LMFDB - Embedded newform 744.2.o.e.557.19

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			557.19
Character	$\chi$	$=$	744.557
Dual form			744.2.o.e.557.17

$q$-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} +(-6.60514 + 4.28628i) 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} +(-9.63099 - 0.493940i) 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	$-0.577388\pi$
$13$	−1.73596			−0.481469			−0.240734	+	0.970591i	$0.577388\pi$
$14$	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	$-0.236356\pi$
$17$	6.07545			1.47351			0.736757	+	0.676158i	$0.236356\pi$
$18$	−4.08562	+	1.14353i	−0.962991	+	0.269534i
$19$			5.82201i			1.33566i	0.744314	+	0.667830i	$0.232777\pi$
$19$			5.82201i			1.33566i	−0.744314	+	0.667830i	$0.767223\pi$
$20$	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	$-0.727983\pi$
$23$	−6.29736			−1.31309			−0.656545	+	0.754287i	$0.727983\pi$
$24$	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	$-0.603139\pi$
$37$	−3.87328			−0.636763			−0.318381	+	0.947963i	$0.603139\pi$
$38$	−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	$-0.764432\pi$
$41$		−	8.63565i		−	1.34866i	0.738429	−	0.674331i	$-0.235568\pi$
$42$	−4.37896	+	1.80457i	−0.675688	+	0.278451i
$43$	−4.82027			−0.735084			−0.367542	−	0.930007i	$-0.619801\pi$
$43$	−4.82027			−0.735084			−0.367542	+	0.930007i	$0.619801\pi$
$44$	−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	$-0.767842\pi$
$47$		−	9.13697i		−	1.33276i	0.745611	−	0.666382i	$-0.232158\pi$
$48$	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	$-0.588163\pi$
$61$	−4.27136			−0.546891			−0.273446	+	0.961887i	$0.588163\pi$
$62$	−6.60514	+	4.28628i	−0.838853	+	0.544358i
$63$	−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	$-0.771192\pi$
$67$		−	10.7801i		−	1.31700i	0.752582	−	0.658498i	$-0.228808\pi$
$68$	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	$-0.886436\pi$
$71$		−	5.88571i		−	0.698505i	0.937029	−	0.349252i	$-0.113564\pi$
$72$	−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	$-0.389737\pi$
$89$	6.40594			0.679028			0.339514	+	0.940601i	$0.389737\pi$
$90$	−6.47014	+	1.81094i	−0.682013	+	0.190890i
$91$	3.35657			0.351864
$92$	−6.61569	+	10.7173i	−0.689733	+	1.11735i
$93$	−9.63099	−	0.493940i	−0.998687	−	0.0512192i
$94$	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	$-0.877774\pi$
$109$		−	7.82222i		−	0.749233i	0.927180	−	0.374617i	$-0.122226\pi$
$110$	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	$0.000844203\pi$
$113$			0.0563852i			0.00530427i	−0.999996	+	0.00265214i	$0.999156\pi$
$114$	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
$124$	5.20422	−	9.84460i	0.467353	−	0.884071i
$125$	−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	$-0.496866\pi$
$137$	0.230447			0.0196884			0.00984420	+	0.999952i	$0.496866\pi$
$138$	−14.2618	+	5.87728i	−1.21404	+	0.500307i
$139$	4.67379			0.396426			0.198213	−	0.980159i	$-0.436486\pi$
$139$	4.67379			0.396426			0.198213	+	0.980159i	$0.436486\pi$
$140$	−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	$-0.905493\pi$
$157$		−	7.33155i		−	0.585122i	0.956247	−	0.292561i	$-0.0945074\pi$
$158$	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	$0.230235\pi$
$163$			16.9003i			1.32373i	−0.749623	+	0.661866i	$0.769765\pi$
$164$	−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	$-0.752548\pi$
$167$	−18.4214			−1.42549			−0.712744	+	0.701424i	$0.752548\pi$
$168$	−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	$-0.429167\pi$
$181$	5.93835			0.441394			0.220697	+	0.975342i	$0.429167\pi$
$182$	−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
$186$	12.2348	−	6.02576i	0.897099	−	0.441830i
$187$		−	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	$-0.971288\pi$
$191$		−	2.48988i		−	0.180161i	0.995934	−	0.0900807i	$-0.0287125\pi$
$192$	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	$-0.888549\pi$
$211$		−	9.96544i		−	0.686049i	0.939326	−	0.343025i	$-0.111451\pi$
$212$	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	$-0.706040\pi$
$229$	−18.2510			−1.20606			−0.603029	+	0.797719i	$0.706040\pi$
$230$	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	$-0.803162\pi$
$233$		−	17.6981i		−	1.15944i	0.814816	−	0.579720i	$-0.196838\pi$
$234$	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	$-0.337361\pi$
$239$	15.1195			0.978002			0.489001	+	0.872283i	$0.337361\pi$
$240$	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
$248$	0.355646	+	15.7440i	0.0225835	+	0.999745i
$249$	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	$-0.789277\pi$
$257$		−	19.7088i		−	1.22940i	0.788760	−	0.614701i	$-0.210723\pi$
$258$	−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	$-0.386858\pi$
$263$	11.2875			0.696018			0.348009	+	0.937491i	$0.386858\pi$
$264$	−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	$-0.273865\pi$
$277$	21.7080			1.30431			0.652154	+	0.758086i	$0.273865\pi$
$278$	−5.77222	+	3.22026i	−0.346195	+	0.193138i
$279$	16.4647	+	2.81318i	0.985715	+	0.168420i
$280$	0.382320	−	8.65232i	0.0228480	−	0.517075i
$281$			1.63148i			0.0973257i	0.998815	+	0.0486629i	$0.0154960\pi$
$281$			1.63148i			0.0973257i	−0.998815	+	0.0486629i	$0.984504\pi$
$282$	−8.52746	−	20.6927i	−0.507803	−	1.23223i
$283$			13.5256i			0.804016i	0.915636	+	0.402008i	$0.131688\pi$
$283$			13.5256i			0.804016i	−0.915636	+	0.402008i	$0.868312\pi$
$284$	−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	$-0.952810\pi$
$307$		−	5.17619i		−	0.295421i	0.989031	−	0.147711i	$-0.0471904\pi$
$308$	17.7784	+	10.9745i	1.01302	+	0.625329i
$309$	24.3972	+	2.89195i	1.38791	+	0.164517i
$310$	−10.4601	+	6.78790i	−0.594096	+	0.385527i
$311$			28.1634i			1.59700i	0.601996	+	0.798499i	$0.294372\pi$
$311$			28.1634i			1.59700i	−0.601996	+	0.798499i	$0.705628\pi$
$312$	−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	$-0.211998\pi$
$331$	28.6107			1.57258			0.786292	+	0.617854i	$0.211998\pi$
$332$	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	$-0.877031\pi$
$349$		−	14.0777i		−	0.753563i	0.926302	−	0.376782i	$-0.122969\pi$
$350$	−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	$-0.642952\pi$
$353$	−16.3140			−0.868306			−0.434153	+	0.900839i	$0.642952\pi$
$354$	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	$-0.919537\pi$
$359$		−	9.47738i		−	0.500197i	0.968220	−	0.250098i	$-0.0804630\pi$
$360$	−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
$372$	−10.9584	+	15.8717i	−0.568169	+	0.822912i
$373$		−	2.65714i		−	0.137582i	−0.997631	−	0.0687908i	$-0.978086\pi$
$373$		−	2.65714i		−	0.137582i	0.997631	−	0.0687908i	$-0.0219141\pi$
$374$	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	$0.300469\pi$
$379$			31.5335i			1.61976i	−0.586592	+	0.809882i	$0.699531\pi$
$380$	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	$-0.606675\pi$
$383$	−12.8731			−0.657783			−0.328892	+	0.944368i	$0.606675\pi$
$384$	−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	$-0.901606\pi$
$397$		−	12.1229i		−	0.608429i	0.952604	−	0.304214i	$-0.0983939\pi$
$398$	−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	$-0.580085\pi$
$401$	−9.97038			−0.497897			−0.248948	+	0.968517i	$0.580085\pi$
$402$	−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	$-0.924945\pi$
$421$		−	9.58670i		−	0.467227i	0.972330	−	0.233614i	$-0.0750550\pi$
$422$	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	$-0.868602\pi$
$431$		−	16.6572i		−	0.802348i	0.916002	−	0.401174i	$-0.131398\pi$
$432$	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	$-0.115613\pi$
$434$	12.7714	−	8.28774i	0.613046	−	0.397824i
$435$	−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	$-0.620033\pi$
$449$	−15.6049			−0.736442			−0.368221	+	0.929738i	$0.620033\pi$
$450$	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
$465$	−15.2520	−	0.782221i	−0.707294	−	0.0362747i
$466$	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	$0.206753\pi$
$479$			26.4740i			1.20963i	−0.796367	+	0.604814i	$0.793247\pi$
$480$	−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
$496$	−11.2869	−	19.1991i	−0.506797	−	0.862066i
$497$			11.3803i			0.510477i
$498$	0.883788	+	2.14459i	0.0396035	+	0.0961016i
$499$	−2.86528			−0.128267			−0.0641337	−	0.997941i	$-0.520428\pi$
$499$	−2.86528			−0.128267			−0.0641337	+	0.997941i	$0.520428\pi$
$500$	−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	$-0.840658\pi$
$503$		−	21.5279i		−	0.959882i	0.877301	−	0.479941i	$-0.159342\pi$
$504$	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	$-0.982498\pi$
$521$		−	2.50887i		−	0.109915i	0.998489	−	0.0549577i	$-0.0175024\pi$
$522$	3.75410	+	13.4127i	0.164313	+	0.587057i
$523$	38.0803			1.66514			0.832568	−	0.553923i	$-0.186870\pi$
$523$	38.0803			1.66514			0.832568	+	0.553923i	$0.186870\pi$
$524$	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	$0.193827\pi$
$541$			26.6081i			1.14397i	−0.820263	+	0.571986i	$0.806173\pi$
$542$	−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	$-0.911528\pi$
$547$		−	12.8343i		−	0.548755i	0.961622	−	0.274377i	$-0.0884717\pi$
$548$	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	$-0.329357\pi$
$558$	−22.2725	+	7.86990i	−0.942871	+	0.333159i
$559$	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	$-0.466011\pi$
$569$	5.08457			0.213156			0.106578	+	0.994304i	$0.466011\pi$
$570$	8.60490	+	20.8806i	0.360420	+	0.874592i
$571$	32.7220			1.36937			0.684686	−	0.728838i	$-0.259939\pi$
$571$	32.7220			1.36937			0.684686	+	0.728838i	$0.259939\pi$
$572$	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	$-0.820009\pi$
$593$		−	26.0953i		−	1.07160i	0.844344	−	0.535802i	$-0.179991\pi$
$594$	−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	$0.235339\pi$
$599$			32.9818i			1.34760i	−0.738915	+	0.673799i	$0.764661\pi$
$600$	−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	$-0.441203\pi$
$613$	9.09480			0.367336			0.183668	+	0.982988i	$0.441203\pi$
$614$	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	$0.133056\pi$
$617$			20.1667i			0.811882i	−0.913899	+	0.405941i	$0.866944\pi$
$618$	−32.1236	+	13.2382i	−1.29220	+	0.532517i
$619$	16.3420			0.656842			0.328421	−	0.944531i	$-0.393484\pi$
$619$	16.3420			0.656842			0.328421	+	0.944531i	$0.393484\pi$
$620$	8.24159	−	15.5903i	0.330990	−	0.626120i
$621$	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	$-0.403797\pi$
$641$	15.0718			0.595299			0.297650	+	0.954675i	$0.403797\pi$
$642$	−6.30307	+	2.59750i	−0.248762	+	0.102515i
$643$	−35.8673			−1.41447			−0.707235	−	0.706979i	$-0.750058\pi$
$643$	−35.8673			−1.41447			−0.707235	+	0.706979i	$0.750058\pi$
$644$	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	$-0.232648\pi$
$647$	37.8787			1.48917			0.744583	+	0.667530i	$0.232648\pi$
$648$	−12.5622	+	22.1402i	−0.493492	+	0.869751i
$649$		−	31.6193i		−	1.24117i
$650$	−5.34292	+	2.98075i	−0.209567	+	0.116915i
$651$	18.6220	+	0.955059i	0.729855	+	0.0374317i
$652$	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	$-0.929817\pi$
$661$		−	11.2458i		−	0.437411i	0.975791	−	0.218706i	$-0.0701835\pi$
$662$	−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
$682$	23.1575	+	35.6856i	0.886746	+	1.36647i
$683$	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	$0.146557\pi$
$691$			23.3599i			0.888653i	−0.895865	+	0.444326i	$0.853443\pi$
$692$	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	$-0.590379\pi$
$709$	−14.9183			−0.560268			−0.280134	+	0.959961i	$0.590379\pi$
$710$	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	$-0.766828\pi$
$719$	−39.8718			−1.48697			−0.743484	+	0.668754i	$0.766828\pi$
$720$	−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	$-0.952801\pi$
$733$		−	7.99972i		−	0.295476i	0.989027	−	0.147738i	$-0.0471993\pi$
$734$	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	$-0.497480\pi$
$739$	0.430479			0.0158354			0.00791771	+	0.999969i	$0.497480\pi$
$740$	−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	$-0.263317\pi$
$743$	36.9027			1.35383			0.676914	+	0.736062i	$0.263317\pi$
$744$	2.59822	−	27.1523i	0.0952553	−	0.995453i
$745$	−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	$-0.635538\pi$
$757$	−22.7293			−0.826110			−0.413055	+	0.910706i	$0.635538\pi$
$758$	−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	$-0.441883\pi$
$761$	10.0175			0.363135			0.181567	+	0.983379i	$0.441883\pi$
$762$	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	$-0.573403\pi$
$787$	−12.8241			−0.457128			−0.228564	+	0.973529i	$0.573403\pi$
$788$	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
$806$	11.4663	−	7.44080i	0.403882	−	0.262091i
$807$	−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	$-0.626623\pi$
$809$	−22.0370			−0.774780			−0.387390	+	0.921916i	$0.626623\pi$
$810$	−20.1426	+	0.744367i	−0.707740	+	0.0261544i
$811$			47.5945i			1.67127i	0.549285	+	0.835635i	$0.314900\pi$
$811$			47.5945i			1.67127i	−0.549285	+	0.835635i	$0.685100\pi$
$812$	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	$-0.304158\pi$
$829$	33.2360			1.15433			0.577167	+	0.816626i	$0.304158\pi$
$830$	−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
$837$	−27.7459	−	8.19556i	−0.959037	−	0.283280i
$838$	−21.5323	+	12.0126i	−0.743822	+	0.414969i
$839$			16.5785i			0.572355i	0.958177	+	0.286177i	$0.0923847\pi$
$839$			16.5785i			0.572355i	−0.958177	+	0.286177i	$0.907615\pi$
$840$	−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	$0.150089\pi$
$853$			26.5331i			0.908476i	−0.890880	+	0.454238i	$0.849911\pi$
$854$	−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	$-0.854759\pi$
$857$		−	25.7978i		−	0.881237i	0.897694	−	0.440618i	$-0.145241\pi$
$858$	8.75324	+	21.2406i	0.298831	+	0.725141i
$859$	5.42634			0.185144			0.0925721	−	0.995706i	$-0.470491\pi$
$859$	5.42634			0.185144			0.0925721	+	0.995706i	$0.470491\pi$
$860$	−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	$-0.538581\pi$
$863$	−7.10387			−0.241819			−0.120909	+	0.992664i	$0.538581\pi$
$864$	−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
$868$	−10.0626	+	19.0350i	−0.341548	+	0.646092i
$869$	−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	$0.0796382\pi$
$877$			14.6643i			0.495177i	−0.968865	+	0.247589i	$0.920362\pi$
$878$	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	$-0.529738\pi$
$881$	−5.53794			−0.186578			−0.0932890	+	0.995639i	$0.529738\pi$
$882$	13.3247	−	3.72949i	0.448668	−	0.125579i
$883$	−42.3487			−1.42515			−0.712574	−	0.701597i	$-0.752471\pi$
$883$	−42.3487			−1.42515			−0.712574	+	0.701597i	$0.752471\pi$
$884$	−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	$-0.843853\pi$
$887$		−	28.0618i		−	0.942223i	0.882074	−	0.471112i	$-0.156147\pi$
$888$	−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	$-0.913759\pi$
$907$		−	16.1201i		−	0.535260i	0.963522	−	0.267630i	$-0.0862405\pi$
$908$	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	$-0.393854\pi$
$911$	19.7589			0.654641			0.327321	+	0.944913i	$0.393854\pi$
$912$	−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	$-0.508744\pi$
$929$	−1.67439			−0.0549351			−0.0274675	+	0.999623i	$0.508744\pi$
$930$	19.3755	−	9.54261i	0.635346	−	0.312915i
$931$		−	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	$-0.219637\pi$
$953$	47.6174			1.54248			0.771240	+	0.636545i	$0.219637\pi$
$954$	−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	$-0.938216\pi$
$977$		−	12.0579i		−	0.385767i	0.981222	−	0.192884i	$-0.0617840\pi$
$978$	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	$-0.607632\pi$
$983$	−20.8014			−0.663461			−0.331730	+	0.943374i	$0.607632\pi$
$984$	−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	$-0.0380533\pi$
$992$	27.1678	+	15.9346i	0.862578	+	0.505923i
$993$	−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	$-0.879755\pi$
$997$		−	23.2925i		−	0.737681i	0.929493	−	0.368840i	$-0.120245\pi$
$998$	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.557.19	yes	96
3.2	odd	2	inner	744.2.o.e.557.77	yes	96
8.5	even	2	inner	744.2.o.e.557.80	yes	96
24.5	odd	2	inner	744.2.o.e.557.18	yes	96
31.30	odd	2	inner	744.2.o.e.557.20	yes	96
93.92	even	2	inner	744.2.o.e.557.78	yes	96
248.61	odd	2	inner	744.2.o.e.557.79	yes	96
744.557	even	2	inner	744.2.o.e.557.17	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
744.2.o.e.557.17	✓	96	744.557	even	2	inner
744.2.o.e.557.18	yes	96	24.5	odd	2	inner
744.2.o.e.557.19	yes	96	1.1	even	1	trivial
744.2.o.e.557.20	yes	96	31.30	odd	2	inner
744.2.o.e.557.77	yes	96	3.2	odd	2	inner
744.2.o.e.557.78	yes	96	93.92	even	2	inner
744.2.o.e.557.79	yes	96	248.61	odd	2	inner
744.2.o.e.557.80	yes	96	8.5	even	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} +(-6.60514 + 4.28628i) 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} +(-9.63099 - 0.493940i) 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

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Database

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