LMFDB - Embedded newform 182.3.k.a.101.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [182,3,Mod(101,182)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(182, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("182.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	182.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.95914081136$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.17
Character	$\chi$	$=$	182.101
Dual form			182.3.k.a.173.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 + 0.707107i) q^{2} +4.02925i q^{3} +(1.00000 + 1.73205i) q^{4} +(4.59702 + 7.96227i) q^{5} +(-2.84911 + 4.93480i) q^{6} +(-5.39829 - 4.45628i) q^{7} +2.82843i q^{8} -7.23484 q^{9} +13.0023i q^{10} -17.1732i q^{11} +(-6.97886 + 4.02925i) q^{12} +(9.51338 - 8.85977i) q^{13} +(-3.46047 - 9.27497i) q^{14} +(-32.0819 + 18.5225i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(3.18575 - 1.83929i) q^{17} +(-8.86083 - 5.11580i) q^{18} +17.2294 q^{19} +(-9.19403 + 15.9245i) q^{20} +(17.9554 - 21.7511i) q^{21} +(12.1433 - 21.0328i) q^{22} +(-3.50087 + 6.06369i) q^{23} -11.3964 q^{24} +(-29.7651 + 51.5547i) q^{25} +(17.9163 - 4.12398i) q^{26} +7.11227i q^{27} +(2.32020 - 13.8064i) q^{28} +(0.359781 + 0.623160i) q^{29} -52.3896 q^{30} +(-22.2101 + 38.4690i) q^{31} +(-4.89898 + 2.82843i) q^{32} +69.1951 q^{33} +5.20230 q^{34} +(10.6660 - 63.4682i) q^{35} +(-7.23484 - 12.5311i) q^{36} +(26.4251 + 15.2565i) q^{37} +(21.1016 + 12.1830i) q^{38} +(35.6982 + 38.3318i) q^{39} +(-22.5207 + 13.0023i) q^{40} +(-16.2530 - 28.1511i) q^{41} +(37.3712 - 13.9431i) q^{42} +(26.8250 - 46.4622i) q^{43} +(29.7449 - 17.1732i) q^{44} +(-33.2587 - 57.6057i) q^{45} +(-8.57536 + 4.95098i) q^{46} +(-36.6987 - 63.5641i) q^{47} +(-13.9577 - 8.05850i) q^{48} +(9.28318 + 48.1126i) q^{49} +(-72.9093 + 42.0942i) q^{50} +(7.41096 + 12.8362i) q^{51} +(24.8590 + 7.61789i) q^{52} +(-4.39981 + 7.62069i) q^{53} +(-5.02914 + 8.71072i) q^{54} +(136.738 - 78.9455i) q^{55} +(12.6043 - 15.2687i) q^{56} +69.4215i q^{57} +1.01762i q^{58} +(-6.58394 - 11.4037i) q^{59} +(-64.1639 - 37.0450i) q^{60} +11.6030i q^{61} +(-54.4034 + 31.4098i) q^{62} +(39.0558 + 32.2405i) q^{63} -8.00000 q^{64} +(114.277 + 35.0196i) q^{65} +(84.7464 + 48.9283i) q^{66} -27.7832i q^{67} +(6.37150 + 3.67858i) q^{68} +(-24.4321 - 14.1059i) q^{69} +(57.9420 - 70.1904i) q^{70} +(-25.6313 - 14.7983i) q^{71} -20.4632i q^{72} +(-30.1279 + 52.1831i) q^{73} +(21.5760 + 37.3707i) q^{74} +(-207.727 - 119.931i) q^{75} +(17.2294 + 29.8422i) q^{76} +(-76.5286 + 92.7060i) q^{77} +(16.6165 + 72.1891i) q^{78} +(-66.3791 - 114.972i) q^{79} -36.7761 q^{80} -93.7707 q^{81} -45.9706i q^{82} +108.148 q^{83} +(55.6294 + 9.34868i) q^{84} +(29.2899 + 16.9105i) q^{85} +(65.7075 - 37.9363i) q^{86} +(-2.51087 + 1.44965i) q^{87} +48.5732 q^{88} +(48.6213 - 84.2145i) q^{89} -94.0697i q^{90} +(-90.8376 + 5.43338i) q^{91} -14.0035 q^{92} +(-155.001 - 89.4900i) q^{93} -103.800i q^{94} +(79.2038 + 137.185i) q^{95} +(-11.3964 - 19.7392i) q^{96} +(39.5728 - 68.5420i) q^{97} +(-22.6512 + 65.4899i) q^{98} +124.245i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{4} + 10 q^{7} - 88 q^{9} - 12 q^{12} - 4 q^{13} - 12 q^{14} + 60 q^{15} - 72 q^{16} + 24 q^{17} - 24 q^{18} + 100 q^{19} - 42 q^{21} + 12 q^{22} + 28 q^{23} - 82 q^{25} + 120 q^{26} + 4 q^{28}+ \cdots + 96 q^{98}+O(q^{100}) $ 36 * q + 36 * q^4 + 10 * q^7 - 88 * q^9 - 12 * q^12 - 4 * q^13 - 12 * q^14 + 60 * q^15 - 72 * q^16 + 24 * q^17 - 24 * q^18 + 100 * q^19 - 42 * q^21 + 12 * q^22 + 28 * q^23 - 82 * q^25 + 120 * q^26 + 4 * q^28 + 40 * q^29 - 112 * q^30 - 10 * q^31 - 192 * q^33 + 130 * q^35 - 88 * q^36 + 60 * q^37 + 60 * q^38 + 198 * q^39 - 90 * q^41 + 16 * q^42 + 20 * q^43 + 24 * q^44 + 48 * q^46 - 108 * q^47 - 24 * q^48 + 186 * q^49 - 192 * q^50 - 36 * q^51 + 80 * q^52 - 218 * q^53 + 144 * q^54 + 282 * q^55 + 120 * q^60 - 180 * q^62 + 252 * q^63 - 288 * q^64 - 368 * q^65 + 96 * q^66 + 48 * q^68 + 18 * q^69 + 144 * q^70 - 18 * q^71 + 74 * q^73 + 24 * q^74 - 1182 * q^75 + 100 * q^76 - 174 * q^77 - 320 * q^78 - 352 * q^79 + 68 * q^81 + 708 * q^83 - 108 * q^84 - 204 * q^85 - 36 * q^86 - 348 * q^87 + 48 * q^88 + 426 * q^89 - 224 * q^91 + 112 * q^92 + 426 * q^93 + 20 * q^95 + 64 * q^97 + 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$			4.02925i			1.34308i	0.740967	+	0.671541i	$0.234367\pi$
$3$			4.02925i			1.34308i	−0.740967	+	0.671541i	$0.765633\pi$
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	4.59702	+	7.96227i	0.919403	+	1.59245i	0.800324	+	0.599568i	$0.204661\pi$
$5$	4.59702	+	7.96227i	0.919403	+	1.59245i	0.119080	+	0.992885i	$0.462006\pi$
$6$	−2.84911	+	4.93480i	−0.474851	+	0.822467i
$7$	−5.39829	−	4.45628i	−0.771185	−	0.636611i
$7$	−5.39829	−	4.45628i	−0.771185	−	0.636611i
$8$			2.82843i			0.353553i
$9$	−7.23484			−0.803871
$10$			13.0023i			1.30023i
$11$		−	17.1732i		−	1.56120i	−0.625030	−	0.780600i	$-0.714913\pi$
$11$		−	17.1732i		−	1.56120i	0.625030	−	0.780600i	$-0.285087\pi$
$12$	−6.97886	+	4.02925i	−0.581572	+	0.335771i
$13$	9.51338	−	8.85977i	0.731799	−	0.681521i
$13$	9.51338	−	8.85977i	0.731799	−	0.681521i
$14$	−3.46047	−	9.27497i	−0.247176	−	0.662498i
$15$	−32.0819	+	18.5225i	−2.13880	+	1.23483i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	3.18575	−	1.83929i	0.187397	−	0.108194i	−0.403366	−	0.915039i	$-0.632160\pi$
$17$	3.18575	−	1.83929i	0.187397	−	0.108194i	0.590763	+	0.806845i	$0.298827\pi$
$18$	−8.86083	−	5.11580i	−0.492268	−	0.284211i
$19$	17.2294			0.906810			0.453405	−	0.891305i	$-0.350209\pi$
$19$	17.2294			0.906810			0.453405	+	0.891305i	$0.350209\pi$
$20$	−9.19403	+	15.9245i	−0.459702	+	0.796227i
$21$	17.9554	−	21.7511i	0.855021	−	1.03577i
$22$	12.1433	−	21.0328i	0.551968	−	0.956036i
$23$	−3.50087	+	6.06369i	−0.152212	+	0.263639i	−0.932040	−	0.362355i	$-0.881973\pi$
$23$	−3.50087	+	6.06369i	−0.152212	+	0.263639i	0.779828	+	0.625993i	$0.215306\pi$
$24$	−11.3964			−0.474851
$25$	−29.7651	+	51.5547i	−1.19060	+	2.06219i
$26$	17.9163	−	4.12398i	0.689087	−	0.158615i
$27$			7.11227i			0.263417i
$28$	2.32020	−	13.8064i	0.0828644	−	0.493086i
$29$	0.359781	+	0.623160i	0.0124063	+	0.0214883i	0.872162	−	0.489217i	$-0.162718\pi$
$29$	0.359781	+	0.623160i	0.0124063	+	0.0214883i	−0.859756	+	0.510706i	$0.829384\pi$
$30$	−52.3896			−1.74632
$31$	−22.2101	+	38.4690i	−0.716455	+	1.24094i	0.245941	+	0.969285i	$0.420903\pi$
$31$	−22.2101	+	38.4690i	−0.716455	+	1.24094i	−0.962396	+	0.271651i	$0.912430\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	69.1951			2.09682
$34$	5.20230			0.153009
$35$	10.6660	−	63.4682i	0.304743	−	1.81338i
$36$	−7.23484	−	12.5311i	−0.200968	−	0.348086i
$37$	26.4251	+	15.2565i	0.714191	+	0.412339i	0.812611	−	0.582806i	$-0.198045\pi$
$37$	26.4251	+	15.2565i	0.714191	+	0.412339i	−0.0984196	+	0.995145i	$0.531379\pi$
$38$	21.1016	+	12.1830i	0.555305	+	0.320606i
$39$	35.6982	+	38.3318i	0.915339	+	0.982866i
$40$	−22.5207	+	13.0023i	−0.563017	+	0.325058i
$41$	−16.2530	−	28.1511i	−0.396416	−	0.686612i	0.596865	−	0.802342i	$-0.296413\pi$
$41$	−16.2530	−	28.1511i	−0.396416	−	0.686612i	−0.993281	+	0.115729i	$0.963079\pi$
$42$	37.3712	−	13.9431i	0.889790	−	0.331978i
$43$	26.8250	−	46.4622i	0.623837	−	1.08052i	−0.364928	−	0.931036i	$-0.618906\pi$
$43$	26.8250	−	46.4622i	0.623837	−	1.08052i	0.988765	−	0.149481i	$-0.0477604\pi$
$44$	29.7449	−	17.1732i	0.676020	−	0.390300i
$45$	−33.2587	−	57.6057i	−0.739082	−	1.28013i
$46$	−8.57536	+	4.95098i	−0.186421	+	0.107630i
$47$	−36.6987	−	63.5641i	−0.780824	−	1.35243i	−0.931462	−	0.363838i	$-0.881466\pi$
$47$	−36.6987	−	63.5641i	−0.780824	−	1.35243i	0.150638	−	0.988589i	$-0.451867\pi$
$48$	−13.9577	−	8.05850i	−0.290786	−	0.167885i
$49$	9.28318	+	48.1126i	0.189453	+	0.981890i
$50$	−72.9093	+	42.0942i	−1.45819	+	0.841884i
$51$	7.41096	+	12.8362i	0.145313	+	0.251690i
$52$	24.8590	+	7.61789i	0.478057	+	0.146498i
$53$	−4.39981	+	7.62069i	−0.0830153	+	0.143787i	−0.904544	−	0.426381i	$-0.859788\pi$
$53$	−4.39981	+	7.62069i	−0.0830153	+	0.143787i	0.821528	+	0.570167i	$0.193122\pi$
$54$	−5.02914	+	8.71072i	−0.0931321	+	0.161310i
$55$	136.738	−	78.9455i	2.48614	−	1.43537i
$56$	12.6043	−	15.2687i	0.225076	−	0.272655i
$57$			69.4215i			1.21792i
$58$			1.01762i			0.0175451i
$59$	−6.58394	−	11.4037i	−0.111592	−	0.193283i	0.804820	−	0.593519i	$-0.202262\pi$
$59$	−6.58394	−	11.4037i	−0.111592	−	0.193283i	−0.916412	+	0.400235i	$0.868928\pi$
$60$	−64.1639	−	37.0450i	−1.06940	−	0.617417i
$61$			11.6030i			0.190212i	0.995467	+	0.0951062i	$0.0303191\pi$
$61$			11.6030i			0.190212i	−0.995467	+	0.0951062i	$0.969681\pi$
$62$	−54.4034	+	31.4098i	−0.877474	+	0.506610i
$63$	39.0558	+	32.2405i	0.619933	+	0.511753i
$64$	−8.00000			−0.125000
$65$	114.277	+	35.0196i	1.75811	+	0.538763i
$66$	84.7464	+	48.9283i	1.28404	+	0.741338i
$67$		−	27.7832i		−	0.414675i	−0.978269	−	0.207338i	$-0.933520\pi$
$67$		−	27.7832i		−	0.414675i	0.978269	−	0.207338i	$-0.0664798\pi$
$68$	6.37150	+	3.67858i	0.0936985	+	0.0540968i
$69$	−24.4321	−	14.1059i	−0.354089	−	0.204433i
$70$	57.9420	−	70.1904i	0.827742	−	1.00272i
$71$	−25.6313	−	14.7983i	−0.361005	−	0.208426i	0.308517	−	0.951219i	$-0.400167\pi$
$71$	−25.6313	−	14.7983i	−0.361005	−	0.208426i	−0.669521	+	0.742793i	$0.733501\pi$
$72$		−	20.4632i		−	0.284211i
$73$	−30.1279	+	52.1831i	−0.412711	+	0.714836i	−0.995185	−	0.0980129i	$-0.968751\pi$
$73$	−30.1279	+	52.1831i	−0.412711	+	0.714836i	0.582474	+	0.812849i	$0.302085\pi$
$74$	21.5760	+	37.3707i	0.291567	+	0.505010i
$75$	−207.727	−	119.931i	−2.76969	−	1.59908i
$76$	17.2294	+	29.8422i	0.226702	+	0.392660i
$77$	−76.5286	+	92.7060i	−0.993878	+	1.20397i
$78$	16.6165	+	72.1891i	0.213033	+	0.925501i
$79$	−66.3791	−	114.972i	−0.840242	−	1.45534i	−0.889690	−	0.456565i	$-0.849080\pi$
$79$	−66.3791	−	114.972i	−0.840242	−	1.45534i	0.0494485	−	0.998777i	$-0.484254\pi$
$80$	−36.7761			−0.459702
$81$	−93.7707			−1.15766
$82$		−	45.9706i		−	0.560617i
$83$	108.148			1.30299			0.651493	−	0.758654i	$-0.274143\pi$
$83$	108.148			1.30299			0.651493	+	0.758654i	$0.274143\pi$
$84$	55.6294	+	9.34868i	0.662255	+	0.111294i
$85$	29.2899	+	16.9105i	0.344587	+	0.198947i
$86$	65.7075	−	37.9363i	0.764041	−	0.441119i
$87$	−2.51087	+	1.44965i	−0.0288605	+	0.0166626i
$88$	48.5732			0.551968
$89$	48.6213	−	84.2145i	0.546307	−	0.946231i	−0.452217	−	0.891908i	$-0.649367\pi$
$89$	48.6213	−	84.2145i	0.546307	−	0.946231i	0.998523	−	0.0543228i	$-0.0173000\pi$
$90$		−	94.0697i		−	1.04522i
$91$	−90.8376	+	5.43338i	−0.998216	+	0.0597074i
$92$	−14.0035			−0.152212
$93$	−155.001	−	89.4900i	−1.66668	−	0.962258i
$94$		−	103.800i		−	1.10425i
$95$	79.2038	+	137.185i	0.833724	+	1.44405i
$96$	−11.3964	−	19.7392i	−0.118713	−	0.205617i
$97$	39.5728	−	68.5420i	0.407967	−	0.706619i	−0.586695	−	0.809808i	$-0.699571\pi$
$97$	39.5728	−	68.5420i	0.407967	−	0.706619i	0.994662	+	0.103189i	$0.0329046\pi$
$98$	−22.6512	+	65.4899i	−0.231135	+	0.668264i
$99$			124.245i			1.25500i
$100$	−119.060			−1.19060
$101$		−	11.0336i		−	0.109243i	−0.998507	−	0.0546216i	$-0.982605\pi$
$101$		−	11.0336i		−	0.109243i	0.998507	−	0.0546216i	$-0.0173952\pi$
$102$			20.9614i			0.205504i
$103$	139.106	−	80.3127i	1.35054	−	0.779735i	0.362215	−	0.932094i	$-0.382020\pi$
$103$	139.106	−	80.3127i	1.35054	−	0.779735i	0.988325	+	0.152360i	$0.0486872\pi$
$104$	25.0592	+	26.9079i	0.240954	+	0.258730i
$105$	255.729	+	42.9760i	2.43552	+	0.409296i
$106$	−10.7773	+	6.22227i	−0.101673	+	0.0587007i
$107$	−67.0302	+	116.100i	−0.626450	+	1.08504i	0.361808	+	0.932253i	$0.382160\pi$
$107$	−67.0302	+	116.100i	−0.626450	+	1.08504i	−0.988258	+	0.152791i	$0.951174\pi$
$108$	−12.3188	+	7.11227i	−0.114063	+	0.0658544i
$109$	53.7515	+	31.0334i	0.493133	+	0.284710i	0.725873	−	0.687829i	$-0.241436\pi$
$109$	53.7515	+	31.0334i	0.493133	+	0.284710i	−0.232740	+	0.972539i	$0.574769\pi$
$110$	223.292			2.02992
$111$	−61.4723	+	106.473i	−0.553805	+	0.959218i
$112$	26.2336	−	9.78769i	0.234228	−	0.0873901i
$113$	−15.4838	+	26.8187i	−0.137024	+	0.237333i	−0.926369	−	0.376617i	$-0.877087\pi$
$113$	−15.4838	+	26.8187i	−0.137024	+	0.237333i	0.789345	+	0.613950i	$0.210421\pi$
$114$	−49.0884	+	85.0236i	−0.430600	+	0.745821i
$115$	−64.3743			−0.559777
$116$	−0.719563	+	1.24632i	−0.00620313	+	0.0107441i
$117$	−68.8278	+	64.0990i	−0.588272	+	0.547855i
$118$		−	18.6222i		−	0.157815i
$119$	−25.3940	−	4.26753i	−0.213395	−	0.0358616i
$120$	−52.3896	−	90.7414i	−0.436580	−	0.756179i
$121$	−173.919			−1.43735
$122$	−8.20453	+	14.2107i	−0.0672502	+	0.116481i
$123$	113.428	−	65.4875i	0.922177	−	0.532419i
$124$	−88.8404			−0.716455
$125$	−317.472			−2.53978
$126$	25.0359	+	67.1029i	0.198698	+	0.532563i
$127$	24.8316	+	43.0096i	0.195524	+	0.338658i	0.947072	−	0.321020i	$-0.104026\pi$
$127$	24.8316	+	43.0096i	0.195524	+	0.338658i	−0.751548	+	0.659678i	$0.770692\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	187.208	+	108.085i	1.45122	+	0.837865i
$130$	115.198	+	123.696i	0.886135	+	0.951508i
$131$	−148.863	+	85.9460i	−1.13636	+	0.656076i	−0.945526	−	0.325547i	$-0.894452\pi$
$131$	−148.863	+	85.9460i	−1.13636	+	0.656076i	−0.190831	+	0.981623i	$0.561118\pi$
$132$	69.1951	+	119.849i	0.524205	+	0.907950i
$133$	−93.0093	−	76.7789i	−0.699318	−	0.577285i
$134$	19.6457	−	34.0274i	0.146610	−	0.253936i
$135$	−56.6298	+	32.6952i	−0.419480	+	0.242187i
$136$	5.20230	+	9.01066i	0.0382522	+	0.0662548i
$137$	37.7134	−	21.7738i	0.275280	−	0.158933i	−0.356005	−	0.934484i	$-0.615861\pi$
$137$	37.7134	−	21.7738i	0.275280	−	0.158933i	0.631285	+	0.775551i	$0.282528\pi$
$138$	−19.9487	−	34.5522i	−0.144556	−	0.250379i
$139$	21.7494	+	12.5570i	0.156471	+	0.0903384i	0.576191	−	0.817315i	$-0.304538\pi$
$139$	21.7494	+	12.5570i	0.156471	+	0.0903384i	−0.419720	+	0.907654i	$0.637872\pi$
$140$	120.596	−	44.9942i	0.861402	−	0.321387i
$141$	256.115	−	147.868i	1.81642	−	1.04871i
$142$	−20.9279	−	36.2482i	−0.147380	−	0.255269i
$143$	−152.151	−	163.375i	−1.06399	−	1.14248i
$144$	14.4697	−	25.0622i	0.100484	−	0.174043i
$145$	−3.30784	+	5.72935i	−0.0228127	+	0.0395128i
$146$	−73.7980	+	42.6073i	−0.505466	+	0.291831i
$147$	−193.858	+	37.4042i	−1.31876	+	0.254450i
$148$			61.0261i			0.412339i
$149$			154.197i			1.03488i	0.855719	+	0.517441i	$0.173115\pi$
$149$			154.197i			1.03488i	−0.855719	+	0.517441i	$0.826885\pi$
$150$	−169.608	−	293.770i	−1.13072	−	1.95847i
$151$	38.2961	+	22.1103i	0.253617	+	0.146426i	0.621419	−	0.783478i	$-0.286556\pi$
$151$	38.2961	+	22.1103i	0.253617	+	0.146426i	−0.367802	+	0.929904i	$0.619890\pi$
$152$			48.7321i			0.320606i
$153$	−23.0484	+	13.3070i	−0.150643	+	0.0869738i
$154$	−159.281	+	59.4274i	−1.03429	+	0.385892i
$155$	−408.401			−2.63484
$156$	−30.6944	+	100.163i	−0.196759	+	0.642070i
$157$	112.372	+	64.8778i	0.715743	+	0.413235i	0.813184	−	0.582007i	$-0.197732\pi$
$157$	112.372	+	64.8778i	0.715743	+	0.413235i	−0.0974406	+	0.995241i	$0.531066\pi$
$158$		−	187.748i		−	1.18828i
$159$	−30.7057	−	17.7279i	−0.193117	−	0.111496i
$160$	−45.0414	−	26.0046i	−0.281509	−	0.162529i
$161$	45.9203	−	17.1327i	0.285219	−	0.106414i
$162$	−114.845	−	66.3059i	−0.708921	−	0.409295i
$163$		−	214.343i		−	1.31499i	−0.753460	−	0.657494i	$-0.771617\pi$
$163$		−	214.343i		−	1.31499i	0.753460	−	0.657494i	$-0.228383\pi$
$164$	32.5061	−	56.3022i	0.198208	−	0.343306i
$165$	318.091	+	550.950i	1.92782	+	3.33909i
$166$	132.454	+	76.4721i	0.797913	+	0.460675i
$167$	70.0407	+	121.314i	0.419405	+	0.726431i	0.995880	−	0.0906838i	$-0.0289053\pi$
$167$	70.0407	+	121.314i	0.419405	+	0.726431i	−0.576474	+	0.817115i	$0.695572\pi$
$168$	61.5213	+	50.7857i	0.366198	+	0.302296i
$169$	12.0089	−	168.573i	0.0710587	−	0.997472i
$170$	23.9151	+	41.4221i	0.140677	+	0.243660i
$171$	−124.652			−0.728958
$172$	107.300			0.623837
$173$		−	302.316i		−	1.74749i	−0.486383	−	0.873746i	$-0.661684\pi$
$173$		−	302.316i		−	1.74749i	0.486383	−	0.873746i	$-0.338316\pi$
$174$	−4.10023			−0.0235645
$175$	390.423	−	145.666i	2.23099	−	0.832376i
$176$	59.4897	+	34.3464i	0.338010	+	0.195150i
$177$	45.9484	−	26.5283i	0.259596	−	0.149878i
$178$	119.097	−	68.7609i	0.669086	−	0.386297i
$179$	−183.417			−1.02468			−0.512339	−	0.858783i	$-0.671221\pi$
$179$	−183.417			−1.02468			−0.512339	+	0.858783i	$0.671221\pi$
$180$	66.5173	−	115.211i	0.369541	−	0.640063i
$181$			220.794i			1.21986i	0.792456	+	0.609929i	$0.208802\pi$
$181$			220.794i			1.21986i	−0.792456	+	0.609929i	$0.791198\pi$
$182$	−115.095	−	57.5774i	−0.632390	−	0.316359i
$183$	−46.7512			−0.255471
$184$	−17.1507	−	9.90197i	−0.0932104	−	0.0538150i
$185$			280.538i			1.51642i
$186$	−126.558	−	219.205i	−0.680419	−	1.17852i
$187$	−31.5866	−	54.7095i	−0.168912	−	0.292564i
$188$	73.3975	−	127.128i	0.390412	−	0.676214i
$189$	31.6943	−	38.3941i	0.167694	−	0.203144i
$190$			224.022i			1.17906i
$191$	−9.41722			−0.0493048			−0.0246524	−	0.999696i	$-0.507848\pi$
$191$	−9.41722			−0.0493048			−0.0246524	+	0.999696i	$0.507848\pi$
$192$		−	32.2340i		−	0.167885i
$193$			34.3839i			0.178155i	0.996025	+	0.0890774i	$0.0283919\pi$
$193$			34.3839i			0.178155i	−0.996025	+	0.0890774i	$0.971608\pi$
$194$	96.9331	−	55.9643i	0.499655	−	0.288476i
$195$	−141.103	+	460.450i	−0.723603	+	2.36128i
$196$	−74.0503	+	64.1915i	−0.377808	+	0.327508i
$197$	100.680	−	58.1276i	0.511065	−	0.295064i	−0.222206	−	0.975000i	$-0.571326\pi$
$197$	100.680	−	58.1276i	0.511065	−	0.295064i	0.733271	+	0.679936i	$0.237992\pi$
$198$	−87.8548	+	152.169i	−0.443711	+	0.768530i
$199$	−86.5735	+	49.9833i	−0.435043	+	0.251172i	−0.701493	−	0.712677i	$-0.747483\pi$
$199$	−86.5735	+	49.9833i	−0.435043	+	0.251172i	0.266450	+	0.963849i	$0.414149\pi$
$200$	−145.819	−	84.1884i	−0.729093	−	0.420942i
$201$	111.946			0.556943
$202$	7.80190	−	13.5133i	0.0386233	−	0.0668975i
$203$	0.834767	−	4.96729i	0.00411215	−	0.0244694i
$204$	−14.8219	+	25.6723i	−0.0726565	+	0.125845i
$205$	149.431	−	258.822i	0.728932	−	1.26255i
$206$	227.159			1.10271
$207$	25.3283	−	43.8698i	0.122359	−	0.211932i
$208$	11.6644	+	50.6749i	0.0560787	+	0.243629i
$209$		−	295.884i		−	1.41571i
$210$	282.814	+	233.463i	1.34674	+	1.11173i
$211$	−160.266	−	277.589i	−0.759555	−	1.31559i	−0.943078	−	0.332573i	$-0.892083\pi$
$211$	−160.266	−	277.589i	−0.759555	−	1.31559i	0.183522	−	0.983016i	$-0.441250\pi$
$212$	−17.5992			−0.0830153
$213$	59.6259	−	103.275i	0.279934	−	0.484859i
$214$	−164.190	+	94.7950i	−0.767242	+	0.442967i
$215$	493.260			2.29423
$216$	−20.1165			−0.0931321
$217$	291.325	−	108.693i	1.34251	−	0.500888i
$218$	43.8879	+	76.0161i	0.201321	+	0.348698i
$219$	−210.258	−	121.393i	−0.960084	−	0.554305i
$220$	273.475	+	157.891i	1.24307	+	0.717687i
$221$	14.0115	−	45.7229i	0.0634006	−	0.206891i
$222$	−150.576	+	86.9350i	−0.678270	+	0.391599i
$223$	158.432	+	274.412i	0.710458	+	1.23055i	0.964686	+	0.263404i	$0.0848453\pi$
$223$	158.432	+	274.412i	0.710458	+	1.23055i	−0.254228	+	0.967144i	$0.581821\pi$
$224$	39.0504	+	6.56253i	0.174332	+	0.0292970i
$225$	215.346	−	372.990i	0.957092	−	1.65773i
$226$	−37.9273	+	21.8973i	−0.167820	+	0.0968909i
$227$	70.5513	+	122.198i	0.310799	+	0.538319i	0.978535	−	0.206078i	$-0.0660702\pi$
$227$	70.5513	+	122.198i	0.310799	+	0.538319i	−0.667737	+	0.744397i	$0.732737\pi$
$228$	−120.241	+	69.4215i	−0.527375	+	0.304480i
$229$	38.3046	+	66.3454i	0.167269	+	0.289718i	0.937459	−	0.348097i	$-0.113172\pi$
$229$	38.3046	+	66.3454i	0.167269	+	0.289718i	−0.770190	+	0.637815i	$0.779839\pi$
$230$	−78.8421	−	45.5195i	−0.342792	−	0.197911i
$231$	−373.536	−	308.353i	−1.61704	−	1.33486i
$232$	−1.76256	+	1.01762i	−0.00759725	+	0.00438627i
$233$	−137.436	−	238.046i	−0.589853	−	1.02166i	−0.994251	−	0.107073i	$-0.965852\pi$
$233$	−137.436	−	238.046i	−0.589853	−	1.02166i	0.404398	−	0.914583i	$-0.367481\pi$
$234$	−129.621	+	29.8363i	−0.553937	+	0.127506i
$235$	337.409	−	584.410i	1.43578	−	2.48685i
$236$	13.1679	−	22.8074i	0.0557961	−	0.0966417i
$237$	463.251	−	267.458i	1.95464	−	1.12851i
$238$	−28.0836	−	23.1829i	−0.117998	−	0.0974072i
$239$			177.253i			0.741646i	0.928704	+	0.370823i	$0.120924\pi$
$239$			177.253i			0.741646i	−0.928704	+	0.370823i	$0.879076\pi$
$240$		−	148.180i		−	0.617417i
$241$	−159.932	−	277.010i	−0.663617	−	1.14942i	−0.979658	−	0.200673i	$-0.935687\pi$
$241$	−159.932	−	277.010i	−0.663617	−	1.14942i	0.316041	−	0.948746i	$-0.397646\pi$
$242$	−213.007	−	122.979i	−0.880192	−	0.508179i
$243$		−	313.815i		−	1.29142i
$244$	−20.0969	+	11.6030i	−0.0823644	+	0.0475531i
$245$	−340.410	+	295.090i	−1.38943	+	1.20445i
$246$	185.227			0.752954
$247$	163.910	−	152.648i	0.663602	−	0.618010i
$248$	−108.807	−	62.8196i	−0.438737	−	0.253305i
$249$			435.755i			1.75002i
$250$	−388.822	−	224.487i	−1.55529	−	0.897946i
$251$	−27.6527	−	15.9653i	−0.110170	−	0.0636067i	0.443902	−	0.896075i	$-0.353594\pi$
$251$	−27.6527	−	15.9653i	−0.110170	−	0.0636067i	−0.554073	+	0.832468i	$0.686927\pi$
$252$	−16.7863	+	99.8871i	−0.0666123	+	0.396377i
$253$	104.133	+	60.1212i	0.411593	+	0.237633i
$254$			70.2344i			0.276513i
$255$	−68.1366	+	118.016i	−0.267203	+	0.462808i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	31.7225	+	18.3150i	0.123434	+	0.0712646i	0.560446	−	0.828191i	$-0.310630\pi$
$257$	31.7225	+	18.3150i	0.123434	+	0.0712646i	−0.437012	+	0.899456i	$0.643963\pi$
$258$	152.855	+	264.752i	0.592460	+	1.02617i
$259$	−74.6631	−	200.117i	−0.288274	−	0.772652i
$260$	53.6213	+	232.953i	0.206236	+	0.895974i
$261$	−2.60296	−	4.50846i	−0.00997303	−	0.0172738i
$262$	−243.092			−0.927832
$263$	−422.407			−1.60611			−0.803056	−	0.595904i	$-0.796794\pi$
$263$	−422.407			−1.60611			−0.803056	+	0.595904i	$0.796794\pi$
$264$			195.713i			0.741338i
$265$	−80.9040			−0.305298
$266$	−59.6218	−	159.802i	−0.224142	−	0.600760i
$267$	339.321	+	195.907i	1.27087	+	0.733735i
$268$	48.1220	−	27.7832i	0.179560	−	0.103669i
$269$	−385.918	+	222.810i	−1.43464	+	0.828290i	−0.997470	−	0.0710895i	$-0.977352\pi$
$269$	−385.918	+	222.810i	−1.43464	+	0.828290i	−0.437170	+	0.899379i	$0.644019\pi$
$270$	−92.4761			−0.342504
$271$	−184.235	+	319.104i	−0.679833	+	1.17750i	0.295198	+	0.955436i	$0.404614\pi$
$271$	−184.235	+	319.104i	−0.679833	+	1.17750i	−0.975031	+	0.222069i	$0.928719\pi$
$272$			14.7143i			0.0540968i
$273$	−21.8924	−	366.007i	−0.0801920	−	1.34069i
$274$	61.5857			0.224765
$275$	885.359	+	511.162i	3.21949	+	1.85877i
$276$		−	56.4236i		−	0.204433i
$277$	−166.583	−	288.530i	−0.601382	−	1.04162i	−0.992612	−	0.121331i	$-0.961284\pi$
$277$	−166.583	−	288.530i	−0.601382	−	1.04162i	0.391230	−	0.920293i	$-0.372050\pi$
$278$	17.7583	+	30.7583i	0.0638789	+	0.110641i
$279$	160.686	−	278.317i	0.575937	−	0.997552i
$280$	179.515	+	30.1681i	0.641126	+	0.107743i
$281$		−	289.853i		−	1.03151i	−0.856738	−	0.515753i	$-0.827512\pi$
$281$		−	289.853i		−	1.03151i	0.856738	−	0.515753i	$-0.172488\pi$
$282$	418.235			1.48310
$283$			15.5507i			0.0549494i	0.999622	+	0.0274747i	$0.00874658\pi$
$283$			15.5507i			0.0549494i	−0.999622	+	0.0274747i	$0.991253\pi$
$284$		−	59.1930i		−	0.208426i
$285$	−552.752	+	319.132i	−1.93948	+	1.11976i
$286$	−70.8220	−	307.680i	−0.247629	−	1.07580i
$287$	−37.7104	+	224.396i	−0.131395	+	0.781868i
$288$	35.4433	−	20.4632i	0.123067	−	0.0710528i
$289$	−137.734	+	238.562i	−0.476588	+	0.825475i
$290$	−8.10253	+	4.67800i	−0.0279397	+	0.0161310i
$291$	276.173	+	159.448i	0.949048	+	0.547933i
$292$	−120.512			−0.412711
$293$	−126.969	+	219.916i	−0.433340	+	0.750566i	−0.997159	−	0.0753321i	$-0.975998\pi$
$293$	−126.969	+	219.916i	−0.433340	+	0.750566i	0.563819	+	0.825899i	$0.309332\pi$
$294$	−263.875	−	91.2674i	−0.897534	−	0.310433i
$295$	60.5330	−	104.846i	0.205197	−	0.355411i
$296$	−43.1520	+	74.7414i	−0.145784	+	0.252505i
$297$	122.141			0.411248
$298$	−109.034	+	188.852i	−0.365886	+	0.633733i
$299$	20.4178	+	88.7032i	0.0682868	+	0.296666i
$300$		−	479.724i		−	1.59908i
$301$	−351.858	+	131.277i	−1.16896	+	0.436137i
$302$	31.2687	+	54.1589i	0.103539	+	0.179334i
$303$	44.4569			0.146723
$304$	−34.4588	+	59.6843i	−0.113351	+	0.196330i
$305$	−92.3858	+	53.3390i	−0.302904	+	0.174882i
$306$	−37.6378			−0.122999
$307$	272.611			0.887982			0.443991	−	0.896031i	$-0.353562\pi$
$307$	272.611			0.887982			0.443991	+	0.896031i	$0.353562\pi$
$308$	−237.100	−	39.8454i	−0.769806	−	0.129368i
$309$	323.600	+	560.491i	1.04725	+	1.81389i
$310$	−500.187	−	288.783i	−1.61350	−	0.931558i
$311$	−250.624	−	144.698i	−0.805866	−	0.465267i	0.0396525	−	0.999214i	$-0.487375\pi$
$311$	−250.624	−	144.698i	−0.805866	−	0.465267i	−0.845518	+	0.533947i	$0.820708\pi$
$312$	−108.419	+	100.970i	−0.347496	+	0.323621i
$313$	248.246	−	143.325i	0.793117	−	0.457906i	−0.0479417	−	0.998850i	$-0.515266\pi$
$313$	248.246	−	143.325i	0.793117	−	0.457906i	0.841059	+	0.540944i	$0.181933\pi$
$314$	91.7511	+	158.918i	0.292201	+	0.506107i
$315$	−77.1669	+	459.182i	−0.244974	+	1.45772i
$316$	132.758	−	229.944i	0.420121	−	0.727671i
$317$	−72.1894	+	41.6786i	−0.227727	+	0.131478i	−0.609523	−	0.792768i	$-0.708639\pi$
$317$	−72.1894	+	41.6786i	−0.227727	+	0.131478i	0.381796	+	0.924247i	$0.375306\pi$
$318$	−25.0711	−	43.4244i	−0.0788399	−	0.136555i
$319$	10.7017	−	6.17860i	0.0335475	−	0.0193687i
$320$	−36.7761	−	63.6981i	−0.114925	−	0.199057i
$321$	−467.794	−	270.081i	−1.45730	−	0.841375i
$322$	68.3553	+	11.4873i	0.212283	+	0.0356748i
$323$	54.8885	−	31.6899i	0.169933	−	0.0981111i
$324$	−93.7707	−	162.416i	−0.289416	−	0.501283i
$325$	173.596	+	754.172i	0.534141	+	2.32053i
$326$	151.563	−	262.515i	0.464918	−	0.805262i
$327$	−125.041	+	216.578i	−0.382389	+	0.662318i
$328$	79.6233	−	45.9706i	0.242754	−	0.140154i
$329$	−85.1486	+	506.677i	−0.258810	+	1.54005i
$330$			899.697i			2.72636i
$331$			299.299i			0.904225i	0.891961	+	0.452113i	$0.149329\pi$
$331$			299.299i			0.904225i	−0.891961	+	0.452113i	$0.850671\pi$
$332$	108.148	+	187.318i	0.325747	+	0.564210i
$333$	−191.181	−	110.379i	−0.574118	−	0.331467i
$334$			198.105i			0.593129i
$335$	221.217	−	127.720i	0.660351	−	0.381254i
$336$	39.4370	+	105.702i	0.117372	+	0.314588i
$337$	−605.486			−1.79669			−0.898347	−	0.439286i	$-0.855232\pi$
$337$	−605.486			−1.79669			−0.898347	+	0.439286i	$0.855232\pi$
$338$	133.907	−	197.967i	0.396174	−	0.585701i
$339$	−108.059	−	62.3879i	−0.318758	−	0.184035i
$340$			67.6421i			0.198947i
$341$	660.636	+	381.419i	1.93735	+	1.11853i
$342$	−152.667	−	88.1421i	−0.446394	−	0.257726i
$343$	164.290	−	301.094i	0.478979	−	0.877826i
$344$	131.415	+	75.8725i	0.382021	+	0.220560i
$345$		−	259.380i		−	0.751826i
$346$	213.770	−	370.260i	0.617832	−	1.07012i
$347$	−12.6363	−	21.8868i	−0.0364159	−	0.0630742i	0.847243	−	0.531205i	$-0.178261\pi$
$347$	−12.6363	−	21.8868i	−0.0364159	−	0.0630742i	−0.883659	+	0.468131i	$0.844927\pi$
$348$	−5.02173	−	2.89930i	−0.0144303	−	0.00833131i
$349$	276.022	+	478.084i	0.790894	+	1.36987i	0.925414	+	0.378958i	$0.123717\pi$
$349$	276.022	+	478.084i	0.790894	+	1.36987i	−0.134520	+	0.990911i	$0.542949\pi$
$350$	581.170	+	97.6672i	1.66048	+	0.279049i
$351$	63.0131	+	67.6618i	0.179524	+	0.192769i
$352$	48.5732	+	84.1312i	0.137992	+	0.239009i
$353$	150.830			0.427279			0.213640	−	0.976913i	$-0.431468\pi$
$353$	150.830			0.427279			0.213640	+	0.976913i	$0.431468\pi$
$354$	75.0335			0.211959
$355$		−	272.111i		−	0.766511i
$356$	194.485			0.546307
$357$	17.1950	−	102.319i	0.0481651	−	0.286607i
$358$	−224.640	−	129.696i	−0.627485	−	0.362279i
$359$	53.1461	−	30.6839i	0.148039	−	0.0854705i	−0.424151	−	0.905592i	$-0.639427\pi$
$359$	53.1461	−	30.6839i	0.148039	−	0.0854705i	0.572190	+	0.820121i	$0.306094\pi$
$360$	162.934	−	94.0697i	0.452593	−	0.261305i
$361$	−64.1483			−0.177696
$362$	−156.125	+	270.417i	−0.431285	+	0.747007i
$363$		−	700.763i		−	1.93048i
$364$	−100.249	−	151.902i	−0.275408	−	0.417313i
$365$	−553.994			−1.51779
$366$	−57.2583	−	33.0581i	−0.156443	−	0.0903226i
$367$			412.194i			1.12314i	0.827428	+	0.561572i	$0.189803\pi$
$367$			412.194i			1.12314i	−0.827428	+	0.561572i	$0.810197\pi$
$368$	−14.0035	−	24.2548i	−0.0380530	−	0.0659097i
$369$	117.588	+	203.669i	0.318667	+	0.551948i
$370$	−198.370	+	343.588i	−0.536136	+	0.928615i
$371$	57.7114	−	21.5320i	0.155556	−	0.0580377i
$372$		−	357.960i		−	0.962258i
$373$	167.917			0.450179			0.225089	−	0.974338i	$-0.427733\pi$
$373$	167.917			0.450179			0.225089	+	0.974338i	$0.427733\pi$
$374$		−	89.3403i		−	0.238878i
$375$		−	1279.17i		−	3.41113i
$376$	179.786	−	103.800i	0.478155	−	0.276063i
$377$	8.94379	+	2.74078i	0.0237236	+	0.00726996i
$378$	65.9661	−	24.6118i	0.174514	−	0.0651106i
$379$	−180.041	+	103.947i	−0.475042	+	0.274266i	−0.718348	−	0.695684i	$-0.755101\pi$
$379$	−180.041	+	103.947i	−0.475042	+	0.274266i	0.243306	+	0.969950i	$0.421768\pi$
$380$	−158.408	+	274.370i	−0.416862	+	0.722026i
$381$	−173.296	+	100.053i	−0.454846	+	0.262605i
$382$	−11.5337	−	6.65898i	−0.0301929	−	0.0174319i
$383$	−506.267			−1.32185			−0.660924	−	0.750453i	$-0.729835\pi$
$383$	−506.267			−1.32185			−0.660924	+	0.750453i	$0.729835\pi$
$384$	22.7929	−	39.4784i	0.0593564	−	0.102808i
$385$	−1089.95	−	183.170i	−2.83105	−	0.475766i
$386$	−24.3131	+	42.1115i	−0.0629873	+	0.109097i
$387$	−194.074	+	336.147i	−0.501484	+	0.868596i
$388$	158.291			0.407967
$389$	−132.829	+	230.066i	−0.341462	+	0.591429i	−0.984704	−	0.174233i	$-0.944255\pi$
$389$	−132.829	+	230.066i	−0.341462	+	0.591429i	0.643243	+	0.765662i	$0.277589\pi$
$390$	−498.402	+	464.160i	−1.27795	+	1.19015i
$391$			25.7565i			0.0658735i
$392$	−136.083	+	26.2568i	−0.347150	+	0.0669816i
$393$	−346.298	−	599.805i	−0.881165	−	1.52622i
$394$	164.410			0.417283
$395$	610.292	−	1057.06i	1.54504	−	2.67609i
$396$	−215.199	+	124.245i	−0.543433	+	0.313751i
$397$	196.496			0.494951			0.247476	−	0.968894i	$-0.420399\pi$
$397$	196.496			0.494951			0.247476	+	0.968894i	$0.420399\pi$
$398$	−141.374			−0.355211
$399$	309.361	−	374.758i	0.775342	−	0.939242i
$400$	−119.060	−	206.219i	−0.297651	−	0.515547i
$401$	−15.8779	−	9.16713i	−0.0395958	−	0.0228607i	0.480071	−	0.877229i	$-0.340611\pi$
$401$	−15.8779	−	9.16713i	−0.0395958	−	0.0228607i	−0.519667	+	0.854369i	$0.673944\pi$
$402$	137.105	+	79.1574i	0.341056	+	0.196909i
$403$	129.533	+	562.747i	0.321423	+	1.39639i
$404$	19.1107	−	11.0336i	0.0473037	−	0.0273108i
$405$	−431.065	−	746.627i	−1.06436	−	1.84352i
$406$	4.53478	−	5.49339i	0.0111694	−	0.0135305i
$407$	262.004	−	453.804i	0.643743	−	1.11500i
$408$	−36.3062	+	20.9614i	−0.0889857	+	0.0513759i
$409$	27.6031	+	47.8100i	0.0674893	+	0.116895i	0.897795	−	0.440413i	$-0.145168\pi$
$409$	27.6031	+	47.8100i	0.0674893	+	0.116895i	−0.830306	+	0.557307i	$0.811834\pi$
$410$	366.030	−	211.327i	0.892755	−	0.515433i
$411$	87.7321	+	151.957i	0.213460	+	0.369724i
$412$	278.211	+	160.625i	0.675270	+	0.389867i
$413$	−15.2761	+	90.9005i	−0.0369881	+	0.220098i
$414$	62.0413	−	35.8196i	0.149858	−	0.0865207i
$415$	497.158	+	861.102i	1.19797	+	2.07495i
$416$	−21.5467	+	70.3117i	−0.0517948	+	0.169019i
$417$	−50.5954	+	87.6338i	−0.121332	+	0.210153i
$418$	209.221	−	362.382i	0.500530	−	0.866943i
$419$	−595.399	+	343.754i	−1.42100	+	0.820415i	−0.996384	−	0.0849586i	$-0.972924\pi$
$419$	−595.399	+	343.754i	−1.42100	+	0.820415i	−0.424616	+	0.905374i	$0.639591\pi$
$420$	181.293	+	485.912i	0.431649	+	1.15693i
$421$		−	584.326i		−	1.38795i	−0.720001	−	0.693973i	$-0.755859\pi$
$421$		−	584.326i		−	1.38795i	0.720001	−	0.693973i	$-0.244141\pi$
$422$		−	453.301i		−	1.07417i
$423$	265.509	+	459.876i	0.627682	+	1.08718i
$424$	−21.5546	−	12.4445i	−0.0508363	−	0.0293503i
$425$			218.987i			0.515263i
$426$	146.053	−	84.3237i	0.342847	−	0.197943i
$427$	51.7060	−	62.6362i	0.121091	−	0.146689i
$428$	−268.121			−0.626450
$429$	658.280	−	613.053i	1.53445	−	1.42903i
$430$	604.117	+	348.787i	1.40492	+	0.811133i
$431$			3.28529i			0.00762248i	0.999993	+	0.00381124i	$0.00121316\pi$
$431$			3.28529i			0.00762248i	−0.999993	+	0.00381124i	$0.998787\pi$
$432$	−24.6376	−	14.2245i	−0.0570315	−	0.0329272i
$433$	−244.440	−	141.128i	−0.564527	−	0.325930i	0.190434	−	0.981700i	$-0.439011\pi$
$433$	−244.440	−	141.128i	−0.564527	−	0.325930i	−0.754960	+	0.655770i	$0.772344\pi$
$434$	433.656	+	72.8772i	0.999208	+	0.167920i
$435$	−23.0850	−	13.3281i	−0.0530689	−	0.0306393i
$436$			124.134i			0.284710i
$437$	−60.3179	+	104.474i	−0.138027	+	0.239070i
$438$	−171.675	−	297.350i	−0.391953	−	0.678882i
$439$	303.629	+	175.300i	0.691638	+	0.399317i	0.804225	−	0.594325i	$-0.202581\pi$
$439$	303.629	+	175.300i	0.691638	+	0.399317i	−0.112588	+	0.993642i	$0.535914\pi$
$440$	223.292	+	386.752i	0.507481	+	0.878983i
$441$	−67.1623	−	348.087i	−0.152295	−	0.789313i
$442$	49.4915	−	46.0912i	0.111972	−	0.104279i
$443$	15.8959	+	27.5325i	0.0358824	+	0.0621501i	0.883409	−	0.468603i	$-0.155243\pi$
$443$	15.8959	+	27.5325i	0.0358824	+	0.0621501i	−0.847527	+	0.530753i	$0.821909\pi$
$444$	−245.889			−0.553805
$445$	894.051			2.00910
$446$			448.113i			1.00474i
$447$	−621.299			−1.38993
$448$	43.1864	+	35.6502i	0.0963981	+	0.0795764i
$449$	−271.586	−	156.800i	−0.604868	−	0.349221i	0.166086	−	0.986111i	$-0.446887\pi$
$449$	−271.586	−	156.800i	−0.604868	−	0.349221i	−0.770954	+	0.636891i	$0.780220\pi$
$450$	527.487	−	304.545i	1.17219	−	0.676767i
$451$	−483.445	+	279.117i	−1.07194	+	0.618885i
$452$	−61.9350			−0.137024
$453$	−89.0878	+	154.305i	−0.196662	+	0.340628i
$454$			199.549i			0.439536i
$455$	−460.844	−	698.296i	−1.01284	−	1.53472i
$456$	−196.354			−0.430600
$457$	84.0335	+	48.5168i	0.183881	+	0.106164i	0.589115	−	0.808049i	$-0.299477\pi$
$457$	84.0335	+	48.5168i	0.183881	+	0.106164i	−0.405234	+	0.914213i	$0.632810\pi$
$458$			108.342i			0.236554i
$459$	13.0815	+	22.6579i	0.0285001	+	0.0493636i
$460$	−64.3743	−	111.500i	−0.139944	−	0.242390i
$461$	244.363	−	423.249i	0.530071	−	0.918110i	−0.469314	−	0.883032i	$-0.655499\pi$
$461$	244.363	−	423.249i	0.530071	−	0.918110i	0.999385	−	0.0350783i	$-0.0111681\pi$
$462$	−239.448	−	641.783i	−0.518285	−	1.38914i
$463$			570.309i			1.23177i	0.787837	+	0.615884i	$0.211201\pi$
$463$			570.309i			1.23177i	−0.787837	+	0.615884i	$0.788799\pi$
$464$	−2.87825			−0.00620313
$465$		−	1645.55i		−	3.53881i
$466$		−	388.727i		−	0.834178i
$467$	−92.0182	+	53.1267i	−0.197041	+	0.113762i	−0.595275	−	0.803522i	$-0.702957\pi$
$467$	−92.0182	+	53.1267i	−0.197041	+	0.113762i	0.398233	+	0.917284i	$0.369623\pi$
$468$	−179.851	−	55.1142i	−0.384296	−	0.117765i
$469$	−123.810	+	149.982i	−0.263987	+	0.319791i
$470$	826.481	−	477.169i	1.75847	−	1.01525i
$471$	−261.409	+	452.773i	−0.555008	+	0.961303i
$472$	32.2546	−	18.6222i	0.0683360	−	0.0394538i
$473$	−797.906	−	460.671i	−1.68690	−	0.973935i
$474$	756.485			1.59596
$475$	−512.835	+	888.255i	−1.07965	+	1.87001i
$476$	−18.0024	−	48.2512i	−0.0378202	−	0.101368i
$477$	31.8319	−	55.1345i	0.0667336	−	0.115586i
$478$	−125.337	+	217.090i	−0.262211	+	0.454163i
$479$	33.2438			0.0694024			0.0347012	−	0.999398i	$-0.488952\pi$
$479$	33.2438			0.0694024			0.0347012	+	0.999398i	$0.488952\pi$
$480$	104.779	−	181.483i	0.218290	−	0.378089i
$481$	386.561	−	88.9790i	0.803662	−	0.184987i
$482$		−	452.355i		−	0.938497i
$483$	69.0320	+	185.024i	0.142923	+	0.383073i
$484$	−173.919	−	301.237i	−0.359337	−	0.622390i
$485$	727.667			1.50034
$486$	221.901	−	384.343i	0.456586	−	0.790829i
$487$	311.789	−	180.011i	0.640223	−	0.369633i	−0.144477	−	0.989508i	$-0.546150\pi$
$487$	311.789	−	180.011i	0.640223	−	0.369633i	0.784701	+	0.619875i	$0.212817\pi$
$488$	−32.8181			−0.0672502
$489$	863.641			1.76614
$490$	−625.576	+	120.703i	−1.27669	+	0.246332i
$491$	242.721	+	420.404i	0.494339	+	0.856221i	0.999979	−	0.00652400i	$-0.00207667\pi$
$491$	242.721	+	420.404i	0.494339	+	0.856221i	−0.505639	+	0.862745i	$0.668743\pi$
$492$	226.856	+	130.975i	0.461088	+	0.266210i
$493$	2.29235	+	1.32349i	0.00464979	+	0.00268456i
$494$	308.686	−	71.0536i	0.624871	−	0.143833i
$495$	−989.275	+	571.158i	−1.99854	+	1.15385i
$496$	−88.8404	−	153.876i	−0.179114	−	0.310234i
$497$	72.4204	+	194.106i	0.145715	+	0.390555i
$498$	−308.125	+	533.688i	−0.618725	+	1.07166i
$499$	295.490	−	170.601i	0.592164	−	0.341886i	−0.173789	−	0.984783i	$-0.555601\pi$
$499$	295.490	−	170.601i	0.592164	−	0.341886i	0.765953	+	0.642897i	$0.222268\pi$
$500$	−317.472	−	549.878i	−0.634944	−	1.09976i
$501$	−488.804	+	282.211i	−0.975657	+	0.563296i
$502$	−22.5783	−	39.1068i	−0.0449767	−	0.0779020i
$503$	227.952	+	131.608i	0.453184	+	0.261646i	0.709174	−	0.705034i	$-0.249068\pi$
$503$	227.952	+	131.608i	0.453184	+	0.261646i	−0.255990	+	0.966679i	$0.582401\pi$
$504$	−91.1898	+	110.466i	−0.180932	+	0.219180i
$505$	87.8521	−	50.7214i	0.173965	−	0.100438i
$506$	85.0243	+	147.266i	0.168032	+	0.291040i
$507$	679.222	+	48.3869i	1.33969	+	0.0954378i
$508$	−49.6632	+	86.0192i	−0.0977622	+	0.169329i
$509$	79.9178	−	138.422i	0.157009	−	0.271948i	−0.776779	−	0.629773i	$-0.783148\pi$
$509$	79.9178	−	138.422i	0.157009	−	0.271948i	0.933789	+	0.357824i	$0.116481\pi$
$510$	−166.900	+	96.3598i	−0.327255	+	0.188941i
$511$	395.181	−	147.441i	0.773349	−	0.288535i
$512$		−	22.6274i		−	0.0441942i
$513$			122.540i			0.238869i
$514$	25.9013	+	44.8624i	0.0503917	+	0.0872810i
$515$	1278.94	+	738.397i	2.48338	+	1.43378i
$516$			432.338i			0.837865i
$517$	−1091.60	+	630.235i	−2.11141	+	1.21902i
$518$	50.0607	−	297.887i	0.0966423	−	0.575071i
$519$	1218.11			2.34703
$520$	−99.0503	+	323.224i	−0.190481	+	0.621585i
$521$	676.625	+	390.650i	1.29870	+	0.749808i	0.980180	−	0.198107i	$-0.0634793\pi$
$521$	676.625	+	390.650i	1.29870	+	0.749808i	0.318525	+	0.947915i	$0.396813\pi$
$522$		−	7.36229i		−	0.0141040i
$523$	−719.435	−	415.366i	−1.37559	−	0.794199i	−0.383967	−	0.923347i	$-0.625442\pi$
$523$	−719.435	−	415.366i	−1.37559	−	0.794199i	−0.991625	+	0.129148i	$0.958776\pi$
$524$	−297.726	−	171.892i	−0.568179	−	0.328038i
$525$	586.924	+	1573.11i	1.11795	+	2.99640i
$526$	−517.341	−	298.687i	−0.983538	−	0.567846i
$527$			163.403i			0.310063i
$528$	−138.390	+	239.699i	−0.262103	+	0.453975i
$529$	239.988	+	415.671i	0.453663	+	0.785767i
$530$	−99.0867	−	57.2078i	−0.186956	−	0.107939i
$531$	47.6338	+	82.5041i	0.0897058	+	0.155375i
$532$	39.9757	−	237.876i	0.0751423	−	0.447135i
$533$	−404.034	−	123.814i	−0.758037	−	0.232296i
$534$	277.055	+	479.873i	0.518829	+	0.898638i
$535$	−1232.56			−2.30384
$536$	78.5828			0.146610
$537$		−	739.034i		−	1.37623i
$538$	−630.202			−1.17138
$539$	826.248	−	159.422i	1.53293	−	0.295774i
$540$	−113.260	−	65.3904i	−0.209740	−	0.121093i
$541$	−55.8428	+	32.2408i	−0.103221	+	0.0595949i	−0.550722	−	0.834689i	$-0.685648\pi$
$541$	−55.8428	+	32.2408i	−0.103221	+	0.0595949i	0.447501	+	0.894284i	$0.352314\pi$
$542$	−451.281	+	260.547i	−0.832621	+	0.480714i
$543$	−889.635			−1.63837
$544$	−10.4046	+	18.0213i	−0.0191261	+	0.0331274i
$545$			570.645i			1.04705i
$546$	231.994	−	463.746i	0.424897	−	0.849352i
$547$	−196.545			−0.359314			−0.179657	−	0.983729i	$-0.557499\pi$
$547$	−196.545			−0.359314			−0.179657	+	0.983729i	$0.557499\pi$
$548$	75.4267	+	43.5477i	0.137640	+	0.0794665i
$549$		−	83.9455i		−	0.152906i
$550$	722.893	+	1252.09i	1.31435	+	2.27652i
$551$	6.19881	+	10.7367i	0.0112501	+	0.0194858i
$552$	39.8975	−	69.1045i	0.0722781	−	0.125189i
$553$	−154.013	+	916.456i	−0.278505	+	1.65724i
$554$		−	471.167i		−	0.850483i
$555$	−1130.36			−2.03668
$556$			50.2281i			0.0903384i
$557$		−	448.600i		−	0.805386i	−0.915335	−	0.402693i	$-0.868074\pi$
$557$		−	448.600i		−	0.805386i	0.915335	−	0.402693i	$-0.131926\pi$
$558$	393.600	−	227.245i	0.705376	−	0.407249i
$559$	−156.448	−	679.676i	−0.279872	−	1.21588i
$560$	198.528	+	163.885i	0.354515	+	0.292651i
$561$	220.438	−	127.270i	0.392938	−	0.226863i
$562$	204.957	−	354.996i	0.364692	−	0.631665i
$563$	448.726	−	259.072i	0.797027	−	0.460164i	−0.0454038	−	0.998969i	$-0.514457\pi$
$563$	448.726	−	259.072i	0.797027	−	0.460164i	0.842430	+	0.538805i	$0.181124\pi$
$564$	512.231	+	295.737i	0.908211	+	0.524356i
$565$	−284.716			−0.503923
$566$	−10.9960	+	19.0456i	−0.0194276	+	0.0336495i
$567$	506.202	+	417.868i	0.892772	+	0.736981i
$568$	41.8558	−	72.4964i	0.0736898	−	0.127634i
$569$	343.450	−	594.874i	0.603604	−	1.04547i	−0.388667	−	0.921378i	$-0.627064\pi$
$569$	343.450	−	594.874i	0.603604	−	1.04547i	0.992271	−	0.124094i	$-0.0396023\pi$
$570$	−902.640			−1.58358
$571$	321.533	−	556.911i	0.563105	−	0.975326i	−0.434118	−	0.900856i	$-0.642940\pi$
$571$	321.533	−	556.911i	0.563105	−	0.975326i	0.997223	−	0.0744705i	$-0.0237267\pi$
$572$	130.824	−	426.908i	0.228713	−	0.746343i
$573$		−	37.9443i		−	0.0662205i
$574$	−204.858	+	248.163i	−0.356895	+	0.432339i
$575$	−208.408	−	360.973i	−0.362448	−	0.627779i
$576$	57.8787			0.100484
$577$	139.909	−	242.329i	0.242476	−	0.419981i	−0.718943	−	0.695069i	$-0.755374\pi$
$577$	139.909	−	242.329i	0.242476	−	0.419981i	0.961419	+	0.275088i	$0.0887071\pi$
$578$	−337.378	+	194.785i	−0.583699	+	0.336999i
$579$	−138.541			−0.239277
$580$	−13.2314			−0.0228127
$581$	−583.814	−	481.937i	−1.00484	−	0.829496i
$582$	225.494	+	390.567i	0.387447	+	0.671078i
$583$	130.872	+	75.5589i	0.224480	+	0.129604i
$584$	−147.596	−	85.2146i	−0.252733	−	0.145915i
$585$	−826.776	−	253.361i	−1.41329	−	0.433096i
$586$	−311.008	+	179.561i	−0.530731	+	0.306417i
$587$	−522.694	−	905.332i	−0.890449	−	1.54230i	−0.839338	−	0.543610i	$-0.817057\pi$
$587$	−522.694	−	905.332i	−0.890449	−	1.54230i	−0.0511114	−	0.998693i	$-0.516276\pi$
$588$	−258.644	−	298.367i	−0.439870	−	0.507427i
$589$	−382.666	+	662.797i	−0.649688	+	1.12529i
$590$	148.275	−	85.6066i	0.251313	−	0.145096i
$591$	234.210	+	405.664i	0.396295	+	0.686403i
$592$	−105.700	+	61.0261i	−0.178548	+	0.103085i
$593$	−300.390	−	520.290i	−0.506559	−	0.877387i	−0.999971	−	0.00759089i	$-0.997584\pi$
$593$	−300.390	−	520.290i	−0.506559	−	0.877387i	0.493412	−	0.869796i	$-0.335750\pi$
$594$	149.591	+	86.3664i	0.251837	+	0.145398i
$595$	−82.7574	−	221.812i	−0.139088	−	0.372793i
$596$	−267.078	+	154.197i	−0.448117	+	0.258720i
$597$	−201.395	−	348.826i	−0.337345	−	0.584299i
$598$	−37.7161	+	123.076i	−0.0630703	+	0.205813i
$599$	−158.885	+	275.197i	−0.265251	+	0.459428i	−0.967629	−	0.252376i	$-0.918788\pi$
$599$	−158.885	+	275.197i	−0.265251	+	0.459428i	0.702378	+	0.711804i	$0.252121\pi$
$600$	339.216	−	587.540i	0.565360	−	0.979233i
$601$	906.763	−	523.520i	1.50876	−	0.871082i	0.508810	−	0.860879i	$-0.330086\pi$
$601$	906.763	−	523.520i	1.50876	−	0.871082i	0.999948	−	0.0102029i	$-0.00324774\pi$
$602$	−523.763	−	88.0199i	−0.870038	−	0.146212i
$603$			201.007i			0.333345i
$604$			88.4411i			0.146426i
$605$	−799.509	−	1384.79i	−1.32150	−	2.28891i
$606$	54.4484	+	31.4358i	0.0898489	+	0.0518743i
$607$			119.972i			0.197647i	0.995105	+	0.0988235i	$0.0315079\pi$
$607$			119.972i			0.197647i	−0.995105	+	0.0988235i	$0.968492\pi$
$608$	−84.4064	+	48.7321i	−0.138826	+	0.0801514i
$609$	20.0144	+	3.36348i	0.0328644	+	0.00552296i
$610$	−150.865			−0.247320
$611$	−912.292	−	279.567i	−1.49311	−	0.457556i
$612$	−46.0967	−	26.6140i	−0.0753215	−	0.0434869i
$613$		−	13.3868i		−	0.0218381i	−0.999940	−	0.0109191i	$-0.996524\pi$
$613$		−	13.3868i		−	0.0218381i	0.999940	−	0.0109191i	$-0.00347572\pi$
$614$	333.878	+	192.765i	0.543776	+	0.313949i
$615$	1042.86	+	602.095i	1.69570	+	0.979016i
$616$	−262.212	−	216.456i	−0.425669	−	0.351389i
$617$	602.948	+	348.112i	0.977225	+	0.564201i	0.901431	−	0.432923i	$-0.142518\pi$
$617$	602.948	+	348.112i	0.977225	+	0.564201i	0.0757935	+	0.997124i	$0.475851\pi$
$618$			915.278i			1.48103i
$619$	−459.302	+	795.534i	−0.742006	+	1.28519i	0.209574	+	0.977793i	$0.432792\pi$
$619$	−459.302	+	795.534i	−0.742006	+	1.28519i	−0.951580	+	0.307400i	$0.900541\pi$
$620$	−408.401	−	707.371i	−0.658711	−	1.14092i
$621$	−43.1266	−	24.8992i	−0.0694471	−	0.0400953i
$622$	−204.634	−	354.436i	−0.328993	−	0.569833i
$623$	−637.755	+	237.945i	−1.02368	+	0.381934i
$624$	−204.182	+	46.9987i	−0.327214	+	0.0753184i
$625$	−715.296	−	1238.93i	−1.14447	−	1.98229i
$626$	405.383			0.647577
$627$	1192.19			1.90142
$628$			259.511i			0.413235i
$629$	112.245			0.178450
$630$	−419.201	+	507.816i	−0.665398	+	0.806057i
$631$	610.860	+	352.680i	0.968082	+	0.558922i	0.898651	−	0.438664i	$-0.144548\pi$
$631$	610.860	+	352.680i	0.968082	+	0.558922i	0.0694309	+	0.997587i	$0.477882\pi$
$632$	325.190	−	187.748i	0.514541	−	0.297070i
$633$	1118.48	−	645.752i	1.76694	−	1.02015i
$634$	−117.885			−0.185938
$635$	−228.302	+	395.431i	−0.359531	+	0.622727i
$636$		−	70.9117i		−	0.111496i
$637$	514.581	+	375.467i	0.807820	+	0.589430i
$638$	17.4757			0.0273914
$639$	185.439	+	107.063i	0.290201	+	0.167548i
$640$		−	104.019i		−	0.162529i
$641$	−396.497	−	686.753i	−0.618560	−	1.07138i	−0.989749	−	0.142820i	$-0.954383\pi$
$641$	−396.497	−	686.753i	−0.618560	−	1.07138i	0.371188	−	0.928558i	$-0.378950\pi$
$642$	−381.953	−	661.561i	−0.594942	−	1.03047i
$643$	420.524	−	728.369i	0.654003	−	1.13277i	−0.328140	−	0.944629i	$-0.606422\pi$
$643$	420.524	−	728.369i	0.654003	−	1.13277i	0.982143	−	0.188137i	$-0.0602450\pi$
$644$	75.5950	+	62.4035i	0.117384	+	0.0968998i
$645$			1987.47i			3.08134i
$646$	89.6325			0.138750
$647$			598.987i			0.925791i	0.886413	+	0.462896i	$0.153189\pi$
$647$			598.987i			0.925791i	−0.886413	+	0.462896i	$0.846811\pi$
$648$		−	265.223i		−	0.409295i
$649$	−195.839	+	113.067i	−0.301754	+	0.174218i
$650$	−320.669	+	1046.42i	−0.493337	+	1.60987i
$651$	437.950	+	1173.82i	0.672734	+	1.80311i
$652$	371.253	−	214.343i	0.569406	−	0.328747i
$653$	206.768	−	358.132i	0.316643	−	0.548442i	−0.663142	−	0.748493i	$-0.730778\pi$
$653$	206.768	−	358.132i	0.316643	−	0.548442i	0.979785	+	0.200052i	$0.0641110\pi$
$654$	−306.288	+	176.835i	−0.468330	+	0.270390i
$655$	−1368.65	−	790.190i	−2.08954	−	1.20640i
$656$	130.024			0.198208
$657$	217.970	−	377.536i	0.331766	−	0.574636i
$658$	−462.560	+	560.341i	−0.702979	+	0.851583i
$659$	9.17613	−	15.8935i	0.0139243	−	0.0241176i	−0.858979	−	0.512010i	$-0.828901\pi$
$659$	9.17613	−	15.8935i	0.0139243	−	0.0241176i	0.872904	+	0.487893i	$0.162234\pi$
$660$	−636.182	+	1101.90i	−0.963912	+	1.66955i
$661$	975.962			1.47649			0.738246	−	0.674531i	$-0.235654\pi$
$661$	975.962			1.47649			0.738246	+	0.674531i	$0.235654\pi$
$662$	−211.636	+	366.564i	−0.319692	+	0.553723i
$663$	184.229	+	56.4559i	0.277872	+	0.0851522i
$664$			305.888i			0.460675i
$665$	183.769	−	1093.52i	0.276344	−	1.64439i
$666$	−156.099	−	270.371i	−0.234383	−	0.405963i
$667$	−5.03820			−0.00755352
$668$	−140.081	+	242.628i	−0.209703	+	0.363216i
$669$	−1105.68	+	638.362i	−1.65273	+	0.954203i
$670$	361.247			0.539174
$671$	199.260			0.296960
$672$	−26.4421	+	157.344i	−0.0393483	+	0.234142i
$673$	478.681	+	829.100i	0.711264	+	1.23195i	0.964383	+	0.264511i	$0.0852104\pi$
$673$	478.681	+	829.100i	0.711264	+	1.23195i	−0.253119	+	0.967435i	$0.581456\pi$
$674$	−741.566	−	428.143i	−1.10025	−	0.635227i
$675$	−366.671	−	211.698i	−0.543216	−	0.313626i
$676$	303.986	−	147.773i	0.449683	−	0.218599i
$677$	−973.555	+	562.082i	−1.43804	+	0.830255i	−0.997714	−	0.0675817i	$-0.978472\pi$
$677$	−973.555	+	562.082i	−1.43804	+	0.830255i	−0.440329	+	0.897836i	$0.645138\pi$
$678$	−88.2298	−	152.819i	−0.130132	−	0.225396i
$679$	−519.068	+	193.663i	−0.764459	+	0.285218i
$680$	−47.8302	+	82.8443i	−0.0703385	+	0.121830i
$681$	−492.368	+	284.269i	−0.723007	+	0.417428i
$682$	539.407	+	934.281i	0.790920	+	1.36991i
$683$	344.216	−	198.733i	0.503976	−	0.290971i	−0.226378	−	0.974040i	$-0.572688\pi$
$683$	344.216	−	198.733i	0.503976	−	0.290971i	0.730354	+	0.683069i	$0.239355\pi$
$684$	−124.652	−	215.903i	−0.182240	−	0.315648i
$685$	346.738	+	200.189i	0.506187	+	0.292247i
$686$	414.119	−	252.593i	0.603672	−	0.368212i
$687$	−267.322	+	154.339i	−0.389115	+	0.224656i
$688$	107.300	+	185.849i	0.155959	+	0.270129i
$689$	25.6605	+	111.480i	0.0372431	+	0.161800i
$690$	183.409	−	317.674i	0.265811	−	0.460398i
$691$	−211.040	+	365.532i	−0.305413	+	0.528990i	−0.977353	−	0.211615i	$-0.932128\pi$
$691$	−211.040	+	365.532i	−0.305413	+	0.528990i	0.671940	+	0.740605i	$0.265461\pi$
$692$	523.627	−	302.316i	0.756686	−	0.436873i
$693$	553.672	−	670.713i	0.798950	−	0.967840i
$694$		−	35.7409i		−	0.0514999i
$695$			230.900i			0.332230i
$696$	−4.10023	−	7.10180i	−0.00589113	−	0.0102037i
$697$	−103.556	−	59.7882i	−0.148574	−	0.0857793i
$698$			780.708i			1.11849i
$699$	959.146	−	553.763i	1.37217	−	0.792222i
$700$	642.723	+	530.566i	0.918176	+	0.757952i
$701$	253.930			0.362240			0.181120	−	0.983461i	$-0.442028\pi$
$701$	253.930			0.362240			0.181120	+	0.983461i	$0.442028\pi$
$702$	29.3309	+	127.425i	0.0417819	+	0.181518i
$703$	455.288	+	262.861i	0.647636	+	0.373913i
$704$			137.386i			0.195150i
$705$	2354.73	+	1359.51i	3.34005	+	1.92838i
$706$	184.728	+	106.653i	0.261654	+	0.151066i
$707$	−49.1686	+	59.5624i	−0.0695454	+	0.0842467i
$708$	91.8969	+	53.0567i	0.129798	+	0.0749388i
$709$			901.522i			1.27154i	0.771878	+	0.635770i	$0.219317\pi$
$709$			901.522i			1.27154i	−0.771878	+	0.635770i	$0.780683\pi$
$710$	192.412	−	333.267i	0.271003	−	0.469390i
$711$	480.242	+	831.804i	0.675446	+	1.16991i
$712$	238.195	+	137.522i	0.334543	+	0.193149i
$713$	−155.509	−	269.350i	−0.218106	−	0.377770i
$714$	93.4097	−	113.156i	0.130826	−	0.158481i
$715$	601.398	−	1962.50i	0.841117	−	2.74476i
$716$	−183.417	−	317.688i	−0.256170	−	0.443699i
$717$	−714.197			−0.996091
$718$	86.7872			0.120874
$719$			1087.25i			1.51217i	0.654474	+	0.756085i	$0.272890\pi$
$719$			1087.25i			1.51217i	−0.654474	+	0.756085i	$0.727110\pi$
$720$	266.069			0.369541
$721$	−1108.83	−	186.342i	−1.53790	−	0.258449i
$722$	−78.5653	−	45.3597i	−0.108816	−	0.0628251i
$723$	1116.14	−	644.405i	1.54376	−	0.891293i
$724$	−382.427	+	220.794i	−0.528214	+	0.304964i
$725$	−42.8357			−0.0590838
$726$	495.514	−	858.256i	0.682527	−	1.18217i
$727$			202.930i			0.279133i	0.990213	+	0.139566i	$0.0445709\pi$
$727$			202.930i			0.279133i	−0.990213	+	0.139566i	$0.955429\pi$
$728$	−15.3679	−	256.928i	−0.0211098	−	0.352923i
$729$	420.502			0.576820
$730$	−678.501	−	391.733i	−0.929453	−	0.536620i
$731$		−	197.356i		−	0.269981i
$732$	−46.7512	−	80.9754i	−0.0638678	−	0.110622i
$733$	−270.224	−	468.041i	−0.368654	−	0.638528i	0.620701	−	0.784047i	$-0.286848\pi$
$733$	−270.224	−	468.041i	−0.368654	−	0.638528i	−0.989355	+	0.145519i	$0.953515\pi$
$734$	−291.465	+	504.832i	−0.397091	+	0.687782i
$735$	−1188.99	−	1371.60i	−1.61767	−	1.86612i
$736$		−	39.6079i		−	0.0538150i
$737$	−477.127			−0.647391
$738$			332.590i			0.450663i
$739$			622.249i			0.842014i	0.907057	+	0.421007i	$0.138323\pi$
$739$			622.249i			0.842014i	−0.907057	+	0.421007i	$0.861677\pi$
$740$	−485.906	+	280.538i	−0.656630	+	0.379105i
$741$	615.058	+	660.433i	0.830038	+	0.891273i
$742$	85.9072	+	14.4369i	0.115778	+	0.0194568i
$743$	330.453	−	190.787i	0.444755	−	0.256780i	−0.260857	−	0.965377i	$-0.584005\pi$
$743$	330.453	−	190.787i	0.444755	−	0.256780i	0.705613	+	0.708598i	$0.250672\pi$
$744$	253.116	−	438.410i	0.340209	−	0.589260i
$745$	−1227.76	+	708.847i	−1.64800	+	0.951473i
$746$	205.655	+	118.735i	0.275677	+	0.159162i
$747$	−782.433			−1.04743
$748$	63.1731	−	109.419i	0.0844560	−	0.146282i
$749$	879.221	−	328.035i	1.17386	−	0.437964i
$750$	904.512	−	1566.66i	1.20602	−	2.08888i
$751$	120.903	−	209.410i	0.160989	−	0.278842i	−0.774234	−	0.632899i	$-0.781865\pi$
$751$	120.903	−	209.410i	0.160989	−	0.278842i	0.935224	+	0.354057i	$0.115198\pi$
$752$	293.590			0.390412
$753$	64.3281	−	111.420i	0.0854291	−	0.147968i
$754$	9.01584	+	9.68097i	0.0119573	+	0.0128395i
$755$			406.565i			0.538497i
$756$	98.1949	+	16.5019i	0.129887	+	0.0218279i
$757$	−277.724	−	481.032i	−0.366874	−	0.635445i	0.622201	−	0.782858i	$-0.286239\pi$
$757$	−277.724	−	481.032i	−0.366874	−	0.635445i	−0.989075	+	0.147413i	$0.952905\pi$
$758$	−294.006			−0.387870
$759$	−242.243	+	419.578i	−0.319161	+	0.552804i
$760$	−388.018	+	224.022i	−0.510549	+	0.294766i
$761$	901.772			1.18498			0.592492	−	0.805577i	$-0.298144\pi$
$761$	901.772			1.18498			0.592492	+	0.805577i	$0.298144\pi$
$762$	−282.992			−0.371380
$763$	−151.873	−	407.059i	−0.199047	−	0.533498i
$764$	−9.41722	−	16.3111i	−0.0123262	−	0.0213496i
$765$	−211.907	−	122.345i	−0.277003	−	0.159928i
$766$	−620.048	−	357.985i	−0.809463	−	0.467343i
$767$	−163.670	−	50.1558i	−0.213390	−	0.0653921i
$768$	55.8309	−	32.2340i	0.0726965	−	0.0419713i
$769$	−27.1659	−	47.0527i	−0.0353263	−	0.0611869i	0.847822	−	0.530281i	$-0.177914\pi$
$769$	−27.1659	−	47.0527i	−0.0353263	−	0.0611869i	−0.883148	+	0.469094i	$0.844580\pi$
$770$	−1205.39	−	995.050i	−1.56545	−	1.29227i
$771$	−73.7957	+	127.818i	−0.0957143	+	0.165782i
$772$	−59.5546	+	34.3839i	−0.0771433	+	0.0445387i
$773$	−242.452	−	419.939i	−0.313651	−	0.543259i	0.665499	−	0.746399i	$-0.268219\pi$
$773$	−242.452	−	419.939i	−0.313651	−	0.543259i	−0.979150	+	0.203140i	$0.934885\pi$
$774$	−475.383	+	274.463i	−0.614190	+	0.354603i
$775$	−1322.17	−	2290.07i	−1.70603	−	2.95493i
$776$	193.866	+	111.929i	0.249828	+	0.144238i
$777$	806.320	−	300.836i	1.03773	−	0.387176i
$778$	−325.362	+	187.848i	−0.418203	+	0.241450i
$779$	−280.030	−	485.026i	−0.359474	−	0.622627i
$780$	−938.626	+	216.054i	−1.20337	+	0.276992i
$781$	−254.134	+	440.172i	−0.325395	+	0.563601i
$782$	−18.2126	+	31.5452i	−0.0232898	+	0.0403391i
$783$	−4.43208	+	2.55886i	−0.00566038	+	0.00326802i
$784$	−185.233	−	64.0673i	−0.236267	−	0.0817185i
$785$			1192.98i			1.51972i
$786$		−	979.478i		−	1.24615i
$787$	−308.817	−	534.888i	−0.392398	−	0.679654i	0.600367	−	0.799725i	$-0.295021\pi$
$787$	−308.817	−	534.888i	−0.392398	−	0.679654i	−0.992765	+	0.120071i	$0.961688\pi$
$788$	201.360	+	116.255i	0.255533	+	0.147532i
$789$		−	1701.98i		−	2.15714i
$790$	1494.90	−	863.083i	1.89228	−	1.09251i
$791$	203.097	−	75.7751i	0.256760	−	0.0957966i
$792$	−351.419			−0.443711
$793$	102.800	+	110.383i	0.129634	+	0.139197i
$794$	240.657	+	138.943i	0.303095	+	0.174992i
$795$		−	325.982i		−	0.410041i
$796$	−173.147	−	99.9665i	−0.217521	−	0.125586i
$797$	45.6634	+	26.3638i	0.0572941	+	0.0330788i	0.528373	−	0.849012i	$-0.322802\pi$
$797$	45.6634	+	26.3638i	0.0572941	+	0.0330788i	−0.471079	+	0.882091i	$0.656135\pi$
$798$	643.882	−	240.231i	0.806870	−	0.301041i
$799$	−233.826	−	134.999i	−0.292648	−	0.168960i
$800$		−	336.754i		−	0.420942i
$801$	−351.767	+	609.279i	−0.439160	+	0.760648i
$802$	−12.9643	−	22.4548i	−0.0161649	−	0.0279985i
$803$	896.150	+	517.393i	1.11600	+	0.644325i
$804$	111.946	+	193.895i	0.139236	+	0.241163i
$805$	347.511	+	286.870i	0.431691	+	0.356360i
$806$	−239.277	+	780.815i	−0.296869	+	0.968753i
$807$	−897.756	−	1554.96i	−1.11246	−	1.92684i
$808$	31.2076			0.0386233
$809$	−623.929			−0.771235			−0.385617	−	0.922659i	$-0.626011\pi$
$809$	−623.929			−0.771235			−0.385617	+	0.922659i	$0.626011\pi$
$810$		−	1219.24i		−	1.50523i
$811$	−10.3713			−0.0127882			−0.00639412	−	0.999980i	$-0.502035\pi$
$811$	−10.3713			−0.0127882			−0.00639412	+	0.999980i	$0.502035\pi$
$812$	9.43836	−	3.52143i	0.0116236	−	0.00433673i
$813$	−1285.75	−	742.327i	−1.58149	−	0.913071i
$814$	641.775	−	370.529i	0.788421	−	0.455195i
$815$	1706.66	−	985.338i	2.09406	−	1.20900i
$816$	−59.2877			−0.0726565
$817$	462.178	−	800.516i	0.565701	−	0.979823i
$818$			78.0734i			0.0954442i
$819$	657.196	−	39.3096i	0.802437	−	0.0479971i
$820$	597.724			0.728932
$821$	84.1426	+	48.5798i	0.102488	+	0.0591715i	0.550368	−	0.834922i	$-0.314487\pi$
$821$	84.1426	+	48.5798i	0.102488	+	0.0591715i	−0.447880	+	0.894094i	$0.647821\pi$
$822$			248.144i			0.301878i
$823$	436.168	+	755.465i	0.529973	+	0.917940i	0.999389	+	0.0349626i	$0.0111312\pi$
$823$	436.168	+	755.465i	0.529973	+	0.917940i	−0.469416	+	0.882977i	$0.655535\pi$
$824$	227.159	+	393.450i	0.275678	+	0.477488i
$825$	−2059.60	+	3567.33i	−2.49649	+	4.32404i
$826$	−82.9857	+	100.528i	−0.100467	+	0.121705i
$827$			246.854i			0.298493i	0.988800	+	0.149247i	$0.0476848\pi$
$827$			246.854i			0.298493i	−0.988800	+	0.149247i	$0.952315\pi$
$828$	101.313			0.122359
$829$			590.402i			0.712186i	0.934451	+	0.356093i	$0.115891\pi$
$829$			590.402i			0.712186i	−0.934451	+	0.356093i	$0.884109\pi$
$830$			1406.17i			1.69419i
$831$	1162.56	−	671.203i	1.39899	−	0.807706i
$832$	−76.1071	+	70.8782i	−0.0914748	+	0.0851901i
$833$	118.067	+	136.200i	0.141737	+	0.163506i
$834$	−123.933	+	71.5527i	−0.148601	+	0.0857946i
$835$	−643.956	+	1115.37i	−0.771205	+	1.33577i
$836$	512.486	−	295.884i	0.613021	−	0.353928i
$837$	−273.602	−	157.964i	−0.326884	−	0.188727i
$838$	−972.283			−1.16024
$839$	−186.954	+	323.815i	−0.222830	+	0.385953i	−0.955666	−	0.294452i	$-0.904863\pi$
$839$	−186.954	+	323.815i	−0.222830	+	0.385953i	0.732836	+	0.680405i	$0.238196\pi$
$840$	−121.555	+	723.312i	−0.144708	+	0.861085i
$841$	420.241	−	727.879i	0.499692	−	0.865492i
$842$	413.181	−	715.650i	0.490713	−	0.849940i
$843$	1167.89			1.38540
$844$	320.532	−	555.178i	0.379778	−	0.657794i
$845$	1397.43	−	679.314i	1.65376	−	0.803921i
$846$			750.974i			0.887676i
$847$	938.867	+	775.032i	1.10846	+	0.915032i
$848$	−17.5992	−	30.4828i	−0.0207538	−	0.0359467i
$849$	−62.6576			−0.0738016
$850$	−154.847	+	268.203i	−0.182173	+	0.315533i
$851$	−185.022	+	106.822i	−0.217417	+	0.125526i
$852$	238.503			0.279934
$853$	1444.14			1.69301			0.846506	−	0.532379i	$-0.178702\pi$
$853$	1444.14			1.69301			0.846506	+	0.532379i	$0.178702\pi$
$854$	107.617	−	40.1517i	0.126015	−	0.0470160i
$855$	−573.026	−	992.511i	−0.670206	−	1.16083i
$856$	−328.380	−	189.590i	−0.383621	−	0.221484i
$857$	641.919	+	370.612i	0.749031	+	0.432453i	0.825344	−	0.564631i	$-0.190981\pi$
$857$	641.919	+	370.612i	0.749031	+	0.432453i	−0.0763129	+	0.997084i	$0.524315\pi$
$858$	1239.72	−	285.359i	1.44489	−	0.332587i
$859$	898.862	−	518.958i	1.04641	−	0.604142i	0.124764	−	0.992186i	$-0.460183\pi$
$859$	898.862	−	518.958i	1.04641	−	0.604142i	0.921641	+	0.388044i	$0.126849\pi$
$860$	493.260	+	854.351i	0.573558	+	0.993431i
$861$	−904.147	−	151.945i	−1.05011	−	0.176474i
$862$	−2.32305	+	4.02364i	−0.00269495	+	0.00466780i
$863$	−301.249	+	173.926i	−0.349071	+	0.201536i	−0.664276	−	0.747487i	$-0.731260\pi$
$863$	−301.249	+	173.926i	−0.349071	+	0.201536i	0.315205	+	0.949024i	$0.397927\pi$
$864$	−20.1165	−	34.8429i	−0.0232830	−	0.0403274i
$865$	2407.12	−	1389.75i	2.78280	−	1.60665i
$866$	−199.584	−	345.690i	−0.230467	−	0.399181i
$867$	−961.227	−	554.964i	−1.10868	−	0.640097i
$868$	479.587	+	395.897i	0.552519	+	0.456103i
$869$	−1974.44	+	1139.94i	−2.27208	+	1.31179i
$870$	−18.8488	−	32.6471i	−0.0216653	−	0.0375254i
$871$	−246.153	−	264.312i	−0.282610	−	0.303459i
$872$	−87.7758	+	152.032i	−0.100660	+	0.174349i
$873$	−286.303	+	495.891i	−0.327953	+	0.568030i
$874$	−147.748	+	85.3024i	−0.169048	+	0.0976000i
$875$	1713.81	+	1414.74i	1.95864	+	1.61685i
$876$		−	485.571i		−	0.554305i
$877$			899.673i			1.02585i	0.858433	+	0.512926i	$0.171439\pi$
$877$			899.673i			1.02585i	−0.858433	+	0.512926i	$0.828561\pi$
$878$	247.912	+	429.396i	0.282360	+	0.489062i
$879$	−886.096	−	511.588i	−1.00807	−	0.582011i
$880$			631.564i			0.717687i
$881$	222.311	−	128.352i	0.252340	−	0.145688i	−0.368495	−	0.929630i	$-0.620127\pi$
$881$	222.311	−	128.352i	0.252340	−	0.145688i	0.620835	+	0.783941i	$0.286794\pi$
$882$	163.878	−	473.809i	0.185803	−	0.537198i
$883$	−774.664			−0.877309			−0.438654	−	0.898656i	$-0.644545\pi$
$883$	−774.664			−0.877309			−0.438654	+	0.898656i	$0.644545\pi$
$884$	93.2059	−	21.4542i	0.105437	−	0.0242695i
$885$	422.451	+	243.902i	0.477346	+	0.275596i
$886$			44.9603i			0.0507453i
$887$	523.734	+	302.378i	0.590456	+	0.340900i	0.765278	−	0.643700i	$-0.222602\pi$
$887$	523.734	+	302.378i	0.590456	+	0.340900i	−0.174822	+	0.984600i	$0.555935\pi$
$888$	−301.152	−	173.870i	−0.339135	−	0.195800i
$889$	57.6144	−	342.835i	0.0648081	−	0.385641i
$890$	1094.98	+	632.190i	1.23032	+	0.710326i
$891$			1610.34i			1.80734i
$892$	−316.864	+	548.825i	−0.355229	+	0.615274i
$893$	−632.297	−	1095.17i	−0.708059	−	1.22639i
$894$	−760.933	−	439.325i	−0.851155	−	0.491415i
$895$	−843.173	−	1460.42i	−0.942093	−	1.63175i
$896$	27.6838	+	74.1998i	0.0308971	+	0.0828123i
$897$	−357.407	+	82.2682i	−0.398447	+	0.0917149i
$898$	−221.749	−	384.080i	−0.246936	−	0.427706i
$899$	−31.9631			−0.0355541
$900$	861.383			0.957092
$901$			32.3701i			0.0359269i
$902$	−789.462			−0.875235
$903$	−528.949	−	1417.72i	−0.585768	−	1.57001i
$904$	−75.8546	−	43.7947i	−0.0839100	−	0.0484454i
$905$	−1758.02	+	1014.99i	−1.94257	+	1.12154i
$906$	−218.220	+	125.989i	−0.240861	+	0.139061i
$907$	−124.385			−0.137139			−0.0685696	−	0.997646i	$-0.521844\pi$
$907$	−124.385			−0.137139			−0.0685696	+	0.997646i	$0.521844\pi$
$908$	−141.103	+	244.397i	−0.155399	+	0.269160i
$909$			79.8260i			0.0878174i
$910$	−70.6465	−	1181.10i	−0.0776335	−	1.29791i
$911$	1162.26			1.27580			0.637902	−	0.770117i	$-0.279802\pi$
$911$	1162.26			1.27580			0.637902	+	0.770117i	$0.279802\pi$
$912$	−240.483	−	138.843i	−0.263687	−	0.152240i
$913$		−	1857.25i		−	2.03422i
$914$	68.6131	+	118.841i	0.0750690	+	0.130023i
$915$	−214.916	−	372.245i	−0.234881	−	0.406826i
$916$	−76.6091	+	132.691i	−0.0836344	+	0.144859i
$917$	1186.60	+	199.412i	1.29401	+	0.217462i
$918$			37.0002i			0.0403052i
$919$	287.881			0.313255			0.156627	−	0.987658i	$-0.449938\pi$
$919$	287.881			0.313255			0.156627	+	0.987658i	$0.449938\pi$
$920$		−	182.078i		−	0.197911i
$921$			1098.42i			1.19263i
$922$	598.564	−	345.581i	0.649202	−	0.374817i
$923$	−374.950	+	86.3063i	−0.406230	+	0.0935063i
$924$	160.547	−	955.335i	0.173752	−	1.03391i
$925$	−1573.09	+	908.225i	−1.70064	+	0.981864i
$926$	−403.269	+	698.483i	−0.435496	+	0.754301i
$927$	−1006.41	+	581.049i	−1.08566	+	0.626806i
$928$	−3.52512	−	2.03523i	−0.00379862	−	0.00219314i
$929$	−1072.18			−1.15412			−0.577061	−	0.816701i	$-0.695800\pi$
$929$	−1072.18			−1.15412			−0.577061	+	0.816701i	$0.695800\pi$
$930$	1163.58	−	2015.38i	1.25116	−	2.16707i
$931$	159.943	+	828.951i	0.171797	+	0.890387i
$932$	274.872	−	476.092i	0.294927	−	0.510828i
$933$	583.024	−	1009.83i	0.624892	−	1.08234i
$934$	−150.265			−0.160883
$935$	290.408	−	503.001i	0.310597	−	0.537969i
$936$	−181.299	−	194.674i	−0.193696	−	0.207985i
$937$			980.365i			1.04628i	0.852247	+	0.523140i	$0.175240\pi$
$937$			980.365i			1.04628i	−0.852247	+	0.523140i	$0.824760\pi$
$938$	−257.689	+	96.1430i	−0.274721	+	0.102498i
$939$	577.491	+	1000.24i	0.615006	+	1.06522i
$940$	1349.64			1.43578
$941$	−355.761	+	616.197i	−0.378067	+	0.654832i	−0.990781	−	0.135473i	$-0.956745\pi$
$941$	−355.761	+	616.197i	−0.378067	+	0.654832i	0.612714	+	0.790305i	$0.290078\pi$
$942$	−640.318	+	369.688i	−0.679744	+	0.392450i
$943$	227.599			0.241357
$944$	52.6715			0.0557961
$945$	451.403	+	75.8596i	0.477675	+	0.0802747i
$946$	−651.487	−	1128.41i	−0.688676	−	1.19282i
$947$	918.273	+	530.165i	0.969665	+	0.559836i	0.899134	−	0.437673i	$-0.144197\pi$
$947$	918.273	+	530.165i	0.969665	+	0.559836i	0.0705309	+	0.997510i	$0.477531\pi$
$948$	926.501	+	534.916i	0.977322	+	0.564257i
$949$	175.712	+	763.364i	0.185154	+	0.804387i
$950$	−1256.18	+	725.258i	−1.32230	+	0.763429i
$951$	−167.933	−	290.869i	−0.176586	−	0.305856i
$952$	12.0704	−	71.8251i	0.0126790	−	0.0754465i
$953$	241.380	−	418.082i	0.253284	−	0.438701i	−0.711144	−	0.703046i	$-0.751823\pi$
$953$	241.380	−	418.082i	0.253284	−	0.438701i	0.964428	+	0.264345i	$0.0851559\pi$
$954$	77.9720	−	45.0171i	0.0817316	−	0.0471878i
$955$	−43.2911	−	74.9824i	−0.0453310	−	0.0785156i
$956$	−307.012	+	177.253i	−0.321142	+	0.185411i
$957$	24.8951	+	43.1196i	0.0260137	+	0.0450571i
$958$	40.7151	+	23.5069i	0.0425001	+	0.0245375i
$959$	−300.618	−	50.5197i	−0.313470	−	0.0526796i
$960$	256.656	−	148.180i	0.267350	−	0.154354i
$961$	−506.076	−	876.550i	−0.526614	−	0.912123i
$962$	536.357	+	164.364i	0.557543	+	0.170856i
$963$	484.953	−	839.963i	0.503585	−	0.872235i
$964$	319.864	−	554.020i	0.331809	−	0.574710i
$965$	−273.774	+	158.063i	−0.283703	+	0.163796i
$966$	−46.2852	+	275.420i	−0.0479142	+	0.285114i
$967$			477.346i			0.493636i	0.969062	+	0.246818i	$0.0793849\pi$
$967$			477.346i			0.493636i	−0.969062	+	0.246818i	$0.920615\pi$
$968$		−	491.918i		−	0.508179i
$969$	127.686	+	221.159i	0.131771	+	0.228235i
$970$	891.206	+	514.538i	0.918769	+	0.530451i
$971$			718.965i			0.740437i	0.928945	+	0.370219i	$0.120717\pi$
$971$			718.965i			0.740437i	−0.928945	+	0.370219i	$0.879283\pi$
$972$	543.543	−	313.815i	0.559201	−	0.322855i
$973$	−61.4522	−	164.708i	−0.0631574	−	0.169279i
$974$	509.149			0.522740
$975$	−3038.74	+	699.460i	−3.11666	+	0.717395i
$976$	−40.1938	−	23.2059i	−0.0411822	−	0.0237766i
$977$			314.676i			0.322084i	0.986948	+	0.161042i	$0.0514855\pi$
$977$			314.676i			0.322084i	−0.986948	+	0.161042i	$0.948515\pi$
$978$	1057.74	+	610.686i	1.08153	+	0.624424i
$979$	−1446.23	−	834.984i	−1.47726	−	0.852894i
$980$	−851.520	−	294.519i	−0.868898	−	0.300529i
$981$	−388.883	−	224.522i	−0.396415	−	0.228870i
$982$			686.518i			0.699101i
$983$	−542.737	+	940.049i	−0.552123	+	0.956306i	0.445998	+	0.895034i	$0.352849\pi$
$983$	−542.737	+	940.049i	−0.552123	+	0.956306i	−0.998121	+	0.0612717i	$0.980484\pi$
$984$	185.227	+	320.822i	0.188239	+	0.326039i
$985$	925.654	+	534.427i	0.939750	+	0.542565i
$986$	1.87169	+	3.24187i	0.00189827	+	0.00328790i
$987$	−2041.53	−	343.085i	−2.06842	−	0.347604i
$988$	428.305	+	131.252i	0.433507	+	0.132846i
$989$	187.822	+	325.317i	0.189911	+	0.328935i
$990$	−1615.48			−1.63180
$991$	−143.491			−0.144794			−0.0723970	−	0.997376i	$-0.523065\pi$
$991$	−143.491			−0.144794			−0.0723970	+	0.997376i	$0.523065\pi$
$992$		−	251.279i		−	0.253305i
$993$	−1205.95			−1.21445
$994$	−48.5570	+	288.939i	−0.0488501	+	0.290683i
$995$	−795.960	−	459.548i	−0.799960	−	0.461857i
$996$	−754.749	+	435.755i	−0.757780	+	0.437505i
$997$	−1204.50	+	695.419i	−1.20813	+	0.697511i	−0.962349	−	0.271815i	$-0.912376\pi$
$997$	−1204.50	+	695.419i	−1.20813	+	0.697511i	−0.245776	+	0.969327i	$0.579043\pi$
$998$	482.533			0.483500
$999$	−108.509	+	187.942i	−0.108617	+	0.188130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.3.k.a.101.17	✓	36
7.5	odd	6		182.3.r.a.75.8	yes	36
13.4	even	6		182.3.r.a.17.17	yes	36
91.82	odd	6	inner	182.3.k.a.173.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.3.k.a.101.17	✓	36	1.1	even	1	trivial
182.3.k.a.173.11	yes	36	91.82	odd	6	inner
182.3.r.a.17.17	yes	36	13.4	even	6
182.3.r.a.75.8	yes	36	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	182.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +4.02925i q^{3} +(1.00000 + 1.73205i) q^{4} +(4.59702 + 7.96227i) q^{5} +(-2.84911 + 4.93480i) q^{6} +(-5.39829 - 4.45628i) q^{7} +2.82843i q^{8} -7.23484 q^{9} +13.0023i q^{10} -17.1732i q^{11} +(-6.97886 + 4.02925i) q^{12} +(9.51338 - 8.85977i) q^{13} +(-3.46047 - 9.27497i) q^{14} +(-32.0819 + 18.5225i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(3.18575 - 1.83929i) q^{17} +(-8.86083 - 5.11580i) q^{18} +17.2294 q^{19} +(-9.19403 + 15.9245i) q^{20} +(17.9554 - 21.7511i) q^{21} +(12.1433 - 21.0328i) q^{22} +(-3.50087 + 6.06369i) q^{23} -11.3964 q^{24} +(-29.7651 + 51.5547i) q^{25} +(17.9163 - 4.12398i) q^{26} +7.11227i q^{27} +(2.32020 - 13.8064i) q^{28} +(0.359781 + 0.623160i) q^{29} -52.3896 q^{30} +(-22.2101 + 38.4690i) q^{31} +(-4.89898 + 2.82843i) q^{32} +69.1951 q^{33} +5.20230 q^{34} +(10.6660 - 63.4682i) q^{35} +(-7.23484 - 12.5311i) q^{36} +(26.4251 + 15.2565i) q^{37} +(21.1016 + 12.1830i) q^{38} +(35.6982 + 38.3318i) q^{39} +(-22.5207 + 13.0023i) q^{40} +(-16.2530 - 28.1511i) q^{41} +(37.3712 - 13.9431i) q^{42} +(26.8250 - 46.4622i) q^{43} +(29.7449 - 17.1732i) q^{44} +(-33.2587 - 57.6057i) q^{45} +(-8.57536 + 4.95098i) q^{46} +(-36.6987 - 63.5641i) q^{47} +(-13.9577 - 8.05850i) q^{48} +(9.28318 + 48.1126i) q^{49} +(-72.9093 + 42.0942i) q^{50} +(7.41096 + 12.8362i) q^{51} +(24.8590 + 7.61789i) q^{52} +(-4.39981 + 7.62069i) q^{53} +(-5.02914 + 8.71072i) q^{54} +(136.738 - 78.9455i) q^{55} +(12.6043 - 15.2687i) q^{56} +69.4215i q^{57} +1.01762i q^{58} +(-6.58394 - 11.4037i) q^{59} +(-64.1639 - 37.0450i) q^{60} +11.6030i q^{61} +(-54.4034 + 31.4098i) q^{62} +(39.0558 + 32.2405i) q^{63} -8.00000 q^{64} +(114.277 + 35.0196i) q^{65} +(84.7464 + 48.9283i) q^{66} -27.7832i q^{67} +(6.37150 + 3.67858i) q^{68} +(-24.4321 - 14.1059i) q^{69} +(57.9420 - 70.1904i) q^{70} +(-25.6313 - 14.7983i) q^{71} -20.4632i q^{72} +(-30.1279 + 52.1831i) q^{73} +(21.5760 + 37.3707i) q^{74} +(-207.727 - 119.931i) q^{75} +(17.2294 + 29.8422i) q^{76} +(-76.5286 + 92.7060i) q^{77} +(16.6165 + 72.1891i) q^{78} +(-66.3791 - 114.972i) q^{79} -36.7761 q^{80} -93.7707 q^{81} -45.9706i q^{82} +108.148 q^{83} +(55.6294 + 9.34868i) q^{84} +(29.2899 + 16.9105i) q^{85} +(65.7075 - 37.9363i) q^{86} +(-2.51087 + 1.44965i) q^{87} +48.5732 q^{88} +(48.6213 - 84.2145i) q^{89} -94.0697i q^{90} +(-90.8376 + 5.43338i) q^{91} -14.0035 q^{92} +(-155.001 - 89.4900i) q^{93} -103.800i q^{94} +(79.2038 + 137.185i) q^{95} +(-11.3964 - 19.7392i) q^{96} +(39.5728 - 68.5420i) q^{97} +(-22.6512 + 65.4899i) q^{98} +124.245i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{4} + 10 q^{7} - 88 q^{9} - 12 q^{12} - 4 q^{13} - 12 q^{14} + 60 q^{15} - 72 q^{16} + 24 q^{17} - 24 q^{18} + 100 q^{19} - 42 q^{21} + 12 q^{22} + 28 q^{23} - 82 q^{25} + 120 q^{26} + 4 q^{28}+ \cdots + 96 q^{98}+O(q^{100}) \) 36 * q + 36 * q^4 + 10 * q^7 - 88 * q^9 - 12 * q^12 - 4 * q^13 - 12 * q^14 + 60 * q^15 - 72 * q^16 + 24 * q^17 - 24 * q^18 + 100 * q^19 - 42 * q^21 + 12 * q^22 + 28 * q^23 - 82 * q^25 + 120 * q^26 + 4 * q^28 + 40 * q^29 - 112 * q^30 - 10 * q^31 - 192 * q^33 + 130 * q^35 - 88 * q^36 + 60 * q^37 + 60 * q^38 + 198 * q^39 - 90 * q^41 + 16 * q^42 + 20 * q^43 + 24 * q^44 + 48 * q^46 - 108 * q^47 - 24 * q^48 + 186 * q^49 - 192 * q^50 - 36 * q^51 + 80 * q^52 - 218 * q^53 + 144 * q^54 + 282 * q^55 + 120 * q^60 - 180 * q^62 + 252 * q^63 - 288 * q^64 - 368 * q^65 + 96 * q^66 + 48 * q^68 + 18 * q^69 + 144 * q^70 - 18 * q^71 + 74 * q^73 + 24 * q^74 - 1182 * q^75 + 100 * q^76 - 174 * q^77 - 320 * q^78 - 352 * q^79 + 68 * q^81 + 708 * q^83 - 108 * q^84 - 204 * q^85 - 36 * q^86 - 348 * q^87 + 48 * q^88 + 426 * q^89 - 224 * q^91 + 112 * q^92 + 426 * q^93 + 20 * q^95 + 64 * q^97 + 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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