LMFDB - Embedded newform 361.2.c.i.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(68,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("361.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			68.3
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	361.68
Dual form			361.2.c.i.292.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26604 - 2.19285i) q^{2} +(0.326352 - 0.565258i) q^{3} +(-2.20574 - 3.82045i) q^{4} +(0.673648 - 1.16679i) q^{5} +(-0.826352 - 1.43128i) q^{6} +1.53209 q^{7} -6.10607 q^{8} +(1.28699 + 2.22913i) q^{9} +O(q^{10})$	\(q+(1.26604 - 2.19285i) q^{2} +(0.326352 - 0.565258i) q^{3} +(-2.20574 - 3.82045i) q^{4} +(0.673648 - 1.16679i) q^{5} +(-0.826352 - 1.43128i) q^{6} +1.53209 q^{7} -6.10607 q^{8} +(1.28699 + 2.22913i) q^{9} +(-1.70574 - 2.95442i) q^{10} -1.18479 q^{11} -2.87939 q^{12} +(-1.35844 - 2.35289i) q^{13} +(1.93969 - 3.35965i) q^{14} +(-0.439693 - 0.761570i) q^{15} +(-3.31908 + 5.74881i) q^{16} +(-1.93969 + 3.35965i) q^{17} +6.51754 q^{18} -5.94356 q^{20} +(0.500000 - 0.866025i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(2.53209 + 4.38571i) q^{23} +(-1.99273 + 3.45150i) q^{24} +(1.59240 + 2.75811i) q^{25} -6.87939 q^{26} +3.63816 q^{27} +(-3.37939 - 5.85327i) q^{28} +(2.32635 + 4.02936i) q^{29} -2.22668 q^{30} -3.83750 q^{31} +(2.29813 + 3.98048i) q^{32} +(-0.386659 + 0.669713i) q^{33} +(4.91147 + 8.50692i) q^{34} +(1.03209 - 1.78763i) q^{35} +(5.67752 - 9.83375i) q^{36} -4.10607 q^{37} -1.77332 q^{39} +(-4.11334 + 7.12452i) q^{40} +(4.99273 - 8.64766i) q^{41} +(-1.26604 - 2.19285i) q^{42} +(4.35117 - 7.53644i) q^{43} +(2.61334 + 4.52644i) q^{44} +3.46791 q^{45} +12.8229 q^{46} +(-0.286989 - 0.497079i) q^{47} +(2.16637 + 3.75227i) q^{48} -4.65270 q^{49} +8.06418 q^{50} +(1.26604 + 2.19285i) q^{51} +(-5.99273 + 10.3797i) q^{52} +(-1.47178 - 2.54920i) q^{53} +(4.60607 - 7.97794i) q^{54} +(-0.798133 + 1.38241i) q^{55} -9.35504 q^{56} +11.7811 q^{58} +(1.96791 - 3.40852i) q^{59} +(-1.93969 + 3.35965i) q^{60} +(2.25877 + 3.91231i) q^{61} +(-4.85844 + 8.41507i) q^{62} +(1.97178 + 3.41523i) q^{63} -1.63816 q^{64} -3.66044 q^{65} +(0.979055 + 1.69577i) q^{66} +(1.94356 + 3.36635i) q^{67} +17.1138 q^{68} +3.30541 q^{69} +(-2.61334 - 4.52644i) q^{70} +(3.46791 - 6.00660i) q^{71} +(-7.85844 - 13.6112i) q^{72} +(-3.06418 + 5.30731i) q^{73} +(-5.19846 + 9.00400i) q^{74} +2.07873 q^{75} -1.81521 q^{77} +(-2.24510 + 3.88863i) q^{78} +(-4.90420 + 8.49432i) q^{79} +(4.47178 + 7.74535i) q^{80} +(-2.67365 + 4.63089i) q^{81} +(-12.6420 - 21.8966i) q^{82} +12.3182 q^{83} -4.41147 q^{84} +(2.61334 + 4.52644i) q^{85} +(-11.0175 - 19.0829i) q^{86} +3.03684 q^{87} +7.23442 q^{88} +(1.21301 + 2.10100i) q^{89} +(4.39053 - 7.60462i) q^{90} +(-2.08125 - 3.60483i) q^{91} +(11.1702 - 19.3474i) q^{92} +(-1.25237 + 2.16918i) q^{93} -1.45336 q^{94} +3.00000 q^{96} +(-3.68479 + 6.38225i) q^{97} +(-5.89053 + 10.2027i) q^{98} +(-1.52481 - 2.64106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - 12 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - 12 * q^8	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - 12 q^{8} - 6 q^{12} + 6 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} - 6 q^{18} - 6 q^{20} + 3 q^{21} - 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} - 30 q^{26} - 12 q^{27} - 9 q^{28} + 15 q^{29} - 18 q^{31} - 9 q^{33} + 9 q^{34} - 3 q^{35} + 9 q^{36} - 24 q^{39} - 18 q^{40} + 12 q^{41} - 3 q^{42} + 9 q^{44} + 30 q^{45} + 36 q^{46} + 6 q^{47} - 6 q^{48} - 30 q^{49} + 30 q^{50} + 3 q^{51} - 18 q^{52} + 6 q^{53} + 3 q^{54} + 9 q^{55} - 6 q^{56} + 36 q^{58} + 21 q^{59} - 6 q^{60} - 9 q^{61} - 21 q^{62} - 3 q^{63} + 24 q^{64} + 24 q^{65} + 9 q^{66} - 18 q^{67} + 30 q^{68} + 24 q^{69} - 9 q^{70} + 30 q^{71} - 39 q^{72} - 3 q^{74} + 30 q^{75} - 18 q^{77} - 12 q^{78} + 9 q^{79} + 12 q^{80} - 15 q^{81} - 18 q^{82} - 6 q^{84} + 9 q^{85} - 21 q^{86} + 42 q^{87} - 18 q^{88} + 15 q^{89} + 9 q^{90} - 15 q^{91} + 24 q^{92} - 24 q^{93} + 18 q^{94} + 18 q^{96} - 15 q^{97} - 18 q^{98} + 18 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - 12 * q^8 - 6 * q^12 + 6 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 - 6 * q^18 - 6 * q^20 + 3 * q^21 - 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 - 30 * q^26 - 12 * q^27 - 9 * q^28 + 15 * q^29 - 18 * q^31 - 9 * q^33 + 9 * q^34 - 3 * q^35 + 9 * q^36 - 24 * q^39 - 18 * q^40 + 12 * q^41 - 3 * q^42 + 9 * q^44 + 30 * q^45 + 36 * q^46 + 6 * q^47 - 6 * q^48 - 30 * q^49 + 30 * q^50 + 3 * q^51 - 18 * q^52 + 6 * q^53 + 3 * q^54 + 9 * q^55 - 6 * q^56 + 36 * q^58 + 21 * q^59 - 6 * q^60 - 9 * q^61 - 21 * q^62 - 3 * q^63 + 24 * q^64 + 24 * q^65 + 9 * q^66 - 18 * q^67 + 30 * q^68 + 24 * q^69 - 9 * q^70 + 30 * q^71 - 39 * q^72 - 3 * q^74 + 30 * q^75 - 18 * q^77 - 12 * q^78 + 9 * q^79 + 12 * q^80 - 15 * q^81 - 18 * q^82 - 6 * q^84 + 9 * q^85 - 21 * q^86 + 42 * q^87 - 18 * q^88 + 15 * q^89 + 9 * q^90 - 15 * q^91 + 24 * q^92 - 24 * q^93 + 18 * q^94 + 18 * q^96 - 15 * q^97 - 18 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.26604	−	2.19285i	0.895229	−	1.55058i	0.0617072	−	0.998094i	$-0.480346\pi$
$2$	1.26604	−	2.19285i	0.895229	−	1.55058i	0.833521	−	0.552487i	$-0.186321\pi$
$3$	0.326352	−	0.565258i	0.188419	−	0.326352i	−0.756304	−	0.654220i	$-0.772997\pi$
$3$	0.326352	−	0.565258i	0.188419	−	0.326352i	0.944723	+	0.327868i	$0.106330\pi$
$4$	−2.20574	−	3.82045i	−1.10287	−	1.91022i
$5$	0.673648	−	1.16679i	0.301265	−	0.521806i	−0.675158	−	0.737673i	$-0.735925\pi$
$5$	0.673648	−	1.16679i	0.301265	−	0.521806i	0.976423	+	0.215867i	$0.0692579\pi$
$6$	−0.826352	−	1.43128i	−0.337357	−	0.584319i
$7$	1.53209			0.579075			0.289538	−	0.957167i	$-0.406498\pi$
$7$	1.53209			0.579075			0.289538	+	0.957167i	$0.406498\pi$
$8$	−6.10607			−2.15882
$9$	1.28699	+	2.22913i	0.428996	+	0.743043i
$10$	−1.70574	−	2.95442i	−0.539401	−	0.934271i
$11$	−1.18479			−0.357228			−0.178614	−	0.983919i	$-0.557161\pi$
$11$	−1.18479			−0.357228			−0.178614	+	0.983919i	$0.557161\pi$
$12$	−2.87939			−0.831207
$13$	−1.35844	−	2.35289i	−0.376764	−	0.652574i	0.613826	−	0.789442i	$-0.289630\pi$
$13$	−1.35844	−	2.35289i	−0.376764	−	0.652574i	−0.990589	+	0.136868i	$0.956296\pi$
$14$	1.93969	−	3.35965i	0.518405	−	0.897903i
$15$	−0.439693	−	0.761570i	−0.113528	−	0.196637i
$16$	−3.31908	+	5.74881i	−0.829769	+	1.43720i
$17$	−1.93969	+	3.35965i	−0.470445	+	0.814834i	−0.999429	−	0.0337978i	$-0.989240\pi$
$17$	−1.93969	+	3.35965i	−0.470445	+	0.814834i	0.528984	+	0.848632i	$0.322573\pi$
$18$	6.51754			1.53620
$19$		0			0
$19$		0			0
$20$	−5.94356			−1.32902
$21$	0.500000	−	0.866025i	0.109109	−	0.188982i
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	2.53209	+	4.38571i	0.527977	+	0.914483i	0.999468	+	0.0326122i	$0.0103826\pi$
$23$	2.53209	+	4.38571i	0.527977	+	0.914483i	−0.471491	+	0.881871i	$0.656284\pi$
$24$	−1.99273	+	3.45150i	−0.406763	+	0.704535i
$25$	1.59240	+	2.75811i	0.318479	+	0.551622i
$26$	−6.87939			−1.34916
$27$	3.63816			0.700163
$28$	−3.37939	−	5.85327i	−0.638644	−	1.10616i
$29$	2.32635	+	4.02936i	0.431993	+	0.748233i	0.997045	−	0.0768219i	$-0.0244773\pi$
$29$	2.32635	+	4.02936i	0.431993	+	0.748233i	−0.565052	+	0.825055i	$0.691144\pi$
$30$	−2.22668			−0.406535
$31$	−3.83750			−0.689235			−0.344617	−	0.938743i	$-0.611991\pi$
$31$	−3.83750			−0.689235			−0.344617	+	0.938743i	$0.611991\pi$
$32$	2.29813	+	3.98048i	0.406256	+	0.703657i
$33$	−0.386659	+	0.669713i	−0.0673087	+	0.116582i
$34$	4.91147	+	8.50692i	0.842311	+	1.45893i
$35$	1.03209	−	1.78763i	0.174455	−	0.302165i
$36$	5.67752	−	9.83375i	0.946253	−	1.63896i
$37$	−4.10607			−0.675033			−0.337517	−	0.941320i	$-0.609587\pi$
$37$	−4.10607			−0.675033			−0.337517	+	0.941320i	$0.609587\pi$
$38$		0			0
$39$	−1.77332			−0.283958
$40$	−4.11334	+	7.12452i	−0.650376	+	1.12648i
$41$	4.99273	−	8.64766i	0.779733	−	1.35054i	−0.152363	−	0.988325i	$-0.548688\pi$
$41$	4.99273	−	8.64766i	0.779733	−	1.35054i	0.932096	−	0.362212i	$-0.117978\pi$
$42$	−1.26604	−	2.19285i	−0.195355	−	0.338365i
$43$	4.35117	−	7.53644i	0.663547	−	1.14930i	−0.316130	−	0.948716i	$-0.602384\pi$
$43$	4.35117	−	7.53644i	0.663547	−	1.14930i	0.979677	−	0.200581i	$-0.0642829\pi$
$44$	2.61334	+	4.52644i	0.393976	+	0.682386i
$45$	3.46791			0.516966
$46$	12.8229			1.89064
$47$	−0.286989	−	0.497079i	−0.0418616	−	0.0725065i	0.844335	−	0.535815i	$-0.179996\pi$
$47$	−0.286989	−	0.497079i	−0.0418616	−	0.0725065i	−0.886197	+	0.463308i	$0.846662\pi$
$48$	2.16637	+	3.75227i	0.312689	+	0.541594i
$49$	−4.65270			−0.664672
$50$	8.06418			1.14045
$51$	1.26604	+	2.19285i	0.177282	+	0.307061i
$52$	−5.99273	+	10.3797i	−0.831042	+	1.43941i
$53$	−1.47178	−	2.54920i	−0.202165	−	0.350160i	0.747061	−	0.664756i	$-0.231464\pi$
$53$	−1.47178	−	2.54920i	−0.202165	−	0.350160i	−0.949226	+	0.314596i	$0.898131\pi$
$54$	4.60607	−	7.97794i	0.626806	−	1.08566i
$55$	−0.798133	+	1.38241i	−0.107620	+	0.186404i
$56$	−9.35504			−1.25012
$57$		0			0
$58$	11.7811			1.54693
$59$	1.96791	−	3.40852i	0.256200	−	0.443752i	−0.709021	−	0.705188i	$-0.750863\pi$
$59$	1.96791	−	3.40852i	0.256200	−	0.443752i	0.965221	+	0.261436i	$0.0841960\pi$
$60$	−1.93969	+	3.35965i	−0.250413	+	0.433728i
$61$	2.25877	+	3.91231i	0.289206	+	0.500919i	0.973620	−	0.228174i	$-0.0732754\pi$
$61$	2.25877	+	3.91231i	0.289206	+	0.500919i	−0.684414	+	0.729093i	$0.739942\pi$
$62$	−4.85844	+	8.41507i	−0.617023	+	1.06871i
$63$	1.97178	+	3.41523i	0.248421	+	0.430278i
$64$	−1.63816			−0.204769
$65$	−3.66044			−0.454022
$66$	0.979055	+	1.69577i	0.120513	+	0.208735i
$67$	1.94356	+	3.36635i	0.237444	+	0.411265i	0.959980	−	0.280068i	$-0.0903570\pi$
$67$	1.94356	+	3.36635i	0.237444	+	0.411265i	−0.722536	+	0.691333i	$0.757024\pi$
$68$	17.1138			2.07535
$69$	3.30541			0.397924
$70$	−2.61334	−	4.52644i	−0.312354	−	0.541013i
$71$	3.46791	−	6.00660i	0.411565	−	0.712852i	−0.583496	−	0.812116i	$-0.698316\pi$
$71$	3.46791	−	6.00660i	0.411565	−	0.712852i	0.995061	+	0.0992641i	$0.0316489\pi$
$72$	−7.85844	−	13.6112i	−0.926126	−	1.60410i
$73$	−3.06418	+	5.30731i	−0.358635	+	0.621174i	−0.987733	−	0.156152i	$-0.950091\pi$
$73$	−3.06418	+	5.30731i	−0.358635	+	0.621174i	0.629098	+	0.777326i	$0.283424\pi$
$74$	−5.19846	+	9.00400i	−0.604309	+	1.04669i
$75$	2.07873			0.240031
$76$		0			0
$77$	−1.81521			−0.206862
$78$	−2.24510	+	3.88863i	−0.254208	+	0.440300i
$79$	−4.90420	+	8.49432i	−0.551766	+	0.955686i	0.446382	+	0.894843i	$0.352712\pi$
$79$	−4.90420	+	8.49432i	−0.551766	+	0.955686i	−0.998147	+	0.0608434i	$0.980621\pi$
$80$	4.47178	+	7.74535i	0.499960	+	0.865957i
$81$	−2.67365	+	4.63089i	−0.297072	+	0.514544i
$82$	−12.6420	−	21.8966i	−1.39608	−	2.41808i
$83$	12.3182			1.35210			0.676049	−	0.736857i	$-0.263691\pi$
$83$	12.3182			1.35210			0.676049	+	0.736857i	$0.263691\pi$
$84$	−4.41147			−0.481331
$85$	2.61334	+	4.52644i	0.283457	+	0.490961i
$86$	−11.0175	−	19.0829i	−1.18805	−	2.05777i
$87$	3.03684			0.325583
$88$	7.23442			0.771192
$89$	1.21301	+	2.10100i	0.128579	+	0.222705i	0.923126	−	0.384497i	$-0.125625\pi$
$89$	1.21301	+	2.10100i	0.128579	+	0.222705i	−0.794547	+	0.607202i	$0.792292\pi$
$90$	4.39053	−	7.60462i	0.462802	−	0.801597i
$91$	−2.08125	−	3.60483i	−0.218174	−	0.377889i
$92$	11.1702	−	19.3474i	1.16458	−	2.01711i
$93$	−1.25237	+	2.16918i	−0.129865	+	0.224933i
$94$	−1.45336			−0.149903
$95$		0			0
$96$	3.00000			0.306186
$97$	−3.68479	+	6.38225i	−0.374134	+	0.648019i	−0.990197	−	0.139678i	$-0.955393\pi$
$97$	−3.68479	+	6.38225i	−0.374134	+	0.648019i	0.616063	+	0.787697i	$0.288727\pi$
$98$	−5.89053	+	10.2027i	−0.595033	+	1.03063i
$99$	−1.52481	−	2.64106i	−0.153250	−	0.265436i
$100$	7.02481	−	12.1673i	0.702481	−	1.21673i
$101$	−1.08512	−	1.87949i	−0.107974	−	0.187016i	0.806976	−	0.590585i	$-0.201103\pi$
$101$	−1.08512	−	1.87949i	−0.107974	−	0.187016i	−0.914949	+	0.403569i	$0.867770\pi$
$102$	6.41147			0.634831
$103$	−12.4757			−1.22926			−0.614631	−	0.788815i	$-0.710695\pi$
$103$	−12.4757			−1.22926			−0.614631	+	0.788815i	$0.710695\pi$
$104$	8.29473	+	14.3669i	0.813365	+	1.40879i
$105$	−0.673648	−	1.16679i	−0.0657413	−	0.113867i
$106$	−7.45336			−0.723935
$107$	−6.68004			−0.645784			−0.322892	−	0.946436i	$-0.604655\pi$
$107$	−6.68004			−0.645784			−0.322892	+	0.946436i	$0.604655\pi$
$108$	−8.02481	−	13.8994i	−0.772188	−	1.33747i
$109$	−4.72668	+	8.18685i	−0.452734	+	0.784158i	−0.998555	−	0.0537437i	$-0.982885\pi$
$109$	−4.72668	+	8.18685i	−0.452734	+	0.784158i	0.545821	+	0.837902i	$0.316218\pi$
$110$	2.02094	+	3.50038i	0.192690	+	0.333748i
$111$	−1.34002	+	2.32099i	−0.127189	+	0.220298i
$112$	−5.08512	+	8.80769i	−0.480499	+	0.832248i
$113$	1.31046			0.123278			0.0616388	−	0.998099i	$-0.480367\pi$
$113$	1.31046			0.123278			0.0616388	+	0.998099i	$0.480367\pi$
$114$		0			0
$115$	6.82295			0.636243
$116$	10.2626	−	17.7754i	0.952862	−	1.65041i
$117$	3.49660	−	6.05628i	0.323260	−	0.559904i
$118$	−4.98293	−	8.63068i	−0.458716	−	0.794519i
$119$	−2.97178	+	5.14728i	−0.272423	+	0.471850i
$120$	2.68479	+	4.65020i	0.245087	+	0.424503i
$121$	−9.59627			−0.872388
$122$	11.4388			1.03562
$123$	−3.25877	−	5.64436i	−0.293833	−	0.508934i
$124$	8.46451	+	14.6610i	0.760135	+	1.31659i
$125$	11.0273			0.986315
$126$	9.98545			0.889575
$127$	7.25150	+	12.5600i	0.643466	+	1.11452i	0.984653	+	0.174521i	$0.0558377\pi$
$127$	7.25150	+	12.5600i	0.643466	+	1.11452i	−0.341187	+	0.939995i	$0.610829\pi$
$128$	−6.67024	+	11.5532i	−0.589572	+	1.02117i
$129$	−2.84002	−	4.91906i	−0.250050	−	0.433099i
$130$	−4.63429	+	8.02682i	−0.406454	+	0.703998i
$131$	9.90420	−	17.1546i	0.865334	−	1.49880i	−0.00138118	−	0.999999i	$-0.500440\pi$
$131$	9.90420	−	17.1546i	0.865334	−	1.49880i	0.866715	−	0.498803i	$-0.166227\pi$
$132$	3.41147			0.296931
$133$		0			0
$134$	9.84255			0.850267
$135$	2.45084	−	4.24497i	0.210934	−	0.365349i
$136$	11.8439	−	20.5142i	1.01561	−	1.75908i
$137$	−5.10220	−	8.83726i	−0.435910	−	0.755018i	0.561459	−	0.827504i	$-0.310240\pi$
$137$	−5.10220	−	8.83726i	−0.435910	−	0.755018i	−0.997369	+	0.0724859i	$0.976907\pi$
$138$	4.18479	−	7.24827i	0.356233	−	0.617014i
$139$	0.830222	+	1.43799i	0.0704185	+	0.121968i	0.899085	−	0.437775i	$-0.144233\pi$
$139$	0.830222	+	1.43799i	0.0704185	+	0.121968i	−0.828666	+	0.559743i	$0.810900\pi$
$140$	−9.10607			−0.769603
$141$	−0.374638			−0.0315502
$142$	−8.78106	−	15.2092i	−0.736890	−	1.27633i
$143$	1.60947	+	2.78768i	0.134591	+	0.233118i
$144$	−17.0865			−1.42387
$145$	6.26857			0.520576
$146$	7.75877	+	13.4386i	0.642120	+	1.11219i
$147$	−1.51842	+	2.62998i	−0.125237	+	0.216917i
$148$	9.05690	+	15.6870i	0.744473	+	1.28946i
$149$	−5.60354	+	9.70562i	−0.459060	+	0.795115i	−0.998912	−	0.0466451i	$-0.985147\pi$
$149$	−5.60354	+	9.70562i	−0.459060	+	0.795115i	0.539852	+	0.841760i	$0.318480\pi$
$150$	2.63176	−	4.55834i	0.214882	−	0.372187i
$151$	−11.0419			−0.898576			−0.449288	−	0.893387i	$-0.648322\pi$
$151$	−11.0419			−0.898576			−0.449288	+	0.893387i	$0.648322\pi$
$152$		0			0
$153$	−9.98545			−0.807276
$154$	−2.29813	+	3.98048i	−0.185189	+	0.320757i
$155$	−2.58512	+	4.47756i	−0.207642	+	0.359647i
$156$	3.91147	+	6.77487i	0.313169	+	0.542424i
$157$	−5.49660	+	9.52038i	−0.438676	+	0.759809i	−0.997588	−	0.0694179i	$-0.977886\pi$
$157$	−5.49660	+	9.52038i	−0.438676	+	0.759809i	0.558912	+	0.829227i	$0.311219\pi$
$158$	12.4179	+	21.5084i	0.987913	+	1.71112i
$159$	−1.92127			−0.152367
$160$	6.19253			0.489563
$161$	3.87939	+	6.71929i	0.305738	+	0.529554i
$162$	6.76991	+	11.7258i	0.531895	+	0.921269i
$163$	−6.33275			−0.496019			−0.248010	−	0.968758i	$-0.579776\pi$
$163$	−6.33275			−0.496019			−0.248010	+	0.968758i	$0.579776\pi$
$164$	−44.0506			−3.43977
$165$	0.520945	+	0.902302i	0.0405555	+	0.0702441i
$166$	15.5954	−	27.0120i	1.21044	−	2.09654i
$167$	6.88919	+	11.9324i	0.533101	+	0.923358i	0.999253	+	0.0386534i	$0.0123068\pi$
$167$	6.88919	+	11.9324i	0.533101	+	0.923358i	−0.466152	+	0.884705i	$0.654360\pi$
$168$	−3.05303	+	5.28801i	−0.235547	+	0.407979i
$169$	2.80928	−	4.86581i	0.216098	−	0.374293i
$170$	13.2344			1.01503
$171$		0			0
$172$	−38.3901			−2.92722
$173$	−12.6236	+	21.8647i	−0.959755	+	1.66234i	−0.236665	+	0.971591i	$0.576054\pi$
$173$	−12.6236	+	21.8647i	−0.959755	+	1.66234i	−0.723091	+	0.690753i	$0.757279\pi$
$174$	3.84477	−	6.65934i	0.291471	−	0.504843i
$175$	2.43969	+	4.22567i	0.184423	+	0.319431i
$176$	3.93242	−	6.81115i	0.296417	−	0.513410i
$177$	−1.28446	−	2.22475i	−0.0965461	−	0.167223i
$178$	6.14290			0.460430
$179$	5.83069			0.435806			0.217903	−	0.975970i	$-0.430078\pi$
$179$	5.83069			0.435806			0.217903	+	0.975970i	$0.430078\pi$
$180$	−7.64930	−	13.2490i	−0.570145	−	0.987520i
$181$	−6.78106	−	11.7451i	−0.504032	−	0.873009i	−0.999989	−	0.00466221i	$-0.998516\pi$
$181$	−6.78106	−	11.7451i	−0.504032	−	0.873009i	0.495957	−	0.868347i	$-0.334817\pi$
$182$	−10.5398			−0.781264
$183$	2.94862			0.217968
$184$	−15.4611	−	26.7794i	−1.13981	−	1.97420i
$185$	−2.76604	+	4.79093i	−0.203364	+	0.352236i
$186$	3.17112	+	5.49254i	0.232518	+	0.402733i
$187$	2.29813	−	3.98048i	0.168056	−	0.291082i
$188$	−1.26604	+	2.19285i	−0.0923358	+	0.159930i
$189$	5.57398			0.405447
$190$		0			0
$191$	−10.2841			−0.744128			−0.372064	−	0.928207i	$-0.621350\pi$
$191$	−10.2841			−0.744128			−0.372064	+	0.928207i	$0.621350\pi$
$192$	−0.534615	+	0.925981i	−0.0385825	+	0.0668269i
$193$	−6.90033	+	11.9517i	−0.496697	+	0.860304i	−0.999993	−	0.00381024i	$-0.998787\pi$
$193$	−6.90033	+	11.9517i	−0.496697	+	0.860304i	0.503296	+	0.864114i	$0.332120\pi$
$194$	9.33022	+	16.1604i	0.669871	+	1.16025i
$195$	−1.19459	+	2.06910i	−0.0855466	+	0.148171i
$196$	10.2626	+	17.7754i	0.733046	+	1.26967i
$197$	−7.94087			−0.565764			−0.282882	−	0.959155i	$-0.591290\pi$
$197$	−7.94087			−0.565764			−0.282882	+	0.959155i	$0.591290\pi$
$198$	−7.72193			−0.548774
$199$	−13.5175	−	23.4131i	−0.958233	−	1.65971i	−0.726790	−	0.686860i	$-0.758989\pi$
$199$	−13.5175	−	23.4131i	−0.958233	−	1.65971i	−0.231443	−	0.972848i	$-0.574345\pi$
$200$	−9.72328	−	16.8412i	−0.687540	−	1.19085i
$201$	2.53714			0.178956
$202$	−5.49525			−0.386645
$203$	3.56418	+	6.17334i	0.250156	+	0.433283i
$204$	5.58512	−	9.67372i	0.391037	−	0.677296i
$205$	−6.72668	−	11.6510i	−0.469812	−	0.813738i
$206$	−15.7947	+	27.3573i	−1.10047	+	1.90607i
$207$	−6.51754	+	11.2887i	−0.453000	+	0.784620i
$208$	18.0351			1.25051
$209$		0			0
$210$	−3.41147			−0.235414
$211$	4.03596	−	6.99049i	0.277847	−	0.481245i	−0.693003	−	0.720935i	$-0.743713\pi$
$211$	4.03596	−	6.99049i	0.277847	−	0.481245i	0.970849	+	0.239690i	$0.0770459\pi$
$212$	−6.49273	+	11.2457i	−0.445922	+	0.772360i
$213$	−2.26352	−	3.92053i	−0.155094	−	0.268630i
$214$	−8.45723	+	14.6484i	−0.578125	+	1.00134i
$215$	−5.86231	−	10.1538i	−0.399806	−	0.692485i
$216$	−22.2148			−1.51153
$217$	−5.87939			−0.399119
$218$	11.9684	+	20.7298i	0.810601	+	1.40400i
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$	7.04189			0.474764
$221$	10.5398			0.708986
$222$	3.39306	+	5.87695i	0.227727	+	0.394435i
$223$	7.73783	−	13.4023i	0.518163	−	0.897485i	−0.481614	−	0.876383i	$-0.659949\pi$
$223$	7.73783	−	13.4023i	0.518163	−	0.897485i	0.999777	−	0.0211016i	$-0.00671733\pi$
$224$	3.52094	+	6.09845i	0.235253	+	0.407470i
$225$	−4.09879	+	7.09932i	−0.273253	+	0.473288i
$226$	1.65910	−	2.87365i	0.110362	−	0.191152i
$227$	9.87258			0.655266			0.327633	−	0.944805i	$-0.393749\pi$
$227$	9.87258			0.655266			0.327633	+	0.944805i	$0.393749\pi$
$228$		0			0
$229$	20.1189			1.32949			0.664746	−	0.747070i	$-0.268540\pi$
$229$	20.1189			1.32949			0.664746	+	0.747070i	$0.268540\pi$
$230$	8.63816	−	14.9617i	0.569583	−	0.986547i
$231$	−0.592396	+	1.02606i	−0.0389768	+	0.0675098i
$232$	−14.2049	−	24.6035i	−0.932595	−	1.61530i
$233$	−1.76739	+	3.06121i	−0.115785	+	0.200546i	−0.918093	−	0.396364i	$-0.870272\pi$
$233$	−1.76739	+	3.06121i	−0.115785	+	0.200546i	0.802308	+	0.596910i	$0.203605\pi$
$234$	−8.85369	−	15.3350i	−0.578784	−	1.00248i
$235$	−0.773318			−0.0504457
$236$	−17.3628			−1.13022
$237$	3.20099	+	5.54428i	0.207927	+	0.360139i
$238$	7.52481	+	13.0334i	0.487761	+	0.844827i
$239$	11.9736			0.774507			0.387254	−	0.921973i	$-0.373424\pi$
$239$	11.9736			0.774507			0.387254	+	0.921973i	$0.373424\pi$
$240$	5.83750			0.376809
$241$	−6.45084	−	11.1732i	−0.415535	−	0.719728i	0.579950	−	0.814652i	$-0.303072\pi$
$241$	−6.45084	−	11.1732i	−0.415535	−	0.719728i	−0.995484	+	0.0949248i	$0.969739\pi$
$242$	−12.1493	+	21.0432i	−0.780987	+	1.35271i
$243$	7.20233	+	12.4748i	0.462030	+	0.800259i
$244$	9.96451	−	17.2590i	0.637912	−	1.10490i
$245$	−3.13429	+	5.42874i	−0.200242	+	0.346830i
$246$	−16.5030			−1.05219
$247$		0			0
$248$	23.4320			1.48793
$249$	4.02007	−	6.96296i	0.254761	−	0.441260i
$250$	13.9611	−	24.1813i	0.882978	−	1.52936i
$251$	−7.18139	−	12.4385i	−0.453285	−	0.785113i	0.545303	−	0.838239i	$-0.316415\pi$
$251$	−7.18139	−	12.4385i	−0.453285	−	0.785113i	−0.998588	+	0.0531262i	$0.983081\pi$
$252$	8.69846	−	15.0662i	0.547952	−	0.949080i
$253$	−3.00000	−	5.19615i	−0.188608	−	0.326679i
$254$	36.7229			2.30420
$255$	3.41147			0.213635
$256$	15.2515	+	26.4164i	0.953219	+	1.65102i
$257$	−2.48886	−	4.31082i	−0.155251	−	0.268902i	0.777900	−	0.628388i	$-0.216285\pi$
$257$	−2.48886	−	4.31082i	−0.155251	−	0.268902i	−0.933150	+	0.359487i	$0.882952\pi$
$258$	−14.3824			−0.895408
$259$	−6.29086			−0.390895
$260$	8.07398	+	13.9845i	0.500727	+	0.867284i
$261$	−5.98798	+	10.3715i	−0.370647	+	0.641979i
$262$	−25.0783	−	43.4369i	−1.54934	−	2.68354i
$263$	12.0214	−	20.8217i	0.741272	−	1.28392i	−0.210644	−	0.977563i	$-0.567556\pi$
$263$	12.0214	−	20.8217i	0.741272	−	1.28392i	0.951916	−	0.306358i	$-0.0991105\pi$
$264$	2.36097	−	4.08931i	0.145307	−	0.251680i
$265$	−3.96585			−0.243620
$266$		0			0
$267$	1.58347			0.0969070
$268$	8.57398	−	14.8506i	0.523739	−	0.907143i
$269$	6.55556	−	11.3546i	0.399700	−	0.692300i	−0.593989	−	0.804473i	$-0.702448\pi$
$269$	6.55556	−	11.3546i	0.399700	−	0.692300i	0.993689	+	0.112173i	$0.0357811\pi$
$270$	−6.20574	−	10.7487i	−0.377669	−	0.654142i
$271$	13.2849	−	23.0102i	0.807002	−	1.39777i	−0.107929	−	0.994159i	$-0.534422\pi$
$271$	13.2849	−	23.0102i	0.807002	−	1.39777i	0.914931	−	0.403610i	$-0.132245\pi$
$272$	−12.8760	−	22.3019i	−0.780721	−	1.35225i
$273$	−2.71688			−0.164433
$274$	−25.8384			−1.56096
$275$	−1.88666	−	3.26779i	−0.113770	−	0.197055i
$276$	−7.29086	−	12.6281i	−0.438858	−	0.760125i
$277$	−16.5107			−0.992034			−0.496017	−	0.868313i	$-0.665205\pi$
$277$	−16.5107			−0.992034			−0.496017	+	0.868313i	$0.665205\pi$
$278$	4.20439			0.252163
$279$	−4.93882	−	8.55428i	−0.295679	−	0.512131i
$280$	−6.30200	+	10.9154i	−0.376617	+	0.652319i
$281$	9.69506	+	16.7923i	0.578359	+	1.00175i	0.995668	+	0.0929821i	$0.0296399\pi$
$281$	9.69506	+	16.7923i	0.578359	+	1.00175i	−0.417309	+	0.908765i	$0.637027\pi$
$282$	−0.474308	+	0.821525i	−0.0282446	+	0.0489211i
$283$	5.65523	−	9.79515i	0.336169	−	0.582261i	−0.647540	−	0.762031i	$-0.724202\pi$
$283$	5.65523	−	9.79515i	0.336169	−	0.582261i	0.983709	+	0.179770i	$0.0575355\pi$
$284$	−30.5972			−1.81561
$285$		0			0
$286$	8.15064			0.481958
$287$	7.64930	−	13.2490i	0.451524	−	0.782062i
$288$	−5.91534	+	10.2457i	−0.348565	+	0.603732i
$289$	0.975185	+	1.68907i	0.0573638	+	0.0993571i
$290$	7.93629	−	13.7461i	0.466035	−	0.807196i
$291$	2.40508	+	4.16572i	0.140988	+	0.244199i
$292$	27.0351			1.58211
$293$	3.89899			0.227781			0.113891	−	0.993493i	$-0.463669\pi$
$293$	3.89899			0.227781			0.113891	+	0.993493i	$0.463669\pi$
$294$	3.84477	+	6.65934i	0.224232	+	0.388380i
$295$	−2.65136	−	4.59229i	−0.154368	−	0.267373i
$296$	25.0719			1.45728
$297$	−4.31046			−0.250118
$298$	14.1887	+	24.5755i	0.821927	+	1.42362i
$299$	6.87939	−	11.9154i	0.397845	−	0.689088i
$300$	−4.58512	−	7.94166i	−0.264722	−	0.458512i
$301$	6.66637	−	11.5465i	0.384243	−	0.665529i
$302$	−13.9795	+	24.2132i	−0.804431	+	1.39332i
$303$	−1.41653			−0.0813773
$304$		0			0
$305$	6.08647			0.348510
$306$	−12.6420	+	21.8966i	−0.722697	+	1.25175i
$307$	−11.5876	+	20.0704i	−0.661342	+	1.14548i	0.318921	+	0.947781i	$0.396679\pi$
$307$	−11.5876	+	20.0704i	−0.661342	+	1.14548i	−0.980263	+	0.197697i	$0.936654\pi$
$308$	4.00387	+	6.93491i	0.228142	+	0.395153i
$309$	−4.07145	+	7.05196i	−0.231617	+	0.401172i
$310$	6.54576	+	11.3376i	0.371774	+	0.643932i
$311$	−3.46110			−0.196261			−0.0981306	−	0.995174i	$-0.531286\pi$
$311$	−3.46110			−0.196261			−0.0981306	+	0.995174i	$0.531286\pi$
$312$	10.8280			0.613015
$313$	11.4449	+	19.8232i	0.646904	+	1.12047i	0.983858	+	0.178950i	$0.0572701\pi$
$313$	11.4449	+	19.8232i	0.646904	+	1.12047i	−0.336954	+	0.941521i	$0.609397\pi$
$314$	13.9179	+	24.1065i	0.785431	+	1.36041i
$315$	5.31315			0.299362
$316$	43.2695			2.43410
$317$	−13.0603	−	22.6211i	−0.733540	−	1.27053i	−0.955361	−	0.295441i	$-0.904533\pi$
$317$	−13.0603	−	22.6211i	−0.733540	−	1.27053i	0.221821	−	0.975087i	$-0.428800\pi$
$318$	−2.43242	+	4.21307i	−0.136403	+	0.236257i
$319$	−2.75624	−	4.77396i	−0.154320	−	0.267290i
$320$	−1.10354	+	1.91139i	−0.0616898	+	0.106850i
$321$	−2.18004	+	3.77595i	−0.121678	+	0.210753i
$322$	19.6459			1.09482
$323$		0			0
$324$	23.5895			1.31053
$325$	4.32635	−	7.49346i	0.239983	−	0.415662i
$326$	−8.01754	+	13.8868i	−0.444051	+	0.769118i
$327$	3.08512	+	5.34359i	0.170608	+	0.295501i
$328$	−30.4859	+	52.8032i	−1.68330	+	2.91557i
$329$	−0.439693	−	0.761570i	−0.0242410	−	0.0419867i
$330$	2.63816			0.145226
$331$	19.0446			1.04678			0.523392	−	0.852092i	$-0.324666\pi$
$331$	19.0446			1.04678			0.523392	+	0.852092i	$0.324666\pi$
$332$	−27.1707	−	47.0611i	−1.49119	−	2.58281i
$333$	−5.28446	−	9.15296i	−0.289587	−	0.501579i
$334$	34.8881			1.90899
$335$	5.23711			0.286134
$336$	3.31908	+	5.74881i	0.181071	+	0.313623i
$337$	−0.850700	+	1.47346i	−0.0463406	+	0.0802642i	−0.888265	−	0.459331i	$-0.848089\pi$
$337$	−0.850700	+	1.47346i	−0.0463406	+	0.0802642i	0.841925	+	0.539595i	$0.181423\pi$
$338$	−7.11334	−	12.3207i	−0.386915	−	0.670156i
$339$	0.427671	−	0.740748i	0.0232279	−	0.0402319i
$340$	11.5287	−	19.9683i	0.625231	−	1.08293i
$341$	4.54664			0.246214
$342$		0			0
$343$	−17.8530			−0.963970
$344$	−26.5685	+	46.0180i	−1.43248	+	2.48113i
$345$	2.22668	−	3.85673i	0.119881	−	0.207639i
$346$	31.9641	+	55.3634i	1.71840	+	2.97636i
$347$	2.45084	−	4.24497i	0.131568	−	0.227882i	−0.792713	−	0.609595i	$-0.791332\pi$
$347$	2.45084	−	4.24497i	0.131568	−	0.227882i	0.924281	+	0.381713i	$0.124666\pi$
$348$	−6.69846	−	11.6021i	−0.359075	−	0.621937i
$349$	−28.1293			−1.50573			−0.752863	−	0.658177i	$-0.771328\pi$
$349$	−28.1293			−1.50573			−0.752863	+	0.658177i	$0.771328\pi$
$350$	12.3550			0.660405
$351$	−4.94222	−	8.56017i	−0.263796	−	0.456908i
$352$	−2.72281	−	4.71605i	−0.145126	−	0.251366i
$353$	−8.31996			−0.442827			−0.221413	−	0.975180i	$-0.571067\pi$
$353$	−8.31996			−0.442827			−0.221413	+	0.975180i	$0.571067\pi$
$354$	−6.50475			−0.345723
$355$	−4.67230	−	8.09267i	−0.247980	−	0.429514i
$356$	5.35117	−	9.26849i	0.283611	−	0.491229i
$357$	1.93969	+	3.35965i	0.102659	+	0.177811i
$358$	7.38191	−	12.7858i	0.390146	−	0.675753i
$359$	−12.4645	+	21.5892i	−0.657852	+	1.13943i	0.323319	+	0.946290i	$0.395201\pi$
$359$	−12.4645	+	21.5892i	−0.657852	+	1.13943i	−0.981171	+	0.193142i	$0.938132\pi$
$360$	−21.1753			−1.11604
$361$		0			0
$362$	−34.3405			−1.80490
$363$	−3.13176	+	5.42437i	−0.164375	+	0.284705i
$364$	−9.18139	+	15.9026i	−0.481236	+	0.833524i
$365$	4.12836	+	7.15052i	0.216088	+	0.374275i
$366$	3.73308	−	6.46588i	0.195131	−	0.337977i
$367$	1.29292	+	2.23940i	0.0674898	+	0.116896i	0.897796	−	0.440412i	$-0.145168\pi$
$367$	1.29292	+	2.23940i	0.0674898	+	0.116896i	−0.830306	+	0.557308i	$0.811834\pi$
$368$	−33.6168			−1.75240
$369$	25.7023			1.33801
$370$	7.00387	+	12.1311i	0.364114	+	0.630664i
$371$	−2.25490	−	3.90560i	−0.117069	−	0.202769i
$372$	11.0496			0.572897
$373$	−23.3833			−1.21074			−0.605371	−	0.795943i	$-0.706975\pi$
$373$	−23.3833			−1.21074			−0.605371	+	0.795943i	$0.706975\pi$
$374$	−5.81908	−	10.0789i	−0.300897	−	0.521170i
$375$	3.59879	−	6.23329i	0.185841	−	0.321886i
$376$	1.75237	+	3.03520i	0.0903718	+	0.156529i
$377$	6.32042	−	10.9473i	0.325518	−	0.563814i
$378$	7.05690	−	12.2229i	0.362968	−	0.628679i
$379$	25.4388			1.30670			0.653352	−	0.757054i	$-0.273362\pi$
$379$	25.4388			1.30670			0.653352	+	0.757054i	$0.273362\pi$
$380$		0			0
$381$	9.46616			0.484966
$382$	−13.0201	+	22.5514i	−0.666165	+	1.15383i
$383$	13.7404	−	23.7990i	0.702099	−	1.21607i	−0.265629	−	0.964075i	$-0.585580\pi$
$383$	13.7404	−	23.7990i	0.702099	−	1.21607i	0.967728	−	0.251996i	$-0.0810870\pi$
$384$	4.35369	+	7.54082i	0.222173	+	0.384816i
$385$	−1.22281	+	2.11797i	−0.0623202	+	0.107942i
$386$	17.4722	+	30.2628i	0.889314	+	1.54034i
$387$	22.3996			1.13864
$388$	32.5107			1.65048
$389$	1.67112	+	2.89447i	0.0847292	+	0.146755i	0.905276	−	0.424824i	$-0.139664\pi$
$389$	1.67112	+	2.89447i	0.0847292	+	0.146755i	−0.820547	+	0.571580i	$0.806331\pi$
$390$	3.02481	+	5.23913i	0.153167	+	0.265294i
$391$	−19.6459			−0.993536
$392$	28.4097			1.43491
$393$	−6.46451	−	11.1969i	−0.326091	−	0.564807i
$394$	−10.0535	+	17.4132i	−0.506488	+	0.877263i
$395$	6.60741	+	11.4444i	0.332455	+	0.575829i
$396$	−6.72668	+	11.6510i	−0.338028	+	0.585482i
$397$	6.56165	−	11.3651i	0.329320	−	0.570399i	−0.653057	−	0.757309i	$-0.726514\pi$
$397$	6.56165	−	11.3651i	0.329320	−	0.570399i	0.982377	+	0.186910i	$0.0598472\pi$
$398$	−68.4552			−3.43135
$399$		0			0
$400$	−21.1411			−1.05706
$401$	−8.55690	+	14.8210i	−0.427311	+	0.740125i	−0.996633	−	0.0819897i	$-0.973873\pi$
$401$	−8.55690	+	14.8210i	−0.427311	+	0.740125i	0.569322	+	0.822115i	$0.307206\pi$
$402$	3.21213	−	5.56358i	0.160207	−	0.277486i
$403$	5.21301	+	9.02920i	0.259679	+	0.449776i
$404$	−4.78699	+	8.29131i	−0.238162	+	0.412508i
$405$	3.60220	+	6.23919i	0.178995	+	0.310028i
$406$	18.0496			0.895788
$407$	4.86484			0.241141
$408$	−7.73055	−	13.3897i	−0.382719	−	0.662889i
$409$	4.39899	+	7.61927i	0.217516	+	0.376748i	0.954048	−	0.299654i	$-0.0968713\pi$
$409$	4.39899	+	7.61927i	0.217516	+	0.376748i	−0.736532	+	0.676403i	$0.763538\pi$
$410$	−34.0651			−1.68236
$411$	−6.66044			−0.328535
$412$	27.5180	+	47.6626i	1.35571	+	2.34817i
$413$	3.01501	−	5.22216i	0.148359	−	0.256966i
$414$	16.5030	+	28.5840i	0.811078	+	1.40483i
$415$	8.29813	−	14.3728i	0.407339	−	0.705532i
$416$	6.24376	−	10.8145i	0.306125	−	0.530225i
$417$	1.08378			0.0530728
$418$		0			0
$419$	6.84018			0.334165			0.167082	−	0.985943i	$-0.446565\pi$
$419$	6.84018			0.334165			0.167082	+	0.985943i	$0.446565\pi$
$420$	−2.97178	+	5.14728i	−0.145008	+	0.251161i
$421$	2.41147	−	4.17680i	0.117528	−	0.203565i	−0.801259	−	0.598317i	$-0.795836\pi$
$421$	2.41147	−	4.17680i	0.117528	−	0.203565i	0.918787	+	0.394752i	$0.129170\pi$
$422$	−10.2194	−	17.7005i	−0.497473	−	0.861648i
$423$	0.738703	−	1.27947i	0.0359170	−	0.0622100i
$424$	8.98680	+	15.5656i	0.436437	+	0.755932i
$425$	−12.3550			−0.599307
$426$	−11.4629			−0.555377
$427$	3.46064	+	5.99400i	0.167472	+	0.290070i
$428$	14.7344	+	25.5208i	0.712215	+	1.23359i
$429$	2.10101			0.101438
$430$	−29.6878			−1.43167
$431$	−0.651826	−	1.12900i	−0.0313974	−	0.0543818i	0.849900	−	0.526944i	$-0.176662\pi$
$431$	−0.651826	−	1.12900i	−0.0313974	−	0.0543818i	−0.881297	+	0.472563i	$0.843329\pi$
$432$	−12.0753	+	20.9151i	−0.580974	+	1.00628i
$433$	−9.91194	−	17.1680i	−0.476337	−	0.825041i	0.523295	−	0.852152i	$-0.324703\pi$
$433$	−9.91194	−	17.1680i	−0.476337	−	0.825041i	−0.999632	+	0.0271109i	$0.991369\pi$
$434$	−7.44356	+	12.8926i	−0.357302	+	0.618866i
$435$	2.04576	−	3.54336i	0.0980867	−	0.169891i
$436$	41.7033			1.99722
$437$		0			0
$438$	10.1284			0.483952
$439$	17.2836	−	29.9360i	0.824901	−	1.42877i	−0.0770948	−	0.997024i	$-0.524564\pi$
$439$	17.2836	−	29.9360i	0.824901	−	1.42877i	0.901995	−	0.431746i	$-0.142102\pi$
$440$	4.87346	−	8.44107i	0.232333	−	0.402412i
$441$	−5.98798	−	10.3715i	−0.285142	−	0.493880i
$442$	13.3439	−	23.1123i	0.634704	−	1.09934i
$443$	−8.50505	−	14.7312i	−0.404087	−	0.699900i	0.590128	−	0.807310i	$-0.299077\pi$
$443$	−8.50505	−	14.7312i	−0.404087	−	0.699900i	−0.994215	+	0.107410i	$0.965744\pi$
$444$	11.8229			0.561092
$445$	3.26857			0.154945
$446$	−19.5929	−	33.9358i	−0.927749	−	1.60691i
$447$	3.65745	+	6.33489i	0.172992	+	0.299630i
$448$	−2.50980			−0.118577
$449$	37.4097			1.76547			0.882737	−	0.469868i	$-0.155698\pi$
$449$	37.4097			1.76547			0.882737	+	0.469868i	$0.155698\pi$
$450$	10.3785	+	17.9761i	0.489248	+	0.847402i
$451$	−5.91534	+	10.2457i	−0.278543	+	0.482450i
$452$	−2.89053	−	5.00654i	−0.135959	−	0.235488i
$453$	−3.60354	+	6.24152i	−0.169309	+	0.293252i
$454$	12.4991	−	21.6491i	0.586613	−	1.01604i
$455$	−5.60813			−0.262913
$456$		0			0
$457$	9.11112			0.426200			0.213100	−	0.977030i	$-0.431644\pi$
$457$	9.11112			0.426200			0.213100	+	0.977030i	$0.431644\pi$
$458$	25.4714	−	44.1177i	1.19020	−	2.06149i
$459$	−7.05690	+	12.2229i	−0.329388	+	0.570517i
$460$	−15.0496	−	26.0667i	−0.701693	−	1.21537i
$461$	12.2242	−	21.1729i	0.569336	−	0.986118i	−0.427296	−	0.904112i	$-0.640534\pi$
$461$	12.2242	−	21.1729i	0.569336	−	0.986118i	0.996632	−	0.0820066i	$-0.0261329\pi$
$462$	1.50000	+	2.59808i	0.0697863	+	0.120873i
$463$	−0.250725			−0.0116522			−0.00582609	−	0.999983i	$-0.501855\pi$
$463$	−0.250725			−0.0116522			−0.00582609	+	0.999983i	$0.501855\pi$
$464$	−30.8854			−1.43382
$465$	1.68732	+	2.92252i	0.0782475	+	0.135529i
$466$	4.47519	+	7.75125i	0.207309	+	0.359070i
$467$	15.3618			0.710861			0.355431	−	0.934703i	$-0.384334\pi$
$467$	15.3618			0.710861			0.355431	+	0.934703i	$0.384334\pi$
$468$	−30.8503			−1.42606
$469$	2.97771	+	5.15755i	0.137498	+	0.238153i
$470$	−0.979055	+	1.69577i	−0.0451605	+	0.0782202i
$471$	3.58765	+	6.21399i	0.165310	+	0.286326i
$472$	−12.0162	+	20.8127i	−0.553090	+	0.957980i
$473$	−5.15523	+	8.92912i	−0.237038	+	0.410561i
$474$	16.2104			0.744567
$475$		0			0
$476$	26.2199			1.20179
$477$	3.78833	−	6.56159i	0.173456	−	0.300434i
$478$	15.1591	−	26.2563i	0.693361	−	1.20094i
$479$	0.359623	+	0.622885i	0.0164316	+	0.0284603i	0.874124	−	0.485702i	$-0.161436\pi$
$479$	0.359623	+	0.622885i	0.0164316	+	0.0284603i	−0.857693	+	0.514163i	$0.828103\pi$
$480$	2.02094	−	3.50038i	0.0922431	−	0.159770i
$481$	5.57785	+	9.66112i	0.254328	+	0.440509i
$482$	−32.6682			−1.48800
$483$	5.06418			0.230428
$484$	21.1668	+	36.6620i	0.962129	+	1.66646i
$485$	4.96451	+	8.59878i	0.225427	+	0.390450i
$486$	36.4739			1.65449
$487$	11.7469			0.532303			0.266152	−	0.963931i	$-0.414248\pi$
$487$	11.7469			0.532303			0.266152	+	0.963931i	$0.414248\pi$
$488$	−13.7922	−	23.8888i	−0.624344	−	1.08140i
$489$	−2.06670	+	3.57964i	−0.0934596	+	0.161877i
$490$	7.93629	+	13.7461i	0.358525	+	0.620984i
$491$	−0.0444153	+	0.0769295i	−0.00200443	+	0.00347178i	−0.867026	−	0.498263i	$-0.833971\pi$
$491$	−0.0444153	+	0.0769295i	−0.00200443	+	0.00347178i	0.865021	+	0.501735i	$0.167305\pi$
$492$	−14.3760	+	24.8999i	−0.648119	+	1.12258i
$493$	−18.0496			−0.812914
$494$		0			0
$495$	−4.10876			−0.184675
$496$	12.7369	−	22.0610i	0.571906	−	0.990570i
$497$	5.31315	−	9.20264i	0.238327	−	0.412795i
$498$	−10.1792	−	17.6308i	−0.456139	−	0.790057i
$499$	−7.34524	+	12.7223i	−0.328818	+	0.569529i	−0.982278	−	0.187432i	$-0.939984\pi$
$499$	−7.34524	+	12.7223i	−0.328818	+	0.569529i	0.653460	+	0.756961i	$0.273317\pi$
$500$	−24.3234	−	42.1294i	−1.08778	−	1.88408i
$501$	8.99319			0.401786
$502$	−36.3678			−1.62318
$503$	2.45202	+	4.24702i	0.109330	+	0.189365i	0.915499	−	0.402320i	$-0.131796\pi$
$503$	2.45202	+	4.24702i	0.109330	+	0.189365i	−0.806169	+	0.591685i	$0.798463\pi$
$504$	−12.0398	−	20.8536i	−0.536297	−	0.928893i
$505$	−2.92396			−0.130115
$506$	−15.1925			−0.675390
$507$	−1.83363	−	3.17593i	−0.0814342	−	0.141048i
$508$	31.9898	−	55.4079i	1.41932	−	2.45833i
$509$	−3.20692	−	5.55455i	−0.142144	−	0.246201i	0.786160	−	0.618023i	$-0.212066\pi$
$509$	−3.20692	−	5.55455i	−0.142144	−	0.246201i	−0.928304	+	0.371823i	$0.878733\pi$
$510$	4.31908	−	7.48086i	0.191252	−	0.331258i
$511$	−4.69459	+	8.13127i	−0.207677	+	0.359706i
$512$	50.5553			2.23425
$513$		0			0
$514$	−12.6040			−0.555939
$515$	−8.40420	+	14.5565i	−0.370333	+	0.641436i
$516$	−12.5287	+	21.7003i	−0.551545	+	0.955303i
$517$	0.340022	+	0.588936i	0.0149542	+	0.0259014i
$518$	−7.96451	+	13.7949i	−0.349940	+	0.606115i
$519$	8.23947	+	14.2712i	0.361673	+	0.626436i
$520$	22.3509			0.980153
$521$	−35.8135			−1.56902			−0.784508	−	0.620119i	$-0.787084\pi$
$521$	−35.8135			−1.56902			−0.784508	+	0.620119i	$0.787084\pi$
$522$	15.1621	+	26.2615i	0.663627	+	1.14944i
$523$	−19.3862	−	33.5780i	−0.847701	−	1.46826i	−0.883254	−	0.468894i	$-0.844653\pi$
$523$	−19.3862	−	33.5780i	−0.847701	−	1.46826i	0.0355529	−	0.999368i	$-0.488681\pi$
$524$	−87.3842			−3.81740
$525$	3.18479			0.138996
$526$	−30.4393	−	52.7224i	−1.32722	−	2.29881i
$527$	7.44356	−	12.8926i	0.324247	−	0.561612i
$528$	−2.56670	−	4.44566i	−0.111701	−	0.193473i
$529$	−1.32295	+	2.29141i	−0.0575195	+	0.0996267i
$530$	−5.02094	+	8.69653i	−0.218096	+	0.377753i
$531$	10.1307			0.439636
$532$		0			0
$533$	−27.1293			−1.17510
$534$	2.00475	−	3.47232i	0.0867539	−	0.150262i
$535$	−4.50000	+	7.79423i	−0.194552	+	0.336974i
$536$	−11.8675	−	20.5552i	−0.512599	−	0.887848i
$537$	1.90286	−	3.29584i	0.0821143	−	0.142226i
$538$	−16.5993	−	28.7508i	−0.715645	−	1.23953i
$539$	5.51249			0.237440
$540$	−21.6236			−0.930532
$541$	−4.74510	−	8.21875i	−0.204008	−	0.353352i	0.745808	−	0.666161i	$-0.232063\pi$
$541$	−4.74510	−	8.21875i	−0.204008	−	0.353352i	−0.949816	+	0.312809i	$0.898730\pi$
$542$	−33.6386	−	58.2638i	−1.44490	−	2.50264i
$543$	−8.85204			−0.379878
$544$	−17.8307			−0.764484
$545$	6.36824	+	11.0301i	0.272785	+	0.472478i
$546$	−3.43969	+	5.95772i	−0.147205	+	0.254967i
$547$	−7.10607	−	12.3081i	−0.303833	−	0.526255i	0.673167	−	0.739490i	$-0.264933\pi$
$547$	−7.10607	−	12.3081i	−0.303833	−	0.526255i	−0.977001	+	0.213235i	$0.931600\pi$
$548$	−22.5082	+	38.9854i	−0.961503	+	1.66537i
$549$	−5.81403	+	10.0702i	−0.248137	+	0.429785i
$550$	−9.55438			−0.407400
$551$		0			0
$552$	−20.1830			−0.859047
$553$	−7.51367	+	13.0141i	−0.319514	+	0.553414i
$554$	−20.9033	+	36.2056i	−0.888097	+	1.53823i
$555$	1.80541	+	3.12706i	0.0766353	+	0.132736i
$556$	3.66250	−	6.34364i	0.155325	−	0.269030i
$557$	−11.2699	−	19.5201i	−0.477522	−	0.827092i	0.522146	−	0.852856i	$-0.325131\pi$
$557$	−11.2699	−	19.5201i	−0.477522	−	0.827092i	−0.999668	+	0.0257641i	$0.991798\pi$
$558$	−25.0110			−1.05880
$559$	−23.6432			−1.00000
$560$	6.85117	+	11.8666i	0.289515	+	0.501454i
$561$	−1.50000	−	2.59808i	−0.0633300	−	0.109691i
$562$	49.0975			2.07105
$563$	−42.9718			−1.81105			−0.905524	−	0.424296i	$-0.860522\pi$
$563$	−42.9718			−1.81105			−0.905524	+	0.424296i	$0.860522\pi$
$564$	0.826352	+	1.43128i	0.0347957	+	0.0602679i
$565$	0.882789	−	1.52904i	0.0371392	−	0.0643270i
$566$	−14.3195	−	24.8022i	−0.601895	−	1.04251i
$567$	−4.09627	+	7.09494i	−0.172027	+	0.297960i
$568$	−21.1753	+	36.6767i	−0.888496	+	1.53892i
$569$	7.42696			0.311354			0.155677	−	0.987808i	$-0.450244\pi$
$569$	7.42696			0.311354			0.155677	+	0.987808i	$0.450244\pi$
$570$		0			0
$571$	4.04458			0.169260			0.0846301	−	0.996412i	$-0.473029\pi$
$571$	4.04458			0.169260			0.0846301	+	0.996412i	$0.473029\pi$
$572$	7.10014	−	12.2978i	0.296872	−	0.514197i
$573$	−3.35622	+	5.81314i	−0.140208	+	0.242847i
$574$	−19.3687	−	33.5476i	−0.808434	−	1.40025i
$575$	−8.06418	+	13.9676i	−0.336299	+	0.582488i
$576$	−2.10829	−	3.65166i	−0.0878453	−	0.152153i
$577$	3.23442			0.134651			0.0673254	−	0.997731i	$-0.478553\pi$
$577$	3.23442			0.134651			0.0673254	+	0.997731i	$0.478553\pi$
$578$	4.93851			0.205415
$579$	4.50387	+	7.80093i	0.187174	+	0.324196i
$580$	−13.8268	−	23.9488i	−0.574127	−	0.994418i
$581$	18.8726			0.782966
$582$	12.1797			0.504866
$583$	1.74376	+	3.02027i	0.0722190	+	0.125087i
$584$	18.7101	−	32.4068i	0.774228	−	1.34100i
$585$	−4.71095	−	8.15961i	−0.194774	−	0.337358i
$586$	4.93629	−	8.54990i	0.203916	−	0.353193i
$587$	20.4042	−	35.3411i	0.842171	−	1.45868i	−0.0458837	−	0.998947i	$-0.514610\pi$
$587$	20.4042	−	35.3411i	0.842171	−	1.45868i	0.888055	−	0.459737i	$-0.152056\pi$
$588$	13.3969			0.552480
$589$		0			0
$590$	−13.4270			−0.552779
$591$	−2.59152	+	4.48864i	−0.106601	+	0.184638i
$592$	13.6284	−	23.6050i	0.560122	−	0.970160i
$593$	5.53209	+	9.58186i	0.227176	+	0.393480i	0.956970	−	0.290187i	$-0.0937175\pi$
$593$	5.53209	+	9.58186i	0.227176	+	0.393480i	−0.729794	+	0.683667i	$0.760384\pi$
$594$	−5.45723	+	9.45221i	−0.223913	+	0.387829i
$595$	4.00387	+	6.93491i	0.164143	+	0.284303i
$596$	49.4397			2.02513
$597$	−17.6459			−0.722198
$598$	−17.4192	−	30.1710i	−0.712325	−	1.23378i
$599$	22.2788	+	38.5881i	0.910289	+	1.57667i	0.813656	+	0.581346i	$0.197474\pi$
$599$	22.2788	+	38.5881i	0.910289	+	1.57667i	0.0966322	+	0.995320i	$0.469193\pi$
$600$	−12.6928			−0.518183
$601$	−4.99907			−0.203916			−0.101958	−	0.994789i	$-0.532511\pi$
$601$	−4.99907			−0.203916			−0.101958	+	0.994789i	$0.532511\pi$
$602$	−16.8799	−	29.2368i	−0.687971	−	1.19160i
$603$	−5.00269	+	8.66491i	−0.203725	+	0.352862i
$604$	24.3555	+	42.1850i	0.991011	+	1.71648i
$605$	−6.46451	+	11.1969i	−0.262820	+	0.455217i
$606$	−1.79339	+	3.10623i	−0.0728513	+	0.126182i
$607$	−31.1881			−1.26589			−0.632943	−	0.774199i	$-0.718153\pi$
$607$	−31.1881			−1.26589			−0.632943	+	0.774199i	$0.718153\pi$
$608$		0			0
$609$	4.65270			0.188537
$610$	7.70574	−	13.3467i	0.311996	−	0.540393i
$611$	−0.779715	+	1.35051i	−0.0315439	+	0.0546356i
$612$	22.0253	+	38.1489i	0.890319	+	1.54208i
$613$	−8.18479	+	14.1765i	−0.330581	+	0.572582i	−0.982626	−	0.185598i	$-0.940578\pi$
$613$	−8.18479	+	14.1765i	−0.330581	+	0.572582i	0.652045	+	0.758180i	$0.273911\pi$
$614$	29.3410	+	50.8200i	1.18410	+	2.05093i
$615$	−8.78106			−0.354086
$616$	11.0838			0.446578
$617$	−8.02915	−	13.9069i	−0.323241	−	0.559871i	0.657913	−	0.753094i	$-0.271439\pi$
$617$	−8.02915	−	13.9069i	−0.323241	−	0.559871i	−0.981155	+	0.193223i	$0.938106\pi$
$618$	10.3093	+	17.8562i	0.414700	+	0.718281i
$619$	23.8425			0.958313			0.479156	−	0.877730i	$-0.340943\pi$
$619$	23.8425			0.958313			0.479156	+	0.877730i	$0.340943\pi$
$620$	22.8084			0.916007
$621$	9.21213	+	15.9559i	0.369670	+	0.640288i
$622$	−4.38191	+	7.58969i	−0.175699	+	0.304319i
$623$	1.85844	+	3.21891i	0.0744569	+	0.128963i
$624$	5.88578	−	10.1945i	0.235620	−	0.408106i
$625$	−0.533433	+	0.923933i	−0.0213373	+	0.0369573i
$626$	57.9590			2.31651
$627$		0			0
$628$	48.4962			1.93521
$629$	7.96451	−	13.7949i	0.317566	−	0.550040i
$630$	6.72668	−	11.6510i	0.267997	−	0.464185i
$631$	−10.7365	−	18.5961i	−0.427413	−	0.740300i	0.569230	−	0.822179i	$-0.307241\pi$
$631$	−10.7365	−	18.5961i	−0.427413	−	0.740300i	−0.996642	+	0.0818782i	$0.973908\pi$
$632$	29.9454	−	51.8669i	1.19116	−	2.06315i
$633$	−2.63429	−	4.56272i	−0.104703	−	0.181352i
$634$	−66.1397			−2.62674
$635$	19.5398			0.775414
$636$	4.23783	+	7.34013i	0.168041	+	0.291055i
$637$	6.32042	+	10.9473i	0.250424	+	0.433748i
$638$	−13.9581			−0.552607
$639$	17.8527			0.706240
$640$	8.98680	+	15.5656i	0.355234	+	0.615284i
$641$	−6.37686	+	11.0450i	−0.251871	+	0.436253i	−0.964041	−	0.265754i	$-0.914379\pi$
$641$	−6.37686	+	11.0450i	−0.251871	+	0.436253i	0.712170	+	0.702007i	$0.247712\pi$
$642$	5.52007	+	9.56104i	0.217860	+	0.377344i
$643$	−14.3041	+	24.7754i	−0.564097	+	0.977045i	0.433036	+	0.901377i	$0.357442\pi$
$643$	−14.3041	+	24.7754i	−0.564097	+	0.977045i	−0.997133	+	0.0756683i	$0.975891\pi$
$644$	17.1138	−	29.6420i	0.674378	−	1.16806i
$645$	−7.65270			−0.301325
$646$		0			0
$647$	16.7128			0.657046			0.328523	−	0.944496i	$-0.393449\pi$
$647$	16.7128			0.657046			0.328523	+	0.944496i	$0.393449\pi$
$648$	16.3255	−	28.2766i	0.641325	−	1.11081i
$649$	−2.33157	+	4.03839i	−0.0915220	+	0.158521i
$650$	−10.9547	−	18.9741i	−0.429679	−	0.744226i
$651$	−1.91875	+	3.32337i	−0.0752017	+	0.130253i
$652$	13.9684	+	24.1939i	0.547044	+	0.947508i
$653$	27.0000			1.05659			0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000			1.05659			0.528296	+	0.849060i	$0.322831\pi$
$654$	15.6236			0.610931
$655$	−13.3439	−	23.1123i	−0.521389	−	0.903072i
$656$	33.1425	+	57.4045i	1.29400	+	2.24127i
$657$	−15.7743			−0.615412
$658$	−2.22668			−0.0868051
$659$	21.9504	+	38.0193i	0.855067	+	1.48102i	0.876583	+	0.481251i	$0.159818\pi$
$659$	21.9504	+	38.0193i	0.855067	+	1.48102i	−0.0215154	+	0.999769i	$0.506849\pi$
$660$	2.29813	−	3.98048i	0.0894547	−	0.154940i
$661$	5.37804	+	9.31504i	0.209182	+	0.362313i	0.951457	−	0.307782i	$-0.0995867\pi$
$661$	5.37804	+	9.31504i	0.209182	+	0.362313i	−0.742275	+	0.670095i	$0.766253\pi$
$662$	24.1113	−	41.7620i	0.937112	−	1.62312i
$663$	3.43969	−	5.95772i	0.133587	−	0.231379i
$664$	−75.2158			−2.91894
$665$		0			0
$666$	−26.7615			−1.03699
$667$	−11.7811	+	20.4054i	−0.456164	+	0.790100i
$668$	30.3915	−	52.6396i	1.17588	−	2.03669i
$669$	−5.05051	−	8.74774i	−0.195264	−	0.338207i
$670$	6.63041	−	11.4842i	0.256155	−	0.443674i
$671$	−2.67617	−	4.63527i	−0.103313	−	0.178943i
$672$	4.59627			0.177305
$673$	4.65776			0.179543			0.0897717	−	0.995962i	$-0.471386\pi$
$673$	4.65776			0.179543			0.0897717	+	0.995962i	$0.471386\pi$
$674$	2.15405	+	3.73092i	0.0829708	+	0.143710i
$675$	5.79339	+	10.0344i	0.222988	+	0.386226i
$676$	−24.7861			−0.953312
$677$	3.26857			0.125621			0.0628107	−	0.998025i	$-0.479994\pi$
$677$	3.26857			0.125621			0.0628107	+	0.998025i	$0.479994\pi$
$678$	−1.08290	−	1.87564i	−0.0415886	−	0.0720335i
$679$	−5.64543	+	9.77817i	−0.216652	+	0.375252i
$680$	−15.9572	−	27.6387i	−0.611932	−	1.05990i
$681$	3.22193	−	5.58055i	0.123465	−	0.213847i
$682$	5.75624	−	9.97011i	0.220418	−	0.381775i
$683$	6.21894			0.237961			0.118981	−	0.992897i	$-0.462037\pi$
$683$	6.21894			0.237961			0.118981	+	0.992897i	$0.462037\pi$
$684$		0			0
$685$	−13.7483			−0.525297
$686$	−22.6027	+	39.1490i	−0.862974	+	1.49471i
$687$	6.56583	−	11.3723i	0.250502	−	0.433882i
$688$	28.8837	+	50.0281i	1.10118	+	1.90730i
$689$	−3.99866	+	6.92588i	−0.152337	+	0.263855i
$690$	−5.63816	−	9.76557i	−0.214641	−	0.371769i
$691$	22.2175			0.845194			0.422597	−	0.906318i	$-0.361119\pi$
$691$	22.2175			0.845194			0.422597	+	0.906318i	$0.361119\pi$
$692$	111.377			4.23393
$693$	−2.33615	−	4.04633i	−0.0887431	−	0.153708i
$694$	−6.20574	−	10.7487i	−0.235567	−	0.408013i
$695$	2.23711			0.0848584
$696$	−18.5431			−0.702875
$697$	19.3687	+	33.5476i	0.733642	+	1.27071i
$698$	−35.6129	+	61.6834i	−1.34797	+	2.33475i
$699$	1.15358	+	1.99806i	0.0436324	+	0.0755736i
$700$	10.7626	−	18.6414i	0.406790	−	0.704580i
$701$	13.8862	−	24.0517i	0.524476	−	0.908420i	−0.475117	−	0.879922i	$-0.657594\pi$
$701$	13.8862	−	24.0517i	0.524476	−	0.908420i	0.999594	−	0.0284974i	$-0.00907222\pi$
$702$	−25.0283			−0.944631
$703$		0			0
$704$	1.94087			0.0731495
$705$	−0.252374	+	0.437124i	−0.00950495	+	0.0164631i
$706$	−10.5334	+	18.2444i	−0.396431	+	0.686639i
$707$	−1.66250	−	2.87954i	−0.0625249	−	0.108296i
$708$	−5.66637	+	9.81445i	−0.212955	+	0.368850i
$709$	3.05391	+	5.28953i	0.114692	+	0.198652i	0.917657	−	0.397374i	$-0.130079\pi$
$709$	3.05391	+	5.28953i	0.114692	+	0.198652i	−0.802965	+	0.596027i	$0.796745\pi$
$710$	−23.6614			−0.887996
$711$	−25.2466			−0.946822
$712$	−7.40673	−	12.8288i	−0.277579	−	0.480781i
$713$	−9.71688	−	16.8301i	−0.363900	−	0.630293i
$714$	9.82295			0.367615
$715$	4.33687			0.162190
$716$	−12.8610	−	22.2758i	−0.480637	−	0.832488i
$717$	3.90760	−	6.76817i	0.145932	−	0.252762i
$718$	31.5612	+	54.6657i	1.17786	+	2.04010i
$719$	−19.3619	+	33.5358i	−0.722077	+	1.25067i	0.238089	+	0.971243i	$0.423479\pi$
$719$	−19.3619	+	33.5358i	−0.722077	+	1.25067i	−0.960166	+	0.279431i	$0.909854\pi$
$720$	−11.5103	+	19.9364i	−0.428962	+	0.742985i
$721$	−19.1138			−0.711835
$722$		0			0
$723$	−8.42097			−0.313179
$724$	−29.9145	+	51.8134i	−1.11176	+	1.92563i
$725$	−7.40895	+	12.8327i	−0.275161	+	0.476594i
$726$	7.92989	+	13.7350i	0.294306	+	0.509753i
$727$	5.53895	−	9.59375i	0.205428	−	0.355812i	−0.744841	−	0.667242i	$-0.767475\pi$
$727$	5.53895	−	9.59375i	0.205428	−	0.355812i	0.950269	+	0.311430i	$0.100808\pi$
$728$	12.7083	+	22.0114i	0.471000	+	0.815795i
$729$	−6.63991			−0.245923
$730$	20.9067			0.773793
$731$	16.8799	+	29.2368i	0.624324	+	1.08136i
$732$	−6.50387	−	11.2650i	−0.240390	−	0.416368i
$733$	−15.8075			−0.583862			−0.291931	−	0.956439i	$-0.594298\pi$
$733$	−15.8075			−0.583862			−0.291931	+	0.956439i	$0.594298\pi$
$734$	6.54757			0.241675
$735$	2.04576	+	3.54336i	0.0754590	+	0.130699i
$736$	−11.6382	+	20.1579i	−0.428988	+	0.743029i
$737$	−2.30272	−	3.98843i	−0.0848217	−	0.146916i
$738$	32.5403	−	56.3614i	1.19782	−	2.07469i
$739$	−0.774663	+	1.34175i	−0.0284964	+	0.0493573i	−0.879922	−	0.475118i	$-0.842405\pi$
$739$	−0.774663	+	1.34175i	−0.0284964	+	0.0493573i	0.851425	+	0.524476i	$0.175739\pi$
$740$	24.4047			0.897133
$741$		0			0
$742$	−11.4192			−0.419213
$743$	−19.0817	+	33.0505i	−0.700040	+	1.21251i	0.268411	+	0.963304i	$0.413501\pi$
$743$	−19.0817	+	33.0505i	−0.700040	+	1.21251i	−0.968452	+	0.249201i	$0.919832\pi$
$744$	7.64708	−	13.2451i	0.280356	−	0.485590i
$745$	7.54963	+	13.0763i	0.276597	+	0.479080i
$746$	−29.6043	+	51.2762i	−1.08389	+	1.87735i
$747$	15.8534	+	27.4589i	0.580045	+	1.00467i
$748$	−20.2763			−0.741375
$749$	−10.2344			−0.373958
$750$	−9.11246	−	15.7832i	−0.332740	−	0.576323i
$751$	12.6741	+	21.9522i	0.462485	+	0.801048i	0.999084	−	0.0427898i	$-0.0136246\pi$
$751$	12.6741	+	21.9522i	0.462485	+	0.801048i	−0.536599	+	0.843837i	$0.680291\pi$
$752$	3.81016			0.138942
$753$	−9.37464			−0.341631
$754$	−16.0039	−	27.7195i	−0.582827	−	1.00949i
$755$	−7.43835	+	12.8836i	−0.270709	+	0.468882i
$756$	−12.2947	−	21.2951i	−0.447155	−	0.774495i
$757$	−21.1853	+	36.6939i	−0.769991	+	1.33366i	0.167576	+	0.985859i	$0.446406\pi$
$757$	−21.1853	+	36.6939i	−0.769991	+	1.33366i	−0.937567	+	0.347805i	$0.886927\pi$
$758$	32.2067	−	55.7836i	1.16980	−	2.02615i
$759$	−3.91622			−0.142150
$760$		0			0
$761$	−2.85710			−0.103570			−0.0517848	−	0.998658i	$-0.516491\pi$
$761$	−2.85710			−0.103570			−0.0517848	+	0.998658i	$0.516491\pi$
$762$	11.9846	−	20.7579i	0.434155	−	0.751979i
$763$	−7.24170	+	12.5430i	−0.262167	+	0.454087i
$764$	22.6839	+	39.2897i	0.820675	+	1.42145i
$765$	−6.72668	+	11.6510i	−0.243204	+	0.421241i
$766$	−34.7918	−	60.2612i	−1.25708	−	2.17732i
$767$	−10.6932			−0.386108
$768$	19.9094			0.718419
$769$	−9.56031	−	16.5589i	−0.344754	−	0.597131i	0.640555	−	0.767912i	$-0.278704\pi$
$769$	−9.56031	−	16.5589i	−0.344754	−	0.597131i	−0.985309	+	0.170781i	$0.945371\pi$
$770$	3.09627	+	5.36289i	0.111582	+	0.193265i
$771$	−3.24897			−0.117009
$772$	60.8813			2.19116
$773$	−1.25743	−	2.17793i	−0.0452265	−	0.0783346i	0.842526	−	0.538656i	$-0.181068\pi$
$773$	−1.25743	−	2.17793i	−0.0452265	−	0.0783346i	−0.887752	+	0.460321i	$0.847734\pi$
$774$	28.3589	−	49.1191i	1.01934	−	1.76555i
$775$	−6.11081	−	10.5842i	−0.219507	−	0.380197i
$776$	22.4996	−	38.9704i	0.807688	−	1.39896i
$777$	−2.05303	+	3.55596i	−0.0736522	+	0.127569i
$778$	8.46286			0.303408
$779$		0			0
$780$	10.5398			0.377386
$781$	−4.10876	+	7.11657i	−0.147023	+	0.254651i
$782$	−24.8726	+	43.0806i	−0.889442	+	1.54056i
$783$	8.46363	+	14.6594i	0.302465	+	0.523886i
$784$	15.4427	−	26.7475i	0.551524	−	0.955268i
$785$	7.40554	+	12.8268i	0.264315	+	0.457807i
$786$	−32.7374			−1.16770
$787$	2.72605			0.0971733			0.0485866	−	0.998819i	$-0.484528\pi$
$787$	2.72605			0.0971733			0.0485866	+	0.998819i	$0.484528\pi$
$788$	17.5155	+	30.3377i	0.623963	+	1.08074i
$789$	−7.84642	−	13.5904i	−0.279340	−	0.483831i
$790$	33.4611			1.19049
$791$	2.00774			0.0713870
$792$	9.31062	+	16.1265i	0.330839	+	0.573029i
$793$	6.13681	−	10.6293i	0.217925	−	0.377456i
$794$	−16.6147	−	28.7775i	−0.589633	−	1.02127i
$795$	−1.29426	+	2.24173i	−0.0459028	+	0.0795059i
$796$	−59.6323	+	103.286i	−2.11361	+	3.66088i
$797$	22.0327			0.780439			0.390219	−	0.920722i	$-0.372399\pi$
$797$	22.0327			0.780439			0.390219	+	0.920722i	$0.372399\pi$
$798$		0			0
$799$	2.22668			0.0787743
$800$	−7.31908	+	12.6770i	−0.258768	+	0.448200i
$801$	−3.12226	+	5.40792i	−0.110320	+	0.191079i
$802$	21.6668	+	37.5281i	0.765083	+	1.32516i
$803$	3.63041	−	6.28806i	0.128115	−	0.221901i
$804$	−5.59627	−	9.69302i	−0.197365	−	0.341846i
$805$	10.4534			0.368433
$806$	26.3996			0.929887
$807$	−4.27884	−	7.41116i	−0.150622	−	0.260885i
$808$	6.62583	+	11.4763i	0.233096	+	0.403734i
$809$	54.7205			1.92387			0.961935	−	0.273278i	$-0.0881077\pi$
$809$	54.7205			1.92387			0.961935	+	0.273278i	$0.0881077\pi$
$810$	18.2422			0.640964
$811$	1.15523	+	2.00092i	0.0405656	+	0.0702617i	0.885595	−	0.464458i	$-0.153751\pi$
$811$	1.15523	+	2.00092i	0.0405656	+	0.0702617i	−0.845030	+	0.534719i	$0.820417\pi$
$812$	15.7233	−	27.2335i	0.551779	−	0.955709i
$813$	−8.67112	−	15.0188i	−0.304110	−	0.526733i
$814$	6.15910	−	10.6679i	0.215876	−	0.373909i
$815$	−4.26604	+	7.38901i	−0.149433	+	0.258826i
$816$	−16.8084			−0.588412
$817$		0			0
$818$	22.2772			0.778906
$819$	5.35710	−	9.27876i	0.187192	−	0.324226i
$820$	−29.6746	+	51.3979i	−1.03628	+	1.79489i
$821$	−0.555560	−	0.962258i	−0.0193892	−	0.0335830i	0.856168	−	0.516698i	$-0.172839\pi$
$821$	−0.555560	−	0.962258i	−0.0193892	−	0.0335830i	−0.875557	+	0.483114i	$0.839505\pi$
$822$	−8.43242	+	14.6054i	−0.294114	+	0.509421i
$823$	−10.3238	−	17.8814i	−0.359866	−	0.623306i	0.628072	−	0.778155i	$-0.283844\pi$
$823$	−10.3238	−	17.8814i	−0.359866	−	0.623306i	−0.987938	+	0.154849i	$0.950511\pi$
$824$	76.1772			2.65376
$825$	−2.46286			−0.0857457
$826$	−7.63429	−	13.2230i	−0.265631	−	0.460086i
$827$	−18.1527	−	31.4414i	−0.631231	−	1.09332i	−0.987300	−	0.158865i	$-0.949217\pi$
$827$	−18.1527	−	31.4414i	−0.631231	−	1.09332i	0.356069	−	0.934460i	$-0.384117\pi$
$828$	57.5039			1.99840
$829$	−7.14971			−0.248320			−0.124160	−	0.992262i	$-0.539624\pi$
$829$	−7.14971			−0.248320			−0.124160	+	0.992262i	$0.539624\pi$
$830$	−21.0116	−	36.3932i	−0.729324	−	1.26323i
$831$	−5.38831	+	9.33282i	−0.186918	+	0.323752i
$832$	2.22534	+	3.85440i	0.0771497	+	0.133627i
$833$	9.02481	−	15.6314i	0.312691	−	0.541597i
$834$	1.37211	−	2.37657i	0.0475123	−	0.0822938i
$835$	18.5635			0.642418
$836$		0			0
$837$	−13.9614			−0.482577
$838$	8.65998	−	14.9995i	0.299154	−	0.518150i
$839$	17.3033	−	29.9703i	0.597378	−	1.03469i	−0.395829	−	0.918324i	$-0.629543\pi$
$839$	17.3033	−	29.9703i	0.597378	−	1.03469i	0.993207	−	0.116365i	$-0.0371241\pi$
$840$	4.11334	+	7.12452i	0.141924	+	0.245819i
$841$	3.67617	−	6.36732i	0.126765	−	0.219563i
$842$	−6.10607	−	10.5760i	−0.210429	−	0.364474i
$843$	12.6560			0.435896
$844$	−35.6091			−1.22571
$845$	−3.78493	−	6.55569i	−0.130206	−	0.225523i
$846$	−1.87046	−	3.23974i	−0.0643078	−	0.111384i
$847$	−14.7023			−0.505178
$848$	19.5398			0.671001
$849$	−3.69119	−	6.39333i	−0.126681	−	0.219418i
$850$	−15.6420	+	27.0928i	−0.536517	+	0.929275i
$851$	−10.3969	−	18.0080i	−0.356402	−	0.617306i
$852$	−9.98545	+	17.2953i	−0.342096	+	0.592528i
$853$	−16.6254	+	28.7961i	−0.569243	+	0.985959i	0.427397	+	0.904064i	$0.359430\pi$
$853$	−16.6254	+	28.7961i	−0.569243	+	0.985959i	−0.996641	+	0.0818948i	$0.973903\pi$
$854$	17.5253			0.599703
$855$		0			0
$856$	40.7888			1.39413
$857$	1.94310	−	3.36554i	0.0663749	−	0.114965i	−0.830928	−	0.556380i	$-0.812190\pi$
$857$	1.94310	−	3.36554i	0.0663749	−	0.114965i	0.897303	+	0.441415i	$0.145523\pi$
$858$	2.65998	−	4.60722i	0.0908101	−	0.157288i
$859$	−0.828878	−	1.43566i	−0.0282810	−	0.0489840i	0.851539	−	0.524292i	$-0.175670\pi$
$859$	−0.828878	−	1.43566i	−0.0282810	−	0.0489840i	−0.879819	+	0.475308i	$0.842337\pi$
$860$	−25.8614	+	44.7933i	−0.881868	+	1.52744i
$861$	−4.99273	−	8.64766i	−0.170152	−	0.294711i
$862$	−3.30096			−0.112431
$863$	−52.7187			−1.79457			−0.897284	−	0.441455i	$-0.854463\pi$
$863$	−52.7187			−1.79457			−0.897284	+	0.441455i	$0.854463\pi$
$864$	8.36097	+	14.4816i	0.284446	+	0.492675i
$865$	17.0077	+	29.4583i	0.578281	+	1.00161i
$866$	−50.1958			−1.70572
$867$	1.27301			0.0432338
$868$	12.9684	+	22.4619i	0.440175	+	0.762406i
$869$	5.81046	−	10.0640i	0.197106	−	0.341398i
$870$	−5.18004	−	8.97210i	−0.175620	−	0.304183i
$871$	5.28043	−	9.14597i	0.178921	−	0.309899i
$872$	28.8614	−	49.9895i	0.977371	−	1.69286i
$873$	−18.9691			−0.642008
$874$		0			0
$875$	16.8949			0.571151
$876$	8.82295	−	15.2818i	0.298100	−	0.516324i
$877$	10.5949	−	18.3509i	0.357765	−	0.619667i	−0.629822	−	0.776739i	$-0.716872\pi$
$877$	10.5949	−	18.3509i	0.357765	−	0.619667i	0.987587	+	0.157072i	$0.0502055\pi$
$878$	−43.7636	−	75.8007i	−1.47695	−	2.55815i
$879$	1.27244	−	2.20393i	0.0429184	−	0.0743368i
$880$	−5.29813	−	9.17664i	−0.178600	−	0.309344i
$881$	32.1010			1.08151			0.540755	−	0.841180i	$-0.318138\pi$
$881$	32.1010			1.08151			0.540755	+	0.841180i	$0.318138\pi$
$882$	−30.3242			−1.02107
$883$	23.6484	+	40.9603i	0.795833	+	1.37842i	0.922309	+	0.386453i	$0.126300\pi$
$883$	23.6484	+	40.9603i	0.795833	+	1.37842i	−0.126476	+	0.991970i	$0.540367\pi$
$884$	−23.2481	−	40.2669i	−0.781918	−	1.35432i
$885$	−3.46110			−0.116344
$886$	−43.0711			−1.44700
$887$	−5.28153	−	9.14787i	−0.177336	−	0.307155i	0.763631	−	0.645653i	$-0.223415\pi$
$887$	−5.28153	−	9.14787i	−0.177336	−	0.307155i	−0.940967	+	0.338497i	$0.890081\pi$
$888$	8.18227	−	14.1721i	0.274579	−	0.475585i
$889$	11.1099	+	19.2430i	0.372615	+	0.645389i
$890$	4.13816	−	7.16750i	0.138711	−	0.240255i
$891$	3.16772	−	5.48665i	0.106123	−	0.183810i
$892$	−68.2704			−2.28586
$893$		0			0
$894$	18.5220			0.619468
$895$	3.92783	−	6.80321i	0.131293	−	0.227406i
$896$	−10.2194	+	17.7005i	−0.341406	+	0.591333i
$897$	−4.49020	−	7.77725i	−0.149923	−	0.259675i
$898$	47.3624	−	82.0340i	1.58050	−	2.73751i
$899$	−8.92737	−	15.4627i	−0.297744	−	0.515708i
$900$	36.1634			1.20545
$901$	11.4192			0.380429
$902$	14.9782	+	25.9430i	0.498719	+	0.863806i
$903$	−4.35117	−	7.53644i	−0.144798	−	0.250797i
$904$	−8.00175			−0.266134
$905$	−18.2722			−0.607388
$906$	9.12449	+	15.8041i	0.303141	+	0.525055i
$907$	−21.4602	+	37.1702i	−0.712575	+	1.23422i	0.251312	+	0.967906i	$0.419138\pi$
$907$	−21.4602	+	37.1702i	−0.712575	+	1.23422i	−0.963887	+	0.266310i	$0.914195\pi$
$908$	−21.7763	−	37.7177i	−0.722672	−	1.25171i
$909$	2.79308	−	4.83776i	0.0926406	−	0.160458i
$910$	−7.10014	+	12.2978i	−0.235367	+	0.407668i
$911$	−55.1411			−1.82691			−0.913454	−	0.406942i	$-0.866595\pi$
$911$	−55.1411			−1.82691			−0.913454	+	0.406942i	$0.866595\pi$
$912$		0			0
$913$	−14.5945			−0.483008
$914$	11.5351	−	19.9793i	0.381547	−	0.660858i
$915$	1.98633	−	3.44042i	0.0656660	−	0.113737i
$916$	−44.3769	−	76.8631i	−1.46625	−	2.53963i
$917$	15.1741	−	26.2823i	0.501093	−	0.867919i
$918$	17.8687	+	30.9495i	0.589755	+	1.02149i
$919$	−24.5577			−0.810083			−0.405041	−	0.914298i	$-0.632743\pi$
$919$	−24.5577			−0.810083			−0.405041	+	0.914298i	$0.632743\pi$
$920$	−41.6614			−1.37353
$921$	7.56330	+	13.1000i	0.249219	+	0.431660i
$922$	−30.9526	−	53.6116i	−1.01937	−	1.76560i
$923$	−18.8438			−0.620251
$924$	5.22668			0.171945
$925$	−6.53849	−	11.3250i	−0.214984	−	0.372363i
$926$	−0.317429	+	0.549803i	−0.0104314	+	0.0180677i
$927$	−16.0560	−	27.8099i	−0.527349	−	0.913395i
$928$	−10.6925	+	18.5200i	−0.351000	+	0.607949i
$929$	11.1386	−	19.2927i	0.365446	−	0.632972i	−0.623401	−	0.781902i	$-0.714250\pi$
$929$	11.1386	−	19.2927i	0.365446	−	0.632972i	0.988848	+	0.148930i	$0.0475830\pi$
$930$	8.54488			0.280198
$931$		0			0
$932$	15.5936			0.510785
$933$	−1.12954	+	1.95642i	−0.0369794	+	0.0640502i
$934$	19.4488	−	33.6863i	0.636383	−	1.10225i
$935$	−3.09627	−	5.36289i	−0.101259	−	0.175385i
$936$	−21.3505	+	36.9801i	−0.697861	+	1.20873i
$937$	4.77584	+	8.27201i	0.156020	+	0.270235i	0.933430	−	0.358760i	$-0.116800\pi$
$937$	4.77584	+	8.27201i	0.156020	+	0.270235i	−0.777410	+	0.628994i	$0.783467\pi$
$938$	15.0797			0.492368
$939$	14.9403			0.487557
$940$	1.70574	+	2.95442i	0.0556350	+	0.0963627i
$941$	27.8628	+	48.2597i	0.908301	+	1.57322i	0.816424	+	0.577452i	$0.195953\pi$
$941$	27.8628	+	48.2597i	0.908301	+	1.57322i	0.0918762	+	0.995770i	$0.470714\pi$
$942$	18.1685			0.591961
$943$	50.5681			1.64672
$944$	13.0633	+	22.6263i	0.425174	+	0.736423i
$945$	3.75490	−	6.50368i	0.122147	−	0.211565i
$946$	13.0535	+	22.6093i	0.424406	+	0.735093i
$947$	13.5214	−	23.4198i	0.439387	−	0.761040i	−0.558255	−	0.829669i	$-0.688529\pi$
$947$	13.5214	−	23.4198i	0.439387	−	0.761040i	0.997642	+	0.0686288i	$0.0218624\pi$
$948$	14.1211	−	24.4584i	0.458631	−	0.794373i
$949$	16.6500			0.540482
$950$		0			0
$951$	−17.0490			−0.552852
$952$	18.1459	−	31.4296i	0.588112	−	1.01864i
$953$	−11.5655	+	20.0321i	−0.374644	+	0.648902i	−0.990274	−	0.139133i	$-0.955568\pi$
$953$	−11.5655	+	20.0321i	−0.374644	+	0.648902i	0.615630	+	0.788036i	$0.288902\pi$
$954$	−9.59240	−	16.6145i	−0.310565	−	0.537915i
$955$	−6.92783	+	11.9994i	−0.224179	+	0.388290i
$956$	−26.4106	−	45.7445i	−0.854180	−	1.47948i
$957$	−3.59802			−0.116308
$958$	1.82119			0.0588401
$959$	−7.81702	−	13.5395i	−0.252425	−	0.437212i
$960$	0.720285	+	1.24757i	0.0232471	+	0.0402652i
$961$	−16.2736			−0.524956
$962$	28.2472			0.910727
$963$	−8.59714	−	14.8907i	−0.277039	−	0.479846i
$964$	−28.4577	+	49.2902i	−0.916561	+	1.58753i
$965$	9.29679	+	16.1025i	0.299274	+	0.518358i
$966$	6.41147	−	11.1050i	0.206286	−	0.357297i
$967$	−19.5175	+	33.8054i	−0.627642	+	1.08711i	0.360382	+	0.932805i	$0.382646\pi$
$967$	−19.5175	+	33.8054i	−0.627642	+	1.08711i	−0.988024	+	0.154303i	$0.950687\pi$
$968$	58.5954			1.88333
$969$		0			0
$970$	25.1411			0.807234
$971$	20.6013	−	35.6825i	0.661128	−	1.14511i	−0.319192	−	0.947690i	$-0.603411\pi$
$971$	20.6013	−	35.6825i	0.661128	−	1.14511i	0.980320	−	0.197417i	$-0.0632552\pi$
$972$	31.7729	−	55.0323i	1.01912	−	1.76516i
$973$	1.27197	+	2.20312i	0.0407776	+	0.0706289i
$974$	14.8721	−	25.7593i	0.476533	−	0.825380i
$975$	−2.82383	−	4.89101i	−0.0904348	−	0.156638i
$976$	−29.9881			−0.959897
$977$	22.4938			0.719641			0.359821	−	0.933022i	$-0.382838\pi$
$977$	22.4938			0.719641			0.359821	+	0.933022i	$0.382838\pi$
$978$	5.23308	+	9.06396i	0.167335	+	0.289833i
$979$	−1.43717	−	2.48925i	−0.0459320	−	0.0795566i
$980$	27.6536			0.883363
$981$	−24.3327			−0.776885
$982$	0.112463	+	0.194792i	0.00358885	+	0.00621608i
$983$	22.2731	−	38.5781i	0.710401	−	1.23045i	−0.254306	−	0.967124i	$-0.581847\pi$
$983$	22.2731	−	38.5781i	0.710401	−	1.23045i	0.964707	−	0.263326i	$-0.0848196\pi$
$984$	19.8983	+	34.4648i	0.634334	+	1.09870i
$985$	−5.34936	+	9.26536i	−0.170445	+	0.295219i
$986$	−22.8516	+	39.5802i	−0.727744	+	1.26049i
$987$	−0.573978			−0.0182699
$988$		0			0
$989$	44.0702			1.40135
$990$	−5.20187	+	9.00990i	−0.165326	+	0.286353i
$991$	22.6648	−	39.2566i	0.719971	−	1.24703i	−0.241040	−	0.970515i	$-0.577489\pi$
$991$	22.6648	−	39.2566i	0.719971	−	1.24703i	0.961011	−	0.276510i	$-0.0891780\pi$
$992$	−8.81908	−	15.2751i	−0.280006	−	0.484985i
$993$	6.21523	−	10.7651i	0.197234	−	0.341620i
$994$	−13.4534	−	23.3019i	−0.426715	−	0.739092i
$995$	−36.4243			−1.15473
$996$	−35.4688			−1.12387
$997$	5.24557	+	9.08559i	0.166129	+	0.287743i	0.937056	−	0.349180i	$-0.113540\pi$
$997$	5.24557	+	9.08559i	0.166129	+	0.287743i	−0.770927	+	0.636924i	$0.780207\pi$
$998$	18.5988	+	32.2141i	0.588735	+	1.01972i
$999$	−14.9385			−0.472634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.c.i.68.3		6
19.2	odd	18		361.2.e.h.234.1		6
19.3	odd	18		361.2.e.a.99.1		6
19.4	even	9		361.2.e.g.62.1		6
19.5	even	9		361.2.e.f.28.1		6
19.6	even	9		19.2.e.a.16.1	yes	6
19.7	even	3	inner	361.2.c.i.292.3		6
19.8	odd	6		361.2.a.h.1.3		3
19.9	even	9		361.2.e.f.245.1		6
19.10	odd	18		361.2.e.b.245.1		6
19.11	even	3		361.2.a.g.1.1		3
19.12	odd	6		361.2.c.h.292.1		6
19.13	odd	18		361.2.e.h.54.1		6
19.14	odd	18		361.2.e.b.28.1		6
19.15	odd	18		361.2.e.a.62.1		6
19.16	even	9		361.2.e.g.99.1		6
19.17	even	9		19.2.e.a.6.1	✓	6
19.18	odd	2		361.2.c.h.68.1		6
57.8	even	6		3249.2.a.s.1.1		3
57.11	odd	6		3249.2.a.z.1.3		3
57.17	odd	18		171.2.u.c.82.1		6
57.44	odd	18		171.2.u.c.73.1		6
76.11	odd	6		5776.2.a.br.1.2		3
76.27	even	6		5776.2.a.bi.1.2		3
76.55	odd	18		304.2.u.b.177.1		6
76.63	odd	18		304.2.u.b.225.1		6
95.17	odd	36		475.2.u.a.424.1		12
95.44	even	18		475.2.l.a.301.1		6
95.49	even	6		9025.2.a.bd.1.3		3
95.63	odd	36		475.2.u.a.149.1		12
95.74	even	18		475.2.l.a.101.1		6
95.82	odd	36		475.2.u.a.149.2		12
95.84	odd	6		9025.2.a.x.1.1		3
95.93	odd	36		475.2.u.a.424.2		12
133.6	odd	18		931.2.w.a.491.1		6
133.17	odd	18		931.2.v.a.177.1		6
133.25	even	9		931.2.x.a.814.1		6
133.44	even	9		931.2.v.b.263.1		6
133.55	odd	18		931.2.w.a.785.1		6
133.74	even	9		931.2.v.b.177.1		6
133.82	odd	18		931.2.v.a.263.1		6
133.93	even	9		931.2.x.a.557.1		6
133.101	odd	18		931.2.x.b.814.1		6
133.131	odd	18		931.2.x.b.557.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	19.17	even	9
19.2.e.a.16.1	yes	6	19.6	even	9
171.2.u.c.73.1		6	57.44	odd	18
171.2.u.c.82.1		6	57.17	odd	18
304.2.u.b.177.1		6	76.55	odd	18
304.2.u.b.225.1		6	76.63	odd	18
361.2.a.g.1.1		3	19.11	even	3
361.2.a.h.1.3		3	19.8	odd	6
361.2.c.h.68.1		6	19.18	odd	2
361.2.c.h.292.1		6	19.12	odd	6
361.2.c.i.68.3		6	1.1	even	1	trivial
361.2.c.i.292.3		6	19.7	even	3	inner
361.2.e.a.62.1		6	19.15	odd	18
361.2.e.a.99.1		6	19.3	odd	18
361.2.e.b.28.1		6	19.14	odd	18
361.2.e.b.245.1		6	19.10	odd	18
361.2.e.f.28.1		6	19.5	even	9
361.2.e.f.245.1		6	19.9	even	9
361.2.e.g.62.1		6	19.4	even	9
361.2.e.g.99.1		6	19.16	even	9
361.2.e.h.54.1		6	19.13	odd	18
361.2.e.h.234.1		6	19.2	odd	18
475.2.l.a.101.1		6	95.74	even	18
475.2.l.a.301.1		6	95.44	even	18
475.2.u.a.149.1		12	95.63	odd	36
475.2.u.a.149.2		12	95.82	odd	36
475.2.u.a.424.1		12	95.17	odd	36
475.2.u.a.424.2		12	95.93	odd	36
931.2.v.a.177.1		6	133.17	odd	18
931.2.v.a.263.1		6	133.82	odd	18
931.2.v.b.177.1		6	133.74	even	9
931.2.v.b.263.1		6	133.44	even	9
931.2.w.a.491.1		6	133.6	odd	18
931.2.w.a.785.1		6	133.55	odd	18
931.2.x.a.557.1		6	133.93	even	9
931.2.x.a.814.1		6	133.25	even	9
931.2.x.b.557.1		6	133.131	odd	18
931.2.x.b.814.1		6	133.101	odd	18
3249.2.a.s.1.1		3	57.8	even	6
3249.2.a.z.1.3		3	57.11	odd	6
5776.2.a.bi.1.2		3	76.27	even	6
5776.2.a.br.1.2		3	76.11	odd	6
9025.2.a.x.1.1		3	95.84	odd	6
9025.2.a.bd.1.3		3	95.49	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 - 2.19285i) q^{2} +(0.326352 - 0.565258i) q^{3} +(-2.20574 - 3.82045i) q^{4} +(0.673648 - 1.16679i) q^{5} +(-0.826352 - 1.43128i) q^{6} +1.53209 q^{7} -6.10607 q^{8} +(1.28699 + 2.22913i) q^{9} +O(q^{10})\)	\(q+(1.26604 - 2.19285i) q^{2} +(0.326352 - 0.565258i) q^{3} +(-2.20574 - 3.82045i) q^{4} +(0.673648 - 1.16679i) q^{5} +(-0.826352 - 1.43128i) q^{6} +1.53209 q^{7} -6.10607 q^{8} +(1.28699 + 2.22913i) q^{9} +(-1.70574 - 2.95442i) q^{10} -1.18479 q^{11} -2.87939 q^{12} +(-1.35844 - 2.35289i) q^{13} +(1.93969 - 3.35965i) q^{14} +(-0.439693 - 0.761570i) q^{15} +(-3.31908 + 5.74881i) q^{16} +(-1.93969 + 3.35965i) q^{17} +6.51754 q^{18} -5.94356 q^{20} +(0.500000 - 0.866025i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(2.53209 + 4.38571i) q^{23} +(-1.99273 + 3.45150i) q^{24} +(1.59240 + 2.75811i) q^{25} -6.87939 q^{26} +3.63816 q^{27} +(-3.37939 - 5.85327i) q^{28} +(2.32635 + 4.02936i) q^{29} -2.22668 q^{30} -3.83750 q^{31} +(2.29813 + 3.98048i) q^{32} +(-0.386659 + 0.669713i) q^{33} +(4.91147 + 8.50692i) q^{34} +(1.03209 - 1.78763i) q^{35} +(5.67752 - 9.83375i) q^{36} -4.10607 q^{37} -1.77332 q^{39} +(-4.11334 + 7.12452i) q^{40} +(4.99273 - 8.64766i) q^{41} +(-1.26604 - 2.19285i) q^{42} +(4.35117 - 7.53644i) q^{43} +(2.61334 + 4.52644i) q^{44} +3.46791 q^{45} +12.8229 q^{46} +(-0.286989 - 0.497079i) q^{47} +(2.16637 + 3.75227i) q^{48} -4.65270 q^{49} +8.06418 q^{50} +(1.26604 + 2.19285i) q^{51} +(-5.99273 + 10.3797i) q^{52} +(-1.47178 - 2.54920i) q^{53} +(4.60607 - 7.97794i) q^{54} +(-0.798133 + 1.38241i) q^{55} -9.35504 q^{56} +11.7811 q^{58} +(1.96791 - 3.40852i) q^{59} +(-1.93969 + 3.35965i) q^{60} +(2.25877 + 3.91231i) q^{61} +(-4.85844 + 8.41507i) q^{62} +(1.97178 + 3.41523i) q^{63} -1.63816 q^{64} -3.66044 q^{65} +(0.979055 + 1.69577i) q^{66} +(1.94356 + 3.36635i) q^{67} +17.1138 q^{68} +3.30541 q^{69} +(-2.61334 - 4.52644i) q^{70} +(3.46791 - 6.00660i) q^{71} +(-7.85844 - 13.6112i) q^{72} +(-3.06418 + 5.30731i) q^{73} +(-5.19846 + 9.00400i) q^{74} +2.07873 q^{75} -1.81521 q^{77} +(-2.24510 + 3.88863i) q^{78} +(-4.90420 + 8.49432i) q^{79} +(4.47178 + 7.74535i) q^{80} +(-2.67365 + 4.63089i) q^{81} +(-12.6420 - 21.8966i) q^{82} +12.3182 q^{83} -4.41147 q^{84} +(2.61334 + 4.52644i) q^{85} +(-11.0175 - 19.0829i) q^{86} +3.03684 q^{87} +7.23442 q^{88} +(1.21301 + 2.10100i) q^{89} +(4.39053 - 7.60462i) q^{90} +(-2.08125 - 3.60483i) q^{91} +(11.1702 - 19.3474i) q^{92} +(-1.25237 + 2.16918i) q^{93} -1.45336 q^{94} +3.00000 q^{96} +(-3.68479 + 6.38225i) q^{97} +(-5.89053 + 10.2027i) q^{98} +(-1.52481 - 2.64106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - 12 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - 12 * q^8	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - 12 q^{8} - 6 q^{12} + 6 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} - 6 q^{18} - 6 q^{20} + 3 q^{21} - 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{25} - 30 q^{26} - 12 q^{27} - 9 q^{28} + 15 q^{29} - 18 q^{31} - 9 q^{33} + 9 q^{34} - 3 q^{35} + 9 q^{36} - 24 q^{39} - 18 q^{40} + 12 q^{41} - 3 q^{42} + 9 q^{44} + 30 q^{45} + 36 q^{46} + 6 q^{47} - 6 q^{48} - 30 q^{49} + 30 q^{50} + 3 q^{51} - 18 q^{52} + 6 q^{53} + 3 q^{54} + 9 q^{55} - 6 q^{56} + 36 q^{58} + 21 q^{59} - 6 q^{60} - 9 q^{61} - 21 q^{62} - 3 q^{63} + 24 q^{64} + 24 q^{65} + 9 q^{66} - 18 q^{67} + 30 q^{68} + 24 q^{69} - 9 q^{70} + 30 q^{71} - 39 q^{72} - 3 q^{74} + 30 q^{75} - 18 q^{77} - 12 q^{78} + 9 q^{79} + 12 q^{80} - 15 q^{81} - 18 q^{82} - 6 q^{84} + 9 q^{85} - 21 q^{86} + 42 q^{87} - 18 q^{88} + 15 q^{89} + 9 q^{90} - 15 q^{91} + 24 q^{92} - 24 q^{93} + 18 q^{94} + 18 q^{96} - 15 q^{97} - 18 q^{98} + 18 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - 12 * q^8 - 6 * q^12 + 6 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 - 6 * q^18 - 6 * q^20 + 3 * q^21 - 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^25 - 30 * q^26 - 12 * q^27 - 9 * q^28 + 15 * q^29 - 18 * q^31 - 9 * q^33 + 9 * q^34 - 3 * q^35 + 9 * q^36 - 24 * q^39 - 18 * q^40 + 12 * q^41 - 3 * q^42 + 9 * q^44 + 30 * q^45 + 36 * q^46 + 6 * q^47 - 6 * q^48 - 30 * q^49 + 30 * q^50 + 3 * q^51 - 18 * q^52 + 6 * q^53 + 3 * q^54 + 9 * q^55 - 6 * q^56 + 36 * q^58 + 21 * q^59 - 6 * q^60 - 9 * q^61 - 21 * q^62 - 3 * q^63 + 24 * q^64 + 24 * q^65 + 9 * q^66 - 18 * q^67 + 30 * q^68 + 24 * q^69 - 9 * q^70 + 30 * q^71 - 39 * q^72 - 3 * q^74 + 30 * q^75 - 18 * q^77 - 12 * q^78 + 9 * q^79 + 12 * q^80 - 15 * q^81 - 18 * q^82 - 6 * q^84 + 9 * q^85 - 21 * q^86 + 42 * q^87 - 18 * q^88 + 15 * q^89 + 9 * q^90 - 15 * q^91 + 24 * q^92 - 24 * q^93 + 18 * q^94 + 18 * q^96 - 15 * q^97 - 18 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more