LMFDB - Embedded newform 182.3.r.a.17.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [182,3,Mod(17,182)]

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, 1]))

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

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

chi := DirichletCharacter("182.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	182.r (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			17.17
Character	$\chi$	$=$	182.17
Dual form			182.3.r.a.75.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} +(3.48943 - 2.01462i) q^{3} -2.00000 q^{4} +(-4.59702 - 7.96227i) q^{5} +(2.84911 + 4.93480i) q^{6} +(-6.55840 + 2.44692i) q^{7} -2.82843i q^{8} +(3.61742 - 6.26555i) q^{9} +(11.2603 - 6.50116i) q^{10} +(14.8724 - 8.58660i) 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} +4.00000 q^{16} +3.67858i q^{17} +(8.86083 + 5.11580i) q^{18} +(8.61469 - 14.9211i) q^{19} +(9.19403 + 15.9245i) q^{20} +(-17.9554 + 21.7511i) q^{21} +(12.1433 + 21.0328i) q^{22} +7.00175 q^{23} +(-5.69822 - 9.86960i) q^{24} +(-29.7651 + 51.5547i) q^{25} +(12.5296 - 13.4540i) q^{26} +7.11227i q^{27} +(13.1168 - 4.89384i) q^{28} +(0.359781 - 0.623160i) q^{29} +(26.1948 - 45.3707i) q^{30} +(22.2101 - 38.4690i) q^{31} +5.65685i q^{32} +(34.5976 - 59.9247i) q^{33} -5.20230 q^{34} +(49.6321 + 40.9712i) q^{35} +(-7.23484 + 12.5311i) q^{36} +30.5131i q^{37} +(21.1016 + 12.1830i) q^{38} +(-51.0454 - 11.7497i) q^{39} +(-22.5207 + 13.0023i) q^{40} +(16.2530 - 28.1511i) q^{41} +(-30.7607 - 25.3928i) q^{42} +(26.8250 + 46.4622i) q^{43} +(-29.7449 + 17.1732i) q^{44} -66.5173 q^{45} +9.90197i q^{46} +(36.6987 + 63.5641i) q^{47} +(13.9577 - 8.05850i) q^{48} +(37.0251 - 32.0958i) q^{49} +(-72.9093 - 42.0942i) q^{50} +(7.41096 + 12.8362i) q^{51} +(19.0268 + 17.7195i) q^{52} +(-4.39981 + 7.62069i) q^{53} -10.0583 q^{54} +(-136.738 - 78.9455i) q^{55} +(6.92094 + 18.5499i) q^{56} -69.4215i q^{57} +(0.881281 + 0.508808i) q^{58} -13.1679 q^{59} +(64.1639 + 37.0450i) q^{60} +(-10.0485 - 5.80148i) q^{61} +(54.4034 + 31.4098i) q^{62} +(-8.39315 + 49.9435i) q^{63} -8.00000 q^{64} +(-26.8107 + 116.477i) q^{65} +(84.7464 + 48.9283i) q^{66} +(24.0610 - 13.8916i) q^{67} -7.35717i q^{68} +(24.4321 - 14.1059i) q^{69} +(-57.9420 + 70.1904i) q^{70} +(-25.6313 + 14.7983i) q^{71} +(-17.7217 - 10.2316i) q^{72} +(30.1279 - 52.1831i) q^{73} -43.1520 q^{74} +239.862i 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} +(-18.3881 - 31.8491i) q^{80} +(46.8853 + 81.2078i) q^{81} +(39.8117 + 22.9853i) q^{82} -108.148 q^{83} +(35.9109 - 43.5021i) q^{84} +(29.2899 - 16.9105i) q^{85} +(-65.7075 + 37.9363i) q^{86} -2.89930i q^{87} +(-24.2866 - 42.0656i) q^{88} +97.2426 q^{89} -94.0697i q^{90} +(84.0717 + 34.8274i) q^{91} -14.0035 q^{92} -178.980i q^{93} +(-89.8932 + 51.8998i) q^{94} -158.408 q^{95} +(11.3964 + 19.7392i) q^{96} +(-39.5728 - 68.5420i) q^{97} +(45.3903 + 52.3615i) q^{98} -124.245i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{3} - 72 q^{4} + 8 q^{7} + 44 q^{9} + 12 q^{11} - 12 q^{12} + 4 q^{13} - 12 q^{14} + 60 q^{15} + 144 q^{16} + 24 q^{18} + 50 q^{19} + 42 q^{21} + 12 q^{22} - 56 q^{23} - 82 q^{25} + 48 q^{26}+ \cdots - 24 q^{98}+O(q^{100}) $ 36 * q + 6 * q^3 - 72 * q^4 + 8 * q^7 + 44 * q^9 + 12 * q^11 - 12 * q^12 + 4 * q^13 - 12 * q^14 + 60 * q^15 + 144 * q^16 + 24 * q^18 + 50 * q^19 + 42 * q^21 + 12 * q^22 - 56 * q^23 - 82 * q^25 + 48 * q^26 - 16 * q^28 + 40 * q^29 + 56 * q^30 + 10 * q^31 - 96 * q^33 - 20 * q^35 - 88 * q^36 + 60 * q^38 - 348 * q^39 + 90 * q^41 - 176 * q^42 + 20 * q^43 - 24 * q^44 + 108 * q^47 + 24 * q^48 - 36 * q^49 - 192 * q^50 - 36 * q^51 - 8 * q^52 - 218 * q^53 + 288 * q^54 - 282 * q^55 + 24 * q^56 + 144 * q^58 - 120 * q^60 + 354 * q^61 + 180 * q^62 + 66 * q^63 - 288 * q^64 + 340 * q^65 + 96 * q^66 + 30 * q^67 - 18 * q^69 - 144 * q^70 - 18 * q^71 - 48 * q^72 - 74 * q^73 - 48 * q^74 - 100 * q^76 - 174 * q^77 - 320 * q^78 - 352 * q^79 - 34 * q^81 - 192 * q^82 - 708 * q^83 - 84 * q^84 - 204 * q^85 + 36 * q^86 - 24 * q^88 + 852 * q^89 + 4 * q^91 + 112 * q^92 + 252 * q^94 - 40 * q^95 - 64 * q^97 - 24 * q^98

Character values

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

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

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	3.48943	−	2.01462i	1.16314	−	0.671541i	0.211088	−	0.977467i	$-0.432299\pi$
$3$	3.48943	−	2.01462i	1.16314	−	0.671541i	0.952055	+	0.305926i	$0.0989659\pi$
$4$	−2.00000			−0.500000
$5$	−4.59702	−	7.96227i	−0.919403	−	1.59245i	−0.800324	−	0.599568i	$-0.795339\pi$
$5$	−4.59702	−	7.96227i	−0.919403	−	1.59245i	−0.119080	−	0.992885i	$-0.537994\pi$
$6$	2.84911	+	4.93480i	0.474851	+	0.822467i
$7$	−6.55840	+	2.44692i	−0.936914	+	0.349560i
$7$	−6.55840	+	2.44692i	−0.936914	+	0.349560i
$8$		−	2.82843i		−	0.353553i
$9$	3.61742	−	6.26555i	0.401936	−	0.696173i
$10$	11.2603	−	6.50116i	1.12603	−	0.650116i
$11$	14.8724	−	8.58660i	1.35204	−	0.780600i	0.363505	−	0.931592i	$-0.381580\pi$
$11$	14.8724	−	8.58660i	1.35204	−	0.780600i	0.988535	+	0.150992i	$0.0482468\pi$
$12$	−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
$16$	4.00000			0.250000
$17$			3.67858i			0.216387i	0.994130	+	0.108194i	$0.0345067\pi$
$17$			3.67858i			0.216387i	−0.994130	+	0.108194i	$0.965493\pi$
$18$	8.86083	+	5.11580i	0.492268	+	0.284211i
$19$	8.61469	−	14.9211i	0.453405	−	0.785320i	−0.545190	−	0.838312i	$-0.683543\pi$
$19$	8.61469	−	14.9211i	0.453405	−	0.785320i	0.998595	+	0.0529922i	$0.0168759\pi$
$20$	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
$23$	7.00175			0.304424			0.152212	−	0.988348i	$-0.451360\pi$
$23$	7.00175			0.304424			0.152212	+	0.988348i	$0.451360\pi$
$24$	−5.69822	−	9.86960i	−0.237426	−	0.411233i
$25$	−29.7651	+	51.5547i	−1.19060	+	2.06219i
$26$	12.5296	−	13.4540i	0.481908	−	0.517460i
$27$			7.11227i			0.263417i
$28$	13.1168	−	4.89384i	0.468457	−	0.174780i
$29$	0.359781	−	0.623160i	0.0124063	−	0.0214883i	−0.859756	−	0.510706i	$-0.829384\pi$
$29$	0.359781	−	0.623160i	0.0124063	−	0.0214883i	0.872162	+	0.489217i	$0.162718\pi$
$30$	26.1948	−	45.3707i	0.873160	−	1.51236i
$31$	22.2101	−	38.4690i	0.716455	−	1.24094i	−0.245941	−	0.969285i	$-0.579097\pi$
$31$	22.2101	−	38.4690i	0.716455	−	1.24094i	0.962396	−	0.271651i	$-0.0875696\pi$
$32$			5.65685i			0.176777i
$33$	34.5976	−	59.9247i	1.04841	−	1.81590i
$34$	−5.20230			−0.153009
$35$	49.6321	+	40.9712i	1.41806	+	1.17060i
$36$	−7.23484	+	12.5311i	−0.200968	+	0.348086i
$37$			30.5131i			0.824677i	0.911031	+	0.412339i	$0.135288\pi$
$37$			30.5131i			0.824677i	−0.911031	+	0.412339i	$0.864712\pi$
$38$	21.1016	+	12.1830i	0.555305	+	0.320606i
$39$	−51.0454	−	11.7497i	−1.30886	−	0.301274i
$40$	−22.5207	+	13.0023i	−0.563017	+	0.325058i
$41$	16.2530	−	28.1511i	0.396416	−	0.686612i	−0.596865	−	0.802342i	$-0.703587\pi$
$41$	16.2530	−	28.1511i	0.396416	−	0.686612i	0.993281	+	0.115729i	$0.0369206\pi$
$42$	−30.7607	−	25.3928i	−0.732397	−	0.604591i
$43$	26.8250	+	46.4622i	0.623837	+	1.08052i	0.988765	+	0.149481i	$0.0477604\pi$
$43$	26.8250	+	46.4622i	0.623837	+	1.08052i	−0.364928	+	0.931036i	$0.618906\pi$
$44$	−29.7449	+	17.1732i	−0.676020	+	0.390300i
$45$	−66.5173			−1.47816
$46$			9.90197i			0.215260i
$47$	36.6987	+	63.5641i	0.780824	+	1.35243i	0.931462	+	0.363838i	$0.118534\pi$
$47$	36.6987	+	63.5641i	0.780824	+	1.35243i	−0.150638	+	0.988589i	$0.548133\pi$
$48$	13.9577	−	8.05850i	0.290786	−	0.167885i
$49$	37.0251	−	32.0958i	0.755615	−	0.655016i
$50$	−72.9093	−	42.0942i	−1.45819	−	0.841884i
$51$	7.41096	+	12.8362i	0.145313	+	0.251690i
$52$	19.0268	+	17.7195i	0.365899	+	0.340760i
$53$	−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	$0.193122\pi$
$54$	−10.0583			−0.186264
$55$	−136.738	−	78.9455i	−2.48614	−	1.43537i
$56$	6.92094	+	18.5499i	0.123588	+	0.331249i
$57$		−	69.4215i		−	1.21792i
$58$	0.881281	+	0.508808i	0.0151945	+	0.00877255i
$59$	−13.1679			−0.223185			−0.111592	−	0.993754i	$-0.535595\pi$
$59$	−13.1679			−0.223185			−0.111592	+	0.993754i	$0.535595\pi$
$60$	64.1639	+	37.0450i	1.06940	+	0.617417i
$61$	−10.0485	−	5.80148i	−0.164729	−	0.0951062i	0.415369	−	0.909653i	$-0.363652\pi$
$61$	−10.0485	−	5.80148i	−0.164729	−	0.0951062i	−0.580098	+	0.814547i	$0.696986\pi$
$62$	54.4034	+	31.4098i	0.877474	+	0.506610i
$63$	−8.39315	+	49.9435i	−0.133225	+	0.792755i
$64$	−8.00000			−0.125000
$65$	−26.8107	+	116.477i	−0.412472	+	1.79195i
$66$	84.7464	+	48.9283i	1.28404	+	0.741338i
$67$	24.0610	−	13.8916i	0.359119	−	0.207338i	−0.309575	−	0.950875i	$-0.600187\pi$
$67$	24.0610	−	13.8916i	0.359119	−	0.207338i	0.668694	+	0.743537i	$0.266854\pi$
$68$		−	7.35717i		−	0.108194i
$69$	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	−0.669521	−	0.742793i	$-0.733501\pi$
$71$	−25.6313	+	14.7983i	−0.361005	+	0.208426i	0.308517	+	0.951219i	$0.400167\pi$
$72$	−17.7217	−	10.2316i	−0.246134	−	0.142106i
$73$	30.1279	−	52.1831i	0.412711	−	0.714836i	−0.582474	−	0.812849i	$-0.697915\pi$
$73$	30.1279	−	52.1831i	0.412711	−	0.714836i	0.995185	+	0.0980129i	$0.0312486\pi$
$74$	−43.1520			−0.583135
$75$			239.862i			3.19816i
$76$	−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	$-0.484254\pi$
$80$	−18.3881	−	31.8491i	−0.229851	−	0.398113i
$81$	46.8853	+	81.2078i	0.578831	+	1.00257i
$82$	39.8117	+	22.9853i	0.485508	+	0.280308i
$83$	−108.148			−1.30299			−0.651493	−	0.758654i	$-0.725857\pi$
$83$	−108.148			−1.30299			−0.651493	+	0.758654i	$0.725857\pi$
$84$	35.9109	−	43.5021i	0.427511	−	0.517883i
$85$	29.2899	−	16.9105i	0.344587	−	0.198947i
$86$	−65.7075	+	37.9363i	−0.764041	+	0.441119i
$87$		−	2.89930i		−	0.0333253i
$88$	−24.2866	−	42.0656i	−0.275984	−	0.478018i
$89$	97.2426			1.09261			0.546307	−	0.837585i	$-0.316033\pi$
$89$	97.2426			1.09261			0.546307	+	0.837585i	$0.316033\pi$
$90$		−	94.0697i		−	1.04522i
$91$	84.0717	+	34.8274i	0.923865	+	0.382719i
$92$	−14.0035			−0.152212
$93$		−	178.980i		−	1.92452i
$94$	−89.8932	+	51.8998i	−0.956310	+	0.552126i
$95$	−158.408			−1.66745
$96$	11.3964	+	19.7392i	0.118713	+	0.205617i
$97$	−39.5728	−	68.5420i	−0.407967	−	0.706619i	0.586695	−	0.809808i	$-0.300429\pi$
$97$	−39.5728	−	68.5420i	−0.407967	−	0.706619i	−0.994662	+	0.103189i	$0.967095\pi$
$98$	45.3903	+	52.3615i	0.463166	+	0.534301i
$99$		−	124.245i		−	1.25500i
$100$	59.5302	−	103.109i	0.595302	−	1.03109i
$101$	−9.55534	+	5.51678i	−0.0946073	+	0.0546216i	−0.546557	−	0.837422i	$-0.684062\pi$
$101$	−9.55534	+	5.51678i	−0.0946073	+	0.0546216i	0.451950	+	0.892043i	$0.350729\pi$
$102$	−18.1531	+	10.4807i	−0.177971	+	0.102752i
$103$	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
$107$	134.060			1.25290			0.626450	−	0.779461i	$-0.284507\pi$
$107$	134.060			1.25290			0.626450	+	0.779461i	$0.284507\pi$
$108$		−	14.2245i		−	0.131709i
$109$	−53.7515	−	31.0334i	−0.493133	−	0.284710i	0.232740	−	0.972539i	$-0.425231\pi$
$109$	−53.7515	−	31.0334i	−0.493133	−	0.284710i	−0.725873	+	0.687829i	$0.758564\pi$
$110$	111.646	−	193.376i	1.01496	−	1.75797i
$111$	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	0.789345	−	0.613950i	$-0.210421\pi$
$113$	−15.4838	−	26.8187i	−0.137024	−	0.237333i	−0.926369	+	0.376617i	$0.877087\pi$
$114$	98.1768			0.861200
$115$	−32.1872	−	55.7498i	−0.279888	−	0.484781i
$116$	−0.719563	+	1.24632i	−0.00620313	+	0.0107441i
$117$	−89.9253	+	27.5571i	−0.768592	+	0.235531i
$118$		−	18.6222i		−	0.157815i
$119$	−9.00121	−	24.1256i	−0.0756404	−	0.202736i
$120$	−52.3896	+	90.7414i	−0.436580	+	0.756179i
$121$	86.9596	−	150.618i	0.718674	−	1.24478i
$122$	8.20453	−	14.2107i	0.0672502	−	0.116481i
$123$		−	130.975i		−	1.06484i
$124$	−44.4202	+	76.9380i	−0.358227	+	0.620468i
$125$	317.472			2.53978
$126$	−70.6308	−	11.8697i	−0.560562	−	0.0942041i
$127$	24.8316	−	43.0096i	0.195524	−	0.338658i	−0.751548	−	0.659678i	$-0.770692\pi$
$127$	24.8316	−	43.0096i	0.195524	−	0.338658i	0.947072	+	0.321020i	$0.104026\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	187.208	+	108.085i	1.45122	+	0.837865i
$130$	−164.723	−	37.9160i	−1.26710	−	0.291662i
$131$	−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
$133$	−19.9878	+	118.938i	−0.150285	+	0.894270i
$134$	19.6457	+	34.0274i	0.146610	+	0.253936i
$135$	56.6298	−	32.6952i	0.419480	−	0.242187i
$136$	10.4046			0.0765045
$137$		−	43.5477i		−	0.317866i	−0.987289	−	0.158933i	$-0.949195\pi$
$137$		−	43.5477i		−	0.317866i	0.987289	−	0.158933i	$-0.0508054\pi$
$138$	19.9487	+	34.5522i	0.144556	+	0.250379i
$139$	−21.7494	+	12.5570i	−0.156471	+	0.0903384i	−0.576191	−	0.817315i	$-0.695462\pi$
$139$	−21.7494	+	12.5570i	−0.156471	+	0.0903384i	0.419720	+	0.907654i	$0.362128\pi$
$140$	−99.2642	−	81.9423i	−0.709030	−	0.585302i
$141$	256.115	+	147.868i	1.81642	+	1.04871i
$142$	−20.9279	−	36.2482i	−0.147380	−	0.255269i
$143$	−217.563	−	50.0787i	−1.52142	−	0.350201i
$144$	14.4697	−	25.0622i	0.100484	−	0.174043i
$145$	−6.61568			−0.0456254
$146$	73.7980	+	42.6073i	0.505466	+	0.291831i
$147$	64.5358	−	186.588i	0.439019	−	1.26930i
$148$		−	61.0261i		−	0.412339i
$149$	133.539	+	77.0987i	0.896233	+	0.517441i	0.875976	−	0.482354i	$-0.160218\pi$
$149$	133.539	+	77.0987i	0.896233	+	0.517441i	0.0202572	+	0.999795i	$0.493551\pi$
$150$	−339.216			−2.26144
$151$	−38.2961	−	22.1103i	−0.253617	−	0.146426i	0.367802	−	0.929904i	$-0.380110\pi$
$151$	−38.2961	−	22.1103i	−0.253617	−	0.146426i	−0.621419	+	0.783478i	$0.713444\pi$
$152$	−42.2032	−	24.3660i	−0.277653	−	0.160303i
$153$	23.0484	+	13.3070i	0.150643	+	0.0869738i
$154$	−131.106	−	108.228i	−0.851339	−	0.702778i
$155$	−408.401			−2.63484
$156$	102.091	+	23.4993i	0.654428	+	0.150637i
$157$	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	$0.531066\pi$
$158$	162.595	−	93.8742i	1.02908	−	0.594141i
$159$			35.4559i			0.222993i
$160$	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
$163$	−185.626	−	107.171i	−1.13881	−	0.657494i	−0.192676	−	0.981262i	$-0.561717\pi$
$163$	−185.626	−	107.171i	−1.13881	−	0.657494i	−0.946136	+	0.323769i	$0.895050\pi$
$164$	−32.5061	+	56.3022i	−0.198208	+	0.343306i
$165$	−636.182			−3.85565
$166$		−	152.944i		−	0.921351i
$167$	−70.0407	+	121.314i	−0.419405	+	0.726431i	−0.995880	−	0.0906838i	$-0.971095\pi$
$167$	−70.0407	+	121.314i	−0.419405	+	0.726431i	0.576474	+	0.817115i	$0.304428\pi$
$168$	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
$171$	−62.3259	−	107.952i	−0.364479	−	0.631296i
$172$	−53.6500	−	92.9245i	−0.311918	−	0.540259i
$173$	261.813	+	151.158i	1.51337	+	0.873746i	0.999877	+	0.0156530i	$0.00498271\pi$
$173$	261.813	+	151.158i	1.51337	+	0.873746i	0.513495	+	0.858093i	$0.328351\pi$
$174$	4.10023			0.0235645
$175$	69.0611	−	410.949i	0.394635	−	2.34828i
$176$	59.4897	−	34.3464i	0.338010	−	0.195150i
$177$	−45.9484	+	26.5283i	−0.259596	+	0.149878i
$178$			137.522i			0.772594i
$179$	91.7087	+	158.844i	0.512339	+	0.887398i	0.999898	+	0.0143073i	$0.00455430\pi$
$179$	91.7087	+	158.844i	0.512339	+	0.887398i	−0.487558	+	0.873090i	$0.662112\pi$
$180$	133.035			0.739082
$181$			220.794i			1.21986i	0.792456	+	0.609929i	$0.208802\pi$
$181$			220.794i			1.21986i	−0.792456	+	0.609929i	$0.791198\pi$
$182$	−49.2534	+	118.895i	−0.270623	+	0.653271i
$183$	−46.7512			−0.255471
$184$		−	19.8039i		−	0.107630i
$185$	242.953	−	140.269i	1.31326	−	0.758211i
$186$	253.116			1.36084
$187$	31.5866	+	54.7095i	0.168912	+	0.292564i
$188$	−73.3975	−	127.128i	−0.390412	−	0.676214i
$189$	−17.4032	−	46.6451i	−0.0920803	−	0.246799i
$190$		−	224.022i		−	1.17906i
$191$	4.70861	−	8.15555i	0.0246524	−	0.0426992i	−0.853436	−	0.521198i	$-0.825485\pi$
$191$	4.70861	−	8.15555i	0.0246524	−	0.0426992i	0.878088	+	0.478498i	$0.158819\pi$
$192$	−27.9154	+	16.1170i	−0.145393	+	0.0839427i
$193$	−29.7773	+	17.1919i	−0.154287	+	0.0890774i	−0.575156	−	0.818044i	$-0.695059\pi$
$193$	−29.7773	+	17.1919i	−0.154287	+	0.0890774i	0.420869	+	0.907121i	$0.361725\pi$
$194$	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	0.733271	−	0.679936i	$-0.237992\pi$
$197$	100.680	+	58.1276i	0.511065	+	0.295064i	−0.222206	+	0.975000i	$0.571326\pi$
$198$	175.710			0.887422
$199$		−	99.9665i		−	0.502344i	−0.967942	−	0.251172i	$-0.919184\pi$
$199$		−	99.9665i		−	0.502344i	0.967942	−	0.251172i	$-0.0808160\pi$
$200$	145.819	+	84.1884i	0.729093	+	0.420942i
$201$	55.9728	−	96.9477i	0.278471	−	0.482327i
$202$	−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
$205$	−298.862			−1.45786
$206$	113.579	+	196.725i	0.551356	+	0.954976i
$207$	25.3283	−	43.8698i	0.122359	−	0.211932i
$208$	−38.0535	−	35.4391i	−0.182950	−	0.170380i
$209$		−	295.884i		−	1.41571i
$210$	−60.7773	+	361.656i	−0.289416	+	1.72217i
$211$	−160.266	+	277.589i	−0.759555	+	1.31559i	0.183522	+	0.983016i	$0.441250\pi$
$211$	−160.266	+	277.589i	−0.759555	+	1.31559i	−0.943078	+	0.332573i	$0.892083\pi$
$212$	8.79962	−	15.2414i	0.0415076	−	0.0718933i
$213$	−59.6259	+	103.275i	−0.279934	+	0.484859i
$214$			189.590i			0.885935i
$215$	246.630	−	427.175i	1.14712	−	1.98686i
$216$	20.1165			0.0931321
$217$	−51.5320	+	306.641i	−0.237474	+	1.41309i
$218$	43.8879	−	76.0161i	0.201321	−	0.348698i
$219$		−	242.786i		−	1.10861i
$220$	273.475	+	157.891i	1.24307	+	0.717687i
$221$	32.5914	−	34.9958i	0.147472	−	0.158352i
$222$	−150.576	+	86.9350i	−0.678270	+	0.391599i
$223$	−158.432	+	274.412i	−0.710458	+	1.23055i	0.254228	+	0.967144i	$0.418179\pi$
$223$	−158.432	+	274.412i	−0.710458	+	1.23055i	−0.964686	+	0.263404i	$0.915155\pi$
$224$	−13.8419	−	37.0999i	−0.0617941	−	0.165625i
$225$	215.346	+	372.990i	0.957092	+	1.65773i
$226$	37.9273	−	21.8973i	0.167820	−	0.0968909i
$227$	141.103			0.621597			0.310799	−	0.950476i	$-0.399404\pi$
$227$	141.103			0.621597			0.310799	+	0.950476i	$0.399404\pi$
$228$			138.843i			0.608960i
$229$	−38.3046	−	66.3454i	−0.167269	−	0.289718i	0.770190	−	0.637815i	$-0.220161\pi$
$229$	−38.3046	−	66.3454i	−0.167269	−	0.289718i	−0.937459	+	0.348097i	$0.886828\pi$
$230$	78.8421	−	45.5195i	0.342792	−	0.197911i
$231$	−80.2734	+	477.668i	−0.347504	+	2.06783i
$232$	−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	$-0.367481\pi$
$234$	−38.9716	−	127.174i	−0.166545	−	0.543477i
$235$	337.409	−	584.410i	1.43578	−	2.48685i
$236$	26.3358			0.111592
$237$	−463.251	−	267.458i	−1.95464	−	1.12851i
$238$	34.1188	−	12.7296i	0.143356	−	0.0534858i
$239$		−	177.253i		−	0.741646i	−0.928704	−	0.370823i	$-0.879076\pi$
$239$		−	177.253i		−	0.741646i	0.928704	−	0.370823i	$-0.120924\pi$
$240$	−128.328	−	74.0901i	−0.534699	−	0.308709i
$241$	−319.864			−1.32723			−0.663617	−	0.748072i	$-0.730980\pi$
$241$	−319.864			−1.32723			−0.663617	+	0.748072i	$0.730980\pi$
$242$	213.007	+	122.979i	0.880192	+	0.508179i
$243$	271.772	+	156.907i	1.11840	+	0.645709i
$244$	20.0969	+	11.6030i	0.0823644	+	0.0475531i
$245$	−425.760	−	147.259i	−1.73780	−	0.601058i
$246$	185.227			0.752954
$247$	−214.152	+	65.6258i	−0.867013	+	0.265691i
$248$	−108.807	−	62.8196i	−0.438737	−	0.253305i
$249$	−377.375	+	217.877i	−1.51556	+	0.875010i
$250$			448.973i			1.79589i
$251$	27.6527	−	15.9653i	0.110170	−	0.0636067i	−0.443902	−	0.896075i	$-0.646406\pi$
$251$	27.6527	−	15.9653i	0.110170	−	0.0636067i	0.554073	+	0.832468i	$0.313073\pi$
$252$	16.7863	−	99.8871i	0.0666123	−	0.396377i
$253$	104.133	−	60.1212i	0.411593	−	0.237633i
$254$	60.8247	+	35.1172i	0.239467	+	0.138257i
$255$	68.1366	−	118.016i	0.267203	−	0.462808i
$256$	16.0000			0.0625000
$257$		−	36.6300i		−	0.142529i	−0.997457	−	0.0712646i	$-0.977297\pi$
$257$		−	36.6300i		−	0.142529i	0.997457	−	0.0712646i	$-0.0227035\pi$
$258$	−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
$262$	−121.546	−	210.524i	−0.463916	−	0.803526i
$263$	211.204	+	365.815i	0.803056	+	1.39093i	0.917596	+	0.397515i	$0.130127\pi$
$263$	211.204	+	365.815i	0.803056	+	1.39093i	−0.114540	+	0.993419i	$0.536539\pi$
$264$	−169.493	−	97.8567i	−0.642018	−	0.370669i
$265$	80.9040			0.305298
$266$	−168.204	−	28.2671i	−0.632344	−	0.106267i
$267$	339.321	−	195.907i	1.27087	−	0.733735i
$268$	−48.1220	+	27.7832i	−0.179560	+	0.103669i
$269$		−	445.620i		−	1.65658i	−0.560300	−	0.828290i	$-0.689314\pi$
$269$		−	445.620i		−	1.65658i	0.560300	−	0.828290i	$-0.310686\pi$
$270$	46.2380	+	80.0866i	0.171252	+	0.296617i
$271$	−368.469			−1.35967			−0.679833	−	0.733367i	$-0.737948\pi$
$271$	−368.469			−1.35967			−0.679833	+	0.733367i	$0.737948\pi$
$272$			14.7143i			0.0540968i
$273$	363.527	−	47.8451i	1.33160	−	0.175257i
$274$	61.5857			0.224765
$275$			1022.32i			3.71755i
$276$	−48.8642	+	28.2118i	−0.177044	+	0.102217i
$277$	333.166			1.20276			0.601382	−	0.798962i	$-0.294617\pi$
$277$	333.166			1.20276			0.601382	+	0.798962i	$0.294617\pi$
$278$	−17.7583	−	30.7583i	−0.0638789	−	0.110641i
$279$	−160.686	−	278.317i	−0.575937	−	0.997552i
$280$	115.884	−	140.381i	0.413871	−	0.501360i
$281$			289.853i			1.03151i	0.856738	+	0.515753i	$0.172488\pi$
$281$			289.853i			1.03151i	−0.856738	+	0.515753i	$0.827512\pi$
$282$	−209.117	+	362.202i	−0.741551	+	1.28440i
$283$	13.4673	−	7.77535i	0.0475876	−	0.0274747i	−0.476017	−	0.879436i	$-0.657920\pi$
$283$	13.4673	−	7.77535i	0.0475876	−	0.0274747i	0.523605	+	0.851961i	$0.324587\pi$
$284$	51.2627	−	29.5965i	0.180502	−	0.104213i
$285$	−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
$289$	275.468			0.953177
$290$		−	9.35599i		−	0.0322620i
$291$	−276.173	−	159.448i	−0.949048	−	0.547933i
$292$	−60.2558	+	104.366i	−0.206355	+	0.357418i
$293$	126.969	+	219.916i	0.433340	+	0.750566i	0.997159	−	0.0753321i	$-0.0240017\pi$
$293$	126.969	+	219.916i	0.433340	+	0.750566i	−0.563819	+	0.825899i	$0.690668\pi$
$294$	263.875	+	91.2674i	0.897534	+	0.310433i
$295$	60.5330	+	104.846i	0.205197	+	0.355411i
$296$	86.3040			0.291567
$297$	61.0703	+	105.777i	0.205624	+	0.356151i
$298$	−109.034	+	188.852i	−0.365886	+	0.633733i
$299$	−66.6103	−	62.0339i	−0.222777	−	0.207471i
$300$		−	479.724i		−	1.59908i
$301$	−289.618	−	239.079i	−0.962187	−	0.794283i
$302$	31.2687	−	54.1589i	0.103539	−	0.179334i
$303$	−22.2285	+	38.5008i	−0.0733613	+	0.127065i
$304$	34.4588	−	59.6843i	0.113351	−	0.196330i
$305$			106.678i			0.349764i
$306$	−18.8189	+	32.5953i	−0.0614997	+	0.106521i
$307$	−272.611			−0.887982			−0.443991	−	0.896031i	$-0.646438\pi$
$307$	−272.611			−0.887982			−0.443991	+	0.896031i	$0.646438\pi$
$308$	153.057	−	185.412i	0.496939	−	0.601987i
$309$	323.600	−	560.491i	1.04725	−	1.81389i
$310$		−	577.566i		−	1.86312i
$311$	−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	$0.820708\pi$
$312$	−33.2331	+	144.378i	−0.106516	+	0.462751i
$313$	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
$315$	436.247	−	162.763i	1.38491	−	0.516707i
$316$	132.758	+	229.944i	0.420121	+	0.727671i
$317$	72.1894	−	41.6786i	0.227727	−	0.131478i	−0.381796	−	0.924247i	$-0.624694\pi$
$317$	72.1894	−	41.6786i	0.227727	−	0.131478i	0.609523	+	0.792768i	$0.291361\pi$
$318$	−50.1421			−0.157680
$319$		−	12.3572i		−	0.0387373i
$320$	36.7761	+	63.6981i	0.114925	+	0.199057i
$321$	467.794	−	270.081i	1.45730	−	0.841375i
$322$	−24.2293	−	64.9410i	−0.0752464	−	0.201680i
$323$	54.8885	+	31.6899i	0.169933	+	0.0981111i
$324$	−93.7707	−	162.416i	−0.289416	−	0.501283i
$325$	739.930	−	226.747i	2.27671	−	0.697684i
$326$	151.563	−	262.515i	0.464918	−	0.805262i
$327$	−250.083			−0.764779
$328$	−79.6233	−	45.9706i	−0.242754	−	0.140154i
$329$	−396.221	−	327.079i	−1.20432	−	0.994163i
$330$		−	899.697i		−	2.72636i
$331$	259.200	+	149.649i	0.783082	+	0.452113i	0.837521	−	0.546404i	$-0.184004\pi$
$331$	259.200	+	149.649i	0.783082	+	0.452113i	−0.0544394	+	0.998517i	$0.517337\pi$
$332$	216.296			0.651493
$333$	191.181	+	110.379i	0.574118	+	0.331467i
$334$	−171.564	−	99.0525i	−0.513665	−	0.296564i
$335$	−221.217	−	127.720i	−0.660351	−	0.381254i
$336$	−71.8218	+	87.0043i	−0.213755	+	0.258941i
$337$	−605.486			−1.79669			−0.898347	−	0.439286i	$-0.855232\pi$
$337$	−605.486			−1.79669			−0.898347	+	0.439286i	$0.855232\pi$
$338$	−238.398	+	16.9832i	−0.705319	+	0.0502461i
$339$	−108.059	−	62.3879i	−0.318758	−	0.184035i
$340$	−58.5797	+	33.8210i	−0.172293	+	0.0994736i
$341$		−	762.837i		−	2.23706i
$342$	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
$345$	−224.630	−	129.690i	−0.651101	−	0.375913i
$346$	−213.770	+	370.260i	−0.617832	+	1.07012i
$347$	25.2726			0.0728318			0.0364159	−	0.999337i	$-0.488406\pi$
$347$	25.2726			0.0728318			0.0364159	+	0.999337i	$0.488406\pi$
$348$			5.79859i			0.0166626i
$349$	−276.022	+	478.084i	−0.790894	+	1.36987i	0.134520	+	0.990911i	$0.457051\pi$
$349$	−276.022	+	478.084i	−0.790894	+	1.36987i	−0.925414	+	0.378958i	$0.876283\pi$
$350$	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
$353$	75.4148	+	130.622i	0.213640	+	0.370035i	0.952851	−	0.303439i	$-0.0981349\pi$
$353$	75.4148	+	130.622i	0.213640	+	0.370035i	−0.739211	+	0.673474i	$0.764802\pi$
$354$	−37.5167	−	64.9809i	−0.105979	−	0.183562i
$355$	235.655	+	136.056i	0.663818	+	0.383255i
$356$	−194.485			−0.546307
$357$	−80.0131	−	66.0506i	−0.224126	−	0.185016i
$358$	−224.640	+	129.696i	−0.627485	+	0.362279i
$359$	−53.1461	+	30.6839i	−0.148039	+	0.0854705i	−0.572190	−	0.820121i	$-0.693906\pi$
$359$	−53.1461	+	30.6839i	−0.148039	+	0.0854705i	0.424151	+	0.905592i	$0.360573\pi$
$360$			188.139i			0.522610i
$361$	32.0742	+	55.5541i	0.0888481	+	0.153889i
$362$	−312.250			−0.862570
$363$		−	700.763i		−	1.93048i
$364$	−168.143	−	69.6548i	−0.461932	−	0.191359i
$365$	−553.994			−1.51779
$366$		−	66.1162i		−	0.180645i
$367$	356.970	−	206.097i	0.972670	−	0.561572i	0.0726211	−	0.997360i	$-0.476864\pi$
$367$	356.970	−	206.097i	0.972670	−	0.561572i	0.900049	+	0.435788i	$0.143530\pi$
$368$	28.0070			0.0761060
$369$	−117.588	−	203.669i	−0.318667	−	0.551948i
$370$	198.370	+	343.588i	0.536136	+	0.928615i
$371$	10.2085	−	60.7455i	0.0275161	−	0.163735i
$372$			357.960i			0.962258i
$373$	−83.9583	+	145.420i	−0.225089	+	0.389866i	−0.956346	−	0.292236i	$-0.905601\pi$
$373$	−83.9583	+	145.420i	−0.225089	+	0.389866i	0.731257	+	0.682102i	$0.238934\pi$
$374$	−77.3709	+	44.6701i	−0.206874	+	0.119439i
$375$	1107.80	−	639.587i	2.95412	−	1.70556i
$376$	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	0.243306	−	0.969950i	$-0.421768\pi$
$379$	−180.041	−	103.947i	−0.475042	−	0.274266i	−0.718348	+	0.695684i	$0.755101\pi$
$380$	316.815			0.833724
$381$		−	200.105i		−	0.525211i
$382$	11.5337	+	6.65898i	0.0301929	+	0.0174319i
$383$	−253.134	+	438.440i	−0.660924	+	1.14475i	0.319450	+	0.947603i	$0.396502\pi$
$383$	−253.134	+	438.440i	−0.660924	+	1.14475i	−0.980373	+	0.197150i	$0.936831\pi$
$384$	−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
$387$	388.149			1.00297
$388$	79.1455	+	137.084i	0.203983	+	0.353309i
$389$	−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	$0.277589\pi$
$390$	−651.175	+	199.549i	−1.66968	+	0.511664i
$391$			25.7565i			0.0658735i
$392$	−90.7805	−	104.723i	−0.231583	−	0.267150i
$393$	−346.298	+	599.805i	−0.881165	+	1.52622i
$394$	−82.2048	+	142.383i	−0.208642	+	0.361378i
$395$	−610.292	+	1057.06i	−1.54504	+	2.67609i
$396$			248.491i			0.627502i
$397$	98.2478	−	170.170i	0.247476	−	0.428640i	−0.715349	−	0.698767i	$-0.753732\pi$
$397$	98.2478	−	170.170i	0.247476	−	0.428640i	0.962825	+	0.270127i	$0.0870656\pi$
$398$	141.374			0.355211
$399$	169.869	+	455.294i	0.425737	+	1.14109i
$400$	−119.060	+	206.219i	−0.297651	+	0.515547i
$401$		−	18.3343i		−	0.0457213i	−0.999739	−	0.0228607i	$-0.992723\pi$
$401$		−	18.3343i		−	0.0457213i	0.999739	−	0.0228607i	$-0.00727741\pi$
$402$	137.105	+	79.1574i	0.341056	+	0.196909i
$403$	−552.120	+	169.194i	−1.37002	+	0.419836i
$404$	19.1107	−	11.0336i	0.0473037	−	0.0273108i
$405$	431.065	−	746.627i	1.06436	−	1.84352i
$406$	−7.02480	−	1.18054i	−0.0173025	−	0.00290773i
$407$	262.004	+	453.804i	0.643743	+	1.11500i
$408$	36.3062	−	20.9614i	0.0889857	−	0.0513759i
$409$	55.2062			0.134979			0.0674893	−	0.997720i	$-0.478501\pi$
$409$	55.2062			0.134979			0.0674893	+	0.997720i	$0.478501\pi$
$410$		−	422.655i		−	1.03087i
$411$	−87.7321	−	151.957i	−0.213460	−	0.369724i
$412$	−278.211	+	160.625i	−0.675270	+	0.389867i
$413$	86.3602	−	32.2208i	0.209105	−	0.0780164i
$414$	62.0413	+	35.8196i	0.149858	+	0.0865207i
$415$	497.158	+	861.102i	1.19797	+	2.07495i
$416$	50.1184	−	53.8158i	0.120477	−	0.129365i
$417$	−50.5954	+	87.6338i	−0.121332	+	0.210153i
$418$	418.443			1.00106
$419$	595.399	+	343.754i	1.42100	+	0.820415i	0.996384	−	0.0849586i	$-0.0270758\pi$
$419$	595.399	+	343.754i	1.42100	+	0.820415i	0.424616	+	0.905374i	$0.360409\pi$
$420$	−511.459	−	85.9521i	−1.21776	−	0.204648i
$421$			584.326i			1.38795i	0.720001	+	0.693973i	$0.244141\pi$
$421$			584.326i			1.38795i	−0.720001	+	0.693973i	$0.755859\pi$
$422$	−392.570	−	226.651i	−0.930261	−	0.537087i
$423$	531.019			1.25536
$424$	21.5546	+	12.4445i	0.0508363	+	0.0293503i
$425$	−189.648	−	109.493i	−0.446231	−	0.257632i
$426$	−146.053	−	84.3237i	−0.342847	−	0.197943i
$427$	80.0975	+	13.4606i	0.187582	+	0.0315237i
$428$	−268.121			−0.626450
$429$	−860.059	+	263.560i	−2.00480	+	0.614360i
$430$	604.117	+	348.787i	1.40492	+	0.811133i
$431$	−2.84514	+	1.64264i	−0.00660126	+	0.00381124i	−0.503297	−	0.864113i	$-0.667880\pi$
$431$	−2.84514	+	1.64264i	−0.00660126	+	0.00381124i	0.496696	+	0.867925i	$0.334546\pi$
$432$			28.4491i			0.0658544i
$433$	244.440	−	141.128i	0.564527	−	0.325930i	−0.190434	−	0.981700i	$-0.560989\pi$
$433$	244.440	−	141.128i	0.564527	−	0.325930i	0.754960	+	0.655770i	$0.227656\pi$
$434$	−433.656	−	72.8772i	−0.999208	−	0.167920i
$435$	−23.0850	+	13.3281i	−0.0530689	+	0.0306393i
$436$	107.503	+	62.0668i	0.246566	+	0.142355i
$437$	60.3179	−	104.474i	0.138027	−	0.239070i
$438$	343.351			0.783906
$439$		−	350.600i		−	0.798634i	−0.916813	−	0.399317i	$-0.869247\pi$
$439$		−	350.600i		−	0.798634i	0.916813	−	0.399317i	$-0.130753\pi$
$440$	−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	$0.821909\pi$
$444$	−122.945	−	212.946i	−0.276902	−	0.479609i
$445$	−447.026	−	774.271i	−1.00455	−	1.73994i
$446$	−388.078	−	224.057i	−0.870129	−	0.502369i
$447$	621.299			1.38993
$448$	52.4672	−	19.5754i	0.117114	−	0.0436950i
$449$	−271.586	+	156.800i	−0.604868	+	0.349221i	−0.770954	−	0.636891i	$-0.780220\pi$
$449$	−271.586	+	156.800i	−0.604868	+	0.349221i	0.166086	+	0.986111i	$0.446887\pi$
$450$	−527.487	+	304.545i	−1.17219	+	0.676767i
$451$		−	558.234i		−	1.23777i
$452$	30.9675	+	53.6373i	0.0685122	+	0.118667i
$453$	−178.176			−0.393324
$454$			199.549i			0.439536i
$455$	−109.174	−	829.503i	−0.239943	−	1.82308i
$456$	−196.354			−0.430600
$457$			97.0336i			0.212327i	0.994349	+	0.106164i	$0.0338567\pi$
$457$			97.0336i			0.212327i	−0.994349	+	0.106164i	$0.966143\pi$
$458$	93.8266	−	54.1708i	0.204862	−	0.118277i
$459$	−26.1631			−0.0570002
$460$	64.3743	+	111.500i	0.139944	+	0.242390i
$461$	−244.363	−	423.249i	−0.530071	−	0.918110i	−0.999385	−	0.0350783i	$-0.988832\pi$
$461$	−244.363	−	423.249i	−0.530071	−	0.918110i	0.469314	−	0.883032i	$-0.344501\pi$
$462$	−675.524	−	113.524i	−1.46217	−	0.245722i
$463$		−	570.309i		−	1.23177i	−0.787837	−	0.615884i	$-0.788799\pi$
$463$		−	570.309i		−	1.23177i	0.787837	−	0.615884i	$-0.211201\pi$
$464$	1.43913	−	2.49264i	0.00310156	−	0.00537207i
$465$	−1425.09	+	822.774i	−3.06470	+	1.76941i
$466$	336.648	−	194.364i	0.722420	−	0.417089i
$467$	−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
$471$	522.818			1.11002
$472$			37.2444i			0.0789076i
$473$	797.906	+	460.671i	1.68690	+	0.973935i
$474$	378.243	−	655.135i	0.797980	−	1.38214i
$475$	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
$478$	250.674			0.524423
$479$	16.6219	+	28.7900i	0.0347012	+	0.0601043i	0.882854	−	0.469647i	$-0.155619\pi$
$479$	16.6219	+	28.7900i	0.0347012	+	0.0601043i	−0.848153	+	0.529751i	$0.822285\pi$
$480$	104.779	−	181.483i	0.218290	−	0.378089i
$481$	270.339	−	290.282i	0.562035	−	0.603498i
$482$		−	452.355i		−	0.938497i
$483$	−125.720	+	152.296i	−0.260289	+	0.315312i
$484$	−173.919	+	301.237i	−0.359337	+	0.622390i
$485$	−363.833	+	630.178i	−0.750172	+	1.29934i
$486$	−221.901	+	384.343i	−0.456586	+	0.790829i
$487$		−	360.023i		−	0.739266i	−0.929178	−	0.369633i	$-0.879483\pi$
$487$		−	360.023i		−	0.739266i	0.929178	−	0.369633i	$-0.120517\pi$
$488$	−16.4091	+	28.4213i	−0.0336251	+	0.0582404i
$489$	−863.641			−1.76614
$490$	208.256	−	602.116i	0.425012	−	1.22881i
$491$	242.721	−	420.404i	0.494339	−	0.856221i	−0.505639	−	0.862745i	$-0.668743\pi$
$491$	242.721	−	420.404i	0.494339	−	0.856221i	0.999979	+	0.00652400i	$0.00207667\pi$
$492$			261.950i			0.532419i
$493$	2.29235	+	1.32349i	0.00464979	+	0.00268456i
$494$	−92.8089	−	302.857i	−0.187872	−	0.613071i
$495$	−989.275	+	571.158i	−1.99854	+	1.15385i
$496$	88.8404	−	153.876i	0.179114	−	0.310234i
$497$	131.890	−	159.771i	0.265373	−	0.321470i
$498$	−308.125	−	533.688i	−0.618725	−	1.07166i
$499$	−295.490	+	170.601i	−0.592164	+	0.341886i	−0.765953	−	0.642897i	$-0.777732\pi$
$499$	−295.490	+	170.601i	−0.592164	+	0.341886i	0.173789	+	0.984783i	$0.444399\pi$
$500$	−634.944			−1.26989
$501$			564.423i			1.12659i
$502$	22.5783	+	39.1068i	0.0449767	+	0.0779020i
$503$	−227.952	+	131.608i	−0.453184	+	0.261646i	−0.709174	−	0.705034i	$-0.750932\pi$
$503$	−227.952	+	131.608i	−0.453184	+	0.261646i	0.255990	+	0.966679i	$0.417599\pi$
$504$	141.262	+	23.7394i	0.280281	+	0.0471020i
$505$	87.8521	+	50.7214i	0.173965	+	0.100438i
$506$	85.0243	+	147.266i	0.168032	+	0.291040i
$507$	381.515	+	564.030i	0.752495	+	1.11248i
$508$	−49.6632	+	86.0192i	−0.0977622	+	0.169329i
$509$	159.836			0.314019			0.157009	−	0.987597i	$-0.449815\pi$
$509$	159.836			0.314019			0.157009	+	0.987597i	$0.449815\pi$
$510$	166.900	+	96.3598i	0.327255	+	0.188941i
$511$	−69.9029	+	415.958i	−0.136796	+	0.814007i
$512$			22.6274i			0.0441942i
$513$	106.123	+	61.2700i	0.206867	+	0.119435i
$514$	51.8027			0.100783
$515$	−1278.94	−	738.397i	−2.48338	−	1.43378i
$516$	−374.416	−	216.169i	−0.725612	−	0.418932i
$517$	1091.60	+	630.235i	2.11141	+	1.21902i
$518$	283.008	−	105.590i	0.546347	−	0.203841i
$519$	1218.11			2.34703
$520$	329.446	+	75.8320i	0.633549	+	0.145831i
$521$	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	$0.396813\pi$
$522$	6.37593	−	3.68114i	0.0122144	−	0.00705200i
$523$			830.732i			1.58840i	0.607658	+	0.794199i	$0.292109\pi$
$523$			830.732i			1.58840i	−0.607658	+	0.794199i	$0.707891\pi$
$524$	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
$527$	141.512	+	81.7017i	0.268523	+	0.155032i
$528$	138.390	−	239.699i	0.262103	−	0.453975i
$529$	−479.976			−0.907326
$530$			114.416i			0.215878i
$531$	−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
$535$	−616.278	−	1067.42i	−1.15192	−	1.99519i
$536$	−39.2914	−	68.0547i	−0.0733049	−	0.126968i
$537$	640.023	+	369.517i	1.19185	+	0.688114i
$538$	630.202			1.17138
$539$	275.060	−	795.263i	0.510316	−	1.47544i
$540$	−113.260	+	65.3904i	−0.209740	+	0.121093i
$541$	55.8428	−	32.2408i	0.103221	−	0.0595949i	−0.447501	−	0.894284i	$-0.647686\pi$
$541$	55.8428	−	32.2408i	0.103221	−	0.0595949i	0.550722	+	0.834689i	$0.314352\pi$
$542$		−	521.094i		−	0.961428i
$543$	444.817	+	770.446i	0.819185	+	1.41887i
$544$	−20.8092			−0.0382522
$545$			570.645i			1.04705i
$546$	67.6632	+	514.104i	0.123925	+	0.941583i
$547$	−196.545			−0.359314			−0.179657	−	0.983729i	$-0.557499\pi$
$547$	−196.545			−0.359314			−0.179657	+	0.983729i	$0.557499\pi$
$548$			87.0953i			0.158933i
$549$	−72.6990	+	41.9728i	−0.132421	+	0.0764531i
$550$	−1445.79			−2.62870
$551$	−6.19881	−	10.7367i	−0.0112501	−	0.0194858i
$552$	−39.8975	−	69.1045i	−0.0722781	−	0.125189i
$553$	716.668	+	591.607i	1.29596	+	1.06981i
$554$			471.167i			0.850483i
$555$	565.179	−	978.918i	1.01834	−	1.76382i
$556$	43.4988	−	25.1141i	0.0782353	−	0.0451692i
$557$	388.499	−	224.300i	0.697485	−	0.402693i	−0.108925	−	0.994050i	$-0.534741\pi$
$557$	388.499	−	224.300i	0.697485	−	0.402693i	0.806410	+	0.591357i	$0.201408\pi$
$558$	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
$562$	−409.914			−0.729384
$563$			518.144i			0.920327i	0.887834	+	0.460164i	$0.152209\pi$
$563$			518.144i			0.920327i	−0.887834	+	0.460164i	$0.847791\pi$
$564$	−512.231	−	295.737i	−0.908211	−	0.524356i
$565$	−142.358	+	246.572i	−0.251961	+	0.436410i
$566$	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
$569$	−686.901			−1.20721			−0.603604	−	0.797285i	$-0.706269\pi$
$569$	−686.901			−1.20721			−0.603604	+	0.797285i	$0.706269\pi$
$570$	−451.320	−	781.709i	−0.791790	−	1.37142i
$571$	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	$-0.0237267\pi$
$572$	435.125	+	100.157i	0.760708	+	0.175100i
$573$		−	37.9443i		−	0.0662205i
$574$	−317.344	−	53.3305i	−0.552864	−	0.0929104i
$575$	−208.408	+	360.973i	−0.362448	+	0.627779i
$576$	−28.9394	+	50.1244i	−0.0502419	+	0.0870216i
$577$	−139.909	+	242.329i	−0.242476	+	0.419981i	−0.961419	−	0.275088i	$-0.911293\pi$
$577$	−139.909	+	242.329i	−0.242476	+	0.419981i	0.718943	+	0.695069i	$0.244626\pi$
$578$			389.571i			0.673998i
$579$	−69.2706	+	119.980i	−0.119638	+	0.207220i
$580$	13.2314			0.0228127
$581$	709.277	−	264.629i	1.22079	−	0.455472i
$582$	225.494	−	390.567i	0.387447	−	0.671078i
$583$			151.118i			0.259207i
$584$	−147.596	−	85.2146i	−0.252733	−	0.145915i
$585$	632.805	+	589.328i	1.08172	+	1.00740i
$586$	−311.008	+	179.561i	−0.530731	+	0.306417i
$587$	522.694	−	905.332i	0.890449	−	1.54230i	0.0511114	−	0.998693i	$-0.483724\pi$
$587$	522.694	−	905.332i	0.890449	−	1.54230i	0.839338	−	0.543610i	$-0.182943\pi$
$588$	−129.072	+	373.175i	−0.219510	+	0.634652i
$589$	−382.666	−	662.797i	−0.649688	−	1.12529i
$590$	−148.275	+	85.6066i	−0.251313	+	0.145096i
$591$	468.421			0.792590
$592$			122.052i			0.206169i
$593$	300.390	+	520.290i	0.506559	+	0.877387i	0.999971	+	0.00759089i	$0.00241628\pi$
$593$	300.390	+	520.290i	0.506559	+	0.877387i	−0.493412	+	0.869796i	$0.664250\pi$
$594$	−149.591	+	86.3664i	−0.251837	+	0.145398i
$595$	−150.716	+	182.576i	−0.253304	+	0.306850i
$596$	−267.078	−	154.197i	−0.448117	−	0.258720i
$597$	−201.395	−	348.826i	−0.337345	−	0.584299i
$598$	87.7292	−	94.2012i	0.146704	−	0.157527i
$599$	−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	$0.252121\pi$
$600$	678.432			1.13072
$601$	−906.763	−	523.520i	−1.50876	−	0.871082i	−0.999948	−	0.0102029i	$-0.996752\pi$
$601$	−906.763	−	523.520i	−1.50876	−	0.871082i	−0.508810	−	0.860879i	$-0.669914\pi$
$602$	338.109	−	409.582i	0.561643	−	0.680369i
$603$		−	201.007i		−	0.333345i
$604$	76.5923	+	44.2206i	0.126808	+	0.0732129i
$605$	−1599.02			−2.64300
$606$	−54.4484	−	31.4358i	−0.0898489	−	0.0518743i
$607$	−103.899	−	59.9859i	−0.171167	−	0.0988235i	0.411969	−	0.911198i	$-0.364841\pi$
$607$	−103.899	−	59.9859i	−0.171167	−	0.0988235i	−0.583136	+	0.812374i	$0.698175\pi$
$608$	84.4064	+	48.7321i	0.138826	+	0.0801514i
$609$	7.09435	+	19.0147i	0.0116492	+	0.0312229i
$610$	−150.865			−0.247320
$611$	214.034	−	929.852i	0.350301	−	1.52185i
$612$	−46.0967	−	26.6140i	−0.0753215	−	0.0434869i
$613$	11.5933	−	6.69339i	0.0189124	−	0.0109191i	−0.490514	−	0.871433i	$-0.663191\pi$
$613$	11.5933	−	6.69339i	0.0189124	−	0.0109191i	0.509426	+	0.860514i	$0.329858\pi$
$614$		−	385.530i		−	0.627898i
$615$	−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	0.0757935	−	0.997124i	$-0.475851\pi$
$617$	602.948	−	348.112i	0.977225	−	0.564201i	0.901431	+	0.432923i	$0.142518\pi$
$618$	792.654	+	457.639i	1.28261	+	0.740516i
$619$	459.302	−	795.534i	0.742006	−	1.28519i	−0.209574	−	0.977793i	$-0.567208\pi$
$619$	459.302	−	795.534i	0.742006	−	1.28519i	0.951580	−	0.307400i	$-0.0994589\pi$
$620$	816.801			1.31742
$621$			49.7983i			0.0801906i
$622$	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
$626$	202.692	+	351.072i	0.323789	+	0.560818i
$627$	−596.095	−	1032.47i	−0.950709	−	1.64668i
$628$	−224.743	−	129.756i	−0.357872	−	0.206617i
$629$	−112.245			−0.178450
$630$	230.181	+	616.947i	0.365367	+	0.979280i
$631$	610.860	−	352.680i	0.968082	−	0.558922i	0.0694309	−	0.997587i	$-0.477882\pi$
$631$	610.860	−	352.680i	0.968082	−	0.558922i	0.898651	+	0.438664i	$0.144548\pi$
$632$	−325.190	+	187.748i	−0.514541	+	0.297070i
$633$			1291.50i			2.04029i
$634$	58.9424	+	102.091i	0.0929691	+	0.161027i
$635$	−456.605			−0.719063
$636$		−	70.9117i		−	0.111496i
$637$	−636.596	−	22.6950i	−0.999365	−	0.0356279i
$638$	17.4757			0.0273914
$639$			214.126i			0.335096i
$640$	−90.0827	+	52.0093i	−0.140754	+	0.0812645i
$641$	792.995			1.23712			0.618560	−	0.785737i	$-0.287716\pi$
$641$	792.995			1.23712			0.618560	+	0.785737i	$0.287716\pi$
$642$	381.953	+	661.561i	0.594942	+	1.03047i
$643$	−420.524	−	728.369i	−0.654003	−	1.13277i	−0.982143	−	0.188137i	$-0.939755\pi$
$643$	−420.524	−	728.369i	−0.654003	−	1.13277i	0.328140	−	0.944629i	$-0.393578\pi$
$644$	91.8405	−	34.2655i	0.142609	−	0.0532072i
$645$		−	1987.47i		−	3.08134i
$646$	−44.8163	+	77.6240i	−0.0693750	+	0.120161i
$647$	518.738	−	299.493i	0.801759	−	0.462896i	−0.0423272	−	0.999104i	$-0.513477\pi$
$647$	518.738	−	299.493i	0.801759	−	0.462896i	0.844086	+	0.536208i	$0.180144\pi$
$648$	229.690	−	132.612i	0.354460	−	0.204648i
$649$	−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
$653$	−413.536			−0.633286			−0.316643	−	0.948545i	$-0.602556\pi$
$653$	−413.536			−0.633286			−0.316643	+	0.948545i	$0.602556\pi$
$654$		−	353.670i		−	0.540780i
$655$	1368.65	+	790.190i	2.08954	+	1.20640i
$656$	65.0122	−	112.604i	0.0991039	−	0.171653i
$657$	−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	0.872904	−	0.487893i	$-0.162234\pi$
$659$	9.17613	+	15.8935i	0.0139243	+	0.0241176i	−0.858979	+	0.512010i	$0.828901\pi$
$660$	1272.36			1.92782
$661$	487.981	+	845.208i	0.738246	+	1.27868i	0.953284	+	0.302075i	$0.0976792\pi$
$661$	487.981	+	845.208i	0.738246	+	1.27868i	−0.215038	+	0.976606i	$0.568988\pi$
$662$	−211.636	+	366.564i	−0.319692	+	0.553723i
$663$	43.2222	−	187.775i	0.0651918	−	0.283220i
$664$			305.888i			0.460675i
$665$	1038.90	−	387.611i	1.56225	−	0.582873i
$666$	−156.099	+	270.371i	−0.234383	+	0.405963i
$667$	2.51910	−	4.36321i	0.00377676	−	0.00654154i
$668$	140.081	−	242.628i	0.209703	−	0.363216i
$669$			1276.72i			1.90841i
$670$	180.623	−	312.849i	0.269587	−	0.466938i
$671$	−199.260			−0.296960
$672$	−123.043	−	101.571i	−0.183099	−	0.151148i
$673$	478.681	−	829.100i	0.711264	−	1.23195i	−0.253119	−	0.967435i	$-0.581456\pi$
$673$	478.681	−	829.100i	0.711264	−	1.23195i	0.964383	−	0.264511i	$-0.0852104\pi$
$674$		−	856.287i		−	1.27045i
$675$	−366.671	−	211.698i	−0.543216	−	0.313626i
$676$	−24.0179	−	337.146i	−0.0355294	−	0.498736i
$677$	−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
$679$	427.251	+	352.694i	0.629236	+	0.519432i
$680$	−47.8302	−	82.8443i	−0.0703385	−	0.121830i
$681$	492.368	−	284.269i	0.723007	−	0.417428i
$682$	1078.81			1.58184
$683$		−	397.466i		−	0.581942i	−0.956732	−	0.290971i	$-0.906022\pi$
$683$		−	397.466i		−	0.581942i	0.956732	−	0.290971i	$-0.0939783\pi$
$684$	124.652	+	215.903i	0.182240	+	0.315648i
$685$	−346.738	+	200.189i	−0.506187	+	0.292247i
$686$	−425.812	−	232.341i	−0.620717	−	0.338689i
$687$	−267.322	−	154.339i	−0.389115	−	0.224656i
$688$	107.300	+	185.849i	0.155959	+	0.270129i
$689$	109.375	−	33.5173i	0.158744	−	0.0486463i
$690$	183.409	−	317.674i	0.265811	−	0.460398i
$691$	−422.080			−0.610825			−0.305413	−	0.952220i	$-0.598794\pi$
$691$	−422.080			−0.610825			−0.305413	+	0.952220i	$0.598794\pi$
$692$	−523.627	−	302.316i	−0.756686	−	0.436873i
$693$	304.019	+	814.851i	0.438700	+	1.17583i
$694$			35.7409i			0.0514999i
$695$	199.965	+	115.450i	0.287719	+	0.166115i
$696$	−8.20045			−0.0117823
$697$	103.556	+	59.7882i	0.148574	+	0.0857793i
$698$	−676.113	−	390.354i	−0.968643	−	0.559247i
$699$	−959.146	−	553.763i	−1.37217	−	0.792222i
$700$	−138.122	+	821.898i	−0.197318	+	1.17414i
$701$	253.930			0.362240			0.181120	−	0.983461i	$-0.442028\pi$
$701$	253.930			0.362240			0.181120	+	0.983461i	$0.442028\pi$
$702$	95.6882	+	89.1140i	0.136308	+	0.126943i
$703$	455.288	+	262.861i	0.647636	+	0.373913i
$704$	−118.979	+	68.6928i	−0.169005	+	0.0975751i
$705$		−	2719.01i		−	3.85675i
$706$	−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
$709$	780.741	+	450.761i	1.10119	+	0.635770i	0.936532	−	0.350581i	$-0.114016\pi$
$709$	780.741	+	450.761i	1.10119	+	0.635770i	0.164654	+	0.986351i	$0.447349\pi$
$710$	−192.412	+	333.267i	−0.271003	+	0.469390i
$711$	−960.484			−1.35089
$712$		−	275.044i		−	0.386297i
$713$	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
$717$	−357.099	−	618.513i	−0.498046	−	0.862640i
$718$	−43.3936	−	75.1599i	−0.0604368	−	0.104680i
$719$	−941.586	−	543.625i	−1.30958	−	0.756085i	−0.327552	−	0.944833i	$-0.606224\pi$
$719$	−941.586	−	543.625i	−1.30958	−	0.756085i	−0.982025	+	0.188749i	$0.939557\pi$
$720$	−266.069			−0.369541
$721$	−715.791	+	867.103i	−0.992776	+	1.20264i
$722$	−78.5653	+	45.3597i	−0.108816	+	0.0628251i
$723$	−1116.14	+	644.405i	−1.54376	+	0.891293i
$724$		−	441.588i		−	0.609929i
$725$	21.4179	+	37.0968i	0.0295419	+	0.0511681i
$726$	991.029			1.36505
$727$			202.930i			0.279133i	0.990213	+	0.139566i	$0.0445709\pi$
$727$			202.930i			0.279133i	−0.990213	+	0.139566i	$0.955429\pi$
$728$	98.5067	−	237.791i	0.135311	−	0.326636i
$729$	420.502			0.576820
$730$		−	783.465i		−	1.07324i
$731$	−170.915	+	98.6780i	−0.233810	+	0.134990i
$732$	93.5024			0.127736
$733$	270.224	+	468.041i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464852\pi$
$733$	270.224	+	468.041i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$734$	291.465	+	504.832i	0.397091	+	0.687782i
$735$	−1782.33	+	343.896i	−2.42494	+	0.467885i
$736$			39.6079i			0.0538150i
$737$	238.564	−	413.204i	0.323695	−	0.560657i
$738$	288.031	−	166.295i	0.390286	−	0.225332i
$739$	−538.883	+	311.124i	−0.729206	+	0.421007i	−0.818132	−	0.575031i	$-0.804990\pi$
$739$	−538.883	+	311.124i	−0.729206	+	0.421007i	0.0889257	+	0.996038i	$0.471657\pi$
$740$	−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	0.705613	−	0.708598i	$-0.250672\pi$
$743$	330.453	+	190.787i	0.444755	+	0.256780i	−0.260857	+	0.965377i	$0.584005\pi$
$744$	−506.232			−0.680419
$745$		−	1417.69i		−	1.90295i
$746$	−205.655	−	118.735i	−0.275677	−	0.159162i
$747$	−391.216	+	677.607i	−0.523717	+	0.907104i
$748$	−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
$751$	−241.806			−0.321979			−0.160989	−	0.986956i	$-0.551469\pi$
$751$	−241.806			−0.321979			−0.160989	+	0.986956i	$0.551469\pi$
$752$	146.795	+	254.256i	0.195206	+	0.338107i
$753$	64.3281	−	111.420i	0.0854291	−	0.147968i
$754$	−3.87604	−	12.6484i	−0.00514064	−	0.0167751i
$755$			406.565i			0.538497i
$756$	34.8063	+	93.2902i	0.0460401	+	0.123400i
$757$	−277.724	+	481.032i	−0.366874	+	0.635445i	−0.989075	−	0.147413i	$-0.952905\pi$
$757$	−277.724	+	481.032i	−0.366874	+	0.635445i	0.622201	+	0.782858i	$0.286239\pi$
$758$	147.003	−	254.616i	0.193935	−	0.335906i
$759$	242.243	−	419.578i	0.319161	−	0.552804i
$760$			448.044i			0.589532i
$761$	450.886	−	780.958i	0.592492	−	1.02623i	−0.401404	−	0.915901i	$-0.631478\pi$
$761$	450.886	−	780.958i	0.592492	−	1.02623i	0.993896	−	0.110325i	$-0.0351890\pi$
$762$	282.992			0.371380
$763$	428.460	+	72.0039i	0.561546	+	0.0943695i
$764$	−9.41722	+	16.3111i	−0.0123262	+	0.0213496i
$765$		−	244.690i		−	0.319856i
$766$	−620.048	−	357.985i	−0.809463	−	0.467343i
$767$	125.271	+	116.664i	0.163326	+	0.152105i
$768$	55.8309	−	32.2340i	0.0726965	−	0.0419713i
$769$	27.1659	−	47.0527i	0.0353263	−	0.0611869i	−0.847822	−	0.530281i	$-0.822086\pi$
$769$	27.1659	−	47.0527i	0.0353263	−	0.0611869i	0.883148	+	0.469094i	$0.155420\pi$
$770$	−259.041	+	1541.43i	−0.336417	+	2.00185i
$771$	−73.7957	−	127.818i	−0.0957143	−	0.165782i
$772$	59.5546	−	34.3839i	0.0771433	−	0.0445387i
$773$	−484.904			−0.627301			−0.313651	−	0.949538i	$-0.601552\pi$
$773$	−484.904			−0.627301			−0.313651	+	0.949538i	$0.601552\pi$
$774$			548.925i			0.709206i
$775$	1322.17	+	2290.07i	1.70603	+	2.95493i
$776$	−193.866	+	111.929i	−0.249828	+	0.144238i
$777$	−663.692	−	547.876i	−0.854172	−	0.705117i
$778$	−325.362	−	187.848i	−0.418203	−	0.241450i
$779$	−280.030	−	485.026i	−0.359474	−	0.622627i
$780$	−282.205	−	920.901i	−0.361801	−	1.18064i
$781$	−254.134	+	440.172i	−0.325395	+	0.563601i
$782$	−36.4252			−0.0465796
$783$	4.43208	+	2.55886i	0.00566038	+	0.00326802i
$784$	148.101	−	128.383i	0.188904	−	0.163754i
$785$		−	1192.98i		−	1.51972i
$786$	−848.253	−	489.739i	−1.07920	−	0.623077i
$787$	−617.635			−0.784797			−0.392398	−	0.919795i	$-0.628354\pi$
$787$	−617.635			−0.784797			−0.392398	+	0.919795i	$0.628354\pi$
$788$	−201.360	−	116.255i	−0.255533	−	0.147532i
$789$	1473.96	+	850.992i	1.86814	+	1.07857i
$790$	−1494.90	−	863.083i	−1.89228	−	1.09251i
$791$	167.172	+	138.000i	0.211342	+	0.174463i
$792$	−351.419			−0.443711
$793$	44.1950	+	144.219i	0.0557315	+	0.181865i
$794$	240.657	+	138.943i	0.303095	+	0.174992i
$795$	282.309	−	162.991i	0.355106	−	0.205020i
$796$			199.933i			0.251172i
$797$	−45.6634	+	26.3638i	−0.0572941	+	0.0330788i	−0.528373	−	0.849012i	$-0.677198\pi$
$797$	−45.6634	+	26.3638i	−0.0572941	+	0.0330788i	0.471079	+	0.882091i	$0.343865\pi$
$798$	−643.882	+	240.231i	−0.806870	+	0.301041i
$799$	−233.826	+	134.999i	−0.292648	+	0.168960i
$800$	−291.637	−	168.377i	−0.364547	−	0.210471i
$801$	351.767	−	609.279i	0.439160	−	0.760648i
$802$	25.9285			0.0323299
$803$		−	1034.79i		−	1.28865i
$804$	−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
$808$	15.6038	+	27.0266i	0.0193116	+	0.0334487i
$809$	311.964	+	540.338i	0.385617	+	0.667909i	0.991855	−	0.127375i	$-0.0406552\pi$
$809$	311.964	+	540.338i	0.385617	+	0.667909i	−0.606237	+	0.795284i	$0.707322\pi$
$810$	1055.89	+	609.618i	1.30357	+	0.752615i
$811$	10.3713			0.0127882			0.00639412	−	0.999980i	$-0.497965\pi$
$811$	10.3713			0.0127882			0.00639412	+	0.999980i	$0.497965\pi$
$812$	1.66953	−	9.93457i	0.00205608	−	0.0122347i
$813$	−1285.75	+	742.327i	−1.58149	+	0.913071i
$814$	−641.775	+	370.529i	−0.788421	+	0.455195i
$815$			1970.68i			2.41801i
$816$	29.6439	+	51.3447i	0.0363283	+	0.0629224i
$817$	924.356			1.13140
$818$			78.0734i			0.0954442i
$819$	522.336	−	400.771i	0.637772	−	0.489341i
$820$	597.724			0.728932
$821$			97.1595i			0.118343i	0.998248	+	0.0591715i	$0.0188459\pi$
$821$			97.1595i			0.118343i	−0.998248	+	0.0591715i	$0.981154\pi$
$822$	214.899	−	124.072i	0.261434	−	0.150939i
$823$	−872.335			−1.05995			−0.529973	−	0.848015i	$-0.677798\pi$
$823$	−872.335			−1.05995			−0.529973	+	0.848015i	$0.677798\pi$
$824$	−227.159	−	393.450i	−0.275678	−	0.477488i
$825$	2059.60	+	3567.33i	2.49649	+	4.32404i
$826$	45.5671	+	122.132i	0.0551659	+	0.147859i
$827$		−	246.854i		−	0.298493i	−0.988800	−	0.149247i	$-0.952315\pi$
$827$		−	246.854i		−	0.298493i	0.988800	−	0.149247i	$-0.0476848\pi$
$828$	−50.6565	+	87.7397i	−0.0611794	+	0.105966i
$829$	511.303	−	295.201i	0.616771	−	0.356093i	−0.158840	−	0.987304i	$-0.550775\pi$
$829$	511.303	−	295.201i	0.616771	−	0.356093i	0.775611	+	0.631211i	$0.217442\pi$
$830$	−1217.78	+	703.087i	−1.46721	+	0.847093i
$831$	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
$835$	1287.91			1.54241
$836$			591.768i			0.707856i
$837$	273.602	+	157.964i	0.326884	+	0.188727i
$838$	−486.141	+	842.022i	−0.580121	+	1.00480i
$839$	186.954	+	323.815i	0.222830	+	0.385953i	0.955666	−	0.294452i	$-0.0951372\pi$
$839$	186.954	+	323.815i	0.222830	+	0.385953i	−0.732836	+	0.680405i	$0.761804\pi$
$840$	121.555	−	723.312i	0.144708	−	0.861085i
$841$	420.241	+	727.879i	0.499692	+	0.865492i
$842$	−826.361			−0.981427
$843$	583.945	+	1011.42i	0.692698	+	1.19979i
$844$	320.532	−	555.178i	0.379778	−	0.657794i
$845$	1287.02	−	870.550i	1.52310	−	1.03024i
$846$			750.974i			0.887676i
$847$	−201.764	+	1200.60i	−0.238210	+	1.41747i
$848$	−17.5992	+	30.4828i	−0.0207538	+	0.0359467i
$849$	31.3288	−	54.2631i	0.0369008	−	0.0639141i
$850$	154.847	−	268.203i	0.182173	−	0.315533i
$851$			213.645i			0.251051i
$852$	119.252	−	206.550i	0.139967	−	0.242430i
$853$	−1444.14			−1.69301			−0.846506	−	0.532379i	$-0.821298\pi$
$853$	−1444.14			−1.69301			−0.846506	+	0.532379i	$0.821298\pi$
$854$	−19.0362	+	113.275i	−0.0222906	+	0.132641i
$855$	−573.026	+	992.511i	−0.670206	+	1.16083i
$856$		−	379.180i		−	0.442967i
$857$	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	$0.524315\pi$
$858$	−372.731	−	1216.31i	−0.434418	−	1.41761i
$859$	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
$861$	320.486	+	858.987i	0.372225	+	0.997662i
$862$	−2.32305	−	4.02364i	−0.00269495	−	0.00466780i
$863$	301.249	−	173.926i	0.349071	−	0.201536i	−0.315205	−	0.949024i	$-0.602073\pi$
$863$	301.249	−	173.926i	0.349071	−	0.201536i	0.664276	+	0.747487i	$0.268740\pi$
$864$	−40.2331			−0.0465661
$865$		−	2779.50i		−	3.21330i
$866$	199.584	+	345.690i	0.230467	+	0.399181i
$867$	961.227	−	554.964i	1.10868	−	0.640097i
$868$	103.064	−	613.283i	0.118737	−	0.706547i
$869$	−1974.44	−	1139.94i	−2.27208	−	1.31179i
$870$	−18.8488	−	32.6471i	−0.0216653	−	0.0375254i
$871$	−351.978	−	81.0185i	−0.404108	−	0.0930178i
$872$	−87.7758	+	152.032i	−0.100660	+	0.174349i
$873$	−572.605			−0.655905
$874$	147.748	+	85.3024i	0.169048	+	0.0976000i
$875$	−2082.11	+	776.829i	−2.37955	+	0.887805i
$876$			485.571i			0.554305i
$877$	779.140	+	449.837i	0.888415	+	0.512926i	0.873424	−	0.486961i	$-0.161895\pi$
$877$	779.140	+	449.837i	0.888415	+	0.512926i	0.0149911	+	0.999888i	$0.495228\pi$
$878$	495.824			0.564720
$879$	886.096	+	511.588i	1.00807	+	0.582011i
$880$	−546.951	−	315.782i	−0.621535	−	0.358843i
$881$	−222.311	−	128.352i	−0.252340	−	0.145688i	0.368495	−	0.929630i	$-0.379873\pi$
$881$	−222.311	−	128.352i	−0.252340	−	0.145688i	−0.620835	+	0.783941i	$0.713206\pi$
$882$	492.269	−	94.9818i	0.558128	−	0.107689i
$883$	−774.664			−0.877309			−0.438654	−	0.898656i	$-0.644545\pi$
$883$	−774.664			−0.877309			−0.438654	+	0.898656i	$0.644545\pi$
$884$	−65.1828	+	69.9916i	−0.0737362	+	0.0791760i
$885$	422.451	+	243.902i	0.477346	+	0.275596i
$886$	−38.9368	+	22.4802i	−0.0439467	+	0.0253727i
$887$		−	604.756i		−	0.681800i	−0.940100	−	0.340900i	$-0.889268\pi$
$887$		−	604.756i		−	0.681800i	0.940100	−	0.340900i	$-0.110732\pi$
$888$	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
$891$	1394.60	+	805.172i	1.56521	+	0.903672i
$892$	316.864	−	548.825i	0.355229	−	0.615274i
$893$	1264.59			1.41612
$894$			878.650i			0.982830i
$895$	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
$899$	−15.9816	−	27.6809i	−0.0177770	−	0.0307907i
$900$	−430.692	−	745.980i	−0.478546	−	0.828866i
$901$	−28.0334	−	16.1851i	−0.0311136	−	0.0179635i
$902$	789.462			0.875235
$903$	−1492.26	−	250.778i	−1.65256	−	0.277717i
$904$	−75.8546	+	43.7947i	−0.0839100	+	0.0484454i
$905$	1758.02	−	1014.99i	1.94257	−	1.12154i
$906$		−	251.978i		−	0.278122i
$907$	62.1926	+	107.721i	0.0685696	+	0.118766i	0.898272	−	0.439440i	$-0.144823\pi$
$907$	62.1926	+	107.721i	0.0685696	+	0.118766i	−0.829702	+	0.558206i	$0.811490\pi$
$908$	−282.205			−0.310799
$909$			79.8260i			0.0878174i
$910$	1173.09	−	154.395i	1.28912	−	0.169665i
$911$	1162.26			1.27580			0.637902	−	0.770117i	$-0.279802\pi$
$911$	1162.26			1.27580			0.637902	+	0.770117i	$0.279802\pi$
$912$		−	277.686i		−	0.304480i
$913$	−1608.42	+	928.623i	−1.76169	+	1.01711i
$914$	−137.226			−0.150138
$915$	214.916	+	372.245i	0.234881	+	0.406826i
$916$	76.6091	+	132.691i	0.0836344	+	0.144859i
$917$	765.998	−	927.923i	0.835331	−	1.01191i
$918$		−	37.0002i		−	0.0403052i
$919$	−143.941	+	249.312i	−0.156627	+	0.271287i	−0.933650	−	0.358186i	$-0.883396\pi$
$919$	−143.941	+	249.312i	−0.156627	+	0.271287i	0.777023	+	0.629472i	$0.216729\pi$
$920$	−157.684	+	91.0390i	−0.171396	+	0.0989554i
$921$	−951.256	+	549.208i	−1.03285	+	0.596317i
$922$	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
$926$	806.539			0.870992
$927$		−	1162.10i		−	1.25361i
$928$	3.52512	+	2.03523i	0.00379862	+	0.00219314i
$929$	−536.089	+	928.534i	−0.577061	+	0.999498i	0.418754	+	0.908100i	$0.362467\pi$
$929$	−536.089	+	928.534i	−0.577061	+	0.999498i	−0.995814	+	0.0913984i	$0.970866\pi$
$930$	−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
$933$	−1166.05			−1.24978
$934$	−75.1325	−	130.133i	−0.0804417	−	0.139329i
$935$	290.408	−	503.001i	0.310597	−	0.537969i
$936$	77.9433	+	254.347i	0.0832727	+	0.271738i
$937$			980.365i			1.04628i	0.852247	+	0.523140i	$0.175240\pi$
$937$			980.365i			1.04628i	−0.852247	+	0.523140i	$0.824760\pi$
$938$	−212.107	−	175.093i	−0.226126	−	0.186667i
$939$	577.491	−	1000.24i	0.615006	−	1.06522i
$940$	−674.819	+	1168.82i	−0.717892	+	1.24343i
$941$	355.761	−	616.197i	0.378067	−	0.654832i	−0.612714	−	0.790305i	$-0.709922\pi$
$941$	355.761	−	616.197i	0.378067	−	0.654832i	0.990781	+	0.135473i	$0.0432554\pi$
$942$			739.376i			0.784900i
$943$	113.800	−	197.107i	0.120678	−	0.209021i
$944$	−52.6715			−0.0557961
$945$	−291.398	+	352.997i	−0.308358	+	0.373542i
$946$	−651.487	+	1128.41i	−0.688676	+	1.19282i
$947$			1060.33i			1.11967i	0.828603	+	0.559836i	$0.189136\pi$
$947$			1060.33i			1.11967i	−0.828603	+	0.559836i	$0.810864\pi$
$948$	926.501	+	534.916i	0.977322	+	0.564257i
$949$	−748.948	+	229.511i	−0.789197	+	0.241845i
$950$	−1256.18	+	725.258i	−1.32230	+	0.763429i
$951$	167.933	−	290.869i	0.176586	−	0.305856i
$952$	−68.2376	+	25.4593i	−0.0716781	+	0.0267429i
$953$	241.380	+	418.082i	0.253284	+	0.438701i	0.964428	−	0.264345i	$-0.0851559\pi$
$953$	241.380	+	418.082i	0.253284	+	0.438701i	−0.711144	+	0.703046i	$0.751823\pi$
$954$	−77.9720	+	45.0171i	−0.0817316	+	0.0471878i
$955$	−86.5822			−0.0906620
$956$			354.507i			0.370823i
$957$	−24.8951	−	43.1196i	−0.0260137	−	0.0450571i
$958$	−40.7151	+	23.5069i	−0.0425001	+	0.0245375i
$959$	106.558	+	285.603i	0.111113	+	0.297813i
$960$	256.656	+	148.180i	0.267350	+	0.154354i
$961$	−506.076	−	876.550i	−0.526614	−	0.912123i
$962$	410.521	+	382.317i	0.426737	+	0.397419i
$963$	484.953	−	839.963i	0.503585	−	0.872235i
$964$	639.727			0.663617
$965$	273.774	+	158.063i	0.283703	+	0.163796i
$966$	−215.378	−	177.794i	−0.222959	−	0.184052i
$967$		−	477.346i		−	0.493636i	−0.969062	−	0.246818i	$-0.920615\pi$
$967$		−	477.346i		−	0.493636i	0.969062	−	0.246818i	$-0.0793849\pi$
$968$	−426.013	−	245.959i	−0.440096	−	0.254090i
$969$	255.373			0.263543
$970$	−891.206	−	514.538i	−0.918769	−	0.530451i
$971$	−622.642	−	359.482i	−0.641237	−	0.370219i	0.143854	−	0.989599i	$-0.454051\pi$
$971$	−622.642	−	359.482i	−0.641237	−	0.370219i	−0.785091	+	0.619380i	$0.787384\pi$
$972$	−543.543	−	313.815i	−0.559201	−	0.322855i
$973$	111.915	−	135.573i	0.115021	−	0.139335i
$974$	509.149			0.522740
$975$	2125.12	−	2281.90i	2.17961	−	2.34041i
$976$	−40.1938	−	23.2059i	−0.0411822	−	0.0237766i
$977$	−272.518	+	157.338i	−0.278933	+	0.161042i	−0.632940	−	0.774201i	$-0.718152\pi$
$977$	−272.518	+	157.338i	−0.278933	+	0.161042i	0.354007	+	0.935243i	$0.384819\pi$
$978$		−	1221.37i		−	1.24885i
$979$	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
$982$	594.542	+	343.259i	0.605440	+	0.349551i
$983$	542.737	−	940.049i	0.552123	−	0.956306i	−0.445998	−	0.895034i	$-0.647151\pi$
$983$	542.737	−	940.049i	0.552123	−	0.956306i	0.998121	−	0.0612717i	$-0.0195156\pi$
$984$	−370.454			−0.376477
$985$		−	1068.85i		−	1.08513i
$986$	−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
$990$	−807.740	−	1399.05i	−0.815899	−	1.41318i
$991$	71.7454	+	124.267i	0.0723970	+	0.125395i	0.899951	−	0.435990i	$-0.143602\pi$
$991$	71.7454	+	124.267i	0.0723970	+	0.125395i	−0.827554	+	0.561386i	$0.810268\pi$
$992$	217.614	+	125.639i	0.219369	+	0.126652i
$993$	1205.95			1.21445
$994$	225.950	+	186.521i	0.227314	+	0.187647i
$995$	−795.960	+	459.548i	−0.799960	+	0.461857i
$996$	754.749	−	435.755i	0.757780	−	0.437505i
$997$		−	1390.84i		−	1.39502i	−0.716574	−	0.697511i	$-0.754291\pi$
$997$		−	1390.84i		−	1.39502i	0.716574	−	0.697511i	$-0.245709\pi$
$998$	−241.266	−	417.886i	−0.241750	−	0.418723i
$999$	−217.017			−0.217234

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.3.k.a.101.17	✓	36	13.10	even	6
182.3.k.a.173.11	yes	36	7.5	odd	6
182.3.r.a.17.17	yes	36	1.1	even	1	trivial
182.3.r.a.75.8	yes	36	91.75	odd	6	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(3.48943 - 2.01462i) q^{3} -2.00000 q^{4} +(-4.59702 - 7.96227i) q^{5} +(2.84911 + 4.93480i) q^{6} +(-6.55840 + 2.44692i) q^{7} -2.82843i q^{8} +(3.61742 - 6.26555i) q^{9} +(11.2603 - 6.50116i) q^{10} +(14.8724 - 8.58660i) 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} +4.00000 q^{16} +3.67858i q^{17} +(8.86083 + 5.11580i) q^{18} +(8.61469 - 14.9211i) q^{19} +(9.19403 + 15.9245i) q^{20} +(-17.9554 + 21.7511i) q^{21} +(12.1433 + 21.0328i) q^{22} +7.00175 q^{23} +(-5.69822 - 9.86960i) q^{24} +(-29.7651 + 51.5547i) q^{25} +(12.5296 - 13.4540i) q^{26} +7.11227i q^{27} +(13.1168 - 4.89384i) q^{28} +(0.359781 - 0.623160i) q^{29} +(26.1948 - 45.3707i) q^{30} +(22.2101 - 38.4690i) q^{31} +5.65685i q^{32} +(34.5976 - 59.9247i) q^{33} -5.20230 q^{34} +(49.6321 + 40.9712i) q^{35} +(-7.23484 + 12.5311i) q^{36} +30.5131i q^{37} +(21.1016 + 12.1830i) q^{38} +(-51.0454 - 11.7497i) q^{39} +(-22.5207 + 13.0023i) q^{40} +(16.2530 - 28.1511i) q^{41} +(-30.7607 - 25.3928i) q^{42} +(26.8250 + 46.4622i) q^{43} +(-29.7449 + 17.1732i) q^{44} -66.5173 q^{45} +9.90197i q^{46} +(36.6987 + 63.5641i) q^{47} +(13.9577 - 8.05850i) q^{48} +(37.0251 - 32.0958i) q^{49} +(-72.9093 - 42.0942i) q^{50} +(7.41096 + 12.8362i) q^{51} +(19.0268 + 17.7195i) q^{52} +(-4.39981 + 7.62069i) q^{53} -10.0583 q^{54} +(-136.738 - 78.9455i) q^{55} +(6.92094 + 18.5499i) q^{56} -69.4215i q^{57} +(0.881281 + 0.508808i) q^{58} -13.1679 q^{59} +(64.1639 + 37.0450i) q^{60} +(-10.0485 - 5.80148i) q^{61} +(54.4034 + 31.4098i) q^{62} +(-8.39315 + 49.9435i) q^{63} -8.00000 q^{64} +(-26.8107 + 116.477i) q^{65} +(84.7464 + 48.9283i) q^{66} +(24.0610 - 13.8916i) q^{67} -7.35717i q^{68} +(24.4321 - 14.1059i) q^{69} +(-57.9420 + 70.1904i) q^{70} +(-25.6313 + 14.7983i) q^{71} +(-17.7217 - 10.2316i) q^{72} +(30.1279 - 52.1831i) q^{73} -43.1520 q^{74} +239.862i 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} +(-18.3881 - 31.8491i) q^{80} +(46.8853 + 81.2078i) q^{81} +(39.8117 + 22.9853i) q^{82} -108.148 q^{83} +(35.9109 - 43.5021i) q^{84} +(29.2899 - 16.9105i) q^{85} +(-65.7075 + 37.9363i) q^{86} -2.89930i q^{87} +(-24.2866 - 42.0656i) q^{88} +97.2426 q^{89} -94.0697i q^{90} +(84.0717 + 34.8274i) q^{91} -14.0035 q^{92} -178.980i q^{93} +(-89.8932 + 51.8998i) q^{94} -158.408 q^{95} +(11.3964 + 19.7392i) q^{96} +(-39.5728 - 68.5420i) q^{97} +(45.3903 + 52.3615i) q^{98} -124.245i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{3} - 72 q^{4} + 8 q^{7} + 44 q^{9} + 12 q^{11} - 12 q^{12} + 4 q^{13} - 12 q^{14} + 60 q^{15} + 144 q^{16} + 24 q^{18} + 50 q^{19} + 42 q^{21} + 12 q^{22} - 56 q^{23} - 82 q^{25} + 48 q^{26}+ \cdots - 24 q^{98}+O(q^{100}) \) 36 * q + 6 * q^3 - 72 * q^4 + 8 * q^7 + 44 * q^9 + 12 * q^11 - 12 * q^12 + 4 * q^13 - 12 * q^14 + 60 * q^15 + 144 * q^16 + 24 * q^18 + 50 * q^19 + 42 * q^21 + 12 * q^22 - 56 * q^23 - 82 * q^25 + 48 * q^26 - 16 * q^28 + 40 * q^29 + 56 * q^30 + 10 * q^31 - 96 * q^33 - 20 * q^35 - 88 * q^36 + 60 * q^38 - 348 * q^39 + 90 * q^41 - 176 * q^42 + 20 * q^43 - 24 * q^44 + 108 * q^47 + 24 * q^48 - 36 * q^49 - 192 * q^50 - 36 * q^51 - 8 * q^52 - 218 * q^53 + 288 * q^54 - 282 * q^55 + 24 * q^56 + 144 * q^58 - 120 * q^60 + 354 * q^61 + 180 * q^62 + 66 * q^63 - 288 * q^64 + 340 * q^65 + 96 * q^66 + 30 * q^67 - 18 * q^69 - 144 * q^70 - 18 * q^71 - 48 * q^72 - 74 * q^73 - 48 * q^74 - 100 * q^76 - 174 * q^77 - 320 * q^78 - 352 * q^79 - 34 * q^81 - 192 * q^82 - 708 * q^83 - 84 * q^84 - 204 * q^85 + 36 * q^86 - 24 * q^88 + 852 * q^89 + 4 * q^91 + 112 * q^92 + 252 * q^94 - 40 * q^95 - 64 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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