LMFDB - Embedded newform 31.3.f.a.15.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,3,Mod(15,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("31.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, 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:	$0.844688819517$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 20 x^{18} - 33 x^{17} + 250 x^{16} - 510 x^{15} + 2908 x^{14} - 6447 x^{13} + \cdots + 731025 $ x^20 - 2x^19 + 20x^18 - 33x^17 + 250x^16 - 510x^15 + 2908x^14 - 6447x^13 + 39842x^12 - 79034x^11 + 199542x^10 - 173039x^9 + 688988x^8 - 636120x^7 + 3401146x^6 - 2156427x^5 + 7116556x^4 - 6139950x^3 + 6454710x^2 - 3116475*x + 731025
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.1
Root			$1.15230 + 3.54642i$ of defining polynomial
Character	$\chi$	$=$	31.15
Dual form			31.3.f.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.01677 + 2.19181i) q^{2} +(-1.12307 + 1.54577i) q^{3} +(3.06079 - 9.42013i) q^{4} -7.37547 q^{5} -7.12479i q^{6} +(-1.10519 + 3.40142i) q^{7} +(6.80424 + 20.9413i) q^{8} +(1.65302 + 5.08748i) q^{9} +O(q^{10})$	\(q+(-3.01677 + 2.19181i) q^{2} +(-1.12307 + 1.54577i) q^{3} +(3.06079 - 9.42013i) q^{4} -7.37547 q^{5} -7.12479i q^{6} +(-1.10519 + 3.40142i) q^{7} +(6.80424 + 20.9413i) q^{8} +(1.65302 + 5.08748i) q^{9} +(22.2501 - 16.1656i) q^{10} +(-4.14078 - 1.34542i) q^{11} +(11.1239 + 15.3107i) q^{12} +(-10.4773 + 14.4207i) q^{13} +(-4.12117 - 12.6837i) q^{14} +(8.28317 - 11.4008i) q^{15} +(-34.3732 - 24.9736i) q^{16} +(16.0233 - 5.20629i) q^{17} +(-16.1376 - 11.7246i) q^{18} +(5.24291 - 3.80920i) q^{19} +(-22.5747 + 69.4779i) q^{20} +(-4.01662 - 5.52840i) q^{21} +(15.4407 - 5.01698i) q^{22} +(4.97511 - 1.61651i) q^{23} +(-40.0122 - 13.0007i) q^{24} +29.3975 q^{25} -66.4681i q^{26} +(-26.0751 - 8.47230i) q^{27} +(28.6591 + 20.8220i) q^{28} +(21.1698 + 29.1378i) q^{29} +52.5487i q^{30} +(-30.8898 - 2.61211i) q^{31} +70.3573 q^{32} +(6.73010 - 4.88970i) q^{33} +(-36.9274 + 50.8262i) q^{34} +(8.15128 - 25.0871i) q^{35} +52.9843 q^{36} +33.2298i q^{37} +(-7.46760 + 22.9829i) q^{38} +(-10.5245 - 32.3909i) q^{39} +(-50.1845 - 154.452i) q^{40} +(-2.36218 + 1.71622i) q^{41} +(24.2344 + 7.87424i) q^{42} +(-12.6063 - 17.3510i) q^{43} +(-25.3481 + 34.8886i) q^{44} +(-12.1918 - 37.5226i) q^{45} +(-11.4657 + 15.7811i) q^{46} +(-10.5593 - 7.67178i) q^{47} +(77.2070 - 25.0861i) q^{48} +(29.2936 + 21.2831i) q^{49} +(-88.6854 + 64.4337i) q^{50} +(-9.94755 + 30.6154i) q^{51} +(103.776 + 142.836i) q^{52} +(-39.1000 + 12.7043i) q^{53} +(97.2320 - 31.5926i) q^{54} +(30.5402 + 9.92310i) q^{55} -78.7501 q^{56} +12.3823i q^{57} +(-127.729 - 41.5016i) q^{58} +(-38.1942 - 27.7497i) q^{59} +(-82.0440 - 112.924i) q^{60} +25.2189i q^{61} +(98.9124 - 59.8243i) q^{62} -19.1316 q^{63} +(-74.7588 + 54.3155i) q^{64} +(77.2747 - 106.359i) q^{65} +(-9.58584 + 29.5022i) q^{66} +63.6335 q^{67} -166.877i q^{68} +(-3.08864 + 9.50585i) q^{69} +(30.3955 + 93.5479i) q^{70} +(37.8748 + 116.567i) q^{71} +(-95.2910 + 69.2330i) q^{72} +(-8.37951 - 2.72267i) q^{73} +(-72.8333 - 100.246i) q^{74} +(-33.0155 + 45.4419i) q^{75} +(-19.8357 - 61.0480i) q^{76} +(9.15268 - 12.5976i) q^{77} +(102.745 + 74.6483i) q^{78} +(120.538 - 39.1653i) q^{79} +(253.518 + 184.192i) q^{80} +(3.43131 - 2.49299i) q^{81} +(3.36451 - 10.3549i) q^{82} +(-42.9969 - 59.1801i) q^{83} +(-64.3723 + 20.9158i) q^{84} +(-118.179 + 38.3988i) q^{85} +(76.0603 + 24.7135i) q^{86} -68.8156 q^{87} -95.8678i q^{88} +(64.4529 + 20.9420i) q^{89} +(119.022 + 86.4747i) q^{90} +(-37.4715 - 51.5752i) q^{91} -51.8140i q^{92} +(38.7291 - 44.8150i) q^{93} +48.6700 q^{94} +(-38.6689 + 28.0946i) q^{95} +(-79.0162 + 108.756i) q^{96} +(-46.0155 + 141.621i) q^{97} -135.020 q^{98} -23.2902i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9	\( 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + 12 q^{10} - 10 q^{11} + 90 q^{12} + 10 q^{13} - 85 q^{15} - 103 q^{16} + 35 q^{17} + 6 q^{18} + 47 q^{19} - 125 q^{20} - 125 q^{21} + 150 q^{22} + 75 q^{23} + 195 q^{24} + 82 q^{25} + 25 q^{27} + 88 q^{28} + 5 q^{29} + 73 q^{31} + 226 q^{32} - 206 q^{33} - 265 q^{34} - 50 q^{35} - 520 q^{36} + 8 q^{38} + 91 q^{39} - 466 q^{40} - 98 q^{41} + 245 q^{43} + 380 q^{44} - 162 q^{45} - 445 q^{46} - 187 q^{47} + 570 q^{48} + 328 q^{49} - 44 q^{50} + 185 q^{51} - 15 q^{52} + 25 q^{53} + 920 q^{54} + 190 q^{55} + 64 q^{56} - 85 q^{58} - 173 q^{59} + 275 q^{60} - 40 q^{62} + 252 q^{63} - 469 q^{64} - 345 q^{65} - 564 q^{66} + 76 q^{67} - 197 q^{69} - 11 q^{70} - 467 q^{71} - 982 q^{72} - 15 q^{73} + 45 q^{74} - 175 q^{75} + 55 q^{76} - 320 q^{77} - 91 q^{78} + 500 q^{79} + 1030 q^{80} + 117 q^{81} + 178 q^{82} - 50 q^{83} + 65 q^{84} + 20 q^{85} + 1125 q^{86} - 366 q^{87} + 55 q^{89} + 444 q^{90} + 300 q^{91} + 502 q^{93} + 62 q^{94} - 559 q^{95} - 10 q^{96} - 405 q^{97} - 1000 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9 + 12 * q^10 - 10 * q^11 + 90 * q^12 + 10 * q^13 - 85 * q^15 - 103 * q^16 + 35 * q^17 + 6 * q^18 + 47 * q^19 - 125 * q^20 - 125 * q^21 + 150 * q^22 + 75 * q^23 + 195 * q^24 + 82 * q^25 + 25 * q^27 + 88 * q^28 + 5 * q^29 + 73 * q^31 + 226 * q^32 - 206 * q^33 - 265 * q^34 - 50 * q^35 - 520 * q^36 + 8 * q^38 + 91 * q^39 - 466 * q^40 - 98 * q^41 + 245 * q^43 + 380 * q^44 - 162 * q^45 - 445 * q^46 - 187 * q^47 + 570 * q^48 + 328 * q^49 - 44 * q^50 + 185 * q^51 - 15 * q^52 + 25 * q^53 + 920 * q^54 + 190 * q^55 + 64 * q^56 - 85 * q^58 - 173 * q^59 + 275 * q^60 - 40 * q^62 + 252 * q^63 - 469 * q^64 - 345 * q^65 - 564 * q^66 + 76 * q^67 - 197 * q^69 - 11 * q^70 - 467 * q^71 - 982 * q^72 - 15 * q^73 + 45 * q^74 - 175 * q^75 + 55 * q^76 - 320 * q^77 - 91 * q^78 + 500 * q^79 + 1030 * q^80 + 117 * q^81 + 178 * q^82 - 50 * q^83 + 65 * q^84 + 20 * q^85 + 1125 * q^86 - 366 * q^87 + 55 * q^89 + 444 * q^90 + 300 * q^91 + 502 * q^93 + 62 * q^94 - 559 * q^95 - 10 * q^96 - 405 * q^97 - 1000 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−3.01677	+	2.19181i	−1.50838	+	1.09590i	−0.541495	+	0.840704i	$0.682142\pi$
$2$	−3.01677	+	2.19181i	−1.50838	+	1.09590i	−0.966888	+	0.255201i	$0.917858\pi$
$3$	−1.12307	+	1.54577i	−0.374357	+	0.515258i	−0.954079	−	0.299557i	$-0.903161\pi$
$3$	−1.12307	+	1.54577i	−0.374357	+	0.515258i	0.579722	+	0.814814i	$0.303161\pi$
$4$	3.06079	−	9.42013i	0.765196	−	2.35503i
$5$	−7.37547			−1.47509			−0.737547	−	0.675296i	$-0.764016\pi$
$5$	−7.37547			−1.47509			−0.737547	+	0.675296i	$0.764016\pi$
$6$		−	7.12479i		−	1.18747i
$7$	−1.10519	+	3.40142i	−0.157884	+	0.485917i	−0.998442	−	0.0558050i	$-0.982227\pi$
$7$	−1.10519	+	3.40142i	−0.157884	+	0.485917i	0.840558	+	0.541722i	$0.182227\pi$
$8$	6.80424	+	20.9413i	0.850530	+	2.61766i
$9$	1.65302	+	5.08748i	0.183669	+	0.565276i
$10$	22.2501	−	16.1656i	2.22501	−	1.61656i
$11$	−4.14078	−	1.34542i	−0.376434	−	0.122311i	0.114688	−	0.993402i	$-0.463413\pi$
$11$	−4.14078	−	1.34542i	−0.376434	−	0.122311i	−0.491122	+	0.871091i	$0.663413\pi$
$12$	11.1239	+	15.3107i	0.926992	+	1.27590i
$13$	−10.4773	+	14.4207i	−0.805943	+	1.10929i	0.185994	+	0.982551i	$0.440450\pi$
$13$	−10.4773	+	14.4207i	−0.805943	+	1.10929i	−0.991937	+	0.126735i	$0.959550\pi$
$14$	−4.12117	−	12.6837i	−0.294369	−	0.905975i
$15$	8.28317	−	11.4008i	0.552211	−	0.760053i
$16$	−34.3732	−	24.9736i	−2.14833	−	1.56085i
$17$	16.0233	−	5.20629i	0.942547	−	0.306252i	0.202864	−	0.979207i	$-0.434975\pi$
$17$	16.0233	−	5.20629i	0.942547	−	0.306252i	0.739684	+	0.672955i	$0.234975\pi$
$18$	−16.1376	−	11.7246i	−0.896532	−	0.651369i
$19$	5.24291	−	3.80920i	0.275943	−	0.200484i	−0.441203	−	0.897407i	$-0.645448\pi$
$19$	5.24291	−	3.80920i	0.275943	−	0.200484i	0.717146	+	0.696923i	$0.245448\pi$
$20$	−22.5747	+	69.4779i	−1.12874	+	3.47389i
$21$	−4.01662	−	5.52840i	−0.191268	−	0.263257i
$22$	15.4407	−	5.01698i	0.701848	−	0.228044i
$23$	4.97511	−	1.61651i	0.216309	−	0.0702831i	−0.198858	−	0.980028i	$-0.563723\pi$
$23$	4.97511	−	1.61651i	0.216309	−	0.0702831i	0.415167	+	0.909745i	$0.363723\pi$
$24$	−40.0122	−	13.0007i	−1.66717	−	0.541697i
$25$	29.3975			1.17590
$26$		−	66.4681i		−	2.55646i
$27$	−26.0751	−	8.47230i	−0.965743	−	0.313789i
$28$	28.6591	+	20.8220i	1.02354	+	0.743644i
$29$	21.1698	+	29.1378i	0.729994	+	1.00475i	0.999132	+	0.0416493i	$0.0132612\pi$
$29$	21.1698	+	29.1378i	0.729994	+	1.00475i	−0.269138	+	0.963102i	$0.586739\pi$
$30$			52.5487i			1.75162i
$31$	−30.8898	−	2.61211i	−0.996444	−	0.0842616i
$31$	−30.8898	−	2.61211i	−0.996444	−	0.0842616i
$32$	70.3573			2.19867
$33$	6.73010	−	4.88970i	0.203942	−	0.148173i
$34$	−36.9274	+	50.8262i	−1.08610	+	1.49489i
$35$	8.15128	−	25.0871i	0.232894	−	0.716773i
$36$	52.9843			1.47179
$37$			33.2298i			0.898102i	0.893506	+	0.449051i	$0.148238\pi$
$37$			33.2298i			0.898102i	−0.893506	+	0.449051i	$0.851762\pi$
$38$	−7.46760	+	22.9829i	−0.196516	+	0.604813i
$39$	−10.5245	−	32.3909i	−0.269858	−	0.830537i
$40$	−50.1845	−	154.452i	−1.25461	−	3.86130i
$41$	−2.36218	+	1.71622i	−0.0576141	+	0.0418591i	−0.616220	−	0.787574i	$-0.711337\pi$
$41$	−2.36218	+	1.71622i	−0.0576141	+	0.0418591i	0.558605	+	0.829434i	$0.311337\pi$
$42$	24.2344	+	7.87424i	0.577010	+	0.187482i
$43$	−12.6063	−	17.3510i	−0.293169	−	0.403512i	0.636871	−	0.770970i	$-0.280228\pi$
$43$	−12.6063	−	17.3510i	−0.293169	−	0.403512i	−0.930040	+	0.367458i	$0.880228\pi$
$44$	−25.3481	+	34.8886i	−0.576092	+	0.792923i
$45$	−12.1918	−	37.5226i	−0.270929	−	0.833835i
$46$	−11.4657	+	15.7811i	−0.249254	+	0.343068i
$47$	−10.5593	−	7.67178i	−0.224666	−	0.163229i	0.469759	−	0.882795i	$-0.344341\pi$
$47$	−10.5593	−	7.67178i	−0.224666	−	0.163229i	−0.694424	+	0.719566i	$0.744341\pi$
$48$	77.2070	−	25.0861i	1.60848	−	0.522627i
$49$	29.2936	+	21.2831i	0.597829	+	0.434348i
$50$	−88.6854	+	64.4337i	−1.77371	+	1.28867i
$51$	−9.94755	+	30.6154i	−0.195050	+	0.600302i
$52$	103.776	+	142.836i	1.99570	+	2.74684i
$53$	−39.1000	+	12.7043i	−0.737735	+	0.239705i	−0.653695	−	0.756758i	$-0.726782\pi$
$53$	−39.1000	+	12.7043i	−0.737735	+	0.239705i	−0.0840397	+	0.996462i	$0.526782\pi$
$54$	97.2320	−	31.5926i	1.80059	−	0.585048i
$55$	30.5402	+	9.92310i	0.555276	+	0.180420i
$56$	−78.7501			−1.40625
$57$			12.3823i			0.217234i
$58$	−127.729	−	41.5016i	−2.20222	−	0.715545i
$59$	−38.1942	−	27.7497i	−0.647360	−	0.470335i	0.215011	−	0.976612i	$-0.431021\pi$
$59$	−38.1942	−	27.7497i	−0.647360	−	0.470335i	−0.862371	+	0.506277i	$0.831021\pi$
$60$	−82.0440	−	112.924i	−1.36740	−	1.88207i
$61$			25.2189i			0.413425i	0.978402	+	0.206712i	$0.0662765\pi$
$61$			25.2189i			0.413425i	−0.978402	+	0.206712i	$0.933724\pi$
$62$	98.9124	−	59.8243i	1.59536	−	0.964908i
$63$	−19.1316			−0.303676
$64$	−74.7588	+	54.3155i	−1.16811	+	0.848679i
$65$	77.2747	−	106.359i	1.18884	−	1.63630i
$66$	−9.58584	+	29.5022i	−0.145240	+	0.447003i
$67$	63.6335			0.949754			0.474877	−	0.880052i	$-0.342493\pi$
$67$	63.6335			0.949754			0.474877	+	0.880052i	$0.342493\pi$
$68$		−	166.877i		−	2.45407i
$69$	−3.08864	+	9.50585i	−0.0447629	+	0.137766i
$70$	30.3955	+	93.5479i	0.434222	+	1.33640i
$71$	37.8748	+	116.567i	0.533448	+	1.64178i	0.746978	+	0.664848i	$0.231504\pi$
$71$	37.8748	+	116.567i	0.533448	+	1.64178i	−0.213530	+	0.976936i	$0.568496\pi$
$72$	−95.2910	+	69.2330i	−1.32349	+	0.961569i
$73$	−8.37951	−	2.72267i	−0.114788	−	0.0372968i	0.251060	−	0.967972i	$-0.419221\pi$
$73$	−8.37951	−	2.72267i	−0.114788	−	0.0372968i	−0.365848	+	0.930675i	$0.619221\pi$
$74$	−72.8333	−	100.246i	−0.984234	−	1.35468i
$75$	−33.0155	+	45.4419i	−0.440206	+	0.605892i
$76$	−19.8357	−	61.0480i	−0.260996	−	0.803263i
$77$	9.15268	−	12.5976i	0.118866	−	0.163605i
$78$	102.745	+	74.6483i	1.31724	+	0.957030i
$79$	120.538	−	39.1653i	1.52580	−	0.495763i	0.578384	−	0.815765i	$-0.303684\pi$
$79$	120.538	−	39.1653i	1.52580	−	0.495763i	0.947417	+	0.320002i	$0.103684\pi$
$80$	253.518	+	184.192i	3.16898	+	2.30240i
$81$	3.43131	−	2.49299i	0.0423618	−	0.0307777i
$82$	3.36451	−	10.3549i	0.0410306	−	0.126279i
$83$	−42.9969	−	59.1801i	−0.518035	−	0.713014i	0.467213	−	0.884145i	$-0.345258\pi$
$83$	−42.9969	−	59.1801i	−0.518035	−	0.713014i	−0.985248	+	0.171131i	$0.945258\pi$
$84$	−64.3723	+	20.9158i	−0.766337	+	0.248998i
$85$	−118.179	+	38.3988i	−1.39035	+	0.451751i
$86$	76.0603	+	24.7135i	0.884422	+	0.287366i
$87$	−68.8156			−0.790984
$88$		−	95.8678i		−	1.08941i
$89$	64.4529	+	20.9420i	0.724190	+	0.235304i	0.647839	−	0.761777i	$-0.275673\pi$
$89$	64.4529	+	20.9420i	0.724190	+	0.235304i	0.0763512	+	0.997081i	$0.475673\pi$
$90$	119.022	+	86.4747i	1.32247	+	0.960830i
$91$	−37.4715	−	51.5752i	−0.411775	−	0.566760i
$92$		−	51.8140i		−	0.563195i
$93$	38.7291	−	44.8150i	0.416442	−	0.481881i
$94$	48.6700			0.517766
$95$	−38.6689	+	28.0946i	−0.407041	+	0.295733i
$96$	−79.0162	+	108.756i	−0.823086	+	1.13288i
$97$	−46.0155	+	141.621i	−0.474386	+	1.46001i	0.372397	+	0.928073i	$0.378536\pi$
$97$	−46.0155	+	141.621i	−0.474386	+	1.46001i	−0.846783	+	0.531938i	$0.821464\pi$
$98$	−135.020			−1.37776
$99$		−	23.2902i		−	0.235254i
$100$	89.9795	−	276.928i	0.899795	−	2.76928i
$101$	5.51111	+	16.9614i	0.0545654	+	0.167935i	0.974625	−	0.223843i	$-0.0718602\pi$
$101$	5.51111	+	16.9614i	0.0545654	+	0.167935i	−0.920060	+	0.391778i	$0.871860\pi$
$102$	−37.0937	−	114.163i	−0.363664	−	1.11924i
$103$	−24.8663	+	18.0664i	−0.241420	+	0.175402i	−0.701916	−	0.712260i	$-0.747672\pi$
$103$	−24.8663	+	18.0664i	−0.241420	+	0.175402i	0.460495	+	0.887662i	$0.347672\pi$
$104$	−373.278	−	121.285i	−3.58922	−	1.16621i
$105$	29.6245	+	40.7746i	0.282138	+	0.388329i
$106$	90.1100	−	124.026i	0.850094	−	1.17005i
$107$	13.0676	+	40.2179i	0.122127	+	0.375869i	0.993367	−	0.114989i	$-0.0366834\pi$
$107$	13.0676	+	40.2179i	0.122127	+	0.375869i	−0.871240	+	0.490858i	$0.836683\pi$
$108$	−159.620	+	219.698i	−1.47797	+	2.03425i
$109$	−19.0809	−	13.8631i	−0.175054	−	0.127184i	0.496808	−	0.867860i	$-0.334505\pi$
$109$	−19.0809	−	13.8631i	−0.175054	−	0.127184i	−0.671862	+	0.740676i	$0.734505\pi$
$110$	−113.882	+	37.0025i	−1.03529	+	0.336387i
$111$	−51.3657	−	37.3194i	−0.462754	−	0.336210i
$112$	122.935	−	89.3172i	1.09763	−	0.797475i
$113$	−21.2095	+	65.2760i	−0.187694	+	0.577664i	−0.999984	−	0.00558998i	$-0.998221\pi$
$113$	−21.2095	+	65.2760i	−0.187694	+	0.577664i	0.812290	+	0.583254i	$0.198221\pi$
$114$	−27.1397	−	37.3546i	−0.238068	−	0.327672i
$115$	−36.6938	+	11.9225i	−0.319076	+	0.103674i
$116$	339.278	−	110.238i	2.92481	−	0.950328i
$117$	−90.6843	−	29.4651i	−0.775080	−	0.251839i
$118$	176.045			1.49191
$119$			60.2559i			0.506352i
$120$	295.108	+	95.8865i	2.45924	+	0.799054i
$121$	−82.5552	−	59.9798i	−0.682274	−	0.495701i
$122$	−55.2751	−	76.0796i	−0.453074	−	0.623603i
$123$		−	5.57883i		−	0.0453564i
$124$	−119.153	+	282.990i	−0.960914	+	2.28218i
$125$	−32.4337			−0.259470
$126$	57.7155	−	41.9328i	0.458060	−	0.332800i
$127$	97.9114	−	134.763i	0.770956	−	1.06113i	−0.225267	−	0.974297i	$-0.572325\pi$
$127$	97.9114	−	134.763i	0.770956	−	1.06113i	0.996223	−	0.0868325i	$-0.0276745\pi$
$128$	19.5144	−	60.0591i	0.152456	−	0.469212i
$129$	40.9785			0.317663
$130$			490.233i			3.77102i
$131$	−39.7089	+	122.212i	−0.303122	+	0.932913i	0.677250	+	0.735753i	$0.263172\pi$
$131$	−39.7089	+	122.212i	−0.303122	+	0.932913i	−0.980371	+	0.197159i	$0.936828\pi$
$132$	−25.4622	−	78.3647i	−0.192896	−	0.593672i
$133$	7.16227	+	22.0432i	0.0538517	+	0.165738i
$134$	−191.967	+	139.473i	−1.43259	+	1.04084i
$135$	192.316	+	62.4872i	1.42456	+	0.462868i
$136$	218.053	+	300.124i	1.60333	+	2.20679i
$137$	128.275	−	176.556i	0.936315	−	1.28873i	−0.0210299	−	0.999779i	$-0.506695\pi$
$137$	128.275	−	176.556i	0.936315	−	1.28873i	0.957345	−	0.288948i	$-0.0933055\pi$
$138$	−11.5173	−	35.4466i	−0.0834588	−	0.256860i
$139$	125.828	−	173.188i	0.905241	−	1.24596i	−0.0635254	−	0.997980i	$-0.520234\pi$
$139$	125.828	−	173.188i	0.905241	−	1.24596i	0.968766	−	0.247977i	$-0.0797656\pi$
$140$	−211.374	−	153.572i	−1.50981	−	1.09694i
$141$	23.7177	−	7.70634i	0.168210	−	0.0546549i
$142$	−369.752	−	268.640i	−2.60388	−	1.89183i
$143$	62.7859	−	45.6166i	0.439062	−	0.318997i
$144$	70.2330	−	216.155i	0.487729	−	1.50108i
$145$	−156.137	−	214.905i	−1.07681	−	1.48210i
$146$	31.2466	−	10.1526i	0.214018	−	0.0695386i
$147$	−65.7976	+	21.3789i	−0.447603	+	0.145435i
$148$	313.029	+	101.709i	2.11506	+	0.687224i
$149$	175.770			1.17967			0.589833	−	0.807525i	$-0.299194\pi$
$149$	175.770			1.17967			0.589833	+	0.807525i	$0.299194\pi$
$150$		−	209.451i		−	1.39634i
$151$	−200.899	−	65.2761i	−1.33046	−	0.432292i	−0.444385	−	0.895836i	$-0.646578\pi$
$151$	−200.899	−	65.2761i	−1.33046	−	0.432292i	−0.886074	+	0.463544i	$0.846578\pi$
$152$	115.444	+	83.8747i	0.759497	+	0.551807i
$153$	52.9738	+	72.9122i	0.346234	+	0.476550i
$154$			58.0649i			0.377045i
$155$	227.826	+	19.2655i	1.46985	+	0.124294i
$156$	−337.340			−2.16244
$157$	−73.4673	+	53.3771i	−0.467945	+	0.339982i	−0.796640	−	0.604454i	$-0.793391\pi$
$157$	−73.4673	+	53.3771i	−0.467945	+	0.339982i	0.328695	+	0.944436i	$0.393391\pi$
$158$	−277.793	+	382.349i	−1.75818	+	2.41993i
$159$	24.2740	−	74.7076i	0.152666	−	0.469859i
$160$	−518.918			−3.24324
$161$			18.7090i			0.116205i
$162$	−4.88729	+	15.0415i	−0.0301685	+	0.0928491i
$163$	68.3485	+	210.355i	0.419316	+	1.29052i	0.908333	+	0.418247i	$0.137355\pi$
$163$	68.3485	+	210.355i	0.419316	+	1.29052i	−0.489017	+	0.872274i	$0.662645\pi$
$164$	8.93692	+	27.5050i	0.0544934	+	0.167714i
$165$	−49.6376	+	36.0638i	−0.300834	+	0.218569i
$166$	259.423	+	84.2917i	1.56279	+	0.507781i
$167$	94.6307	+	130.248i	0.566651	+	0.779928i	0.992153	−	0.125029i	$-0.0399025\pi$
$167$	94.6307	+	130.248i	0.566651	+	0.779928i	−0.425502	+	0.904957i	$0.639903\pi$
$168$	88.4419	−	121.730i	0.526440	−	0.724583i
$169$	−45.9601	−	141.451i	−0.271953	−	0.836985i
$170$	272.357	−	374.867i	1.60210	−	2.20510i
$171$	28.0459	+	20.3765i	0.164011	+	0.119161i
$172$	−202.034	+	65.6448i	−1.17462	+	0.381656i
$173$	−147.394	−	107.088i	−0.851988	−	0.619005i	0.0737057	−	0.997280i	$-0.476517\pi$
$173$	−147.394	−	107.088i	−0.851988	−	0.619005i	−0.925693	+	0.378275i	$0.876517\pi$
$174$	207.601	−	150.831i	1.19311	−	0.866843i
$175$	−32.4898	+	99.9933i	−0.185656	+	0.571390i
$176$	108.732	+	149.656i	0.617794	+	0.850321i
$177$	85.7896	−	27.8747i	0.484687	−	0.157484i
$178$	−240.340	+	78.0913i	−1.35023	+	0.438715i
$179$	201.417	+	65.4444i	1.12524	+	0.365611i	0.811763	−	0.583986i	$-0.198508\pi$
$179$	201.417	+	65.4444i	1.12524	+	0.365611i	0.313472	+	0.949598i	$0.398508\pi$
$180$	−390.784			−2.17102
$181$			21.6213i			0.119455i	0.998215	+	0.0597275i	$0.0190232\pi$
$181$			21.6213i			0.119455i	−0.998215	+	0.0597275i	$0.980977\pi$
$182$	226.086	+	73.4597i	1.24223	+	0.403625i
$183$	−38.9827	−	28.3226i	−0.213020	−	0.154768i
$184$	67.7037	+	93.1862i	0.367955	+	0.506447i
$185$		−	245.085i		−	1.32478i
$186$	−18.6108	+	220.083i	−0.100058	+	1.18324i
$187$	−73.3536			−0.392265
$188$	−104.589	+	75.9883i	−0.556324	+	0.404193i
$189$	57.6357	−	79.3287i	0.304951	−	0.419729i
$190$	55.0770	−	169.510i	0.289879	−	0.892156i
$191$	−135.594			−0.709919			−0.354959	−	0.934882i	$-0.615505\pi$
$191$	−135.594			−0.709919			−0.354959	+	0.934882i	$0.615505\pi$
$192$		−	176.560i		−	0.919585i
$193$	32.8765	−	101.183i	0.170344	−	0.524266i	−0.829046	−	0.559181i	$-0.811116\pi$
$193$	32.8765	−	101.183i	0.170344	−	0.524266i	0.999390	+	0.0349144i	$0.0111159\pi$
$194$	−171.588	−	528.095i	−0.884477	−	2.72214i
$195$	77.6228	+	238.898i	0.398065	+	1.22512i
$196$	290.151	−	210.807i	1.48036	−	1.07554i
$197$	−298.018	−	96.8320i	−1.51278	−	0.491533i	−0.569067	−	0.822291i	$-0.692696\pi$
$197$	−298.018	−	96.8320i	−1.51278	−	0.491533i	−0.943716	+	0.330758i	$0.892696\pi$
$198$	51.0476	+	70.2610i	0.257816	+	0.354853i
$199$	−202.935	+	279.315i	−1.01977	+	1.40360i	−0.107408	+	0.994215i	$0.534255\pi$
$199$	−202.935	+	279.315i	−1.01977	+	1.40360i	−0.912364	+	0.409380i	$0.865745\pi$
$200$	200.028	+	615.622i	1.00014	+	3.07811i
$201$	−71.4649	+	98.3630i	−0.355547	+	0.489368i
$202$	−53.8020	−	39.0894i	−0.266346	−	0.193512i
$203$	−122.506	+	39.8048i	−0.603480	+	0.196083i
$204$	257.954	+	187.415i	1.26448	+	0.918699i
$205$	17.4222	−	12.6579i	0.0849862	−	0.0617461i
$206$	35.4177	−	109.004i	0.171930	−	0.529148i
$207$	16.4480	+	22.6387i	0.0794587	+	0.109366i
$208$	720.274	−	234.031i	3.46286	−	1.12515i
$209$	−26.8347	+	8.71912i	−0.128396	+	0.0417183i
$210$	−178.740	−	58.0762i	−0.851143	−	0.276553i
$211$	−62.8035			−0.297647			−0.148824	−	0.988864i	$-0.547549\pi$
$211$	−62.8035			−0.297647			−0.148824	+	0.988864i	$0.547549\pi$
$212$			407.212i			1.92081i
$213$	−222.722	−	72.3667i	−1.04564	−	0.339750i
$214$	−127.572	−	92.6865i	−0.596131	−	0.433114i
$215$	92.9771	+	127.972i	0.432451	+	0.595218i
$216$		−	603.693i		−	2.79488i
$217$	43.0239	−	102.182i	0.198267	−	0.470885i
$218$	87.9478			0.403430
$219$	13.6194	−	9.89508i	0.0621891	−	0.0451830i
$220$	186.954	−	257.320i	0.849790	−	1.16964i
$221$	−92.8020	+	285.615i	−0.419918	+	1.29238i
$222$	236.755			1.06647
$223$		−	425.325i		−	1.90729i	−0.300938	−	0.953644i	$-0.597300\pi$
$223$		−	425.325i		−	1.90729i	0.300938	−	0.953644i	$-0.402700\pi$
$224$	−77.7581	+	239.315i	−0.347134	+	1.06837i
$225$	48.5948	+	149.559i	0.215977	+	0.664708i
$226$	−79.0886	−	243.410i	−0.349949	−	1.07703i
$227$	30.8765	−	22.4331i	0.136020	−	0.0988241i	−0.517695	−	0.855565i	$-0.673210\pi$
$227$	30.8765	−	22.4331i	0.136020	−	0.0988241i	0.653715	+	0.756741i	$0.273210\pi$
$228$	116.643	+	37.8997i	0.511593	+	0.166227i
$229$	111.386	+	153.309i	0.486401	+	0.669473i	0.979719	−	0.200376i	$-0.0642162\pi$
$229$	111.386	+	153.309i	0.486401	+	0.669473i	−0.493318	+	0.869849i	$0.664216\pi$
$230$	84.5646	−	116.393i	0.367672	−	0.506057i
$231$	9.19390	+	28.2959i	0.0398005	+	0.122493i
$232$	−466.138	+	641.584i	−2.00922	+	2.76545i
$233$	274.179	+	199.203i	1.17673	+	0.854947i	0.991800	−	0.127804i	$-0.0407927\pi$
$233$	274.179	+	199.203i	1.17673	+	0.854947i	0.184935	+	0.982751i	$0.440793\pi$
$234$	338.155	−	109.873i	1.44511	−	0.469544i
$235$	77.8797	+	56.5829i	0.331403	+	0.240779i
$236$	−378.311	+	274.859i	−1.60301	+	1.16466i
$237$	−74.8323	+	230.310i	−0.315748	+	0.971773i
$238$	−132.069	−	181.778i	−0.554914	−	0.763773i
$239$	−318.956	+	103.635i	−1.33454	+	0.433620i	−0.887465	−	0.460875i	$-0.847536\pi$
$239$	−318.956	+	103.635i	−1.33454	+	0.433620i	−0.447079	+	0.894495i	$0.647536\pi$
$240$	−569.438	+	185.022i	−2.37266	+	0.770923i
$241$	124.245	+	40.3696i	0.515539	+	0.167509i	0.555220	−	0.831704i	$-0.312634\pi$
$241$	124.245	+	40.3696i	0.515539	+	0.167509i	−0.0396810	+	0.999212i	$0.512634\pi$
$242$	380.514			1.57237
$243$		−	238.649i		−	0.982093i
$244$	237.565	+	77.1897i	0.973629	+	0.316351i
$245$	−216.054	−	156.972i	−0.881854	−	0.640704i
$246$	12.2277	+	16.8300i	0.0497062	+	0.0684148i
$247$			115.516i			0.467678i
$248$	−155.480	−	664.645i	−0.626937	−	2.68002i
$249$	139.768			0.561316
$250$	97.8450	−	71.0885i	0.391380	−	0.284354i
$251$	63.6126	−	87.5553i	0.253437	−	0.348826i	−0.663274	−	0.748376i	$-0.730834\pi$
$251$	63.6126	−	87.5553i	0.253437	−	0.348826i	0.916711	+	0.399551i	$0.130834\pi$
$252$	−58.5576	+	180.222i	−0.232372	+	0.715166i
$253$	−22.7757			−0.0900226
$254$			621.153i			2.44548i
$255$	73.3679	−	225.803i	0.287717	−	0.885502i
$256$	−41.4536	−	127.581i	−0.161928	−	0.498364i
$257$	83.1137	+	255.798i	0.323399	+	0.995321i	0.972158	+	0.234327i	$0.0752886\pi$
$257$	83.1137	+	255.798i	0.323399	+	0.995321i	−0.648758	+	0.760994i	$0.724711\pi$
$258$	−123.623	+	89.8170i	−0.479157	+	0.348128i
$259$	−113.028	−	36.7252i	−0.436403	−	0.141796i
$260$	−765.399	−	1053.48i	−2.94384	−	4.05185i
$261$	−113.244	+	155.867i	−0.433884	+	0.597190i
$262$	−148.072	−	455.718i	−0.565160	−	1.73938i
$263$	162.782	−	224.050i	0.618942	−	0.851901i	−0.378333	−	0.925669i	$-0.623503\pi$
$263$	162.782	−	224.050i	0.618942	−	0.851901i	0.997275	+	0.0737688i	$0.0235027\pi$
$264$	148.190	+	107.666i	0.561326	+	0.407827i
$265$	288.380	−	93.7005i	1.08823	−	0.353587i
$266$	−69.9214	−	50.8009i	−0.262862	−	0.190981i
$267$	−104.757	+	76.1102i	−0.392347	+	0.285057i
$268$	194.769	−	599.436i	0.726748	−	2.23670i
$269$	−160.796	−	221.316i	−0.597754	−	0.822738i	0.397746	−	0.917495i	$-0.369792\pi$
$269$	−160.796	−	221.316i	−0.597754	−	0.822738i	−0.995500	+	0.0947575i	$0.969792\pi$
$270$	−717.132	+	233.010i	−2.65604	+	0.863001i
$271$	228.416	−	74.2167i	0.842862	−	0.273862i	0.144409	−	0.989518i	$-0.453872\pi$
$271$	228.416	−	74.2167i	0.842862	−	0.273862i	0.698453	+	0.715656i	$0.253872\pi$
$272$	−680.792	−	221.203i	−2.50291	−	0.813245i
$273$	121.807			0.446178
$274$			813.782i			2.97001i
$275$	−121.729	−	39.5520i	−0.442649	−	0.143825i
$276$	80.0927	+	58.1907i	0.290191	+	0.210836i
$277$	−9.54891	−	13.1429i	−0.0344726	−	0.0474475i	0.791433	−	0.611256i	$-0.209336\pi$
$277$	−9.54891	−	13.1429i	−0.0344726	−	0.0474475i	−0.825905	+	0.563809i	$0.809336\pi$
$278$			798.260i			2.87144i
$279$	−37.7724	−	161.469i	−0.135385	−	0.578742i
$280$	580.819			2.07435
$281$	256.905	−	186.652i	0.914253	−	0.664244i	−0.0278341	−	0.999613i	$-0.508861\pi$
$281$	256.905	−	186.652i	0.914253	−	0.664244i	0.942087	+	0.335369i	$0.108861\pi$
$282$	−54.6598	+	75.2328i	−0.193829	+	0.266783i
$283$	38.4191	−	118.242i	0.135757	−	0.417816i	−0.859950	−	0.510378i	$-0.829506\pi$
$283$	38.4191	−	118.242i	0.135757	−	0.417816i	0.995707	+	0.0925618i	$0.0295056\pi$
$284$	1214.00			4.27465
$285$		−	91.3256i		−	0.320441i
$286$	−89.4275	+	275.230i	−0.312684	+	0.962341i
$287$	−3.22694	−	9.93151i	−0.0112437	−	0.0346046i
$288$	116.302	+	357.942i	0.403828	+	1.24285i
$289$	−4.16506	+	3.02609i	−0.0144120	+	0.0104709i
$290$	942.060	+	306.094i	3.24848	+	1.05550i
$291$	−167.236	−	230.180i	−0.574692	−	0.790996i
$292$	−51.2958	+	70.6026i	−0.175670	+	0.241790i
$293$	125.972	+	387.703i	0.429940	+	1.32322i	0.898184	+	0.439620i	$0.144887\pi$
$293$	125.972	+	387.703i	0.429940	+	1.32322i	−0.468244	+	0.883599i	$0.655113\pi$
$294$	151.637	−	208.711i	0.515773	−	0.709901i
$295$	281.700	+	204.667i	0.954917	+	0.693788i
$296$	−695.875	+	226.103i	−2.35093	+	0.763863i
$297$	96.5722	+	70.1638i	0.325159	+	0.236242i
$298$	−530.258	+	385.255i	−1.77939	+	1.29280i
$299$	−28.8143	+	88.6812i	−0.0963688	+	0.296593i
$300$	327.015	+	450.098i	1.09005	+	1.50033i
$301$	72.9504	−	23.7030i	0.242360	−	0.0787476i
$302$	749.139	−	243.410i	2.48059	−	0.805994i
$303$	−32.4079	−	10.5300i	−0.106957	−	0.0347524i
$304$	−275.345			−0.905740
$305$		−	186.001i		−	0.609840i
$306$	−319.619	−	103.851i	−1.04451	−	0.339381i
$307$	4.53444	+	3.29446i	0.0147702	+	0.0107312i	0.595146	−	0.803618i	$-0.297094\pi$
$307$	4.53444	+	3.29446i	0.0147702	+	0.0107312i	−0.580376	+	0.814349i	$0.697094\pi$
$308$	−90.6564	−	124.778i	−0.294339	−	0.405123i
$309$		−	58.7275i		−	0.190057i
$310$	−729.525	+	441.232i	−2.35331	+	1.42333i
$311$	−447.602			−1.43924			−0.719618	−	0.694370i	$-0.755683\pi$
$311$	−447.602			−1.43924			−0.719618	+	0.694370i	$0.755683\pi$
$312$	606.698	−	440.792i	1.94454	−	1.41279i
$313$	−63.4004	+	87.2632i	−0.202557	+	0.278796i	−0.898196	−	0.439596i	$-0.855122\pi$
$313$	−63.4004	+	87.2632i	−0.202557	+	0.278796i	0.695638	+	0.718392i	$0.255122\pi$
$314$	104.641	−	322.053i	0.333252	−	1.02565i
$315$	141.104			0.447950
$316$		−	1255.36i		−	3.97267i
$317$	101.657	−	312.869i	0.320686	−	0.986969i	−0.652665	−	0.757647i	$-0.726349\pi$
$317$	101.657	−	312.869i	0.320686	−	0.986969i	0.973351	−	0.229322i	$-0.0736509\pi$
$318$	90.5159	+	278.579i	0.284641	+	0.876035i
$319$	−48.4570	−	149.135i	−0.151903	−	0.467509i
$320$	551.381	−	400.602i	1.72307	−	1.25188i
$321$	−76.8437	−	24.9680i	−0.239388	−	0.0777820i
$322$	−41.0065	−	56.4407i	−0.127349	−	0.175282i
$323$	64.1769	−	88.3320i	0.198690	−	0.273474i
$324$	−12.9818	−	39.9539i	−0.0400673	−	0.123314i
$325$	−308.005	+	423.933i	−0.947709	+	1.30441i
$326$	−667.249	−	484.785i	−2.04678	−	1.48707i
$327$	42.8584	−	13.9255i	0.131065	−	0.0425857i
$328$	−52.0128	−	37.7895i	−0.158576	−	0.115212i
$329$	37.7649	−	27.4378i	0.114787	−	0.0833977i
$330$	70.7000	−	217.592i	0.214243	−	0.659371i
$331$	289.311	+	398.202i	0.874051	+	1.20303i	0.978033	+	0.208449i	$0.0668416\pi$
$331$	289.311	+	398.202i	0.874051	+	1.20303i	−0.103982	+	0.994579i	$0.533158\pi$
$332$	−689.089	+	223.899i	−2.07557	+	0.674393i
$333$	−169.056	+	54.9296i	−0.507675	+	0.164954i
$334$	−570.958	−	185.515i	−1.70945	−	0.555435i
$335$	−469.327			−1.40098
$336$			290.338i			0.864102i
$337$	143.542	+	46.6395i	0.425940	+	0.138396i	0.514139	−	0.857707i	$-0.328111\pi$
$337$	143.542	+	46.6395i	0.425940	+	0.138396i	−0.0881998	+	0.996103i	$0.528111\pi$
$338$	448.683	+	325.988i	1.32747	+	0.964460i
$339$	−77.0822	−	106.095i	−0.227381	−	0.312963i
$340$			1230.80i			3.61999i
$341$	124.393	+	52.3759i	0.364789	+	0.153595i
$342$	−129.269			−0.377980
$343$	−246.545	+	179.126i	−0.718791	+	0.522232i
$344$	277.577	−	382.052i	0.806910	−	1.11062i
$345$	22.7801	−	70.1101i	0.0660294	−	0.203218i
$346$	679.369			1.96349
$347$			112.647i			0.324630i	0.986739	+	0.162315i	$0.0518961\pi$
$347$			112.647i			0.324630i	−0.986739	+	0.162315i	$0.948104\pi$
$348$	−210.630	+	648.252i	−0.605258	+	1.86279i
$349$	13.9512	+	42.9375i	0.0399749	+	0.123030i	0.969052	−	0.246855i	$-0.0793971\pi$
$349$	13.9512	+	42.9375i	0.0399749	+	0.123030i	−0.929078	+	0.369885i	$0.879397\pi$
$350$	−121.152	−	372.868i	−0.346149	−	1.06534i
$351$	395.372	−	287.254i	1.12641	−	0.818388i
$352$	−291.334	−	94.6602i	−0.827653	−	0.268921i
$353$	−89.9734	−	123.838i	−0.254882	−	0.350815i	0.662332	−	0.749211i	$-0.269567\pi$
$353$	−89.9734	−	123.838i	−0.254882	−	0.350815i	−0.917214	+	0.398396i	$0.869567\pi$
$354$	−197.711	+	272.126i	−0.558506	+	0.768718i
$355$	−279.345	−	859.734i	−0.786886	−	2.42179i
$356$	394.553	−	543.056i	1.10830	−	1.52544i
$357$	−93.1420	−	67.6716i	−0.260902	−	0.189556i
$358$	−751.070	+	244.037i	−2.09796	+	0.681669i
$359$	262.911	+	191.016i	0.732343	+	0.532078i	0.890304	−	0.455367i	$-0.150492\pi$
$359$	262.911	+	191.016i	0.732343	+	0.532078i	−0.157961	+	0.987445i	$0.550492\pi$
$360$	702.816	−	510.625i	1.95227	−	1.41840i
$361$	−98.5770	+	303.389i	−0.273067	+	0.840412i
$362$	−47.3899	−	65.2266i	−0.130911	−	0.180184i
$363$	185.431	−	60.2500i	0.510828	−	0.165978i
$364$	−600.537	+	195.126i	−1.64983	+	0.536061i
$365$	61.8028	+	20.0810i	0.169323	+	0.0550163i
$366$	179.680			0.490928
$367$			12.0557i			0.0328493i	0.999865	+	0.0164247i	$0.00522836\pi$
$367$			12.0557i			0.0328493i	−0.999865	+	0.0164247i	$0.994772\pi$
$368$	−211.381	−	68.6817i	−0.574404	−	0.186635i
$369$	−12.6360	−	9.18059i	−0.0342439	−	0.0248796i
$370$	537.180	+	739.364i	1.45184	+	1.99828i
$371$		−	147.036i		−	0.396324i
$372$	−303.621	−	502.002i	−0.816187	−	1.34947i
$373$	586.802			1.57320			0.786598	−	0.617465i	$-0.211840\pi$
$373$	586.802			1.57320			0.786598	+	0.617465i	$0.211840\pi$
$374$	221.291	−	160.777i	0.591686	−	0.429885i
$375$	36.4253	−	50.1352i	0.0971343	−	0.133694i
$376$	88.8090	−	273.326i	0.236194	−	0.726931i
$377$	−641.989			−1.70289
$378$			365.643i			0.967309i
$379$	−227.668	+	700.691i	−0.600708	+	1.84879i	−0.0767384	+	0.997051i	$0.524451\pi$
$379$	−227.668	+	700.691i	−0.600708	+	1.84879i	−0.523969	+	0.851737i	$0.675549\pi$
$380$	146.298	+	450.258i	0.384994	+	1.18489i
$381$	98.3524	+	302.698i	0.258143	+	0.794482i
$382$	409.057	−	297.197i	1.07083	−	0.778003i
$383$	−75.9542	−	24.6790i	−0.198314	−	0.0644360i	0.208176	−	0.978091i	$-0.433247\pi$
$383$	−75.9542	−	24.6790i	−0.198314	−	0.0644360i	−0.406490	+	0.913655i	$0.633247\pi$
$384$	70.9217	+	97.6154i	0.184692	+	0.254207i
$385$	−67.5053	+	92.9130i	−0.175338	+	0.241333i
$386$	122.594	+	377.306i	0.317601	+	0.977475i
$387$	67.4346	−	92.8158i	0.174250	−	0.239834i
$388$	1193.25	+	866.944i	3.07538	+	2.23439i
$389$	179.869	−	58.4430i	0.462389	−	0.150239i	−0.0685532	−	0.997647i	$-0.521838\pi$
$389$	179.869	−	58.4430i	0.462389	−	0.150239i	0.530942	+	0.847408i	$0.321838\pi$
$390$	−757.789	−	550.566i	−1.94305	−	1.41171i
$391$	71.3017	−	51.8037i	0.182357	−	0.132490i
$392$	−246.374	+	758.262i	−0.628506	+	1.93434i
$393$	−144.315	−	198.633i	−0.367215	−	0.505428i
$394$	1111.29	−	361.080i	2.82053	−	0.916446i
$395$	−889.026	+	288.862i	−2.25070	+	0.731296i
$396$	−219.396	−	71.2862i	−0.554031	−	0.180016i
$397$	322.751			0.812974			0.406487	−	0.913657i	$-0.366754\pi$
$397$	322.751			0.812974			0.406487	+	0.913657i	$0.366754\pi$
$398$		−	1287.42i		−	3.23473i
$399$	−42.1175	−	13.6848i	−0.105558	−	0.0342978i
$400$	−1010.49	−	734.162i	−2.52622	−	1.83540i
$401$	−55.2544	−	76.0511i	−0.137792	−	0.189654i	0.734545	−	0.678560i	$-0.237396\pi$
$401$	−55.2544	−	76.0511i	−0.137792	−	0.189654i	−0.872336	+	0.488907i	$0.837396\pi$
$402$		−	453.376i		−	1.12780i
$403$	361.308	−	418.084i	0.896547	−	1.03743i
$404$	176.647			0.437246
$405$	−25.3075	+	18.3870i	−0.0624877	+	0.0453999i
$406$	282.329	−	388.593i	0.695392	−	0.957124i
$407$	44.7080	−	137.597i	0.109848	−	0.338076i
$408$	−708.813			−1.73729
$409$			240.778i			0.588700i	0.955698	+	0.294350i	$0.0951031\pi$
$409$			240.778i			0.588700i	−0.955698	+	0.294350i	$0.904897\pi$
$410$	−24.8148	+	76.3722i	−0.0605239	+	0.186274i
$411$	128.853	+	396.569i	0.313511	+	0.964887i
$412$	94.0777	+	289.541i	0.228344	+	0.702770i
$413$	136.600	−	99.2460i	0.330751	−	0.240305i
$414$	−99.2393	−	32.2448i	−0.239708	−	0.0778860i
$415$	317.122	+	436.481i	0.764150	+	1.05176i
$416$	−737.152	+	1014.60i	−1.77200	+	2.43895i
$417$	126.395	+	389.005i	0.303106	+	0.932865i
$418$	61.8433	−	85.1200i	0.147951	−	0.203636i
$419$	−574.377	−	417.309i	−1.37083	−	0.995965i	−0.997672	−	0.0681963i	$-0.978276\pi$
$419$	−574.377	−	417.309i	−1.37083	−	0.995965i	−0.373156	−	0.927769i	$-0.621724\pi$
$420$	474.776	−	154.264i	1.13042	−	0.367295i
$421$	9.97296	+	7.24578i	0.0236887	+	0.0172109i	0.599567	−	0.800325i	$-0.295340\pi$
$421$	9.97296	+	7.24578i	0.0236887	+	0.0172109i	−0.575878	+	0.817536i	$0.695340\pi$
$422$	189.464	−	137.653i	0.448966	−	0.326193i
$423$	21.5753	−	66.4019i	0.0510054	−	0.156978i
$424$	−532.091	−	732.361i	−1.25493	−	1.72727i
$425$	471.045	−	153.052i	1.10834	−	0.360122i
$426$	830.514	−	269.850i	1.94956	−	0.633451i
$427$	−85.7801	−	27.8717i	−0.200890	−	0.0652732i
$428$	418.855			0.978634
$429$			148.283i			0.345649i
$430$	−560.980	−	182.274i	−1.30461	−	0.423892i
$431$	−24.6913	−	17.9393i	−0.0572884	−	0.0416224i	0.558773	−	0.829321i	$-0.311272\pi$
$431$	−24.6913	−	17.9393i	−0.0572884	−	0.0416224i	−0.616061	+	0.787699i	$0.711272\pi$
$432$	684.699	+	942.408i	1.58495	+	2.18150i
$433$		−	206.190i		−	0.476189i	−0.971242	−	0.238095i	$-0.923477\pi$
$433$		−	206.190i		−	0.476189i	0.971242	−	0.238095i	$-0.0765228\pi$
$434$	94.1708	+	402.560i	0.216983	+	0.927557i
$435$	507.547			1.16678
$436$	−188.995	+	137.313i	−0.433474	+	0.314937i
$437$	19.9264	−	27.4264i	0.0455983	−	0.0627606i
$438$	−19.3985	+	59.7023i	−0.0442887	+	0.136307i
$439$	−152.080			−0.346423			−0.173211	−	0.984885i	$-0.555414\pi$
$439$	−152.080			−0.346423			−0.173211	+	0.984885i	$0.555414\pi$
$440$			707.070i			1.60698i
$441$	−59.8542	+	184.212i	−0.135724	+	0.417715i
$442$	−346.052	−	1065.04i	−0.782923	−	2.40959i
$443$	−96.8338	−	298.024i	−0.218586	−	0.672740i	−0.998880	−	0.0473257i	$-0.984930\pi$
$443$	−96.8338	−	298.024i	−0.218586	−	0.672740i	0.780293	−	0.625414i	$-0.215070\pi$
$444$	−508.773	+	369.645i	−1.14588	+	0.832534i
$445$	−475.370	−	154.457i	−1.06825	−	0.347095i
$446$	932.232	+	1283.11i	2.09021	+	2.87692i
$447$	−197.402	+	271.701i	−0.441616	+	0.607832i
$448$	−102.127	−	314.315i	−0.227962	−	0.701596i
$449$	−110.208	+	151.689i	−0.245453	+	0.337837i	−0.913912	−	0.405912i	$-0.866954\pi$
$449$	−110.208	+	151.689i	−0.245453	+	0.337837i	0.668460	+	0.743748i	$0.266954\pi$
$450$	−474.405	−	344.675i	−1.05423	−	0.765945i
$451$	12.0903	−	3.92838i	0.0268078	−	0.00871037i
$452$	549.991	+	399.592i	1.21679	+	0.884052i
$453$	326.526	−	237.235i	0.720808	−	0.523698i
$454$	−43.9781	+	135.351i	−0.0968681	+	0.298129i
$455$	276.370	+	380.391i	0.607407	+	0.836024i
$456$	−259.302	+	84.2525i	−0.568646	+	0.184764i
$457$	171.813	−	55.8253i	0.375958	−	0.122156i	−0.114942	−	0.993372i	$-0.536668\pi$
$457$	171.813	−	55.8253i	0.375958	−	0.122156i	0.490900	+	0.871216i	$0.336668\pi$
$458$	−672.050	−	218.362i	−1.46736	−	0.476773i
$459$	−461.918			−1.00636
$460$			382.152i			0.830766i
$461$	765.975	+	248.880i	1.66155	+	0.539871i	0.981196	−	0.193013i	$-0.0618258\pi$
$461$	765.975	+	248.880i	1.66155	+	0.539871i	0.680354	+	0.732883i	$0.261826\pi$
$462$	−89.7551	−	65.2109i	−0.194275	−	0.141149i
$463$	−186.120	−	256.172i	−0.401987	−	0.553288i	0.559254	−	0.828996i	$-0.311088\pi$
$463$	−186.120	−	256.172i	−0.401987	−	0.553288i	−0.961241	+	0.275708i	$0.911088\pi$
$464$		−	1530.25i		−	3.29794i
$465$	−285.645	+	330.531i	−0.614291	+	0.710820i
$466$	−1263.75			−2.71191
$467$	−43.6169	+	31.6895i	−0.0933981	+	0.0678577i	−0.633504	−	0.773739i	$-0.718384\pi$
$467$	−43.6169	+	31.6895i	−0.0933981	+	0.0678577i	0.540106	+	0.841597i	$0.318384\pi$
$468$	−555.130	+	764.072i	−1.18618	+	1.63263i
$469$	−70.3270	+	216.444i	−0.149951	+	0.461502i
$470$	−358.964			−0.763753
$471$		−	173.510i		−	0.368387i
$472$	321.233	−	988.653i	0.680578	−	2.09460i
$473$	28.8553	+	88.8075i	0.0610049	+	0.187754i
$474$	−279.044	−	858.810i	−0.588701	−	1.81184i
$475$	154.128	−	111.981i	0.324481	−	0.235749i
$476$	567.619	+	184.430i	1.19248	+	0.387459i
$477$	−129.266	−	177.920i	−0.270999	−	0.372998i
$478$	735.068	−	1011.73i	1.53780	−	2.11660i
$479$	39.0062	+	120.049i	0.0814326	+	0.250624i	0.983481	−	0.181011i	$-0.0579369\pi$
$479$	39.0062	+	120.049i	0.0814326	+	0.250624i	−0.902048	+	0.431635i	$0.857937\pi$
$480$	582.781	−	802.130i	1.21413	−	1.67110i
$481$	−479.197	−	348.157i	−0.996251	−	0.723819i
$482$	−463.300	+	150.535i	−0.961204	+	0.312314i
$483$	−28.9199	−	21.0115i	−0.0598755	−	0.0435021i
$484$	−817.702	+	594.095i	−1.68947	+	1.22747i
$485$	339.386	−	1044.52i	0.699764	−	2.15365i
$486$	523.072	+	719.947i	1.07628	+	1.48137i
$487$	298.190	−	96.8878i	0.612300	−	0.198948i	0.0135814	−	0.999908i	$-0.495677\pi$
$487$	298.190	−	96.8878i	0.612300	−	0.198948i	0.598719	+	0.800959i	$0.295677\pi$
$488$	−528.117	+	171.596i	−1.08221	+	0.351630i
$489$	−401.921	−	130.592i	−0.821925	−	0.267060i
$490$	995.839			2.03232
$491$			709.358i			1.44472i	0.691517	+	0.722360i	$0.256943\pi$
$491$			709.358i			1.44472i	−0.691517	+	0.722360i	$0.743057\pi$
$492$	−52.5533	−	17.0756i	−0.106816	−	0.0347065i
$493$	490.910	+	356.667i	0.995761	+	0.723463i
$494$	−253.190	−	348.486i	−0.512530	−	0.705437i
$495$			171.776i			0.347022i
$496$	996.546	+	861.215i	2.00917	+	1.73632i
$497$	−438.351			−0.881994
$498$	−421.646	+	306.344i	−0.846679	+	0.615149i
$499$	−57.3336	+	78.9129i	−0.114897	+	0.158142i	−0.862592	−	0.505900i	$-0.831160\pi$
$499$	−57.3336	+	78.9129i	−0.114897	+	0.158142i	0.747695	+	0.664042i	$0.231160\pi$
$500$	−99.2727	+	305.530i	−0.198545	+	0.611060i
$501$	−307.611			−0.613994
$502$			403.561i			0.803905i
$503$	−102.762	+	316.268i	−0.204297	+	0.628763i	0.795444	+	0.606027i	$0.207238\pi$
$503$	−102.762	+	316.268i	−0.204297	+	0.628763i	−0.999742	+	0.0227359i	$0.992762\pi$
$504$	−130.176	−	400.640i	−0.258285	−	0.794921i
$505$	−40.6470	−	125.099i	−0.0804891	−	0.247720i
$506$	68.7090	−	49.9200i	0.135789	−	0.0986562i
$507$	270.267	+	87.8150i	0.533071	+	0.173205i
$508$	−969.804	−	1334.82i	−1.90906	−	2.62760i
$509$	115.703	−	159.251i	0.227314	−	0.312871i	−0.680091	−	0.733128i	$-0.738060\pi$
$509$	115.703	−	159.251i	0.227314	−	0.312871i	0.907405	+	0.420256i	$0.138060\pi$
$510$	273.584	+	842.004i	0.536438	+	1.65099i
$511$	18.5219	−	25.4932i	0.0362463	−	0.0498888i
$512$	609.047	+	442.498i	1.18954	+	0.864254i
$513$	−168.982	+	54.9055i	−0.329399	+	0.107028i
$514$	−811.394	−	589.512i	−1.57859	−	1.14691i
$515$	183.401	−	133.248i	0.356118	−	0.258735i
$516$	125.426	−	386.023i	0.243074	−	0.748106i
$517$	33.4019	+	45.9738i	0.0646072	+	0.0889242i
$518$	421.475	−	136.945i	0.813658	−	0.264374i
$519$	331.067	−	107.570i	0.637895	−	0.207265i
$520$	2753.10	+	894.537i	5.29443	+	1.72026i
$521$	−751.787			−1.44297			−0.721485	−	0.692430i	$-0.756540\pi$
$521$	−751.787			−1.44297			−0.721485	+	0.692430i	$0.756540\pi$
$522$		−	718.422i		−	1.37629i
$523$	187.841	+	61.0334i	0.359161	+	0.116699i	0.483039	−	0.875599i	$-0.339533\pi$
$523$	187.841	+	61.0334i	0.359161	+	0.116699i	−0.123877	+	0.992298i	$0.539533\pi$
$524$	1029.71	+	748.127i	1.96509	+	1.42772i
$525$	−118.079	−	162.521i	−0.224912	−	0.309564i
$526$			1032.69i			1.96329i
$527$	−508.555	+	118.966i	−0.965001	+	0.225742i
$528$	−353.448			−0.669410
$529$	−405.831	+	294.854i	−0.767167	+	0.557379i
$530$	−664.603	+	914.748i	−1.25397	+	1.72594i
$531$	78.0404	−	240.184i	0.146969	−	0.452323i
$532$	229.572			0.431526
$533$		−	52.0456i		−	0.0976466i
$534$	149.208	−	459.214i	0.279415	−	0.859951i
$535$	−96.3797	−	296.626i	−0.180149	−	0.554441i
$536$	432.978	+	1332.57i	0.807794	+	2.48614i
$537$	−327.368	+	237.847i	−0.609623	+	0.442917i
$538$	970.167	+	315.226i	1.80328	+	0.585923i
$539$	−92.6637	−	127.541i	−0.171918	−	0.236625i
$540$	1177.27	−	1620.38i	2.18014	−	3.00070i
$541$	−103.255	−	317.785i	−0.190859	−	0.587403i	0.809141	−	0.587614i	$-0.199933\pi$
$541$	−103.255	−	317.785i	−0.190859	−	0.587403i	−1.00000		0.000211431i	$0.999933\pi$
$542$	−526.408	+	724.538i	−0.971232	+	1.33679i
$543$	−33.4217	−	24.2823i	−0.0615501	−	0.0447188i
$544$	1127.36	−	366.300i	2.07235	−	0.673346i
$545$	140.730	+	102.247i	0.258221	+	0.187609i
$546$	−367.462	+	266.977i	−0.673008	+	0.488969i
$547$	−23.8250	+	73.3258i	−0.0435557	+	0.134051i	−0.970470	−	0.241223i	$-0.922451\pi$
$547$	−23.8250	+	73.3258i	−0.0435557	+	0.134051i	0.926914	+	0.375274i	$0.122451\pi$
$548$	−1270.55	−	1748.77i	−2.31853	−	3.19118i
$549$	−128.301	+	41.6875i	−0.233699	+	0.0759335i
$550$	453.917	−	147.487i	0.825304	−	0.268157i
$551$	221.983	+	72.1266i	0.402873	+	0.130901i
$552$	−220.081			−0.398697
$553$			453.286i			0.819686i
$554$	57.6137	+	18.7198i	0.103996	+	0.0337903i
$555$	378.846	+	275.248i	0.682605	+	0.495942i
$556$	−1246.32	−	1715.41i	−2.24158	−	3.08527i
$557$		−	970.890i		−	1.74307i	−0.490333	−	0.871535i	$-0.663125\pi$
$557$		−	970.890i		−	1.74307i	0.490333	−	0.871535i	$-0.336875\pi$
$558$	467.860	+	404.324i	0.838459	+	0.724596i
$559$	382.293			0.683888
$560$	−906.700	+	658.756i	−1.61911	+	1.17635i
$561$	82.3812	−	113.388i	0.146847	−	0.202118i
$562$	−365.916	+	1126.17i	−0.651096	+	2.00387i
$563$	435.344			0.773257			0.386629	−	0.922236i	$-0.373640\pi$
$563$	435.344			0.773257			0.386629	+	0.922236i	$0.373640\pi$
$564$		−	247.011i		−	0.437963i
$565$	156.430	−	481.441i	0.276867	−	0.852108i
$566$	143.262	+	440.916i	0.253113	+	0.779003i
$567$	4.68747	+	14.4265i	0.00826714	+	0.0254436i
$568$	−2183.35	+	1586.30i	−3.84393	+	2.79278i
$569$	−253.356	−	82.3203i	−0.445265	−	0.144675i	0.0777984	−	0.996969i	$-0.475211\pi$
$569$	−253.356	−	82.3203i	−0.445265	−	0.144675i	−0.523064	+	0.852294i	$0.675211\pi$
$570$	200.168	+	275.508i	0.351172	+	0.483347i
$571$	145.123	−	199.745i	0.254156	−	0.349815i	−0.662806	−	0.748792i	$-0.730634\pi$
$571$	145.123	−	199.745i	0.254156	−	0.349815i	0.916961	+	0.398976i	$0.130634\pi$
$572$	−237.540	−	731.074i	−0.415280	−	1.27810i
$573$	152.282	−	209.598i	0.265763	−	0.365791i
$574$	31.5029	+	22.8882i	0.0548831	+	0.0398749i
$575$	146.256	−	47.5214i	0.254358	−	0.0826459i
$576$	−399.907	−	290.550i	−0.694284	−	0.504427i
$577$	53.8913	−	39.1543i	0.0933991	−	0.0678584i	−0.540106	−	0.841597i	$-0.681616\pi$
$577$	53.8913	−	39.1543i	0.0933991	−	0.0678584i	0.633505	+	0.773739i	$0.281616\pi$
$578$	5.93240	−	18.2580i	0.0102637	−	0.0315883i
$579$	119.484	+	164.456i	0.206363	+	0.284034i
$580$	−2502.33	+	813.057i	−4.31437	+	1.40182i
$581$	248.816	−	80.8453i	0.428255	−	0.139149i
$582$	1009.02	+	327.851i	1.73371	+	0.563318i
$583$	178.997			0.307027
$584$		−	194.004i		−	0.332198i
$585$	668.839	+	217.319i	1.14331	+	0.371485i
$586$	−1229.80	−	893.503i	−2.09864	−	1.52475i
$587$	203.093	+	279.534i	0.345985	+	0.476207i	0.946177	−	0.323648i	$-0.104909\pi$
$587$	203.093	+	279.534i	0.345985	+	0.476207i	−0.600193	+	0.799855i	$0.704909\pi$
$588$			685.258i			1.16540i
$589$	−171.902	+	103.970i	−0.291854	+	0.176520i
$590$	−1298.42			−2.20071
$591$	484.376	−	351.919i	0.819587	−	0.595464i
$592$	829.867	−	1142.21i	1.40180	−	1.92941i
$593$	108.215	−	333.052i	0.182488	−	0.561639i	−0.817408	−	0.576059i	$-0.804590\pi$
$593$	108.215	−	333.052i	0.182488	−	0.561639i	0.999896	+	0.0144195i	$0.00459004\pi$
$594$	−445.121			−0.749363
$595$		−	444.415i		−	0.746917i
$596$	537.995	−	1655.78i	0.902676	−	2.77815i
$597$	−203.849	−	627.382i	−0.341455	−	1.05089i
$598$	−107.446	−	330.686i	−0.179676	−	0.552987i
$599$	74.0813	−	53.8232i	0.123675	−	0.0898551i	−0.524228	−	0.851578i	$-0.675646\pi$
$599$	74.0813	−	53.8232i	0.123675	−	0.0898551i	0.647903	+	0.761723i	$0.275646\pi$
$600$	−1176.26	−	382.189i	−1.96043	−	0.636982i
$601$	−147.383	−	202.856i	−0.245230	−	0.337530i	0.668604	−	0.743619i	$-0.266892\pi$
$601$	−147.383	−	202.856i	−0.245230	−	0.337530i	−0.913834	+	0.406089i	$0.866892\pi$
$602$	−168.122	+	231.400i	−0.279272	+	0.384385i
$603$	105.188	+	323.734i	0.174441	+	0.536873i
$604$	−1229.82	+	1692.70i	−2.03613	+	2.80249i
$605$	608.883	+	442.379i	1.00642	+	0.731206i
$606$	120.847	−	39.2655i	0.199417	−	0.0647946i
$607$	833.849	+	605.826i	1.37372	+	0.998067i	0.997436	+	0.0715626i	$0.0227986\pi$
$607$	833.849	+	605.826i	1.37372	+	0.998067i	0.376285	+	0.926504i	$0.377201\pi$
$608$	368.877	−	268.005i	0.606706	−	0.440797i
$609$	76.0542	−	234.071i	0.124884	−	0.384353i
$610$	407.679	+	561.123i	0.668327	+	0.919873i
$611$	221.265	−	71.8934i	0.362136	−	0.117665i
$612$	848.984	−	275.852i	1.38723	−	0.450738i
$613$	422.533	+	137.289i	0.689287	+	0.223963i	0.632657	−	0.774432i	$-0.281964\pi$
$613$	422.533	+	137.289i	0.689287	+	0.223963i	0.0566303	+	0.998395i	$0.481964\pi$
$614$	−20.9002			−0.0340394
$615$			41.1465i			0.0669049i
$616$	326.087	+	105.952i	0.529362	+	0.172000i
$617$	−346.471	−	251.726i	−0.561541	−	0.407984i	0.270481	−	0.962725i	$-0.412817\pi$
$617$	−346.471	−	251.726i	−0.561541	−	0.407984i	−0.832023	+	0.554742i	$0.812817\pi$
$618$	128.720	+	177.167i	0.208284	+	0.286678i
$619$		−	139.551i		−	0.225445i	−0.993626	−	0.112723i	$-0.964043\pi$
$619$		−	139.551i		−	0.225445i	0.993626	−	0.112723i	$-0.0359572\pi$
$620$	878.812	−	2087.19i	1.41744	−	3.36643i
$621$	−143.422			−0.230953
$622$	1350.31	−	981.059i	2.17092	−	1.57727i
$623$	−142.465	+	196.087i	−0.228676	+	0.314746i
$624$	−447.159	+	1376.21i	−0.716601	+	2.20547i
$625$	−495.724			−0.793158
$626$		−	402.214i		−	0.642515i
$627$	16.6595	−	51.2725i	0.0265701	−	0.0817743i
$628$	277.952	+	855.448i	0.442598	+	1.36218i
$629$	173.004	+	532.451i	0.275046	+	0.846503i
$630$	−425.679	+	309.274i	−0.675681	+	0.490911i
$631$	−1049.84	−	341.115i	−1.66378	−	0.540594i	−0.682120	−	0.731241i	$-0.738942\pi$
$631$	−1049.84	−	341.115i	−1.66378	−	0.540594i	−0.981659	+	0.190646i	$0.938942\pi$
$632$	1640.34	+	2257.74i	2.59548	+	3.57237i
$633$	70.5328	−	97.0800i	0.111426	−	0.153365i
$634$	379.073	+	1166.67i	0.597907	+	1.84017i
$635$	−722.142	+	993.943i	−1.13723	+	1.56527i
$636$	−629.457	−	457.328i	−0.989713	−	0.719069i
$637$	−613.834	+	199.447i	−0.963632	+	0.313103i
$638$	473.060	+	343.698i	0.741473	+	0.538712i
$639$	−530.423	+	385.375i	−0.830084	+	0.603091i
$640$	−143.928	+	442.964i	−0.224887	+	0.692131i
$641$	241.959	+	333.027i	0.377470	+	0.519544i	0.954912	−	0.296888i	$-0.0959489\pi$
$641$	241.959	+	333.027i	0.377470	+	0.519544i	−0.577442	+	0.816432i	$0.695949\pi$
$642$	286.545	−	93.1040i	0.446331	−	0.145022i
$643$	−613.968	+	199.490i	−0.954849	+	0.310249i	−0.744684	−	0.667417i	$-0.767400\pi$
$643$	−613.968	+	199.490i	−0.954849	+	0.310249i	−0.210165	+	0.977666i	$0.567400\pi$
$644$	176.241	+	57.2642i	0.273666	+	0.0889196i
$645$	−302.235			−0.468582
$646$			407.141i			0.630249i
$647$	419.167	+	136.196i	0.647862	+	0.210503i	0.614471	−	0.788939i	$-0.289369\pi$
$647$	419.167	+	136.196i	0.647862	+	0.210503i	0.0333910	+	0.999442i	$0.489369\pi$
$648$	75.5539	+	54.8932i	0.116596	+	0.0847117i
$649$	120.819	+	166.293i	0.186161	+	0.256229i
$650$		−	1954.00i		−	3.00615i
$651$	109.632	+	181.263i	0.168405	+	0.278438i
$652$	2190.77			3.36008
$653$	−287.365	+	208.783i	−0.440069	+	0.319729i	−0.785662	−	0.618656i	$-0.787678\pi$
$653$	−287.365	+	208.783i	−0.440069	+	0.319729i	0.345594	+	0.938384i	$0.387678\pi$
$654$	−98.7716	+	135.947i	−0.151027	+	0.207871i
$655$	292.872	−	901.367i	0.447133	−	1.37613i
$656$	124.056			0.189110
$657$		−	47.1313i		−	0.0717371i
$658$	−53.7895	+	165.547i	−0.0817470	+	0.251591i
$659$	26.6633	+	82.0613i	0.0404603	+	0.124524i	0.969246	−	0.246092i	$-0.0791466\pi$
$659$	26.6633	+	82.0613i	0.0404603	+	0.124524i	−0.928786	+	0.370616i	$0.879147\pi$
$660$	187.796	+	577.976i	0.284539	+	0.875722i
$661$	131.869	−	95.8088i	0.199500	−	0.144945i	−0.483550	−	0.875317i	$-0.660653\pi$
$661$	131.869	−	95.8088i	0.199500	−	0.144945i	0.683050	+	0.730371i	$0.260653\pi$
$662$	−1745.57	−	567.169i	−2.63681	−	0.856751i
$663$	−337.273	−	464.217i	−0.508708	−	0.700176i
$664$	946.748	−	1303.09i	1.42583	−	1.96248i
$665$	−52.8251	−	162.579i	−0.0794363	−	0.244480i
$666$	389.607	−	536.248i	0.584996	−	0.805177i
$667$	152.424	+	110.742i	0.228521	+	0.166031i
$668$	1516.60	−	492.772i	2.27036	−	0.737683i
$669$	657.456	+	477.670i	0.982745	+	0.714006i
$670$	1415.85	−	1028.67i	2.11321	−	1.53534i
$671$	33.9300	−	104.426i	0.0505664	−	0.155627i
$672$	−282.599	−	388.964i	−0.420534	−	0.578815i
$673$	−369.934	+	120.199i	−0.549680	+	0.178602i	−0.570672	−	0.821178i	$-0.693317\pi$
$673$	−369.934	+	120.199i	−0.549680	+	0.178602i	0.0209927	+	0.999780i	$0.493317\pi$
$674$	−535.256	+	173.915i	−0.794149	+	0.258035i
$675$	−766.542	−	249.064i	−1.13562	−	0.368984i
$676$	−1473.16			−2.17923
$677$		−	119.049i		−	0.175847i	−0.996127	−	0.0879237i	$-0.971977\pi$
$677$		−	119.049i		−	0.175847i	0.996127	−	0.0879237i	$-0.0280232\pi$
$678$	465.078	+	151.113i	0.685956	+	0.222881i
$679$	−430.857	−	313.036i	−0.634546	−	0.461025i
$680$	−1608.24	−	2213.56i	−2.36506	−	3.25523i
$681$			72.9219i			0.107081i
$682$	−490.063	+	114.640i	−0.718568	+	0.168094i
$683$	1323.40			1.93763			0.968816	−	0.247782i	$-0.0797015\pi$
$683$	1323.40			1.93763			0.968816	+	0.247782i	$0.0797015\pi$
$684$	277.792	−	201.828i	0.406129	−	0.295070i
$685$	−946.089	+	1302.18i	−1.38115	+	1.90099i
$686$	351.160	−	1080.76i	0.511895	−	1.57545i
$687$	−362.076			−0.527039
$688$			911.234i			1.32447i
$689$	226.455	−	696.956i	0.328672	−	1.01155i
$690$	84.9455	+	261.435i	0.123109	+	0.378892i
$691$	−232.175	−	714.562i	−0.335999	−	1.03410i	−0.966228	−	0.257689i	$-0.917039\pi$
$691$	−232.175	−	714.562i	−0.335999	−	1.03410i	0.630229	−	0.776410i	$-0.282961\pi$
$692$	−1459.92	+	1060.70i	−2.10972	+	1.53280i
$693$	79.2196	+	25.7400i	0.114314	+	0.0371429i
$694$	−246.900	−	339.829i	−0.355763	−	0.489666i
$695$	−928.044	+	1277.34i	−1.33531	+	1.83790i
$696$	−468.238	−	1441.09i	−0.672756	−	2.07053i
$697$	−28.9148	+	39.7977i	−0.0414846	+	0.0570986i
$698$	−136.198	−	98.9539i	−0.195127	−	0.141768i
$699$	−615.845	+	200.100i	−0.881037	+	0.286266i
$700$	842.506	+	612.116i	1.20358	+	0.874452i
$701$	116.275	−	84.4786i	0.165870	−	0.120512i	−0.501754	−	0.865011i	$-0.667312\pi$
$701$	116.275	−	84.4786i	0.165870	−	0.120512i	0.667624	+	0.744499i	$0.267312\pi$
$702$	−563.137	+	1733.16i	−0.802190	+	2.46889i
$703$	126.579	+	174.221i	0.180055	+	0.247824i
$704$	382.637	−	124.326i	0.543518	−	0.176600i
$705$	−174.929	+	56.8378i	−0.248126	+	0.0806210i
$706$	542.857	+	176.385i	0.768920	+	0.249837i
$707$	−63.7838			−0.0902176
$708$		−	893.468i		−	1.26196i
$709$	−233.484	−	75.8637i	−0.329315	−	0.107001i	0.139693	−	0.990195i	$-0.455388\pi$
$709$	−233.484	−	75.8637i	−0.329315	−	0.107001i	−0.469008	+	0.883194i	$0.655388\pi$
$710$	2727.09	+	1981.35i	3.84097	+	2.79063i
$711$	398.505	+	548.495i	0.560486	+	0.771442i
$712$			1492.22i			2.09582i
$713$	−157.902	+	36.9381i	−0.221462	+	0.0518066i
$714$	429.311			0.601276
$715$	−463.075	+	336.444i	−0.647658	+	0.470551i
$716$	1232.99	−	1697.06i	1.72205	−	2.37020i
$717$	198.014	−	609.423i	0.276170	−	0.849963i
$718$	−1211.81			−1.68776
$719$		−	418.100i		−	0.581502i	−0.956799	−	0.290751i	$-0.906095\pi$
$719$		−	418.100i		−	0.581502i	0.956799	−	0.290751i	$-0.0939051\pi$
$720$	−518.002	+	1594.24i	−0.719447	+	2.21423i
$721$	−33.9696	−	104.548i	−0.0471145	−	0.145004i
$722$	−367.587	−	1131.32i	−0.509123	−	1.56692i
$723$	−201.938	+	146.716i	−0.279306	+	0.202927i
$724$	203.676	+	66.1783i	0.281320	+	0.0914065i
$725$	622.340	+	856.578i	0.858401	+	1.18149i
$726$	−427.344	+	588.189i	−0.588628	+	0.810177i
$727$	318.711	+	980.891i	0.438392	+	1.34923i	0.889571	+	0.456797i	$0.151004\pi$
$727$	318.711	+	980.891i	0.438392	+	1.34923i	−0.451179	+	0.892433i	$0.648996\pi$
$728$	825.086	−	1135.63i	1.13336	−	1.55994i
$729$	399.778	+	290.456i	0.548393	+	0.398431i
$730$	−230.458	+	74.8804i	−0.315696	+	0.102576i
$731$	−292.328	−	212.389i	−0.399902	−	0.290546i
$732$	−386.120	+	280.533i	−0.527487	+	0.383242i
$733$	287.480	−	884.772i	0.392196	−	1.20706i	−0.538927	−	0.842352i	$-0.681170\pi$
$733$	287.480	−	884.772i	0.392196	−	1.20706i	0.931124	−	0.364704i	$-0.118830\pi$
$734$	−26.4238	−	36.3692i	−0.0359997	−	0.0495494i
$735$	485.288	−	157.680i	0.660256	−	0.214530i
$736$	350.035	−	113.733i	0.475592	−	0.154529i
$737$	−263.492	−	85.6138i	−0.357520	−	0.116165i
$738$	58.2420			0.0789186
$739$		−	1011.09i		−	1.36818i	−0.729397	−	0.684090i	$-0.760199\pi$
$739$		−	1011.09i		−	1.36818i	0.729397	−	0.684090i	$-0.239801\pi$
$740$	−2308.73	−	750.153i	−3.11991	−	1.01372i
$741$	−178.562	−	129.733i	−0.240975	−	0.175078i
$742$	322.275	+	443.574i	0.434333	+	0.597808i
$743$			1217.22i			1.63825i	0.573612	+	0.819127i	$0.305542\pi$
$743$			1217.22i			1.63825i	−0.573612	+	0.819127i	$0.694458\pi$
$744$	1202.01	+	506.106i	1.61560	+	0.680250i
$745$	−1296.39			−1.74012
$746$	−1770.25	+	1286.16i	−2.37298	+	1.72407i
$747$	230.003	−	316.572i	0.307903	−	0.423791i
$748$	−224.520	+	691.000i	−0.300160	+	0.923797i
$749$	−151.240			−0.201923
$750$			231.084i			0.308111i
$751$	−0.142556	+	0.438743i	−0.000189822	+	0.000584212i	−0.951151	−	0.308725i	$-0.900098\pi$
$751$	−0.142556	+	0.438743i	−0.000189822	+	0.000584212i	0.950962	+	0.309309i	$0.100098\pi$
$752$	171.365	+	527.407i	0.227879	+	0.701339i
$753$	63.8992	+	196.661i	0.0848594	+	0.261171i
$754$	1936.73	−	1407.12i	2.56861	−	1.86620i
$755$	1481.73	+	481.442i	1.96255	+	0.637672i
$756$	−570.876	−	785.744i	−0.755127	−	1.03934i
$757$	636.684	−	876.321i	0.841062	−	1.15762i	−0.144699	−	0.989476i	$-0.546222\pi$
$757$	636.684	−	876.321i	0.841062	−	1.15762i	0.985762	−	0.168148i	$-0.0537785\pi$
$758$	−848.959	−	2612.83i	−1.12000	−	3.44700i
$759$	25.5787	−	35.2061i	0.0337006	−	0.0463848i
$760$	−851.450	−	618.615i	−1.12033	−	0.813967i
$761$	51.3287	−	16.6777i	0.0674490	−	0.0219155i	−0.275098	−	0.961416i	$-0.588710\pi$
$761$	51.3287	−	16.6777i	0.0674490	−	0.0219155i	0.342547	+	0.939501i	$0.388710\pi$
$762$	−960.162	−	697.598i	−1.26005	−	0.915483i
$763$	68.2421	−	49.5808i	0.0894392	−	0.0649814i
$764$	−415.026	+	1277.32i	−0.543227	+	1.67188i
$765$	−390.707	−	537.762i	−0.510728	−	0.702956i
$766$	283.228	−	92.0263i	0.369749	−	0.120139i
$767$	800.342	−	260.047i	1.04347	−	0.339044i
$768$	243.767	+	79.2046i	0.317405	+	0.103131i
$769$	697.424			0.906924			0.453462	−	0.891276i	$-0.350189\pi$
$769$	697.424			0.906924			0.453462	+	0.891276i	$0.350189\pi$
$770$		−	428.256i		−	0.556176i
$771$	−488.747	−	158.804i	−0.633914	−	0.205971i
$772$	−852.533	−	619.401i	−1.10432	−	0.802333i
$773$	466.722	+	642.388i	0.603780	+	0.831032i	0.996048	−	0.0888193i	$-0.0283094\pi$
$773$	466.722	+	642.388i	0.603780	+	0.831032i	−0.392268	+	0.919851i	$0.628309\pi$
$774$			427.808i			0.552723i
$775$	−908.082	−	76.7896i	−1.17172	−	0.0990833i
$776$	−3278.83			−4.22530
$777$	183.708	−	133.471i	0.236432	−	0.171778i
$778$	−414.527	+	570.548i	−0.532811	+	0.733352i
$779$	−5.84726	+	17.9960i	−0.00750610	+	0.0231014i
$780$	2488.04			3.18979
$781$		−	533.634i		−	0.683271i
$782$	−101.557	+	312.559i	−0.129868	+	0.399692i
$783$	−305.141	−	939.126i	−0.389707	−	1.19939i
$784$	−475.401	−	1463.13i	−0.606379	−	1.86624i
$785$	541.856	−	393.681i	0.690262	−	0.501505i
$786$	870.732	+	282.918i	1.10780	+	0.359947i
$787$	287.650	+	395.917i	0.365502	+	0.503071i	0.951671	−	0.307118i	$-0.0993646\pi$
$787$	287.650	+	395.917i	0.365502	+	0.503071i	−0.586169	+	0.810189i	$0.699365\pi$
$788$	−1824.34	+	2510.99i	−2.31515	+	3.18653i
$789$	163.515	+	503.247i	0.207243	+	0.637829i
$790$	2048.85	−	2820.01i	2.59349	−	3.56963i
$791$	−198.591	−	144.285i	−0.251063	−	0.182408i
$792$	487.726	−	158.472i	0.615816	−	0.200091i
$793$	−363.675	−	264.225i	−0.458606	−	0.333197i
$794$	−973.664	+	707.408i	−1.22628	+	0.890942i
$795$	−179.032	+	551.003i	−0.225197	+	0.693086i
$796$	2010.05	+	2766.59i	2.52519	+	3.47562i
$797$	−380.814	+	123.734i	−0.477809	+	0.155250i	−0.538013	−	0.842936i	$-0.680825\pi$
$797$	−380.814	+	123.734i	−0.477809	+	0.155250i	0.0602038	+	0.998186i	$0.480825\pi$
$798$	157.053	−	51.0297i	0.196809	−	0.0639470i
$799$	−209.136	−	67.9525i	−0.261748	−	0.0850469i
$800$	2068.33			2.58541
$801$			362.521i			0.452585i
$802$	333.379	+	108.321i	0.415685	+	0.135064i
$803$	31.0346	+	22.5479i	0.0386483	+	0.0280796i
$804$	707.853	+	974.277i	0.880415	+	1.21179i
$805$		−	137.988i		−	0.171413i
$806$	−173.622	+	2053.18i	−0.215412	+	2.54737i
$807$	522.690			0.647695
$808$	−317.696	+	230.820i	−0.393188	+	0.285668i
$809$	−320.601	+	441.269i	−0.396292	+	0.545450i	−0.959809	−	0.280655i	$-0.909448\pi$
$809$	−320.601	+	441.269i	−0.396292	+	0.545450i	0.563516	+	0.826105i	$0.309448\pi$
$810$	36.0461	−	110.938i	0.0445013	−	0.136961i
$811$	1016.49			1.25337			0.626687	−	0.779271i	$-0.284411\pi$
$811$	1016.49			1.25337			0.626687	+	0.779271i	$0.284411\pi$
$812$			1275.86i			1.57126i
$813$	−141.804	+	436.429i	−0.174421	+	0.536813i
$814$	166.713	+	513.090i	0.204807	+	0.630331i
$815$	−504.102	−	1551.47i	−0.618530	−	1.90364i
$816$	1106.51	−	803.924i	1.35601	−	0.985201i
$817$	−132.187	−	42.9501i	−0.161796	−	0.0525706i
$818$	−527.740	−	726.372i	−0.645159	−	0.887985i
$819$	200.446	−	275.891i	0.244745	−	0.336863i
$820$	−65.9140	−	202.862i	−0.0803829	−	0.247393i
$821$	322.706	−	444.167i	0.393064	−	0.541007i	−0.565922	−	0.824459i	$-0.691480\pi$
$821$	322.706	−	444.167i	0.393064	−	0.541007i	0.958986	+	0.283452i	$0.0914797\pi$
$822$	−1257.92	−	913.934i	−1.53032	−	1.11184i
$823$	100.513	−	32.6587i	0.122130	−	0.0396825i	−0.247314	−	0.968935i	$-0.579548\pi$
$823$	100.513	−	32.6587i	0.122130	−	0.0396825i	0.369444	+	0.929253i	$0.379548\pi$
$824$	−547.531	−	397.805i	−0.664479	−	0.482773i
$825$	197.848	−	143.745i	0.239816	−	0.174236i
$826$	−194.563	+	598.804i	−0.235549	+	0.724944i
$827$	−91.3056	−	125.671i	−0.110406	−	0.151961i	0.750238	−	0.661168i	$-0.229939\pi$
$827$	−91.3056	−	125.671i	−0.110406	−	0.151961i	−0.860644	+	0.509207i	$0.829939\pi$
$828$	263.603	−	85.6498i	0.318361	−	0.103442i
$829$	1183.36	−	384.498i	1.42746	−	0.463810i	0.509496	−	0.860473i	$-0.329832\pi$
$829$	1183.36	−	384.498i	1.42746	−	0.463810i	0.917964	+	0.396663i	$0.129832\pi$
$830$	−1913.37	−	621.691i	−2.30526	−	0.749025i
$831$	31.0401			0.0373527
$832$		−	1647.15i		−	1.97975i
$833$	580.186	+	188.514i	0.696502	+	0.226307i
$834$	−1233.93	−	896.502i	−1.47953	−	1.07494i
$835$	−697.946	−	960.640i	−0.835863	−	1.15047i
$836$			279.474i			0.334298i
$837$	783.321	+	329.818i	0.935868	+	0.394048i
$838$	2647.42			3.15922
$839$	1037.22	−	753.585i	1.23626	−	0.898194i	0.238915	−	0.971041i	$-0.423208\pi$
$839$	1037.22	−	753.585i	1.23626	−	0.898194i	0.997343	+	0.0728468i	$0.0232084\pi$
$840$	−652.301	+	897.815i	−0.776548	+	1.06883i
$841$	−140.965	+	433.845i	−0.167616	+	0.515868i
$842$	−45.9674			−0.0545932
$843$			606.741i			0.719740i
$844$	−192.228	+	591.617i	−0.227758	+	0.700969i
$845$	338.977	+	1043.26i	0.401156	+	1.23463i
$846$	80.4527	+	247.608i	0.0950978	+	0.292681i
$847$	295.256	−	214.516i	0.348590	−	0.253265i
$848$	1661.26	+	539.777i	1.95904	+	0.636530i
$849$	139.628	+	192.181i	0.164462	+	0.226362i
$850$	−1085.57	+	1494.16i	−1.27715	+	1.75784i
$851$	53.7163	+	165.322i	0.0631214	+	0.194268i
$852$	−1363.41	+	1876.57i	−1.60024	+	2.20255i
$853$	−706.128	−	513.032i	−0.827818	−	0.601445i	0.0911235	−	0.995840i	$-0.470954\pi$
$853$	−706.128	−	513.032i	−0.827818	−	0.601445i	−0.918941	+	0.394395i	$0.870954\pi$
$854$	319.868	−	103.931i	0.374553	−	0.121700i
$855$	−206.851	−	150.286i	−0.241932	−	0.175774i
$856$	−753.301	+	547.305i	−0.880025	+	0.639375i
$857$	126.023	−	387.859i	0.147051	−	0.452577i	−0.850218	−	0.526431i	$-0.823530\pi$
$857$	126.023	−	387.859i	0.147051	−	0.452577i	0.997269	+	0.0738539i	$0.0235299\pi$
$858$	−325.009	−	447.337i	−0.378799	−	0.521371i
$859$	698.608	−	226.991i	0.813280	−	0.264251i	0.127294	−	0.991865i	$-0.459371\pi$
$859$	698.608	−	226.991i	0.813280	−	0.264251i	0.685987	+	0.727614i	$0.259371\pi$
$860$	1490.10	−	484.161i	1.73267	−	0.562978i
$861$	18.9759	+	6.16566i	0.0220394	+	0.00716105i
$862$	113.807			0.132027
$863$		−	800.658i		−	0.927762i	−0.885898	−	0.463881i	$-0.846457\pi$
$863$		−	800.658i		−	0.927762i	0.885898	−	0.463881i	$-0.153543\pi$
$864$	−1834.57	−	596.088i	−2.12335	−	0.689917i
$865$	1087.10	+	789.823i	1.25676	+	0.913091i
$866$	451.929	+	622.027i	0.521858	+	0.718276i
$867$		−	9.83675i		−	0.0113457i
$868$	−830.882	−	718.048i	−0.957238	−	0.827244i
$869$	−551.816			−0.635001
$870$	−1531.15	+	1112.45i	−1.75994	+	1.27867i
$871$	−666.705	+	917.640i	−0.765447	+	1.05355i
$872$	160.480	−	493.907i	0.184037	−	0.566407i
$873$	−796.560			−0.912440
$874$			126.414i			0.144638i
$875$	35.8454	−	110.321i	0.0409661	−	0.126081i
$876$	−51.5268	−	158.583i	−0.0588206	−	0.181031i
$877$	−181.836	−	559.634i	−0.207339	−	0.638123i	−0.999609	−	0.0279529i	$-0.991101\pi$
$877$	−181.836	−	559.634i	−0.207339	−	0.638123i	0.792271	−	0.610170i	$-0.208899\pi$
$878$	458.789	−	333.329i	0.522538	−	0.379646i
$879$	−740.778	−	240.693i	−0.842750	−	0.273826i
$880$	−801.948	−	1103.79i	−0.911304	−	1.25430i
$881$	400.196	−	550.822i	0.454252	−	0.625224i	−0.519052	−	0.854742i	$-0.673715\pi$
$881$	400.196	−	550.822i	0.454252	−	0.625224i	0.973304	+	0.229518i	$0.0737151\pi$
$882$	−223.192	−	686.914i	−0.253052	−	0.778814i
$883$	−152.024	+	209.243i	−0.172168	+	0.236968i	−0.886377	−	0.462963i	$-0.846786\pi$
$883$	−152.024	+	209.243i	−0.172168	+	0.236968i	0.714210	+	0.699932i	$0.246786\pi$
$884$	2406.48	+	1748.41i	2.72227	+	1.97784i
$885$	−632.739	+	205.589i	−0.714959	+	0.232304i
$886$	945.336	+	686.827i	1.06697	+	0.775200i
$887$	−256.650	+	186.467i	−0.289346	+	0.210222i	−0.722984	−	0.690865i	$-0.757230\pi$
$887$	−256.650	+	186.467i	−0.289346	+	0.210222i	0.433638	+	0.901087i	$0.357230\pi$
$888$	432.012	−	1329.59i	0.486499	−	1.49729i
$889$	350.177	+	481.977i	0.393899	+	0.542156i
$890$	1772.62	−	575.960i	1.99171	−	0.647146i
$891$	−17.5624	+	5.70637i	−0.0197109	+	0.00640446i
$892$	−4006.62	−	1301.83i	−4.49172	−	1.45945i
$893$	−84.5847			−0.0947197
$894$		−	1252.33i		−	1.40081i
$895$	−1485.55	−	482.683i	−1.65983	−	0.539310i
$896$	182.719	+	132.753i	0.203928	+	0.148162i
$897$	−104.721	−	144.136i	−0.116745	−	0.160686i
$898$		−	699.165i		−	0.778580i
$899$	−577.820	−	955.357i	−0.642736	−	1.06269i
$900$	1557.61			1.73067
$901$	−560.368	+	407.131i	−0.621940	+	0.451866i
$902$	−27.8634	+	38.3506i	−0.0308906	+	0.0425173i
$903$	−45.2889	+	139.385i	−0.0501539	+	0.154358i
$904$	−1511.28			−1.67177
$905$		−	159.468i		−	0.176207i
$906$	−465.079	+	1431.37i	−0.513332	+	1.57987i
$907$	352.338	+	1084.39i	0.388465	+	1.19557i	0.933935	+	0.357443i	$0.116351\pi$
$907$	352.338	+	1084.39i	0.388465	+	1.19557i	−0.545470	+	0.838131i	$0.683649\pi$
$908$	−116.816	−	359.523i	−0.128652	−	0.395951i
$909$	−77.1811	+	56.0754i	−0.0849077	+	0.0616891i
$910$	−1667.49	−	541.800i	−1.83241	−	0.595385i
$911$	−645.558	−	888.534i	−0.708626	−	0.975339i	−0.999826	−	0.0186772i	$-0.994055\pi$
$911$	−645.558	−	888.534i	−0.708626	−	0.975339i	0.291200	−	0.956662i	$-0.405945\pi$
$912$	309.232	−	425.621i	0.339070	−	0.466689i
$913$	98.4184	+	302.901i	0.107797	+	0.331764i
$914$	−395.960	+	544.992i	−0.433217	+	0.596272i
$915$	287.516	+	208.893i	0.314225	+	0.228298i
$916$	1785.12	−	580.021i	1.94882	−	0.633211i
$917$	−371.807	−	270.134i	−0.405460	−	0.294584i
$918$	1393.50	−	1012.44i	1.51797	−	1.10287i
$919$	−320.840	+	987.443i	−0.349118	+	1.07448i	0.610223	+	0.792229i	$0.291080\pi$
$919$	−320.840	+	987.443i	−0.349118	+	1.07448i	−0.959342	+	0.282247i	$0.908920\pi$
$920$	−499.347	−	687.292i	−0.542768	−	0.747056i
$921$	−10.1850	+	3.30930i	−0.0110586	+	0.00359316i
$922$	−2856.27	+	928.057i	−3.09790	+	1.00657i
$923$	−2077.80	−	675.118i	−2.25114	−	0.731439i
$924$	294.692			0.318931
$925$			976.873i			1.05608i
$926$	1122.96	+	364.872i	1.21270	+	0.394031i
$927$	−133.017	−	96.6427i	−0.143492	−	0.104253i
$928$	1489.45	+	2050.06i	1.60501	+	2.20911i
$929$			427.048i			0.459685i	0.973228	+	0.229843i	$0.0738212\pi$
$929$			427.048i			0.459685i	−0.973228	+	0.229843i	$0.926179\pi$
$930$	137.263	−	1623.22i	0.147595	−	1.74539i
$931$	234.655			0.252046
$932$	2715.72	−	1973.09i	2.91386	−	2.11704i
$933$	502.689	−	691.892i	0.538788	−	0.741577i
$934$	62.1246	−	191.200i	0.0665145	−	0.204711i
$935$	541.017			0.578628
$936$		−	2099.54i		−	2.24309i
$937$	−292.809	+	901.174i	−0.312496	+	0.961765i	0.664276	+	0.747487i	$0.268740\pi$
$937$	−292.809	+	901.174i	−0.312496	+	0.961765i	−0.976773	+	0.214278i	$0.931260\pi$
$938$	−262.244	−	807.105i	−0.279578	−	0.860453i
$939$	−63.6860	−	196.005i	−0.0678232	−	0.208738i
$940$	771.392	−	560.449i	0.820630	−	0.596222i
$941$	1462.24	+	475.110i	1.55392	+	0.504899i	0.955175	−	0.296041i	$-0.0956667\pi$
$941$	1462.24	+	475.110i	1.55392	+	0.504899i	0.598744	+	0.800940i	$0.295667\pi$
$942$	380.301	+	523.440i	0.403717	+	0.555668i
$943$	−8.97780	+	12.3569i	−0.00952047	+	0.0131038i
$944$	619.848	+	1907.70i	0.656618	+	2.02086i
$945$	−425.090	+	585.086i	−0.449831	+	0.619139i
$946$	−281.699	−	204.666i	−0.297779	−	0.216349i
$947$	116.227	−	37.7643i	0.122731	−	0.0398779i	−0.247007	−	0.969014i	$-0.579447\pi$
$947$	116.227	−	37.7643i	0.122731	−	0.0398779i	0.369739	+	0.929136i	$0.379447\pi$
$948$	1940.51	+	1409.86i	2.04695	+	1.48719i
$949$	127.057	−	92.3124i	0.133885	−	0.0972734i
$950$	−219.529	+	675.640i	−0.231083	+	0.711200i
$951$	369.456	+	508.513i	0.388492	+	0.534714i
$952$	−1261.84	+	409.996i	−1.32546	+	0.430668i
$953$	−1730.28	+	562.202i	−1.81561	+	0.589929i	−0.815680	+	0.578503i	$0.803637\pi$
$953$	−1730.28	+	562.202i	−1.81561	+	0.589929i	−0.999935	+	0.0114257i	$0.996363\pi$
$954$	779.933	+	253.416i	0.817540	+	0.265635i
$955$	1000.07			1.04720
$956$			3321.81i			3.47470i
$957$	284.950	+	92.5859i	0.297753	+	0.0967460i
$958$	−380.797	−	276.665i	−0.397491	−	0.288794i
$959$	458.771	+	631.445i	0.478385	+	0.658441i
$960$			1302.21i			1.35647i
$961$	947.354	+	161.375i	0.985800	+	0.167924i
$962$	2208.72			2.29597
$963$	−183.007	+	132.962i	−0.190039	+	0.138071i
$964$	760.574	−	1046.84i	0.788977	−	1.08593i
$965$	−242.479	+	746.274i	−0.251274	+	0.773341i
$966$	133.298			0.137989
$967$		−	203.154i		−	0.210087i	−0.994468	−	0.105043i	$-0.966502\pi$
$967$		−	203.154i		−	0.210087i	0.994468	−	0.105043i	$-0.0334981\pi$
$968$	694.331	−	2136.93i	0.717284	−	2.20757i
$969$	64.4660	+	198.406i	0.0665284	+	0.204753i
$970$	1265.55	+	3894.95i	1.30469	+	4.01541i
$971$	−52.4883	+	38.1350i	−0.0540559	+	0.0392739i	−0.614485	−	0.788928i	$-0.710636\pi$
$971$	−52.4883	+	38.1350i	−0.0540559	+	0.0392739i	0.560429	+	0.828202i	$0.310636\pi$
$972$	−2248.10	−	730.452i	−2.31286	−	0.751494i
$973$	450.021	+	619.401i	0.462509	+	0.636589i
$974$	−687.210	+	945.864i	−0.705555	+	0.971113i
$975$	−309.393	−	952.213i	−0.317326	−	0.976629i
$976$	629.807	−	866.855i	0.645294	−	0.888171i
$977$	−1106.26	−	803.745i	−1.13230	−	0.822666i	−0.146275	−	0.989244i	$-0.546728\pi$
$977$	−1106.26	−	803.745i	−1.13230	−	0.822666i	−0.986028	+	0.166578i	$0.946728\pi$
$978$	1498.74	−	486.969i	1.53245	−	0.497923i
$979$	−238.709	−	173.432i	−0.243830	−	0.177153i
$980$	−2140.00	+	1554.80i	−2.18367	+	1.58653i
$981$	38.9870	−	119.990i	0.0397421	−	0.122314i
$982$	−1554.78	−	2139.97i	−1.58328	−	2.17919i
$983$	−925.344	+	300.662i	−0.941347	+	0.305862i	−0.739195	−	0.673492i	$-0.764794\pi$
$983$	−925.344	+	300.662i	−0.941347	+	0.305862i	−0.202152	+	0.979354i	$0.564794\pi$
$984$	116.828	−	37.9597i	0.118728	−	0.0385770i
$985$	2198.02	+	714.181i	2.23150	+	0.725057i
$986$	−2262.71			−2.29484
$987$			89.1907i			0.0903654i
$988$	1088.18	+	353.571i	1.10140	+	0.357865i
$989$	−90.7657	−	65.9451i	−0.0917752	−	0.0666786i
$990$	−376.500	−	518.207i	−0.380303	−	0.523442i
$991$		−	906.532i		−	0.914764i	−0.889270	−	0.457382i	$-0.848787\pi$
$991$		−	906.532i		−	0.914764i	0.889270	−	0.457382i	$-0.151213\pi$
$992$	−2173.32	−	183.781i	−2.19085	−	0.185263i
$993$	−940.447			−0.947077
$994$	1322.40	−	960.782i	1.33039	−	0.966582i
$995$	1496.74	−	2060.08i	1.50426	−	2.07043i
$996$	427.799	−	1316.63i	0.429517	−	1.32192i
$997$	1406.53			1.41076			0.705381	−	0.708829i	$-0.250776\pi$
$997$	1406.53			1.41076			0.705381	+	0.708829i	$0.250776\pi$
$998$		−	363.726i		−	0.364455i
$999$	281.532	−	866.468i	0.281814	−	0.867335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.3.f.a.15.1	✓	20
3.2	odd	2		279.3.v.a.46.5		20
31.29	odd	10	inner	31.3.f.a.29.1	yes	20
93.29	even	10		279.3.v.a.91.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.3.f.a.15.1	✓	20	1.1	even	1	trivial
31.3.f.a.29.1	yes	20	31.29	odd	10	inner
279.3.v.a.46.5		20	3.2	odd	2
279.3.v.a.91.5		20	93.29	even	10

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.01677 + 2.19181i) q^{2} +(-1.12307 + 1.54577i) q^{3} +(3.06079 - 9.42013i) q^{4} -7.37547 q^{5} -7.12479i q^{6} +(-1.10519 + 3.40142i) q^{7} +(6.80424 + 20.9413i) q^{8} +(1.65302 + 5.08748i) q^{9} +O(q^{10})\)	\(q+(-3.01677 + 2.19181i) q^{2} +(-1.12307 + 1.54577i) q^{3} +(3.06079 - 9.42013i) q^{4} -7.37547 q^{5} -7.12479i q^{6} +(-1.10519 + 3.40142i) q^{7} +(6.80424 + 20.9413i) q^{8} +(1.65302 + 5.08748i) q^{9} +(22.2501 - 16.1656i) q^{10} +(-4.14078 - 1.34542i) q^{11} +(11.1239 + 15.3107i) q^{12} +(-10.4773 + 14.4207i) q^{13} +(-4.12117 - 12.6837i) q^{14} +(8.28317 - 11.4008i) q^{15} +(-34.3732 - 24.9736i) q^{16} +(16.0233 - 5.20629i) q^{17} +(-16.1376 - 11.7246i) q^{18} +(5.24291 - 3.80920i) q^{19} +(-22.5747 + 69.4779i) q^{20} +(-4.01662 - 5.52840i) q^{21} +(15.4407 - 5.01698i) q^{22} +(4.97511 - 1.61651i) q^{23} +(-40.0122 - 13.0007i) q^{24} +29.3975 q^{25} -66.4681i q^{26} +(-26.0751 - 8.47230i) q^{27} +(28.6591 + 20.8220i) q^{28} +(21.1698 + 29.1378i) q^{29} +52.5487i q^{30} +(-30.8898 - 2.61211i) q^{31} +70.3573 q^{32} +(6.73010 - 4.88970i) q^{33} +(-36.9274 + 50.8262i) q^{34} +(8.15128 - 25.0871i) q^{35} +52.9843 q^{36} +33.2298i q^{37} +(-7.46760 + 22.9829i) q^{38} +(-10.5245 - 32.3909i) q^{39} +(-50.1845 - 154.452i) q^{40} +(-2.36218 + 1.71622i) q^{41} +(24.2344 + 7.87424i) q^{42} +(-12.6063 - 17.3510i) q^{43} +(-25.3481 + 34.8886i) q^{44} +(-12.1918 - 37.5226i) q^{45} +(-11.4657 + 15.7811i) q^{46} +(-10.5593 - 7.67178i) q^{47} +(77.2070 - 25.0861i) q^{48} +(29.2936 + 21.2831i) q^{49} +(-88.6854 + 64.4337i) q^{50} +(-9.94755 + 30.6154i) q^{51} +(103.776 + 142.836i) q^{52} +(-39.1000 + 12.7043i) q^{53} +(97.2320 - 31.5926i) q^{54} +(30.5402 + 9.92310i) q^{55} -78.7501 q^{56} +12.3823i q^{57} +(-127.729 - 41.5016i) q^{58} +(-38.1942 - 27.7497i) q^{59} +(-82.0440 - 112.924i) q^{60} +25.2189i q^{61} +(98.9124 - 59.8243i) q^{62} -19.1316 q^{63} +(-74.7588 + 54.3155i) q^{64} +(77.2747 - 106.359i) q^{65} +(-9.58584 + 29.5022i) q^{66} +63.6335 q^{67} -166.877i q^{68} +(-3.08864 + 9.50585i) q^{69} +(30.3955 + 93.5479i) q^{70} +(37.8748 + 116.567i) q^{71} +(-95.2910 + 69.2330i) q^{72} +(-8.37951 - 2.72267i) q^{73} +(-72.8333 - 100.246i) q^{74} +(-33.0155 + 45.4419i) q^{75} +(-19.8357 - 61.0480i) q^{76} +(9.15268 - 12.5976i) q^{77} +(102.745 + 74.6483i) q^{78} +(120.538 - 39.1653i) q^{79} +(253.518 + 184.192i) q^{80} +(3.43131 - 2.49299i) q^{81} +(3.36451 - 10.3549i) q^{82} +(-42.9969 - 59.1801i) q^{83} +(-64.3723 + 20.9158i) q^{84} +(-118.179 + 38.3988i) q^{85} +(76.0603 + 24.7135i) q^{86} -68.8156 q^{87} -95.8678i q^{88} +(64.4529 + 20.9420i) q^{89} +(119.022 + 86.4747i) q^{90} +(-37.4715 - 51.5752i) q^{91} -51.8140i q^{92} +(38.7291 - 44.8150i) q^{93} +48.6700 q^{94} +(-38.6689 + 28.0946i) q^{95} +(-79.0162 + 108.756i) q^{96} +(-46.0155 + 141.621i) q^{97} -135.020 q^{98} -23.2902i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9	\( 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + 12 q^{10} - 10 q^{11} + 90 q^{12} + 10 q^{13} - 85 q^{15} - 103 q^{16} + 35 q^{17} + 6 q^{18} + 47 q^{19} - 125 q^{20} - 125 q^{21} + 150 q^{22} + 75 q^{23} + 195 q^{24} + 82 q^{25} + 25 q^{27} + 88 q^{28} + 5 q^{29} + 73 q^{31} + 226 q^{32} - 206 q^{33} - 265 q^{34} - 50 q^{35} - 520 q^{36} + 8 q^{38} + 91 q^{39} - 466 q^{40} - 98 q^{41} + 245 q^{43} + 380 q^{44} - 162 q^{45} - 445 q^{46} - 187 q^{47} + 570 q^{48} + 328 q^{49} - 44 q^{50} + 185 q^{51} - 15 q^{52} + 25 q^{53} + 920 q^{54} + 190 q^{55} + 64 q^{56} - 85 q^{58} - 173 q^{59} + 275 q^{60} - 40 q^{62} + 252 q^{63} - 469 q^{64} - 345 q^{65} - 564 q^{66} + 76 q^{67} - 197 q^{69} - 11 q^{70} - 467 q^{71} - 982 q^{72} - 15 q^{73} + 45 q^{74} - 175 q^{75} + 55 q^{76} - 320 q^{77} - 91 q^{78} + 500 q^{79} + 1030 q^{80} + 117 q^{81} + 178 q^{82} - 50 q^{83} + 65 q^{84} + 20 q^{85} + 1125 q^{86} - 366 q^{87} + 55 q^{89} + 444 q^{90} + 300 q^{91} + 502 q^{93} + 62 q^{94} - 559 q^{95} - 10 q^{96} - 405 q^{97} - 1000 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9 + 12 * q^10 - 10 * q^11 + 90 * q^12 + 10 * q^13 - 85 * q^15 - 103 * q^16 + 35 * q^17 + 6 * q^18 + 47 * q^19 - 125 * q^20 - 125 * q^21 + 150 * q^22 + 75 * q^23 + 195 * q^24 + 82 * q^25 + 25 * q^27 + 88 * q^28 + 5 * q^29 + 73 * q^31 + 226 * q^32 - 206 * q^33 - 265 * q^34 - 50 * q^35 - 520 * q^36 + 8 * q^38 + 91 * q^39 - 466 * q^40 - 98 * q^41 + 245 * q^43 + 380 * q^44 - 162 * q^45 - 445 * q^46 - 187 * q^47 + 570 * q^48 + 328 * q^49 - 44 * q^50 + 185 * q^51 - 15 * q^52 + 25 * q^53 + 920 * q^54 + 190 * q^55 + 64 * q^56 - 85 * q^58 - 173 * q^59 + 275 * q^60 - 40 * q^62 + 252 * q^63 - 469 * q^64 - 345 * q^65 - 564 * q^66 + 76 * q^67 - 197 * q^69 - 11 * q^70 - 467 * q^71 - 982 * q^72 - 15 * q^73 + 45 * q^74 - 175 * q^75 + 55 * q^76 - 320 * q^77 - 91 * q^78 + 500 * q^79 + 1030 * q^80 + 117 * q^81 + 178 * q^82 - 50 * q^83 + 65 * q^84 + 20 * q^85 + 1125 * q^86 - 366 * q^87 + 55 * q^89 + 444 * q^90 + 300 * q^91 + 502 * q^93 + 62 * q^94 - 559 * q^95 - 10 * q^96 - 405 * q^97 - 1000 * q^98

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