LMFDB - Embedded newform 169.4.c.j.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(22,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.c (of order $3$, degree $2$, not 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.j.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28078 - 2.21837i) q^{2} +(1.84233 - 3.19101i) q^{3} +(0.719224 + 1.24573i) q^{4} -0.561553 q^{5} +(-4.71922 - 8.17394i) q^{6} +(9.08854 + 15.7418i) q^{7} +24.1771 q^{8} +(6.71165 + 11.6249i) q^{9} +O(q^{10})$	\(q+(1.28078 - 2.21837i) q^{2} +(1.84233 - 3.19101i) q^{3} +(0.719224 + 1.24573i) q^{4} -0.561553 q^{5} +(-4.71922 - 8.17394i) q^{6} +(9.08854 + 15.7418i) q^{7} +24.1771 q^{8} +(6.71165 + 11.6249i) q^{9} +(-0.719224 + 1.24573i) q^{10} +(32.3693 - 56.0653i) q^{11} +5.30019 q^{12} +46.5616 q^{14} +(-1.03457 + 1.79192i) q^{15} +(25.2116 - 43.6679i) q^{16} +(12.7732 + 22.1238i) q^{17} +34.3845 q^{18} +(-53.9848 - 93.5045i) q^{19} +(-0.403882 - 0.699544i) q^{20} +66.9763 q^{21} +(-82.9157 - 143.614i) q^{22} +(-36.6307 + 63.4462i) q^{23} +(44.5421 - 77.1493i) q^{24} -124.685 q^{25} +148.946 q^{27} +(-13.0734 + 22.6438i) q^{28} +(-87.9545 + 152.342i) q^{29} +(2.65009 + 4.59010i) q^{30} +113.093 q^{31} +(32.1274 + 55.6462i) q^{32} +(-119.270 - 206.581i) q^{33} +65.4384 q^{34} +(-5.10370 - 8.83986i) q^{35} +(-9.65435 + 16.7218i) q^{36} +(57.4039 - 99.4264i) q^{37} -276.570 q^{38} -13.5767 q^{40} +(-34.8229 + 60.3151i) q^{41} +(85.7817 - 148.578i) q^{42} +(-219.151 - 379.581i) q^{43} +93.1231 q^{44} +(-3.76894 - 6.52800i) q^{45} +(93.8314 + 162.521i) q^{46} +31.9479 q^{47} +(-92.8963 - 160.901i) q^{48} +(6.29686 - 10.9065i) q^{49} +(-159.693 + 276.597i) q^{50} +94.1298 q^{51} +2.84658 q^{53} +(190.767 - 330.417i) q^{54} +(-18.1771 + 31.4836i) q^{55} +(219.734 + 380.591i) q^{56} -397.831 q^{57} +(225.300 + 390.231i) q^{58} +(35.8163 + 62.0356i) q^{59} -2.97633 q^{60} +(460.348 + 797.345i) q^{61} +(144.847 - 250.882i) q^{62} +(-121.998 + 211.307i) q^{63} +567.978 q^{64} -611.032 q^{66} +(-222.140 + 384.758i) q^{67} +(-18.3736 + 31.8240i) q^{68} +(134.972 + 233.778i) q^{69} -26.1468 q^{70} +(-270.859 - 469.142i) q^{71} +(162.268 + 281.056i) q^{72} -764.004 q^{73} +(-147.043 - 254.686i) q^{74} +(-229.710 + 397.870i) q^{75} +(77.6543 - 134.501i) q^{76} +1176.76 q^{77} -421.538 q^{79} +(-14.1577 + 24.5218i) q^{80} +(93.1932 - 161.415i) q^{81} +(89.2007 + 154.500i) q^{82} -603.797 q^{83} +(48.1710 + 83.4346i) q^{84} +(-7.17283 - 12.4237i) q^{85} -1122.73 q^{86} +(324.082 + 561.327i) q^{87} +(782.596 - 1355.50i) q^{88} +(-579.941 + 1004.49i) q^{89} -19.3087 q^{90} -105.383 q^{92} +(208.354 - 360.880i) q^{93} +(40.9181 - 70.8722i) q^{94} +(30.3153 + 52.5077i) q^{95} +236.757 q^{96} +(291.634 + 505.126i) q^{97} +(-16.1298 - 27.9375i) q^{98} +869.006 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9}+O(q^{10}) $ 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9	\( 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9} - 7 q^{10} + 80 q^{11} - 86 q^{12} + 178 q^{14} - 33 q^{15} + 39 q^{16} - 19 q^{17} + 220 q^{18} - 84 q^{19} + 19 q^{20} + 606 q^{21} - 142 q^{22} - 196 q^{23} + 273 q^{24} - 474 q^{25} + 670 q^{27} + 125 q^{28} + 44 q^{29} - 43 q^{30} + 172 q^{31} - 123 q^{32} - 106 q^{33} + 270 q^{34} - 107 q^{35} + 250 q^{36} + 209 q^{37} - 628 q^{38} - 178 q^{40} - 230 q^{41} - 197 q^{42} - 287 q^{43} + 356 q^{44} - 180 q^{45} - 4 q^{46} - 870 q^{47} - 285 q^{48} - 383 q^{49} - 144 q^{50} + 962 q^{51} - 236 q^{53} + 91 q^{54} + 18 q^{55} + 1015 q^{56} - 1212 q^{57} + 794 q^{58} - 368 q^{59} - 350 q^{60} + 1058 q^{61} + 332 q^{62} - 1560 q^{63} + 1538 q^{64} - 1636 q^{66} + 68 q^{67} + 211 q^{68} - 796 q^{69} + 250 q^{70} - 131 q^{71} + 1350 q^{72} - 912 q^{73} - 147 q^{74} + 516 q^{75} + 22 q^{76} + 1524 q^{77} - 2016 q^{79} - 69 q^{80} - 122 q^{81} - 72 q^{82} - 3916 q^{83} + 1409 q^{84} - 173 q^{85} - 2718 q^{86} + 2558 q^{87} + 1242 q^{88} - 720 q^{89} + 500 q^{90} - 1576 q^{92} + 652 q^{93} + 811 q^{94} + 146 q^{95} + 3726 q^{96} - 928 q^{97} - 650 q^{98} + 260 q^{99}+O(q^{100}) \) 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9 - 7 * q^10 + 80 * q^11 - 86 * q^12 + 178 * q^14 - 33 * q^15 + 39 * q^16 - 19 * q^17 + 220 * q^18 - 84 * q^19 + 19 * q^20 + 606 * q^21 - 142 * q^22 - 196 * q^23 + 273 * q^24 - 474 * q^25 + 670 * q^27 + 125 * q^28 + 44 * q^29 - 43 * q^30 + 172 * q^31 - 123 * q^32 - 106 * q^33 + 270 * q^34 - 107 * q^35 + 250 * q^36 + 209 * q^37 - 628 * q^38 - 178 * q^40 - 230 * q^41 - 197 * q^42 - 287 * q^43 + 356 * q^44 - 180 * q^45 - 4 * q^46 - 870 * q^47 - 285 * q^48 - 383 * q^49 - 144 * q^50 + 962 * q^51 - 236 * q^53 + 91 * q^54 + 18 * q^55 + 1015 * q^56 - 1212 * q^57 + 794 * q^58 - 368 * q^59 - 350 * q^60 + 1058 * q^61 + 332 * q^62 - 1560 * q^63 + 1538 * q^64 - 1636 * q^66 + 68 * q^67 + 211 * q^68 - 796 * q^69 + 250 * q^70 - 131 * q^71 + 1350 * q^72 - 912 * q^73 - 147 * q^74 + 516 * q^75 + 22 * q^76 + 1524 * q^77 - 2016 * q^79 - 69 * q^80 - 122 * q^81 - 72 * q^82 - 3916 * q^83 + 1409 * q^84 - 173 * q^85 - 2718 * q^86 + 2558 * q^87 + 1242 * q^88 - 720 * q^89 + 500 * q^90 - 1576 * q^92 + 652 * q^93 + 811 * q^94 + 146 * q^95 + 3726 * q^96 - 928 * q^97 - 650 * q^98 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.28078	−	2.21837i	0.452823	−	0.784312i	−0.545737	−	0.837956i	$-0.683750\pi$
$2$	1.28078	−	2.21837i	0.452823	−	0.784312i	0.998560	+	0.0536442i	$0.0170837\pi$
$3$	1.84233	−	3.19101i	0.354556	−	0.614110i	−0.632486	−	0.774572i	$-0.717965\pi$
$3$	1.84233	−	3.19101i	0.354556	−	0.614110i	0.987042	+	0.160462i	$0.0512985\pi$
$4$	0.719224	+	1.24573i	0.0899029	+	0.155716i
$5$	−0.561553			−0.0502268			−0.0251134	−	0.999685i	$-0.507995\pi$
$5$	−0.561553			−0.0502268			−0.0251134	+	0.999685i	$0.507995\pi$
$6$	−4.71922	−	8.17394i	−0.321102	−	0.556166i
$7$	9.08854	+	15.7418i	0.490735	+	0.849978i	0.999943	−	0.0106654i	$-0.00339497\pi$
$7$	9.08854	+	15.7418i	0.490735	+	0.849978i	−0.509208	+	0.860643i	$0.670062\pi$
$8$	24.1771			1.06849
$9$	6.71165	+	11.6249i	0.248579	+	0.430552i
$10$	−0.719224	+	1.24573i	−0.0227438	+	0.0393935i
$11$	32.3693	−	56.0653i	0.887247	−	1.53676i	0.0441305	−	0.999026i	$-0.485948\pi$
$11$	32.3693	−	56.0653i	0.887247	−	1.53676i	0.843116	−	0.537731i	$-0.180718\pi$
$12$	5.30019			0.127503
$13$		0			0
$13$		0			0
$14$	46.5616			0.888864
$15$	−1.03457	+	1.79192i	−0.0178082	+	0.0308448i
$16$	25.2116	−	43.6679i	0.393932	−	0.682310i
$17$	12.7732	+	22.1238i	0.182233	+	0.315636i	0.942641	−	0.333810i	$-0.108334\pi$
$17$	12.7732	+	22.1238i	0.182233	+	0.315636i	−0.760408	+	0.649446i	$0.775001\pi$
$18$	34.3845			0.450250
$19$	−53.9848	−	93.5045i	−0.651841	−	1.12902i	−0.982676	−	0.185333i	$-0.940664\pi$
$19$	−53.9848	−	93.5045i	−0.651841	−	1.12902i	0.330835	−	0.943689i	$-0.392670\pi$
$20$	−0.403882	−	0.699544i	−0.00451554	−	0.00782114i
$21$	66.9763			0.695973
$22$	−82.9157	−	143.614i	−0.803531	−	1.39176i
$23$	−36.6307	+	63.4462i	−0.332088	+	0.575193i	−0.982921	−	0.184027i	$-0.941086\pi$
$23$	−36.6307	+	63.4462i	−0.332088	+	0.575193i	0.650833	+	0.759221i	$0.274420\pi$
$24$	44.5421	−	77.1493i	0.378839	−	0.656168i
$25$	−124.685			−0.997477
$26$		0			0
$27$	148.946			1.06165
$28$	−13.0734	+	22.6438i	−0.0882371	+	0.152831i
$29$	−87.9545	+	152.342i	−0.563198	+	0.975488i	0.434017	+	0.900905i	$0.357096\pi$
$29$	−87.9545	+	152.342i	−0.563198	+	0.975488i	−0.997215	+	0.0745830i	$0.976237\pi$
$30$	2.65009	+	4.59010i	0.0161280	+	0.0279344i
$31$	113.093			0.655228			0.327614	−	0.944812i	$-0.393755\pi$
$31$	113.093			0.655228			0.327614	+	0.944812i	$0.393755\pi$
$32$	32.1274	+	55.6462i	0.177480	+	0.307405i
$33$	−119.270	−	206.581i	−0.629158	−	1.08973i
$34$	65.4384			0.330077
$35$	−5.10370	−	8.83986i	−0.0246481	−	0.0426917i
$36$	−9.65435	+	16.7218i	−0.0446961	+	0.0774158i
$37$	57.4039	−	99.4264i	0.255058	−	0.441773i	−0.709853	−	0.704349i	$-0.751239\pi$
$37$	57.4039	−	99.4264i	0.255058	−	0.441773i	0.964911	+	0.262576i	$0.0845722\pi$
$38$	−276.570			−1.18067
$39$		0			0
$40$	−13.5767			−0.0536666
$41$	−34.8229	+	60.3151i	−0.132645	+	0.229747i	−0.924695	−	0.380708i	$-0.875680\pi$
$41$	−34.8229	+	60.3151i	−0.132645	+	0.229747i	0.792051	+	0.610455i	$0.209014\pi$
$42$	85.7817	−	148.578i	0.315153	−	0.545860i
$43$	−219.151	−	379.581i	−0.777214	−	1.34617i	−0.933541	−	0.358469i	$-0.883299\pi$
$43$	−219.151	−	379.581i	−0.777214	−	1.34617i	0.156327	−	0.987705i	$-0.450035\pi$
$44$	93.1231			0.319064
$45$	−3.76894	−	6.52800i	−0.0124854	−	0.0216253i
$46$	93.8314	+	162.521i	0.300754	+	0.520921i
$47$	31.9479			0.0991506			0.0495753	−	0.998770i	$-0.484213\pi$
$47$	31.9479			0.0991506			0.0495753	+	0.998770i	$0.484213\pi$
$48$	−92.8963	−	160.901i	−0.279342	−	0.483835i
$49$	6.29686	−	10.9065i	0.0183582	−	0.0317973i
$50$	−159.693	+	276.597i	−0.451680	+	0.782334i
$51$	94.1298			0.258447
$52$		0			0
$53$	2.84658			0.00737752			0.00368876	−	0.999993i	$-0.498826\pi$
$53$	2.84658			0.00737752			0.00368876	+	0.999993i	$0.498826\pi$
$54$	190.767	−	330.417i	0.480741	−	0.832669i
$55$	−18.1771	+	31.4836i	−0.0445636	+	0.0771864i
$56$	219.734	+	380.591i	0.524344	+	0.908190i
$57$	−397.831			−0.924457
$58$	225.300	+	390.231i	0.510058	+	0.883446i
$59$	35.8163	+	62.0356i	0.0790319	+	0.136887i	0.902832	−	0.429992i	$-0.141484\pi$
$59$	35.8163	+	62.0356i	0.0790319	+	0.136887i	−0.823801	+	0.566880i	$0.808150\pi$
$60$	−2.97633			−0.00640405
$61$	460.348	+	797.345i	0.966253	+	1.67360i	0.706209	+	0.708003i	$0.250404\pi$
$61$	460.348	+	797.345i	0.966253	+	1.67360i	0.260044	+	0.965597i	$0.416263\pi$
$62$	144.847	−	250.882i	0.296702	−	0.513903i
$63$	−121.998	+	211.307i	−0.243973	+	0.422574i
$64$	567.978			1.10933
$65$		0			0
$66$	−611.032			−1.13959
$67$	−222.140	+	384.758i	−0.405056	+	0.701577i	−0.994328	−	0.106357i	$-0.966081\pi$
$67$	−222.140	+	384.758i	−0.405056	+	0.701577i	0.589272	+	0.807935i	$0.299415\pi$
$68$	−18.3736	+	31.8240i	−0.0327665	+	0.0567533i
$69$	134.972	+	233.778i	0.235488	+	0.407877i
$70$	−26.1468			−0.0446448
$71$	−270.859	−	469.142i	−0.452748	−	0.784182i	0.545808	−	0.837910i	$-0.316223\pi$
$71$	−270.859	−	469.142i	−0.452748	−	0.784182i	−0.998556	+	0.0537283i	$0.982890\pi$
$72$	162.268	+	281.056i	0.265604	+	0.460039i
$73$	−764.004			−1.22493			−0.612465	−	0.790498i	$-0.709822\pi$
$73$	−764.004			−1.22493			−0.612465	+	0.790498i	$0.709822\pi$
$74$	−147.043	−	254.686i	−0.230992	−	0.400090i
$75$	−229.710	+	397.870i	−0.353662	+	0.612561i
$76$	77.6543	−	134.501i	0.117205	−	0.203005i
$77$	1176.76			1.74161
$78$		0			0
$79$	−421.538			−0.600338			−0.300169	−	0.953886i	$-0.597043\pi$
$79$	−421.538			−0.600338			−0.300169	+	0.953886i	$0.597043\pi$
$80$	−14.1577	+	24.5218i	−0.0197859	+	0.0342703i
$81$	93.1932	−	161.415i	0.127837	−	0.221420i
$82$	89.2007	+	154.500i	0.120129	+	0.208069i
$83$	−603.797			−0.798498			−0.399249	−	0.916842i	$-0.630729\pi$
$83$	−603.797			−0.798498			−0.399249	+	0.916842i	$0.630729\pi$
$84$	48.1710	+	83.4346i	0.0625700	+	0.108374i
$85$	−7.17283	−	12.4237i	−0.00915297	−	0.0158534i
$86$	−1122.73			−1.40776
$87$	324.082	+	561.327i	0.399371	+	0.691731i
$88$	782.596	−	1355.50i	0.948011	−	1.64200i
$89$	−579.941	+	1004.49i	−0.690715	+	1.19635i	0.280889	+	0.959740i	$0.409371\pi$
$89$	−579.941	+	1004.49i	−0.690715	+	1.19635i	−0.971604	+	0.236613i	$0.923963\pi$
$90$	−19.3087			−0.0226146
$91$		0			0
$92$	−105.383			−0.119423
$93$	208.354	−	360.880i	0.232315	−	0.402382i
$94$	40.9181	−	70.8722i	0.0448977	−	0.0777650i
$95$	30.3153	+	52.5077i	0.0327399	+	0.0567071i
$96$	236.757			0.251707
$97$	291.634	+	505.126i	0.305268	+	0.528740i	0.977321	−	0.211763i	$-0.0679206\pi$
$97$	291.634	+	505.126i	0.305268	+	0.528740i	−0.672053	+	0.740503i	$0.734587\pi$
$98$	−16.1298	−	27.9375i	−0.0166260	−	0.0287971i
$99$	869.006			0.882206
$100$	−89.6761	−	155.324i	−0.0896761	−	0.155324i
$101$	−460.870	+	798.251i	−0.454043	+	0.786425i	−0.998633	−	0.0522775i	$-0.983352\pi$
$101$	−460.870	+	798.251i	−0.454043	+	0.786425i	0.544590	+	0.838702i	$0.316685\pi$
$102$	120.559	−	208.815i	0.117031	−	0.202703i
$103$	−930.712			−0.890347			−0.445174	−	0.895444i	$-0.646858\pi$
$103$	−930.712			−0.890347			−0.445174	+	0.895444i	$0.646858\pi$
$104$		0			0
$105$	−37.6107			−0.0349565
$106$	3.64584	−	6.31478i	0.00334071	−	0.00578628i
$107$	−428.691	+	742.515i	−0.387319	+	0.670857i	−0.992088	−	0.125545i	$-0.959932\pi$
$107$	−428.691	+	742.515i	−0.387319	+	0.670857i	0.604769	+	0.796401i	$0.293266\pi$
$108$	107.125	+	185.547i	0.0954459	+	0.165317i
$109$	−671.853			−0.590384			−0.295192	−	0.955438i	$-0.595384\pi$
$109$	−671.853			−0.590384			−0.295192	+	0.955438i	$0.595384\pi$
$110$	46.5616	+	80.6470i	0.0403588	+	0.0699035i
$111$	−211.514	−	366.352i	−0.180865	−	0.313267i
$112$	916.548			0.773265
$113$	−320.737	−	555.532i	−0.267012	−	0.462479i	0.701077	−	0.713086i	$-0.252703\pi$
$113$	−320.737	−	555.532i	−0.267012	−	0.462479i	−0.968089	+	0.250607i	$0.919370\pi$
$114$	−509.533	+	882.537i	−0.418615	+	0.725063i
$115$	20.5701	−	35.6284i	0.0166797	−	0.0288901i
$116$	−253.036			−0.202533
$117$		0			0
$118$	183.491			0.143150
$119$	−232.179	+	402.147i	−0.178856	+	0.309788i
$120$	−25.0128	+	43.3234i	−0.0190279	+	0.0329572i
$121$	−1430.05	−	2476.91i	−1.07441	−	1.86094i
$122$	2358.41			1.75017
$123$	128.311	+	222.240i	0.0940599	+	0.162917i
$124$	81.3390	+	140.883i	0.0589069	+	0.102030i
$125$	140.211			0.100327
$126$	312.505	+	541.274i	0.220953	+	0.382703i
$127$	276.587	−	479.063i	0.193253	−	0.334724i	−0.753073	−	0.657937i	$-0.771430\pi$
$127$	276.587	−	479.063i	0.193253	−	0.334724i	0.946326	+	0.323212i	$0.104763\pi$
$128$	470.434	−	814.816i	0.324851	−	0.562658i
$129$	−1614.99			−1.10227
$130$		0			0
$131$	2056.40			1.37152			0.685758	−	0.727830i	$-0.259471\pi$
$131$	2056.40			1.37152			0.685758	+	0.727830i	$0.259471\pi$
$132$	171.563	−	297.157i	0.113126	−	0.195941i
$133$	981.287	−	1699.64i	0.639762	−	1.10810i
$134$	569.024	+	985.578i	0.366837	+	0.635380i
$135$	−83.6411			−0.0533235
$136$	308.819	+	534.890i	0.194713	+	0.337253i
$137$	−904.283	−	1566.26i	−0.563928	−	0.976752i	−0.997149	−	0.0754639i	$-0.975956\pi$
$137$	−904.283	−	1566.26i	−0.563928	−	0.976752i	0.433221	−	0.901288i	$-0.357377\pi$
$138$	691.474			0.426537
$139$	−746.818	−	1293.53i	−0.455714	−	0.789320i	0.543015	−	0.839723i	$-0.317283\pi$
$139$	−746.818	−	1293.53i	−0.455714	−	0.789320i	−0.998729	+	0.0504032i	$0.983949\pi$
$140$	7.34140	−	12.7157i	0.00443187	−	0.00767622i
$141$	58.8585	−	101.946i	0.0351545	−	0.0608894i
$142$	−1387.64			−0.820058
$143$		0			0
$144$	676.847			0.391694
$145$	49.3911	−	85.5479i	0.0282876	−	0.0489956i
$146$	−978.518	+	1694.84i	−0.554676	+	0.960727i
$147$	−23.2018	−	40.1867i	−0.0130180	−	0.0225479i
$148$	165.145			0.0917218
$149$	−1379.51	−	2389.38i	−0.758482	−	1.31373i	−0.943625	−	0.331018i	$-0.892608\pi$
$149$	−1379.51	−	2389.38i	−0.758482	−	1.31373i	0.185143	−	0.982712i	$-0.440725\pi$
$150$	588.415	+	1019.16i	0.320292	+	0.554763i
$151$	976.355			0.526190			0.263095	−	0.964770i	$-0.415257\pi$
$151$	976.355			0.526190			0.263095	+	0.964770i	$0.415257\pi$
$152$	−1305.20	−	2260.67i	−0.696483	−	1.20634i
$153$	−171.458	+	296.975i	−0.0905986	+	0.156921i
$154$	1507.17	−	2610.49i	0.788642	−	1.36597i
$155$	−63.5076			−0.0329100
$156$		0			0
$157$	−564.875			−0.287146			−0.143573	−	0.989640i	$-0.545859\pi$
$157$	−564.875			−0.287146			−0.143573	+	0.989640i	$0.545859\pi$
$158$	−539.896	+	935.127i	−0.271847	+	0.470853i
$159$	5.24435	−	9.08347i	0.00261575	−	0.00453061i
$160$	−18.0412	−	31.2483i	−0.00891427	−	0.0154400i
$161$	−1331.68			−0.651869
$162$	−238.719	−	413.474i	−0.115775	−	0.200528i
$163$	754.266	+	1306.43i	0.362446	+	0.627775i	0.988363	−	0.152115i	$-0.0486084\pi$
$163$	754.266	+	1306.43i	0.362446	+	0.627775i	−0.625917	+	0.779890i	$0.715275\pi$
$164$	−100.182			−0.0477005
$165$	66.9763	+	116.006i	0.0316006	+	0.0547339i
$166$	−773.329	+	1339.45i	−0.361578	+	0.626272i
$167$	296.260	−	513.138i	0.137277	−	0.237771i	−0.789188	−	0.614152i	$-0.789498\pi$
$167$	296.260	−	513.138i	0.137277	−	0.237771i	0.926465	+	0.376381i	$0.122832\pi$
$168$	1619.29			0.743638
$169$		0			0
$170$	−36.7471			−0.0165787
$171$	724.654	−	1255.14i	0.324068	−	0.561303i
$172$	315.237	−	546.007i	0.139748	−	0.242050i
$173$	2247.78	+	3893.28i	0.987838	+	1.71099i	0.628576	+	0.777748i	$0.283638\pi$
$173$	2247.78	+	3893.28i	0.987838	+	1.71099i	0.359262	+	0.933237i	$0.383028\pi$
$174$	1660.31			0.723377
$175$	−1133.20	−	1962.76i	−0.489497	−	0.847834i
$176$	−1632.17	−	2827.00i	−0.699030	−	1.21076i
$177$	263.941			0.112085
$178$	1485.55	+	2573.05i	0.625543	+	1.08347i
$179$	77.1425	−	133.615i	0.0322117	−	0.0557924i	−0.849470	−	0.527637i	$-0.823078\pi$
$179$	77.1425	−	133.615i	0.0322117	−	0.0557924i	0.881682	+	0.471844i	$0.156412\pi$
$180$	5.42143	−	9.39019i	0.00224494	−	0.00388835i
$181$	1071.35			0.439959			0.219979	−	0.975505i	$-0.429401\pi$
$181$	1071.35			0.439959			0.219979	+	0.975505i	$0.429401\pi$
$182$		0			0
$183$	3392.45			1.37037
$184$	−885.623	+	1533.94i	−0.354831	+	0.614586i
$185$	−32.2353	+	55.8332i	−0.0128107	+	0.0221889i
$186$	−533.710	−	924.413i	−0.210395	−	0.364415i
$187$	1653.84			0.646742
$188$	22.9777	+	39.7985i	0.00891393	+	0.0154394i
$189$	1353.70	+	2344.68i	0.520991	+	0.902383i
$190$	155.309			0.0593015
$191$	−338.601	−	586.475i	−0.128274	−	0.222177i	0.794734	−	0.606958i	$-0.207610\pi$
$191$	−338.601	−	586.475i	−0.128274	−	0.222177i	−0.923008	+	0.384781i	$0.874277\pi$
$192$	1046.40	−	1812.42i	0.393321	−	0.681252i
$193$	660.840	−	1144.61i	0.246468	−	0.426895i	−0.716075	−	0.698023i	$-0.754063\pi$
$193$	660.840	−	1144.61i	0.246468	−	0.426895i	0.962543	+	0.271128i	$0.0873967\pi$
$194$	1494.07			0.552929
$195$		0			0
$196$	18.1154			0.00660183
$197$	633.683	−	1097.57i	0.229178	−	0.396948i	−0.728387	−	0.685166i	$-0.759730\pi$
$197$	633.683	−	1097.57i	0.229178	−	0.396948i	0.957565	+	0.288218i	$0.0930629\pi$
$198$	1113.00	−	1927.78i	0.399483	−	0.691925i
$199$	−1198.12	−	2075.21i	−0.426796	−	0.739233i	0.569790	−	0.821790i	$-0.307025\pi$
$199$	−1198.12	−	2075.21i	−0.426796	−	0.739233i	−0.996586	+	0.0825573i	$0.973691\pi$
$200$	−3014.51			−1.06579
$201$	818.510	+	1417.70i	0.287230	+	0.497497i
$202$	1180.54	+	2044.76i	0.411202	+	0.712222i
$203$	−3197.51			−1.10552
$204$	67.7003	+	117.260i	0.0232352	+	0.0402445i
$205$	19.5549	−	33.8701i	0.00666231	−	0.0115395i
$206$	−1192.03	+	2064.66i	−0.403170	+	0.698310i
$207$	−983.409			−0.330201
$208$		0			0
$209$	−6989.81			−2.31337
$210$	−48.1710	+	83.4346i	−0.0158291	+	0.0274168i
$211$	45.7769	−	79.2880i	0.0149356	−	0.0258692i	−0.858461	−	0.512879i	$-0.828579\pi$
$211$	45.7769	−	79.2880i	0.0149356	−	0.0258692i	0.873397	+	0.487010i	$0.161912\pi$
$212$	2.04733	+	3.54608i	0.000663261	+	0.00114880i
$213$	−1996.05			−0.642099
$214$	1098.12	+	1901.99i	0.350774	+	0.607558i
$215$	123.065	+	213.155i	0.0390370	+	0.0676141i
$216$	3601.08			1.13436
$217$	1027.85	+	1780.29i	0.321543	+	0.556929i
$218$	−860.494	+	1490.42i	−0.267339	+	0.463045i
$219$	−1407.55	+	2437.94i	−0.434307	+	0.752241i
$220$	−52.2935			−0.0160256
$221$		0			0
$222$	−1083.61			−0.327599
$223$	617.709	−	1069.90i	0.185493	−	0.321282i	−0.758250	−	0.651964i	$-0.773945\pi$
$223$	617.709	−	1069.90i	0.185493	−	0.321282i	0.943742	+	0.330682i	$0.107279\pi$
$224$	−583.982	+	1011.49i	−0.174192	+	0.301709i
$225$	−836.839	−	1449.45i	−0.247952	−	0.429466i
$226$	−1643.17			−0.483637
$227$	1650.83	+	2859.32i	0.482685	+	0.836035i	0.999802	−	0.0198797i	$-0.00632833\pi$
$227$	1650.83	+	2859.32i	0.482685	+	0.836035i	−0.517118	+	0.855914i	$0.672995\pi$
$228$	−286.130	−	495.591i	−0.0831114	−	0.143953i
$229$	−211.283			−0.0609694			−0.0304847	−	0.999535i	$-0.509705\pi$
$229$	−211.283			−0.0609694			−0.0304847	+	0.999535i	$0.509705\pi$
$230$	−52.6913	−	91.2640i	−0.0151059	−	0.0261642i
$231$	2167.98	−	3755.05i	0.617500	−	1.06954i
$232$	−2126.48	+	3683.18i	−0.601769	+	1.04230i
$233$	−256.724			−0.0721827			−0.0360913	−	0.999348i	$-0.511491\pi$
$233$	−256.724			−0.0721827			−0.0360913	+	0.999348i	$0.511491\pi$
$234$		0			0
$235$	−17.9404			−0.00498002
$236$	−51.5198	+	89.2349i	−0.0142104	+	0.0246131i
$237$	−776.612	+	1345.13i	−0.212854	+	0.368674i
$238$	594.740	+	1030.12i	0.161980	+	0.280558i
$239$	3549.62			0.960694			0.480347	−	0.877078i	$-0.340511\pi$
$239$	3549.62			0.960694			0.480347	+	0.877078i	$0.340511\pi$
$240$	52.1662	+	90.3545i	0.0140305	+	0.0243015i
$241$	−2515.05	−	4356.19i	−0.672235	−	1.16434i	−0.977269	−	0.212003i	$-0.932001\pi$
$241$	−2515.05	−	4356.19i	−0.672235	−	1.16434i	0.305034	−	0.952341i	$-0.401332\pi$
$242$	−7326.27			−1.94608
$243$	1667.39	+	2888.00i	0.440176	+	0.762408i
$244$	−662.186	+	1146.94i	−0.173738	+	0.300923i
$245$	−3.53602	+	6.12457i	−0.000922074	+	0.00159708i
$246$	657.349			0.170370
$247$		0			0
$248$	2734.25			0.700102
$249$	−1112.39	+	1926.72i	−0.283113	+	0.490366i
$250$	179.579	−	311.040i	0.0454303	−	0.0786876i
$251$	359.392	+	622.485i	0.0903770	+	0.156538i	0.907670	−	0.419685i	$-0.137859\pi$
$251$	359.392	+	622.485i	0.0903770	+	0.156538i	−0.817293	+	0.576223i	$0.804526\pi$
$252$	−350.976			−0.0877357
$253$	2371.42	+	4107.42i	0.589288	+	1.02068i
$254$	−708.492	−	1227.14i	−0.175019	−	0.303141i
$255$	−52.8588			−0.0129810
$256$	1066.87	+	1847.87i	0.260466	+	0.451141i
$257$	−640.397	+	1109.20i	−0.155435	+	0.269222i	−0.933217	−	0.359312i	$-0.883011\pi$
$257$	−640.397	+	1109.20i	−0.155435	+	0.269222i	0.777782	+	0.628534i	$0.216345\pi$
$258$	−2068.45	+	3582.65i	−0.499131	+	0.864520i
$259$	2086.87			0.500663
$260$		0			0
$261$	−2361.28			−0.559998
$262$	2633.79	−	4561.86i	0.621054	−	1.07570i
$263$	−2612.77	+	4525.46i	−0.612587	+	1.06103i	0.378215	+	0.925718i	$0.376538\pi$
$263$	−2612.77	+	4525.46i	−0.612587	+	1.06103i	−0.990803	+	0.135315i	$0.956795\pi$
$264$	−2883.60	−	4994.54i	−0.672247	−	1.16437i
$265$	−1.59851			−0.000370549
$266$	−2513.62	−	4353.71i	−0.579398	−	1.00355i
$267$	2136.89	+	3701.19i	0.489795	+	0.848350i
$268$	−639.074			−0.145663
$269$	−3221.90	−	5580.50i	−0.730270	−	1.26487i	−0.956768	−	0.290854i	$-0.906061\pi$
$269$	−3221.90	−	5580.50i	−0.730270	−	1.26487i	0.226497	−	0.974012i	$-0.427273\pi$
$270$	−107.125	+	185.547i	−0.0241461	+	0.0418223i
$271$	−1964.97	+	3403.42i	−0.440455	+	0.762890i	−0.997723	−	0.0674426i	$-0.978516\pi$
$271$	−1964.97	+	3403.42i	−0.440455	+	0.762890i	0.557269	+	0.830332i	$0.311849\pi$
$272$	1288.13			0.287149
$273$		0			0
$274$	−4632.74			−1.02144
$275$	−4035.96	+	6990.48i	−0.885009	+	1.53288i
$276$	−194.149	+	336.277i	−0.0423421	+	0.0733387i
$277$	2942.20	+	5096.04i	0.638194	+	1.10538i	0.985829	+	0.167754i	$0.0536516\pi$
$277$	2942.20	+	5096.04i	0.638194	+	1.10538i	−0.347635	+	0.937630i	$0.613015\pi$
$278$	−3826.03			−0.825431
$279$	759.039	+	1314.69i	0.162876	+	0.282110i
$280$	−123.392	−	213.722i	−0.0263361	−	0.0456155i
$281$	−3529.79			−0.749358			−0.374679	−	0.927155i	$-0.622247\pi$
$281$	−3529.79			−0.749358			−0.374679	+	0.927155i	$0.622247\pi$
$282$	−150.769	−	261.140i	−0.0318375	−	0.0551442i
$283$	1305.50	−	2261.19i	0.274219	−	0.474961i	−0.695719	−	0.718314i	$-0.744914\pi$
$283$	1305.50	−	2261.19i	0.274219	−	0.474961i	0.969938	+	0.243353i	$0.0782474\pi$
$284$	389.617	−	674.836i	0.0814067	−	0.141001i
$285$	223.403			0.0464325
$286$		0			0
$287$	−1265.96			−0.260373
$288$	−431.255	+	746.955i	−0.0882359	+	0.152829i
$289$	2130.19	−	3689.60i	0.433582	−	0.750987i
$290$	−126.518	−	219.136i	−0.0256186	−	0.0443727i
$291$	2149.15			0.432939
$292$	−549.490	−	951.744i	−0.110125	−	0.190742i
$293$	−2745.51	−	4755.37i	−0.547422	−	0.948163i	−0.998450	−	0.0556531i	$-0.982276\pi$
$293$	−2745.51	−	4755.37i	−0.547422	−	0.948163i	0.451028	−	0.892510i	$-0.351057\pi$
$294$	−118.865			−0.0235795
$295$	−20.1127	−	34.8363i	−0.00396952	−	0.00687541i
$296$	1387.86	−	2403.84i	0.272526	−	0.472028i
$297$	4821.28	−	8350.70i	0.941950	−	1.63150i
$298$	−7067.37			−1.37383
$299$		0			0
$300$	−660.852			−0.127181
$301$	3983.53	−	6899.67i	0.762813	−	1.32123i
$302$	1250.49	−	2165.92i	0.238271	−	0.412697i
$303$	1698.15	+	2941.28i	0.321967	+	0.557664i
$304$	−5444.19			−1.02712
$305$	−258.509	−	447.751i	−0.0485318	−	0.0840596i
$306$	439.200	+	760.716i	0.0820502	+	0.142115i
$307$	7307.59			1.35852			0.679261	−	0.733897i	$-0.262300\pi$
$307$	7307.59			1.35852			0.679261	+	0.733897i	$0.262300\pi$
$308$	846.353	+	1465.93i	0.156576	+	0.271198i
$309$	−1714.68	+	2969.91i	−0.315678	+	0.546771i
$310$	−81.3390	+	140.883i	−0.0149024	+	0.0258117i
$311$	7904.92			1.44131			0.720654	−	0.693295i	$-0.243842\pi$
$311$	7904.92			1.44131			0.720654	+	0.693295i	$0.243842\pi$
$312$		0			0
$313$	10002.4			1.80629			0.903145	−	0.429336i	$-0.141252\pi$
$313$	10002.4			1.80629			0.903145	+	0.429336i	$0.141252\pi$
$314$	−723.478	+	1253.10i	−0.130026	+	0.225212i
$315$	68.5084	−	118.660i	0.0122540	−	0.0212246i
$316$	−303.180	−	525.123i	−0.0539722	−	0.0934825i
$317$	6230.81			1.10397			0.551983	−	0.833856i	$-0.313871\pi$
$317$	6230.81			1.10397			0.551983	+	0.833856i	$0.313871\pi$
$318$	−13.4337	−	23.2678i	−0.00236894	−	0.00410312i
$319$	5694.06	+	9862.40i	0.999392	+	1.73100i
$320$	−318.950			−0.0557182
$321$	1579.58	+	2735.91i	0.274653	+	0.475713i
$322$	−1705.58	+	2954.15i	−0.295181	+	0.511269i
$323$	1379.12	−	2388.70i	0.237573	−	0.411489i
$324$	268.107			0.0459717
$325$		0			0
$326$	3864.19			0.656495
$327$	−1237.77	+	2143.89i	−0.209324	+	0.362561i
$328$	−841.917	+	1458.24i	−0.141729	+	0.245482i
$329$	290.360	+	502.918i	0.0486567	+	0.0842758i
$330$	343.127			0.0572379
$331$	−2317.25	−	4013.60i	−0.384797	−	0.666488i	0.606944	−	0.794745i	$-0.292395\pi$
$331$	−2317.25	−	4013.60i	−0.384797	−	0.666488i	−0.991741	+	0.128257i	$0.959062\pi$
$332$	−434.265	−	752.170i	−0.0717874	−	0.124339i
$333$	1541.10			0.253609
$334$	−758.886	−	1314.43i	−0.124325	−	0.215337i
$335$	124.743	−	216.062i	0.0203447	−	0.0352380i
$336$	1688.58	−	2924.71i	0.274166	−	0.474870i
$337$	3029.82			0.489747			0.244874	−	0.969555i	$-0.421254\pi$
$337$	3029.82			0.489747			0.244874	+	0.969555i	$0.421254\pi$
$338$		0			0
$339$	−2363.61			−0.378684
$340$	10.3177	−	17.8708i	0.00164576	−	0.00285054i
$341$	3660.74	−	6340.58i	0.581349	−	1.00693i
$342$	−1856.24	−	3215.10i	−0.293491	−	0.508342i
$343$	6463.66			1.01751
$344$	−5298.43	−	9177.15i	−0.830443	−	1.43837i
$345$	−75.7937	−	131.278i	−0.0118278	−	0.0204864i
$346$	11515.6			1.78926
$347$	−1420.80	−	2460.90i	−0.219805	−	0.380714i	0.734943	−	0.678129i	$-0.237209\pi$
$347$	−1420.80	−	2460.90i	−0.219805	−	0.380714i	−0.954748	+	0.297415i	$0.903876\pi$
$348$	−466.175	+	807.440i	−0.0718093	+	0.124377i
$349$	3782.84	−	6552.07i	0.580202	−	1.00494i	−0.415252	−	0.909706i	$-0.636307\pi$
$349$	3782.84	−	6552.07i	0.580202	−	1.00494i	0.995455	−	0.0952339i	$-0.0303599\pi$
$350$	−5805.51			−0.886622
$351$		0			0
$352$	4159.76			0.629875
$353$	−1169.72	+	2026.01i	−0.176368	+	0.305478i	−0.940634	−	0.339423i	$-0.889768\pi$
$353$	−1169.72	+	2026.01i	−0.176368	+	0.305478i	0.764266	+	0.644901i	$0.223101\pi$
$354$	338.050	−	585.520i	0.0507547	−	0.0879097i
$355$	152.102	+	263.448i	0.0227401	+	0.0393870i
$356$	−1668.43			−0.248389
$357$	855.502	+	1481.77i	0.126829	+	0.219674i
$358$	−197.605	−	342.261i	−0.0291724	−	0.0505281i
$359$	2531.68			0.372192			0.186096	−	0.982532i	$-0.440417\pi$
$359$	2531.68			0.372192			0.186096	+	0.982532i	$0.440417\pi$
$360$	−91.1221	−	157.828i	−0.0133404	−	0.0231063i
$361$	−2399.23	+	4155.58i	−0.349793	+	0.605858i
$362$	1372.16	−	2376.64i	0.199223	−	0.345065i
$363$	−10538.5			−1.52376
$364$		0			0
$365$	429.028			0.0615243
$366$	4344.97	−	7525.70i	0.620533	−	1.07479i
$367$	−3288.91	+	5696.55i	−0.467792	+	0.810239i	−0.999323	−	0.0368000i	$-0.988284\pi$
$367$	−3288.91	+	5696.55i	−0.467792	+	0.810239i	0.531531	+	0.847039i	$0.321617\pi$
$368$	1847.04	+	3199.17i	0.261640	+	0.453174i
$369$	−934.876			−0.131891
$370$	82.5725	+	143.020i	0.0116020	+	0.0200952i
$371$	25.8713	+	44.8104i	0.00362041	+	0.00627073i
$372$	599.413			0.0835433
$373$	−1451.36	−	2513.83i	−0.201471	−	0.348958i	0.747532	−	0.664226i	$-0.231239\pi$
$373$	−1451.36	−	2513.83i	−0.201471	−	0.348958i	−0.949003	+	0.315268i	$0.897905\pi$
$374$	2118.20	−	3668.83i	0.292859	−	0.507247i
$375$	258.315	−	447.415i	0.0355716	−	0.0616117i
$376$	772.407			0.105941
$377$		0			0
$378$	6935.16			0.943667
$379$	−932.867	+	1615.77i	−0.126433	+	0.218989i	−0.922292	−	0.386493i	$-0.873686\pi$
$379$	−932.867	+	1615.77i	−0.126433	+	0.218989i	0.795859	+	0.605482i	$0.207020\pi$
$380$	−43.6070	+	75.5296i	−0.00588682	+	0.0101963i
$381$	−1019.13	−	1765.18i	−0.137038	−	0.237357i
$382$	−1734.69			−0.232342
$383$	5417.99	+	9384.24i	0.722837	+	1.25199i	0.959858	+	0.280486i	$0.0904955\pi$
$383$	5417.99	+	9384.24i	0.722837	+	1.25199i	−0.237021	+	0.971504i	$0.576171\pi$
$384$	−1733.39	−	3002.32i	−0.230356	−	0.398988i
$385$	−660.813			−0.0874757
$386$	−1692.78	−	2931.97i	−0.223213	−	0.386616i
$387$	2941.73	−	5095.22i	0.386399	−	0.669263i
$388$	−419.501	+	726.597i	−0.0548890	+	0.0950705i
$389$	−9520.34			−1.24088			−0.620438	−	0.784256i	$-0.713045\pi$
$389$	−9520.34			−1.24088			−0.620438	+	0.784256i	$0.713045\pi$
$390$		0			0
$391$	−1871.56			−0.242069
$392$	152.240	−	263.687i	0.0196155	−	0.0339750i
$393$	3788.57	−	6561.99i	0.486280	−	0.842261i
$394$	−1623.21	−	2811.49i	−0.207554	−	0.359494i
$395$	236.716			0.0301531
$396$	625.009	+	1082.55i	0.0793129	+	0.137374i
$397$	−5054.42	−	8754.51i	−0.638978	−	1.10674i	−0.985657	−	0.168758i	$-0.946024\pi$
$397$	−5054.42	−	8754.51i	−0.638978	−	1.10674i	0.346680	−	0.937983i	$-0.387309\pi$
$398$	−6138.10			−0.773053
$399$	−3615.71	−	6262.59i	−0.453664	−	0.785768i
$400$	−3143.51	+	5444.71i	−0.392938	+	0.680589i
$401$	1042.19	−	1805.12i	0.129787	−	0.224797i	−0.793807	−	0.608169i	$-0.791904\pi$
$401$	1042.19	−	1805.12i	0.129787	−	0.224797i	0.923594	+	0.383373i	$0.125237\pi$
$402$	4193.32			0.520258
$403$		0			0
$404$	−1325.88			−0.163279
$405$	−52.3329	+	90.6432i	−0.00642084	+	0.0111212i
$406$	−4095.30	+	7093.27i	−0.500607	+	0.867076i
$407$	−3716.25	−	6436.73i	−0.452599	−	0.783924i
$408$	2275.78			0.276147
$409$	−4858.26	−	8414.76i	−0.587349	−	1.01732i	−0.994578	−	0.103992i	$-0.966838\pi$
$409$	−4858.26	−	8414.76i	−0.587349	−	1.01732i	0.407229	−	0.913326i	$-0.366495\pi$
$410$	−50.0909	−	86.7600i	−0.00603369	−	0.0104507i
$411$	−6663.95			−0.799777
$412$	−669.390	−	1159.42i	−0.0800449	−	0.138642i
$413$	−651.035	+	1127.63i	−0.0775674	+	0.134351i
$414$	−1259.53	+	2181.56i	−0.149523	+	0.258981i
$415$	339.064			0.0401060
$416$		0			0
$417$	−5503.54			−0.646305
$418$	−8952.38	+	15506.0i	−1.04755	+	1.81441i
$419$	−6690.94	+	11589.1i	−0.780129	+	1.35122i	0.151737	+	0.988421i	$0.451513\pi$
$419$	−6690.94	+	11589.1i	−0.780129	+	1.35122i	−0.931866	+	0.362802i	$0.881820\pi$
$420$	−27.0505	−	46.8529i	−0.00314269	−	0.00544330i
$421$	9463.37			1.09553			0.547763	−	0.836633i	$-0.315479\pi$
$421$	9463.37			1.09553			0.547763	+	0.836633i	$0.315479\pi$
$422$	−117.260	−	203.100i	−0.0135264	−	0.0234284i
$423$	214.423	+	371.391i	0.0246468	+	0.0426895i
$424$	68.8221			0.00788278
$425$	−1592.62	−	2758.50i	−0.181773	−	0.314840i
$426$	−2556.49	+	4427.97i	−0.290757	+	0.503606i
$427$	−8367.77	+	14493.4i	−0.948349	+	1.64259i
$428$	−1233.30			−0.139285
$429$		0			0
$430$	630.474			0.0707074
$431$	2426.14	−	4202.20i	0.271144	−	0.469635i	−0.698011	−	0.716087i	$-0.745931\pi$
$431$	2426.14	−	4202.20i	0.271144	−	0.469635i	0.969155	+	0.246452i	$0.0792647\pi$
$432$	3755.17	−	6504.15i	0.418220	−	0.724378i
$433$	4104.00	+	7108.33i	0.455486	+	0.788925i	0.998716	−	0.0506587i	$-0.0161321\pi$
$433$	4104.00	+	7108.33i	0.455486	+	0.788925i	−0.543230	+	0.839584i	$0.682799\pi$
$434$	5265.78			0.582409
$435$	−181.989	−	315.215i	−0.0200591	−	0.0347434i
$436$	−483.213	−	836.949i	−0.0530773	−	0.0919325i
$437$	7910.01			0.865874
$438$	3605.50	+	6244.92i	0.393328	+	0.681264i
$439$	1496.90	−	2592.71i	0.162741	−	0.281875i	−0.773110	−	0.634272i	$-0.781300\pi$
$439$	1496.90	−	2592.71i	0.162741	−	0.281875i	0.935851	+	0.352397i	$0.114633\pi$
$440$	−439.469	+	761.182i	−0.0476156	+	0.0824726i
$441$	169.049			0.0182539
$442$		0			0
$443$	9743.67			1.04500			0.522501	−	0.852639i	$-0.324999\pi$
$443$	9743.67			1.04500			0.522501	+	0.852639i	$0.324999\pi$
$444$	304.251	−	526.979i	0.0325206	−	0.0563273i
$445$	325.668	−	564.073i	0.0346924	−	0.0600890i
$446$	−1582.29	−	2740.61i	−0.167990	−	0.290968i
$447$	−10166.0			−1.07570
$448$	5162.09	+	8941.01i	0.544388	+	0.942908i
$449$	−280.729	−	486.237i	−0.0295065	−	0.0511068i	0.850895	−	0.525336i	$-0.176060\pi$
$449$	−280.729	−	486.237i	−0.0295065	−	0.0511068i	−0.880402	+	0.474229i	$0.842727\pi$
$450$	−4287.22			−0.449114
$451$	2254.39	+	3904.71i	0.235377	+	0.407685i
$452$	461.363	−	799.104i	0.0480104	−	0.0831564i
$453$	1798.77	−	3115.56i	0.186564	−	0.323138i
$454$	8457.38			0.874283
$455$		0			0
$456$	−9618.40			−0.987770
$457$	6879.20	−	11915.1i	0.704148	−	1.21962i	−0.262851	−	0.964837i	$-0.584663\pi$
$457$	6879.20	−	11915.1i	0.704148	−	1.21962i	0.966998	−	0.254783i	$-0.0820040\pi$
$458$	−270.606	+	468.704i	−0.0276083	+	0.0478190i
$459$	1902.52	+	3295.26i	0.193468	+	0.335097i
$460$	59.1779			0.00599823
$461$	6004.62	+	10400.3i	0.606644	+	1.05074i	0.991789	+	0.127882i	$0.0408179\pi$
$461$	6004.62	+	10400.3i	0.606644	+	1.05074i	−0.385145	+	0.922856i	$0.625849\pi$
$462$	−5553.39	−	9618.75i	−0.559236	−	0.968625i
$463$	−13635.7			−1.36870			−0.684348	−	0.729156i	$-0.739913\pi$
$463$	−13635.7			−1.36870			−0.684348	+	0.729156i	$0.739913\pi$
$464$	4434.96	+	7681.57i	0.443724	+	0.768552i
$465$	−117.002	+	202.653i	−0.0116685	+	0.0202104i
$466$	−328.806	+	569.509i	−0.0326860	+	0.0566138i
$467$	8821.95			0.874157			0.437079	−	0.899423i	$-0.356013\pi$
$467$	8821.95			0.874157			0.437079	+	0.899423i	$0.356013\pi$
$468$		0			0
$469$	−8075.72			−0.795100
$470$	−22.9777	+	39.7985i	−0.00225507	+	0.00390589i
$471$	−1040.69	+	1802.52i	−0.101809	+	0.176339i
$472$	865.933	+	1499.84i	0.0844445	+	0.146262i
$473$	−28375.1			−2.75832
$474$	1989.33	+	3445.62i	0.192770	+	0.333888i
$475$	6731.08	+	11658.6i	0.650196	+	1.12617i
$476$	−667.956			−0.0643187
$477$	19.1053	+	33.0913i	0.00183390	+	0.00317641i
$478$	4546.27	−	7874.37i	0.435024	−	0.753484i
$479$	−7310.02	+	12661.3i	−0.697293	+	1.20775i	0.272109	+	0.962267i	$0.412279\pi$
$479$	−7310.02	+	12661.3i	−0.697293	+	1.20775i	−0.969402	+	0.245480i	$0.921054\pi$
$480$	−132.951			−0.0126424
$481$		0			0
$482$	−12884.9			−1.21761
$483$	−2453.39	+	4249.39i	−0.231124	+	0.400319i
$484$	2057.04	−	3562.91i	0.193186	−	0.334608i
$485$	−163.768	−	283.655i	−0.0153326	−	0.0265569i
$486$	8542.20			0.797288
$487$	−4899.43	−	8486.06i	−0.455882	−	0.789610i	0.542857	−	0.839825i	$-0.317343\pi$
$487$	−4899.43	−	8486.06i	−0.455882	−	0.789610i	−0.998738	+	0.0502150i	$0.984009\pi$
$488$	11129.9	+	19277.5i	1.03243	+	1.78822i
$489$	5558.43			0.514030
$490$	9.05771	+	15.6884i	0.000835072	+	0.00144639i
$491$	5418.03	−	9384.31i	0.497989	−	0.862542i	−0.502009	−	0.864863i	$-0.667405\pi$
$491$	5418.03	−	9384.31i	0.497989	−	0.862542i	0.999997	+	0.00232091i	$0.000738769\pi$
$492$	−184.568	+	319.681i	−0.0169125	+	0.0292934i
$493$	−4493.84			−0.410532
$494$		0			0
$495$	−487.993			−0.0443104
$496$	2851.26	−	4938.52i	0.258115	−	0.447069i
$497$	4923.43	−	8527.63i	0.444358	−	0.769651i
$498$	2849.45	+	4935.40i	0.256400	+	0.444098i
$499$	−2589.96			−0.232349			−0.116175	−	0.993229i	$-0.537063\pi$
$499$	−2589.96			−0.232349			−0.116175	+	0.993229i	$0.537063\pi$
$500$	100.843	+	174.665i	0.00901969	+	0.0156226i
$501$	−1091.62	−	1890.74i	−0.0973451	−	0.168607i
$502$	1841.20			0.163699
$503$	8533.73	+	14780.9i	0.756462	+	1.31023i	0.944644	+	0.328096i	$0.106407\pi$
$503$	8533.73	+	14780.9i	0.756462	+	1.31023i	−0.188183	+	0.982134i	$0.560260\pi$
$504$	−2949.56	+	5108.79i	−0.260682	+	0.451515i
$505$	258.803	−	448.260i	0.0228051	−	0.0394996i
$506$	12149.0			1.06737
$507$		0			0
$508$	795.712			0.0694961
$509$	−506.447	+	877.192i	−0.0441019	+	0.0763867i	−0.887234	−	0.461320i	$-0.847376\pi$
$509$	−506.447	+	877.192i	−0.0441019	+	0.0763867i	0.843132	+	0.537707i	$0.180709\pi$
$510$	−67.7003	+	117.260i	−0.00587808	+	0.0101811i
$511$	−6943.68	−	12026.8i	−0.601116	−	1.04116i
$512$	12992.6			1.12148
$513$	−8040.83	−	13927.1i	−0.692030	−	1.19863i
$514$	1640.41	+	2841.28i	0.140769	+	0.243820i
$515$	522.644			0.0447193
$516$	−1161.54	−	2011.85i	−0.0990969	−	0.171641i
$517$	1034.13	−	1791.17i	0.0879711	−	0.152370i
$518$	2672.81	−	4629.45i	0.226712	−	0.392676i
$519$	16564.6			1.40098
$520$		0			0
$521$	−14367.7			−1.20818			−0.604089	−	0.796917i	$-0.706463\pi$
$521$	−14367.7			−1.20818			−0.604089	+	0.796917i	$0.706463\pi$
$522$	−3024.27	+	5238.19i	−0.253580	+	0.439213i
$523$	8109.96	−	14046.9i	0.678057	−	1.17443i	−0.297509	−	0.954719i	$-0.596156\pi$
$523$	8109.96	−	14046.9i	0.678057	−	1.17443i	0.975565	−	0.219709i	$-0.0705109\pi$
$524$	1479.01	+	2561.72i	0.123303	+	0.213568i
$525$	−8350.92			−0.694217
$526$	6692.76	+	11592.2i	0.554787	+	0.960919i
$527$	1444.56	+	2502.05i	0.119404	+	0.206814i
$528$	−12028.0			−0.991382
$529$	3399.89	+	5888.78i	0.279435	+	0.483996i
$530$	−2.04733	+	3.54608i	−0.000167793	+	0.000290626i
$531$	−480.772	+	832.722i	−0.0392914	+	0.0680547i
$532$	2823.06			0.230066
$533$		0			0
$534$	10947.5			0.887161
$535$	240.733	−	416.961i	0.0194538	−	0.0336950i
$536$	−5370.70	+	9302.32i	−0.432796	+	0.749625i
$537$	−284.244	−	492.325i	−0.0228418	−	0.0395631i
$538$	−16506.1			−1.32273
$539$	−407.650	−	706.071i	−0.0325765	−	0.0564242i
$540$	−60.1566	−	104.194i	−0.00479394	−	0.00830335i
$541$	−17592.2			−1.39806			−0.699029	−	0.715094i	$-0.746384\pi$
$541$	−17592.2			−1.39806			−0.699029	+	0.715094i	$0.746384\pi$
$542$	5033.36	+	8718.04i	0.398896	+	0.690908i
$543$	1973.77	−	3418.67i	0.155990	−	0.270183i
$544$	−820.738	+	1421.56i	−0.0646854	+	0.112038i
$545$	377.281			0.0296531
$546$		0			0
$547$	10504.6			0.821103			0.410552	−	0.911837i	$-0.365336\pi$
$547$	10504.6			0.821103			0.410552	+	0.911837i	$0.365336\pi$
$548$	1300.76	−	2252.99i	0.101398	−	0.175626i
$549$	−6179.38	+	10703.0i	−0.480382	+	0.832045i
$550$	10338.3	+	17906.5i	0.801504	+	1.38825i
$551$	18992.8			1.46846
$552$	3263.22	+	5652.06i	0.251616	+	0.435811i
$553$	−3831.16	−	6635.77i	−0.294607	−	0.510274i
$554$	15073.2			1.15596
$555$	118.776	+	205.726i	0.00908426	+	0.0157344i
$556$	1074.26	−	1860.67i	0.0819401	−	0.141924i
$557$	−253.779	+	439.558i	−0.0193051	+	0.0334375i	−0.875517	−	0.483188i	$-0.839479\pi$
$557$	−253.779	+	439.558i	−0.0193051	+	0.0334375i	0.856211	+	0.516626i	$0.172812\pi$
$558$	3888.64			0.295016
$559$		0			0
$560$	−514.690			−0.0388386
$561$	3046.92	−	5277.41i	0.229306	−	0.397170i
$562$	−4520.87	+	7830.38i	−0.339327	+	0.587731i
$563$	1721.57	+	2981.85i	0.128873	+	0.223215i	0.923240	−	0.384223i	$-0.125531\pi$
$563$	1721.57	+	2981.85i	0.128873	+	0.223215i	−0.794367	+	0.607438i	$0.792197\pi$
$564$	169.330			0.0126420
$565$	180.111	+	311.961i	0.0134112	+	0.0232288i
$566$	−3344.11	−	5792.16i	−0.248345	−	0.430146i
$567$	3387.96			0.250936
$568$	−6548.59	−	11342.5i	−0.483755	−	0.837888i
$569$	−11986.1	+	20760.5i	−0.883098	+	1.52957i	−0.0352188	+	0.999380i	$0.511213\pi$
$569$	−11986.1	+	20760.5i	−0.883098	+	1.52957i	−0.847879	+	0.530190i	$0.822121\pi$
$570$	286.130	−	495.591i	0.0210257	−	0.0364176i
$571$	−7458.32			−0.546622			−0.273311	−	0.961926i	$-0.588119\pi$
$571$	−7458.32			−0.546622			−0.273311	+	0.961926i	$0.588119\pi$
$572$		0			0
$573$	−2495.26			−0.181922
$574$	−1621.41	+	2808.36i	−0.117903	+	0.204214i
$575$	4567.28	−	7910.77i	0.331250	−	0.573742i
$576$	3812.07	+	6602.70i	0.275757	+	0.477626i
$577$	−5669.57			−0.409059			−0.204530	−	0.978860i	$-0.565566\pi$
$577$	−5669.57			−0.409059			−0.204530	+	0.978860i	$0.565566\pi$
$578$	−5456.60	−	9451.10i	−0.392672	−	0.680128i
$579$	−2434.97	−	4217.49i	−0.174774	−	0.302717i
$580$	142.093			0.0101726
$581$	−5487.64	−	9504.87i	−0.391851	−	0.678706i
$582$	2752.58	−	4767.60i	0.196045	−	0.339559i
$583$	92.1420	−	159.595i	0.00654568	−	0.0113375i
$584$	−18471.4			−1.30882
$585$		0			0
$586$	−14065.6			−0.991541
$587$	508.696	−	881.087i	0.0357685	−	0.0619529i	−0.847587	−	0.530657i	$-0.821945\pi$
$587$	508.696	−	881.087i	0.0357685	−	0.0619529i	0.883355	+	0.468704i	$0.155279\pi$
$588$	33.3746	−	57.8064i	0.00234072	−	0.00405425i
$589$	−6105.30	−	10574.7i	−0.427104	−	0.739766i
$590$	−103.040			−0.00718996
$591$	−2334.91	−	4044.18i	−0.162513	−	0.281481i
$592$	−2894.49	−	5013.41i	−0.200951	−	0.348057i
$593$	10198.2			0.706221			0.353111	−	0.935582i	$-0.385124\pi$
$593$	10198.2			0.706221			0.353111	+	0.935582i	$0.385124\pi$
$594$	−12350.0	−	21390.8i	−0.853073	−	1.47757i
$595$	130.381	−	225.827i	0.00898336	−	0.0155596i
$596$	1984.35	−	3437.00i	0.136380	−	0.236216i
$597$	−8829.33			−0.605294
$598$		0			0
$599$	12516.3			0.853763			0.426881	−	0.904308i	$-0.359612\pi$
$599$	12516.3			0.853763			0.426881	+	0.904308i	$0.359612\pi$
$600$	−5553.72	+	9619.33i	−0.377883	+	0.654512i
$601$	−4813.73	+	8337.63i	−0.326716	+	0.565888i	−0.981858	−	0.189617i	$-0.939275\pi$
$601$	−4813.73	+	8337.63i	−0.326716	+	0.565888i	0.655142	+	0.755505i	$0.272609\pi$
$602$	−10204.0	−	17673.9i	−0.690838	−	1.19657i
$603$	−5963.70			−0.402754
$604$	702.218	+	1216.28i	0.0473060	+	0.0819364i
$605$	803.046	+	1390.92i	0.0539644	+	0.0934691i
$606$	8699.80			0.583177
$607$	−3333.60	−	5773.96i	−0.222910	−	0.386092i	0.732780	−	0.680466i	$-0.238222\pi$
$607$	−3333.60	−	5773.96i	−0.222910	−	0.386092i	−0.955690	+	0.294373i	$0.904889\pi$
$608$	3468.78	−	6008.11i	0.231378	−	0.400758i
$609$	−5890.87	+	10203.3i	−0.391971	+	0.678913i
$610$	−1324.37			−0.0879053
$611$		0			0
$612$	−493.268			−0.0325803
$613$	−11542.7	+	19992.5i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$613$	−11542.7	+	19992.5i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$614$	9359.39	−	16210.9i	0.615170	−	1.06551i
$615$	−72.0532	−	124.800i	−0.00472433	−	0.00818278i
$616$	28450.6			1.86089
$617$	1524.62	+	2640.72i	0.0994796	+	0.172304i	0.911469	−	0.411368i	$-0.134949\pi$
$617$	1524.62	+	2640.72i	0.0994796	+	0.172304i	−0.811990	+	0.583672i	$0.801616\pi$
$618$	4392.24	+	7607.58i	0.285893	+	0.495181i
$619$	−7296.58			−0.473787			−0.236894	−	0.971536i	$-0.576129\pi$
$619$	−7296.58			−0.473787			−0.236894	+	0.971536i	$0.576129\pi$
$620$	−45.6761	−	79.1134i	−0.00295871	−	0.00512463i
$621$	−5455.99	+	9450.06i	−0.352563	+	0.610657i
$622$	10124.4	−	17536.0i	0.652657	−	1.13044i
$623$	−21083.3			−1.35583
$624$		0			0
$625$	15506.8			0.992438
$626$	12810.8	−	22189.0i	0.817929	−	1.41670i
$627$	−12877.5	+	22304.5i	−0.820222	+	1.42067i
$628$	−406.271	−	703.683i	−0.0258153	−	0.0447134i
$629$	2932.92			0.185920
$630$	−175.488	−	303.954i	−0.0110978	−	0.0192219i
$631$	−11914.8	−	20637.0i	−0.751694	−	1.30197i	−0.947001	−	0.321230i	$-0.895904\pi$
$631$	−11914.8	−	20637.0i	−0.751694	−	1.30197i	0.195307	−	0.980742i	$-0.437430\pi$
$632$	−10191.6			−0.641453
$633$	−168.672	−	292.149i	−0.0105910	−	0.0183442i
$634$	7980.27	−	13822.2i	0.499901	−	0.865853i
$635$	−155.318	+	269.019i	−0.00970648	+	0.0168121i
$636$	15.0874			0.000940653
$637$		0			0
$638$	29171.3			1.81019
$639$	3635.82	−	6297.43i	0.225088	−	0.389863i
$640$	−264.174	+	457.562i	−0.0163162	+	0.0282605i
$641$	−6702.63	−	11609.3i	−0.413008	−	0.715351i	0.582209	−	0.813039i	$-0.302188\pi$
$641$	−6702.63	−	11609.3i	−0.413008	−	0.715351i	−0.995217	+	0.0976883i	$0.968855\pi$
$642$	8092.36			0.497477
$643$	2625.76	+	4547.94i	0.161042	+	0.278932i	0.935243	−	0.354008i	$-0.115181\pi$
$643$	2625.76	+	4547.94i	0.161042	+	0.278932i	−0.774201	+	0.632940i	$0.781848\pi$
$644$	−957.774	−	1658.91i	−0.0586049	−	0.101507i
$645$	906.904			0.0553633
$646$	−3532.68	−	6118.79i	−0.215157	−	0.372663i
$647$	−10805.7	+	18716.1i	−0.656595	+	1.13726i	0.324897	+	0.945749i	$0.394670\pi$
$647$	−10805.7	+	18716.1i	−0.656595	+	1.13726i	−0.981492	+	0.191506i	$0.938663\pi$
$648$	2253.14	−	3902.55i	0.136592	−	0.236584i
$649$	4637.39			0.280483
$650$		0			0
$651$	7574.54			0.456021
$652$	−1084.97	+	1879.23i	−0.0651699	+	0.112878i
$653$	10797.9	−	18702.6i	0.647099	−	1.12081i	−0.336714	−	0.941607i	$-0.609316\pi$
$653$	10797.9	−	18702.6i	0.647099	−	1.12081i	0.983813	−	0.179201i	$-0.0573512\pi$
$654$	3170.63	+	5491.68i	0.189574	+	0.328351i
$655$	−1154.78			−0.0688869
$656$	1755.89	+	3041.28i	0.104506	+	0.181009i
$657$	−5127.72	−	8881.48i	−0.304492	−	0.527396i
$658$	1487.54			0.0881314
$659$	8321.30	+	14412.9i	0.491884	+	0.851968i	0.999956	−	0.00934609i	$-0.00297500\pi$
$659$	8321.30	+	14412.9i	0.491884	+	0.851968i	−0.508072	+	0.861315i	$0.669642\pi$
$660$	−96.3419	+	166.869i	−0.00568198	+	0.00984147i
$661$	13490.6	−	23366.3i	0.793831	−	1.37495i	−0.129748	−	0.991547i	$-0.541417\pi$
$661$	13490.6	−	23366.3i	0.793831	−	1.37495i	0.923579	−	0.383408i	$-0.125250\pi$
$662$	−11871.5			−0.696980
$663$		0			0
$664$	−14598.1			−0.853185
$665$	−551.044	+	954.437i	−0.0321332	+	0.0556564i
$666$	1973.80	−	3418.73i	0.114840	−	0.198908i
$667$	−6443.67	−	11160.8i	−0.374063	−	0.647896i
$668$	852.310			0.0493665
$669$	−2276.05	−	3942.23i	−0.131535	−	0.227826i
$670$	−319.537	−	553.454i	−0.0184251	−	0.0319131i
$671$	59604.5			3.42922
$672$	2151.77	+	3726.98i	0.123521	+	0.213945i
$673$	−5574.62	+	9655.53i	−0.319296	+	0.553036i	−0.980341	−	0.197309i	$-0.936780\pi$
$673$	−5574.62	+	9655.53i	−0.319296	+	0.553036i	0.661046	+	0.750346i	$0.270113\pi$
$674$	3880.52	−	6721.26i	0.221769	−	0.384115i
$675$	−18571.3			−1.05898
$676$		0			0
$677$	3314.33			0.188154			0.0940769	−	0.995565i	$-0.470010\pi$
$677$	3314.33			0.188154			0.0940769	+	0.995565i	$0.470010\pi$
$678$	−3027.26	+	5243.36i	−0.171477	+	0.297006i
$679$	−5301.06	+	9181.71i	−0.299611	+	0.518942i
$680$	−173.418	−	300.369i	−0.00977982	−	0.0169391i
$681$	12165.5			0.684556
$682$	−9377.17	−	16241.7i	−0.526496	−	0.911918i
$683$	12252.6	+	21222.2i	0.686433	+	1.18894i	0.972984	+	0.230872i	$0.0741577\pi$
$683$	12252.6	+	21222.2i	0.686433	+	1.18894i	−0.286552	+	0.958065i	$0.592509\pi$
$684$	2084.75			0.116539
$685$	507.803	+	879.540i	0.0283243	+	0.0490591i
$686$	8278.50	−	14338.8i	0.460750	−	0.798042i
$687$	−389.253	+	674.206i	−0.0216171	+	0.0374419i
$688$	−22100.6			−1.22468
$689$		0			0
$690$	−388.299			−0.0214236
$691$	−10876.4	+	18838.5i	−0.598782	+	1.03712i	0.394219	+	0.919017i	$0.371015\pi$
$691$	−10876.4	+	18838.5i	−0.598782	+	1.03712i	−0.993001	+	0.118105i	$0.962318\pi$
$692$	−3233.32	+	5600.27i	−0.177619	+	0.307645i
$693$	7897.99	+	13679.7i	0.432929	+	0.749855i
$694$	−7278.90			−0.398132
$695$	419.378	+	726.383i	0.0228891	+	0.0396450i
$696$	7835.37	+	13571.3i	0.426722	+	0.739105i
$697$	−1779.20			−0.0966887
$698$	−9689.94	−	16783.5i	−0.525458	−	0.910120i
$699$	−472.971	+	819.209i	−0.0255928	+	0.0443281i
$700$	1630.05	−	2823.33i	0.0880145	−	0.152446i
$701$	34250.9			1.84542			0.922709	−	0.385496i	$-0.125970\pi$
$701$	34250.9			1.84542			0.922709	+	0.385496i	$0.125970\pi$
$702$		0			0
$703$	−12395.8			−0.665028
$704$	18385.1	−	31843.9i	0.984252	−	1.70477i
$705$	−33.0522	+	57.2480i	−0.00176570	+	0.00305828i
$706$	2996.30	+	5189.74i	0.159727	+	0.276655i
$707$	−16754.6			−0.891259
$708$	189.833	+	328.800i	0.0100768	+	0.0174535i
$709$	−2763.56	−	4786.62i	−0.146386	−	0.253548i	0.783503	−	0.621388i	$-0.213431\pi$
$709$	−2763.56	−	4786.62i	−0.146386	−	0.253548i	−0.929889	+	0.367840i	$0.880097\pi$
$710$	779.234			0.0411889
$711$	−2829.21	−	4900.34i	−0.149232	−	0.258477i
$712$	−14021.3	+	24285.6i	−0.738020	+	1.27829i
$713$	−4142.67	+	7175.31i	−0.217593	+	0.376883i
$714$	4382.83			0.229724
$715$		0			0
$716$	221.931			0.0115837
$717$	6539.57	−	11326.9i	0.340620	−	0.589972i
$718$	3242.51	−	5616.19i	0.168537	−	0.291914i
$719$	1888.89	+	3271.65i	0.0979745	+	0.169697i	0.910846	−	0.412746i	$-0.135430\pi$
$719$	1888.89	+	3271.65i	0.0979745	+	0.169697i	−0.812872	+	0.582443i	$0.802097\pi$
$720$	−380.085			−0.0196735
$721$	−8458.81	−	14651.1i	−0.436925	−	0.756776i
$722$	6145.75	+	10644.7i	0.316788	+	0.548693i
$723$	−18534.2			−0.953380
$724$	770.538	+	1334.61i	0.0395536	+	0.0685088i
$725$	10966.6	−	18994.7i	0.561777	−	0.973027i
$726$	−13497.4	+	23378.2i	−0.689994	+	1.19510i
$727$	19076.8			0.973204			0.486602	−	0.873624i	$-0.338236\pi$
$727$	19076.8			0.973204			0.486602	+	0.873624i	$0.338236\pi$
$728$		0			0
$729$	17319.9			0.879944
$730$	549.490	−	951.744i	0.0278596	−	0.0482543i
$731$	5598.52	−	9696.92i	0.283268	−	0.490634i
$732$	2439.93	+	4226.08i	0.123200	+	0.213388i
$733$	−7997.30			−0.402984			−0.201492	−	0.979490i	$-0.564579\pi$
$733$	−7997.30			−0.402984			−0.201492	+	0.979490i	$0.564579\pi$
$734$	8424.71	+	14592.0i	0.423653	+	0.733789i
$735$	13.0290	+	22.5669i	0.000653855	+	0.00113251i
$736$	−4707.39			−0.235756
$737$	14381.0	+	24908.7i	0.718769	+	1.24494i
$738$	−1197.37	+	2073.90i	−0.0597232	+	0.103444i
$739$	14491.8	−	25100.6i	0.721367	−	1.24944i	−0.239086	−	0.970998i	$-0.576848\pi$
$739$	14491.8	−	25100.6i	0.721367	−	1.24944i	0.960452	−	0.278445i	$-0.0898190\pi$
$740$	−92.7376			−0.00460689
$741$		0			0
$742$	132.541			0.00655761
$743$	−9572.69	+	16580.4i	−0.472662	+	0.818674i	−0.999511	−	0.0312847i	$-0.990040\pi$
$743$	−9572.69	+	16580.4i	−0.472662	+	0.818674i	0.526849	+	0.849959i	$0.323373\pi$
$744$	5037.40	−	8725.02i	0.248226	−	0.429939i
$745$	774.667	+	1341.76i	0.0380961	+	0.0659844i
$746$	−7435.47			−0.364922
$747$	−4052.47	−	7019.09i	−0.198490	−	0.343795i
$748$	1189.48	+	2060.24i	0.0581440	+	0.100708i
$749$	−15584.7			−0.760284
$750$	−661.688	−	1146.08i	−0.0322152	−	0.0557984i
$751$	12758.4	−	22098.3i	0.619923	−	1.07374i	−0.369576	−	0.929200i	$-0.620497\pi$
$751$	12758.4	−	22098.3i	0.619923	−	1.07374i	0.989499	−	0.144538i	$-0.0461695\pi$
$752$	805.459	−	1395.10i	0.0390586	−	0.0676515i
$753$	2648.47			0.128175
$754$		0			0
$755$	−548.275			−0.0264288
$756$	−1947.23	+	3372.70i	−0.0936773	+	0.162254i
$757$	8615.31	−	14922.2i	0.413645	−	0.716453i	−0.581641	−	0.813446i	$-0.697589\pi$
$757$	8615.31	−	14922.2i	0.413645	−	0.716453i	0.995285	+	0.0969925i	$0.0309223\pi$
$758$	2389.59	+	4138.89i	0.114504	+	0.198326i
$759$	17475.7			0.835744
$760$	732.936	+	1269.48i	0.0349821	+	0.0605908i
$761$	−1171.53	−	2029.15i	−0.0558053	−	0.0966576i	0.836773	−	0.547550i	$-0.184439\pi$
$761$	−1171.53	−	2029.15i	−0.0558053	−	0.0966576i	−0.892579	+	0.450892i	$0.851106\pi$
$762$	−5221.11			−0.248216
$763$	−6106.17	−	10576.2i	−0.289722	−	0.501814i
$764$	487.060	−	843.613i	0.0230644	−	0.0399488i
$765$	96.2829	−	166.767i	0.00455048	−	0.00788166i
$766$	27756.9			1.30927
$767$		0			0
$768$	7862.11			0.369400
$769$	−3550.09	+	6148.93i	−0.166475	+	0.288344i	−0.937178	−	0.348851i	$-0.886572\pi$
$769$	−3550.09	+	6148.93i	−0.166475	+	0.288344i	0.770703	+	0.637195i	$0.219905\pi$
$770$	−846.353	+	1465.93i	−0.0396110	+	0.0686082i
$771$	2359.65	+	4087.03i	0.110221	+	0.190909i
$772$	1901.17			0.0886328
$773$	6135.22	+	10626.5i	0.285470	+	0.494449i	0.972723	−	0.231969i	$-0.0745169\pi$
$773$	6135.22	+	10626.5i	0.285470	+	0.494449i	−0.687253	+	0.726418i	$0.741184\pi$
$774$	−7535.39	−	13051.7i	−0.349941	−	0.606115i
$775$	−14100.9			−0.653575
$776$	7050.87	+	12212.5i	0.326175	+	0.564951i
$777$	3844.70	−	6659.22i	0.177513	−	0.307462i
$778$	−12193.4	+	21119.6i	−0.561897	+	0.973233i
$779$	7519.64			0.345852
$780$		0			0
$781$	−35070.1			−1.60680
$782$	−2397.06	+	4151.82i	−0.109614	+	0.189858i
$783$	−13100.5	+	22690.7i	−0.597922	+	1.03563i
$784$	−317.509	−	549.941i	−0.0144638	−	0.0250520i
$785$	317.207			0.0144224
$786$	−9704.61	−	16808.9i	−0.440397	−	0.762790i
$787$	1712.52	+	2966.17i	0.0775663	+	0.134349i	0.902199	−	0.431319i	$-0.141952\pi$
$787$	1712.52	+	2966.17i	0.0775663	+	0.134349i	−0.824633	+	0.565668i	$0.808618\pi$
$788$	1823.04			0.0824151
$789$	9627.17	+	16674.8i	0.434394	+	0.752392i
$790$	303.180	−	525.123i	0.0136540	−	0.0236494i
$791$	5830.06	−	10098.0i	0.262064	−	0.453909i
$792$	21010.0			0.942624
$793$		0			0
$794$	−25894.3			−1.15737
$795$	−2.94498	+	5.10085i	−0.000131381	+	0.000227558i
$796$	1723.43	−	2985.07i	0.0767405	−	0.132918i
$797$	5890.57	+	10202.8i	0.261800	+	0.453451i	0.966720	−	0.255836i	$-0.0823506\pi$
$797$	5890.57	+	10202.8i	0.261800	+	0.453451i	−0.704920	+	0.709286i	$0.749017\pi$
$798$	−18523.6			−0.821717
$799$	408.077	+	706.810i	0.0180685	+	0.0312955i
$800$	−4005.79	−	6938.23i	−0.177033	−	0.306629i
$801$	−15569.4			−0.686790
$802$	−2669.62	−	4623.92i	−0.117541	−	0.203586i
$803$	−24730.3	+	42834.1i	−1.08682	+	1.88242i
$804$	−1177.38	+	2039.29i	−0.0516457	+	0.0894530i
$805$	747.807			0.0327413
$806$		0			0
$807$	−23743.2			−1.03569
$808$	−11142.5	+	19299.4i	−0.485138	+	0.840284i
$809$	−9455.06	+	16376.7i	−0.410905	+	0.711709i	−0.994989	−	0.0999847i	$-0.968121\pi$
$809$	−9455.06	+	16376.7i	−0.410905	+	0.711709i	0.584084	+	0.811693i	$0.301454\pi$
$810$	134.053	+	232.187i	0.00581501	+	0.0100719i
$811$	−12803.3			−0.554359			−0.277180	−	0.960818i	$-0.589400\pi$
$811$	−12803.3			−0.554359			−0.277180	+	0.960818i	$0.589400\pi$
$812$	−2299.73	−	3983.24i	−0.0993899	−	0.172148i
$813$	7240.23	+	12540.4i	0.312332	+	0.540975i
$814$	−19038.7			−0.819788
$815$	−423.560	−	733.628i	−0.0182045	−	0.0315311i
$816$	2373.17	−	4110.44i	0.101811	−	0.176341i
$817$	−23661.7	+	40983.2i	−1.01324	+	1.75498i
$818$	−24889.4			−1.06386
$819$		0			0
$820$	56.2574			0.00239585
$821$	9667.54	−	16744.7i	0.410962	−	0.711806i	−0.584033	−	0.811730i	$-0.698526\pi$
$821$	9667.54	−	16744.7i	0.410962	−	0.711806i	0.994995	+	0.0999231i	$0.0318597\pi$
$822$	−8535.03	+	14783.1i	−0.362157	+	0.627275i
$823$	1062.95	+	1841.09i	0.0450209	+	0.0779784i	0.887658	−	0.460504i	$-0.152331\pi$
$823$	1062.95	+	1841.09i	0.0450209	+	0.0779784i	−0.842637	+	0.538482i	$0.818998\pi$
$824$	−22501.9			−0.951324
$825$	14871.1	+	25757.5i	0.627571	+	1.08698i
$826$	1667.66	+	2888.47i	0.0702486	+	0.121674i
$827$	6989.24			0.293881			0.146941	−	0.989145i	$-0.453057\pi$
$827$	6989.24			0.293881			0.146941	+	0.989145i	$0.453057\pi$
$828$	−707.291	−	1225.06i	−0.0296861	−	0.0514178i
$829$	16324.8	−	28275.4i	0.683938	−	1.18462i	−0.289831	−	0.957078i	$-0.593599\pi$
$829$	16324.8	−	28275.4i	0.683938	−	1.18462i	0.973769	−	0.227538i	$-0.0730676\pi$
$830$	434.265	−	752.170i	0.0181609	−	0.0314556i
$831$	21682.0			0.905103
$832$		0			0
$833$	321.724			0.0133819
$834$	−7048.80	+	12208.9i	−0.292662	+	0.506905i
$835$	−166.366	+	288.154i	−0.00689500	+	0.0119425i
$836$	−5027.24	−	8707.43i	−0.207979	−	0.360231i
$837$	16844.7			0.695626
$838$	17139.2	+	29686.0i	0.706520	+	1.22373i
$839$	−2019.12	−	3497.21i	−0.0830841	−	0.143906i	0.821489	−	0.570224i	$-0.193144\pi$
$839$	−2019.12	−	3497.21i	−0.0830841	−	0.143906i	−0.904573	+	0.426318i	$0.859810\pi$
$840$	−909.318			−0.0373505
$841$	−3277.50	−	5676.80i	−0.134384	−	0.232761i
$842$	12120.5	−	20993.3i	0.496079	−	0.859235i
$843$	−6503.04	+	11263.6i	−0.265690	+	0.460188i
$844$	131.695			0.00537102
$845$		0			0
$846$	1098.51			0.0446426
$847$	25994.1	−	45023.0i	1.05451	−	1.82646i
$848$	71.7671	−	124.304i	0.00290624	−	0.00503376i
$849$	−4810.32	−	8331.72i	−0.194452	−	0.336801i
$850$	−8159.17			−0.329244
$851$	4205.49	+	7284.12i	0.169403	+	0.293415i
$852$	−1435.61	−	2486.54i	−0.0577265	−	0.0999853i
$853$	−8114.12			−0.325700			−0.162850	−	0.986651i	$-0.552069\pi$
$853$	−8114.12			−0.325700			−0.162850	+	0.986651i	$0.552069\pi$
$854$	21434.5	+	37125.6i	0.858868	+	1.48760i
$855$	−406.932	+	704.826i	−0.0162769	+	0.0281925i
$856$	−10364.5	+	17951.8i	−0.413845	+	0.716801i
$857$	−22298.1			−0.888786			−0.444393	−	0.895832i	$-0.646581\pi$
$857$	−22298.1			−0.888786			−0.444393	+	0.895832i	$0.646581\pi$
$858$		0			0
$859$	33550.5			1.33263			0.666315	−	0.745670i	$-0.267870\pi$
$859$	33550.5			1.33263			0.666315	+	0.745670i	$0.267870\pi$
$860$	−177.022	+	306.612i	−0.00701908	+	0.0121574i
$861$	−2332.31	+	4039.68i	−0.0923170	+	0.159898i
$862$	−6214.69	−	10764.2i	−0.245560	−	0.425323i
$863$	14120.5			0.556972			0.278486	−	0.960440i	$-0.410167\pi$
$863$	14120.5			0.556972			0.278486	+	0.960440i	$0.410167\pi$
$864$	4785.24	+	8288.28i	0.188423	+	0.326358i
$865$	−1262.25	−	2186.28i	−0.0496159	−	0.0859373i
$866$	21025.2			0.825018
$867$	−7849.03	−	13594.9i	−0.307459	−	0.532534i
$868$	−1478.51	+	2560.85i	−0.0578154	+	0.100139i
$869$	−13644.9	+	23633.6i	−0.532648	+	0.922574i
$870$	−932.351			−0.0363329
$871$		0			0
$872$	−16243.4			−0.630817
$873$	−3914.69	+	6780.45i	−0.151767	+	0.262868i
$874$	10131.0	−	17547.3i	0.392088	−	0.679116i
$875$	1274.31	+	2207.18i	0.0492339	+	0.0852757i
$876$	−4049.36			−0.156182
$877$	−970.844	−	1681.55i	−0.0373809	−	0.0647457i	0.846730	−	0.532023i	$-0.178568\pi$
$877$	−970.844	−	1681.55i	−0.0373809	−	0.0647457i	−0.884111	+	0.467278i	$0.845235\pi$
$878$	−3834.39	−	6641.36i	−0.147385	−	0.255279i
$879$	−20232.6			−0.776368
$880$	916.548	+	1587.51i	0.0351100	+	0.0608124i
$881$	395.116	−	684.360i	0.0151099	−	0.0261710i	−0.858372	−	0.513028i	$-0.828524\pi$
$881$	395.116	−	684.360i	0.0151099	−	0.0261710i	0.873481	+	0.486857i	$0.161857\pi$
$882$	216.514	−	375.014i	0.00826578	−	0.0143167i
$883$	−36638.6			−1.39636			−0.698180	−	0.715922i	$-0.746007\pi$
$883$	−36638.6			−1.39636			−0.698180	+	0.715922i	$0.746007\pi$
$884$		0			0
$885$	−148.217			−0.00562968
$886$	12479.5	−	21615.1i	0.473201	−	0.819607i
$887$	20343.2	−	35235.4i	0.770075	−	1.33381i	−0.167447	−	0.985881i	$-0.553552\pi$
$887$	20343.2	−	35235.4i	0.770075	−	1.33381i	0.937522	−	0.347927i	$-0.113114\pi$
$888$	−5113.78	−	8857.33i	−0.193252	−	0.334721i
$889$	10055.1			0.379344
$890$	−834.215	−	1444.90i	−0.0314190	−	0.0544194i
$891$	−6033.20	−	10449.8i	−0.226846	−	0.392909i
$892$	1777.08			0.0667053
$893$	−1724.70	−	2987.27i	−0.0646304	−	0.111943i
$894$	−13020.4	+	22552.0i	−0.487101	+	0.843684i
$895$	−43.3196	+	75.0317i	−0.00161789	+	0.00280227i
$896$	17102.2			0.637663
$897$		0			0
$898$	−1438.21			−0.0534449
$899$	−9947.02	+	17228.8i	−0.369023	+	0.639167i
$900$	1203.75	−	2084.95i	0.0445833	−	0.0772205i
$901$	36.3600	+	62.9773i	0.00134442	+	0.00232861i
$902$	11549.5			0.426336
$903$	−14677.9	−	25422.9i	−0.540920	−	0.936901i
$904$	−7754.48	−	13431.2i	−0.285299	−	0.494152i
$905$	−601.618			−0.0220977
$906$	−4607.64	−	7980.66i	−0.168961	−	0.292649i
$907$	5232.22	−	9062.46i	0.191547	−	0.331769i	−0.754216	−	0.656626i	$-0.771983\pi$
$907$	5232.22	−	9062.46i	0.191547	−	0.331769i	0.945763	+	0.324857i	$0.105316\pi$
$908$	−2374.63	+	4112.98i	−0.0867896	+	0.150324i
$909$	−12372.8			−0.451463
$910$		0			0
$911$	−35611.5			−1.29513			−0.647563	−	0.762011i	$-0.724212\pi$
$911$	−35611.5			−1.29513			−0.647563	+	0.762011i	$0.724212\pi$
$912$	−10030.0	+	17372.4i	−0.364173	+	0.630767i
$913$	−19544.5	+	33852.1i	−0.708465	+	1.22710i
$914$	−17621.4	−	30521.2i	−0.637708	−	1.10454i
$915$	−1905.04			−0.0688291
$916$	−151.960	−	263.202i	−0.00548133	−	0.00949393i
$917$	18689.7	+	32371.5i	0.673051	+	1.16576i
$918$	9746.80			0.350427
$919$	−538.627	−	932.930i	−0.0193337	−	0.0334870i	0.856197	−	0.516650i	$-0.172821\pi$
$919$	−538.627	−	932.930i	−0.0193337	−	0.0334870i	−0.875530	+	0.483163i	$0.839488\pi$
$920$	497.324	−	861.391i	0.0178221	−	0.0308687i
$921$	13463.0	−	23318.6i	0.481673	−	0.834282i
$922$	30762.3			1.09881
$923$		0			0
$924$	6237.04			0.222060
$925$	−7157.38	+	12397.0i	−0.254414	+	0.440659i
$926$	−17464.3	+	30249.1i	−0.619777	+	1.07348i
$927$	−6246.61	−	10819.4i	−0.221322	−	0.383341i
$928$	−11303.0			−0.399826
$929$	27866.9	+	48266.9i	0.984159	+	1.70461i	0.645617	+	0.763661i	$0.276600\pi$
$929$	27866.9	+	48266.9i	0.984159	+	1.70461i	0.338542	+	0.940951i	$0.390066\pi$
$930$	299.706	+	519.107i	0.0105675	+	0.0183034i
$931$	−1359.74			−0.0478665
$932$	−184.642	−	319.810i	−0.00648944	−	0.0112400i
$933$	14563.5	−	25224.7i	0.511025	−	0.885121i
$934$	11299.0	−	19570.4i	0.395838	−	0.685612i
$935$	−928.718			−0.0324838
$936$		0			0
$937$	−3198.60			−0.111519			−0.0557596	−	0.998444i	$-0.517758\pi$
$937$	−3198.60			−0.111519			−0.0557596	+	0.998444i	$0.517758\pi$
$938$	−10343.2	+	17914.9i	−0.360040	+	0.623607i
$939$	18427.7	−	31917.7i	0.640432	−	1.10926i
$940$	−12.9032	−	22.3490i	−0.000447718	−	0.000775471i
$941$	−8823.35			−0.305667			−0.152834	−	0.988252i	$-0.548840\pi$
$941$	−8823.35			−0.305667			−0.152834	+	0.988252i	$0.548840\pi$
$942$	2665.77	+	4617.25i	0.0922033	+	0.159701i
$943$	−2551.17	−	4418.76i	−0.0880993	−	0.152593i
$944$	3611.95			0.124533
$945$	−760.175	−	1316.66i	−0.0261677	−	0.0453238i
$946$	−36342.1	+	62946.4i	−1.24903	+	2.16339i
$947$	14145.2	−	24500.2i	0.485383	−	0.840708i	−0.514476	−	0.857505i	$-0.672013\pi$
$947$	14145.2	−	24500.2i	0.485383	−	0.840708i	0.999859	+	0.0167965i	$0.00534675\pi$
$948$	−2234.23			−0.0765447
$949$		0			0
$950$	34484.0			1.17769
$951$	11479.2	−	19882.6i	0.391418	−	0.677956i
$952$	−5613.42	+	9722.73i	−0.191105	+	0.331004i
$953$	6199.52	+	10737.9i	0.210726	+	0.364988i	0.951942	−	0.306278i	$-0.0990838\pi$
$953$	6199.52	+	10737.9i	0.210726	+	0.364988i	−0.741216	+	0.671267i	$0.765750\pi$
$954$	97.8783			0.00332173
$955$	190.143	+	329.337i	0.00644280	+	0.0111592i
$956$	2552.97	+	4421.88i	0.0863693	+	0.149596i
$957$	41961.3			1.41736
$958$	18725.0	+	32432.7i	0.631500	+	1.09379i
$959$	16437.2	−	28470.1i	0.553478	−	0.958653i
$960$	−587.610	+	1017.77i	−0.0197553	+	0.0342171i
$961$	−17001.0			−0.570676
$962$		0			0
$963$	−11508.9			−0.385118
$964$	3617.77	−	6266.15i	0.120872	−	0.209356i
$965$	−371.097	+	642.758i	−0.0123793	+	0.0214416i
$966$	6284.49	+	10885.0i	0.209317	+	0.362547i
$967$	26667.1			0.886820			0.443410	−	0.896319i	$-0.353769\pi$
$967$	26667.1			0.886820			0.443410	+	0.896319i	$0.353769\pi$
$968$	−34574.3	−	59884.5i	−1.14800	−	1.98839i
$969$	−5081.58	−	8801.55i	−0.168466	−	0.291792i
$970$	−839.001			−0.0277719
$971$	−24710.3	−	42799.6i	−0.816676	−	1.41453i	−0.908118	−	0.418715i	$-0.862481\pi$
$971$	−24710.3	−	42799.6i	−0.816676	−	1.41453i	0.0914414	−	0.995810i	$-0.470853\pi$
$972$	−2398.45	+	4154.23i	−0.0791463	+	0.137085i
$973$	13575.0	−	23512.5i	0.447270	−	0.774694i
$974$	−25100.3			−0.825735
$975$		0			0
$976$	46424.5			1.52255
$977$	389.380	−	674.425i	0.0127506	−	0.0220847i	−0.859580	−	0.511002i	$-0.829275\pi$
$977$	389.380	−	674.425i	0.0127506	−	0.0220847i	0.872330	+	0.488917i	$0.162608\pi$
$978$	7119.10	−	12330.6i	0.232765	−	0.403160i
$979$	37544.6	+	65029.2i	1.22567	+	2.12292i
$980$	−10.1728			−0.000331589
$981$	−4509.24	−	7810.23i	−0.146757	−	0.254191i
$982$	−13878.6	−	24038.4i	−0.451001	−	0.781157i
$983$	−5997.90			−0.194612			−0.0973059	−	0.995255i	$-0.531023\pi$
$983$	−5997.90			−0.194612			−0.0973059	+	0.995255i	$0.531023\pi$
$984$	3102.17	+	5373.12i	0.100502	+	0.174074i
$985$	−355.847	+	616.344i	−0.0115109	+	0.0199374i
$986$	−5755.61	+	9969.01i	−0.185898	+	0.321986i
$987$	2139.75			0.0690062
$988$		0			0
$989$	32110.6			1.03241
$990$	−625.009	+	1082.55i	−0.0200647	+	0.0347532i
$991$	−4487.47	+	7772.53i	−0.143844	+	0.249145i	−0.928941	−	0.370228i	$-0.879280\pi$
$991$	−4487.47	+	7772.53i	−0.143844	+	0.249145i	0.785097	+	0.619373i	$0.212613\pi$
$992$	3633.37	+	6293.19i	0.116290	+	0.201420i
$993$	−17076.6			−0.545729
$994$	−12611.6	−	21844.0i	−0.402431	−	0.697031i
$995$	672.808	+	1165.34i	0.0214366	+	0.0371293i
$996$	−3200.24			−0.101811
$997$	−14265.1	−	24707.9i	−0.453140	−	0.784861i	0.545439	−	0.838150i	$-0.316363\pi$
$997$	−14265.1	−	24707.9i	−0.453140	−	0.784861i	−0.998579	+	0.0532892i	$0.983029\pi$
$998$	−3317.16	+	5745.48i	−0.105213	+	0.182234i
$999$	8550.08	−	14809.2i	0.270783	−	0.469011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.j.22.2		4
13.2	odd	12		169.4.e.f.23.4		8
13.3	even	3	inner	169.4.c.j.146.2		4
13.4	even	6		13.4.a.b.1.2	✓	2
13.5	odd	4		169.4.e.f.147.1		8
13.6	odd	12		169.4.b.f.168.4		4
13.7	odd	12		169.4.b.f.168.1		4
13.8	odd	4		169.4.e.f.147.4		8
13.9	even	3		169.4.a.g.1.1		2
13.10	even	6		169.4.c.g.146.1		4
13.11	odd	12		169.4.e.f.23.1		8
13.12	even	2		169.4.c.g.22.1		4
39.17	odd	6		117.4.a.d.1.1		2
39.35	odd	6		1521.4.a.r.1.2		2
52.43	odd	6		208.4.a.h.1.2		2
65.4	even	6		325.4.a.f.1.1		2
65.17	odd	12		325.4.b.e.274.4		4
65.43	odd	12		325.4.b.e.274.1		4
91.69	odd	6		637.4.a.b.1.2		2
104.43	odd	6		832.4.a.z.1.1		2
104.69	even	6		832.4.a.s.1.2		2
143.43	odd	6		1573.4.a.b.1.1		2
156.95	even	6		1872.4.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.b.1.2	✓	2	13.4	even	6
117.4.a.d.1.1		2	39.17	odd	6
169.4.a.g.1.1		2	13.9	even	3
169.4.b.f.168.1		4	13.7	odd	12
169.4.b.f.168.4		4	13.6	odd	12
169.4.c.g.22.1		4	13.12	even	2
169.4.c.g.146.1		4	13.10	even	6
169.4.c.j.22.2		4	1.1	even	1	trivial
169.4.c.j.146.2		4	13.3	even	3	inner
169.4.e.f.23.1		8	13.11	odd	12
169.4.e.f.23.4		8	13.2	odd	12
169.4.e.f.147.1		8	13.5	odd	4
169.4.e.f.147.4		8	13.8	odd	4
208.4.a.h.1.2		2	52.43	odd	6
325.4.a.f.1.1		2	65.4	even	6
325.4.b.e.274.1		4	65.43	odd	12
325.4.b.e.274.4		4	65.17	odd	12
637.4.a.b.1.2		2	91.69	odd	6
832.4.a.s.1.2		2	104.69	even	6
832.4.a.z.1.1		2	104.43	odd	6
1521.4.a.r.1.2		2	39.35	odd	6
1573.4.a.b.1.1		2	143.43	odd	6
1872.4.a.bb.1.1		2	156.95	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.28078 - 2.21837i) q^{2} +(1.84233 - 3.19101i) q^{3} +(0.719224 + 1.24573i) q^{4} -0.561553 q^{5} +(-4.71922 - 8.17394i) q^{6} +(9.08854 + 15.7418i) q^{7} +24.1771 q^{8} +(6.71165 + 11.6249i) q^{9} +O(q^{10})\)	\(q+(1.28078 - 2.21837i) q^{2} +(1.84233 - 3.19101i) q^{3} +(0.719224 + 1.24573i) q^{4} -0.561553 q^{5} +(-4.71922 - 8.17394i) q^{6} +(9.08854 + 15.7418i) q^{7} +24.1771 q^{8} +(6.71165 + 11.6249i) q^{9} +(-0.719224 + 1.24573i) q^{10} +(32.3693 - 56.0653i) q^{11} +5.30019 q^{12} +46.5616 q^{14} +(-1.03457 + 1.79192i) q^{15} +(25.2116 - 43.6679i) q^{16} +(12.7732 + 22.1238i) q^{17} +34.3845 q^{18} +(-53.9848 - 93.5045i) q^{19} +(-0.403882 - 0.699544i) q^{20} +66.9763 q^{21} +(-82.9157 - 143.614i) q^{22} +(-36.6307 + 63.4462i) q^{23} +(44.5421 - 77.1493i) q^{24} -124.685 q^{25} +148.946 q^{27} +(-13.0734 + 22.6438i) q^{28} +(-87.9545 + 152.342i) q^{29} +(2.65009 + 4.59010i) q^{30} +113.093 q^{31} +(32.1274 + 55.6462i) q^{32} +(-119.270 - 206.581i) q^{33} +65.4384 q^{34} +(-5.10370 - 8.83986i) q^{35} +(-9.65435 + 16.7218i) q^{36} +(57.4039 - 99.4264i) q^{37} -276.570 q^{38} -13.5767 q^{40} +(-34.8229 + 60.3151i) q^{41} +(85.7817 - 148.578i) q^{42} +(-219.151 - 379.581i) q^{43} +93.1231 q^{44} +(-3.76894 - 6.52800i) q^{45} +(93.8314 + 162.521i) q^{46} +31.9479 q^{47} +(-92.8963 - 160.901i) q^{48} +(6.29686 - 10.9065i) q^{49} +(-159.693 + 276.597i) q^{50} +94.1298 q^{51} +2.84658 q^{53} +(190.767 - 330.417i) q^{54} +(-18.1771 + 31.4836i) q^{55} +(219.734 + 380.591i) q^{56} -397.831 q^{57} +(225.300 + 390.231i) q^{58} +(35.8163 + 62.0356i) q^{59} -2.97633 q^{60} +(460.348 + 797.345i) q^{61} +(144.847 - 250.882i) q^{62} +(-121.998 + 211.307i) q^{63} +567.978 q^{64} -611.032 q^{66} +(-222.140 + 384.758i) q^{67} +(-18.3736 + 31.8240i) q^{68} +(134.972 + 233.778i) q^{69} -26.1468 q^{70} +(-270.859 - 469.142i) q^{71} +(162.268 + 281.056i) q^{72} -764.004 q^{73} +(-147.043 - 254.686i) q^{74} +(-229.710 + 397.870i) q^{75} +(77.6543 - 134.501i) q^{76} +1176.76 q^{77} -421.538 q^{79} +(-14.1577 + 24.5218i) q^{80} +(93.1932 - 161.415i) q^{81} +(89.2007 + 154.500i) q^{82} -603.797 q^{83} +(48.1710 + 83.4346i) q^{84} +(-7.17283 - 12.4237i) q^{85} -1122.73 q^{86} +(324.082 + 561.327i) q^{87} +(782.596 - 1355.50i) q^{88} +(-579.941 + 1004.49i) q^{89} -19.3087 q^{90} -105.383 q^{92} +(208.354 - 360.880i) q^{93} +(40.9181 - 70.8722i) q^{94} +(30.3153 + 52.5077i) q^{95} +236.757 q^{96} +(291.634 + 505.126i) q^{97} +(-16.1298 - 27.9375i) q^{98} +869.006 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9}+O(q^{10}) \) 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9	\( 4 q + q^{2} - 5 q^{3} + 7 q^{4} + 6 q^{5} - 23 q^{6} - 9 q^{7} + 6 q^{8} - 35 q^{9} - 7 q^{10} + 80 q^{11} - 86 q^{12} + 178 q^{14} - 33 q^{15} + 39 q^{16} - 19 q^{17} + 220 q^{18} - 84 q^{19} + 19 q^{20} + 606 q^{21} - 142 q^{22} - 196 q^{23} + 273 q^{24} - 474 q^{25} + 670 q^{27} + 125 q^{28} + 44 q^{29} - 43 q^{30} + 172 q^{31} - 123 q^{32} - 106 q^{33} + 270 q^{34} - 107 q^{35} + 250 q^{36} + 209 q^{37} - 628 q^{38} - 178 q^{40} - 230 q^{41} - 197 q^{42} - 287 q^{43} + 356 q^{44} - 180 q^{45} - 4 q^{46} - 870 q^{47} - 285 q^{48} - 383 q^{49} - 144 q^{50} + 962 q^{51} - 236 q^{53} + 91 q^{54} + 18 q^{55} + 1015 q^{56} - 1212 q^{57} + 794 q^{58} - 368 q^{59} - 350 q^{60} + 1058 q^{61} + 332 q^{62} - 1560 q^{63} + 1538 q^{64} - 1636 q^{66} + 68 q^{67} + 211 q^{68} - 796 q^{69} + 250 q^{70} - 131 q^{71} + 1350 q^{72} - 912 q^{73} - 147 q^{74} + 516 q^{75} + 22 q^{76} + 1524 q^{77} - 2016 q^{79} - 69 q^{80} - 122 q^{81} - 72 q^{82} - 3916 q^{83} + 1409 q^{84} - 173 q^{85} - 2718 q^{86} + 2558 q^{87} + 1242 q^{88} - 720 q^{89} + 500 q^{90} - 1576 q^{92} + 652 q^{93} + 811 q^{94} + 146 q^{95} + 3726 q^{96} - 928 q^{97} - 650 q^{98} + 260 q^{99}+O(q^{100}) \) 4 * q + q^2 - 5 * q^3 + 7 * q^4 + 6 * q^5 - 23 * q^6 - 9 * q^7 + 6 * q^8 - 35 * q^9 - 7 * q^10 + 80 * q^11 - 86 * q^12 + 178 * q^14 - 33 * q^15 + 39 * q^16 - 19 * q^17 + 220 * q^18 - 84 * q^19 + 19 * q^20 + 606 * q^21 - 142 * q^22 - 196 * q^23 + 273 * q^24 - 474 * q^25 + 670 * q^27 + 125 * q^28 + 44 * q^29 - 43 * q^30 + 172 * q^31 - 123 * q^32 - 106 * q^33 + 270 * q^34 - 107 * q^35 + 250 * q^36 + 209 * q^37 - 628 * q^38 - 178 * q^40 - 230 * q^41 - 197 * q^42 - 287 * q^43 + 356 * q^44 - 180 * q^45 - 4 * q^46 - 870 * q^47 - 285 * q^48 - 383 * q^49 - 144 * q^50 + 962 * q^51 - 236 * q^53 + 91 * q^54 + 18 * q^55 + 1015 * q^56 - 1212 * q^57 + 794 * q^58 - 368 * q^59 - 350 * q^60 + 1058 * q^61 + 332 * q^62 - 1560 * q^63 + 1538 * q^64 - 1636 * q^66 + 68 * q^67 + 211 * q^68 - 796 * q^69 + 250 * q^70 - 131 * q^71 + 1350 * q^72 - 912 * q^73 - 147 * q^74 + 516 * q^75 + 22 * q^76 + 1524 * q^77 - 2016 * q^79 - 69 * q^80 - 122 * q^81 - 72 * q^82 - 3916 * q^83 + 1409 * q^84 - 173 * q^85 - 2718 * q^86 + 2558 * q^87 + 1242 * q^88 - 720 * q^89 + 500 * q^90 - 1576 * q^92 + 652 * q^93 + 811 * q^94 + 146 * q^95 + 3726 * q^96 - 928 * q^97 - 650 * q^98 + 260 * q^99

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