LMFDB - Embedded newform 169.4.e.h.23.5

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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.5
Character	$\chi$	$=$	169.23
Dual form			169.4.e.h.147.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.73781 + 1.58068i) q^{2} +(-3.54442 - 6.13911i) q^{3} +(0.997073 - 1.72698i) q^{4} -13.6039i q^{5} +(19.4079 + 11.2051i) q^{6} +(12.4114 + 7.16574i) q^{7} -18.9866i q^{8} +(-11.6258 + 20.1364i) q^{9} +O(q^{10})$	\(q+(-2.73781 + 1.58068i) q^{2} +(-3.54442 - 6.13911i) q^{3} +(0.997073 - 1.72698i) q^{4} -13.6039i q^{5} +(19.4079 + 11.2051i) q^{6} +(12.4114 + 7.16574i) q^{7} -18.9866i q^{8} +(-11.6258 + 20.1364i) q^{9} +(21.5034 + 37.2450i) q^{10} +(58.6492 - 33.8611i) q^{11} -14.1362 q^{12} -45.3068 q^{14} +(-83.5160 + 48.2180i) q^{15} +(37.9883 + 65.7976i) q^{16} +(0.168897 - 0.292539i) q^{17} -73.5064i q^{18} +(-35.0939 - 20.2615i) q^{19} +(-23.4937 - 13.5641i) q^{20} -101.593i q^{21} +(-107.047 + 185.411i) q^{22} +(-77.8158 - 134.781i) q^{23} +(-116.561 + 67.2965i) q^{24} -60.0670 q^{25} -26.5720 q^{27} +(24.7502 - 14.2895i) q^{28} +(16.8963 + 29.2652i) q^{29} +(152.434 - 264.024i) q^{30} -157.397i q^{31} +(-76.4663 - 44.1478i) q^{32} +(-415.754 - 240.036i) q^{33} +1.06789i q^{34} +(97.4822 - 168.844i) q^{35} +(23.1835 + 40.1550i) q^{36} +(50.7667 - 29.3102i) q^{37} +128.107 q^{38} -258.293 q^{40} +(51.3976 - 29.6744i) q^{41} +(160.586 + 278.144i) q^{42} +(-104.155 + 180.402i) q^{43} -135.048i q^{44} +(273.935 + 158.156i) q^{45} +(426.090 + 246.003i) q^{46} +221.212i q^{47} +(269.293 - 466.428i) q^{48} +(-68.8044 - 119.173i) q^{49} +(164.452 - 94.9464i) q^{50} -2.39457 q^{51} -409.639 q^{53} +(72.7491 - 42.0017i) q^{54} +(-460.645 - 797.860i) q^{55} +(136.053 - 235.651i) q^{56} +287.260i q^{57} +(-92.5175 - 53.4150i) q^{58} +(150.331 + 86.7937i) q^{59} +192.308i q^{60} +(-280.398 + 485.664i) q^{61} +(248.793 + 430.922i) q^{62} +(-288.585 + 166.615i) q^{63} -328.679 q^{64} +1517.68 q^{66} +(-233.025 + 134.537i) q^{67} +(-0.336806 - 0.583366i) q^{68} +(-551.623 + 955.440i) q^{69} +616.351i q^{70} +(-52.8062 - 30.4877i) q^{71} +(382.323 + 220.734i) q^{72} -282.066i q^{73} +(-92.6598 + 160.491i) q^{74} +(212.902 + 368.758i) q^{75} +(-69.9823 + 40.4043i) q^{76} +970.560 q^{77} +984.026 q^{79} +(895.106 - 516.790i) q^{80} +(408.078 + 706.813i) q^{81} +(-93.8112 + 162.486i) q^{82} +1201.86i q^{83} +(-175.450 - 101.296i) q^{84} +(-3.97968 - 2.29767i) q^{85} -658.543i q^{86} +(119.775 - 207.456i) q^{87} +(-642.908 - 1113.55i) q^{88} +(467.566 - 269.949i) q^{89} -999.976 q^{90} -310.352 q^{92} +(-966.275 + 557.879i) q^{93} +(-349.664 - 605.636i) q^{94} +(-275.636 + 477.415i) q^{95} +625.913i q^{96} +(-1374.60 - 793.627i) q^{97} +(376.747 + 217.515i) q^{98} +1574.65i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * 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 $

$2$	−2.73781	+	1.58068i	−0.967962	+	0.558853i	−0.898614	−	0.438739i	$-0.855425\pi$
$2$	−2.73781	+	1.58068i	−0.967962	+	0.558853i	−0.0693479	+	0.997593i	$0.522092\pi$
$3$	−3.54442	−	6.13911i	−0.682123	−	1.18147i	−0.974332	−	0.225118i	$-0.927723\pi$
$3$	−3.54442	−	6.13911i	−0.682123	−	1.18147i	0.292208	−	0.956355i	$-0.405610\pi$
$4$	0.997073	−	1.72698i	0.124634	−	0.215873i
$5$		−	13.6039i		−	1.21677i	−0.793641	−	0.608386i	$-0.791817\pi$
$5$		−	13.6039i		−	1.21677i	0.793641	−	0.608386i	$-0.208183\pi$
$6$	19.4079	+	11.2051i	1.32054	+	0.762414i
$7$	12.4114	+	7.16574i	0.670154	+	0.386913i	0.796135	−	0.605119i	$-0.206875\pi$
$7$	12.4114	+	7.16574i	0.670154	+	0.386913i	−0.125981	+	0.992033i	$0.540208\pi$
$8$		−	18.9866i		−	0.839098i
$9$	−11.6258	+	20.1364i	−0.430585	+	0.745794i
$10$	21.5034	+	37.2450i	0.679998	+	1.17779i
$11$	58.6492	−	33.8611i	1.60758	−	0.928138i	0.617672	−	0.786436i	$-0.288076\pi$
$11$	58.6492	−	33.8611i	1.60758	−	0.928138i	0.989909	−	0.141702i	$-0.0452575\pi$
$12$	−14.1362			−0.340063
$13$		0			0
$13$		0			0
$14$	−45.3068			−0.864911
$15$	−83.5160	+	48.2180i	−1.43758	+	0.829989i
$16$	37.9883	+	65.7976i	0.593567	+	1.02809i
$17$	0.168897	−	0.292539i	0.00240963	−	0.00417360i	−0.864818	−	0.502085i	$-0.832566\pi$
$17$	0.168897	−	0.292539i	0.00240963	−	0.00417360i	0.867228	+	0.497912i	$0.165900\pi$
$18$		−	73.5064i		−	0.962535i
$19$	−35.0939	−	20.2615i	−0.423741	−	0.244647i	0.272935	−	0.962032i	$-0.412005\pi$
$19$	−35.0939	−	20.2615i	−0.423741	−	0.244647i	−0.696677	+	0.717385i	$0.745339\pi$
$20$	−23.4937	−	13.5641i	−0.262668	−	0.151651i
$21$		−	101.593i		−	1.05569i
$22$	−107.047	+	185.411i	−1.03739	+	1.79680i
$23$	−77.8158	−	134.781i	−0.705466	−	1.22190i	−0.966523	−	0.256580i	$-0.917404\pi$
$23$	−77.8158	−	134.781i	−0.705466	−	1.22190i	0.261057	−	0.965323i	$-0.415929\pi$
$24$	−116.561	+	67.2965i	−0.991371	+	0.572368i
$25$	−60.0670			−0.480536
$26$		0			0
$27$	−26.5720			−0.189399
$28$	24.7502	−	14.2895i	0.167048	−	0.0964452i
$29$	16.8963	+	29.2652i	0.108192	+	0.187393i	0.915038	−	0.403368i	$-0.132161\pi$
$29$	16.8963	+	29.2652i	0.108192	+	0.187393i	−0.806846	+	0.590762i	$0.798827\pi$
$30$	152.434	−	264.024i	0.927684	−	1.60680i
$31$		−	157.397i		−	0.911911i	−0.890003	−	0.455956i	$-0.849298\pi$
$31$		−	157.397i		−	0.911911i	0.890003	−	0.455956i	$-0.150702\pi$
$32$	−76.4663	−	44.1478i	−0.422421	−	0.243885i
$33$	−415.754	−	240.036i	−2.19314	−	1.26621i
$34$			1.06789i			0.00538651i
$35$	97.4822	−	168.844i	0.470786	−	0.815425i
$36$	23.1835	+	40.1550i	0.107331	+	0.185903i
$37$	50.7667	−	29.3102i	0.225567	−	0.130231i	−0.382958	−	0.923766i	$-0.625095\pi$
$37$	50.7667	−	29.3102i	0.225567	−	0.130231i	0.608526	+	0.793534i	$0.291761\pi$
$38$	128.107			0.546888
$39$		0			0
$40$	−258.293			−1.02099
$41$	51.3976	−	29.6744i	0.195779	−	0.113033i	−0.398906	−	0.916992i	$-0.630610\pi$
$41$	51.3976	−	29.6744i	0.195779	−	0.113033i	0.594685	+	0.803959i	$0.297277\pi$
$42$	160.586	+	278.144i	0.589976	+	1.02187i
$43$	−104.155	+	180.402i	−0.369385	+	0.639793i	−0.989469	−	0.144742i	$-0.953765\pi$
$43$	−104.155	+	180.402i	−0.369385	+	0.639793i	0.620085	+	0.784535i	$0.287098\pi$
$44$		−	135.048i		−	0.462711i
$45$	273.935	+	158.156i	0.907462	+	0.523924i
$46$	426.090	+	246.003i	1.36573	+	0.788504i
$47$			221.212i			0.686533i	0.939238	+	0.343266i	$0.111533\pi$
$47$			221.212i			0.686533i	−0.939238	+	0.343266i	$0.888467\pi$
$48$	269.293	−	466.428i	0.809772	−	1.40257i
$49$	−68.8044	−	119.173i	−0.200596	−	0.347442i
$50$	164.452	−	94.9464i	0.465141	−	0.268549i
$51$	−2.39457			−0.00657465
$52$		0			0
$53$	−409.639			−1.06167			−0.530833	−	0.847477i	$-0.678121\pi$
$53$	−409.639			−1.06167			−0.530833	+	0.847477i	$0.678121\pi$
$54$	72.7491	−	42.0017i	0.183332	−	0.105847i
$55$	−460.645	−	797.860i	−1.12933	−	1.95606i
$56$	136.053	−	235.651i	0.324658	−	0.562325i
$57$			287.260i			0.667518i
$58$	−92.5175	−	53.4150i	−0.209451	−	0.120927i
$59$	150.331	+	86.7937i	0.331719	+	0.191518i	0.656604	−	0.754235i	$-0.271992\pi$
$59$	150.331	+	86.7937i	0.331719	+	0.191518i	−0.324885	+	0.945754i	$0.605326\pi$
$60$			192.308i			0.413780i
$61$	−280.398	+	485.664i	−0.588546	+	1.01939i	0.405877	+	0.913928i	$0.366966\pi$
$61$	−280.398	+	485.664i	−0.588546	+	1.01939i	−0.994423	+	0.105464i	$0.966367\pi$
$62$	248.793	+	430.922i	0.509625	+	0.882696i
$63$	−288.585	+	166.615i	−0.577116	+	0.333198i
$64$	−328.679			−0.641951
$65$		0			0
$66$	1517.68			2.83050
$67$	−233.025	+	134.537i	−0.424903	+	0.245318i	−0.697173	−	0.716903i	$-0.745559\pi$
$67$	−233.025	+	134.537i	−0.424903	+	0.245318i	0.272270	+	0.962221i	$0.412226\pi$
$68$	−0.336806	−	0.583366i	−0.000600644	−	0.00104035i
$69$	−551.623	+	955.440i	−0.962430	+	1.66698i
$70$			616.351i			1.05240i
$71$	−52.8062	−	30.4877i	−0.0882669	−	0.0509609i	0.455217	−	0.890381i	$-0.349562\pi$
$71$	−52.8062	−	30.4877i	−0.0882669	−	0.0509609i	−0.543484	+	0.839420i	$0.682895\pi$
$72$	382.323	+	220.734i	0.625794	+	0.361303i
$73$		−	282.066i		−	0.452238i	−0.974100	−	0.226119i	$-0.927396\pi$
$73$		−	282.066i		−	0.452238i	0.974100	−	0.226119i	$-0.0726038\pi$
$74$	−92.6598	+	160.491i	−0.145561	+	0.252118i
$75$	212.902	+	368.758i	0.327785	+	0.567740i
$76$	−69.9823	+	40.4043i	−0.105625	+	0.0609828i
$77$	970.560			1.43644
$78$		0			0
$79$	984.026			1.40141			0.700706	−	0.713450i	$-0.252868\pi$
$79$	984.026			1.40141			0.700706	+	0.713450i	$0.252868\pi$
$80$	895.106	−	516.790i	1.25095	−	0.722236i
$81$	408.078	+	706.813i	0.559778	+	0.969565i
$82$	−93.8112	+	162.486i	−0.126338	+	0.218824i
$83$			1201.86i			1.58942i	0.606991	+	0.794709i	$0.292376\pi$
$83$			1201.86i			1.58942i	−0.606991	+	0.794709i	$0.707624\pi$
$84$	−175.450	−	101.296i	−0.227895	−	0.131575i
$85$	−3.97968	−	2.29767i	−0.00507832	−	0.00293197i
$86$		−	658.543i		−	0.825727i
$87$	119.775	−	207.456i	0.147600	−	0.255651i
$88$	−642.908	−	1113.55i	−0.778798	−	1.34892i
$89$	467.566	−	269.949i	0.556875	−	0.321512i	−0.195015	−	0.980800i	$-0.562476\pi$
$89$	467.566	−	269.949i	0.556875	−	0.321512i	0.751890	+	0.659288i	$0.229142\pi$
$90$	−999.976			−1.17119
$91$		0			0
$92$	−310.352			−0.351701
$93$	−966.275	+	557.879i	−1.07740	+	0.622036i
$94$	−349.664	−	605.636i	−0.383671	−	0.664538i
$95$	−275.636	+	477.415i	−0.297680	+	0.515597i
$96$			625.913i			0.665438i
$97$	−1374.60	−	793.627i	−1.43886	−	0.830728i	−0.441093	−	0.897461i	$-0.645409\pi$
$97$	−1374.60	−	793.627i	−1.43886	−	0.830728i	−0.997771	+	0.0667329i	$0.978742\pi$
$98$	376.747	+	217.515i	0.388339	+	0.224207i
$99$			1574.65i			1.59857i
$100$	−59.8912	+	103.735i	−0.0598912	+	0.103735i
$101$	580.363	+	1005.22i	0.571765	+	0.990326i	0.996385	+	0.0849545i	$0.0270745\pi$
$101$	580.363	+	1005.22i	0.571765	+	0.990326i	−0.424620	+	0.905372i	$0.639592\pi$
$102$	6.55589	−	3.78504i	0.00636402	−	0.00367427i
$103$	82.2962			0.0787270			0.0393635	−	0.999225i	$-0.487467\pi$
$103$	82.2962			0.0787270			0.0393635	+	0.999225i	$0.487467\pi$
$104$		0			0
$105$	−1382.07			−1.28454
$106$	1121.51	−	647.507i	1.02765	−	0.593315i
$107$	−661.022	−	1144.92i	−0.597229	−	1.03443i	−0.993228	−	0.116180i	$-0.962935\pi$
$107$	−661.022	−	1144.92i	−0.597229	−	1.03443i	0.396000	−	0.918251i	$-0.370398\pi$
$108$	−26.4942	+	45.8894i	−0.0236056	+	0.0408862i
$109$		−	2073.41i		−	1.82199i	−0.412420	−	0.910994i	$-0.635316\pi$
$109$		−	2073.41i		−	1.82199i	0.412420	−	0.910994i	$-0.364684\pi$
$110$	2522.32	+	1456.26i	2.18630	+	1.26226i
$111$	−359.877	−	207.775i	−0.307730	−	0.177668i
$112$			1088.86i			0.918636i
$113$	801.411	−	1388.09i	0.667172	−	1.15558i	−0.311519	−	0.950240i	$-0.600838\pi$
$113$	801.411	−	1388.09i	0.667172	−	1.15558i	0.978691	−	0.205336i	$-0.0658288\pi$
$114$	−454.065	−	786.464i	−0.373045	−	0.646133i
$115$	−1833.55	+	1058.60i	−1.48678	+	0.858392i
$116$	67.3872			0.0539375
$117$		0			0
$118$	−548.771			−0.428122
$119$	4.19252	−	2.42055i	0.00322964	−	0.00186463i
$120$	915.497	+	1585.69i	0.696442	+	1.20627i
$121$	1627.65	−	2819.18i	1.22288	−	2.11809i
$122$		−	1772.87i		−	1.31564i
$123$	−364.349	−	210.357i	−0.267091	−	0.154205i
$124$	−271.821	−	156.936i	−0.196857	−	0.113655i
$125$		−	883.344i		−	0.632070i
$126$	526.727	−	912.319i	0.372418	−	0.645046i
$127$	307.248	+	532.169i	0.214676	+	0.371829i	0.953172	−	0.302428i	$-0.0977972\pi$
$127$	307.248	+	532.169i	0.214676	+	0.371829i	−0.738496	+	0.674257i	$0.764464\pi$
$128$	1511.59	−	872.717i	1.04380	−	0.602641i
$129$	1476.68			1.00786
$130$		0			0
$131$	−330.171			−0.220208			−0.110104	−	0.993920i	$-0.535118\pi$
$131$	−330.171			−0.220208			−0.110104	+	0.993920i	$0.535118\pi$
$132$	−829.075	+	478.667i	−0.546680	+	0.315626i
$133$	−290.377	−	502.947i	−0.189315	−	0.327902i
$134$	425.318	−	736.673i	0.274193	−	0.474917i
$135$			361.484i			0.230456i
$136$	−5.55433	−	3.20679i	−0.00350206	−	0.00202191i
$137$	−1994.06	−	1151.27i	−1.24353	−	0.717953i	−0.273720	−	0.961809i	$-0.588254\pi$
$137$	−1994.06	−	1151.27i	−1.24353	−	0.717953i	−0.969811	+	0.243856i	$0.921587\pi$
$138$		−	3487.75i		−	2.15143i
$139$	−603.611	+	1045.48i	−0.368328	+	0.637963i	−0.989304	−	0.145866i	$-0.953403\pi$
$139$	−603.611	+	1045.48i	−0.368328	+	0.637963i	0.620976	+	0.783829i	$0.286736\pi$
$140$	−194.394	−	336.700i	−0.117352	−	0.203260i
$141$	1358.04	−	784.066i	0.811119	−	0.468300i
$142$	192.765			0.113919
$143$		0			0
$144$	−1766.57			−1.02232
$145$	398.122	−	229.856i	0.228015	−	0.131645i
$146$	445.856	+	772.245i	0.252735	+	0.437750i
$147$	−487.743	+	844.796i	−0.273662	+	0.473997i
$148$		−	116.898i		−	0.0649251i
$149$	293.529	+	169.469i	0.161388	+	0.0931774i	0.578519	−	0.815669i	$-0.303631\pi$
$149$	293.529	+	169.469i	0.161388	+	0.0931774i	−0.417131	+	0.908846i	$0.636964\pi$
$150$	−1165.77	−	673.060i	−0.634567	−	0.366367i
$151$			1694.81i			0.913386i	0.889624	+	0.456693i	$0.150966\pi$
$151$			1694.81i			0.913386i	−0.889624	+	0.456693i	$0.849034\pi$
$152$	−384.697	+	666.314i	−0.205283	+	0.355561i
$153$	3.92713	+	6.80199i	0.00207510	+	0.00359417i
$154$	−2657.21	+	1534.14i	−1.39042	+	0.802757i
$155$	−2141.21			−1.10959
$156$		0			0
$157$	9.59250			0.00487621			0.00243811	−	0.999997i	$-0.499224\pi$
$157$	9.59250			0.00487621			0.00243811	+	0.999997i	$0.499224\pi$
$158$	−2694.08	+	1555.43i	−1.35651	+	0.783184i
$159$	1451.93	+	2514.82i	0.724187	+	1.25433i
$160$	−600.584	+	1040.24i	−0.296752	+	0.513990i
$161$		−	2230.43i		−	1.09182i
$162$	−2234.48	−	1290.08i	−1.08369	−	0.625668i
$163$	−105.742	−	61.0501i	−0.0508119	−	0.0293363i	0.474379	−	0.880321i	$-0.342673\pi$
$163$	−105.742	−	61.0501i	−0.0508119	−	0.0293363i	−0.525191	+	0.850985i	$0.676006\pi$
$164$		−	118.350i		−	0.0563512i
$165$	−3265.43	+	5655.90i	−1.54069	+	2.66855i
$166$	−1899.76	−	3290.48i	−0.888251	−	1.53850i
$167$	1914.99	−	1105.62i	0.887346	−	0.512309i	0.0142723	−	0.999898i	$-0.495457\pi$
$167$	1914.99	−	1105.62i	0.887346	−	0.512309i	0.873073	+	0.487589i	$0.162123\pi$
$168$	−1928.92			−0.885828
$169$		0			0
$170$	14.5275			0.00655416
$171$	815.988	−	471.111i	0.364913	−	0.210683i
$172$	207.701	+	359.749i	0.0920758	+	0.159480i
$173$	−106.937	+	185.220i	−0.0469957	+	0.0813989i	−0.888566	−	0.458748i	$-0.848298\pi$
$173$	−106.937	+	185.220i	−0.0469957	+	0.0813989i	0.841571	+	0.540147i	$0.181631\pi$
$174$			757.301i			0.329947i
$175$	−745.517	−	430.424i	−0.322033	−	0.185926i
$176$	4455.96	+	2572.65i	1.90841	+	1.10182i
$177$		−	1230.53i		−	0.522556i
$178$	−853.405	+	1478.14i	−0.359356	+	0.622423i
$179$	1483.70	+	2569.85i	0.619537	+	1.07307i	0.989570	+	0.144051i	$0.0460130\pi$
$179$	1483.70	+	2569.85i	0.619537	+	1.07307i	−0.370033	+	0.929019i	$0.620654\pi$
$180$	546.266	−	315.387i	0.226202	−	0.130598i
$181$	−2329.44			−0.956609			−0.478304	−	0.878194i	$-0.658748\pi$
$181$	−2329.44			−0.956609			−0.478304	+	0.878194i	$0.658748\pi$
$182$		0			0
$183$	3975.39			1.60584
$184$	−2559.03	+	1477.46i	−1.02530	+	0.591955i
$185$	−398.734	−	690.627i	−0.158462	−	0.274464i
$186$	1763.65	−	3054.73i	0.695254	−	1.20421i
$187$		−	22.8762i		−	0.00894586i
$188$	382.028	+	220.564i	0.148204	+	0.0855654i
$189$	−329.796	−	190.408i	−0.126927	−	0.0732812i
$190$		−	1742.76i		−	0.665438i
$191$	2239.88	−	3879.58i	0.848544	−	1.46972i	−0.0339639	−	0.999423i	$-0.510813\pi$
$191$	2239.88	−	3879.58i	0.848544	−	1.46972i	0.882508	−	0.470298i	$-0.155854\pi$
$192$	1164.97	+	2017.79i	0.437890	+	0.758447i
$193$	1128.11	−	651.313i	0.420741	−	0.242915i	−0.274653	−	0.961543i	$-0.588563\pi$
$193$	1128.11	−	651.313i	0.420741	−	0.242915i	0.695394	+	0.718629i	$0.255230\pi$
$194$	5017.87			1.85702
$195$		0			0
$196$	−274.412			−0.100004
$197$	641.685	−	370.477i	0.232072	−	0.133987i	−0.379456	−	0.925210i	$-0.623889\pi$
$197$	641.685	−	370.477i	0.232072	−	0.133987i	0.611528	+	0.791223i	$0.290555\pi$
$198$	−2489.01	−	4311.09i	−0.893365	−	1.54735i
$199$	−2344.37	+	4060.57i	−0.835115	+	1.44646i	0.0588210	+	0.998269i	$0.481266\pi$
$199$	−2344.37	+	4060.57i	−0.835115	+	1.44646i	−0.893936	+	0.448194i	$0.852067\pi$
$200$			1140.47i			0.403217i
$201$	1651.87	+	953.709i	0.579672	+	0.334674i
$202$	−3177.85	−	1834.73i	−1.10689	−	0.639066i
$203$			484.297i			0.167443i
$204$	−2.38756	+	4.13538i	−0.000819426	+	0.00141929i
$205$	−403.688	−	699.209i	−0.137536	−	0.238219i
$206$	−225.311	+	130.084i	−0.0762048	+	0.0439969i
$207$	3618.68			1.21505
$208$		0			0
$209$	−2744.30			−0.908265
$210$	3783.85	−	2184.61i	1.24338	−	0.717867i
$211$	1602.56	+	2775.71i	0.522865	+	0.905628i	0.999646	+	0.0266064i	$0.00847009\pi$
$211$	1602.56	+	2775.71i	0.522865	+	0.905628i	−0.476781	+	0.879022i	$0.658197\pi$
$212$	−408.440	+	707.439i	−0.132320	+	0.229185i
$213$			432.244i			0.139046i
$214$	3619.51	+	2089.72i	1.15619	+	0.667526i
$215$	2454.18	+	1416.92i	0.778482	+	0.449457i
$216$			504.513i			0.158925i
$217$	1127.86	−	1953.51i	0.352831	−	0.611121i
$218$	3277.39	+	5676.60i	1.01822	+	1.76362i
$219$	−1731.64	+	999.761i	−0.534307	+	0.308482i
$220$	−1837.18			−0.563014
$221$		0			0
$222$	1313.70			0.397161
$223$	−915.726	+	528.695i	−0.274984	+	0.158762i	−0.631151	−	0.775660i	$-0.717417\pi$
$223$	−915.726	+	528.695i	−0.274984	+	0.158762i	0.356166	+	0.934423i	$0.384084\pi$
$224$	−632.704	−	1095.87i	−0.188724	−	0.326880i
$225$	698.326	−	1209.54i	0.206911	−	0.358381i
$226$			5067.09i			1.49141i
$227$	4468.42	+	2579.84i	1.30652	+	0.754317i	0.981513	−	0.191396i	$-0.0613013\pi$
$227$	4468.42	+	2579.84i	1.30652	+	0.754317i	0.325003	+	0.945713i	$0.394635\pi$
$228$	496.093	+	286.419i	0.144099	+	0.0831956i
$229$			1698.25i			0.490059i	0.969516	+	0.245030i	$0.0787977\pi$
$229$			1698.25i			0.490059i	−0.969516	+	0.245030i	$0.921202\pi$
$230$	3346.61	−	5796.50i	0.959430	−	1.66178i
$231$	−3440.07	−	5958.37i	−0.979826	−	1.69711i
$232$	555.647	−	320.803i	0.157241	−	0.0907834i
$233$	−3162.23			−0.889119			−0.444559	−	0.895749i	$-0.646640\pi$
$233$	−3162.23			−0.889119			−0.444559	+	0.895749i	$0.646640\pi$
$234$		0			0
$235$	3009.35			0.835354
$236$	299.782	−	173.079i	0.0826871	−	0.0477394i
$237$	−3487.80	−	6041.04i	−0.955936	−	1.65573i
$238$	−7.65221	+	13.2540i	−0.00208411	+	0.00360979i
$239$		−	2350.04i		−	0.636030i	−0.948086	−	0.318015i	$-0.896984\pi$
$239$		−	2350.04i		−	0.636030i	0.948086	−	0.318015i	$-0.103016\pi$
$240$	−6345.26	−	3663.44i	−1.70660	−	0.985308i
$241$	4474.91	+	2583.59i	1.19608	+	0.690555i	0.959678	−	0.281102i	$-0.0906998\pi$
$241$	4474.91	+	2583.59i	1.19608	+	0.690555i	0.236398	+	0.971656i	$0.424033\pi$
$242$			10291.2i			2.73364i
$243$	2534.08	−	4389.15i	0.668976	−	1.15870i
$244$	559.155	+	968.485i	0.146706	+	0.254102i
$245$	−1621.22	+	936.011i	−0.422759	+	0.244080i
$246$	1330.02			0.344712
$247$		0			0
$248$	−2988.43			−0.765183
$249$	7378.37	−	4259.91i	1.87785	−	1.08418i
$250$	1396.28	+	2418.43i	0.353234	+	0.611820i
$251$	1447.00	−	2506.28i	0.363880	−	0.630259i	−0.624715	−	0.780853i	$-0.714785\pi$
$251$	1447.00	−	2506.28i	0.363880	−	0.630259i	0.988596	+	0.150593i	$0.0481183\pi$
$252$			664.508i			0.166111i
$253$	−9127.67	−	5269.86i	−2.26819	−	1.30954i
$254$	−1682.37	−	971.318i	−0.415596	−	0.239945i
$255$			32.5756i			0.00799986i
$256$	−1444.25	+	2501.52i	−0.352600	+	0.610722i
$257$	−3081.31	−	5336.99i	−0.747887	−	1.29538i	−0.948834	−	0.315776i	$-0.897735\pi$
$257$	−3081.31	−	5336.99i	−0.747887	−	1.29538i	0.200946	−	0.979602i	$-0.435598\pi$
$258$	−4042.87	+	2334.15i	−0.975574	+	0.563248i
$259$	840.116			0.201553
$260$		0			0
$261$	−785.729			−0.186343
$262$	903.946	−	521.894i	0.213153	−	0.123064i
$263$	99.7136	+	172.709i	0.0233787	+	0.0404931i	0.877478	−	0.479617i	$-0.159224\pi$
$263$	99.7136	+	172.709i	0.0233787	+	0.0404931i	−0.854099	+	0.520110i	$0.825891\pi$
$264$	−4557.47	+	7893.77i	−1.06247	+	1.84026i
$265$			5572.70i			1.29181i
$266$	1589.99	+	917.982i	0.366499	+	0.211598i
$267$	−3314.50	−	1913.63i	−0.759715	−	0.438622i
$268$			536.572i			0.122300i
$269$	−554.001	+	959.559i	−0.125569	+	0.217492i	−0.921955	−	0.387296i	$-0.873409\pi$
$269$	−554.001	+	959.559i	−0.125569	+	0.217492i	0.796386	+	0.604788i	$0.206742\pi$
$270$	−571.389	−	989.675i	−0.128791	−	0.223073i
$271$	351.653	−	203.027i	0.0788244	−	0.0455093i	−0.460070	−	0.887883i	$-0.652176\pi$
$271$	351.653	−	203.027i	0.0788244	−	0.0455093i	0.538894	+	0.842373i	$0.318842\pi$
$272$	25.6645			0.00572110
$273$		0			0
$274$	7279.13			1.60492
$275$	−3522.88	+	2033.94i	−0.772501	+	0.446003i
$276$	1100.02	+	1905.29i	0.239903	+	0.415525i
$277$	144.405	−	250.117i	0.0313230	−	0.0542530i	−0.849939	−	0.526881i	$-0.823361\pi$
$277$	144.405	−	250.117i	0.0313230	−	0.0542530i	0.881262	+	0.472628i	$0.156695\pi$
$278$		−	3816.45i		−	0.823366i
$279$	3169.41	+	1829.86i	0.680098	+	0.392655i
$280$	−3205.78	−	1850.86i	−0.684221	−	0.395035i
$281$		−	5134.93i		−	1.09012i	−0.838396	−	0.545061i	$-0.816506\pi$
$281$		−	5134.93i		−	1.09012i	0.838396	−	0.545061i	$-0.183494\pi$
$282$	−2478.71	+	4293.25i	−0.523422	+	0.906593i
$283$	2637.20	+	4567.76i	0.553940	+	0.959453i	0.997985	+	0.0634483i	$0.0202098\pi$
$283$	2637.20	+	4567.76i	0.553940	+	0.959453i	−0.444045	+	0.896005i	$0.646457\pi$
$284$	−105.303	+	60.7969i	−0.0220021	+	0.0127029i
$285$	3907.87			0.812218
$286$		0			0
$287$	850.556			0.174936
$288$	1777.96	−	1026.51i	0.363776	−	0.210026i
$289$	2456.44	+	4254.68i	0.499988	+	0.866005i
$290$	−726.655	+	1258.60i	−0.147140	+	0.254854i
$291$			11251.8i			2.26664i
$292$	−487.124	−	281.241i	−0.0976258	−	0.0563643i
$293$	1252.00	+	722.845i	0.249634	+	0.144127i	0.619597	−	0.784920i	$-0.287296\pi$
$293$	1252.00	+	722.845i	0.249634	+	0.144127i	−0.369962	+	0.929047i	$0.620629\pi$
$294$		−	3083.86i		−	0.611749i
$295$	1180.74	−	2045.09i	0.233034	−	0.403627i
$296$	−556.501	−	963.888i	−0.109277	−	0.189273i
$297$	−1558.43	+	899.758i	−0.304475	+	0.175789i
$298$	−1071.50			−0.208290
$299$		0			0
$300$	849.117			0.163413
$301$	−2585.43	+	1492.70i	−0.495089	+	0.285840i
$302$	−2678.94	−	4640.06i	−0.510449	−	0.884124i
$303$	4114.10	−	7125.83i	0.780029	−	1.35105i
$304$		−	3078.79i		−	0.580858i
$305$	6606.94	+	3814.52i	1.24037	+	0.716127i
$306$	−21.5035	−	12.4150i	−0.00401723	−	0.00231935i
$307$		−	9421.42i		−	1.75149i	−0.482770	−	0.875747i	$-0.660369\pi$
$307$		−	9421.42i		−	1.75149i	0.482770	−	0.875747i	$-0.339631\pi$
$308$	967.719	−	1676.14i	0.179029	−	0.310087i
$309$	−291.692	−	505.225i	−0.0537015	−	0.0930138i
$310$	5862.23	−	3384.56i	1.07404	−	0.620097i
$311$	−7885.87			−1.43784			−0.718918	−	0.695095i	$-0.755362\pi$
$311$	−7885.87			−1.43784			−0.718918	+	0.695095i	$0.755362\pi$
$312$		0			0
$313$	−550.423			−0.0993986			−0.0496993	−	0.998764i	$-0.515826\pi$
$313$	−550.423			−0.0993986			−0.0496993	+	0.998764i	$0.515826\pi$
$314$	−26.2625	+	15.1626i	−0.00471999	+	0.00272509i
$315$	2266.61	+	3925.89i	0.405426	+	0.702219i
$316$	981.146	−	1699.39i	0.174664	−	0.302527i
$317$		−	150.974i		−	0.0267494i	−0.999911	−	0.0133747i	$-0.995743\pi$
$317$		−	150.974i		−	0.0267494i	0.999911	−	0.0133747i	$-0.00425742\pi$
$318$	−7950.23	−	4590.07i	−1.40197	−	0.809428i
$319$	1981.90	+	1144.25i	0.347854	+	0.200833i
$320$			4471.32i			0.781108i
$321$	−4685.88	+	8116.18i	−0.814767	+	1.41122i
$322$	3525.59	+	6106.50i	0.610166	+	1.05684i
$323$	−11.8545	+	6.84422i	−0.00204212	+	0.00117902i
$324$	1627.54			0.279070
$325$		0			0
$326$	386.002			0.0655787
$327$	−12728.9	+	7349.03i	−2.15263	+	1.24282i
$328$	−563.416	−	975.866i	−0.0948459	−	0.164278i
$329$	−1585.14	+	2745.55i	−0.265629	+	0.460082i
$330$		−	20646.4i		−	3.44408i
$331$	6130.84	+	3539.64i	1.01807	+	0.587784i	0.913545	−	0.406738i	$-0.133334\pi$
$331$	6130.84	+	3539.64i	1.01807	+	0.587784i	0.104527	+	0.994522i	$0.466667\pi$
$332$	2075.60	+	1198.35i	0.343112	+	0.198096i
$333$			1363.02i			0.224303i
$334$	−3495.26	+	6053.97i	−0.572612	+	0.991792i
$335$	1830.23	+	3170.05i	0.298496	+	0.517010i
$336$	6684.61	−	3859.36i	1.08534	−	0.626623i
$337$	6633.34			1.07223			0.536114	−	0.844145i	$-0.319892\pi$
$337$	6633.34			1.07223			0.536114	+	0.844145i	$0.319892\pi$
$338$		0			0
$339$	−11362.1			−1.82037
$340$	−7.93607	+	4.58189i	−0.00126586	+	0.000730847i
$341$	−5329.62	−	9231.18i	−0.846379	−	1.46597i
$342$	−1489.35	+	2579.62i	−0.235481	+	0.407866i
$343$		−	6887.83i		−	1.08428i
$344$	3425.23	+	1977.56i	0.536849	+	0.309950i
$345$	12997.7	+	7504.25i	2.02833	+	1.17106i
$346$		−	676.130i		−	0.105055i
$347$	−3202.08	+	5546.17i	−0.495380	+	0.858023i	−0.999986	−	0.00532645i	$-0.998305\pi$
$347$	−3202.08	+	5546.17i	−0.495380	+	0.858023i	0.504606	+	0.863350i	$0.331638\pi$
$348$	−238.848	−	413.698i	−0.0367920	−	0.0637256i
$349$	145.577	−	84.0492i	0.0223283	−	0.0128913i	−0.488794	−	0.872399i	$-0.662563\pi$
$349$	145.577	−	84.0492i	0.0223283	−	0.0128913i	0.511123	+	0.859508i	$0.329230\pi$
$350$	2721.45			0.415621
$351$		0			0
$352$	−5979.58			−0.905434
$353$	7319.58	−	4225.96i	1.10363	−	0.637182i	0.166459	−	0.986048i	$-0.446767\pi$
$353$	7319.58	−	4225.96i	1.10363	−	0.637182i	0.937172	+	0.348866i	$0.113433\pi$
$354$	1945.07	+	3368.96i	0.292032	+	0.505815i
$355$	−414.753	+	718.373i	−0.0620078	+	0.107401i
$356$		−	1076.64i		−	0.160285i
$357$	−29.7200	−	17.1589i	−0.00440603	−	0.00254382i
$358$	−8124.20	−	4690.51i	−1.19938	−	0.692461i
$359$			2631.92i			0.386929i	0.981107	+	0.193464i	$0.0619724\pi$
$359$			2631.92i			0.386929i	−0.981107	+	0.193464i	$0.938028\pi$
$360$	3002.85	−	5201.10i	0.439623	−	0.761450i
$361$	−2608.45	−	4517.96i	−0.380295	−	0.658691i
$362$	6377.58	−	3682.09i	0.925961	−	0.534604i
$363$	−23076.3			−3.33662
$364$		0			0
$365$	−3837.21			−0.550271
$366$	−10883.9	+	6283.81i	−1.55440	+	0.897431i
$367$	6634.93	+	11492.0i	0.943708	+	1.63455i	0.758318	+	0.651885i	$0.226021\pi$
$367$	6634.93	+	11492.0i	0.943708	+	1.63455i	0.185390	+	0.982665i	$0.440645\pi$
$368$	5912.18	−	10240.2i	0.837482	−	1.45056i
$369$			1379.95i			0.194681i
$370$	2183.31	+	1260.54i	0.306771	+	0.177114i
$371$	−5084.20	−	2935.37i	−0.711479	−	0.410773i
$372$			2224.98i			0.310108i
$373$	5840.03	−	10115.2i	0.810684	−	1.40415i	−0.101701	−	0.994815i	$-0.532429\pi$
$373$	5840.03	−	10115.2i	0.810684	−	1.40415i	0.912386	−	0.409332i	$-0.134238\pi$
$374$	36.1599	+	62.6308i	0.00499943	+	0.00865926i
$375$	−5422.95	+	3130.94i	−0.746773	+	0.431150i
$376$	4200.06			0.576068
$377$		0			0
$378$	1203.89			0.163814
$379$	2925.63	−	1689.11i	0.396516	−	0.228928i	−0.288464	−	0.957491i	$-0.593144\pi$
$379$	2925.63	−	1689.11i	0.396516	−	0.228928i	0.684979	+	0.728562i	$0.259811\pi$
$380$	549.657	+	952.035i	0.0742022	+	0.128522i
$381$	2178.03	−	3772.46i	0.292871	−	0.507267i
$382$			14162.1i			1.89685i
$383$	−3793.98	−	2190.46i	−0.506171	−	0.292238i	0.225087	−	0.974339i	$-0.427733\pi$
$383$	−3793.98	−	2190.46i	−0.506171	−	0.292238i	−0.731258	+	0.682101i	$0.761067\pi$
$384$	−10715.4	−	6186.55i	−1.42401	−	0.822151i
$385$		−	13203.4i		−	1.74782i
$386$	−2059.03	+	3566.35i	−0.271507	+	0.470265i
$387$	−2421.77	−	4194.64i	−0.318103	−	0.550970i
$388$	−2741.16	+	1582.61i	−0.358663	+	0.207074i
$389$	12484.0			1.62716			0.813578	−	0.581456i	$-0.197517\pi$
$389$	12484.0			1.62716			0.813578	+	0.581456i	$0.197517\pi$
$390$		0			0
$391$	−52.5716			−0.00679964
$392$	−2262.69	+	1306.36i	−0.291538	+	0.168320i
$393$	1170.26	+	2026.96i	0.150209	+	0.260169i
$394$	−1171.21	+	2028.59i	−0.149758	+	0.259388i
$395$		−	13386.6i		−	1.70520i
$396$	2719.39	+	1570.04i	0.345087	+	0.199236i
$397$	−8184.36	−	4725.24i	−1.03466	−	0.597363i	−0.116346	−	0.993209i	$-0.537118\pi$
$397$	−8184.36	−	4725.24i	−1.03466	−	0.597363i	−0.918317	+	0.395846i	$0.870451\pi$
$398$		−	14822.8i		−	1.86683i
$399$	−2058.43	+	3565.31i	−0.258272	+	0.447340i
$400$	−2281.84	−	3952.27i	−0.285230	−	0.494033i
$401$	2516.69	−	1453.01i	0.313411	−	0.180948i	−0.335041	−	0.942204i	$-0.608750\pi$
$401$	2516.69	−	1453.01i	0.313411	−	0.180948i	0.648452	+	0.761256i	$0.275417\pi$
$402$	−6030.02			−0.748134
$403$		0			0
$404$	2314.66			0.285046
$405$	9615.43	−	5551.47i	1.17974	−	0.681123i
$406$	−765.516	−	1325.91i	−0.0935762	−	0.162079i
$407$	1984.95	−	3438.04i	0.241745	−	0.418715i
$408$			45.4648i			0.00551678i
$409$	−5019.42	−	2897.96i	−0.606832	−	0.350355i	0.164892	−	0.986312i	$-0.447272\pi$
$409$	−5019.42	−	2897.96i	−0.606832	−	0.350355i	−0.771725	+	0.635957i	$0.780606\pi$
$410$	2210.45	+	1276.20i	0.266259	+	0.153725i
$411$			16322.3i			1.95893i
$412$	82.0553	−	142.124i	0.00981208	−	0.0169950i
$413$	1243.88	+	2154.47i	0.148202	+	0.256693i
$414$	−9907.26	+	5719.96i	−1.17612	+	0.679036i
$415$	16350.1			1.93396
$416$		0			0
$417$	8557.79			1.00498
$418$	7513.38	−	4337.85i	0.879167	−	0.507587i
$419$	2071.23	+	3587.48i	0.241495	+	0.418281i	0.961140	−	0.276060i	$-0.0890290\pi$
$419$	2071.23	+	3587.48i	0.241495	+	0.418281i	−0.719645	+	0.694342i	$0.755696\pi$
$420$	−1378.03	+	2386.81i	−0.160097	+	0.277296i
$421$			1426.92i			0.165187i	0.996583	+	0.0825935i	$0.0263203\pi$
$421$			1426.92i			0.165187i	−0.996583	+	0.0825935i	$0.973680\pi$
$422$	−8774.99	−	5066.24i	−1.01223	−	0.584410i
$423$	−4454.42	−	2571.76i	−0.512012	−	0.295610i
$424$			7777.66i			0.890841i
$425$	−10.1452	+	17.5719i	−0.00115791	+	0.00200556i
$426$	−683.238	−	1183.40i	−0.0777066	−	0.134592i
$427$	−6960.28	+	4018.52i	−0.788833	+	0.455433i
$428$	−2636.35			−0.297740
$429$		0			0
$430$	−8958.78			−1.00472
$431$	−2202.37	+	1271.54i	−0.246136	+	0.142106i	−0.617994	−	0.786183i	$-0.712054\pi$
$431$	−2202.37	+	1271.54i	−0.246136	+	0.142106i	0.371858	+	0.928290i	$0.378721\pi$
$432$	−1009.42	−	1748.38i	−0.112421	−	0.194719i
$433$	−1724.22	+	2986.43i	−0.191364	+	0.331452i	−0.945703	−	0.325033i	$-0.894624\pi$
$433$	−1724.22	+	2986.43i	−0.191364	+	0.331452i	0.754338	+	0.656486i	$0.227958\pi$
$434$			7131.14i			0.788723i
$435$	−2822.22	−	1629.41i	−0.311069	−	0.179596i
$436$	−3580.74	−	2067.34i	−0.393317	−	0.227082i
$437$			6306.65i			0.690361i
$438$	3160.60	−	5474.31i	0.344793	−	0.597198i
$439$	−6321.28	−	10948.8i	−0.687240	−	1.19033i	−0.972727	−	0.231952i	$-0.925489\pi$
$439$	−6321.28	−	10948.8i	−0.687240	−	1.19033i	0.285487	−	0.958382i	$-0.407845\pi$
$440$	−15148.7	+	8746.08i	−1.64133	+	0.947621i
$441$	3199.62			0.345494
$442$		0			0
$443$	8486.59			0.910181			0.455091	−	0.890445i	$-0.349607\pi$
$443$	8486.59			0.910181			0.455091	+	0.890445i	$0.349607\pi$
$444$	−717.647	+	414.334i	−0.0767072	+	0.0442870i
$445$	−3672.37	−	6360.73i	−0.391207	−	0.677590i
$446$	1671.39	−	2894.93i	0.177450	−	0.307352i
$447$		−	2402.67i		−	0.254234i
$448$	−4079.37	−	2355.23i	−0.430206	−	0.248379i
$449$	9846.32	+	5684.77i	1.03491	+	0.597508i	0.918389	−	0.395680i	$-0.129491\pi$
$449$	9846.32	+	5684.77i	1.03491	+	0.597508i	0.116526	+	0.993188i	$0.462824\pi$
$450$			4415.31i			0.462532i
$451$	2009.62	−	3480.76i	0.209821	−	0.363420i
$452$	−1598.13	−	2768.05i	−0.166305	−	0.288048i
$453$	10404.6	−	6007.10i	1.07914	−	0.623042i
$454$	−16311.6			−1.68621
$455$		0			0
$456$	5454.10			0.560113
$457$	9776.58	−	5644.51i	1.00072	−	0.577766i	0.0922591	−	0.995735i	$-0.470591\pi$
$457$	9776.58	−	5644.51i	1.00072	−	0.577766i	0.908461	+	0.417969i	$0.137258\pi$
$458$	−2684.38	−	4649.49i	−0.273871	−	0.474359i
$459$	−4.48795	+	7.77335i	−0.000456382	+	0.000790477i
$460$			4222.01i			0.427940i
$461$	−3320.44	−	1917.06i	−0.335463	−	0.193680i	0.322801	−	0.946467i	$-0.395376\pi$
$461$	−3320.44	−	1917.06i	−0.335463	−	0.193680i	−0.658264	+	0.752787i	$0.728709\pi$
$462$	18836.5	+	10875.3i	1.89687	+	1.09516i
$463$		−	1294.44i		−	0.129930i	−0.997888	−	0.0649651i	$-0.979306\pi$
$463$		−	1294.44i		−	0.129930i	0.997888	−	0.0649651i	$-0.0206936\pi$
$464$	−1283.72	+	2223.47i	−0.128438	+	0.222461i
$465$	7589.35	+	13145.1i	0.756876	+	1.31095i
$466$	8657.59	−	4998.46i	0.860634	−	0.496887i
$467$	−13861.5			−1.37352			−0.686760	−	0.726884i	$-0.740968\pi$
$467$	−13861.5			−1.37352			−0.686760	+	0.726884i	$0.740968\pi$
$468$		0			0
$469$	−3856.22			−0.379667
$470$	−8239.03	+	4756.80i	−0.808591	+	0.466840i
$471$	−33.9998	−	58.8894i	−0.00332618	−	0.00576111i
$472$	1647.92	−	2854.28i	0.160703	−	0.278345i
$473$			14107.3i			1.37136i
$474$	19097.9	+	11026.2i	1.85062	+	1.06846i
$475$	2107.98	+	1217.04i	0.203623	+	0.117562i
$476$		−	9.65386i		−	0.000929588i
$477$	4762.38	−	8248.68i	0.457137	−	0.791784i
$478$	3714.65	+	6433.96i	0.355448	+	0.615653i
$479$	8337.79	−	4813.83i	0.795331	−	0.459185i	−0.0465049	−	0.998918i	$-0.514808\pi$
$479$	8337.79	−	4813.83i	0.795331	−	0.459185i	0.841836	+	0.539733i	$0.181475\pi$
$480$	8514.88			0.809686
$481$		0			0
$482$	−16335.3			−1.54368
$483$	−13692.9	+	7905.58i	−1.28995	+	0.744754i
$484$	−3245.78	−	5621.85i	−0.304825	−	0.527972i
$485$	−10796.5	+	18700.0i	−1.01081	+	1.75077i
$486$			16022.2i			1.49544i
$487$	10351.5	+	5976.42i	0.963183	+	0.556094i	0.897151	−	0.441724i	$-0.145633\pi$
$487$	10351.5	+	5976.42i	0.963183	+	0.556094i	0.0660314	+	0.997818i	$0.478966\pi$
$488$	9221.11	+	5323.81i	0.855369	+	0.493848i
$489$			865.548i			0.0800438i
$490$	2959.06	−	5125.24i	0.272810	−	0.472520i
$491$	2705.06	+	4685.30i	0.248631	+	0.430641i	0.963146	−	0.268979i	$-0.0866862\pi$
$491$	2705.06	+	4685.30i	0.248631	+	0.430641i	−0.714516	+	0.699620i	$0.753353\pi$
$492$	−726.565	+	419.482i	−0.0665774	+	0.0384385i
$493$	11.4149			0.00104281
$494$		0			0
$495$	21421.4			1.94509
$496$	10356.3	−	5979.22i	0.937525	−	0.541280i
$497$	−436.934	−	756.791i	−0.0394349	−	0.0683033i
$498$	−13467.1	+	23325.6i	−1.21179	+	2.09889i
$499$		−	14472.9i		−	1.29838i	−0.760624	−	0.649192i	$-0.775107\pi$
$499$		−	14472.9i		−	1.29838i	0.760624	−	0.649192i	$-0.224893\pi$
$500$	−1525.52	−	880.759i	−0.136447	−	0.0787775i
$501$	−13575.1	−	7837.58i	−1.21056	−	0.698916i
$502$			9148.97i			0.813423i
$503$	300.970	−	521.296i	0.0266791	−	0.0462096i	−0.852378	−	0.522927i	$-0.824840\pi$
$503$	300.970	−	521.296i	0.0266791	−	0.0462096i	0.879057	+	0.476717i	$0.158173\pi$
$504$	3163.45	+	5479.25i	0.279586	+	0.484257i
$505$	13674.9	−	7895.22i	1.20500	−	0.695708i
$506$	33319.8			2.92736
$507$		0			0
$508$	1225.39			0.107024
$509$	15086.9	−	8710.42i	1.31378	−	0.758512i	0.331061	−	0.943609i	$-0.392593\pi$
$509$	15086.9	−	8710.42i	1.31378	−	0.758512i	0.982720	+	0.185097i	$0.0592599\pi$
$510$	−51.4915	−	89.1859i	−0.00447075	−	0.00774356i
$511$	2021.21	−	3500.85i	0.174977	−	0.303069i
$512$			4831.90i			0.417074i
$513$	932.515	+	538.388i	0.0802564	+	0.0463361i
$514$	16872.1	+	9741.11i	1.44785	+	0.835919i
$515$		−	1119.55i		−	0.0957929i
$516$	1472.36	−	2550.20i	0.125614	−	0.217570i
$517$	7490.48	+	12973.9i	0.637197	+	1.10366i
$518$	−2300.08	+	1327.95i	−0.195096	+	0.112639i
$519$	1516.11			0.128227
$520$		0			0
$521$	12881.5			1.08320			0.541601	−	0.840636i	$-0.317818\pi$
$521$	12881.5			1.08320			0.541601	+	0.840636i	$0.317818\pi$
$522$	2151.18	−	1241.98i	0.180373	−	0.104138i
$523$	−8267.01	−	14318.9i	−0.691188	−	1.19717i	−0.971449	−	0.237249i	$-0.923754\pi$
$523$	−8267.01	−	14318.9i	−0.691188	−	1.19717i	0.280261	−	0.959924i	$-0.409579\pi$
$524$	−329.205	+	570.199i	−0.0274454	+	0.0475368i
$525$			6102.41i			0.507297i
$526$	−545.994	−	315.230i	−0.0452594	−	0.0261305i
$527$	−46.0446	−	26.5839i	−0.00380595	−	0.00219737i
$528$		−	36474.2i		−	3.00632i
$529$	−6027.10	+	10439.2i	−0.495365	+	0.857997i
$530$	−8808.64	−	15257.0i	−0.721930	−	1.25042i
$531$	−3495.43	+	2018.09i	−0.285666	+	0.164930i
$532$	−1158.11			−0.0943802
$533$		0			0
$534$	12099.3			0.980501
$535$	−15575.5	+	8992.50i	−1.25867	+	0.726691i
$536$	2554.40	+	4424.35i	0.205846	+	0.356535i
$537$	10517.7	−	18217.2i	0.845202	−	1.46393i
$538$		−	3502.79i		−	0.280699i
$539$	−8070.65	−	4659.59i	−0.644949	−	0.372361i
$540$	624.276	+	360.426i	0.0497492	+	0.0287227i
$541$			19026.9i			1.51207i	0.654531	+	0.756035i	$0.272866\pi$
$541$			19026.9i			1.51207i	−0.654531	+	0.756035i	$0.727134\pi$
$542$	−641.840	+	1111.70i	−0.0508660	+	0.0881025i
$543$	8256.52	+	14300.7i	0.652525	+	1.13021i
$544$	−25.8299	+	14.9129i	−0.00203575	+	0.00117534i
$545$	−28206.5			−2.21694
$546$		0			0
$547$	8153.61			0.637336			0.318668	−	0.947866i	$-0.396764\pi$
$547$	8153.61			0.637336			0.318668	+	0.947866i	$0.396764\pi$
$548$	−3976.44	+	2295.80i	−0.309973	+	0.178963i
$549$	−6519.70	−	11292.4i	−0.506838	−	0.877869i
$550$	6429.99	−	11137.1i	0.498501	−	0.863429i
$551$		−	1369.37i		−	0.105875i
$552$	18140.6	+	10473.5i	1.39876	+	0.807573i
$553$	12213.2	+	7051.27i	0.939162	+	0.542225i
$554$			913.031i			0.0700198i
$555$	−2826.56	+	4895.74i	−0.216181	+	0.374437i
$556$	1203.69	+	2084.85i	0.0918125	+	0.159024i
$557$	−1132.81	+	654.031i	−0.0861739	+	0.0497525i	−0.542468	−	0.840077i	$-0.682510\pi$
$557$	−1132.81	+	654.031i	−0.0861739	+	0.0497525i	0.456294	+	0.889829i	$0.349177\pi$
$558$	−11569.7			−0.877746
$559$		0			0
$560$	14812.7			1.11777
$561$	−140.440	+	81.0829i	−0.0105693	+	0.00610218i
$562$	8116.66	+	14058.5i	0.609218	+	1.05520i
$563$	−10368.0	+	17958.0i	−0.776129	+	1.34429i	0.158029	+	0.987434i	$0.449486\pi$
$563$	−10368.0	+	17958.0i	−0.776129	+	1.34429i	−0.934158	+	0.356860i	$0.883847\pi$
$564$		−	3127.09i		−	0.233465i
$565$	−18883.4	−	10902.3i	−1.40607	−	0.811797i
$566$	−14440.3	−	8337.11i	−1.07239	−	0.619143i
$567$			11696.7i			0.866343i
$568$	−578.858	+	1002.61i	−0.0427612	+	0.0740645i
$569$	−7490.98	−	12974.8i	−0.551913	−	0.955941i	−0.998137	−	0.0610196i	$-0.980565\pi$
$569$	−7490.98	−	12974.8i	−0.551913	−	0.955941i	0.446224	−	0.894921i	$-0.352769\pi$
$570$	−10699.0	+	6177.07i	−0.786197	+	0.453911i
$571$	5668.79			0.415467			0.207734	−	0.978185i	$-0.433391\pi$
$571$	5668.79			0.415467			0.207734	+	0.978185i	$0.433391\pi$
$572$		0			0
$573$	−31756.2			−2.31525
$574$	−2328.66	+	1344.45i	−0.169332	+	0.0977637i
$575$	4674.16	+	8095.89i	0.339002	+	0.587168i
$576$	3821.15	−	6618.42i	0.276414	−	0.478763i
$577$			6872.94i			0.495882i	0.968775	+	0.247941i	$0.0797540\pi$
$577$			6872.94i			0.495882i	−0.968775	+	0.247941i	$0.920246\pi$
$578$	−13450.6	−	7765.68i	−0.967940	−	0.558840i
$579$	−7996.97	−	4617.05i	−0.573994	−	0.331396i
$580$		−	916.731i		−	0.0656297i
$581$	−8612.24	+	14916.8i	−0.614967	+	1.06515i
$582$	−17785.4	−	30805.3i	−1.26672	−	2.19402i
$583$	−24025.0	+	13870.8i	−1.70671	+	0.985372i
$584$	−5355.49			−0.379472
$585$		0			0
$586$	−4570.34			−0.322182
$587$	16102.4	−	9296.71i	1.13223	−	0.653691i	0.187732	−	0.982220i	$-0.439886\pi$
$587$	16102.4	−	9296.71i	1.13223	−	0.653691i	0.944494	+	0.328530i	$0.106553\pi$
$588$	972.631	+	1684.65i	0.0682154	+	0.118152i
$589$	−3189.08	+	5523.65i	−0.223097	+	0.386415i
$590$			7465.44i			0.520928i
$591$	−4548.80	−	2626.25i	−0.316603	−	0.182791i
$592$	3857.08	+	2226.89i	0.267779	+	0.154602i
$593$		−	15612.6i		−	1.08117i	−0.841291	−	0.540583i	$-0.818204\pi$
$593$		−	15612.6i		−	1.08117i	0.841291	−	0.540583i	$-0.181796\pi$
$594$	2844.45	−	4926.74i	0.196480	−	0.340314i
$595$	−32.9290	−	57.0347i	−0.00226884	−	0.00392974i
$596$	585.339	−	337.946i	0.0402289	−	0.0232262i
$597$	33237.7			2.27861
$598$		0			0
$599$	−22979.8			−1.56749			−0.783747	−	0.621081i	$-0.786694\pi$
$599$	−22979.8			−1.56749			−0.783747	+	0.621081i	$0.786694\pi$
$600$	7001.46	−	4042.30i	0.476389	−	0.275044i
$601$	−1390.88	−	2409.08i	−0.0944015	−	0.163508i	0.814957	−	0.579521i	$-0.196760\pi$
$601$	−1390.88	−	2409.08i	−0.0944015	−	0.163508i	−0.909359	+	0.416013i	$0.863427\pi$
$602$	4718.95	−	8173.46i	0.319485	−	0.553364i
$603$		−	6256.38i		−	0.422520i
$604$	2926.90	+	1689.85i	0.197175	+	0.113839i
$605$	−38351.9	−	22142.5i	−2.57723	−	1.48797i
$606$			26012.2i			1.74369i
$607$	2039.29	−	3532.15i	0.136363	−	0.236187i	−0.789755	−	0.613423i	$-0.789792\pi$
$607$	2039.29	−	3532.15i	0.136363	−	0.236187i	0.926117	+	0.377236i	$0.123125\pi$
$608$	1789.00	+	3098.64i	0.119331	+	0.206688i
$609$	2973.15	−	1716.55i	0.197829	−	0.114217i
$610$	−24118.1			−1.60084
$611$		0			0
$612$	15.6625			0.00103451
$613$	−22767.9	+	13145.1i	−1.50014	+	0.866107i	−0.500142	+	0.865944i	$0.666719\pi$
$613$	−22767.9	+	13145.1i	−1.50014	+	0.866107i	−1.00000		0.000163453i	$0.999948\pi$
$614$	14892.2	+	25794.1i	0.978828	+	1.69538i
$615$	−2861.68	+	4956.58i	−0.187633	+	0.324989i
$616$		−	18427.6i		−	1.20531i
$617$	−4201.69	−	2425.85i	−0.274155	−	0.158283i	0.356619	−	0.934250i	$-0.383929\pi$
$617$	−4201.69	−	2425.85i	−0.274155	−	0.158283i	−0.630774	+	0.775966i	$0.717263\pi$
$618$	1597.20	+	922.141i	0.103962	+	0.0600226i
$619$		−	4957.05i		−	0.321875i	−0.986965	−	0.160937i	$-0.948548\pi$
$619$		−	4957.05i		−	0.321875i	0.986965	−	0.160937i	$-0.0514517\pi$
$620$	−2134.94	+	3697.83i	−0.138293	+	0.239530i
$621$	2067.72	+	3581.40i	0.133615	+	0.231428i
$622$	21590.0	−	12465.0i	1.39177	−	0.803539i
$623$	7737.54			0.497589
$624$		0			0
$625$	−19525.3			−1.24962
$626$	1506.95	−	870.041i	0.0962141	−	0.0555492i
$627$	9726.96	+	16847.6i	0.619549	+	1.07309i
$628$	9.56443	−	16.5661i	0.000607742	−	0.00105264i
$629$		−	19.8017i		−	0.00125524i
$630$	−12411.1	−	7165.56i	−0.784875	−	0.453148i
$631$	2360.01	+	1362.55i	0.148892	+	0.0859627i	0.572595	−	0.819838i	$-0.305937\pi$
$631$	2360.01	+	1362.55i	0.148892	+	0.0859627i	−0.423703	+	0.905801i	$0.639270\pi$
$632$		−	18683.3i		−	1.17592i
$633$	11360.3	−	19676.5i	0.713317	−	1.23550i
$634$	238.641	+	413.339i	0.0149490	+	0.0258924i
$635$	7239.59	−	4179.78i	0.452432	−	0.261212i
$636$	5790.73			0.361034
$637$		0			0
$638$	−7234.77			−0.448946
$639$	1227.83	−	708.887i	0.0760127	−	0.0438860i
$640$	−11872.4	−	20563.6i	−0.733277	−	1.27007i
$641$	10698.2	−	18529.7i	0.659207	−	1.14178i	−0.321614	−	0.946871i	$-0.604225\pi$
$641$	10698.2	−	18529.7i	0.659207	−	1.14178i	0.980821	−	0.194909i	$-0.0624413\pi$
$642$		−	29627.4i		−	1.82134i
$643$	18908.6	+	10916.9i	1.15969	+	0.669549i	0.951230	−	0.308481i	$-0.0998208\pi$
$643$	18908.6	+	10916.9i	1.15969	+	0.669549i	0.208462	+	0.978030i	$0.433154\pi$
$644$	−3851.91	−	2223.90i	−0.235693	−	0.136078i
$645$		−	20088.6i		−	1.22634i
$646$	21.6370	−	37.4764i	0.00131780	−	0.00228249i
$647$	−2434.53	−	4216.73i	−0.147931	−	0.256224i	0.782532	−	0.622611i	$-0.213928\pi$
$647$	−2434.53	−	4216.73i	−0.147931	−	0.256224i	−0.930463	+	0.366387i	$0.880595\pi$
$648$	13420.0	−	7748.03i	0.813560	−	0.469709i
$649$	11755.7			0.711021
$650$		0			0
$651$	−15990.5			−0.962696
$652$	−210.865	+	121.743i	−0.0126658	+	0.00731260i
$653$	8423.48	+	14589.9i	0.504803	+	0.874344i	0.999985	+	0.00555458i	$0.00176809\pi$
$653$	8423.48	+	14589.9i	0.504803	+	0.874344i	−0.495182	+	0.868789i	$0.664899\pi$
$654$	23232.9	−	40240.5i	1.38911	−	2.40601i
$655$			4491.63i			0.267943i
$656$	3905.01	+	2254.56i	0.232416	+	0.134186i
$657$	5679.82	+	3279.24i	0.337277	+	0.194727i
$658$		−	10022.4i		−	0.593790i
$659$	12370.5	−	21426.4i	0.731240	−	1.26654i	−0.225114	−	0.974332i	$-0.572275\pi$
$659$	12370.5	−	21426.4i	0.731240	−	1.26654i	0.956354	−	0.292212i	$-0.0943912\pi$
$660$	6511.75	+	11278.7i	0.384045	+	0.665185i
$661$	−14308.5	+	8261.00i	−0.841959	+	0.486105i	−0.857930	−	0.513767i	$-0.828249\pi$
$661$	−14308.5	+	8261.00i	−0.841959	+	0.486105i	0.0159708	+	0.999872i	$0.494916\pi$
$662$	−22380.1			−1.31394
$663$		0			0
$664$	22819.3			1.33368
$665$	−6842.06	+	3950.26i	−0.398983	+	0.230353i
$666$	−2154.49	−	3731.68i	−0.125352	−	0.217116i
$667$	2629.59	−	4554.59i	0.152651	−	0.264399i
$668$		−	4409.55i		−	0.255405i
$669$	6491.43	+	3747.83i	0.375147	+	0.216591i
$670$	−10021.6	−	5786.00i	−0.577866	−	0.333631i
$671$			37978.4i			2.18501i
$672$	−4485.13	+	7768.47i	−0.257467	+	0.445946i
$673$	−10360.8	−	17945.4i	−0.593429	−	1.02785i	−0.993766	−	0.111482i	$-0.964440\pi$
$673$	−10360.8	−	17945.4i	−0.593429	−	1.02785i	0.400337	−	0.916368i	$-0.368893\pi$
$674$	−18160.8	+	10485.2i	−1.03788	+	0.599219i
$675$	1596.10			0.0910133
$676$		0			0
$677$	32407.3			1.83975			0.919877	−	0.392207i	$-0.128288\pi$
$677$	32407.3			1.83975			0.919877	+	0.392207i	$0.128288\pi$
$678$	31107.4	−	17959.9i	1.76205	−	1.01732i
$679$	−11373.9	−	19700.1i	−0.642840	−	1.11343i
$680$	−43.6250	+	75.5607i	−0.00246021	+	0.00426121i
$681$		−	36576.1i		−	2.05815i
$682$	29183.0	+	16848.8i	1.63853	+	0.946004i
$683$	−8767.45	−	5061.89i	−0.491182	−	0.283584i	0.233883	−	0.972265i	$-0.424857\pi$
$683$	−8767.45	−	5061.89i	−0.491182	−	0.283584i	−0.725065	+	0.688681i	$0.758190\pi$
$684$		−	1878.93i		−	0.105033i
$685$	−15661.8	+	27127.0i	−0.873586	+	1.51309i
$686$	10887.4	+	18857.6i	0.605954	+	1.04954i
$687$	10425.7	−	6019.31i	0.578991	−	0.334281i
$688$	−15826.7			−0.877018
$689$		0			0
$690$	−47447.1			−2.61780
$691$	−25724.9	+	14852.2i	−1.41624	+	0.817665i	−0.995966	−	0.0897342i	$-0.971398\pi$
$691$	−25724.9	+	14852.2i	−1.41624	+	0.817665i	−0.420271	+	0.907399i	$0.638065\pi$
$692$	213.248	+	369.356i	0.0117145	+	0.0202902i
$693$	−11283.5	+	19543.6i	−0.618507	+	1.07129i
$694$		−	20245.8i		−	1.10738i
$695$	14222.7	+	8211.48i	0.776256	+	0.448172i
$696$	−3938.89	−	2274.12i	−0.214516	−	0.123851i
$697$		−	20.0477i		−	0.00108947i
$698$	−265.709	+	460.221i	−0.0144086	+	0.0249565i
$699$	11208.3	+	19413.3i	0.606489	+	1.05047i
$700$	−1486.67	+	858.329i	−0.0802726	+	0.0463454i
$701$	20585.2			1.10912			0.554558	−	0.832145i	$-0.312887\pi$
$701$	20585.2			1.10912			0.554558	+	0.832145i	$0.312887\pi$
$702$		0			0
$703$	−2375.47			−0.127443
$704$	−19276.7	+	11129.4i	−1.03199	+	0.595819i
$705$	−10666.4	−	18474.7i	−0.569815	−	0.986948i
$706$	−13359.8	+	23139.8i	−0.712183	+	1.23354i
$707$			16634.9i			0.884894i
$708$	−2125.11	−	1226.93i	−0.112806	−	0.0651283i
$709$	25686.5	+	14830.1i	1.36062	+	0.785552i	0.989706	−	0.143117i	$-0.0457125\pi$
$709$	25686.5	+	14830.1i	1.36062	+	0.785552i	0.370910	+	0.928669i	$0.379046\pi$
$710$		−	2622.36i		−	0.138613i
$711$	−11440.1	+	19814.8i	−0.603427	+	1.04517i
$712$	−5125.42	−	8877.49i	−0.269780	−	0.467273i
$713$	−21214.1	+	12247.9i	−1.11427	+	0.643322i
$714$	108.491			0.00568649
$715$		0			0
$716$	5917.44			0.308862
$717$	−14427.1	+	8329.51i	−0.751452	+	0.433851i
$718$	−4160.21	−	7205.70i	−0.216236	−	0.374532i
$719$	639.842	−	1108.24i	0.0331879	−	0.0574831i	−0.848954	−	0.528466i	$-0.822767\pi$
$719$	639.842	−	1108.24i	0.0331879	−	0.0574831i	0.882142	+	0.470983i	$0.156101\pi$
$720$			24032.4i			1.24393i
$721$	1021.41	+	589.713i	0.0527592	+	0.0304605i
$722$	14282.9	+	8246.22i	0.736223	+	0.425059i
$723$		−	36629.3i		−	1.88417i
$724$	−2322.62	+	4022.90i	−0.119226	+	0.206506i
$725$	−1014.91	−	1757.87i	−0.0519900	−	0.0900493i
$726$	63178.6	−	36476.2i	3.22972	−	1.86468i
$727$	−6202.77			−0.316435			−0.158217	−	0.987404i	$-0.550575\pi$
$727$	−6202.77			−0.316435			−0.158217	+	0.987404i	$0.550575\pi$
$728$		0			0
$729$	−13891.1			−0.705740
$730$	10505.6	−	6065.39i	0.532642	−	0.307521i
$731$	35.1831	+	60.9390i	0.00178016	+	0.00308332i
$732$	3963.76	−	6865.43i	0.200143	−	0.346658i
$733$		−	35501.2i		−	1.78891i	−0.447162	−	0.894453i	$-0.647565\pi$
$733$		−	35501.2i		−	1.78891i	0.447162	−	0.894453i	$-0.352435\pi$
$734$	−36330.4	−	20975.4i	−1.82695	−	1.05479i
$735$	11492.5	+	6635.23i	0.576747	+	0.332985i
$736$			13741.6i			0.688209i
$737$	−9111.13	+	15780.9i	−0.455377	+	0.788736i
$738$	−2181.26	−	3778.05i	−0.108798	−	0.188444i
$739$	3371.89	−	1946.76i	0.167844	−	0.0969050i	−0.413725	−	0.910402i	$-0.635772\pi$
$739$	3371.89	−	1946.76i	0.167844	−	0.0969050i	0.581569	+	0.813497i	$0.302439\pi$
$740$	−1590.27			−0.0789991
$741$		0			0
$742$	18559.5			0.918247
$743$	−1918.24	+	1107.50i	−0.0947152	+	0.0546839i	−0.546609	−	0.837388i	$-0.684082\pi$
$743$	−1918.24	+	1107.50i	−0.0947152	+	0.0546839i	0.451894	+	0.892072i	$0.350748\pi$
$744$	10592.2	+	18346.3i	0.521949	+	0.904042i
$745$	2305.44	−	3993.15i	0.113376	−	0.196373i
$746$			36924.8i			1.81221i
$747$	−24201.3	−	13972.6i	−1.18538	−	0.684379i
$748$	−39.5068	−	22.8093i	−0.00193117	−	0.00111496i
$749$		−	18946.9i		−	0.924303i
$750$	9898.01	−	17143.8i	0.481899	−	0.834673i
$751$	1302.17	+	2255.42i	0.0632714	+	0.109589i	0.895926	−	0.444204i	$-0.146513\pi$
$751$	1302.17	+	2255.42i	0.0632714	+	0.109589i	−0.832655	+	0.553793i	$0.813180\pi$
$752$	−14555.2	+	8403.45i	−0.705816	+	0.407503i
$753$	−20515.1			−0.992845
$754$		0			0
$755$	23056.0			1.11138
$756$	−657.662	+	379.701i	−0.0316388	+	0.0182667i
$757$	4842.86	+	8388.08i	0.232519	+	0.402734i	0.958549	−	0.284929i	$-0.0919700\pi$
$757$	4842.86	+	8388.08i	0.232519	+	0.402734i	−0.726030	+	0.687663i	$0.758637\pi$
$758$	−5339.88	+	9248.94i	−0.255875	+	0.443188i
$759$			74714.4i			3.57307i
$760$	9064.49	+	5233.39i	0.432636	+	0.249783i
$761$	−8751.73	−	5052.81i	−0.416885	−	0.240689i	0.276858	−	0.960911i	$-0.410707\pi$
$761$	−8751.73	−	5052.81i	−0.416885	−	0.240689i	−0.693744	+	0.720222i	$0.744040\pi$
$762$			13771.0i			0.654687i
$763$	14857.5	−	25734.0i	0.704951	−	1.22101i
$764$	−4466.64	−	7736.45i	−0.211515	−	0.366355i
$765$	92.5338	−	53.4244i	0.00437329	−	0.00252492i
$766$	13849.6			0.653273
$767$		0			0
$768$	20476.1			0.962068
$769$	−3960.50	+	2286.60i	−0.185721	+	0.107226i	−0.589978	−	0.807419i	$-0.700864\pi$
$769$	−3960.50	+	2286.60i	−0.185721	+	0.107226i	0.404257	+	0.914646i	$0.367530\pi$
$770$	20870.3	+	36148.5i	0.976773	+	1.69182i
$771$	−21842.9	+	37833.0i	−1.02030	+	1.76722i
$772$		−	2597.63i		−	0.121102i
$773$	−6448.54	−	3723.07i	−0.300049	−	0.173233i	0.342416	−	0.939548i	$-0.388755\pi$
$773$	−6448.54	−	3723.07i	−0.300049	−	0.173233i	−0.642465	+	0.766315i	$0.722088\pi$
$774$	13260.7	+	7656.08i	0.615823	+	0.355545i
$775$			9454.34i			0.438206i
$776$	−15068.3	+	26099.1i	−0.697062	+	1.20735i
$777$	−2977.72	−	5157.57i	−0.137484	−	0.238129i
$778$	−34178.8	+	19733.1i	−1.57503	+	0.909341i
$779$	−2404.99			−0.110613
$780$		0			0
$781$	−4129.39			−0.189195
$782$	143.931	−	83.0986i	0.00658180	−	0.00380000i
$783$	−448.968	−	777.635i	−0.0204914	−	0.0354922i
$784$	5227.52	−	9054.34i	0.238134	−	0.412461i
$785$		−	130.496i		−	0.00593324i
$786$	−6407.92	−	3699.62i	−0.290793	−	0.167889i
$787$	2829.40	+	1633.56i	0.128154	+	0.0739898i	0.562707	−	0.826657i	$-0.309760\pi$
$787$	2829.40	+	1633.56i	0.128154	+	0.0739898i	−0.434552	+	0.900647i	$0.643093\pi$
$788$		−	1477.57i		−	0.0667973i
$789$	706.853	−	1224.31i	0.0318943	−	0.0552426i
$790$	21159.9	+	36650.0i	0.952957	+	1.65057i
$791$	19893.3	−	11485.4i	0.894216	−	0.516276i
$792$	29897.3			1.34135
$793$		0			0
$794$	29876.3			1.33535
$795$	34211.4	−	19752.0i	1.52623	−	0.881171i
$796$	4675.02	+	8097.37i	0.208168	+	0.360557i
$797$	−1582.88	+	2741.62i	−0.0703492	+	0.121848i	−0.899054	−	0.437837i	$-0.855745\pi$
$797$	−1582.88	+	2741.62i	−0.0703492	+	0.121848i	0.828705	+	0.559685i	$0.189078\pi$
$798$		−	13014.9i		−	0.577344i
$799$	64.7130	+	37.3621i	0.00286531	+	0.00165429i
$800$	4593.10	+	2651.83i	0.202988	+	0.117195i
$801$			12553.5i			0.553752i
$802$	−4593.49	+	7956.15i	−0.202246	+	0.350301i
$803$	−9551.09	−	16543.0i	−0.419739	−	0.727010i
$804$	3294.07	−	1901.84i	0.144494	−	0.0834236i
$805$	−30342.6			−1.32849
$806$		0			0
$807$	7854.45			0.342614
$808$	19085.7	−	11019.1i	0.830981	−	0.479767i
$809$	−6794.86	−	11769.0i	−0.295296	−	0.511468i	0.679758	−	0.733437i	$-0.262085\pi$
$809$	−6794.86	−	11769.0i	−0.295296	−	0.511468i	−0.975054	+	0.221969i	$0.928752\pi$
$810$	−17550.2	+	30397.8i	−0.761296	+	1.31860i
$811$			24977.7i			1.08149i	0.841188	+	0.540744i	$0.181857\pi$
$811$			24977.7i			1.08149i	−0.841188	+	0.540744i	$0.818143\pi$
$812$	836.371	+	482.879i	0.0361464	+	0.0208691i
$813$	−2492.81	−	1439.22i	−0.107536	−	0.0620859i
$814$			12550.3i			0.540401i
$815$	−830.521	+	1438.50i	−0.0356956	+	0.0618265i
$816$	−90.9657	−	157.557i	−0.00390249	−	0.00675932i
$817$	7310.43	−	4220.68i	0.313047	−	0.180738i
$818$	18323.0			0.783188
$819$		0			0
$820$	−1610.03			−0.0685666
$821$	−7203.06	+	4158.69i	−0.306198	+	0.176784i	−0.645224	−	0.763993i	$-0.723236\pi$
$821$	−7203.06	+	4158.69i	−0.306198	+	0.176784i	0.339026	+	0.940777i	$0.389903\pi$
$822$	−25800.3	−	44687.4i	−1.09475	−	1.89617i
$823$	7231.47	−	12525.3i	0.306286	−	0.530502i	−0.671261	−	0.741221i	$-0.734247\pi$
$823$	7231.47	−	12525.3i	0.306286	−	0.530502i	0.977547	+	0.210719i	$0.0675804\pi$
$824$		−	1562.53i		−	0.0660597i
$825$	24973.1	+	14418.2i	1.05388	+	0.608459i
$826$	−6811.02	−	3932.35i	−0.286908	−	0.165646i
$827$		−	17881.0i		−	0.751854i	−0.926649	−	0.375927i	$-0.877324\pi$
$827$		−	17881.0i		−	0.751854i	0.926649	−	0.375927i	$-0.122676\pi$
$828$	3608.09	−	6249.39i	0.151437	−	0.262296i
$829$	175.584	+	304.121i	0.00735620	+	0.0127413i	0.869680	−	0.493616i	$-0.164325\pi$
$829$	175.584	+	304.121i	0.00735620	+	0.0127413i	−0.862324	+	0.506357i	$0.830992\pi$
$830$	−44763.4	+	25844.2i	−1.87200	+	1.08080i
$831$	−2047.33			−0.0854646
$832$		0			0
$833$	−46.4836			−0.00193345
$834$	−23429.6	+	13527.1i	−0.972784	+	0.561637i
$835$	−15040.8	−	26051.5i	−0.623364	−	1.07970i
$836$	−2736.27	+	4739.36i	−0.113201	+	0.196070i
$837$			4182.34i			0.172716i
$838$	−11341.3	−	6547.90i	−0.467516	−	0.269920i
$839$	−28947.7	−	16712.9i	−1.19116	−	0.687717i	−0.232592	−	0.972575i	$-0.574721\pi$
$839$	−28947.7	−	16712.9i	−1.19116	−	0.687717i	−0.958570	+	0.284857i	$0.908054\pi$
$840$			26240.8i			1.07785i
$841$	11623.5	−	20132.5i	0.476589	−	0.825477i
$842$	−2255.50	−	3906.63i	−0.0923153	−	0.159895i
$843$	−31523.9	+	18200.3i	−1.28795	+	0.743598i
$844$	6391.46			0.260667
$845$		0			0
$846$	16260.5			0.660811
$847$	40402.9	−	23326.7i	1.63903	−	0.946297i
$848$	−15561.5	−	26953.3i	−0.630169	−	1.09149i
$849$	18694.7	−	32380.1i	0.755711	−	1.30893i
$850$		−	64.1449i		−	0.00258841i
$851$	−7900.91	−	4561.59i	−0.318260	−	0.183748i
$852$	746.478	+	430.979i	0.0300163	+	0.0173299i
$853$			35097.5i			1.40881i	0.709797	+	0.704406i	$0.248787\pi$
$853$			35097.5i			1.40881i	−0.709797	+	0.704406i	$0.751213\pi$
$854$	12704.0	−	22003.9i	0.509040	−	0.881684i
$855$	−6408.96	−	11100.6i	−0.256353	−	0.444016i
$856$	−21738.2	+	12550.6i	−0.867988	+	0.501133i
$857$	−15015.8			−0.598519			−0.299259	−	0.954172i	$-0.596740\pi$
$857$	−15015.8			−0.598519			−0.299259	+	0.954172i	$0.596740\pi$
$858$		0			0
$859$	19647.1			0.780383			0.390192	−	0.920734i	$-0.372409\pi$
$859$	19647.1			0.780383			0.390192	+	0.920734i	$0.372409\pi$
$860$	4893.99	−	2825.55i	0.194051	−	0.112035i
$861$	−3014.72	−	5221.65i	−0.119328	−	0.206682i
$862$	4019.78	−	6962.47i	0.158833	−	0.275107i
$863$		−	9035.14i		−	0.356385i	−0.983996	−	0.178192i	$-0.942975\pi$
$863$		−	9035.14i		−	0.356385i	0.983996	−	0.178192i	$-0.0570249\pi$
$864$	2031.86	+	1173.10i	0.0800062	+	0.0461916i
$865$	2519.72	+	1454.76i	0.0990440	+	0.0571831i
$866$		−	10901.7i		−	0.427778i
$867$	17413.3	−	30160.7i	0.682108	−	1.18144i
$868$	−2249.12	−	3895.59i	−0.0879495	−	0.152333i
$869$	57712.3	−	33320.2i	2.25288	−	1.30070i
$870$	10302.3			0.401471
$871$		0			0
$872$	−39367.0			−1.52883
$873$	31961.7	−	18453.1i	1.23911	−	0.715398i
$874$	−9968.77	−	17266.4i	−0.385811	−	0.668244i
$875$	6329.81	−	10963.6i	0.244556	−	0.423584i
$876$			3987.34i			0.153790i
$877$	7148.31	+	4127.08i	0.275235	+	0.158907i	0.631264	−	0.775568i	$-0.282536\pi$
$877$	7148.31	+	4127.08i	0.275235	+	0.158907i	−0.356029	+	0.934475i	$0.615870\pi$
$878$	34612.9	+	19983.8i	1.33044	+	0.768133i
$879$		−	10248.3i		−	0.393248i
$880$	34998.2	−	60618.6i	1.34067	−	2.32211i
$881$	−21053.7	−	36466.1i	−0.805128	−	1.39452i	−0.916205	−	0.400710i	$-0.868763\pi$
$881$	−21053.7	−	36466.1i	−0.805128	−	1.39452i	0.111077	−	0.993812i	$-0.464570\pi$
$882$	−8759.96	+	5057.57i	−0.334425	+	0.193081i
$883$	17584.7			0.670183			0.335091	−	0.942186i	$-0.391233\pi$
$883$	17584.7			0.670183			0.335091	+	0.942186i	$0.391233\pi$
$884$		0			0
$885$	−16740.1			−0.635832
$886$	−23234.7	+	13414.6i	−0.881021	+	0.508658i
$887$	11922.9	+	20651.1i	0.451333	+	0.781731i	0.998469	−	0.0553122i	$-0.0176154\pi$
$887$	11922.9	+	20651.1i	0.451333	+	0.781731i	−0.547136	+	0.837043i	$0.684282\pi$
$888$	−3944.94	+	6832.84i	−0.149081	+	0.258215i
$889$			8806.63i			0.332244i
$890$	20108.5	+	11609.7i	0.757347	+	0.437255i
$891$	47866.9	+	27636.0i	1.79978	+	1.03910i
$892$			2108.59i			0.0791488i
$893$	4482.07	−	7763.17i	0.167958	−	0.290912i
$894$	3797.85	+	6578.07i	0.142079	+	0.246089i
$895$	34960.0	−	20184.2i	1.30568	−	0.753836i
$896$	25014.6			0.932679
$897$		0			0
$898$	−35943.1			−1.33568
$899$	4606.24	−	2659.41i	0.170886	−	0.0986612i
$900$	−1392.56	−	2411.99i	−0.0515764	−	0.0893330i
$901$	−69.1870	+	119.835i	−0.00255822	+	0.00443096i
$902$			12706.2i			0.469036i
$903$	18327.7	+	10581.5i	0.675423	+	0.389956i
$904$	−26355.0	−	15216.1i	−0.969641	−	0.559823i
$905$			31689.6i			1.16398i
$906$	−18990.5	+	32892.6i	−0.696378	+	1.20616i
$907$	15282.9	+	26470.7i	0.559492	+	0.969069i	0.997539	+	0.0701164i	$0.0223371\pi$
$907$	15282.9	+	26470.7i	0.559492	+	0.969069i	−0.438047	+	0.898952i	$0.644330\pi$
$908$	8910.67	−	5144.58i	0.325673	−	0.188027i
$909$	−26988.7			−0.984773
$910$		0			0
$911$	18556.9			0.674882			0.337441	−	0.941347i	$-0.390439\pi$
$911$	18556.9			0.674882			0.337441	+	0.941347i	$0.390439\pi$
$912$	−18901.0	+	10912.5i	−0.686268	+	0.396217i
$913$	40696.5	+	70488.3i	1.47520	+	2.55512i
$914$	−17844.3	+	30907.2i	−0.645773	+	1.11851i
$915$		−	54081.0i		−	1.95395i
$916$	2932.85	+	1693.28i	0.105790	+	0.0610781i
$917$	−4097.89	−	2365.92i	−0.147573	−	0.0852012i
$918$		−	28.3760i		−	0.00102020i
$919$	4969.41	−	8607.27i	0.178374	−	0.308953i	−0.762950	−	0.646458i	$-0.776250\pi$
$919$	4969.41	−	8607.27i	0.178374	−	0.308953i	0.941324	+	0.337505i	$0.109583\pi$
$920$	20099.3	+	34812.9i	0.720275	+	1.24755i
$921$	−57839.1	+	33393.4i	−2.06934	+	1.19474i
$922$	12121.0			0.432954
$923$		0			0
$924$	−13720.0			−0.488479
$925$	−3049.40	+	1760.57i	−0.108393	+	0.0625809i
$926$	2046.09	+	3543.93i	0.0726119	+	0.125768i
$927$	−956.758	+	1657.15i	−0.0338986	+	0.0587142i
$928$		−	2983.73i		−	0.105545i
$929$	5155.97	+	2976.80i	0.182090	+	0.105130i	0.588274	−	0.808661i	$-0.299807\pi$
$929$	5155.97	+	2976.80i	0.182090	+	0.105130i	−0.406184	+	0.913791i	$0.633141\pi$
$930$	−41556.4	−	23992.6i	−1.46526	−	0.845966i
$931$			5576.31i			0.196301i
$932$	−3152.98	+	5461.11i	−0.110815	+	0.191936i
$933$	27950.8	+	48412.2i	0.980781	+	1.69876i
$934$	37950.2	−	21910.6i	1.32952	−	0.767597i
$935$	−311.207			−0.0108851
$936$		0			0
$937$	−24568.0			−0.856564			−0.428282	−	0.903645i	$-0.640881\pi$
$937$	−24568.0			−0.856564			−0.428282	+	0.903645i	$0.640881\pi$
$938$	10557.6	−	6095.44i	0.367503	−	0.212178i
$939$	1950.93	+	3379.11i	0.0678021	+	0.117437i
$940$	3000.54	−	5197.09i	0.104114	−	0.180330i
$941$		−	11024.8i		−	0.381931i	−0.981597	−	0.190965i	$-0.938838\pi$
$941$		−	11024.8i		−	0.381931i	0.981597	−	0.190965i	$-0.0611618\pi$
$942$	186.170	+	107.485i	0.00643923	+	0.00371769i
$943$	−7999.09	−	4618.27i	−0.276231	−	0.159482i
$944$			13188.6i			0.454715i
$945$	−2590.30	+	4486.53i	−0.0891666	+	0.154441i
$946$	−22299.0	−	38623.0i	−0.766388	−	1.32742i
$947$	−5344.64	+	3085.73i	−0.183398	+	0.105885i	−0.588888	−	0.808215i	$-0.700434\pi$
$947$	−5344.64	+	3085.73i	−0.183398	+	0.105885i	0.405490	+	0.914099i	$0.367101\pi$
$948$	−13910.4			−0.476569
$949$		0			0
$950$	−7695.01			−0.262799
$951$	−926.847	+	535.116i	−0.0316037	+	0.0182464i
$952$	−45.9581	−	79.6017i	−0.00156461	−	0.00270998i
$953$	−9419.22	+	16314.6i	−0.320166	+	0.554544i	−0.980522	−	0.196408i	$-0.937072\pi$
$953$	−9419.22	+	16314.6i	−0.320166	+	0.554544i	0.660356	+	0.750953i	$0.270405\pi$
$954$			30111.1i			1.02189i
$955$	−52777.6	−	30471.1i	−1.78832	−	1.03248i
$956$	−4058.47	−	2343.16i	−0.137302	−	0.0792711i
$957$		−	16222.8i		−	0.547973i
$958$	−15218.2	+	26358.7i	−0.513234	+	0.888947i
$959$	−16499.4	−	28577.8i	−0.555571	−	0.962278i
$960$	27449.9	−	15848.2i	0.922857	−	0.532812i
$961$	5017.33			0.168418
$962$		0			0
$963$	30739.6			1.02863
$964$	8923.62	−	5152.06i	0.298144	−	0.172133i
$965$	−8860.42	−	15346.7i	−0.295572	−	0.511946i
$966$	24992.3	−	43288.0i	0.832417	−	1.44179i
$967$			24934.5i			0.829203i	0.910003	+	0.414602i	$0.136079\pi$
$967$			24934.5i			0.829203i	−0.910003	+	0.414602i	$0.863921\pi$
$968$	−53526.6	−	30903.6i	−1.77728	−	1.02612i
$969$	84.0348	+	48.5175i	0.00278595	+	0.00160847i
$970$		−	68262.8i		−	2.25957i
$971$	−16080.6	+	27852.4i	−0.531463	+	0.920520i	0.467863	+	0.883801i	$0.345024\pi$
$971$	−16080.6	+	27852.4i	−0.531463	+	0.920520i	−0.999326	+	0.0367194i	$0.988309\pi$
$972$	−5053.32	−	8752.61i	−0.166755	−	0.288827i
$973$	−14983.3	+	8650.63i	−0.493673	+	0.285022i
$974$	−37787.2			−1.24310
$975$		0			0
$976$	−42607.4			−1.39737
$977$	−16336.7	+	9432.00i	−0.534961	+	0.308860i	−0.743034	−	0.669253i	$-0.766614\pi$
$977$	−16336.7	+	9432.00i	−0.534961	+	0.308860i	0.208073	+	0.978113i	$0.433281\pi$
$978$	−1368.15	−	2369.71i	−0.0447327	−	0.0774794i
$979$	18281.6	−	31664.6i	0.596815	−	1.03371i
$980$			3733.08i			0.121683i
$981$	41751.1	+	24105.0i	1.35883	+	0.784520i
$982$	−14811.9	−	8551.64i	−0.481330	−	0.277896i
$983$			7883.83i			0.255804i	0.991787	+	0.127902i	$0.0408243\pi$
$983$			7883.83i			0.255804i	−0.991787	+	0.127902i	$0.959176\pi$
$984$	−3993.97	+	6917.75i	−0.129393	+	0.224116i
$985$	−5039.94	−	8729.44i	−0.163031	−	0.282379i
$986$	−31.2520	+	18.0433i	−0.00100940	+	0.000582776i
$987$	22473.6			0.724766
$988$		0			0
$989$	32419.7			1.04235
$990$	−58647.8	+	33860.3i	−1.88278	+	1.08702i
$991$	−7086.14	−	12273.6i	−0.227143	−	0.393423i	0.729817	−	0.683642i	$-0.239605\pi$
$991$	−7086.14	−	12273.6i	−0.227143	−	0.393423i	−0.956960	+	0.290219i	$0.906272\pi$
$992$	−6948.72	+	12035.5i	−0.222401	+	0.385210i
$993$		−	50183.9i		−	1.60376i
$994$	2392.48	+	1381.30i	0.0763430	+	0.0440767i
$995$	55239.7	+	31892.6i	1.76002	+	1.01615i
$996$		−	16989.7i		−	0.540503i
$997$	−26231.4	+	45434.1i	−0.833256	+	1.44324i	0.0621870	+	0.998065i	$0.480192\pi$
$997$	−26231.4	+	45434.1i	−0.833256	+	1.44324i	−0.895443	+	0.445177i	$0.853141\pi$
$998$	22876.9	+	39623.9i	0.725607	+	1.25679i
$999$	−1348.97	+	778.830i	−0.0427224	+	0.0246658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.h.23.5		36
13.2	odd	12		169.4.a.k.1.3	✓	9
13.3	even	3		169.4.b.g.168.5		18
13.4	even	6	inner	169.4.e.h.147.5		36
13.5	odd	4		169.4.c.l.146.7		18
13.6	odd	12		169.4.c.l.22.7		18
13.7	odd	12		169.4.c.k.22.3		18
13.8	odd	4		169.4.c.k.146.3		18
13.9	even	3	inner	169.4.e.h.147.14		36
13.10	even	6		169.4.b.g.168.14		18
13.11	odd	12		169.4.a.l.1.7	yes	9
13.12	even	2	inner	169.4.e.h.23.14		36
39.2	even	12		1521.4.a.bh.1.7		9
39.11	even	12		1521.4.a.bg.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.3	✓	9	13.2	odd	12
169.4.a.l.1.7	yes	9	13.11	odd	12
169.4.b.g.168.5		18	13.3	even	3
169.4.b.g.168.14		18	13.10	even	6
169.4.c.k.22.3		18	13.7	odd	12
169.4.c.k.146.3		18	13.8	odd	4
169.4.c.l.22.7		18	13.6	odd	12
169.4.c.l.146.7		18	13.5	odd	4
169.4.e.h.23.5		36	1.1	even	1	trivial
169.4.e.h.23.14		36	13.12	even	2	inner
169.4.e.h.147.5		36	13.4	even	6	inner
169.4.e.h.147.14		36	13.9	even	3	inner
1521.4.a.bg.1.3		9	39.11	even	12
1521.4.a.bh.1.7		9	39.2	even	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)

\(f(q)\)	\(=\)	\(q+(-2.73781 + 1.58068i) q^{2} +(-3.54442 - 6.13911i) q^{3} +(0.997073 - 1.72698i) q^{4} -13.6039i q^{5} +(19.4079 + 11.2051i) q^{6} +(12.4114 + 7.16574i) q^{7} -18.9866i q^{8} +(-11.6258 + 20.1364i) q^{9} +O(q^{10})\)	\(q+(-2.73781 + 1.58068i) q^{2} +(-3.54442 - 6.13911i) q^{3} +(0.997073 - 1.72698i) q^{4} -13.6039i q^{5} +(19.4079 + 11.2051i) q^{6} +(12.4114 + 7.16574i) q^{7} -18.9866i q^{8} +(-11.6258 + 20.1364i) q^{9} +(21.5034 + 37.2450i) q^{10} +(58.6492 - 33.8611i) q^{11} -14.1362 q^{12} -45.3068 q^{14} +(-83.5160 + 48.2180i) q^{15} +(37.9883 + 65.7976i) q^{16} +(0.168897 - 0.292539i) q^{17} -73.5064i q^{18} +(-35.0939 - 20.2615i) q^{19} +(-23.4937 - 13.5641i) q^{20} -101.593i q^{21} +(-107.047 + 185.411i) q^{22} +(-77.8158 - 134.781i) q^{23} +(-116.561 + 67.2965i) q^{24} -60.0670 q^{25} -26.5720 q^{27} +(24.7502 - 14.2895i) q^{28} +(16.8963 + 29.2652i) q^{29} +(152.434 - 264.024i) q^{30} -157.397i q^{31} +(-76.4663 - 44.1478i) q^{32} +(-415.754 - 240.036i) q^{33} +1.06789i q^{34} +(97.4822 - 168.844i) q^{35} +(23.1835 + 40.1550i) q^{36} +(50.7667 - 29.3102i) q^{37} +128.107 q^{38} -258.293 q^{40} +(51.3976 - 29.6744i) q^{41} +(160.586 + 278.144i) q^{42} +(-104.155 + 180.402i) q^{43} -135.048i q^{44} +(273.935 + 158.156i) q^{45} +(426.090 + 246.003i) q^{46} +221.212i q^{47} +(269.293 - 466.428i) q^{48} +(-68.8044 - 119.173i) q^{49} +(164.452 - 94.9464i) q^{50} -2.39457 q^{51} -409.639 q^{53} +(72.7491 - 42.0017i) q^{54} +(-460.645 - 797.860i) q^{55} +(136.053 - 235.651i) q^{56} +287.260i q^{57} +(-92.5175 - 53.4150i) q^{58} +(150.331 + 86.7937i) q^{59} +192.308i q^{60} +(-280.398 + 485.664i) q^{61} +(248.793 + 430.922i) q^{62} +(-288.585 + 166.615i) q^{63} -328.679 q^{64} +1517.68 q^{66} +(-233.025 + 134.537i) q^{67} +(-0.336806 - 0.583366i) q^{68} +(-551.623 + 955.440i) q^{69} +616.351i q^{70} +(-52.8062 - 30.4877i) q^{71} +(382.323 + 220.734i) q^{72} -282.066i q^{73} +(-92.6598 + 160.491i) q^{74} +(212.902 + 368.758i) q^{75} +(-69.9823 + 40.4043i) q^{76} +970.560 q^{77} +984.026 q^{79} +(895.106 - 516.790i) q^{80} +(408.078 + 706.813i) q^{81} +(-93.8112 + 162.486i) q^{82} +1201.86i q^{83} +(-175.450 - 101.296i) q^{84} +(-3.97968 - 2.29767i) q^{85} -658.543i q^{86} +(119.775 - 207.456i) q^{87} +(-642.908 - 1113.55i) q^{88} +(467.566 - 269.949i) q^{89} -999.976 q^{90} -310.352 q^{92} +(-966.275 + 557.879i) q^{93} +(-349.664 - 605.636i) q^{94} +(-275.636 + 477.415i) q^{95} +625.913i q^{96} +(-1374.60 - 793.627i) q^{97} +(376.747 + 217.515i) q^{98} +1574.65i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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