LMFDB - Embedded newform 169.4.c.g.146.1

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			146.1
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	169.146
Dual form			169.4.c.g.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28078 - 2.21837i) q^{2} +(1.84233 + 3.19101i) q^{3} +(0.719224 - 1.24573i) q^{4} +0.561553 q^{5} +(4.71922 - 8.17394i) q^{6} +(-9.08854 + 15.7418i) q^{7} -24.1771 q^{8} +(6.71165 - 11.6249i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.28078	−	2.21837i	−0.452823	−	0.784312i	0.545737	−	0.837956i	$-0.316250\pi$
$2$	−1.28078	−	2.21837i	−0.452823	−	0.784312i	−0.998560	+	0.0536442i	$0.982916\pi$
$3$	1.84233	+	3.19101i	0.354556	+	0.614110i	0.987042	−	0.160462i	$-0.0512985\pi$
$3$	1.84233	+	3.19101i	0.354556	+	0.614110i	−0.632486	+	0.774572i	$0.717965\pi$
$4$	0.719224	−	1.24573i	0.0899029	−	0.155716i
$5$	0.561553			0.0502268			0.0251134	−	0.999685i	$-0.492005\pi$
$5$	0.561553			0.0502268			0.0251134	+	0.999685i	$0.492005\pi$
$6$	4.71922	−	8.17394i	0.321102	−	0.556166i
$7$	−9.08854	+	15.7418i	−0.490735	+	0.849978i	−0.999943	−	0.0106654i	$-0.996605\pi$
$7$	−9.08854	+	15.7418i	−0.490735	+	0.849978i	0.509208	+	0.860643i	$0.329938\pi$
$8$	−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	−0.843116	−	0.537731i	$-0.819282\pi$
$11$	−32.3693	−	56.0653i	−0.887247	−	1.53676i	−0.0441305	−	0.999026i	$-0.514052\pi$
$12$	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	−0.760408	−	0.649446i	$-0.775001\pi$
$17$	12.7732	−	22.1238i	0.182233	−	0.315636i	0.942641	+	0.333810i	$0.108334\pi$
$18$	−34.3845			−0.450250
$19$	53.9848	−	93.5045i	0.651841	−	1.12902i	−0.330835	−	0.943689i	$-0.607330\pi$
$19$	53.9848	−	93.5045i	0.651841	−	1.12902i	0.982676	−	0.185333i	$-0.0593363\pi$
$20$	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	0.650833	−	0.759221i	$-0.274420\pi$
$23$	−36.6307	−	63.4462i	−0.332088	−	0.575193i	−0.982921	+	0.184027i	$0.941086\pi$
$24$	−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	−0.997215	−	0.0745830i	$-0.976237\pi$
$29$	−87.9545	−	152.342i	−0.563198	−	0.975488i	0.434017	−	0.900905i	$-0.357096\pi$
$30$	2.65009	−	4.59010i	0.0161280	−	0.0279344i
$31$	−113.093			−0.655228			−0.327614	−	0.944812i	$-0.606245\pi$
$31$	−113.093			−0.655228			−0.327614	+	0.944812i	$0.606245\pi$
$32$	−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	$-0.248761\pi$
$37$	−57.4039	−	99.4264i	−0.255058	−	0.441773i	−0.964911	+	0.262576i	$0.915428\pi$
$38$	−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	$-0.124320\pi$
$41$	34.8229	+	60.3151i	0.132645	+	0.229747i	−0.792051	+	0.610455i	$0.790986\pi$
$42$	85.7817	+	148.578i	0.315153	+	0.545860i
$43$	−219.151	+	379.581i	−0.777214	+	1.34617i	0.156327	+	0.987705i	$0.450035\pi$
$43$	−219.151	+	379.581i	−0.777214	+	1.34617i	−0.933541	+	0.358469i	$0.883299\pi$
$44$	−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	$-0.515787\pi$
$47$	−31.9479			−0.0991506			−0.0495753	+	0.998770i	$0.515787\pi$
$48$	−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	$-0.858516\pi$
$59$	−35.8163	+	62.0356i	−0.0790319	+	0.136887i	0.823801	+	0.566880i	$0.191850\pi$
$60$	2.97633			0.00640405
$61$	460.348	−	797.345i	0.966253	−	1.67360i	0.260044	−	0.965597i	$-0.416263\pi$
$61$	460.348	−	797.345i	0.966253	−	1.67360i	0.706209	−	0.708003i	$-0.250404\pi$
$62$	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	$-0.0339188\pi$
$67$	222.140	+	384.758i	0.405056	+	0.701577i	−0.589272	+	0.807935i	$0.700585\pi$
$68$	−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	$-0.683777\pi$
$71$	270.859	−	469.142i	0.452748	−	0.784182i	0.998556	+	0.0537283i	$0.0171105\pi$
$72$	−162.268	+	281.056i	−0.265604	+	0.460039i
$73$	764.004			1.22493			0.612465	−	0.790498i	$-0.290178\pi$
$73$	764.004			1.22493			0.612465	+	0.790498i	$0.290178\pi$
$74$	−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	$-0.369271\pi$
$83$	603.797			0.798498			0.399249	+	0.916842i	$0.369271\pi$
$84$	−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	0.971604	+	0.236613i	$0.0760375\pi$
$89$	579.941	+	1004.49i	0.690715	+	1.19635i	−0.280889	+	0.959740i	$0.590629\pi$
$90$	−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	$-0.932079\pi$
$97$	−291.634	+	505.126i	−0.305268	+	0.528740i	0.672053	+	0.740503i	$0.265413\pi$
$98$	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	0.544590	−	0.838702i	$-0.316685\pi$
$101$	−460.870	−	798.251i	−0.454043	−	0.786425i	−0.998633	+	0.0522775i	$0.983352\pi$
$102$	−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	0.604769	−	0.796401i	$-0.293266\pi$
$107$	−428.691	−	742.515i	−0.387319	−	0.670857i	−0.992088	+	0.125545i	$0.959932\pi$
$108$	107.125	−	185.547i	0.0954459	−	0.165317i
$109$	671.853			0.590384			0.295192	−	0.955438i	$-0.404616\pi$
$109$	671.853			0.590384			0.295192	+	0.955438i	$0.404616\pi$
$110$	−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	−0.968089	−	0.250607i	$-0.919370\pi$
$113$	−320.737	+	555.532i	−0.267012	+	0.462479i	0.701077	+	0.713086i	$0.252703\pi$
$114$	−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	0.946326	−	0.323212i	$-0.104763\pi$
$127$	276.587	+	479.063i	0.193253	+	0.334724i	−0.753073	+	0.657937i	$0.771430\pi$
$128$	−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	−0.433221	−	0.901288i	$-0.642623\pi$
$137$	904.283	−	1566.26i	0.563928	−	0.976752i	0.997149	−	0.0754639i	$-0.0240438\pi$
$138$	−691.474			−0.426537
$139$	−746.818	+	1293.53i	−0.455714	+	0.789320i	−0.998729	−	0.0504032i	$-0.983949\pi$
$139$	−746.818	+	1293.53i	−0.455714	+	0.789320i	0.543015	+	0.839723i	$0.317283\pi$
$140$	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	−0.185143	−	0.982712i	$-0.559275\pi$
$149$	1379.51	−	2389.38i	0.758482	−	1.31373i	0.943625	−	0.331018i	$-0.107392\pi$
$150$	−588.415	+	1019.16i	−0.320292	+	0.554763i
$151$	−976.355			−0.526190			−0.263095	−	0.964770i	$-0.584743\pi$
$151$	−976.355			−0.526190			−0.263095	+	0.964770i	$0.584743\pi$
$152$	−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	$-0.951392\pi$
$163$	−754.266	+	1306.43i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$164$	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	$-0.210502\pi$
$167$	−296.260	−	513.138i	−0.137277	−	0.237771i	−0.926465	+	0.376381i	$0.877168\pi$
$168$	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	0.359262	−	0.933237i	$-0.383028\pi$
$173$	2247.78	−	3893.28i	0.987838	−	1.71099i	0.628576	−	0.777748i	$-0.283638\pi$
$174$	−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	0.881682	−	0.471844i	$-0.156412\pi$
$179$	77.1425	+	133.615i	0.0322117	+	0.0557924i	−0.849470	+	0.527637i	$0.823078\pi$
$180$	−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	−0.923008	−	0.384781i	$-0.874277\pi$
$191$	−338.601	+	586.475i	−0.128274	+	0.222177i	0.794734	+	0.606958i	$0.207610\pi$
$192$	1046.40	+	1812.42i	0.393321	+	0.681252i
$193$	−660.840	−	1144.61i	−0.246468	−	0.426895i	0.716075	−	0.698023i	$-0.245937\pi$
$193$	−660.840	−	1144.61i	−0.246468	−	0.426895i	−0.962543	+	0.271128i	$0.912603\pi$
$194$	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	$-0.240270\pi$
$197$	−633.683	−	1097.57i	−0.229178	−	0.396948i	−0.957565	+	0.288218i	$0.906937\pi$
$198$	1113.00	+	1927.78i	0.399483	+	0.691925i
$199$	−1198.12	+	2075.21i	−0.426796	+	0.739233i	−0.996586	−	0.0825573i	$-0.973691\pi$
$199$	−1198.12	+	2075.21i	−0.426796	+	0.739233i	0.569790	+	0.821790i	$0.307025\pi$
$200$	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	0.873397	−	0.487010i	$-0.161912\pi$
$211$	45.7769	+	79.2880i	0.0149356	+	0.0258692i	−0.858461	+	0.512879i	$0.828579\pi$
$212$	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	$-0.226055\pi$
$223$	−617.709	−	1069.90i	−0.185493	−	0.321282i	−0.943742	+	0.330682i	$0.892721\pi$
$224$	−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	$-0.993672\pi$
$227$	−1650.83	+	2859.32i	−0.482685	+	0.836035i	0.517118	+	0.855914i	$0.327005\pi$
$228$	286.130	−	495.591i	0.0831114	−	0.143953i
$229$	211.283			0.0609694			0.0304847	−	0.999535i	$-0.490295\pi$
$229$	211.283			0.0609694			0.0304847	+	0.999535i	$0.490295\pi$
$230$	−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	$-0.659489\pi$
$239$	−3549.62			−0.960694			−0.480347	+	0.877078i	$0.659489\pi$
$240$	−52.1662	+	90.3545i	−0.0140305	+	0.0243015i
$241$	2515.05	−	4356.19i	0.672235	−	1.16434i	−0.305034	−	0.952341i	$-0.598668\pi$
$241$	2515.05	−	4356.19i	0.672235	−	1.16434i	0.977269	−	0.212003i	$-0.0679987\pi$
$242$	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	−0.817293	−	0.576223i	$-0.804526\pi$
$251$	359.392	−	622.485i	0.0903770	−	0.156538i	0.907670	+	0.419685i	$0.137859\pi$
$252$	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	0.777782	−	0.628534i	$-0.216345\pi$
$257$	−640.397	−	1109.20i	−0.155435	−	0.269222i	−0.933217	+	0.359312i	$0.883011\pi$
$258$	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	−0.990803	−	0.135315i	$-0.956795\pi$
$263$	−2612.77	−	4525.46i	−0.612587	−	1.06103i	0.378215	−	0.925718i	$-0.376538\pi$
$264$	−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	0.226497	+	0.974012i	$0.427273\pi$
$269$	−3221.90	+	5580.50i	−0.730270	+	1.26487i	−0.956768	+	0.290854i	$0.906061\pi$
$270$	−107.125	−	185.547i	−0.0241461	−	0.0418223i
$271$	1964.97	+	3403.42i	0.440455	+	0.762890i	0.997723	−	0.0674426i	$-0.0214839\pi$
$271$	1964.97	+	3403.42i	0.440455	+	0.762890i	−0.557269	+	0.830332i	$0.688151\pi$
$272$	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	−0.347635	−	0.937630i	$-0.613015\pi$
$277$	2942.20	−	5096.04i	0.638194	−	1.10538i	0.985829	−	0.167754i	$-0.0536516\pi$
$278$	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	$-0.377753\pi$
$281$	3529.79			0.749358			0.374679	+	0.927155i	$0.377753\pi$
$282$	−150.769	+	261.140i	−0.0318375	+	0.0551442i
$283$	1305.50	+	2261.19i	0.274219	+	0.474961i	0.969938	−	0.243353i	$-0.0782474\pi$
$283$	1305.50	+	2261.19i	0.274219	+	0.474961i	−0.695719	+	0.718314i	$0.744914\pi$
$284$	−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	−0.451028	−	0.892510i	$-0.648943\pi$
$293$	2745.51	−	4755.37i	0.547422	−	0.948163i	0.998450	−	0.0556531i	$-0.0177241\pi$
$294$	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	$-0.737700\pi$
$307$	−7307.59			−1.35852			−0.679261	+	0.733897i	$0.737700\pi$
$308$	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	$-0.686129\pi$
$317$	−6230.81			−1.10397			−0.551983	+	0.833856i	$0.686129\pi$
$318$	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	$-0.707605\pi$
$331$	2317.25	−	4013.60i	0.384797	−	0.666488i	0.991741	+	0.128257i	$0.0409381\pi$
$332$	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	−0.954748	−	0.297415i	$-0.903876\pi$
$347$	−1420.80	+	2460.90i	−0.219805	+	0.380714i	0.734943	+	0.678129i	$0.237209\pi$
$348$	−466.175	−	807.440i	−0.0718093	−	0.124377i
$349$	−3782.84	−	6552.07i	−0.580202	−	1.00494i	−0.995455	−	0.0952339i	$-0.969640\pi$
$349$	−3782.84	−	6552.07i	−0.580202	−	1.00494i	0.415252	−	0.909706i	$-0.363693\pi$
$350$	−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	$-0.110232\pi$
$353$	1169.72	+	2026.01i	0.176368	+	0.305478i	−0.764266	+	0.644901i	$0.776899\pi$
$354$	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	$-0.559583\pi$
$359$	−2531.68			−0.372192			−0.186096	+	0.982532i	$0.559583\pi$
$360$	−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	0.531531	−	0.847039i	$-0.321617\pi$
$367$	−3288.91	−	5696.55i	−0.467792	−	0.810239i	−0.999323	+	0.0368000i	$0.988284\pi$
$368$	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	−0.949003	−	0.315268i	$-0.897905\pi$
$373$	−1451.36	+	2513.83i	−0.201471	+	0.348958i	0.747532	+	0.664226i	$0.231239\pi$
$374$	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	$-0.126314\pi$
$379$	932.867	+	1615.77i	0.126433	+	0.218989i	−0.795859	+	0.605482i	$0.792980\pi$
$380$	−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	0.237021	+	0.971504i	$0.423829\pi$
$383$	−5417.99	+	9384.24i	−0.722837	+	1.25199i	−0.959858	+	0.280486i	$0.909504\pi$
$384$	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	−0.346680	−	0.937983i	$-0.612691\pi$
$397$	5054.42	−	8754.51i	0.638978	−	1.10674i	0.985657	−	0.168758i	$-0.0539757\pi$
$398$	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	$-0.208096\pi$
$401$	−1042.19	−	1805.12i	−0.129787	−	0.224797i	−0.923594	+	0.383373i	$0.874763\pi$
$402$	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	−0.407229	−	0.913326i	$-0.633505\pi$
$409$	4858.26	−	8414.76i	0.587349	−	1.01732i	0.994578	−	0.103992i	$-0.0331617\pi$
$410$	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	−0.931866	−	0.362802i	$-0.881820\pi$
$419$	−6690.94	−	11589.1i	−0.780129	−	1.35122i	0.151737	−	0.988421i	$-0.451513\pi$
$420$	−27.0505	+	46.8529i	−0.00314269	+	0.00544330i
$421$	−9463.37			−1.09553			−0.547763	−	0.836633i	$-0.684521\pi$
$421$	−9463.37			−1.09553			−0.547763	+	0.836633i	$0.684521\pi$
$422$	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	$-0.254069\pi$
$431$	−2426.14	−	4202.20i	−0.271144	−	0.469635i	−0.969155	+	0.246452i	$0.920735\pi$
$432$	3755.17	+	6504.15i	0.418220	+	0.724378i
$433$	4104.00	−	7108.33i	0.455486	−	0.788925i	−0.543230	−	0.839584i	$-0.682799\pi$
$433$	4104.00	−	7108.33i	0.455486	−	0.788925i	0.998716	+	0.0506587i	$0.0161321\pi$
$434$	−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	0.935851	−	0.352397i	$-0.114633\pi$
$439$	1496.90	+	2592.71i	0.162741	+	0.281875i	−0.773110	+	0.634272i	$0.781300\pi$
$440$	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	$-0.823940\pi$
$449$	280.729	−	486.237i	0.0295065	−	0.0511068i	0.880402	+	0.474229i	$0.157273\pi$
$450$	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	−0.966998	−	0.254783i	$-0.917996\pi$
$457$	−6879.20	−	11915.1i	−0.704148	−	1.21962i	0.262851	−	0.964837i	$-0.415337\pi$
$458$	−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	0.385145	+	0.922856i	$0.374151\pi$
$461$	−6004.62	+	10400.3i	−0.606644	+	1.05074i	−0.991789	+	0.127882i	$0.959182\pi$
$462$	5553.39	−	9618.75i	0.559236	−	0.968625i
$463$	13635.7			1.36870			0.684348	−	0.729156i	$-0.260087\pi$
$463$	13635.7			1.36870			0.684348	+	0.729156i	$0.260087\pi$
$464$	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	0.969402	+	0.245480i	$0.0789456\pi$
$479$	7310.02	+	12661.3i	0.697293	+	1.20775i	−0.272109	+	0.962267i	$0.587721\pi$
$480$	−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	$-0.682657\pi$
$487$	4899.43	−	8486.06i	0.455882	−	0.789610i	0.998738	+	0.0502150i	$0.0159907\pi$
$488$	−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	0.999997	−	0.00232091i	$-0.000738769\pi$
$491$	5418.03	+	9384.31i	0.497989	+	0.862542i	−0.502009	+	0.864863i	$0.667405\pi$
$492$	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	$-0.462937\pi$
$499$	2589.96			0.232349			0.116175	+	0.993229i	$0.462937\pi$
$500$	−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	−0.188183	−	0.982134i	$-0.560260\pi$
$503$	8533.73	−	14780.9i	0.756462	−	1.31023i	0.944644	−	0.328096i	$-0.106407\pi$
$504$	−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	$-0.152624\pi$
$509$	506.447	+	877.192i	0.0441019	+	0.0763867i	−0.843132	+	0.537707i	$0.819291\pi$
$510$	−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	0.975565	+	0.219709i	$0.0705109\pi$
$523$	8109.96	+	14046.9i	0.678057	+	1.17443i	−0.297509	+	0.954719i	$0.596156\pi$
$524$	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	$-0.253616\pi$
$541$	17592.2			1.39806			0.699029	+	0.715094i	$0.253616\pi$
$542$	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	$-0.160521\pi$
$557$	253.779	+	439.558i	0.0193051	+	0.0334375i	−0.856211	+	0.516626i	$0.827188\pi$
$558$	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	−0.794367	−	0.607438i	$-0.792197\pi$
$563$	1721.57	−	2981.85i	0.128873	−	0.223215i	0.923240	+	0.384223i	$0.125531\pi$
$564$	−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	−0.847879	−	0.530190i	$-0.822121\pi$
$569$	−11986.1	−	20760.5i	−0.883098	−	1.52957i	−0.0352188	−	0.999380i	$-0.511213\pi$
$570$	−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	$-0.434434\pi$
$577$	5669.57			0.409059			0.204530	+	0.978860i	$0.434434\pi$
$578$	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	$-0.178055\pi$
$587$	−508.696	−	881.087i	−0.0357685	−	0.0619529i	−0.883355	+	0.468704i	$0.844721\pi$
$588$	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	$-0.614876\pi$
$593$	−10198.2			−0.706221			−0.353111	+	0.935582i	$0.614876\pi$
$594$	−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	0.655142	−	0.755505i	$-0.272609\pi$
$601$	−4813.73	−	8337.63i	−0.326716	−	0.565888i	−0.981858	+	0.189617i	$0.939275\pi$
$602$	−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	−0.955690	−	0.294373i	$-0.904889\pi$
$607$	−3333.60	+	5773.96i	−0.222910	+	0.386092i	0.732780	+	0.680466i	$0.238222\pi$
$608$	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	0.942578	+	0.333987i	$0.108394\pi$
$613$	11542.7	+	19992.5i	0.760530	+	1.31728i	−0.182047	+	0.983290i	$0.558272\pi$
$614$	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	$-0.865051\pi$
$617$	−1524.62	+	2640.72i	−0.0994796	+	0.172304i	0.811990	+	0.583672i	$0.198384\pi$
$618$	−4392.24	+	7607.58i	−0.285893	+	0.495181i
$619$	7296.58			0.473787			0.236894	−	0.971536i	$-0.423871\pi$
$619$	7296.58			0.473787			0.236894	+	0.971536i	$0.423871\pi$
$620$	−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	−0.195307	−	0.980742i	$-0.562570\pi$
$631$	11914.8	−	20637.0i	0.751694	−	1.30197i	0.947001	−	0.321230i	$-0.104096\pi$
$632$	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	−0.995217	−	0.0976883i	$-0.968855\pi$
$641$	−6702.63	+	11609.3i	−0.413008	+	0.715351i	0.582209	+	0.813039i	$0.302188\pi$
$642$	−8092.36			−0.497477
$643$	−2625.76	+	4547.94i	−0.161042	+	0.278932i	−0.935243	−	0.354008i	$-0.884819\pi$
$643$	−2625.76	+	4547.94i	−0.161042	+	0.278932i	0.774201	+	0.632940i	$0.218152\pi$
$644$	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	−0.981492	−	0.191506i	$-0.938663\pi$
$647$	−10805.7	−	18716.1i	−0.656595	−	1.13726i	0.324897	−	0.945749i	$-0.394670\pi$
$648$	−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	0.983813	+	0.179201i	$0.0573512\pi$
$653$	10797.9	+	18702.6i	0.647099	+	1.12081i	−0.336714	+	0.941607i	$0.609316\pi$
$654$	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	−0.508072	−	0.861315i	$-0.669642\pi$
$659$	8321.30	−	14412.9i	0.491884	−	0.851968i	0.999956	+	0.00934609i	$0.00297500\pi$
$660$	−96.3419	−	166.869i	−0.00568198	−	0.00984147i
$661$	−13490.6	−	23366.3i	−0.793831	−	1.37495i	−0.923579	−	0.383408i	$-0.874750\pi$
$661$	−13490.6	−	23366.3i	−0.793831	−	1.37495i	0.129748	−	0.991547i	$-0.458583\pi$
$662$	−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	0.661046	−	0.750346i	$-0.270113\pi$
$673$	−5574.62	−	9655.53i	−0.319296	−	0.553036i	−0.980341	+	0.197309i	$0.936780\pi$
$674$	−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	0.286552	+	0.958065i	$0.407491\pi$
$683$	−12252.6	+	21222.2i	−0.686433	+	1.18894i	−0.972984	+	0.230872i	$0.925842\pi$
$684$	−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	0.993001	+	0.118105i	$0.0376818\pi$
$691$	10876.4	+	18838.5i	0.598782	+	1.03712i	−0.394219	+	0.919017i	$0.628985\pi$
$692$	−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	$-0.786569\pi$
$709$	2763.56	−	4786.62i	0.146386	−	0.253548i	0.929889	+	0.367840i	$0.119903\pi$
$710$	−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	−0.812872	−	0.582443i	$-0.802097\pi$
$719$	1888.89	−	3271.65i	0.0979745	−	0.169697i	0.910846	+	0.412746i	$0.135430\pi$
$720$	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	$-0.435421\pi$
$733$	7997.30			0.402984			0.201492	+	0.979490i	$0.435421\pi$
$734$	−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	−0.960452	−	0.278445i	$-0.910181\pi$
$739$	−14491.8	−	25100.6i	−0.721367	−	1.24944i	0.239086	−	0.970998i	$-0.423152\pi$
$740$	−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	$-0.00995986\pi$
$743$	9572.69	+	16580.4i	0.472662	+	0.818674i	−0.526849	+	0.849959i	$0.676627\pi$
$744$	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	0.989499	+	0.144538i	$0.0461695\pi$
$751$	12758.4	+	22098.3i	0.619923	+	1.07374i	−0.369576	+	0.929200i	$0.620497\pi$
$752$	−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	0.995285	−	0.0969925i	$-0.0309223\pi$
$757$	8615.31	+	14922.2i	0.413645	+	0.716453i	−0.581641	+	0.813446i	$0.697589\pi$
$758$	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	$-0.815561\pi$
$761$	1171.53	−	2029.15i	0.0558053	−	0.0966576i	0.892579	+	0.450892i	$0.148894\pi$
$762$	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	$-0.113428\pi$
$769$	3550.09	+	6148.93i	0.166475	+	0.288344i	−0.770703	+	0.637195i	$0.780095\pi$
$770$

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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