LMFDB - Embedded newform 97.3.l.a.5.6

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			5.6
Character	$\chi$	$=$	97.5
Dual form			97.3.l.a.39.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.390169 - 0.791184i) q^{2} +(-2.36070 + 2.69186i) q^{3} +(1.96131 - 2.55602i) q^{4} +(0.944383 + 0.0309159i) q^{5} +(3.05082 + 0.817466i) q^{6} +(5.11796 + 8.23036i) q^{7} +(-6.24836 - 1.24288i) q^{8} +(-0.498478 - 3.78632i) q^{9} +(-0.344009 - 0.759243i) q^{10} +(16.4218 - 5.57444i) q^{11} +(2.25041 + 11.3135i) q^{12} +(14.8094 + 15.8118i) q^{13} +(4.51486 - 7.26048i) q^{14} +(-2.31262 + 2.46916i) q^{15} +(-1.88088 - 7.01954i) q^{16} +(-5.75252 + 1.34130i) q^{17} +(-2.80118 + 1.87169i) q^{18} +(-12.3640 + 6.60870i) q^{19} +(1.93125 - 2.35323i) q^{20} +(-34.2369 - 5.65254i) q^{21} +(-10.8177 - 10.8177i) q^{22} +(22.1208 - 15.8516i) q^{23} +(18.0961 - 13.8856i) q^{24} +(-24.0556 - 1.57669i) q^{25} +(6.73189 - 17.8862i) q^{26} +(-15.4237 - 10.3058i) q^{27} +(31.0749 + 3.06061i) q^{28} +(-18.2105 - 8.25106i) q^{29} +(2.85588 + 0.866320i) q^{30} +(-0.759147 - 11.5823i) q^{31} +(-23.9791 + 21.0291i) q^{32} +(-23.7612 + 57.3646i) q^{33} +(3.30567 + 4.02797i) q^{34} +(4.57887 + 7.93084i) q^{35} +(-10.6556 - 6.15200i) q^{36} +(-37.4880 + 6.18930i) q^{37} +(10.0527 + 7.20369i) q^{38} +(-77.5235 + 2.53786i) q^{39} +(-5.86242 - 1.36692i) q^{40} +(43.9870 - 16.5556i) q^{41} +(8.88598 + 29.2931i) q^{42} +(66.6522 + 8.77493i) q^{43} +(17.9597 - 52.9076i) q^{44} +(-0.353697 - 3.59114i) q^{45} +(-21.1724 - 11.3169i) q^{46} +(-4.94197 + 2.04703i) q^{47} +(23.3358 + 11.5079i) q^{48} +(-19.8731 + 40.2986i) q^{49} +(8.13828 + 19.6476i) q^{50} +(9.96937 - 18.6514i) q^{51} +(69.4610 - 6.84131i) q^{52} +(-38.2883 - 12.9971i) q^{53} +(-2.13592 + 16.2240i) q^{54} +(15.6808 - 4.75671i) q^{55} +(-21.7496 - 57.7872i) q^{56} +(11.3980 - 48.8833i) q^{57} +(0.577053 + 17.6271i) q^{58} +(33.2212 - 46.3602i) q^{59} +(1.77548 + 10.7539i) q^{60} +(-30.6509 + 53.0890i) q^{61} +(-8.86757 + 5.11969i) q^{62} +(28.6115 - 23.4809i) q^{63} +(-0.862159 - 0.357118i) q^{64} +(13.4969 + 15.3902i) q^{65} +(54.6568 - 3.58240i) q^{66} +(30.6554 - 101.057i) q^{67} +(-7.85406 + 17.3343i) q^{68} +(-9.55040 + 96.9669i) q^{69} +(4.48822 - 6.71709i) q^{70} +(-127.326 - 47.9219i) q^{71} +(-1.59125 + 24.2778i) q^{72} +(25.5819 + 33.3390i) q^{73} +(19.5235 + 27.2451i) q^{74} +(61.0321 - 61.0321i) q^{75} +(-7.35761 + 44.5644i) q^{76} +(129.926 + 106.627i) q^{77} +(32.2552 + 60.3452i) q^{78} +(44.4620 + 66.5420i) q^{79} +(-1.55926 - 6.68728i) q^{80} +(97.3520 - 26.0854i) q^{81} +(-30.2609 - 28.3424i) q^{82} +(-72.3684 - 45.0016i) q^{83} +(-81.5971 + 76.4240i) q^{84} +(-5.47405 + 1.08886i) q^{85} +(-19.0630 - 56.1579i) q^{86} +(65.2001 - 29.5418i) q^{87} +(-109.537 + 14.4209i) q^{88} +(-2.26477 + 11.3858i) q^{89} +(-2.70325 + 1.68099i) q^{90} +(-54.3429 + 202.811i) q^{91} +(2.86875 - 87.6311i) q^{92} +(32.9701 + 25.2989i) q^{93} +(3.54778 + 3.11132i) q^{94} +(-11.8807 + 5.85890i) q^{95} -114.192i q^{96} +(-90.1938 + 35.6943i) q^{97} +39.6374 q^{98} +(-29.2925 - 59.3992i) 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 $

$2$	−0.390169	−	0.791184i	−0.195084	−	0.395592i	0.777248	−	0.629195i	$-0.216615\pi$
$2$	−0.390169	−	0.791184i	−0.195084	−	0.395592i	−0.972332	+	0.233603i	$0.924948\pi$
$3$	−2.36070	+	2.69186i	−0.786899	+	0.897286i	−0.996759	−	0.0804453i	$-0.974366\pi$
$3$	−2.36070	+	2.69186i	−0.786899	+	0.897286i	0.209860	+	0.977731i	$0.432699\pi$
$4$	1.96131	−	2.55602i	0.490326	−	0.639006i
$5$	0.944383	+	0.0309159i	0.188877	+	0.00618318i	0.127011	−	0.991901i	$-0.459462\pi$
$5$	0.944383	+	0.0309159i	0.188877	+	0.00618318i	0.0618657	+	0.998084i	$0.480295\pi$
$6$	3.05082	+	0.817466i	0.508471	+	0.136244i
$7$	5.11796	+	8.23036i	0.731138	+	1.17577i	0.978381	+	0.206812i	$0.0663087\pi$
$7$	5.11796	+	8.23036i	0.731138	+	1.17577i	−0.247243	+	0.968954i	$0.579525\pi$
$8$	−6.24836	−	1.24288i	−0.781045	−	0.155359i
$9$	−0.498478	−	3.78632i	−0.0553864	−	0.420702i
$10$	−0.344009	−	0.759243i	−0.0344009	−	0.0759243i
$11$	16.4218	−	5.57444i	1.49289	−	0.506767i	0.548655	−	0.836049i	$-0.315140\pi$
$11$	16.4218	−	5.57444i	1.49289	−	0.506767i	0.944232	+	0.329282i	$0.106807\pi$
$12$	2.25041	+	11.3135i	0.187534	+	0.942796i
$13$	14.8094	+	15.8118i	1.13918	+	1.21629i	0.973150	+	0.230171i	$0.0739287\pi$
$13$	14.8094	+	15.8118i	1.13918	+	1.21629i	0.166032	+	0.986120i	$0.446905\pi$
$14$	4.51486	−	7.26048i	0.322490	−	0.518606i
$15$	−2.31262	+	2.46916i	−0.154175	+	0.164611i
$16$	−1.88088	−	7.01954i	−0.117555	−	0.438721i
$17$	−5.75252	+	1.34130i	−0.338384	+	0.0789000i	−0.392815	−	0.919618i	$-0.628499\pi$
$17$	−5.75252	+	1.34130i	−0.338384	+	0.0789000i	0.0544314	+	0.998518i	$0.482665\pi$
$18$	−2.80118	+	1.87169i	−0.155621	+	0.103983i
$19$	−12.3640	+	6.60870i	−0.650737	+	0.347826i	−0.763511	−	0.645794i	$-0.776526\pi$
$19$	−12.3640	+	6.60870i	−0.650737	+	0.347826i	0.112774	+	0.993621i	$0.464026\pi$
$20$	1.93125	−	2.35323i	0.0965623	−	0.117662i
$21$	−34.2369	−	5.65254i	−1.63033	−	0.269168i
$22$	−10.8177	−	10.8177i	−0.491712	−	0.491712i
$23$	22.1208	−	15.8516i	0.961775	−	0.689198i	0.0112796	−	0.999936i	$-0.496410\pi$
$23$	22.1208	−	15.8516i	0.961775	−	0.689198i	0.950496	+	0.310738i	$0.100576\pi$
$24$	18.0961	−	13.8856i	0.754005	−	0.578568i
$25$	−24.0556	−	1.57669i	−0.962223	−	0.0630674i
$26$	6.73189	−	17.8862i	0.258919	−	0.687931i
$27$	−15.4237	−	10.3058i	−0.571247	−	0.381695i
$28$	31.0749	+	3.06061i	1.10982	+	0.109307i
$29$	−18.2105	−	8.25106i	−0.627947	−	0.284519i	0.0734399	−	0.997300i	$-0.476602\pi$
$29$	−18.2105	−	8.25106i	−0.627947	−	0.284519i	−0.701387	+	0.712780i	$0.747436\pi$
$30$	2.85588	+	0.866320i	0.0951959	+	0.0288773i
$31$	−0.759147	−	11.5823i	−0.0244886	−	0.373624i	−0.992460	−	0.122565i	$-0.960888\pi$
$31$	−0.759147	−	11.5823i	−0.0244886	−	0.373624i	0.967972	−	0.251059i	$-0.0807787\pi$
$32$	−23.9791	+	21.0291i	−0.749346	+	0.657159i
$33$	−23.7612	+	57.3646i	−0.720036	+	1.73832i
$34$	3.30567	+	4.02797i	0.0972255	+	0.118470i
$35$	4.57887	+	7.93084i	0.130825	+	0.226595i
$36$	−10.6556	−	6.15200i	−0.295988	−	0.170889i
$37$	−37.4880	+	6.18930i	−1.01319	+	0.167278i	−0.646379	−	0.763017i	$-0.723717\pi$
$37$	−37.4880	+	6.18930i	−1.01319	+	0.167278i	−0.366812	+	0.930295i	$0.619551\pi$
$38$	10.0527	+	7.20369i	0.264546	+	0.189571i
$39$	−77.5235	+	2.53786i	−1.98778	+	0.0650733i
$40$	−5.86242	−	1.36692i	−0.146560	−	0.0341731i
$41$	43.9870	−	16.5556i	1.07285	−	0.403794i	0.247779	−	0.968817i	$-0.420299\pi$
$41$	43.9870	−	16.5556i	1.07285	−	0.403794i	0.825075	+	0.565023i	$0.191133\pi$
$42$	8.88598	+	29.2931i	0.211571	+	0.697456i
$43$	66.6522	+	8.77493i	1.55005	+	0.204068i	0.856427	−	0.516268i	$-0.172679\pi$
$43$	66.6522	+	8.77493i	1.55005	+	0.204068i	0.693625	+	0.720336i	$0.256012\pi$
$44$	17.9597	−	52.9076i	0.408175	−	1.20244i
$45$	−0.353697	−	3.59114i	−0.00785993	−	0.0798032i
$46$	−21.1724	−	11.3169i	−0.460269	−	0.246019i
$47$	−4.94197	+	2.04703i	−0.105148	+	0.0435539i	−0.434638	−	0.900605i	$-0.643124\pi$
$47$	−4.94197	+	2.04703i	−0.105148	+	0.0435539i	0.329489	+	0.944159i	$0.393124\pi$
$48$	23.3358	+	11.5079i	0.486162	+	0.239749i
$49$	−19.8731	+	40.2986i	−0.405573	+	0.822420i
$50$	8.13828	+	19.6476i	0.162766	+	0.392951i
$51$	9.96937	−	18.6514i	0.195478	−	0.365713i
$52$	69.4610	−	6.84131i	1.33579	−	0.131564i
$53$	−38.2883	−	12.9971i	−0.722420	−	0.245229i	−0.0640754	−	0.997945i	$-0.520410\pi$
$53$	−38.2883	−	12.9971i	−0.722420	−	0.245229i	−0.658345	+	0.752716i	$0.728743\pi$
$54$	−2.13592	+	16.2240i	−0.0395541	+	0.300444i
$55$	15.6808	−	4.75671i	0.285105	−	0.0864857i
$56$	−21.7496	−	57.7872i	−0.388385	−	1.03191i
$57$	11.3980	−	48.8833i	0.199965	−	0.857601i
$58$	0.577053	+	17.6271i	0.00994919	+	0.303916i
$59$	33.2212	−	46.3602i	0.563072	−	0.785766i	−0.430056	−	0.902802i	$-0.641506\pi$
$59$	33.2212	−	46.3602i	0.563072	−	0.785766i	0.993128	+	0.117036i	$0.0373394\pi$
$60$	1.77548	+	10.7539i	0.0295913	+	0.179232i
$61$	−30.6509	+	53.0890i	−0.502474	+	0.870311i	0.497522	+	0.867452i	$0.334244\pi$
$61$	−30.6509	+	53.0890i	−0.502474	+	0.870311i	−0.999996	+	0.00285944i	$0.999090\pi$
$62$	−8.86757	+	5.11969i	−0.143025	+	0.0825757i
$63$	28.6115	−	23.4809i	0.454151	−	0.372712i
$64$	−0.862159	−	0.357118i	−0.0134712	−	0.00557997i
$65$	13.4969	+	15.3902i	0.207644	+	0.236773i
$66$	54.6568	−	3.58240i	0.828134	−	0.0542787i
$67$	30.6554	−	101.057i	0.457544	−	1.50832i	−0.360277	−	0.932845i	$-0.617318\pi$
$67$	30.6554	−	101.057i	0.457544	−	1.50832i	0.817820	−	0.575474i	$-0.195182\pi$
$68$	−7.85406	+	17.3343i	−0.115501	+	0.254916i
$69$	−9.55040	+	96.9669i	−0.138412	+	1.40532i
$70$	4.48822	−	6.71709i	0.0641174	−	0.0959585i
$71$	−127.326	−	47.9219i	−1.79332	−	0.674957i	−0.997596	−	0.0692931i	$-0.977926\pi$
$71$	−127.326	−	47.9219i	−1.79332	−	0.674957i	−0.795721	−	0.605664i	$-0.792908\pi$
$72$	−1.59125	+	24.2778i	−0.0221007	+	0.337192i
$73$	25.5819	+	33.3390i	0.350437	+	0.456699i	0.934999	−	0.354651i	$-0.115400\pi$
$73$	25.5819	+	33.3390i	0.350437	+	0.456699i	−0.584562	+	0.811349i	$0.698734\pi$
$74$	19.5235	+	27.2451i	0.263832	+	0.368177i
$75$	61.0321	−	61.0321i	0.813761	−	0.813761i
$76$	−7.35761	+	44.5644i	−0.0968106	+	0.586373i
$77$	129.926	+	106.627i	1.68734	+	1.38477i
$78$	32.2552	+	60.3452i	0.413528	+	0.773656i
$79$	44.4620	+	66.5420i	0.562810	+	0.842304i	0.998324	−	0.0578779i	$-0.0184334\pi$
$79$	44.4620	+	66.5420i	0.562810	+	0.842304i	−0.435514	+	0.900182i	$0.643433\pi$
$80$	−1.55926	−	6.68728i	−0.0194907	−	0.0835910i
$81$	97.3520	−	26.0854i	1.20188	−	0.322042i
$82$	−30.2609	−	28.3424i	−0.369035	−	0.345639i
$83$	−72.3684	−	45.0016i	−0.871909	−	0.542188i	0.0172165	−	0.999852i	$-0.494520\pi$
$83$	−72.3684	−	45.0016i	−0.871909	−	0.542188i	−0.889125	+	0.457664i	$0.848686\pi$
$84$	−81.5971	+	76.4240i	−0.971394	+	0.909809i
$85$	−5.47405	+	1.08886i	−0.0644006	+	0.0128101i
$86$	−19.0630	−	56.1579i	−0.221663	−	0.652999i
$87$	65.2001	−	29.5418i	0.749426	−	0.339561i
$88$	−109.537	+	14.4209i	−1.24474	+	0.163873i
$89$	−2.26477	+	11.3858i	−0.0254468	+	0.127930i	−0.991421	−	0.130710i	$-0.958274\pi$
$89$	−2.26477	+	11.3858i	−0.0254468	+	0.127930i	0.965974	+	0.258640i	$0.0832743\pi$
$90$	−2.70325	+	1.68099i	−0.0300362	+	0.0186777i
$91$	−54.3429	+	202.811i	−0.597175	+	2.22869i
$92$	2.86875	−	87.6311i	0.0311820	−	0.952512i
$93$	32.9701	+	25.2989i	0.354518	+	0.272031i
$94$	3.54778	+	3.11132i	0.0377424	+	0.0330992i
$95$	−11.8807	+	5.85890i	−0.125060	+	0.0616726i
$96$		−	114.192i		−	1.18950i
$97$	−90.1938	+	35.6943i	−0.929833	+	0.367983i
$97$	−90.1938	+	35.6943i	−0.929833	+	0.367983i
$98$	39.6374			0.404464
$99$	−29.2925	−	59.3992i	−0.295883	−	0.599992i
$100$	−51.2104	+	58.3942i	−0.512104	+	0.583942i
$101$	18.7751	−	24.4682i	0.185892	−	0.242259i	−0.691106	−	0.722754i	$-0.742876\pi$
$101$	18.7751	−	24.4682i	0.185892	−	0.242259i	0.876998	+	0.480495i	$0.159543\pi$
$102$	−18.6464	−	0.610420i	−0.182808	−	0.00598451i
$103$	21.0453	+	5.63908i	0.204324	+	0.0547483i	0.359529	−	0.933134i	$-0.382937\pi$
$103$	21.0453	+	5.63908i	0.204324	+	0.0547483i	−0.155206	+	0.987882i	$0.549604\pi$
$104$	−72.8821	−	117.204i	−0.700789	−	1.12696i
$105$	−32.1580	−	6.39663i	−0.306267	−	0.0609203i
$106$	4.65578	+	35.3641i	0.0439224	+	0.333624i
$107$	−43.3312	−	95.6339i	−0.404964	−	0.893775i	−0.996185	−	0.0872654i	$-0.972187\pi$
$107$	−43.3312	−	95.6339i	−0.404964	−	0.893775i	0.591221	−	0.806510i	$-0.298646\pi$
$108$	−56.5923	+	19.2105i	−0.524003	+	0.177875i
$109$	−30.9869	−	155.782i	−0.284284	−	1.42919i	−0.813925	−	0.580970i	$-0.802674\pi$
$109$	−30.9869	−	155.782i	−0.284284	−	1.42919i	0.529641	−	0.848222i	$-0.322326\pi$
$110$	−9.88158	−	10.5505i	−0.0898326	−	0.0959132i
$111$	71.8372	−	115.524i	0.647182	−	1.04075i
$112$	48.1470	−	51.4060i	0.429884	−	0.458982i
$113$	3.74267	+	13.9678i	0.0331210	+	0.123609i	0.980507	−	0.196484i	$-0.0629524\pi$
$113$	3.74267	+	13.9678i	0.0331210	+	0.123609i	−0.947386	+	0.320093i	$0.896286\pi$
$114$	−43.1228	+	10.0548i	−0.378270	+	0.0882002i
$115$	21.3806	−	14.2861i	0.185918	−	0.124227i
$116$	−56.8062	+	30.3635i	−0.489709	+	0.261755i
$117$	52.4863	−	63.9547i	0.448601	−	0.546622i
$118$	−49.6413	−	8.19582i	−0.420689	−	0.0694561i
$119$	−40.4806	−	40.4806i	−0.340173	−	0.340173i
$120$	17.5190	−	12.5539i	0.145991	−	0.104616i
$121$	142.604	−	109.424i	1.17855	−	0.904330i
$122$	53.9622	+	3.53687i	0.442313	+	0.0289907i
$123$	−59.2749	+	157.490i	−0.481909	+	1.28040i
$124$	−31.0937	−	20.7761i	−0.250755	−	0.167549i
$125$	−46.1774	−	4.54808i	−0.369419	−	0.0363846i
$126$	−29.7410	−	13.4755i	−0.236040	−	0.106948i
$127$	−6.28900	−	1.90775i	−0.0495197	−	0.0150216i	0.265428	−	0.964131i	$-0.414487\pi$
$127$	−6.28900	−	1.90775i	−0.0495197	−	0.0150216i	−0.314947	+	0.949109i	$0.601987\pi$
$128$	8.39767	+	128.124i	0.0656068	+	1.00097i
$129$	−180.967	+	158.703i	−1.40284	+	1.23026i
$130$	6.91045	−	16.6833i	0.0531573	−	0.128333i
$131$	53.5499	+	65.2508i	0.408778	+	0.498098i	0.936181	−	0.351518i	$-0.114334\pi$
$131$	53.5499	+	65.2508i	0.408778	+	0.498098i	−0.527403	+	0.849615i	$0.676834\pi$
$132$	100.022	+	173.244i	0.757744	+	1.31245i
$133$	−117.670	−	67.9371i	−0.884740	−	0.510805i
$134$	−91.9158	+	15.1754i	−0.685938	+	0.113249i
$135$	−14.2473	−	10.2094i	−0.105535	−	0.0756255i
$136$	37.6109	−	1.23125i	0.276551	−	0.00905333i
$137$	60.0855	+	14.0100i	0.438580	+	0.102263i	0.440535	−	0.897735i	$-0.354789\pi$
$137$	60.0855	+	14.0100i	0.438580	+	0.102263i	−0.00195449	+	0.999998i	$0.500622\pi$
$138$	80.4449	−	30.2773i	0.582934	−	0.219401i
$139$	−30.0712	−	99.1314i	−0.216339	−	0.713176i	−0.996190	−	0.0872098i	$-0.972205\pi$
$139$	−30.0712	−	99.1314i	−0.216339	−	0.713176i	0.779851	−	0.625966i	$-0.215295\pi$
$140$	29.2520	+	3.85110i	0.208943	+	0.0275078i
$141$	6.15618	−	18.1355i	0.0436608	−	0.128621i
$142$	11.7634	+	119.436i	0.0828407	+	0.841095i
$143$	331.338	+	177.104i	2.31705	+	1.23849i
$144$	−25.6406	+	10.6207i	−0.178060	+	0.0737548i
$145$	−16.9426	−	8.35516i	−0.116845	−	0.0576218i
$146$	16.3960	−	33.2478i	0.112301	−	0.227725i
$147$	−61.5638	−	148.628i	−0.418801	−	1.01108i
$148$	−57.7055	+	107.959i	−0.389902	+	0.729455i
$149$	−53.9557	+	5.31417i	−0.362119	+	0.0356656i	−0.277441	−	0.960743i	$-0.589486\pi$
$149$	−53.9557	+	5.31417i	−0.362119	+	0.0356656i	−0.0846780	+	0.996408i	$0.526986\pi$
$150$	−72.1004	−	24.4748i	−0.480670	−	0.163165i
$151$	1.99296	−	15.1381i	0.0131984	−	0.100252i	−0.983578	−	0.180485i	$-0.942233\pi$
$151$	1.99296	−	15.1381i	0.0131984	−	0.100252i	0.996776	+	0.0802333i	$0.0255665\pi$
$152$	85.4685	−	25.9266i	0.562293	−	0.170570i
$153$	7.94609	+	21.1123i	0.0519352	+	0.137989i
$154$	33.6688	−	144.398i	0.218629	−	0.937647i
$155$	−0.358847	−	10.9616i	−0.00231514	−	0.0707203i
$156$	−145.560	+	203.129i	−0.933080	+	1.30211i
$157$	−23.1308	−	140.101i	−0.147330	−	0.892363i	−0.953658	−	0.300894i	$-0.902715\pi$
$157$	−23.1308	−	140.101i	−0.147330	−	0.892363i	0.806328	−	0.591469i	$-0.201452\pi$
$158$	35.2993	−	61.1402i	0.223413	−	0.386963i
$159$	125.373	−	72.3844i	0.788512	−	0.455248i
$160$	−23.2956	+	19.1182i	−0.145597	+	0.119489i
$161$	243.678	+	100.935i	1.51353	+	0.626923i
$162$	−58.6221	−	66.8456i	−0.361865	−	0.412627i
$163$	54.3367	−	3.56141i	0.333354	−	0.0218492i	0.102193	−	0.994765i	$-0.467414\pi$
$163$	54.3367	−	3.56141i	0.333354	−	0.0218492i	0.231161	+	0.972915i	$0.425748\pi$
$164$	43.9557	−	144.902i	0.268022	−	0.883551i
$165$	−24.2132	+	53.4396i	−0.146746	+	0.323876i
$166$	−7.36863	+	74.8149i	−0.0443893	+	0.450692i
$167$	−156.231	+	233.816i	−0.935512	+	1.40009i	−0.0191175	+	0.999817i	$0.506086\pi$
$167$	−156.231	+	233.816i	−0.935512	+	1.40009i	−0.916395	+	0.400276i	$0.868914\pi$
$168$	206.899	+	77.8713i	1.23154	+	0.463520i
$169$	−19.6425	+	299.687i	−0.116228	+	1.77330i
$170$	2.99729	+	3.90614i	0.0176311	+	0.0229773i
$171$	31.1858	+	43.5197i	0.182373	+	0.254501i
$172$	153.154	−	153.154i	0.890432	−	0.890432i
$173$	22.6043	−	136.912i	0.130661	−	0.791399i	−0.838488	−	0.544921i	$-0.816560\pi$
$173$	22.6043	−	136.912i	0.130661	−	0.791399i	0.969148	−	0.246479i	$-0.0792735\pi$
$174$	−48.8120	−	40.0590i	−0.280529	−	0.230224i
$175$	−110.139	−	206.055i	−0.629365	−	1.17746i
$176$	−70.0173	−	104.788i	−0.397825	−	0.595388i
$177$	46.3698	+	198.869i	0.261976	+	1.12355i
$178$	9.89186	−	2.65052i	0.0555723	−	0.0148905i
$179$	−118.847	−	111.312i	−0.663949	−	0.621856i	0.276813	−	0.960924i	$-0.410722\pi$
$179$	−118.847	−	111.312i	−0.663949	−	0.621856i	−0.940762	+	0.339068i	$0.889888\pi$
$180$	−9.87276	−	6.13927i	−0.0548486	−	0.0341071i
$181$	−4.49774	+	4.21259i	−0.0248494	+	0.0232740i	−0.695918	−	0.718121i	$-0.745002\pi$
$181$	−4.49774	+	4.21259i	−0.0248494	+	0.0232740i	0.671069	+	0.741395i	$0.265836\pi$
$182$	181.663	−	36.1351i	0.998150	−	0.198544i
$183$	−70.5504	−	207.835i	−0.385522	−	1.13571i
$184$	−157.920	+	71.5528i	−0.858263	+	0.388874i
$185$	−35.5944	+	4.68610i	−0.192402	+	0.0253302i
$186$	7.15215	−	35.9563i	0.0384524	−	0.193313i
$187$	−86.9895	+	54.0936i	−0.465185	+	0.289270i
$188$	−4.46046	+	16.6467i	−0.0237258	+	0.0885460i
$189$	5.88234	−	179.687i	0.0311235	−	0.950724i
$190$	9.27094	+	7.11384i	0.0487944	+	0.0374413i
$191$	182.658	+	160.187i	0.956323	+	0.838673i	0.986978	−	0.160857i	$-0.0514258\pi$
$191$	182.658	+	160.187i	0.956323	+	0.838673i	−0.0306545	+	0.999530i	$0.509759\pi$
$192$	2.99661	−	1.47776i	0.0156073	−	0.00769668i
$193$			5.82114i			0.0301613i	0.999886	+	0.0150807i	$0.00480051\pi$
$193$			5.82114i			0.0301613i	−0.999886	+	0.0150807i	$0.995199\pi$
$194$	63.4316	+	57.4330i	0.326967	+	0.296047i
$195$	−73.2904			−0.375848
$196$	64.0270	+	129.834i	0.326668	+	0.662417i
$197$	−90.3500	+	103.024i	−0.458629	+	0.522967i	−0.934219	−	0.356701i	$-0.883902\pi$
$197$	−90.3500	+	103.024i	−0.458629	+	0.522967i	0.475589	+	0.879667i	$0.342235\pi$
$198$	−35.5667	+	46.3514i	−0.179630	+	0.234098i
$199$	335.251	+	10.9750i	1.68468	+	0.0551507i	0.859950	−	0.510378i	$-0.170495\pi$
$199$	335.251	+	10.9750i	1.68468	+	0.0551507i	0.824728	+	0.565529i	$0.191328\pi$
$200$	148.348	+	39.7498i	0.741741	+	0.198749i
$201$	199.664	+	321.086i	0.993353	+	1.59744i
$202$	−26.6843	−	5.30783i	−0.132100	−	0.0262764i
$203$	−25.2914	−	192.107i	−0.124588	−	0.946341i
$204$	−28.1204	−	62.0630i	−0.137845	−	0.304230i
$205$	42.0525	−	14.2749i	0.205134	−	0.0696336i
$206$	−3.74968	−	18.8509i	−0.0182023	−	0.0915093i
$207$	−71.0458	−	75.8548i	−0.343216	−	0.366448i
$208$	83.1368	−	133.695i	0.399696	−	0.642764i
$209$	−166.199	+	177.449i	−0.795210	+	0.849037i
$210$	7.48614	+	27.9387i	0.0356483	+	0.133041i
$211$	−168.969	+	39.3980i	−0.800800	+	0.186720i	−0.607396	−	0.794399i	$-0.707786\pi$
$211$	−168.969	+	39.3980i	−0.800800	+	0.186720i	−0.193404	+	0.981119i	$0.561953\pi$
$212$	−108.316	+	72.3744i	−0.510924	+	0.341389i
$213$	429.576	−	229.613i	2.01679	−	1.07800i
$214$	−58.7576	+	71.5963i	−0.274568	+	0.334562i
$215$	62.6740	+	10.3475i	0.291507	+	0.0481280i
$216$	83.5638	+	83.5638i	0.386870	+	0.386870i
$217$	91.4415	−	65.5261i	0.421389	−	0.301963i
$218$	−111.162	+	85.2976i	−0.509917	+	0.391273i
$219$	−150.135	−	9.84037i	−0.685548	−	0.0449332i
$220$	18.5965	−	49.4098i	0.0845297	−	0.224590i
$221$	−106.400	−	71.0939i	−0.481446	−	0.321692i
$222$	−119.429	−	11.7627i	−0.537968	−	0.0529853i
$223$	298.405	+	135.206i	1.33814	+	0.606304i	0.949117	−	0.314924i	$-0.101979\pi$
$223$	298.405	+	135.206i	1.33814	+	0.606304i	0.389024	+	0.921228i	$0.372812\pi$
$224$	−295.801	−	89.7302i	−1.32054	−	0.400581i
$225$	6.02134	+	91.8679i	0.0267615	+	0.408302i
$226$	9.59085	−	8.41095i	0.0424374	−	0.0372166i
$227$	108.154	−	261.106i	0.476447	−	1.15025i	−0.484817	−	0.874616i	$-0.661114\pi$
$227$	108.154	−	261.106i	0.476447	−	1.15025i	0.961264	−	0.275630i	$-0.0888864\pi$
$228$	−102.592	−	125.009i	−0.449964	−	0.548283i
$229$	−15.6135	−	27.0433i	−0.0681811	−	0.118093i	0.829920	−	0.557883i	$-0.188386\pi$
$229$	−15.6135	−	27.0433i	−0.0681811	−	0.118093i	−0.898101	+	0.439790i	$0.855053\pi$
$230$	−19.6450	−	11.3420i	−0.0854128	−	0.0493131i
$231$	−593.740	+	98.0269i	−2.57030	+	0.424359i
$232$	103.530	+	74.1889i	0.446252	+	0.319780i
$233$	53.9454	−	1.76599i	0.231525	−	0.00757935i	0.0832638	−	0.996528i	$-0.473466\pi$
$233$	53.9454	−	1.76599i	0.231525	−	0.00757935i	0.148262	+	0.988948i	$0.452632\pi$
$234$	−71.0785	−	16.5732i	−0.303754	−	0.0708255i
$235$	−4.73040	+	1.78040i	−0.0201294	+	0.00757616i
$236$	−53.3407	−	175.841i	−0.226020	−	0.745088i
$237$	−284.083	−	37.4002i	−1.19866	−	0.157807i
$238$	−16.2333	+	47.8218i	−0.0682072	+	0.200932i
$239$	−17.3336	−	175.991i	−0.0725254	−	0.736363i	−0.960836	−	0.277119i	$-0.910620\pi$
$239$	−17.3336	−	175.991i	−0.0725254	−	0.736363i	0.888310	−	0.459244i	$-0.151880\pi$
$240$	21.6821	+	11.5893i	0.0903423	+	0.0482890i
$241$	−21.8559	+	9.05302i	−0.0906884	+	0.0375644i	−0.427566	−	0.903984i	$-0.640629\pi$
$241$	−21.8559	+	9.05302i	−0.0906884	+	0.0375644i	0.336878	+	0.941548i	$0.390629\pi$
$242$	−142.214	−	70.1322i	−0.587661	−	0.289803i
$243$	−85.7607	+	173.905i	−0.352925	+	0.715660i
$244$	75.5808	+	182.468i	0.309757	+	0.747820i
$245$	−20.0137	+	37.4429i	−0.0816884	+	0.152828i
$246$	147.730	−	14.5502i	0.600530	−	0.0591470i
$247$	−287.598	−	97.6265i	−1.16437	−	0.395249i
$248$	−9.65199	+	73.3141i	−0.0389193	+	0.295621i
$249$	291.978	−	88.5705i	1.17260	−	0.355705i
$250$	14.4186	+	38.3094i	0.0576745	+	0.153237i
$251$	−18.4566	+	79.1562i	−0.0735325	+	0.315364i	−0.997793	−	0.0663983i	$-0.978849\pi$
$251$	−18.4566	+	79.1562i	−0.0735325	+	0.315364i	0.924261	+	0.381762i	$0.124683\pi$
$252$	−3.90171	−	119.185i	−0.0154830	−	0.472956i
$253$	274.899	−	383.622i	1.08656	−	1.51629i
$254$	0.944392	+	5.72010i	0.00371808	+	0.0225201i
$255$	9.99153	−	17.3058i	0.0391825	−	0.0678660i
$256$	94.8603	−	54.7676i	0.370548	−	0.213936i
$257$	−341.409	+	280.187i	−1.32844	+	1.09022i	−0.339705	+	0.940532i	$0.610327\pi$
$257$	−341.409	+	280.187i	−1.32844	+	1.09022i	−0.988733	+	0.149688i	$0.952173\pi$
$258$	196.171	+	81.2567i	0.760353	+	0.314949i
$259$	−242.803	−	276.863i	−0.937462	−	1.06897i
$260$	65.8093	−	4.31337i	0.253113	−	0.0165899i
$261$	−22.1636	+	73.0636i	−0.0849180	+	0.279937i
$262$	30.7319	−	67.8267i	0.117297	−	0.258880i
$263$	−42.0410	+	426.849i	−0.159852	+	1.62300i	0.496147	+	0.868239i	$0.334748\pi$
$263$	−42.0410	+	426.849i	−0.159852	+	1.62300i	−0.655998	+	0.754762i	$0.727752\pi$
$264$	219.765	−	328.902i	0.832445	−	1.24584i
$265$	−35.7570	−	13.4580i	−0.134932	−	0.0507848i
$266$	−7.83939	+	119.606i	−0.0294714	+	0.449646i
$267$	−25.3024	−	32.9747i	−0.0947656	−	0.123501i
$268$	−198.180	−	276.560i	−0.739479	−	1.03194i
$269$	61.1176	−	61.1176i	0.227203	−	0.227203i	−0.584320	−	0.811523i	$-0.698639\pi$
$269$	61.1176	−	61.1176i	0.227203	−	0.227203i	0.811523	+	0.584320i	$0.198639\pi$
$270$	−2.51871	+	15.2556i	−0.00932855	+	0.0565022i
$271$	44.2036	+	36.2770i	0.163113	+	0.133863i	0.712409	−	0.701764i	$-0.247604\pi$
$271$	44.2036	+	36.2770i	0.163113	+	0.133863i	−0.549296	+	0.835628i	$0.685104\pi$
$272$	20.2351	+	37.8572i	0.0743937	+	0.139181i
$273$	−417.650	−	625.057i	−1.52985	−	2.28959i
$274$	−12.3590	−	53.0049i	−0.0451059	−	0.193449i
$275$	−403.824	+	108.204i	−1.46845	+	0.393470i
$276$	229.118	+	214.593i	0.830139	+	0.777510i
$277$	296.914	+	184.633i	1.07189	+	0.666546i	0.945562	−	0.325442i	$-0.105513\pi$
$277$	296.914	+	184.633i	1.07189	+	0.666546i	0.126331	+	0.991988i	$0.459680\pi$
$278$	−66.6983	+	62.4698i	−0.239922	+	0.224712i
$279$	−43.4760	+	8.64791i	−0.155828	+	0.0309961i
$280$	−18.7534	−	55.2457i	−0.0669764	−	0.197306i
$281$	−404.809	+	183.417i	−1.44060	+	0.652729i	−0.972915	−	0.231165i	$-0.925746\pi$
$281$	−404.809	+	183.417i	−1.44060	+	0.652729i	−0.467688	+	0.883894i	$0.654913\pi$
$282$	−16.7505	+	2.20524i	−0.0593989	+	0.00782001i
$283$	−7.60519	+	38.2339i	−0.0268735	+	0.135102i	−0.991893	−	0.127076i	$-0.959441\pi$
$283$	−7.60519	+	38.2339i	−0.0268735	+	0.135102i	0.965020	+	0.262178i	$0.0844408\pi$
$284$	−372.214	+	231.457i	−1.31061	+	0.814991i
$285$	12.2753	−	45.8122i	0.0430714	−	0.160744i
$286$	10.8440	−	331.249i	0.0379160	−	1.15821i
$287$	361.382	+	277.298i	1.25917	+	0.966196i
$288$	91.5758	+	80.3098i	0.317971	+	0.278853i
$289$	−227.904	+	112.390i	−0.788595	+	0.388892i
$290$			16.6646i			0.0574642i
$291$	116.836	−	327.052i	0.401498	−	1.12389i
$292$	135.389			0.463662
$293$	196.128	+	397.708i	0.669378	+	1.35736i	0.921009	+	0.389541i	$0.127366\pi$
$293$	196.128	+	397.708i	0.669378	+	1.35736i	−0.251631	+	0.967823i	$0.580967\pi$
$294$	−93.5719	+	106.698i	−0.318272	+	0.362920i
$295$	32.8069	−	42.7547i	0.111210	−	0.144931i
$296$	241.931	+	7.92001i	0.817335	+	0.0267568i
$297$	−310.733	−	83.2606i	−1.04624	−	0.280339i
$298$	25.2563	+	40.6154i	0.0847527	+	0.136293i
$299$	578.237	+	115.018i	1.93390	+	0.384677i
$300$	−36.2969	−	275.702i	−0.120990	−	0.919007i
$301$	268.903	+	593.481i	0.893365	+	1.97170i
$302$	−12.7546	+	4.32959i	−0.0422337	+	0.0143364i
$303$	21.5426	+	108.302i	0.0710976	+	0.357432i
$304$	69.6452	+	74.3594i	0.229096	+	0.244603i
$305$	−30.5875	+	49.1887i	−0.100287	+	0.161275i
$306$	13.6034	−	14.5242i	0.0444554	−	0.0474646i
$307$	−1.47447	−	5.50281i	−0.00480284	−	0.0179244i	0.963483	−	0.267770i	$-0.0862868\pi$
$307$	−1.47447	−	5.50281i	−0.00480284	−	0.0179244i	−0.968286	+	0.249846i	$0.919620\pi$
$308$	527.365	−	122.964i	1.71222	−	0.399235i
$309$	−64.8612	+	43.3389i	−0.209907	+	0.140255i
$310$	−8.53266	+	4.56080i	−0.0275247	+	0.0147123i
$311$	189.219	−	230.564i	0.608421	−	0.741363i	−0.374126	−	0.927378i	$-0.622057\pi$
$311$	189.219	−	230.564i	0.608421	−	0.741363i	0.982547	+	0.186015i	$0.0595572\pi$
$312$	487.549	+	80.4946i	1.56266	+	0.257996i
$313$	−367.621	−	367.621i	−1.17451	−	1.17451i	−0.981123	−	0.193386i	$-0.938053\pi$
$313$	−367.621	−	367.621i	−1.17451	−	1.17451i	−0.193386	−	0.981123i	$-0.561947\pi$
$314$	−101.821	+	72.9637i	−0.324270	+	0.232368i
$315$	27.7462	−	21.2904i	0.0880831	−	0.0675886i
$316$	257.286	+	16.8634i	0.814197	+	0.0533653i
$317$	−191.645	+	509.190i	−0.604560	+	1.60628i	0.178230	+	0.983989i	$0.442963\pi$
$317$	−191.645	+	509.190i	−0.604560	+	1.60628i	−0.782789	+	0.622287i	$0.786204\pi$
$318$	−106.186	−	70.9513i	−0.333919	−	0.223117i
$319$	−345.043	−	33.9838i	−1.08164	−	0.106532i
$320$	−0.803168	−	0.363911i	−0.00250990	−	0.00113722i
$321$	359.725	+	109.121i	1.12064	+	0.339942i
$322$	−15.2176	−	232.175i	−0.0472595	−	0.721041i
$323$	62.2600	−	54.6005i	0.192755	−	0.169042i
$324$	124.262	−	299.995i	0.383525	−	0.925912i
$325$	−331.317	−	403.711i	−1.01944	−	1.24219i
$326$	−24.0182	−	41.6007i	−0.0736755	−	0.127610i
$327$	492.493	+	284.341i	1.50610	+	0.869545i
$328$	−295.423	+	48.7746i	−0.900680	+	0.148703i
$329$	−42.1407	−	30.1976i	−0.128087	−	0.0917859i
$330$	51.7277	−	1.69339i	0.156751	−	0.00513149i
$331$	471.805	+	110.009i	1.42539	+	0.332355i	0.867449	−	0.497525i	$-0.165758\pi$
$331$	471.805	+	110.009i	1.42539	+	0.332355i	0.557942	+	0.829880i	$0.311591\pi$
$332$	−256.962	+	96.7135i	−0.773981	+	0.291306i
$333$	42.1216	+	138.856i	0.126491	+	0.416986i
$334$	245.947	+	32.3796i	0.736369	+	0.0969449i
$335$	32.0748	−	94.4892i	0.0957455	−	0.282057i
$336$	24.7173	+	250.959i	0.0735634	+	0.746902i
$337$	317.028	+	169.455i	0.940736	+	0.502834i	0.869121	−	0.494599i	$-0.164685\pi$
$337$	317.028	+	169.455i	0.940736	+	0.502834i	0.0716142	+	0.997432i	$0.477185\pi$
$338$	244.771	−	101.388i	0.724176	−	0.299963i
$339$	−46.4347	−	22.8991i	−0.136976	−	0.0675489i
$340$	−7.95315	+	16.1274i	−0.0233916	+	0.0474335i
$341$	−77.0315	−	185.971i	−0.225899	−	0.545368i
$342$	22.2644	−	41.6537i	0.0651005	−	0.121795i
$343$	39.2335	−	3.86417i	0.114383	−	0.0112658i
$344$	−405.561	−	137.669i	−1.17896	−	0.400202i
$345$	−12.0171	+	91.2786i	−0.0348321	+	0.264576i
$346$	−117.142	+	35.5347i	−0.338561	+	0.102701i
$347$	−60.5571	−	160.896i	−0.174516	−	0.463679i	0.819478	−	0.573111i	$-0.194263\pi$
$347$	−60.5571	−	160.896i	−0.174516	−	0.463679i	−0.993994	+	0.109432i	$0.965097\pi$
$348$	52.3678	−	224.593i	0.150482	−	0.645383i
$349$	−11.1571	−	340.813i	−0.0319687	−	0.976542i	−0.888063	−	0.459722i	$-0.847949\pi$
$349$	−11.1571	−	340.813i	−0.0319687	−	0.976542i	0.856094	−	0.516820i	$-0.172884\pi$
$350$	−120.055	+	167.536i	−0.343014	+	0.478676i
$351$	−65.4621	−	396.498i	−0.186502	−	1.12962i
$352$	−276.553	+	479.004i	−0.785663	+	1.36081i
$353$	267.014	−	154.161i	0.756415	−	0.436716i	−0.0715924	−	0.997434i	$-0.522808\pi$
$353$	267.014	−	154.161i	0.756415	−	0.436716i	0.828007	+	0.560718i	$0.189475\pi$
$354$	139.250	−	114.280i	0.393362	−	0.322824i
$355$	−118.763	−	49.1931i	−0.334542	−	0.138572i
$356$	24.6603	+	28.1197i	0.0692706	+	0.0789880i
$357$	204.530	−	13.4056i	0.572914	−	0.0375508i
$358$	−41.6981	+	137.460i	−0.116475	+	0.383967i
$359$	−78.5181	+	173.293i	−0.218714	+	0.482711i	−0.987662	−	0.156600i	$-0.949947\pi$
$359$	−78.5181	+	173.293i	−0.218714	+	0.482711i	0.768949	+	0.639311i	$0.220780\pi$
$360$	−2.25332	+	22.8784i	−0.00625922	+	0.0635510i
$361$	−91.3671	+	136.741i	−0.253095	+	0.378783i
$362$	5.08781	+	1.91492i	0.0140547	+	0.00528982i
$363$	−42.0911	+	642.186i	−0.115954	+	1.76911i
$364$	411.805	+	536.675i	1.13133	+	1.47438i
$365$	23.1284	+	32.2757i	0.0633656	+	0.0884266i
$366$	−136.909	+	136.909i	−0.374068	+	0.374068i
$367$	−38.3183	+	232.091i	−0.104410	+	0.632399i	0.882398	+	0.470503i	$0.155928\pi$
$367$	−38.3183	+	232.091i	−0.104410	+	0.632399i	−0.986808	+	0.161896i	$0.948239\pi$
$368$	−152.877	−	125.463i	−0.415427	−	0.340932i
$369$	−84.6111	−	158.296i	−0.229298	−	0.428987i
$370$	17.5954	+	26.3334i	0.0475551	+	0.0711713i
$371$	−88.9871	−	381.645i	−0.239857	−	1.02869i
$372$	129.329	−	34.6536i	0.347659	−	0.0931549i
$373$	−316.471	−	296.407i	−0.848448	−	0.794658i	0.132039	−	0.991245i	$-0.457848\pi$
$373$	−316.471	−	296.407i	−0.848448	−	0.794658i	−0.980486	+	0.196587i	$0.937014\pi$
$374$	76.7385	+	47.7191i	0.205183	+	0.127591i
$375$	121.254	−	113.566i	0.323343	−	0.302844i
$376$	33.4234	−	6.64833i	0.0888921	−	0.0176817i
$377$	−139.221	−	410.133i	−0.369288	−	1.08789i
$378$	−144.460	+	65.4542i	−0.382171	+	0.173159i
$379$	104.780	−	13.7946i	0.276465	−	0.0363972i	0.00898097	−	0.999960i	$-0.497141\pi$
$379$	104.780	−	13.7946i	0.276465	−	0.0363972i	0.267484	+	0.963562i	$0.413808\pi$
$380$	−8.32615	+	41.8584i	−0.0219109	+	0.110154i
$381$	19.9818	−	12.4255i	0.0524457	−	0.0326128i
$382$	55.4697	−	207.016i	0.145209	−	0.541926i
$383$	−8.69387	+	265.570i	−0.0226994	+	0.693395i	0.926056	+	0.377385i	$0.123177\pi$
$383$	−8.69387	+	265.570i	−0.0226994	+	0.693395i	−0.948756	+	0.316010i	$0.897657\pi$
$384$	−364.715	−	279.856i	−0.949780	−	0.728791i
$385$	119.403	+	104.714i	0.310138	+	0.271984i
$386$	4.60559	−	2.27123i	0.0119316	−	0.00588400i
$387$		−	256.741i		−	0.663412i
$388$	−85.6620	+	300.545i	−0.220778	+	0.774600i
$389$	87.5787			0.225138			0.112569	−	0.993644i	$-0.464092\pi$
$389$	87.5787			0.225138			0.112569	+	0.993644i	$0.464092\pi$
$390$	28.5956	+	57.9862i	0.0733221	+	0.148682i
$391$	−105.989	+	120.857i	−0.271071	+	0.309097i
$392$	174.260	−	227.100i	0.444541	−	0.579337i
$393$	−302.061	−	9.88845i	−0.768603	−	0.0251615i
$394$	116.763	+	31.2866i	0.296353	+	0.0794075i
$395$	39.9319	+	64.2158i	0.101093	+	0.162572i
$396$	−209.277	−	41.6278i	−0.528478	−	0.105121i
$397$	−26.3574	−	200.204i	−0.0663913	−	0.504292i	−0.992041	−	0.125912i	$-0.959814\pi$
$397$	−26.3574	−	200.204i	−0.0663913	−	0.504292i	0.925650	−	0.378380i	$-0.123519\pi$
$398$	−122.121	−	269.527i	−0.306837	−	0.677204i
$399$	460.661	−	156.373i	1.15454	−	0.391913i
$400$	34.1780	+	171.824i	0.0854450	+	0.429561i
$401$	1.57554	+	1.68219i	0.00392903	+	0.00419498i	0.731826	−	0.681492i	$-0.238669\pi$
$401$	1.57554	+	1.68219i	0.00392903	+	0.00419498i	−0.727897	+	0.685687i	$0.759502\pi$
$402$	176.135	−	283.249i	0.438147	−	0.704598i
$403$	171.895	−	183.531i	0.426539	−	0.455411i
$404$	−25.7175	−	95.9791i	−0.0636572	−	0.237572i
$405$	92.7441	−	21.6249i	0.228998	−	0.0533948i
$406$	−142.124	+	94.9644i	−0.350060	+	0.233903i
$407$	−581.118	+	310.614i	−1.42781	+	0.763179i
$408$	−85.4735	+	104.150i	−0.209494	+	0.255269i
$409$	−646.820	−	106.790i	−1.58147	−	0.261101i	−0.693309	−	0.720641i	$-0.743848\pi$
$409$	−646.820	−	106.790i	−1.58147	−	0.261101i	−0.888157	+	0.459540i	$0.848014\pi$
$410$	−27.7016	−	27.7016i	−0.0675649	−	0.0675649i
$411$	−179.557	+	128.668i	−0.436877	+	0.313062i
$412$	55.6899	−	42.7324i	0.135170	−	0.103719i
$413$	551.586	+	36.1529i	1.33556	+	0.0875372i
$414$	−32.2953	+	85.8064i	−0.0780079	+	0.207262i
$415$	−66.9523	−	44.7361i	−0.161331	−	0.107798i
$416$	−687.622	−	67.7249i	−1.65294	−	0.162800i
$417$	337.837	+	153.072i	0.810160	+	0.367079i
$418$	205.240	+	62.2589i	0.491005	+	0.148945i
$419$	33.8410	+	516.314i	0.0807661	+	1.23225i	0.825310	+	0.564679i	$0.191000\pi$
$419$	33.8410	+	516.314i	0.0807661	+	1.23225i	−0.744544	+	0.667573i	$0.767333\pi$
$420$	−79.4216	+	69.6509i	−0.189099	+	0.165835i
$421$	116.791	−	281.959i	0.277414	−	0.669737i	−0.722348	−	0.691529i	$-0.756937\pi$
$421$	116.791	−	281.959i	0.277414	−	0.669737i	0.999763	+	0.0217924i	$0.00693729\pi$
$422$	97.0974	+	118.314i	0.230089	+	0.280364i
$423$	10.2142	+	17.6915i	0.0241470	+	0.0418238i
$424$	223.085	+	128.798i	0.526144	+	0.303769i
$425$	140.495	−	23.1958i	0.330576	−	0.0545784i
$426$	−349.273	−	250.286i	−0.819890	−	0.587525i
$427$	−593.812	+	19.4394i	−1.39066	+	0.0455255i
$428$	−329.428	−	76.8119i	−0.769692	−	0.179467i
$429$	−1258.93	+	473.826i	−2.93456	+	1.10449i
$430$	−16.2666	−	53.6239i	−0.0378294	−	0.124707i
$431$	835.523	+	109.999i	1.93857	+	0.255217i	0.996727	−	0.0808430i	$-0.0257612\pi$
$431$	835.523	+	109.999i	1.93857	+	0.255217i	0.941840	+	0.336060i	$0.109095\pi$
$432$	−43.3317	+	127.651i	−0.100305	+	0.295488i
$433$	26.1707	+	265.716i	0.0604405	+	0.613663i	0.976924	+	0.213589i	$0.0685154\pi$
$433$	26.1707	+	265.716i	0.0604405	+	0.613663i	−0.916483	+	0.400074i	$0.868985\pi$
$434$	−87.5208	−	46.7808i	−0.201661	−	0.107790i
$435$	62.4872	−	25.8830i	0.143649	−	0.0595012i
$436$	−458.957	−	226.332i	−1.05265	−	0.519111i
$437$	−168.744	+	342.179i	−0.386142	+	0.783018i
$438$	50.7924	+	122.624i	0.115964	+	0.279963i
$439$	49.0658	−	91.7957i	0.111767	−	0.209102i	−0.819818	−	0.572624i	$-0.805926\pi$
$439$	49.0658	−	91.7957i	0.111767	−	0.209102i	0.931586	+	0.363522i	$0.118426\pi$
$440$	−103.891	+	10.2324i	−0.236116	+	0.0232554i
$441$	162.489	+	55.1577i	0.368457	+	0.125074i
$442$	−14.7346	+	111.920i	−0.0333361	+	0.253213i
$443$	49.6633	−	15.0652i	0.112107	−	0.0340072i	−0.233733	−	0.972301i	$-0.575094\pi$
$443$	49.6633	−	15.0652i	0.112107	−	0.0340072i	0.345840	+	0.938294i	$0.387594\pi$
$444$	−154.386	−	410.194i	−0.347717	−	0.923861i
$445$	−2.49081	+	10.6825i	−0.00559732	+	0.0240056i
$446$	−9.45586	−	288.846i	−0.0212015	−	0.647638i
$447$	113.068	−	157.786i	0.252948	−	0.352989i
$448$	−1.47329	−	8.92359i	−0.00328860	−	0.0199187i
$449$	377.225	−	653.373i	0.840145	−	1.45517i	−0.0496262	−	0.998768i	$-0.515803\pi$
$449$	377.225	−	653.373i	0.840145	−	1.45517i	0.889771	−	0.456406i	$-0.150864\pi$
$450$	70.3351	−	40.6080i	0.156300	−	0.0902399i
$451$	630.057	−	517.074i	1.39702	−	1.14651i
$452$	43.0426	+	17.8288i	0.0952270	+	0.0394443i
$453$	36.0447	+	41.1011i	0.0795689	+	0.0907309i
$454$	−248.781	+	16.3060i	−0.547975	+	0.0359162i
$455$	−57.5906	+	189.851i	−0.126573	+	0.417255i
$456$	−131.974	+	291.274i	−0.289418	+	0.638758i
$457$	34.0730	−	345.949i	0.0745580	−	0.757000i	−0.883118	−	0.469151i	$-0.844560\pi$
$457$	34.0730	−	345.949i	0.0745580	−	0.757000i	0.957676	−	0.287849i	$-0.0929401\pi$
$458$	−15.3044	+	22.9046i	−0.0334156	+	0.0500100i
$459$	102.548	+	38.5964i	0.223416	+	0.0840880i
$460$	5.41839	−	82.6687i	0.0117791	−	0.179715i
$461$	29.7800	+	38.8101i	0.0645987	+	0.0841867i	0.824535	−	0.565811i	$-0.191437\pi$
$461$	29.7800	+	38.8101i	0.0645987	+	0.0841867i	−0.759937	+	0.649997i	$0.774770\pi$
$462$	309.216	+	431.510i	0.669299	+	0.934005i
$463$	−284.003	+	284.003i	−0.613396	+	0.613396i	−0.943829	−	0.330433i	$-0.892805\pi$
$463$	−284.003	+	284.003i	−0.613396	+	0.613396i	0.330433	+	0.943829i	$0.392805\pi$
$464$	−23.6669	+	143.348i	−0.0510063	+	0.308940i
$465$	30.3543	+	24.9111i	0.0652781	+	0.0535724i
$466$	−22.4450	−	41.9917i	−0.0481653	−	0.0901109i
$467$	−416.289	−	623.020i	−0.891410	−	1.33409i	−0.942085	−	0.335374i	$-0.891137\pi$
$467$	−416.289	−	623.020i	−0.891410	−	1.33409i	0.0506747	−	0.998715i	$-0.483863\pi$
$468$	−60.5281	−	259.591i	−0.129334	−	0.554682i
$469$	988.632	−	264.903i	2.10796	−	0.564825i
$470$	3.25428	+	3.04796i	0.00692400	+	0.00648503i
$471$	431.737	+	268.471i	0.916638	+	0.570002i
$472$	−265.198	+	248.385i	−0.561860	+	0.526240i
$473$	1143.46	−	227.449i	2.41747	−	0.480864i
$474$	81.2498	+	239.354i	0.171413	+	0.504967i
$475$	307.843	−	139.482i	0.648091	−	0.293646i
$476$	−182.864	+	24.0745i	−0.384168	+	0.0505767i
$477$	−30.1253	+	151.450i	−0.0631558	+	0.317506i
$478$	−132.478	+	82.3801i	−0.277151	+	0.172343i
$479$	−17.2927	+	64.5372i	−0.0361017	+	0.134733i	−0.981625	−	0.190822i	$-0.938885\pi$
$479$	−17.2927	+	64.5372i	−0.0361017	+	0.134733i	0.945523	+	0.325555i	$0.105551\pi$
$480$	3.53034	−	107.841i	0.00735487	−	0.224668i
$481$	−653.038	−	501.094i	−1.35767	−	1.04177i
$482$	15.6901	+	13.7598i	0.0325521	+	0.0285474i
$483$	−846.950	+	417.670i	−1.75352	+	0.864741i
$484$		−	579.113i		−	1.19651i
$485$	−86.2810	+	30.9207i	−0.177899	+	0.0637540i
$486$	171.052			0.351959
$487$	272.488	+	552.551i	0.559523	+	1.13460i	0.974420	+	0.224732i	$0.0721508\pi$
$487$	272.488	+	552.551i	0.559523	+	1.13460i	−0.414897	+	0.909868i	$0.636183\pi$
$488$	257.501	−	293.624i	0.527666	−	0.601688i
$489$	−118.686	+	154.674i	−0.242711	+	0.316307i
$490$	37.4329	+	1.22543i	0.0763937	+	0.00250087i
$491$	223.495	+	59.8853i	0.455183	+	0.121966i	0.479124	−	0.877747i	$-0.340955\pi$
$491$	223.495	+	59.8853i	0.455183	+	0.121966i	−0.0239404	+	0.999713i	$0.507621\pi$
$492$	286.291	+	460.393i	0.581892	+	0.935758i
$493$	115.823	+	23.0387i	0.234936	+	0.0467316i
$494$	34.9714	+	265.634i	0.0707923	+	0.537721i
$495$	−25.8269	−	57.0012i	−0.0521756	−	0.115154i
$496$	−79.8748	+	27.1138i	−0.161038	+	0.0546650i
$497$	−257.233	−	1293.20i	−0.517571	−	2.60201i
$498$	−183.996	−	196.451i	−0.369470	−	0.394479i
$499$	22.3089	−	35.8756i	0.0447071	−	0.0718949i	−0.826087	−	0.563542i	$-0.809438\pi$
$499$	22.3089	−	35.8756i	0.0447071	−	0.0718949i	0.870795	+	0.491647i	$0.163605\pi$
$500$	−102.193	+	109.110i	−0.204386	+	0.218221i
$501$	−260.585	−	972.518i	−0.520131	−	1.94115i
$502$	69.8283	−	16.2817i	0.139100	−	0.0324336i
$503$	−82.8003	+	55.3254i	−0.164613	+	0.109991i	−0.635148	−	0.772390i	$-0.719061\pi$
$503$	−82.8003	+	55.3254i	−0.164613	+	0.109991i	0.470535	+	0.882381i	$0.344061\pi$
$504$	−207.959	+	111.156i	−0.412617	+	0.220548i
$505$	18.4873	−	22.5269i	0.0366086	−	0.0446077i
$506$	−410.772	−	67.8188i	−0.811803	−	0.134029i
$507$	−760.345	−	760.345i	−1.49969	−	1.49969i
$508$	−17.2109	+	12.3332i	−0.0338797	+	0.0242779i
$509$	−315.970	+	242.452i	−0.620766	+	0.476330i	−0.870622	−	0.491953i	$-0.836283\pi$
$509$	−315.970	+	242.452i	−0.620766	+	0.476330i	0.249856	+	0.968283i	$0.419617\pi$
$510$	−17.5905	−	1.15294i	−0.0344911	−	0.00226067i
$511$	−143.465	+	381.176i	−0.280753	+	0.745942i
$512$	346.696	+	231.655i	0.677140	+	0.452450i
$513$	258.806	+	25.4902i	0.504495	+	0.0496885i
$514$	354.886	+	160.797i	0.690440	+	0.312834i
$515$	19.7005	+	5.97609i	0.0382534	+	0.0116041i
$516$	50.7189	+	773.821i	0.0982924	+	1.49965i
$517$	−69.7449	+	61.1646i	−0.134903	+	0.118307i
$518$	−124.316	+	300.125i	−0.239992	+	0.579392i
$519$	315.186	+	384.055i	0.607295	+	0.739991i
$520$	−65.2052	−	112.939i	−0.125395	−	0.217190i
$521$	93.8952	+	54.2104i	0.180221	+	0.104051i	0.587397	−	0.809299i	$-0.300153\pi$
$521$	93.8952	+	54.2104i	0.180221	+	0.104051i	−0.407175	+	0.913350i	$0.633486\pi$
$522$	66.4543	−	10.9716i	0.127307	−	0.0210185i
$523$	401.603	+	287.785i	0.767884	+	0.550258i	0.897347	−	0.441326i	$-0.145492\pi$
$523$	401.603	+	287.785i	0.767884	+	0.550258i	−0.129463	+	0.991584i	$0.541325\pi$
$524$	271.810	−	8.89815i	0.518722	−	0.0169812i
$525$	814.676	+	189.956i	1.55176	+	0.361821i
$526$	354.119	−	133.281i	0.673231	−	0.253386i
$527$	19.9024	+	65.6094i	0.0377655	+	0.124496i
$528$	447.365	+	58.8967i	0.847282	+	0.111547i
$529$	68.0176	−	200.373i	0.128578	−	0.378778i
$530$	3.30352	+	33.5412i	0.00623306	+	0.0632854i
$531$	−192.094	−	102.677i	−0.361760	−	0.193365i
$532$	−404.436	+	167.523i	−0.760219	+	0.314893i
$533$	913.193	+	450.337i	1.71331	+	0.844910i
$534$	−16.2169	+	32.8846i	−0.0303687	+	0.0615816i
$535$	−37.9646	−	91.6547i	−0.0709619	−	0.171317i
$536$	−317.148	+	593.342i	−0.591693	+	1.10698i
$537$	580.198	−	57.1445i	1.08044	−	0.106414i
$538$	−72.2014	−	24.5091i	−0.134203	−	0.0455559i
$539$	−101.709	+	772.555i	−0.188699	+	1.43331i
$540$	−54.0388	+	16.3925i	−0.100072	+	0.0303564i
$541$	−167.898	−	446.094i	−0.310347	−	0.824572i	−0.995376	−	0.0960563i	$-0.969377\pi$
$541$	−167.898	−	446.094i	−0.310347	−	0.824572i	0.685029	−	0.728516i	$-0.259790\pi$
$542$	11.4549	−	49.1273i	0.0211345	−	0.0906408i
$543$	−0.721905	−	22.0519i	−0.00132948	−	0.0406113i
$544$	109.734	−	153.133i	0.201717	−	0.281495i
$545$	−24.4474	−	148.076i	−0.0448576	−	0.271699i
$546$	−331.581	+	574.316i	−0.607292	+	1.05186i
$547$	−786.084	+	453.846i	−1.43708	+	0.829700i	−0.997646	−	0.0685731i	$-0.978155\pi$
$547$	−786.084	+	453.846i	−1.43708	+	0.829700i	−0.439437	+	0.898273i	$0.644822\pi$
$548$	153.656	−	126.102i	0.280394	−	0.230113i
$549$	216.290	+	89.5904i	0.393972	+	0.163188i
$550$	243.169	+	277.281i	0.442125	+	0.504147i
$551$	279.683	−	18.3314i	0.507592	−	0.0332693i
$552$	180.192	−	594.014i	0.326435	−	1.07611i
$553$	−320.110	+	706.497i	−0.578860	+	1.27757i
$554$	30.2321	−	306.952i	0.0545707	−	0.554065i
$555$	71.4133	−	106.878i	0.128673	−	0.192572i
$556$	−312.361	−	117.564i	−0.561800	−	0.211447i
$557$	20.4555	−	312.090i	0.0367243	−	0.560305i	−0.939363	−	0.342925i	$-0.888582\pi$
$557$	20.4555	−	312.090i	0.0367243	−	0.560305i	0.976087	−	0.217380i	$-0.0697511\pi$
$558$	23.8051	+	31.0234i	0.0426614	+	0.0555974i
$559$	848.330	+	1183.84i	1.51758	+	2.11779i
$560$	47.0585	−	47.0585i	0.0840330	−	0.0840330i
$561$	59.7436	−	361.862i	0.106495	−	0.645030i
$562$	303.060	+	248.715i	0.539253	+	0.442554i
$563$	−350.284	−	655.335i	−0.622173	−	1.16400i	−0.973702	−	0.227827i	$-0.926838\pi$
$563$	−350.284	−	655.335i	−0.622173	−	1.16400i	0.351528	−	0.936177i	$-0.385662\pi$
$564$	−34.2807	−	51.3046i	−0.0607813	−	0.0909656i
$565$	3.10269	+	13.3067i	0.00549148	+	0.0235517i
$566$	33.2173	−	8.90056i	0.0586879	−	0.0157254i
$567$	712.936	+	667.738i	1.25738	+	1.17767i
$568$	736.014	+	457.683i	1.29580	+	0.805780i
$569$	372.206	−	348.609i	0.654141	−	0.612670i	−0.284041	−	0.958812i	$-0.591675\pi$
$569$	372.206	−	348.609i	0.654141	−	0.612670i	0.938182	+	0.346142i	$0.112508\pi$
$570$	−41.0353	+	8.16243i	−0.0719918	+	0.0143201i
$571$	−257.817	−	759.505i	−0.451519	−	1.33013i	−0.899825	−	0.436251i	$-0.856306\pi$
$571$	−257.817	−	759.505i	−0.451519	−	1.33013i	0.448306	−	0.893880i	$-0.352027\pi$
$572$	1102.54	−	499.552i	1.92751	−	0.873343i
$573$	−862.399	+	113.537i	−1.50506	+	0.198145i
$574$	78.3939	−	394.113i	0.136575	−	0.686608i
$575$	−557.122	+	346.441i	−0.968908	+	0.602506i
$576$	−0.922394	+	3.44242i	−0.00160138	+	0.00597643i
$577$	−30.2211	+	923.160i	−0.0523763	+	1.59993i	0.572965	+	0.819580i	$0.305793\pi$
$577$	−30.2211	+	923.160i	−0.0523763	+	1.59993i	−0.625342	+	0.780351i	$0.715040\pi$
$578$	177.842	+	136.463i	0.307685	+	0.236095i
$579$	−15.6697	−	13.7419i	−0.0270633	−	0.0237339i
$580$	−54.5856	+	26.9186i	−0.0941130	+	0.0464114i
$581$		−	825.934i		−	1.42157i
$582$	−304.344	+	35.1668i	−0.522928	+	0.0604240i
$583$	−701.212			−1.20277
$584$	−118.409	−	240.109i	−0.202755	−	0.411146i
$585$	51.5444	−	58.7751i	0.0881101	−	0.100470i
$586$	238.137	−	310.346i	0.406377	−	0.529601i
$587$	−822.769	−	26.9347i	−1.40165	−	0.0458853i	−0.677498	−	0.735525i	$-0.736936\pi$
$587$	−822.769	−	26.9347i	−1.40165	−	0.0458853i	−0.724153	+	0.689640i	$0.757769\pi$
$588$	−500.642	−	134.147i	−0.851433	−	0.228141i
$589$	85.9303	+	138.187i	0.145892	+	0.234613i
$590$	−46.6271	−	9.27470i	−0.0790289	−	0.0157198i
$591$	−64.0382	−	486.419i	−0.108356	−	0.823044i
$592$	113.956	+	251.507i	0.192494	+	0.424843i
$593$	−502.863	+	170.699i	−0.847999	+	0.287857i	−0.711415	−	0.702772i	$-0.751946\pi$
$593$	−502.863	+	170.699i	−0.847999	+	0.287857i	−0.136583	+	0.990629i	$0.543612\pi$
$594$	55.3638	+	278.332i	0.0932050	+	0.468573i
$595$	−36.9777	−	39.4807i	−0.0621474	−	0.0663541i
$596$	−92.2404	+	148.335i	−0.154766	+	0.248884i
$597$	−820.969	+	876.539i	−1.37516	+	1.46824i
$598$	−134.609	−	502.368i	−0.225099	−	0.840081i
$599$	737.054	−	171.857i	1.23047	−	0.286907i	0.439212	−	0.898383i	$-0.355258\pi$
$599$	737.054	−	171.857i	1.23047	−	0.286907i	0.791262	+	0.611477i	$0.209424\pi$
$600$	−457.206	+	305.495i	−0.762009	+	0.509158i
$601$	−50.3878	+	26.9329i	−0.0838400	+	0.0448134i	−0.512784	−	0.858518i	$-0.671386\pi$
$601$	−50.3878	+	26.9329i	−0.0838400	+	0.0448134i	0.428944	+	0.903331i	$0.358886\pi$
$602$	364.635	−	444.310i	0.605707	−	0.738056i
$603$	−397.916	−	65.6962i	−0.659894	−	0.108949i
$604$	−34.7844	−	34.7844i	−0.0575901	−	0.0575901i
$605$	138.056	−	98.9294i	0.228191	−	0.163520i
$606$	77.2814	−	59.3001i	0.127527	−	0.0978549i
$607$	9.04054	+	0.592548i	0.0148938	+	0.000976191i	0.0728482	−	0.997343i	$-0.476791\pi$
$607$	9.04054	+	0.592548i	0.0148938	+	0.000976191i	−0.0579544	+	0.998319i	$0.518458\pi$
$608$	157.503	−	418.474i	0.259050	−	0.688280i
$609$	576.831	+	385.426i	0.947177	+	0.632884i
$610$	50.8516	+	5.00845i	0.0833633	+	0.00821057i
$611$	−105.555	−	47.8262i	−0.172757	−	0.0782753i
$612$	69.5481	+	21.0972i	0.113641	+	0.0344725i
$613$	−46.0307	−	702.292i	−0.0750908	−	1.14566i	−0.854605	−	0.519279i	$-0.826201\pi$
$613$	−46.0307	−	702.292i	−0.0750908	−	1.14566i	0.779514	−	0.626385i	$-0.215466\pi$
$614$	−3.77844	+	3.31360i	−0.00615381	+	0.00539675i
$615$	−60.8471	+	146.898i	−0.0989384	+	0.238858i
$616$	−679.297	−	827.726i	−1.10275	−	1.34371i
$617$	168.954	+	292.636i	0.273831	+	0.474289i	0.969839	−	0.243745i	$-0.0783758\pi$
$617$	168.954	+	292.636i	0.273831	+	0.474289i	−0.696009	+	0.718033i	$0.745043\pi$
$618$	59.5959	+	34.4077i	0.0964334	+	0.0556759i
$619$	−140.733	+	23.2350i	−0.227355	+	0.0375364i	−0.275488	−	0.961305i	$-0.588839\pi$
$619$	−140.733	+	23.2350i	−0.227355	+	0.0375364i	0.0481333	+	0.998841i	$0.484673\pi$
$620$	−28.7220	−	20.5819i	−0.0463258	−	0.0331966i
$621$	−504.547	+	16.5172i	−0.812475	+	0.0265977i
$622$	−256.246	−	59.7481i	−0.411971	−	0.0960581i
$623$	−105.300	+	39.6320i	−0.169021	+	0.0636148i
$624$	163.627	+	539.406i	0.262223	+	0.864432i
$625$	554.055	+	72.9427i	0.886488	+	0.116708i
$626$	−147.422	+	434.290i	−0.235498	+	0.693755i
$627$	−85.3218	−	866.287i	−0.136079	−	1.38164i
$628$	−403.468	−	215.658i	−0.642465	−	0.343405i
$629$	207.349	−	85.8868i	0.329649	−	0.136545i
$630$	−27.6703	−	13.6455i	−0.0439211	−	0.0216595i
$631$	499.731	−	1013.35i	0.791966	−	1.60595i	−0.00353240	−	0.999994i	$-0.501124\pi$
$631$	499.731	−	1013.35i	0.791966	−	1.60595i	0.795499	−	0.605955i	$-0.207209\pi$
$632$	−195.111	−	471.039i	−0.308719	−	0.745315i
$633$	292.830	−	547.847i	0.462607	−	0.865477i
$634$	477.637	−	47.0431i	0.753370	−	0.0742005i
$635$	−5.88025	−	1.99608i	−0.00926023	−	0.00314343i
$636$	60.8794	−	462.425i	0.0957224	−	0.727084i
$637$	−931.500	+	282.567i	−1.46232	+	0.443591i
$638$	107.738	+	286.252i	0.168868	+	0.448671i
$639$	−117.979	+	505.983i	−0.184630	+	0.791835i
$640$	3.96956	+	121.258i	0.00620244	+	0.189465i
$641$	317.682	−	443.325i	0.495604	−	0.691615i	−0.487818	−	0.872945i	$-0.662207\pi$
$641$	317.682	−	443.325i	0.495604	−	0.691615i	0.983422	+	0.181330i	$0.0580403\pi$
$642$	−54.0183	−	327.184i	−0.0841407	−	0.509633i
$643$	−202.896	+	351.426i	−0.315545	+	0.546541i	−0.979553	−	0.201185i	$-0.935521\pi$
$643$	−202.896	+	351.426i	−0.315545	+	0.546541i	0.664008	+	0.747726i	$0.268854\pi$
$644$	735.917	−	424.882i	1.14273	−	0.659755i
$645$	−175.808	+	144.282i	−0.272571	+	0.223693i
$646$	−67.4909	−	27.9557i	−0.104475	−	0.0432750i
$647$	−615.267	−	701.578i	−0.950954	−	1.08436i	−0.996348	−	0.0853859i	$-0.972788\pi$
$647$	−615.267	−	701.578i	−0.950954	−	1.08436i	0.0453941	−	0.998969i	$-0.485546\pi$
$648$	−640.711	+	41.9944i	−0.988751	+	0.0648062i
$649$	287.119	−	946.505i	0.442403	−	1.45841i
$650$	−190.140	+	419.649i	−0.292524	+	0.645613i
$651$	−39.4788	+	400.835i	−0.0606433	+	0.615722i
$652$	97.4678	−	145.871i	0.149490	−	0.223728i
$653$	−601.533	−	226.401i	−0.921184	−	0.346709i	−0.153952	−	0.988078i	$-0.549200\pi$
$653$	−601.533	−	226.401i	−0.921184	−	0.346709i	−0.767232	+	0.641369i	$0.778367\pi$
$654$	32.8107	−	500.594i	0.0501692	−	0.765434i
$655$	48.5544	+	63.2773i	0.0741288	+	0.0966066i
$656$	−198.947	−	277.630i	−0.303272	−	0.423216i
$657$	113.480	−	113.480i	0.172724	−	0.172724i
$658$	−7.44986	+	45.1232i	−0.0113220	+	0.0685762i
$659$	−116.491	−	95.6016i	−0.176769	−	0.145071i	0.541848	−	0.840476i	$-0.317725\pi$
$659$	−116.491	−	95.6016i	−0.176769	−	0.145071i	−0.718617	+	0.695406i	$0.755225\pi$
$660$	89.1034	+	166.701i	0.135005	+	0.252577i
$661$	586.700	+	878.059i	0.887594	+	1.32838i	0.943991	+	0.329971i	$0.107039\pi$
$661$	586.700	+	878.059i	0.887594	+	1.32838i	−0.0563968	+	0.998408i	$0.517961\pi$
$662$	−97.0457	−	416.206i	−0.146595	−	0.628711i
$663$	442.552	−	118.581i	0.667499	−	0.178856i
$664$	396.252	+	371.131i	0.596765	+	0.558932i
$665$	−109.026	−	67.7965i	−0.163948	−	0.101950i
$666$	93.4264	−	87.5033i	0.140280	−	0.131386i
$667$	−533.623	+	106.144i	−0.800034	+	0.159137i
$668$	291.222	+	857.913i	0.435961	+	1.28430i
$669$	−1068.40	+	484.085i	−1.59701	+	0.723595i
$670$	−87.2729	+	11.4897i	−0.130258	+	0.0171488i
$671$	−207.401	+	1042.68i	−0.309093	+	1.55391i
$672$	939.837	−	584.428i	1.39857	−	0.869685i
$673$	−175.045	+	653.279i	−0.260097	+	0.970696i	0.705086	+	0.709122i	$0.250908\pi$
$673$	−175.045	+	653.279i	−0.260097	+	0.970696i	−0.965183	+	0.261574i	$0.915758\pi$
$674$	10.3757	−	316.943i	0.0153941	−	0.470242i
$675$	354.776	+	272.229i	0.525595	+	0.403303i
$676$	727.482	+	637.985i	1.07616	+	0.943764i
$677$	−608.206	+	299.934i	−0.898384	+	0.443034i	−0.832010	−	0.554761i	$-0.812810\pi$
$677$	−608.206	+	299.934i	−0.898384	+	0.443034i	−0.0663743	+	0.997795i	$0.521143\pi$
$678$			45.6729i			0.0673642i
$679$	−755.385	−	559.645i	−1.11250	−	0.824219i
$680$	35.5571			0.0522899
$681$	447.542	+	907.525i	0.657184	+	1.33264i
$682$	−117.082	+	133.506i	−0.171674	+	0.195757i
$683$	−693.332	+	903.568i	−1.01513	+	1.32294i	−0.0695377	+	0.997579i	$0.522152\pi$
$683$	−693.332	+	903.568i	−1.01513	+	1.32294i	−0.945590	+	0.325361i	$0.894514\pi$
$684$	172.402	+	5.64387i	0.252050	+	0.00825127i
$685$	56.3106	+	15.0884i	0.0822053	+	0.0220268i
$686$	−18.3650	−	29.5333i	−0.0267711	−	0.0430514i
$687$	109.655	+	21.8118i	0.159615	+	0.0317494i
$688$	−63.7688	−	484.372i	−0.0926873	−	0.704030i
$689$	−361.517	−	797.885i	−0.524698	−	1.15803i
$690$	76.9069	−	26.1064i	0.111459	−	0.0378353i
$691$	266.858	+	1341.58i	0.386190	+	1.94151i	0.333005	+	0.942925i	$0.391938\pi$
$691$	266.858	+	1341.58i	0.386190	+	1.94151i	0.0531858	+	0.998585i	$0.483062\pi$
$692$	−305.616	−	326.303i	−0.441642	−	0.471537i
$693$	338.959	−	545.090i	0.489118	−	0.786566i
$694$	−103.671	+	110.689i	−0.149382	+	0.159494i
$695$	−25.3340	−	94.5477i	−0.0364518	−	0.136040i
$696$	−444.110	+	103.552i	−0.638089	+	0.148782i
$697$	−230.830	+	154.236i	−0.331177	+	0.221285i
$698$	−265.293	+	141.802i	−0.380076	+	0.203155i
$699$	−122.595	+	149.382i	−0.175386	+	0.213709i
$700$	−742.698	−	122.620i	−1.06100	−	0.175171i
$701$	620.175	+	620.175i	0.884700	+	0.884700i	0.994008	−	0.109308i	$-0.0348634\pi$
$701$	620.175	+	620.175i	0.884700	+	0.884700i	−0.109308	+	0.994008i	$0.534863\pi$
$702$	−288.161	+	206.494i	−0.410486	+	0.294150i
$703$	422.599	−	324.272i	0.601137	−	0.461268i
$704$	−16.1489	−	1.05845i	−0.0229388	−	0.00150349i
$705$	6.37447	−	16.9366i	0.00904180	−	0.0240235i
$706$	−226.150	−	151.109i	−0.320326	−	0.214035i
$707$	297.472	+	29.2984i	0.420752	+	0.0414405i
$708$	599.260	+	271.521i	0.846412	+	0.383504i
$709$	−213.322	−	64.7107i	−0.300878	−	0.0912703i	0.136236	−	0.990676i	$-0.456499\pi$
$709$	−213.322	−	64.7107i	−0.300878	−	0.0912703i	−0.437114	+	0.899406i	$0.643999\pi$
$710$	7.41668	+	113.157i	0.0104460	+	0.159376i
$711$	229.786	−	201.517i	0.323187	−	0.283427i
$712$	28.3021	−	68.3274i	0.0397502	−	0.0959655i
$713$	−200.391	−	244.177i	−0.281054	−	0.342465i
$714$	−90.4076	−	156.591i	−0.126621	−	0.219315i
$715$	307.434	+	177.497i	0.429978	+	0.248248i
$716$	−517.612	+	85.4580i	−0.722921	+	0.119355i
$717$	514.661	+	368.801i	0.717798	+	0.514367i
$718$	167.742	−	5.49131i	0.233624	−	0.00764806i
$719$	−551.839	−	128.671i	−0.767509	−	0.178958i	−0.175051	−	0.984559i	$-0.556009\pi$
$719$	−551.839	−	128.671i	−0.767509	−	0.178958i	−0.592458	+	0.805601i	$0.701842\pi$
$720$	−24.5429	+	9.23730i	−0.0340874	+	0.0128296i
$721$	61.2976	+	202.071i	0.0850175	+	0.280265i
$722$	143.836	+	18.9363i	0.199218	+	0.0262276i
$723$	27.2257	−	80.2044i	0.0376566	−	0.110933i
$724$	1.94604	+	19.7585i	0.00268790	+	0.0272907i
$725$	425.054	+	227.196i	0.586281	+	0.313374i
$726$	524.510	−	217.259i	0.722466	−	0.299255i
$727$	30.9670	+	15.2712i	0.0425955	+	0.0210058i	0.463462	−	0.886117i	$-0.346607\pi$
$727$	30.9670	+	15.2712i	0.0425955	+	0.0210058i	−0.420866	+	0.907123i	$0.638274\pi$
$728$	591.622	−	1199.69i	0.812668	−	1.64793i
$729$	81.4491	+	196.635i	0.111727	+	0.269733i
$730$	16.5120	−	30.8918i	0.0226192	−	0.0423175i
$731$	−395.188	+	38.9226i	−0.540613	+	0.0532457i
$732$	−669.602	−	227.299i	−0.914756	−	0.310518i
$733$	−28.3312	+	215.197i	−0.0386511	+	0.293584i	0.961192	+	0.275880i	$0.0889691\pi$
$733$	−28.3312	+	215.197i	−0.0386511	+	0.293584i	−0.999843	+	0.0177044i	$0.994364\pi$
$734$	198.577	−	60.2377i	0.270541	−	0.0820677i
$735$	−53.5449	−	142.265i	−0.0728501	−	0.193558i
$736$	−197.093	+	845.287i	−0.267790	+	1.14849i
$737$	−59.9220	−	1830.43i	−0.0813052	−	2.48362i
$738$	−92.2288	+	128.705i	−0.124971	+	0.174397i
$739$	−9.38986	−	56.8735i	−0.0127062	−	0.0769601i	0.979540	−	0.201252i	$-0.0645009\pi$
$739$	−9.38986	−	56.8735i	−0.0127062	−	0.0769601i	−0.992246	+	0.124291i	$0.960334\pi$
$740$	−57.8338	+	100.171i	−0.0781538	+	0.135366i
$741$	941.729	−	543.708i	1.27089	−	0.733748i
$742$	−267.231	+	219.311i	−0.360150	+	0.295568i
$743$	−985.921	−	408.382i	−1.32695	−	0.549639i	−0.397164	−	0.917748i	$-0.630006\pi$
$743$	−985.921	−	408.382i	−1.32695	−	0.549639i	−0.929783	+	0.368108i	$0.880006\pi$
$744$	−174.566	−	199.054i	−0.234631	−	0.267546i
$745$	−51.1191	+	3.35052i	−0.0686163	+	0.00449735i
$746$	−111.036	+	366.036i	−0.148841	+	0.490664i
$747$	−134.316	+	296.442i	−0.179807	+	0.396843i
$748$	−32.3486	+	328.441i	−0.0432468	+	0.439092i
$749$	565.334	−	846.082i	0.754785	−	1.12962i
$750$	−137.161	−	51.6239i	−0.182882	−	0.0688318i
$751$	−19.3722	+	295.563i	−0.0257953	+	0.393560i	0.965366	+	0.260899i	$0.0840188\pi$
$751$	−19.3722	+	295.563i	−0.0257953	+	0.393560i	−0.991161	+	0.132661i	$0.957648\pi$
$752$	23.6645	+	30.8401i	0.0314687	+	0.0410108i
$753$	−169.507	−	236.547i	−0.225109	−	0.314139i
$754$	−270.171	+	270.171i	−0.358317	+	0.358317i
$755$	2.35013	−	14.2345i	0.00311275	−	0.0188537i
$756$	−447.747	−	367.456i	−0.592258	−	0.486053i
$757$	160.706	+	300.659i	0.212293	+	0.397172i	0.965419	−	0.260704i	$-0.0839548\pi$
$757$	160.706	+	300.659i	0.212293	+	0.397172i	−0.753126	+	0.657877i	$0.771455\pi$
$758$	−51.7959	−	77.5181i	−0.0683324	−	0.102267i
$759$	383.701	+	1645.60i	0.505535	+	2.16812i
$760$	81.5166	−	21.8423i	0.107259	−	0.0287399i
$761$	270.460	+	253.314i	0.355401	+	0.332869i	0.840722	−	0.541467i	$-0.182131\pi$
$761$	270.460	+	253.314i	0.355401	+	0.332869i	−0.485321	+	0.874336i	$0.661297\pi$
$762$	−17.6271	−	10.9612i	−0.0231327	−	0.0143848i
$763$	1123.55	−	1052.32i	1.47254	−	1.37919i
$764$	767.688	−	152.703i	1.00483	−	0.199873i
$765$	6.85145	+	20.1837i	0.00895614	+	0.0263839i
$766$	213.507	−	96.7387i	0.278730	−	0.126291i
$767$	1225.02	−	161.277i	1.59716	−	0.210270i
$768$	−76.5097	+	384.640i	−0.0996220	+	0.500833i
$769$	−44.2598	+	27.5225i	−0.0575550	+	0.0357900i	−0.556542	−	0.830819i	$-0.687872\pi$
$769$	−44.2598	+	27.5225i	−0.0575550	+	0.0357900i	0.498987	+	0.866609i	$0.333706\pi$
$770$	36.2604	−	135.326i	0.0470915	−	0.175748i
$771$	51.7389	−	1580.46i	0.0671062	−	2.04988i
$772$	14.8790	+	11.4170i	0.0192733	+	0.0147889i
$773$	28.3297	+	24.8444i	0.0366490	+	0.0321403i	0.677474	−	0.735546i	$-0.263074\pi$
$773$	28.3297	+	24.8444i	0.0366490	+	0.0321403i	−0.640825	+	0.767687i	$0.721408\pi$
$774$	−203.129	+	100.172i	−0.262441	+	0.129421i
$775$			279.817i			0.361054i
$776$	607.926	−	110.931i	0.783410	−	0.142953i
$777$	1318.46			1.69686
$778$	−34.1705	−	69.2908i	−0.0439209	−	0.0890628i
$779$	−434.445	+	495.390i	−0.557696	+	0.635931i
$780$	−143.745	+	187.332i	−0.184288	+	0.240169i
$781$	−2358.05	−	77.1944i	−3.01927	−	0.0988405i
$782$	136.974	+	36.7020i	0.175158	+	0.0469335i
$783$	195.839	+	314.935i	0.250114	+	0.402215i
$784$	320.256	+	63.7029i	0.408490	+	0.0812537i
$785$	−17.5130	−	133.024i	−0.0223095	−	0.169458i
$786$	110.031	+	242.844i	0.139989	+	0.308962i
$787$	1265.01	−	429.413i	1.60738	−	0.545632i	0.633706	−	0.773574i	$-0.281533\pi$
$787$	1265.01	−	429.413i	1.60738	−	0.545632i	0.973675	+	0.227942i	$0.0731995\pi$
$788$	86.1289	+	432.999i	0.109301	+	0.549491i
$789$	−1049.77	−	1120.83i	−1.33051	−	1.42057i
$790$	35.2263	−	56.6485i	0.0445902	−	0.0717069i
$791$	−95.8054	+	102.290i	−0.121119	+	0.129318i
$792$	109.204	+	407.554i	0.137884	+	0.514589i
$793$	−1293.35	+	301.568i	−1.63096	+	0.380287i
$794$	−148.114	+	98.9668i	−0.186542	+	0.124643i
$795$	120.638	−	64.4826i	0.151746	−	0.0811101i
$796$	685.582	−	835.384i	0.861284	−	1.04948i
$797$	1169.14	+	193.026i	1.46692	+	0.242190i	0.842416	−	0.538828i	$-0.181133\pi$
$797$	1169.14	+	193.026i	1.46692	+	0.242190i	0.624509	+	0.781018i	$0.285299\pi$
$798$	−303.456	−	303.456i	−0.380270	−	0.380270i
$799$	25.6831	−	18.4043i	0.0321441	−	0.0230341i
$800$	609.987	−	468.059i	0.762483	−	0.585074i
$801$	44.2390	+	2.89958i	0.0552297	+	0.00361995i
$802$	0.716193	−	1.90288i	0.000893008	−	0.00237267i
$803$	605.946	+	404.880i	0.754603	+	0.504210i
$804$	1212.30	+	119.402i	1.50784	+	0.148509i
$805$	227.005	+	102.854i	0.281993	+	0.127770i
$806$	−212.275	−	64.3928i	−0.263368	−	0.0798918i
$807$	20.2398	+	308.800i	0.0250803	+	0.382652i
$808$	−147.724	+	129.551i	−0.182827	+	0.160335i
$809$	−211.517	+	510.648i	−0.261455	+	0.631209i	−0.999029	−	0.0440576i	$-0.985971\pi$
$809$	−211.517	+	510.648i	−0.261455	+	0.631209i	0.737574	+	0.675267i	$0.235971\pi$
$810$	−53.2951	−	64.9403i	−0.0657964	−	0.0801732i
$811$	696.171	+	1205.80i	0.858411	+	1.48681i	0.873445	+	0.486924i	$0.161881\pi$
$811$	696.171	+	1205.80i	0.858411	+	1.48681i	−0.0150340	+	0.999887i	$0.504786\pi$
$812$	−540.635	−	312.136i	−0.665807	−	0.384404i
$813$	−202.004	+	33.3510i	−0.248467	+	0.0410221i
$814$	472.487	+	338.579i	0.580450	+	0.415945i
$815$	51.4248	−	1.68347i	0.0630979	−	0.00206561i
$816$	−149.675	−	34.8993i	−0.183425	−	0.0427688i
$817$	−882.080	+	331.991i	−1.07966	+	0.406354i
$818$	167.878	+	553.419i	0.205230	+	0.676552i
$819$	794.993	+	104.663i	0.970688	+	0.127793i
$820$	45.9908	−	135.484i	0.0560863	−	0.165225i
$821$	50.0562	+	508.229i	0.0609698	+	0.619037i	0.976313	+	0.216363i	$0.0694193\pi$
$821$	50.0562	+	508.229i	0.0609698	+	0.619037i	−0.915343	+	0.402674i	$0.868081\pi$
$822$	171.858	+	91.8599i	0.209073	+	0.111752i
$823$	−544.825	+	225.674i	−0.661998	+	0.274209i	−0.688279	−	0.725446i	$-0.741634\pi$
$823$	−544.825	+	225.674i	−0.661998	+	0.274209i	0.0262808	+	0.999655i	$0.491634\pi$
$824$	−124.490	−	61.3917i	−0.151080	−	0.0745045i
$825$	662.035	−	1342.47i	0.802467	−	1.62724i
$826$	−186.608	−	450.512i	−0.225918	−	0.545414i
$827$	−667.600	+	1248.99i	−0.807256	+	1.51027i	0.0519563	+	0.998649i	$0.483454\pi$
$827$	−667.600	+	1248.99i	−0.807256	+	1.51027i	−0.859212	+	0.511620i	$0.829046\pi$
$828$	−333.229	+	32.8202i	−0.402451	+	0.0396379i
$829$	125.531	+	42.6122i	0.151425	+	0.0514019i	0.396123	−	0.918198i	$-0.370355\pi$
$829$	125.531	+	42.6122i	0.151425	+	0.0514019i	−0.244698	+	0.969599i	$0.578689\pi$
$830$	−9.27178	+	70.4262i	−0.0111708	+	0.0848508i
$831$	−1197.93	+	363.389i	−1.44155	+	0.437291i
$832$	−7.12135	−	18.9210i	−0.00855931	−	0.0227415i
$833$	60.2677	−	258.474i	0.0723502	−	0.310293i
$834$	−10.7054	−	327.015i	−0.0128362	−	0.392104i
$835$	−154.770	+	215.982i	−0.185353	+	0.258660i
$836$	127.596	+	772.840i	0.152627	+	0.924449i
$837$	−107.656	+	186.466i	−0.128621	+	0.222779i
$838$	395.295	−	228.224i	0.471713	−	0.272344i
$839$	−871.284	+	715.045i	−1.03848	+	0.852258i	−0.989207	−	0.146527i	$-0.953190\pi$
$839$	−871.284	+	715.045i	−1.03848	+	0.852258i	−0.0492730	+	0.998785i	$0.515690\pi$
$840$	192.985	+	79.9368i	0.229744	+	0.0951629i
$841$	−290.968	−	331.786i	−0.345979	−	0.394514i
$842$	−268.650	+	17.6082i	−0.319062	+	0.0209124i
$843$	461.900	−	1522.68i	0.547924	−	1.80626i
$844$	−230.697	+	509.160i	−0.273338	+	0.603270i
$845$	−27.8152	+	282.412i	−0.0329174	+	0.334216i
$846$	10.0120	−	14.9840i	0.0118345	−	0.0177115i
$847$	1630.44	+	613.654i	1.92496	+	0.724503i
$848$	−19.2181	+	293.212i	−0.0226629	+	0.345769i
$849$	−84.9666	−	110.731i	−0.100078	−	0.130425i
$850$	−73.1689	−	102.107i	−0.0860811	−	0.120126i
$851$	−731.157	+	731.157i	−0.859173	+	0.859173i
$852$	255.633	−	1548.35i	0.300039	−	1.81731i
$853$	181.913	+	149.292i	0.213262	+	0.175020i	0.734960	−	0.678111i	$-0.237201\pi$
$853$	181.913	+	149.292i	0.213262	+	0.175020i	−0.521698	+	0.853131i	$0.674701\pi$
$854$	247.067	+	462.229i	0.289305	+	0.541252i
$855$	28.1059	+	42.0635i	0.0328724	+	0.0491970i
$856$	151.888	+	651.410i	0.177439	+	0.760993i
$857$	753.455	−	201.888i	0.879178	−	0.235575i	0.209125	−	0.977889i	$-0.432938\pi$
$857$	753.455	−	201.888i	0.879178	−	0.235575i	0.670052	+	0.742314i	$0.266272\pi$
$858$	866.077	+	811.169i	1.00941	+	0.945419i
$859$	−464.747	−	288.998i	−0.541032	−	0.336436i	0.230042	−	0.973181i	$-0.426114\pi$
$859$	−464.747	−	288.998i	−0.541032	−	0.336436i	−0.771074	+	0.636745i	$0.780280\pi$
$860$	149.371	−	139.902i	0.173688	−	0.162676i
$861$	−1599.56	+	318.173i	−1.85779	+	0.369538i
$862$	−238.966	−	703.970i	−0.277222	−	0.816670i
$863$	254.174	−	115.165i	0.294523	−	0.133447i	−0.260016	−	0.965604i	$-0.583728\pi$
$863$	254.174	−	115.165i	0.294523	−	0.133447i	0.554539	+	0.832157i	$0.312894\pi$
$864$	586.566	−	77.2229i	0.678896	−	0.0893784i
$865$	25.5799	−	128.599i	0.0295721	−	0.148669i
$866$	200.019	−	124.380i	0.230969	−	0.143626i
$867$	235.474	−	878.803i	0.271597	−	1.01361i
$868$	11.8586	−	362.243i	0.0136620	−	0.417331i
$869$	1101.08	+	844.887i	1.26706	+	0.972251i
$870$	−44.8588	−	39.3401i	−0.0515618	−	0.0452185i
$871$	2051.89	−	1011.88i	2.35578	−	1.16174i
$872$			1011.89i			1.16043i
$873$	180.110	+	323.709i	0.206311	+	0.370801i
$874$	336.565			0.385086
$875$	−198.902	−	403.334i	−0.227317	−	0.460953i
$876$	−319.613	+	364.449i	−0.364855	+	0.416037i
$877$	−486.398	+	633.886i	−0.554615	+	0.722789i	−0.983568	−	0.180538i	$-0.942216\pi$
$877$	−486.398	+	633.886i	−0.554615	+	0.722789i	0.428953	+	0.903327i	$0.358883\pi$
$878$	−91.7713	−	3.00428i	−0.104523	−	0.00342173i
$879$	−1533.57	−	410.919i	−1.74468	−	0.467485i
$880$	−62.8835	−	101.125i	−0.0714586	−	0.114915i
$881$	−440.311	−	87.5832i	−0.499785	−	0.0994134i	−0.0612408	−	0.998123i	$-0.519506\pi$
$881$	−440.311	−	87.5832i	−0.499785	−	0.0994134i	−0.438544	+	0.898710i	$0.644506\pi$
$882$	−19.7584	−	150.080i	−0.0224018	−	0.170159i
$883$	−662.308	−	1461.74i	−0.750066	−	1.65543i	−0.755244	−	0.655444i	$-0.772482\pi$
$883$	−662.308	−	1461.74i	−0.750066	−	1.65543i	0.00517830	−	0.999987i	$-0.498352\pi$
$884$	−390.400	+	132.523i	−0.441628	+	0.149913i
$885$	37.6426	+	189.242i	0.0425341	+	0.213833i
$886$	−31.2964	−	33.4148i	−0.0353232	−	0.0377142i
$887$	779.269	−	1253.17i	0.878545	−	1.41281i	−0.0320378	−	0.999487i	$-0.510200\pi$
$887$	779.269	−	1253.17i	0.878545	−	1.41281i	0.910582	−	0.413328i	$-0.135634\pi$
$888$	−592.446	+	632.548i	−0.667168	+	0.712328i
$889$	−16.4854	−	61.5245i	−0.0185438	−	0.0692064i
$890$	9.42366	−	2.19729i	0.0105884	−	0.00246886i
$891$	1453.28	−	971.051i	1.63107	−	1.08984i
$892$	930.853	−	497.551i	1.04356	−	0.557793i
$893$	47.5744	−	57.9695i	0.0532748	−	0.0649155i
$894$	−168.953	−	27.8943i	−0.188986	−	0.0312017i
$895$	−108.796	−	108.796i	−0.121559	−	0.121559i
$896$	−1011.53	+	724.849i	−1.12893	+	0.808983i
$897$	−1674.66	+	1285.01i	−1.86695	+	1.43256i
$898$	−664.120	−	43.5287i	−0.739554	−	0.0484730i
$899$	−81.7422	+	217.184i	−0.0909257	+	0.241584i
$900$	246.626	+	164.790i	0.274029	+	0.183100i
$901$	237.687	+	23.4101i	0.263804	+	0.0259824i
$902$	−654.929	−	296.745i	−0.726086	−	0.328985i
$903$	−2232.37	−	677.181i	−2.47217	−	0.749923i
$904$	−6.02526	−	91.9277i	−0.00666511	−	0.101690i
$905$	−4.37783	+	3.83925i	−0.00483738	+	0.00424226i
$906$	18.4550	−	44.5544i	0.0203698	−	0.0491770i
$907$	−583.287	−	710.737i	−0.643094	−	0.783613i	0.344811	−	0.938672i	$-0.387943\pi$
$907$	−583.287	−	710.737i	−0.643094	−	0.783613i	−0.987905	+	0.155060i	$0.950443\pi$
$908$	−455.270	−	788.551i	−0.501399	−	0.868448i
$909$	−102.003	−	58.8916i	−0.112215	−	0.0647872i
$910$	172.677	−	28.5091i	0.189755	−	0.0313287i
$911$	91.5601	+	65.6110i	0.100505	+	0.0720209i	0.631616	−	0.775281i	$-0.282392\pi$
$911$	91.5601	+	65.6110i	0.100505	+	0.0720209i	−0.531111	+	0.847302i	$0.678225\pi$
$912$	−364.576	+	11.9350i	−0.399755	+	0.0130866i
$913$	−1439.27	−	335.592i	−1.57642	−	0.367570i
$914$	−287.004	+	108.020i	−0.314008	+	0.118184i
$915$	−60.2013	−	198.457i	−0.0657937	−	0.216893i
$916$	−99.7462	−	13.1318i	−0.108893	−	0.0143361i
$917$	−262.971	+	774.686i	−0.286773	+	0.844805i
$918$	−9.47424	−	96.1935i	−0.0103205	−	0.104786i
$919$	247.287	+	132.177i	0.269082	+	0.143828i	0.600420	−	0.799685i	$-0.295000\pi$
$919$	247.287	+	132.177i	0.269082	+	0.143828i	−0.331338	+	0.943512i	$0.607500\pi$
$920$	−151.349	+	62.6910i	−0.164510	+	0.0681424i
$921$	18.2936	+	9.02138i	0.0198627	+	0.00979520i
$922$	19.0867	−	38.7039i	0.0207014	−	0.0419782i
$923$	−1127.88	−	2722.94i	−1.22197	−	2.95010i
$924$	−913.946	+	1709.87i	−0.989120	+	1.85051i
$925$	911.555	−	89.7803i	0.985465	−	0.0970598i
$926$	335.507	+	113.889i	0.362319	+	0.122991i
$927$	10.8607	−	82.4952i	0.0117160	−	0.0889916i
$928$	610.183	−	185.097i	0.657524	−	0.199458i
$929$	521.138	+	1384.63i	0.560967	+	1.49045i	0.846661	+	0.532132i	$0.178609\pi$
$929$	521.138	+	1384.63i	0.560967	+	1.49045i	−0.285695	+	0.958321i	$0.592224\pi$
$930$	7.86599	−	33.7354i	0.00845805	−	0.0362746i
$931$	−20.6105	−	629.587i	−0.0221381	−	0.676248i
$932$	101.289	−	141.349i	0.108680	−	0.151662i
$933$	173.957	+	1053.64i	0.186449	+	1.12931i
$934$	−330.500	+	572.444i	−0.353855	+	0.612895i
$935$	−83.8238	+	48.3957i	−0.0896511	+	0.0517601i
$936$	−407.441	+	334.378i	−0.435300	+	0.357242i
$937$	−821.749	−	340.379i	−0.877000	−	0.363265i	−0.101667	−	0.994818i	$-0.532418\pi$
$937$	−821.749	−	340.379i	−0.877000	−	0.363265i	−0.775332	+	0.631553i	$0.782418\pi$
$938$	−595.320	−	678.832i	−0.634670	−	0.723702i
$939$	1857.43	−	121.742i	1.97809	−	0.129651i
$940$	−4.72703	+	15.5829i	−0.00502875	+	0.0165776i
$941$	−326.621	+	720.867i	−0.347100	+	0.766065i	0.652864	+	0.757475i	$0.273567\pi$
$941$	−326.621	+	720.867i	−0.347100	+	0.766065i	−0.999963	+	0.00858944i	$0.997266\pi$
$942$	43.9599	−	446.332i	0.0466665	−	0.473813i
$943$	710.599	−	1063.49i	0.753551	−	1.12777i
$944$	−387.912	−	146.000i	−0.410924	−	0.154661i
$945$	11.1104	−	169.511i	0.0117570	−	0.179377i
$946$	−626.097	−	815.945i	−0.661836	−	0.862522i
$947$	314.502	+	438.887i	0.332103	+	0.463449i	0.945169	−	0.326583i	$-0.105897\pi$
$947$	314.502	+	438.887i	0.332103	+	0.463449i	−0.613065	+	0.790032i	$0.710064\pi$
$948$	−652.769	+	652.769i	−0.688575	+	0.688575i
$949$	−148.298	+	898.225i	−0.156267	+	0.946497i
$950$	−230.467	−	189.139i	−0.242596	−	0.199094i
$951$	−918.249	−	1717.92i	−0.965562	−	1.80644i
$952$	202.625	+	303.249i	0.212841	+	0.318539i
$953$	−181.656	−	779.078i	−0.190614	−	0.817501i	−0.979253	−	0.202643i	$-0.935047\pi$
$953$	−181.656	−	779.078i	−0.190614	−	0.817501i	0.788638	−	0.614858i	$-0.210787\pi$
$954$	131.579	−	35.2565i	0.137923	−	0.0369565i
$955$	167.547	+	156.925i	0.175441	+	0.164319i
$956$	−483.833	−	300.866i	−0.506101	−	0.314714i
$957$	906.021	−	848.581i	0.946731	−	0.886710i
$958$	57.8079	−	11.4987i	0.0603423	−	0.0120028i
$959$	192.208	+	566.228i	0.200426	+	0.590436i
$960$	2.87563	−	1.30293i	0.00299545	−	0.00135722i
$961$	819.204	−	107.850i	0.852450	−	0.112227i
$962$	−141.662	+	712.184i	−0.147258	+	0.740316i
$963$	−340.501	+	211.737i	−0.353583	+	0.219872i
$964$	−19.7264	+	73.6199i	−0.0204631	+	0.0763692i
$965$	−0.179966	+	5.49739i	−0.000186493	+	0.00569677i
$966$	660.907	+	507.132i	0.684169	+	0.524981i
$967$	−355.457	−	311.727i	−0.367587	−	0.322365i	0.455548	−	0.890211i	$-0.349444\pi$
$967$	−355.457	−	311.727i	−0.367587	−	0.322365i	−0.823135	+	0.567846i	$0.807777\pi$
$968$	−1027.04	+	506.481i	−1.06099	+	0.523224i
$969$			296.490i			0.305975i
$970$	58.1281	+	56.1999i	0.0599259	+	0.0579380i
$971$	−300.980			−0.309969			−0.154984	−	0.987917i	$-0.549533\pi$
$971$	−300.980			−0.309969			−0.154984	+	0.987917i	$0.549533\pi$
$972$	276.303	+	560.288i	0.284263	+	0.576428i
$973$	661.984	−	754.848i	0.680353	−	0.775794i
$974$	330.853	−	431.176i	0.339685	−	0.442686i
$975$	1868.87	+	61.1806i	1.91679	+	0.0627493i
$976$	430.311	+	115.301i	0.440892	+	0.118137i
$977$	−412.554	−	663.441i	−0.422266	−	0.679059i	0.567240	−	0.823553i	$-0.308011\pi$
$977$	−412.554	−	663.441i	−0.422266	−	0.679059i	−0.989506	+	0.144494i	$0.953845\pi$
$978$	168.683	+	33.5531i	0.172478	+	0.0343079i
$979$	26.2777	+	199.599i	0.0268414	+	0.203880i
$980$	56.4521	+	124.592i	0.0576041	+	0.127135i
$981$	−574.393	+	194.980i	−0.585518	+	0.198756i
$982$	−39.8205	−	200.191i	−0.0405504	−	0.203860i
$983$	−834.925	−	891.440i	−0.849364	−	0.906856i	0.147249	−	0.989100i	$-0.452958\pi$
$983$	−834.925	−	891.440i	−0.849364	−	0.906856i	−0.996612	+	0.0822431i	$0.973792\pi$
$984$	566.110	−	910.379i	0.575315	−	0.925182i
$985$	−88.5101	+	94.5013i	−0.0898580	+	0.0959404i
$986$	−26.9628	−	100.626i	−0.0273456	−	0.102055i
$987$	180.769	−	42.1494i	0.183150	−	0.0427045i
$988$	−813.604	+	543.633i	−0.823486	+	0.550236i
$989$	1613.50	−	862.433i	1.63145	−	0.872026i
$990$	−35.0216	+	42.6740i	−0.0353754	+	0.0431050i
$991$	51.4172	+	8.48901i	0.0518841	+	0.00856611i	0.188781	−	0.982019i	$-0.439546\pi$
$991$	51.4172	+	8.48901i	0.0518841	+	0.00856611i	−0.136897	+	0.990585i	$0.543713\pi$
$992$	261.770	+	261.770i	0.263881	+	0.263881i
$993$	−1409.92	+	1010.33i	−1.41986	+	1.01745i
$994$	−922.792	+	708.084i	−0.928363	+	0.712358i
$995$	316.266	+	20.7292i	0.317855	+	0.0208333i
$996$	346.269	−	920.015i	0.347660	−	0.923710i
$997$	979.877	+	654.733i	0.982826	+	0.656703i	0.939568	−	0.342361i	$-0.111227\pi$
$997$	979.877	+	654.733i	0.982826	+	0.656703i	0.0432570	+	0.999064i	$0.486227\pi$
$998$	−37.0884	−	3.65289i	−0.0371627	−	0.00366021i
$999$	641.989	+	290.881i	0.642632	+	0.291173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.3.l.a.5.6	✓	480
97.39	odd	96	inner	97.3.l.a.39.6	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.3.l.a.5.6	✓	480	1.1	even	1	trivial
97.3.l.a.39.6	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+(-0.390169 - 0.791184i) q^{2} +(-2.36070 + 2.69186i) q^{3} +(1.96131 - 2.55602i) q^{4} +(0.944383 + 0.0309159i) q^{5} +(3.05082 + 0.817466i) q^{6} +(5.11796 + 8.23036i) q^{7} +(-6.24836 - 1.24288i) q^{8} +(-0.498478 - 3.78632i) q^{9} +(-0.344009 - 0.759243i) q^{10} +(16.4218 - 5.57444i) q^{11} +(2.25041 + 11.3135i) q^{12} +(14.8094 + 15.8118i) q^{13} +(4.51486 - 7.26048i) q^{14} +(-2.31262 + 2.46916i) q^{15} +(-1.88088 - 7.01954i) q^{16} +(-5.75252 + 1.34130i) q^{17} +(-2.80118 + 1.87169i) q^{18} +(-12.3640 + 6.60870i) q^{19} +(1.93125 - 2.35323i) q^{20} +(-34.2369 - 5.65254i) q^{21} +(-10.8177 - 10.8177i) q^{22} +(22.1208 - 15.8516i) q^{23} +(18.0961 - 13.8856i) q^{24} +(-24.0556 - 1.57669i) q^{25} +(6.73189 - 17.8862i) q^{26} +(-15.4237 - 10.3058i) q^{27} +(31.0749 + 3.06061i) q^{28} +(-18.2105 - 8.25106i) q^{29} +(2.85588 + 0.866320i) q^{30} +(-0.759147 - 11.5823i) q^{31} +(-23.9791 + 21.0291i) q^{32} +(-23.7612 + 57.3646i) q^{33} +(3.30567 + 4.02797i) q^{34} +(4.57887 + 7.93084i) q^{35} +(-10.6556 - 6.15200i) q^{36} +(-37.4880 + 6.18930i) q^{37} +(10.0527 + 7.20369i) q^{38} +(-77.5235 + 2.53786i) q^{39} +(-5.86242 - 1.36692i) q^{40} +(43.9870 - 16.5556i) q^{41} +(8.88598 + 29.2931i) q^{42} +(66.6522 + 8.77493i) q^{43} +(17.9597 - 52.9076i) q^{44} +(-0.353697 - 3.59114i) q^{45} +(-21.1724 - 11.3169i) q^{46} +(-4.94197 + 2.04703i) q^{47} +(23.3358 + 11.5079i) q^{48} +(-19.8731 + 40.2986i) q^{49} +(8.13828 + 19.6476i) q^{50} +(9.96937 - 18.6514i) q^{51} +(69.4610 - 6.84131i) q^{52} +(-38.2883 - 12.9971i) q^{53} +(-2.13592 + 16.2240i) q^{54} +(15.6808 - 4.75671i) q^{55} +(-21.7496 - 57.7872i) q^{56} +(11.3980 - 48.8833i) q^{57} +(0.577053 + 17.6271i) q^{58} +(33.2212 - 46.3602i) q^{59} +(1.77548 + 10.7539i) q^{60} +(-30.6509 + 53.0890i) q^{61} +(-8.86757 + 5.11969i) q^{62} +(28.6115 - 23.4809i) q^{63} +(-0.862159 - 0.357118i) q^{64} +(13.4969 + 15.3902i) q^{65} +(54.6568 - 3.58240i) q^{66} +(30.6554 - 101.057i) q^{67} +(-7.85406 + 17.3343i) q^{68} +(-9.55040 + 96.9669i) q^{69} +(4.48822 - 6.71709i) q^{70} +(-127.326 - 47.9219i) q^{71} +(-1.59125 + 24.2778i) q^{72} +(25.5819 + 33.3390i) q^{73} +(19.5235 + 27.2451i) q^{74} +(61.0321 - 61.0321i) q^{75} +(-7.35761 + 44.5644i) q^{76} +(129.926 + 106.627i) q^{77} +(32.2552 + 60.3452i) q^{78} +(44.4620 + 66.5420i) q^{79} +(-1.55926 - 6.68728i) q^{80} +(97.3520 - 26.0854i) q^{81} +(-30.2609 - 28.3424i) q^{82} +(-72.3684 - 45.0016i) q^{83} +(-81.5971 + 76.4240i) q^{84} +(-5.47405 + 1.08886i) q^{85} +(-19.0630 - 56.1579i) q^{86} +(65.2001 - 29.5418i) q^{87} +(-109.537 + 14.4209i) q^{88} +(-2.26477 + 11.3858i) q^{89} +(-2.70325 + 1.68099i) q^{90} +(-54.3429 + 202.811i) q^{91} +(2.86875 - 87.6311i) q^{92} +(32.9701 + 25.2989i) q^{93} +(3.54778 + 3.11132i) q^{94} +(-11.8807 + 5.85890i) q^{95} -114.192i q^{96} +(-90.1938 + 35.6943i) q^{97} +39.6374 q^{98} +(-29.2925 - 59.3992i) 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

Varieties

Fields

Representations

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Database

Properties

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