LMFDB - Embedded newform 744.2.o.e.557.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [744,2,Mod(557,744)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(744, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))

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

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

chi := DirichletCharacter("744.557");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 744 = 2^{3} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	744.o (of order $2$, degree $1$, 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:	$5.94086991038$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			557.18
Character	$\chi$	$=$	744.557
Dual form			744.2.o.e.557.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23502 - 0.689003i) q^{2} +(1.72001 - 0.203883i) q^{3} +(1.05055 + 1.70187i) q^{4} +1.58364 q^{5} +(-2.26472 - 0.933293i) q^{6} -1.93355 q^{7} +(-0.124858 - 2.82567i) q^{8} +(2.91686 - 0.701361i) q^{9} +O(q^{10})$	\(q+(-1.23502 - 0.689003i) q^{2} +(1.72001 - 0.203883i) q^{3} +(1.05055 + 1.70187i) q^{4} +1.58364 q^{5} +(-2.26472 - 0.933293i) q^{6} -1.93355 q^{7} +(-0.124858 - 2.82567i) q^{8} +(2.91686 - 0.701361i) q^{9} +(-1.95582 - 1.09113i) q^{10} -5.40271i q^{11} +(2.15394 + 2.71304i) q^{12} +1.73596 q^{13} +(2.38798 + 1.33222i) q^{14} +(2.72387 - 0.322876i) q^{15} +(-1.79269 + 3.57579i) q^{16} -6.07545 q^{17} +(-4.08562 - 1.14353i) q^{18} -5.82201i q^{19} +(1.66369 + 2.69514i) q^{20} +(-3.32573 + 0.394218i) q^{21} +(-3.72248 + 6.67245i) q^{22} +6.29736 q^{23} +(-0.790862 - 4.83472i) q^{24} -2.49210 q^{25} +(-2.14395 - 1.19608i) q^{26} +(4.87404 - 1.80105i) q^{27} +(-2.03129 - 3.29065i) q^{28} -3.28289i q^{29} +(-3.58649 - 1.47800i) q^{30} +(5.55537 - 0.371337i) q^{31} +(4.67774 - 3.18100i) q^{32} +(-1.10152 - 9.29271i) q^{33} +(7.50331 + 4.18601i) q^{34} -3.06204 q^{35} +(4.25793 + 4.22730i) q^{36} +3.87328 q^{37} +(-4.01138 + 7.19030i) q^{38} +(2.98587 - 0.353932i) q^{39} +(-0.197729 - 4.47483i) q^{40} +8.63565i q^{41} +(4.37896 + 1.80457i) q^{42} +4.82027 q^{43} +(9.19468 - 5.67581i) q^{44} +(4.61925 - 1.11070i) q^{45} +(-7.77737 - 4.33890i) q^{46} +9.13697i q^{47} +(-2.35441 + 6.51589i) q^{48} -3.26137 q^{49} +(3.07779 + 1.71706i) q^{50} +(-10.4498 + 1.23868i) q^{51} +(1.82371 + 2.95437i) q^{52} +2.07629i q^{53} +(-7.26046 - 1.13390i) q^{54} -8.55592i q^{55} +(0.241419 + 5.46358i) q^{56} +(-1.18701 - 10.0139i) q^{57} +(-2.26193 + 4.05444i) q^{58} +5.85249 q^{59} +(3.41105 + 4.29646i) q^{60} +4.27136 q^{61} +(-7.11684 - 3.36906i) q^{62} +(-5.63991 + 1.35612i) q^{63} +(-7.96882 + 0.705614i) q^{64} +2.74913 q^{65} +(-5.04231 + 12.2356i) q^{66} +10.7801i q^{67} +(-6.38256 - 10.3396i) q^{68} +(10.8315 - 1.28392i) q^{69} +(3.78169 + 2.10976i) q^{70} +5.88571i q^{71} +(-2.34601 - 8.15452i) q^{72} -11.2016i q^{73} +(-4.78357 - 2.66870i) q^{74} +(-4.28643 + 0.508096i) q^{75} +(9.90828 - 6.11630i) q^{76} +10.4464i q^{77} +(-3.93147 - 1.62016i) q^{78} -16.0486i q^{79} +(-2.83897 + 5.66274i) q^{80} +(8.01619 - 4.09155i) q^{81} +(5.94999 - 10.6652i) q^{82} +0.946957i q^{83} +(-4.16475 - 5.24580i) q^{84} -9.62131 q^{85} +(-5.95313 - 3.32118i) q^{86} +(-0.669326 - 5.64661i) q^{87} +(-15.2663 + 0.674570i) q^{88} -6.40594 q^{89} +(-6.47014 - 1.81094i) q^{90} -3.35657 q^{91} +(6.61569 + 10.7173i) q^{92} +(9.47957 - 1.77135i) q^{93} +(6.29540 - 11.2843i) q^{94} -9.21994i q^{95} +(7.39721 - 6.42505i) q^{96} +4.03258 q^{97} +(4.02786 + 2.24710i) q^{98} +(-3.78925 - 15.7590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9}+O(q^{10}) $ 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9	$ 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9} - 52 q^{10} - 60 q^{16} - 4 q^{18} + 168 q^{25} - 20 q^{28} + 16 q^{31} + 8 q^{33} + 8 q^{39} - 64 q^{40} - 64 q^{49} + 56 q^{63} + 72 q^{64} + 4 q^{66} - 84 q^{70} - 44 q^{72} - 28 q^{76} + 56 q^{78} - 112 q^{81} - 108 q^{82} - 168 q^{87} + 104 q^{90} + 8 q^{94} + 72 q^{97}+O(q^{100}) $ 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9 - 52 * q^10 - 60 * q^16 - 4 * q^18 + 168 * q^25 - 20 * q^28 + 16 * q^31 + 8 * q^33 + 8 * q^39 - 64 * q^40 - 64 * q^49 + 56 * q^63 + 72 * q^64 + 4 * q^66 - 84 * q^70 - 44 * q^72 - 28 * q^76 + 56 * q^78 - 112 * q^81 - 108 * q^82 - 168 * q^87 + 104 * q^90 + 8 * q^94 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/744\mathbb{Z}\right)^\times$.

$n$	$313$	$373$	$497$	$559$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.23502	−	0.689003i	−0.873291	−	0.487199i
$2$	−1.23502	−	0.689003i	−0.873291	−	0.487199i
$3$	1.72001	−	0.203883i	0.993048	−	0.117712i
$3$	1.72001	−	0.203883i	0.993048	−	0.117712i
$4$	1.05055	+	1.70187i	0.525274	+	0.850933i
$5$	1.58364			0.708224			0.354112	−	0.935203i	$-0.384783\pi$
$5$	1.58364			0.708224			0.354112	+	0.935203i	$0.384783\pi$
$6$	−2.26472	−	0.933293i	−0.924569	−	0.381015i
$7$	−1.93355			−0.730814			−0.365407	−	0.930848i	$-0.619070\pi$
$7$	−1.93355			−0.730814			−0.365407	+	0.930848i	$0.619070\pi$
$8$	−0.124858	−	2.82567i	−0.0441439	−	0.999025i
$9$	2.91686	−	0.701361i	0.972288	−	0.233787i
$10$	−1.95582	−	1.09113i	−0.618485	−	0.345046i
$11$		−	5.40271i		−	1.62898i	−0.580179	−	0.814489i	$-0.697018\pi$
$11$		−	5.40271i		−	1.62898i	0.580179	−	0.814489i	$-0.302982\pi$
$12$	2.15394	+	2.71304i	0.621787	+	0.783186i
$13$	1.73596			0.481469			0.240734	−	0.970591i	$-0.422612\pi$
$13$	1.73596			0.481469			0.240734	+	0.970591i	$0.422612\pi$
$14$	2.38798	+	1.33222i	0.638214	+	0.356052i
$15$	2.72387	−	0.322876i	0.703300	−	0.0833663i
$16$	−1.79269	+	3.57579i	−0.448173	+	0.893947i
$17$	−6.07545			−1.47351			−0.736757	−	0.676158i	$-0.763644\pi$
$17$	−6.07545			−1.47351			−0.736757	+	0.676158i	$0.763644\pi$
$18$	−4.08562	−	1.14353i	−0.962991	−	0.269534i
$19$		−	5.82201i		−	1.33566i	−0.744314	−	0.667830i	$-0.767223\pi$
$19$		−	5.82201i		−	1.33566i	0.744314	−	0.667830i	$-0.232777\pi$
$20$	1.66369	+	2.69514i	0.372012	+	0.602651i
$21$	−3.32573	+	0.394218i	−0.725733	+	0.0860255i
$22$	−3.72248	+	6.67245i	−0.793636	+	1.42257i
$23$	6.29736			1.31309			0.656545	−	0.754287i	$-0.272017\pi$
$23$	6.29736			1.31309			0.656545	+	0.754287i	$0.272017\pi$
$24$	−0.790862	−	4.83472i	−0.161434	−	0.986883i
$25$	−2.49210			−0.498419
$26$	−2.14395	−	1.19608i	−0.420462	−	0.234571i
$27$	4.87404	−	1.80105i	0.938009	−	0.346611i
$28$	−2.03129	−	3.29065i	−0.383878	−	0.621874i
$29$		−	3.28289i		−	0.609618i	−0.952413	−	0.304809i	$-0.901407\pi$
$29$		−	3.28289i		−	0.609618i	0.952413	−	0.304809i	$-0.0985927\pi$
$30$	−3.58649	−	1.47800i	−0.654801	−	0.269844i
$31$	5.55537	−	0.371337i	0.997773	−	0.0666942i
$31$	5.55537	−	0.371337i	0.997773	−	0.0666942i
$32$	4.67774	−	3.18100i	0.826916	−	0.562326i
$33$	−1.10152	−	9.29271i	−0.191750	−	1.61765i
$34$	7.50331	+	4.18601i	1.28681	+	0.717894i
$35$	−3.06204			−0.517580
$36$	4.25793	+	4.22730i	0.709655	+	0.704549i
$37$	3.87328			0.636763			0.318381	−	0.947963i	$-0.396861\pi$
$37$	3.87328			0.636763			0.318381	+	0.947963i	$0.396861\pi$
$38$	−4.01138	+	7.19030i	−0.650732	+	1.16642i
$39$	2.98587	−	0.353932i	0.478121	−	0.0566745i
$40$	−0.197729	−	4.47483i	−0.0312638	−	0.707533i
$41$			8.63565i			1.34866i	0.738429	+	0.674331i	$0.235568\pi$
$41$			8.63565i			1.34866i	−0.738429	+	0.674331i	$0.764432\pi$
$42$	4.37896	+	1.80457i	0.675688	+	0.278451i
$43$	4.82027			0.735084			0.367542	−	0.930007i	$-0.380199\pi$
$43$	4.82027			0.735084			0.367542	+	0.930007i	$0.380199\pi$
$44$	9.19468	−	5.67581i	1.38615	−	0.855660i
$45$	4.61925	−	1.11070i	0.688597	−	0.165573i
$46$	−7.77737	−	4.33890i	−1.14671	−	0.639736i
$47$			9.13697i			1.33276i	0.745611	+	0.666382i	$0.232158\pi$
$47$			9.13697i			1.33276i	−0.745611	+	0.666382i	$0.767842\pi$
$48$	−2.35441	+	6.51589i	−0.339830	+	0.940487i
$49$	−3.26137			−0.465911
$50$	3.07779	+	1.71706i	0.435265	+	0.242829i
$51$	−10.4498	+	1.23868i	−1.46327	+	0.173450i
$52$	1.82371	+	2.95437i	0.252903	+	0.409698i
$53$			2.07629i			0.285201i	0.989780	+	0.142600i	$0.0455464\pi$
$53$			2.07629i			0.285201i	−0.989780	+	0.142600i	$0.954454\pi$
$54$	−7.26046	−	1.13390i	−0.988023	−	0.154304i
$55$		−	8.55592i		−	1.15368i
$56$	0.241419	+	5.46358i	0.0322610	+	0.730102i
$57$	−1.18701	−	10.0139i	−0.157223	−	1.32637i
$58$	−2.26193	+	4.05444i	−0.297005	+	0.532374i
$59$	5.85249			0.761930			0.380965	−	0.924590i	$-0.375592\pi$
$59$	5.85249			0.761930			0.380965	+	0.924590i	$0.375592\pi$
$60$	3.41105	+	4.29646i	0.440365	+	0.554671i
$61$	4.27136			0.546891			0.273446	−	0.961887i	$-0.411837\pi$
$61$	4.27136			0.546891			0.273446	+	0.961887i	$0.411837\pi$
$62$	−7.11684	−	3.36906i	−0.903840	−	0.427871i
$63$	−5.63991	+	1.35612i	−0.710562	+	0.170855i
$64$	−7.96882	+	0.705614i	−0.996103	+	0.0882018i
$65$	2.74913			0.340987
$66$	−5.04231	+	12.2356i	−0.620665	+	1.50610i
$67$			10.7801i			1.31700i	0.752582	+	0.658498i	$0.228808\pi$
$67$			10.7801i			1.31700i	−0.752582	+	0.658498i	$0.771192\pi$
$68$	−6.38256	−	10.3396i	−0.773999	−	1.25386i
$69$	10.8315	−	1.28392i	1.30396	−	0.154566i
$70$	3.78169	+	2.10976i	0.451998	+	0.252164i
$71$			5.88571i			0.698505i	0.937029	+	0.349252i	$0.113564\pi$
$71$			5.88571i			0.698505i	−0.937029	+	0.349252i	$0.886436\pi$
$72$	−2.34601	−	8.15452i	−0.276480	−	0.961020i
$73$		−	11.2016i		−	1.31105i	−0.755173	−	0.655525i	$-0.772447\pi$
$73$		−	11.2016i		−	1.31105i	0.755173	−	0.655525i	$-0.227553\pi$
$74$	−4.78357	−	2.66870i	−0.556079	−	0.310230i
$75$	−4.28643	+	0.508096i	−0.494954	+	0.0586698i
$76$	9.90828	−	6.11630i	1.13656	−	0.701588i
$77$			10.4464i			1.19048i
$78$	−3.93147	−	1.62016i	−0.445151	−	0.183447i
$79$		−	16.0486i		−	1.80561i	−0.430048	−	0.902806i	$-0.641504\pi$
$79$		−	16.0486i		−	1.80561i	0.430048	−	0.902806i	$-0.358496\pi$
$80$	−2.83897	+	5.66274i	−0.317407	+	0.633114i
$81$	8.01619	−	4.09155i	0.890687	−	0.454616i
$82$	5.94999	−	10.6652i	0.657067	−	1.17777i
$83$			0.946957i			0.103942i	0.998649	+	0.0519710i	$0.0165503\pi$
$83$			0.946957i			0.103942i	−0.998649	+	0.0519710i	$0.983450\pi$
$84$	−4.16475	−	5.24580i	−0.454411	−	0.572364i
$85$	−9.62131			−1.04358
$86$	−5.95313	−	3.32118i	−0.641942	−	0.358132i
$87$	−0.669326	−	5.64661i	−0.0717593	−	0.605380i
$88$	−15.2663	+	0.674570i	−1.62739	+	0.0719094i
$89$	−6.40594			−0.679028			−0.339514	−	0.940601i	$-0.610263\pi$
$89$	−6.40594			−0.679028			−0.339514	+	0.940601i	$0.610263\pi$
$90$	−6.47014	−	1.81094i	−0.682013	−	0.190890i
$91$	−3.35657			−0.351864
$92$	6.61569	+	10.7173i	0.689733	+	1.11735i
$93$	9.47957	−	1.77135i	0.982986	−	0.183680i
$94$	6.29540	−	11.2843i	0.649321	−	1.16389i
$95$		−	9.21994i		−	0.945946i
$96$	7.39721	−	6.42505i	0.754974	−	0.655754i
$97$	4.03258			0.409446			0.204723	−	0.978820i	$-0.434371\pi$
$97$	4.03258			0.409446			0.204723	+	0.978820i	$0.434371\pi$
$98$	4.02786	+	2.24710i	0.406875	+	0.226991i
$99$	−3.78925	−	15.7590i	−0.380834	−	1.58383i
$100$	−2.61807	−	4.24121i	−0.261807	−	0.424121i
$101$	−10.7901			−1.07365			−0.536827	−	0.843692i	$-0.680377\pi$
$101$	−10.7901			−1.07365			−0.536827	+	0.843692i	$0.680377\pi$
$102$	13.7592	+	5.67018i	1.36236	+	0.561431i
$103$	−14.1844			−1.39763			−0.698814	−	0.715304i	$-0.746288\pi$
$103$	−14.1844			−1.39763			−0.698814	+	0.715304i	$0.746288\pi$
$104$	−0.216748	−	4.90525i	−0.0212539	−	0.480999i
$105$	−5.26674	+	0.624298i	−0.513982	+	0.0609253i
$106$	1.43057	−	2.56426i	0.138949	−	0.249063i
$107$	−2.78315			−0.269058			−0.134529	−	0.990910i	$-0.542952\pi$
$107$	−2.78315			−0.269058			−0.134529	+	0.990910i	$0.542952\pi$
$108$	8.18555	+	6.40287i	0.787655	+	0.616116i
$109$			7.82222i			0.749233i	0.927180	+	0.374617i	$0.122226\pi$
$109$			7.82222i			0.749233i	−0.927180	+	0.374617i	$0.877774\pi$
$110$	−5.89506	+	10.5667i	−0.562072	+	1.00750i
$111$	6.66207	−	0.789695i	0.632336	−	0.0749545i
$112$	3.46627	−	6.91397i	0.327532	−	0.653309i
$113$		−	0.0563852i		−	0.00530427i	−0.999996	−	0.00265214i	$-0.999156\pi$
$113$		−	0.0563852i		−	0.00530427i	0.999996	−	0.00265214i	$-0.000844203\pi$
$114$	−5.43364	+	13.1852i	−0.508907	+	1.23491i
$115$	9.97273			0.929962
$116$	5.58705	−	3.44884i	0.518744	−	0.320217i
$117$	5.06356	−	1.21753i	0.468126	−	0.112561i
$118$	−7.22794	−	4.03239i	−0.665386	−	0.371211i
$119$	11.7472			1.07686
$120$	−1.25244	−	7.65644i	−0.114331	−	0.698934i
$121$	−18.1892			−1.65357
$122$	−5.27521	−	2.94298i	−0.477595	−	0.266445i
$123$	1.76066	+	14.8534i	0.158753	+	1.33929i
$124$	6.46815	+	9.06438i	0.580857	+	0.814005i
$125$	−11.8648			−1.06122
$126$	7.89977	+	2.21108i	0.703768	+	0.196979i
$127$			18.2101i			1.61589i	0.589261	+	0.807943i	$0.299419\pi$
$127$			18.2101i			1.61589i	−0.589261	+	0.807943i	$0.700581\pi$
$128$	10.3278	+	4.61910i	0.912859	+	0.408274i
$129$	8.29091	−	0.982770i	0.729974	−	0.0865281i
$130$	−3.39523	−	1.89416i	−0.297781	−	0.166129i
$131$	7.32770			0.640224			0.320112	−	0.947380i	$-0.396279\pi$
$131$	7.32770			0.640224			0.320112	+	0.947380i	$0.396279\pi$
$132$	14.6577	−	11.6371i	1.27579	−	1.01288i
$133$			11.2572i			0.976120i
$134$	7.42751	−	13.3136i	0.641639	−	1.15012i
$135$	7.71870	−	2.85220i	0.664320	−	0.245478i
$136$	0.758568	+	17.1672i	0.0650467	+	1.47208i
$137$	−0.230447			−0.0196884			−0.00984420	−	0.999952i	$-0.503134\pi$
$137$	−0.230447			−0.0196884			−0.00984420	+	0.999952i	$0.503134\pi$
$138$	−14.2618	−	5.87728i	−1.21404	−	0.500307i
$139$	−4.67379			−0.396426			−0.198213	−	0.980159i	$-0.563514\pi$
$139$	−4.67379			−0.396426			−0.198213	+	0.980159i	$0.563514\pi$
$140$	−3.21683	−	5.21119i	−0.271871	−	0.440426i
$141$	1.86287	+	15.7157i	0.156882	+	1.32350i
$142$	4.05527	−	7.26896i	0.340311	−	0.609998i
$143$		−	9.37888i		−	0.784302i
$144$	−2.72113	+	11.6874i	−0.226761	+	0.973951i
$145$		−	5.19891i		−	0.431746i
$146$	−7.71795	+	13.8342i	−0.638742	+	1.14493i
$147$	−5.60959	+	0.664938i	−0.462671	+	0.0548432i
$148$	4.06907	+	6.59180i	0.334475	+	0.541842i
$149$	−12.7714			−1.04628			−0.523138	−	0.852248i	$-0.675239\pi$
$149$	−12.7714			−1.04628			−0.523138	+	0.852248i	$0.675239\pi$
$150$	5.64391	+	2.32586i	0.460823	+	0.189905i
$151$			13.0233i			1.05982i	0.848053	+	0.529911i	$0.177775\pi$
$151$			13.0233i			1.05982i	−0.848053	+	0.529911i	$0.822225\pi$
$152$	−16.4511	+	0.726923i	−1.33436	+	0.0589613i
$153$	−17.7213	+	4.26108i	−1.43268	+	0.344488i
$154$	7.19762	−	12.9015i	0.580001	−	1.03964i
$155$	8.79768	−	0.588063i	0.706647	−	0.0472344i
$156$	3.73915	+	4.70972i	0.299371	+	0.377080i
$157$			7.33155i			0.585122i	0.956247	+	0.292561i	$0.0945074\pi$
$157$			7.33155i			0.585122i	−0.956247	+	0.292561i	$0.905493\pi$
$158$	−11.0576	+	19.8204i	−0.879692	+	1.57682i
$159$	0.423320	+	3.57124i	0.0335715	+	0.283218i
$160$	7.40784	−	5.03754i	0.585641	−	0.398252i
$161$	−12.1763			−0.959625
$162$	−12.7192	−	0.470036i	−0.999318	−	0.0369295i
$163$		−	16.9003i		−	1.32373i	−0.749623	−	0.661866i	$-0.769765\pi$
$163$		−	16.9003i		−	1.32373i	0.749623	−	0.661866i	$-0.230235\pi$
$164$	−14.6967	+	9.07217i	−1.14762	+	0.708418i
$165$	−1.74441	−	14.7163i	−0.135802	−	1.14566i
$166$	0.652456	−	1.16951i	0.0506404	−	0.0907716i
$167$	18.4214			1.42549			0.712744	−	0.701424i	$-0.247452\pi$
$167$	18.4214			1.42549			0.712744	+	0.701424i	$0.247452\pi$
$168$	1.52917	+	9.34819i	0.117978	+	0.721229i
$169$	−9.98644			−0.768188
$170$	11.8825	+	6.62911i	0.911347	+	0.508430i
$171$	−4.08333	−	16.9820i	−0.312260	−	1.29865i
$172$	5.06393	+	8.20345i	0.386121	+	0.625507i
$173$	19.3371			1.47017			0.735087	−	0.677972i	$-0.237141\pi$
$173$	19.3371			1.47017			0.735087	+	0.677972i	$0.237141\pi$
$174$	−3.06390	+	7.43484i	−0.232274	+	0.563634i
$175$	4.81860			0.364252
$176$	19.3189	+	9.68540i	1.45622	+	0.730064i
$177$	10.0663	−	1.19322i	0.756632	−	0.0896881i
$178$	7.91147	+	4.41372i	0.592989	+	0.330822i
$179$		−	6.86378i		−	0.513023i	−0.966541	−	0.256511i	$-0.917427\pi$
$179$		−	6.86378i		−	0.513023i	0.966541	−	0.256511i	$-0.0825731\pi$
$180$	6.74301	+	6.69450i	0.502594	+	0.498978i
$181$	−5.93835			−0.441394			−0.220697	−	0.975342i	$-0.570833\pi$
$181$	−5.93835			−0.441394			−0.220697	+	0.975342i	$0.570833\pi$
$182$	4.14543	+	2.31269i	0.307280	+	0.171428i
$183$	7.34678	−	0.870857i	0.543089	−	0.0643756i
$184$	−0.786275	−	17.7943i	−0.0579650	−	1.31181i
$185$	6.13386			0.450970
$186$	−12.9279	−	4.34381i	−0.947922	−	0.318503i
$187$			32.8239i			2.40032i
$188$	−15.5499	+	9.59883i	−1.13409	+	0.700067i
$189$	−9.42421	+	3.48242i	−0.685510	+	0.253308i
$190$	−6.35257	+	11.3868i	−0.460864	+	0.826086i
$191$			2.48988i			0.180161i	0.995934	+	0.0900807i	$0.0287125\pi$
$191$			2.48988i			0.180161i	−0.995934	+	0.0900807i	$0.971288\pi$
$192$	−13.5626	+	2.83837i	−0.978795	+	0.204842i
$193$	23.2978			1.67701			0.838505	−	0.544895i	$-0.183430\pi$
$193$	23.2978			1.67701			0.838505	+	0.544895i	$0.183430\pi$
$194$	−4.98032	−	2.77846i	−0.357566	−	0.199482i
$195$	4.72853	−	0.560500i	0.338617	−	0.0401382i
$196$	−3.42623	−	5.55042i	−0.244731	−	0.396459i
$197$			21.1706i			1.50834i	0.656677	+	0.754172i	$0.271962\pi$
$197$			21.1706i			1.50834i	−0.656677	+	0.754172i	$0.728038\pi$
$198$	−6.17818	+	22.0734i	−0.439064	+	1.56869i
$199$			13.0368i			0.924156i	0.886839	+	0.462078i	$0.152896\pi$
$199$			13.0368i			0.924156i	−0.886839	+	0.462078i	$0.847104\pi$
$200$	0.311158	+	7.04184i	0.0220022	+	0.497934i
$201$	2.19787	+	18.5418i	0.155026	+	1.30784i
$202$	13.3260	+	7.43441i	0.937612	+	0.523083i
$203$			6.34765i			0.445518i
$204$	−13.0861	−	16.4829i	−0.916212	−	1.15404i
$205$			13.6757i			0.955154i
$206$	17.5180	+	9.77308i	1.22054	+	0.680922i
$207$	18.3685	−	4.41672i	1.27670	−	0.306983i
$208$	−3.11204	+	6.20742i	−0.215781	+	0.430407i
$209$	−31.4546			−2.17576
$210$	6.93468	+	2.85778i	0.478538	+	0.197206i
$211$			9.96544i			0.686049i	0.939326	+	0.343025i	$0.111451\pi$
$211$			9.96544i			0.686049i	−0.939326	+	0.343025i	$0.888549\pi$
$212$	−3.53357	+	2.18125i	−0.242687	+	0.149809i
$213$	1.19999	+	10.1235i	0.0822223	+	0.693649i
$214$	3.43725	+	1.91760i	0.234966	+	0.131085i
$215$	7.63355			0.520604
$216$	−5.69772	−	13.5475i	−0.387681	−	0.921794i
$217$	−10.7416	+	0.718001i	−0.729187	+	0.0487411i
$218$	5.38954	−	9.66060i	0.365026	−	0.654298i
$219$	−2.28382	−	19.2669i	−0.154326	−	1.30194i
$220$	14.5610	−	8.98841i	0.981704	−	0.605999i
$221$	−10.5467			−0.709451
$222$	−8.77189	−	3.61490i	−0.588731	−	0.242616i
$223$		−	3.95369i		−	0.264759i	−0.991199	−	0.132379i	$-0.957738\pi$
$223$		−	3.95369i		−	0.264759i	0.991199	−	0.132379i	$-0.0422617\pi$
$224$	−9.04466	+	6.15062i	−0.604322	+	0.410956i
$225$	−7.26911	+	1.74786i	−0.484607	+	0.116524i
$226$	−0.0388496	+	0.0696369i	−0.00258424	+	0.00463218i
$227$	23.2022			1.53999			0.769993	−	0.638052i	$-0.220259\pi$
$227$	23.2022			1.53999			0.769993	+	0.638052i	$0.220259\pi$
$228$	15.7953	−	12.5402i	1.04607	−	0.830497i
$229$	18.2510			1.20606			0.603029	−	0.797719i	$-0.293960\pi$
$229$	18.2510			1.20606			0.603029	+	0.797719i	$0.293960\pi$
$230$	−12.3165	−	6.87124i	−0.812127	−	0.453076i
$231$	2.12985	+	17.9679i	0.140134	+	1.18220i
$232$	−9.27638	+	0.409895i	−0.609024	+	0.0269109i
$233$			17.6981i			1.15944i	0.814816	+	0.579720i	$0.196838\pi$
$233$			17.6981i			1.15944i	−0.814816	+	0.579720i	$0.803162\pi$
$234$	−7.09248	−	1.98513i	−0.463650	−	0.129772i
$235$			14.4696i			0.943894i
$236$	6.14833	+	9.96016i	0.400222	+	0.648351i
$237$	−3.27204	−	27.6038i	−0.212542	−	1.79306i
$238$	−14.5080	−	8.09387i	−0.940417	−	0.524647i
$239$	−15.1195			−0.978002			−0.489001	−	0.872283i	$-0.662639\pi$
$239$	−15.1195			−0.978002			−0.489001	+	0.872283i	$0.662639\pi$
$240$	−3.72853	+	10.3188i	−0.240675	+	0.666075i
$241$		−	4.80092i		−	0.309255i	−0.987973	−	0.154627i	$-0.950582\pi$
$241$		−	4.80092i		−	0.309255i	0.987973	−	0.154627i	$-0.0494177\pi$
$242$	22.4641	+	12.5324i	1.44405	+	0.805616i
$243$	12.9537	−	8.67186i	0.830981	−	0.556300i
$244$	4.48727	+	7.26928i	0.287268	+	0.465368i
$245$	−5.16483			−0.329969
$246$	8.05959	−	19.5573i	0.513861	−	1.24693i
$247$		−	10.1068i		−	0.643079i
$248$	−1.74291	−	15.6513i	−0.110675	−	0.993857i
$249$	0.193068	+	1.62877i	0.0122352	+	0.103219i
$250$	14.6532	+	8.17485i	0.926750	+	0.517023i
$251$		−	23.1138i		−	1.45893i	−0.684017	−	0.729466i	$-0.739768\pi$
$251$		−	23.1138i		−	1.45893i	0.684017	−	0.729466i	$-0.260232\pi$
$252$	−8.23293	−	8.17370i	−0.518626	−	0.514895i
$253$		−	34.0228i		−	2.13900i
$254$	12.5468	−	22.4899i	0.787258	−	1.41114i
$255$	−16.5487	+	1.96162i	−1.03632	+	0.122841i
$256$	−9.57250	−	12.8206i	−0.598281	−	0.801286i
$257$			19.7088i			1.22940i	0.788760	+	0.614701i	$0.210723\pi$
$257$			19.7088i			1.22940i	−0.788760	+	0.614701i	$0.789277\pi$
$258$	−10.9166	−	4.49872i	−0.679636	−	0.280078i
$259$	−7.48919			−0.465355
$260$	2.88809	+	4.67865i	0.179112	+	0.290157i
$261$	−2.30249	−	9.57576i	−0.142521	−	0.592724i
$262$	−9.04985	−	5.04881i	−0.559102	−	0.311916i
$263$	−11.2875			−0.696018			−0.348009	−	0.937491i	$-0.613142\pi$
$263$	−11.2875			−0.696018			−0.348009	+	0.937491i	$0.613142\pi$
$264$	−26.1206	+	4.27280i	−1.60761	+	0.262972i
$265$			3.28809i			0.201986i
$266$	7.75622	−	13.9028i	0.475564	−	0.852436i
$267$	−11.0183	+	1.30606i	−0.674308	+	0.0799297i
$268$	−18.3463	+	11.3250i	−1.12068	+	0.691785i
$269$		−	0.109173i		−	0.00665640i	−0.999994	−	0.00332820i	$-0.998941\pi$
$269$		−	0.109173i		−	0.00665640i	0.999994	−	0.00332820i	$-0.00105940\pi$
$270$	−11.4979	−	1.79569i	−0.699741	−	0.109282i
$271$			24.1318i			1.46590i	0.680281	+	0.732952i	$0.261858\pi$
$271$			24.1318i			1.46590i	−0.680281	+	0.732952i	$0.738142\pi$
$272$	10.8914	−	21.7245i	0.660390	−	1.31724i
$273$	−5.77333	+	0.684347i	−0.349418	+	0.0414186i
$274$	0.284606	+	0.158779i	0.0171937	+	0.00959216i
$275$			13.4641i			0.811914i
$276$	13.5641	+	17.0850i	0.816463	+	1.02839i
$277$	−21.7080			−1.30431			−0.652154	−	0.758086i	$-0.726135\pi$
$277$	−21.7080			−1.30431			−0.652154	+	0.758086i	$0.726135\pi$
$278$	5.77222	+	3.22026i	0.346195	+	0.193138i
$279$	15.9438	−	4.97946i	0.954531	−	0.298112i
$280$	0.382320	+	8.65232i	0.0228480	+	0.517075i
$281$		−	1.63148i		−	0.0973257i	−0.998815	−	0.0486629i	$-0.984504\pi$
$281$		−	1.63148i		−	0.0973257i	0.998815	−	0.0486629i	$-0.0154960\pi$
$282$	8.52746	−	20.6927i	0.507803	−	1.23223i
$283$		−	13.5256i		−	0.804016i	−0.915636	−	0.402008i	$-0.868312\pi$
$283$		−	13.5256i		−	0.804016i	0.915636	−	0.402008i	$-0.131688\pi$
$284$	−10.0167	+	6.18322i	−0.594381	+	0.366907i
$285$	−1.87979	−	15.8584i	−0.111349	−	0.939370i
$286$	−6.46208	+	11.5831i	−0.382111	+	0.684924i
$287$		−	16.6975i		−	0.985621i
$288$	11.4133	−	12.5593i	0.672536	−	0.740065i
$289$	19.9111			1.17124
$290$	−3.58207	+	6.42076i	−0.210346	+	0.377040i
$291$	6.93607	−	0.822173i	0.406600	−	0.0481967i
$292$	19.0637	−	11.7679i	1.11562	−	0.688661i
$293$	−6.33849			−0.370299			−0.185149	−	0.982710i	$-0.559277\pi$
$293$	−6.33849			−0.370299			−0.185149	+	0.982710i	$0.559277\pi$
$294$	7.38610	+	3.04382i	0.430766	+	0.177519i
$295$	9.26822			0.539616
$296$	−0.483609	−	10.9446i	−0.0281092	−	0.636142i
$297$	−9.73052	−	26.3330i	−0.564622	−	1.52800i
$298$	15.7730	+	8.79955i	0.913703	+	0.509744i
$299$	10.9320			0.632212
$300$	−5.36782	−	6.76115i	−0.309911	−	0.390355i
$301$	−9.32024			−0.537210
$302$	8.97310	−	16.0840i	0.516344	−	0.925533i
$303$	−18.5591	+	2.19991i	−1.06619	+	0.126382i
$304$	20.8183	+	10.4371i	1.19401	+	0.598608i
$305$	6.76428			0.387321
$306$	24.8220	+	6.94749i	1.41898	+	0.397161i
$307$			5.17619i			0.295421i	0.989031	+	0.147711i	$0.0471904\pi$
$307$			5.17619i			0.295421i	−0.989031	+	0.147711i	$0.952810\pi$
$308$	−17.7784	+	10.9745i	−1.01302	+	0.625329i
$309$	−24.3972	+	2.89195i	−1.38791	+	0.164517i
$310$	−11.2705	−	5.33536i	−0.640121	−	0.303028i
$311$		−	28.1634i		−	1.59700i	−0.601996	−	0.798499i	$-0.705628\pi$
$311$		−	28.1634i		−	1.59700i	0.601996	−	0.798499i	$-0.294372\pi$
$312$	−1.37291	−	8.39288i	−0.0777255	−	0.475153i
$313$			28.5259i			1.61238i	0.591655	+	0.806191i	$0.298475\pi$
$313$			28.5259i			1.61238i	−0.591655	+	0.806191i	$0.701525\pi$
$314$	5.05146	−	9.05462i	0.285071	−	0.510982i
$315$	−8.93156	+	2.14760i	−0.503237	+	0.121003i
$316$	27.3126	−	16.8599i	1.53645	−	0.948442i
$317$	−2.47581			−0.139055			−0.0695277	−	0.997580i	$-0.522149\pi$
$317$	−2.47581			−0.139055			−0.0695277	+	0.997580i	$0.522149\pi$
$318$	1.93779	−	4.70222i	0.108666	−	0.263688i
$319$	−17.7365			−0.993054
$320$	−12.6197	+	1.11744i	−0.705463	+	0.0624666i
$321$	−4.78705	+	0.567437i	−0.267187	+	0.0316713i
$322$	15.0380	+	8.38950i	0.838032	+	0.467528i
$323$			35.3713i			1.96811i
$324$	15.3847	+	9.34410i	0.854703	+	0.519117i
$325$	−4.32618			−0.239973
$326$	−11.6443	+	20.8722i	−0.644920	+	1.15600i
$327$	1.59482	+	13.4543i	0.0881936	+	0.744024i
$328$	24.4015	−	1.07823i	1.34735	−	0.0595352i
$329$		−	17.6668i		−	0.974003i
$330$	−7.98518	+	19.3768i	−0.439570	+	1.06666i
$331$	−28.6107			−1.57258			−0.786292	−	0.617854i	$-0.788002\pi$
$331$	−28.6107			−1.57258			−0.786292	+	0.617854i	$0.788002\pi$
$332$	−1.61159	+	0.994825i	−0.0884477	+	0.0545981i
$333$	11.2978	−	2.71656i	0.619117	−	0.148867i
$334$	−22.7508	−	12.6924i	−1.24487	−	0.694497i
$335$			17.0717i			0.932728i
$336$	4.55237	−	12.5988i	0.248352	−	0.687321i
$337$			19.2589i			1.04910i	0.851379	+	0.524551i	$0.175767\pi$
$337$			19.2589i			1.04910i	−0.851379	+	0.524551i	$0.824233\pi$
$338$	12.3335	+	6.88069i	0.670852	+	0.374260i
$339$	−0.0114960	−	0.0969831i	−0.000624376	−	0.00526740i
$340$	−10.1077	−	16.3742i	−0.548164	−	0.888014i
$341$	−2.00623	−	30.0140i	−0.108643	−	1.62535i
$342$	−6.65766	+	23.7865i	−0.360005	+	1.28623i
$343$	19.8409			1.07131
$344$	−0.601848	−	13.6205i	−0.0324495	−	0.734368i
$345$	17.1532	−	2.03327i	0.923496	−	0.109467i
$346$	−23.8817	−	13.3233i	−1.28389	−	0.716268i
$347$		−	17.2373i		−	0.925344i	−0.886529	−	0.462672i	$-0.846891\pi$
$347$		−	17.2373i		−	0.925344i	0.886529	−	0.462672i	$-0.153109\pi$
$348$	8.90661	−	7.07114i	0.477445	−	0.379053i
$349$			14.0777i			0.753563i	0.926302	+	0.376782i	$0.122969\pi$
$349$			14.0777i			0.753563i	−0.926302	+	0.376782i	$0.877031\pi$
$350$	−5.95107	−	3.32003i	−0.318098	−	0.177463i
$351$	8.46113	−	3.12654i	0.451622	−	0.166882i
$352$	−17.1860	−	25.2725i	−0.916016	−	1.34703i
$353$	16.3140			0.868306			0.434153	−	0.900839i	$-0.357048\pi$
$353$	16.3140			0.868306			0.434153	+	0.900839i	$0.357048\pi$
$354$	−13.2543	−	5.46209i	−0.704456	−	0.290307i
$355$			9.32082i			0.494698i
$356$	−6.72976	−	10.9021i	−0.356676	−	0.577808i
$357$	20.2053	−	2.39505i	1.06938	−	0.126760i
$358$	−4.72916	+	8.47690i	−0.249944	+	0.448018i
$359$			9.47738i			0.500197i	0.968220	+	0.250098i	$0.0804630\pi$
$359$			9.47738i			0.500197i	−0.968220	+	0.250098i	$0.919537\pi$
$360$	−3.71522	−	12.9138i	−0.195809	−	0.680617i
$361$	−14.8958			−0.783988
$362$	7.33398	+	4.09154i	0.385466	+	0.215047i
$363$	−31.2857	+	3.70847i	−1.64207	+	0.194644i
$364$	−3.52624	−	5.71243i	−0.184825	−	0.299413i
$365$		−	17.7393i		−	0.928517i
$366$	−9.67344	−	3.98643i	−0.505639	−	0.208374i
$367$		−	33.2819i		−	1.73730i	−0.495424	−	0.868651i	$-0.664987\pi$
$367$		−	33.2819i		−	1.73730i	0.495424	−	0.868651i	$-0.335013\pi$
$368$	−11.2892	+	22.5180i	−0.588492	+	1.17383i
$369$	6.05671	+	25.1890i	0.315300	+	1.31129i
$370$	−7.57544	−	4.22625i	−0.393828	−	0.219712i
$371$		−	4.01462i		−	0.208429i
$372$	12.9734	+	14.2721i	0.672637	+	0.739973i
$373$			2.65714i			0.137582i	0.997631	+	0.0687908i	$0.0219141\pi$
$373$			2.65714i			0.137582i	−0.997631	+	0.0687908i	$0.978086\pi$
$374$	22.6158	−	40.5382i	1.16943	−	2.09618i
$375$	−20.4075	+	2.41902i	−1.05384	+	0.124918i
$376$	25.8180	−	1.14082i	1.33146	−	0.0588334i
$377$		−	5.69897i		−	0.293512i
$378$	14.0385	+	2.19246i	0.722062	+	0.112768i
$379$		−	31.5335i		−	1.61976i	−0.586592	−	0.809882i	$-0.699531\pi$
$379$		−	31.5335i		−	1.61976i	0.586592	−	0.809882i	$-0.300469\pi$
$380$	15.6911	−	9.68600i	0.804937	−	0.496881i
$381$	3.71273	+	31.3216i	0.190209	+	1.60465i
$382$	1.71553	−	3.07505i	0.0877744	−	0.157333i
$383$	12.8731			0.657783			0.328892	−	0.944368i	$-0.393325\pi$
$383$	12.8731			0.657783			0.328892	+	0.944368i	$0.393325\pi$
$384$	18.7057	+	5.83922i	0.954572	+	0.297982i
$385$			16.5433i			0.843126i
$386$	−28.7732	−	16.0522i	−1.46452	−	0.817037i
$387$	14.0601	−	3.38075i	0.714713	−	0.171853i
$388$	4.23642	+	6.86291i	0.215072	+	0.348411i
$389$			8.92812i			0.452673i	0.974049	+	0.226337i	$0.0726750\pi$
$389$			8.92812i			0.452673i	−0.974049	+	0.226337i	$0.927325\pi$
$390$	−6.22601	−	2.56574i	−0.315266	−	0.129921i
$391$	−38.2593			−1.93486
$392$	0.407208	+	9.21557i	0.0205671	+	0.465456i
$393$	12.6037	−	1.49399i	0.635773	−	0.0753619i
$394$	14.5866	−	26.1461i	0.734864	−	1.31722i
$395$		−	25.4152i		−	1.27878i
$396$	22.8388	−	23.0043i	1.14770	−	1.15601i
$397$			12.1229i			0.608429i	0.952604	+	0.304214i	$0.0983939\pi$
$397$			12.1229i			0.608429i	−0.952604	+	0.304214i	$0.901606\pi$
$398$	8.98242	−	16.1007i	0.450248	−	0.807058i
$399$	2.29514	+	19.3624i	0.114901	+	0.969333i
$400$	4.46757	−	8.91121i	0.223378	−	0.445560i
$401$	9.97038			0.497897			0.248948	−	0.968517i	$-0.419915\pi$
$401$	9.97038			0.497897			0.248948	+	0.968517i	$0.419915\pi$
$402$	10.0610	−	24.4139i	0.501796	−	1.21765i
$403$	9.64390	−	0.644627i	0.480397	−	0.0321112i
$404$	−11.3355	−	18.3633i	−0.563963	−	0.913608i
$405$	12.6947	−	6.47952i	0.630806	−	0.321970i
$406$	4.37355	−	7.83948i	0.217056	−	0.389067i
$407$		−	20.9262i		−	1.03727i
$408$	4.80485	+	29.3731i	0.237875	+	1.45419i
$409$		−	17.1712i		−	0.849062i	−0.905413	−	0.424531i	$-0.860439\pi$
$409$		−	17.1712i		−	0.849062i	0.905413	−	0.424531i	$-0.139561\pi$
$410$	9.42262	−	16.8898i	0.465350	−	0.834128i
$411$	−0.396371	+	0.0469841i	−0.0195515	+	0.00231756i
$412$	−14.9014	−	24.1399i	−0.734138	−	1.18929i
$413$	−11.3161			−0.556829
$414$	−25.7287	−	7.20125i	−1.26449	−	0.353922i
$415$			1.49964i			0.0736142i
$416$	8.12037	−	5.52208i	0.398134	−	0.270742i
$417$	−8.03896	+	0.952905i	−0.393670	+	0.0466640i
$418$	38.8471	+	21.6723i	1.90007	+	1.06003i
$419$	17.4348			0.851745			0.425873	−	0.904783i	$-0.359967\pi$
$419$	17.4348			0.851745			0.425873	+	0.904783i	$0.359967\pi$
$420$	−6.59544	−	8.30743i	−0.321825	−	0.405361i
$421$			9.58670i			0.467227i	0.972330	+	0.233614i	$0.0750550\pi$
$421$			9.58670i			0.467227i	−0.972330	+	0.233614i	$0.924945\pi$
$422$	6.86622	−	12.3075i	0.334243	−	0.599121i
$423$	6.40831	+	26.6513i	0.311583	+	1.29583i
$424$	5.86692	−	0.259241i	0.284923	−	0.0125899i
$425$	15.1406			0.734428
$426$	5.49309	−	13.3295i	0.266141	−	0.645816i
$427$	−8.25890			−0.399676
$428$	−2.92384	−	4.73656i	−0.141329	−	0.228950i
$429$	−1.91219	−	16.1318i	−0.0923216	−	0.778849i
$430$	−9.42759	−	5.25954i	−0.454639	−	0.253638i
$431$			16.6572i			0.802348i	0.916002	+	0.401174i	$0.131398\pi$
$431$			16.6572i			0.802348i	−0.916002	+	0.401174i	$0.868602\pi$
$432$	−2.29750	+	20.6572i	−0.110539	+	0.993872i
$433$		−	14.7856i		−	0.710551i	−0.934762	−	0.355276i	$-0.884387\pi$
$433$		−	14.7856i		−	0.710551i	0.934762	−	0.355276i	$-0.115613\pi$
$434$	13.7608	+	6.51425i	0.660539	+	0.312694i
$435$	−1.05997	−	8.94217i	−0.0508216	−	0.428744i
$436$	−13.3124	+	8.21763i	−0.637547	+	0.393553i
$437$		−	36.6633i		−	1.75384i
$438$	−10.4544	+	25.3686i	−0.499530	+	1.21216i
$439$	−6.52703			−0.311518			−0.155759	−	0.987795i	$-0.549782\pi$
$439$	−6.52703			−0.311518			−0.155759	+	0.987795i	$0.549782\pi$
$440$	−24.1762	+	1.06827i	−1.15256	+	0.0509280i
$441$	−9.51298	+	2.28740i	−0.452999	+	0.108924i
$442$	13.0254	+	7.26674i	0.619557	+	0.345644i
$443$	−3.27834			−0.155759			−0.0778793	−	0.996963i	$-0.524815\pi$
$443$	−3.27834			−0.155759			−0.0778793	+	0.996963i	$0.524815\pi$
$444$	8.34279	+	10.5083i	0.395931	+	0.498704i
$445$	−10.1447			−0.480904
$446$	−2.72411	+	4.88289i	−0.128990	+	0.231211i
$447$	−21.9670	+	2.60387i	−1.03900	+	0.123159i
$448$	15.4081	−	1.36434i	0.727966	−	0.0644591i
$449$	15.6049			0.736442			0.368221	−	0.929738i	$-0.379967\pi$
$449$	15.6049			0.736442			0.368221	+	0.929738i	$0.379967\pi$
$450$	10.1818	+	2.84980i	0.479973	+	0.134341i
$451$	46.6559			2.19694
$452$	0.0959601	−	0.0592354i	0.00451358	−	0.00278620i
$453$	2.65523	+	22.4002i	0.124754	+	1.05245i
$454$	−28.6552	−	15.9864i	−1.34486	−	0.750280i
$455$	−5.31559			−0.249198
$456$	−28.1478	+	4.60441i	−1.31814	+	0.215621i
$457$			12.4020i			0.580142i	0.957005	+	0.290071i	$0.0936789\pi$
$457$			12.4020i			0.580142i	−0.957005	+	0.290071i	$0.906321\pi$
$458$	−22.5403	−	12.5750i	−1.05324	−	0.587590i
$459$	−29.6120	+	10.9422i	−1.38217	+	0.510737i
$460$	10.4768	+	16.9722i	0.488485	+	0.791335i
$461$			8.88419i			0.413778i	0.978364	+	0.206889i	$0.0663339\pi$
$461$			8.88419i			0.413778i	−0.978364	+	0.206889i	$0.933666\pi$
$462$	9.74957	−	23.6582i	0.453591	−	1.10068i
$463$			8.56406i			0.398006i	0.979999	+	0.199003i	$0.0637703\pi$
$463$			8.56406i			0.398006i	−0.979999	+	0.199003i	$0.936230\pi$
$464$	11.7389	+	5.88523i	0.544966	+	0.273215i
$465$	15.0122	−	2.80517i	0.696174	−	0.130087i
$466$	12.1940	−	21.8575i	0.564878	−	1.01253i
$467$	−9.00042			−0.416490			−0.208245	−	0.978077i	$-0.566775\pi$
$467$	−9.00042			−0.416490			−0.208245	+	0.978077i	$0.566775\pi$
$468$	7.39160	+	7.33842i	0.341677	+	0.339218i
$469$		−	20.8439i		−	0.962480i
$470$	9.96962	−	17.8703i	0.459864	−	0.824295i
$471$	1.49478	+	12.6103i	0.0688757	+	0.581054i
$472$	−0.730730	−	16.5372i	−0.0336346	−	0.761187i
$473$		−	26.0425i		−	1.19744i
$474$	−14.9781	+	36.3457i	−0.687965	+	1.66941i
$475$			14.5090i			0.665719i
$476$	12.3410	+	19.9922i	0.565650	+	0.916340i
$477$	1.45623	+	6.05626i	0.0666762	+	0.277297i
$478$	18.6729	+	10.4174i	0.854080	+	0.476482i
$479$		−	26.4740i		−	1.20963i	−0.796367	−	0.604814i	$-0.793247\pi$
$479$		−	26.4740i		−	1.20963i	0.796367	−	0.604814i	$-0.206753\pi$
$480$	11.7145	−	10.1749i	0.534691	−	0.464421i
$481$	6.72385			0.306581
$482$	−3.30785	+	5.92924i	−0.150669	+	0.270069i
$483$	−20.9433	+	2.48253i	−0.952954	+	0.112959i
$484$	−19.1087	−	30.9556i	−0.868577	−	1.40707i
$485$	6.38614			0.289980
$486$	−21.9730	+	1.78477i	−0.996717	+	0.0809587i
$487$		−	18.2134i		−	0.825327i	−0.910884	−	0.412664i	$-0.864599\pi$
$487$		−	18.2134i		−	0.825327i	0.910884	−	0.412664i	$-0.135401\pi$
$488$	−0.533313	−	12.0694i	−0.0241419	−	0.546358i
$489$	−3.44567	−	29.0686i	−0.155819	−	1.31453i
$490$	6.37867	+	3.55858i	0.288159	+	0.160760i
$491$		−	9.62164i		−	0.434219i	−0.976147	−	0.217109i	$-0.930337\pi$
$491$		−	9.62164i		−	0.434219i	0.976147	−	0.217109i	$-0.0696628\pi$
$492$	−23.4288	+	18.6006i	−1.05625	+	0.838581i
$493$			19.9451i			0.898281i
$494$	−6.96360	+	12.4821i	−0.313307	+	0.561595i
$495$	−6.00079	−	24.9565i	−0.269715	−	1.12171i
$496$	−8.63125	+	20.5305i	−0.387555	+	0.921847i
$497$		−	11.3803i		−	0.510477i
$498$	0.883788	−	2.14459i	0.0396035	−	0.0961016i
$499$	2.86528			0.128267			0.0641337	−	0.997941i	$-0.479572\pi$
$499$	2.86528			0.128267			0.0641337	+	0.997941i	$0.479572\pi$
$500$	−12.4645	−	20.1922i	−0.557430	−	0.903023i
$501$	31.6849	−	3.75580i	1.41558	−	0.167797i
$502$	−15.9255	+	28.5461i	−0.710790	+	1.27407i
$503$			21.5279i			0.959882i	0.877301	+	0.479941i	$0.159342\pi$
$503$			21.5279i			0.959882i	−0.877301	+	0.479941i	$0.840658\pi$
$504$	4.53613	+	15.7672i	0.202055	+	0.702327i
$505$	−17.0876			−0.760387
$506$	−23.4418	+	42.0188i	−1.04212	+	1.86797i
$507$	−17.1768	+	2.03606i	−0.762847	+	0.0904248i
$508$	−30.9912	+	19.1306i	−1.37501	+	0.848784i
$509$			37.2926i			1.65296i	0.562963	+	0.826482i	$0.309661\pi$
$509$			37.2926i			1.65296i	−0.562963	+	0.826482i	$0.690339\pi$
$510$	21.7896	+	8.97949i	0.964859	+	0.397619i
$511$			21.6589i			0.958135i
$512$	2.98880	+	22.4292i	0.132088	+	0.991238i
$513$	−10.4857	−	28.3767i	−0.462955	−	1.25286i
$514$	13.5794	−	24.3408i	0.598963	−	1.07363i
$515$	−22.4629			−0.989833
$516$	10.3825	+	13.0776i	0.457066	+	0.575708i
$517$	49.3643			2.17104
$518$	9.24929	+	5.16007i	0.406391	+	0.226721i
$519$	33.2600	−	3.94251i	1.45995	−	0.173057i
$520$	−0.343250	−	7.76813i	−0.0150525	−	0.340655i
$521$			2.50887i			0.109915i	0.998489	+	0.0549577i	$0.0175024\pi$
$521$			2.50887i			0.109915i	−0.998489	+	0.0549577i	$0.982498\pi$
$522$	−3.75410	+	13.4127i	−0.164313	+	0.587057i
$523$	−38.0803			−1.66514			−0.832568	−	0.553923i	$-0.813130\pi$
$523$	−38.0803			−1.66514			−0.832568	+	0.553923i	$0.813130\pi$
$524$	7.69810	+	12.4708i	0.336293	+	0.544788i
$525$	8.28804	−	0.982430i	0.361720	−	0.0428768i
$526$	13.9403	+	7.77714i	0.607826	+	0.339099i
$527$	−33.7514	+	2.25604i	−1.47023	+	0.0982748i
$528$	35.2034	+	12.7202i	1.53203	+	0.553575i
$529$	16.6568			0.724207
$530$	2.26551	−	4.06086i	0.0984073	−	0.176392i
$531$	17.0709	−	4.10471i	0.740815	−	0.178129i
$532$	−19.1582	+	11.8262i	−0.830612	+	0.512731i
$533$			14.9911i			0.649339i
$534$	14.5077	+	5.97862i	0.627809	+	0.258720i
$535$	−4.40750			−0.190553
$536$	30.4610	−	1.34598i	1.31571	−	0.0581374i
$537$	−1.39941	−	11.8058i	−0.0603888	−	0.509456i
$538$	−0.0752206	+	0.134831i	−0.00324299	+	0.00581298i
$539$			17.6202i			0.758958i
$540$	12.9629	+	10.1398i	0.557836	+	0.436348i
$541$		−	26.6081i		−	1.14397i	−0.820263	−	0.571986i	$-0.806173\pi$
$541$		−	26.6081i		−	1.14397i	0.820263	−	0.571986i	$-0.193827\pi$
$542$	16.6269	−	29.8033i	0.714187	−	1.28016i
$543$	−10.2140	+	1.21073i	−0.438325	+	0.0519573i
$544$	−28.4194	+	19.3260i	−1.21847	+	0.828595i
$545$			12.3876i			0.530624i
$546$	7.60170	+	3.13266i	0.325323	+	0.134066i
$547$			12.8343i			0.548755i	0.961622	+	0.274377i	$0.0884717\pi$
$547$			12.8343i			0.548755i	−0.961622	+	0.274377i	$0.911528\pi$
$548$	−0.242096	−	0.392189i	−0.0103418	−	0.0167535i
$549$	12.4590	−	2.99576i	0.531736	−	0.127856i
$550$	9.27679	−	16.6284i	0.395564	−	0.709037i
$551$	−19.1130			−0.814243
$552$	−4.98035	−	30.4460i	−0.211978	−	1.29587i
$553$			31.0309i			1.31957i
$554$	26.8098	+	14.9569i	1.13904	+	0.635458i
$555$	10.5503	−	1.25059i	0.447835	−	0.0530845i
$556$	−4.91004	−	7.95416i	−0.208232	−	0.337332i
$557$		−	40.5799i		−	1.71943i	−0.510778	−	0.859713i	$-0.670643\pi$
$557$		−	40.5799i		−	1.71943i	0.510778	−	0.859713i	$-0.329357\pi$
$558$	−23.1218	−	4.83561i	−0.978823	−	0.204708i
$559$	8.36779			0.353920
$560$	5.48931	−	10.9492i	0.231966	−	0.462689i
$561$	6.69223	+	56.4574i	0.282546	+	2.38363i
$562$	−1.12409	+	2.01491i	−0.0474170	+	0.0849937i
$563$	−20.6428			−0.869991			−0.434996	−	0.900433i	$-0.643250\pi$
$563$	−20.6428			−0.869991			−0.434996	+	0.900433i	$0.643250\pi$
$564$	−24.7889	+	19.6804i	−1.04380	+	0.828696i
$565$		−	0.0892937i		−	0.00375661i
$566$	−9.31921	+	16.7044i	−0.391716	+	0.702140i
$567$	−15.4997	+	7.91122i	−0.650927	+	0.332240i
$568$	16.6311	−	0.734877i	0.697824	−	0.0308347i
$569$	−5.08457			−0.213156			−0.106578	−	0.994304i	$-0.533989\pi$
$569$	−5.08457			−0.213156			−0.106578	+	0.994304i	$0.533989\pi$
$570$	−8.60490	+	20.8806i	−0.360420	+	0.874592i
$571$	−32.7220			−1.36937			−0.684686	−	0.728838i	$-0.740061\pi$
$571$	−32.7220			−1.36937			−0.684686	+	0.728838i	$0.740061\pi$
$572$	15.9616	−	9.85298i	0.667388	−	0.411974i
$573$	0.507644	+	4.28262i	0.0212071	+	0.178909i
$574$	−11.5046	+	20.6217i	−0.480194	+	0.860734i
$575$	−15.6936			−0.654470
$576$	−22.7491	+	7.64720i	−0.947878	+	0.318633i
$577$	2.77291			0.115438			0.0577189	−	0.998333i	$-0.481617\pi$
$577$	2.77291			0.115438			0.0577189	+	0.998333i	$0.481617\pi$
$578$	−24.5906	−	13.7188i	−1.02284	−	0.570628i
$579$	40.0724	−	4.75001i	1.66535	−	0.197404i
$580$	8.84785	−	5.46171i	0.367387	−	0.226785i
$581$		−	1.83099i		−	0.0759623i
$582$	−9.13267	−	3.76358i	−0.378561	−	0.156005i
$583$	11.2176			0.464585
$584$	−31.6521	+	1.39861i	−1.30977	+	0.0578749i
$585$	8.01883	−	1.92813i	0.331538	−	0.0797184i
$586$	7.82816	+	4.36724i	0.323378	+	0.180409i
$587$			29.8154i			1.23061i	0.788288	+	0.615307i	$0.210968\pi$
$587$			29.8154i			1.23061i	−0.788288	+	0.615307i	$0.789032\pi$
$588$	−7.02479	−	8.84822i	−0.289697	−	0.364895i
$589$	−2.16193	−	32.3434i	−0.0890808	−	1.33269i
$590$	−11.4464	−	6.38583i	−0.471242	−	0.262901i
$591$	4.31633	+	36.4137i	0.177550	+	1.49786i
$592$	−6.94360	+	13.8500i	−0.285380	+	0.569232i
$593$			26.0953i			1.07160i	0.844344	+	0.535802i	$0.179991\pi$
$593$			26.0953i			1.07160i	−0.844344	+	0.535802i	$0.820009\pi$
$594$	−6.12613	+	39.2261i	−0.251358	+	1.60947i
$595$	18.6033			0.762661
$596$	−13.4170	−	21.7352i	−0.549582	−	0.890310i
$597$	2.65799	+	22.4235i	0.108784	+	0.917732i
$598$	−13.5012	−	7.53216i	−0.552105	−	0.308013i
$599$		−	32.9818i		−	1.34760i	−0.738915	−	0.673799i	$-0.764661\pi$
$599$		−	32.9818i		−	1.34760i	0.738915	−	0.673799i	$-0.235339\pi$
$600$	1.97091	+	12.0486i	0.0804619	+	0.491882i
$601$		−	12.7924i		−	0.521814i	−0.965364	−	0.260907i	$-0.915978\pi$
$601$		−	12.7924i		−	0.521814i	0.965364	−	0.260907i	$-0.0840216\pi$
$602$	11.5107	+	6.42168i	0.469141	+	0.261728i
$603$	7.56073	+	31.4440i	0.307897	+	1.28050i
$604$	−22.1639	+	13.6816i	−0.901837	+	0.556697i
$605$	−28.8051			−1.17110
$606$	24.4366	+	10.0703i	0.992667	+	0.409078i
$607$	−12.8573			−0.521861			−0.260930	−	0.965358i	$-0.584029\pi$
$607$	−12.8573			−0.521861			−0.260930	+	0.965358i	$0.584029\pi$
$608$	−18.5198	−	27.2338i	−0.751076	−	1.10448i
$609$	1.29418	+	10.9180i	0.0524427	+	0.442420i
$610$	−8.35402	−	4.66061i	−0.338244	−	0.188703i
$611$			15.8614i			0.641684i
$612$	−25.8689	−	25.6827i	−1.04569	−	1.03816i
$613$	−9.09480			−0.367336			−0.183668	−	0.982988i	$-0.558797\pi$
$613$	−9.09480			−0.367336			−0.183668	+	0.982988i	$0.558797\pi$
$614$	3.56642	−	6.39270i	0.143929	−	0.257989i
$615$	2.78825	+	23.5224i	0.112433	+	0.948514i
$616$	29.5181	−	1.30432i	1.18932	−	0.0525524i
$617$		−	20.1667i		−	0.811882i	−0.913899	−	0.405941i	$-0.866944\pi$
$617$		−	20.1667i		−	0.811882i	0.913899	−	0.405941i	$-0.133056\pi$
$618$	32.1236	+	13.2382i	1.29220	+	0.532517i
$619$	−16.3420			−0.656842			−0.328421	−	0.944531i	$-0.606516\pi$
$619$	−16.3420			−0.656842			−0.328421	+	0.944531i	$0.606516\pi$
$620$	10.2432	+	14.3547i	0.411377	+	0.576498i
$621$	30.6936	−	11.3418i	1.23169	−	0.455132i
$622$	−19.4047	+	34.7823i	−0.778056	+	1.39464i
$623$	12.3862			0.496244
$624$	−4.08716	+	11.3113i	−0.163617	+	0.452815i
$625$	−6.32897			−0.253159
$626$	19.6545	−	35.2301i	0.785551	−	1.40808i
$627$	−54.1022	+	6.41305i	−2.16063	+	0.256113i
$628$	−12.4773	+	7.70216i	−0.497899	+	0.307349i
$629$	−23.5319			−0.938279
$630$	12.5104	+	3.50155i	0.498425	+	0.139505i
$631$			12.0870i			0.481174i	0.970628	+	0.240587i	$0.0773400\pi$
$631$			12.0870i			0.481174i	−0.970628	+	0.240587i	$0.922660\pi$
$632$	−45.3481	+	2.00380i	−1.80385	+	0.0797068i
$633$	2.03178	+	17.1407i	0.0807561	+	0.681280i
$634$	3.05768	+	1.70584i	0.121436	+	0.0677477i
$635$			28.8382i			1.14441i
$636$	−5.63306	+	4.47220i	−0.223365	+	0.177334i
$637$	−5.66161			−0.224321
$638$	21.9050	+	12.2205i	0.867226	+	0.483815i
$639$	4.12800	+	17.1678i	0.163301	+	0.679148i
$640$	16.3555	+	7.31497i	0.646508	+	0.289149i
$641$	−15.0718			−0.595299			−0.297650	−	0.954675i	$-0.596203\pi$
$641$	−15.0718			−0.595299			−0.297650	+	0.954675i	$0.596203\pi$
$642$	6.30307	+	2.59750i	0.248762	+	0.102515i
$643$	35.8673			1.41447			0.707235	−	0.706979i	$-0.249942\pi$
$643$	35.8673			1.41447			0.707235	+	0.706979i	$0.249942\pi$
$644$	−12.7918	−	20.7224i	−0.504067	−	0.816577i
$645$	13.1298	−	1.55635i	0.516985	−	0.0612812i
$646$	24.3710	−	43.6843i	0.958863	−	1.71874i
$647$	−37.8787			−1.48917			−0.744583	−	0.667530i	$-0.767352\pi$
$647$	−37.8787			−1.48917			−0.744583	+	0.667530i	$0.767352\pi$
$648$	−12.5622	−	22.1402i	−0.493492	−	0.869751i
$649$		−	31.6193i		−	1.24117i
$650$	5.34292	+	2.98075i	0.209567	+	0.116915i
$651$	−18.3293	+	3.42499i	−0.718380	+	0.134236i
$652$	28.7620	−	17.7546i	1.12641	−	0.695322i
$653$	4.27059			0.167121			0.0835606	−	0.996503i	$-0.473371\pi$
$653$	4.27059			0.167121			0.0835606	+	0.996503i	$0.473371\pi$
$654$	7.30042	−	17.7152i	0.285469	−	0.692717i
$655$	11.6044			0.453422
$656$	−30.8792	−	15.4811i	−1.20563	−	0.604435i
$657$	−7.85638	−	32.6736i	−0.306506	−	1.27472i
$658$	−12.1725	+	21.8189i	−0.474533	+	0.850588i
$659$	45.1891			1.76032			0.880158	−	0.474681i	$-0.157436\pi$
$659$	45.1891			1.76032			0.880158	+	0.474681i	$0.157436\pi$
$660$	23.2125	−	18.4289i	0.903546	−	0.717344i
$661$			11.2458i			0.437411i	0.975791	+	0.218706i	$0.0701835\pi$
$661$			11.2458i			0.437411i	−0.975791	+	0.218706i	$0.929817\pi$
$662$	35.3348	+	19.7128i	1.37332	+	0.766162i
$663$	−18.1405	+	2.15030i	−0.704519	+	0.0835107i
$664$	2.67579	−	0.118235i	0.103841	−	0.00458841i
$665$			17.8272i			0.691311i
$666$	−15.8248	−	4.42922i	−0.613197	−	0.171629i
$667$		−	20.6736i		−	0.800484i
$668$	19.3526	+	31.3507i	0.748773	+	1.21300i
$669$	−0.806090	−	6.80039i	−0.0311652	−	0.262918i
$670$	11.7625	−	21.0839i	0.454424	−	0.814543i
$671$		−	23.0769i		−	0.890874i
$672$	−14.3029	+	12.4232i	−0.551746	+	0.479235i
$673$			6.32918i			0.243972i	0.992532	+	0.121986i	$0.0389263\pi$
$673$			6.32918i			0.243972i	−0.992532	+	0.121986i	$0.961074\pi$
$674$	13.2695	−	23.7852i	0.511121	−	0.916171i
$675$	−12.1466	+	4.48838i	−0.467522	+	0.172758i
$676$	−10.4912	−	16.9956i	−0.403509	−	0.653676i
$677$		−	9.84163i		−	0.378245i	−0.981954	−	0.189122i	$-0.939436\pi$
$677$		−	9.84163i		−	0.378245i	0.981954	−	0.189122i	$-0.0605643\pi$
$678$	−0.0526239	+	0.127697i	−0.00202101	+	0.00490417i
$679$	−7.79720			−0.299229
$680$	1.20130	+	27.1866i	0.0460676	+	1.04256i
$681$	39.9081	−	4.73054i	1.52928	−	0.181275i
$682$	−18.2020	+	38.4502i	−0.696992	+	1.47233i
$683$	31.4121			1.20195			0.600975	−	0.799268i	$-0.294779\pi$
$683$	31.4121			1.20195			0.600975	+	0.799268i	$0.294779\pi$
$684$	24.6114	−	24.7897i	0.941039	−	0.947858i
$685$	−0.364944			−0.0139438
$686$	−24.5039	−	13.6705i	−0.935564	−	0.521940i
$687$	31.3918	−	3.72106i	1.19767	−	0.141967i
$688$	−8.64127	+	17.2363i	−0.329445	+	0.657126i
$689$			3.60436i			0.137315i
$690$	−22.5855	−	9.30747i	−0.859814	−	0.354330i
$691$		−	23.3599i		−	0.888653i	−0.895865	−	0.444326i	$-0.853443\pi$
$691$		−	23.3599i		−	0.888653i	0.895865	−	0.444326i	$-0.146557\pi$
$692$	20.3146	+	32.9092i	0.772245	+	1.25102i
$693$	7.32671	+	30.4708i	0.278319	+	1.15749i
$694$	−11.8765	+	21.2884i	−0.450827	+	0.808095i
$695$	−7.40158			−0.280758
$696$	−15.8719	+	2.59632i	−0.601622	+	0.0984132i
$697$		−	52.4655i		−	1.98727i
$698$	9.69960	−	17.3863i	0.367135	−	0.658080i
$699$	3.60834	+	30.4409i	0.136480	+	1.15138i
$700$	5.06218	+	8.20061i	0.191332	+	0.309954i
$701$	33.8118			1.27706			0.638528	−	0.769599i	$-0.279544\pi$
$701$	33.8118			1.27706			0.638528	+	0.769599i	$0.279544\pi$
$702$	−12.6039	−	1.96841i	−0.475702	−	0.0742927i
$703$		−	22.5503i		−	0.850499i
$704$	3.81223	+	43.0532i	0.143679	+	1.62263i
$705$	2.95011	+	24.8879i	0.111108	+	0.937332i
$706$	−20.1481	−	11.2404i	−0.758284	−	0.423038i
$707$	20.8632			0.784642
$708$	12.6059	+	15.8780i	0.473758	+	0.596733i
$709$	14.9183			0.560268			0.280134	−	0.959961i	$-0.409621\pi$
$709$	14.9183			0.560268			0.280134	+	0.959961i	$0.409621\pi$
$710$	6.42207	−	11.5114i	0.241016	−	0.432015i
$711$	−11.2559	−	46.8117i	−0.422128	−	1.75557i
$712$	0.799832	+	18.1011i	0.0299750	+	0.678367i
$713$	34.9842	−	2.33845i	1.31017	−	0.0875755i
$714$	−26.6042	−	10.9636i	−0.995636	−	0.410302i
$715$		−	14.8527i		−	0.555461i
$716$	11.6812	−	7.21073i	0.436548	−	0.269478i
$717$	−26.0058	+	3.08262i	−0.971203	+	0.115122i
$718$	6.52995	−	11.7048i	0.243695	−	0.436817i
$719$	39.8718			1.48697			0.743484	−	0.668754i	$-0.233172\pi$
$719$	39.8718			1.48697			0.743484	+	0.668754i	$0.233172\pi$
$720$	−4.30928	+	18.5086i	−0.160597	+	0.689775i
$721$	27.4262			1.02141
$722$	18.3966	+	10.2632i	0.684650	+	0.381958i
$723$	−0.978826	−	8.25763i	−0.0364029	−	0.307105i
$724$	−6.23853	−	10.1063i	−0.231853	−	0.375597i
$725$			8.18129i			0.303846i
$726$	41.1936	+	16.9759i	1.52884	+	0.630034i
$727$	19.0749			0.707448			0.353724	−	0.935350i	$-0.384915\pi$
$727$	19.0749			0.707448			0.353724	+	0.935350i	$0.384915\pi$
$728$	0.419094	+	9.48456i	0.0155327	+	0.351521i
$729$	20.5125	−	17.5567i	0.759721	−	0.650249i
$730$	−12.2224	+	21.9084i	−0.452372	+	0.810866i
$731$	−29.2853			−1.08316
$732$	9.20023	+	11.5883i	0.340050	+	0.428318i
$733$			7.99972i			0.295476i	0.989027	+	0.147738i	$0.0471993\pi$
$733$			7.99972i			0.295476i	−0.989027	+	0.147738i	$0.952801\pi$
$734$	−22.9314	+	41.1039i	−0.846412	+	1.51717i
$735$	−8.88355	+	1.05302i	−0.327675	+	0.0388412i
$736$	29.4574	−	20.0319i	1.08582	−	0.738385i
$737$	58.2416			2.14536
$738$	9.87516	−	35.2820i	0.363510	−	1.29875i
$739$	−0.430479			−0.0158354			−0.00791771	−	0.999969i	$-0.502520\pi$
$739$	−0.430479			−0.0158354			−0.00791771	+	0.999969i	$0.502520\pi$
$740$	6.44392	+	10.4390i	0.236883	+	0.383746i
$741$	−2.06060	−	17.3837i	−0.0756979	−	0.638608i
$742$	−2.76609	+	4.95814i	−0.101546	+	0.182019i
$743$	−36.9027			−1.35383			−0.676914	−	0.736062i	$-0.736683\pi$
$743$	−36.9027			−1.35383			−0.676914	+	0.736062i	$0.736683\pi$
$744$	−6.18884	−	26.5650i	−0.226894	−	0.973919i
$745$	−20.2253			−0.740997
$746$	1.83078	−	3.28162i	0.0670296	−	0.120149i
$747$	0.664158	+	2.76214i	0.0243003	+	0.101062i
$748$	−55.8619	+	34.4831i	−2.04251	+	1.26083i
$749$	5.38138			0.196631
$750$	26.8704	+	11.0733i	0.981167	+	0.404339i
$751$	25.8808			0.944405			0.472202	−	0.881490i	$-0.343459\pi$
$751$	25.8808			0.944405			0.472202	+	0.881490i	$0.343459\pi$
$752$	−32.6718	−	16.3798i	−1.19142	−	0.597309i
$753$	−4.71252	−	39.7560i	−0.171734	−	1.44879i
$754$	−3.92661	+	7.03835i	−0.142999	+	0.256321i
$755$			20.6242i			0.750591i
$756$	−15.8272	−	12.3803i	−0.575630	−	0.450267i
$757$	22.7293			0.826110			0.413055	−	0.910706i	$-0.364462\pi$
$757$	22.7293			0.826110			0.413055	+	0.910706i	$0.364462\pi$
$758$	−21.7267	+	38.9444i	−0.789148	+	1.41453i
$759$	−6.93666	−	58.5195i	−0.251785	−	2.12412i
$760$	−26.0525	+	1.15118i	−0.945024	+	0.0417578i
$761$	−10.0175			−0.363135			−0.181567	−	0.983379i	$-0.558117\pi$
$761$	−10.0175			−0.363135			−0.181567	+	0.983379i	$0.558117\pi$
$762$	16.9954	−	41.2408i	0.615677	−	1.49400i
$763$		−	15.1247i		−	0.547550i
$764$	−4.23744	+	2.61574i	−0.153305	+	0.0946341i
$765$	−28.0640	+	6.74801i	−1.01466	+	0.243975i
$766$	−15.8985	−	8.86959i	−0.574436	−	0.320471i
$767$	10.1597			0.366845
$768$	−19.0787	−	20.0999i	−0.688443	−	0.725291i
$769$	−22.5073			−0.811635			−0.405817	−	0.913954i	$-0.633013\pi$
$769$	−22.5073			−0.811635			−0.405817	+	0.913954i	$0.633013\pi$
$770$	11.3984	−	20.4313i	0.410770	−	0.736294i
$771$	4.01829	+	33.8993i	0.144715	+	1.22086i
$772$	24.4754	+	39.6496i	0.880890	+	1.42702i
$773$			46.5416i			1.67399i	0.547214	+	0.836993i	$0.315689\pi$
$773$			46.5416i			1.67399i	−0.547214	+	0.836993i	$0.684311\pi$
$774$	−19.6938	−	5.51214i	−0.707879	−	0.198130i
$775$	−13.8445	+	0.925409i	−0.497310	+	0.0332417i
$776$	−0.503499	−	11.3947i	−0.0180746	−	0.409047i
$777$	−12.8815	+	1.52692i	−0.462120	+	0.0547778i
$778$	6.15150	−	11.0264i	0.220542	−	0.395316i
$779$	50.2768			1.80135
$780$	5.92144	+	7.45848i	0.212022	+	0.267057i
$781$	31.7987			1.13785
$782$	47.2510	+	26.3608i	1.68969	+	0.942660i
$783$	−5.91264	−	16.0010i	−0.211301	−	0.571827i
$784$	5.84664	−	11.6620i	0.208809	−	0.416499i
$785$			11.6105i			0.414397i
$786$	−16.5952	−	6.83889i	−0.591931	−	0.243935i
$787$	12.8241			0.457128			0.228564	−	0.973529i	$-0.426597\pi$
$787$	12.8241			0.457128			0.228564	+	0.973529i	$0.426597\pi$
$788$	−36.0296	+	22.2408i	−1.28350	+	0.792295i
$789$	−19.4146	+	2.30133i	−0.691179	+	0.0819295i
$790$	−17.5111	+	31.3883i	−0.623019	+	1.11674i
$791$			0.109024i			0.00387644i
$792$	−44.0565	+	12.6748i	−1.56548	+	0.450379i
$793$	7.41491			0.263311
$794$	8.35269	−	14.9720i	0.296426	−	0.531335i
$795$	0.670385	+	5.65555i	0.0237761	+	0.200582i
$796$	−22.1869	+	13.6958i	−0.786395	+	0.485436i
$797$		−	1.46281i		−	0.0518155i	−0.999664	−	0.0259078i	$-0.991752\pi$
$797$		−	1.46281i		−	0.0518155i	0.999664	−	0.0259078i	$-0.00824762\pi$
$798$	10.5062	−	25.4943i	0.371916	−	0.902490i
$799$		−	55.5112i		−	1.96385i
$800$	−11.6574	+	7.92735i	−0.412151	+	0.280274i
$801$	−18.6853	+	4.49288i	−0.660211	+	0.158748i
$802$	−12.3136	−	6.86962i	−0.434809	−	0.242575i
$803$	−60.5191			−2.13567
$804$	−29.2467	+	23.2196i	−1.03145	+	0.818892i
$805$	−19.2828			−0.679629
$806$	−12.3546	−	5.84855i	−0.435171	−	0.206006i
$807$	−0.0222585	−	0.187779i	−0.000783537	−	0.00661013i
$808$	1.34723	+	30.4892i	0.0473953	+	1.07261i
$809$	22.0370			0.774780			0.387390	−	0.921916i	$-0.373377\pi$
$809$	22.0370			0.774780			0.387390	+	0.921916i	$0.373377\pi$
$810$	−20.1426	−	0.744367i	−0.707740	−	0.0261544i
$811$		−	47.5945i		−	1.67127i	−0.549285	−	0.835635i	$-0.685100\pi$
$811$		−	47.5945i		−	1.67127i	0.549285	−	0.835635i	$-0.314900\pi$
$812$	−10.8028	+	6.66852i	−0.379106	+	0.234019i
$813$	4.92006	+	41.5070i	0.172554	+	1.45571i
$814$	−14.4182	+	25.8443i	−0.505358	+	0.905841i
$815$		−	26.7639i		−	0.937498i
$816$	14.3041	−	39.5870i	0.500744	−	1.38582i
$817$		−	28.0636i		−	0.981823i
$818$	−11.8310	+	21.2068i	−0.413662	+	0.741478i
$819$	−9.79066	+	2.35417i	−0.342113	+	0.0822612i
$820$	−23.2743	+	14.3670i	−0.812772	+	0.501718i
$821$		−	36.8010i		−	1.28436i	−0.766553	−	0.642181i	$-0.778030\pi$
$821$		−	36.8010i		−	1.28436i	0.766553	−	0.642181i	$-0.221970\pi$
$822$	0.521898	+	0.215074i	0.0182033	+	0.00750158i
$823$		−	21.6818i		−	0.755779i	−0.925851	−	0.377889i	$-0.876650\pi$
$823$		−	21.6818i		−	0.755779i	0.925851	−	0.377889i	$-0.123350\pi$
$824$	1.77103	+	40.0803i	0.0616967	+	1.39626i
$825$	2.74509	+	23.1583i	0.0955719	+	0.806269i
$826$	13.9756	+	7.79683i	0.486274	+	0.271286i
$827$		−	14.7171i		−	0.511765i	−0.966708	−	0.255883i	$-0.917634\pi$
$827$		−	14.7171i		−	0.511765i	0.966708	−	0.255883i	$-0.0823661\pi$
$828$	26.8137	+	26.6208i	0.931841	+	0.925137i
$829$	−33.2360			−1.15433			−0.577167	−	0.816626i	$-0.695842\pi$
$829$	−33.2360			−1.15433			−0.577167	+	0.816626i	$0.695842\pi$
$830$	1.03325	−	1.85208i	0.0358648	−	0.0642866i
$831$	−37.3380	+	4.42589i	−1.29524	+	0.153533i
$832$	−13.8336	+	1.22492i	−0.479592	+	0.0424664i
$833$	19.8143			0.686526
$834$	10.5848	+	4.36201i	0.366523	+	0.151044i
$835$	29.1728			1.00956
$836$	−33.0446	−	53.5315i	−1.14287	−	1.85143i
$837$	26.4083	−	11.8154i	0.912803	−	0.408399i
$838$	−21.5323	−	12.0126i	−0.743822	−	0.414969i
$839$		−	16.5785i		−	0.572355i	−0.958177	−	0.286177i	$-0.907615\pi$
$839$		−	16.5785i		−	0.572355i	0.958177	−	0.286177i	$-0.0923847\pi$
$840$	2.42165	+	14.8041i	0.0835550	+	0.510791i
$841$	18.2226			0.628366
$842$	6.60527	−	11.8398i	0.227633	−	0.408025i
$843$	−0.332630	−	2.80615i	−0.0114564	−	0.0966491i
$844$	−16.9598	+	10.4692i	−0.583782	+	0.360364i
$845$	−15.8149			−0.544049
$846$	10.4484	−	37.3302i	0.359225	−	1.28344i
$847$	35.1699			1.20845
$848$	−7.42438	−	3.72216i	−0.254954	−	0.127819i
$849$	−2.75764	−	23.2642i	−0.0946421	−	0.798426i
$850$	−18.6990	−	10.4319i	−0.641369	−	0.357812i
$851$	24.3914			0.836127
$852$	−15.9681	+	12.6774i	−0.547059	+	0.434322i
$853$		−	26.5331i		−	0.908476i	−0.890880	−	0.454238i	$-0.849911\pi$
$853$		−	26.5331i		−	0.908476i	0.890880	−	0.454238i	$-0.150089\pi$
$854$	10.1999	+	5.69041i	0.349034	+	0.194722i
$855$	−6.46650	−	26.8933i	−0.221150	−	0.919732i
$856$	0.347499	+	7.86428i	0.0118773	+	0.268795i
$857$			25.7978i			0.881237i	0.897694	+	0.440618i	$0.145241\pi$
$857$			25.7978i			0.881237i	−0.897694	+	0.440618i	$0.854759\pi$
$858$	−8.75324	+	21.2406i	−0.298831	+	0.725141i
$859$	−5.42634			−0.185144			−0.0925721	−	0.995706i	$-0.529509\pi$
$859$	−5.42634			−0.185144			−0.0925721	+	0.995706i	$0.529509\pi$
$860$	8.01942	+	12.9913i	0.273460	+	0.442999i
$861$	−3.40433	−	28.7198i	−0.116019	−	0.978769i
$862$	11.4769	−	20.5720i	0.390903	−	0.700684i
$863$	7.10387			0.241819			0.120909	−	0.992664i	$-0.461419\pi$
$863$	7.10387			0.241819			0.120909	+	0.992664i	$0.461419\pi$
$864$	17.0704	−	23.9291i	0.580746	−	0.814085i
$865$	30.6230			1.04121
$866$	−10.1873	+	18.2605i	−0.346180	+	0.620518i
$867$	34.2473	−	4.05954i	1.16310	−	0.137869i
$868$	−12.5065	−	17.5265i	−0.424499	−	0.594887i
$869$	−86.7060			−2.94130
$870$	−4.85211	+	11.7741i	−0.164502	+	0.399179i
$871$			18.7138i			0.634093i
$872$	22.1030	−	0.976666i	0.748503	−	0.0330741i
$873$	11.7625	−	2.82829i	0.398100	−	0.0957232i
$874$	−25.2611	+	45.2799i	−0.854470	+	1.53162i
$875$	22.9411			0.775552
$876$	30.3904	−	24.1276i	1.02680	−	0.815195i
$877$		−	14.6643i		−	0.495177i	−0.968865	−	0.247589i	$-0.920362\pi$
$877$		−	14.6643i		−	0.495177i	0.968865	−	0.247589i	$-0.0796382\pi$
$878$	8.06101	+	4.49714i	0.272046	+	0.151771i
$879$	−10.9023	+	1.29231i	−0.367724	+	0.0435885i
$880$	30.5941	+	15.3381i	1.03133	+	0.517049i
$881$	5.53794			0.186578			0.0932890	−	0.995639i	$-0.470262\pi$
$881$	5.53794			0.186578			0.0932890	+	0.995639i	$0.470262\pi$
$882$	13.3247	+	3.72949i	0.448668	+	0.125579i
$883$	42.3487			1.42515			0.712574	−	0.701597i	$-0.247529\pi$
$883$	42.3487			1.42515			0.712574	+	0.701597i	$0.247529\pi$
$884$	−11.0799	−	17.9491i	−0.372656	−	0.603695i
$885$	15.9414	−	1.88963i	0.535865	−	0.0635192i
$886$	4.04882	+	2.25879i	0.136023	+	0.0758854i
$887$			28.0618i			0.942223i	0.882074	+	0.471112i	$0.156147\pi$
$887$			28.0618i			0.942223i	−0.882074	+	0.471112i	$0.843853\pi$
$888$	−3.06323	−	18.7262i	−0.102795	−	0.628411i
$889$		−	35.2102i		−	1.18091i
$890$	12.5289	+	6.98972i	0.419969	+	0.234296i
$891$	−22.1054	−	43.3091i	−0.740560	−	1.45091i
$892$	6.72865	−	4.15355i	0.225292	−	0.139071i
$893$	53.1955			1.78012
$894$	28.9237	+	11.9195i	0.967353	+	0.398647i
$895$		−	10.8697i		−	0.363335i
$896$	−19.9694	−	8.93127i	−0.667131	−	0.298373i
$897$	18.8031	−	2.22884i	0.627817	−	0.0744188i
$898$	−19.2724	−	10.7518i	−0.643128	−	0.358794i
$899$	−1.21906	−	18.2377i	−0.0406580	−	0.608261i
$900$	−10.6112	−	10.5348i	−0.353706	−	0.351161i
$901$		−	12.6144i		−	0.420247i
$902$	−57.6210	−	32.1461i	−1.91857	−	1.07035i
$903$	−16.0309	+	1.90024i	−0.533475	+	0.0632360i
$904$	−0.159326	+	0.00704014i	−0.00529910	+	0.000234151i
$905$	−9.40419			−0.312606
$906$	12.1546	−	29.4942i	0.403808	−	0.979878i
$907$			16.1201i			0.535260i	0.963522	+	0.267630i	$0.0862405\pi$
$907$			16.1201i			0.535260i	−0.963522	+	0.267630i	$0.913759\pi$
$908$	24.3751	+	39.4871i	0.808916	+	1.31043i
$909$	−31.4732	+	7.56774i	−1.04390	+	0.251006i
$910$	6.56485	+	3.66246i	0.217623	+	0.121409i
$911$	−19.7589			−0.654641			−0.327321	−	0.944913i	$-0.606146\pi$
$911$	−19.7589			−0.654641			−0.327321	+	0.944913i	$0.606146\pi$
$912$	37.9355	+	13.7074i	1.25617	+	0.453897i
$913$	5.11613			0.169319
$914$	8.54503	−	15.3167i	0.282645	−	0.506633i
$915$	11.6346	−	1.37912i	0.384629	−	0.0455923i
$916$	19.1735	+	31.0607i	0.633511	+	1.02627i
$917$	−14.1685			−0.467885
$918$	44.1106	+	6.88896i	1.45587	+	0.227370i
$919$	11.9387			0.393820			0.196910	−	0.980422i	$-0.436909\pi$
$919$	11.9387			0.393820			0.196910	+	0.980422i	$0.436909\pi$
$920$	−1.24517	−	28.1796i	−0.0410522	−	0.929055i
$921$	1.05534	+	8.90310i	0.0347745	+	0.293367i
$922$	6.12124	−	10.9722i	0.201592	−	0.361349i
$923$			10.2174i			0.336308i
$924$	−28.3415	+	22.5009i	−0.932367	+	0.740226i
$925$	−9.65258			−0.317375
$926$	5.90066	−	10.5768i	0.193908	−	0.347575i
$927$	−41.3739	+	9.94836i	−1.35890	+	0.326747i
$928$	−10.4429	−	15.3565i	−0.342804	−	0.504103i
$929$	1.67439			0.0549351			0.0274675	−	0.999623i	$-0.491256\pi$
$929$	1.67439			0.0549351			0.0274675	+	0.999623i	$0.491256\pi$
$930$	−20.4731	−	6.87901i	−0.671340	−	0.225572i
$931$			18.9877i			0.622298i
$932$	−30.1198	+	18.5927i	−0.986606	+	0.609024i
$933$	−5.74203	−	48.4413i	−0.187986	−	1.58590i
$934$	11.1157	+	6.20132i	0.363717	+	0.202913i
$935$			51.9811i			1.69996i
$936$	−4.07257	−	14.1559i	−0.133116	−	0.462701i
$937$	−9.86622			−0.322315			−0.161158	−	0.986929i	$-0.551523\pi$
$937$	−9.86622			−0.322315			−0.161158	+	0.986929i	$0.551523\pi$
$938$	−14.3615	+	25.7426i	−0.468919	+	0.840525i
$939$	5.81595	+	49.0649i	0.189796	+	1.60117i
$940$	−24.6254	+	15.2011i	−0.803191	+	0.495804i
$941$		−	47.1471i		−	1.53695i	−0.639879	−	0.768476i	$-0.721015\pi$
$941$		−	47.1471i		−	1.53695i	0.639879	−	0.768476i	$-0.278985\pi$
$942$	6.84249	−	16.6039i	0.222940	−	0.540985i
$943$			54.3818i			1.77092i
$944$	−10.4917	+	20.9273i	−0.341477	+	0.681124i
$945$	−14.9245	+	5.51488i	−0.485494	+	0.179399i
$946$	−17.9434	+	32.1630i	−0.583389	+	1.04571i
$947$			29.5704i			0.960907i	0.877020	+	0.480454i	$0.159528\pi$
$947$			29.5704i			0.960907i	−0.877020	+	0.480454i	$0.840472\pi$
$948$	43.5405	−	34.5677i	1.41413	−	1.12271i
$949$		−	19.4456i		−	0.631230i
$950$	9.99676	−	17.9189i	0.324338	−	0.581366i
$951$	−4.25842	+	0.504776i	−0.138089	+	0.0163685i
$952$	−1.46673	−	33.1937i	−0.0475370	−	1.07582i
$953$	−47.6174			−1.54248			−0.771240	−	0.636545i	$-0.780363\pi$
$953$	−47.6174			−1.54248			−0.771240	+	0.636545i	$0.780363\pi$
$954$	2.37431	−	8.48295i	0.0768712	−	0.274646i
$955$			3.94306i			0.127594i
$956$	−15.8838	−	25.7314i	−0.513720	−	0.832214i
$957$	−30.5070	+	3.61617i	−0.986150	+	0.116894i
$958$	−18.2407	+	32.6959i	−0.589330	+	1.05636i
$959$	0.445581			0.0143886
$960$	−21.4782	+	4.49494i	−0.693206	+	0.145074i
$961$	30.7242	−	4.12583i	0.991104	−	0.133091i
$962$	−8.30409	−	4.63276i	−0.267735	−	0.149366i
$963$	−8.11808	+	1.95200i	−0.261602	+	0.0629022i
$964$	8.17053	−	5.04361i	0.263155	−	0.162444i
$965$	36.8952			1.18770
$966$	27.5759	+	11.3640i	0.887240	+	0.365632i
$967$		−	23.2802i		−	0.748639i	−0.927300	−	0.374320i	$-0.877876\pi$
$967$		−	23.2802i		−	0.748639i	0.927300	−	0.374320i	$-0.122124\pi$
$968$	2.27107	+	51.3968i	0.0729949	+	1.65196i
$969$	7.21161	+	60.8390i	0.231670	+	1.95443i
$970$	−7.88701	−	4.40007i	−0.253237	−	0.141278i
$971$	−1.16482			−0.0373807			−0.0186904	−	0.999825i	$-0.505950\pi$
$971$	−1.16482			−0.0373807			−0.0186904	+	0.999825i	$0.505950\pi$
$972$	28.3669	+	12.9353i	0.909867	+	0.414899i
$973$	9.03702			0.289713
$974$	−12.5491	+	22.4939i	−0.402098	+	0.720751i
$975$	−7.44107	+	0.882034i	−0.238305	+	0.0282477i
$976$	−7.65724	+	15.2735i	−0.245102	+	0.488892i
$977$			12.0579i			0.385767i	0.981222	+	0.192884i	$0.0617840\pi$
$977$			12.0579i			0.385767i	−0.981222	+	0.192884i	$0.938216\pi$
$978$	−15.7729	+	38.2744i	−0.504362	+	1.22388i
$979$			34.6094i			1.10612i
$980$	−5.42591	−	8.78984i	−0.173324	−	0.280781i
$981$	5.48620	+	22.8164i	0.175161	+	0.728470i
$982$	−6.62934	+	11.8829i	−0.211551	+	0.379199i
$983$	20.8014			0.663461			0.331730	−	0.943374i	$-0.392368\pi$
$983$	20.8014			0.663461			0.331730	+	0.943374i	$0.392368\pi$
$984$	41.7510	−	6.82961i	1.33097	−	0.217720i
$985$			33.5266i			1.06825i
$986$	13.7422	−	24.6326i	0.437642	−	0.784461i
$987$	−3.60196	−	30.3871i	−0.114652	−	0.967231i
$988$	17.2004	−	10.6177i	0.547217	−	0.337793i
$989$	30.3550			0.965232
$990$	−9.78399	+	34.9563i	−0.310956	+	1.11098i
$991$		−	7.50887i		−	0.238527i	−0.992863	−	0.119264i	$-0.961947\pi$
$991$		−	7.50887i		−	0.238527i	0.992863	−	0.119264i	$-0.0380533\pi$
$992$	24.8054	−	19.4086i	0.787571	−	0.616224i
$993$	−49.2106	+	5.83323i	−1.56165	+	0.185112i
$994$	−7.84108	+	14.0549i	−0.248704	+	0.445795i
$995$			20.6456i			0.654509i
$996$	−2.56913	+	2.03968i	−0.0814059	+	0.0646299i
$997$			23.2925i			0.737681i	0.929493	+	0.368840i	$0.120245\pi$
$997$			23.2925i			0.737681i	−0.929493	+	0.368840i	$0.879755\pi$
$998$	−3.53867	−	1.97418i	−0.112015	−	0.0624917i
$999$	18.8785	−	6.97595i	0.597289	−	0.220709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	744.2.o.e.557.18	yes	96
3.2	odd	2	inner	744.2.o.e.557.80	yes	96
8.5	even	2	inner	744.2.o.e.557.77	yes	96
24.5	odd	2	inner	744.2.o.e.557.19	yes	96
31.30	odd	2	inner	744.2.o.e.557.17	✓	96
93.92	even	2	inner	744.2.o.e.557.79	yes	96
248.61	odd	2	inner	744.2.o.e.557.78	yes	96
744.557	even	2	inner	744.2.o.e.557.20	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
744.2.o.e.557.17	✓	96	31.30	odd	2	inner
744.2.o.e.557.18	yes	96	1.1	even	1	trivial
744.2.o.e.557.19	yes	96	24.5	odd	2	inner
744.2.o.e.557.20	yes	96	744.557	even	2	inner
744.2.o.e.557.77	yes	96	8.5	even	2	inner
744.2.o.e.557.78	yes	96	248.61	odd	2	inner
744.2.o.e.557.79	yes	96	93.92	even	2	inner
744.2.o.e.557.80	yes	96	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 744 = 2^{3} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	744.o (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23502 - 0.689003i) q^{2} +(1.72001 - 0.203883i) q^{3} +(1.05055 + 1.70187i) q^{4} +1.58364 q^{5} +(-2.26472 - 0.933293i) q^{6} -1.93355 q^{7} +(-0.124858 - 2.82567i) q^{8} +(2.91686 - 0.701361i) q^{9} +O(q^{10})\)	\(q+(-1.23502 - 0.689003i) q^{2} +(1.72001 - 0.203883i) q^{3} +(1.05055 + 1.70187i) q^{4} +1.58364 q^{5} +(-2.26472 - 0.933293i) q^{6} -1.93355 q^{7} +(-0.124858 - 2.82567i) q^{8} +(2.91686 - 0.701361i) q^{9} +(-1.95582 - 1.09113i) q^{10} -5.40271i q^{11} +(2.15394 + 2.71304i) q^{12} +1.73596 q^{13} +(2.38798 + 1.33222i) q^{14} +(2.72387 - 0.322876i) q^{15} +(-1.79269 + 3.57579i) q^{16} -6.07545 q^{17} +(-4.08562 - 1.14353i) q^{18} -5.82201i q^{19} +(1.66369 + 2.69514i) q^{20} +(-3.32573 + 0.394218i) q^{21} +(-3.72248 + 6.67245i) q^{22} +6.29736 q^{23} +(-0.790862 - 4.83472i) q^{24} -2.49210 q^{25} +(-2.14395 - 1.19608i) q^{26} +(4.87404 - 1.80105i) q^{27} +(-2.03129 - 3.29065i) q^{28} -3.28289i q^{29} +(-3.58649 - 1.47800i) q^{30} +(5.55537 - 0.371337i) q^{31} +(4.67774 - 3.18100i) q^{32} +(-1.10152 - 9.29271i) q^{33} +(7.50331 + 4.18601i) q^{34} -3.06204 q^{35} +(4.25793 + 4.22730i) q^{36} +3.87328 q^{37} +(-4.01138 + 7.19030i) q^{38} +(2.98587 - 0.353932i) q^{39} +(-0.197729 - 4.47483i) q^{40} +8.63565i q^{41} +(4.37896 + 1.80457i) q^{42} +4.82027 q^{43} +(9.19468 - 5.67581i) q^{44} +(4.61925 - 1.11070i) q^{45} +(-7.77737 - 4.33890i) q^{46} +9.13697i q^{47} +(-2.35441 + 6.51589i) q^{48} -3.26137 q^{49} +(3.07779 + 1.71706i) q^{50} +(-10.4498 + 1.23868i) q^{51} +(1.82371 + 2.95437i) q^{52} +2.07629i q^{53} +(-7.26046 - 1.13390i) q^{54} -8.55592i q^{55} +(0.241419 + 5.46358i) q^{56} +(-1.18701 - 10.0139i) q^{57} +(-2.26193 + 4.05444i) q^{58} +5.85249 q^{59} +(3.41105 + 4.29646i) q^{60} +4.27136 q^{61} +(-7.11684 - 3.36906i) q^{62} +(-5.63991 + 1.35612i) q^{63} +(-7.96882 + 0.705614i) q^{64} +2.74913 q^{65} +(-5.04231 + 12.2356i) q^{66} +10.7801i q^{67} +(-6.38256 - 10.3396i) q^{68} +(10.8315 - 1.28392i) q^{69} +(3.78169 + 2.10976i) q^{70} +5.88571i q^{71} +(-2.34601 - 8.15452i) q^{72} -11.2016i q^{73} +(-4.78357 - 2.66870i) q^{74} +(-4.28643 + 0.508096i) q^{75} +(9.90828 - 6.11630i) q^{76} +10.4464i q^{77} +(-3.93147 - 1.62016i) q^{78} -16.0486i q^{79} +(-2.83897 + 5.66274i) q^{80} +(8.01619 - 4.09155i) q^{81} +(5.94999 - 10.6652i) q^{82} +0.946957i q^{83} +(-4.16475 - 5.24580i) q^{84} -9.62131 q^{85} +(-5.95313 - 3.32118i) q^{86} +(-0.669326 - 5.64661i) q^{87} +(-15.2663 + 0.674570i) q^{88} -6.40594 q^{89} +(-6.47014 - 1.81094i) q^{90} -3.35657 q^{91} +(6.61569 + 10.7173i) q^{92} +(9.47957 - 1.77135i) q^{93} +(6.29540 - 11.2843i) q^{94} -9.21994i q^{95} +(7.39721 - 6.42505i) q^{96} +4.03258 q^{97} +(4.02786 + 2.24710i) q^{98} +(-3.78925 - 15.7590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9}+O(q^{10}) \) 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9	\( 96 q + 12 q^{4} - 32 q^{7} + 32 q^{9} - 52 q^{10} - 60 q^{16} - 4 q^{18} + 168 q^{25} - 20 q^{28} + 16 q^{31} + 8 q^{33} + 8 q^{39} - 64 q^{40} - 64 q^{49} + 56 q^{63} + 72 q^{64} + 4 q^{66} - 84 q^{70} - 44 q^{72} - 28 q^{76} + 56 q^{78} - 112 q^{81} - 108 q^{82} - 168 q^{87} + 104 q^{90} + 8 q^{94} + 72 q^{97}+O(q^{100}) \) 96 * q + 12 * q^4 - 32 * q^7 + 32 * q^9 - 52 * q^10 - 60 * q^16 - 4 * q^18 + 168 * q^25 - 20 * q^28 + 16 * q^31 + 8 * q^33 + 8 * q^39 - 64 * q^40 - 64 * q^49 + 56 * q^63 + 72 * q^64 + 4 * q^66 - 84 * q^70 - 44 * q^72 - 28 * q^76 + 56 * q^78 - 112 * q^81 - 108 * q^82 - 168 * q^87 + 104 * q^90 + 8 * q^94 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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