$
$439$	−397.678	+	744.003i	−0.905872	+	1.69477i	−0.697325	+	0.716755i	$0.745626\pi$
$440$	−27.7480	+	2.73294i	−0.0630636	+	0.00621122i
$441$	−144.290	−	48.9797i	−0.327187	−	0.111065i
$442$	13.3816	−	101.643i	0.0302751	−	0.229962i
$443$	121.813	−	36.9514i	0.274972	−	0.0834118i	−0.149787	−	0.988718i	$-0.547859\pi$
$443$	121.813	−	36.9514i	0.274972	−	0.0834118i	0.424759	+	0.905306i	$0.360359\pi$
$444$	−222.030	−	589.920i	−0.500068	−	1.32865i
$445$	12.8581	−	55.1454i	0.0288946	−	0.123922i
$446$	−14.8315	−	453.055i	−0.0332544	−	1.01582i
$447$	−267.626	+	373.472i	−0.598716	+	0.835507i
$448$	95.3403	+	577.468i	0.212813	+	1.28899i
$449$	−226.819	+	392.862i	−0.505164	+	0.874970i	0.494818	+	0.868997i	$0.335235\pi$
$449$	−226.819	+	392.862i	−0.505164	+	0.874970i	−0.999982	+	0.00597362i	$0.998099\pi$
$450$	581.345	−	335.640i	1.29188	−	0.745866i
$451$	−78.8931	+	64.7459i	−0.174929	+	0.143561i
$452$	20.4219	+	8.45902i	0.0451812	+	0.0187147i
$453$	745.991	+	850.640i	1.64678	+	1.87779i
$454$	714.620	−	46.8387i	1.57405	−	0.103169i
$455$	−3.55734	+	11.7270i	−0.00781834	+	0.0257736i
$456$	−176.060	+	388.573i	−0.386096	+	0.852133i
$457$	61.9940	−	629.436i	0.135654	−	1.37732i	−0.650601	−	0.759419i	$-0.725483\pi$
$457$	61.9940	−	629.436i	0.135654	−	1.37732i	0.786256	−	0.617901i	$-0.212017\pi$
$458$	−302.389	+	452.557i	−0.660238	+	0.988116i
$459$	13.1316	+	4.94240i	0.0286092	+	0.0107678i
$460$	14.1406	−	215.744i	0.0307404	−	0.469008i
$461$	−287.163	−	374.238i	−0.622913	−	0.811796i	0.370201	−	0.928952i	$-0.379289\pi$
$461$	−287.163	−	374.238i	−0.622913	−	0.811796i	−0.993114	+	0.117156i	$0.962622\pi$
$462$	212.901	+	297.103i	0.460825	+	0.643080i
$463$	364.181	−	364.181i	0.786569	−	0.786569i	−0.194361	−	0.980930i	$-0.562263\pi$
$463$	364.181	−	364.181i	0.786569	−	0.786569i	0.980930	+	0.194361i	$0.0622634\pi$
$464$	−19.0398	+	115.322i	−0.0410340	+	0.248539i
$465$	136.158	+	111.742i	0.292812	+	0.240305i
$466$	−293.947	−	549.937i	−0.630788	−	1.18012i
$467$	447.761	+	670.122i	0.958804	+	1.43495i	0.899605	+	0.436705i	$0.143855\pi$
$467$	447.761	+	670.122i	0.958804	+	1.43495i	0.0591989	+	0.998246i	$0.481145\pi$
$468$	29.6186	+	127.027i	0.0632877	+	0.271426i
$469$	524.774	−	140.613i	1.11892	−	0.299814i
$470$	−74.3712	−	69.6563i	−0.158237	−	0.148205i
$471$	−845.922	−	526.028i	−1.79601	−	1.11683i
$472$	190.753	−	178.660i	0.404138	−	0.378517i
$473$	284.551	−	56.6006i	0.601587	−	0.119663i
$474$	−257.657	−	759.032i	−0.543580	−	1.60133i
$475$	344.970	−	156.304i	0.726252	−	0.329061i
$476$	441.372	−	58.1077i	0.927251	−	0.122075i
$477$	−17.6081	+	88.5218i	−0.0369142	+	0.185580i
$478$	−908.369	+	564.860i	−1.90035	+	1.18172i
$479$	−243.358	+	908.225i	−0.508055	+	1.89609i	−0.0690203	+	0.997615i	$0.521987\pi$
$479$	−243.358	+	908.225i	−0.508055	+	1.89609i	−0.439034	+	0.898470i	$0.644679\pi$
$480$	−4.56436	+	139.427i	−0.00950908	+	0.290472i
$481$	−48.4731	−	37.1947i	−0.100776	−	0.0773279i
$482$	126.972	+	111.351i	0.263427	+	0.231019i
$483$	−859.501	+	423.859i	−1.77951	+	0.877555i
$484$		−	587.797i		−	1.21446i
$485$	−84.8423	−	12.2327i	−0.174933	−	0.0252220i
$486$	−1080.51			−2.22327
$487$	32.3517	+	65.6027i	0.0664305	+	0.134708i	0.927555	−	0.373686i	$-0.121906\pi$
$487$	32.3517	+	65.6027i	0.0664305	+	0.134708i	−0.861125	+	0.508394i	$0.830240\pi$
$488$	−281.802	+	321.333i	−0.577463	+	0.658470i
$489$	−389.254	+	507.285i	−0.796020	+	1.03739i
$490$	48.7673	+	1.59648i	0.0995251	+	0.00325811i
$491$	720.334	+	193.013i	1.46708	+	0.393102i	0.901927	−	0.431888i	$-0.142152\pi$
$491$	720.334	+	193.013i	1.46708	+	0.393102i	0.565148	+	0.824990i	$0.308819\pi$
$492$	−281.615	−	452.874i	−0.572388	−	0.920475i
$493$	411.633	+	81.8790i	0.834956	+	0.166083i
$494$	15.9630	+	121.251i	0.0323137	+	0.245447i
$495$	15.5409	+	34.2995i	0.0313957	+	0.0692918i
$496$	163.568	−	55.5237i	0.329774	−	0.111943i
$497$	−31.8564	−	160.153i	−0.0640973	−	0.322239i
$498$	−1221.69	−	1304.39i	−2.45320	−	2.61925i
$499$	348.219	−	559.982i	0.697834	−	1.12221i	−0.288504	−	0.957479i	$-0.593158\pi$
$499$	348.219	−	559.982i	0.697834	−	1.12221i	0.986339	−	0.164730i	$-0.0526754\pi$
$500$	−179.689	+	191.852i	−0.359378	+	0.383704i
$501$	124.572	+	464.908i	0.248646	+	0.927959i
$502$	−682.477	+	159.131i	−1.35952	+	0.316994i
$503$	−345.626	+	230.940i	−0.687129	+	0.459125i	−0.849489	−	0.527607i	$-0.823090\pi$
$503$	−345.626	+	230.940i	−0.687129	+	0.459125i	0.162360	+	0.986732i	$0.448090\pi$
$504$	−280.687	+	150.030i	−0.556919	+	0.297680i
$505$	42.7781	−	52.1253i	0.0847091	−	0.103218i
$506$	−616.736	−	101.823i	−1.21884	−	0.201232i
$507$	−485.269	−	485.269i	−0.957137	−	0.957137i
$508$	246.557	−	176.680i	0.485348	−	0.347795i
$509$	−373.141	+	286.321i	−0.733087	+	0.562518i	−0.906436	−	0.422343i	$-0.861208\pi$
$509$	−373.141	+	286.321i	−0.733087	+	0.562518i	0.173349	+	0.984860i	$0.444541\pi$
$510$	154.324	+	10.1149i	0.302595	+	0.0198331i
$511$	209.602	−	556.899i	0.410180	−	1.08982i
$512$	192.378	+	128.543i	0.375739	+	0.251061i
$513$	−16.6570	−	1.64057i	−0.0324698	−	0.00319799i
$514$	220.365	+	99.8459i	0.428725	+	0.194253i
$515$	67.8858	+	20.5929i	0.131817	+	0.0399863i
$516$	99.1508	+	1512.75i	0.192153	+	2.93168i
$517$	−133.278	+	116.882i	−0.257791	+	0.226077i
$518$	168.732	−	407.356i	0.325738	−	0.786401i
$519$	−816.028	−	994.332i	−1.57231	−	1.91586i
$520$	−7.06126	−	12.2305i	−0.0135794	−	0.0235201i
$521$	−615.748	−	355.502i	−1.18186	−	0.682346i	−0.225415	−	0.974263i	$-0.572374\pi$
$521$	−615.748	−	355.502i	−1.18186	−	0.682346i	−0.956444	+	0.291917i	$0.905707\pi$
$522$	−875.546	+	144.553i	−1.67729	+	0.276922i
$523$	472.028	+	338.251i	0.902540	+	0.646751i	0.935737	−	0.352698i	$-0.114736\pi$
$523$	472.028	+	338.251i	0.902540	+	0.646751i	−0.0331976	+	0.999449i	$0.510569\pi$
$524$	578.516	−	18.9387i	1.10404	−	0.0361425i
$525$	558.341	+	130.187i	1.06351	+	0.247975i
$526$	214.910	−	80.8863i	0.408574	−	0.153776i
$527$	−180.048	−	593.538i	−0.341647	−	1.12626i
$528$	74.2879	+	9.78018i	0.140697	+	0.0185231i
$529$	356.770	−	1051.01i	0.674423	−	1.98679i
$530$	−2.83284	−	28.7623i	−0.00534498	−	0.0542685i
$531$	−311.291	−	166.388i	−0.586235	−	0.313349i
$532$	−490.634	+	203.227i	−0.922244	+	0.382006i
$533$	−46.3628	−	22.8636i	−0.0869845	−	0.0428960i
$534$	378.349	−	767.217i	0.708519	−	1.43674i
$535$	1.47859	+	3.56963i	0.00276372	+	0.00667221i
$536$	−295.139	+	552.166i	−0.550632	+	1.03016i
$537$	1062.21	−	104.619i	1.97804	−	0.194820i
$538$	925.639	+	314.212i	1.72052	+	0.584037i
$539$	11.0797	−	84.1590i	0.0205561	−	0.156139i
$540$	5.47014	−	1.65935i	0.0101299	−	0.00307287i
$541$	158.910	+	422.214i	0.293734	+	0.780432i	0.997544	+	0.0700440i	$0.0223140\pi$
$541$	158.910	+	422.214i	0.293734	+	0.780432i	−0.703810	+	0.710388i	$0.748519\pi$
$542$	−175.813	+	754.019i	−0.324378	+	1.39118i
$543$	7.34702	+	224.428i	0.0135304	+	0.413312i
$544$	286.131	−	399.295i	0.525976	−	0.733998i
$545$	24.8274	+	150.377i	0.0455549	+	0.275922i
$546$	−92.5664	+	160.330i	−0.169536	+	0.293644i
$547$	−323.333	+	186.676i	−0.591103	+	0.341273i	−0.765533	−	0.643396i	$-0.777525\pi$
$547$	−323.333	+	186.676i	−0.591103	+	0.341273i	0.174431	+	0.984669i	$0.444191\pi$
$548$	746.711	−	612.810i	1.36261	−	1.11827i
$549$	533.276	+	220.890i	0.971360	+	0.402350i
$550$	246.565	+	281.153i	0.448300	+	0.511188i
$551$	−499.588	+	32.7447i	−0.906693	+	0.0594278i
$552$	320.590	−	1056.84i	0.580779	−	1.91457i
$553$	139.246	−	307.322i	0.251801	−	0.555737i
$554$	19.7539	−	200.564i	0.0356568	−	0.362029i
$555$	51.2066	−	76.6361i	0.0922641	−	0.138083i
$556$	−1273.24	−	479.213i	−2.29000	−	0.861894i
$557$	−27.7774	+	423.801i	−0.0498696	+	0.760864i	0.897559	+	0.440895i	$0.145339\pi$
$557$	−27.7774	+	423.801i	−0.0498696	+	0.760864i	−0.947428	+	0.319968i	$0.896328\pi$
$558$	798.349	+	1040.43i	1.43073	+	1.86457i
$559$	85.5952	+	119.448i	0.153122	+	0.213682i
$560$	−12.8192	+	12.8192i	−0.0228915	+	0.0228915i
$561$	43.8271	−	265.457i	0.0781231	−	0.473185i
$562$	812.403	+	666.722i	1.44556	+	1.18634i
$563$	45.9525	+	85.9711i	0.0816208	+	0.152702i	0.919420	−	0.393276i	$-0.128658\pi$
$563$	45.9525	+	85.9711i	0.0816208	+	0.152702i	−0.837800	+	0.545978i	$0.816158\pi$
$564$	−514.618	−	770.180i	−0.912443	−	1.36557i
$565$	0.733969	+	3.14782i	0.00129906	+	0.00557137i
$566$	1305.84	−	349.898i	2.30713	−	0.618194i
$567$	−341.326	−	319.687i	−0.601986	−	0.563822i
$568$	159.802	+	99.3712i	0.281341	+	0.174949i
$569$	−555.369	+	520.160i	−0.976044	+	0.914165i	−0.996327	−	0.0856295i	$-0.972710\pi$
$569$	−555.369	+	520.160i	−0.976044	+	0.914165i	0.0202833	+	0.999794i	$0.493543\pi$
$570$	−180.944	+	35.9919i	−0.317445	+	0.0631437i
$571$	−93.7644	−	276.221i	−0.164211	−	0.483750i	0.833413	−	0.552651i	$-0.186384\pi$
$571$	−93.7644	−	276.221i	−0.164211	−	0.483750i	−0.997623	+	0.0689017i	$0.978051\pi$
$572$	−66.1852	+	29.9881i	−0.115708	+	0.0524268i
$573$	−175.518	+	23.1074i	−0.306314	+	0.0403270i
$574$	72.7778	−	365.879i	0.126791	−	0.637419i
$575$	−832.619	+	517.756i	−1.44803	+	0.900445i
$576$	−235.766	+	879.890i	−0.409316	+	1.52759i
$577$	8.75988	−	267.587i	0.0151818	−	0.463755i	−0.964604	−	0.263704i	$-0.915056\pi$
$577$	8.75988	−	267.587i	0.0151818	−	0.463755i	0.979785	−	0.200051i	$-0.0641108\pi$
$578$	294.565	+	226.027i	0.509627	+	0.391051i
$579$	484.764	+	425.126i	0.837243	+	0.734242i
$580$	153.354	−	75.6257i	0.264403	−	0.130389i
$581$		−	752.252i		−	1.29475i
$582$	−1206.28	−	471.022i	−2.07264	−	0.809315i
$583$	−50.2795			−0.0862426
$584$	303.292	+	615.014i	0.519335	+	1.05311i
$585$	−12.5757	+	14.3398i	−0.0214969	+	0.0245125i
$586$	135.333	−	176.370i	0.230944	−	0.300972i
$587$	240.181	+	7.86270i	0.409166	+	0.0133947i	0.236609	−	0.971605i	$-0.423964\pi$
$587$	240.181	+	7.86270i	0.409166	+	0.0133947i	0.172557	+	0.985000i	$0.444797\pi$
$588$	428.438	+	114.800i	0.728636	+	0.195237i
$589$	390.715	+	628.320i	0.663352	+	1.06676i
$590$	110.855	+	22.0504i	0.187889	+	0.0373735i
$591$	−82.6766	−	627.991i	−0.139893	−	1.06259i
$592$	−37.3036	−	82.3309i	−0.0630129	−	0.139072i
$593$	−402.051	+	136.478i	−0.677995	+	0.230148i	−0.639133	−	0.769096i	$-0.720707\pi$
$593$	−402.051	+	136.478i	−0.677995	+	0.230148i	−0.0388620	+	0.999245i	$0.512373\pi$
$594$	−3.22418	−	16.2090i	−0.00542791	−	0.0272879i
$595$	44.4998	+	47.5120i	0.0747897	+	0.0798521i
$596$	348.075	−	559.750i	0.584018	−	0.939178i
$597$	−66.9376	+	71.4686i	−0.112123	+	0.119713i
$598$	−81.9445	−	305.821i	−0.137031	−	0.511406i
$599$	−787.886	+	183.709i	−1.31534	+	0.306693i	−0.825144	−	0.564922i	$-0.808906\pi$
$599$	−787.886	+	183.709i	−1.31534	+	0.306693i	−0.490191	+	0.871615i	$0.663073\pi$
$600$	−549.354	+	367.066i	−0.915589	+	0.611777i
$601$	−509.755	+	272.469i	−0.848177	+	0.453360i	−0.837406	−	0.546582i	$-0.815929\pi$
$601$	−509.755	+	272.469i	−0.848177	+	0.453360i	−0.0107715	+	0.999942i	$0.503429\pi$
$602$	−672.750	+	819.748i	−1.11752	+	1.36171i
$603$	834.269	+	137.738i	1.38353	+	0.228422i
$604$	−1147.73	−	1147.73i	−1.90021	−	1.90021i
$605$	69.8653	−	50.0647i	0.115480	−	0.0827516i
$606$	808.186	−	620.143i	1.33364	−	1.02334i
$607$	−374.081	−	24.5186i	−0.616279	−	0.0403931i	−0.245933	−	0.969287i	$-0.579094\pi$
$607$	−374.081	−	24.5186i	−0.616279	−	0.0403931i	−0.370346	+	0.928894i	$0.620761\pi$
$608$	−206.416	+	548.433i	−0.339499	+	0.902028i
$609$	−630.168	−	421.065i	−1.03476	−	0.691404i
$610$	−183.944	−	18.1169i	−0.301547	−	0.0296998i
$611$	−81.7847	−	37.0562i	−0.133854	−	0.0606484i
$612$	663.037	+	201.130i	1.08339	+	0.328644i
$613$	2.73704	+	41.7591i	0.00446498	+	0.0681225i	0.999510	−	0.0313038i	$-0.00996593\pi$
$613$	2.73704	+	41.7591i	0.00446498	+	0.0681225i	−0.995045	+	0.0994263i	$0.968299\pi$
$614$	−1344.36	+	1178.97i	−2.18950	+	1.92014i
$615$	29.8422	−	72.0455i	0.0485239	−	0.117147i
$616$	−112.478	−	137.054i	−0.182594	−	0.222491i
$617$	124.011	+	214.793i	0.200990	+	0.348126i	0.948848	−	0.315734i	$-0.102251\pi$
$617$	124.011	+	214.793i	0.200990	+	0.348126i	−0.747857	+	0.663859i	$0.768917\pi$
$618$	928.124	+	535.853i	1.50182	+	0.867076i
$619$	−573.235	+	94.6414i	−0.926066	+	0.152894i	−0.606876	−	0.794797i	$-0.707577\pi$
$619$	−573.235	+	94.6414i	−0.926066	+	0.152894i	−0.319190	+	0.947691i	$0.603411\pi$
$620$	−205.400	−	147.187i	−0.331290	−	0.237399i
$621$	43.3080	−	1.41776i	0.0697391	−	0.00228302i
$622$	−909.724	−	212.118i	−1.46258	−	0.341025i
$623$	336.991	−	126.834i	0.540916	−	0.203586i
$624$	11.0169	+	36.3178i	0.0176552	+	0.0582015i
$625$	562.188	+	74.0135i	0.899501	+	0.118422i
$626$	262.189	−	772.384i	0.418832	−	1.23384i
$627$	31.4588	+	319.406i	0.0501735	+	0.509420i
$628$	1260.33	+	673.658i	2.00689	+	1.07270i
$629$	−299.853	+	124.203i	−0.476714	+	0.197461i
$630$	−123.445	−	60.8764i	−0.195945	−	0.0966292i
$631$	−358.439	+	726.843i	−0.568050	+	1.15189i	0.403483	+	0.914987i	$0.367799\pi$
$631$	−358.439	+	726.843i	−0.568050	+	1.15189i	−0.971533	+	0.236904i	$0.923867\pi$
$632$	148.796	+	359.225i	0.235437	+	0.568394i
$633$	379.566	−	710.119i	0.599631	−	1.12183i
$634$	−778.816	+	76.7067i	−1.22842	+	0.120988i
$635$	42.0002	+	14.2572i	0.0661421	+	0.0224522i
$636$	34.2926	−	260.478i	0.0539192	−	0.409557i
$637$	41.1435	−	12.4808i	0.0645895	−	0.0195930i
$638$	−174.134	−	462.664i	−0.272938	−	0.725178i
$639$	57.7097	−	247.504i	0.0903126	−	0.387329i
$640$	−5.20997	−	159.148i	−0.00814057	−	0.248669i
$641$	502.474	−	701.201i	0.783890	−	1.09392i	−0.209350	−	0.977841i	$-0.567135\pi$
$641$	502.474	−	701.201i	0.783890	−	1.09392i	0.993240	−	0.116077i	$-0.0370319\pi$
$642$	9.50822	+	57.5904i	0.0148103	+	0.0897047i
$643$	−297.456	+	515.210i	−0.462607	+	0.801259i	−0.999090	−	0.0426521i	$-0.986419\pi$
$643$	−297.456	+	515.210i	−0.462607	+	0.801259i	0.536483	+	0.843911i	$0.319753\pi$
$644$	1190.64	−	687.416i	1.84882	−	1.06742i
$645$	−171.360	+	140.631i	−0.265674	+	0.218033i
$646$	600.193	+	248.608i	0.929091	+	0.384842i
$647$	−353.378	−	402.950i	−0.546179	−	0.622797i	0.411231	−	0.911531i	$-0.365099\pi$
$647$	−353.378	−	402.950i	−0.546179	−	0.622797i	−0.957409	+	0.288734i	$0.906766\pi$
$648$	537.783	−	35.2482i	0.829912	−	0.0543953i
$649$	57.0788	−	188.164i	0.0879489	−	0.289929i
$650$	−78.1709	+	172.527i	−0.120263	+	0.265426i
$651$	−109.784	+	1114.66i	−0.168639	+	1.71222i
$652$	509.634	−	762.721i	0.781647	−	1.16982i
$653$	1045.88	+	393.642i	1.60166	+	0.602820i	0.983124	−	0.182940i	$-0.0585614\pi$
$653$	1045.88	+	393.642i	1.60166	+	0.602820i	0.618531	+	0.785760i	$0.287728\pi$
$654$	−150.592	+	2297.59i	−0.230263	+	3.51314i
$655$	51.5253	+	67.1491i	0.0786646	+	0.102518i
$656$	−44.5444	−	62.1616i	−0.0679030	−	0.0947586i
$657$	654.856	−	654.856i	0.996737	−	0.996737i
$658$	105.548	−	639.298i	0.160408	−	0.971577i
$659$	−592.787	−	486.488i	−0.899525	−	0.738221i	0.0661951	−	0.997807i	$-0.478914\pi$
$659$	−592.787	−	486.488i	−0.899525	−	0.738221i	−0.965720	+	0.259586i	$0.916414\pi$
$660$	−51.6710	−	96.6697i	−0.0782895	−	0.146469i
$661$	−616.140	−	922.118i	−0.932133	−	1.39504i	−0.918627	−	0.395127i	$-0.870701\pi$
$661$	−616.140	−	922.118i	−0.932133	−	1.39504i	−0.0135063	−	0.999909i	$-0.504299\pi$
$662$	35.7089	+	153.147i	0.0539410	+	0.231340i
$663$	131.632	−	35.2707i	0.198540	−	0.0531987i
$664$	632.726	+	592.613i	0.952901	+	0.892489i
$665$	−65.9445	−	41.0069i	−0.0991647	−	0.0616645i
$666$	500.861	−	469.108i	0.752044	−	0.704366i
$667$	1271.23	−	252.863i	1.90589	−	0.379106i
$668$	−221.950	−	653.845i	−0.332261	−	0.978809i
$669$	548.839	−	248.676i	0.820387	−	0.371713i
$670$	−268.447	+	35.3417i	−0.400667	+	0.0527488i
$671$	−62.7317	+	315.374i	−0.0934899	+	0.470006i
$672$	−753.303	+	468.434i	−1.12099	+	0.697074i
$673$	234.277	−	874.332i	0.348108	−	1.29916i	−0.540832	−	0.841131i	$-0.681890\pi$
$673$	234.277	−	874.332i	0.348108	−	1.29916i	0.888939	−	0.458025i	$-0.151443\pi$
$674$	−7.97188	+	243.516i	−0.0118277	+	0.361299i
$675$	−20.5658	−	15.7807i	−0.0304679	−	0.0233788i
$676$	740.212	+	649.149i	1.09499	+	0.960279i
$677$	397.668	−	196.108i	0.587398	−	0.289672i	−0.124203	−	0.992257i	$-0.539637\pi$
$677$	397.668	−	196.108i	0.587398	−	0.289672i	0.711600	+	0.702584i	$0.247971\pi$
$678$			48.8301i			0.0720208i
$679$	−235.054	−	491.794i	−0.346177	−	0.724292i
$680$	−75.0191			−0.110322
$681$	421.037	+	853.778i	0.618263	+	1.25371i
$682$	−481.696	+	549.270i	−0.706300	+	0.805381i
$683$	307.481	−	400.717i	0.450192	−	0.586701i	−0.512030	−	0.858967i	$-0.671106\pi$
$683$	307.481	−	400.717i	0.450192	−	0.586701i	0.962222	+	0.272266i	$0.0877731\pi$
$684$	−826.088	−	27.0433i	−1.20773	−	0.0395370i
$685$	136.438	+	36.5586i	0.199180	+	0.0533702i
$686$	624.647	+	1004.51i	0.910564	+	1.46431i
$687$	−709.593	−	141.147i	−1.03289	−	0.205454i
$688$	28.3755	+	215.533i	0.0412434	+	0.313275i
$689$	−10.5104	−	23.1968i	−0.0152545	−	0.0336674i
$690$	452.267	−	153.524i	0.655459	−	0.222498i
$691$	−74.8465	−	376.279i	−0.108316	−	0.544543i	−0.996394	−	0.0848489i	$-0.972959\pi$
$691$	−74.8465	−	376.279i	−0.108316	−	0.544543i	0.888078	−	0.459694i	$-0.152041\pi$
$692$	1261.47	+	1346.86i	1.82293	+	1.94633i
$693$	−126.446	+	203.341i	−0.182461	+	0.293421i
$694$	−675.437	+	721.157i	−0.973252	+	1.03913i
$695$	−51.4872	−	192.153i	−0.0740824	−	0.276479i
$696$	850.599	−	198.332i	1.22212	−	0.284960i
$697$	−228.320	+	152.559i	−0.327576	+	0.218879i
$698$	136.156	−	72.7769i	0.195066	−	0.104265i
$699$	525.836	−	640.732i	0.752268	−	0.916642i
$700$	−811.501	−	133.979i	−1.15929	−	0.191399i
$701$	880.888	+	880.888i	1.25662	+	1.25662i	0.952698	+	0.303918i	$0.0982950\pi$
$701$	880.888	+	880.888i	1.25662	+	1.25662i	0.303918	+	0.952698i	$0.401705\pi$
$702$	6.80420	−	4.87582i	0.00969259	−	0.00694561i
$703$	307.161	−	235.693i	0.436929	−	0.335267i
$704$	−506.370	−	33.1893i	−0.719276	−	0.0471438i
$705$	47.7114	−	126.766i	0.0676758	−	0.179810i
$706$	470.864	+	314.622i	0.666947	+	0.445640i
$707$	426.724	+	42.0286i	0.603570	+	0.0594464i
$708$	935.873	+	424.038i	1.32185	+	0.598924i
$709$	−612.339	−	185.751i	−0.863665	−	0.261990i	−0.172785	−	0.984960i	$-0.555277\pi$
$709$	−612.339	−	185.751i	−0.863665	−	0.261990i	−0.690880	+	0.722970i	$0.742777\pi$
$710$	5.32255	+	81.2064i	0.00749655	+	0.114375i
$711$	394.805	−	346.235i	0.555282	−	0.486969i
$712$	−158.795	+	383.364i	−0.223026	+	0.538433i
$713$	−1215.17	−	1480.68i	−1.70430	−	2.07670i
$714$	491.714	+	851.674i	0.688676	+	1.19282i
$715$	−9.20161	−	5.31255i	−0.0128694	−	0.00743014i
$716$	−1510.78	+	249.430i	−2.11002	+	0.348367i
$717$	−1155.76	−	828.207i	−1.61194	−	1.15510i
$718$	−1462.21	+	47.8678i	−2.03651	+	0.0666683i
$719$	938.220	+	218.762i	1.30490	+	0.304259i	0.821031	−	0.570884i	$-0.193399\pi$
$719$	938.220	+	218.762i	1.30490	+	0.304259i	0.483865	+	0.875143i	$0.339233\pi$
$720$	−26.4074	+	9.93906i	−0.0366770	+	0.0138042i
$721$	130.948	+	431.677i	0.181620	+	0.598720i
$722$	365.936	+	48.1764i	0.506837	+	0.0667263i
$723$	−72.1589	+	212.573i	−0.0998048	+	0.294016i
$724$	−31.5752	−	320.588i	−0.0436121	−	0.442801i
$725$	−683.848	−	365.524i	−0.943238	−	0.504171i
$726$	1199.64	−	496.906i	1.65239	−	0.684443i
$727$	−361.682	−	178.362i	−0.497499	−	0.245339i	0.176187	−	0.984357i	$-0.443624\pi$
$727$	−361.682	−	178.362i	−0.497499	−	0.245339i	−0.673686	+	0.739017i	$0.735290\pi$
$728$	39.7190	−	80.5421i	0.0545591	−	0.110635i
$729$	−263.008	−	634.959i	−0.360780	−	0.870999i
$730$	−139.795	+	261.538i	−0.191500	+	0.358271i
$731$	776.843	−	76.5124i	1.06271	−	0.104668i
$732$	−1591.04	−	540.086i	−2.17356	−	0.737823i
$733$	−49.3509	+	374.857i	−0.0673273	+	0.511402i	0.924240	+	0.381811i	$0.124700\pi$
$733$	−49.3509	+	374.857i	−0.0673273	+	0.511402i	−0.991568	+	0.129590i	$0.958634\pi$
$734$	−180.756	+	54.8316i	−0.246261	+	0.0747024i
$735$	22.8466	+	60.7018i	0.0310837	+	0.0825875i
$736$	344.485	−	1477.42i	0.468051	−	2.00736i
$737$	15.4121	+	470.791i	0.0209119	+	0.638793i
$738$	338.189	−	471.942i	0.458250	−	0.639488i
$739$	−163.512	−	990.375i	−0.221261	−	1.34016i	−0.834827	−	0.550512i	$-0.814432\pi$
$739$	−163.512	−	990.375i	−0.221261	−	1.34016i	0.613567	−	0.789643i	$-0.289734\pi$
$740$	−66.1136	+	114.512i	−0.0893426	+	0.154746i
$741$	−140.785	+	81.2820i	−0.189993	+	0.109692i
$742$	142.064	−	116.589i	0.191462	−	0.157128i
$743$	1258.26	+	521.187i	1.69348	+	0.701463i	0.999823	−	0.0188397i	$-0.00599721\pi$
$743$	1258.26	+	521.187i	1.69348	+	0.701463i	0.693660	+	0.720303i	$0.255997\pi$
$744$	−851.061	−	970.450i	−1.14390	−	1.30437i
$745$	96.1784	−	6.30387i	0.129099	−	0.00846157i
$746$	130.191	−	429.184i	0.174519	−	0.575313i
$747$	483.195	−	1066.43i	0.646847	−	1.42762i
$748$	−37.8329	+	384.124i	−0.0505787	+	0.513534i
$749$	−13.6498	+	20.4284i	−0.0182241	+	0.0272743i
$750$	−543.456	−	204.542i	−0.724608	−	0.272723i
$751$	17.5887	−	268.352i	0.0234204	−	0.357326i	−0.970024	−	0.243009i	$-0.921865\pi$
$751$	17.5887	−	268.352i	0.0234204	−	0.357326i	0.993444	−	0.114317i	$-0.0364679\pi$
$752$	−80.8613	−	105.381i	−0.107528	−	0.140134i
$753$	−542.589	−	757.183i	−0.720570	−	1.00555i
$754$	177.053	−	177.053i	0.234818	−	0.234818i
$755$	38.6624	−	234.175i	0.0512085	−	0.310165i
$756$	28.0982	+	23.0596i	0.0371670	+	0.0305022i
$757$	−17.5323	−	32.8007i	−0.0231603	−	0.0433298i	0.870075	−	0.492919i	$-0.164070\pi$
$757$	−17.5323	−	32.8007i	−0.0231603	−	0.0433298i	−0.893235	+	0.449590i	$0.851570\pi$
$758$	−738.346	−	1105.01i	−0.974071	−	1.45780i
$759$	−188.677	−	809.191i	−0.248586	−	1.06613i
$760$	86.4414	−	23.1619i	0.113739	−	0.0304762i
$761$	297.247	+	278.403i	0.390601	+	0.365838i	0.853965	−	0.520330i	$-0.174191\pi$
$761$	297.247	+	278.403i	0.390601	+	0.365838i	−0.463364	+	0.886168i	$0.653358\pi$
$762$	569.018	+	353.838i	0.746743	+	0.464355i
$763$	−707.366	+	662.521i	−0.927086	+	0.868311i
$764$	249.093	−	49.5476i	0.326037	−	0.0648529i
$765$	32.5670	+	95.9392i	0.0425712	+	0.125411i
$766$	−2097.80	+	950.500i	−2.73864	+	1.24086i
$767$	98.7426	−	12.9997i	0.128739	−	0.0169488i
$768$	126.908	−	638.011i	0.165245	−	0.830743i
$769$	20.4908	−	12.7420i	0.0266460	−	0.0165696i	−0.514680	−	0.857382i	$-0.672089\pi$
$769$	20.4908	−	12.7420i	0.0266460	−	0.0165696i	0.541326	+	0.840813i	$0.317923\pi$
$770$	19.8451	−	74.0631i	0.0257729	−	0.0961858i
$771$	−10.5220	+	321.414i	−0.0136472	+	0.416879i
$772$	−733.846	−	563.100i	−0.950578	−	0.729404i
$773$	409.590	+	359.201i	0.529870	+	0.464684i	0.881988	−	0.471272i	$-0.156205\pi$
$773$	409.590	+	359.201i	0.529870	+	0.464684i	−0.352118	+	0.935956i	$0.614538\pi$
$774$	−1480.28	+	729.991i	−1.91250	+	0.943141i
$775$			1145.93i			1.47861i
$776$	598.825	+	189.722i	0.771682	+	0.244487i
$777$	586.093			0.754303
$778$	−269.436	−	546.362i	−0.346319	−	0.702265i
$779$	215.982	−	246.280i	0.277255	−	0.316149i
$780$	33.7981	−	44.0466i	0.0433309	−	0.0564700i
$781$	141.501	+	4.63226i	0.181179	+	0.00593119i
$782$	−1624.53	−	435.291i	−2.07740	−	0.556638i
$783$	18.0961	+	29.1009i	0.0231112	+	0.0371659i
$784$	62.3830	+	12.4087i	0.0795701	+	0.0158275i
$785$	27.2757	+	207.180i	0.0347461	+	0.263923i
$786$	527.712	+	1164.69i	0.671389	+	1.48179i
$787$	−225.963	+	76.7041i	−0.287120	+	0.0974639i	−0.461284	−	0.887253i	$-0.652611\pi$
$787$	−225.963	+	76.7041i	−0.287120	+	0.0974639i	0.174164	+	0.984717i	$0.444278\pi$
$788$	177.278	+	891.235i	0.224972	+	1.13101i
$789$	208.655	+	222.779i	0.264456	+	0.282356i
$790$	−88.7956	+	142.795i	−0.112399	+	0.180753i
$791$	−14.0502	+	15.0013i	−0.0177626	+	0.0189649i
$792$	−71.4201	−	266.544i	−0.0901769	−	0.336545i
$793$	−158.614	+	36.9835i	−0.200017	+	0.0466375i
$794$	445.997	−	298.006i	0.561710	−	0.375322i
$795$	33.8812	−	18.1099i	0.0426178	−	0.0227797i
$796$	89.1180	−	108.591i	0.111957	−	0.136420i
$797$	−54.3492	−	8.97309i	−0.0681922	−	0.0112586i	0.128702	−	0.991683i	$-0.458919\pi$
$797$	−54.3492	−	8.97309i	−0.0681922	−	0.0112586i	−0.196894	+	0.980425i	$0.563086\pi$
$798$	−829.534	−	829.534i	−1.03952	−	1.03952i
$799$	−387.692	+	277.816i	−0.485221	+	0.347705i
$800$	−720.020	+	552.491i	−0.900026	+	0.690614i
$801$	559.206	+	36.6523i	0.698134	+	0.0457581i
$802$	−576.260	+	1531.09i	−0.718529	+	1.90908i
$803$	428.965	+	286.625i	0.534203	+	0.356943i
$804$	−2449.49	−	241.254i	−3.04663	−	0.300067i
$805$	183.117	+	82.9692i	0.227474	+	0.103067i
$806$	−354.103	−	107.416i	−0.439334	−	0.133271i
$807$	84.9827	+	1296.59i	0.105307	+	1.60667i
$808$	−371.517	+	325.812i	−0.459799	+	0.403233i
$809$	−257.622	+	621.955i	−0.318445	+	0.768795i	0.680892	+	0.732384i	$0.261592\pi$
$809$	−257.622	+	621.955i	−0.318445	+	0.768795i	−0.999337	+	0.0364107i	$0.988408\pi$
$810$	147.859	+	180.166i	0.182542	+	0.222428i
$811$	249.033	+	431.338i	0.307069	+	0.531860i	0.977720	−	0.209914i	$-0.0673183\pi$
$811$	249.033	+	431.338i	0.307069	+	0.531860i	−0.670650	+	0.741774i	$0.733985\pi$
$812$	941.617	+	543.643i	1.15963	+	0.669511i
$813$	−1015.42	+	167.647i	−1.24898	+	0.206208i
$814$	310.741	+	222.674i	0.381746	+	0.273555i
$815$	134.064	−	4.38880i	0.164496	−	0.00538503i
$816$	196.335	+	45.7789i	0.240607	+	0.0561016i
$817$	−871.502	+	328.010i	−1.06671	+	0.401481i
$818$	−106.839	−	352.201i	−0.130610	−	0.430563i
$819$	−120.245	−	15.8306i	−0.146819	−	0.0193291i
$820$	−35.9604	+	105.936i	−0.0438541	+	0.129190i
$821$	139.632	+	1417.71i	0.170076	+	1.72681i	0.579935	+	0.814663i	$0.303078\pi$
$821$	139.632	+	1417.71i	0.170076	+	1.72681i	−0.409859	+	0.912149i	$0.634422\pi$
$822$	1881.93	+	1005.91i	2.28946	+	1.22374i
$823$	631.995	−	261.781i	0.767916	−	0.318081i	0.0358882	−	0.999356i	$-0.488574\pi$
$823$	631.995	−	261.781i	0.767916	−	0.318081i	0.732028	+	0.681274i	$0.238574\pi$
$824$	−466.246	−	229.927i	−0.565833	−	0.279038i
$825$	−219.853	+	445.818i	−0.266488	+	0.540385i
$826$	275.043	+	664.012i	0.332981	+	0.803888i
$827$	17.0044	−	31.8130i	0.0205616	−	0.0384680i	−0.871431	−	0.490519i	$-0.836807\pi$
$827$	17.0044	−	31.8130i	0.0205616	−	0.0384680i	0.891992	+	0.452051i	$0.149307\pi$
$828$	2129.46	−	209.734i	2.57181	−	0.253302i
$829$	−1350.74	−	458.514i	−1.62936	−	0.553093i	−0.650834	−	0.759220i	$-0.725581\pi$
$829$	−1350.74	−	458.514i	−1.62936	−	0.553093i	−0.978525	+	0.206127i	$0.933914\pi$
$830$	−48.9353	+	371.700i	−0.0589582	+	0.447832i
$831$	256.356	−	77.7647i	0.308491	−	0.0935796i
$832$	−90.5389	−	240.556i	−0.108821	−	0.289130i
$833$	51.8618	−	222.423i	0.0622591	−	0.267015i
$834$	−98.3300	−	3003.67i	−0.117902	−	3.60152i
$835$	58.8114	−	82.0712i	0.0704328	−	0.0982889i
$836$	−75.0036	−	454.290i	−0.0897173	−	0.543410i
$837$	25.3216	−	43.8584i	0.0302529	−	0.0523995i
$838$	−274.847	+	158.683i	−0.327979	+	0.189359i
$839$	40.2943	−	33.0687i	0.0480266	−	0.0394144i	−0.610074	−	0.792345i	$-0.708860\pi$
$839$	40.2943	−	33.0687i	0.0480266	−	0.0394144i	0.658100	+	0.752930i	$0.271360\pi$
$840$	125.159	+	51.8424i	0.148998	+	0.0617171i
$841$	121.352	+	138.376i	0.144295	+	0.164537i
$842$	1365.10	−	89.4737i	1.62126	−	0.106263i
$843$	−405.526	+	1336.84i	−0.481051	+	1.58581i
$844$	−476.735	+	1052.18i	−0.564852	+	1.24665i
$845$	−14.1110	+	143.272i	−0.0166994	+	0.169552i
$846$	560.272	−	838.506i	0.662260	−	0.991142i
$847$	511.523	+	192.524i	0.603923	+	0.227300i
$848$	2.46405	−	37.5941i	0.00290572	−	0.0443327i
$849$	1093.96	+	1425.67i	1.28853	+	1.67924i
$850$	586.060	+	817.845i	0.689482	+	0.962171i
$851$	−708.748	+	708.748i	−0.832842	+	0.832842i
$852$	−120.507	+	729.901i	−0.141440	+	0.856692i
$853$	364.032	+	298.753i	0.426766	+	0.350238i	0.823128	−	0.567857i	$-0.192227\pi$
$853$	364.032	+	298.753i	0.426766	+	0.350238i	−0.396361	+	0.918095i	$0.629727\pi$
$854$	−554.048	−	1036.55i	−0.648768	−	1.21376i
$855$	−67.1465	−	100.492i	−0.0785339	−	0.117534i
$856$	−6.42940	−	27.5742i	−0.00751099	−	0.0322129i
$857$	−1284.13	+	344.080i	−1.49840	+	0.401494i	−0.912562	−	0.408937i	$-0.865899\pi$
$857$	−1284.13	+	344.080i	−1.49840	+	0.401494i	−0.585834	+	0.810431i	$0.699233\pi$
$858$	−117.154	−	109.727i	−0.136543	−	0.127887i
$859$	−302.272	−	187.965i	−0.351888	−	0.218818i	0.340665	−	0.940185i	$-0.389348\pi$
$859$	−302.272	−	187.965i	−0.351888	−	0.218818i	−0.692553	+	0.721367i	$0.743514\pi$
$860$	232.113	−	217.397i	0.269899	−	0.252788i
$861$	486.346	−	96.7402i	0.564862	−	0.112358i
$862$	−768.368	−	2263.54i	−0.891378	−	2.62591i
$863$	−1121.45	+	508.123i	−1.29948	+	0.588787i	−0.938980	−	0.343973i	$-0.888227\pi$
$863$	−1121.45	+	508.123i	−1.29948	+	0.588787i	−0.360500	+	0.932759i	$0.617394\pi$
$864$	39.7660	−	5.23529i	0.0460255	−	0.00605937i
$865$	−52.6431	+	264.655i	−0.0608590	+	0.305959i
$866$	1376.20	−	855.777i	1.58915	−	0.988195i
$867$	−127.738	+	476.723i	−0.147333	+	0.549853i
$868$	52.5741	−	1605.97i	0.0605693	−	1.85020i
$869$	232.081	+	178.082i	0.267066	+	0.204927i
$870$	283.986	+	249.049i	0.326420	+	0.286263i
$871$	−213.981	+	105.524i	−0.245673	+	0.121153i
$872$		−	1116.90i		−	1.28084i
$873$	−17.3308	−	848.177i	−0.0198520	−	0.971566i
$874$	2006.27			2.29550
$875$	−108.103	−	219.210i	−0.123546	−	0.250526i
$876$	−1777.46	+	2026.81i	−2.02907	+	2.31371i
$877$	468.278	−	610.271i	0.533954	−	0.695862i	−0.446012	−	0.895027i	$-0.647156\pi$
$877$	468.278	−	610.271i	0.533954	−	0.695862i	0.979966	+	0.199165i	$0.0638228\pi$
$878$	2672.10	+	87.4756i	3.04340	+	0.0996305i
$879$	285.437	+	76.4825i	0.324729	+	0.0870108i
$880$	−8.30039	−	13.3481i	−0.00943226	−	0.0151683i
$881$	208.920	+	41.5568i	0.237140	+	0.0471701i	0.312229	−	0.950007i	$-0.398924\pi$
$881$	208.920	+	41.5568i	0.237140	+	0.0471701i	−0.0750895	+	0.997177i	$0.523924\pi$
$882$	63.0312	+	478.770i	0.0714640	+	0.542823i
$883$	−365.020	−	805.617i	−0.413386	−	0.912363i	−0.995091	−	0.0989631i	$-0.968447\pi$
$883$	−365.020	−	805.617i	−0.413386	−	0.912363i	0.581705	−	0.813400i	$-0.302386\pi$
$884$	−185.127	+	62.8422i	−0.209420	+	0.0710884i
$885$	29.3106	+	147.354i	0.0331193	+	0.166502i
$886$	−275.769	−	294.435i	−0.311251	−	0.332320i
$887$	264.964	−	426.096i	0.298719	−	0.480379i	−0.665167	−	0.746695i	$-0.731640\pi$
$887$	264.964	−	426.096i	0.298719	−	0.480379i	0.963886	+	0.266315i	$0.0858063\pi$
$888$	−461.716	+	492.969i	−0.519950	+	0.555145i
$889$	72.9978	+	272.432i	0.0821123	+	0.306447i
$890$	−174.763	+	40.7491i	−0.196363	+	0.0457855i
$891$	337.136	−	225.267i	0.378380	−	0.252825i
$892$	−762.351	+	407.485i	−0.854654	+	0.456822i
$893$	360.946	−	439.814i	0.404195	−	0.492513i
$894$	1436.65	+	237.191i	1.60699	+	0.265315i
$895$	−158.326	−	158.326i	−0.176900	−	0.176900i
$896$	823.043	−	589.784i	0.918574	−	0.658241i
$897$	333.886	−	256.200i	0.372226	−	0.285619i
$898$	1434.56	+	94.0261i	1.59751	+	0.104706i
$899$	533.609	−	1417.76i	0.593558	−	1.57705i
$900$	−1064.37	−	711.188i	−1.18263	−	0.790209i
$901$	−134.629	−	13.2598i	−0.149422	−	0.0147168i
$902$	294.610	+	133.486i	0.326619	+	0.147989i
$903$	−1348.93	−	409.192i	−1.49383	−	0.453148i
$904$	−1.54916	−	23.6356i	−0.00171367	−	0.0261455i
$905$	35.4156	−	31.0586i	0.0391333	−	0.0343189i
$906$	1372.15	−	3312.66i	1.51451	−	3.65636i
$907$	990.192	+	1206.55i	1.09172	+	1.33027i	0.939742	+	0.341883i	$0.111065\pi$
$907$	990.192	+	1206.55i	1.09172	+	1.33027i	0.151979	+	0.988384i	$0.451435\pi$
$908$	−682.838	−	1182.71i	−0.752025	−	1.30255i
$909$	577.951	+	333.680i	0.635809	+	0.367085i
$910$	38.3180	−	6.32633i	0.0421077	−	0.00695201i
$911$	193.168	+	138.422i	0.212039	+	0.151945i	0.683521	−	0.729930i	$-0.260448\pi$
$911$	193.168	+	138.422i	0.212039	+	0.151945i	−0.471482	+	0.881875i	$0.656281\pi$
$912$	−240.363	+	7.86866i	−0.263556	+	0.00862792i
$913$	635.183	+	148.104i	0.695710	+	0.162217i
$914$	−1875.95	+	706.057i	−2.05246	+	0.772491i
$915$	−71.3203	−	235.112i	−0.0779457	−	0.256953i
$916$	1029.05	+	135.477i	1.12342	+	0.147901i
$917$	−173.003	+	509.649i	−0.188662	+	0.555779i
$918$	−4.35843	−	44.2518i	−0.00474774	−	0.0482046i
$919$	−1026.35	−	548.596i	−1.11681	−	0.596949i	−0.193539	−	0.981093i	$-0.561997\pi$
$919$	−1026.35	−	548.596i	−1.11681	−	0.596949i	−0.923273	+	0.384144i	$0.874497\pi$
$920$	−214.043	+	88.6595i	−0.232655	+	0.0963690i
$921$	−2131.71	−	1051.24i	−2.31456	−	1.14141i
$922$	−661.192	+	1340.77i	−0.717129	+	1.45419i
$923$	27.4420	+	66.2509i	0.0297314	+	0.0717778i
$924$	328.569	−	614.710i	0.355595	−	0.665271i
$925$	596.747	−	58.7744i	0.645132	−	0.0635399i
$926$	−1545.58	−	524.654i	−1.66909	−	0.566581i
$927$	−91.6407	+	696.080i	−0.0988573	+	0.750896i
$928$	1148.10	−	348.271i	1.23717	−	0.375292i
$929$	−632.587	−	1680.74i	−0.680933	−	1.80920i	−0.580513	−	0.814251i	$-0.697148\pi$
$929$	−632.587	−	1680.74i	−0.680933	−	1.80920i	−0.100420	−	0.994945i	$-0.532019\pi$
$930$	126.756	−	543.628i	0.136297	−	0.584547i
$931$	8.91422	+	272.301i	0.00957489	+	0.292483i
$932$	−692.635	+	966.571i	−0.743171	+	1.03709i
$933$	−202.266	−	1225.11i	−0.216791	−	1.31308i
$934$	1277.08	−	2211.97i	1.36732	−	2.36828i
$935$	−48.8791	+	28.2204i	−0.0522771	+	0.0301822i
$936$	108.043	−	88.6682i	0.115430	−	0.0947310i
$937$	−886.499	−	367.200i	−0.946104	−	0.391889i	−0.144339	−	0.989528i	$-0.546105\pi$
$937$	−886.499	−	367.200i	−0.946104	−	0.391889i	−0.801765	+	0.597639i	$0.796105\pi$
$938$	−1135.23	−	1294.48i	−1.21026	−	1.38004i
$939$	1081.91	−	70.9124i	1.15220	−	0.0755191i
$940$	−56.4065	+	185.947i	−0.0600069	+	0.197816i
$941$	−237.683	+	524.577i	−0.252585	+	0.557468i	−0.993461	−	0.114175i	$-0.963578\pi$
$941$	−237.683	+	524.577i	−0.252585	+	0.557468i	0.740875	+	0.671643i	$0.234411\pi$
$942$	−309.430	+	3141.69i	−0.328482	+	3.33513i
$943$	−471.141	+	705.112i	−0.499619	+	0.747732i
$944$	137.893	+	51.8994i	0.146073	+	0.0549782i
$945$	−0.347631	+	5.30382i	−0.000367863	+	0.00561251i
$946$	−559.723	−	729.446i	−0.591674	−	0.771084i
$947$	−212.656	−	296.761i	−0.224557	−	0.313369i	0.685324	−	0.728238i	$-0.259661\pi$
$947$	−212.656	−	296.761i	−0.224557	−	0.313369i	−0.909881	+	0.414869i	$0.863827\pi$
$948$	−1080.86	+	1080.86i	−1.14015	+	1.14015i
$949$	−42.5666	+	257.822i	−0.0448542	+	0.271678i
$950$	−927.799	−	761.425i	−0.976631	−	0.801500i
$951$	−490.372	−	917.422i	−0.515639	−	0.964692i
$952$	−265.027	−	396.642i	−0.278390	−	0.416640i
$953$	136.587	+	585.790i	0.143323	+	0.614680i	0.995771	+	0.0918680i	$0.0292838\pi$
$953$	136.587	+	585.790i	0.143323	+	0.614680i	−0.852448	+	0.522812i	$0.824883\pi$
$954$	276.287	−	74.0309i	0.289609	−	0.0776005i
$955$	27.1053	+	25.3869i	0.0283825	+	0.0265831i
$956$	1732.23	+	1077.17i	1.81195	+	1.12674i
$957$	479.605	−	449.199i	0.501154	−	0.469382i
$958$	2922.57	−	581.335i	3.05070	−	0.606821i
$959$	288.717	+	850.532i	0.301060	+	0.886895i
$960$	353.175	−	160.022i	0.367891	−	0.166689i
$961$	−1266.78	+	166.775i	−1.31819	+	0.173543i
$962$	−37.7755	+	189.910i	−0.0392677	+	0.197412i
$963$	−32.4726	+	20.1927i	−0.0337202	+	0.0209686i
$964$	83.3529	−	311.077i	0.0864656	−	0.322694i
$965$	4.42553	−	135.186i	0.00458604	−	0.140089i
$966$	2409.48	+	1848.86i	2.49428	+	1.91393i
$967$	289.035	+	253.477i	0.298899	+	0.262127i	0.795638	−	0.605773i	$-0.207136\pi$
$967$	289.035	+	253.477i	0.298899	+	0.262127i	−0.496739	+	0.867900i	$0.665469\pi$
$968$	−564.903	+	278.579i	−0.583578	+	0.287789i
$969$			863.543i			0.891169i
$970$	84.1521	+	258.294i	0.0867547	+	0.266283i
$971$	1215.57			1.25187			0.625935	−	0.779875i	$-0.284718\pi$
$971$	1215.57			1.25187			0.625935	+	0.779875i	$0.284718\pi$
$972$	911.332	+	1848.00i	0.937585	+	1.90123i
$973$	834.059	−	951.062i	0.857203	−	0.977453i
$974$	141.117	−	183.907i	0.144884	−	0.188816i
$975$	−251.639	−	8.23782i	−0.258092	−	0.00844905i
$976$	−232.732	−	62.3603i	−0.238455	−	0.0638937i
$977$	607.134	+	976.351i	0.621427	+	0.999335i	0.997355	+	0.0726865i	$0.0231572\pi$
$977$	607.134	+	976.351i	0.621427	+	0.999335i	−0.375928	+	0.926649i	$0.622676\pi$
$978$	1987.47	+	395.332i	2.03218	+	0.404225i
$979$	40.7488	+	309.518i	0.0416229	+	0.316157i
$980$	−38.4012	−	84.7533i	−0.0391849	−	0.0864830i
$981$	−1428.36	+	484.863i	−1.45602	+	0.494253i
$982$	−461.070	−	2317.95i	−0.469521	−	2.36044i
$983$	652.898	+	697.092i	0.664189	+	0.709148i	0.970044	−	0.242931i	$-0.0781088\pi$
$983$	652.898	+	697.092i	0.664189	+	0.709148i	−0.305854	+	0.952078i	$0.598942\pi$
$984$	−301.767	+	485.281i	−0.306674	+	0.493171i
$985$	−90.8325	+	96.9808i	−0.0922157	+	0.0984577i
$986$	−344.250	−	1284.76i	−0.349138	−	1.30300i
$987$	838.794	−	195.579i	0.849842	−	0.198155i
$988$	193.912	−	129.568i	0.196267	−	0.131142i
$989$	2126.05	−	1136.40i	2.14970	−	1.14904i
$990$	75.7065	−	92.2487i	0.0764712	−	0.0931805i
$991$	249.739	+	41.2320i	0.252007	+	0.0416065i	0.287565	−	0.957761i	$-0.407154\pi$
$991$	249.739	+	41.2320i	0.252007	+	0.0416065i	−0.0355583	+	0.999368i	$0.511321\pi$
$992$	−1253.73	−	1253.73i	−1.26384	−	1.26384i
$993$	−169.911	+	121.757i	−0.171109	+	0.122615i
$994$	−410.552	+	315.027i	−0.413030	+	0.316929i
$995$	20.4975	+	1.34348i	0.0206005	+	0.00135023i
$996$	−1200.49	+	3189.62i	−1.20531	+	3.20243i
$997$	865.982	+	578.631i	0.868588	+	0.580372i	0.908056	−	0.418849i	$-0.137566\pi$
$997$	865.982	+	578.631i	0.868588	+	0.580372i	−0.0394679	+	0.999221i	$0.512566\pi$
$998$	−2079.73	−	204.836i	−2.08390	−	0.205246i
$999$	−24.1382	−	10.9369i	−0.0241624	−	0.0109478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.3.l.a.5.2	✓	480
97.39	odd	96	inner	97.3.l.a.39.2	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.3.l.a.5.2	✓	480	1.1	even	1	trivial
97.3.l.a.39.2	yes	480	97.39	odd	96	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	97.l (of order \(96\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40167 - 2.84231i) q^{2} +(2.77755 - 3.16719i) q^{3} +(-3.67900 + 4.79457i) q^{4} +(-0.883234 - 0.0289141i) q^{5} +(-12.8954 - 3.45530i) q^{6} +(-2.96741 - 4.77199i) q^{7} +(6.35145 + 1.26338i) q^{8} +(-1.14157 - 8.67110i) q^{9} +(1.15582 + 2.55096i) q^{10} +(4.61358 - 1.56610i) q^{11} +(4.96670 + 24.9693i) q^{12} +(1.68695 + 1.80114i) q^{13} +(-9.40414 + 15.1231i) q^{14} +(-2.54481 + 2.71706i) q^{15} +(0.944879 + 3.52634i) q^{16} +(12.7664 - 2.97671i) q^{17} +(-23.0458 + 15.3987i) q^{18} +(-13.7911 + 7.37152i) q^{19} +(3.38805 - 4.12835i) q^{20} +(-23.3560 - 3.85609i) q^{21} +(-10.9181 - 10.9181i) q^{22} +(32.9069 - 23.5807i) q^{23} +(21.6429 - 16.6072i) q^{24} +(-24.1672 - 1.58400i) q^{25} +(2.75484 - 7.31944i) q^{26} +(0.889957 + 0.594650i) q^{27} +(33.7968 + 3.32869i) q^{28} +(29.1626 + 13.2134i) q^{29} +(11.2897 + 3.42470i) q^{30} +(-3.09455 - 47.2138i) q^{31} +(28.1738 - 24.7078i) q^{32} +(7.85432 - 18.9620i) q^{33} +(-26.3550 - 32.1137i) q^{34} +(2.48294 + 4.30059i) q^{35} +(45.7740 + 26.4276i) q^{36} +(-24.4281 + 4.03309i) q^{37} +(40.2828 + 28.8663i) q^{38} +(10.3901 - 0.340138i) q^{39} +(-5.57329 - 1.29951i) q^{40} +(-19.6050 + 7.37878i) q^{41} +(21.7772 + 71.7899i) q^{42} +(59.0383 + 7.77254i) q^{43} +(-9.46460 + 27.8818i) q^{44} +(0.757558 + 7.69162i) q^{45} +(-113.148 - 60.4791i) q^{46} +(-33.6147 + 13.9237i) q^{47} +(13.7930 + 6.80198i) q^{48} +(7.70580 - 15.6258i) q^{49} +(29.3723 + 70.9110i) q^{50} +(26.0316 - 48.7016i) q^{51} +(-14.8420 + 1.46181i) q^{52} +(-9.77212 - 3.31719i) q^{53} +(0.442752 - 3.36304i) q^{54} +(-4.12015 + 1.24983i) q^{55} +(-12.8185 - 34.0580i) q^{56} +(-14.9586 + 64.1540i) q^{57} +(-3.31982 - 101.410i) q^{58} +(23.5077 - 32.8050i) q^{59} +(-3.66480 - 22.1973i) q^{60} +(-32.9991 + 57.1561i) q^{61} +(-129.859 + 74.9739i) q^{62} +(-37.9909 + 31.1783i) q^{63} +(-96.2264 - 39.8583i) q^{64} +(-1.43789 - 1.63960i) q^{65} +(-64.9052 + 4.25411i) q^{66} +(-28.0650 + 92.5178i) q^{67} +(-32.6956 + 72.1607i) q^{68} +(16.7159 - 169.719i) q^{69} +(8.74333 - 13.0853i) q^{70} +(27.1959 + 10.2358i) q^{71} +(3.70427 - 56.5163i) q^{72} +(64.4618 + 84.0083i) q^{73} +(45.7035 + 63.7791i) q^{74} +(-72.1426 + 72.1426i) q^{75} +(15.3944 - 93.2424i) q^{76} +(-21.1638 - 17.3687i) q^{77} +(-15.5304 - 29.0553i) q^{78} +(33.3573 + 49.9228i) q^{79} +(-0.732589 - 3.14190i) q^{80} +(80.3864 - 21.5395i) q^{81} +(48.4525 + 45.3807i) q^{82} +(113.681 + 70.6911i) q^{83} +(104.415 - 97.7953i) q^{84} +(-11.3618 + 2.26000i) q^{85} +(-60.6604 - 178.700i) q^{86} +(122.850 - 55.6626i) q^{87} +(31.2815 - 4.11829i) q^{88} +(-12.5007 + 62.8450i) q^{89} +(20.8001 - 12.9343i) q^{90} +(3.58913 - 13.3948i) q^{91} +(-8.00501 + 244.528i) q^{92} +(-158.130 - 121.338i) q^{93} +(86.6922 + 76.0270i) q^{94} +(12.3940 - 6.11202i) q^{95} -157.859i q^{96} +(96.4087 + 10.6938i) q^{97} -55.2144 q^{98} +(-18.8465 - 38.2170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) \) 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Introduction

L-functions

Modular forms

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Database

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