LMFDB - Embedded newform 117.3.bb.a.76.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(7,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 11]))

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

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

chi := DirichletCharacter("117.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.bb (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.24
Character	$\chi$	$=$	117.76
Dual form			117.3.bb.a.97.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.36624 - 0.901981i) q^{2} +(2.98988 + 0.246189i) q^{3} +(7.05390 - 4.07257i) q^{4} +(-8.54788 + 2.29040i) q^{5} +(10.2867 - 1.86808i) q^{6} +(-1.24140 + 1.24140i) q^{7} +(10.2147 - 10.2147i) q^{8} +(8.87878 + 1.47215i) q^{9} +(-26.7083 + 15.4201i) q^{10} +(-3.67551 - 13.7172i) q^{11} +(22.0930 - 10.4399i) q^{12} +(0.387122 + 12.9942i) q^{13} +(-3.05913 + 5.29856i) q^{14} +(-26.1210 + 4.74362i) q^{15} +(8.88141 - 15.3831i) q^{16} +(-7.58364 - 4.37842i) q^{17} +(31.2160 - 3.05287i) q^{18} +(-12.9554 + 3.47139i) q^{19} +(-50.9681 + 50.9681i) q^{20} +(-4.01725 + 3.40601i) q^{21} +(-24.7453 - 42.8602i) q^{22} +16.8226i q^{23} +(33.0555 - 28.0260i) q^{24} +(46.1697 - 26.6561i) q^{25} +(13.0237 + 43.3925i) q^{26} +(26.1841 + 6.58743i) q^{27} +(-3.70102 + 13.8124i) q^{28} +(20.5574 - 35.6065i) q^{29} +(-83.6510 + 39.5288i) q^{30} +(6.32358 - 1.69440i) q^{31} +(1.06636 - 3.97970i) q^{32} +(-7.61232 - 41.9177i) q^{33} +(-29.4776 - 7.89851i) q^{34} +(7.76803 - 13.4546i) q^{35} +(68.6255 - 25.7751i) q^{36} +(35.5862 + 9.53529i) q^{37} +(-40.4799 + 23.3711i) q^{38} +(-2.04160 + 38.9465i) q^{39} +(-63.9184 + 110.710i) q^{40} +(-38.2367 - 38.2367i) q^{41} +(-10.4509 + 15.0890i) q^{42} -13.5933i q^{43} +(-81.7910 - 81.7910i) q^{44} +(-79.2666 + 7.75214i) q^{45} +(15.1737 + 56.6290i) q^{46} +(43.2515 + 11.5892i) q^{47} +(30.3415 - 43.8070i) q^{48} +45.9179i q^{49} +(131.375 - 131.375i) q^{50} +(-21.5963 - 14.9580i) q^{51} +(55.6507 + 90.0835i) q^{52} +38.3056 q^{53} +(94.0836 - 1.44268i) q^{54} +(62.8357 + 108.835i) q^{55} +25.3611i q^{56} +(-39.5897 + 7.18956i) q^{57} +(37.0848 - 138.403i) q^{58} +(-10.3255 - 2.76672i) q^{59} +(-164.936 + 139.841i) q^{60} -34.3952 q^{61} +(19.7584 - 11.4075i) q^{62} +(-12.8496 + 9.19458i) q^{63} +56.6928i q^{64} +(-33.0710 - 110.186i) q^{65} +(-63.4339 - 134.239i) q^{66} +(-61.0077 - 61.0077i) q^{67} -71.3257 q^{68} +(-4.14155 + 50.2976i) q^{69} +(14.0132 - 52.2981i) q^{70} +(-108.463 + 29.0626i) q^{71} +(105.732 - 75.6566i) q^{72} +(60.2281 - 60.2281i) q^{73} +128.392 q^{74} +(144.604 - 68.3320i) q^{75} +(-77.2486 + 77.2486i) q^{76} +(21.5913 + 12.4657i) q^{77} +(28.2565 + 132.945i) q^{78} +(3.19706 + 5.53747i) q^{79} +(-40.6839 + 151.834i) q^{80} +(76.6655 + 26.1419i) q^{81} +(-163.203 - 94.2252i) q^{82} +(-3.70698 + 13.8346i) q^{83} +(-14.4661 + 40.3863i) q^{84} +(74.8524 + 20.0566i) q^{85} +(-12.2609 - 45.7582i) q^{86} +(70.2302 - 101.398i) q^{87} +(-177.662 - 102.573i) q^{88} +(-30.6602 - 8.21537i) q^{89} +(-259.838 + 97.5925i) q^{90} +(-16.6116 - 15.6505i) q^{91} +(68.5113 + 118.665i) q^{92} +(19.3239 - 3.50925i) q^{93} +156.048 q^{94} +(102.790 - 59.3460i) q^{95} +(4.16804 - 11.6363i) q^{96} +(133.294 + 133.294i) q^{97} +(41.4171 + 154.571i) q^{98} +(-12.4402 - 127.203i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 2 q^{5} + 10 q^{6} - 6 q^{7} + 18 q^{8} - 2 q^{9} - 12 q^{10} - 14 q^{11} - 54 q^{12} - 2 q^{13} - 4 q^{14} - 44 q^{15} + 162 q^{16} - 12 q^{17} + 34 q^{18} - 36 q^{19}+ \cdots - 524 q^{99}+O(q^{100}) $ 104 * q - 2 * q^2 - 2 * q^3 - 6 * q^4 - 2 * q^5 + 10 * q^6 - 6 * q^7 + 18 * q^8 - 2 * q^9 - 12 * q^10 - 14 * q^11 - 54 * q^12 - 2 * q^13 - 4 * q^14 - 44 * q^15 + 162 * q^16 - 12 * q^17 + 34 * q^18 - 36 * q^19 - 82 * q^20 + 106 * q^21 + 2 * q^22 - 66 * q^24 + 52 * q^26 + 4 * q^27 + 56 * q^28 + 74 * q^29 - 438 * q^30 - 34 * q^31 + 22 * q^32 - 68 * q^33 + 6 * q^34 - 106 * q^35 - 6 * q^36 + 14 * q^37 - 216 * q^38 - 176 * q^39 - 36 * q^40 - 26 * q^41 - 220 * q^42 + 496 * q^44 - 50 * q^45 + 118 * q^47 + 130 * q^48 + 92 * q^50 + 76 * q^52 - 208 * q^53 + 904 * q^54 - 4 * q^55 - 86 * q^57 - 76 * q^58 + 430 * q^59 - 358 * q^60 - 4 * q^61 - 282 * q^62 - 326 * q^63 + 406 * q^65 - 412 * q^66 - 72 * q^67 - 1068 * q^68 + 204 * q^69 - 106 * q^70 - 8 * q^71 - 642 * q^72 + 90 * q^73 + 356 * q^74 + 204 * q^75 - 194 * q^76 + 432 * q^77 + 646 * q^78 - 16 * q^79 - 278 * q^80 - 182 * q^81 - 12 * q^82 - 536 * q^83 + 310 * q^84 - 234 * q^85 + 414 * q^86 + 434 * q^87 - 6 * q^88 + 400 * q^89 + 798 * q^90 + 120 * q^91 + 48 * q^92 - 116 * q^93 - 244 * q^94 + 858 * q^95 + 1528 * q^96 + 344 * q^97 + 280 * q^98 - 524 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.36624	−	0.901981i	1.68312	−	0.450991i	0.714520	−	0.699615i	$-0.246645\pi$
$2$	3.36624	−	0.901981i	1.68312	−	0.450991i	0.968600	+	0.248624i	$0.0799784\pi$
$3$	2.98988	+	0.246189i	0.996627	+	0.0820632i
$3$	2.98988	+	0.246189i	0.996627	+	0.0820632i
$4$	7.05390	−	4.07257i	1.76348	−	1.01814i
$5$	−8.54788	+	2.29040i	−1.70958	+	0.458079i	−0.975321	−	0.220794i	$-0.929135\pi$
$5$	−8.54788	+	2.29040i	−1.70958	+	0.458079i	−0.734255	+	0.678873i	$0.762469\pi$
$6$	10.2867	−	1.86808i	1.71445	−	0.311347i
$7$	−1.24140	+	1.24140i	−0.177343	+	0.177343i	−0.790196	−	0.612854i	$-0.790021\pi$
$7$	−1.24140	+	1.24140i	−0.177343	+	0.177343i	0.612854	+	0.790196i	$0.290021\pi$
$8$	10.2147	−	10.2147i	1.27684	−	1.27684i
$9$	8.87878	+	1.47215i	0.986531	+	0.163573i
$10$	−26.7083	+	15.4201i	−2.67083	+	1.54201i
$11$	−3.67551	−	13.7172i	−0.334138	−	1.24702i	−0.904801	−	0.425835i	$-0.859981\pi$
$11$	−3.67551	−	13.7172i	−0.334138	−	1.24702i	0.570663	−	0.821184i	$-0.306686\pi$
$12$	22.0930	−	10.4399i	1.84108	−	0.869993i
$13$	0.387122	+	12.9942i	0.0297786	+	0.999557i
$13$	0.387122	+	12.9942i	0.0297786	+	0.999557i
$14$	−3.05913	+	5.29856i	−0.218509	+	0.378469i
$15$	−26.1210	+	4.74362i	−1.74140	+	0.316241i
$16$	8.88141	−	15.3831i	0.555088	−	0.961441i
$17$	−7.58364	−	4.37842i	−0.446097	−	0.257554i	0.260084	−	0.965586i	$-0.416250\pi$
$17$	−7.58364	−	4.37842i	−0.446097	−	0.257554i	−0.706180	+	0.708032i	$0.749583\pi$
$18$	31.2160	−	3.05287i	1.73422	−	0.169604i
$19$	−12.9554	+	3.47139i	−0.681863	+	0.182705i	−0.583093	−	0.812406i	$-0.698158\pi$
$19$	−12.9554	+	3.47139i	−0.681863	+	0.182705i	−0.0987703	+	0.995110i	$0.531491\pi$
$20$	−50.9681	+	50.9681i	−2.54841	+	2.54841i
$21$	−4.01725	+	3.40601i	−0.191298	+	0.162191i
$22$	−24.7453	−	42.8602i	−1.12479	−	1.94819i
$23$			16.8226i			0.731418i	0.930729	+	0.365709i	$0.119173\pi$
$23$			16.8226i			0.731418i	−0.930729	+	0.365709i	$0.880827\pi$
$24$	33.0555	−	28.0260i	1.37731	−	1.16775i
$25$	46.1697	−	26.6561i	1.84679	−	1.06624i
$26$	13.0237	+	43.3925i	0.500912	+	1.66894i
$27$	26.1841	+	6.58743i	0.969781	+	0.243979i
$28$	−3.70102	+	13.8124i	−0.132179	+	0.493300i
$29$	20.5574	−	35.6065i	0.708877	−	1.22781i	−0.256397	−	0.966572i	$-0.582535\pi$
$29$	20.5574	−	35.6065i	0.708877	−	1.22781i	0.965274	−	0.261239i	$-0.0841312\pi$
$30$	−83.6510	+	39.5288i	−2.78837	+	1.31763i
$31$	6.32358	−	1.69440i	0.203986	−	0.0546580i	−0.155379	−	0.987855i	$-0.549660\pi$
$31$	6.32358	−	1.69440i	0.203986	−	0.0546580i	0.359365	+	0.933197i	$0.382993\pi$
$32$	1.06636	−	3.97970i	0.0333237	−	0.124366i
$33$	−7.61232	−	41.9177i	−0.230676	−	1.27023i
$34$	−29.4776	−	7.89851i	−0.866989	−	0.232309i
$35$	7.76803	−	13.4546i	0.221944	−	0.384418i
$36$	68.6255	−	25.7751i	1.90626	−	0.715974i
$37$	35.5862	+	9.53529i	0.961789	+	0.257711i	0.705357	−	0.708852i	$-0.250787\pi$
$37$	35.5862	+	9.53529i	0.961789	+	0.257711i	0.256432	+	0.966562i	$0.417453\pi$
$38$	−40.4799	+	23.3711i	−1.06526	+	0.615028i
$39$	−2.04160	+	38.9465i	−0.0523486	+	0.998629i
$40$	−63.9184	+	110.710i	−1.59796	+	2.76775i
$41$	−38.2367	−	38.2367i	−0.932603	−	0.932603i	0.0652647	−	0.997868i	$-0.479211\pi$
$41$	−38.2367	−	38.2367i	−0.932603	−	0.932603i	−0.997868	+	0.0652647i	$0.979211\pi$
$42$	−10.4509	+	15.0890i	−0.248830	+	0.359261i
$43$		−	13.5933i		−	0.316122i	−0.987429	−	0.158061i	$-0.949476\pi$
$43$		−	13.5933i		−	0.316122i	0.987429	−	0.158061i	$-0.0505243\pi$
$44$	−81.7910	−	81.7910i	−1.85889	−	1.85889i
$45$	−79.2666	+	7.75214i	−1.76148	+	0.172270i
$46$	15.1737	+	56.6290i	0.329863	+	1.23106i
$47$	43.2515	+	11.5892i	0.920246	+	0.246579i	0.687690	−	0.726004i	$-0.258625\pi$
$47$	43.2515	+	11.5892i	0.920246	+	0.246579i	0.232555	+	0.972583i	$0.425291\pi$
$48$	30.3415	−	43.8070i	0.632115	−	0.912646i
$49$			45.9179i			0.937099i
$50$	131.375	−	131.375i	2.62750	−	2.62750i
$51$	−21.5963	−	14.9580i	−0.423456	−	0.293293i
$52$	55.6507	+	90.0835i	1.07021	+	1.73237i
$53$	38.3056			0.722747			0.361373	−	0.932421i	$-0.382308\pi$
$53$	38.3056			0.722747			0.361373	+	0.932421i	$0.382308\pi$
$54$	94.0836	−	1.44268i	1.74229	−	0.0267162i
$55$	62.8357	+	108.835i	1.14247	+	1.97881i
$56$			25.3611i			0.452876i
$57$	−39.5897	+	7.18956i	−0.694557	+	0.126133i
$58$	37.0848	−	138.403i	0.639394	−	2.38625i
$59$	−10.3255	−	2.76672i	−0.175009	−	0.0468935i	0.170250	−	0.985401i	$-0.445542\pi$
$59$	−10.3255	−	2.76672i	−0.175009	−	0.0468935i	−0.345259	+	0.938507i	$0.612209\pi$
$60$	−164.936	+	139.841i	−2.74894	+	2.33068i
$61$	−34.3952			−0.563856			−0.281928	−	0.959436i	$-0.590974\pi$
$61$	−34.3952			−0.563856			−0.281928	+	0.959436i	$0.590974\pi$
$62$	19.7584	−	11.4075i	0.318683	−	0.183992i
$63$	−12.8496	+	9.19458i	−0.203962	+	0.145946i
$64$			56.6928i			0.885826i
$65$	−33.0710	−	110.186i	−0.508785	−	1.69518i
$66$	−63.4339	−	134.239i	−0.961119	−	2.03392i
$67$	−61.0077	−	61.0077i	−0.910563	−	0.910563i	0.0857532	−	0.996316i	$-0.472670\pi$
$67$	−61.0077	−	61.0077i	−0.910563	−	0.910563i	−0.996316	+	0.0857532i	$0.972670\pi$
$68$	−71.3257			−1.04891
$69$	−4.14155	+	50.2976i	−0.0600225	+	0.728951i
$70$	14.0132	−	52.2981i	0.200189	−	0.747116i
$71$	−108.463	+	29.0626i	−1.52765	+	0.409332i	−0.922251	−	0.386591i	$-0.873652\pi$
$71$	−108.463	+	29.0626i	−1.52765	+	0.409332i	−0.605397	+	0.795924i	$0.706986\pi$
$72$	105.732	−	75.6566i	1.46850	−	1.05079i
$73$	60.2281	−	60.2281i	0.825042	−	0.825042i	−0.161784	−	0.986826i	$-0.551725\pi$
$73$	60.2281	−	60.2281i	0.825042	−	0.825042i	0.986826	+	0.161784i	$0.0517248\pi$
$74$	128.392			1.73503
$75$	144.604	−	68.3320i	1.92806	−	0.911094i
$76$	−77.2486	+	77.2486i	−1.01643	+	1.01643i
$77$	21.5913	+	12.4657i	0.280406	+	0.161893i
$78$	28.2565	+	132.945i	0.362263	+	1.70442i
$79$	3.19706	+	5.53747i	0.0404691	+	0.0700945i	0.885550	−	0.464543i	$-0.153781\pi$
$79$	3.19706	+	5.53747i	0.0404691	+	0.0700945i	−0.845081	+	0.534638i	$0.820448\pi$
$80$	−40.6839	+	151.834i	−0.508549	+	1.89793i
$81$	76.6655	+	26.1419i	0.946488	+	0.322739i
$82$	−163.203	−	94.2252i	−1.99028	−	1.14909i
$83$	−3.70698	+	13.8346i	−0.0446624	+	0.166682i	−0.984655	−	0.174513i	$-0.944165\pi$
$83$	−3.70698	+	13.8346i	−0.0446624	+	0.166682i	0.939993	+	0.341195i	$0.110832\pi$
$84$	−14.4661	+	40.3863i	−0.172215	+	0.480789i
$85$	74.8524	+	20.0566i	0.880617	+	0.235960i
$86$	−12.2609	−	45.7582i	−0.142568	−	0.532072i
$87$	70.2302	−	101.398i	0.807244	−	1.16550i
$88$	−177.662	−	102.573i	−2.01888	−	1.16560i
$89$	−30.6602	−	8.21537i	−0.344496	−	0.0923075i	0.0824224	−	0.996597i	$-0.473734\pi$
$89$	−30.6602	−	8.21537i	−0.344496	−	0.0923075i	−0.426919	+	0.904290i	$0.640401\pi$
$90$	−259.838	+	97.5925i	−2.88709	+	1.08436i
$91$	−16.6116	−	15.6505i	−0.182545	−	0.171983i
$92$	68.5113	+	118.665i	0.744689	+	1.28984i
$93$	19.3239	−	3.50925i	0.207784	−	0.0377339i
$94$	156.048			1.66009
$95$	102.790	−	59.3460i	1.08200	−	0.624695i
$96$	4.16804	−	11.6363i	0.0434171	−	0.121212i
$97$	133.294	+	133.294i	1.37417	+	1.37417i	0.854162	+	0.520008i	$0.174071\pi$
$97$	133.294	+	133.294i	1.37417	+	1.37417i	0.520008	+	0.854162i	$0.325929\pi$
$98$	41.4171	+	154.571i	0.422623	+	1.57725i
$99$	−12.4402	−	127.203i	−0.125659	−	1.28488i
$100$	217.118	−	376.059i	2.17118	−	3.76059i
$101$	−78.0149	−	45.0419i	−0.772425	−	0.445960i	0.0613141	−	0.998119i	$-0.480471\pi$
$101$	−78.0149	−	45.0419i	−0.772425	−	0.445960i	−0.833739	+	0.552159i	$0.813804\pi$
$102$	−86.1901	−	30.8727i	−0.845001	−	0.302673i
$103$	−8.07065	−	4.65959i	−0.0783559	−	0.0452388i	0.460310	−	0.887758i	$-0.347738\pi$
$103$	−8.07065	−	4.65959i	−0.0783559	−	0.0452388i	−0.538666	+	0.842519i	$0.681072\pi$
$104$	136.687	+	128.778i	1.31430	+	1.23825i
$105$	26.5379	−	38.3153i	0.252742	−	0.364908i
$106$	128.946	−	34.5509i	1.21647	−	0.325952i
$107$	−34.8068	−	60.2872i	−0.325298	−	0.563432i	0.656275	−	0.754522i	$-0.272131\pi$
$107$	−34.8068	−	60.2872i	−0.325298	−	0.563432i	−0.981573	+	0.191090i	$0.938798\pi$
$108$	211.528	−	60.1695i	1.95859	−	0.557125i
$109$	8.55814	+	8.55814i	0.0785150	+	0.0785150i	0.745274	−	0.666759i	$-0.232319\pi$
$109$	8.55814	+	8.55814i	0.0785150	+	0.0785150i	−0.666759	+	0.745274i	$0.732319\pi$
$110$	309.687	+	309.687i	2.81534	+	2.81534i
$111$	104.051	+	37.2703i	0.937396	+	0.335769i
$112$	8.07113	+	30.1219i	0.0720637	+	0.268945i
$113$	32.7142	+	56.6626i	0.289506	+	0.501439i	0.973692	−	0.227869i	$-0.0731757\pi$
$113$	32.7142	+	56.6626i	0.289506	+	0.501439i	−0.684186	+	0.729308i	$0.739842\pi$
$114$	−126.784	+	59.9110i	−1.11214	+	0.525535i
$115$	−38.5305	−	143.798i	−0.335048	−	1.25041i
$116$		−	334.887i		−	2.88695i
$117$	−15.6924	+	115.943i	−0.134123	+	0.990965i
$118$	−37.2538			−0.315710
$119$	14.8497	−	3.97896i	0.124787	−	0.0334367i
$120$	−218.364	+	315.273i	−1.81970	+	2.62728i
$121$	−69.8632	+	40.3355i	−0.577382	+	0.333352i
$122$	−115.783	+	31.0238i	−0.949038	+	0.254294i
$123$	−104.910	−	123.737i	−0.852925	−	1.00599i
$124$	37.7054	−	37.7054i	0.304076	−	0.304076i
$125$	−177.163	+	177.163i	−1.41730	+	1.41730i
$126$	−34.9616	+	42.5413i	−0.277473	+	0.337629i
$127$	−136.317	+	78.7026i	−1.07336	+	0.619705i	−0.929098	−	0.369834i	$-0.879415\pi$
$127$	−136.317	+	78.7026i	−1.07336	+	0.619705i	−0.144263	+	0.989539i	$0.546081\pi$
$128$	55.4013	+	206.761i	0.432823	+	1.61532i
$129$	3.34652	−	40.6422i	0.0259420	−	0.315056i
$130$	−210.711	−	341.085i	−1.62086	−	2.62373i
$131$	−23.9115	+	41.4159i	−0.182530	+	0.316152i	−0.942742	−	0.333524i	$-0.891762\pi$
$131$	−23.9115	+	41.4159i	−0.182530	+	0.316152i	0.760211	+	0.649676i	$0.225095\pi$
$132$	−224.409	−	264.682i	−1.70007	−	2.00516i
$133$	11.7734	−	20.3922i	0.0885221	−	0.153325i
$134$	−260.395	−	150.339i	−1.94324	−	1.12193i
$135$	−238.906	+	3.66338i	−1.76968	+	0.0271361i
$136$	−122.189	+	32.7405i	−0.898449	+	0.240739i
$137$	−135.124	+	135.124i	−0.986304	+	0.986304i	−0.999907	−	0.0136038i	$-0.995670\pi$
$137$	−135.124	+	135.124i	−0.986304	+	0.986304i	0.0136038	+	0.999907i	$0.495670\pi$
$138$	31.4261	+	173.050i	0.227725	+	1.25398i
$139$	−21.4784	−	37.2017i	−0.154521	−	0.267638i	0.778364	−	0.627814i	$-0.216050\pi$
$139$	−21.4784	−	37.2017i	−0.154521	−	0.267638i	−0.932884	+	0.360176i	$0.882717\pi$
$140$		−	126.543i		−	0.903882i
$141$	126.464	+	45.2985i	0.896907	+	0.321266i
$142$	−338.899	+	195.663i	−2.38661	+	1.37791i
$143$	176.822	−	53.0707i	1.23652	−	0.371124i
$144$	101.502	−	123.508i	0.704877	−	0.857694i
$145$	−94.1694	+	351.445i	−0.649444	+	2.42376i
$146$	148.418	−	257.067i	1.01656	−	1.76073i
$147$	−11.3045	+	137.289i	−0.0769013	+	0.933938i
$148$	289.855	−	77.6663i	1.95848	−	0.524773i
$149$	−12.4653	+	46.5210i	−0.0836596	+	0.312222i	−0.995057	−	0.0993056i	$-0.968338\pi$
$149$	−12.4653	+	46.5210i	−0.0836596	+	0.312222i	0.911397	+	0.411527i	$0.135005\pi$
$150$	425.139	−	360.453i	2.83426	−	2.40302i
$151$	128.197	+	34.3503i	0.848987	+	0.227485i	0.656980	−	0.753908i	$-0.271834\pi$
$151$	128.197	+	34.3503i	0.848987	+	0.227485i	0.192007	+	0.981394i	$0.438500\pi$
$152$	−96.8765	+	167.795i	−0.637345	+	1.10391i
$153$	−60.8878	−	50.0393i	−0.397960	−	0.327054i
$154$	83.9254	+	22.4877i	0.544970	+	0.146024i
$155$	−50.1724	+	28.9670i	−0.323693	+	0.186884i
$156$	144.211	+	283.040i	0.924432	+	1.81436i
$157$	−40.4006	+	69.9759i	−0.257329	+	0.445707i	−0.965525	−	0.260309i	$-0.916176\pi$
$157$	−40.4006	+	69.9759i	−0.257329	+	0.445707i	0.708197	+	0.706015i	$0.249509\pi$
$158$	15.7568	+	15.7568i	0.0997263	+	0.0997263i
$159$	114.529	+	9.43043i	0.720309	+	0.0593109i
$160$			36.4604i			0.227877i
$161$	−20.8836	−	20.8836i	−0.129712	−	0.129712i
$162$	281.654	+	18.8490i	1.73861	+	0.116352i
$163$	−72.3197	−	269.901i	−0.443679	−	1.65583i	−0.719401	−	0.694595i	$-0.755584\pi$
$163$	−72.3197	−	269.901i	−0.443679	−	1.65583i	0.275722	−	0.961237i	$-0.411083\pi$
$164$	−425.440	−	113.996i	−2.59415	−	0.695100i
$165$	161.077	+	340.872i	0.976226	+	2.06589i
$166$			49.9143i			0.300689i
$167$	−32.4680	+	32.4680i	−0.194419	+	0.194419i	−0.797602	−	0.603183i	$-0.793899\pi$
$167$	−32.4680	+	32.4680i	−0.194419	+	0.194419i	0.603183	+	0.797602i	$0.293899\pi$
$168$	−6.24363	+	75.8266i	−0.0371644	+	0.451349i
$169$	−168.700	+	10.0607i	−0.998226	+	0.0595308i
$170$	270.062			1.58860
$171$	−120.139	+	11.7494i	−0.702565	+	0.0687097i
$172$	−55.3596	−	95.8856i	−0.321858	−	0.557474i
$173$		−	41.1884i		−	0.238083i	−0.992889	−	0.119041i	$-0.962018\pi$
$173$		−	41.1884i		−	0.238083i	0.992889	−	0.119041i	$-0.0379821\pi$
$174$	144.953	−	404.677i	0.833060	−	2.32573i
$175$	−24.2242	+	90.4058i	−0.138424	+	0.516605i
$176$	−243.656	−	65.2875i	−1.38441	−	0.370952i
$177$	−30.1910	−	10.8142i	−0.170570	−	0.0610971i
$178$	−110.620			−0.621459
$179$	261.123	−	150.760i	1.45879	−	0.842233i	0.459838	−	0.888003i	$-0.347907\pi$
$179$	261.123	−	150.760i	1.45879	−	0.842233i	0.998952	+	0.0457701i	$0.0145742\pi$
$180$	−527.568	+	377.502i	−2.93093	+	2.09723i
$181$		−	98.1005i		−	0.541992i	−0.962580	−	0.270996i	$-0.912647\pi$
$181$		−	98.1005i		−	0.541992i	0.962580	−	0.270996i	$-0.0873530\pi$
$182$	−70.0350	−	37.6998i	−0.384808	−	0.207142i
$183$	−102.838	−	8.46774i	−0.561954	−	0.0462718i
$184$	171.838	+	171.838i	0.933904	+	0.933904i
$185$	−326.026			−1.76230
$186$	61.8836	−	29.2428i	0.332708	−	0.157219i
$187$	−32.1859	+	120.119i	−0.172117	+	0.642349i
$188$	352.290	−	94.3959i	1.87388	−	0.502106i
$189$	−40.6825	+	24.3272i	−0.215251	+	0.128716i
$190$	292.488	−	292.488i	1.53941	−	1.53941i
$191$	−90.6647			−0.474684			−0.237342	−	0.971426i	$-0.576276\pi$
$191$	−90.6647			−0.474684			−0.237342	+	0.971426i	$0.576276\pi$
$192$	−13.9572	+	169.505i	−0.0726936	+	0.882838i
$193$	14.4313	−	14.4313i	0.0747735	−	0.0747735i	−0.668731	−	0.743504i	$-0.733162\pi$
$193$	14.4313	−	14.4313i	0.0747735	−	0.0747735i	0.743504	+	0.668731i	$0.233162\pi$
$194$	568.930	+	328.472i	2.93263	+	1.69315i
$195$	−71.7517	−	337.586i	−0.367957	−	1.73121i
$196$	187.004	+	323.900i	0.954101	+	1.65255i
$197$	−68.1531	+	254.351i	−0.345955	+	1.29112i	0.545537	+	0.838086i	$0.316326\pi$
$197$	−68.1531	+	254.351i	−0.345955	+	1.29112i	−0.891493	+	0.453035i	$0.850341\pi$
$198$	−156.612	−	416.975i	−0.790968	−	2.10593i
$199$	43.9695	+	25.3858i	0.220952	+	0.127567i	0.606391	−	0.795167i	$-0.292617\pi$
$199$	43.9695	+	25.3858i	0.220952	+	0.127567i	−0.385439	+	0.922733i	$0.625950\pi$
$200$	199.326	−	743.895i	0.996630	−	3.71947i
$201$	−167.386	−	197.425i	−0.832768	−	0.982216i
$202$	−303.244	−	81.2540i	−1.50121	−	0.402247i
$203$	18.6819	+	69.7218i	0.0920291	+	0.343457i
$204$	−213.255	−	17.5596i	−1.04537	−	0.0860767i
$205$	414.420	+	239.266i	2.02156	+	1.16715i
$206$	−31.3706	−	8.40574i	−0.152285	−	0.0408045i
$207$	−24.7655	+	149.364i	−0.119640	+	0.721567i
$208$	203.329	+	109.452i	0.977544	+	0.526212i
$209$	95.2355	+	164.953i	0.455672	+	0.789247i
$210$	54.7732	−	152.915i	0.260825	−	0.728168i
$211$	66.4434			0.314898			0.157449	−	0.987527i	$-0.449673\pi$
$211$	66.4434			0.314898			0.157449	+	0.987527i	$0.449673\pi$
$212$	270.204	−	156.002i	1.27455	−	0.735860i
$213$	−331.446	+	60.1912i	−1.55609	+	0.282588i
$214$	−171.546	−	171.546i	−0.801618	−	0.801618i
$215$	31.1340	+	116.194i	0.144809	+	0.540435i
$216$	334.752	−	200.174i	1.54978	−	0.926732i
$217$	−5.74666	+	9.95351i	−0.0264823	+	0.0458687i
$218$	36.5280	+	21.0895i	0.167560	+	0.0967407i
$219$	194.902	−	165.247i	0.889965	−	0.754554i
$220$	886.474	+	511.806i	4.02943	+	2.32639i
$221$	53.9584	−	100.239i	0.244156	−	0.453569i
$222$	383.878	+	31.6088i	1.72918	+	0.142382i
$223$	104.945	−	28.1199i	0.470605	−	0.126098i	−0.0157198	−	0.999876i	$-0.505004\pi$
$223$	104.945	−	28.1199i	0.470605	−	0.126098i	0.486324	+	0.873778i	$0.338337\pi$
$224$	3.61662	+	6.26417i	0.0161456	+	0.0279650i
$225$	449.172	−	168.705i	1.99632	−	0.749798i
$226$	161.232	+	161.232i	0.713418	+	0.713418i
$227$	−179.988	−	179.988i	−0.792900	−	0.792900i	0.189065	−	0.981965i	$-0.439454\pi$
$227$	−179.988	−	179.988i	−0.792900	−	0.792900i	−0.981965	+	0.189065i	$0.939454\pi$
$228$	−249.982	+	211.946i	−1.09641	+	0.929590i
$229$	−23.1134	−	86.2605i	−0.100932	−	0.376683i	0.896920	−	0.442193i	$-0.145799\pi$
$229$	−23.1134	−	86.2605i	−0.100932	−	0.376683i	−0.997852	+	0.0655096i	$0.979133\pi$
$230$	−259.406	−	449.304i	−1.12785	−	1.95350i
$231$	61.4865	+	42.5866i	0.266175	+	0.184358i
$232$	−153.722	−	573.699i	−0.662595	−	2.47284i
$233$		−	52.3389i		−	0.224630i	−0.993673	−	0.112315i	$-0.964173\pi$
$233$		−	52.3389i		−	0.224630i	0.993673	−	0.112315i	$-0.0358266\pi$
$234$	51.7541	+	404.446i	0.221171	+	1.72840i
$235$	−396.253			−1.68618
$236$	−84.1030	+	22.5353i	−0.356368	+	0.0954886i
$237$	8.19556	+	17.3435i	0.0345804	+	0.0731791i
$238$	46.3987	−	26.7883i	0.194952	−	0.112556i
$239$	251.363	−	67.3526i	1.05173	−	0.281810i	0.308763	−	0.951139i	$-0.400085\pi$
$239$	251.363	−	67.3526i	1.05173	−	0.281810i	0.742966	+	0.669329i	$0.233418\pi$
$240$	−159.020	+	443.951i	−0.662584	+	1.84980i
$241$	79.5206	−	79.5206i	0.329961	−	0.329961i	−0.522611	−	0.852572i	$-0.675042\pi$
$241$	79.5206	−	79.5206i	0.329961	−	0.329961i	0.852572	+	0.522611i	$0.175042\pi$
$242$	−198.794	+	198.794i	−0.821465	+	0.821465i
$243$	222.785	+	97.0354i	0.916811	+	0.399322i
$244$	−242.621	+	140.077i	−0.994347	+	0.574086i
$245$	−105.170	−	392.500i	−0.429266	−	1.60204i
$246$	−464.760	−	321.901i	−1.88927	−	1.30854i
$247$	−50.1233	−	167.002i	−0.202929	−	0.676120i
$248$	47.2858	−	81.9014i	0.190668	−	0.330247i
$249$	−14.4894	+	40.4513i	−0.0581902	+	0.162455i
$250$	−436.575	+	756.171i	−1.74630	+	3.02468i
$251$	239.559	+	138.309i	0.954417	+	0.551033i	0.894450	−	0.447168i	$-0.147567\pi$
$251$	239.559	+	138.309i	0.954417	+	0.551033i	0.0599666	+	0.998200i	$0.480901\pi$
$252$	−53.1945	+	117.189i	−0.211089	+	0.465035i
$253$	230.759	−	61.8318i	0.912092	−	0.244394i
$254$	−387.887	+	387.887i	−1.52711	+	1.52711i
$255$	218.862	+	78.3949i	0.858283	+	0.307431i
$256$	259.603	+	449.645i	1.01407	+	1.75643i
$257$			379.147i			1.47528i	0.675195	+	0.737639i	$0.264060\pi$
$257$			379.147i			1.47528i	−0.675195	+	0.737639i	$0.735940\pi$
$258$	−25.3934	−	139.830i	−0.0984239	−	0.541977i
$259$	−56.0137	+	32.3395i	−0.216269	+	0.124863i
$260$	−682.022	−	642.561i	−2.62316	−	2.47139i
$261$	234.943	−	285.879i	0.900166	−	1.09532i
$262$	−43.1354	+	160.984i	−0.164639	+	0.614441i
$263$	32.0652	−	55.5385i	0.121921	−	0.211173i	−0.798604	−	0.601856i	$-0.794428\pi$
$263$	32.0652	−	55.5385i	0.121921	−	0.211173i	0.920525	+	0.390683i	$0.127761\pi$
$264$	−505.935	−	350.420i	−1.91642	−	1.32735i
$265$	−327.431	+	87.7350i	−1.23559	+	0.331075i
$266$	21.2388	−	79.2644i	0.0798453	−	0.297987i
$267$	−89.6478	−	32.1112i	−0.335759	−	0.120267i
$268$	−678.801	−	181.884i	−2.53284	−	0.678672i
$269$	−99.5264	+	172.385i	−0.369987	+	0.640836i	−0.989563	−	0.144101i	$-0.953971\pi$
$269$	−99.5264	+	172.385i	−0.369987	+	0.640836i	0.619576	+	0.784936i	$0.287304\pi$
$270$	−800.911	+	227.821i	−2.96634	+	0.843781i
$271$	−33.4259	−	8.95645i	−0.123343	−	0.0330496i	0.196620	−	0.980480i	$-0.437004\pi$
$271$	−33.4259	−	8.95645i	−0.123343	−	0.0330496i	−0.319962	+	0.947430i	$0.603670\pi$
$272$	−134.707	+	77.7731i	−0.495246	+	0.285931i
$273$	−45.8137	−	50.8826i	−0.167816	−	0.186383i
$274$	−332.980	+	576.738i	−1.21525	+	2.10488i
$275$	−535.344	−	535.344i	−1.94671	−	1.94671i
$276$	175.627	+	371.661i	0.636329	+	1.34660i
$277$		−	183.943i		−	0.664053i	−0.943270	−	0.332027i	$-0.892268\pi$
$277$		−	183.943i		−	0.664053i	0.943270	−	0.332027i	$-0.107732\pi$
$278$	−105.857	−	105.857i	−0.380780	−	0.380780i
$279$	58.6401	−	5.73490i	0.210180	−	0.0205552i
$280$	−58.0869	−	216.783i	−0.207453	−	0.774226i
$281$	439.299	+	117.710i	1.56334	+	0.418896i	0.933720	−	0.358005i	$-0.116543\pi$
$281$	439.299	+	117.710i	1.56334	+	0.418896i	0.629622	+	0.776901i	$0.283210\pi$
$282$	466.566	+	38.4175i	1.65449	+	0.136232i
$283$		−	232.049i		−	0.819961i	−0.912094	−	0.409981i	$-0.865535\pi$
$283$		−	232.049i		−	0.819961i	0.912094	−	0.409981i	$-0.134465\pi$
$284$	−646.728	+	646.728i	−2.27721	+	2.27721i
$285$	321.941	−	152.132i	1.12962	−	0.533795i
$286$	547.356	−	338.139i	1.91383	−	1.18230i
$287$	94.9340			0.330781
$288$	15.3267	−	33.7651i	0.0532177	−	0.117240i
$289$	−106.159	−	183.873i	−0.367332	−	0.636237i
$290$			1267.99i			4.37237i
$291$	365.719	+	431.350i	1.25677	+	1.48230i
$292$	179.560	−	670.126i	0.614931	−	2.29495i
$293$	189.026	+	50.6495i	0.645141	+	0.172865i	0.566531	−	0.824040i	$-0.308285\pi$
$293$	189.026	+	50.6495i	0.645141	+	0.172865i	0.0786102	+	0.996905i	$0.474952\pi$
$294$	85.7784	+	472.344i	0.291763	+	1.60661i
$295$	94.5983			0.320672
$296$	460.903	−	266.103i	1.55710	−	0.898995i
$297$	−5.87880	−	383.384i	−0.0197940	−	1.29086i
$298$			167.844i			0.563237i
$299$	−218.597	+	6.51240i	−0.731094	+	0.0217806i
$300$	741.738	−	1070.92i	2.47246	−	3.56973i
$301$	16.8747	+	16.8747i	0.0560620	+	0.0560620i
$302$	462.525			1.53154
$303$	−222.166	−	153.876i	−0.733223	−	0.507843i
$304$	−61.6617	+	230.124i	−0.202834	+	0.756988i
$305$	294.006	−	78.7787i	0.963955	−	0.258291i
$306$	−250.098	−	113.525i	−0.817312	−	0.370996i
$307$	−179.861	+	179.861i	−0.585866	+	0.585866i	−0.936509	−	0.350643i	$-0.885963\pi$
$307$	−179.861	+	179.861i	−0.585866	+	0.585866i	0.350643	+	0.936509i	$0.385963\pi$
$308$	203.071			0.659320
$309$	−22.9832	−	15.9185i	−0.0743792	−	0.0515163i
$310$	−142.765	+	142.765i	−0.460531	+	0.460531i
$311$	−379.944	−	219.361i	−1.22168	−	0.705340i	−0.256407	−	0.966569i	$-0.582539\pi$
$311$	−379.944	−	219.361i	−1.22168	−	0.705340i	−0.965277	+	0.261229i	$0.915872\pi$
$312$	376.973	+	418.682i	1.20825	+	1.34193i
$313$	−147.788	−	255.976i	−0.472166	−	0.817815i	0.527327	−	0.849663i	$-0.323194\pi$
$313$	−147.788	−	255.976i	−0.472166	−	0.817815i	−0.999493	+	0.0318471i	$0.989861\pi$
$314$	−72.8812	+	271.996i	−0.232106	+	0.866231i
$315$	88.7779	−	108.025i	0.281835	−	0.342936i
$316$	45.1035	+	26.0405i	0.142733	+	0.0824067i
$317$	−3.00092	+	11.1996i	−0.00946663	+	0.0353299i	−0.970498	−	0.241111i	$-0.922488\pi$
$317$	−3.00092	+	11.1996i	−0.00946663	+	0.0353299i	0.961031	+	0.276441i	$0.0891549\pi$
$318$	394.039	−	71.5580i	1.23912	−	0.225025i
$319$	−563.981	−	151.118i	−1.76797	−	0.473725i
$320$	−129.849	−	484.604i	−0.405779	−	1.51439i
$321$	−89.2263	−	188.821i	−0.277963	−	0.588227i
$322$	−89.1357	−	51.4625i	−0.276819	−	0.159822i
$323$	113.448	+	30.3984i	0.351233	+	0.0941127i
$324$	647.256	−	127.824i	1.99770	−	0.394517i
$325$	364.249	+	589.621i	1.12077	+	1.81422i
$326$	−486.891	−	843.320i	−1.49353	−	2.58687i
$327$	23.4809	+	27.6947i	0.0718070	+	0.0846934i
$328$	−781.155			−2.38157
$329$	−68.0792	+	39.3056i	−0.206928	+	0.119470i
$330$	849.685	+	1002.17i	2.57480	+	3.03687i
$331$	175.222	+	175.222i	0.529371	+	0.529371i	0.920385	−	0.391014i	$-0.127876\pi$
$331$	175.222	+	175.222i	0.529371	+	0.529371i	−0.391014	+	0.920385i	$0.627876\pi$
$332$	30.1939	+	112.685i	0.0909454	+	0.339413i
$333$	301.925	+	137.050i	0.906680	+	0.411562i
$334$	−80.0095	+	138.581i	−0.239549	+	0.414912i
$335$	661.219	+	381.755i	1.97379	+	1.13957i
$336$	16.7160	+	92.0479i	0.0497501	+	0.273952i
$337$	−223.836	−	129.232i	−0.664201	−	0.383477i	0.129674	−	0.991557i	$-0.458607\pi$
$337$	−223.836	−	129.232i	−0.664201	−	0.383477i	−0.793876	+	0.608080i	$0.791940\pi$
$338$	−558.811	+	186.031i	−1.65329	+	0.550388i
$339$	83.8617	+	177.468i	0.247380	+	0.523505i
$340$	609.684	−	163.364i	1.79319	−	0.480483i
$341$	−46.4848	−	80.5141i	−0.136319	−	0.236112i
$342$	−393.818	+	147.914i	−1.15151	+	0.432497i
$343$	−117.831	−	117.831i	−0.343530	−	0.343530i
$344$	−138.851	−	138.851i	−0.403638	−	0.403638i
$345$	−79.8001	−	439.424i	−0.231305	−	1.27369i
$346$	−37.1511	−	138.650i	−0.107373	−	0.400722i
$347$	265.380	+	459.652i	0.764784	+	1.32464i	0.940361	+	0.340179i	$0.110488\pi$
$347$	265.380	+	459.652i	0.764784	+	1.32464i	−0.175577	+	0.984466i	$0.556179\pi$
$348$	82.4455	−	1001.27i	0.236912	−	2.87722i
$349$	−83.1673	−	310.385i	−0.238302	−	0.889355i	−0.976633	−	0.214916i	$-0.931052\pi$
$349$	−83.1673	−	310.385i	−0.238302	−	0.889355i	0.738331	−	0.674439i	$-0.235614\pi$
$350$			326.177i			0.931936i
$351$	−75.4622	+	342.792i	−0.214992	+	0.976616i
$352$	−58.5098			−0.166221
$353$	537.883	−	144.125i	1.52375	−	0.408287i	0.602774	−	0.797912i	$-0.294062\pi$
$353$	537.883	−	144.125i	1.52375	−	0.408287i	0.920974	+	0.389625i	$0.127395\pi$
$354$	−111.384	−	9.17148i	−0.314645	−	0.0259081i
$355$	860.564	−	496.847i	2.42412	−	1.39957i
$356$	−249.732	+	66.9154i	−0.701493	+	0.187965i
$357$	45.3784	−	8.24079i	0.127110	−	0.0230834i
$358$	743.022	−	743.022i	2.07548	−	2.07548i
$359$	−372.001	+	372.001i	−1.03622	+	1.03622i	−0.0368966	+	0.999319i	$0.511747\pi$
$359$	−372.001	+	372.001i	−1.03622	+	1.03622i	−0.999319	+	0.0368966i	$0.988253\pi$
$360$	−730.500	+	888.871i	−2.02917	+	2.46909i
$361$	−156.843	+	90.5536i	−0.434469	+	0.250841i
$362$	−88.4849	−	330.230i	−0.244433	−	0.912238i
$363$	−218.813	+	103.399i	−0.602790	+	0.284845i
$364$	−180.914	−	42.7448i	−0.497017	−	0.117431i
$365$	−376.876	+	652.768i	−1.03254	+	1.78841i
$366$	−353.814	+	64.2532i	−0.966705	+	0.175555i
$367$	160.753	−	278.432i	0.438019	−	0.758670i	−0.559518	−	0.828818i	$-0.689014\pi$
$367$	160.753	−	278.432i	0.438019	−	0.758670i	0.997537	+	0.0701478i	$0.0223471\pi$
$368$	258.783	+	149.409i	0.703215	+	0.406002i
$369$	−283.205	−	395.786i	−0.767494	−	1.07259i
$370$	−1097.48	+	294.069i	−2.96617	+	0.794782i
$371$	−47.5525	+	47.5525i	−0.128174	+	0.128174i
$372$	122.017	−	103.452i	0.328003	−	0.278097i
$373$	−84.0740	−	145.620i	−0.225399	−	0.390403i	0.731040	−	0.682335i	$-0.239035\pi$
$373$	−84.0740	−	145.620i	−0.225399	−	0.390403i	−0.956439	+	0.291932i	$0.905702\pi$
$374$			433.382i			1.15877i
$375$	−573.312	+	486.080i	−1.52883	+	1.29621i
$376$	560.183	−	323.422i	1.48985	−	0.860164i
$377$	470.638	+	253.344i	1.24838	+	0.672000i
$378$	−115.004	+	118.586i	−0.304244	+	0.313720i
$379$	144.324	−	538.624i	0.380802	−	1.42117i	−0.463878	−	0.885899i	$-0.653542\pi$
$379$	144.324	−	538.624i	0.380802	−	1.42117i	0.844679	−	0.535272i	$-0.179791\pi$
$380$	483.382	−	837.242i	1.27206	−	2.20327i
$381$	−426.947	+	201.752i	−1.12060	+	0.529532i
$382$	−305.199	+	81.7778i	−0.798950	+	0.214078i
$383$	139.897	−	522.102i	0.365266	−	1.36319i	−0.501794	−	0.864987i	$-0.667326\pi$
$383$	139.897	−	522.102i	0.365266	−	1.36319i	0.867060	−	0.498204i	$-0.166007\pi$
$384$	114.741	+	631.829i	0.298805	+	1.64539i
$385$	−213.111	−	57.1030i	−0.553536	−	0.148319i
$386$	35.5624	−	61.5959i	0.0921306	−	0.159575i
$387$	20.0114	−	120.692i	0.0517090	−	0.311865i
$388$	1483.10	+	397.395i	3.82242	+	1.02421i
$389$	−126.133	+	72.8229i	−0.324249	+	0.187205i	−0.653285	−	0.757112i	$-0.726610\pi$
$389$	−126.133	+	72.8229i	−0.324249	+	0.187205i	0.329036	+	0.944317i	$0.393276\pi$
$390$	−546.030	−	1071.68i	−1.40008	−	2.74789i
$391$	73.6565	−	127.577i	0.188380	−	0.326283i
$392$	469.038	+	469.038i	1.19653	+	1.19653i
$393$	−81.6886	+	117.942i	−0.207859	+	0.300106i
$394$			917.680i			2.32914i
$395$	−40.0111	−	40.0111i	−0.101294	−	0.101294i
$396$	−605.796	−	846.614i	−1.52979	−	2.13791i
$397$	−17.1546	−	64.0220i	−0.0432107	−	0.161264i	0.940949	−	0.338548i	$-0.109936\pi$
$397$	−17.1546	−	64.0220i	−0.0432107	−	0.161264i	−0.984160	+	0.177283i	$0.943269\pi$
$398$	170.909	+	45.7950i	0.429420	+	0.115063i
$399$	40.2215	−	58.0717i	0.100806	−	0.145543i
$400$		−	946.975i		−	2.36744i
$401$	−246.564	+	246.564i	−0.614873	+	0.614873i	−0.944212	−	0.329339i	$-0.893174\pi$
$401$	−246.564	+	246.564i	−0.614873	+	0.614873i	0.329339	+	0.944212i	$0.393174\pi$
$402$	−741.537	−	513.602i	−1.84462	−	1.27762i
$403$	24.4654	+	81.5141i	0.0607082	+	0.202268i
$404$	−733.746			−1.81620
$405$	−715.203	−	47.8631i	−1.76593	−	0.118181i
$406$	125.776	+	217.850i	0.309792	+	0.536576i
$407$		−	523.190i		−	1.28548i
$408$	−373.391	+	67.8084i	−0.915175	+	0.166197i
$409$	−120.177	+	448.505i	−0.293830	+	1.09659i	0.648311	+	0.761375i	$0.275476\pi$
$409$	−120.177	+	448.505i	−0.293830	+	1.09659i	−0.942142	+	0.335215i	$0.891191\pi$
$410$	1610.85	+	431.626i	3.92891	+	1.05275i
$411$	−437.270	+	370.738i	−1.06392	+	0.902038i
$412$	−75.9062			−0.184238
$413$	16.2527	−	9.38350i	0.0393528	−	0.0227203i
$414$	51.3573	+	525.134i	0.124051	+	1.26844i
$415$		−	126.747i		−	0.305415i
$416$	52.1260	+	12.3159i	0.125303	+	0.0296055i
$417$	−55.0592	−	116.516i	−0.132036	−	0.279416i
$418$	469.370	+	469.370i	1.12289	+	1.12289i
$419$	675.726			1.61271			0.806356	−	0.591431i	$-0.201437\pi$
$419$	675.726			1.61271			0.806356	+	0.591431i	$0.201437\pi$
$420$	31.1537	−	378.350i	0.0741754	−	0.900833i
$421$	−135.788	+	506.768i	−0.322537	+	1.20372i	0.594228	+	0.804297i	$0.297458\pi$
$421$	−135.788	+	506.768i	−0.322537	+	1.20372i	−0.916765	+	0.399427i	$0.869209\pi$
$422$	223.665	−	59.9307i	0.530011	−	0.142016i
$423$	366.960	+	166.571i	0.867517	+	0.393785i
$424$	391.280	−	391.280i	0.922831	−	0.922831i
$425$	−466.846			−1.09846
$426$	−1061.44	+	501.577i	−2.49164	+	1.17741i
$427$	42.6982	−	42.6982i	0.0999957	−	0.0999957i
$428$	−491.048	−	283.507i	−1.14731	−	0.662399i
$429$	541.741	−	115.144i	1.26280	−	0.268400i
$430$	209.609	+	363.053i	0.487463	+	0.844310i
$431$	160.021	−	597.207i	0.371279	−	1.38563i	−0.487428	−	0.873163i	$-0.662065\pi$
$431$	160.021	−	597.207i	0.371279	−	1.38563i	0.858707	−	0.512467i	$-0.171268\pi$
$432$	333.886	−	344.285i	0.772885	−	0.796957i
$433$	420.399	+	242.717i	0.970897	+	0.560548i	0.899510	−	0.436901i	$-0.143924\pi$
$433$	420.399	+	242.717i	0.970897	+	0.560548i	0.0713877	+	0.997449i	$0.477257\pi$
$434$	−10.3668	+	38.6893i	−0.0238865	+	0.0891458i
$435$	−368.077	+	1027.60i	−0.846155	+	2.36229i
$436$	95.2219	+	25.5146i	0.218399	+	0.0585198i
$437$	−58.3978	−	217.944i	−0.133633	−	0.498727i
$438$	507.038	−	732.060i	1.15762	−	1.67137i
$439$	−108.169	−	62.4512i	−0.246398	−	0.142258i	0.371716	−	0.928347i	$-0.378770\pi$
$439$	−108.169	−	62.4512i	−0.246398	−	0.142258i	−0.618114	+	0.786089i	$0.712103\pi$
$440$	1753.56	+	469.866i	3.98537	+	1.06788i
$441$	−67.5982	+	407.695i	−0.153284	+	0.924478i
$442$	91.2236	−	386.097i	0.206388	−	0.873522i
$443$	−307.260	−	532.190i	−0.693589	−	1.20133i	−0.970654	−	0.240481i	$-0.922695\pi$
$443$	−307.260	−	532.190i	−0.693589	−	1.20133i	0.277065	−	0.960851i	$-0.410638\pi$
$444$	885.752	−	160.854i	1.99494	−	0.362284i
$445$	280.896			0.631227
$446$	327.906	−	189.317i	0.735215	−	0.424477i
$447$	−48.7227	+	136.024i	−0.108999	+	0.304303i
$448$	−70.3784	−	70.3784i	−0.157095	−	0.157095i
$449$	−139.464	−	520.486i	−0.310610	−	1.15921i	−0.928008	−	0.372560i	$-0.878480\pi$
$449$	−139.464	−	520.486i	−0.310610	−	1.15921i	0.617398	−	0.786651i	$-0.288187\pi$
$450$	1359.85	−	973.046i	3.02190	−	2.16232i
$451$	−383.961	+	665.041i	−0.851356	+	1.47459i
$452$	461.525	+	266.462i	1.02107	+	0.589517i
$453$	374.837	+	134.264i	0.827455	+	0.296388i
$454$	−768.230	−	443.538i	−1.69214	−	0.976955i
$455$	177.840	+	95.7310i	0.390856	+	0.210398i
$456$	−330.958	+	477.837i	−0.725786	+	1.04789i
$457$	234.126	−	62.7339i	0.512311	−	0.137273i	0.00660319	−	0.999978i	$-0.497898\pi$
$457$	234.126	−	62.7339i	0.512311	−	0.137273i	0.505708	+	0.862705i	$0.331231\pi$
$458$	−155.611	−	269.526i	−0.339761	−	0.588484i
$459$	−169.728	−	164.602i	−0.369778	−	0.358609i
$460$	−857.417	−	857.417i	−1.86395	−	1.86395i
$461$	−168.101	−	168.101i	−0.364644	−	0.364644i	0.500876	−	0.865519i	$-0.333011\pi$
$461$	−168.101	−	168.101i	−0.364644	−	0.364644i	−0.865519	+	0.500876i	$0.833011\pi$
$462$	245.391	+	87.8972i	0.531149	+	0.190254i
$463$	115.605	+	431.444i	0.249687	+	0.931844i	0.970970	+	0.239203i	$0.0768862\pi$
$463$	115.605	+	431.444i	0.249687	+	0.931844i	−0.721283	+	0.692641i	$0.756447\pi$
$464$	−365.158	−	632.472i	−0.786979	−	1.36309i
$465$	−157.141	+	74.2561i	−0.337937	+	0.159690i
$466$	−47.2087	−	176.185i	−0.101306	−	0.378080i
$467$			120.666i			0.258386i	0.991619	+	0.129193i	$0.0412387\pi$
$467$			120.666i			0.258386i	−0.991619	+	0.129193i	$0.958761\pi$
$468$	361.493	+	881.758i	0.772422	+	1.88410i
$469$	151.470			0.322963
$470$	−1333.88	+	357.413i	−2.83805	+	0.760453i
$471$	−138.020	+	199.274i	−0.293037	+	0.423086i
$472$	−133.734	+	77.2111i	−0.283334	+	0.163583i
$473$	−186.462	+	49.9622i	−0.394211	+	0.105628i
$474$	43.2317	+	50.9900i	0.0912061	+	0.107574i
$475$	−505.613	+	505.613i	−1.06445	+	1.06445i
$476$	88.5437	−	88.5437i	0.186016	−	0.186016i
$477$	340.107	+	56.3917i	0.713012	+	0.118222i
$478$	785.399	−	453.450i	1.64309	−	0.948640i
$479$	161.742	+	603.628i	0.337665	+	1.26018i	0.900951	+	0.433921i	$0.142870\pi$
$479$	161.742	+	603.628i	0.337665	+	1.26018i	−0.563286	+	0.826262i	$0.690463\pi$
$480$	−8.97616	+	109.012i	−0.0187003	+	0.227109i
$481$	−110.128	+	466.107i	−0.228956	+	0.969037i
$482$	195.959	−	339.412i	0.406555	−	0.704173i
$483$	−57.2981	−	67.5807i	−0.118630	−	0.139919i
$484$	−328.539	+	569.046i	−0.678799	+	1.17572i
$485$	−1444.68	−	834.087i	−2.97873	−	1.71977i
$486$	837.472	+	125.696i	1.72319	+	0.258635i
$487$	−108.024	+	28.9450i	−0.221815	+	0.0594353i	−0.368015	−	0.929820i	$-0.619963\pi$
$487$	−108.024	+	28.9450i	−0.221815	+	0.0594353i	0.146200	+	0.989255i	$0.453296\pi$
$488$	−351.337	+	351.337i	−0.719954	+	0.719954i
$489$	−149.781	−	824.775i	−0.306300	−	1.68666i
$490$	−708.056	−	1226.39i	−1.44501	−	2.50283i
$491$		−	349.844i		−	0.712513i	−0.934388	−	0.356256i	$-0.884053\pi$
$491$		−	349.844i		−	0.712513i	0.934388	−	0.356256i	$-0.115947\pi$
$492$	−1243.95	−	445.574i	−2.52836	−	0.905639i
$493$	−311.801	+	180.018i	−0.632455	+	0.365148i
$494$	−319.360	−	516.957i	−0.646477	−	1.04647i
$495$	397.683	+	1058.82i	0.803400	+	2.13904i
$496$	30.0973	−	112.325i	0.0606800	−	0.226461i
$497$	98.5676	−	170.724i	0.198325	−	0.343509i
$498$	−12.2884	+	149.238i	−0.0246754	+	0.299674i
$499$	651.681	−	174.617i	1.30597	−	0.349934i	0.462268	−	0.886740i	$-0.347036\pi$
$499$	651.681	−	174.617i	1.30597	−	0.349934i	0.843706	+	0.536806i	$0.180369\pi$
$500$	−528.181	+	1971.20i	−1.05636	+	3.94240i
$501$	−105.069	+	89.0821i	−0.209718	+	0.177809i
$502$	931.164	+	249.505i	1.85491	+	0.497021i
$503$	213.872	−	370.437i	0.425192	−	0.736455i	−0.571246	−	0.820779i	$-0.693540\pi$
$503$	213.872	−	370.437i	0.425192	−	0.736455i	0.996438	+	0.0843240i	$0.0268731\pi$
$504$	−37.3354	+	225.175i	−0.0740782	+	0.446776i
$505$	770.026	+	206.328i	1.52480	+	0.408570i
$506$	721.020	−	416.281i	1.42494	−	0.822690i
$507$	−506.871	−	11.4519i	−0.999745	−	0.0225876i
$508$	−641.044	+	1110.32i	−1.26190	+	2.18567i
$509$	151.564	+	151.564i	0.297768	+	0.297768i	0.840139	−	0.542371i	$-0.182473\pi$
$509$	151.564	+	151.564i	0.297768	+	0.297768i	−0.542371	+	0.840139i	$0.682473\pi$
$510$	807.453	+	66.4864i	1.58324	+	0.130365i
$511$			149.534i			0.292630i
$512$	674.020	+	674.020i	1.31644	+	1.31644i
$513$	−362.093	+	5.55232i	−0.705834	+	0.0108232i
$514$	341.983	+	1276.30i	0.665337	+	2.48307i
$515$	79.6593	+	21.3446i	0.154678	+	0.0414459i
$516$	−141.913	−	300.315i	−0.275024	−	0.582007i
$517$		−	635.887i		−	1.22995i
$518$	−159.386	+	159.386i	−0.307695	+	0.307695i
$519$	10.1401	−	123.148i	0.0195378	−	0.237280i
$520$	−1463.33	−	787.712i	−2.81411	−	1.51483i
$521$	692.479			1.32913			0.664567	−	0.747228i	$-0.268616\pi$
$521$	692.479			1.32913			0.664567	+	0.747228i	$0.268616\pi$
$522$	533.018	−	1174.25i	1.02111	−	2.24952i
$523$	−267.793	−	463.831i	−0.512033	−	0.886867i	−0.999903	−	0.0139505i	$-0.995559\pi$
$523$	−267.793	−	463.831i	−0.512033	−	0.886867i	0.487870	−	0.872916i	$-0.337774\pi$
$524$			389.525i			0.743368i
$525$	−94.6843	+	264.339i	−0.180351	+	0.503503i
$526$	57.8444	−	215.878i	0.109970	−	0.410415i
$527$	−55.3746	−	14.8376i	−0.105075	−	0.0281548i
$528$	−712.430	−	255.188i	−1.34930	−	0.483310i
$529$	246.000			0.465027
$530$	−1023.08	+	590.674i	−1.93033	+	1.11448i
$531$	−87.6051	−	39.7659i	−0.164981	−	0.0748886i
$532$		−	191.793i		−	0.360513i
$533$	482.055	−	511.659i	0.904418	−	0.959961i
$534$	−330.740	−	27.2334i	−0.619363	−	0.0509989i
$535$	435.606	+	435.606i	0.814218	+	0.814218i
$536$	−1246.35			−2.32529
$537$	817.843	−	386.468i	1.52299	−	0.719679i
$538$	−179.542	+	670.060i	−0.333721	+	1.24546i
$539$	629.865	−	168.772i	1.16858	−	0.313120i
$540$	−1670.30	+	998.804i	−3.09315	+	1.84964i
$541$	314.860	−	314.860i	0.581997	−	0.581997i	−0.353455	−	0.935452i	$-0.614993\pi$
$541$	314.860	−	314.860i	0.581997	−	0.581997i	0.935452	+	0.353455i	$0.114993\pi$
$542$	−120.598			−0.222506
$543$	24.1513	−	293.309i	0.0444776	−	0.540164i
$544$	−25.5117	+	25.5117i	−0.0468965	+	0.0468965i
$545$	−92.7555	−	53.5524i	−0.170194	−	0.0982613i
$546$	−200.115	−	129.960i	−0.366511	−	0.238022i
$547$	−314.476	−	544.689i	−0.574911	−	0.995776i	−0.996051	−	0.0887799i	$-0.971703\pi$
$547$	−314.476	−	544.689i	−0.574911	−	0.995776i	0.421140	−	0.906996i	$-0.361630\pi$
$548$	−402.848	+	1503.45i	−0.735124	+	2.74352i
$549$	−305.388	−	50.6351i	−0.556262	−	0.0922315i
$550$	−2284.97	−	1319.23i	−4.15449	−	2.39859i
$551$	−142.726	+	532.659i	−0.259030	+	0.966714i
$552$	471.471	+	556.081i	0.854115	+	1.00739i
$553$	−10.8430	−	2.90538i	−0.0196076	−	0.00525385i
$554$	−165.913	−	619.196i	−0.299482	−	1.11768i
$555$	−974.779	−	80.2642i	−1.75636	−	0.144620i
$556$	−303.013	−	174.945i	−0.544988	−	0.314649i
$557$	610.140	+	163.487i	1.09540	+	0.293513i	0.760892	−	0.648879i	$-0.224762\pi$
$557$	610.140	+	163.487i	1.09540	+	0.293513i	0.334512	+	0.942391i	$0.391428\pi$
$558$	192.224	−	72.1974i	0.344487	−	0.129386i
$559$	176.634	−	5.26225i	0.315982	−	0.00941368i
$560$	−137.982	−	238.992i	−0.246397	−	0.426772i
$561$	−125.804	+	351.219i	−0.224250	+	0.626058i
$562$	1584.96			2.82021
$563$	−338.112	+	195.209i	−0.600554	+	0.346730i	−0.769259	−	0.638937i	$-0.779375\pi$
$563$	−338.112	+	195.209i	−0.600554	+	0.346730i	0.168706	+	0.985666i	$0.446041\pi$
$564$	1076.55	−	195.502i	1.90877	−	0.346635i
$565$	−409.417	−	409.417i	−0.724631	−	0.724631i
$566$	−209.304	−	781.133i	−0.369795	−	1.38009i
$567$	−127.625	+	62.7200i	−0.225088	+	0.110617i
$568$	−811.053	+	1404.78i	−1.42791	+	2.47321i
$569$	−263.144	−	151.926i	−0.462468	−	0.267006i	0.250613	−	0.968087i	$-0.419368\pi$
$569$	−263.144	−	151.926i	−0.462468	−	0.267006i	−0.713081	+	0.701081i	$0.752701\pi$
$570$	946.512	−	802.497i	1.66055	−	1.40789i
$571$	294.359	+	169.948i	0.515515	+	0.297632i	0.735098	−	0.677961i	$-0.237136\pi$
$571$	294.359	+	169.948i	0.515515	+	0.297632i	−0.219583	+	0.975594i	$0.570470\pi$
$572$	1031.15	−	1094.48i	1.80271	−	1.91342i
$573$	−271.077	−	22.3207i	−0.473083	−	0.0389541i
$574$	319.571	−	85.6287i	0.556744	−	0.149179i
$575$	448.425	+	776.695i	0.779870	+	1.35077i
$576$	−83.4606	+	503.363i	−0.144897	+	0.873895i
$577$	112.123	+	112.123i	0.194321	+	0.194321i	0.797560	−	0.603239i	$-0.206124\pi$
$577$	112.123	+	112.123i	0.194321	+	0.194321i	−0.603239	+	0.797560i	$0.706124\pi$
$578$	−523.206	−	523.206i	−0.905201	−	0.905201i
$579$	46.7006	−	39.5950i	0.0806574	−	0.0683851i
$580$	767.023	+	2862.57i	1.32245	+	4.93547i
$581$	−12.5724	−	21.7761i	−0.0216393	−	0.0374804i
$582$	1620.17	+	1122.16i	2.78379	+	1.92810i
$583$	−140.793	−	525.445i	−0.241497	−	0.901278i
$584$		−	1230.43i		−	2.10689i
$585$	−131.419	−	1027.01i	−0.224648	−	1.75557i
$586$	681.993			1.16381
$587$	−167.063	+	44.7645i	−0.284605	+	0.0762597i	−0.398298	−	0.917256i	$-0.630399\pi$
$587$	−167.063	+	44.7645i	−0.284605	+	0.0762597i	0.113692	+	0.993516i	$0.463732\pi$
$588$	479.379	+	1014.46i	0.815270	+	1.72527i
$589$	−76.0426	+	43.9032i	−0.129105	+	0.0745385i
$590$	318.441	−	85.3259i	0.539730	−	0.144620i
$591$	−266.388	+	743.701i	−0.450742	+	1.25838i
$592$	462.738	−	462.738i	0.781651	−	0.781651i
$593$	−221.043	+	221.043i	−0.372754	+	0.372754i	−0.868479	−	0.495725i	$-0.834902\pi$
$593$	−221.043	+	221.043i	−0.372754	+	0.372754i	0.495725	+	0.868479i	$0.334902\pi$
$594$	−365.595	−	1285.26i	−0.615480	−	2.16374i
$595$	−117.820	+	68.0234i	−0.198017	+	0.114325i
$596$	101.532	+	378.921i	0.170355	+	0.635773i
$597$	125.214	+	86.7253i	0.209738	+	0.145269i
$598$	−729.976	+	219.093i	−1.22070	+	0.366376i
$599$	−372.714	+	645.560i	−0.622227	+	1.07773i	0.366843	+	0.930283i	$0.380439\pi$
$599$	−372.714	+	645.560i	−0.622227	+	1.07773i	−0.989070	+	0.147446i	$0.952895\pi$
$600$	779.100	−	2175.08i	1.29850	−	3.62514i
$601$	−8.42382	+	14.5905i	−0.0140163	+	0.0242770i	−0.872948	−	0.487812i	$-0.837795\pi$
$601$	−8.42382	+	14.5905i	−0.0140163	+	0.0242770i	0.858932	+	0.512089i	$0.171128\pi$
$602$	72.0248	+	41.5835i	0.119642	+	0.0690756i
$603$	−451.862	−	631.487i	−0.749356	−	1.04724i
$604$	1044.18	−	279.788i	1.72878	−	0.463225i
$605$	504.798	−	504.798i	0.834377	−	0.834377i
$606$	−886.659	−	317.595i	−1.46313	−	0.524084i
$607$	46.9804	+	81.3724i	0.0773976	+	0.134057i	0.902126	−	0.431472i	$-0.142006\pi$
$607$	46.9804	+	81.3724i	0.0773976	+	0.134057i	−0.824729	+	0.565528i	$0.808672\pi$
$608$			55.2603i			0.0908887i
$609$	38.6919	+	213.059i	0.0635335	+	0.349851i
$610$	918.639	−	530.376i	1.50597	−	0.869469i
$611$	−133.849	+	566.507i	−0.219066	+	0.927180i
$612$	−633.286	−	105.003i	−1.03478	−	0.171573i
$613$	179.037	−	668.174i	0.292066	−	1.09001i	−0.651453	−	0.758689i	$-0.725840\pi$
$613$	179.037	−	668.174i	0.292066	−	1.09001i	0.943519	−	0.331318i	$-0.107493\pi$
$614$	−443.224	+	767.686i	−0.721863	+	1.25030i
$615$	1180.16	+	817.402i	1.91896	+	1.32911i
$616$	347.883	−	93.2149i	0.564745	−	0.151323i
$617$	−36.8843	+	137.654i	−0.0597800	+	0.223102i	−0.989353	−	0.145536i	$-0.953509\pi$
$617$	−36.8843	+	137.654i	−0.0597800	+	0.223102i	0.929573	+	0.368638i	$0.120176\pi$
$618$	−91.7251	−	32.8553i	−0.148422	−	0.0531639i
$619$	−1105.29	−	296.163i	−1.78561	−	0.478454i	−0.794025	−	0.607885i	$-0.792018\pi$
$619$	−1105.29	−	296.163i	−1.78561	−	0.478454i	−0.991588	+	0.129431i	$0.958685\pi$
$620$	−235.941	+	408.661i	−0.380549	+	0.659131i
$621$	−110.818	+	440.485i	−0.178451	+	0.709315i
$622$	−1476.84	−	395.718i	−2.37434	−	0.636203i
$623$	48.2600	−	27.8630i	0.0774640	−	0.0447238i
$624$	580.984	+	377.306i	0.931065	+	0.604657i
$625$	442.192	−	765.898i	0.707507	−	1.22544i
$626$	−728.376	−	728.376i	−1.16354	−	1.16354i
$627$	244.133	+	516.635i	0.389367	+	0.823979i
$628$			658.138i			1.04799i
$629$	−228.124	−	228.124i	−0.362677	−	0.362677i
$630$	201.411	−	443.714i	0.319701	−	0.704308i
$631$	48.5261	+	181.102i	0.0769034	+	0.287007i	0.993658	−	0.112443i	$-0.0358676\pi$
$631$	48.5261	+	181.102i	0.0769034	+	0.287007i	−0.916755	+	0.399451i	$0.869201\pi$
$632$	89.2207	+	23.9066i	0.141172	+	0.0378269i
$633$	198.658	+	16.3577i	0.313836	+	0.0258415i
$634$			40.4073i			0.0637339i
$635$	984.960	−	984.960i	1.55112	−	1.55112i
$636$	846.283	−	399.907i	1.33063	−	0.628784i
$637$	−596.667	+	17.7758i	−0.936684	+	0.0279055i
$638$	−2034.80			−3.18934
$639$	−1005.80	+	98.3660i	−1.57403	+	0.153937i
$640$	−947.128	−	1640.47i	−1.47989	−	2.56324i
$641$			1237.03i			1.92984i	0.262536	+	0.964922i	$0.415441\pi$
$641$			1237.03i			1.92984i	−0.262536	+	0.964922i	$0.584559\pi$
$642$	−470.670	−	555.136i	−0.733131	−	0.864697i
$643$	−116.580	+	435.081i	−0.181306	+	0.676642i	0.814085	+	0.580745i	$0.197239\pi$
$643$	−116.580	+	435.081i	−0.181306	+	0.676642i	−0.995391	+	0.0958972i	$0.969428\pi$
$644$	−232.361	−	62.2608i	−0.360808	−	0.0966783i
$645$	64.4813	+	355.070i	0.0999709	+	0.550496i
$646$	409.313			0.633612
$647$	579.143	−	334.368i	0.895120	−	0.516798i	0.0195064	−	0.999810i	$-0.493791\pi$
$647$	579.143	−	334.368i	0.895120	−	0.516798i	0.875614	+	0.483012i	$0.160457\pi$
$648$	1050.15	−	516.085i	1.62060	−	0.796427i
$649$			151.807i			0.233908i
$650$	1757.98	+	1656.26i	2.70458	+	2.54809i
$651$	−19.6323	+	28.3450i	−0.0301571	+	0.0435408i
$652$	−1609.33	−	1609.33i	−2.46829	−	2.46829i
$653$	−1028.38			−1.57485			−0.787427	−	0.616407i	$-0.788587\pi$
$653$	−1028.38			−1.57485			−0.787427	+	0.616407i	$0.788587\pi$
$654$	104.022	+	72.0478i	0.159056	+	0.110165i
$655$	109.534	−	408.785i	0.167227	−	0.624099i
$656$	−927.794	+	248.602i	−1.41432	+	0.378966i
$657$	623.417	−	446.087i	0.948884	−	0.678975i
$658$	−193.718	+	193.718i	−0.294405	+	0.294405i
$659$	455.413			0.691067			0.345533	−	0.938406i	$-0.387698\pi$
$659$	455.413			0.691067			0.345533	+	0.938406i	$0.387698\pi$
$660$	2524.45	+	1748.48i	3.82493	+	2.64921i
$661$	390.004	−	390.004i	0.590021	−	0.590021i	−0.347616	−	0.937637i	$-0.613009\pi$
$661$	390.004	−	390.004i	0.590021	−	0.590021i	0.937637	+	0.347616i	$0.113009\pi$
$662$	747.885	+	431.792i	1.12974	+	0.652253i
$663$	186.007	−	286.418i	0.280553	−	0.432003i
$664$	103.451	+	179.182i	0.155800	+	0.269853i
$665$	−53.9317	+	201.276i	−0.0811003	+	0.302670i
$666$	1139.97	+	189.013i	1.71166	+	0.283804i
$667$	598.995	+	345.830i	0.898043	+	0.518485i
$668$	−96.7978	+	361.254i	−0.144907	+	0.540800i
$669$	320.695	−	58.2388i	0.479365	−	0.0870535i
$670$	2570.16	+	688.672i	3.83606	+	1.02787i
$671$	126.420	+	471.806i	0.188406	+	0.703139i
$672$	9.27109	+	19.6195i	0.0137963	+	0.0291957i
$673$	902.052	+	520.800i	1.34035	+	0.773849i	0.986858	−	0.161590i	$-0.0516624\pi$
$673$	902.052	+	520.800i	1.34035	+	0.773849i	0.353487	+	0.935439i	$0.384996\pi$
$674$	−870.050	−	233.129i	−1.29088	−	0.345889i
$675$	1384.51	−	393.825i	2.05112	−	0.583445i
$676$	−1149.02	+	758.011i	−1.69974	+	1.12132i
$677$	−356.857	−	618.095i	−0.527115	−	0.912990i	−0.999501	−	0.0315983i	$-0.989940\pi$
$677$	−356.857	−	618.095i	−0.527115	−	0.912990i	0.472385	−	0.881392i	$-0.343393\pi$
$678$	442.372	+	521.759i	0.652466	+	0.769557i
$679$	−330.943			−0.487398
$680$	969.469	−	559.723i	1.42569	−	0.823122i
$681$	−493.832	−	582.455i	−0.725157	−	0.855293i
$682$	−229.101	−	229.101i	−0.335926	−	0.335926i
$683$	20.8652	+	77.8698i	0.0305493	+	0.114011i	0.979517	−	0.201362i	$-0.0645368\pi$
$683$	20.8652	+	77.8698i	0.0305493	+	0.114011i	−0.948968	+	0.315374i	$0.897870\pi$
$684$	−799.596	+	572.152i	−1.16900	+	0.836479i
$685$	845.534	−	1464.51i	1.23436	−	2.13797i
$686$	−502.928	−	290.366i	−0.733132	−	0.423274i
$687$	−47.8700	−	263.599i	−0.0696798	−	0.383696i
$688$	−209.106	−	120.727i	−0.303933	−	0.175476i
$689$	14.8289	+	497.752i	0.0215224	+	0.722426i
$690$	−664.979	−	1407.23i	−0.963737	−	2.03946i
$691$	−31.3291	+	8.39461i	−0.0453388	+	0.0121485i	−0.281417	−	0.959586i	$-0.590804\pi$
$691$	−31.3291	+	8.39461i	−0.0453388	+	0.0121485i	0.236078	+	0.971734i	$0.424138\pi$
$692$	−167.743	−	290.539i	−0.242403	−	0.419854i
$693$	173.353	+	142.466i	0.250148	+	0.205579i
$694$	1307.93	+	1307.93i	1.88463	+	1.88463i
$695$	268.801	+	268.801i	0.386765	+	0.386765i
$696$	−318.372	−	1753.14i	−0.457431	−	2.51887i
$697$	122.557	+	457.390i	0.175836	+	0.656227i
$698$	−559.923	−	969.814i	−0.802181	−	1.38942i
$699$	12.8853	−	156.487i	0.0184339	−	0.223873i
$700$	197.309	+	736.369i	0.281871	+	1.05196i
$701$			1211.96i			1.72890i	0.502723	+	0.864448i	$0.332332\pi$
$701$			1211.96i			1.72890i	−0.502723	+	0.864448i	$0.667668\pi$
$702$	55.1683	+	1221.99i	0.0785873	+	1.74072i
$703$	−494.134			−0.702893
$704$	777.667	−	208.375i	1.10464	−	0.295988i
$705$	−1184.75	−	97.5533i	−1.68050	−	0.138373i
$706$	1680.65	−	970.321i	2.38052	−	1.37439i
$707$	152.763	−	40.9326i	0.216072	−	0.0578962i
$708$	−257.006	+	46.6727i	−0.363003	+	0.0659219i
$709$	−690.230	+	690.230i	−0.973526	+	0.973526i	−0.999658	−	0.0261329i	$-0.991681\pi$
$709$	−690.230	+	690.230i	−0.973526	+	0.973526i	0.0261329	+	0.999658i	$0.491681\pi$
$710$	2448.72	−	2448.72i	3.44890	−	3.44890i
$711$	20.2340	+	53.8725i	0.0284585	+	0.0757701i
$712$	−397.103	+	229.267i	−0.557728	+	0.322005i
$713$	28.5042	+	106.379i	0.0399779	+	0.149199i
$714$	145.322	−	68.6709i	0.203532	−	0.0961778i
$715$	−1389.90	+	858.634i	−1.94391	+	1.20089i
$716$	1227.96	−	2126.89i	1.71503	−	2.97051i
$717$	768.128	−	139.493i	1.07131	−	0.194551i
$718$	−916.708	+	1587.78i	−1.27675	+	2.21140i
$719$	−583.567	−	336.922i	−0.811636	−	0.468598i	0.0358874	−	0.999356i	$-0.488574\pi$
$719$	−583.567	−	336.922i	−0.811636	−	0.468598i	−0.847524	+	0.530757i	$0.821908\pi$
$720$	−584.748	+	1288.21i	−0.812149	+	1.78918i
$721$	15.8033	−	4.23448i	0.0219186	−	0.00587307i
$722$	−446.295	+	446.295i	−0.618137	+	0.618137i
$723$	257.334	−	218.180i	0.355926	−	0.301770i
$724$	−399.522	−	691.992i	−0.551825	−	0.955790i
$725$		−	2191.92i		−	3.02334i
$726$	−643.313	+	545.431i	−0.886106	+	0.751282i
$727$	−867.103	+	500.622i	−1.19271	+	0.688614i	−0.958921	−	0.283673i	$-0.908447\pi$
$727$	−867.103	+	500.622i	−1.19271	+	0.688614i	−0.233793	+	0.972286i	$0.575114\pi$
$728$	−329.548	+	9.81782i	−0.452675	+	0.0134860i
$729$	642.212	+	344.972i	0.880949	+	0.473212i
$730$	−679.870	+	2537.31i	−0.931329	+	3.47577i
$731$	−59.5170	+	103.086i	−0.0814186	+	0.141021i
$732$	−759.892	+	359.083i	−1.03810	+	0.490551i
$733$	−1368.42	+	366.667i	−1.86688	+	0.500228i	−0.866877	+	0.498522i	$0.833876\pi$
$733$	−1368.42	+	366.667i	−1.86688	+	0.500228i	−0.999999	+	0.00170628i	$0.999457\pi$
$734$	289.992	−	1082.27i	0.395085	−	1.47448i
$735$	−217.817	−	1199.42i	−0.296349	−	1.63187i
$736$	66.9490	+	17.9389i	0.0909633	+	0.0243735i
$737$	−612.621	+	1061.09i	−0.831236	+	1.43974i
$738$	−1310.33	−	1076.87i	−1.77551	−	1.45917i
$739$	−699.273	−	187.370i	−0.946243	−	0.253545i	−0.247475	−	0.968894i	$-0.579601\pi$
$739$	−699.273	−	187.370i	−0.946243	−	0.253545i	−0.698767	+	0.715349i	$0.746268\pi$
$740$	−2299.76	+	1327.77i	−3.10778	+	1.79428i
$741$	−108.749	−	511.655i	−0.146760	−	0.690492i
$742$	−117.182	+	202.965i	−0.157927	+	0.273537i
$743$	164.322	+	164.322i	0.221160	+	0.221160i	0.808987	−	0.587827i	$-0.200016\pi$
$743$	164.322	+	164.322i	0.221160	+	0.221160i	−0.587827	+	0.808987i	$0.700016\pi$
$744$	161.542	−	233.234i	0.217126	−	0.313487i
$745$		−	426.207i		−	0.572090i
$746$	−414.360	−	414.360i	−0.555442	−	0.555442i
$747$	−53.2801	+	117.377i	−0.0713255	+	0.157132i
$748$	262.159	+	978.390i	0.350480	+	1.30801i
$749$	118.050	+	31.6313i	0.157610	+	0.0422314i
$750$	−1491.47	+	2153.38i	−1.98863	+	2.87117i
$751$			426.882i			0.568418i	0.958762	+	0.284209i	$0.0917309\pi$
$751$			426.882i			0.568418i	−0.958762	+	0.284209i	$0.908269\pi$
$752$	562.412	−	562.412i	0.747889	−	0.747889i
$753$	682.202	+	472.505i	0.905978	+	0.627497i
$754$	1812.79	+	428.311i	2.40423	+	0.568051i
$755$	−1174.49			−1.55561
$756$	−187.896	+	337.284i	−0.248540	+	0.446143i
$757$	−328.020	−	568.148i	−0.433316	−	0.750525i	0.563841	−	0.825884i	$-0.309323\pi$
$757$	−328.020	−	568.148i	−0.433316	−	0.750525i	−0.997157	+	0.0753585i	$0.975990\pi$
$758$		−	1943.32i		−	2.56374i
$759$	705.165	−	128.059i	0.929071	−	0.168721i
$760$	443.771	−	1656.18i	0.583909	−	2.17918i
$761$	−1256.00	−	336.544i	−1.65046	−	0.442239i	−0.690718	−	0.723125i	$-0.742705\pi$
$761$	−1256.00	−	336.544i	−1.65046	−	0.442239i	−0.959741	+	0.280885i	$0.909372\pi$
$762$	−1255.23	+	1064.24i	−1.64728	+	1.39664i
$763$	−21.2481			−0.0278481
$764$	−639.540	+	369.238i	−0.837094	+	0.483296i
$765$	635.072	+	288.273i	0.830159	+	0.376827i
$766$		−	1883.71i		−	2.45915i
$767$	31.9541	−	135.243i	0.0416612	−	0.176328i
$768$	665.483	+	1408.30i	0.866515	+	1.83372i
$769$	1041.17	+	1041.17i	1.35392	+	1.35392i	0.881225	+	0.472697i	$0.156720\pi$
$769$	1041.17	+	1041.17i	1.35392	+	1.35392i	0.472697	+	0.881225i	$0.343280\pi$
$770$	−768.890			−0.998558
$771$	−93.3419	+	1133.60i	−0.121066	+	1.47030i
$772$	43.0244	−	160.569i	0.0557311	−	0.207991i
$773$	113.735	−	30.4751i	0.147134	−	0.0394244i	−0.184500	−	0.982832i	$-0.559067\pi$
$773$	113.735	−	30.4751i	0.147134	−	0.0394244i	0.331634	+	0.943408i	$0.392400\pi$
$774$	−41.4985	−	424.327i	−0.0536156	−	0.548226i
$775$	246.792	−	246.792i	0.318441	−	0.318441i
$776$	2723.13			3.50919
$777$	−175.436	+	82.9014i	−0.225786	+	0.106694i
$778$	−358.909	+	358.909i	−0.461323	+	0.461323i
$779$	628.107	+	362.638i	0.806299	+	0.465517i
$780$	−1880.97	−	2089.09i	−2.41151	−	2.67832i
$781$	797.315	+	1380.99i	1.02089	+	1.76823i
$782$	132.874	−	495.891i	0.169915	−	0.634132i
$783$	772.833	−	796.903i	0.987015	−	1.01776i
$784$	706.357	+	407.815i	0.900966	+	0.520173i
$785$	185.067	−	690.679i	0.235754	−	0.879846i
$786$	−168.602	+	470.702i	−0.214507	+	0.598858i
$787$	112.850	+	30.2381i	0.143393	+	0.0384220i	0.329801	−	0.944050i	$-0.393018\pi$
$787$	112.850	+	30.2381i	0.143393	+	0.0384220i	−0.186409	+	0.982472i	$0.559685\pi$
$788$	555.117	+	2071.73i	0.704464	+	2.62909i
$789$	109.544	−	158.159i	0.138839	−	0.200456i
$790$	−170.776	−	98.5977i	−0.216172	−	0.124807i
$791$	−110.952	−	29.7295i	−0.140268	−	0.0375848i
$792$	−1426.42	−	1172.27i	−1.80103	−	1.48014i
$793$	−13.3151	−	446.940i	−0.0167908	−	0.563606i
$794$	−115.493	−	200.040i	−0.145458	−	0.251940i
$795$	−1000.58	+	181.707i	−1.25859	+	0.228562i
$796$	413.542			0.519525
$797$	−628.151	+	362.663i	−0.788144	+	0.455035i	−0.839309	−	0.543655i	$-0.817040\pi$
$797$	−628.151	+	362.663i	−0.788144	+	0.455035i	0.0511646	+	0.998690i	$0.483707\pi$
$798$	83.0157	−	231.762i	0.104030	−	0.290429i
$799$	−277.262	−	277.262i	−0.347011	−	0.347011i
$800$	−56.8498	−	212.166i	−0.0710623	−	0.265208i
$801$	−260.131	−	118.079i	−0.324757	−	0.147414i
$802$	−607.597	+	1052.39i	−0.757603	+	1.31221i
$803$	−1047.53	−	604.792i	−1.30452	−	0.753165i
$804$	−1984.76	−	710.926i	−2.46860	−	0.884236i
$805$	226.342	+	130.679i	0.281170	+	0.162334i
$806$	155.881	+	252.329i	0.193400	+	0.313063i
$807$	−340.012	+	490.908i	−0.421328	+	0.608312i
$808$	−1256.99	+	336.810i	−1.55568	+	0.416844i
$809$	54.6391	+	94.6376i	0.0675390	+	0.116981i	0.897817	−	0.440368i	$-0.145152\pi$
$809$	54.6391	+	94.6376i	0.0675390	+	0.116981i	−0.830278	+	0.557349i	$0.811819\pi$
$810$	−2450.72	+	483.981i	−3.02558	+	0.597507i
$811$	−585.721	−	585.721i	−0.722221	−	0.722221i	0.246837	−	0.969057i	$-0.420609\pi$
$811$	−585.721	−	585.721i	−0.722221	−	0.722221i	−0.969057	+	0.246837i	$0.920609\pi$
$812$	415.728	+	415.728i	0.511980	+	0.511980i
$813$	−97.7346	−	35.0078i	−0.120215	−	0.0430601i
$814$	−471.908	−	1761.18i	−0.579739	−	2.16362i
$815$	1236.36	+	2141.44i	1.51701	+	2.62753i
$816$	−421.905	+	199.369i	−0.517040	+	0.244325i
$817$	47.1875	+	176.106i	0.0577570	+	0.215552i
$818$			1618.17i			1.97821i
$819$	−124.451	−	163.412i	−0.151955	−	0.199526i
$820$	3897.71			4.75330
$821$	−120.861	+	32.3846i	−0.147212	+	0.0394453i	−0.331673	−	0.943395i	$-0.607613\pi$
$821$	−120.861	+	32.3846i	−0.147212	+	0.0394453i	0.184460	+	0.982840i	$0.440946\pi$
$822$	−1137.56	+	1642.40i	−1.38389	+	1.99805i
$823$	41.3630	−	23.8809i	0.0502588	−	0.0290169i	−0.474660	−	0.880169i	$-0.657429\pi$
$823$	41.3630	−	23.8809i	0.0502588	−	0.0290169i	0.524919	+	0.851152i	$0.324096\pi$
$824$	−130.036	+	34.8430i	−0.157811	+	0.0422852i
$825$	−1468.82	−	1732.41i	−1.78039	−	2.09989i
$826$	46.2467	−	46.2467i	0.0559888	−	0.0559888i
$827$	423.155	−	423.155i	0.511674	−	0.511674i	−0.403365	−	0.915039i	$-0.632160\pi$
$827$	423.155	−	423.155i	0.511674	−	0.511674i	0.915039	+	0.403365i	$0.132160\pi$
$828$	433.604	+	1154.46i	0.523676	+	1.39428i
$829$	−839.134	+	484.474i	−1.01222	+	0.584408i	−0.911842	−	0.410541i	$-0.865340\pi$
$829$	−839.134	+	484.474i	−1.01222	+	0.584408i	−0.100382	+	0.994949i	$0.532006\pi$
$830$	−114.324	−	426.661i	−0.137739	−	0.514050i
$831$	45.2848	−	549.967i	0.0544943	−	0.661814i
$832$	−736.680	+	21.9470i	−0.885433	+	0.0263786i
$833$	201.048	−	348.225i	0.241354	−	0.418037i
$834$	−290.438	−	342.560i	−0.348247	−	0.410743i
$835$	203.168	−	351.897i	0.243315	−	0.421433i
$836$	1343.56	+	775.707i	1.60713	+	0.927879i
$837$	176.739	−	2.71011i	0.211157	−	0.00323788i
$838$	2274.66	−	609.493i	2.71439	−	0.727318i
$839$	−293.438	+	293.438i	−0.349747	+	0.349747i	−0.860015	−	0.510268i	$-0.829546\pi$
$839$	−293.438	+	293.438i	−0.349747	+	0.349747i	0.510268	+	0.860015i	$0.329546\pi$
$840$	−120.303	−	662.457i	−0.143218	−	0.788639i
$841$	−424.716	−	735.630i	−0.505013	−	0.874708i
$842$			1828.38i			2.17147i
$843$	1284.47	+	460.089i	1.52369	+	0.545776i
$844$	468.686	−	270.596i	0.555315	−	0.320611i
$845$	1418.99	−	472.388i	1.67927	−	0.559039i
$846$	1385.52	+	229.727i	1.63773	+	0.271545i
$847$	36.6556	−	136.801i	0.0432770	−	0.161512i
$848$	340.208	−	589.257i	0.401188	−	0.694878i
$849$	57.1280	−	693.799i	0.0672886	−	0.817196i
$850$	−1571.52	+	421.086i	−1.84884	+	0.495396i
$851$	−160.409	+	598.653i	−0.188494	+	0.703470i
$852$	−2092.86	+	1774.42i	−2.45641	+	2.08266i
$853$	982.405	+	263.235i	1.15171	+	0.308598i	0.783648	−	0.621205i	$-0.213356\pi$
$853$	982.405	+	263.235i	1.15171	+	0.308598i	0.368057	+	0.929803i	$0.380023\pi$
$854$	105.219	−	182.245i	0.123208	−	0.213402i
$855$	1000.02	−	375.597i	1.16961	−	0.439295i
$856$	−971.359	−	260.275i	−1.13477	−	0.304059i
$857$	−277.234	+	160.061i	−0.323493	+	0.186769i	−0.652948	−	0.757402i	$-0.726468\pi$
$857$	−277.234	+	160.061i	−0.323493	+	0.186769i	0.329455	+	0.944171i	$0.393135\pi$
$858$	1719.77	−	876.241i	2.00440	−	1.02126i
$859$	826.114	−	1430.87i	0.961716	−	1.66574i	0.243526	−	0.969894i	$-0.421696\pi$
$859$	826.114	−	1430.87i	0.961716	−	1.66574i	0.718190	−	0.695847i	$-0.244971\pi$
$860$	692.823	+	692.823i	0.805608	+	0.805608i
$861$	283.842	+	23.3718i	0.329665	+	0.0271449i
$862$		−	2154.68i		−	2.49963i
$863$	279.041	+	279.041i	0.323339	+	0.323339i	0.850046	−	0.526708i	$-0.176574\pi$
$863$	279.041	+	279.041i	0.323339	+	0.323339i	−0.526708	+	0.850046i	$0.676574\pi$
$864$	54.1376	−	97.1802i	0.0626592	−	0.112477i
$865$	94.3377	+	352.073i	0.109061	+	0.407021i
$866$	1634.09	+	437.853i	1.88694	+	0.505604i
$867$	−272.135	−	575.892i	−0.313881	−	0.664236i
$868$			93.6148i			0.107851i
$869$	64.2077	−	64.2077i	0.0738869	−	0.0738869i
$870$	−312.165	+	3791.13i	−0.358810	+	4.35762i
$871$	769.131	−	816.366i	0.883044	−	0.937275i
$872$	174.838			0.200502
$873$	987.262	+	1379.72i	1.13088	+	1.58044i
$874$	−393.162	−	680.977i	−0.449843	−	0.779150i
$875$		−	439.859i		−	0.502697i
$876$	701.840	−	1959.39i	0.801188	−	2.23675i
$877$	−180.179	+	672.438i	−0.205450	+	0.766748i	0.783862	+	0.620935i	$0.213247\pi$
$877$	−180.179	+	672.438i	−0.205450	+	0.766748i	−0.989312	+	0.145814i	$0.953420\pi$
$878$	−420.452	−	112.660i	−0.478874	−	0.128314i
$879$	552.697	+	197.972i	0.628780	+	0.225224i
$880$	2232.28			2.53668
$881$	−108.150	+	62.4404i	−0.122758	+	0.0708745i	−0.560122	−	0.828410i	$-0.689246\pi$
$881$	−108.150	+	62.4404i	−0.122758	+	0.0708745i	0.437363	+	0.899285i	$0.355912\pi$
$882$	140.181	+	1433.37i	0.158936	+	1.62514i
$883$		−	511.184i		−	0.578917i	−0.957191	−	0.289459i	$-0.906525\pi$
$883$		−	511.184i		−	0.578917i	0.957191	−	0.289459i	$-0.0934752\pi$
$884$	−27.6117	−	926.823i	−0.0312350	−	1.04844i
$885$	282.838	+	23.2891i	0.319591	+	0.0263154i
$886$	−1514.34	−	1514.34i	−1.70918	−	1.70918i
$887$	−324.174			−0.365473			−0.182736	−	0.983162i	$-0.558496\pi$
$887$	−324.174			−0.365473			−0.182736	+	0.983162i	$0.558496\pi$
$888$	1443.56	−	682.145i	1.62563	−	0.768182i
$889$	71.5223	−	266.925i	0.0804525	−	0.300253i
$890$	945.563	−	253.363i	1.06243	−	0.284677i
$891$	76.8083	−	1147.72i	0.0862046	−	1.28813i
$892$	625.751	−	625.751i	0.701514	−	0.701514i
$893$	−600.572			−0.672533
$894$	−41.3215	+	501.835i	−0.0462210	+	0.561337i
$895$	−1886.75	+	1886.75i	−2.10810	+	2.10810i
$896$	−325.447	−	187.897i	−0.363222	−	0.209707i
$897$	−655.183	−	34.3450i	−0.730415	−	0.0382887i
$898$	−938.937	−	1626.29i	−1.04559	−	1.81101i
$899$	69.6649	−	259.993i	0.0774916	−	0.289203i
$900$	2481.36	−	3019.31i	2.75706	−	3.35479i
$901$	−290.496	−	167.718i	−0.322415	−	0.186146i
$902$	−692.652	+	2585.01i	−0.767907	+	2.86587i
$903$	46.2989	+	54.6076i	0.0512723	+	0.0604735i
$904$	912.958	+	244.626i	1.00991	+	0.270604i
$905$	224.689	+	838.552i	0.248275	+	0.926576i
$906$	1382.90	+	113.869i	1.52637	+	0.125683i
$907$	−202.750	−	117.057i	−0.223539	−	0.129060i	0.384049	−	0.923313i	$-0.374529\pi$
$907$	−202.750	−	117.057i	−0.223539	−	0.129060i	−0.607588	+	0.794253i	$0.707863\pi$
$908$	−2002.63	−	536.604i	−2.20554	−	0.590974i
$909$	−626.369	−	514.767i	−0.689074	−	0.566301i
$910$	684.999	+	161.846i	0.752746	+	0.177852i
$911$	240.121	+	415.901i	0.263579	+	0.456533i	0.967190	−	0.254053i	$-0.0817636\pi$
$911$	240.121	+	415.901i	0.263579	+	0.456533i	−0.703611	+	0.710585i	$0.748430\pi$
$912$	−241.015	+	672.864i	−0.264271	+	0.737790i
$913$	203.397			0.222779
$914$	731.540	−	422.355i	0.800372	−	0.462095i
$915$	898.438	−	163.158i	0.981900	−	0.178315i
$916$	−514.342	−	514.342i	−0.561509	−	0.561509i
$917$	−21.7300	−	81.0973i	−0.0236968	−	0.0884376i
$918$	−719.814	−	400.997i	−0.784111	−	0.436816i
$919$	−803.073	+	1390.96i	−0.873855	+	1.51356i	−0.0158776	+	0.999874i	$0.505054\pi$
$919$	−803.073	+	1390.96i	−0.873855	+	1.51356i	−0.857977	+	0.513687i	$0.828279\pi$
$920$	−1862.43	−	1075.27i	−2.02438	−	1.16878i
$921$	−582.042	+	493.483i	−0.631968	+	0.535812i
$922$	−717.491	−	414.244i	−0.778190	−	0.449288i
$923$	−419.634	−	1398.14i	−0.454642	−	1.51478i
$924$	607.157	+	49.9938i	0.657096	+	0.0541059i
$925$	1897.18	−	508.347i	2.05100	−	0.549564i
$926$	778.309	+	1348.07i	0.840506	+	1.45580i
$927$	−64.7979	−	53.2528i	−0.0699007	−	0.0574464i
$928$	−119.782	−	119.782i	−0.129075	−	0.129075i
$929$	161.051	+	161.051i	0.173359	+	0.173359i	0.788454	−	0.615094i	$-0.210882\pi$
$929$	161.051	+	161.051i	0.173359	+	0.173359i	−0.615094	+	0.788454i	$0.710882\pi$
$930$	−461.996	+	391.702i	−0.496770	+	0.421185i
$931$	−159.399	−	594.884i	−0.171212	−	0.638973i
$932$	−213.154	−	369.193i	−0.228706	−	0.396130i
$933$	−1081.98	−	749.400i	−1.15968	−	0.803216i
$934$	108.839	+	406.192i	0.116530	+	0.434895i
$935$		−	1100.48i		−	1.17699i
$936$	1024.03	+	1344.62i	1.09405	+	1.43656i
$937$	−48.4170			−0.0516723			−0.0258362	−	0.999666i	$-0.508225\pi$
$937$	−48.4170			−0.0516723			−0.0258362	+	0.999666i	$0.508225\pi$
$938$	509.884	−	136.623i	0.543586	−	0.145653i
$939$	−378.850	−	801.722i	−0.403461	−	0.853804i
$940$	−2795.13	+	1613.77i	−2.97354	+	1.71678i
$941$	717.693	−	192.305i	0.762692	−	0.204363i	0.143551	−	0.989643i	$-0.454148\pi$
$941$	717.693	−	192.305i	0.762692	−	0.204363i	0.619141	+	0.785280i	$0.287481\pi$
$942$	−284.869	+	795.294i	−0.302409	+	0.844262i
$943$	643.242	−	643.242i	0.682123	−	0.682123i
$944$	−134.266	+	134.266i	−0.142231	+	0.142231i
$945$	292.030	−	301.125i	0.309026	−	0.318651i
$946$	−582.610	+	336.370i	−0.615866	+	0.355571i
$947$	394.869	+	1473.67i	0.416969	+	1.55615i	0.780860	+	0.624706i	$0.214781\pi$
$947$	394.869	+	1473.67i	0.416969	+	1.55615i	−0.363891	+	0.931441i	$0.618552\pi$
$948$	128.443	+	88.9620i	0.135489	+	0.0938418i
$949$	805.933	+	759.302i	0.849245	+	0.800108i
$950$	−1245.96	+	2158.07i	−1.31154	+	2.27165i
$951$	−11.7296	+	32.7466i	−0.0123340	+	0.0344339i
$952$	111.041	−	192.329i	0.116640	−	0.202027i
$953$	776.026	+	448.039i	0.814298	+	0.470135i	0.848446	−	0.529282i	$-0.177539\pi$
$953$	776.026	+	448.039i	0.814298	+	0.470135i	−0.0341484	+	0.999417i	$0.510872\pi$
$954$	1195.75	−	116.942i	1.25340	−	0.122581i
$955$	774.991	−	207.658i	0.811509	−	0.217443i
$956$	1498.79	−	1498.79i	1.56778	−	1.56778i
$957$	−1649.03	−	590.672i	−1.72313	−	0.617212i
$958$	1088.92	+	1886.07i	1.13666	+	1.96876i
$959$		−	335.484i		−	0.349827i
$960$	−268.929	−	1480.87i	−0.280135	−	1.54258i
$961$	−795.134	+	459.071i	−0.827402	+	0.477701i
$962$	49.7034	+	1668.36i	0.0516668	+	1.73426i
$963$	−220.290	−	586.518i	−0.228754	−	0.609053i
$964$	237.077	−	884.784i	0.245931	−	0.917826i
$965$	−90.3035	+	156.410i	−0.0935787	+	0.162083i
$966$	−253.836	−	175.811i	−0.262770	−	0.181999i
$967$	1598.82	−	428.403i	1.65338	−	0.443023i	0.692826	−	0.721105i	$-0.256365\pi$
$967$	1598.82	−	428.403i	1.65338	−	0.443023i	0.960557	+	0.278082i	$0.0896987\pi$
$968$	−301.617	+	1125.65i	−0.311588	+	1.16286i
$969$	331.713	+	118.817i	0.342325	+	0.122619i
$970$	−5615.48	−	1504.66i	−5.78915	−	1.55120i
$971$	539.004	−	933.583i	0.555102	−	0.961465i	−0.442793	−	0.896624i	$-0.646012\pi$
$971$	539.004	−	933.583i	0.555102	−	0.961465i	0.997896	−	0.0648416i	$-0.0206542\pi$
$972$	1966.69	−	222.830i	2.02334	−	0.229249i
$973$	72.8454	+	19.5189i	0.0748668	+	0.0200605i
$974$	−337.527	+	194.872i	−0.346537	+	0.200073i
$975$	943.902	+	1852.57i	0.968105	+	1.90007i
$976$	−305.478	+	529.104i	−0.312990	+	0.542114i
$977$	−843.034	−	843.034i	−0.862880	−	0.862880i	0.128792	−	0.991672i	$-0.458890\pi$
$977$	−843.034	−	843.034i	−0.862880	−	0.862880i	−0.991672	+	0.128792i	$0.958890\pi$
$978$	−1248.13	−	2641.29i	−1.27621	−	2.70071i
$979$			450.768i			0.460437i
$980$	−2340.35	−	2340.35i	−2.38811	−	2.38811i
$981$	63.3869	+	88.5847i	0.0646146	+	0.0903004i
$982$	−315.553	−	1177.66i	−0.321337	−	1.19924i
$983$	−1175.21	−	314.896i	−1.19553	−	0.320342i	−0.394461	−	0.918912i	$-0.629069\pi$
$983$	−1175.21	−	314.896i	−1.19553	−	0.320342i	−0.801070	+	0.598571i	$0.795736\pi$
$984$	−2335.56	−	192.312i	−2.37354	−	0.195439i
$985$		−	2330.26i		−	2.36575i
$986$	−887.223	+	887.223i	−0.899820	+	0.899820i
$987$	−213.225	+	100.759i	−0.216034	+	0.102086i
$988$	−1033.69	−	973.882i	−1.04625	−	0.985711i
$989$	228.674			0.231218
$990$	2293.74	+	3205.55i	2.31690	+	3.23793i
$991$	167.362	+	289.880i	0.168882	+	0.292513i	0.938027	−	0.346562i	$-0.112651\pi$
$991$	167.362	+	289.880i	0.168882	+	0.292513i	−0.769145	+	0.639075i	$0.779318\pi$
$992$		−	26.9728i		−	0.0271903i
$993$	480.754	+	567.030i	0.484143	+	0.571027i
$994$	177.812	−	663.604i	0.178886	−	0.667610i
$995$	−433.989	−	116.287i	−0.436170	−	0.116871i
$996$	62.5342	+	344.348i	0.0627853	+	0.345731i
$997$	−846.364			−0.848911			−0.424455	−	0.905449i	$-0.639534\pi$
$997$	−846.364			−0.848911			−0.424455	+	0.905449i	$0.639534\pi$
$998$	2036.21	−	1175.61i	2.04029	−	1.17796i
$999$	868.978	+	484.094i	0.869848	+	0.484579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.bb.a.76.24	yes	104
3.2	odd	2		351.3.be.a.37.3		104
9.2	odd	6		351.3.z.a.154.24		104
9.7	even	3		117.3.w.a.115.3	yes	104
13.6	odd	12		117.3.w.a.58.3	✓	104
39.32	even	12		351.3.z.a.253.24		104
117.97	odd	12	inner	117.3.bb.a.97.24	yes	104
117.110	even	12		351.3.be.a.19.3		104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.w.a.58.3	✓	104	13.6	odd	12
117.3.w.a.115.3	yes	104	9.7	even	3
117.3.bb.a.76.24	yes	104	1.1	even	1	trivial
117.3.bb.a.97.24	yes	104	117.97	odd	12	inner
351.3.z.a.154.24		104	9.2	odd	6
351.3.z.a.253.24		104	39.32	even	12
351.3.be.a.19.3		104	117.110	even	12
351.3.be.a.37.3		104	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.36624 - 0.901981i) q^{2} +(2.98988 + 0.246189i) q^{3} +(7.05390 - 4.07257i) q^{4} +(-8.54788 + 2.29040i) q^{5} +(10.2867 - 1.86808i) q^{6} +(-1.24140 + 1.24140i) q^{7} +(10.2147 - 10.2147i) q^{8} +(8.87878 + 1.47215i) q^{9} +(-26.7083 + 15.4201i) q^{10} +(-3.67551 - 13.7172i) q^{11} +(22.0930 - 10.4399i) q^{12} +(0.387122 + 12.9942i) q^{13} +(-3.05913 + 5.29856i) q^{14} +(-26.1210 + 4.74362i) q^{15} +(8.88141 - 15.3831i) q^{16} +(-7.58364 - 4.37842i) q^{17} +(31.2160 - 3.05287i) q^{18} +(-12.9554 + 3.47139i) q^{19} +(-50.9681 + 50.9681i) q^{20} +(-4.01725 + 3.40601i) q^{21} +(-24.7453 - 42.8602i) q^{22} +16.8226i q^{23} +(33.0555 - 28.0260i) q^{24} +(46.1697 - 26.6561i) q^{25} +(13.0237 + 43.3925i) q^{26} +(26.1841 + 6.58743i) q^{27} +(-3.70102 + 13.8124i) q^{28} +(20.5574 - 35.6065i) q^{29} +(-83.6510 + 39.5288i) q^{30} +(6.32358 - 1.69440i) q^{31} +(1.06636 - 3.97970i) q^{32} +(-7.61232 - 41.9177i) q^{33} +(-29.4776 - 7.89851i) q^{34} +(7.76803 - 13.4546i) q^{35} +(68.6255 - 25.7751i) q^{36} +(35.5862 + 9.53529i) q^{37} +(-40.4799 + 23.3711i) q^{38} +(-2.04160 + 38.9465i) q^{39} +(-63.9184 + 110.710i) q^{40} +(-38.2367 - 38.2367i) q^{41} +(-10.4509 + 15.0890i) q^{42} -13.5933i q^{43} +(-81.7910 - 81.7910i) q^{44} +(-79.2666 + 7.75214i) q^{45} +(15.1737 + 56.6290i) q^{46} +(43.2515 + 11.5892i) q^{47} +(30.3415 - 43.8070i) q^{48} +45.9179i q^{49} +(131.375 - 131.375i) q^{50} +(-21.5963 - 14.9580i) q^{51} +(55.6507 + 90.0835i) q^{52} +38.3056 q^{53} +(94.0836 - 1.44268i) q^{54} +(62.8357 + 108.835i) q^{55} +25.3611i q^{56} +(-39.5897 + 7.18956i) q^{57} +(37.0848 - 138.403i) q^{58} +(-10.3255 - 2.76672i) q^{59} +(-164.936 + 139.841i) q^{60} -34.3952 q^{61} +(19.7584 - 11.4075i) q^{62} +(-12.8496 + 9.19458i) q^{63} +56.6928i q^{64} +(-33.0710 - 110.186i) q^{65} +(-63.4339 - 134.239i) q^{66} +(-61.0077 - 61.0077i) q^{67} -71.3257 q^{68} +(-4.14155 + 50.2976i) q^{69} +(14.0132 - 52.2981i) q^{70} +(-108.463 + 29.0626i) q^{71} +(105.732 - 75.6566i) q^{72} +(60.2281 - 60.2281i) q^{73} +128.392 q^{74} +(144.604 - 68.3320i) q^{75} +(-77.2486 + 77.2486i) q^{76} +(21.5913 + 12.4657i) q^{77} +(28.2565 + 132.945i) q^{78} +(3.19706 + 5.53747i) q^{79} +(-40.6839 + 151.834i) q^{80} +(76.6655 + 26.1419i) q^{81} +(-163.203 - 94.2252i) q^{82} +(-3.70698 + 13.8346i) q^{83} +(-14.4661 + 40.3863i) q^{84} +(74.8524 + 20.0566i) q^{85} +(-12.2609 - 45.7582i) q^{86} +(70.2302 - 101.398i) q^{87} +(-177.662 - 102.573i) q^{88} +(-30.6602 - 8.21537i) q^{89} +(-259.838 + 97.5925i) q^{90} +(-16.6116 - 15.6505i) q^{91} +(68.5113 + 118.665i) q^{92} +(19.3239 - 3.50925i) q^{93} +156.048 q^{94} +(102.790 - 59.3460i) q^{95} +(4.16804 - 11.6363i) q^{96} +(133.294 + 133.294i) q^{97} +(41.4171 + 154.571i) q^{98} +(-12.4402 - 127.203i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 2 q^{2} - 2 q^{3} - 6 q^{4} - 2 q^{5} + 10 q^{6} - 6 q^{7} + 18 q^{8} - 2 q^{9} - 12 q^{10} - 14 q^{11} - 54 q^{12} - 2 q^{13} - 4 q^{14} - 44 q^{15} + 162 q^{16} - 12 q^{17} + 34 q^{18} - 36 q^{19}+ \cdots - 524 q^{99}+O(q^{100}) \) 104 * q - 2 * q^2 - 2 * q^3 - 6 * q^4 - 2 * q^5 + 10 * q^6 - 6 * q^7 + 18 * q^8 - 2 * q^9 - 12 * q^10 - 14 * q^11 - 54 * q^12 - 2 * q^13 - 4 * q^14 - 44 * q^15 + 162 * q^16 - 12 * q^17 + 34 * q^18 - 36 * q^19 - 82 * q^20 + 106 * q^21 + 2 * q^22 - 66 * q^24 + 52 * q^26 + 4 * q^27 + 56 * q^28 + 74 * q^29 - 438 * q^30 - 34 * q^31 + 22 * q^32 - 68 * q^33 + 6 * q^34 - 106 * q^35 - 6 * q^36 + 14 * q^37 - 216 * q^38 - 176 * q^39 - 36 * q^40 - 26 * q^41 - 220 * q^42 + 496 * q^44 - 50 * q^45 + 118 * q^47 + 130 * q^48 + 92 * q^50 + 76 * q^52 - 208 * q^53 + 904 * q^54 - 4 * q^55 - 86 * q^57 - 76 * q^58 + 430 * q^59 - 358 * q^60 - 4 * q^61 - 282 * q^62 - 326 * q^63 + 406 * q^65 - 412 * q^66 - 72 * q^67 - 1068 * q^68 + 204 * q^69 - 106 * q^70 - 8 * q^71 - 642 * q^72 + 90 * q^73 + 356 * q^74 + 204 * q^75 - 194 * q^76 + 432 * q^77 + 646 * q^78 - 16 * q^79 - 278 * q^80 - 182 * q^81 - 12 * q^82 - 536 * q^83 + 310 * q^84 - 234 * q^85 + 414 * q^86 + 434 * q^87 - 6 * q^88 + 400 * q^89 + 798 * q^90 + 120 * q^91 + 48 * q^92 - 116 * q^93 - 244 * q^94 + 858 * q^95 + 1528 * q^96 + 344 * q^97 + 280 * q^98 - 524 * q^99

Introduction

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