LMFDB - Embedded newform 224.2.u.c.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, degree $4$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			197.1
Character	$\chi$	$=$	224.197
Dual form			224.2.u.c.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37975 - 0.310320i) q^{2} +(0.424336 + 1.02444i) q^{3} +(1.80740 + 0.856327i) q^{4} +(3.70330 + 1.53396i) q^{5} +(-0.267572 - 1.54514i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.22802 - 1.74239i) q^{8} +(1.25191 - 1.25191i) q^{9} +O(q^{10})$	\(q+(-1.37975 - 0.310320i) q^{2} +(0.424336 + 1.02444i) q^{3} +(1.80740 + 0.856327i) q^{4} +(3.70330 + 1.53396i) q^{5} +(-0.267572 - 1.54514i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.22802 - 1.74239i) q^{8} +(1.25191 - 1.25191i) q^{9} +(-4.63360 - 3.26568i) q^{10} +(-1.32694 + 3.20352i) q^{11} +(-0.110307 + 2.21494i) q^{12} +(-1.88338 + 0.780120i) q^{13} +(0.756199 + 1.19506i) q^{14} +4.44471i q^{15} +(2.53341 + 3.09545i) q^{16} -3.99616i q^{17} +(-2.11581 + 1.33883i) q^{18} +(-2.05694 + 0.852011i) q^{19} +(5.37979 + 5.94372i) q^{20} +(0.424336 - 1.02444i) q^{21} +(2.82496 - 4.00827i) q^{22} +(5.08811 - 5.08811i) q^{23} +(0.839537 - 3.02183i) q^{24} +(7.82588 + 7.82588i) q^{25} +(2.84067 - 0.491918i) q^{26} +(4.88704 + 2.02428i) q^{27} +(-0.672512 - 1.88354i) q^{28} +(2.71380 + 6.55170i) q^{29} +(1.37928 - 6.13258i) q^{30} -8.51005 q^{31} +(-2.53488 - 5.05711i) q^{32} -3.84487 q^{33} +(-1.24009 + 5.51369i) q^{34} +(-1.53396 - 3.70330i) q^{35} +(3.33475 - 1.19066i) q^{36} +(-6.76303 - 2.80134i) q^{37} +(3.10245 - 0.537250i) q^{38} +(-1.59837 - 1.59837i) q^{39} +(-5.57829 - 9.87028i) q^{40} +(-1.33578 + 1.33578i) q^{41} +(-0.903379 + 1.28178i) q^{42} +(-1.30662 + 3.15446i) q^{43} +(-5.14157 + 4.65375i) q^{44} +(6.55658 - 2.71582i) q^{45} +(-8.59925 + 5.44136i) q^{46} -3.16999i q^{47} +(-2.09608 + 3.90883i) q^{48} +1.00000i q^{49} +(-8.36921 - 13.2263i) q^{50} +(4.09381 - 1.69571i) q^{51} +(-4.07206 - 0.202795i) q^{52} +(4.79044 - 11.5651i) q^{53} +(-6.11471 - 4.30954i) q^{54} +(-9.82812 + 9.82812i) q^{55} +(0.343395 + 2.80750i) q^{56} +(-1.74566 - 1.74566i) q^{57} +(-1.71124 - 9.88184i) q^{58} +(2.39858 + 0.993524i) q^{59} +(-3.80613 + 8.03338i) q^{60} +(-3.85768 - 9.31326i) q^{61} +(11.7417 + 2.64084i) q^{62} -1.77047 q^{63} +(1.92817 + 7.76416i) q^{64} -8.17138 q^{65} +(5.30495 + 1.19314i) q^{66} +(-0.315504 - 0.761694i) q^{67} +(3.42202 - 7.22266i) q^{68} +(7.37152 + 3.05338i) q^{69} +(0.967264 + 5.58564i) q^{70} +(-6.21830 - 6.21830i) q^{71} +(-4.97060 + 0.607971i) q^{72} +(-2.09089 + 2.09089i) q^{73} +(8.46196 + 5.96385i) q^{74} +(-4.69632 + 11.3379i) q^{75} +(-4.44731 - 0.221483i) q^{76} +(3.20352 - 1.32694i) q^{77} +(1.70934 + 2.70135i) q^{78} -9.23644i q^{79} +(4.63368 + 15.3495i) q^{80} +0.554037i q^{81} +(2.25756 - 1.42852i) q^{82} +(4.95210 - 2.05123i) q^{83} +(1.64420 - 1.48820i) q^{84} +(6.12994 - 14.7990i) q^{85} +(2.78170 - 3.94689i) q^{86} +(-5.56024 + 5.56024i) q^{87} +(8.53822 - 4.82546i) q^{88} +(9.12026 + 9.12026i) q^{89} +(-9.88919 + 1.71251i) q^{90} +(1.88338 + 0.780120i) q^{91} +(13.5534 - 4.83918i) q^{92} +(-3.61112 - 8.71801i) q^{93} +(-0.983711 + 4.37378i) q^{94} -8.92440 q^{95} +(4.10505 - 4.74274i) q^{96} -9.76692 q^{97} +(0.310320 - 1.37975i) q^{98} +(2.34931 + 5.67173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−1.37975	−	0.310320i	−0.975628	−	0.219430i
$2$	−1.37975	−	0.310320i	−0.975628	−	0.219430i
$3$	0.424336	+	1.02444i	0.244990	+	0.591459i	0.997765	−	0.0668192i	$-0.0212851\pi$
$3$	0.424336	+	1.02444i	0.244990	+	0.591459i	−0.752775	+	0.658278i	$0.771285\pi$
$4$	1.80740	+	0.856327i	0.903701	+	0.428163i
$5$	3.70330	+	1.53396i	1.65617	+	0.686007i	0.997775	−	0.0666689i	$-0.0212371\pi$
$5$	3.70330	+	1.53396i	1.65617	+	0.686007i	0.658392	+	0.752676i	$0.271237\pi$
$6$	−0.267572	−	1.54514i	−0.109236	−	0.630802i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−2.22802	−	1.74239i	−0.787725	−	0.616027i
$9$	1.25191	−	1.25191i	0.417303	−	0.417303i
$10$	−4.63360	−	3.26568i	−1.46527	−	1.03270i
$11$	−1.32694	+	3.20352i	−0.400088	+	0.965897i	0.587557	+	0.809183i	$0.300090\pi$
$11$	−1.32694	+	3.20352i	−0.400088	+	0.965897i	−0.987644	+	0.156714i	$0.949910\pi$
$12$	−0.110307	+	2.21494i	−0.0318430	+	0.639398i
$13$	−1.88338	+	0.780120i	−0.522354	+	0.216366i	−0.628251	−	0.778011i	$-0.716229\pi$
$13$	−1.88338	+	0.780120i	−0.522354	+	0.216366i	0.105896	+	0.994377i	$0.466229\pi$
$14$	0.756199	+	1.19506i	0.202103	+	0.319393i
$15$			4.44471i			1.14762i
$16$	2.53341	+	3.09545i	0.633352	+	0.773864i
$17$		−	3.99616i		−	0.969210i	−0.874733	−	0.484605i	$-0.838963\pi$
$17$		−	3.99616i		−	0.969210i	0.874733	−	0.484605i	$-0.161037\pi$
$18$	−2.11581	+	1.33883i	−0.498702	+	0.315564i
$19$	−2.05694	+	0.852011i	−0.471893	+	0.195465i	−0.605940	−	0.795510i	$-0.707203\pi$
$19$	−2.05694	+	0.852011i	−0.471893	+	0.195465i	0.134047	+	0.990975i	$0.457203\pi$
$20$	5.37979	+	5.94372i	1.20296	+	1.32906i
$21$	0.424336	−	1.02444i	0.0925976	−	0.223550i
$22$	2.82496	−	4.00827i	0.602283	−	0.854565i
$23$	5.08811	−	5.08811i	1.06094	−	1.06094i	0.0629268	−	0.998018i	$-0.479957\pi$
$23$	5.08811	−	5.08811i	1.06094	−	1.06094i	0.998018	−	0.0629268i	$-0.0200435\pi$
$24$	0.839537	−	3.02183i	0.171370	−	0.616828i
$25$	7.82588	+	7.82588i	1.56518	+	1.56518i
$26$	2.84067	−	0.491918i	0.557101	−	0.0964731i
$27$	4.88704	+	2.02428i	0.940512	+	0.389573i
$28$	−0.672512	−	1.88354i	−0.127093	−	0.355956i
$29$	2.71380	+	6.55170i	0.503941	+	1.21662i	0.947321	+	0.320287i	$0.103779\pi$
$29$	2.71380	+	6.55170i	0.503941	+	1.21662i	−0.443380	+	0.896334i	$0.646221\pi$
$30$	1.37928	−	6.13258i	0.251822	−	1.11965i
$31$	−8.51005			−1.52845			−0.764225	−	0.644950i	$-0.776878\pi$
$31$	−8.51005			−1.52845			−0.764225	+	0.644950i	$0.776878\pi$
$32$	−2.53488	−	5.05711i	−0.448108	−	0.893980i
$33$	−3.84487			−0.669306
$34$	−1.24009	+	5.51369i	−0.212673	+	0.945589i
$35$	−1.53396	−	3.70330i	−0.259286	−	0.625972i
$36$	3.33475	−	1.19066i	0.555792	−	0.198444i
$37$	−6.76303	−	2.80134i	−1.11184	−	0.460537i	−0.250266	−	0.968177i	$-0.580518\pi$
$37$	−6.76303	−	2.80134i	−1.11184	−	0.460537i	−0.861570	+	0.507640i	$0.830518\pi$
$38$	3.10245	−	0.537250i	0.503283	−	0.0871535i
$39$	−1.59837	−	1.59837i	−0.255944	−	0.255944i
$40$	−5.57829	−	9.87028i	−0.882005	−	1.56063i
$41$	−1.33578	+	1.33578i	−0.208614	+	0.208614i	−0.803678	−	0.595064i	$-0.797127\pi$
$41$	−1.33578	+	1.33578i	−0.208614	+	0.208614i	0.595064	+	0.803678i	$0.297127\pi$
$42$	−0.903379	+	1.28178i	−0.139394	+	0.197783i
$43$	−1.30662	+	3.15446i	−0.199258	+	0.481051i	−0.991650	−	0.128962i	$-0.958836\pi$
$43$	−1.30662	+	3.15446i	−0.199258	+	0.481051i	0.792392	+	0.610012i	$0.208836\pi$
$44$	−5.14157	+	4.65375i	−0.775121	+	0.701579i
$45$	6.55658	−	2.71582i	0.977397	−	0.404851i
$46$	−8.59925	+	5.44136i	−1.26789	+	0.802285i
$47$		−	3.16999i		−	0.462390i	−0.972907	−	0.231195i	$-0.925736\pi$
$47$		−	3.16999i		−	0.462390i	0.972907	−	0.231195i	$-0.0742636\pi$
$48$	−2.09608	+	3.90883i	−0.302543	+	0.564191i
$49$			1.00000i			0.142857i
$50$	−8.36921	−	13.2263i	−1.18358	−	1.87048i
$51$	4.09381	−	1.69571i	0.573248	−	0.237447i
$52$	−4.07206	−	0.202795i	−0.564693	−	0.0281226i
$53$	4.79044	−	11.5651i	0.658017	−	1.58859i	−0.142845	−	0.989745i	$-0.545625\pi$
$53$	4.79044	−	11.5651i	0.658017	−	1.58859i	0.800862	−	0.598849i	$-0.204375\pi$
$54$	−6.11471	−	4.30954i	−0.832106	−	0.586454i
$55$	−9.82812	+	9.82812i	−1.32522	+	1.32522i
$56$	0.343395	+	2.80750i	0.0458881	+	0.375169i
$57$	−1.74566	−	1.74566i	−0.231219	−	0.231219i
$58$	−1.71124	−	9.88184i	−0.224696	−	1.29755i
$59$	2.39858	+	0.993524i	0.312268	+	0.129346i	0.533313	−	0.845918i	$-0.320947\pi$
$59$	2.39858	+	0.993524i	0.312268	+	0.129346i	−0.221045	+	0.975264i	$0.570947\pi$
$60$	−3.80613	+	8.03338i	−0.491369	+	1.03711i
$61$	−3.85768	−	9.31326i	−0.493925	−	1.19244i	−0.952707	−	0.303891i	$-0.901714\pi$
$61$	−3.85768	−	9.31326i	−0.493925	−	1.19244i	0.458782	−	0.888549i	$-0.348286\pi$
$62$	11.7417	+	2.64084i	1.49120	+	0.335387i
$63$	−1.77047			−0.223058
$64$	1.92817	+	7.76416i	0.241021	+	0.970520i
$65$	−8.17138			−1.01353
$66$	5.30495	+	1.19314i	0.652994	+	0.146865i
$67$	−0.315504	−	0.761694i	−0.0385449	−	0.0930557i	0.903435	−	0.428726i	$-0.141037\pi$
$67$	−0.315504	−	0.761694i	−0.0385449	−	0.0930557i	−0.941980	+	0.335670i	$0.891037\pi$
$68$	3.42202	−	7.22266i	0.414980	−	0.875877i
$69$	7.37152	+	3.05338i	0.887427	+	0.367584i
$70$	0.967264	+	5.58564i	0.115610	+	0.667611i
$71$	−6.21830	−	6.21830i	−0.737977	−	0.737977i	0.234210	−	0.972186i	$-0.424750\pi$
$71$	−6.21830	−	6.21830i	−0.737977	−	0.737977i	−0.972186	+	0.234210i	$0.924750\pi$
$72$	−4.97060	+	0.607971i	−0.585791	+	0.0716500i
$73$	−2.09089	+	2.09089i	−0.244720	+	0.244720i	−0.818800	−	0.574079i	$-0.805360\pi$
$73$	−2.09089	+	2.09089i	−0.244720	+	0.244720i	0.574079	+	0.818800i	$0.305360\pi$
$74$	8.46196	+	5.96385i	0.983683	+	0.693283i
$75$	−4.69632	+	11.3379i	−0.542284	+	1.30919i
$76$	−4.44731	−	0.221483i	−0.510141	−	0.0254058i
$77$	3.20352	−	1.32694i	0.365075	−	0.151219i
$78$	1.70934	+	2.70135i	0.193544	+	0.305867i
$79$		−	9.23644i		−	1.03918i	−0.854416	−	0.519590i	$-0.826085\pi$
$79$		−	9.23644i		−	1.03918i	0.854416	−	0.519590i	$-0.173915\pi$
$80$	4.63368	+	15.3495i	0.518061	+	1.71613i
$81$			0.554037i			0.0615596i
$82$	2.25756	−	1.42852i	0.249306	−	0.157754i
$83$	4.95210	−	2.05123i	0.543563	−	0.225151i	−0.0939688	−	0.995575i	$-0.529955\pi$
$83$	4.95210	−	2.05123i	0.543563	−	0.225151i	0.637532	+	0.770424i	$0.279955\pi$
$84$	1.64420	−	1.48820i	0.179397	−	0.162376i
$85$	6.12994	−	14.7990i	0.664885	−	1.60517i
$86$	2.78170	−	3.94689i	0.299958	−	0.425604i
$87$	−5.56024	+	5.56024i	−0.596121	+	0.596121i
$88$	8.53822	−	4.82546i	0.910178	−	0.514396i
$89$	9.12026	+	9.12026i	0.966745	+	0.966745i	0.999465	−	0.0327193i	$-0.0104167\pi$
$89$	9.12026	+	9.12026i	0.966745	+	0.966745i	−0.0327193	+	0.999465i	$0.510417\pi$
$90$	−9.88919	+	1.71251i	−1.04241	+	0.180514i
$91$	1.88338	+	0.780120i	0.197431	+	0.0817788i
$92$	13.5534	−	4.83918i	1.41304	−	0.504519i
$93$	−3.61112	−	8.71801i	−0.374455	−	0.904015i
$94$	−0.983711	+	4.37378i	−0.101462	+	0.451121i
$95$	−8.92440			−0.915624
$96$	4.10505	−	4.74274i	0.418970	−	0.484054i
$97$	−9.76692			−0.991681			−0.495840	−	0.868414i	$-0.665140\pi$
$97$	−9.76692			−0.991681			−0.495840	+	0.868414i	$0.665140\pi$
$98$	0.310320	−	1.37975i	0.0313471	−	0.139375i
$99$	2.34931	+	5.67173i	0.236114	+	0.570030i
$100$	7.44301	+	20.8460i	0.744301	+	2.08460i
$101$	−10.9249	−	4.52526i	−1.08707	−	0.450280i	−0.234088	−	0.972216i	$-0.575210\pi$
$101$	−10.9249	−	4.52526i	−1.08707	−	0.450280i	−0.852985	+	0.521935i	$0.825210\pi$
$102$	−6.17464	+	1.06926i	−0.611380	+	0.105873i
$103$	0.574490	+	0.574490i	0.0566061	+	0.0566061i	0.734843	−	0.678237i	$-0.237256\pi$
$103$	0.574490	+	0.574490i	0.0566061	+	0.0566061i	−0.678237	+	0.734843i	$0.737256\pi$
$104$	5.55548	+	1.54345i	0.544759	+	0.151347i
$105$	3.14289	−	3.14289i	0.306714	−	0.306714i
$106$	−10.1985	+	14.4704i	−0.990565	+	1.40549i
$107$	−0.927686	+	2.23963i	−0.0896828	+	0.216513i	−0.962356	−	0.271790i	$-0.912384\pi$
$107$	−0.927686	+	2.23963i	−0.0896828	+	0.216513i	0.872674	+	0.488304i	$0.162384\pi$
$108$	7.09941	+	7.84360i	0.683141	+	0.754750i
$109$	4.13881	−	1.71435i	0.396426	−	0.164205i	−0.175560	−	0.984469i	$-0.556173\pi$
$109$	4.13881	−	1.71435i	0.396426	−	0.164205i	0.571985	+	0.820264i	$0.306173\pi$
$110$	16.6102	−	10.5105i	1.58372	−	1.00213i
$111$		−	8.11701i		−	0.770432i
$112$	0.397427	−	3.98021i	0.0375533	−	0.376094i
$113$			0.128309i			0.0120703i	0.999982	+	0.00603513i	$0.00192105\pi$
$113$			0.128309i			0.0120703i	−0.999982	+	0.00603513i	$0.998079\pi$
$114$	1.86686	+	2.95029i	0.174847	+	0.276320i
$115$	26.6478	−	11.0379i	2.48492	−	1.02929i
$116$	−0.705463	+	14.1655i	−0.0655006	+	1.31523i
$117$	−1.38118	+	3.33446i	−0.127690	+	0.308271i
$118$	−3.00112	−	2.11514i	−0.276275	−	0.194714i
$119$	−2.82571	+	2.82571i	−0.259032	+	0.259032i
$120$	7.74441	−	9.90292i	0.706965	−	0.904008i
$121$	−0.723576	−	0.723576i	−0.0657796	−	0.0657796i
$122$	2.43253	+	14.0471i	0.220231	+	1.27176i
$123$	−1.93524	−	0.801605i	−0.174495	−	0.0722782i
$124$	−15.3811	−	7.28738i	−1.38126	−	0.654426i
$125$	9.30724	+	22.4697i	0.832465	+	2.00975i
$126$	2.44280	+	0.549412i	0.217622	+	0.0489455i
$127$	−6.89025			−0.611411			−0.305705	−	0.952126i	$-0.598892\pi$
$127$	−6.89025			−0.611411			−0.305705	+	0.952126i	$0.598892\pi$
$128$	−0.251008	−	11.3109i	−0.0221862	−	0.999754i
$129$	−3.78599			−0.333338
$130$	11.2744	+	2.53574i	0.988833	+	0.222400i
$131$	0.879601	+	2.12354i	0.0768511	+	0.185535i	0.957636	−	0.287982i	$-0.0929843\pi$
$131$	0.879601	+	2.12354i	0.0768511	+	0.185535i	−0.880785	+	0.473517i	$0.842984\pi$
$132$	−6.94923	−	3.29246i	−0.604853	−	0.286572i
$133$	2.05694	+	0.852011i	0.178359	+	0.0738787i
$134$	0.198946	+	1.14885i	0.0171864	+	0.0992457i
$135$	14.9930	+	14.9930i	1.29040	+	1.29040i
$136$	−6.96286	+	8.90353i	−0.597060	+	0.763471i
$137$	1.06584	−	1.06584i	0.0910611	−	0.0910611i	−0.660109	−	0.751170i	$-0.729490\pi$
$137$	1.06584	−	1.06584i	0.0910611	−	0.0910611i	0.751170	+	0.660109i	$0.229490\pi$
$138$	−9.22330	−	6.50043i	−0.785140	−	0.553353i
$139$	1.68081	−	4.05783i	0.142564	−	0.344181i	−0.836428	−	0.548076i	$-0.815360\pi$
$139$	1.68081	−	4.05783i	0.142564	−	0.344181i	0.978993	+	0.203895i	$0.0653603\pi$
$140$	0.398757	−	8.00693i	0.0337011	−	0.676709i
$141$	3.24745	−	1.34514i	0.273485	−	0.113281i
$142$	6.65002	+	10.5093i	0.558057	+	0.881925i
$143$		−	7.06860i		−	0.591106i
$144$	7.04683	+	0.703631i	0.587236	+	0.0586360i
$145$			28.4258i			2.36063i
$146$	3.53375	−	2.23605i	0.292455	−	0.185057i
$147$	−1.02444	+	0.424336i	−0.0844941	+	0.0349986i
$148$	−9.82466	−	10.8545i	−0.807582	−	0.892236i
$149$	1.61740	−	3.90476i	0.132503	−	0.319890i	−0.843678	−	0.536850i	$-0.819614\pi$
$149$	1.61740	−	3.90476i	0.132503	−	0.319890i	0.976181	+	0.216960i	$0.0696140\pi$
$150$	9.99812	−	14.1861i	0.816343	−	1.15829i
$151$	14.4036	−	14.4036i	1.17214	−	1.17214i	0.190448	−	0.981697i	$-0.439006\pi$
$151$	14.4036	−	14.4036i	1.17214	−	1.17214i	0.981697	−	0.190448i	$-0.0609939\pi$
$152$	6.06743	+	1.68568i	0.492134	+	0.136727i
$153$	−5.00283	−	5.00283i	−0.404455	−	0.404455i
$154$	−4.83182	+	0.836725i	−0.389359	+	0.0674252i
$155$	−31.5153	−	13.0541i	−2.53137	−	1.04853i
$156$	−1.52017	−	4.25762i	−0.121711	−	0.340882i
$157$	3.52753	+	8.51620i	0.281527	+	0.679667i	0.999872	−	0.0160208i	$-0.00509978\pi$
$157$	3.52753	+	8.51620i	0.281527	+	0.679667i	−0.718344	+	0.695688i	$0.755100\pi$
$158$	−2.86625	+	12.7439i	−0.228027	+	1.01385i
$159$	13.8805			1.10080
$160$	−1.63003	−	22.6164i	−0.128865	−	1.78798i
$161$	−7.19568			−0.567099
$162$	0.171929	−	0.764430i	0.0135080	−	0.0600593i
$163$	−3.75784	−	9.07224i	−0.294337	−	0.710593i	−0.999998	−	0.00204276i	$-0.999350\pi$
$163$	−3.75784	−	9.07224i	−0.294337	−	0.710593i	0.705661	−	0.708550i	$-0.250650\pi$
$164$	−3.55816	+	1.27043i	−0.277846	+	0.0992039i
$165$	−14.2387	−	5.89787i	−1.10848	−	0.459148i
$166$	−7.46917	+	1.29344i	−0.579720	+	0.100390i
$167$	5.75159	+	5.75159i	0.445071	+	0.445071i	0.893712	−	0.448641i	$-0.148092\pi$
$167$	5.75159	+	5.75159i	0.445071	+	0.445071i	−0.448641	+	0.893712i	$0.648092\pi$
$168$	−2.73040	+	1.54311i	−0.210655	+	0.119054i
$169$	−6.25387	+	6.25387i	−0.481067	+	0.481067i
$170$	−13.0502	+	18.5166i	−1.00090	+	1.42016i
$171$	−1.50846	+	3.64174i	−0.115355	+	0.278491i
$172$	−5.06284	+	4.58249i	−0.386038	+	0.349411i
$173$	−16.1234	+	6.67853i	−1.22584	+	0.507759i	−0.899262	−	0.437411i	$-0.855895\pi$
$173$	−16.1234	+	6.67853i	−1.22584	+	0.507759i	−0.326578	+	0.945170i	$0.605895\pi$
$174$	9.39718	−	5.94627i	0.712399	−	0.450786i
$175$		−	11.0675i		−	0.836622i
$176$	−13.2780	+	4.00833i	−1.00087	+	0.302140i
$177$			2.87878i			0.216382i
$178$	−9.75344	−	15.4138i	−0.731052	−	1.15532i
$179$	−14.3176	+	5.93053i	−1.07014	+	0.443269i	−0.847042	−	0.531526i	$-0.821619\pi$
$179$	−14.3176	+	5.93053i	−1.07014	+	0.443269i	−0.223103	+	0.974795i	$0.571619\pi$
$180$	14.1760	+	0.705987i	1.05662	+	0.0526212i
$181$	−8.21076	+	19.8225i	−0.610301	+	1.47340i	0.252370	+	0.967631i	$0.418790\pi$
$181$	−8.21076	+	19.8225i	−0.610301	+	1.47340i	−0.862671	+	0.505766i	$0.831210\pi$
$182$	−2.35649	−	1.66082i	−0.174675	−	0.123108i
$183$	7.90389	−	7.90389i	0.584273	−	0.584273i
$184$	−20.2019	+	2.47096i	−1.48930	+	0.182162i
$185$	−20.7484	−	20.7484i	−1.52545	−	1.52545i
$186$	2.27705	+	13.1492i	0.166962	+	0.964149i
$187$	12.8018	+	5.30266i	0.936157	+	0.387769i
$188$	2.71455	−	5.72944i	0.197979	−	0.417863i
$189$	−2.02428	−	4.88704i	−0.147245	−	0.355480i
$190$	12.3134	+	2.76942i	0.893309	+	0.200915i
$191$	10.2155			0.739164			0.369582	−	0.929198i	$-0.379501\pi$
$191$	10.2155			0.739164			0.369582	+	0.929198i	$0.379501\pi$
$192$	−7.13570	+	5.26990i	−0.514975	+	0.380322i
$193$	1.33660			0.0962108			0.0481054	−	0.998842i	$-0.484682\pi$
$193$	1.33660			0.0962108			0.0481054	+	0.998842i	$0.484682\pi$
$194$	13.4759	+	3.03087i	0.967512	+	0.217604i
$195$	−3.46741	−	8.37106i	−0.248306	−	0.599464i
$196$	−0.856327	+	1.80740i	−0.0611662	+	0.129100i
$197$	−4.81759	−	1.99551i	−0.343239	−	0.142174i	0.204403	−	0.978887i	$-0.434475\pi$
$197$	−4.81759	−	1.99551i	−0.343239	−	0.142174i	−0.547642	+	0.836712i	$0.684475\pi$
$198$	−1.48140	−	8.55458i	−0.105278	−	0.607948i
$199$	14.6883	+	14.6883i	1.04123	+	1.04123i	0.999113	+	0.0421136i	$0.0134091\pi$
$199$	14.6883	+	14.6883i	1.04123	+	1.04123i	0.0421136	+	0.999113i	$0.486591\pi$
$200$	−3.80052	−	31.0720i	−0.268737	−	2.19712i
$201$	0.646428	−	0.646428i	0.0455955	−	0.0455955i
$202$	13.6694	+	9.63395i	0.961774	+	0.677842i
$203$	2.71380	−	6.55170i	0.190472	−	0.459840i
$204$	8.85125	+	0.440806i	0.619711	+	0.0308626i
$205$	−6.99584	+	2.89777i	−0.488610	+	0.202389i
$206$	−0.614374	−	0.970926i	−0.0428055	−	0.0676476i
$207$		−	12.7397i		−	0.885472i
$208$	−7.18619	−	3.85354i	−0.498272	−	0.267195i
$209$		−	7.71999i		−	0.534003i
$210$	−5.31169	+	3.36109i	−0.366541	+	0.231937i
$211$	21.1265	−	8.75089i	1.45441	−	0.602436i	0.491165	−	0.871066i	$-0.336571\pi$
$211$	21.1265	−	8.75089i	1.45441	−	0.602436i	0.963243	+	0.268631i	$0.0865711\pi$
$212$	18.5618	−	16.8007i	1.27483	−	1.15388i
$213$	3.73161	−	9.00890i	0.255686	−	0.617280i
$214$	1.97498	−	2.80225i	0.135007	−	0.191558i
$215$	−9.67762	+	9.67762i	−0.660008	+	0.660008i
$216$	−7.36136	−	13.0253i	−0.500877	−	0.886257i
$217$	6.01751	+	6.01751i	0.408495	+	0.408495i
$218$	−6.24250	+	1.08101i	−0.422796	+	0.0732154i
$219$	−3.02923	−	1.25475i	−0.204696	−	0.0847879i
$220$	−26.1795	+	9.34729i	−1.76502	+	0.630194i
$221$	3.11748	+	7.52627i	0.209704	+	0.506271i
$222$	−2.51887	+	11.1994i	−0.169056	+	0.751656i
$223$	−23.8764			−1.59888			−0.799442	−	0.600743i	$-0.794871\pi$
$223$	−23.8764			−1.59888			−0.799442	+	0.600743i	$0.794871\pi$
$224$	−1.78349	+	5.36835i	−0.119164	+	0.358688i
$225$	19.5946			1.30631
$226$	0.0398167	−	0.177033i	0.00264857	−	0.0117761i
$227$	7.83210	+	18.9084i	0.519835	+	1.25499i	0.938004	+	0.346624i	$0.112672\pi$
$227$	7.83210	+	18.9084i	0.519835	+	1.25499i	−0.418169	+	0.908369i	$0.637328\pi$
$228$	−1.66026	−	4.64997i	−0.109953	−	0.307952i
$229$	1.72921	+	0.716263i	0.114270	+	0.0473320i	0.439086	−	0.898445i	$-0.355302\pi$
$229$	1.72921	+	0.716263i	0.114270	+	0.0473320i	−0.324816	+	0.945777i	$0.605302\pi$
$230$	−40.1924	+	6.96012i	−2.65021	+	0.458937i
$231$	2.71873	+	2.71873i	0.178879	+	0.178879i
$232$	5.36919	−	19.3258i	0.352505	−	1.26880i
$233$	5.83290	−	5.83290i	0.382126	−	0.382126i	−0.489742	−	0.871868i	$-0.662909\pi$
$233$	5.83290	−	5.83290i	0.382126	−	0.382126i	0.871868	+	0.489742i	$0.162909\pi$
$234$	2.94043	−	4.17210i	0.192222	−	0.272739i
$235$	4.86263	−	11.7394i	0.317203	−	0.765795i
$236$	3.48442	+	3.84966i	0.226816	+	0.250592i
$237$	9.46214	−	3.91935i	0.614632	−	0.254589i
$238$	4.77564	−	3.02189i	0.309559	−	0.195880i
$239$			24.2326i			1.56748i	0.621092	+	0.783738i	$0.286689\pi$
$239$			24.2326i			1.56748i	−0.621092	+	0.783738i	$0.713311\pi$
$240$	−13.7584	+	11.2603i	−0.888101	+	0.726847i
$241$			2.18918i			0.141017i	0.997511	+	0.0705087i	$0.0224622\pi$
$241$			2.18918i			0.141017i	−0.997511	+	0.0705087i	$0.977538\pi$
$242$	0.773811	+	1.22289i	0.0497425	+	0.0786105i
$243$	14.0936	−	5.83774i	0.904102	−	0.374491i
$244$	1.00282	−	20.1362i	0.0641987	−	1.28909i
$245$	−1.53396	+	3.70330i	−0.0980010	+	0.236595i
$246$	2.42139	+	1.70656i	0.154382	+	0.108806i
$247$	3.20931	−	3.20931i	0.204204	−	0.204204i
$248$	18.9606	+	14.8278i	1.20400	+	0.941567i
$249$	4.20270	+	4.20270i	0.266335	+	0.266335i
$250$	−5.86884	−	33.8907i	−0.371178	−	2.14343i
$251$	10.0634	+	4.16841i	0.635199	+	0.263108i	0.676960	−	0.736020i	$-0.263297\pi$
$251$	10.0634	+	4.16841i	0.635199	+	0.263108i	−0.0417613	+	0.999128i	$0.513297\pi$
$252$	−3.19995	−	1.51610i	−0.201578	−	0.0955053i
$253$	9.54823	+	23.0515i	0.600292	+	1.44923i
$254$	9.50680	+	2.13818i	0.596510	+	0.134162i
$255$	17.7618			1.11228
$256$	−3.16368	+	15.6841i	−0.197730	+	0.980256i
$257$	−24.7180			−1.54187			−0.770934	−	0.636915i	$-0.780210\pi$
$257$	−24.7180			−1.54187			−0.770934	+	0.636915i	$0.780210\pi$
$258$	5.22371	+	1.17487i	0.325214	+	0.0731442i
$259$	2.80134	+	6.76303i	0.174067	+	0.420234i
$260$	−14.7690	−	6.99737i	−0.915933	−	0.433959i
$261$	11.5996	+	4.80471i	0.717996	+	0.297404i
$262$	−0.554648	−	3.20291i	−0.0342662	−	0.197877i
$263$	−3.13019	−	3.13019i	−0.193016	−	0.193016i	0.603982	−	0.796998i	$-0.293580\pi$
$263$	−3.13019	−	3.13019i	−0.193016	−	0.193016i	−0.796998	+	0.603982i	$0.793580\pi$
$264$	8.56645	+	6.69925i	0.527229	+	0.412311i
$265$	35.4809	−	35.4809i	2.17957	−	2.17957i
$266$	−2.57365	−	1.81387i	−0.157801	−	0.111215i
$267$	−5.47308	+	13.2132i	−0.334947	+	0.808633i
$268$	0.0820163	−	1.64686i	0.00500994	−	0.100598i
$269$	−19.0188	+	7.87784i	−1.15960	+	0.480320i	−0.877740	−	0.479137i	$-0.840950\pi$
$269$	−19.0188	+	7.87784i	−1.15960	+	0.480320i	−0.281855	+	0.959457i	$0.590950\pi$
$270$	−16.0340	−	25.3392i	−0.975795	−	1.54210i
$271$			6.36191i			0.386458i	0.981154	+	0.193229i	$0.0618961\pi$
$271$			6.36191i			0.386458i	−0.981154	+	0.193229i	$0.938104\pi$
$272$	12.3699	−	10.1239i	0.750037	−	0.613852i
$273$			2.26043i			0.136808i
$274$	−1.80135	+	1.13984i	−0.108823	+	0.0688603i
$275$	−35.4548	+	14.6859i	−2.13801	+	0.885591i
$276$	10.7086	+	11.8311i	0.644582	+	0.712150i
$277$	−0.769977	+	1.85889i	−0.0462635	+	0.111690i	−0.945322	−	0.326139i	$-0.894252\pi$
$277$	−0.769977	+	1.85889i	−0.0462635	+	0.111690i	0.899058	+	0.437829i	$0.144252\pi$
$278$	−3.57832	+	5.07719i	−0.214613	+	0.304510i
$279$	−10.6538	+	10.6538i	−0.637827	+	0.637827i
$280$	−3.03490	+	10.9238i	−0.181370	+	0.652821i
$281$	16.6647	+	16.6647i	0.994135	+	0.994135i	0.999983	−	0.00584778i	$-0.00186142\pi$
$281$	16.6647	+	16.6647i	0.994135	+	0.994135i	−0.00584778	+	0.999983i	$0.501861\pi$
$282$	−4.89808	+	0.848200i	−0.291677	+	0.0505096i
$283$	5.33995	+	2.21188i	0.317427	+	0.131483i	0.535708	−	0.844403i	$-0.320045\pi$
$283$	5.33995	+	2.21188i	0.317427	+	0.131483i	−0.218281	+	0.975886i	$0.570045\pi$
$284$	−5.91408	−	16.5639i	−0.350936	−	0.982885i
$285$	−3.78694	−	9.14248i	−0.224319	−	0.541554i
$286$	−2.19353	+	9.75288i	−0.129706	+	0.576700i
$287$	1.88908			0.111509
$288$	−9.50449	−	3.15761i	−0.560058	−	0.186064i
$289$	1.03073			0.0606311
$290$	8.82110	−	39.2204i	0.517993	−	2.30310i
$291$	−4.14445	−	10.0056i	−0.242952	−	0.586538i
$292$	−5.56957	+	1.98860i	−0.325934	+	0.116374i
$293$	12.1989	+	5.05294i	0.712666	+	0.295196i	0.709407	−	0.704799i	$-0.248963\pi$
$293$	12.1989	+	5.05294i	0.712666	+	0.295196i	0.00325849	+	0.999995i	$0.498963\pi$
$294$	1.54514	−	0.267572i	0.0901146	−	0.0156051i
$295$	7.35863	+	7.35863i	0.428436	+	0.428436i
$296$	10.1872	+	18.0253i	0.592117	+	1.04770i
$297$	−12.9696	+	12.9696i	−0.752574	+	0.752574i
$298$	−3.44334	+	4.88567i	−0.199467	+	0.283019i
$299$	−5.61349	+	13.5522i	−0.324637	+	0.783742i
$300$	−18.1971	+	16.4706i	−1.05061	+	0.950931i
$301$	3.15446	−	1.30662i	0.181820	−	0.0753123i
$302$	−24.3430	+	15.4035i	−1.40078	+	0.886375i
$303$		−	13.1121i		−	0.753273i
$304$	−7.84842	−	4.20866i	−0.450138	−	0.241383i
$305$		−	40.4073i		−	2.31372i
$306$	5.35016	+	8.45512i	0.305848	+	0.483347i
$307$	8.01235	−	3.31882i	0.457289	−	0.189415i	−0.142135	−	0.989847i	$-0.545397\pi$
$307$	8.01235	−	3.31882i	0.457289	−	0.189415i	0.599423	+	0.800432i	$0.295397\pi$
$308$	6.92634	+	0.344942i	0.394665	+	0.0196549i
$309$	−0.344752	+	0.832305i	−0.0196123	+	0.0473482i
$310$	39.4322	+	27.7911i	2.23960	+	1.57843i
$311$	21.3528	−	21.3528i	1.21081	−	1.21081i	0.240043	−	0.970762i	$-0.422838\pi$
$311$	21.3528	−	21.3528i	1.21081	−	1.21081i	0.970762	−	0.240043i	$-0.0771616\pi$
$312$	0.776222	+	6.34617i	0.0439449	+	0.359281i
$313$	−6.73094	−	6.73094i	−0.380455	−	0.380455i	0.490811	−	0.871266i	$-0.336701\pi$
$313$	−6.73094	−	6.73094i	−0.380455	−	0.380455i	−0.871266	+	0.490811i	$0.836701\pi$
$314$	−2.22434	−	12.8449i	−0.125527	−	0.724878i
$315$	−6.55658	−	2.71582i	−0.369421	−	0.153019i
$316$	7.90941	−	16.6940i	0.444939	−	0.939108i
$317$	0.0760844	+	0.183684i	0.00427333	+	0.0103167i	0.926002	−	0.377519i	$-0.123223\pi$
$317$	0.0760844	+	0.183684i	0.00427333	+	0.0103167i	−0.921728	+	0.387836i	$0.873223\pi$
$318$	−19.1516	−	4.30740i	−1.07397	−	0.241547i
$319$	−24.5896			−1.37675
$320$	−4.76930	+	31.7107i	−0.266612	+	1.77268i
$321$	−2.68801			−0.150030
$322$	9.92821	+	2.23297i	0.553278	+	0.124438i
$323$	3.40477	+	8.21984i	0.189446	+	0.457364i
$324$	−0.474437	+	1.00137i	−0.0263576	+	0.0556315i
$325$	−20.8442	−	8.63395i	−1.15623	−	0.478925i
$326$	2.36957	+	13.6835i	0.131239	+	0.757860i
$327$	3.51249	+	3.51249i	0.194241	+	0.194241i
$328$	5.30360	−	0.648702i	0.292843	−	0.0358186i
$329$	−2.24152	+	2.24152i	−0.123579	+	0.123579i
$330$	17.8156	+	12.5561i	0.980716	+	0.691192i
$331$	−3.22280	+	7.78053i	−0.177141	+	0.427657i	−0.987365	−	0.158464i	$-0.949346\pi$
$331$	−3.22280	+	7.78053i	−0.177141	+	0.427657i	0.810223	+	0.586121i	$0.199346\pi$
$332$	10.7069	+	0.533223i	0.587620	+	0.0292644i
$333$	−11.9737	+	4.95968i	−0.656157	+	0.271789i
$334$	−6.15090	−	9.72057i	−0.336562	−	0.531886i
$335$		−	3.30475i		−	0.180558i
$336$	4.24611	−	1.28181i	0.231644	−	0.0699282i
$337$			23.3157i			1.27009i	0.772476	+	0.635044i	$0.219018\pi$
$337$			23.3157i			1.27009i	−0.772476	+	0.635044i	$0.780982\pi$
$338$	10.5695	−	6.68805i	0.574903	−	0.363782i
$339$	−0.131444	+	0.0544459i	−0.00713906	+	0.00295709i
$340$	23.7520	−	21.4985i	1.28813	−	1.16592i
$341$	11.2923	−	27.2621i	0.611514	−	1.47632i
$342$	3.21140	−	4.55657i	0.173652	−	0.246391i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	8.40747	−	4.75157i	0.453301	−	0.256187i
$345$	22.6152	+	22.6152i	1.21756	+	1.21756i
$346$	24.3187	−	4.21126i	1.30738	−	0.226399i
$347$	20.3270	+	8.41971i	1.09121	+	0.451994i	0.854428	−	0.519569i	$-0.173908\pi$
$347$	20.3270	+	8.41971i	1.09121	+	0.451994i	0.236781	+	0.971563i	$0.423908\pi$
$348$	−14.8110	+	5.28821i	−0.793952	+	0.283478i
$349$	−8.67368	−	20.9401i	−0.464292	−	1.12090i	−0.966618	−	0.256221i	$-0.917522\pi$
$349$	−8.67368	−	20.9401i	−0.464292	−	1.12090i	0.502327	−	0.864678i	$-0.332478\pi$
$350$	−3.43446	+	15.2703i	−0.183580	+	0.816232i
$351$	−10.7833			−0.575571
$352$	19.5642	−	1.41005i	1.04277	−	0.0751557i
$353$	−11.8631			−0.631409			−0.315704	−	0.948858i	$-0.602241\pi$
$353$	−11.8631			−0.631409			−0.315704	+	0.948858i	$0.602241\pi$
$354$	0.893344	−	3.97199i	0.0474807	−	0.211109i
$355$	−13.4896	−	32.5669i	−0.715955	−	1.72847i
$356$	8.67406	+	24.2939i	0.459724	+	1.28757i
$357$	−4.09381	−	1.69571i	−0.216667	−	0.0897466i
$358$	21.5950	−	3.73960i	1.14133	−	0.197644i
$359$	−0.519581	−	0.519581i	−0.0274225	−	0.0274225i	0.693263	−	0.720685i	$-0.256173\pi$
$359$	−0.519581	−	0.519581i	−0.0274225	−	0.0274225i	−0.720685	+	0.693263i	$0.756173\pi$
$360$	−19.3402	−	5.37319i	−1.01932	−	0.283192i
$361$	−9.92997	+	9.92997i	−0.522630	+	0.522630i
$362$	17.4801	−	24.8021i	0.918734	−	1.30357i
$363$	0.434219	−	1.04830i	0.0227906	−	0.0550213i
$364$	2.73598	+	3.02278i	0.143404	+	0.158437i
$365$	−10.9505	+	4.53586i	−0.573177	+	0.237418i
$366$	−13.3581	+	8.45263i	−0.698240	+	0.441826i
$367$			20.8905i			1.09048i	0.838281	+	0.545239i	$0.183561\pi$
$367$			20.8905i			1.09048i	−0.838281	+	0.545239i	$0.816439\pi$
$368$	28.6403	+	2.85976i	1.49298	+	0.149075i
$369$			3.34456i			0.174111i
$370$	22.1889	+	35.0662i	1.15355	+	1.82301i
$371$	−11.5651	+	4.79044i	−0.600432	+	0.248707i
$372$	0.938722	−	18.8492i	0.0486705	−	0.977288i
$373$	−0.402626	+	0.972025i	−0.0208472	+	0.0503296i	−0.933960	−	0.357377i	$-0.883671\pi$
$373$	−0.402626	+	0.972025i	−0.0208472	+	0.0503296i	0.913113	+	0.407706i	$0.133671\pi$
$374$	−16.0177	−	11.2890i	−0.828254	−	0.583739i
$375$	−19.0694	+	19.0694i	−0.984737	+	0.984737i
$376$	−5.52335	+	7.06280i	−0.284845	+	0.364236i
$377$	−10.2222	−	10.2222i	−0.526472	−	0.526472i
$378$	1.27644	+	7.37106i	0.0656532	+	0.379126i
$379$	−20.1406	−	8.34251i	−1.03455	−	0.428526i	−0.200199	−	0.979755i	$-0.564159\pi$
$379$	−20.1406	−	8.34251i	−1.03455	−	0.428526i	−0.834354	+	0.551230i	$0.814159\pi$
$380$	−16.1300	−	7.64220i	−0.827451	−	0.392037i
$381$	−2.92378	−	7.05862i	−0.149790	−	0.361624i
$382$	−14.0947	−	3.17006i	−0.721149	−	0.162194i
$383$	2.87465			0.146888			0.0734438	−	0.997299i	$-0.476601\pi$
$383$	2.87465			0.146888			0.0734438	+	0.997299i	$0.476601\pi$
$384$	11.4808	−	5.05677i	0.585878	−	0.258052i
$385$	13.8991			0.708362
$386$	−1.84417	−	0.414775i	−0.0938660	−	0.0211115i
$387$	2.31333	+	5.58487i	0.117593	+	0.283895i
$388$	−17.6528	−	8.36368i	−0.896183	−	0.424601i
$389$	34.3165	+	14.2143i	1.73991	+	0.720696i	0.998782	+	0.0493368i	$0.0157108\pi$
$389$	34.3165	+	14.2143i	1.73991	+	0.720696i	0.741132	+	0.671359i	$0.234289\pi$
$390$	2.18643	+	12.6260i	0.110714	+	0.639340i
$391$	−20.3329	−	20.3329i	−1.02828	−	1.02828i
$392$	1.74239	−	2.22802i	0.0880039	−	0.112532i
$393$	−1.80219	+	1.80219i	−0.0909085	+	0.0909085i
$394$	6.02781	+	4.24830i	0.303676	+	0.214026i
$395$	14.1683	−	34.2053i	0.712885	−	1.72106i
$396$	−0.610710	+	12.2629i	−0.0306893	+	0.616232i
$397$	−30.2593	+	12.5338i	−1.51867	+	0.629054i	−0.977325	−	0.211745i	$-0.932085\pi$
$397$	−30.2593	+	12.5338i	−1.51867	+	0.629054i	−0.541347	+	0.840799i	$0.682085\pi$
$398$	−15.7081	−	24.8242i	−0.787374	−	1.24433i
$399$			2.46874i			0.123592i
$400$	−4.39851	+	44.0508i	−0.219925	+	2.20254i
$401$		−	36.1292i		−	1.80421i	−0.431522	−	0.902103i	$-0.642023\pi$
$401$		−	36.1292i		−	1.80421i	0.431522	−	0.902103i	$-0.357977\pi$
$402$	−1.09251	+	0.691307i	−0.0544893	+	0.0344793i
$403$	16.0276	−	6.63886i	0.798393	−	0.330705i
$404$	−15.8707	−	17.5343i	−0.789595	−	0.872364i
$405$	−0.849869	+	2.05176i	−0.0422303	+	0.101953i
$406$	−5.77749	+	8.19754i	−0.286732	+	0.406837i
$407$	17.9483	−	17.9483i	0.889663	−	0.889663i
$408$	−12.0757	−	3.35492i	−0.597836	−	0.166093i
$409$	12.5036	+	12.5036i	0.618265	+	0.618265i	0.945086	−	0.326821i	$-0.105978\pi$
$409$	12.5036	+	12.5036i	0.618265	+	0.618265i	−0.326821	+	0.945086i	$0.605978\pi$
$410$	10.5517	−	1.82724i	0.521112	−	0.0902409i
$411$	1.54416	+	0.639613i	0.0761679	+	0.0315498i
$412$	0.546383	+	1.53028i	0.0269184	+	0.0753917i
$413$	−0.993524	−	2.39858i	−0.0488881	−	0.118026i
$414$	−3.95339	+	17.5776i	−0.194299	+	0.863891i
$415$	21.4856			1.05469
$416$	8.71929	+	7.54693i	0.427498	+	0.370019i
$417$	4.87022			0.238496
$418$	−2.39567	+	10.6516i	−0.117176	+	0.520989i
$419$	−5.45653	−	13.1732i	−0.266569	−	0.643554i	0.732749	−	0.680500i	$-0.238237\pi$
$419$	−5.45653	−	13.1732i	−0.266569	−	0.643554i	−0.999317	+	0.0369456i	$0.988237\pi$
$420$	8.37180	−	2.98912i	0.408502	−	0.145854i
$421$	−0.496953	−	0.205845i	−0.0242200	−	0.0100323i	0.370541	−	0.928816i	$-0.379172\pi$
$421$	−0.496953	−	0.205845i	−0.0242200	−	0.0100323i	−0.394761	+	0.918784i	$0.629172\pi$
$422$	−31.8648	+	5.51802i	−1.55115	+	0.268613i
$423$	−3.96854	−	3.96854i	−0.192957	−	0.192957i
$424$	−30.8242	+	17.4206i	−1.49695	+	0.846019i
$425$	31.2735	−	31.2735i	1.51699	−	1.51699i
$426$	−7.94432	+	11.2720i	−0.384904	+	0.546131i
$427$	−3.85768	+	9.31326i	−0.186686	+	0.450700i
$428$	−3.59456	+	3.25351i	−0.173750	+	0.157265i
$429$	7.24133	−	2.99946i	0.349615	−	0.144815i
$430$	16.3558	−	10.3495i	0.788748	−	0.499097i
$431$			26.8787i			1.29470i	0.762193	+	0.647350i	$0.224123\pi$
$431$			26.8787i			1.29470i	−0.762193	+	0.647350i	$0.775877\pi$
$432$	6.11481	+	20.2560i	0.294199	+	0.974565i
$433$			1.35555i			0.0651438i	0.999469	+	0.0325719i	$0.0103698\pi$
$433$			1.35555i			0.0651438i	−0.999469	+	0.0325719i	$0.989630\pi$
$434$	−6.43529	−	10.1700i	−0.308904	−	0.488176i
$435$	−29.1204	+	12.0621i	−1.39622	+	0.578332i
$436$	8.94853	+	0.445651i	0.428557	+	0.0213428i
$437$	−6.13079	+	14.8010i	−0.293276	+	0.708030i
$438$	3.79019	+	2.67126i	0.181102	+	0.127638i
$439$	21.2655	−	21.2655i	1.01495	−	1.01495i	0.0150600	−	0.999887i	$-0.495206\pi$
$439$	21.2655	−	21.2655i	1.01495	−	1.01495i	0.999887	−	0.0150600i	$-0.00479394\pi$
$440$	39.0217	−	4.77287i	1.86028	−	0.227538i
$441$	1.25191	+	1.25191i	0.0596148	+	0.0596148i
$442$	−1.96578	−	11.3518i	−0.0935027	−	0.539948i
$443$	−2.39845	−	0.993471i	−0.113954	−	0.0472012i	0.324978	−	0.945722i	$-0.394643\pi$
$443$	−2.39845	−	0.993471i	−0.113954	−	0.0472012i	−0.438932	+	0.898520i	$0.644643\pi$
$444$	6.95081	−	14.6707i	0.329871	−	0.696241i
$445$	19.7850	+	47.7651i	0.937898	+	2.26429i
$446$	32.9434	+	7.40934i	1.55992	+	0.350843i
$447$	4.68650			0.221664
$448$	4.12667	−	6.85351i	0.194967	−	0.323798i
$449$	32.1967			1.51945			0.759727	−	0.650242i	$-0.225332\pi$
$449$	32.1967			1.51945			0.759727	+	0.650242i	$0.225332\pi$
$450$	−27.0356	−	6.08060i	−1.27447	−	0.286642i
$451$	−2.50670	−	6.05170i	−0.118036	−	0.284964i
$452$	−0.109874	+	0.231905i	−0.00516804	+	0.0109079i
$453$	20.8675	+	8.64359i	0.980440	+	0.406111i
$454$	−4.93867	−	28.5192i	−0.231783	−	1.33847i
$455$	5.77804	+	5.77804i	0.270879	+	0.270879i
$456$	0.847754	+	6.93099i	0.0396997	+	0.324574i
$457$	−15.6589	+	15.6589i	−0.732492	+	0.732492i	−0.971113	−	0.238621i	$-0.923305\pi$
$457$	−15.6589	+	15.6589i	−0.732492	+	0.732492i	0.238621	+	0.971113i	$0.423305\pi$
$458$	−2.16360	−	1.52487i	−0.101099	−	0.0712526i
$459$	8.08934	−	19.5294i	0.377578	−	0.911554i
$460$	57.6153	+	2.86933i	2.68633	+	0.133783i
$461$	−11.9675	+	4.95708i	−0.557380	+	0.230874i	−0.643547	−	0.765406i	$-0.722538\pi$
$461$	−11.9675	+	4.95708i	−0.557380	+	0.230874i	0.0861675	+	0.996281i	$0.472538\pi$
$462$	−2.90749	−	4.59484i	−0.135268	−	0.213771i
$463$		−	30.8800i		−	1.43512i	−0.696499	−	0.717558i	$-0.745260\pi$
$463$		−	30.8800i		−	1.43512i	0.696499	−	0.717558i	$-0.254740\pi$
$464$	−13.4053	+	24.9986i	−0.622327	+	1.16053i
$465$		−	37.8247i		−	1.75408i
$466$	−9.85799	+	6.23786i	−0.456663	+	0.288963i
$467$	−25.2521	+	10.4598i	−1.16853	+	0.484020i	−0.880706	−	0.473663i	$-0.842931\pi$
$467$	−25.2521	+	10.4598i	−1.16853	+	0.484020i	−0.287823	+	0.957684i	$0.592931\pi$
$468$	−5.35173	+	4.84397i	−0.247384	+	0.223912i
$469$	−0.315504	+	0.761694i	−0.0145686	+	0.0351718i
$470$	−10.3522	+	14.6885i	−0.477510	+	0.677528i
$471$	−7.22746	+	7.22746i	−0.333024	+	0.333024i
$472$	−3.61298	−	6.39285i	−0.166301	−	0.294255i
$473$	−8.37156	−	8.37156i	−0.384925	−	0.384925i
$474$	−14.2716	+	2.47141i	−0.655517	+	0.113516i
$475$	−22.7651	−	9.42960i	−1.04453	−	0.432660i
$476$	−7.52693	+	2.68746i	−0.344996	+	0.123180i
$477$	−8.48132	−	20.4757i	−0.388333	−	0.937519i
$478$	7.51986	−	33.4348i	0.343950	−	1.52927i
$479$	−17.3650			−0.793426			−0.396713	−	0.917943i	$-0.629849\pi$
$479$	−17.3650			−0.793426			−0.396713	+	0.917943i	$0.629849\pi$
$480$	22.4774	−	11.2668i	1.02595	−	0.514257i
$481$	14.9227			0.680417
$482$	0.679346	−	3.02051i	0.0309434	−	0.137580i
$483$	−3.05338	−	7.37152i	−0.138934	−	0.335416i
$484$	−0.688176	−	1.92741i	−0.0312807	−	0.0876096i
$485$	−36.1699	−	14.9820i	−1.64239	−	0.680300i
$486$	−21.2571	+	3.68109i	−0.964242	+	0.166978i
$487$	5.96219	+	5.96219i	0.270173	+	0.270173i	0.829170	−	0.558997i	$-0.188814\pi$
$487$	5.96219	+	5.96219i	0.270173	+	0.270173i	−0.558997	+	0.829170i	$0.688814\pi$
$488$	−7.63232	+	27.4717i	−0.345499	+	1.24359i
$489$	7.69935	−	7.69935i	0.348177	−	0.348177i
$490$	3.26568	−	4.63360i	0.147529	−	0.209325i
$491$	−11.0080	+	26.5757i	−0.496785	+	1.19934i	0.454421	+	0.890787i	$0.349846\pi$
$491$	−11.0080	+	26.5757i	−0.496785	+	1.19934i	−0.951206	+	0.308557i	$0.900154\pi$
$492$	−2.81133	−	3.10602i	−0.126745	−	0.140030i
$493$	26.1816	−	10.8448i	1.17916	−	0.488425i
$494$	−5.42395	+	3.43212i	−0.244035	+	0.154419i
$495$			24.6078i			1.10604i
$496$	−21.5594	−	26.3425i	−0.968047	−	1.18281i
$497$			8.79401i			0.394465i
$498$	−4.49448	−	7.10285i	−0.201402	−	0.318286i
$499$	−12.3497	+	5.11543i	−0.552850	+	0.228998i	−0.641578	−	0.767058i	$-0.721720\pi$
$499$	−12.3497	+	5.11543i	−0.552850	+	0.228998i	0.0887276	+	0.996056i	$0.471720\pi$
$500$	−2.41945	+	48.5818i	−0.108201	+	2.17264i
$501$	−3.45154	+	8.33274i	−0.154203	+	0.372279i
$502$	−12.5915	−	8.87425i	−0.561984	−	0.396077i
$503$	−16.4206	+	16.4206i	−0.732158	+	0.732158i	−0.971047	−	0.238889i	$-0.923217\pi$
$503$	−16.4206	+	16.4206i	−0.732158	+	0.732158i	0.238889	+	0.971047i	$0.423217\pi$
$504$	3.94464	+	3.08484i	0.175708	+	0.137410i
$505$	−33.5168	−	33.5168i	−1.49148	−	1.49148i
$506$	−6.02081	−	34.7682i	−0.267657	−	1.54564i
$507$	−9.06044	−	3.75296i	−0.402388	−	0.166675i
$508$	−12.4535	−	5.90030i	−0.552533	−	0.261784i
$509$	−1.21719	−	2.93855i	−0.0539509	−	0.130249i	0.894606	−	0.446856i	$-0.147456\pi$
$509$	−1.21719	−	2.93855i	−0.0539509	−	0.130249i	−0.948557	+	0.316607i	$0.897456\pi$
$510$	−24.5067	−	5.51184i	−1.08518	−	0.244068i
$511$	2.95697			0.130809
$512$	9.23218	−	20.6583i	0.408008	−	0.912978i
$513$	−11.7770			−0.519969
$514$	34.1046	+	7.67050i	1.50429	+	0.338331i
$515$	1.24627	+	3.00875i	0.0549170	+	0.132581i
$516$	−6.84281	−	3.24205i	−0.301238	−	0.142723i
$517$	10.1551	+	4.20638i	0.446621	+	0.184997i
$518$	−1.76643	−	10.2006i	−0.0776126	−	0.448188i
$519$	−13.6835	−	13.6835i	−0.600637	−	0.600637i
$520$	18.2060	+	14.2377i	0.798387	+	0.624365i
$521$	2.47792	−	2.47792i	0.108560	−	0.108560i	−0.650741	−	0.759300i	$-0.725541\pi$
$521$	2.47792	−	2.47792i	0.108560	−	0.108560i	0.759300	+	0.650741i	$0.225541\pi$
$522$	−14.5135	−	10.2289i	−0.635238	−	0.447705i
$523$	−6.15101	+	14.8499i	−0.268965	+	0.649339i	−0.999435	−	0.0336055i	$-0.989301\pi$
$523$	−6.15101	+	14.8499i	−0.268965	+	0.649339i	0.730470	+	0.682945i	$0.239301\pi$
$524$	−0.228655	+	4.59133i	−0.00998885	+	0.200573i
$525$	11.3379	−	4.69632i	0.494827	−	0.204964i
$526$	3.34751	+	5.29023i	0.145958	+	0.230665i
$527$			34.0075i			1.48139i
$528$	−9.74062	−	11.9016i	−0.423906	−	0.517951i
$529$		−	28.7778i		−	1.25121i
$530$	−59.9651	+	37.9442i	−2.60472	+	1.64819i
$531$	4.24661	−	1.75900i	0.184287	−	0.0763342i
$532$	2.98811	+	3.30134i	0.129551	+	0.143131i
$533$	1.47371	−	3.55785i	0.0638335	−	0.154108i
$534$	11.6518	−	16.5324i	0.504222	−	0.715428i
$535$	−6.87100	+	6.87100i	−0.297059	+	0.297059i
$536$	−0.624216	+	2.24680i	−0.0269620	+	0.0970470i
$537$	−12.1509	−	12.1509i	−0.524350	−	0.524350i
$538$	28.6858	−	4.96751i	1.23673	−	0.214164i
$539$	−3.20352	−	1.32694i	−0.137985	−	0.0571554i
$540$	14.2595	+	39.9374i	0.613632	+	1.71863i
$541$	−0.620742	−	1.49860i	−0.0266878	−	0.0644300i	0.909974	−	0.414666i	$-0.136101\pi$
$541$	−0.620742	−	1.49860i	−0.0266878	−	0.0644300i	−0.936662	+	0.350236i	$0.886101\pi$
$542$	1.97423	−	8.77782i	0.0848004	−	0.377040i
$543$	−23.7910			−1.02097
$544$	−20.2090	+	10.1298i	−0.866454	+	0.434311i
$545$	17.9570			0.769193
$546$	0.701458	−	3.11882i	0.0300196	−	0.133473i
$547$	−13.7263	−	33.1383i	−0.586896	−	1.41689i	−0.886455	−	0.462815i	$-0.846840\pi$
$547$	−13.7263	−	33.1383i	−0.586896	−	1.41689i	0.299559	−	0.954078i	$-0.403160\pi$
$548$	2.83912	−	1.01370i	0.121281	−	0.0433030i
$549$	−16.4888	−	6.82990i	−0.703726	−	0.291493i
$550$	53.4760	−	9.26043i	2.28022	−	0.394866i
$551$	−11.1642	−	11.1642i	−0.475613	−	0.475613i
$552$	−11.1037	−	19.6471i	−0.472606	−	0.836234i
$553$	−6.53115	+	6.53115i	−0.277733	+	0.277733i
$554$	1.63922	−	2.32586i	0.0696440	−	0.0988162i
$555$	12.4511	−	30.0597i	0.528522	−	1.27596i
$556$	6.51273	−	5.89482i	0.276201	−	0.249996i
$557$	15.8664	−	6.57207i	0.672280	−	0.278468i	−0.0203155	−	0.999794i	$-0.506467\pi$
$557$	15.8664	−	6.57207i	0.672280	−	0.278468i	0.692596	+	0.721326i	$0.256467\pi$
$558$	18.0057	−	11.3935i	0.762241	−	0.482324i
$559$		−	6.96035i		−	0.294392i
$560$	7.57726	−	14.1303i	0.320198	−	0.597113i
$561$			15.3647i			0.648698i
$562$	−17.8217	−	28.1645i	−0.751764	−	1.18805i
$563$	−31.6643	+	13.1158i	−1.33449	+	0.552765i	−0.931934	−	0.362629i	$-0.881879\pi$
$563$	−31.6643	+	13.1158i	−1.33449	+	0.552765i	−0.402559	+	0.915394i	$0.631879\pi$
$564$	7.02133	+	0.349673i	0.295651	+	0.0147239i
$565$	−0.196820	+	0.475165i	−0.00828027	+	0.0199903i
$566$	−6.68139	−	4.70893i	−0.280840	−	0.197931i
$567$	0.391763	−	0.391763i	0.0164525	−	0.0164525i
$568$	3.01982	+	24.6892i	0.126709	+	1.03594i
$569$	−2.50103	−	2.50103i	−0.104849	−	0.104849i	0.652736	−	0.757585i	$-0.273621\pi$
$569$	−2.50103	−	2.50103i	−0.104849	−	0.104849i	−0.757585	+	0.652736i	$0.773621\pi$
$570$	2.38792	+	13.7895i	0.100019	+	0.577578i
$571$	−10.0887	−	4.17887i	−0.422198	−	0.174880i	0.161461	−	0.986879i	$-0.448379\pi$
$571$	−10.0887	−	4.17887i	−0.422198	−	0.174880i	−0.583659	+	0.811999i	$0.698379\pi$
$572$	6.05303	−	12.7758i	0.253090	−	0.534183i
$573$	4.33478	+	10.4651i	0.181088	+	0.437185i
$574$	−2.60645	−	0.586220i	−0.108791	−	0.0244684i
$575$	79.6379			3.32113
$576$	12.1339	+	7.30614i	0.505580	+	0.304422i
$577$	6.21937			0.258916			0.129458	−	0.991585i	$-0.458676\pi$
$577$	6.21937			0.258916			0.129458	+	0.991585i	$0.458676\pi$
$578$	−1.42214	−	0.319856i	−0.0591534	−	0.0133042i
$579$	0.567168	+	1.36927i	0.0235707	+	0.0569047i
$580$	−24.3418	+	51.3769i	−1.01074	+	2.13331i
$581$	−4.95210	−	2.05123i	−0.205448	−	0.0850992i
$582$	2.61336	+	15.0913i	0.108327	+	0.625554i
$583$	30.6925	+	30.6925i	1.27115	+	1.27115i
$584$	8.30170	−	1.01541i	0.343527	−	0.0420179i
$585$	−10.2298	+	10.2298i	−0.422952	+	0.422952i
$586$	−15.2633	−	10.7573i	−0.630522	−	0.444381i
$587$	−3.46382	+	8.36239i	−0.142967	+	0.345153i	−0.979102	−	0.203371i	$-0.934810\pi$
$587$	−3.46382	+	8.36239i	−0.142967	+	0.345153i	0.836135	+	0.548524i	$0.184810\pi$
$588$	−2.21494	−	0.110307i	−0.0913426	−	0.00454900i
$589$	17.5046	−	7.25065i	0.721265	−	0.298758i
$590$	−7.86952	−	12.4366i	−0.323983	−	0.512006i
$591$		−	5.78208i		−	0.237843i
$592$	−8.46210	−	28.0316i	−0.347790	−	1.15209i
$593$			2.15762i			0.0886029i	0.999018	+	0.0443014i	$0.0141062\pi$
$593$			2.15762i			0.0886029i	−0.999018	+	0.0443014i	$0.985894\pi$
$594$	21.9195	−	13.8701i	0.899370	−	0.569096i
$595$	−14.7990	+	6.12994i	−0.606699	+	0.251303i
$596$	6.26705	−	5.67245i	0.256709	−	0.232353i
$597$	−8.81447	+	21.2800i	−0.360752	+	0.870933i
$598$	11.9507	−	16.9566i	0.488701	−	0.693406i
$599$	−19.8845	+	19.8845i	−0.812458	+	0.812458i	−0.985002	−	0.172544i	$-0.944801\pi$
$599$	−19.8845	+	19.8845i	−0.812458	+	0.812458i	0.172544	+	0.985002i	$0.444801\pi$
$600$	30.2186	−	17.0783i	1.23367	−	0.697220i
$601$	−9.17640	−	9.17640i	−0.374313	−	0.374313i	0.494732	−	0.869045i	$-0.335266\pi$
$601$	−9.17640	−	9.17640i	−0.374313	−	0.374313i	−0.869045	+	0.494732i	$0.835266\pi$
$602$	−4.75783	+	0.823912i	−0.193915	+	0.0335801i
$603$	−1.34855	−	0.558590i	−0.0549174	−	0.0227475i
$604$	38.3672	−	13.6989i	1.56114	−	0.557399i
$605$	−1.56969	−	3.78956i	−0.0638168	−	0.154067i
$606$	−4.06896	+	18.0914i	−0.165290	+	0.734915i
$607$	33.4990			1.35968			0.679842	−	0.733359i	$-0.262048\pi$
$607$	33.4990			1.35968			0.679842	+	0.733359i	$0.262048\pi$
$608$	9.52280	+	8.24241i	0.386200	+	0.334274i
$609$	7.86337			0.318640
$610$	−12.5392	+	55.7519i	−0.507698	+	2.25733i
$611$	2.47297	+	5.97028i	0.100046	+	0.241532i
$612$	−4.75807	−	13.3262i	−0.192334	−	0.538679i
$613$	16.4402	+	6.80976i	0.664014	+	0.275044i	0.689127	−	0.724641i	$-0.257994\pi$
$613$	16.4402	+	6.80976i	0.664014	+	0.275044i	−0.0251123	+	0.999685i	$0.507994\pi$
$614$	−12.0849	+	2.09274i	−0.487707	+	0.0844562i
$615$	−5.93717	−	5.93717i	−0.239410	−	0.239410i
$616$	−9.44955	−	2.62532i	−0.380733	−	0.105777i
$617$	12.4869	−	12.4869i	0.502702	−	0.502702i	−0.409575	−	0.912277i	$-0.634323\pi$
$617$	12.4869	−	12.4869i	0.502702	−	0.502702i	0.912277	+	0.409575i	$0.134323\pi$
$618$	0.733951	−	1.04139i	0.0295239	−	0.0418907i
$619$	−2.94179	+	7.10210i	−0.118240	+	0.285458i	−0.971908	−	0.235360i	$-0.924373\pi$
$619$	−2.94179	+	7.10210i	−0.118240	+	0.285458i	0.853668	+	0.520818i	$0.174373\pi$
$620$	−45.7823	−	50.5813i	−1.83866	−	2.03139i
$621$	35.1656	−	14.5661i	1.41115	−	0.584516i
$622$	−36.0876	+	22.8352i	−1.44698	+	0.915609i
$623$		−	12.8980i		−	0.516747i
$624$	0.898356	−	8.99699i	0.0359630	−	0.360168i
$625$			42.1515i			1.68606i
$626$	7.19825	+	11.3757i	0.287700	+	0.454666i
$627$	7.90865	−	3.27587i	0.315841	−	0.130826i
$628$	−0.916992	+	18.4129i	−0.0365920	+	0.734756i
$629$	−11.1946	+	27.0261i	−0.446358	+	1.07760i
$630$	8.20364	+	5.78179i	0.326841	+	0.230352i
$631$	−11.1311	+	11.1311i	−0.443121	+	0.443121i	−0.893060	−	0.449938i	$-0.851446\pi$
$631$	−11.1311	+	11.1311i	−0.443121	+	0.443121i	0.449938	+	0.893060i	$0.351446\pi$
$632$	−16.0935	+	20.5790i	−0.640163	+	0.818588i
$633$	17.9295	+	17.9295i	0.712632	+	0.712632i
$634$	−0.0479764	−	0.277048i	−0.00190538	−	0.0110030i
$635$	−25.5167	−	10.5693i	−1.01260	−	0.419432i
$636$	25.0877	+	11.8863i	0.994791	+	0.471321i
$637$	−0.780120	−	1.88338i	−0.0309095	−	0.0746221i
$638$	33.9274	+	7.63064i	1.34320	+	0.302100i
$639$	−15.5695			−0.615920
$640$	16.4209	−	42.2728i	0.649094	−	1.67098i
$641$	14.5343			0.574072			0.287036	−	0.957920i	$-0.407330\pi$
$641$	14.5343			0.574072			0.287036	+	0.957920i	$0.407330\pi$
$642$	3.70878	+	0.834145i	0.146374	+	0.0329211i
$643$	17.7274	+	42.7978i	0.699101	+	1.68778i	0.725587	+	0.688130i	$0.241568\pi$
$643$	17.7274	+	42.7978i	0.699101	+	1.68778i	−0.0264860	+	0.999649i	$0.508432\pi$
$644$	−13.0055	−	6.16185i	−0.512488	−	0.242811i
$645$	−14.0207	−	5.80755i	−0.552063	−	0.228672i
$646$	−2.14694	−	12.3979i	−0.0844701	−	0.487787i
$647$	1.39587	+	1.39587i	0.0548772	+	0.0548772i	0.734013	−	0.679136i	$-0.237645\pi$
$647$	1.39587	+	1.39587i	0.0548772	+	0.0548772i	−0.679136	+	0.734013i	$0.737645\pi$
$648$	0.965347	−	1.23441i	0.0379224	−	0.0484921i
$649$	−6.36554	+	6.36554i	−0.249869	+	0.249869i
$650$	26.0804	+	18.3810i	1.02296	+	0.720964i
$651$	−3.61112	+	8.71801i	−0.141531	+	0.341686i
$652$	0.976864	−	19.6151i	0.0382569	−	0.768188i
$653$	34.2784	−	14.1986i	1.34142	−	0.555633i	0.407527	−	0.913193i	$-0.366391\pi$
$653$	34.2784	−	14.1986i	1.34142	−	0.555633i	0.933890	+	0.357560i	$0.116391\pi$
$654$	−3.75635	−	5.93634i	−0.146885	−	0.232129i
$655$			9.21340i			0.359997i
$656$	−7.51894	−	0.750771i	−0.293565	−	0.0293127i
$657$			5.23522i			0.204245i
$658$	3.78832	−	2.39714i	0.147684	−	0.0934503i
$659$	23.3595	−	9.67583i	0.909958	−	0.376917i	0.121917	−	0.992540i	$-0.461096\pi$
$659$	23.3595	−	9.67583i	0.909958	−	0.376917i	0.788040	+	0.615623i	$0.211096\pi$
$660$	−20.6846	−	22.8528i	−0.805146	−	0.889544i
$661$	−6.63744	+	16.0242i	−0.258167	+	0.623269i	−0.998817	−	0.0486210i	$-0.984517\pi$
$661$	−6.63744	+	16.0242i	−0.258167	+	0.623269i	0.740651	+	0.671890i	$0.234517\pi$
$662$	6.86111	−	9.73507i	0.266665	−	0.378364i
$663$	−6.38733	+	6.38733i	−0.248063	+	0.248063i
$664$	−14.6074	−	4.05830i	−0.566877	−	0.157492i
$665$	6.31050	+	6.31050i	0.244711	+	0.244711i
$666$	18.0598	−	3.12742i	0.699804	−	0.121185i
$667$	47.1440	+	19.5277i	1.82542	+	0.756114i
$668$	5.47020	+	15.3207i	0.211648	+	0.592775i
$669$	−10.1316	−	24.4599i	−0.391711	−	0.945674i
$670$	−1.02553	+	4.55972i	−0.0396197	+	0.176157i
$671$	34.9541			1.34939
$672$	−6.25633	+	0.450912i	−0.241343	+	0.0173943i
$673$	−30.1958			−1.16396			−0.581980	−	0.813203i	$-0.697722\pi$
$673$	−30.1958			−1.16396			−0.581980	+	0.813203i	$0.697722\pi$
$674$	7.23534	−	32.1698i	0.278695	−	1.23913i
$675$	22.4037	+	54.0872i	0.862317	+	2.08182i
$676$	−16.6586	+	5.94790i	−0.640716	+	0.228766i
$677$	44.6271	+	18.4851i	1.71516	+	0.710442i	0.999933	+	0.0115465i	$0.00367546\pi$
$677$	44.6271	+	18.4851i	1.71516	+	0.710442i	0.715224	+	0.698895i	$0.246325\pi$
$678$	0.198255	−	0.0343318i	0.00761394	−	0.00131850i
$679$	6.90626	+	6.90626i	0.265038	+	0.265038i
$680$	−39.4432	+	22.2917i	−1.51258	+	0.854848i
$681$	−16.0470	+	16.0470i	−0.614922	+	0.614922i
$682$	−24.0405	+	34.1105i	−0.920559	+	1.30616i
$683$	9.95564	−	24.0350i	0.380942	−	0.919675i	−0.610842	−	0.791752i	$-0.709169\pi$
$683$	9.95564	−	24.0350i	0.380942	−	0.919675i	0.991784	−	0.127923i	$-0.0408309\pi$
$684$	−5.84491	+	5.29036i	−0.223486	+	0.202282i
$685$	5.58209	−	2.31218i	0.213281	−	0.0883438i
$686$	−1.19506	+	0.756199i	−0.0456275	+	0.0288718i
$687$			2.07540i			0.0791816i
$688$	−13.0747	+	3.94695i	−0.498468	+	0.150476i
$689$			25.5186i			0.972182i
$690$	−24.1853	−	38.2212i	−0.920718	−	1.45506i
$691$	38.8924	−	16.1098i	1.47954	−	0.612844i	0.510525	−	0.859863i	$-0.329451\pi$
$691$	38.8924	−	16.1098i	1.47954	−	0.612844i	0.969011	+	0.247019i	$0.0794510\pi$
$692$	−34.8605	−	1.73611i	−1.32520	−	0.0659968i
$693$	2.34931	−	5.67173i	0.0892427	−	0.215451i
$694$	−25.4333	−	17.9249i	−0.965434	−	0.680421i
$695$	12.4491	−	12.4491i	0.472221	−	0.472221i
$696$	22.0764	−	2.70025i	0.836806	−	0.102353i
$697$	5.33800	+	5.33800i	0.202191	+	0.202191i
$698$	5.46934	+	31.5837i	0.207018	+	1.19546i
$699$	8.45054	+	3.50033i	0.319629	+	0.132395i
$700$	9.47737	−	20.0034i	0.358211	−	0.756056i
$701$	−17.1972	−	41.5176i	−0.649528	−	1.56810i	−0.813456	−	0.581626i	$-0.802417\pi$
$701$	−17.1972	−	41.5176i	−0.649528	−	1.56810i	0.163929	−	0.986472i	$-0.447583\pi$
$702$	14.8783	+	3.34628i	0.561543	+	0.126297i
$703$	16.2979			0.614687
$704$	−27.4312	−	4.12566i	−1.03385	−	0.155491i
$705$	14.0897			0.530648
$706$	16.3681	+	3.68136i	0.616020	+	0.138550i
$707$	4.52526	+	10.9249i	0.170190	+	0.410875i
$708$	−2.46518	+	5.20311i	−0.0926470	+	0.195545i
$709$	−32.3176	−	13.3864i	−1.21371	−	0.502736i	−0.318306	−	0.947988i	$-0.603114\pi$
$709$	−32.3176	−	13.3864i	−1.21371	−	0.502736i	−0.895405	+	0.445252i	$0.853114\pi$
$710$	8.50612	+	49.1201i	0.319229	+	1.84345i
$711$	−11.5632	−	11.5632i	−0.433653	−	0.433653i
$712$	−4.42911	−	36.2112i	−0.165988	−	1.35707i
$713$	−43.3001	+	43.3001i	−1.62160	+	1.62160i
$714$	5.12221	+	3.61005i	0.191694	+	0.135103i
$715$	10.8429	−	26.1772i	0.405503	−	0.978970i
$716$	−30.9561	−	1.54166i	−1.15688	−	0.0576146i
$717$	−24.8247	+	10.2827i	−0.927097	+	0.384016i
$718$	0.555654	+	0.878127i	0.0207368	+	0.0327714i
$719$			8.83327i			0.329426i	0.986342	+	0.164713i	$0.0526697\pi$
$719$			8.83327i			0.329426i	−0.986342	+	0.164713i	$0.947330\pi$
$720$	25.0172	+	13.4153i	0.932336	+	0.499959i
$721$		−	0.812451i		−	0.0302573i
$722$	16.7823	−	10.6194i	0.624573	−	0.395212i
$723$	−2.24267	+	0.928946i	−0.0834059	+	0.0345479i
$724$	−31.8147	+	28.7962i	−1.18238	+	1.07020i
$725$	−30.0349	+	72.5108i	−1.11547	+	2.69298i
$726$	−0.924420	+	1.31164i	−0.0343084	+	0.0486794i
$727$	10.6261	−	10.6261i	0.394099	−	0.394099i	−0.482046	−	0.876146i	$-0.660106\pi$
$727$	10.6261	−	10.6261i	0.394099	−	0.394099i	0.876146	+	0.482046i	$0.160106\pi$
$728$	−2.83693	−	5.01970i	−0.105144	−	0.186042i
$729$	13.1361	+	13.1361i	0.486522	+	0.486522i
$730$	16.5165	−	2.86017i	0.611305	−	0.105860i
$731$	12.6057	+	5.22146i	0.466239	+	0.193123i
$732$	21.0538	−	7.51720i	0.778172	−	0.277844i
$733$	−6.91692	−	16.6989i	−0.255482	−	0.616789i	0.743147	−	0.669128i	$-0.233332\pi$
$733$	−6.91692	−	16.6989i	−0.255482	−	0.616789i	−0.998629	+	0.0523392i	$0.983332\pi$
$734$	6.48276	−	28.8237i	0.239283	−	1.06390i
$735$	−4.44471			−0.163946
$736$	−38.6289	−	12.8334i	−1.42388	−	0.473045i
$737$	2.85875			0.105304
$738$	1.03788	−	4.61464i	0.0382051	−	0.169867i
$739$	9.07991	+	21.9208i	0.334010	+	0.806371i	0.998266	+	0.0588659i	$0.0187484\pi$
$739$	9.07991	+	21.9208i	0.334010	+	0.806371i	−0.664256	+	0.747505i	$0.731252\pi$
$740$	−19.7333	−	55.2682i	−0.725411	−	2.03170i
$741$	4.64956	+	1.92591i	0.170806	+	0.0707502i
$742$	17.4435	−	3.02069i	0.640372	−	0.110893i
$743$	−19.1248	−	19.1248i	−0.701621	−	0.701621i	0.263137	−	0.964758i	$-0.415243\pi$
$743$	−19.1248	−	19.1248i	−0.701621	−	0.701621i	−0.964758	+	0.263137i	$0.915243\pi$
$744$	−7.14450	+	25.7159i	−0.261930	+	0.942790i
$745$	11.9795	−	11.9795i	0.438894	−	0.438894i
$746$	0.857161	−	1.21621i	0.0313829	−	0.0445285i
$747$	3.63163	−	8.76753i	0.132874	−	0.320787i
$748$	18.5971	+	20.5465i	0.679978	+	0.751256i
$749$	2.23963	−	0.927686i	0.0818344	−	0.0338969i
$750$	32.2285	−	20.3933i	1.17682	−	0.744657i
$751$		−	25.3046i		−	0.923380i	−0.887041	−	0.461690i	$-0.847243\pi$
$751$		−	25.3046i		−	0.923380i	0.887041	−	0.461690i	$-0.152757\pi$
$752$	9.81255	−	8.03087i	0.357827	−	0.292856i
$753$			12.0782i			0.440153i
$754$	10.9319	+	17.2763i	0.398117	+	0.629164i
$755$	75.4352	−	31.2463i	2.74537	−	1.13717i
$756$	0.526218	−	10.5663i	0.0191384	−	0.384293i
$757$	3.78355	−	9.13430i	0.137516	−	0.331992i	−0.840087	−	0.542452i	$-0.817496\pi$
$757$	3.78355	−	9.13430i	0.137516	−	0.331992i	0.977602	+	0.210460i	$0.0674961\pi$
$758$	25.2001	+	17.7606i	0.915308	+	0.645093i
$759$	−19.5631	+	19.5631i	−0.710097	+	0.710097i
$760$	19.8838	+	15.5498i	0.721260	+	0.564049i
$761$	−28.0212	−	28.0212i	−1.01577	−	1.01577i	−0.999874	−	0.0158923i	$-0.994941\pi$
$761$	−28.0212	−	28.0212i	−1.01577	−	1.01577i	−0.0158923	−	0.999874i	$-0.505059\pi$
$762$	1.84364	+	10.6464i	0.0667880	+	0.385679i
$763$	−4.13881	−	1.71435i	−0.149835	−	0.0620636i
$764$	18.4634	+	8.74777i	0.667984	+	0.316483i
$765$	−10.8529	−	26.2011i	−0.392386	−	0.947303i
$766$	−3.96629	−	0.892062i	−0.143308	−	0.0322315i
$767$	−5.29249			−0.191101
$768$	−17.4098	+	3.41433i	−0.628223	+	0.123204i
$769$	6.76588			0.243984			0.121992	−	0.992531i	$-0.461072\pi$
$769$	6.76588			0.243984			0.121992	+	0.992531i	$0.461072\pi$
$770$	−19.1772	−	4.31316i	−0.691098	−	0.155435i
$771$	−10.4887	−	25.3221i	−0.377743	−	0.911952i
$772$	2.41578	+	1.14457i	0.0869458	+	0.0411940i
$773$	28.0963	+	11.6379i	1.01055	+	0.418585i	0.825657	−	0.564173i	$-0.190805\pi$
$773$	28.0963	+	11.6379i	1.01055	+	0.418585i	0.184897	+	0.982758i	$0.440805\pi$
$774$	−1.45871	−	8.42358i	−0.0524323	−	0.302779i
$775$	−66.5986	−	66.5986i	−2.39229	−	2.39229i
$776$	21.7609	+	17.0178i	0.781172	+	0.610902i
$777$	−5.73959	+	5.73959i	−0.205907	+	0.205907i
$778$	−42.9370	−	30.2613i	−1.53937	−	1.08492i
$779$	1.60952	−	3.88572i	0.0576669	−	0.139220i
$780$	0.901364	−	18.0991i	0.0322740	−	0.648052i
$781$	28.1717	−	11.6691i	1.00806	−	0.417554i
$782$	21.7445	+	34.3640i	0.777583	+	1.22885i
$783$			37.5120i			1.34057i
$784$	−3.09545	+	2.53341i	−0.110552	+	0.0904789i
$785$			36.9491i			1.31877i
$786$	3.04582	−	1.92731i	0.108641	−	0.0687449i
$787$	−13.6911	+	5.67103i	−0.488034	+	0.202150i	−0.613111	−	0.789997i	$-0.710082\pi$
$787$	−13.6911	+	5.67103i	−0.488034	+	0.202150i	0.125077	+	0.992147i	$0.460082\pi$
$788$	−6.99851	−	7.73212i	−0.249312	−	0.275445i
$789$	1.87843	−	4.53493i	0.0668739	−	0.161448i
$790$	−30.1633	+	42.7979i	−1.07316	+	1.52268i
$791$	0.0907278	−	0.0907278i	0.00322591	−	0.00322591i
$792$	4.64804	−	16.7301i	0.165161	−	0.594479i
$793$	14.5309	+	14.5309i	0.516008	+	0.516008i
$794$	45.6397	−	7.90342i	1.61969	−	0.280482i
$795$	51.4037	+	21.2921i	1.82310	+	0.755153i
$796$	13.9697	+	39.1257i	0.495143	+	1.38677i
$797$	−0.393333	−	0.949589i	−0.0139326	−	0.0336362i	0.916760	−	0.399438i	$-0.130795\pi$
$797$	−0.393333	−	0.949589i	−0.0139326	−	0.0336362i	−0.930693	+	0.365802i	$0.880795\pi$
$798$	0.766100	−	3.40623i	0.0271196	−	0.120579i
$799$	−12.6678			−0.448153
$800$	19.7387	−	59.4140i	0.697868	−	2.10060i
$801$	22.8355			0.806852
$802$	−11.2116	+	49.8491i	−0.395896	+	1.76023i
$803$	−3.92372	−	9.47269i	−0.138465	−	0.334284i
$804$	1.72191	−	0.614802i	0.0607270	−	0.0216824i
$805$	−26.6478	−	11.0379i	−0.939210	−	0.389034i
$806$	−24.1742	+	4.18625i	−0.851501	+	0.147454i
$807$	−16.1407	−	16.1407i	−0.568179	−	0.568179i
$808$	16.4563	+	29.1179i	0.578929	+	1.02436i
$809$	21.5861	−	21.5861i	0.758926	−	0.758926i	−0.217201	−	0.976127i	$-0.569693\pi$
$809$	21.5861	−	21.5861i	0.758926	−	0.758926i	0.976127	+	0.217201i	$0.0696927\pi$
$810$	1.80931	−	2.56718i	0.0635726	−	0.0902017i
$811$	−0.128421	+	0.310037i	−0.00450948	+	0.0108869i	−0.926118	−	0.377233i	$-0.876875\pi$
$811$	−0.128421	+	0.310037i	−0.00450948	+	0.0108869i	0.921609	+	0.388120i	$0.126875\pi$
$812$	10.5153	−	9.51766i	0.369016	−	0.334005i
$813$	−6.51737	+	2.69958i	−0.228574	+	0.0946786i
$814$	−30.3338	+	19.1944i	−1.06320	+	0.672762i
$815$		−	39.3616i		−	1.37878i
$816$	15.6203	+	8.37628i	0.546820	+	0.293228i
$817$		−	7.60177i		−	0.265952i
$818$	−13.3717	−	21.1320i	−0.467531	−	0.738862i
$819$	3.33446	−	1.38118i	0.116515	−	0.0482622i
$820$	−15.1257	−	0.753285i	−0.528214	−	0.0263059i
$821$	11.6283	−	28.0731i	0.405829	−	0.979758i	−0.580394	−	0.814336i	$-0.697101\pi$
$821$	11.6283	−	28.0731i	0.405829	−	0.979758i	0.986223	−	0.165422i	$-0.0528986\pi$
$822$	−1.93207	−	1.36169i	−0.0673886	−	0.0474944i
$823$	11.4890	−	11.4890i	0.400482	−	0.400482i	−0.477921	−	0.878403i	$-0.658609\pi$
$823$	11.4890	−	11.4890i	0.400482	−	0.400482i	0.878403	+	0.477921i	$0.158609\pi$
$824$	−0.278992	−	2.28096i	−0.00971915	−	0.0794610i
$825$	−30.0895	−	30.0895i	−1.04758	−	1.04758i
$826$	0.626484	+	3.61774i	0.0217982	+	0.125877i
$827$	22.7523	+	9.42431i	0.791175	+	0.327715i	0.741416	−	0.671046i	$-0.234155\pi$
$827$	22.7523	+	9.42431i	0.791175	+	0.327715i	0.0497589	+	0.998761i	$0.484155\pi$
$828$	10.9094	−	23.0258i	0.379127	−	0.800202i
$829$	13.0923	+	31.6076i	0.454714	+	1.09778i	0.970509	+	0.241065i	$0.0774966\pi$
$829$	13.0923	+	31.6076i	0.454714	+	1.09778i	−0.515795	+	0.856712i	$0.672503\pi$
$830$	−29.6447	−	6.66742i	−1.02898	−	0.231429i
$831$	−2.23104			−0.0773941
$832$	−9.68844	−	13.1186i	−0.335886	−	0.454807i
$833$	3.99616			0.138459
$834$	−6.71967	−	1.51133i	−0.232683	−	0.0523330i
$835$	12.4772	+	30.1226i	0.431790	+	1.04243i
$836$	6.61084	−	13.9531i	0.228641	−	0.482579i
$837$	−41.5890	−	17.2267i	−1.43753	−	0.595443i
$838$	3.44071	+	19.8690i	0.118857	+	0.686362i
$839$	−12.2520	−	12.2520i	−0.422984	−	0.422984i	0.463246	−	0.886230i	$-0.346685\pi$
$839$	−12.2520	−	12.2520i	−0.422984	−	0.422984i	−0.886230	+	0.463246i	$0.846685\pi$
$840$	−12.4785	+	1.52629i	−0.430551	+	0.0526621i
$841$	−15.0540	+	15.0540i	−0.519103	+	0.519103i
$842$	0.621791	+	0.438228i	0.0214283	+	0.0151023i
$843$	−10.0005	+	24.1434i	−0.344437	+	0.831544i
$844$	45.6777	+	2.27482i	1.57229	+	0.0783026i
$845$	−32.7531	+	13.5668i	−1.12674	+	0.466712i
$846$	4.24406	+	6.70710i	0.145914	+	0.230595i
$847$			1.02329i			0.0351607i
$848$	47.9355	−	14.4706i	1.64611	−	0.496924i
$849$			6.40902i			0.219957i
$850$	−52.8542	+	33.4447i	−1.81289	+	1.14714i
$851$	−48.6646	+	20.1575i	−1.66820	+	0.690992i
$852$	14.4591	−	13.0872i	0.495360	−	0.448361i
$853$	8.77174	−	21.1769i	0.300339	−	0.725082i	−0.699606	−	0.714529i	$-0.746641\pi$
$853$	8.77174	−	21.1769i	0.300339	−	0.725082i	0.999944	−	0.0105525i	$-0.00335903\pi$
$854$	8.21271	−	11.6528i	0.281033	−	0.398751i
$855$	−11.1725	+	11.1725i	−0.382093	+	0.382093i
$856$	5.96921	−	3.37356i	0.204024	−	0.115306i
$857$	−13.5063	−	13.5063i	−0.461368	−	0.461368i	0.437736	−	0.899104i	$-0.355781\pi$
$857$	−13.5063	−	13.5063i	−0.461368	−	0.461368i	−0.899104	+	0.437736i	$0.855781\pi$
$858$	−10.9220	+	1.89136i	−0.372871	+	0.0645700i
$859$	−36.2180	−	15.0020i	−1.23574	−	0.511861i	−0.333361	−	0.942799i	$-0.608183\pi$
$859$	−36.2180	−	15.0020i	−1.23574	−	0.511861i	−0.902381	+	0.430938i	$0.858183\pi$
$860$	−25.7786	+	9.20415i	−0.879041	+	0.313859i
$861$	0.801605	+	1.93524i	0.0273186	+	0.0659530i
$862$	8.34100	−	37.0858i	0.284096	−	1.26315i
$863$	−21.7052			−0.738852			−0.369426	−	0.929260i	$-0.620446\pi$
$863$	−21.7052			−0.738852			−0.369426	+	0.929260i	$0.620446\pi$
$864$	−2.15106	−	29.8456i	−0.0731805	−	1.01537i
$865$	−69.9544			−2.37852
$866$	0.420656	−	1.87032i	0.0142945	−	0.0635561i
$867$	0.437375	+	1.05592i	0.0148540	+	0.0358608i
$868$	5.72311	+	16.0290i	0.194255	+	0.544061i
$869$	29.5891	+	12.2562i	1.00374	+	0.415763i
$870$	43.9219	−	7.60595i	1.48909	−	0.257866i
$871$	1.18842	+	1.18842i	0.0402682	+	0.0402682i
$872$	−12.2084	−	3.39180i	−0.413429	−	0.114861i
$873$	−12.2273	+	12.2273i	−0.413832	+	0.413832i
$874$	13.0520	−	18.5192i	0.441491	−	0.626421i
$875$	9.30724	−	22.4697i	0.314642	−	0.759613i
$876$	−4.40056	−	4.86184i	−0.148681	−	0.164266i
$877$	−6.12246	+	2.53600i	−0.206741	+	0.0856348i	−0.483651	−	0.875261i	$-0.660690\pi$
$877$	−6.12246	+	2.53600i	−0.206741	+	0.0856348i	0.276910	+	0.960896i	$0.410690\pi$
$878$	−35.9401	+	22.7419i	−1.21292	+	0.767501i
$879$			14.6411i			0.493833i
$880$	−55.3211	−	5.52386i	−1.86488	−	0.186209i
$881$		−	30.4993i		−	1.02755i	−0.857926	−	0.513773i	$-0.828247\pi$
$881$		−	30.4993i		−	1.02755i	0.857926	−	0.513773i	$-0.171753\pi$
$882$	−1.33883	−	2.11581i	−0.0450806	−	0.0712431i
$883$	−31.8467	+	13.1913i	−1.07173	+	0.443924i	−0.847600	−	0.530636i	$-0.821953\pi$
$883$	−31.8467	+	13.1913i	−1.07173	+	0.443924i	−0.224127	+	0.974560i	$0.571953\pi$
$884$	−0.810400	+	16.2726i	−0.0272567	+	0.547306i
$885$	−4.41593	+	10.6610i	−0.148440	+	0.358365i
$886$	3.00096	+	2.11503i	0.100819	+	0.0710557i
$887$	17.0240	−	17.0240i	0.571610	−	0.571610i	−0.360968	−	0.932578i	$-0.617554\pi$
$887$	17.0240	−	17.0240i	0.571610	−	0.571610i	0.932578	+	0.360968i	$0.117554\pi$
$888$	−14.1430	+	18.0849i	−0.474607	+	0.606889i
$889$	4.87214	+	4.87214i	0.163406	+	0.163406i
$890$	−12.4758	−	72.0435i	−0.418188	−	2.41490i
$891$	−1.77487	−	0.735174i	−0.0594603	−	0.0246292i
$892$	−43.1543	−	20.4460i	−1.44491	−	0.684584i
$893$	2.70086	+	6.52046i	0.0903809	+	0.218199i
$894$	−6.46619	−	1.45432i	−0.216262	−	0.0486396i
$895$	−62.1194			−2.07642
$896$	−7.82054	+	8.17552i	−0.261266	+	0.273125i
$897$	−16.2653			−0.543084
$898$	−44.4232	−	9.99128i	−1.48242	−	0.333413i
$899$	−23.0946	−	55.7553i	−0.770248	−	1.85954i
$900$	35.4153	+	16.7794i	1.18051	+	0.559313i
$901$	−46.2161	−	19.1433i	−1.53968	−	0.637757i
$902$	1.58064	+	9.12770i	0.0526296	+	0.303919i
$903$	2.67710	+	2.67710i	0.0890883	+	0.0890883i
$904$	0.223563	−	0.285874i	0.00743560	−	0.00950804i
$905$	−60.8138	+	60.8138i	−2.02152	+	2.02152i
$906$	−26.1096	−	18.4016i	−0.867432	−	0.611351i
$907$	0.156780	−	0.378501i	0.00520580	−	0.0125679i	−0.921255	−	0.388959i	$-0.872835\pi$
$907$	0.156780	−	0.378501i	0.00520580	−	0.0125679i	0.926461	+	0.376391i	$0.122835\pi$
$908$	−2.03598	+	40.8819i	−0.0675664	+	1.35671i
$909$	−19.3423	+	8.01183i	−0.641543	+	0.265736i
$910$	−6.17919	−	9.76527i	−0.204838	−	0.323716i
$911$		−	48.2167i		−	1.59749i	−0.601669	−	0.798745i	$-0.705497\pi$
$911$		−	48.2167i		−	1.59749i	0.601669	−	0.798745i	$-0.294503\pi$
$912$	0.981143	−	9.82609i	0.0324889	−	0.325374i
$913$			18.5860i			0.615106i
$914$	26.4646	−	16.7460i	0.875370	−	0.553909i
$915$	41.3947	−	17.1463i	1.36847	−	0.566838i
$916$	2.51203	+	2.77535i	0.0829997	+	0.0917000i
$917$	0.879601	−	2.12354i	0.0290470	−	0.0701256i
$918$	−17.2216	+	24.4353i	−0.568398	+	0.806486i
$919$	20.5977	−	20.5977i	0.679454	−	0.679454i	−0.280423	−	0.959877i	$-0.590475\pi$
$919$	20.5977	−	20.5977i	0.679454	−	0.679454i	0.959877	+	0.280423i	$0.0904746\pi$
$920$	−78.6041	−	21.8381i	−2.59150	−	0.719982i
$921$	6.79985	+	6.79985i	0.224063	+	0.224063i
$922$	18.0503	−	3.12577i	0.594456	−	0.102942i
$923$	16.5624	+	6.86038i	0.545159	+	0.225812i
$924$	2.58572	+	7.24197i	0.0850640	+	0.238243i
$925$	−31.0037	−	74.8497i	−1.01940	−	2.46104i
$926$	−9.58269	+	42.6066i	−0.314907	+	1.40014i
$927$	1.43842			0.0472439
$928$	26.2535	−	30.3318i	0.861815	−	0.995690i
$929$	47.7474			1.56654			0.783271	−	0.621681i	$-0.213550\pi$
$929$	47.7474			1.56654			0.783271	+	0.621681i	$0.213550\pi$
$930$	−11.7378	+	52.1885i	−0.384897	+	1.71133i
$931$	−0.852011	−	2.05694i	−0.0279235	−	0.0674133i
$932$	15.5373	−	5.54753i	0.508940	−	0.181715i
$933$	30.9353	+	12.8138i	1.01278	+	0.419506i
$934$	38.0874	−	6.59559i	1.24626	−	0.215814i
$935$	39.2747	+	39.2747i	1.28442	+	1.28442i
$936$	8.88721	−	5.02270i	0.290488	−	0.164172i
$937$	19.5686	−	19.5686i	0.639279	−	0.639279i	−0.311099	−	0.950378i	$-0.600697\pi$
$937$	19.5686	−	19.5686i	0.639279	−	0.639279i	0.950378	+	0.311099i	$0.100697\pi$
$938$	0.671685	−	0.953037i	0.0219313	−	0.0311178i
$939$	4.03925	−	9.75160i	0.131816	−	0.318231i
$940$	18.8415	−	17.0539i	0.614542	−	0.556235i
$941$	38.4802	−	15.9390i	1.25442	−	0.519598i	0.346227	−	0.938151i	$-0.387463\pi$
$941$	38.4802	−	15.9390i	1.25442	−	0.519598i	0.908192	+	0.418553i	$0.137463\pi$
$942$	12.2149	−	7.72923i	0.397982	−	0.251832i
$943$			13.5932i			0.442656i
$944$	3.00117	+	9.94169i	0.0976798	+	0.323574i
$945$		−	21.2034i		−	0.689745i
$946$	8.95277	+	14.1485i	0.291080	+	0.460007i
$947$	4.44575	−	1.84149i	0.144467	−	0.0598404i	−0.309278	−	0.950972i	$-0.600087\pi$
$947$	4.44575	−	1.84149i	0.144467	−	0.0598404i	0.453746	+	0.891131i	$0.350087\pi$
$948$	20.4581	+	1.01885i	0.664450	+	0.0330906i
$949$	2.30679	−	5.56908i	0.0748815	−	0.180780i
$950$	28.4838	+	20.0749i	0.924138	+	0.651316i
$951$	−0.155887	+	0.155887i	−0.00505500	+	0.00505500i
$952$	11.2192	−	1.37226i	0.363617	−	0.0444753i
$953$	16.5975	+	16.5975i	0.537645	+	0.537645i	0.922837	−	0.385192i	$-0.125865\pi$
$953$	16.5975	+	16.5975i	0.537645	+	0.537645i	−0.385192	+	0.922837i	$0.625865\pi$
$954$	5.34804	+	30.8832i	0.173149	+	0.999881i
$955$	37.8309	+	15.6701i	1.22418	+	0.507072i
$956$	−20.7510	+	43.7980i	−0.671136	+	1.41653i
$957$	−10.4342	−	25.1904i	−0.337291	−	0.814291i
$958$	23.9593	+	5.38870i	0.774089	+	0.174101i
$959$	−1.50733			−0.0486742
$960$	−34.5094	+	8.57015i	−1.11379	+	0.276600i
$961$	41.4209			1.33616
$962$	−20.5896	−	4.63082i	−0.663834	−	0.149304i
$963$	1.64244	+	3.96520i	0.0529268	+	0.127777i
$964$	−1.87465	+	3.95672i	−0.0603785	+	0.127438i
$965$	4.94984	+	2.05029i	0.159341	+	0.0660013i
$966$	1.92536	+	11.1184i	0.0619476	+	0.357727i
$967$	26.8258	+	26.8258i	0.862659	+	0.862659i	0.991646	−	0.128987i	$-0.0411725\pi$
$967$	26.8258	+	26.8258i	0.862659	+	0.862659i	−0.128987	+	0.991646i	$0.541173\pi$
$968$	0.351393	+	2.87289i	0.0112942	+	0.0923383i
$969$	−6.97594	+	6.97594i	−0.224099	+	0.224099i
$970$	45.2560	+	31.8957i	1.45308	+	1.02411i
$971$	5.46841	−	13.2019i	0.175490	−	0.423670i	−0.811521	−	0.584323i	$-0.801360\pi$
$971$	5.46841	−	13.2019i	0.175490	−	0.423670i	0.987011	+	0.160653i	$0.0513601\pi$
$972$	30.4717	+	1.51754i	0.977382	+	0.0486751i
$973$	−4.05783	+	1.68081i	−0.130088	+	0.0538843i
$974$	−6.37613	−	10.0765i	−0.204304	−	0.322872i
$975$		−	25.0173i		−	0.801194i
$976$	19.0557	−	35.5356i	0.609958	−	1.13747i
$977$		−	4.18523i		−	0.133897i	−0.997756	−	0.0669487i	$-0.978674\pi$
$977$		−	4.18523i		−	0.133897i	0.997756	−	0.0669487i	$-0.0213264\pi$
$978$	−13.0124	+	8.23389i	−0.416091	+	0.263291i
$979$	−41.3189	+	17.1149i	−1.32056	+	0.546993i
$980$	−5.94372	+	5.37979i	−0.189865	+	0.171851i
$981$	3.03520	−	7.32763i	0.0969065	−	0.233953i
$982$	23.4353	−	33.2517i	0.747849	−	1.06111i
$983$	−17.4458	+	17.4458i	−0.556435	+	0.556435i	−0.928291	−	0.371856i	$-0.878722\pi$
$983$	−17.4458	+	17.4458i	−0.556435	+	0.556435i	0.371856	+	0.928291i	$0.378722\pi$
$984$	2.91506	+	5.15794i	0.0929288	+	0.164429i
$985$	−14.7800	−	14.7800i	−0.470929	−	0.470929i
$986$	−39.4894	+	6.83837i	−1.25760	+	0.217778i
$987$	−3.24745	−	1.34514i	−0.103368	−	0.0428162i
$988$	8.54874	−	3.05230i	0.271972	−	0.0971066i
$989$	9.40202	+	22.6985i	0.298967	+	0.721770i
$990$	7.63631	−	33.9526i	0.242698	−	1.07908i
$991$	−25.9523			−0.824401			−0.412201	−	0.911093i	$-0.635240\pi$
$991$	−25.9523			−0.824401			−0.412201	+	0.911093i	$0.635240\pi$
$992$	21.5720	+	43.0363i	0.684910	+	1.36640i
$993$	−9.33822			−0.296339
$994$	2.72896	−	12.1335i	0.0865573	−	0.384851i
$995$	31.8640	+	76.9265i	1.01016	+	2.43873i
$996$	3.99709	+	11.1949i	0.126653	+	0.354723i
$997$	21.1077	+	8.74308i	0.668486	+	0.276896i	0.691005	−	0.722850i	$-0.257168\pi$
$997$	21.1077	+	8.74308i	0.668486	+	0.276896i	−0.0225183	+	0.999746i	$0.507168\pi$
$998$	18.6269	−	3.22562i	0.589626	−	0.102105i
$999$	−27.3805	−	27.3805i	−0.866282	−	0.866282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.197.1	yes	52
4.3	odd	2		896.2.u.c.113.5		52
32.13	even	8	inner	224.2.u.c.141.1	✓	52
32.19	odd	8		896.2.u.c.785.5		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.141.1	✓	52	32.13	even	8	inner
224.2.u.c.197.1	yes	52	1.1	even	1	trivial
896.2.u.c.113.5		52	4.3	odd	2
896.2.u.c.785.5		52	32.19	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37975 - 0.310320i) q^{2} +(0.424336 + 1.02444i) q^{3} +(1.80740 + 0.856327i) q^{4} +(3.70330 + 1.53396i) q^{5} +(-0.267572 - 1.54514i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.22802 - 1.74239i) q^{8} +(1.25191 - 1.25191i) q^{9} +O(q^{10})\)	\(q+(-1.37975 - 0.310320i) q^{2} +(0.424336 + 1.02444i) q^{3} +(1.80740 + 0.856327i) q^{4} +(3.70330 + 1.53396i) q^{5} +(-0.267572 - 1.54514i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.22802 - 1.74239i) q^{8} +(1.25191 - 1.25191i) q^{9} +(-4.63360 - 3.26568i) q^{10} +(-1.32694 + 3.20352i) q^{11} +(-0.110307 + 2.21494i) q^{12} +(-1.88338 + 0.780120i) q^{13} +(0.756199 + 1.19506i) q^{14} +4.44471i q^{15} +(2.53341 + 3.09545i) q^{16} -3.99616i q^{17} +(-2.11581 + 1.33883i) q^{18} +(-2.05694 + 0.852011i) q^{19} +(5.37979 + 5.94372i) q^{20} +(0.424336 - 1.02444i) q^{21} +(2.82496 - 4.00827i) q^{22} +(5.08811 - 5.08811i) q^{23} +(0.839537 - 3.02183i) q^{24} +(7.82588 + 7.82588i) q^{25} +(2.84067 - 0.491918i) q^{26} +(4.88704 + 2.02428i) q^{27} +(-0.672512 - 1.88354i) q^{28} +(2.71380 + 6.55170i) q^{29} +(1.37928 - 6.13258i) q^{30} -8.51005 q^{31} +(-2.53488 - 5.05711i) q^{32} -3.84487 q^{33} +(-1.24009 + 5.51369i) q^{34} +(-1.53396 - 3.70330i) q^{35} +(3.33475 - 1.19066i) q^{36} +(-6.76303 - 2.80134i) q^{37} +(3.10245 - 0.537250i) q^{38} +(-1.59837 - 1.59837i) q^{39} +(-5.57829 - 9.87028i) q^{40} +(-1.33578 + 1.33578i) q^{41} +(-0.903379 + 1.28178i) q^{42} +(-1.30662 + 3.15446i) q^{43} +(-5.14157 + 4.65375i) q^{44} +(6.55658 - 2.71582i) q^{45} +(-8.59925 + 5.44136i) q^{46} -3.16999i q^{47} +(-2.09608 + 3.90883i) q^{48} +1.00000i q^{49} +(-8.36921 - 13.2263i) q^{50} +(4.09381 - 1.69571i) q^{51} +(-4.07206 - 0.202795i) q^{52} +(4.79044 - 11.5651i) q^{53} +(-6.11471 - 4.30954i) q^{54} +(-9.82812 + 9.82812i) q^{55} +(0.343395 + 2.80750i) q^{56} +(-1.74566 - 1.74566i) q^{57} +(-1.71124 - 9.88184i) q^{58} +(2.39858 + 0.993524i) q^{59} +(-3.80613 + 8.03338i) q^{60} +(-3.85768 - 9.31326i) q^{61} +(11.7417 + 2.64084i) q^{62} -1.77047 q^{63} +(1.92817 + 7.76416i) q^{64} -8.17138 q^{65} +(5.30495 + 1.19314i) q^{66} +(-0.315504 - 0.761694i) q^{67} +(3.42202 - 7.22266i) q^{68} +(7.37152 + 3.05338i) q^{69} +(0.967264 + 5.58564i) q^{70} +(-6.21830 - 6.21830i) q^{71} +(-4.97060 + 0.607971i) q^{72} +(-2.09089 + 2.09089i) q^{73} +(8.46196 + 5.96385i) q^{74} +(-4.69632 + 11.3379i) q^{75} +(-4.44731 - 0.221483i) q^{76} +(3.20352 - 1.32694i) q^{77} +(1.70934 + 2.70135i) q^{78} -9.23644i q^{79} +(4.63368 + 15.3495i) q^{80} +0.554037i q^{81} +(2.25756 - 1.42852i) q^{82} +(4.95210 - 2.05123i) q^{83} +(1.64420 - 1.48820i) q^{84} +(6.12994 - 14.7990i) q^{85} +(2.78170 - 3.94689i) q^{86} +(-5.56024 + 5.56024i) q^{87} +(8.53822 - 4.82546i) q^{88} +(9.12026 + 9.12026i) q^{89} +(-9.88919 + 1.71251i) q^{90} +(1.88338 + 0.780120i) q^{91} +(13.5534 - 4.83918i) q^{92} +(-3.61112 - 8.71801i) q^{93} +(-0.983711 + 4.37378i) q^{94} -8.92440 q^{95} +(4.10505 - 4.74274i) q^{96} -9.76692 q^{97} +(0.310320 - 1.37975i) q^{98} +(2.34931 + 5.67173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more