LMFDB - Embedded newform 169.4.e.f.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.1
Root			$-2.21837 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	169.23
Dual form			169.4.e.f.147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21837 + 1.28078i) q^{2} +(1.84233 + 3.19101i) q^{3} +(-0.719224 + 1.24573i) q^{4} -0.561553i q^{5} +(-8.17394 - 4.71922i) q^{6} +(-15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 - 11.6249i) q^{9} +O(q^{10})$	\(q+(-2.21837 + 1.28078i) q^{2} +(1.84233 + 3.19101i) q^{3} +(-0.719224 + 1.24573i) q^{4} -0.561553i q^{5} +(-8.17394 - 4.71922i) q^{6} +(-15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 - 11.6249i) q^{9} +(0.719224 + 1.24573i) q^{10} +(56.0653 - 32.3693i) q^{11} -5.30019 q^{12} +46.5616 q^{14} +(1.79192 - 1.03457i) q^{15} +(25.2116 + 43.6679i) q^{16} +(-12.7732 + 22.1238i) q^{17} +34.3845i q^{18} +(-93.5045 - 53.9848i) q^{19} +(0.699544 + 0.403882i) q^{20} -66.9763i q^{21} +(-82.9157 + 143.614i) q^{22} +(36.6307 + 63.4462i) q^{23} +(77.1493 - 44.5421i) q^{24} +124.685 q^{25} +148.946 q^{27} +(22.6438 - 13.0734i) q^{28} +(-87.9545 - 152.342i) q^{29} +(-2.65009 + 4.59010i) q^{30} +113.093i q^{31} +(55.6462 + 32.1274i) q^{32} +(206.581 + 119.270i) q^{33} -65.4384i q^{34} +(-5.10370 + 8.83986i) q^{35} +(9.65435 + 16.7218i) q^{36} +(99.4264 - 57.4039i) q^{37} +276.570 q^{38} -13.5767 q^{40} +(60.3151 - 34.8229i) q^{41} +(85.7817 + 148.578i) q^{42} +(219.151 - 379.581i) q^{43} +93.1231i q^{44} +(-6.52800 - 3.76894i) q^{45} +(-162.521 - 93.8314i) q^{46} -31.9479i q^{47} +(-92.8963 + 160.901i) q^{48} +(-6.29686 - 10.9065i) q^{49} +(-276.597 + 159.693i) q^{50} -94.1298 q^{51} +2.84658 q^{53} +(-330.417 + 190.767i) q^{54} +(-18.1771 - 31.4836i) q^{55} +(-219.734 + 380.591i) q^{56} -397.831i q^{57} +(390.231 + 225.300i) q^{58} +(-62.0356 - 35.8163i) q^{59} +2.97633i q^{60} +(460.348 - 797.345i) q^{61} +(-144.847 - 250.882i) q^{62} +(-211.307 + 121.998i) q^{63} -567.978 q^{64} -611.032 q^{66} +(384.758 - 222.140i) q^{67} +(-18.3736 - 31.8240i) q^{68} +(-134.972 + 233.778i) q^{69} -26.1468i q^{70} +(-469.142 - 270.859i) q^{71} +(-281.056 - 162.268i) q^{72} +764.004i q^{73} +(-147.043 + 254.686i) q^{74} +(229.710 + 397.870i) q^{75} +(134.501 - 77.6543i) q^{76} -1176.76 q^{77} -421.538 q^{79} +(24.5218 - 14.1577i) q^{80} +(93.1932 + 161.415i) q^{81} +(-89.2007 + 154.500i) q^{82} -603.797i q^{83} +(83.4346 + 48.1710i) q^{84} +(12.4237 + 7.17283i) q^{85} +1122.73i q^{86} +(324.082 - 561.327i) q^{87} +(-782.596 - 1355.50i) q^{88} +(-1004.49 + 579.941i) q^{89} +19.3087 q^{90} -105.383 q^{92} +(-360.880 + 208.354i) q^{93} +(40.9181 + 70.8722i) q^{94} +(-30.3153 + 52.5077i) q^{95} +236.757i q^{96} +(505.126 + 291.634i) q^{97} +(27.9375 + 16.1298i) q^{98} -869.006i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9}+O(q^{10}) $ 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9	$ 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9} + 14 q^{10} + 172 q^{12} + 356 q^{14} + 78 q^{16} + 38 q^{17} - 284 q^{22} + 392 q^{23} + 948 q^{25} + 1340 q^{27} + 88 q^{29} + 86 q^{30} - 214 q^{35} - 500 q^{36} + 1256 q^{38} - 356 q^{40} - 394 q^{42} + 574 q^{43} - 570 q^{48} + 766 q^{49} - 1924 q^{51} - 472 q^{53} + 36 q^{55} - 2030 q^{56} + 2116 q^{61} - 664 q^{62} - 3076 q^{64} - 3272 q^{66} + 422 q^{68} + 1592 q^{69} - 294 q^{74} - 1032 q^{75} - 3048 q^{77} - 4032 q^{79} - 244 q^{81} + 144 q^{82} + 5116 q^{87} - 2484 q^{88} - 1000 q^{90} - 3152 q^{92} + 1622 q^{94} - 292 q^{95}+O(q^{100}) $ 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9 + 14 * q^10 + 172 * q^12 + 356 * q^14 + 78 * q^16 + 38 * q^17 - 284 * q^22 + 392 * q^23 + 948 * q^25 + 1340 * q^27 + 88 * q^29 + 86 * q^30 - 214 * q^35 - 500 * q^36 + 1256 * q^38 - 356 * q^40 - 394 * q^42 + 574 * q^43 - 570 * q^48 + 766 * q^49 - 1924 * q^51 - 472 * q^53 + 36 * q^55 - 2030 * q^56 + 2116 * q^61 - 664 * q^62 - 3076 * q^64 - 3272 * q^66 + 422 * q^68 + 1592 * q^69 - 294 * q^74 - 1032 * q^75 - 3048 * q^77 - 4032 * q^79 - 244 * q^81 + 144 * q^82 + 5116 * q^87 - 2484 * q^88 - 1000 * q^90 - 3152 * q^92 + 1622 * q^94 - 292 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.21837	+	1.28078i	−0.784312	+	0.452823i	−0.837956	−	0.545737i	$-0.816250\pi$
$2$	−2.21837	+	1.28078i	−0.784312	+	0.452823i	0.0536442	+	0.998560i	$0.482916\pi$
$3$	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
$5$		−	0.561553i		−	0.0502268i	−0.999685	−	0.0251134i	$-0.992005\pi$
$5$		−	0.561553i		−	0.0502268i	0.999685	−	0.0251134i	$-0.00799469\pi$
$6$	−8.17394	−	4.71922i	−0.556166	−	0.321102i
$7$	−15.7418	−	9.08854i	−0.849978	−	0.490735i	0.0106654	−	0.999943i	$-0.496605\pi$
$7$	−15.7418	−	9.08854i	−0.849978	−	0.490735i	−0.860643	+	0.509208i	$0.829938\pi$
$8$		−	24.1771i		−	1.06849i
$9$	6.71165	−	11.6249i	0.248579	−	0.430552i
$10$	0.719224	+	1.24573i	0.0227438	+	0.0393935i
$11$	56.0653	−	32.3693i	1.53676	−	0.887247i	0.537731	−	0.843116i	$-0.319282\pi$
$11$	56.0653	−	32.3693i	1.53676	−	0.887247i	0.999026	−	0.0441305i	$-0.0140517\pi$
$12$	−5.30019			−0.127503
$13$		0			0
$13$		0			0
$14$	46.5616			0.888864
$15$	1.79192	−	1.03457i	0.0308448	−	0.0178082i
$16$	25.2116	+	43.6679i	0.393932	+	0.682310i
$17$	−12.7732	+	22.1238i	−0.182233	+	0.315636i	−0.942641	−	0.333810i	$-0.891666\pi$
$17$	−12.7732	+	22.1238i	−0.182233	+	0.315636i	0.760408	+	0.649446i	$0.224999\pi$
$18$			34.3845i			0.450250i
$19$	−93.5045	−	53.9848i	−1.12902	−	0.651841i	−0.185333	−	0.982676i	$-0.559336\pi$
$19$	−93.5045	−	53.9848i	−1.12902	−	0.651841i	−0.943689	+	0.330835i	$0.892670\pi$
$20$	0.699544	+	0.403882i	0.00782114	+	0.00451554i
$21$		−	66.9763i		−	0.695973i
$22$	−82.9157	+	143.614i	−0.803531	+	1.39176i
$23$	36.6307	+	63.4462i	0.332088	+	0.575193i	0.982921	−	0.184027i	$-0.0589135\pi$
$23$	36.6307	+	63.4462i	0.332088	+	0.575193i	−0.650833	+	0.759221i	$0.725580\pi$
$24$	77.1493	−	44.5421i	0.656168	−	0.378839i
$25$	124.685			0.997477
$26$		0			0
$27$	148.946			1.06165
$28$	22.6438	−	13.0734i	0.152831	−	0.0882371i
$29$	−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
$31$			113.093i			0.655228i	0.944812	+	0.327614i	$0.106245\pi$
$31$			113.093i			0.655228i	−0.944812	+	0.327614i	$0.893755\pi$
$32$	55.6462	+	32.1274i	0.307405	+	0.177480i
$33$	206.581	+	119.270i	1.08973	+	0.629158i
$34$		−	65.4384i		−	0.330077i
$35$	−5.10370	+	8.83986i	−0.0246481	+	0.0426917i
$36$	9.65435	+	16.7218i	0.0446961	+	0.0774158i
$37$	99.4264	−	57.4039i	0.441773	−	0.255058i	−0.262576	−	0.964911i	$-0.584572\pi$
$37$	99.4264	−	57.4039i	0.441773	−	0.255058i	0.704349	+	0.709853i	$0.251239\pi$
$38$	276.570			1.18067
$39$		0			0
$40$	−13.5767			−0.0536666
$41$	60.3151	−	34.8229i	0.229747	−	0.132645i	−0.380708	−	0.924695i	$-0.624320\pi$
$41$	60.3151	−	34.8229i	0.229747	−	0.132645i	0.610455	+	0.792051i	$0.290986\pi$
$42$	85.7817	+	148.578i	0.315153	+	0.545860i
$43$	219.151	−	379.581i	0.777214	−	1.34617i	−0.156327	−	0.987705i	$-0.549965\pi$
$43$	219.151	−	379.581i	0.777214	−	1.34617i	0.933541	−	0.358469i	$-0.116701\pi$
$44$			93.1231i			0.319064i
$45$	−6.52800	−	3.76894i	−0.0216253	−	0.0124854i
$46$	−162.521	−	93.8314i	−0.520921	−	0.300754i
$47$		−	31.9479i		−	0.0991506i	−0.998770	−	0.0495753i	$-0.984213\pi$
$47$		−	31.9479i		−	0.0991506i	0.998770	−	0.0495753i	$-0.0157868\pi$
$48$	−92.8963	+	160.901i	−0.279342	+	0.483835i
$49$	−6.29686	−	10.9065i	−0.0183582	−	0.0317973i
$50$	−276.597	+	159.693i	−0.782334	+	0.451680i
$51$	−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	$0.498826\pi$
$54$	−330.417	+	190.767i	−0.832669	+	0.480741i
$55$	−18.1771	−	31.4836i	−0.0445636	−	0.0771864i
$56$	−219.734	+	380.591i	−0.524344	+	0.908190i
$57$		−	397.831i		−	0.924457i
$58$	390.231	+	225.300i	0.883446	+	0.510058i
$59$	−62.0356	−	35.8163i	−0.136887	−	0.0790319i	0.429992	−	0.902832i	$-0.358516\pi$
$59$	−62.0356	−	35.8163i	−0.136887	−	0.0790319i	−0.566880	+	0.823801i	$0.691850\pi$
$60$			2.97633i			0.00640405i
$61$	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
$63$	−211.307	+	121.998i	−0.422574	+	0.243973i
$64$	−567.978			−1.10933
$65$		0			0
$66$	−611.032			−1.13959
$67$	384.758	−	222.140i	0.701577	−	0.405056i	−0.106357	−	0.994328i	$-0.533919\pi$
$67$	384.758	−	222.140i	0.701577	−	0.405056i	0.807935	+	0.589272i	$0.200585\pi$
$68$	−18.3736	−	31.8240i	−0.0327665	−	0.0567533i
$69$	−134.972	+	233.778i	−0.235488	+	0.407877i
$70$		−	26.1468i		−	0.0446448i
$71$	−469.142	−	270.859i	−0.784182	−	0.452748i	0.0537283	−	0.998556i	$-0.482890\pi$
$71$	−469.142	−	270.859i	−0.784182	−	0.452748i	−0.837910	+	0.545808i	$0.816223\pi$
$72$	−281.056	−	162.268i	−0.460039	−	0.265604i
$73$			764.004i			1.22493i	0.790498	+	0.612465i	$0.209822\pi$
$73$			764.004i			1.22493i	−0.790498	+	0.612465i	$0.790178\pi$
$74$	−147.043	+	254.686i	−0.230992	+	0.400090i
$75$	229.710	+	397.870i	0.353662	+	0.612561i
$76$	134.501	−	77.6543i	0.203005	−	0.117205i
$77$	−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	$0.597043\pi$
$80$	24.5218	−	14.1577i	0.0342703	−	0.0197859i
$81$	93.1932	+	161.415i	0.127837	+	0.221420i
$82$	−89.2007	+	154.500i	−0.120129	+	0.208069i
$83$		−	603.797i		−	0.798498i	−0.916842	−	0.399249i	$-0.869271\pi$
$83$		−	603.797i		−	0.798498i	0.916842	−	0.399249i	$-0.130729\pi$
$84$	83.4346	+	48.1710i	0.108374	+	0.0625700i
$85$	12.4237	+	7.17283i	0.0158534	+	0.00915297i
$86$			1122.73i			1.40776i
$87$	324.082	−	561.327i	0.399371	−	0.691731i
$88$	−782.596	−	1355.50i	−0.948011	−	1.64200i
$89$	−1004.49	+	579.941i	−1.19635	+	0.690715i	−0.959740	−	0.280889i	$-0.909371\pi$
$89$	−1004.49	+	579.941i	−1.19635	+	0.690715i	−0.236613	+	0.971604i	$0.576037\pi$
$90$	19.3087			0.0226146
$91$		0			0
$92$	−105.383			−0.119423
$93$	−360.880	+	208.354i	−0.402382	+	0.232315i
$94$	40.9181	+	70.8722i	0.0448977	+	0.0777650i
$95$	−30.3153	+	52.5077i	−0.0327399	+	0.0567071i
$96$			236.757i			0.251707i
$97$	505.126	+	291.634i	0.528740	+	0.305268i	0.740503	−	0.672053i	$-0.234587\pi$
$97$	505.126	+	291.634i	0.528740	+	0.305268i	−0.211763	+	0.977321i	$0.567921\pi$
$98$	27.9375	+	16.1298i	0.0287971	+	0.0166260i
$99$		−	869.006i		−	0.882206i
$100$	−89.6761	+	155.324i	−0.0896761	+	0.155324i
$101$	460.870	+	798.251i	0.454043	+	0.786425i	0.998633	−	0.0522775i	$-0.0166480\pi$
$101$	460.870	+	798.251i	0.454043	+	0.786425i	−0.544590	+	0.838702i	$0.683315\pi$
$102$	208.815	−	120.559i	0.202703	−	0.117031i
$103$	930.712			0.890347			0.445174	−	0.895444i	$-0.353142\pi$
$103$	930.712			0.890347			0.445174	+	0.895444i	$0.353142\pi$
$104$		0			0
$105$	−37.6107			−0.0349565
$106$	−6.31478	+	3.64584i	−0.00578628	+	0.00334071i
$107$	−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
$109$		−	671.853i		−	0.590384i	−0.955438	−	0.295192i	$-0.904616\pi$
$109$		−	671.853i		−	0.590384i	0.955438	−	0.295192i	$-0.0953836\pi$
$110$	80.6470	+	46.5616i	0.0699035	+	0.0403588i
$111$	366.352	+	211.514i	0.313267	+	0.180865i
$112$		−	916.548i		−	0.773265i
$113$	−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
$115$	35.6284	−	20.5701i	0.0288901	−	0.0166797i
$116$	253.036			0.202533
$117$		0			0
$118$	183.491			0.143150
$119$	402.147	−	232.179i	0.309788	−	0.178856i
$120$	−25.0128	−	43.3234i	−0.0190279	−	0.0329572i
$121$	1430.05	−	2476.91i	1.07441	−	1.86094i
$122$			2358.41i			1.75017i
$123$	222.240	+	128.311i	0.162917	+	0.0940599i
$124$	−140.883	−	81.3390i	−0.102030	−	0.0589069i
$125$		−	140.211i		−	0.100327i
$126$	312.505	−	541.274i	0.220953	−	0.382703i
$127$	−276.587	−	479.063i	−0.193253	−	0.334724i	0.753073	−	0.657937i	$-0.228570\pi$
$127$	−276.587	−	479.063i	−0.193253	−	0.334724i	−0.946326	+	0.323212i	$0.895237\pi$
$128$	814.816	−	470.434i	0.562658	−	0.324851i
$129$	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	$0.259471\pi$
$132$	−297.157	+	171.563i	−0.195941	+	0.113126i
$133$	981.287	+	1699.64i	0.639762	+	1.10810i
$134$	−569.024	+	985.578i	−0.366837	+	0.635380i
$135$		−	83.6411i		−	0.0533235i
$136$	534.890	+	308.819i	0.337253	+	0.194713i
$137$	1566.26	+	904.283i	0.976752	+	0.563928i	0.901288	−	0.433221i	$-0.142623\pi$
$137$	1566.26	+	904.283i	0.976752	+	0.563928i	0.0754639	+	0.997149i	$0.475956\pi$
$138$		−	691.474i		−	0.426537i
$139$	−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
$141$	101.946	−	58.8585i	0.0608894	−	0.0351545i
$142$	1387.64			0.820058
$143$		0			0
$144$	676.847			0.391694
$145$	−85.5479	+	49.3911i	−0.0489956	+	0.0282876i
$146$	−978.518	−	1694.84i	−0.554676	−	0.960727i
$147$	23.2018	−	40.1867i	0.0130180	−	0.0225479i
$148$			165.145i			0.0917218i
$149$	−2389.38	−	1379.51i	−1.31373	−	0.758482i	−0.331018	−	0.943625i	$-0.607392\pi$
$149$	−2389.38	−	1379.51i	−1.31373	−	0.758482i	−0.982712	+	0.185143i	$0.940725\pi$
$150$	−1019.16	−	588.415i	−0.554763	−	0.320292i
$151$		−	976.355i		−	0.526190i	−0.964770	−	0.263095i	$-0.915257\pi$
$151$		−	976.355i		−	0.526190i	0.964770	−	0.263095i	$-0.0847432\pi$
$152$	−1305.20	+	2260.67i	−0.696483	+	1.20634i
$153$	171.458	+	296.975i	0.0905986	+	0.156921i
$154$	2610.49	−	1507.17i	1.36597	−	0.788642i
$155$	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	$0.545859\pi$
$158$	935.127	−	539.896i	0.470853	−	0.271847i
$159$	5.24435	+	9.08347i	0.00261575	+	0.00453061i
$160$	18.0412	−	31.2483i	0.00891427	−	0.0154400i
$161$		−	1331.68i		−	0.651869i
$162$	−413.474	−	238.719i	−0.200528	−	0.115775i
$163$	−1306.43	−	754.266i	−0.627775	−	0.362446i	0.152115	−	0.988363i	$-0.451392\pi$
$163$	−1306.43	−	754.266i	−0.627775	−	0.362446i	−0.779890	+	0.625917i	$0.784725\pi$
$164$			100.182i			0.0477005i
$165$	66.9763	−	116.006i	0.0316006	−	0.0547339i
$166$	773.329	+	1339.45i	0.361578	+	0.626272i
$167$	513.138	−	296.260i	0.237771	−	0.137277i	−0.376381	−	0.926465i	$-0.622832\pi$
$167$	513.138	−	296.260i	0.237771	−	0.137277i	0.614152	+	0.789188i	$0.289498\pi$
$168$	−1619.29			−0.743638
$169$		0			0
$170$	−36.7471			−0.0165787
$171$	−1255.14	+	724.654i	−0.561303	+	0.324068i
$172$	315.237	+	546.007i	0.139748	+	0.242050i
$173$	−2247.78	+	3893.28i	−0.987838	+	1.71099i	−0.359262	+	0.933237i	$0.616972\pi$
$173$	−2247.78	+	3893.28i	−0.987838	+	1.71099i	−0.628576	+	0.777748i	$0.716362\pi$
$174$			1660.31i			0.723377i
$175$	−1962.76	−	1133.20i	−0.847834	−	0.489497i
$176$	2827.00	+	1632.17i	1.21076	+	0.699030i
$177$		−	263.941i		−	0.112085i
$178$	1485.55	−	2573.05i	0.625543	−	1.08347i
$179$	−77.1425	−	133.615i	−0.0322117	−	0.0557924i	0.849470	−	0.527637i	$-0.176922\pi$
$179$	−77.1425	−	133.615i	−0.0322117	−	0.0557924i	−0.881682	+	0.471844i	$0.843588\pi$
$180$	9.39019	−	5.42143i	0.00388835	−	0.00224494i
$181$	−1071.35			−0.439959			−0.219979	−	0.975505i	$-0.570599\pi$
$181$	−1071.35			−0.439959			−0.219979	+	0.975505i	$0.570599\pi$
$182$		0			0
$183$	3392.45			1.37037
$184$	1533.94	−	885.623i	0.614586	−	0.354831i
$185$	−32.2353	−	55.8332i	−0.0128107	−	0.0221889i
$186$	533.710	−	924.413i	0.210395	−	0.364415i
$187$			1653.84i			0.646742i
$188$	39.7985	+	22.9777i	0.0154394	+	0.00891393i
$189$	−2344.68	−	1353.70i	−0.902383	−	0.520991i
$190$		−	155.309i		−	0.0593015i
$191$	−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
$193$	1144.61	−	660.840i	0.426895	−	0.246468i	−0.271128	−	0.962543i	$-0.587397\pi$
$193$	1144.61	−	660.840i	0.426895	−	0.246468i	0.698023	+	0.716075i	$0.254063\pi$
$194$	−1494.07			−0.552929
$195$		0			0
$196$	18.1154			0.00660183
$197$	−1097.57	+	633.683i	−0.396948	+	0.229178i	−0.685166	−	0.728387i	$-0.740270\pi$
$197$	−1097.57	+	633.683i	−0.396948	+	0.229178i	0.288218	+	0.957565i	$0.406937\pi$
$198$	1113.00	+	1927.78i	0.399483	+	0.691925i
$199$	1198.12	−	2075.21i	0.426796	−	0.739233i	−0.569790	−	0.821790i	$-0.692975\pi$
$199$	1198.12	−	2075.21i	0.426796	−	0.739233i	0.996586	+	0.0825573i	$0.0263088\pi$
$200$		−	3014.51i		−	1.06579i
$201$	1417.70	+	818.510i	0.497497	+	0.287230i
$202$	−2044.76	−	1180.54i	−0.712222	−	0.411202i
$203$			3197.51i			1.10552i
$204$	67.7003	−	117.260i	0.0232352	−	0.0402445i
$205$	−19.5549	−	33.8701i	−0.00666231	−	0.0115395i
$206$	−2064.66	+	1192.03i	−0.698310	+	0.403170i
$207$	983.409			0.330201
$208$		0			0
$209$	−6989.81			−2.31337
$210$	83.4346	−	48.1710i	0.0274168	−	0.0158291i
$211$	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
$213$		−	1996.05i		−	0.642099i
$214$	1901.99	+	1098.12i	0.607558	+	0.350774i
$215$	−213.155	−	123.065i	−0.0676141	−	0.0390370i
$216$		−	3601.08i		−	1.13436i
$217$	1027.85	−	1780.29i	0.321543	−	0.556929i
$218$	860.494	+	1490.42i	0.267339	+	0.463045i
$219$	−2437.94	+	1407.55i	−0.752241	+	0.434307i
$220$	52.2935			0.0160256
$221$		0			0
$222$	−1083.61			−0.327599
$223$	−1069.90	+	617.709i	−0.321282	+	0.185493i	−0.651964	−	0.758250i	$-0.726055\pi$
$223$	−1069.90	+	617.709i	−0.321282	+	0.185493i	0.330682	+	0.943742i	$0.392721\pi$
$224$	−583.982	−	1011.49i	−0.174192	−	0.301709i
$225$	836.839	−	1449.45i	0.247952	−	0.429466i
$226$		−	1643.17i		−	0.483637i
$227$	2859.32	+	1650.83i	0.836035	+	0.482685i	0.855914	−	0.517118i	$-0.172995\pi$
$227$	2859.32	+	1650.83i	0.836035	+	0.482685i	−0.0198797	+	0.999802i	$0.506328\pi$
$228$	495.591	+	286.130i	0.143953	+	0.0831114i
$229$			211.283i			0.0609694i	0.999535	+	0.0304847i	$0.00970508\pi$
$229$			211.283i			0.0609694i	−0.999535	+	0.0304847i	$0.990295\pi$
$230$	−52.6913	+	91.2640i	−0.0151059	+	0.0261642i
$231$	−2167.98	−	3755.05i	−0.617500	−	1.06954i
$232$	−3683.18	+	2126.48i	−1.04230	+	0.601769i
$233$	256.724			0.0721827			0.0360913	−	0.999348i	$-0.488509\pi$
$233$	256.724			0.0721827			0.0360913	+	0.999348i	$0.488509\pi$
$234$		0			0
$235$	−17.9404			−0.00498002
$236$	89.2349	−	51.5198i	0.0246131	−	0.0142104i
$237$	−776.612	−	1345.13i	−0.212854	−	0.368674i
$238$	−594.740	+	1030.12i	−0.161980	+	0.280558i
$239$			3549.62i			0.960694i	0.877078	+	0.480347i	$0.159489\pi$
$239$			3549.62i			0.960694i	−0.877078	+	0.480347i	$0.840511\pi$
$240$	90.3545	+	52.1662i	0.0243015	+	0.0140305i
$241$	4356.19	+	2515.05i	1.16434	+	0.672235i	0.952341	−	0.305034i	$-0.0986679\pi$
$241$	4356.19	+	2515.05i	1.16434	+	0.672235i	0.212003	+	0.977269i	$0.432001\pi$
$242$			7326.27i			1.94608i
$243$	1667.39	−	2888.00i	0.440176	−	0.762408i
$244$	662.186	+	1146.94i	0.173738	+	0.300923i
$245$	−6.12457	+	3.53602i	−0.00159708	+	0.000922074i
$246$	−657.349			−0.170370
$247$		0			0
$248$	2734.25			0.700102
$249$	1926.72	−	1112.39i	0.490366	−	0.283113i
$250$	179.579	+	311.040i	0.0454303	+	0.0786876i
$251$	−359.392	+	622.485i	−0.0903770	+	0.156538i	−0.907670	−	0.419685i	$-0.862141\pi$
$251$	−359.392	+	622.485i	−0.0903770	+	0.156538i	0.817293	+	0.576223i	$0.195474\pi$
$252$		−	350.976i		−	0.0877357i
$253$	4107.42	+	2371.42i	1.02068	+	0.589288i
$254$	1227.14	+	708.492i	0.303141	+	0.175019i
$255$			52.8588i			0.0129810i
$256$	1066.87	−	1847.87i	0.260466	−	0.451141i
$257$	640.397	+	1109.20i	0.155435	+	0.269222i	0.933217	−	0.359312i	$-0.116989\pi$
$257$	640.397	+	1109.20i	0.155435	+	0.269222i	−0.777782	+	0.628534i	$0.783655\pi$
$258$	−3582.65	+	2068.45i	−0.864520	+	0.499131i
$259$	−2086.87			−0.500663
$260$		0			0
$261$	−2361.28			−0.559998
$262$	−4561.86	+	2633.79i	−1.07570	+	0.621054i
$263$	−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
$265$		−	1.59851i		−	0.000370549i
$266$	−4353.71	−	2513.62i	−1.00355	−	0.579398i
$267$	−3701.19	−	2136.89i	−0.848350	−	0.489795i
$268$			639.074i			0.145663i
$269$	−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
$271$	−3403.42	+	1964.97i	−0.762890	+	0.440455i	−0.830332	−	0.557269i	$-0.811849\pi$
$271$	−3403.42	+	1964.97i	−0.762890	+	0.440455i	0.0674426	+	0.997723i	$0.478516\pi$
$272$	−1288.13			−0.287149
$273$		0			0
$274$	−4632.74			−1.02144
$275$	6990.48	−	4035.96i	1.53288	−	0.885009i
$276$	−194.149	−	336.277i	−0.0423421	−	0.0733387i
$277$	−2942.20	+	5096.04i	−0.638194	+	1.10538i	0.347635	+	0.937630i	$0.386985\pi$
$277$	−2942.20	+	5096.04i	−0.638194	+	1.10538i	−0.985829	+	0.167754i	$0.946348\pi$
$278$		−	3826.03i		−	0.825431i
$279$	1314.69	+	759.039i	0.282110	+	0.162876i
$280$	213.722	+	123.392i	0.0456155	+	0.0263361i
$281$			3529.79i			0.749358i	0.927155	+	0.374679i	$0.122247\pi$
$281$			3529.79i			0.749358i	−0.927155	+	0.374679i	$0.877753\pi$
$282$	−150.769	+	261.140i	−0.0318375	+	0.0551442i
$283$	−1305.50	−	2261.19i	−0.274219	−	0.474961i	0.695719	−	0.718314i	$-0.255086\pi$
$283$	−1305.50	−	2261.19i	−0.274219	−	0.474961i	−0.969938	+	0.243353i	$0.921753\pi$
$284$	674.836	−	389.617i	0.141001	−	0.0814067i
$285$	−223.403			−0.0464325
$286$		0			0
$287$	−1265.96			−0.260373
$288$	746.955	−	431.255i	0.152829	−	0.0882359i
$289$	2130.19	+	3689.60i	0.433582	+	0.750987i
$290$	126.518	−	219.136i	0.0256186	−	0.0443727i
$291$			2149.15i			0.432939i
$292$	−951.744	−	549.490i	−0.190742	−	0.110125i
$293$	4755.37	+	2745.51i	0.948163	+	0.547422i	0.892510	−	0.451028i	$-0.148943\pi$
$293$	4755.37	+	2745.51i	0.948163	+	0.547422i	0.0556531	+	0.998450i	$0.482276\pi$
$294$			118.865i			0.0235795i
$295$	−20.1127	+	34.8363i	−0.00396952	+	0.00687541i
$296$	−1387.86	−	2403.84i	−0.272526	−	0.472028i
$297$	8350.70	−	4821.28i	1.63150	−	0.941950i
$298$	7067.37			1.37383
$299$		0			0
$300$	−660.852			−0.127181
$301$	−6899.67	+	3983.53i	−1.32123	+	0.762813i
$302$	1250.49	+	2165.92i	0.238271	+	0.412697i
$303$	−1698.15	+	2941.28i	−0.321967	+	0.557664i
$304$		−	5444.19i		−	1.02712i
$305$	−447.751	−	258.509i	−0.0840596	−	0.0485318i
$306$	−760.716	−	439.200i	−0.142115	−	0.0820502i
$307$		−	7307.59i		−	1.35852i	−0.733897	−	0.679261i	$-0.762300\pi$
$307$		−	7307.59i		−	1.35852i	0.733897	−	0.679261i	$-0.237700\pi$
$308$	846.353	−	1465.93i	0.156576	−	0.271198i
$309$	1714.68	+	2969.91i	0.315678	+	0.546771i
$310$	−140.883	+	81.3390i	−0.0258117	+	0.0149024i
$311$	−7904.92			−1.44131			−0.720654	−	0.693295i	$-0.756158\pi$
$311$	−7904.92			−1.44131			−0.720654	+	0.693295i	$0.756158\pi$
$312$		0			0
$313$	10002.4			1.80629			0.903145	−	0.429336i	$-0.141252\pi$
$313$	10002.4			1.80629			0.903145	+	0.429336i	$0.141252\pi$
$314$	1253.10	−	723.478i	0.225212	−	0.130026i
$315$	68.5084	+	118.660i	0.0122540	+	0.0212246i
$316$	303.180	−	525.123i	0.0539722	−	0.0934825i
$317$			6230.81i			1.10397i	0.833856	+	0.551983i	$0.186129\pi$
$317$			6230.81i			1.10397i	−0.833856	+	0.551983i	$0.813871\pi$
$318$	−23.2678	−	13.4337i	−0.00410312	−	0.00236894i
$319$	−9862.40	−	5694.06i	−1.73100	−	0.999392i
$320$			318.950i			0.0557182i
$321$	1579.58	−	2735.91i	0.274653	−	0.475713i
$322$	1705.58	+	2954.15i	0.295181	+	0.511269i
$323$	2388.70	−	1379.12i	0.411489	−	0.237573i
$324$	−268.107			−0.0459717
$325$		0			0
$326$	3864.19			0.656495
$327$	2143.89	−	1237.77i	0.362561	−	0.209324i
$328$	−841.917	−	1458.24i	−0.141729	−	0.245482i
$329$	−290.360	+	502.918i	−0.0486567	+	0.0842758i
$330$			343.127i			0.0572379i
$331$	−4013.60	−	2317.25i	−0.666488	−	0.384797i	0.128257	−	0.991741i	$-0.459062\pi$
$331$	−4013.60	−	2317.25i	−0.666488	−	0.384797i	−0.794745	+	0.606944i	$0.792395\pi$
$332$	752.170	+	434.265i	0.124339	+	0.0717874i
$333$		−	1541.10i		−	0.253609i
$334$	−758.886	+	1314.43i	−0.124325	+	0.215337i
$335$	−124.743	−	216.062i	−0.0203447	−	0.0352380i
$336$	2924.71	−	1688.58i	0.474870	−	0.274166i
$337$	−3029.82			−0.489747			−0.244874	−	0.969555i	$-0.578746\pi$
$337$	−3029.82			−0.489747			−0.244874	+	0.969555i	$0.578746\pi$
$338$		0			0
$339$	−2363.61			−0.378684
$340$	−17.8708	+	10.3177i	−0.00285054	+	0.00164576i
$341$	3660.74	+	6340.58i	0.581349	+	1.00693i
$342$	1856.24	−	3215.10i	0.293491	−	0.508342i
$343$			6463.66i			1.01751i
$344$	−9177.15	−	5298.43i	−1.43837	−	0.830443i
$345$	131.278	+	75.7937i	0.0204864	+	0.0118278i
$346$		−	11515.6i		−	1.78926i
$347$	−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
$349$	6552.07	−	3782.84i	1.00494	−	0.580202i	0.0952339	−	0.995455i	$-0.469640\pi$
$349$	6552.07	−	3782.84i	1.00494	−	0.580202i	0.909706	+	0.415252i	$0.136307\pi$
$350$	5805.51			0.886622
$351$		0			0
$352$	4159.76			0.629875
$353$	2026.01	−	1169.72i	0.305478	−	0.176368i	−0.339423	−	0.940634i	$-0.610232\pi$
$353$	2026.01	−	1169.72i	0.305478	−	0.176368i	0.644901	+	0.764266i	$0.276899\pi$
$354$	338.050	+	585.520i	0.0507547	+	0.0879097i
$355$	−152.102	+	263.448i	−0.0227401	+	0.0393870i
$356$		−	1668.43i		−	0.248389i
$357$	1481.77	+	855.502i	0.219674	+	0.126829i
$358$	342.261	+	197.605i	0.0505281	+	0.0291724i
$359$		−	2531.68i		−	0.372192i	−0.982532	−	0.186096i	$-0.940417\pi$
$359$		−	2531.68i		−	0.372192i	0.982532	−	0.186096i	$-0.0595835\pi$
$360$	−91.1221	+	157.828i	−0.0133404	+	0.0231063i
$361$	2399.23	+	4155.58i	0.349793	+	0.605858i
$362$	2376.64	−	1372.16i	0.345065	−	0.199223i
$363$	10538.5			1.52376
$364$		0			0
$365$	429.028			0.0615243
$366$	−7525.70	+	4344.97i	−1.07479	+	0.620533i
$367$	−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
$369$		−	934.876i		−	0.131891i
$370$	143.020	+	82.5725i	0.0200952	+	0.0116020i
$371$	−44.8104	−	25.8713i	−0.00627073	−	0.00362041i
$372$		−	599.413i		−	0.0835433i
$373$	−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
$375$	447.415	−	258.315i	0.0616117	−	0.0355716i
$376$	−772.407			−0.105941
$377$		0			0
$378$	6935.16			0.943667
$379$	1615.77	−	932.867i	0.218989	−	0.126433i	−0.386493	−	0.922292i	$-0.626314\pi$
$379$	1615.77	−	932.867i	0.218989	−	0.126433i	0.605482	+	0.795859i	$0.292980\pi$
$380$	−43.6070	−	75.5296i	−0.00588682	−	0.0101963i
$381$	1019.13	−	1765.18i	0.137038	−	0.237357i
$382$		−	1734.69i		−	0.232342i
$383$	9384.24	+	5417.99i	1.25199	+	0.722837i	0.971504	−	0.237021i	$-0.0761712\pi$
$383$	9384.24	+	5417.99i	1.25199	+	0.722837i	0.280486	+	0.959858i	$0.409504\pi$
$384$	3002.32	+	1733.39i	0.398988	+	0.230356i
$385$			660.813i			0.0874757i
$386$	−1692.78	+	2931.97i	−0.223213	+	0.386616i
$387$	−2941.73	−	5095.22i	−0.386399	−	0.669263i
$388$	−726.597	+	419.501i	−0.0950705	+	0.0548890i
$389$	9520.34			1.24088			0.620438	−	0.784256i	$-0.286955\pi$
$389$	9520.34			1.24088			0.620438	+	0.784256i	$0.286955\pi$
$390$		0			0
$391$	−1871.56			−0.242069
$392$	−263.687	+	152.240i	−0.0339750	+	0.0196155i
$393$	3788.57	+	6561.99i	0.486280	+	0.842261i
$394$	1623.21	−	2811.49i	0.207554	−	0.359494i
$395$			236.716i			0.0301531i
$396$	1082.55	+	625.009i	0.137374	+	0.0793129i
$397$	8754.51	+	5054.42i	1.10674	+	0.638978i	0.937983	−	0.346680i	$-0.112691\pi$
$397$	8754.51	+	5054.42i	1.10674	+	0.638978i	0.168758	+	0.985657i	$0.446024\pi$
$398$			6138.10i			0.773053i
$399$	−3615.71	+	6262.59i	−0.453664	+	0.785768i
$400$	3143.51	+	5444.71i	0.392938	+	0.680589i
$401$	1805.12	−	1042.19i	0.224797	−	0.129787i	−0.383373	−	0.923594i	$-0.625237\pi$
$401$	1805.12	−	1042.19i	0.224797	−	0.129787i	0.608169	+	0.793807i	$0.291904\pi$
$402$	−4193.32			−0.520258
$403$		0			0
$404$	−1325.88			−0.163279
$405$	90.6432	−	52.3329i	0.0111212	−	0.00642084i
$406$	−4095.30	−	7093.27i	−0.500607	−	0.867076i
$407$	3716.25	−	6436.73i	0.452599	−	0.783924i
$408$			2275.78i			0.276147i
$409$	−8414.76	−	4858.26i	−1.01732	−	0.587349i	−0.103992	−	0.994578i	$-0.533162\pi$
$409$	−8414.76	−	4858.26i	−1.01732	−	0.587349i	−0.913326	+	0.407229i	$0.866495\pi$
$410$	86.7600	+	50.0909i	0.0104507	+	0.00603369i
$411$			6663.95i			0.799777i
$412$	−669.390	+	1159.42i	−0.0800449	+	0.138642i
$413$	651.035	+	1127.63i	0.0775674	+	0.134351i
$414$	−2181.56	+	1259.53i	−0.258981	+	0.149523i
$415$	−339.064			−0.0401060
$416$		0			0
$417$	−5503.54			−0.646305
$418$	15506.0	−	8952.38i	1.81441	−	1.04755i
$419$	−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
$421$			9463.37i			1.09553i	0.836633	+	0.547763i	$0.184521\pi$
$421$			9463.37i			1.09553i	−0.836633	+	0.547763i	$0.815479\pi$
$422$	−203.100	−	117.260i	−0.0234284	−	0.0135264i
$423$	−371.391	−	214.423i	−0.0426895	−	0.0246468i
$424$		−	68.8221i		−	0.00788278i
$425$	−1592.62	+	2758.50i	−0.181773	+	0.314840i
$426$	2556.49	+	4427.97i	0.290757	+	0.503606i
$427$	−14493.4	+	8367.77i	−1.64259	+	0.948349i
$428$	1233.30			0.139285
$429$		0			0
$430$	630.474			0.0707074
$431$	−4202.20	+	2426.14i	−0.469635	+	0.271144i	−0.716087	−	0.698011i	$-0.754069\pi$
$431$	−4202.20	+	2426.14i	−0.469635	+	0.271144i	0.246452	+	0.969155i	$0.420735\pi$
$432$	3755.17	+	6504.15i	0.418220	+	0.724378i
$433$	−4104.00	+	7108.33i	−0.455486	+	0.788925i	−0.998716	−	0.0506587i	$-0.983868\pi$
$433$	−4104.00	+	7108.33i	−0.455486	+	0.788925i	0.543230	+	0.839584i	$0.317201\pi$
$434$			5265.78i			0.582409i
$435$	−315.215	−	181.989i	−0.0347434	−	0.0200591i
$436$	836.949	+	483.213i	0.0919325	+	0.0530773i
$437$		−	7910.01i		−	0.865874i
$438$	3605.50	−	6244.92i	0.393328	−	0.681264i
$439$	−1496.90	−	2592.71i	−0.162741	−	0.281875i	0.773110	−	0.634272i	$-0.218700\pi$
$439$	−1496.90	−	2592.71i	−0.162741	−	0.281875i	−0.935851	+	0.352397i	$0.885367\pi$
$440$	−761.182	+	439.469i	−0.0824726	+	0.0476156i
$441$	−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	$0.324999\pi$
$444$	−526.979	+	304.251i	−0.0563273	+	0.0325206i
$445$	325.668	+	564.073i	0.0346924	+	0.0600890i
$446$	1582.29	−	2740.61i	0.167990	−	0.290968i
$447$		−	10166.0i		−	1.07570i
$448$	8941.01	+	5162.09i	0.942908	+	0.544388i
$449$	486.237	+	280.729i	0.0511068	+	0.0295065i	0.525336	−	0.850895i	$-0.323940\pi$
$449$	486.237	+	280.729i	0.0511068	+	0.0295065i	−0.474229	+	0.880402i	$0.657273\pi$
$450$			4287.22i			0.449114i
$451$	2254.39	−	3904.71i	0.235377	−	0.407685i
$452$	−461.363	−	799.104i	−0.0480104	−	0.0831564i
$453$	3115.56	−	1798.77i	0.323138	−	0.186564i
$454$	−8457.38			−0.874283
$455$		0			0
$456$	−9618.40			−0.987770
$457$	−11915.1	+	6879.20i	−1.21962	+	0.704148i	−0.964837	−	0.262851i	$-0.915337\pi$
$457$	−11915.1	+	6879.20i	−1.21962	+	0.704148i	−0.254783	+	0.966998i	$0.582004\pi$
$458$	−270.606	−	468.704i	−0.0276083	−	0.0478190i
$459$	−1902.52	+	3295.26i	−0.193468	+	0.335097i
$460$			59.1779i			0.00599823i
$461$	10400.3	+	6004.62i	1.05074	+	0.606644i	0.922856	−	0.385145i	$-0.125849\pi$
$461$	10400.3	+	6004.62i	1.05074	+	0.606644i	0.127882	+	0.991789i	$0.459182\pi$
$462$	9618.75	+	5553.39i	0.968625	+	0.559236i
$463$			13635.7i			1.36870i	0.729156	+	0.684348i	$0.239913\pi$
$463$			13635.7i			1.36870i	−0.729156	+	0.684348i	$0.760087\pi$
$464$	4434.96	−	7681.57i	0.443724	−	0.768552i
$465$	117.002	+	202.653i	0.0116685	+	0.0202104i
$466$	−569.509	+	328.806i	−0.0566138	+	0.0326860i
$467$	−8821.95			−0.874157			−0.437079	−	0.899423i	$-0.643987\pi$
$467$	−8821.95			−0.874157			−0.437079	+	0.899423i	$0.643987\pi$
$468$		0			0
$469$	−8075.72			−0.795100
$470$	39.7985	−	22.9777i	0.00390589	−	0.00225507i
$471$	−1040.69	−	1802.52i	−0.101809	−	0.176339i
$472$	−865.933	+	1499.84i	−0.0844445	+	0.146262i
$473$		−	28375.1i		−	2.75832i
$474$	3445.62	+	1989.33i	0.333888	+	0.192770i
$475$	−11658.6	−	6731.08i	−1.12617	−	0.650196i
$476$			667.956i			0.0643187i
$477$	19.1053	−	33.0913i	0.00183390	−	0.00317641i
$478$	−4546.27	−	7874.37i	−0.435024	−	0.753484i
$479$	−12661.3	+	7310.02i	−1.20775	+	0.697293i	−0.962267	−	0.272109i	$-0.912279\pi$
$479$	−12661.3	+	7310.02i	−1.20775	+	0.697293i	−0.245480	+	0.969402i	$0.578946\pi$
$480$	132.951			0.0126424
$481$		0			0
$482$	−12884.9			−1.21761
$483$	4249.39	−	2453.39i	0.400319	−	0.231124i
$484$	2057.04	+	3562.91i	0.193186	+	0.334608i
$485$	163.768	−	283.655i	0.0153326	−	0.0265569i
$486$			8542.20i			0.797288i
$487$	−8486.06	−	4899.43i	−0.789610	−	0.455882i	0.0502150	−	0.998738i	$-0.484009\pi$
$487$	−8486.06	−	4899.43i	−0.789610	−	0.455882i	−0.839825	+	0.542857i	$0.817343\pi$
$488$	−19277.5	−	11129.9i	−1.78822	−	1.03243i
$489$		−	5558.43i		−	0.514030i
$490$	9.05771	−	15.6884i	0.000835072	−	0.00144639i
$491$	−5418.03	−	9384.31i	−0.497989	−	0.862542i	0.502009	−	0.864863i	$-0.332595\pi$
$491$	−5418.03	−	9384.31i	−0.497989	−	0.862542i	−0.999997	+	0.00232091i	$0.999261\pi$
$492$	−319.681	+	184.568i	−0.0292934	+	0.0169125i
$493$	4493.84			0.410532
$494$		0			0
$495$	−487.993			−0.0443104
$496$	−4938.52	+	2851.26i	−0.447069	+	0.258115i
$497$	4923.43	+	8527.63i	0.444358	+	0.769651i
$498$	−2849.45	+	4935.40i	−0.256400	+	0.444098i
$499$		−	2589.96i		−	0.232349i	−0.993229	−	0.116175i	$-0.962937\pi$
$499$		−	2589.96i		−	0.232349i	0.993229	−	0.116175i	$-0.0370633\pi$
$500$	174.665	+	100.843i	0.0156226	+	0.00901969i
$501$	1890.74	+	1091.62i	0.168607	+	0.0973451i
$502$		−	1841.20i		−	0.163699i
$503$	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
$505$	448.260	−	258.803i	0.0394996	−	0.0228051i
$506$	−12149.0			−1.06737
$507$		0			0
$508$	795.712			0.0694961
$509$	877.192	−	506.447i	0.0763867	−	0.0441019i	−0.461320	−	0.887234i	$-0.652624\pi$
$509$	877.192	−	506.447i	0.0763867	−	0.0441019i	0.537707	+	0.843132i	$0.319291\pi$
$510$	−67.7003	−	117.260i	−0.00587808	−	0.0101811i
$511$	6943.68	−	12026.8i	0.601116	−	1.04116i
$512$			12992.6i			1.12148i
$513$	−13927.1	−	8040.83i	−1.19863	−	0.692030i
$514$	−2841.28	−	1640.41i	−0.243820	−	0.140769i
$515$		−	522.644i		−	0.0447193i
$516$	−1161.54	+	2011.85i	−0.0990969	+	0.171641i
$517$	−1034.13	−	1791.17i	−0.0879711	−	0.152370i
$518$	4629.45	−	2672.81i	0.392676	−	0.226712i
$519$	−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	$0.706463\pi$
$522$	5238.19	−	3024.27i	0.439213	−	0.253580i
$523$	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
$525$		−	8350.92i		−	0.694217i
$526$	11592.2	+	6692.76i	0.960919	+	0.554787i
$527$	−2502.05	−	1444.56i	−0.206814	−	0.119404i
$528$			12028.0i			0.991382i
$529$	3399.89	−	5888.78i	0.279435	−	0.483996i
$530$	2.04733	+	3.54608i	0.000167793	+	0.000290626i
$531$	−832.722	+	480.772i	−0.0680547	+	0.0392914i
$532$	−2823.06			−0.230066
$533$		0			0
$534$	10947.5			0.887161
$535$	−416.961	+	240.733i	−0.0336950	+	0.0194538i
$536$	−5370.70	−	9302.32i	−0.432796	−	0.749625i
$537$	284.244	−	492.325i	0.0228418	−	0.0395631i
$538$		−	16506.1i		−	1.32273i
$539$	−706.071	−	407.650i	−0.0564242	−	0.0325765i
$540$	104.194	+	60.1566i	0.00830335	+	0.00479394i
$541$			17592.2i			1.39806i	0.715094	+	0.699029i	$0.246384\pi$
$541$			17592.2i			1.39806i	−0.715094	+	0.699029i	$0.753616\pi$
$542$	5033.36	−	8718.04i	0.398896	−	0.690908i
$543$	−1973.77	−	3418.67i	−0.155990	−	0.270183i
$544$	−1421.56	+	820.738i	−0.112038	+	0.0646854i
$545$	−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	$0.365336\pi$
$548$	−2252.99	+	1300.76i	−0.175626	+	0.101398i
$549$	−6179.38	−	10703.0i	−0.480382	−	0.832045i
$550$	−10338.3	+	17906.5i	−0.801504	+	1.38825i
$551$			18992.8i			1.46846i
$552$	5652.06	+	3263.22i	0.435811	+	0.251616i
$553$	6635.77	+	3831.16i	0.510274	+	0.294607i
$554$		−	15073.2i		−	1.15596i
$555$	118.776	−	205.726i	0.00908426	−	0.0157344i
$556$	−1074.26	−	1860.67i	−0.0819401	−	0.141924i
$557$	−439.558	+	253.779i	−0.0334375	+	0.0193051i	−0.516626	−	0.856211i	$-0.672812\pi$
$557$	−439.558	+	253.779i	−0.0334375	+	0.0193051i	0.483188	+	0.875517i	$0.339479\pi$
$558$	−3888.64			−0.295016
$559$		0			0
$560$	−514.690			−0.0388386
$561$	−5277.41	+	3046.92i	−0.397170	+	0.229306i
$562$	−4520.87	−	7830.38i	−0.339327	−	0.587731i
$563$	−1721.57	+	2981.85i	−0.128873	+	0.223215i	−0.923240	−	0.384223i	$-0.874469\pi$
$563$	−1721.57	+	2981.85i	−0.128873	+	0.223215i	0.794367	+	0.607438i	$0.207803\pi$
$564$			169.330i			0.0126420i
$565$	311.961	+	180.111i	0.0232288	+	0.0134112i
$566$	5792.16	+	3344.11i	0.430146	+	0.248345i
$567$		−	3387.96i		−	0.250936i
$568$	−6548.59	+	11342.5i	−0.483755	+	0.837888i
$569$	11986.1	+	20760.5i	0.883098	+	1.52957i	0.847879	+	0.530190i	$0.177879\pi$
$569$	11986.1	+	20760.5i	0.883098	+	1.52957i	0.0352188	+	0.999380i	$0.488787\pi$
$570$	495.591	−	286.130i	0.0364176	−	0.0210257i
$571$	7458.32			0.546622			0.273311	−	0.961926i	$-0.411881\pi$
$571$	7458.32			0.546622			0.273311	+	0.961926i	$0.411881\pi$
$572$		0			0
$573$	−2495.26			−0.181922
$574$	2808.36	−	1621.41i	0.204214	−	0.117903i
$575$	4567.28	+	7910.77i	0.331250	+	0.573742i
$576$	−3812.07	+	6602.70i	−0.275757	+	0.477626i
$577$		−	5669.57i		−	0.409059i	−0.978860	−	0.204530i	$-0.934434\pi$
$577$		−	5669.57i		−	0.409059i	0.978860	−	0.204530i	$-0.0655665\pi$
$578$	−9451.10	−	5456.60i	−0.680128	−	0.392672i
$579$	4217.49	+	2434.97i	0.302717	+	0.174774i
$580$		−	142.093i		−	0.0101726i
$581$	−5487.64	+	9504.87i	−0.391851	+	0.678706i
$582$	−2752.58	−	4767.60i	−0.196045	−	0.339559i
$583$	159.595	−	92.1420i	0.0113375	−	0.00654568i
$584$	18471.4			1.30882
$585$		0			0
$586$	−14065.6			−0.991541
$587$	−881.087	+	508.696i	−0.0619529	+	0.0357685i	−0.530657	−	0.847587i	$-0.678055\pi$
$587$	−881.087	+	508.696i	−0.0619529	+	0.0357685i	0.468704	+	0.883355i	$0.344721\pi$
$588$	33.3746	+	57.8064i	0.00234072	+	0.00405425i
$589$	6105.30	−	10574.7i	0.427104	−	0.739766i
$590$		−	103.040i		−	0.00718996i
$591$	−4044.18	−	2334.91i	−0.281481	−	0.162513i
$592$	5013.41	+	2894.49i	0.348057	+	0.200951i
$593$		−	10198.2i		−	0.706221i	−0.935582	−	0.353111i	$-0.885124\pi$
$593$		−	10198.2i		−	0.706221i	0.935582	−	0.353111i	$-0.114876\pi$
$594$	−12350.0	+	21390.8i	−0.853073	+	1.47757i
$595$	−130.381	−	225.827i	−0.00898336	−	0.0155596i
$596$	3437.00	−	1984.35i	0.236216	−	0.136380i
$597$	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	$0.359612\pi$
$600$	9619.33	−	5553.72i	0.654512	−	0.377883i
$601$	−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
$603$		−	5963.70i		−	0.402754i
$604$	1216.28	+	702.218i	0.0819364	+	0.0473060i
$605$	−1390.92	−	803.046i	−0.0934691	−	0.0539644i
$606$		−	8699.80i		−	0.583177i
$607$	−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
$609$	−10203.3	+	5890.87i	−0.678913	+	0.391971i
$610$	1324.37			0.0879053
$611$		0			0
$612$	−493.268			−0.0325803
$613$	19992.5	−	11542.7i	1.31728	−	0.760530i	0.333987	−	0.942578i	$-0.391606\pi$
$613$	19992.5	−	11542.7i	1.31728	−	0.760530i	0.983290	+	0.182047i	$0.0582724\pi$
$614$	9359.39	+	16210.9i	0.615170	+	1.06551i
$615$	72.0532	−	124.800i	0.00472433	−	0.00818278i
$616$			28450.6i			1.86089i
$617$	2640.72	+	1524.62i	0.172304	+	0.0994796i	0.583672	−	0.811990i	$-0.301616\pi$
$617$	2640.72	+	1524.62i	0.172304	+	0.0994796i	−0.411368	+	0.911469i	$0.634949\pi$
$618$	−7607.58	−	4392.24i	−0.495181	−	0.285893i
$619$			7296.58i			0.473787i	0.971536	+	0.236894i	$0.0761293\pi$
$619$			7296.58i			0.473787i	−0.971536	+	0.236894i	$0.923871\pi$
$620$	−45.6761	+	79.1134i	−0.00295871	+	0.00512463i
$621$	5455.99	+	9450.06i	0.352563	+	0.610657i
$622$	17536.0	−	10124.4i	1.13044	−	0.652657i
$623$	21083.3			1.35583
$624$		0			0
$625$	15506.8			0.992438
$626$	−22189.0	+	12810.8i	−1.41670	+	0.817929i
$627$	−12877.5	−	22304.5i	−0.820222	−	1.42067i
$628$	406.271	−	703.683i	0.0258153	−	0.0447134i
$629$			2932.92i			0.185920i
$630$	−303.954	−	175.488i	−0.0192219	−	0.0110978i
$631$	20637.0	+	11914.8i	1.30197	+	0.751694i	0.980742	−	0.195307i	$-0.0625703\pi$
$631$	20637.0	+	11914.8i	1.30197	+	0.751694i	0.321230	+	0.947001i	$0.395904\pi$
$632$			10191.6i			0.641453i
$633$	−168.672	+	292.149i	−0.0105910	+	0.0183442i
$634$	−7980.27	−	13822.2i	−0.499901	−	0.865853i
$635$	−269.019	+	155.318i	−0.0168121	+	0.00970648i
$636$	−15.0874			−0.000940653
$637$		0			0
$638$	29171.3			1.81019
$639$	−6297.43	+	3635.82i	−0.389863	+	0.225088i
$640$	−264.174	−	457.562i	−0.0163162	−	0.0282605i
$641$	6702.63	−	11609.3i	0.413008	−	0.715351i	−0.582209	−	0.813039i	$-0.697812\pi$
$641$	6702.63	−	11609.3i	0.413008	−	0.715351i	0.995217	+	0.0976883i	$0.0311448\pi$
$642$			8092.36i			0.497477i
$643$	4547.94	+	2625.76i	0.278932	+	0.161042i	0.632940	−	0.774201i	$-0.281848\pi$
$643$	4547.94	+	2625.76i	0.278932	+	0.161042i	−0.354008	+	0.935243i	$0.615181\pi$
$644$	1658.91	+	957.774i	0.101507	+	0.0586049i
$645$		−	906.904i		−	0.0553633i
$646$	−3532.68	+	6118.79i	−0.215157	+	0.372663i
$647$	10805.7	+	18716.1i	0.656595	+	1.13726i	0.981492	+	0.191506i	$0.0613370\pi$
$647$	10805.7	+	18716.1i	0.656595	+	1.13726i	−0.324897	+	0.945749i	$0.605330\pi$
$648$	3902.55	−	2253.14i	0.236584	−	0.136592i
$649$	−4637.39			−0.280483
$650$		0			0
$651$	7574.54			0.456021
$652$	1879.23	−	1084.97i	0.112878	−	0.0651699i
$653$	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
$655$		−	1154.78i		−	0.0688869i
$656$	3041.28	+	1755.89i	0.181009	+	0.104506i
$657$	8881.48	+	5127.72i	0.527396	+	0.304492i
$658$		−	1487.54i		−	0.0881314i
$659$	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
$661$	23366.3	−	13490.6i	1.37495	−	0.793831i	0.383408	−	0.923579i	$-0.374750\pi$
$661$	23366.3	−	13490.6i	1.37495	−	0.793831i	0.991547	+	0.129748i	$0.0414170\pi$
$662$	11871.5			0.696980
$663$		0			0
$664$	−14598.1			−0.853185
$665$	954.437	−	551.044i	0.0556564	−	0.0321332i
$666$	1973.80	+	3418.73i	0.114840	+	0.198908i
$667$	6443.67	−	11160.8i	0.374063	−	0.647896i
$668$			852.310i			0.0493665i
$669$	−3942.23	−	2276.05i	−0.227826	−	0.131535i
$670$	553.454	+	319.537i	0.0319131	+	0.0184251i
$671$		−	59604.5i		−	3.42922i
$672$	2151.77	−	3726.98i	0.123521	−	0.213945i
$673$	5574.62	+	9655.53i	0.319296	+	0.553036i	0.980341	−	0.197309i	$-0.0632204\pi$
$673$	5574.62	+	9655.53i	0.319296	+	0.553036i	−0.661046	+	0.750346i	$0.729887\pi$
$674$	6721.26	−	3880.52i	0.384115	−	0.221769i
$675$	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	$0.470010\pi$
$678$	5243.36	−	3027.26i	0.297006	−	0.171477i
$679$	−5301.06	−	9181.71i	−0.299611	−	0.518942i
$680$	173.418	−	300.369i	0.00977982	−	0.0169391i
$681$			12165.5i			0.684556i
$682$	−16241.7	−	9377.17i	−0.911918	−	0.526496i
$683$	−21222.2	−	12252.6i	−1.18894	−	0.686433i	−0.230872	−	0.972984i	$-0.574158\pi$
$683$	−21222.2	−	12252.6i	−1.18894	−	0.686433i	−0.958065	+	0.286552i	$0.907491\pi$
$684$		−	2084.75i		−	0.116539i
$685$	507.803	−	879.540i	0.0283243	−	0.0490591i
$686$	−8278.50	−	14338.8i	−0.460750	−	0.798042i
$687$	−674.206	+	389.253i	−0.0374419	+	0.0216171i
$688$	22100.6			1.22468
$689$		0			0
$690$	−388.299			−0.0214236
$691$	18838.5	−	10876.4i	1.03712	−	0.598782i	0.118105	−	0.993001i	$-0.462318\pi$
$691$	18838.5	−	10876.4i	1.03712	−	0.598782i	0.919017	+	0.394219i	$0.128985\pi$
$692$	−3233.32	−	5600.27i	−0.177619	−	0.307645i
$693$	−7897.99	+	13679.7i	−0.432929	+	0.749855i
$694$		−	7278.90i		−	0.398132i
$695$	726.383	+	419.378i	0.0396450	+	0.0228891i
$696$	−13571.3	−	7835.37i	−0.739105	−	0.426722i
$697$			1779.20i			0.0966887i
$698$	−9689.94	+	16783.5i	−0.525458	+	0.910120i
$699$	472.971	+	819.209i	0.0255928	+	0.0443281i
$700$	2823.33	−	1630.05i	0.152446	−	0.0880145i
$701$	−34250.9			−1.84542			−0.922709	−	0.385496i	$-0.874030\pi$
$701$	−34250.9			−1.84542			−0.922709	+	0.385496i	$0.874030\pi$
$702$		0			0
$703$	−12395.8			−0.665028
$704$	−31843.9	+	18385.1i	−1.70477	+	0.984252i
$705$	−33.0522	−	57.2480i	−0.00176570	−	0.00305828i
$706$	−2996.30	+	5189.74i	−0.159727	+	0.276655i
$707$		−	16754.6i		−	0.891259i
$708$	328.800	+	189.833i	0.0174535	+	0.0100768i
$709$	4786.62	+	2763.56i	0.253548	+	0.146386i	0.621388	−	0.783503i	$-0.286569\pi$
$709$	4786.62	+	2763.56i	0.253548	+	0.146386i	−0.367840	+	0.929889i	$0.619903\pi$
$710$		−	779.234i		−	0.0411889i
$711$	−2829.21	+	4900.34i	−0.149232	+	0.258477i
$712$	14021.3	+	24285.6i	0.738020	+	1.27829i
$713$	−7175.31	+	4142.67i	−0.376883	+	0.217593i
$714$	−4382.83			−0.229724
$715$		0			0
$716$	221.931			0.0115837
$717$	−11326.9	+	6539.57i	−0.589972	+	0.340620i
$718$	3242.51	+	5616.19i	0.168537	+	0.291914i
$719$	−1888.89	+	3271.65i	−0.0979745	+	0.169697i	−0.910846	−	0.412746i	$-0.864570\pi$
$719$	−1888.89	+	3271.65i	−0.0979745	+	0.169697i	0.812872	+	0.582443i	$0.197903\pi$
$720$		−	380.085i		−	0.0196735i
$721$	−14651.1	−	8458.81i	−0.756776	−	0.436925i
$722$	−10644.7	−	6145.75i	−0.548693	−	0.316788i
$723$			18534.2i			0.953380i
$724$	770.538	−	1334.61i	0.0395536	−	0.0685088i
$725$	−10966.6	−	18994.7i	−0.561777	−	0.973027i
$726$	−23378.2	+	13497.4i	−1.19510	+	0.689994i
$727$	−19076.8			−0.973204			−0.486602	−	0.873624i	$-0.661764\pi$
$727$	−19076.8			−0.973204			−0.486602	+	0.873624i	$0.661764\pi$
$728$		0			0
$729$	17319.9			0.879944
$730$	−951.744	+	549.490i	−0.0482543	+	0.0278596i
$731$	5598.52	+	9696.92i	0.283268	+	0.490634i
$732$	−2439.93	+	4226.08i	−0.123200	+	0.213388i
$733$		−	7997.30i		−	0.402984i	−0.979490	−	0.201492i	$-0.935421\pi$
$733$		−	7997.30i		−	0.402984i	0.979490	−	0.201492i	$-0.0645790\pi$
$734$	14592.0	+	8424.71i	0.733789	+	0.423653i
$735$	−22.5669	−	13.0290i	−0.00113251	−	0.000653855i
$736$			4707.39i			0.235756i
$737$	14381.0	−	24908.7i	0.718769	−	1.24494i
$738$	1197.37	+	2073.90i	0.0597232	+	0.103444i
$739$	25100.6	−	14491.8i	1.24944	−	0.721367i	0.278445	−	0.960452i	$-0.410181\pi$
$739$	25100.6	−	14491.8i	1.24944	−	0.721367i	0.970998	+	0.239086i	$0.0768477\pi$
$740$	92.7376			0.00460689
$741$		0			0
$742$	132.541			0.00655761
$743$	16580.4	−	9572.69i	0.818674	−	0.472662i	−0.0312847	−	0.999511i	$-0.509960\pi$
$743$	16580.4	−	9572.69i	0.818674	−	0.472662i	0.849959	+	0.526849i	$0.176627\pi$
$744$	5037.40	+	8725.02i	0.248226	+	0.429939i
$745$	−774.667	+	1341.76i	−0.0380961	+	0.0659844i
$746$		−	7435.47i		−	0.364922i
$747$	−7019.09	−	4052.47i	−0.343795	−	0.198490i
$748$	−2060.24	−	1189.48i	−0.100708	−	0.0581440i
$749$			15584.7i			0.760284i
$750$	−661.688	+	1146.08i	−0.0322152	+	0.0557984i
$751$	−12758.4	−	22098.3i	−0.619923	−	1.07374i	−0.989499	−	0.144538i	$-0.953830\pi$
$751$	−12758.4	−	22098.3i	−0.619923	−	1.07374i	0.369576	−	0.929200i	$-0.379503\pi$
$752$	1395.10	−	805.459i	0.0676515	−	0.0390586i
$753$	−2648.47			−0.128175
$754$		0			0
$755$	−548.275			−0.0264288
$756$	3372.70	−	1947.23i	0.162254	−	0.0936773i
$757$	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
$759$			17475.7i			0.835744i
$760$	1269.48	+	732.936i	0.0605908	+	0.0349821i
$761$	2029.15	+	1171.53i	0.0966576	+	0.0558053i	0.547550	−	0.836773i	$-0.315561\pi$
$761$	2029.15	+	1171.53i	0.0966576	+	0.0558053i	−0.450892	+	0.892579i	$0.648894\pi$
$762$			5221.11i			0.248216i
$763$	−6106.17	+	10576.2i	−0.289722	+	0.501814i
$764$	−487.060	−	843.613i	−0.0230644	−	0.0399488i
$765$	166.767	−	96.2829i	0.00788166	−	0.00455048i
$766$	−27756.9			−1.30927
$767$		0			0
$768$	7862.11			0.369400
$769$	6148.93	−	3550.09i	0.288344	−	0.166475i	−0.348851	−	0.937178i	$-0.613428\pi$
$769$	6148.93	−	3550.09i	0.288344	−	0.166475i	0.637195	+	0.770703i	$0.280095\pi$
$770$	−846.353	−	1465.93i	−0.0396110	−	0.0686082i
$771$	−2359.65	+	4087.03i	−0.110221	+	0.190909i
$772$			1901.17i			0.0886328i
$773$	10626.5	+	6135.22i	0.494449	+	0.285470i	0.726418	−	0.687253i	$-0.241184\pi$
$773$	10626.5	+	6135.22i	0.494449	+	0.285470i	−0.231969	+	0.972723i	$0.574517\pi$
$774$	13051.7	+	7535.39i	0.606115	+	0.349941i
$775$			14100.9i			0.653575i
$776$	7050.87	−	12212.5i	0.326175	−	0.564951i
$777$	−3844.70	−	6659.22i	−0.177513	−	0.307462i
$778$	−21119.6	+	12193.4i	−0.973233	+	0.561897i
$779$	−7519.64			−0.345852
$780$		0			0
$781$	−35070.1			−1.60680
$782$	4151.82	−	2397.06i	0.189858	−	0.109614i
$783$	−13100.5	−	22690.7i	−0.597922	−	1.03563i
$784$	317.509	−	549.941i	0.0144638	−	0.0250520i
$785$			317.207i			0.0144224i
$786$	−16808.9	−	9704.61i	−0.762790	−	0.440397i
$787$	−2966.17	−	1712.52i	−0.134349	−	0.0775663i	0.431319	−	0.902199i	$-0.358048\pi$
$787$	−2966.17	−	1712.52i	−0.134349	−	0.0775663i	−0.565668	+	0.824633i	$0.691382\pi$
$788$		−	1823.04i		−	0.0824151i
$789$	9627.17	−	16674.8i	0.434394	−	0.752392i
$790$	−303.180	−	525.123i	−0.0136540	−	0.0236494i
$791$	10098.0	−	5830.06i	0.453909	−	0.262064i
$792$	−21010.0			−0.942624
$793$		0			0
$794$	−25894.3			−1.15737
$795$	5.10085	−	2.94498i	0.000227558	−	0.000131381i
$796$	1723.43	+	2985.07i	0.0767405	+	0.132918i
$797$	−5890.57	+	10202.8i	−0.261800	+	0.453451i	−0.966720	−	0.255836i	$-0.917649\pi$
$797$	−5890.57	+	10202.8i	−0.261800	+	0.453451i	0.704920	+	0.709286i	$0.250983\pi$
$798$		−	18523.6i		−	0.821717i
$799$	706.810	+	408.077i	0.0312955	+	0.0180685i
$800$	6938.23	+	4005.79i	0.306629	+	0.177033i
$801$			15569.4i			0.686790i
$802$	−2669.62	+	4623.92i	−0.117541	+	0.203586i
$803$	24730.3	+	42834.1i	1.08682	+	1.88242i
$804$	−2039.29	+	1177.38i	−0.0894530	+	0.0516457i
$805$	−747.807			−0.0327413
$806$		0			0
$807$	−23743.2			−1.03569
$808$	19299.4	−	11142.5i	0.840284	−	0.485138i
$809$	−9455.06	−	16376.7i	−0.410905	−	0.711709i	0.584084	−	0.811693i	$-0.301454\pi$
$809$	−9455.06	−	16376.7i	−0.410905	−	0.711709i	−0.994989	+	0.0999847i	$0.968121\pi$
$810$	−134.053	+	232.187i	−0.00581501	+	0.0100719i
$811$		−	12803.3i		−	0.554359i	−0.960818	−	0.277180i	$-0.910600\pi$
$811$		−	12803.3i		−	0.554359i	0.960818	−	0.277180i	$-0.0893997\pi$
$812$	−3983.24	−	2299.73i	−0.172148	−	0.0993899i
$813$	−12540.4	−	7240.23i	−0.540975	−	0.312332i
$814$			19038.7i			0.819788i
$815$	−423.560	+	733.628i	−0.0182045	+	0.0315311i
$816$	−2373.17	−	4110.44i	−0.101811	−	0.176341i
$817$	−40983.2	+	23661.7i	−1.75498	+	1.01324i
$818$	24889.4			1.06386
$819$		0			0
$820$	56.2574			0.00239585
$821$	−16744.7	+	9667.54i	−0.711806	+	0.410962i	−0.811730	−	0.584033i	$-0.801474\pi$
$821$	−16744.7	+	9667.54i	−0.711806	+	0.410962i	0.0999231	+	0.994995i	$0.468140\pi$
$822$	−8535.03	−	14783.1i	−0.362157	−	0.627275i
$823$	−1062.95	+	1841.09i	−0.0450209	+	0.0779784i	−0.887658	−	0.460504i	$-0.847669\pi$
$823$	−1062.95	+	1841.09i	−0.0450209	+	0.0779784i	0.842637	+	0.538482i	$0.181002\pi$
$824$		−	22501.9i		−	0.951324i
$825$	25757.5	+	14871.1i	1.08698	+	0.627571i
$826$	−2888.47	−	1667.66i	−0.121674	−	0.0702486i
$827$		−	6989.24i		−	0.293881i	−0.989145	−	0.146941i	$-0.953057\pi$
$827$		−	6989.24i		−	0.293881i	0.989145	−	0.146941i	$-0.0469426\pi$
$828$	−707.291	+	1225.06i	−0.0296861	+	0.0514178i
$829$	−16324.8	−	28275.4i	−0.683938	−	1.18462i	−0.973769	−	0.227538i	$-0.926932\pi$
$829$	−16324.8	−	28275.4i	−0.683938	−	1.18462i	0.289831	−	0.957078i	$-0.406401\pi$
$830$	752.170	−	434.265i	0.0314556	−	0.0181609i
$831$	−21682.0			−0.905103
$832$		0			0
$833$	321.724			0.0133819
$834$	12208.9	−	7048.80i	0.506905	−	0.292662i
$835$	−166.366	−	288.154i	−0.00689500	−	0.0119425i
$836$	5027.24	−	8707.43i	0.207979	−	0.360231i
$837$			16844.7i			0.695626i
$838$	29686.0	+	17139.2i	1.22373	+	0.706520i
$839$	3497.21	+	2019.12i	0.143906	+	0.0830841i	0.570224	−	0.821489i	$-0.306856\pi$
$839$	3497.21	+	2019.12i	0.143906	+	0.0830841i	−0.426318	+	0.904573i	$0.640190\pi$
$840$			909.318i			0.0373505i
$841$	−3277.50	+	5676.80i	−0.134384	+	0.232761i
$842$	−12120.5	−	20993.3i	−0.496079	−	0.859235i
$843$	−11263.6	+	6503.04i	−0.460188	+	0.265690i
$844$	−131.695			−0.00537102
$845$		0			0
$846$	1098.51			0.0446426
$847$	−45023.0	+	25994.1i	−1.82646	+	1.05451i
$848$	71.7671	+	124.304i	0.00290624	+	0.00503376i
$849$	4810.32	−	8331.72i	0.194452	−	0.336801i
$850$		−	8159.17i		−	0.329244i
$851$	7284.12	+	4205.49i	0.293415	+	0.169403i
$852$	2486.54	+	1435.61i	0.0999853	+	0.0577265i
$853$			8114.12i			0.325700i	0.986651	+	0.162850i	$0.0520687\pi$
$853$			8114.12i			0.325700i	−0.986651	+	0.162850i	$0.947931\pi$
$854$	21434.5	−	37125.6i	0.858868	−	1.48760i
$855$	406.932	+	704.826i	0.0162769	+	0.0281925i
$856$	−17951.8	+	10364.5i	−0.716801	+	0.413845i
$857$	22298.1			0.888786			0.444393	−	0.895832i	$-0.353419\pi$
$857$	22298.1			0.888786			0.444393	+	0.895832i	$0.353419\pi$
$858$		0			0
$859$	33550.5			1.33263			0.666315	−	0.745670i	$-0.267870\pi$
$859$	33550.5			1.33263			0.666315	+	0.745670i	$0.267870\pi$
$860$	306.612	−	177.022i	0.0121574	−	0.00701908i
$861$	−2332.31	−	4039.68i	−0.0923170	−	0.159898i
$862$	6214.69	−	10764.2i	0.245560	−	0.425323i
$863$			14120.5i			0.556972i	0.960440	+	0.278486i	$0.0898326\pi$
$863$			14120.5i			0.556972i	−0.960440	+	0.278486i	$0.910167\pi$
$864$	8288.28	+	4785.24i	0.326358	+	0.188423i
$865$	2186.28	+	1262.25i	0.0859373	+	0.0496159i
$866$		−	21025.2i		−	0.825018i
$867$	−7849.03	+	13594.9i	−0.307459	+	0.532534i
$868$	1478.51	+	2560.85i	0.0578154	+	0.100139i
$869$	−23633.6	+	13644.9i	−0.922574	+	0.532648i
$870$	932.351			0.0363329
$871$		0			0
$872$	−16243.4			−0.630817
$873$	6780.45	−	3914.69i	0.262868	−	0.151767i
$874$	10131.0	+	17547.3i	0.392088	+	0.679116i
$875$	−1274.31	+	2207.18i	−0.0492339	+	0.0852757i
$876$		−	4049.36i		−	0.156182i
$877$	−1681.55	−	970.844i	−0.0647457	−	0.0373809i	0.467278	−	0.884111i	$-0.345235\pi$
$877$	−1681.55	−	970.844i	−0.0647457	−	0.0373809i	−0.532023	+	0.846730i	$0.678568\pi$
$878$	6641.36	+	3834.39i	0.255279	+	0.147385i
$879$			20232.6i			0.776368i
$880$	916.548	−	1587.51i	0.0351100	−	0.0608124i
$881$	−395.116	−	684.360i	−0.0151099	−	0.0261710i	0.858372	−	0.513028i	$-0.171476\pi$
$881$	−395.116	−	684.360i	−0.0151099	−	0.0261710i	−0.873481	+	0.486857i	$0.838143\pi$
$882$	375.014	−	216.514i	0.0143167	−	0.00826578i
$883$	36638.6			1.39636			0.698180	−	0.715922i	$-0.253993\pi$
$883$	36638.6			1.39636			0.698180	+	0.715922i	$0.253993\pi$
$884$		0			0
$885$	−148.217			−0.00562968
$886$	−21615.1	+	12479.5i	−0.819607	+	0.473201i
$887$	20343.2	+	35235.4i	0.770075	+	1.33381i	0.937522	+	0.347927i	$0.113114\pi$
$887$	20343.2	+	35235.4i	0.770075	+	1.33381i	−0.167447	+	0.985881i	$0.553552\pi$
$888$	5113.78	−	8857.33i	0.193252	−	0.334721i
$889$			10055.1i			0.379344i
$890$	−1444.90	−	834.215i	−0.0544194	−	0.0314190i
$891$	10449.8	+	6033.20i	0.392909	+	0.226846i
$892$		−	1777.08i		−	0.0667053i
$893$	−1724.70	+	2987.27i	−0.0646304	+	0.111943i
$894$	13020.4	+	22552.0i	0.487101	+	0.843684i
$895$	−75.0317	+	43.3196i	−0.00280227	+	0.00161789i
$896$	−17102.2			−0.637663
$897$		0			0
$898$	−1438.21			−0.0534449
$899$	17228.8	−	9947.02i	0.639167	−	0.369023i
$900$	1203.75	+	2084.95i	0.0445833	+	0.0772205i
$901$	−36.3600	+	62.9773i	−0.00134442	+	0.00232861i
$902$			11549.5i			0.426336i
$903$	−25422.9	−	14677.9i	−0.936901	−	0.540920i
$904$	13431.2	+	7754.48i	0.494152	+	0.285299i
$905$			601.618i			0.0220977i
$906$	−4607.64	+	7980.66i	−0.168961	+	0.292649i
$907$	−5232.22	−	9062.46i	−0.191547	−	0.331769i	0.754216	−	0.656626i	$-0.228017\pi$
$907$	−5232.22	−	9062.46i	−0.191547	−	0.331769i	−0.945763	+	0.324857i	$0.894684\pi$
$908$	−4112.98	+	2374.63i	−0.150324	+	0.0867896i
$909$	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	$0.724212\pi$
$912$	17372.4	−	10030.0i	0.630767	−	0.364173i
$913$	−19544.5	−	33852.1i	−0.708465	−	1.22710i
$914$	17621.4	−	30521.2i	0.637708	−	1.10454i
$915$		−	1905.04i		−	0.0688291i
$916$	−263.202	−	151.960i	−0.00949393	−	0.00548133i
$917$	−32371.5	−	18689.7i	−1.16576	−	0.673051i
$918$		−	9746.80i		−	0.350427i
$919$	−538.627	+	932.930i	−0.0193337	+	0.0334870i	−0.875530	−	0.483163i	$-0.839488\pi$
$919$	−538.627	+	932.930i	−0.0193337	+	0.0334870i	0.856197	+	0.516650i	$0.172821\pi$
$920$	−497.324	−	861.391i	−0.0178221	−	0.0308687i
$921$	23318.6	−	13463.0i	0.834282	−	0.481673i
$922$	−30762.3			−1.09881
$923$		0			0
$924$	6237.04			0.222060
$925$	12397.0	−	7157.38i	0.440659	−	0.254414i
$926$	−17464.3	−	30249.1i	−0.619777	−	1.07348i
$927$	6246.61	−	10819.4i	0.221322	−	0.383341i
$928$		−	11303.0i		−	0.399826i
$929$	48266.9	+	27866.9i	1.70461	+	0.984159i	0.940951	+	0.338542i	$0.109934\pi$
$929$	48266.9	+	27866.9i	1.70461	+	0.984159i	0.763661	+	0.645617i	$0.223400\pi$
$930$	−519.107	−	299.706i	−0.0183034	−	0.0105675i
$931$			1359.74i			0.0478665i
$932$	−184.642	+	319.810i	−0.00648944	+	0.0112400i
$933$	−14563.5	−	25224.7i	−0.511025	−	0.885121i
$934$	19570.4	−	11299.0i	0.685612	−	0.395838i
$935$	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	$0.517758\pi$
$938$	17914.9	−	10343.2i	0.623607	−	0.360040i
$939$	18427.7	+	31917.7i	0.640432	+	1.10926i
$940$	12.9032	−	22.3490i	0.000447718	−	0.000775471i
$941$		−	8823.35i		−	0.305667i	−0.988252	−	0.152834i	$-0.951160\pi$
$941$		−	8823.35i		−	0.305667i	0.988252	−	0.152834i	$-0.0488399\pi$
$942$	4617.25	+	2665.77i	0.159701	+	0.0922033i
$943$	4418.76	+	2551.17i	0.152593	+	0.0880993i
$944$		−	3611.95i		−	0.124533i
$945$	−760.175	+	1316.66i	−0.0261677	+	0.0453238i
$946$	36342.1	+	62946.4i	1.24903	+	2.16339i
$947$	24500.2	−	14145.2i	0.840708	−	0.485383i	−0.0167965	−	0.999859i	$-0.505347\pi$
$947$	24500.2	−	14145.2i	0.840708	−	0.485383i	0.857505	+	0.514476i	$0.172013\pi$
$948$	2234.23			0.0765447
$949$		0			0
$950$	34484.0			1.17769
$951$	−19882.6	+	11479.2i	−0.677956	+	0.391418i
$952$	−5613.42	−	9722.73i	−0.191105	−	0.331004i
$953$	−6199.52	+	10737.9i	−0.210726	+	0.364988i	−0.951942	−	0.306278i	$-0.900916\pi$
$953$	−6199.52	+	10737.9i	−0.210726	+	0.364988i	0.741216	+	0.671267i	$0.234250\pi$
$954$			97.8783i			0.00332173i
$955$	329.337	+	190.143i	0.0111592	+	0.00644280i
$956$	−4421.88	−	2552.97i	−0.149596	−	0.0863693i
$957$		−	41961.3i		−	1.41736i
$958$	18725.0	−	32432.7i	0.631500	−	1.09379i
$959$	−16437.2	−	28470.1i	−0.553478	−	0.958653i
$960$	−1017.77	+	587.610i	−0.0342171	+	0.0197553i
$961$	17001.0			0.570676
$962$		0			0
$963$	−11508.9			−0.385118
$964$	−6266.15	+	3617.77i	−0.209356	+	0.120872i
$965$	−371.097	−	642.758i	−0.0123793	−	0.0214416i
$966$	−6284.49	+	10885.0i	−0.209317	+	0.362547i
$967$			26667.1i			0.886820i	0.896319	+	0.443410i	$0.146231\pi$
$967$			26667.1i			0.886820i	−0.896319	+	0.443410i	$0.853769\pi$
$968$	−59884.5	−	34574.3i	−1.98839	−	1.14800i
$969$	8801.55	+	5081.58i	0.291792	+	0.168466i
$970$			839.001i			0.0277719i
$971$	−24710.3	+	42799.6i	−0.816676	+	1.41453i	0.0914414	+	0.995810i	$0.470853\pi$
$971$	−24710.3	+	42799.6i	−0.816676	+	1.41453i	−0.908118	+	0.418715i	$0.862481\pi$
$972$	2398.45	+	4154.23i	0.0791463	+	0.137085i
$973$	23512.5	−	13575.0i	0.774694	−	0.447270i
$974$	25100.3			0.825735
$975$		0			0
$976$	46424.5			1.52255
$977$	−674.425	+	389.380i	−0.0220847	+	0.0127506i	−0.511002	−	0.859580i	$-0.670725\pi$
$977$	−674.425	+	389.380i	−0.0220847	+	0.0127506i	0.488917	+	0.872330i	$0.337392\pi$
$978$	7119.10	+	12330.6i	0.232765	+	0.403160i
$979$	−37544.6	+	65029.2i	−1.22567	+	2.12292i
$980$		−	10.1728i		−	0.000331589i
$981$	−7810.23	−	4509.24i	−0.254191	−	0.146757i
$982$	24038.4	+	13878.6i	0.781157	+	0.451001i
$983$			5997.90i			0.194612i	0.995255	+	0.0973059i	$0.0310225\pi$
$983$			5997.90i			0.194612i	−0.995255	+	0.0973059i	$0.968977\pi$
$984$	3102.17	−	5373.12i	0.100502	−	0.174074i
$985$	355.847	+	616.344i	0.0115109	+	0.0199374i
$986$	−9969.01	+	5755.61i	−0.321986	+	0.185898i
$987$	−2139.75			−0.0690062
$988$		0			0
$989$	32110.6			1.03241
$990$	1082.55	−	625.009i	0.0347532	−	0.0200647i
$991$	−4487.47	−	7772.53i	−0.143844	−	0.249145i	0.785097	−	0.619373i	$-0.212613\pi$
$991$	−4487.47	−	7772.53i	−0.143844	−	0.249145i	−0.928941	+	0.370228i	$0.879280\pi$
$992$	−3633.37	+	6293.19i	−0.116290	+	0.201420i
$993$		−	17076.6i		−	0.545729i
$994$	−21844.0	−	12611.6i	−0.697031	−	0.402431i
$995$	−1165.34	−	672.808i	−0.0371293	−	0.0214366i
$996$			3200.24i			0.101811i
$997$	−14265.1	+	24707.9i	−0.453140	+	0.784861i	−0.998579	−	0.0532892i	$-0.983029\pi$
$997$	−14265.1	+	24707.9i	−0.453140	+	0.784861i	0.545439	+	0.838150i	$0.316363\pi$
$998$	3317.16	+	5745.48i	0.105213	+	0.182234i
$999$	14809.2	−	8550.08i	0.469011	−	0.270783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.f.23.1		8
13.2	odd	12		169.4.a.g.1.1		2
13.3	even	3		169.4.b.f.168.1		4
13.4	even	6	inner	169.4.e.f.147.1		8
13.5	odd	4		169.4.c.j.146.2		4
13.6	odd	12		169.4.c.j.22.2		4
13.7	odd	12		169.4.c.g.22.1		4
13.8	odd	4		169.4.c.g.146.1		4
13.9	even	3	inner	169.4.e.f.147.4		8
13.10	even	6		169.4.b.f.168.4		4
13.11	odd	12		13.4.a.b.1.2	✓	2
13.12	even	2	inner	169.4.e.f.23.4		8
39.2	even	12		1521.4.a.r.1.2		2
39.11	even	12		117.4.a.d.1.1		2
52.11	even	12		208.4.a.h.1.2		2
65.24	odd	12		325.4.a.f.1.1		2
65.37	even	12		325.4.b.e.274.4		4
65.63	even	12		325.4.b.e.274.1		4
91.76	even	12		637.4.a.b.1.2		2
104.11	even	12		832.4.a.z.1.1		2
104.37	odd	12		832.4.a.s.1.2		2
143.76	even	12		1573.4.a.b.1.1		2
156.11	odd	12		1872.4.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.b.1.2	✓	2	13.11	odd	12
117.4.a.d.1.1		2	39.11	even	12
169.4.a.g.1.1		2	13.2	odd	12
169.4.b.f.168.1		4	13.3	even	3
169.4.b.f.168.4		4	13.10	even	6
169.4.c.g.22.1		4	13.7	odd	12
169.4.c.g.146.1		4	13.8	odd	4
169.4.c.j.22.2		4	13.6	odd	12
169.4.c.j.146.2		4	13.5	odd	4
169.4.e.f.23.1		8	1.1	even	1	trivial
169.4.e.f.23.4		8	13.12	even	2	inner
169.4.e.f.147.1		8	13.4	even	6	inner
169.4.e.f.147.4		8	13.9	even	3	inner
208.4.a.h.1.2		2	52.11	even	12
325.4.a.f.1.1		2	65.24	odd	12
325.4.b.e.274.1		4	65.63	even	12
325.4.b.e.274.4		4	65.37	even	12
637.4.a.b.1.2		2	91.76	even	12
832.4.a.s.1.2		2	104.37	odd	12
832.4.a.z.1.1		2	104.11	even	12
1521.4.a.r.1.2		2	39.2	even	12
1573.4.a.b.1.1		2	143.76	even	12
1872.4.a.bb.1.1		2	156.11	odd	12

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.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.21837 + 1.28078i) q^{2} +(1.84233 + 3.19101i) q^{3} +(-0.719224 + 1.24573i) q^{4} -0.561553i q^{5} +(-8.17394 - 4.71922i) q^{6} +(-15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 - 11.6249i) q^{9} +O(q^{10})\)	\(q+(-2.21837 + 1.28078i) q^{2} +(1.84233 + 3.19101i) q^{3} +(-0.719224 + 1.24573i) q^{4} -0.561553i q^{5} +(-8.17394 - 4.71922i) q^{6} +(-15.7418 - 9.08854i) q^{7} -24.1771i q^{8} +(6.71165 - 11.6249i) q^{9} +(0.719224 + 1.24573i) q^{10} +(56.0653 - 32.3693i) q^{11} -5.30019 q^{12} +46.5616 q^{14} +(1.79192 - 1.03457i) q^{15} +(25.2116 + 43.6679i) q^{16} +(-12.7732 + 22.1238i) q^{17} +34.3845i q^{18} +(-93.5045 - 53.9848i) q^{19} +(0.699544 + 0.403882i) q^{20} -66.9763i q^{21} +(-82.9157 + 143.614i) q^{22} +(36.6307 + 63.4462i) q^{23} +(77.1493 - 44.5421i) q^{24} +124.685 q^{25} +148.946 q^{27} +(22.6438 - 13.0734i) q^{28} +(-87.9545 - 152.342i) q^{29} +(-2.65009 + 4.59010i) q^{30} +113.093i q^{31} +(55.6462 + 32.1274i) q^{32} +(206.581 + 119.270i) q^{33} -65.4384i q^{34} +(-5.10370 + 8.83986i) q^{35} +(9.65435 + 16.7218i) q^{36} +(99.4264 - 57.4039i) q^{37} +276.570 q^{38} -13.5767 q^{40} +(60.3151 - 34.8229i) q^{41} +(85.7817 + 148.578i) q^{42} +(219.151 - 379.581i) q^{43} +93.1231i q^{44} +(-6.52800 - 3.76894i) q^{45} +(-162.521 - 93.8314i) q^{46} -31.9479i q^{47} +(-92.8963 + 160.901i) q^{48} +(-6.29686 - 10.9065i) q^{49} +(-276.597 + 159.693i) q^{50} -94.1298 q^{51} +2.84658 q^{53} +(-330.417 + 190.767i) q^{54} +(-18.1771 - 31.4836i) q^{55} +(-219.734 + 380.591i) q^{56} -397.831i q^{57} +(390.231 + 225.300i) q^{58} +(-62.0356 - 35.8163i) q^{59} +2.97633i q^{60} +(460.348 - 797.345i) q^{61} +(-144.847 - 250.882i) q^{62} +(-211.307 + 121.998i) q^{63} -567.978 q^{64} -611.032 q^{66} +(384.758 - 222.140i) q^{67} +(-18.3736 - 31.8240i) q^{68} +(-134.972 + 233.778i) q^{69} -26.1468i q^{70} +(-469.142 - 270.859i) q^{71} +(-281.056 - 162.268i) q^{72} +764.004i q^{73} +(-147.043 + 254.686i) q^{74} +(229.710 + 397.870i) q^{75} +(134.501 - 77.6543i) q^{76} -1176.76 q^{77} -421.538 q^{79} +(24.5218 - 14.1577i) q^{80} +(93.1932 + 161.415i) q^{81} +(-89.2007 + 154.500i) q^{82} -603.797i q^{83} +(83.4346 + 48.1710i) q^{84} +(12.4237 + 7.17283i) q^{85} +1122.73i q^{86} +(324.082 - 561.327i) q^{87} +(-782.596 - 1355.50i) q^{88} +(-1004.49 + 579.941i) q^{89} +19.3087 q^{90} -105.383 q^{92} +(-360.880 + 208.354i) q^{93} +(40.9181 + 70.8722i) q^{94} +(-30.3153 + 52.5077i) q^{95} +236.757i q^{96} +(505.126 + 291.634i) q^{97} +(27.9375 + 16.1298i) q^{98} -869.006i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9}+O(q^{10}) \) 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9	\( 8 q - 10 q^{3} - 14 q^{4} - 70 q^{9} + 14 q^{10} + 172 q^{12} + 356 q^{14} + 78 q^{16} + 38 q^{17} - 284 q^{22} + 392 q^{23} + 948 q^{25} + 1340 q^{27} + 88 q^{29} + 86 q^{30} - 214 q^{35} - 500 q^{36} + 1256 q^{38} - 356 q^{40} - 394 q^{42} + 574 q^{43} - 570 q^{48} + 766 q^{49} - 1924 q^{51} - 472 q^{53} + 36 q^{55} - 2030 q^{56} + 2116 q^{61} - 664 q^{62} - 3076 q^{64} - 3272 q^{66} + 422 q^{68} + 1592 q^{69} - 294 q^{74} - 1032 q^{75} - 3048 q^{77} - 4032 q^{79} - 244 q^{81} + 144 q^{82} + 5116 q^{87} - 2484 q^{88} - 1000 q^{90} - 3152 q^{92} + 1622 q^{94} - 292 q^{95}+O(q^{100}) \) 8 * q - 10 * q^3 - 14 * q^4 - 70 * q^9 + 14 * q^10 + 172 * q^12 + 356 * q^14 + 78 * q^16 + 38 * q^17 - 284 * q^22 + 392 * q^23 + 948 * q^25 + 1340 * q^27 + 88 * q^29 + 86 * q^30 - 214 * q^35 - 500 * q^36 + 1256 * q^38 - 356 * q^40 - 394 * q^42 + 574 * q^43 - 570 * q^48 + 766 * q^49 - 1924 * q^51 - 472 * q^53 + 36 * q^55 - 2030 * q^56 + 2116 * q^61 - 664 * q^62 - 3076 * q^64 - 3272 * q^66 + 422 * q^68 + 1592 * q^69 - 294 * q^74 - 1032 * q^75 - 3048 * q^77 - 4032 * q^79 - 244 * q^81 + 144 * q^82 + 5116 * q^87 - 2484 * q^88 - 1000 * q^90 - 3152 * q^92 + 1622 * q^94 - 292 * q^95

Introduction

L-functions

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