LMFDB - Embedded newform 31.3.h.a.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,3,Mod(3,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.3"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	31.h (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.844688819517$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	31.17
Dual form			31.3.h.a.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.331437 + 1.02006i) q^{2} +(0.293175 + 0.263976i) q^{3} +(2.30540 + 1.67497i) q^{4} +(-0.793103 + 1.37369i) q^{5} +(-0.366440 + 0.211564i) q^{6} +(0.503493 - 4.79042i) q^{7} +(-5.94352 + 4.31822i) q^{8} +(-0.924488 - 8.79591i) q^{9} +(-1.13839 - 1.26431i) q^{10} +(-3.31607 - 7.44800i) q^{11} +(0.233734 + 1.09963i) q^{12} +(0.723920 - 3.40578i) q^{13} +(4.71963 + 2.10131i) q^{14} +(-0.595141 + 0.193373i) q^{15} +(1.08740 + 3.34669i) q^{16} +(-8.55661 + 19.2185i) q^{17} +(9.27876 + 1.97226i) q^{18} +(5.81404 - 1.23581i) q^{19} +(-4.12932 + 1.83849i) q^{20} +(1.41217 - 1.27152i) q^{21} +(8.69647 - 0.914036i) q^{22} +(3.72284 + 5.12405i) q^{23} +(-2.88240 - 0.302952i) q^{24} +(11.2420 + 19.4717i) q^{25} +(3.23416 + 1.86724i) q^{26} +(4.13784 - 5.69524i) q^{27} +(9.18456 - 10.2005i) q^{28} +(-23.1587 - 7.52470i) q^{29} -0.671169i q^{30} +(19.3654 - 24.2071i) q^{31} -33.1606 q^{32} +(0.993907 - 3.05893i) q^{33} +(-16.7680 - 15.0980i) q^{34} +(6.18125 + 4.49094i) q^{35} +(12.6016 - 21.8266i) q^{36} +(-58.1388 + 33.5665i) q^{37} +(-0.666387 + 6.34025i) q^{38} +(1.11128 - 0.807391i) q^{39} +(-1.21809 - 11.5894i) q^{40} +(20.8583 + 23.1655i) q^{41} +(0.828981 + 1.86192i) q^{42} +(-9.34191 - 43.9502i) q^{43} +(4.83033 - 22.7249i) q^{44} +(12.8161 + 5.70610i) q^{45} +(-6.46072 + 2.09922i) q^{46} +(15.6666 + 48.2168i) q^{47} +(-0.564645 + 1.26821i) q^{48} +(25.2346 + 5.36379i) q^{49} +(-23.5882 + 5.01384i) q^{50} +(-7.58180 + 3.37564i) q^{51} +(7.37350 - 6.63913i) q^{52} +(10.4475 - 1.09807i) q^{53} +(4.43805 + 6.10845i) q^{54} +(12.8613 + 1.35177i) q^{55} +(17.6935 + 30.6461i) q^{56} +(2.03076 + 1.17246i) q^{57} +(15.3513 - 21.1292i) q^{58} +(52.3153 - 58.1020i) q^{59} +(-1.69593 - 0.551041i) q^{60} +91.3284i q^{61} +(18.2742 + 27.7769i) q^{62} -42.6016 q^{63} +(6.64103 - 20.4390i) q^{64} +(4.10435 + 3.69558i) q^{65} +(2.79087 + 2.02769i) q^{66} +(-32.1730 + 55.7253i) q^{67} +(-51.9168 + 29.9742i) q^{68} +(-0.261183 + 2.48499i) q^{69} +(-6.62972 + 4.81677i) q^{70} +(-14.6133 - 139.036i) q^{71} +(43.4774 + 48.2865i) q^{72} +(-41.2139 - 92.5678i) q^{73} +(-14.9704 - 70.4302i) q^{74} +(-1.84419 + 8.67622i) q^{75} +(15.4736 + 6.88930i) q^{76} +(-37.3487 + 12.1353i) q^{77} +(0.455267 + 1.40117i) q^{78} +(-13.2762 + 29.8189i) q^{79} +(-5.45975 - 1.16051i) q^{80} +(-75.1433 + 15.9722i) q^{81} +(-30.5434 + 13.5988i) q^{82} +(57.5526 - 51.8206i) q^{83} +(5.38537 - 0.566025i) q^{84} +(-19.6140 - 26.9964i) q^{85} +(47.9281 + 5.03744i) q^{86} +(-4.80320 - 8.31938i) q^{87} +(51.8712 + 29.9478i) q^{88} +(82.1472 - 113.066i) q^{89} +(-10.0683 + 11.1820i) q^{90} +(-15.9506 - 5.18266i) q^{91} +18.0486i q^{92} +(12.0675 - 1.98492i) q^{93} -54.3764 q^{94} +(-2.91350 + 8.96684i) q^{95} +(-9.72186 - 8.75360i) q^{96} +(74.1883 + 53.9009i) q^{97} +(-13.8351 + 23.9630i) q^{98} +(-62.4464 + 36.0534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 6 q^{2} - 10 q^{3} - 18 q^{4} - 7 q^{5} - 9 q^{6} - 22 q^{7} + 43 q^{8} - 2 q^{9} + 18 q^{10} - 5 q^{11} - 87 q^{12} - 49 q^{13} + 12 q^{14} + 70 q^{15} + 102 q^{16} - 62 q^{17} - 69 q^{18} - 132 q^{19}+ \cdots - 606 q^{99}+O(q^{100}) $ 32 * q - 6 * q^2 - 10 * q^3 - 18 * q^4 - 7 * q^5 - 9 * q^6 - 22 * q^7 + 43 * q^8 - 2 * q^9 + 18 * q^10 - 5 * q^11 - 87 * q^12 - 49 * q^13 + 12 * q^14 + 70 * q^15 + 102 * q^16 - 62 * q^17 - 69 * q^18 - 132 * q^19 + 41 * q^20 + 71 * q^21 + 27 * q^22 + 15 * q^23 + 204 * q^24 + 85 * q^25 + 93 * q^26 + 95 * q^27 + 56 * q^28 + 10 * q^29 + 75 * q^31 - 274 * q^32 + 77 * q^33 - 146 * q^34 - 61 * q^35 - 137 * q^36 - 354 * q^37 - 218 * q^38 - 133 * q^39 + 37 * q^40 - 40 * q^41 - 375 * q^42 - 157 * q^43 - 329 * q^44 + 159 * q^45 + 430 * q^46 + 442 * q^47 - 204 * q^48 - 256 * q^49 + 317 * q^50 + 574 * q^51 + 351 * q^52 + 14 * q^53 + 220 * q^54 + 437 * q^55 + 566 * q^56 + 219 * q^57 + 385 * q^58 + 254 * q^59 - 5 * q^60 - 11 * q^62 - 318 * q^63 - 241 * q^64 - 468 * q^65 - 588 * q^66 - 293 * q^67 - 654 * q^68 - 700 * q^69 - 442 * q^70 + 74 * q^71 - 215 * q^72 - 522 * q^73 - 417 * q^74 - 845 * q^75 + 98 * q^76 + 500 * q^77 + 955 * q^78 - 150 * q^79 + 278 * q^80 - 21 * q^81 + 386 * q^82 + 512 * q^83 + 1360 * q^84 + 385 * q^85 - 234 * q^86 + 411 * q^87 + 537 * q^88 + 155 * q^89 + 387 * q^90 - 250 * q^91 - 19 * q^93 - 728 * q^94 + 178 * q^95 - 1250 * q^96 - 3 * q^97 - 458 * q^98 - 606 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{30}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.331437	+	1.02006i	−0.165719	+	0.510029i	−0.999089	−	0.0426863i	$-0.986408\pi$
$2$	−0.331437	+	1.02006i	−0.165719	+	0.510029i	0.833370	+	0.552716i	$0.186408\pi$
$3$	0.293175	+	0.263976i	0.0977250	+	0.0879920i	0.716545	−	0.697541i	$-0.245722\pi$
$3$	0.293175	+	0.263976i	0.0977250	+	0.0879920i	−0.618820	+	0.785533i	$0.712389\pi$
$4$	2.30540	+	1.67497i	0.576350	+	0.418743i
$5$	−0.793103	+	1.37369i	−0.158621	+	0.274739i	−0.934371	−	0.356300i	$-0.884038\pi$
$5$	−0.793103	+	1.37369i	−0.158621	+	0.274739i	0.775751	+	0.631039i	$0.217371\pi$
$6$	−0.366440	+	0.211564i	−0.0610733	+	0.0352607i
$7$	0.503493	−	4.79042i	0.0719276	−	0.684345i	−0.897841	−	0.440320i	$-0.854865\pi$
$7$	0.503493	−	4.79042i	0.0719276	−	0.684345i	0.969769	−	0.244026i	$-0.0784682\pi$
$8$	−5.94352	+	4.31822i	−0.742940	+	0.539777i
$9$	−0.924488	−	8.79591i	−0.102721	−	0.977324i
$10$	−1.13839	−	1.26431i	−0.113839	−	0.126431i
$11$	−3.31607	−	7.44800i	−0.301460	−	0.677091i	0.697770	−	0.716322i	$-0.254176\pi$
$11$	−3.31607	−	7.44800i	−0.301460	−	0.677091i	−0.999230	+	0.0392308i	$0.987509\pi$
$12$	0.233734	+	1.09963i	0.0194778	+	0.0916358i
$13$	0.723920	−	3.40578i	0.0556862	−	0.261983i	−0.941494	−	0.337030i	$-0.890578\pi$
$13$	0.723920	−	3.40578i	0.0556862	−	0.261983i	0.997180	+	0.0750475i	$0.0239109\pi$
$14$	4.71963	+	2.10131i	0.337116	+	0.150094i
$15$	−0.595141	+	0.193373i	−0.0396760	+	0.0128915i
$16$	1.08740	+	3.34669i	0.0679628	+	0.209168i
$17$	−8.55661	+	19.2185i	−0.503330	+	1.13050i	0.466011	+	0.884779i	$0.345691\pi$
$17$	−8.55661	+	19.2185i	−0.503330	+	1.13050i	−0.969341	+	0.245719i	$0.920976\pi$
$18$	9.27876	+	1.97226i	0.515486	+	0.109570i
$19$	5.81404	−	1.23581i	0.306002	−	0.0650427i	−0.0523515	−	0.998629i	$-0.516672\pi$
$19$	5.81404	−	1.23581i	0.306002	−	0.0650427i	0.358353	+	0.933586i	$0.383338\pi$
$20$	−4.12932	+	1.83849i	−0.206466	+	0.0919245i
$21$	1.41217	−	1.27152i	0.0672461	−	0.0605486i
$22$	8.69647	−	0.914036i	0.395294	−	0.0415471i
$23$	3.72284	+	5.12405i	0.161863	+	0.222785i	0.882243	−	0.470794i	$-0.156033\pi$
$23$	3.72284	+	5.12405i	0.161863	+	0.222785i	−0.720380	+	0.693579i	$0.756033\pi$
$24$	−2.88240	−	0.302952i	−0.120100	−	0.0126230i
$25$	11.2420	+	19.4717i	0.449679	+	0.778867i
$26$	3.23416	+	1.86724i	0.124391	+	0.0718170i
$27$	4.13784	−	5.69524i	0.153253	−	0.210935i
$28$	9.18456	−	10.2005i	0.328020	−	0.364303i
$29$	−23.1587	−	7.52470i	−0.798574	−	0.259472i	−0.118823	−	0.992915i	$-0.537912\pi$
$29$	−23.1587	−	7.52470i	−0.798574	−	0.259472i	−0.679751	+	0.733443i	$0.737912\pi$
$30$		−	0.671169i		−	0.0223723i
$31$	19.3654	−	24.2071i	0.624689	−	0.780873i
$31$	19.3654	−	24.2071i	0.624689	−	0.780873i
$32$	−33.1606			−1.03627
$33$	0.993907	−	3.05893i	0.0301184	−	0.0926949i
$34$	−16.7680	−	15.0980i	−0.493176	−	0.444058i
$35$	6.18125	+	4.49094i	0.176607	+	0.128313i
$36$	12.6016	−	21.8266i	0.350044	−	0.606294i
$37$	−58.1388	+	33.5665i	−1.57132	+	0.907202i	−0.575312	+	0.817934i	$0.695119\pi$
$37$	−58.1388	+	33.5665i	−1.57132	+	0.907202i	−0.996008	+	0.0892674i	$0.971547\pi$
$38$	−0.666387	+	6.34025i	−0.0175365	+	0.166849i
$39$	1.11128	−	0.807391i	0.0284943	−	0.0207023i
$40$	−1.21809	−	11.5894i	−0.0304523	−	0.289734i
$41$	20.8583	+	23.1655i	0.508739	+	0.565012i	0.941723	−	0.336390i	$-0.109206\pi$
$41$	20.8583	+	23.1655i	0.508739	+	0.565012i	−0.432984	+	0.901402i	$0.642539\pi$
$42$	0.828981	+	1.86192i	0.0197376	+	0.0443315i
$43$	−9.34191	−	43.9502i	−0.217254	−	1.02210i	−0.942654	−	0.333771i	$-0.891679\pi$
$43$	−9.34191	−	43.9502i	−0.217254	−	1.02210i	0.725400	−	0.688327i	$-0.241655\pi$
$44$	4.83033	−	22.7249i	0.109780	−	0.516476i
$45$	12.8161	+	5.70610i	0.284803	+	0.126802i
$46$	−6.46072	+	2.09922i	−0.140450	+	0.0456351i
$47$	15.6666	+	48.2168i	0.333332	+	1.02589i	0.967538	+	0.252725i	$0.0813269\pi$
$47$	15.6666	+	48.2168i	0.333332	+	1.02589i	−0.634207	+	0.773164i	$0.718673\pi$
$48$	−0.564645	+	1.26821i	−0.0117634	+	0.0264211i
$49$	25.2346	+	5.36379i	0.514993	+	0.109465i
$50$	−23.5882	+	5.01384i	−0.471765	+	0.100277i
$51$	−7.58180	+	3.37564i	−0.148663	+	0.0661889i
$52$	7.37350	−	6.63913i	0.141798	−	0.127676i
$53$	10.4475	−	1.09807i	0.197122	−	0.0207183i	−0.00545293	−	0.999985i	$-0.501736\pi$
$53$	10.4475	−	1.09807i	0.197122	−	0.0207183i	0.202575	+	0.979267i	$0.435069\pi$
$54$	4.43805	+	6.10845i	0.0821861	+	0.113119i
$55$	12.8613	+	1.35177i	0.233841	+	0.0245777i
$56$	17.6935	+	30.6461i	0.315956	+	0.547252i
$57$	2.03076	+	1.17246i	0.0356273	+	0.0205694i
$58$	15.3513	−	21.1292i	0.264677	−	0.364297i
$59$	52.3153	−	58.1020i	0.886700	−	0.984780i	−0.113261	−	0.993565i	$-0.536130\pi$
$59$	52.3153	−	58.1020i	0.886700	−	0.984780i	0.999961	+	0.00878481i	$0.00279633\pi$
$60$	−1.69593	−	0.551041i	−0.0282655	−	0.00918402i
$61$			91.3284i			1.49719i	0.663030	+	0.748593i	$0.269270\pi$
$61$			91.3284i			1.49719i	−0.663030	+	0.748593i	$0.730730\pi$
$62$	18.2742	+	27.7769i	0.294746	+	0.448015i
$63$	−42.6016			−0.676216
$64$	6.64103	−	20.4390i	0.103766	−	0.319359i
$65$	4.10435	+	3.69558i	0.0631439	+	0.0568550i
$66$	2.79087	+	2.02769i	0.0422859	+	0.0307225i
$67$	−32.1730	+	55.7253i	−0.480194	+	0.831720i	−0.999742	−	0.0227210i	$-0.992767\pi$
$67$	−32.1730	+	55.7253i	−0.480194	+	0.831720i	0.519548	+	0.854441i	$0.326100\pi$
$68$	−51.9168	+	29.9742i	−0.763482	+	0.440797i
$69$	−0.261183	+	2.48499i	−0.00378525	+	0.0360143i
$70$	−6.62972	+	4.81677i	−0.0947103	+	0.0688110i
$71$	−14.6133	−	139.036i	−0.205821	−	1.95825i	−0.277221	−	0.960806i	$-0.589413\pi$
$71$	−14.6133	−	139.036i	−0.205821	−	1.95825i	0.0714000	−	0.997448i	$-0.477253\pi$
$72$	43.4774	+	48.2865i	0.603853	+	0.670646i
$73$	−41.2139	−	92.5678i	−0.564573	−	1.26805i	−0.939992	−	0.341197i	$-0.889168\pi$
$73$	−41.2139	−	92.5678i	−0.564573	−	1.26805i	0.375418	−	0.926855i	$-0.377499\pi$
$74$	−14.9704	−	70.4302i	−0.202303	−	0.951759i
$75$	−1.84419	+	8.67622i	−0.0245892	+	0.115683i
$76$	15.4736	+	6.88930i	0.203600	+	0.0906487i
$77$	−37.3487	+	12.1353i	−0.485048	+	0.157602i
$78$	0.455267	+	1.40117i	0.00583676	+	0.0179637i
$79$	−13.2762	+	29.8189i	−0.168053	+	0.377454i	−0.977865	−	0.209236i	$-0.932902\pi$
$79$	−13.2762	+	29.8189i	−0.168053	+	0.377454i	0.809812	+	0.586690i	$0.199569\pi$
$80$	−5.45975	−	1.16051i	−0.0682469	−	0.0145063i
$81$	−75.1433	+	15.9722i	−0.927695	+	0.197188i
$82$	−30.5434	+	13.5988i	−0.372480	+	0.165839i
$83$	57.5526	−	51.8206i	0.693405	−	0.624344i	−0.245146	−	0.969486i	$-0.578836\pi$
$83$	57.5526	−	51.8206i	0.693405	−	0.624344i	0.938551	+	0.345142i	$0.112169\pi$
$84$	5.38537	−	0.566025i	0.0641115	−	0.00673839i
$85$	−19.6140	−	26.9964i	−0.230753	−	0.317605i
$86$	47.9281	+	5.03744i	0.557303	+	0.0585749i
$87$	−4.80320	−	8.31938i	−0.0552092	−	0.0956251i
$88$	51.8712	+	29.9478i	0.589445	+	0.340316i
$89$	82.1472	−	113.066i	0.923002	−	1.27040i	−0.0395249	−	0.999219i	$-0.512584\pi$
$89$	82.1472	−	113.066i	0.923002	−	1.27040i	0.962527	−	0.271185i	$-0.0874155\pi$
$90$	−10.0683	+	11.1820i	−0.111870	+	0.124244i
$91$	−15.9506	−	5.18266i	−0.175281	−	0.0569524i
$92$			18.0486i			0.196181i
$93$	12.0675	−	1.98492i	0.129758	−	0.0213432i
$94$	−54.3764			−0.578473
$95$	−2.91350	+	8.96684i	−0.0306684	+	0.0943878i
$96$	−9.72186	−	8.75360i	−0.101269	−	0.0911833i
$97$	74.1883	+	53.9009i	0.764827	+	0.555680i	0.900387	−	0.435089i	$-0.143283\pi$
$97$	74.1883	+	53.9009i	0.764827	+	0.555680i	−0.135560	+	0.990769i	$0.543283\pi$
$98$	−13.8351	+	23.9630i	−0.141174	+	0.244521i
$99$	−62.4464	+	36.0534i	−0.630771	+	0.364176i
$100$	−6.69724	+	63.7200i	−0.0669724	+	0.637200i
$101$	−45.6950	+	33.1994i	−0.452426	+	0.328707i	−0.790553	−	0.612394i	$-0.790207\pi$
$101$	−45.6950	+	33.1994i	−0.452426	+	0.328707i	0.338127	+	0.941101i	$0.390207\pi$
$102$	−0.930455	−	8.85269i	−0.00912211	−	0.0867911i
$103$	65.9717	+	73.2690i	0.640502	+	0.711349i	0.972754	−	0.231841i	$-0.0744750\pi$
$103$	65.9717	+	73.2690i	0.640502	+	0.711349i	−0.332252	+	0.943191i	$0.607808\pi$
$104$	10.4043	+	23.3683i	0.100041	+	0.224695i
$105$	0.626688	+	2.94833i	0.00596845	+	0.0280794i
$106$	−2.34258	+	11.0210i	−0.0220998	+	0.103971i
$107$	96.5514	+	42.9875i	0.902350	+	0.401752i	0.804846	−	0.593483i	$-0.202248\pi$
$107$	96.5514	+	42.9875i	0.902350	+	0.401752i	0.0975033	+	0.995235i	$0.468914\pi$
$108$	19.0787	−	6.19906i	0.176655	−	0.0573987i
$109$	−8.41814	−	25.9084i	−0.0772307	−	0.237692i	0.904986	−	0.425441i	$-0.139881\pi$
$109$	−8.41814	−	25.9084i	−0.0772307	−	0.237692i	−0.982217	+	0.187749i	$0.939881\pi$
$110$	−5.64159	+	12.6712i	−0.0512872	+	0.115193i
$111$	−25.9056	−	5.50640i	−0.233384	−	0.0496072i
$112$	16.5795	−	3.52409i	0.148031	−	0.0314651i
$113$	88.8851	−	39.5742i	0.786594	−	0.350214i	0.0261836	−	0.999657i	$-0.491665\pi$
$113$	88.8851	−	39.5742i	0.786594	−	0.350214i	0.760410	+	0.649443i	$0.224998\pi$
$114$	−1.86904	+	1.68289i	−0.0163951	+	0.0147622i
$115$	−9.99149	+	1.05015i	−0.0868825	+	0.00913172i
$116$	−40.7863	−	56.1375i	−0.351606	−	0.483944i
$117$	−30.6262	−	3.21894i	−0.261762	−	0.0275123i
$118$	41.9282	+	72.6219i	0.355324	+	0.615439i
$119$	87.7563	+	50.6661i	0.737448	+	0.425766i
$120$	2.70220	−	3.71926i	0.0225183	−	0.0309938i
$121$	36.4883	−	40.5244i	0.301556	−	0.334912i
$122$	−93.1603	−	30.2696i	−0.763609	−	0.248111i
$123$			12.2976i			0.0999808i
$124$	85.1910	−	23.3705i	0.687025	−	0.188472i
$125$	−75.3193			−0.602555
$126$	14.1197	−	43.4561i	0.112061	−	0.344890i
$127$	−142.422	−	128.237i	−1.12143	−	1.00974i	−0.999853	−	0.0171624i	$-0.994537\pi$
$127$	−142.422	−	128.237i	−1.12143	−	1.00974i	−0.121581	−	0.992581i	$-0.538797\pi$
$128$	−88.6620	−	64.4167i	−0.692672	−	0.503256i
$129$	8.86299	−	15.3512i	0.0687054	−	0.119001i
$130$	−5.13004	+	2.96183i	−0.0394618	+	0.0227833i
$131$	−11.4758	+	109.185i	−0.0876013	+	0.833470i	0.859197	+	0.511644i	$0.170963\pi$
$131$	−11.4758	+	109.185i	−0.0876013	+	0.833470i	−0.946799	+	0.321826i	$0.895703\pi$
$132$	7.41497	−	5.38729i	0.0561740	−	0.0408128i
$133$	−2.99273	−	28.4739i	−0.0225017	−	0.214089i
$134$	−46.1797	−	51.2878i	−0.344625	−	0.382744i
$135$	4.54180	+	10.2010i	0.0336429	+	0.0755633i
$136$	−32.1332	−	151.175i	−0.236273	−	1.11158i
$137$	4.76048	−	22.3963i	0.0347480	−	0.163477i	−0.957352	−	0.288923i	$-0.906703\pi$
$137$	4.76048	−	22.3963i	0.0347480	−	0.163477i	0.992100	+	0.125446i	$0.0400362\pi$
$138$	−2.44827	−	1.09004i	−0.0177411	−	0.00789883i
$139$	−157.299	+	51.1096i	−1.13165	+	0.367695i	−0.814203	−	0.580581i	$-0.802826\pi$
$139$	−157.299	+	51.1096i	−1.13165	+	0.367695i	−0.317447	+	0.948276i	$0.602826\pi$
$140$	6.72806	+	20.7068i	0.0480575	+	0.147906i
$141$	−8.13502	+	18.2716i	−0.0576952	+	0.129586i
$142$	146.668	+	31.1753i	1.03288	+	0.219544i
$143$	−27.7668	+	5.90202i	−0.194173	+	0.0412728i
$144$	28.4319	−	12.6587i	0.197444	−	0.0879075i
$145$	28.7038	−	25.8451i	0.197958	−	0.178242i
$146$	108.084	−	11.3601i	0.740304	−	0.0778091i
$147$	5.98225	+	8.23387i	0.0406956	+	0.0560127i
$148$	−190.256	−	19.9967i	−1.28551	−	0.135113i
$149$	14.7814	+	25.6022i	0.0992044	+	0.171827i	0.911356	−	0.411620i	$-0.135037\pi$
$149$	14.7814	+	25.6022i	0.0992044	+	0.171827i	−0.812151	+	0.583447i	$0.801704\pi$
$150$	−8.23902	−	4.75680i	−0.0549268	−	0.0317120i
$151$	−67.1873	+	92.4754i	−0.444949	+	0.612420i	−0.971303	−	0.237846i	$-0.923559\pi$
$151$	−67.1873	+	92.4754i	−0.444949	+	0.612420i	0.526354	+	0.850266i	$0.323559\pi$
$152$	−29.2193	+	32.4513i	−0.192232	+	0.213496i
$153$	176.955	+	57.4960i	1.15657	+	0.375791i
$154$		−	42.1199i		−	0.273506i
$155$	17.8944	+	45.8008i	0.115448	+	0.295489i
$156$	3.91430			0.0250916
$157$	−3.45203	+	10.6243i	−0.0219875	+	0.0676705i	−0.961448	−	0.274986i	$-0.911327\pi$
$157$	−3.45203	+	10.6243i	−0.0219875	+	0.0676705i	0.939461	+	0.342657i	$0.111327\pi$
$158$	−26.0168	−	23.4256i	−0.164663	−	0.148263i
$159$	3.35280	+	2.43595i	0.0210868	+	0.0153205i
$160$	26.2998	−	45.5525i	0.164374	−	0.284703i
$161$	26.4208	−	15.2540i	0.164104	−	0.0947456i
$162$	8.61270	−	81.9444i	0.0531648	−	0.505829i
$163$	−75.9325	+	55.1682i	−0.465843	+	0.338455i	−0.795819	−	0.605534i	$-0.792959\pi$
$163$	−75.9325	+	55.1682i	−0.465843	+	0.338455i	0.329976	+	0.943989i	$0.392959\pi$
$164$	9.28520	+	88.3428i	0.0566171	+	0.538676i
$165$	3.41377	+	3.79137i	0.0206895	+	0.0229780i
$166$	33.7850	+	75.8823i	0.203524	+	0.457122i
$167$	32.8405	+	154.502i	0.196650	+	0.925164i	0.960178	+	0.279389i	$0.0901320\pi$
$167$	32.8405	+	154.502i	0.196650	+	0.925164i	−0.763528	+	0.645774i	$0.776535\pi$
$168$	−2.90253	+	13.6554i	−0.0172770	+	0.0812819i
$169$	143.314	+	63.8075i	0.848011	+	0.377559i
$170$	34.0387	−	11.0599i	0.200228	−	0.0650580i
$171$	−16.2451	−	49.9973i	−0.0950006	−	0.292382i
$172$	52.0785	−	116.970i	0.302782	−	0.680060i
$173$	−100.585	−	21.3799i	−0.581414	−	0.123583i	−0.0921898	−	0.995741i	$-0.529387\pi$
$173$	−100.585	−	21.3799i	−0.581414	−	0.123583i	−0.489224	+	0.872158i	$0.662720\pi$
$174$	10.0782	−	2.14219i	0.0579208	−	0.0123114i
$175$	98.9377	−	44.0499i	0.565358	−	0.251714i
$176$	21.3202	−	19.1968i	0.121138	−	0.109073i
$177$	30.6751	−	3.22408i	0.173306	−	0.0182152i
$178$	88.1072	+	121.269i	0.494984	+	0.681288i
$179$	68.1316	+	7.16092i	0.380624	+	0.0400052i	0.292909	−	0.956140i	$-0.405377\pi$
$179$	68.1316	+	7.16092i	0.380624	+	0.0400052i	0.0877151	+	0.996146i	$0.472044\pi$
$180$	19.9887	+	34.6215i	0.111048	+	0.192341i
$181$	−109.526	−	63.2349i	−0.605116	−	0.349364i	0.165935	−	0.986137i	$-0.446936\pi$
$181$	−109.526	−	63.2349i	−0.605116	−	0.349364i	−0.771052	+	0.636773i	$0.780269\pi$
$182$	10.5732	−	14.5528i	0.0580947	−	0.0799605i
$183$	−24.1085	+	26.7752i	−0.131740	+	0.146313i
$184$	−44.2536	−	14.3789i	−0.240508	−	0.0781459i
$185$		−	106.487i		−	0.575604i
$186$	−1.97490	+	12.9675i	−0.0106177	+	0.0697175i
$187$	171.514			0.917185
$188$	−44.6440	+	137.400i	−0.237468	+	0.730851i
$189$	−25.1992	−	22.6895i	−0.133329	−	0.120050i
$190$	−8.18106	−	5.94389i	−0.0430582	−	0.0312836i
$191$	−112.099	+	194.161i	−0.586906	+	1.01655i	0.407729	+	0.913103i	$0.366321\pi$
$191$	−112.099	+	194.161i	−0.586906	+	1.01655i	−0.994635	+	0.103448i	$0.967012\pi$
$192$	7.34239	−	4.23913i	0.0382416	−	0.0220788i
$193$	18.6790	−	177.718i	0.0967822	−	0.920821i	−0.833139	−	0.553063i	$-0.813459\pi$
$193$	18.6790	−	177.718i	0.0967822	−	0.920821i	0.929922	−	0.367758i	$-0.119875\pi$
$194$	−79.5708	+	57.8116i	−0.410159	+	0.297998i
$195$	0.227751	+	2.16690i	0.00116795	+	0.0111123i
$196$	49.1917	+	54.6329i	0.250978	+	0.278740i
$197$	−64.6732	−	145.258i	−0.328290	−	0.737352i	0.671704	−	0.740820i	$-0.265563\pi$
$197$	−64.6732	−	145.258i	−0.328290	−	0.737352i	−0.999994	+	0.00346803i	$0.998896\pi$
$198$	−16.0796	−	75.6484i	−0.0812099	−	0.382062i
$199$	−3.82129	+	17.9778i	−0.0192025	+	0.0903405i	−0.986705	−	0.162520i	$-0.948038\pi$
$199$	−3.82129	+	17.9778i	−0.0192025	+	0.0903405i	0.967503	+	0.252860i	$0.0813712\pi$
$200$	−150.900	−	67.1849i	−0.754499	−	0.335925i
$201$	−24.1425	+	7.84436i	−0.120112	+	0.0390267i
$202$	−18.7203	−	57.6151i	−0.0926747	−	0.285223i
$203$	−47.7067	+	107.151i	−0.235008	+	0.527837i
$204$	−23.1332	−	4.91711i	−0.113398	−	0.0241035i
$205$	−48.3651	+	10.2803i	−0.235927	+	0.0501479i
$206$	−96.6041	+	43.0109i	−0.468952	+	0.208791i
$207$	41.6290	−	37.4829i	0.201106	−	0.181077i
$208$	12.1853	−	1.28072i	0.0585830	−	0.00615732i
$209$	−28.4841	−	39.2049i	−0.136287	−	0.187583i
$210$	−3.21518	−	0.337929i	−0.0153104	−	0.00160919i
$211$	−192.984	−	334.258i	−0.914616	−	1.58416i	−0.807463	−	0.589919i	$-0.799160\pi$
$211$	−192.984	−	334.258i	−0.914616	−	1.58416i	−0.107153	−	0.994242i	$-0.534174\pi$
$212$	25.9248	+	14.9677i	0.122287	+	0.0706023i
$213$	32.4179	−	44.6195i	0.152197	−	0.209481i
$214$	−75.8504	+	84.2404i	−0.354441	+	0.393647i
$215$	67.7833	+	22.0241i	0.315271	+	0.102438i
$216$			51.7179i			0.239435i
$217$	−106.212	−	104.956i	−0.489455	−	0.483670i
$218$	29.2181			0.134028
$219$	12.3528	−	38.0181i	0.0564055	−	0.173598i
$220$	27.3862	+	24.6586i	0.124483	+	0.112085i
$221$	59.2595	+	43.0545i	0.268143	+	0.194817i
$222$	14.2029	−	24.6002i	0.0639772	−	0.110812i
$223$	218.226	−	125.993i	0.978594	−	0.564991i	0.0767484	−	0.997050i	$-0.475546\pi$
$223$	218.226	−	125.993i	0.978594	−	0.564991i	0.901845	+	0.432059i	$0.142213\pi$
$224$	−16.6961	+	158.853i	−0.0745363	+	0.709165i
$225$	160.878	−	116.885i	0.715014	−	0.519488i
$226$	10.9082	+	103.784i	0.0482663	+	0.459223i
$227$	−212.245	−	235.722i	−0.935001	−	1.03842i	−0.999180	−	0.0404852i	$-0.987110\pi$
$227$	−212.245	−	235.722i	−0.935001	−	1.03842i	0.0641794	−	0.997938i	$-0.479557\pi$
$228$	2.71787	+	6.10444i	0.0119205	+	0.0267738i
$229$	67.7235	+	318.614i	0.295736	+	1.39133i	0.835490	+	0.549506i	$0.185184\pi$
$229$	67.7235	+	318.614i	0.295736	+	1.39133i	−0.539754	+	0.841823i	$0.681483\pi$
$230$	2.24034	−	10.5400i	0.00974060	−	0.0458259i
$231$	−14.1531	−	6.30138i	−0.0612690	−	0.0272787i
$232$	170.137	−	55.2809i	0.733350	−	0.238280i
$233$	−14.1471	−	43.5404i	−0.0607173	−	0.186868i	0.916097	−	0.400956i	$-0.131322\pi$
$233$	−14.1471	−	43.5404i	−0.0607173	−	0.186868i	−0.976814	+	0.214088i	$0.931322\pi$
$234$	13.4342	−	30.1736i	0.0574109	−	0.128947i
$235$	−78.6604	−	16.7198i	−0.334725	−	0.0711480i
$236$	217.927	−	46.3218i	0.923419	−	0.196279i
$237$	−11.7637	+	5.23755i	−0.0496360	+	0.0220994i
$238$	−80.7681	+	72.7239i	−0.339362	+	0.305563i
$239$	−292.680	+	30.7619i	−1.22460	+	0.128711i	−0.694669	−	0.719329i	$-0.744449\pi$
$239$	−292.680	+	30.7619i	−1.22460	+	0.128711i	−0.529932	+	0.848040i	$0.677783\pi$
$240$	−1.29432	−	1.78147i	−0.00539299	−	0.00742281i
$241$	286.887	+	30.1531i	1.19040	+	0.125116i	0.678943	−	0.734191i	$-0.262438\pi$
$241$	286.887	+	30.1531i	1.19040	+	0.125116i	0.511460	+	0.859307i	$0.329105\pi$
$242$	29.2437	+	50.6515i	0.120842	+	0.209304i
$243$	−81.1155	−	46.8321i	−0.333809	−	0.192725i
$244$	−152.972	+	210.548i	−0.626936	+	0.862903i
$245$	−27.3819	+	30.4107i	−0.111763	+	0.124125i
$246$	−12.5443	−	4.07589i	−0.0509931	−	0.0165687i
$247$		−	20.6959i		−	0.0837892i
$248$	−10.5670	+	227.499i	−0.0426088	+	0.917335i
$249$	30.5524			0.122700
$250$	24.9636	−	76.8301i	0.0998545	−	0.307321i
$251$	286.661	+	258.111i	1.14208	+	1.02833i	0.999255	+	0.0385823i	$0.0122842\pi$
$251$	286.661	+	258.111i	1.14208	+	1.02833i	0.142822	+	0.989748i	$0.454382\pi$
$252$	−98.2137	−	71.3564i	−0.389737	−	0.283160i
$253$	25.8188	−	44.7195i	0.102051	−	0.176757i
$254$	178.014	−	102.776i	0.700841	−	0.404631i
$255$	1.37606	−	13.0923i	0.00539630	−	0.0513424i
$256$	164.640	−	119.618i	0.643127	−	0.467259i
$257$	−0.288749	−	2.74726i	−0.00112354	−	0.0106897i	0.993946	−	0.109872i	$-0.0350440\pi$
$257$	−0.288749	−	2.74726i	−0.00112354	−	0.0106897i	−0.995069	+	0.0991821i	$0.968377\pi$
$258$	12.7215	+	14.1287i	0.0493083	+	0.0547624i
$259$	131.525	+	295.410i	0.507818	+	1.14058i
$260$	3.27219	+	15.3945i	0.0125854	+	0.0592094i
$261$	−44.7767	+	210.658i	−0.171558	+	0.807119i
$262$	−107.571	−	47.8938i	−0.410577	−	0.182801i
$263$	180.074	−	58.5097i	0.684694	−	0.222470i	0.0540445	−	0.998539i	$-0.482789\pi$
$263$	180.074	−	58.5097i	0.684694	−	0.222470i	0.630649	+	0.776068i	$0.282789\pi$
$264$	7.30183	+	22.4727i	0.0276584	+	0.0851239i
$265$	−6.77750	+	15.2225i	−0.0255755	+	0.0574434i
$266$	30.0369	+	6.38455i	0.112921	+	0.0240021i
$267$	53.9302	−	11.4632i	0.201986	−	0.0429334i
$268$	−167.510	+	74.5802i	−0.625037	+	0.278284i
$269$	−273.941	+	246.658i	−1.01837	+	0.916942i	−0.996565	−	0.0828198i	$-0.973607\pi$
$269$	−273.941	+	246.658i	−1.01837	+	0.916942i	−0.0218032	+	0.999762i	$0.506941\pi$
$270$	−11.9110	+	1.25189i	−0.0441147	+	0.00463665i
$271$	−98.1285	−	135.062i	−0.362098	−	0.498385i	0.588634	−	0.808400i	$-0.299666\pi$
$271$	−98.1285	−	135.062i	−0.362098	−	0.498385i	−0.950732	+	0.310015i	$0.899666\pi$
$272$	−73.6227	−	7.73806i	−0.270672	−	0.0284487i
$273$	−3.30822	−	5.73000i	−0.0121180	−	0.0209890i
$274$	21.2677	+	12.2789i	0.0776194	+	0.0448136i
$275$	107.746	−	148.300i	0.391804	−	0.539271i
$276$	−4.76441	+	5.29141i	−0.0172624	+	0.0191718i
$277$	74.3015	+	24.1420i	0.268237	+	0.0871553i	0.440047	−	0.897975i	$-0.354962\pi$
$277$	74.3015	+	24.1420i	0.268237	+	0.0871553i	−0.171811	+	0.985130i	$0.554962\pi$
$278$		−	177.394i		−	0.638108i
$279$	−230.826	−	147.957i	−0.827335	−	0.530312i
$280$	−56.1312			−0.200469
$281$	−47.6399	+	146.621i	−0.169537	+	0.521781i	−0.999342	−	0.0362723i	$-0.988452\pi$
$281$	−47.6399	+	146.621i	−0.169537	+	0.521781i	0.829805	+	0.558054i	$0.188452\pi$
$282$	−15.9418	−	14.3541i	−0.0565312	−	0.0509010i
$283$	−18.2600	−	13.2666i	−0.0645228	−	0.0468786i	0.555056	−	0.831813i	$-0.312697\pi$
$283$	−18.2600	−	13.2666i	−0.0645228	−	0.0468786i	−0.619579	+	0.784934i	$0.712697\pi$
$284$	199.192	−	345.010i	0.701380	−	1.21483i
$285$	−3.22120	+	1.85976i	−0.0113024	+	0.00652547i
$286$	3.18255	−	30.2799i	0.0111278	−	0.105874i
$287$	121.474	−	88.2563i	0.423256	−	0.307513i
$288$	30.6566	+	291.678i	0.106446	+	1.01277i
$289$	−102.755	−	114.121i	−0.355554	−	0.394883i
$290$	16.8500	+	37.8456i	0.0581033	+	0.130502i
$291$	7.52160	+	35.3863i	0.0258474	+	0.121603i
$292$	60.0340	−	282.438i	0.205596	−	0.967253i
$293$	−476.320	−	212.071i	−1.62566	−	0.723793i	−0.627183	−	0.778872i	$-0.715792\pi$
$293$	−476.320	−	212.071i	−1.62566	−	0.723793i	−0.998482	+	0.0550795i	$0.982459\pi$
$294$	−10.3818	+	3.37324i	−0.0353121	+	0.0114736i
$295$	38.3230	+	117.946i	0.129909	+	0.399818i
$296$	200.602	−	450.559i	0.677709	−	1.52216i
$297$	−56.1395	−	11.9328i	−0.189022	−	0.0401779i
$298$	−31.0149	+	6.59242i	−0.104077	+	0.0221222i
$299$	20.1464	−	8.96976i	0.0673793	−	0.0299992i
$300$	−18.7840	+	16.9132i	−0.0626133	+	0.0563773i
$301$	−215.244	+	22.6230i	−0.715095	+	0.0751595i
$302$	−72.0620	−	99.1848i	−0.238616	−	0.328426i
$303$	−22.1605	−	2.32916i	−0.0731369	−	0.00768700i
$304$	10.4581	+	18.1139i	0.0344016	+	0.0595853i
$305$	−125.457	−	72.4328i	−0.411335	−	0.237485i
$306$	−117.299	+	161.448i	−0.383329	+	0.527607i
$307$	−20.0369	+	22.2532i	−0.0652668	+	0.0724861i	−0.774894	−	0.632091i	$-0.782197\pi$
$307$	−20.0369	+	22.2532i	−0.0652668	+	0.0724861i	0.709627	+	0.704577i	$0.248863\pi$
$308$	−106.430	−	34.5812i	−0.345552	−	0.112277i
$309$			38.8956i			0.125876i
$310$	−52.6504	+	3.07324i	−0.169840	+	0.00991369i
$311$	403.956			1.29889			0.649447	−	0.760407i	$-0.275000\pi$
$311$	403.956			1.29889			0.649447	+	0.760407i	$0.275000\pi$
$312$	−3.11841	+	9.59748i	−0.00999491	+	0.0307612i
$313$	319.331	+	287.527i	1.02023	+	0.918618i	0.996706	−	0.0811055i	$-0.0258451\pi$
$313$	319.331	+	287.527i	1.02023	+	0.918618i	0.0235229	+	0.999723i	$0.492512\pi$
$314$	−9.69324	−	7.04255i	−0.0308702	−	0.0224285i
$315$	33.7874	−	58.5216i	0.107262	−	0.185783i
$316$	−80.5527	+	46.5071i	−0.254914	+	0.147174i
$317$	22.6302	−	215.312i	0.0713885	−	0.679216i	−0.899046	−	0.437853i	$-0.855739\pi$
$317$	22.6302	−	215.312i	0.0713885	−	0.679216i	0.970435	−	0.241363i	$-0.0775944\pi$
$318$	−3.59606	+	2.61269i	−0.0113083	+	0.00821600i
$319$	20.7516	+	197.438i	0.0650520	+	0.618928i
$320$	22.8099	+	25.3330i	0.0712810	+	0.0791656i
$321$	16.9588	+	38.0901i	0.0528312	+	0.118661i
$322$	6.80319	+	32.0065i	0.0211279	+	0.0993991i
$323$	−25.9981	+	122.311i	−0.0804893	+	0.378673i
$324$	−199.988	−	89.0406i	−0.617248	−	0.274817i
$325$	74.4544	−	24.1917i	0.229091	−	0.0744360i
$326$	−31.1079	−	95.7403i	−0.0954231	−	0.293682i
$327$	4.37120	−	9.81788i	0.0133676	−	0.0300241i
$328$	−224.005	−	47.6138i	−0.682943	−	0.145164i
$329$	238.867	−	50.7727i	0.726038	−	0.154324i
$330$	−4.99887	+	2.22564i	−0.0151481	+	0.00674437i
$331$	−164.493	+	148.111i	−0.496959	+	0.447464i	−0.879098	−	0.476641i	$-0.841854\pi$
$331$	−164.493	+	148.111i	−0.496959	+	0.447464i	0.382139	+	0.924105i	$0.375187\pi$
$332$	219.480	−	23.0682i	0.661083	−	0.0694827i
$333$	348.996	+	480.352i	1.04804	+	1.44250i
$334$	−168.486	−	17.7086i	−0.504449	−	0.0530197i
$335$	−51.0330	−	88.3918i	−0.152337	−	0.263856i
$336$	5.79098	+	3.34342i	0.0172351	+	0.00995066i
$337$	−294.142	+	404.852i	−0.872826	+	1.20134i	0.105531	+	0.994416i	$0.466346\pi$
$337$	−294.142	+	404.852i	−0.872826	+	1.20134i	−0.978357	+	0.206926i	$0.933654\pi$
$338$	−112.587	+	125.040i	−0.333097	+	0.369942i
$339$	36.5055	+	11.8614i	0.107686	+	0.0349893i
$340$		−	95.0904i		−	0.279678i
$341$	−244.511	−	63.9611i	−0.717042	−	0.187569i
$342$	56.3844			0.164867
$343$	111.336	−	342.655i	0.324593	−	0.998995i
$344$	245.310	+	220.879i	0.713112	+	0.642089i
$345$	−3.20647	−	2.32964i	−0.00929411	−	0.00675257i
$346$	55.1462	−	95.5161i	0.159382	−	0.276058i
$347$	354.472	−	204.654i	1.02153	−	0.589782i	0.106985	−	0.994261i	$-0.465880\pi$
$347$	354.472	−	204.654i	1.02153	−	0.589782i	0.914547	+	0.404479i	$0.132547\pi$
$348$	2.86143	−	27.2247i	0.00822251	−	0.0782319i
$349$	49.4165	−	35.9032i	0.141595	−	0.102875i	−0.514733	−	0.857351i	$-0.672109\pi$
$349$	49.4165	−	35.9032i	0.141595	−	0.102875i	0.656328	+	0.754476i	$0.272109\pi$
$350$	12.1419	+	115.522i	0.0346910	+	0.330063i
$351$	−16.4013	−	18.2154i	−0.0467272	−	0.0518959i
$352$	109.963	+	246.980i	0.312394	+	0.701648i
$353$	76.0559	+	357.815i	0.215456	+	1.01364i	0.944332	+	0.328994i	$0.106710\pi$
$353$	76.0559	+	357.815i	0.215456	+	1.01364i	−0.728876	+	0.684645i	$0.759957\pi$
$354$	−6.87811	+	32.3590i	−0.0194297	+	0.0914095i
$355$	202.583	+	90.1957i	0.570656	+	0.254072i
$356$	378.764	−	123.068i	1.06394	−	0.345696i
$357$	12.3533	+	38.0196i	0.0346031	+	0.106497i
$358$	−29.8859	+	67.1249i	−0.0834802	+	0.187500i
$359$	12.1064	+	2.57330i	0.0337226	+	0.00716795i	0.224742	−	0.974418i	$-0.427846\pi$
$359$	12.1064	+	2.57330i	0.0337226	+	0.00716795i	−0.191020	+	0.981586i	$0.561179\pi$
$360$	−100.813	+	21.4285i	−0.280036	+	0.0595235i
$361$	−297.514	+	132.462i	−0.824139	+	0.366930i
$362$	100.804	−	90.7646i	0.278465	−	0.250731i
$363$	21.3949	−	2.24870i	0.0589392	−	0.00619476i
$364$	−28.0917	−	38.6649i	−0.0771750	−	0.106222i
$365$	159.847	+	16.8006i	0.437936	+	0.0460290i
$366$	−19.3218	−	33.4664i	−0.0527918	−	0.0914382i
$367$	−375.366	−	216.718i	−1.02280	−	0.590512i	−0.107884	−	0.994163i	$-0.534408\pi$
$367$	−375.366	−	216.718i	−1.02280	−	0.590512i	−0.914913	+	0.403651i	$0.867741\pi$
$368$	−13.1004	+	18.0311i	−0.0355988	+	0.0489976i
$369$	184.479	−	204.884i	0.499942	−	0.555242i
$370$	108.623	+	35.2936i	0.293575	+	0.0953882i
$371$		−	50.6006i		−	0.136390i
$372$	31.1452	+	15.6367i	0.0837235	+	0.0420342i
$373$	431.656			1.15725			0.578627	−	0.815592i	$-0.303589\pi$
$373$	431.656			1.15725			0.578627	+	0.815592i	$0.303589\pi$
$374$	−56.8460	+	174.954i	−0.151995	+	0.467791i
$375$	−22.0818	−	19.8825i	−0.0588847	−	0.0530200i
$376$	−301.325	−	218.926i	−0.801397	−	0.582249i
$377$	−42.3925	+	73.4259i	−0.112447	+	0.194764i
$378$	31.4966	−	18.1845i	0.0833242	−	0.0481073i
$379$	29.9238	−	284.706i	0.0789546	−	0.751203i	−0.881390	−	0.472389i	$-0.843392\pi$
$379$	29.9238	−	284.706i	0.0789546	−	0.751203i	0.960345	−	0.278814i	$-0.0899414\pi$
$380$	−21.7360	+	15.7921i	−0.0571999	+	0.0415582i
$381$	−7.90300	−	75.1921i	−0.0207428	−	0.197354i
$382$	−160.902	−	178.700i	−0.421210	−	0.467801i
$383$	−233.144	−	523.649i	−0.608730	−	1.36723i	−0.910365	−	0.413807i	$-0.864199\pi$
$383$	−233.144	−	523.649i	−0.608730	−	1.36723i	0.301634	−	0.953424i	$-0.402468\pi$
$384$	−8.98902	−	42.2900i	−0.0234089	−	0.110130i
$385$	12.9511	−	60.9302i	0.0336393	−	0.158260i
$386$	175.092	+	77.9561i	0.453607	+	0.201959i
$387$	−377.946	+	122.802i	−0.976605	+	0.317318i
$388$	80.7511	+	248.526i	0.208121	+	0.640532i
$389$	−212.502	+	477.287i	−0.546277	+	1.22696i	0.403773	+	0.914859i	$0.367699\pi$
$389$	−212.502	+	477.287i	−0.546277	+	1.22696i	−0.950050	+	0.312099i	$0.898968\pi$
$390$	−2.28585	−	0.485873i	−0.00586116	−	0.00124583i
$391$	−130.331	+	27.7028i	−0.333328	+	0.0708511i
$392$	−173.144	+	77.0889i	−0.441695	+	0.196655i
$393$	−32.1865	+	28.9809i	−0.0818996	+	0.0737427i
$394$	169.607	−	17.8264i	0.430475	−	0.0452447i
$395$	−30.4326	−	41.8869i	−0.0770446	−	0.106043i
$396$	−204.352	−	21.4783i	−0.516041	−	0.0542381i
$397$	−199.641	−	345.789i	−0.502874	−	0.871004i	−0.999994	−	0.00332219i	$-0.998943\pi$
$397$	−199.641	−	345.789i	−0.502874	−	0.871004i	0.497120	−	0.867682i	$-0.334391\pi$
$398$	−17.0718	−	9.85643i	−0.0428941	−	0.0247649i
$399$	6.63903	−	9.13784i	0.0166392	−	0.0229019i
$400$	−52.9410	+	58.7969i	−0.132352	+	0.146992i
$401$	−272.820	−	88.6444i	−0.680348	−	0.221058i	−0.0516002	−	0.998668i	$-0.516432\pi$
$401$	−272.820	−	88.6444i	−0.680348	−	0.221058i	−0.628748	+	0.777609i	$0.716432\pi$
$402$		−	27.2266i		−	0.0677279i
$403$	−68.4249	−	83.4781i	−0.169789	−	0.207142i
$404$	−160.953			−0.398399
$405$	37.6555	−	115.892i	0.0929765	−	0.286152i
$406$	−93.4885	−	84.1774i	−0.230267	−	0.207334i
$407$	442.795	+	321.710i	1.08795	+	0.790441i
$408$	30.4858	−	52.8030i	0.0747202	−	0.129419i
$409$	127.882	−	73.8326i	0.312669	−	0.180520i	−0.335451	−	0.942058i	$-0.608889\pi$
$409$	127.882	−	73.8326i	0.312669	−	0.180520i	0.648120	+	0.761538i	$0.275555\pi$
$410$	5.54346	−	52.7425i	0.0135206	−	0.128640i
$411$	7.30774	−	5.30938i	0.0177804	−	0.0129182i
$412$	29.3677	+	279.415i	0.0712808	+	0.678192i
$413$	−251.993	−	279.866i	−0.610152	−	0.677642i
$414$	24.4374	+	54.8873i	0.0590275	+	0.132578i
$415$	25.5405	+	120.159i	0.0615435	+	0.289539i
$416$	−24.0056	+	112.938i	−0.0577058	+	0.271484i
$417$	−59.6080	−	26.5392i	−0.142945	−	0.0636431i
$418$	49.4320	−	16.0614i	0.118258	−	0.0384245i
$419$	−208.754	−	642.478i	−0.498219	−	1.53336i	−0.811880	−	0.583824i	$-0.801556\pi$
$419$	−208.754	−	642.478i	−0.498219	−	1.53336i	0.313661	−	0.949535i	$-0.398444\pi$
$420$	−3.49361	+	7.84677i	−0.00831811	+	0.0186828i
$421$	106.705	+	22.6808i	0.253455	+	0.0538735i	0.332887	−	0.942967i	$-0.391977\pi$
$421$	106.705	+	22.6808i	0.253455	+	0.0538735i	−0.0794318	+	0.996840i	$0.525311\pi$
$422$	404.925	−	86.0694i	0.959537	−	0.203956i
$423$	409.627	−	182.378i	0.968386	−	0.431153i
$424$	−57.3529	+	51.6408i	−0.135266	+	0.121794i
$425$	−470.409	+	49.4420i	−1.10684	+	0.116334i
$426$	34.7699	+	47.8567i	0.0816196	+	0.112340i
$427$	437.501	+	45.9832i	1.02459	+	0.107689i
$428$	150.587	+	260.824i	0.351838	+	0.609402i
$429$	−9.69852	−	5.59945i	−0.0226073	−	0.0130523i
$430$	−44.9318	+	61.8433i	−0.104493	+	0.143822i
$431$	−384.324	+	426.835i	−0.891702	+	0.990335i	−0.999993	−	0.00378395i	$-0.998796\pi$
$431$	−384.324	+	426.835i	−0.891702	+	0.990335i	0.108291	+	0.994119i	$0.465462\pi$
$432$	23.5597	+	7.65501i	0.0545363	+	0.0177199i
$433$		−	124.085i		−	0.286570i	−0.989681	−	0.143285i	$-0.954234\pi$
$433$		−	124.085i		−	0.286570i	0.989681	−	0.143285i	$-0.0457665\pi$
$434$	142.264	−	73.5557i	0.327797	−	0.169483i
$435$	15.2377			0.0350293
$436$	23.9886	−	73.8293i	0.0550197	−	0.169333i
$437$	27.9771	+	25.1907i	0.0640208	+	0.0576446i
$438$	34.6865	+	25.2012i	0.0791928	+	0.0575369i
$439$	−93.9586	+	162.741i	−0.214029	+	0.370708i	−0.952972	−	0.303059i	$-0.901992\pi$
$439$	−93.9586	+	162.741i	−0.214029	+	0.370708i	0.738943	+	0.673768i	$0.235325\pi$
$440$	−82.2784	+	47.5035i	−0.186996	+	0.107962i
$441$	23.8503	−	226.920i	0.0540823	−	0.514559i
$442$	−63.5589	+	46.1783i	−0.143799	+	0.104476i
$443$	−18.1478	−	172.664i	−0.0409656	−	0.389762i	−0.995724	−	0.0923788i	$-0.970553\pi$
$443$	−18.1478	−	172.664i	−0.0409656	−	0.389762i	0.954758	−	0.297383i	$-0.0961137\pi$
$444$	−50.4997	−	56.0856i	−0.113738	−	0.126319i
$445$	90.1669	+	202.518i	0.202622	+	0.455097i
$446$	56.1920	+	264.362i	0.125991	+	0.592741i
$447$	−2.42482	+	11.4079i	−0.00542465	+	0.0255210i
$448$	−94.5676	−	42.1042i	−0.211088	−	0.0939826i
$449$	76.5710	−	24.8794i	0.170537	−	0.0554108i	−0.222504	−	0.974932i	$-0.571423\pi$
$449$	76.5710	−	24.8794i	0.170537	−	0.0554108i	0.393041	+	0.919521i	$0.371423\pi$
$450$	65.9083	+	202.845i	0.146463	+	0.450767i
$451$	103.369	−	232.171i	0.229200	−	0.514792i
$452$	271.201	+	57.6456i	0.600003	+	0.127535i
$453$	−44.1089	+	9.37564i	−0.0973707	+	0.0206968i
$454$	310.796	−	138.375i	0.684573	−	0.304792i
$455$	19.7699	−	17.8009i	0.0434503	−	0.0391228i
$456$	−17.1328	+	1.80072i	−0.0375718	+	0.00394896i
$457$	122.368	+	168.425i	0.267764	+	0.368545i	0.921633	−	0.388062i	$-0.126855\pi$
$457$	122.368	+	168.425i	0.267764	+	0.368545i	−0.653870	+	0.756607i	$0.726855\pi$
$458$	−347.451	−	36.5186i	−0.758627	−	0.0797349i
$459$	74.0480	+	128.255i	0.161325	+	0.279422i
$460$	−24.7933	−	14.3144i	−0.0538985	−	0.0311183i
$461$	323.021	−	444.600i	0.700697	−	0.964426i	−0.299251	−	0.954174i	$-0.596737\pi$
$461$	323.021	−	444.600i	0.700697	−	0.964426i	0.999947	−	0.0102516i	$-0.00326324\pi$
$462$	11.1186	−	12.3485i	0.0240663	−	0.0267284i
$463$	275.358	+	89.4694i	0.594727	+	0.193238i	0.590887	−	0.806754i	$-0.298778\pi$
$463$	275.358	+	89.4694i	0.594727	+	0.193238i	0.00383954	+	0.999993i	$0.498778\pi$
$464$		−	85.6871i		−	0.184671i
$465$	−6.84413	+	18.1514i	−0.0147186	+	0.0390352i
$466$	49.1026			0.105370
$467$	−220.746	+	679.388i	−0.472691	+	1.45479i	0.376357	+	0.926475i	$0.377177\pi$
$467$	−220.746	+	679.388i	−0.472691	+	1.45479i	−0.849047	+	0.528317i	$0.822823\pi$
$468$	−65.2139	−	58.7189i	−0.139346	−	0.125468i
$469$	250.748	+	182.179i	0.534645	+	0.388442i
$470$	43.1261	−	74.6966i	0.0917577	−	0.158929i
$471$	−3.81660	+	2.20352i	−0.00810319	+	0.00467838i
$472$	−60.0397	+	571.239i	−0.127203	+	1.21025i
$473$	−296.363	+	215.320i	−0.626561	+	0.455223i
$474$	−1.44367	−	13.7356i	−0.00304572	−	0.0289781i
$475$	89.4246	+	99.3160i	0.188262	+	0.209086i
$476$	117.449	+	263.795i	0.246742	+	0.554191i
$477$	−19.3171	−	90.8798i	−0.0404971	−	0.190524i
$478$	65.6260	−	308.746i	0.137293	−	0.645912i
$479$	−14.4676	−	6.44139i	−0.0302037	−	0.0134476i	0.391579	−	0.920144i	$-0.371929\pi$
$479$	−14.4676	−	6.44139i	−0.0302037	−	0.0134476i	−0.421783	+	0.906697i	$0.638596\pi$
$480$	19.7352	−	6.41236i	0.0411150	−	0.0133591i
$481$	72.2320	+	222.307i	0.150170	+	0.462177i
$482$	−125.843	+	282.648i	−0.261085	+	0.586406i
$483$	11.7726	+	2.50235i	0.0243740	+	0.00518084i
$484$	151.997	−	32.3080i	0.314044	−	0.0667521i
$485$	−132.882	+	59.1630i	−0.273984	+	0.121986i
$486$	74.6561	−	67.2207i	0.153613	−	0.138314i
$487$	228.440	−	24.0101i	0.469077	−	0.0493020i	0.132958	−	0.991122i	$-0.457552\pi$
$487$	228.440	−	24.0101i	0.469077	−	0.0493020i	0.336119	+	0.941820i	$0.390886\pi$
$488$	−394.376	−	542.812i	−0.808147	−	1.11232i
$489$	−36.8246	−	3.87042i	−0.0753059	−	0.00791497i
$490$	−21.9453	−	38.0103i	−0.0447863	−	0.0775721i
$491$	484.089	+	279.489i	0.985924	+	0.569223i	0.904053	−	0.427420i	$-0.140577\pi$
$491$	484.089	+	279.489i	0.985924	+	0.569223i	0.0818704	+	0.996643i	$0.473911\pi$
$492$	−20.5982	+	28.3510i	−0.0418662	+	0.0576239i
$493$	342.773	−	380.688i	0.695280	−	0.772186i
$494$	21.1111	+	6.85940i	0.0427349	+	0.0138854i
$495$		−	114.376i		−	0.231063i
$496$	102.071	+	38.4869i	0.205789	+	0.0775946i
$497$	−673.398			−1.35493
$498$	−10.1262	+	31.1652i	−0.0203337	+	0.0625807i
$499$	−593.874	−	534.727i	−1.19013	−	1.07160i	−0.995883	−	0.0906434i	$-0.971108\pi$
$499$	−593.874	−	534.727i	−1.19013	−	1.07160i	−0.194245	−	0.980953i	$-0.562226\pi$
$500$	−173.641	−	126.158i	−0.347282	−	0.252315i
$501$	−31.1569	+	53.9653i	−0.0621894	+	0.107715i
$502$	−358.299	+	206.864i	−0.713742	+	0.412079i
$503$	−26.2910	+	250.142i	−0.0522684	+	0.497301i	0.936802	+	0.349859i	$0.113771\pi$
$503$	−26.2910	+	250.142i	−0.0522684	+	0.497301i	−0.989071	+	0.147442i	$0.952896\pi$
$504$	253.203	−	183.963i	0.502387	−	0.365006i
$505$	−9.36495	−	89.1016i	−0.0185445	−	0.176439i
$506$	37.0591	+	41.1584i	0.0732394	+	0.0813406i
$507$	25.1724	+	56.5382i	0.0496498	+	0.111515i
$508$	−113.546	−	534.191i	−0.223516	−	1.05156i
$509$	55.8352	−	262.684i	0.109696	−	0.516079i	−0.888650	−	0.458586i	$-0.848356\pi$
$509$	55.8352	−	262.684i	0.109696	−	0.516079i	0.998346	−	0.0574927i	$-0.0183106\pi$
$510$	12.8988	+	5.74294i	0.0252919	+	0.0112607i
$511$	−464.189	+	150.824i	−0.908394	+	0.295155i
$512$	−68.0138	−	209.325i	−0.132839	−	0.408838i
$513$	17.0193	−	38.2259i	0.0331760	−	0.0745145i
$514$	2.89807	+	0.616004i	0.00563827	+	0.00119845i
$515$	−152.972	+	32.5151i	−0.297032	+	0.0631361i
$516$	46.1455	−	20.5453i	0.0894292	−	0.0398164i
$517$	307.167	−	276.575i	0.594134	−	0.534961i
$518$	−344.927	+	36.2533i	−0.665883	+	0.0699871i
$519$	−23.8451	−	32.8200i	−0.0459443	−	0.0632370i
$520$	−40.3526	−	4.24123i	−0.0776012	−	0.00815621i
$521$	102.483	+	177.506i	0.196704	+	0.340702i	0.947458	−	0.319881i	$-0.103643\pi$
$521$	102.483	+	177.506i	0.196704	+	0.340702i	−0.750754	+	0.660582i	$0.770309\pi$
$522$	−200.043	−	115.495i	−0.383224	−	0.221254i
$523$	16.0466	−	22.0862i	0.0306818	−	0.0422298i	−0.793401	−	0.608700i	$-0.791691\pi$
$523$	16.0466	−	22.0862i	0.0306818	−	0.0422298i	0.824082	+	0.566470i	$0.191691\pi$
$524$	−209.337	+	232.493i	−0.399499	+	0.443688i
$525$	40.6342	+	13.2028i	0.0773984	+	0.0251483i
$526$			203.079i			0.386081i
$527$	299.521	+	579.303i	0.568351	+	1.09925i
$528$	11.3181			0.0214357
$529$	151.074	−	464.957i	0.285583	−	0.878935i
$530$	−13.2815	−	11.9587i	−0.0250595	−	0.0225637i
$531$	−559.426	−	406.446i	−1.05353	−	0.765436i
$532$	40.7935	−	70.6564i	0.0766795	−	0.132813i
$533$	93.9963	−	54.2688i	0.176353	−	0.101818i
$534$	−6.18132	+	58.8113i	−0.0115755	+	0.110134i
$535$	−135.627	+	98.5387i	−0.253508	+	0.184184i
$536$	−49.4131	−	470.134i	−0.0921886	−	0.877116i
$537$	18.0842	+	20.0845i	0.0336763	+	0.0374013i
$538$	−160.811	−	361.187i	−0.298905	−	0.671352i
$539$	−43.7302	−	205.734i	−0.0811321	−	0.381696i
$540$	−6.61579	+	31.1249i	−0.0122515	+	0.0576386i
$541$	503.888	+	224.345i	0.931401	+	0.414686i	0.815620	−	0.578588i	$-0.196396\pi$
$541$	503.888	+	224.345i	0.931401	+	0.414686i	0.115781	+	0.993275i	$0.463063\pi$
$542$	170.295	−	55.3321i	0.314197	−	0.102089i
$543$	−15.4178	−	47.4512i	−0.0283938	−	0.0873870i
$544$	283.742	−	637.296i	0.521585	−	1.17150i
$545$	42.2667	+	8.98406i	0.0775535	+	0.0164845i
$546$	6.94141	−	1.47544i	0.0127132	−	0.00270227i
$547$	−157.582	+	70.1601i	−0.288084	+	0.128263i	−0.545691	−	0.837986i	$-0.683733\pi$
$547$	−157.582	+	70.1601i	−0.288084	+	0.128263i	0.257607	+	0.966250i	$0.417066\pi$
$548$	48.4879	−	43.6587i	0.0884816	−	0.0796692i
$549$	803.316	−	84.4320i	1.46324	−	0.153792i
$550$	115.563	+	159.059i	0.210115	+	0.289199i
$551$	−143.944	−	15.1292i	−0.261242	−	0.0274576i
$552$	−9.17837	−	15.8974i	−0.0166275	−	0.0287996i
$553$	136.160	+	78.6122i	0.246221	+	0.142156i
$554$	−49.2526	+	67.7903i	−0.0889035	+	0.122365i
$555$	28.1099	−	31.2192i	0.0506485	−	0.0562509i
$556$	−448.245	−	145.644i	−0.806196	−	0.261949i
$557$			664.803i			1.19354i	0.802411	+	0.596771i	$0.203550\pi$
$557$			664.803i			1.19354i	−0.802411	+	0.596771i	$0.796450\pi$
$558$	227.429	−	186.418i	0.407579	−	0.334082i
$559$	−156.447			−0.279870
$560$	−8.30825	+	25.5702i	−0.0148362	+	0.0456610i
$561$	50.2835	+	45.2755i	0.0896319	+	0.0807049i
$562$	−133.772	−	97.1910i	−0.238028	−	0.172938i
$563$	−328.910	+	569.689i	−0.584210	+	1.01188i	0.410764	+	0.911742i	$0.365262\pi$
$563$	−328.910	+	569.689i	−0.584210	+	1.01188i	−0.994973	+	0.100139i	$0.968071\pi$
$564$	−49.3588	+	28.4973i	−0.0875156	+	0.0505272i
$565$	−16.1322	+	153.487i	−0.0285525	+	0.271659i
$566$	19.5848	−	14.2292i	0.0346021	−	0.0251399i
$567$	38.6794	+	368.010i	0.0682176	+	0.649047i
$568$	687.242	+	763.260i	1.20993	+	1.34377i
$569$	−160.816	−	361.198i	−0.282629	−	0.634795i	0.715321	−	0.698796i	$-0.246281\pi$
$569$	−160.816	−	361.198i	−0.282629	−	0.634795i	−0.997950	+	0.0640013i	$0.979614\pi$
$570$	−0.829439	−	3.90220i	−0.00145516	−	0.00684597i
$571$	−197.701	+	930.112i	−0.346237	+	1.62892i	0.368573	+	0.929599i	$0.379846\pi$
$571$	−197.701	+	930.112i	−0.346237	+	1.62892i	−0.714810	+	0.699319i	$0.753487\pi$
$572$	−73.8993	−	32.9021i	−0.129195	−	0.0575211i
$573$	−84.1186	+	27.3318i	−0.146804	+	0.0476995i
$574$	49.7655	+	153.162i	0.0866995	+	0.266834i
$575$	−57.9218	+	130.094i	−0.100734	+	0.226251i
$576$	−185.919	−	39.5183i	−0.322776	−	0.0686082i
$577$	−675.100	+	143.497i	−1.17002	+	0.248695i	−0.751637	−	0.659577i	$-0.770736\pi$
$577$	−675.100	+	143.497i	−1.17002	+	0.248695i	−0.418381	+	0.908272i	$0.637402\pi$
$578$	150.467	−	66.9923i	0.260324	−	0.115904i
$579$	52.3896	−	47.1718i	0.0904829	−	0.0814712i
$580$	109.464	−	11.5051i	0.188730	−	0.0198363i
$581$	−219.265	−	301.792i	−0.377392	−	0.519436i
$582$	−38.5891	−	4.05587i	−0.0663042	−	0.00696886i
$583$	−42.8229	−	74.1715i	−0.0734527	−	0.127224i
$584$	644.683	+	372.208i	1.10391	+	0.637343i
$585$	28.7116	−	39.5181i	0.0490796	−	0.0675522i
$586$	374.195	−	415.586i	0.638558	−	0.709191i
$587$	599.072	+	194.650i	1.02056	+	0.331602i	0.771054	−	0.636770i	$-0.219730\pi$
$587$	599.072	+	194.650i	1.02056	+	0.331602i	0.249511	+	0.968372i	$0.419730\pi$
$588$			29.0025i			0.0493239i
$589$	82.6756	−	164.673i	0.140366	−	0.279580i
$590$	−133.014			−0.225447
$591$	19.3841	−	59.6583i	0.0327989	−	0.100945i
$592$	−175.557	−	158.072i	−0.296549	−	0.267014i
$593$	439.691	+	319.454i	0.741468	+	0.538708i	0.893171	−	0.449718i	$-0.148476\pi$
$593$	439.691	+	319.454i	0.741468	+	0.538708i	−0.151702	+	0.988426i	$0.548476\pi$
$594$	30.7789	−	53.3106i	0.0518163	−	0.0897485i
$595$	−139.200	+	80.3669i	−0.233949	+	0.135070i
$596$	−8.80583	+	83.7818i	−0.0147749	+	0.140574i
$597$	−5.86600	+	4.26190i	−0.00982580	+	0.00713886i
$598$	2.47241	+	23.5234i	0.00413447	+	0.0393369i
$599$	524.983	+	583.053i	0.876433	+	0.973377i	0.999820	−	0.0189813i	$-0.00604228\pi$
$599$	524.983	+	583.053i	0.876433	+	0.973377i	−0.123387	+	0.992359i	$0.539376\pi$
$600$	−26.5048	−	59.5309i	−0.0441747	−	0.0992181i
$601$	−176.351	−	829.668i	−0.293430	−	1.38048i	−0.839782	−	0.542923i	$-0.817317\pi$
$601$	−176.351	−	829.668i	−0.293430	−	1.38048i	0.546353	−	0.837555i	$-0.316016\pi$
$602$	48.2629	−	227.059i	0.0801709	−	0.377175i
$603$	519.898	+	231.474i	0.862186	+	0.383870i
$604$	−309.787	+	100.656i	−0.512893	+	0.166649i
$605$	26.7291	+	82.2638i	0.0441804	+	0.135973i
$606$	9.72069	−	21.8330i	0.0160407	−	0.0360281i
$607$	−264.987	−	56.3247i	−0.436552	−	0.0927919i	−0.0156068	−	0.999878i	$-0.504968\pi$
$607$	−264.987	−	56.3247i	−0.436552	−	0.0927919i	−0.420945	+	0.907086i	$0.638301\pi$
$608$	−192.797	+	40.9802i	−0.317100	+	0.0674017i
$609$	−42.2717	+	18.8206i	−0.0694117	+	0.0309041i
$610$	115.467	−	103.967i	0.189290	−	0.170437i
$611$	175.557	−	18.4518i	0.287327	−	0.0301993i
$612$	311.647	+	428.945i	0.509227	+	0.700890i
$613$	325.667	+	34.2290i	0.531267	+	0.0558384i	0.366365	−	0.930471i	$-0.380602\pi$
$613$	325.667	+	34.2290i	0.531267	+	0.0558384i	0.164903	+	0.986310i	$0.447269\pi$
$614$	−16.0586	−	27.8144i	−0.0261541	−	0.0453003i
$615$	−16.8932	−	9.75330i	−0.0274686	−	0.0158590i
$616$	169.580	−	233.406i	0.275291	−	0.378906i
$617$	−61.3393	+	68.1242i	−0.0994155	+	0.110412i	−0.790799	−	0.612076i	$-0.790335\pi$
$617$	−61.3393	+	68.1242i	−0.0994155	+	0.110412i	0.691384	+	0.722488i	$0.257001\pi$
$618$	−39.6758	−	12.8914i	−0.0642003	−	0.0208599i
$619$			14.1597i			0.0228751i	0.999935	+	0.0114375i	$0.00364076\pi$
$619$			14.1597i			0.0228751i	−0.999935	+	0.0114375i	$0.996359\pi$
$620$	−35.4613	+	135.562i	−0.0571956	+	0.218648i
$621$	44.5873			0.0717991
$622$	−133.886	+	412.059i	−0.215251	+	0.662474i
$623$	−500.272	−	450.447i	−0.803006	−	0.723029i
$624$	3.91049	+	2.84114i	0.00626682	+	0.00455311i
$625$	−221.313	+	383.326i	−0.354101	+	0.613322i
$626$	−399.133	+	230.440i	−0.637593	+	0.368114i
$627$	1.99835	−	19.0130i	0.00318716	−	0.0303238i
$628$	−25.7536	+	18.7111i	−0.0410090	+	0.0297948i
$629$	−147.625	−	1404.55i	−0.234697	−	2.23300i
$630$	48.4970	+	53.8614i	0.0769794	+	0.0854943i
$631$	6.67975	+	15.0030i	0.0105860	+	0.0237765i	0.918761	−	0.394814i	$-0.129191\pi$
$631$	6.67975	+	15.0030i	0.0105860	+	0.0237765i	−0.908175	+	0.418590i	$0.862524\pi$
$632$	−49.8570	−	234.559i	−0.0788876	−	0.371137i
$633$	31.6580	−	148.939i	0.0500127	−	0.235291i
$634$	212.130	+	94.4463i	0.334590	+	0.148969i
$635$	289.115	−	93.9390i	0.455299	−	0.147935i
$636$	3.64939	+	11.2317i	0.00573804	+	0.0176599i
$637$	36.5357	−	82.0606i	0.0573559	−	0.128823i
$638$	−208.276	−	44.2705i	−0.326452	−	0.0693895i
$639$	−1209.44	+	257.074i	−1.89271	+	0.402307i
$640$	158.807	−	70.7055i	0.248136	−	0.110477i
$641$	309.300	−	278.495i	0.482528	−	0.434470i	−0.391622	−	0.920126i	$-0.628086\pi$
$641$	309.300	−	278.495i	0.482528	−	0.434470i	0.874150	+	0.485656i	$0.161419\pi$
$642$	−44.4749	+	4.67450i	−0.0692756	+	0.00728116i
$643$	4.91634	+	6.76677i	0.00764595	+	0.0105237i	0.812823	−	0.582511i	$-0.197930\pi$
$643$	4.91634	+	6.76677i	0.00764595	+	0.0105237i	−0.805177	+	0.593035i	$0.797930\pi$
$644$	86.4605	+	9.08737i	0.134256	+	0.0141108i
$645$	14.0585	+	24.3501i	0.0217962	+	0.0377521i
$646$	−116.148	−	67.0580i	−0.179796	−	0.103805i
$647$	670.469	−	922.822i	1.03627	−	1.42631i	0.136143	−	0.990689i	$-0.456529\pi$
$647$	670.469	−	922.822i	1.03627	−	1.42631i	0.900131	−	0.435619i	$-0.143471\pi$
$648$	377.644	−	419.416i	0.582784	−	0.647247i
$649$	−606.225	−	196.975i	−0.934091	−	0.303505i
$650$			83.9659i			0.129178i
$651$	−3.43266	−	58.8079i	−0.00527291	−	0.0903347i
$652$	−267.460			−0.410214
$653$	240.465	−	740.076i	0.368247	−	1.13335i	−0.579676	−	0.814847i	$-0.696821\pi$
$653$	240.465	−	740.076i	0.368247	−	1.13335i	0.947923	−	0.318500i	$-0.103179\pi$
$654$	8.56603	+	7.71289i	0.0130979	+	0.0117934i
$655$	−140.885	−	102.359i	−0.215091	−	0.156273i
$656$	−54.8462	+	94.9965i	−0.0836071	+	0.144812i
$657$	−776.117	+	448.091i	−1.18130	+	0.682026i
$658$	−27.3782	+	260.486i	−0.0416081	+	0.395875i
$659$	−621.919	+	451.850i	−0.943731	+	0.685661i	−0.949316	−	0.314324i	$-0.898222\pi$
$659$	−621.919	+	451.850i	−0.943731	+	0.685661i	0.00558479	+	0.999984i	$0.498222\pi$
$660$	1.51966	+	14.4586i	0.00230251	+	0.0219070i
$661$	141.236	+	156.859i	0.213671	+	0.237306i	0.840447	−	0.541894i	$-0.182293\pi$
$661$	141.236	+	156.859i	0.213671	+	0.237306i	−0.626776	+	0.779199i	$0.715626\pi$
$662$	−96.5622	−	216.882i	−0.145864	−	0.327617i
$663$	6.00804	+	28.2656i	0.00906190	+	0.0426329i
$664$	−118.292	+	556.521i	−0.178151	+	0.838134i
$665$	41.4880	+	18.4716i	0.0623879	+	0.0277769i
$666$	−605.658	+	196.790i	−0.909396	+	0.295481i
$667$	−47.6590	−	146.679i	−0.0714528	−	0.219909i
$668$	−183.076	+	411.197i	−0.274067	+	0.615564i
$669$	97.2377	+	20.6685i	0.145348	+	0.0308946i
$670$	107.079	−	22.7603i	0.159819	−	0.0339707i
$671$	680.214	−	302.851i	1.01373	−	0.451342i
$672$	−46.8283	+	42.1644i	−0.0696849	+	0.0627446i
$673$	−319.271	+	33.5567i	−0.474399	+	0.0498613i	−0.338711	−	0.940890i	$-0.609991\pi$
$673$	−319.271	+	33.5567i	−0.474399	+	0.0498613i	−0.135688	+	0.990752i	$0.543324\pi$
$674$	−315.483	−	434.225i	−0.468076	−	0.644251i
$675$	157.413	+	16.5448i	0.233205	+	0.0245108i
$676$	223.520	+	387.148i	0.330651	+	0.572705i
$677$	413.415	+	238.685i	0.610657	+	0.352563i	0.773222	−	0.634135i	$-0.218644\pi$
$677$	413.415	+	238.685i	0.610657	+	0.352563i	−0.162566	+	0.986698i	$0.551977\pi$
$678$	−24.1986	+	33.3065i	−0.0356911	+	0.0491246i
$679$	295.561	−	328.254i	0.435289	−	0.483437i
$680$	233.153	+	75.7559i	0.342872	+	0.111406i
$681$		−	125.135i		−	0.183753i
$682$	146.284	−	228.217i	0.214493	−	0.334629i
$683$	−778.801			−1.14026			−0.570132	−	0.821553i	$-0.693108\pi$
$683$	−778.801			−1.14026			−0.570132	+	0.821553i	$0.693108\pi$
$684$	46.2925	−	142.474i	0.0676791	−	0.208295i
$685$	26.9901	+	24.3020i	0.0394016	+	0.0354774i
$686$	312.628	+	227.137i	0.455726	+	0.331104i
$687$	−64.2517	+	111.287i	−0.0935250	+	0.161990i
$688$	136.929	−	79.0561i	0.199025	−	0.114907i
$689$	3.82334	−	36.3766i	0.00554911	−	0.0527963i
$690$	3.43911	−	2.49866i	0.00498421	−	0.00362124i
$691$	−62.2099	−	591.887i	−0.0900288	−	0.856566i	−0.942593	−	0.333944i	$-0.891620\pi$
$691$	−62.2099	−	591.887i	−0.0900288	−	0.856566i	0.852564	−	0.522623i	$-0.175046\pi$
$692$	−196.077	−	217.766i	−0.283348	−	0.314690i
$693$	141.270	+	317.297i	0.203852	+	0.457860i
$694$	91.2743	+	429.412i	0.131519	+	0.618749i
$695$	54.5455	−	256.617i	0.0784828	−	0.369232i
$696$	64.4728	+	28.7051i	0.0926333	+	0.0412430i
$697$	−623.682	+	202.647i	−0.894809	+	0.290741i
$698$	20.2449	+	62.3074i	0.0290042	+	0.0892656i
$699$	7.34603	−	16.4994i	0.0105093	−	0.0236044i
$700$	301.873	+	64.1651i	0.431247	+	0.0916645i
$701$	1064.62	−	226.293i	1.51872	−	0.322814i	0.628307	−	0.777965i	$-0.283748\pi$
$701$	1064.62	−	226.293i	1.51872	−	0.322814i	0.890414	+	0.455151i	$0.150415\pi$
$702$	24.0168	−	10.6930i	0.0342120	−	0.0152322i
$703$	−296.539	+	267.005i	−0.421820	+	0.379808i
$704$	−174.252	+	18.3146i	−0.247517	+	0.0260151i
$705$	−18.6476	−	25.6663i	−0.0264506	−	0.0364061i
$706$	−390.200	−	41.0116i	−0.552691	−	0.0580901i
$707$	136.032	+	235.614i	0.192407	+	0.333259i
$708$	76.1186	+	43.9471i	0.107512	+	0.0620722i
$709$	−123.204	+	169.575i	−0.173771	+	0.239175i	−0.887015	−	0.461741i	$-0.847225\pi$
$709$	−123.204	+	169.575i	−0.173771	+	0.239175i	0.713244	+	0.700916i	$0.247225\pi$
$710$	−159.148	+	176.752i	−0.224153	+	0.248947i
$711$	274.558	+	89.2093i	0.386157	+	0.125470i
$712$			1026.74i			1.44205i
$713$	196.133	+	9.11007i	0.275081	+	0.0127771i
$714$	−42.8766			−0.0600512
$715$	13.9144	−	42.8240i	0.0194607	−	0.0598937i
$716$	145.076	+	130.627i	0.202621	+	0.182440i
$717$	−93.9268	−	68.2418i	−0.131000	−	0.0951769i
$718$	−6.63742	+	11.4964i	−0.00924432	+	0.0160116i
$719$	112.384	−	64.8851i	0.156306	−	0.0902436i	−0.419807	−	0.907614i	$-0.637902\pi$
$719$	112.384	−	64.8851i	0.156306	−	0.0902436i	0.576113	+	0.817370i	$0.304569\pi$
$720$	−5.16024	+	49.0964i	−0.00716699	+	0.0681894i
$721$	384.205	−	279.142i	0.532878	−	0.387159i
$722$	−36.5116	−	347.385i	−0.0505701	−	0.481142i
$723$	76.1485	+	84.5715i	0.105323	+	0.116973i
$724$	−146.585	−	329.235i	−0.202465	−	0.454744i
$725$	−113.830	−	535.530i	−0.157008	−	0.738662i
$726$	−4.79727	+	22.5694i	−0.00660781	+	0.0310873i
$727$	73.8162	+	32.8651i	0.101535	+	0.0452065i	0.456876	−	0.889530i	$-0.348968\pi$
$727$	73.8162	+	32.8651i	0.101535	+	0.0452065i	−0.355340	+	0.934737i	$0.615635\pi$
$728$	117.183	−	38.0749i	0.160965	−	0.0523007i
$729$	202.235	+	622.417i	0.277415	+	0.853795i
$730$	−70.1167	+	157.485i	−0.0960503	+	0.215733i
$731$	924.591	+	196.528i	1.26483	+	0.268848i
$732$	−100.427	+	21.3465i	−0.137196	+	0.0291619i
$733$	−263.219	+	117.193i	−0.359098	+	0.159881i	−0.578353	−	0.815787i	$-0.696304\pi$
$733$	−263.219	+	117.193i	−0.359098	+	0.159881i	0.219254	+	0.975668i	$0.429638\pi$
$734$	345.475	−	311.067i	0.470675	−	0.423797i
$735$	−16.0554	+	1.68749i	−0.0218440	+	0.00229590i
$736$	−123.452	−	169.917i	−0.167733	−	0.230865i
$737$	521.730	+	54.8360i	0.707910	+	0.0744044i
$738$	147.851	+	256.085i	0.200340	+	0.346999i
$739$	352.645	+	203.600i	0.477192	+	0.275507i	0.719246	−	0.694756i	$-0.244488\pi$
$739$	352.645	+	203.600i	0.477192	+	0.275507i	−0.242053	+	0.970263i	$0.577821\pi$
$740$	178.362	−	245.494i	0.241030	−	0.331749i
$741$	5.46323	−	6.06753i	0.00737278	−	0.00818830i
$742$	51.6155	+	16.7709i	0.0695627	+	0.0226023i
$743$		−	101.567i		−	0.136699i	−0.997661	−	0.0683493i	$-0.978227\pi$
$743$		−	101.567i		−	0.136699i	0.997661	−	0.0683493i	$-0.0217732\pi$
$744$	−63.1523	+	63.9076i	−0.0848821	+	0.0858973i
$745$	−46.8929			−0.0629434
$746$	−143.067	+	440.314i	−0.191779	+	0.590234i
$747$	−509.016	−	458.320i	−0.681414	−	0.613548i
$748$	395.407	+	287.280i	0.528619	+	0.384064i
$749$	254.541	−	440.878i	0.339841	−	0.588622i
$750$	27.6000	−	15.9349i	0.0368000	−	0.0212465i
$751$	−51.0899	+	486.088i	−0.0680292	+	0.647255i	0.906378	+	0.422467i	$0.138836\pi$
$751$	−51.0899	+	486.088i	−0.0680292	+	0.647255i	−0.974408	+	0.224788i	$0.927831\pi$
$752$	−144.331	+	104.862i	−0.191929	+	0.139444i
$753$	15.9068	+	151.343i	0.0211246	+	0.200987i
$754$	−60.8483	−	67.5788i	−0.0807006	−	0.0896271i
$755$	−73.7465	−	165.637i	−0.0976775	−	0.219387i
$756$	−20.0901	−	94.5163i	−0.0265741	−	0.125022i
$757$	182.072	−	856.582i	0.240518	−	1.13155i	−0.677659	−	0.735377i	$-0.737005\pi$
$757$	182.072	−	856.582i	0.240518	−	1.13155i	0.918177	−	0.396171i	$-0.129661\pi$
$758$	280.499	+	124.886i	0.370051	+	0.164757i
$759$	19.3743	−	6.29509i	0.0255261	−	0.00829392i
$760$	−21.4043	−	65.8757i	−0.0281636	−	0.0866785i
$761$	−539.888	+	1212.61i	−0.709446	+	1.59344i	0.0922692	+	0.995734i	$0.470588\pi$
$761$	−539.888	+	1212.61i	−0.709446	+	1.59344i	−0.801715	+	0.597707i	$0.796079\pi$
$762$	79.3196	+	16.8599i	0.104094	+	0.0221259i
$763$	−128.350	+	27.2817i	−0.168218	+	0.0357559i
$764$	−583.648	+	259.857i	−0.763937	+	0.340127i
$765$	−219.325	+	197.481i	−0.286700	+	0.258145i
$766$	611.426	−	64.2634i	0.798206	−	0.0838948i
$767$	−160.010	−	220.235i	−0.208619	−	0.287139i
$768$	79.8449	+	8.39203i	0.103965	+	0.0109271i
$769$	572.747	+	992.027i	0.744794	+	1.29002i	0.950291	+	0.311364i	$0.100786\pi$
$769$	572.747	+	992.027i	0.744794	+	1.29002i	−0.205497	+	0.978658i	$0.565881\pi$
$770$	57.8599	+	33.4054i	0.0751428	+	0.0433837i
$771$	0.640557	−	0.881652i	0.000830814	−	0.00114352i
$772$	340.736	−	378.425i	0.441368	−	0.490188i
$773$	−1221.64	−	396.935i	−1.58039	−	0.513499i	−0.618231	−	0.785997i	$-0.712150\pi$
$773$	−1221.64	−	396.935i	−1.58039	−	0.513499i	−0.962156	+	0.272498i	$0.912150\pi$
$774$		−	426.228i		−	0.550682i
$775$	689.057	+	104.941i	0.889106	+	0.135408i
$776$	−673.695			−0.868164
$777$	−39.4213	+	121.326i	−0.0507352	+	0.156147i
$778$	−416.429	−	374.955i	−0.535256	−	0.481947i
$779$	149.899	+	108.908i	0.192425	+	0.139805i
$780$	−3.10444	+	5.37705i	−0.00398005	+	0.00689365i
$781$	−987.082	+	569.892i	−1.26387	+	0.729696i
$782$	14.9382	−	142.127i	0.0191025	−	0.181749i
$783$	−138.682	+	100.758i	−0.177116	+	0.128682i
$784$	9.48934	+	90.2850i	0.0121037	+	0.115159i
$785$	−11.8567	−	13.1682i	−0.0151040	−	0.0167747i
$786$	−18.8944	−	42.4375i	−0.0240387	−	0.0539917i
$787$	−82.5673	−	388.449i	−0.104914	−	0.493581i	−0.998960	−	0.0456054i	$-0.985478\pi$
$787$	−82.5673	−	388.449i	−0.104914	−	0.493581i	0.894046	−	0.447976i	$-0.147855\pi$
$788$	94.2059	−	443.204i	0.119551	−	0.562442i
$789$	68.2385	+	30.3817i	0.0864873	+	0.0385066i
$790$	52.8136	−	17.1602i	0.0668526	−	0.0217217i
$791$	−144.824	−	445.722i	−0.183090	−	0.563492i
$792$	215.464	−	483.941i	0.272051	−	0.611037i
$793$	311.044	+	66.1144i	0.392237	+	0.0833725i
$794$	418.893	−	89.0385i	0.527573	−	0.112139i
$795$	−6.00537	+	2.67376i	−0.00755393	+	0.00336322i
$796$	−38.9218	+	35.0454i	−0.0488967	+	0.0440268i
$797$	−371.680	+	39.0651i	−0.466348	+	0.0490152i	−0.334789	−	0.942293i	$-0.608665\pi$
$797$	−371.680	+	39.0651i	−0.466348	+	0.0490152i	−0.131559	+	0.991308i	$0.541998\pi$
$798$	7.12071	+	9.80082i	0.00892320	+	0.0122817i
$799$	−1060.71	−	111.485i	−1.32754	−	0.139530i
$800$	−372.790	−	645.692i	−0.465988	−	0.807115i
$801$	−1070.46	−	618.032i	−1.33641	−	0.771575i
$802$	180.845	−	248.912i	0.225493	−	0.310364i
$803$	−552.778	+	613.922i	−0.688391	+	0.764535i
$804$	−68.7971	−	22.3535i	−0.0855685	−	0.0278029i
$805$			48.3921i			0.0601145i
$806$	107.831	−	42.1296i	0.133785	−	0.0522700i
$807$	−145.424			−0.180204
$808$	128.227	−	394.642i	0.158697	−	0.488419i
$809$	727.568	+	655.105i	0.899343	+	0.809772i	0.982403	−	0.186773i	$-0.0598028\pi$
$809$	727.568	+	655.105i	0.899343	+	0.809772i	−0.0830604	+	0.996545i	$0.526469\pi$
$810$	105.736	+	76.8216i	0.130538	+	0.0948414i
$811$	187.290	−	324.396i	0.230937	−	0.399995i	−0.727147	−	0.686482i	$-0.759154\pi$
$811$	187.290	−	324.396i	0.230937	−	0.399995i	0.958084	+	0.286487i	$0.0924875\pi$
$812$	−289.458	+	167.118i	−0.356475	+	0.205811i
$813$	6.88437	−	65.5004i	0.00846787	−	0.0805664i
$814$	−474.921	+	345.051i	−0.583441	+	0.423895i
$815$	−15.5620	−	148.062i	−0.0190944	−	0.181671i
$816$	−19.5417	−	21.7032i	−0.0239481	−	0.0265971i
$817$	−108.628	−	243.983i	−0.132960	−	0.298633i
$818$	32.9288	+	154.918i	0.0402552	+	0.189386i
$819$	−30.8401	+	145.091i	−0.0376558	+	0.177157i
$820$	−128.720	−	57.3099i	−0.156976	−	0.0698901i
$821$	1280.95	−	416.205i	1.56023	−	0.506949i	0.603360	−	0.797469i	$-0.293828\pi$
$821$	1280.95	−	416.205i	1.56023	−	0.506949i	0.956869	+	0.290520i	$0.0938282\pi$
$822$	2.99382	+	9.21405i	0.00364212	+	0.0112093i
$823$	112.027	−	251.617i	0.136120	−	0.305731i	−0.832605	−	0.553868i	$-0.813151\pi$
$823$	112.027	−	251.617i	0.136120	−	0.305731i	0.968725	+	0.248136i	$0.0798180\pi$
$824$	−708.495	−	150.595i	−0.859824	−	0.182761i
$825$	70.7360	−	15.0354i	0.0857406	−	0.0182247i
$826$	369.000	−	164.289i	0.446731	−	0.198897i
$827$	1006.50	−	906.256i	1.21705	−	1.09584i	0.224439	−	0.974488i	$-0.427945\pi$
$827$	1006.50	−	906.256i	1.21705	−	1.09584i	0.992610	−	0.121348i	$-0.0387217\pi$
$828$	158.754	−	16.6858i	0.191732	−	0.0201519i
$829$	558.974	+	769.361i	0.674275	+	0.928059i	0.999848	−	0.0174574i	$-0.00555716\pi$
$829$	558.974	+	769.361i	0.674275	+	0.928059i	−0.325573	+	0.945517i	$0.605557\pi$
$830$	−131.034	−	13.7722i	−0.157872	−	0.0165931i
$831$	15.4104	+	26.6917i	0.0185445	+	0.0321199i
$832$	−64.8030	−	37.4141i	−0.0778883	−	0.0449688i
$833$	−319.007	+	439.075i	−0.382961	+	0.527101i
$834$	46.8278	−	52.0075i	0.0561484	−	0.0623592i
$835$	−238.285	−	77.4235i	−0.285371	−	0.0927228i
$836$		−	138.093i		−	0.165183i
$837$	−57.7344	−	210.455i	−0.0689778	−	0.251440i
$838$	724.553			0.864622
$839$	−171.570	+	528.039i	−0.204494	+	0.629367i	0.795240	+	0.606295i	$0.207345\pi$
$839$	−171.570	+	528.039i	−0.204494	+	0.629367i	−0.999734	+	0.0230726i	$0.992655\pi$
$840$	−16.4563	−	14.8173i	−0.0195908	−	0.0176396i
$841$	−200.681	−	145.804i	−0.238622	−	0.173369i
$842$	−58.5015	+	101.328i	−0.0694793	+	0.120342i
$843$	−52.6711	+	30.4097i	−0.0624806	+	0.0360732i
$844$	114.967	−	1093.84i	0.136217	−	1.29602i
$845$	−201.315	+	146.264i	−0.238242	+	0.173093i
$846$	50.2703	+	478.290i	0.0594212	+	0.565355i
$847$	−175.757	−	195.198i	−0.207505	−	0.230458i
$848$	15.0355	+	33.7703i	0.0177306	+	0.0398235i
$849$	−1.85129	−	8.70964i	−0.00218055	−	0.0102587i
$850$	105.477	−	496.232i	0.124091	−	0.583802i
$851$	−388.438	−	172.944i	−0.456449	−	0.203224i
$852$	149.473	−	48.5666i	0.175437	−	0.0570030i
$853$	295.744	+	910.206i	0.346710	+	1.06706i	0.960662	+	0.277721i	$0.0895790\pi$
$853$	295.744	+	910.206i	0.346710	+	1.06706i	−0.613952	+	0.789344i	$0.710421\pi$
$854$	−191.910	+	431.036i	−0.224718	+	0.504726i
$855$	81.5650	+	17.3372i	0.0953977	+	0.0202774i
$856$	−759.484	+	161.433i	−0.887248	+	0.188590i
$857$	−1120.21	+	498.749i	−1.30713	+	0.581971i	−0.937751	−	0.347309i	$-0.887096\pi$
$857$	−1120.21	+	498.749i	−1.30713	+	0.581971i	−0.369377	+	0.929280i	$0.620429\pi$
$858$	8.92621	−	8.03720i	0.0104035	−	0.00936736i
$859$	1025.79	−	107.815i	1.19417	−	0.125513i	0.513493	−	0.858094i	$-0.328351\pi$
$859$	1025.79	−	107.815i	1.19417	−	0.125513i	0.680679	+	0.732581i	$0.261685\pi$
$860$	119.378	+	164.309i	0.138811	+	0.191058i
$861$	58.9108	+	6.19178i	0.0684214	+	0.00719138i
$862$	−308.017	−	533.501i	−0.357328	−	0.618911i
$863$	672.485	+	388.259i	0.779241	+	0.449895i	0.836161	−	0.548484i	$-0.184795\pi$
$863$	672.485	+	388.259i	0.779241	+	0.449895i	−0.0569205	+	0.998379i	$0.518128\pi$
$864$	−137.213	+	188.858i	−0.158811	+	0.218585i
$865$	109.143	−	121.216i	0.126177	−	0.140134i
$866$	126.574	+	41.1263i	0.146159	+	0.0474899i
$867$		−	60.5824i		−	0.0698759i
$868$	−69.0616	−	419.868i	−0.0795640	−	0.483718i
$869$	266.116			0.306232
$870$	−5.05035	+	15.5434i	−0.00580500	+	0.0178659i
$871$	166.497	+	149.915i	0.191156	+	0.172118i
$872$	161.911	+	117.636i	0.185678	+	0.134903i
$873$	405.522	−	702.384i	0.464515	−	0.804564i
$874$	−34.9686	+	20.1892i	−0.0400099	+	0.0230997i
$875$	−37.9228	+	360.811i	−0.0433403	+	0.412356i
$876$	92.1573	−	66.9562i	0.105202	−	0.0764340i
$877$	119.718	+	1139.04i	0.136509	+	1.29879i	0.821486	+	0.570229i	$0.193145\pi$
$877$	119.718	+	1139.04i	0.136509	+	1.29879i	−0.684977	+	0.728564i	$0.740188\pi$
$878$	−134.864	−	149.782i	−0.153604	−	0.170594i
$879$	−83.6634	−	187.911i	−0.0951802	−	0.213778i
$880$	9.46143	+	44.5125i	0.0107516	+	0.0505824i
$881$	−90.3860	+	425.233i	−0.102595	+	0.482671i	0.896611	+	0.442819i	$0.146022\pi$
$881$	−90.3860	+	425.233i	−0.102595	+	0.482671i	−0.999206	+	0.0398511i	$0.987312\pi$
$882$	223.567	+	99.5386i	0.253478	+	0.112856i
$883$	−604.712	+	196.483i	−0.684838	+	0.222517i	−0.630712	−	0.776017i	$-0.717237\pi$
$883$	−604.712	+	196.483i	−0.684838	+	0.222517i	−0.0541255	+	0.998534i	$0.517237\pi$
$884$	64.5017	+	198.516i	0.0729657	+	0.224565i
$885$	−19.8996	+	44.6953i	−0.0224854	+	0.0505031i
$886$	182.143	+	38.7156i	0.205579	+	0.0436971i
$887$	1115.38	−	237.082i	1.25748	−	0.267285i	0.469469	−	0.882949i	$-0.344445\pi$
$887$	1115.38	−	237.082i	1.25748	−	0.267285i	0.788009	+	0.615663i	$0.211112\pi$
$888$	177.748	−	79.1386i	0.200167	−	0.0891200i
$889$	−686.020	+	617.695i	−0.771676	+	0.694820i
$890$	−236.465	+	24.8535i	−0.265691	+	0.0279252i
$891$	368.141	+	506.703i	0.413178	+	0.568690i
$892$	714.134	+	75.0585i	0.800598	+	0.0841463i
$893$	150.673	+	260.973i	0.168727	+	0.292243i
$894$	−10.8330	−	6.25445i	−0.0121175	−	0.00699603i
$895$	−63.8723	+	87.9127i	−0.0713657	+	0.0982265i
$896$	−353.224	+	392.295i	−0.394223	+	0.437829i
$897$	8.27423	+	2.68846i	0.00922434	+	0.00299717i
$898$			86.3529i			0.0961613i
$899$	−630.627	+	414.885i	−0.701476	+	0.461496i
$900$	566.667			0.629630
$901$	−68.2916	+	210.180i	−0.0757954	+	0.233274i
$902$	202.568	+	182.393i	0.224576	+	0.202209i
$903$	−69.0760	−	50.1866i	−0.0764961	−	0.0555777i
$904$	−357.400	+	619.035i	−0.395354	+	0.684773i
$905$	173.731	−	100.304i	0.191968	−	0.110833i
$906$	5.05563	−	48.1011i	0.00558017	−	0.0530918i
$907$	1241.09	−	901.704i	1.36834	−	0.994161i	0.370480	−	0.928840i	$-0.379193\pi$
$907$	1241.09	−	901.704i	1.36834	−	0.994161i	0.997864	−	0.0653201i	$-0.0208069\pi$
$908$	−94.4822	−	898.938i	−0.104055	−	0.990020i
$909$	334.263	+	371.237i	0.367727	+	0.408402i
$910$	11.6055	+	26.0663i	0.0127533	+	0.0286443i
$911$	6.23822	+	29.3485i	0.00684766	+	0.0322157i	0.981439	−	0.191776i	$-0.0614246\pi$
$911$	6.23822	+	29.3485i	0.00684766	+	0.0322157i	−0.974591	+	0.223991i	$0.928091\pi$
$912$	−1.71559	+	8.07123i	−0.00188113	+	0.00885004i
$913$	−576.808	−	256.812i	−0.631772	−	0.281283i
$914$	−212.361	+	69.0002i	−0.232342	+	0.0754925i
$915$	−17.6604	−	54.3532i	−0.0193010	−	0.0594024i
$916$	−377.540	+	847.968i	−0.412161	+	0.925729i
$917$	517.262	+	109.947i	0.564081	+	0.119899i
$918$	−155.370	+	33.0249i	−0.169248	+	0.0359748i
$919$	378.302	−	168.431i	0.411646	−	0.183276i	−0.190456	−	0.981696i	$-0.560997\pi$
$919$	378.302	−	168.431i	0.411646	−	0.183276i	0.602102	+	0.798419i	$0.294330\pi$
$920$	54.8498	−	49.3870i	0.0596193	−	0.0536815i
$921$	−11.7486	+	1.23483i	−0.0127564	+	0.00134075i
$922$	346.457	+	476.857i	0.375767	+	0.517199i
$923$	−484.104	−	50.8814i	−0.524490	−	0.0551261i
$924$	−22.0740	−	38.2333i	−0.0238896	−	0.0413780i
$925$	−1307.19	−	754.707i	−1.41318	−	0.815899i
$926$	−182.528	+	251.228i	−0.197114	+	0.271305i
$927$	583.478	−	648.018i	0.629426	−	0.699048i
$928$	767.954	+	249.524i	0.827537	+	0.268883i
$929$			610.357i			0.657005i	0.944503	+	0.328502i	$0.106544\pi$
$929$			610.357i			0.657005i	−0.944503	+	0.328502i	$0.893456\pi$
$930$	−16.2470	−	12.9974i	−0.0174699	−	0.0139757i
$931$	153.344			0.164709
$932$	40.3141	−	124.074i	0.0432554	−	0.133127i
$933$	118.430	+	106.635i	0.126934	+	0.114292i
$934$	−619.852	−	450.349i	−0.663653	−	0.482172i
$935$	−136.028	+	235.607i	−0.145484	+	0.251986i
$936$	195.927	−	113.119i	0.209324	−	0.120853i
$937$	125.007	−	1189.36i	0.133412	−	1.26933i	−0.698980	−	0.715141i	$-0.746363\pi$
$937$	125.007	−	1189.36i	0.133412	−	1.26933i	0.832392	−	0.554187i	$-0.186971\pi$
$938$	−268.941	+	195.397i	−0.286717	+	0.208312i
$939$	17.7197	+	168.592i	0.0188708	+	0.179544i
$940$	−153.338	−	170.300i	−0.163126	−	0.181170i
$941$	15.9325	+	35.7850i	0.0169315	+	0.0380287i	0.921813	−	0.387634i	$-0.126708\pi$
$941$	15.9325	+	35.7850i	0.0169315	+	0.0380287i	−0.904882	+	0.425663i	$0.860041\pi$
$942$	−0.982751	−	4.62348i	−0.00104326	−	0.00490816i
$943$	−41.0491	+	193.121i	−0.0435303	+	0.204794i
$944$	251.337	+	111.903i	0.266247	+	0.118541i
$945$	51.1540	−	16.6209i	0.0541312	−	0.0175883i
$946$	−121.414	−	373.673i	−0.128344	−	0.395003i
$947$	432.824	−	972.138i	0.457047	−	1.02655i	−0.527199	−	0.849742i	$-0.676758\pi$
$947$	432.824	−	972.138i	0.457047	−	1.02655i	0.984246	−	0.176803i	$-0.0565756\pi$
$948$	−35.8928	−	7.62925i	−0.0378616	−	0.00804773i
$949$	−345.101	+	73.3534i	−0.363647	+	0.0772955i
$950$	−130.947	+	58.3013i	−0.137839	+	0.0613698i
$951$	63.4717	−	57.1502i	0.0667421	−	0.0600948i
$952$	−740.368	+	77.8159i	−0.777698	+	0.0817393i
$953$	−685.510	−	943.524i	−0.719318	−	0.990057i	−0.999546	−	0.0301234i	$-0.990410\pi$
$953$	−685.510	−	943.524i	−0.719318	−	0.990057i	0.280228	−	0.959934i	$-0.409590\pi$
$954$	99.1051	+	10.4164i	0.103884	+	0.0109186i
$955$	−177.812	−	307.980i	−0.186191	−	0.322492i
$956$	−726.269	−	419.312i	−0.759696	−	0.438611i
$957$	−46.0351	+	63.3619i	−0.0481035	+	0.0662088i
$958$	11.3657	−	12.6229i	0.0118640	−	0.0131763i
$959$	−104.891	−	34.0811i	−0.109375	−	0.0355381i
$960$			13.4483i			0.0140086i
$961$	−210.965	−	937.558i	−0.219526	−	0.975607i
$962$	−250.707			−0.260610
$963$	288.853	−	888.999i	0.299952	−	0.923156i
$964$	610.884	+	550.042i	0.633697	+	0.570583i
$965$	229.317	+	166.608i	0.237634	+	0.172651i
$966$	−6.45442	+	11.1794i	−0.00668160	+	0.0115729i
$967$	732.012	−	422.627i	0.756992	−	0.437050i	−0.0712224	−	0.997460i	$-0.522690\pi$
$967$	732.012	−	422.627i	0.756992	−	0.437050i	0.828215	+	0.560411i	$0.189357\pi$
$968$	−41.8758	+	398.422i	−0.0432601	+	0.411593i
$969$	−39.9092	+	28.9957i	−0.0411860	+	0.0299234i
$970$	−16.3076	−	155.157i	−0.0168120	−	0.159955i
$971$	−752.418	−	835.645i	−0.774890	−	0.860603i	0.218447	−	0.975849i	$-0.429901\pi$
$971$	−752.418	−	835.645i	−0.774890	−	0.860603i	−0.993337	+	0.115246i	$0.963234\pi$
$972$	−108.561	−	243.833i	−0.111689	−	0.250857i
$973$	165.637	+	779.263i	0.170234	+	0.800887i
$974$	−51.2220	+	240.980i	−0.0525893	+	0.247413i
$975$	28.2142	+	12.5618i	0.0289377	+	0.0128839i
$976$	−305.647	+	99.3108i	−0.313163	+	0.101753i
$977$	97.4901	+	300.044i	0.0997852	+	0.307107i	0.988471	−	0.151409i	$-0.0483811\pi$
$977$	97.4901	+	300.044i	0.0997852	+	0.307107i	−0.888686	+	0.458516i	$0.848381\pi$
$978$	16.1531	−	36.2804i	0.0165164	−	0.0370966i
$979$	−1114.52	−	236.899i	−1.13843	−	0.241980i
$980$	−114.063	+	24.2449i	−0.116391	+	0.0247397i
$981$	−220.105	+	97.9972i	−0.224368	+	0.0998952i
$982$	−445.540	+	401.166i	−0.453706	+	0.408519i
$983$	−910.097	+	95.6550i	−0.925836	+	0.0973093i	−0.555432	−	0.831562i	$-0.687447\pi$
$983$	−910.097	+	95.6550i	−0.925836	+	0.0973093i	−0.370403	+	0.928871i	$0.620781\pi$
$984$	−53.1039	−	73.0912i	−0.0539674	−	0.0742797i
$985$	250.833	+	26.3636i	0.254653	+	0.0267651i
$986$	274.716	+	475.822i	0.278617	+	0.482579i
$987$	83.4325	+	48.1698i	0.0845314	+	0.0488042i
$988$	34.6651	−	47.7124i	0.0350861	−	0.0482919i
$989$	190.425	−	211.488i	0.192543	−	0.213841i
$990$	116.671	+	37.9086i	0.117849	+	0.0382915i
$991$		−	1157.93i		−	1.16845i	−0.811593	−	0.584224i	$-0.801399\pi$
$991$		−	1157.93i		−	1.16845i	0.811593	−	0.584224i	$-0.198601\pi$
$992$	−642.167	+	802.721i	−0.647346	+	0.809194i
$993$	−87.3230			−0.0879386
$994$	223.189	−	686.906i	0.224536	−	0.691052i
$995$	−21.6653	−	19.5075i	−0.0217741	−	0.0196055i
$996$	70.4354	+	51.1743i	0.0707183	+	0.0513799i
$997$	540.163	−	935.590i	0.541788	−	0.938405i	−0.457013	−	0.889460i	$-0.651081\pi$
$997$	540.163	−	935.590i	0.541788	−	0.938405i	0.998801	−	0.0489449i	$-0.0155859\pi$
$998$	742.284	−	428.558i	0.743772	−	0.429417i
$999$	−49.3998	+	470.007i	−0.0494492	+	0.470478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.3.h.a.17.2	yes	32
3.2	odd	2		279.3.bc.b.172.3		32
31.11	odd	30	inner	31.3.h.a.11.2	✓	32
93.11	even	30		279.3.bc.b.73.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.3.h.a.11.2	✓	32	31.11	odd	30	inner
31.3.h.a.17.2	yes	32	1.1	even	1	trivial
279.3.bc.b.73.3		32	93.11	even	30
279.3.bc.b.172.3		32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.331437 + 1.02006i) q^{2} +(0.293175 + 0.263976i) q^{3} +(2.30540 + 1.67497i) q^{4} +(-0.793103 + 1.37369i) q^{5} +(-0.366440 + 0.211564i) q^{6} +(0.503493 - 4.79042i) q^{7} +(-5.94352 + 4.31822i) q^{8} +(-0.924488 - 8.79591i) q^{9} +(-1.13839 - 1.26431i) q^{10} +(-3.31607 - 7.44800i) q^{11} +(0.233734 + 1.09963i) q^{12} +(0.723920 - 3.40578i) q^{13} +(4.71963 + 2.10131i) q^{14} +(-0.595141 + 0.193373i) q^{15} +(1.08740 + 3.34669i) q^{16} +(-8.55661 + 19.2185i) q^{17} +(9.27876 + 1.97226i) q^{18} +(5.81404 - 1.23581i) q^{19} +(-4.12932 + 1.83849i) q^{20} +(1.41217 - 1.27152i) q^{21} +(8.69647 - 0.914036i) q^{22} +(3.72284 + 5.12405i) q^{23} +(-2.88240 - 0.302952i) q^{24} +(11.2420 + 19.4717i) q^{25} +(3.23416 + 1.86724i) q^{26} +(4.13784 - 5.69524i) q^{27} +(9.18456 - 10.2005i) q^{28} +(-23.1587 - 7.52470i) q^{29} -0.671169i q^{30} +(19.3654 - 24.2071i) q^{31} -33.1606 q^{32} +(0.993907 - 3.05893i) q^{33} +(-16.7680 - 15.0980i) q^{34} +(6.18125 + 4.49094i) q^{35} +(12.6016 - 21.8266i) q^{36} +(-58.1388 + 33.5665i) q^{37} +(-0.666387 + 6.34025i) q^{38} +(1.11128 - 0.807391i) q^{39} +(-1.21809 - 11.5894i) q^{40} +(20.8583 + 23.1655i) q^{41} +(0.828981 + 1.86192i) q^{42} +(-9.34191 - 43.9502i) q^{43} +(4.83033 - 22.7249i) q^{44} +(12.8161 + 5.70610i) q^{45} +(-6.46072 + 2.09922i) q^{46} +(15.6666 + 48.2168i) q^{47} +(-0.564645 + 1.26821i) q^{48} +(25.2346 + 5.36379i) q^{49} +(-23.5882 + 5.01384i) q^{50} +(-7.58180 + 3.37564i) q^{51} +(7.37350 - 6.63913i) q^{52} +(10.4475 - 1.09807i) q^{53} +(4.43805 + 6.10845i) q^{54} +(12.8613 + 1.35177i) q^{55} +(17.6935 + 30.6461i) q^{56} +(2.03076 + 1.17246i) q^{57} +(15.3513 - 21.1292i) q^{58} +(52.3153 - 58.1020i) q^{59} +(-1.69593 - 0.551041i) q^{60} +91.3284i q^{61} +(18.2742 + 27.7769i) q^{62} -42.6016 q^{63} +(6.64103 - 20.4390i) q^{64} +(4.10435 + 3.69558i) q^{65} +(2.79087 + 2.02769i) q^{66} +(-32.1730 + 55.7253i) q^{67} +(-51.9168 + 29.9742i) q^{68} +(-0.261183 + 2.48499i) q^{69} +(-6.62972 + 4.81677i) q^{70} +(-14.6133 - 139.036i) q^{71} +(43.4774 + 48.2865i) q^{72} +(-41.2139 - 92.5678i) q^{73} +(-14.9704 - 70.4302i) q^{74} +(-1.84419 + 8.67622i) q^{75} +(15.4736 + 6.88930i) q^{76} +(-37.3487 + 12.1353i) q^{77} +(0.455267 + 1.40117i) q^{78} +(-13.2762 + 29.8189i) q^{79} +(-5.45975 - 1.16051i) q^{80} +(-75.1433 + 15.9722i) q^{81} +(-30.5434 + 13.5988i) q^{82} +(57.5526 - 51.8206i) q^{83} +(5.38537 - 0.566025i) q^{84} +(-19.6140 - 26.9964i) q^{85} +(47.9281 + 5.03744i) q^{86} +(-4.80320 - 8.31938i) q^{87} +(51.8712 + 29.9478i) q^{88} +(82.1472 - 113.066i) q^{89} +(-10.0683 + 11.1820i) q^{90} +(-15.9506 - 5.18266i) q^{91} +18.0486i q^{92} +(12.0675 - 1.98492i) q^{93} -54.3764 q^{94} +(-2.91350 + 8.96684i) q^{95} +(-9.72186 - 8.75360i) q^{96} +(74.1883 + 53.9009i) q^{97} +(-13.8351 + 23.9630i) q^{98} +(-62.4464 + 36.0534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 6 q^{2} - 10 q^{3} - 18 q^{4} - 7 q^{5} - 9 q^{6} - 22 q^{7} + 43 q^{8} - 2 q^{9} + 18 q^{10} - 5 q^{11} - 87 q^{12} - 49 q^{13} + 12 q^{14} + 70 q^{15} + 102 q^{16} - 62 q^{17} - 69 q^{18} - 132 q^{19}+ \cdots - 606 q^{99}+O(q^{100}) \) 32 * q - 6 * q^2 - 10 * q^3 - 18 * q^4 - 7 * q^5 - 9 * q^6 - 22 * q^7 + 43 * q^8 - 2 * q^9 + 18 * q^10 - 5 * q^11 - 87 * q^12 - 49 * q^13 + 12 * q^14 + 70 * q^15 + 102 * q^16 - 62 * q^17 - 69 * q^18 - 132 * q^19 + 41 * q^20 + 71 * q^21 + 27 * q^22 + 15 * q^23 + 204 * q^24 + 85 * q^25 + 93 * q^26 + 95 * q^27 + 56 * q^28 + 10 * q^29 + 75 * q^31 - 274 * q^32 + 77 * q^33 - 146 * q^34 - 61 * q^35 - 137 * q^36 - 354 * q^37 - 218 * q^38 - 133 * q^39 + 37 * q^40 - 40 * q^41 - 375 * q^42 - 157 * q^43 - 329 * q^44 + 159 * q^45 + 430 * q^46 + 442 * q^47 - 204 * q^48 - 256 * q^49 + 317 * q^50 + 574 * q^51 + 351 * q^52 + 14 * q^53 + 220 * q^54 + 437 * q^55 + 566 * q^56 + 219 * q^57 + 385 * q^58 + 254 * q^59 - 5 * q^60 - 11 * q^62 - 318 * q^63 - 241 * q^64 - 468 * q^65 - 588 * q^66 - 293 * q^67 - 654 * q^68 - 700 * q^69 - 442 * q^70 + 74 * q^71 - 215 * q^72 - 522 * q^73 - 417 * q^74 - 845 * q^75 + 98 * q^76 + 500 * q^77 + 955 * q^78 - 150 * q^79 + 278 * q^80 - 21 * q^81 + 386 * q^82 + 512 * q^83 + 1360 * q^84 + 385 * q^85 - 234 * q^86 + 411 * q^87 + 537 * q^88 + 155 * q^89 + 387 * q^90 - 250 * q^91 - 19 * q^93 - 728 * q^94 + 178 * q^95 - 1250 * q^96 - 3 * q^97 - 458 * q^98 - 606 * q^99

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