LMFDB - Embedded newform 722.2.e.s.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			415.1
Character	$\chi$	$=$	722.415
Dual form			722.2.e.s.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-2.36816 + 0.861941i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.427114 + 2.42228i) q^{5} +(2.36816 + 0.861941i) q^{6} +(1.39680 + 2.41933i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.56712 - 2.15407i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-2.36816 + 0.861941i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.427114 + 2.42228i) q^{5} +(2.36816 + 0.861941i) q^{6} +(1.39680 + 2.41933i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.56712 - 2.15407i) q^{9} +(1.88420 - 1.58103i) q^{10} +(0.839266 - 1.45365i) q^{11} +(-1.26007 - 2.18251i) q^{12} +(5.96195 + 2.16997i) q^{13} +(0.485104 - 2.75116i) q^{14} +(-1.07639 - 6.10451i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(3.80661 + 3.19412i) q^{17} -3.35114 q^{18} -2.45965 q^{20} +(-5.39318 - 4.52541i) q^{21} +(-1.57730 + 0.574092i) q^{22} +(-0.433930 - 2.46094i) q^{23} +(-0.437619 + 2.48186i) q^{24} +(-0.986561 - 0.359079i) q^{25} +(-3.17229 - 5.49456i) q^{26} +(-0.442463 + 0.766369i) q^{27} +(-2.14003 + 1.79569i) q^{28} +(-4.54401 + 3.81288i) q^{29} +(-3.09934 + 5.36821i) q^{30} +(3.64204 + 6.30820i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.734557 + 4.16588i) q^{33} +(-0.862888 - 4.89368i) q^{34} +(-6.45690 + 2.35012i) q^{35} +(2.56712 + 2.15407i) q^{36} -0.550972 q^{37} -15.9893 q^{39} +(1.88420 + 1.58103i) q^{40} +(-2.45017 + 0.891788i) q^{41} +(1.22253 + 6.93334i) q^{42} +(0.498594 - 2.82767i) q^{43} +(1.57730 + 0.574092i) q^{44} +(4.12132 + 7.13833i) q^{45} +(-1.24945 + 2.16411i) q^{46} +(0.571158 - 0.479258i) q^{47} +(1.93054 - 1.61992i) q^{48} +(-0.402113 + 0.696480i) q^{49} +(0.524938 + 0.909219i) q^{50} +(-11.7678 - 4.28314i) q^{51} +(-1.10172 + 6.24819i) q^{52} +(0.255310 + 1.44793i) q^{53} +(0.831559 - 0.302663i) q^{54} +(3.16269 + 2.65381i) q^{55} +2.79360 q^{56} +5.93179 q^{58} +(3.80158 + 3.18990i) q^{59} +(5.82485 - 2.12007i) q^{60} +(1.62133 + 9.19501i) q^{61} +(1.26487 - 7.17342i) q^{62} +(8.79718 + 3.20191i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-7.80272 + 13.5147i) q^{65} +(3.24048 - 2.71909i) q^{66} +(-8.85581 + 7.43091i) q^{67} +(-2.48459 + 4.30343i) q^{68} +(3.14880 + 5.45389i) q^{69} +(6.45690 + 2.35012i) q^{70} +(1.21501 - 6.89068i) q^{71} +(-0.581920 - 3.30023i) q^{72} +(5.81312 - 2.11580i) q^{73} +(0.422069 + 0.354158i) q^{74} +2.64584 q^{75} +4.68915 q^{77} +(12.2485 + 10.2777i) q^{78} +(-5.55507 + 2.02188i) q^{79} +(-0.427114 - 2.42228i) q^{80} +(-1.35850 + 7.70442i) q^{81} +(2.45017 + 0.891788i) q^{82} +(-7.58866 - 13.1439i) q^{83} +(3.52015 - 6.09707i) q^{84} +(-9.36292 + 7.85643i) q^{85} +(-2.19953 + 1.84563i) q^{86} +(7.47449 - 12.9462i) q^{87} +(-0.839266 - 1.45365i) q^{88} +(6.48859 + 2.36166i) q^{89} +(1.43132 - 8.11741i) q^{90} +(3.07778 + 17.4550i) q^{91} +(2.34820 - 0.854675i) q^{92} +(-14.0622 - 11.7996i) q^{93} -0.745593 q^{94} -2.52015 q^{96} +(-11.0214 - 9.24803i) q^{97} +(0.755725 - 0.275062i) q^{98} +(-0.976770 - 5.53954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{7} + 12 q^{8}+O(q^{10}) $ 24 * q + 6 * q^7 + 12 * q^8	$ 24 q + 6 q^{7} + 12 q^{8} - 6 q^{11} + 6 q^{12} - 24 q^{18} - 12 q^{20} - 54 q^{26} - 12 q^{27} - 12 q^{30} + 78 q^{31} - 24 q^{37} - 36 q^{39} + 66 q^{45} - 30 q^{46} + 36 q^{49} + 18 q^{50} + 12 q^{56} - 12 q^{58} - 12 q^{64} - 12 q^{65} - 18 q^{68} - 60 q^{69} - 48 q^{75} + 24 q^{77} + 36 q^{83} + 12 q^{84} + 78 q^{87} + 6 q^{88} + 72 q^{94} + 12 q^{96}+O(q^{100}) $ 24 * q + 6 * q^7 + 12 * q^8 - 6 * q^11 + 6 * q^12 - 24 * q^18 - 12 * q^20 - 54 * q^26 - 12 * q^27 - 12 * q^30 + 78 * q^31 - 24 * q^37 - 36 * q^39 + 66 * q^45 - 30 * q^46 + 36 * q^49 + 18 * q^50 + 12 * q^56 - 12 * q^58 - 12 * q^64 - 12 * q^65 - 18 * q^68 - 60 * q^69 - 48 * q^75 + 24 * q^77 + 36 * q^83 + 12 * q^84 + 78 * q^87 + 6 * q^88 + 72 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−2.36816	+	0.861941i	−1.36726	+	0.497642i	−0.918291	−	0.395906i	$-0.870431\pi$
$3$	−2.36816	+	0.861941i	−1.36726	+	0.497642i	−0.448969	+	0.893548i	$0.648209\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.427114	+	2.42228i	−0.191011	+	1.08328i	0.726975	+	0.686664i	$0.240926\pi$
$5$	−0.427114	+	2.42228i	−0.191011	+	1.08328i	−0.917986	+	0.396613i	$0.870185\pi$
$6$	2.36816	+	0.861941i	0.966799	+	0.351886i
$7$	1.39680	+	2.41933i	0.527942	+	0.914422i	0.999469	+	0.0325705i	$0.0103694\pi$
$7$	1.39680	+	2.41933i	0.527942	+	0.914422i	−0.471528	+	0.881851i	$0.656297\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.56712	−	2.15407i	0.855708	−	0.718024i
$10$	1.88420	−	1.58103i	0.595837	−	0.499966i
$11$	0.839266	−	1.45365i	0.253048	−	0.438292i	−0.711315	−	0.702873i	$-0.751900\pi$
$11$	0.839266	−	1.45365i	0.253048	−	0.438292i	0.964364	+	0.264581i	$0.0852336\pi$
$12$	−1.26007	−	2.18251i	−0.363752	−	0.630037i
$13$	5.96195	+	2.16997i	1.65355	+	0.601842i	0.989329	−	0.145696i	$-0.0465422\pi$
$13$	5.96195	+	2.16997i	1.65355	+	0.601842i	0.664219	+	0.747538i	$0.268764\pi$
$14$	0.485104	−	2.75116i	0.129650	−	0.735279i
$15$	−1.07639	−	6.10451i	−0.277923	−	1.57618i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.80661	+	3.19412i	0.923238	+	0.774689i	0.974591	−	0.223992i	$-0.0719088\pi$
$17$	3.80661	+	3.19412i	0.923238	+	0.774689i	−0.0513528	+	0.998681i	$0.516353\pi$
$18$	−3.35114			−0.789872
$19$		0			0
$19$		0			0
$20$	−2.45965			−0.549994
$21$	−5.39318	−	4.52541i	−1.17689	−	0.987526i
$22$	−1.57730	+	0.574092i	−0.336282	+	0.122397i
$23$	−0.433930	−	2.46094i	−0.0904807	−	0.513141i	−0.996039	−	0.0889193i	$-0.971659\pi$
$23$	−0.433930	−	2.46094i	−0.0904807	−	0.513141i	0.905558	−	0.424222i	$-0.139452\pi$
$24$	−0.437619	+	2.48186i	−0.0893286	+	0.506608i
$25$	−0.986561	−	0.359079i	−0.197312	−	0.0718157i
$26$	−3.17229	−	5.49456i	−0.622137	−	1.07757i
$27$	−0.442463	+	0.766369i	−0.0851521	+	0.147488i
$28$	−2.14003	+	1.79569i	−0.404427	+	0.339354i
$29$	−4.54401	+	3.81288i	−0.843802	+	0.708034i	−0.958416	−	0.285376i	$-0.907881\pi$
$29$	−4.54401	+	3.81288i	−0.843802	+	0.708034i	0.114614	+	0.993410i	$0.463437\pi$
$30$	−3.09934	+	5.36821i	−0.565859	+	0.980097i
$31$	3.64204	+	6.30820i	0.654130	+	1.13299i	0.982111	+	0.188302i	$0.0602983\pi$
$31$	3.64204	+	6.30820i	0.654130	+	1.13299i	−0.327982	+	0.944684i	$0.606368\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−0.734557	+	4.16588i	−0.127870	+	0.725187i
$34$	−0.862888	−	4.89368i	−0.147984	−	0.839260i
$35$	−6.45690	+	2.35012i	−1.09142	+	0.397243i
$36$	2.56712	+	2.15407i	0.427854	+	0.359012i
$37$	−0.550972			−0.0905792			−0.0452896	−	0.998974i	$-0.514421\pi$
$37$	−0.550972			−0.0905792			−0.0452896	+	0.998974i	$0.514421\pi$
$38$		0			0
$39$	−15.9893			−2.56033
$40$	1.88420	+	1.58103i	0.297918	+	0.249983i
$41$	−2.45017	+	0.891788i	−0.382652	+	0.139274i	−0.526182	−	0.850372i	$-0.676377\pi$
$41$	−2.45017	+	0.891788i	−0.382652	+	0.139274i	0.143530	+	0.989646i	$0.454155\pi$
$42$	1.22253	+	6.93334i	0.188641	+	1.06984i
$43$	0.498594	−	2.82767i	0.0760349	−	0.431215i	−0.922899	−	0.385043i	$-0.874187\pi$
$43$	0.498594	−	2.82767i	0.0760349	−	0.431215i	0.998933	−	0.0461721i	$-0.0147023\pi$
$44$	1.57730	+	0.574092i	0.237787	+	0.0865476i
$45$	4.12132	+	7.13833i	0.614370	+	1.06412i
$46$	−1.24945	+	2.16411i	−0.184222	+	0.319081i
$47$	0.571158	−	0.479258i	0.0833119	−	0.0699070i	−0.600181	−	0.799865i	$-0.704905\pi$
$47$	0.571158	−	0.479258i	0.0833119	−	0.0699070i	0.683493	+	0.729958i	$0.260460\pi$
$48$	1.93054	−	1.61992i	0.278650	−	0.233815i
$49$	−0.402113	+	0.696480i	−0.0574447	+	0.0994972i
$50$	0.524938	+	0.909219i	0.0742374	+	0.128583i
$51$	−11.7678	−	4.28314i	−1.64782	−	0.599759i
$52$	−1.10172	+	6.24819i	−0.152782	+	0.866468i
$53$	0.255310	+	1.44793i	0.0350695	+	0.198889i	0.997309	−	0.0733160i	$-0.0233582\pi$
$53$	0.255310	+	1.44793i	0.0350695	+	0.198889i	−0.962239	+	0.272205i	$0.912247\pi$
$54$	0.831559	−	0.302663i	0.113161	−	0.0411872i
$55$	3.16269	+	2.65381i	0.426457	+	0.357840i
$56$	2.79360			0.373311
$57$		0			0
$58$	5.93179			0.778882
$59$	3.80158	+	3.18990i	0.494924	+	0.415290i	0.855787	−	0.517329i	$-0.173073\pi$
$59$	3.80158	+	3.18990i	0.494924	+	0.415290i	−0.360863	+	0.932619i	$0.617518\pi$
$60$	5.82485	−	2.12007i	0.751985	−	0.273700i
$61$	1.62133	+	9.19501i	0.207590	+	1.17730i	0.893312	+	0.449437i	$0.148375\pi$
$61$	1.62133	+	9.19501i	0.207590	+	1.17730i	−0.685722	+	0.727863i	$0.740513\pi$
$62$	1.26487	−	7.17342i	0.160638	−	0.911025i
$63$	8.79718	+	3.20191i	1.10834	+	0.403403i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−7.80272	+	13.5147i	−0.967808	+	1.67629i
$66$	3.24048	−	2.71909i	0.398876	−	0.334696i
$67$	−8.85581	+	7.43091i	−1.08191	+	0.907830i	−0.996078	−	0.0884797i	$-0.971799\pi$
$67$	−8.85581	+	7.43091i	−1.08191	+	0.907830i	−0.0858316	+	0.996310i	$0.527355\pi$
$68$	−2.48459	+	4.30343i	−0.301300	+	0.521868i
$69$	3.14880	+	5.45389i	0.379071	+	0.656571i
$70$	6.45690	+	2.35012i	0.771747	+	0.280893i
$71$	1.21501	−	6.89068i	0.144196	−	0.817774i	−0.823814	−	0.566860i	$-0.808158\pi$
$71$	1.21501	−	6.89068i	0.144196	−	0.817774i	0.968010	−	0.250913i	$-0.0807309\pi$
$72$	−0.581920	−	3.30023i	−0.0685799	−	0.388936i
$73$	5.81312	−	2.11580i	0.680374	−	0.247636i	0.0213660	−	0.999772i	$-0.493198\pi$
$73$	5.81312	−	2.11580i	0.680374	−	0.247636i	0.659008	+	0.752136i	$0.270976\pi$
$74$	0.422069	+	0.354158i	0.0490645	+	0.0411700i
$75$	2.64584			0.305515
$76$		0			0
$77$	4.68915			0.534379
$78$	12.2485	+	10.2777i	1.38687	+	1.16372i
$79$	−5.55507	+	2.02188i	−0.624994	+	0.227479i	−0.635051	−	0.772470i	$-0.719021\pi$
$79$	−5.55507	+	2.02188i	−0.624994	+	0.227479i	0.0100569	+	0.999949i	$0.496799\pi$
$80$	−0.427114	−	2.42228i	−0.0477528	−	0.270819i
$81$	−1.35850	+	7.70442i	−0.150944	+	0.856047i
$82$	2.45017	+	0.891788i	0.270576	+	0.0984815i
$83$	−7.58866	−	13.1439i	−0.832964	−	1.44274i	−0.895678	−	0.444704i	$-0.853309\pi$
$83$	−7.58866	−	13.1439i	−0.832964	−	1.44274i	0.0627138	−	0.998032i	$-0.480024\pi$
$84$	3.52015	−	6.09707i	0.384080	−	0.665245i
$85$	−9.36292	+	7.85643i	−1.01555	+	0.852149i
$86$	−2.19953	+	1.84563i	−0.237182	+	0.199019i
$87$	7.47449	−	12.9462i	0.801349	−	1.38798i
$88$	−0.839266	−	1.45365i	−0.0894660	−	0.154960i
$89$	6.48859	+	2.36166i	0.687790	+	0.250335i	0.662189	−	0.749337i	$-0.269628\pi$
$89$	6.48859	+	2.36166i	0.687790	+	0.250335i	0.0256011	+	0.999672i	$0.491850\pi$
$90$	1.43132	−	8.11741i	0.150874	−	0.855650i
$91$	3.07778	+	17.4550i	0.322639	+	1.82978i
$92$	2.34820	−	0.854675i	0.244817	−	0.0891061i
$93$	−14.0622	−	11.7996i	−1.45819	−	1.22356i
$94$	−0.745593			−0.0769021
$95$		0			0
$96$	−2.52015			−0.257211
$97$	−11.0214	−	9.24803i	−1.11905	−	0.938995i	−0.120495	−	0.992714i	$-0.538448\pi$
$97$	−11.0214	−	9.24803i	−1.11905	−	0.938995i	−0.998556	+	0.0537190i	$0.982892\pi$
$98$	0.755725	−	0.275062i	0.0763398	−	0.0277854i
$99$	−0.976770	−	5.53954i	−0.0981691	−	0.556745i
$100$	0.182309	−	1.03393i	0.0182309	−	0.103393i
$101$	−10.6025	−	3.85899i	−1.05499	−	0.383984i	−0.244444	−	0.969663i	$-0.578605\pi$
$101$	−10.6025	−	3.85899i	−1.05499	−	0.383984i	−0.810543	+	0.585680i	$0.800828\pi$
$102$	6.26153	+	10.8453i	0.619983	+	1.07384i
$103$	7.41399	−	12.8414i	0.730522	−	1.26530i	−0.226138	−	0.974095i	$-0.572610\pi$
$103$	7.41399	−	12.8414i	0.730522	−	1.26530i	0.956660	−	0.291206i	$-0.0940565\pi$
$104$	4.86023	−	4.07822i	0.476585	−	0.399902i
$105$	13.2653	−	11.1309i	1.29456	−	1.08627i
$106$	0.735136	−	1.27329i	0.0714027	−	0.123673i
$107$	−1.41424	−	2.44954i	−0.136720	−	0.236806i	0.789533	−	0.613708i	$-0.210323\pi$
$107$	−1.41424	−	2.44954i	−0.136720	−	0.236806i	−0.926253	+	0.376902i	$0.876989\pi$
$108$	−0.831559	−	0.302663i	−0.0800168	−	0.0291237i
$109$	−0.299611	+	1.69918i	−0.0286975	+	0.162752i	−0.995789	−	0.0916785i	$-0.970777\pi$
$109$	−0.299611	+	1.69918i	−0.0286975	+	0.162752i	0.967091	+	0.254430i	$0.0818879\pi$
$110$	−0.716924	−	4.06588i	−0.0683560	−	0.387666i
$111$	1.30479	−	0.474905i	0.123845	−	0.0450760i
$112$	−2.14003	−	1.79569i	−0.202213	−	0.169677i
$113$	0.427785			0.0402426			0.0201213	−	0.999798i	$-0.493595\pi$
$113$	0.427785			0.0402426			0.0201213	+	0.999798i	$0.493595\pi$
$114$		0			0
$115$	6.14643			0.573157
$116$	−4.54401	−	3.81288i	−0.421901	−	0.354017i
$117$	19.9793	−	7.27189i	1.84709	−	0.672286i
$118$	−0.861748	−	4.88722i	−0.0793304	−	0.449905i
$119$	−2.41057	+	13.6710i	−0.220976	+	1.25322i
$120$	−5.82485	−	2.12007i	−0.531734	−	0.193535i
$121$	4.09127	+	7.08628i	0.371933	+	0.644207i
$122$	4.66843	−	8.08596i	0.422660	−	0.732068i
$123$	5.03373	−	4.22380i	0.453876	−	0.380847i
$124$	−5.57993	+	4.68212i	−0.501092	+	0.420466i
$125$	−4.85796	+	8.41423i	−0.434509	+	0.752592i
$126$	−4.68088	−	8.10752i	−0.417006	−	0.722276i
$127$	−1.06779	−	0.388643i	−0.0947509	−	0.0344865i	0.294210	−	0.955741i	$-0.404944\pi$
$127$	−1.06779	−	0.388643i	−0.0947509	−	0.0344865i	−0.388961	+	0.921254i	$0.627166\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	1.25653	+	7.12614i	0.110631	+	0.627421i
$130$	14.6643	−	5.33737i	1.28615	−	0.468119i
$131$	−13.6674	−	11.4683i	−1.19412	−	1.00199i	−0.999778	−	0.0210568i	$-0.993297\pi$
$131$	−13.6674	−	11.4683i	−1.19412	−	1.00199i	−0.194347	−	0.980933i	$-0.562259\pi$
$132$	−4.23015			−0.368187
$133$		0			0
$134$	11.5604			0.998670
$135$	−1.66738	−	1.39910i	−0.143505	−	0.120415i
$136$	4.66950	−	1.69956i	0.400406	−	0.145736i
$137$	−2.76372	−	15.6738i	−0.236121	−	1.33911i	−0.840241	−	0.542214i	$-0.817586\pi$
$137$	−2.76372	−	15.6738i	−0.236121	−	1.33911i	0.604120	−	0.796893i	$-0.293525\pi$
$138$	1.09357	−	6.20193i	0.0930907	−	0.527943i
$139$	−9.50985	−	3.46130i	−0.806615	−	0.293584i	−0.0943901	−	0.995535i	$-0.530090\pi$
$139$	−9.50985	−	3.46130i	−0.806615	−	0.293584i	−0.712225	+	0.701951i	$0.752312\pi$
$140$	−3.43564	−	5.95071i	−0.290365	−	0.502927i
$141$	−0.939503	+	1.62727i	−0.0791204	+	0.137041i
$142$	−5.36000	+	4.49757i	−0.449801	+	0.377428i
$143$	8.15804	−	6.84541i	0.682210	−	0.572442i
$144$	−1.67557	+	2.90217i	−0.139631	+	0.241848i
$145$	−7.29506	−	12.6354i	−0.605821	−	1.04931i
$146$	−5.81312	−	2.11580i	−0.481097	−	0.175105i
$147$	0.351945	−	1.99598i	0.0290279	−	0.164625i
$148$	−0.0956753	−	0.542602i	−0.00786446	−	0.0446016i
$149$	−8.83171	+	3.21448i	−0.723522	+	0.263340i	−0.677420	−	0.735596i	$-0.736902\pi$
$149$	−8.83171	+	3.21448i	−0.723522	+	0.263340i	−0.0461017	+	0.998937i	$0.514680\pi$
$150$	−2.02683	−	1.70071i	−0.165490	−	0.138863i
$151$	10.2632			0.835210			0.417605	−	0.908629i	$-0.362870\pi$
$151$	10.2632			0.835210			0.417605	+	0.908629i	$0.362870\pi$
$152$		0			0
$153$	16.6524			1.34627
$154$	−3.59210	−	3.01413i	−0.289460	−	0.242885i
$155$	−16.8358	+	6.12773i	−1.35228	+	0.492191i
$156$	−2.77651	−	15.7464i	−0.222298	−	1.26072i
$157$	0.516408	−	2.92869i	0.0412138	−	0.233735i	−0.957242	−	0.289289i	$-0.906581\pi$
$157$	0.516408	−	2.92869i	0.0412138	−	0.233735i	0.998456	+	0.0555535i	$0.0176923\pi$
$158$	5.55507	+	2.02188i	0.441938	+	0.160852i
$159$	−1.85265	−	3.20888i	−0.146925	−	0.254481i
$160$	−1.22982	+	2.13012i	−0.0972262	+	0.168401i
$161$	5.34772	−	4.48727i	0.421459	−	0.353646i
$162$	5.99298	−	5.02871i	0.470853	−	0.395092i
$163$	−2.79595	+	4.84273i	−0.218996	+	0.379312i	−0.954501	−	0.298207i	$-0.903612\pi$
$163$	−2.79595	+	4.84273i	−0.218996	+	0.379312i	0.735505	+	0.677519i	$0.236945\pi$
$164$	−1.30371	−	2.25809i	−0.101802	−	0.176327i
$165$	−9.77720	−	3.55861i	−0.761154	−	0.277037i
$166$	−2.63551	+	14.9467i	−0.204556	+	1.16009i
$167$	1.23006	+	6.97599i	0.0951845	+	0.539818i	0.994691	+	0.102910i	$0.0328154\pi$
$167$	1.23006	+	6.97599i	0.0951845	+	0.539818i	−0.899506	+	0.436908i	$0.856073\pi$
$168$	−6.61571	+	2.40792i	−0.510413	+	0.185775i
$169$	20.8775	+	17.5183i	1.60596	+	1.34756i
$170$	12.2224			0.937418
$171$		0			0
$172$	2.87129			0.218934
$173$	17.6350	+	14.7975i	1.34076	+	1.12503i	0.981430	+	0.191822i	$0.0614396\pi$
$173$	17.6350	+	14.7975i	1.34076	+	1.12503i	0.359331	+	0.933210i	$0.383005\pi$
$174$	−14.0474	+	5.11285i	−1.06493	+	0.387604i
$175$	−0.509299	−	2.88838i	−0.0384994	−	0.218341i
$176$	−0.291474	+	1.65303i	−0.0219707	+	0.124602i
$177$	−11.7523	−	4.27748i	−0.883355	−	0.321515i
$178$	−3.45251	−	5.97992i	−0.258776	−	0.448214i
$179$	4.10736	−	7.11415i	0.306998	−	0.531736i	−0.670706	−	0.741723i	$-0.734009\pi$
$179$	4.10736	−	7.11415i	0.306998	−	0.531736i	0.977704	+	0.209987i	$0.0673421\pi$
$180$	−6.31422	+	5.29826i	−0.470634	+	0.394909i
$181$	9.95849	−	8.35617i	0.740209	−	0.621109i	−0.192685	−	0.981261i	$-0.561720\pi$
$181$	9.95849	−	8.35617i	0.740209	−	0.621109i	0.932894	+	0.360152i	$0.117275\pi$
$182$	8.86212	−	15.3496i	0.656904	−	1.13779i
$183$	−11.7651	−	20.3778i	−0.869703	−	1.50637i
$184$	−2.34820	−	0.854675i	−0.173112	−	0.0630075i
$185$	0.235328	−	1.33461i	0.0173016	−	0.0981224i
$186$	3.18765	+	18.0781i	0.233730	+	1.32555i
$187$	7.83790	−	2.85276i	0.573164	−	0.208615i
$188$	0.571158	+	0.479258i	0.0416560	+	0.0349535i
$189$	−2.47214			−0.179821
$190$		0			0
$191$	6.57479			0.475735			0.237868	−	0.971298i	$-0.423552\pi$
$191$	6.57479			0.475735			0.237868	+	0.971298i	$0.423552\pi$
$192$	1.93054	+	1.61992i	0.139325	+	0.116908i
$193$	25.2614	−	9.19440i	1.81836	−	0.661827i	0.822726	−	0.568439i	$-0.192452\pi$
$193$	25.2614	−	9.19440i	1.81836	−	0.661827i	0.995630	−	0.0933887i	$-0.0297699\pi$
$194$	2.49834	+	14.1688i	0.179370	+	1.01726i
$195$	6.82923	−	38.7305i	0.489052	−	2.77355i
$196$	−0.755725	−	0.275062i	−0.0539804	−	0.0196473i
$197$	4.92470	+	8.52983i	0.350870	+	0.607725i	0.986402	−	0.164349i	$-0.0525524\pi$
$197$	4.92470	+	8.52983i	0.350870	+	0.607725i	−0.635532	+	0.772075i	$0.719219\pi$
$198$	−2.81250	+	4.87139i	−0.199876	+	0.346195i
$199$	−15.6779	+	13.1554i	−1.11138	+	0.932558i	−0.998137	−	0.0610089i	$-0.980568\pi$
$199$	−15.6779	+	13.1554i	−1.11138	+	0.932558i	−0.113243	+	0.993567i	$0.536124\pi$
$200$	−0.804252	+	0.674847i	−0.0568692	+	0.0477189i
$201$	14.5670	−	25.2308i	1.02748	−	1.77964i
$202$	5.64146	+	9.77130i	0.396932	+	0.687506i
$203$	−15.5717	−	5.66764i	−1.09292	−	0.397790i
$204$	2.17461	−	12.3328i	0.152253	−	0.863469i
$205$	−1.11366	−	6.31589i	−0.0777815	−	0.441121i
$206$	−13.9337	+	5.07147i	−0.970810	+	0.353346i
$207$	−6.41499	−	5.38282i	−0.445873	−	0.374132i
$208$	−6.34458			−0.439917
$209$		0			0
$210$	−17.3167			−1.19496
$211$	−6.21744	−	5.21705i	−0.428026	−	0.359157i	0.403180	−	0.915121i	$-0.367905\pi$
$211$	−6.21744	−	5.21705i	−0.428026	−	0.359157i	−0.831206	+	0.555964i	$0.812349\pi$
$212$	−1.38160	+	0.502862i	−0.0948889	+	0.0345367i
$213$	3.06201	+	17.3655i	0.209806	+	1.18987i
$214$	−0.491162	+	2.78552i	−0.0335751	+	0.190414i
$215$	6.63645	+	2.41547i	0.452602	+	0.164734i
$216$	0.442463	+	0.766369i	0.0301058	+	0.0521448i
$217$	−10.1744	+	17.6226i	−0.690684	+	1.19630i
$218$	1.32173	−	1.10906i	0.0895185	−	0.0751150i
$219$	−11.9427	+	10.0211i	−0.807014	+	0.677165i
$220$	−2.06430	+	3.57547i	−0.139175	+	0.241058i
$221$	15.7637	+	27.3035i	1.06038	+	1.83663i
$222$	−1.30479	−	0.474905i	−0.0875719	−	0.0318736i
$223$	−1.86742	+	10.5906i	−0.125051	+	0.709202i	0.856226	+	0.516602i	$0.172803\pi$
$223$	−1.86742	+	10.5906i	−0.125051	+	0.709202i	−0.981277	+	0.192600i	$0.938308\pi$
$224$	0.485104	+	2.75116i	0.0324124	+	0.183820i
$225$	−3.30610	+	1.20332i	−0.220407	+	0.0802216i
$226$	−0.327702	−	0.274975i	−0.0217984	−	0.0182911i
$227$	−27.0936			−1.79827			−0.899133	−	0.437676i	$-0.855802\pi$
$227$	−27.0936			−1.79827			−0.899133	+	0.437676i	$0.855802\pi$
$228$		0			0
$229$	9.46557			0.625503			0.312751	−	0.949835i	$-0.398749\pi$
$229$	9.46557			0.625503			0.312751	+	0.949835i	$0.398749\pi$
$230$	−4.70844	−	3.95085i	−0.310465	−	0.260511i
$231$	−11.1047	+	4.04177i	−0.730634	+	0.265929i
$232$	1.03004	+	5.84167i	0.0676257	+	0.383524i
$233$	3.96996	−	22.5148i	0.260081	−	1.47499i	−0.522605	−	0.852575i	$-0.675040\pi$
$233$	3.96996	−	22.5148i	0.260081	−	1.47499i	0.782686	−	0.622417i	$-0.213849\pi$
$234$	−19.9793	−	7.27189i	−1.30609	−	0.475378i
$235$	0.916949	+	1.58820i	0.0598152	+	0.103603i
$236$	−2.48131	+	4.29775i	−0.161519	+	0.279759i
$237$	11.4126	−	9.57629i	0.741326	−	0.622047i
$238$	10.6342	−	8.92312i	0.689310	−	0.578400i
$239$	−4.33306	+	7.50508i	−0.280282	+	0.485463i	−0.971454	−	0.237227i	$-0.923761\pi$
$239$	−4.33306	+	7.50508i	−0.280282	+	0.485463i	0.691172	+	0.722690i	$0.257095\pi$
$240$	3.09934	+	5.36821i	0.200061	+	0.346517i
$241$	5.31702	+	1.93524i	0.342500	+	0.124660i	0.507542	−	0.861627i	$-0.330554\pi$
$241$	5.31702	+	1.93524i	0.342500	+	0.124660i	−0.165043	+	0.986286i	$0.552776\pi$
$242$	1.42088	−	8.05822i	0.0913377	−	0.518002i
$243$	−3.88461	−	22.0307i	−0.249198	−	1.41327i
$244$	−8.77378	+	3.19339i	−0.561684	+	0.204436i
$245$	−1.51532	−	1.27151i	−0.0968105	−	0.0812336i
$246$	−6.57106			−0.418956
$247$		0			0
$248$	7.28408			0.462539
$249$	29.3005	+	24.5860i	1.85684	+	1.55808i
$250$	9.12998	−	3.32304i	0.577431	−	0.210168i
$251$	−2.35384	−	13.3493i	−0.148573	−	0.842600i	−0.964428	−	0.264344i	$-0.914845\pi$
$251$	−2.35384	−	13.3493i	−0.148573	−	0.842600i	0.815855	−	0.578256i	$-0.196267\pi$
$252$	−1.62565	+	9.21954i	−0.102407	+	0.580776i
$253$	−3.94153	−	1.43460i	−0.247802	−	0.0901925i
$254$	0.568158	+	0.984079i	0.0356494	+	0.0617466i
$255$	15.4012	−	26.6756i	0.964458	−	1.67049i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−7.69051	+	6.45311i	−0.479721	+	0.402534i	−0.850326	−	0.526257i	$-0.823595\pi$
$257$	−7.69051	+	6.45311i	−0.479721	+	0.402534i	0.370604	+	0.928791i	$0.379151\pi$
$258$	3.61803	−	6.26662i	0.225249	−	0.390143i
$259$	−0.769599	−	1.33298i	−0.0478206	−	0.0828276i
$260$	−14.6643	−	5.33737i	−0.909442	−	0.331010i
$261$	−3.45182	+	19.5763i	−0.213662	+	1.21174i
$262$	3.09814	+	17.5705i	0.191404	+	1.08551i
$263$	17.6908	−	6.43893i	1.09086	−	0.397042i	0.266922	−	0.963718i	$-0.413993\pi$
$263$	17.6908	−	6.43893i	1.09086	−	0.397042i	0.823940	+	0.566676i	$0.191771\pi$
$264$	3.24048	+	2.71909i	0.199438	+	0.167348i
$265$	−3.61635			−0.222151
$266$		0			0
$267$	−17.4017			−1.06496
$268$	−8.85581	−	7.43091i	−0.540955	−	0.453915i
$269$	−15.3947	+	5.60321i	−0.938630	+	0.341633i	−0.765625	−	0.643287i	$-0.777570\pi$
$269$	−15.3947	+	5.60321i	−0.938630	+	0.341633i	−0.173005	+	0.984921i	$0.555348\pi$
$270$	0.377964	+	2.14354i	0.0230022	+	0.130452i
$271$	−0.480456	+	2.72480i	−0.0291856	+	0.165520i	−0.995917	−	0.0902740i	$-0.971226\pi$
$271$	−0.480456	+	2.72480i	−0.0291856	+	0.165520i	0.966731	+	0.255794i	$0.0823368\pi$
$272$	−4.66950	−	1.69956i	−0.283130	−	0.103051i
$273$	−22.3338	−	38.6833i	−1.35171	−	2.34122i
$274$	−7.95782	+	13.7833i	−0.480749	+	0.832682i
$275$	−1.34996	+	1.13275i	−0.0814057	+	0.0683075i
$276$	−4.82425	+	4.04802i	−0.290385	+	0.243662i
$277$	−12.2661	+	21.2454i	−0.736996	+	1.27651i	0.216846	+	0.976206i	$0.430423\pi$
$277$	−12.2661	+	21.2454i	−0.736996	+	1.27651i	−0.953842	+	0.300309i	$0.902910\pi$
$278$	5.06008	+	8.76432i	0.303484	+	0.525649i
$279$	22.9379	+	8.34870i	1.37325	+	0.499824i
$280$	−1.19319	+	6.76690i	−0.0713065	+	0.404399i
$281$	−1.76606	−	10.0159i	−0.105355	−	0.597496i	−0.991078	−	0.133282i	$-0.957448\pi$
$281$	−1.76606	−	10.0159i	−0.105355	−	0.597496i	0.885724	−	0.464213i	$-0.153663\pi$
$282$	1.76569	−	0.642658i	0.105145	−	0.0382697i
$283$	21.1948	+	17.7845i	1.25990	+	1.05718i	0.995693	+	0.0927133i	$0.0295540\pi$
$283$	21.1948	+	17.7845i	1.25990	+	1.05718i	0.264205	+	0.964467i	$0.414890\pi$
$284$	6.99698			0.415195
$285$		0			0
$286$	−10.6496			−0.629722
$287$	−5.57993	−	4.68212i	−0.329373	−	0.276377i
$288$	3.14904	−	1.14616i	0.185559	−	0.0675380i
$289$	1.33582	+	7.57583i	0.0785778	+	0.445637i
$290$	−2.53355	+	14.3685i	−0.148775	+	0.843745i
$291$	34.0717	+	12.4011i	1.99732	+	0.726964i
$292$	3.09310	+	5.35740i	0.181010	+	0.313518i
$293$	11.9193	−	20.6448i	0.696333	−	1.20608i	−0.273396	−	0.961901i	$-0.588147\pi$
$293$	11.9193	−	20.6448i	0.696333	−	1.20608i	0.969729	−	0.244182i	$-0.0785196\pi$
$294$	−1.55259	+	1.30278i	−0.0905491	+	0.0759797i
$295$	−9.35056	+	7.84605i	−0.544410	+	0.456815i
$296$	−0.275486	+	0.477156i	−0.0160123	+	0.0277341i
$297$	0.742689	+	1.28637i	0.0430952	+	0.0746430i
$298$	8.83171	+	3.21448i	0.511607	+	0.186210i
$299$	2.75310	−	15.6136i	0.159216	−	0.902959i
$300$	0.459446	+	2.60565i	0.0265261	+	0.150437i
$301$	7.53750	−	2.74343i	0.434454	−	0.158128i
$302$	−7.86209	−	6.59708i	−0.452413	−	0.379619i
$303$	28.4346			1.63353
$304$		0			0
$305$	−22.9654			−1.31500
$306$	−12.7565	−	10.7040i	−0.729240	−	0.611905i
$307$	24.4211	−	8.88857i	1.39379	−	0.507297i	0.467460	−	0.884014i	$-0.345169\pi$
$307$	24.4211	−	8.88857i	1.39379	−	0.507297i	0.926328	+	0.376717i	$0.122947\pi$
$308$	0.814263	+	4.61791i	0.0463969	+	0.263130i
$309$	−6.48900	+	36.8010i	−0.369147	+	2.09353i
$310$	16.8358	+	6.12773i	0.956209	+	0.348032i
$311$	11.5522	+	20.0089i	0.655063	+	1.13460i	0.981878	+	0.189515i	$0.0606914\pi$
$311$	11.5522	+	20.0089i	0.655063	+	1.13460i	−0.326814	+	0.945089i	$0.605975\pi$
$312$	−7.99463	+	13.8471i	−0.452607	+	0.783938i
$313$	9.39531	−	7.88360i	0.531054	−	0.445607i	−0.337411	−	0.941357i	$-0.609551\pi$
$313$	9.39531	−	7.88360i	0.531054	−	0.445607i	0.868465	+	0.495750i	$0.165107\pi$
$314$	−2.27812	+	1.91157i	−0.128562	+	0.107876i
$315$	−11.5133	+	19.9417i	−0.648703	+	1.12359i
$316$	−2.95579	−	5.11958i	−0.166276	−	0.287999i
$317$	−0.255883	−	0.0931338i	−0.0143718	−	0.00523091i	0.334824	−	0.942281i	$-0.391323\pi$
$317$	−0.255883	−	0.0931338i	−0.0143718	−	0.00523091i	−0.349196	+	0.937050i	$0.613545\pi$
$318$	−0.643418	+	3.64901i	−0.0360811	+	0.204626i
$319$	1.72896	+	9.80542i	0.0968032	+	0.548998i
$320$	2.31131	−	0.841250i	0.129206	−	0.0470273i
$321$	5.46052	+	4.58192i	0.304776	+	0.255738i
$322$	−6.98095			−0.389033
$323$		0			0
$324$	−7.82328			−0.434626
$325$	−5.10264	−	4.28162i	−0.283043	−	0.237502i
$326$	5.25468	−	1.91255i	0.291030	−	0.105926i
$327$	−0.755063	−	4.28218i	−0.0417551	−	0.236805i
$328$	−0.452772	+	2.56780i	−0.0250002	+	0.141783i
$329$	1.95728	+	0.712391i	0.107908	+	0.0392754i
$330$	5.20234	+	9.01071i	0.286379	+	0.496024i
$331$	−9.99650	+	17.3144i	−0.549457	+	0.951688i	0.448855	+	0.893605i	$0.351832\pi$
$331$	−9.99650	+	17.3144i	−0.549457	+	0.951688i	−0.998312	+	0.0580830i	$0.981501\pi$
$332$	11.6265	−	9.75579i	0.638087	−	0.535419i
$333$	−1.41441	+	1.18683i	−0.0775094	+	0.0650381i
$334$	3.54180	−	6.13458i	0.193799	−	0.335669i
$335$	−14.2173	−	24.6251i	−0.776775	−	1.34541i
$336$	6.61571	+	2.40792i	0.360917	+	0.131363i
$337$	3.00106	−	17.0199i	0.163478	−	0.927131i	−0.787141	−	0.616772i	$-0.788440\pi$
$337$	3.00106	−	17.0199i	0.163478	−	0.927131i	0.950620	−	0.310358i	$-0.100449\pi$
$338$	−4.73255	−	26.8396i	−0.257417	−	1.45988i
$339$	−1.01306	+	0.368725i	−0.0550221	+	0.0200264i
$340$	−9.36292	−	7.85643i	−0.507776	−	0.426075i
$341$	12.2266			0.662105
$342$		0			0
$343$	17.3085			0.934573
$344$	−2.19953	−	1.84563i	−0.118591	−	0.0995096i
$345$	−14.5557	+	5.29786i	−0.783655	+	0.285227i
$346$	−3.99752	−	22.6711i	−0.214908	−	1.21880i
$347$	−3.22041	+	18.2638i	−0.172880	+	0.980454i	0.767681	+	0.640832i	$0.221410\pi$
$347$	−3.22041	+	18.2638i	−0.172880	+	0.980454i	−0.940562	+	0.339622i	$0.889701\pi$
$348$	14.0474	+	5.11285i	0.753022	+	0.274077i
$349$	10.0605	+	17.4253i	0.538527	+	0.932755i	0.998984	+	0.0450735i	$0.0143522\pi$
$349$	10.0605	+	17.4253i	0.538527	+	0.932755i	−0.460457	+	0.887682i	$0.652314\pi$
$350$	−1.46647	+	2.54000i	−0.0783861	+	0.135769i
$351$	−4.30095	+	3.60892i	−0.229568	+	0.192630i
$352$	1.28583	−	1.07894i	0.0685350	−	0.0575077i
$353$	−12.0278	+	20.8328i	−0.640177	+	1.10882i	0.345215	+	0.938523i	$0.387806\pi$
$353$	−12.0278	+	20.8328i	−0.640177	+	1.10882i	−0.985393	+	0.170296i	$0.945527\pi$
$354$	6.25325	+	10.8310i	0.332357	+	0.575659i
$355$	16.1722	+	5.88621i	0.858333	+	0.312408i
$356$	−1.19904	+	6.80011i	−0.0635492	+	0.360405i
$357$	−6.07499	−	34.4530i	−0.321522	−	1.82344i
$358$	−7.71930	+	2.80960i	−0.407978	+	0.148492i
$359$	−8.31423	−	6.97647i	−0.438808	−	0.368204i	0.396455	−	0.918054i	$-0.370240\pi$
$359$	−8.31423	−	6.97647i	−0.438808	−	0.368204i	−0.835263	+	0.549850i	$0.814685\pi$
$360$	8.24263			0.434425
$361$		0			0
$362$	−12.9999			−0.683259
$363$	−15.7967	−	13.2550i	−0.829114	−	0.695709i
$364$	−16.6553	+	6.06205i	−0.872977	+	0.317738i
$365$	2.64221	+	14.9847i	0.138299	+	0.784335i
$366$	−4.08599	+	23.1728i	−0.213578	+	1.21126i
$367$	30.6453	+	11.1540i	1.59967	+	0.582233i	0.979360	−	0.202122i	$-0.0647836\pi$
$367$	30.6453	+	11.1540i	1.59967	+	0.582233i	0.620312	+	0.784355i	$0.287006\pi$
$368$	1.24945	+	2.16411i	0.0651322	+	0.112812i
$369$	−4.36890	+	7.56716i	−0.227436	+	0.393931i
$370$	−1.03814	+	0.871105i	−0.0539704	+	0.0452866i
$371$	−3.14642	+	2.64016i	−0.163354	+	0.137070i
$372$	9.17848	−	15.8976i	0.475882	−	0.824251i
$373$	−2.65099	−	4.59165i	−0.137263	−	0.237746i	0.789197	−	0.614141i	$-0.210497\pi$
$373$	−2.65099	−	4.59165i	−0.137263	−	0.237746i	−0.926460	+	0.376394i	$0.877164\pi$
$374$	−7.83790	−	2.85276i	−0.405288	−	0.147513i
$375$	4.25187	−	24.1136i	0.219566	−	1.24522i
$376$	−0.129471	−	0.734266i	−0.00667695	−	0.0378669i
$377$	−35.3650	+	12.8718i	−1.82139	+	0.662932i
$378$	1.89377	+	1.58906i	0.0974048	+	0.0817323i
$379$	−24.6656			−1.26699			−0.633494	−	0.773748i	$-0.718380\pi$
$379$	−24.6656			−1.26699			−0.633494	+	0.773748i	$0.718380\pi$
$380$		0			0
$381$	2.86368			0.146711
$382$	−5.03658	−	4.22620i	−0.257694	−	0.216231i
$383$	3.42439	−	1.24638i	0.174978	−	0.0636868i	−0.253045	−	0.967454i	$-0.581432\pi$
$383$	3.42439	−	1.24638i	0.174978	−	0.0636868i	0.428024	+	0.903768i	$0.359210\pi$
$384$	−0.437619	−	2.48186i	−0.0223321	−	0.126652i
$385$	−2.00280	+	11.3585i	−0.102072	+	0.578880i
$386$	−25.2614	−	9.19440i	−1.28577	−	0.467983i
$387$	−4.81105	−	8.33298i	−0.244559	−	0.423589i
$388$	7.19369	−	12.4598i	0.365204	−	0.632552i
$389$	2.13997	−	1.79565i	0.108501	−	0.0910430i	−0.586923	−	0.809643i	$-0.699661\pi$
$389$	2.13997	−	1.79565i	0.108501	−	0.0910430i	0.695424	+	0.718600i	$0.255217\pi$
$390$	−30.1270	+	25.2795i	−1.52554	+	1.28008i
$391$	6.20875	−	10.7539i	0.313990	−	0.543846i
$392$	0.402113	+	0.696480i	0.0203098	+	0.0351776i
$393$	42.2516	+	15.3783i	2.13131	+	0.775734i
$394$	1.71033	−	9.69977i	0.0861652	−	0.488667i
$395$	−2.52492	−	14.3195i	−0.127042	−	0.720493i
$396$	5.28577	−	1.92386i	0.265620	−	0.0966777i
$397$	−30.2665	−	25.3966i	−1.51903	−	1.27462i	−0.843254	−	0.537515i	$-0.819363\pi$
$397$	−30.2665	−	25.3966i	−1.51903	−	1.27462i	−0.675778	−	0.737105i	$-0.736192\pi$
$398$	20.4661			1.02587
$399$		0			0
$400$	1.04988			0.0524938
$401$	14.2649	+	11.9696i	0.712354	+	0.597736i	0.925258	−	0.379337i	$-0.123848\pi$
$401$	14.2649	+	11.9696i	0.712354	+	0.597736i	−0.212905	+	0.977073i	$0.568292\pi$
$402$	−27.3770	+	9.96442i	−1.36544	+	0.496980i
$403$	8.02505	+	45.5123i	0.399756	+	2.26713i
$404$	1.95926	−	11.1115i	0.0974768	−	0.552818i
$405$	−18.0821	−	6.58133i	−0.898504	−	0.327029i
$406$	8.28553	+	14.3510i	0.411204	+	0.712226i
$407$	−0.462412	+	0.800921i	−0.0229209	+	0.0397002i
$408$	−9.59321	+	8.04966i	−0.474935	+	0.398518i
$409$	13.1325	−	11.0195i	0.649361	−	0.544879i	−0.257516	−	0.966274i	$-0.582904\pi$
$409$	13.1325	−	11.0195i	0.649361	−	0.544879i	0.906877	+	0.421395i	$0.138460\pi$
$410$	−3.20666	+	5.55410i	−0.158366	+	0.274297i
$411$	20.0549	+	34.7361i	0.989234	+	1.71340i
$412$	13.9337	+	5.07147i	0.686466	+	0.249853i
$413$	−2.40738	+	13.6530i	−0.118460	+	0.671818i
$414$	1.45416	+	8.24696i	0.0714681	+	0.405316i
$415$	35.0796	−	12.7679i	1.72199	−	0.626752i
$416$	4.86023	+	4.07822i	0.238292	+	0.199951i
$417$	25.5043			1.24895
$418$		0			0
$419$	−18.5042			−0.903989			−0.451995	−	0.892021i	$-0.649287\pi$
$419$	−18.5042			−0.903989			−0.451995	+	0.892021i	$0.649287\pi$
$420$	13.2653	+	11.1309i	0.647282	+	0.543134i
$421$	−15.2226	+	5.54059i	−0.741907	+	0.270032i	−0.685196	−	0.728359i	$-0.740283\pi$
$421$	−15.2226	+	5.54059i	−0.741907	+	0.270032i	−0.0567106	+	0.998391i	$0.518061\pi$
$422$	1.40938	+	7.99299i	0.0686075	+	0.389093i
$423$	0.433875	−	2.46063i	0.0210957	−	0.119640i
$424$	1.38160	+	0.502862i	0.0670966	+	0.0244212i
$425$	−2.60851	−	4.51807i	−0.126531	−	0.219159i
$426$	8.81671	−	15.2710i	0.427171	−	0.739882i
$427$	−19.9811	+	16.7661i	−0.966954	+	0.811371i
$428$	2.16675	−	1.81812i	0.104734	−	0.0878820i
$429$	−13.4192	+	23.2428i	−0.647887	+	1.12217i
$430$	−3.53118	−	6.11619i	−0.170289	−	0.294949i
$431$	11.9338	+	4.34354i	0.574830	+	0.209221i	0.613044	−	0.790049i	$-0.289945\pi$
$431$	11.9338	+	4.34354i	0.574830	+	0.209221i	−0.0382143	+	0.999270i	$0.512167\pi$
$432$	0.153666	−	0.871483i	0.00739326	−	0.0419292i
$433$	−2.47189	−	14.0188i	−0.118791	−	0.673699i	−0.984803	−	0.173675i	$-0.944436\pi$
$433$	−2.47189	−	14.0188i	−0.118791	−	0.673699i	0.866012	−	0.500024i	$-0.166675\pi$
$434$	19.1217	−	6.95971i	0.917869	−	0.334077i
$435$	28.1669	+	23.6348i	1.35050	+	1.13320i
$436$	−1.72539			−0.0826312
$437$		0			0
$438$	15.5901			0.744924
$439$	−21.5948	−	18.1202i	−1.03066	−	0.864830i	−0.0397343	−	0.999210i	$-0.512651\pi$
$439$	−21.5948	−	18.1202i	−1.03066	−	0.864830i	−0.990930	+	0.134380i	$0.957096\pi$
$440$	3.87961	−	1.41206i	0.184953	−	0.0673175i
$441$	0.467995	+	2.65413i	0.0222855	+	0.126387i
$442$	5.47466	−	31.0483i	0.260403	−	1.47682i
$443$	31.0046	+	11.2847i	1.47307	+	0.536154i	0.948933	−	0.315479i	$-0.102165\pi$
$443$	31.0046	+	11.2847i	1.47307	+	0.536154i	0.524138	+	0.851633i	$0.324387\pi$
$444$	0.694265	+	1.20250i	0.0329484	+	0.0570683i
$445$	−8.49196	+	14.7085i	−0.402558	+	0.697250i
$446$	8.23806	−	6.91255i	0.390083	−	0.327319i
$447$	18.1442	−	15.2248i	0.858193	−	0.720110i
$448$	1.39680	−	2.41933i	0.0659927	−	0.114303i
$449$	−8.59876	−	14.8935i	−0.405801	−	0.702867i	0.588614	−	0.808415i	$-0.299674\pi$
$449$	−8.59876	−	14.8935i	−0.405801	−	0.702867i	−0.994414	+	0.105547i	$0.966341\pi$
$450$	3.30610	+	1.20332i	0.155851	+	0.0567252i
$451$	−0.759993	+	4.31013i	−0.0357867	+	0.202956i
$452$	0.0742841	+	0.421286i	0.00349403	+	0.0198156i
$453$	−24.3050	+	8.84630i	−1.14195	+	0.415636i
$454$	20.7549	+	17.4154i	0.974076	+	0.817347i
$455$	−43.5954			−2.04378
$456$		0			0
$457$	−31.1517			−1.45722			−0.728608	−	0.684931i	$-0.759832\pi$
$457$	−31.1517			−1.45722			−0.728608	+	0.684931i	$0.759832\pi$
$458$	−7.25105	−	6.08435i	−0.338819	−	0.284303i
$459$	−4.13216	+	1.50398i	−0.192873	+	0.0702000i
$460$	1.06732	+	6.05305i	0.0497639	+	0.282225i
$461$	2.69867	−	15.3049i	0.125689	−	0.712820i	−0.855207	−	0.518287i	$-0.826570\pi$
$461$	2.69867	−	15.3049i	0.125689	−	0.712820i	0.980896	−	0.194533i	$-0.0623190\pi$
$462$	11.1047	+	4.04177i	0.516637	+	0.188040i
$463$	−10.3324	−	17.8962i	−0.480187	−	0.831708i	0.519555	−	0.854437i	$-0.326098\pi$
$463$	−10.3324	−	17.8962i	−0.480187	−	0.831708i	−0.999742	+	0.0227291i	$0.992764\pi$
$464$	2.96589	−	5.13708i	0.137688	−	0.238483i
$465$	34.5882	−	29.0229i	1.60399	−	1.34591i
$466$	−17.5134	+	14.6955i	−0.811292	+	0.680755i
$467$	14.2415	−	24.6670i	0.659017	−	1.14145i	−0.321853	−	0.946790i	$-0.604306\pi$
$467$	14.2415	−	24.6670i	0.659017	−	1.14145i	0.980870	−	0.194662i	$-0.0623609\pi$
$468$	10.6308	+	18.4131i	0.491408	+	0.851144i
$469$	−30.3477	−	11.0456i	−1.40132	−	0.510040i
$470$	0.318453	−	1.80604i	0.0146891	−	0.0833063i
$471$	1.30142	+	7.38074i	0.0599664	+	0.340087i
$472$	4.66333	−	1.69731i	0.214647	−	0.0781252i
$473$	−3.69199	−	3.09795i	−0.169758	−	0.142444i
$474$	−14.8981			−0.684290
$475$		0			0
$476$	−13.8819			−0.636276
$477$	3.77437	+	3.16707i	0.172816	+	0.145010i
$478$	8.14348	−	2.96399i	0.372474	−	0.135570i
$479$	−1.81856	−	10.3135i	−0.0830919	−	0.471238i	−0.997752	−	0.0670140i	$-0.978653\pi$
$479$	−1.81856	−	10.3135i	−0.0830919	−	0.471238i	0.914660	−	0.404224i	$-0.132458\pi$
$480$	1.07639	−	6.10451i	0.0491302	−	0.278631i
$481$	−3.28487	−	1.19559i	−0.149777	−	0.0545144i
$482$	−2.82913	−	4.90020i	−0.128863	−	0.223198i
$483$	−8.79651	+	15.2360i	−0.400255	+	0.693262i
$484$	−6.26818	+	5.25963i	−0.284917	+	0.239074i
$485$	27.1087	−	22.7469i	1.23094	−	1.03288i
$486$	−11.1853	+	19.3735i	−0.507375	+	0.878800i
$487$	1.14947	+	1.99094i	0.0520875	+	0.0902181i	0.890894	−	0.454212i	$-0.150079\pi$
$487$	1.14947	+	1.99094i	0.0520875	+	0.0902181i	−0.838806	+	0.544430i	$0.816746\pi$
$488$	8.77378	+	3.19339i	0.397170	+	0.144558i
$489$	2.44713	−	13.8783i	0.110663	−	0.627600i
$490$	0.343496	+	1.94806i	0.0155176	+	0.0880045i
$491$	−11.4278	+	4.15937i	−0.515728	+	0.187710i	−0.586755	−	0.809765i	$-0.699595\pi$
$491$	−11.4278	+	4.15937i	−0.515728	+	0.187710i	0.0710267	+	0.997474i	$0.477372\pi$
$492$	5.03373	+	4.22380i	0.226938	+	0.190424i
$493$	−29.4761			−1.32754
$494$		0			0
$495$	13.8355			0.621860
$496$	−5.57993	−	4.68212i	−0.250546	−	0.210233i
$497$	18.3680	−	6.68540i	0.823917	−	0.299881i
$498$	−6.64188	−	37.6680i	−0.297630	−	1.68794i
$499$	2.62814	−	14.9049i	0.117652	−	0.667235i	−0.867752	−	0.496998i	$-0.834436\pi$
$499$	2.62814	−	14.9049i	0.117652	−	0.667235i	0.985403	−	0.170237i	$-0.0544533\pi$
$500$	−9.12998	−	3.32304i	−0.408305	−	0.148611i
$501$	−8.92586	−	15.4600i	−0.398778	−	0.690704i
$502$	−6.77762	+	11.7392i	−0.302500	+	0.523945i
$503$	−0.439467	+	0.368756i	−0.0195948	+	0.0164420i	−0.652532	−	0.757761i	$-0.726293\pi$
$503$	−0.439467	+	0.368756i	−0.0195948	+	0.0164420i	0.632938	+	0.774203i	$0.281849\pi$
$504$	7.17153	−	6.01762i	0.319445	−	0.268046i
$505$	13.8760	−	24.0340i	0.617475	−	1.06950i
$506$	2.09724	+	3.63253i	0.0932339	+	0.161486i
$507$	−64.5411	−	23.4910i	−2.86637	−	1.04327i
$508$	0.197319	−	1.11905i	0.00875463	−	0.0496499i
$509$	4.55241	+	25.8180i	0.201782	+	1.14436i	0.902424	+	0.430849i	$0.141786\pi$
$509$	4.55241	+	25.8180i	0.201782	+	1.14436i	−0.700642	+	0.713513i	$0.747103\pi$
$510$	−28.9447	+	10.5350i	−1.28169	+	0.466498i
$511$	13.2386	+	11.1085i	0.585641	+	0.491412i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	10.0393			0.442813
$515$	27.9389	+	23.4435i	1.23113	+	1.03304i
$516$	−6.79968	+	2.47488i	−0.299339	+	0.108951i
$517$	−0.217321	−	1.23249i	−0.00955777	−	0.0542048i
$518$	−0.267279	+	1.51581i	−0.0117436	+	0.0666010i
$519$	−54.5170	−	19.8426i	−2.39303	−	0.870992i
$520$	7.80272	+	13.5147i	0.342172	+	0.592659i
$521$	−6.48183	+	11.2269i	−0.283974	+	0.491857i	−0.972360	−	0.233487i	$-0.924986\pi$
$521$	−6.48183	+	11.2269i	−0.283974	+	0.491857i	0.688386	+	0.725345i	$0.258320\pi$
$522$	15.2276	−	12.7775i	0.666495	−	0.559256i
$523$	−13.6197	+	11.4283i	−0.595548	+	0.499724i	−0.890011	−	0.455939i	$-0.849304\pi$
$523$	−13.6197	+	11.4283i	−0.595548	+	0.499724i	0.294463	+	0.955663i	$0.404859\pi$
$524$	8.92075	−	15.4512i	0.389705	−	0.674989i
$525$	3.69572	+	6.40117i	0.161294	+	0.279370i
$526$	−17.6908	−	6.43893i	−0.771357	−	0.280751i
$527$	−6.28535	+	35.6460i	−0.273794	+	1.55276i
$528$	−0.734557	−	4.16588i	−0.0319675	−	0.181297i
$529$	15.7450	−	5.73071i	0.684565	−	0.249161i
$530$	2.77029	+	2.32455i	0.120334	+	0.100972i
$531$	16.6304			0.721698
$532$		0			0
$533$	−16.5429			−0.716554
$534$	13.3304	+	11.1856i	0.576865	+	0.484047i
$535$	6.53752	−	2.37946i	0.282642	−	0.102873i
$536$	2.00745	+	11.3848i	0.0867086	+	0.491749i
$537$	−3.59491	+	20.3878i	−0.155132	+	0.879797i
$538$	15.3947	+	5.60321i	0.663712	+	0.241571i
$539$	0.674959	+	1.16906i	0.0290726	+	0.0503551i
$540$	1.08831	−	1.88500i	0.0468332	−	0.0811175i
$541$	−4.09388	+	3.43517i	−0.176010	+	0.147690i	−0.726537	−	0.687128i	$-0.758871\pi$
$541$	−4.09388	+	3.43517i	−0.176010	+	0.147690i	0.550527	+	0.834817i	$0.314427\pi$
$542$	2.11952	−	1.77849i	0.0910412	−	0.0763926i
$543$	−16.3808	+	28.3724i	−0.702968	+	1.21758i
$544$	2.48459	+	4.30343i	0.106526	+	0.184508i
$545$	−3.98792	−	1.45148i	−0.170824	−	0.0621747i
$546$	−7.75646	+	43.9891i	−0.331946	+	1.88256i
$547$	−0.885800	−	5.02362i	−0.0378741	−	0.214795i	0.959997	−	0.280010i	$-0.0903377\pi$
$547$	−0.885800	−	5.02362i	−0.0378741	−	0.214795i	−0.997871	+	0.0652152i	$0.979227\pi$
$548$	14.9558	−	5.44347i	0.638880	−	0.232533i
$549$	23.9689	+	20.1123i	1.02297	+	0.858371i
$550$	1.76225			0.0751426
$551$		0			0
$552$	6.29761			0.268044
$553$	−12.6509	−	10.6154i	−0.537972	−	0.451412i
$554$	23.0527	−	8.39048i	0.979413	−	0.356477i
$555$	0.593060	+	3.36341i	0.0251740	+	0.142769i
$556$	1.75735	−	9.96642i	0.0745282	−	0.422670i
$557$	10.0768	+	3.66766i	0.426968	+	0.155404i	0.546561	−	0.837419i	$-0.315937\pi$
$557$	10.0768	+	3.66766i	0.426968	+	0.155404i	−0.119593	+	0.992823i	$0.538159\pi$
$558$	−12.2050	−	21.1397i	−0.516678	−	0.894913i
$559$	9.10855	−	15.7765i	0.385251	−	0.667274i
$560$	5.26371	−	4.41678i	0.222432	−	0.186643i
$561$	−16.1025	+	13.5116i	−0.679849	+	0.570461i
$562$	−5.08518	+	8.80779i	−0.214505	+	0.371534i
$563$	4.88142	+	8.45488i	0.205728	+	0.356331i	0.950364	−	0.311139i	$-0.100711\pi$
$563$	4.88142	+	8.45488i	0.205728	+	0.356331i	−0.744637	+	0.667470i	$0.767377\pi$
$564$	−1.76569	−	0.642658i	−0.0743488	−	0.0270608i
$565$	−0.182713	+	1.03622i	−0.00768678	+	0.0435939i
$566$	−4.80446	−	27.2475i	−0.201947	−	1.14530i
$567$	−20.5371	+	7.47490i	−0.862478	+	0.313916i
$568$	−5.36000	−	4.49757i	−0.224901	−	0.188714i
$569$	8.84194			0.370674			0.185337	−	0.982675i	$-0.440662\pi$
$569$	8.84194			0.370674			0.185337	+	0.982675i	$0.440662\pi$
$570$		0			0
$571$	22.8411			0.955871			0.477935	−	0.878395i	$-0.341385\pi$
$571$	22.8411			0.955871			0.477935	+	0.878395i	$0.341385\pi$
$572$	8.15804	+	6.84541i	0.341105	+	0.286221i
$573$	−15.5702	+	5.66708i	−0.650454	+	0.236746i
$574$	1.26487	+	7.17342i	0.0527945	+	0.299413i
$575$	−0.455573	+	2.58368i	−0.0189987	+	0.107747i
$576$	−3.14904	−	1.14616i	−0.131210	−	0.0477566i
$577$	7.00879	+	12.1396i	0.291780	+	0.505377i	0.974231	−	0.225554i	$-0.0724192\pi$
$577$	7.00879	+	12.1396i	0.291780	+	0.505377i	−0.682451	+	0.730931i	$0.739086\pi$
$578$	3.84635	−	6.66207i	0.159987	−	0.277106i
$579$	−51.8981	+	43.5477i	−2.15681	+	1.80978i
$580$	11.1767	−	9.37834i	0.464086	−	0.389415i
$581$	21.1997	−	36.7190i	0.879513	−	1.52336i
$582$	−18.1292	−	31.4006i	−0.751478	−	1.30160i
$583$	2.31906	+	0.844070i	0.0960458	+	0.0349578i
$584$	1.07422	−	6.09221i	0.0444516	−	0.252097i
$585$	9.08111	+	51.5015i	0.375458	+	2.12933i
$586$	−22.4010	+	8.15328i	−0.925375	+	0.336809i
$587$	16.1142	+	13.5214i	0.665104	+	0.558089i	0.911612	−	0.411052i	$-0.134839\pi$
$587$	16.1142	+	13.5214i	0.665104	+	0.558089i	−0.246508	+	0.969141i	$0.579283\pi$
$588$	2.02677			0.0835825
$589$		0			0
$590$	12.2063			0.502525
$591$	−19.0147	−	15.9552i	−0.782161	−	0.656311i
$592$	0.517744	−	0.188444i	0.0212792	−	0.00774498i
$593$	−6.06367	−	34.3888i	−0.249005	−	1.41218i	−0.811005	−	0.585040i	$-0.801079\pi$
$593$	−6.06367	−	34.3888i	−0.249005	−	1.41218i	0.562000	−	0.827137i	$-0.310032\pi$
$594$	0.257933	−	1.46281i	0.0105831	−	0.0600199i
$595$	−32.0855	−	11.6782i	−1.31538	−	0.478758i
$596$	−4.69925	−	8.13935i	−0.192489	−	0.333401i
$597$	25.7888	−	44.6675i	1.05546	−	1.82812i
$598$	−12.1452	+	10.1911i	−0.496656	+	0.416744i
$599$	−16.4781	+	13.8268i	−0.673277	+	0.564946i	−0.914033	−	0.405639i	$-0.867049\pi$
$599$	−16.4781	+	13.8268i	−0.673277	+	0.564946i	0.240756	+	0.970586i	$0.422605\pi$
$600$	1.32292	−	2.29137i	0.0540080	−	0.0935446i
$601$	−7.17087	−	12.4203i	−0.292506	−	0.506635i	0.681896	−	0.731449i	$-0.261156\pi$
$601$	−7.17087	−	12.4203i	−0.292506	−	0.506635i	−0.974402	+	0.224814i	$0.927822\pi$
$602$	−7.53750	−	2.74343i	−0.307206	−	0.111814i
$603$	−6.72725	+	38.1521i	−0.273955	+	1.55367i
$604$	1.78219	+	10.1073i	0.0725164	+	0.411261i
$605$	−18.9124	+	6.88355i	−0.768899	+	0.279856i
$606$	−21.7822	−	18.2774i	−0.884841	−	0.742470i
$607$	10.3488			0.420046			0.210023	−	0.977696i	$-0.432646\pi$
$607$	10.3488			0.420046			0.210023	+	0.977696i	$0.432646\pi$
$608$		0			0
$609$	41.7615			1.69226
$610$	17.5925	+	14.7619i	0.712300	+	0.597691i
$611$	4.44519	−	1.61792i	0.179833	−	0.0654539i
$612$	2.89166	+	16.3994i	0.116888	+	0.662907i
$613$	3.39784	−	19.2701i	0.137238	−	0.778313i	−0.836038	−	0.548672i	$-0.815134\pi$
$613$	3.39784	−	19.2701i	0.137238	−	0.778313i	0.973275	−	0.229641i	$-0.0737553\pi$
$614$	−24.4211	−	8.88857i	−0.985557	−	0.358713i
$615$	8.08126	+	13.9971i	0.325868	+	0.564419i
$616$	2.34458	−	4.06093i	0.0944657	−	0.163619i
$617$	−4.53898	+	3.80866i	−0.182733	+	0.153331i	−0.729566	−	0.683911i	$-0.760278\pi$
$617$	−4.53898	+	3.80866i	−0.182733	+	0.153331i	0.546833	+	0.837242i	$0.315833\pi$
$618$	28.6261	−	24.0201i	1.15151	−	0.966231i
$619$	−4.01979	+	6.96248i	−0.161569	+	0.279846i	−0.935432	−	0.353508i	$-0.884989\pi$
$619$	−4.01979	+	6.96248i	−0.161569	+	0.279846i	0.773863	+	0.633354i	$0.218322\pi$
$620$	−8.95814	−	15.5160i	−0.359768	−	0.623136i
$621$	2.07799	+	0.756325i	0.0833867	+	0.0303503i
$622$	4.01203	−	22.7533i	0.160868	−	0.912325i
$623$	3.34965	+	18.9968i	0.134201	+	0.761092i
$624$	15.0250	−	5.46865i	0.601481	−	0.218921i
$625$	−22.3280	−	18.7354i	−0.893120	−	0.749417i
$626$	−12.2647			−0.490196
$627$		0			0
$628$	2.97387			0.118671
$629$	−2.09734	−	1.75987i	−0.0836262	−	0.0701707i
$630$	21.6380	−	7.87558i	0.862078	−	0.313771i
$631$	−2.24017	−	12.7047i	−0.0891799	−	0.505764i	−0.996376	−	0.0850566i	$-0.972893\pi$
$631$	−2.24017	−	12.7047i	−0.0891799	−	0.505764i	0.907196	−	0.420708i	$-0.138218\pi$
$632$	−1.02654	+	5.82177i	−0.0408334	+	0.231578i
$633$	19.2207	+	6.99577i	0.763955	+	0.278057i
$634$	0.136152	+	0.235823i	0.00540731	+	0.00936573i
$635$	1.39747	−	2.42049i	0.0554569	−	0.0960542i
$636$	2.83842	−	2.38172i	0.112551	−	0.0944414i
$637$	−3.90872	+	3.27981i	−0.154869	+	0.129951i
$638$	4.97834	−	8.62275i	0.197095	−	0.341378i
$639$	−11.7239	−	20.3065i	−0.463792	−	0.803311i
$640$	−2.31131	−	0.841250i	−0.0913627	−	0.0332533i
$641$	5.01216	−	28.4254i	0.197969	−	1.12274i	−0.710159	−	0.704041i	$-0.751377\pi$
$641$	5.01216	−	28.4254i	0.197969	−	1.12274i	0.908127	−	0.418694i	$-0.137512\pi$
$642$	−1.23780	−	7.01991i	−0.0488520	−	0.277054i
$643$	−24.7510	+	9.00862i	−0.976083	+	0.355265i	−0.780316	−	0.625385i	$-0.784942\pi$
$643$	−24.7510	+	9.00862i	−0.976083	+	0.355265i	−0.195767	+	0.980650i	$0.562720\pi$
$644$	5.34772	+	4.48727i	0.210730	+	0.176823i
$645$	−17.7982			−0.700803
$646$		0			0
$647$	−3.04601			−0.119751			−0.0598756	−	0.998206i	$-0.519070\pi$
$647$	−3.04601			−0.119751			−0.0598756	+	0.998206i	$0.519070\pi$
$648$	5.99298	+	5.02871i	0.235426	+	0.197546i
$649$	7.82754	−	2.84899i	0.307258	−	0.111833i
$650$	1.15667	+	6.55982i	0.0453685	+	0.257297i
$651$	8.90504	−	50.5030i	0.349016	−	1.97937i
$652$	−5.25468	−	1.91255i	−0.205789	−	0.0749011i
$653$	7.59866	+	13.1613i	0.297359	+	0.515040i	0.975531	−	0.219863i	$-0.0705610\pi$
$653$	7.59866	+	13.1613i	0.297359	+	0.515040i	−0.678172	+	0.734903i	$0.737228\pi$
$654$	−2.17412	+	3.76568i	−0.0850148	+	0.147250i
$655$	33.6170	−	28.2080i	1.31352	−	1.10218i
$656$	1.99739	−	1.67601i	0.0779851	−	0.0654373i
$657$	10.3654	−	17.9534i	0.404393	−	0.700429i
$658$	−1.04145	−	1.80384i	−0.0405998	−	0.0703209i
$659$	16.7961	+	6.11330i	0.654285	+	0.238140i	0.647767	−	0.761839i	$-0.275703\pi$
$659$	16.7961	+	6.11330i	0.654285	+	0.238140i	0.00651784	+	0.999979i	$0.497925\pi$
$660$	1.80675	−	10.2466i	0.0703278	−	0.398849i
$661$	−6.57302	−	37.2775i	−0.255661	−	1.44993i	−0.794371	−	0.607434i	$-0.792199\pi$
$661$	−6.57302	−	37.2775i	−0.255661	−	1.44993i	0.538710	−	0.842492i	$-0.318912\pi$
$662$	18.7873	−	6.83801i	0.730188	−	0.265767i
$663$	−60.8649	−	51.0717i	−2.36380	−	1.98346i
$664$	−15.1773			−0.588994
$665$		0			0
$666$	1.84638			0.0715460
$667$	11.3550	+	9.52802i	0.439669	+	0.368926i
$668$	−6.65641	+	2.42274i	−0.257544	+	0.0937385i
$669$	−4.70616	−	26.6900i	−0.181951	−	1.03189i
$670$	−4.93762	+	28.0026i	−0.190757	+	1.08184i
$671$	14.7271	+	5.36021i	0.568532	+	0.206929i
$672$	−3.52015	−	6.09707i	−0.135793	−	0.235200i
$673$	−4.14230	+	7.17468i	−0.159674	+	0.276564i	−0.934751	−	0.355303i	$-0.884378\pi$
$673$	−4.14230	+	7.17468i	−0.159674	+	0.276564i	0.775077	+	0.631867i	$0.217711\pi$
$674$	−13.2391	+	11.1089i	−0.509951	+	0.427900i
$675$	0.711704	−	0.597191i	0.0273935	−	0.0229859i
$676$	−13.6268	+	23.6024i	−0.524109	+	0.907783i
$677$	−9.16167	−	15.8685i	−0.352111	−	0.609875i	0.634508	−	0.772917i	$-0.281203\pi$
$677$	−9.16167	−	15.8685i	−0.352111	−	0.609875i	−0.986619	+	0.163042i	$0.947870\pi$
$678$	1.01306	+	0.368725i	0.0389065	+	0.0141608i
$679$	6.97938	−	39.5820i	0.267844	−	1.51902i
$680$	2.12240	+	12.0367i	0.0813904	+	0.461588i
$681$	64.1621	−	23.3531i	2.45870	−	0.894892i
$682$	−9.36609	−	7.85908i	−0.358646	−	0.300940i
$683$	49.2217			1.88342			0.941709	−	0.336429i	$-0.109219\pi$
$683$	49.2217			1.88342			0.941709	+	0.336429i	$0.109219\pi$
$684$		0			0
$685$	39.1469			1.49573
$686$	−13.2591	−	11.1257i	−0.506235	−	0.424782i
$687$	−22.4160	+	8.15876i	−0.855225	+	0.311276i
$688$	0.498594	+	2.82767i	0.0190087	+	0.107804i
$689$	−1.61983	+	9.18653i	−0.0617107	+	0.349979i
$690$	14.5557	+	5.29786i	0.554128	+	0.201686i
$691$	−8.33895	−	14.4435i	−0.317229	−	0.549456i	0.662680	−	0.748903i	$-0.269419\pi$
$691$	−8.33895	−	14.4435i	−0.317229	−	0.549456i	−0.979909	+	0.199446i	$0.936086\pi$
$692$	−11.5104	+	19.9366i	−0.437560	+	0.757876i
$693$	12.0376	−	10.1008i	0.457272	−	0.383697i
$694$	14.2067	−	11.9209i	0.539280	−	0.452510i
$695$	12.4460	−	21.5572i	0.472105	−	0.817710i
$696$	−7.47449	−	12.9462i	−0.283320	−	0.490724i
$697$	−12.1753	−	4.43145i	−0.461173	−	0.167853i
$698$	3.49398	−	19.8153i	0.132249	−	0.750021i
$699$	10.0049	+	56.7405i	0.378420	+	2.14612i
$700$	2.75606	−	1.00312i	0.104169	−	0.0379145i
$701$	−23.6758	−	19.8664i	−0.894223	−	0.750342i	0.0748294	−	0.997196i	$-0.476159\pi$
$701$	−23.6758	−	19.8664i	−0.894223	−	0.750342i	−0.969053	+	0.246854i	$0.920603\pi$
$702$	5.61449			0.211905
$703$		0			0
$704$	−1.67853			−0.0632620
$705$	−3.54042	−	2.97077i	−0.133340	−	0.111886i
$706$	22.6049	−	8.22753i	0.850749	−	0.309647i
$707$	−5.47340	−	31.0412i	−0.205848	−	1.16742i
$708$	2.17173	−	12.3165i	0.0816187	−	0.462883i
$709$	−37.6869	−	13.7169i	−1.41536	−	0.515150i	−0.482663	−	0.875806i	$-0.660330\pi$
$709$	−37.6869	−	13.7169i	−1.41536	−	0.515150i	−0.932699	+	0.360656i	$0.882553\pi$
$710$	−8.60506	−	14.9044i	−0.322942	−	0.559352i
$711$	−9.90527	+	17.1564i	−0.371477	+	0.643417i
$712$	5.28955	−	4.43846i	0.198234	−	0.166338i
$713$	13.9437	−	11.7002i	0.522196	−	0.438174i
$714$	−17.4922	+	30.2974i	−0.654630	+	1.13385i
$715$	13.0971	+	22.6849i	0.489804	+	0.848365i
$716$	7.71930	+	2.80960i	0.288484	+	0.105000i
$717$	3.79246	−	21.5081i	0.141632	−	0.803234i
$718$	1.88468	+	10.6886i	0.0703358	+	0.398894i
$719$	42.8997	−	15.6142i	1.59989	−	0.582311i	0.620483	−	0.784220i	$-0.286937\pi$
$719$	42.8997	−	15.6142i	1.59989	−	0.582311i	0.979404	+	0.201908i	$0.0647143\pi$
$720$	−6.31422	−	5.29826i	−0.235317	−	0.197455i
$721$	41.4235			1.54269
$722$		0			0
$723$	−14.2596			−0.530322
$724$	9.95849	+	8.35617i	0.370104	+	0.310554i
$725$	5.85207	−	2.12998i	0.217340	−	0.0791054i
$726$	3.58083	+	20.3079i	0.132897	+	0.753697i
$727$	−2.63616	+	14.9504i	−0.0977698	+	0.554480i	0.896093	+	0.443865i	$0.146393\pi$
$727$	−2.63616	+	14.9504i	−0.0977698	+	0.554480i	−0.993863	+	0.110615i	$0.964718\pi$
$728$	16.6553	+	6.06205i	0.617288	+	0.224674i
$729$	16.4537	+	28.4986i	0.609395	+	1.05550i
$730$	7.60793	−	13.1773i	0.281582	−	0.487715i
$731$	10.9299	−	9.17125i	0.404256	−	0.339211i
$732$	18.0252	−	15.1250i	0.666231	−	0.559035i
$733$	13.4993	−	23.3815i	0.498608	−	0.863615i	−0.501390	−	0.865221i	$-0.667178\pi$
$733$	13.4993	−	23.3815i	0.498608	−	0.863615i	0.999999	+	0.00160611i	$0.000511240\pi$
$734$	−16.3060	−	28.2429i	−0.601867	−	1.04246i
$735$	4.68450	+	1.70502i	0.172790	+	0.0628905i
$736$	0.433930	−	2.46094i	0.0159949	−	0.0907114i
$737$	3.36957	+	19.1098i	0.124120	+	0.703917i
$738$	8.21085	−	2.98851i	0.302246	−	0.110008i
$739$	−3.98942	−	3.34752i	−0.146753	−	0.123141i	0.566455	−	0.824092i	$-0.308314\pi$
$739$	−3.98942	−	3.34752i	−0.146753	−	0.123141i	−0.713209	+	0.700952i	$0.752759\pi$
$740$	1.35520			0.0498181
$741$		0			0
$742$	4.10736			0.150786
$743$	−16.9356	−	14.2107i	−0.621307	−	0.521339i	0.276907	−	0.960897i	$-0.410691\pi$
$743$	−16.9356	−	14.2107i	−0.621307	−	0.521339i	−0.898214	+	0.439558i	$0.855135\pi$
$744$	−17.2499	+	6.27845i	−0.632412	+	0.230179i
$745$	−4.01423	−	22.7658i	−0.147070	−	0.834076i
$746$	−0.920679	+	5.22143i	−0.0337084	+	0.191170i
$747$	−47.7940	−	17.3956i	−1.74869	−	0.636472i
$748$	4.17046	+	7.22345i	0.152487	+	0.264115i
$749$	3.95084	−	6.84305i	0.144360	−	0.250040i
$750$	−18.7570	+	15.7390i	−0.684909	+	0.574707i
$751$	9.57247	−	8.03225i	0.349304	−	0.293101i	−0.451206	−	0.892420i	$-0.649006\pi$
$751$	9.57247	−	8.03225i	0.349304	−	0.293101i	0.800511	+	0.599319i	$0.204562\pi$
$752$	−0.372797	+	0.645703i	−0.0135945	+	0.0235464i
$753$	17.0806	+	29.5844i	0.622451	+	1.07812i
$754$	35.3650	+	12.8718i	1.28792	+	0.468764i
$755$	−4.38357	+	24.8604i	−0.159534	+	0.904764i
$756$	−0.429282	−	2.43458i	−0.0156128	−	0.0885448i
$757$	29.1294	−	10.6022i	1.05873	−	0.385345i	0.246776	−	0.969072i	$-0.420629\pi$
$757$	29.1294	−	10.6022i	1.05873	−	0.385345i	0.811949	+	0.583728i	$0.198407\pi$
$758$	18.8949	+	15.8547i	0.686295	+	0.575870i
$759$	10.5707			0.383693
$760$		0			0
$761$	1.96398			0.0711941			0.0355971	−	0.999366i	$-0.488667\pi$
$761$	1.96398			0.0711941			0.0355971	+	0.999366i	$0.488667\pi$
$762$	−2.19371	−	1.84074i	−0.0794697	−	0.0666830i
$763$	−4.52937	+	1.64856i	−0.163974	+	0.0596818i
$764$	1.14170	+	6.47491i	0.0413053	+	0.234254i
$765$	−7.11247	+	40.3368i	−0.257152	+	1.45838i
$766$	−3.42439	−	1.24638i	−0.123728	−	0.0450334i
$767$	15.7428	+	27.2674i	0.568441	+	0.984568i
$768$	−1.26007	+	2.18251i	−0.0454690	+	0.0787546i
$769$	−17.1074	+	14.3548i	−0.616910	+	0.517649i	−0.896830	−	0.442374i	$-0.854136\pi$
$769$	−17.1074	+	14.3548i	−0.616910	+	0.517649i	0.279921	+	0.960023i	$0.409692\pi$
$770$	8.83531	−	7.41370i	0.318402	−	0.267171i
$771$	12.6502	−	21.9108i	0.455586	−	0.789098i
$772$	13.4413	+	23.2810i	0.483763	+	0.837903i
$773$	25.7056	+	9.35606i	0.924565	+	0.336514i	0.760053	−	0.649861i	$-0.225173\pi$
$773$	25.7056	+	9.35606i	0.924565	+	0.336514i	0.164512	+	0.986375i	$0.447395\pi$
$774$	−1.67086	+	9.47591i	−0.0600578	+	0.340605i
$775$	−1.32795	−	7.53120i	−0.0477015	−	0.270529i
$776$	−13.5197	+	4.92077i	−0.485329	+	0.176645i
$777$	2.97149	+	2.49338i	0.106602	+	0.0894494i
$778$	−2.79353			−0.100153
$779$		0			0
$780$	39.3280			1.40817
$781$	−8.99693	−	7.54932i	−0.321935	−	0.270136i
$782$	−11.6686	+	4.24703i	−0.417269	+	0.151874i
$783$	−0.911513	−	5.16945i	−0.0325748	−	0.184741i
$784$	0.139652	−	0.792008i	0.00498759	−	0.0282860i
$785$	6.87356	+	2.50177i	0.245328	+	0.0892920i
$786$	−22.4816	−	38.9393i	−0.801892	−	1.38892i
$787$	3.89481	−	6.74601i	0.138835	−	0.240469i	−0.788221	−	0.615392i	$-0.788998\pi$
$787$	3.89481	−	6.74601i	0.138835	−	0.240469i	0.927056	+	0.374923i	$0.122331\pi$
$788$	−7.54508	+	6.33107i	−0.268782	+	0.225535i
$789$	−36.3448	+	30.4969i	−1.29391	+	1.08572i
$790$	−7.27021	+	12.5924i	−0.258662	+	0.448017i
$791$	0.597531	+	1.03495i	0.0212457	+	0.0367987i
$792$	−5.28577	−	1.92386i	−0.187822	−	0.0683615i
$793$	−10.2866	+	58.3385i	−0.365289	+	2.07166i
$794$	6.86086	+	38.9099i	0.243483	+	1.38086i
$795$	8.56411	−	3.11708i	0.303738	−	0.110552i
$796$	−15.6779	−	13.1554i	−0.555690	−	0.466279i
$797$	6.09655			0.215951			0.107975	−	0.994154i	$-0.465563\pi$
$797$	6.09655			0.215951			0.107975	+	0.994154i	$0.465563\pi$
$798$		0			0
$799$	3.70498			0.131073
$800$	−0.804252	−	0.674847i	−0.0284346	−	0.0238595i
$801$	21.7442	−	7.91424i	0.768293	−	0.279636i
$802$	−3.23358	−	18.3386i	−0.114182	−	0.647557i
$803$	1.80311	−	10.2260i	0.0636305	−	0.360867i
$804$	27.3770	+	9.96442i	0.965513	+	0.351418i
$805$	8.58534	+	14.8703i	0.302594	+	0.524108i
$806$	23.1072	−	40.0228i	0.813916	−	1.40974i
$807$	31.6275	−	26.5386i	1.11334	−	0.934204i
$808$	−8.64322	+	7.25253i	−0.304068	+	0.255143i
$809$	−28.4228	+	49.2297i	−0.999291	+	1.73082i	−0.467047	+	0.884232i	$0.654682\pi$
$809$	−28.4228	+	49.2297i	−0.999291	+	1.73082i	−0.532244	+	0.846591i	$0.678651\pi$
$810$	9.62126	+	16.6645i	0.338057	+	0.585531i
$811$	−19.6592	−	7.15536i	−0.690327	−	0.251259i	−0.0270520	−	0.999634i	$-0.508612\pi$
$811$	−19.6592	−	7.15536i	−0.690327	−	0.251259i	−0.663275	+	0.748375i	$0.730834\pi$
$812$	2.87753	−	16.3193i	0.100982	−	0.572696i
$813$	−1.21082	−	6.86690i	−0.0424653	−	0.240833i
$814$	0.869050	−	0.316308i	0.0304602	−	0.0110866i
$815$	−10.5363	−	8.84099i	−0.369070	−	0.309686i
$816$	12.5231			0.438394
$817$		0			0
$818$	−17.1433			−0.599401
$819$	45.5003	+	38.1793i	1.58991	+	1.33409i
$820$	6.02655	−	2.19348i	0.210456	−	0.0765998i
$821$	2.82321	+	16.0112i	0.0985308	+	0.558796i	0.993608	+	0.112885i	$0.0360092\pi$
$821$	2.82321	+	16.0112i	0.0985308	+	0.558796i	−0.895077	+	0.445911i	$0.852880\pi$
$822$	6.96499	−	39.5004i	0.242932	−	1.37773i
$823$	16.4755	+	5.99659i	0.574299	+	0.209028i	0.612810	−	0.790230i	$-0.290039\pi$
$823$	16.4755	+	5.99659i	0.574299	+	0.209028i	−0.0385106	+	0.999258i	$0.512261\pi$
$824$	−7.41399	−	12.8414i	−0.258279	−	0.447352i
$825$	2.22056	−	3.84613i	0.0773101	−	0.133905i
$826$	10.6201	−	8.91133i	0.369521	−	0.310065i
$827$	13.0422	−	10.9437i	0.453521	−	0.380550i	−0.387219	−	0.921988i	$-0.626564\pi$
$827$	13.0422	−	10.9437i	0.453521	−	0.380550i	0.840741	+	0.541438i	$0.182120\pi$
$828$	4.18709	−	7.25225i	0.145511	−	0.252033i
$829$	−2.88103	−	4.99010i	−0.100062	−	0.173313i	0.811648	−	0.584147i	$-0.198571\pi$
$829$	−2.88103	−	4.99010i	−0.100062	−	0.173313i	−0.911710	+	0.410834i	$0.865238\pi$
$830$	−35.0796	−	12.7679i	−1.21763	−	0.443181i
$831$	10.7357	−	60.8853i	0.372418	−	2.11209i
$832$	−1.10172	−	6.24819i	−0.0381954	−	0.216617i
$833$	−3.75533	+	1.36683i	−0.130115	+	0.0473578i
$834$	−19.5374	−	16.3939i	−0.676526	−	0.567673i
$835$	−17.4232			−0.602954
$836$		0			0
$837$	−6.44588			−0.222802
$838$	14.1750	+	11.8943i	0.489669	+	0.410881i
$839$	8.36283	−	3.04382i	0.288717	−	0.105084i	−0.193602	−	0.981080i	$-0.562017\pi$
$839$	8.36283	−	3.04382i	0.288717	−	0.105084i	0.482319	+	0.875996i	$0.339795\pi$
$840$	−3.00701	−	17.0536i	−0.103752	−	0.588404i
$841$	1.07420	−	6.09210i	0.0370414	−	0.210072i
$842$	15.2226	+	5.54059i	0.524607	+	0.190941i
$843$	12.8154	+	22.1969i	0.441386	+	0.764503i
$844$	4.05815	−	7.02892i	0.139687	−	0.241945i
$845$	−51.3514	+	43.0889i	−1.76654	+	1.48230i
$846$	−1.91403	+	1.60606i	−0.0658057	+	0.0552175i
$847$	−11.4294	+	19.7963i	−0.392718	+	0.680208i
$848$	−0.735136	−	1.27329i	−0.0252447	−	0.0437250i
$849$	−65.5219	−	23.8480i	−2.24870	−	0.818462i
$850$	−0.905926	+	5.13776i	−0.0310730	+	0.176224i
$851$	0.239083	+	1.35591i	0.00819567	+	0.0464800i
$852$	−16.5700	+	6.03099i	−0.567679	+	0.206618i
$853$	2.13661	+	1.79283i	0.0731562	+	0.0613854i	0.678633	−	0.734478i	$-0.262573\pi$
$853$	2.13661	+	1.79283i	0.0731562	+	0.0613854i	−0.605476	+	0.795863i	$0.707017\pi$
$854$	26.0835			0.892559
$855$		0			0
$856$	−2.82849			−0.0966757
$857$	−12.5589	−	10.5382i	−0.429004	−	0.359977i	0.402572	−	0.915388i	$-0.368116\pi$
$857$	−12.5589	−	10.5382i	−0.429004	−	0.359977i	−0.831576	+	0.555412i	$0.812561\pi$
$858$	25.2199	−	9.17930i	0.860994	−	0.313376i
$859$	1.65401	+	9.38034i	0.0564340	+	0.320053i	0.999936	−	0.0113137i	$-0.00360134\pi$
$859$	1.65401	+	9.38034i	0.0564340	+	0.320053i	−0.943502	+	0.331367i	$0.892490\pi$
$860$	−1.22637	+	6.95507i	−0.0418187	+	0.237166i
$861$	17.2499	+	6.27845i	0.587875	+	0.213969i
$862$	−6.34983	−	10.9982i	−0.216276	−	0.374601i
$863$	−25.3382	+	43.8871i	−0.862523	+	1.49393i	0.00696312	+	0.999976i	$0.497784\pi$
$863$	−25.3382	+	43.8871i	−0.862523	+	1.49393i	−0.869486	+	0.493958i	$0.835550\pi$
$864$	−0.677893	+	0.568820i	−0.0230624	+	0.0193517i
$865$	−43.3758	+	36.3966i	−1.47482	+	1.23752i
$866$	−7.11751	+	12.3279i	−0.241863	+	0.418919i
$867$	−9.69337	−	16.7894i	−0.329204	−	0.570198i
$868$	−19.1217	−	6.95971i	−0.649031	−	0.236228i
$869$	−1.72307	+	9.77203i	−0.0584512	+	0.331493i
$870$	−6.38491	−	36.2106i	−0.216469	−	1.22766i
$871$	−68.9228	+	25.0858i	−2.33536	+	0.850001i
$872$	1.32173	+	1.10906i	0.0447593	+	0.0375575i
$873$	−48.2141			−1.63180
$874$		0			0
$875$	−27.1424			−0.917582
$876$	−11.9427	−	10.0211i	−0.403507	−	0.338583i
$877$	18.0965	−	6.58657i	0.611074	−	0.222413i	−0.0178993	−	0.999840i	$-0.505698\pi$
$877$	18.0965	−	6.58657i	0.611074	−	0.222413i	0.628973	+	0.777427i	$0.283476\pi$
$878$	4.89515	+	27.7618i	0.165203	+	0.936914i
$879$	−10.4322	+	59.1641i	−0.351870	+	1.99555i
$880$	−3.87961	−	1.41206i	−0.130782	−	0.0476007i
$881$	−9.55379	−	16.5476i	−0.321875	−	0.557504i	0.659000	−	0.752143i	$-0.270980\pi$
$881$	−9.55379	−	16.5476i	−0.321875	−	0.557504i	−0.980875	+	0.194639i	$0.937646\pi$
$882$	1.34754	−	2.33400i	0.0453739	−	0.0785900i
$883$	38.3007	−	32.1381i	1.28892	−	1.08153i	0.296972	−	0.954886i	$-0.404023\pi$
$883$	38.3007	−	32.1381i	1.28892	−	1.08153i	0.991948	−	0.126646i	$-0.0404214\pi$
$884$	−24.1513	+	20.2654i	−0.812297	+	0.681598i
$885$	15.3808	−	26.6404i	0.517020	−	0.895506i
$886$	−16.4972	−	28.5740i	−0.554234	−	0.959961i
$887$	37.2301	+	13.5507i	1.25007	+	0.454987i	0.880424	−	0.474188i	$-0.157258\pi$
$887$	37.2301	+	13.5507i	1.25007	+	0.454987i	0.369642	+	0.929174i	$0.379480\pi$
$888$	0.241116	−	1.36744i	0.00809132	−	0.0458881i
$889$	−0.551232	−	3.12619i	−0.0184877	−	0.104849i
$890$	15.9597	−	5.80884i	0.534969	−	0.194713i
$891$	10.0594	+	8.44084i	0.337003	+	0.282779i
$892$	−10.7540			−0.360071
$893$		0			0
$894$	−23.6856			−0.792166
$895$	15.4782	+	12.9877i	0.517378	+	0.434132i
$896$	−2.62513	+	0.955469i	−0.0876994	+	0.0319200i
$897$	6.93822	+	39.3486i	0.231661	+	1.31381i
$898$	−2.98632	+	16.9363i	−0.0996548	+	0.565170i
$899$	−40.6019	−	14.7779i	−1.35415	−	0.492869i
$900$	−1.75914	−	3.04692i	−0.0586380	−	0.101564i
$901$	−3.65302	+	6.32721i	−0.121700	+	0.210790i
$902$	3.35269	−	2.81324i	0.111632	−	0.0936706i
$903$	−15.4854	+	12.9938i	−0.515321	+	0.432405i
$904$	0.213892	−	0.370473i	0.00711396	−	0.0123217i
$905$	15.9876	+	27.6913i	0.531445	+	0.920490i
$906$	24.3050	+	8.84630i	0.807480	+	0.293899i
$907$	−9.59484	+	54.4151i	−0.318592	+	1.80682i	0.232743	+	0.972538i	$0.425230\pi$
$907$	−9.59484	+	54.4151i	−0.318592	+	1.80682i	−0.551335	+	0.834284i	$0.685881\pi$
$908$	−4.70476	−	26.6820i	−0.156133	−	0.885473i
$909$	−35.5304	+	12.9320i	−1.17847	+	0.428928i
$910$	33.3960	+	28.0226i	1.10707	+	0.928940i
$911$	−27.7087			−0.918031			−0.459015	−	0.888428i	$-0.651798\pi$
$911$	−27.7087			−0.918031			−0.459015	+	0.888428i	$0.651798\pi$
$912$		0			0
$913$	−25.4756			−0.843120
$914$	23.8636	+	20.0239i	0.789337	+	0.662333i
$915$	54.3858	−	19.7948i	1.79794	−	0.654397i
$916$	1.64368	+	9.32177i	0.0543087	+	0.308000i
$917$	8.65499	−	49.0849i	0.285813	−	1.62093i
$918$	4.13216	+	1.50398i	0.136382	+	0.0496389i
$919$	−13.6250	−	23.5992i	−0.449447	−	0.778465i	0.548903	−	0.835886i	$-0.315046\pi$
$919$	−13.6250	−	23.5992i	−0.449447	−	0.778465i	−0.998350	+	0.0574208i	$0.981712\pi$
$920$	3.07321	−	5.32296i	0.101321	−	0.175493i
$921$	−50.1718	+	42.0992i	−1.65322	+	1.38722i
$922$	−11.9051	+	9.98956i	−0.392073	+	0.328989i
$923$	22.1964	−	38.4454i	0.730605	−	1.26544i
$924$	−5.90868	−	10.2341i	−0.194381	−	0.336678i
$925$	0.543567	+	0.197842i	0.0178724	+	0.00650502i
$926$	−3.58840	+	20.3508i	−0.117922	+	0.668770i
$927$	−8.62869	−	48.9357i	−0.283403	−	1.60726i
$928$	−5.57406	+	2.02879i	−0.182977	+	0.0665983i
$929$	34.0438	+	28.5661i	1.11694	+	0.937224i	0.998446	−	0.0557312i	$-0.0177490\pi$
$929$	34.0438	+	28.5661i	1.11694	+	0.937224i	0.118494	+	0.992955i	$0.462193\pi$
$930$	−45.1517			−1.48058
$931$		0			0
$932$	22.8621			0.748873
$933$	−44.6040	−	37.4272i	−1.46027	−	1.22531i
$934$	−26.7652	+	9.74175i	−0.875785	+	0.318760i
$935$	3.56252	+	20.2041i	0.116507	+	0.660743i
$936$	3.69203	−	20.9386i	0.120678	−	0.684398i
$937$	17.1115	+	6.22808i	0.559009	+	0.203463i	0.606045	−	0.795431i	$-0.292755\pi$
$937$	17.1115	+	6.22808i	0.559009	+	0.203463i	−0.0470358	+	0.998893i	$0.514977\pi$
$938$	16.1477	+	27.9686i	0.527239	+	0.913206i
$939$	−15.4544	+	26.7678i	−0.504336	+	0.873536i
$940$	−1.40485	+	1.17881i	−0.0458211	+	0.0384485i
$941$	30.8471	−	25.8838i	1.00559	−	0.843787i	0.0178380	−	0.999841i	$-0.494322\pi$
$941$	30.8471	−	25.8838i	1.00559	−	0.843787i	0.987749	+	0.156054i	$0.0498773\pi$
$942$	3.74730	−	6.49052i	0.122094	−	0.211472i
$943$	3.25784	+	5.64274i	0.106090	+	0.183753i
$944$	−4.66333	−	1.69731i	−0.151778	−	0.0552428i
$945$	1.05588	−	5.98821i	0.0343479	−	0.194796i
$946$	0.836906	+	4.74633i	0.0272101	+	0.154316i
$947$	−5.98171	+	2.17717i	−0.194380	+	0.0707484i	−0.437376	−	0.899279i	$-0.644092\pi$
$947$	−5.98171	+	2.17717i	−0.194380	+	0.0707484i	0.242996	+	0.970027i	$0.421870\pi$
$948$	11.4126	+	9.57629i	0.370663	+	0.311023i
$949$	39.2488			1.27407
$950$		0			0
$951$	0.686248			0.0222531
$952$	10.6342	+	8.92312i	0.344655	+	0.289200i
$953$	−30.7227	+	11.1821i	−0.995205	+	0.362225i	−0.787734	−	0.616016i	$-0.788746\pi$
$953$	−30.7227	+	11.1821i	−0.995205	+	0.362225i	−0.207471	+	0.978241i	$0.566523\pi$
$954$	−0.855579	−	4.85223i	−0.0277004	−	0.157097i
$955$	−2.80818	+	15.9260i	−0.0908707	+	0.515353i
$956$	−8.14348	−	2.96399i	−0.263379	−	0.0958622i
$957$	−12.5462	−	21.7306i	−0.405560	−	0.702450i
$958$	−5.23632	+	9.06958i	−0.169178	+	0.293025i
$959$	34.0599	−	28.5796i	1.09985	−	0.922884i
$960$	−4.74846	+	3.98443i	−0.153256	+	0.128597i
$961$	−11.0289	+	19.1026i	−0.355771	+	0.616214i
$962$	1.74784	+	3.02735i	0.0563527	+	0.0976057i
$963$	−8.90702	−	3.24189i	−0.287025	−	0.104469i
$964$	−0.982546	+	5.57230i	−0.0316457	+	0.179472i
$965$	11.4819	+	65.1173i	0.369617	+	2.09620i
$966$	16.5320	−	6.01717i	0.531909	−	0.193599i
$967$	6.55685	+	5.50185i	0.210854	+	0.176928i	0.742098	−	0.670291i	$-0.233831\pi$
$967$	6.55685	+	5.50185i	0.210854	+	0.176928i	−0.531244	+	0.847219i	$0.678275\pi$
$968$	8.18253			0.262997
$969$		0			0
$970$	−35.3879			−1.13624
$971$	32.0811	+	26.9192i	1.02953	+	0.863879i	0.990795	−	0.135371i	$-0.0432225\pi$
$971$	32.0811	+	26.9192i	1.02953	+	0.863879i	0.0387357	+	0.999249i	$0.487667\pi$
$972$	21.0215	−	7.65119i	0.674264	−	0.245412i
$973$	−4.90934	−	27.8422i	−0.157386	−	0.892581i
$974$	0.399207	−	2.26401i	0.0127914	−	0.0725437i
$975$	15.7744	+	5.74140i	0.505184	+	0.183872i
$976$	−4.66843	−	8.08596i	−0.149433	−	0.258825i
$977$	−3.09010	+	5.35222i	−0.0988612	+	0.171233i	−0.911214	−	0.411934i	$-0.864853\pi$
$977$	−3.09010	+	5.35222i	−0.0988612	+	0.171233i	0.812352	+	0.583167i	$0.198187\pi$
$978$	−10.7954	+	9.05844i	−0.345200	+	0.289657i
$979$	8.87868	−	7.45009i	0.283764	−	0.238106i
$980$	0.989057	−	1.71310i	0.0315943	−	0.0547229i
$981$	2.89101	+	5.00738i	0.0923029	+	0.159873i
$982$	11.4278	+	4.15937i	0.364675	+	0.132731i
$983$	−5.83009	+	33.0641i	−0.185951	+	1.05458i	0.738776	+	0.673951i	$0.235404\pi$
$983$	−5.83009	+	33.0641i	−0.185951	+	1.05458i	−0.924727	+	0.380630i	$0.875707\pi$
$984$	−1.14105	−	6.47123i	−0.0363754	−	0.206295i
$985$	−22.7651	+	8.28581i	−0.725355	+	0.264008i
$986$	22.5800	+	18.9469i	0.719093	+	0.603391i
$987$	−5.24920			−0.167084
$988$		0			0
$989$	−7.17507			−0.228154
$990$	−10.5986	−	8.89330i	−0.336846	−	0.282648i
$991$	−43.3899	+	15.7927i	−1.37833	+	0.501670i	−0.921671	−	0.387973i	$-0.873175\pi$
$991$	−43.3899	+	15.7927i	−1.37833	+	0.501670i	−0.456656	+	0.889643i	$0.650953\pi$
$992$	1.26487	+	7.17342i	0.0401596	+	0.227756i
$993$	8.74931	−	49.6198i	0.277651	−	1.57464i
$994$	−18.3680	−	6.68540i	−0.582597	−	0.212048i
$995$	−25.1697	−	43.5952i	−0.797934	−	1.38206i
$996$	−19.1245	+	33.1247i	−0.605984	+	1.04960i
$997$	−0.627490	+	0.526527i	−0.0198728	+	0.0166753i	−0.652670	−	0.757642i	$-0.726351\pi$
$997$	−0.627490	+	0.526527i	−0.0198728	+	0.0166753i	0.632797	+	0.774318i	$0.281907\pi$
$998$	−11.5940	+	9.72849i	−0.367000	+	0.307950i
$999$	0.243785	−	0.422248i	0.00771302	−	0.0133593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.s.415.1		24
19.2	odd	18		722.2.c.m.653.4		8
19.3	odd	18		722.2.c.m.429.4		8
19.4	even	9	inner	722.2.e.s.389.4		24
19.5	even	9		722.2.a.m.1.4	✓	4
19.6	even	9	inner	722.2.e.s.595.1		24
19.7	even	3	inner	722.2.e.s.423.4		24
19.8	odd	6		722.2.e.r.245.1		24
19.9	even	9	inner	722.2.e.s.99.4		24
19.10	odd	18		722.2.e.r.99.1		24
19.11	even	3	inner	722.2.e.s.245.4		24
19.12	odd	6		722.2.e.r.423.1		24
19.13	odd	18		722.2.e.r.595.4		24
19.14	odd	18		722.2.a.n.1.1	yes	4
19.15	odd	18		722.2.e.r.389.1		24
19.16	even	9		722.2.c.n.429.1		8
19.17	even	9		722.2.c.n.653.1		8
19.18	odd	2		722.2.e.r.415.4		24
57.5	odd	18		6498.2.a.ca.1.4		4
57.14	even	18		6498.2.a.bx.1.4		4
76.43	odd	18		5776.2.a.bv.1.1		4
76.71	even	18		5776.2.a.bt.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.4	✓	4	19.5	even	9
722.2.a.n.1.1	yes	4	19.14	odd	18
722.2.c.m.429.4		8	19.3	odd	18
722.2.c.m.653.4		8	19.2	odd	18
722.2.c.n.429.1		8	19.16	even	9
722.2.c.n.653.1		8	19.17	even	9
722.2.e.r.99.1		24	19.10	odd	18
722.2.e.r.245.1		24	19.8	odd	6
722.2.e.r.389.1		24	19.15	odd	18
722.2.e.r.415.4		24	19.18	odd	2
722.2.e.r.423.1		24	19.12	odd	6
722.2.e.r.595.4		24	19.13	odd	18
722.2.e.s.99.4		24	19.9	even	9	inner
722.2.e.s.245.4		24	19.11	even	3	inner
722.2.e.s.389.4		24	19.4	even	9	inner
722.2.e.s.415.1		24	1.1	even	1	trivial
722.2.e.s.423.4		24	19.7	even	3	inner
722.2.e.s.595.1		24	19.6	even	9	inner
5776.2.a.bt.1.4		4	76.71	even	18
5776.2.a.bv.1.1		4	76.43	odd	18
6498.2.a.bx.1.4		4	57.14	even	18
6498.2.a.ca.1.4		4	57.5	odd	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-2.36816 + 0.861941i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.427114 + 2.42228i) q^{5} +(2.36816 + 0.861941i) q^{6} +(1.39680 + 2.41933i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.56712 - 2.15407i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-2.36816 + 0.861941i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.427114 + 2.42228i) q^{5} +(2.36816 + 0.861941i) q^{6} +(1.39680 + 2.41933i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.56712 - 2.15407i) q^{9} +(1.88420 - 1.58103i) q^{10} +(0.839266 - 1.45365i) q^{11} +(-1.26007 - 2.18251i) q^{12} +(5.96195 + 2.16997i) q^{13} +(0.485104 - 2.75116i) q^{14} +(-1.07639 - 6.10451i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(3.80661 + 3.19412i) q^{17} -3.35114 q^{18} -2.45965 q^{20} +(-5.39318 - 4.52541i) q^{21} +(-1.57730 + 0.574092i) q^{22} +(-0.433930 - 2.46094i) q^{23} +(-0.437619 + 2.48186i) q^{24} +(-0.986561 - 0.359079i) q^{25} +(-3.17229 - 5.49456i) q^{26} +(-0.442463 + 0.766369i) q^{27} +(-2.14003 + 1.79569i) q^{28} +(-4.54401 + 3.81288i) q^{29} +(-3.09934 + 5.36821i) q^{30} +(3.64204 + 6.30820i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.734557 + 4.16588i) q^{33} +(-0.862888 - 4.89368i) q^{34} +(-6.45690 + 2.35012i) q^{35} +(2.56712 + 2.15407i) q^{36} -0.550972 q^{37} -15.9893 q^{39} +(1.88420 + 1.58103i) q^{40} +(-2.45017 + 0.891788i) q^{41} +(1.22253 + 6.93334i) q^{42} +(0.498594 - 2.82767i) q^{43} +(1.57730 + 0.574092i) q^{44} +(4.12132 + 7.13833i) q^{45} +(-1.24945 + 2.16411i) q^{46} +(0.571158 - 0.479258i) q^{47} +(1.93054 - 1.61992i) q^{48} +(-0.402113 + 0.696480i) q^{49} +(0.524938 + 0.909219i) q^{50} +(-11.7678 - 4.28314i) q^{51} +(-1.10172 + 6.24819i) q^{52} +(0.255310 + 1.44793i) q^{53} +(0.831559 - 0.302663i) q^{54} +(3.16269 + 2.65381i) q^{55} +2.79360 q^{56} +5.93179 q^{58} +(3.80158 + 3.18990i) q^{59} +(5.82485 - 2.12007i) q^{60} +(1.62133 + 9.19501i) q^{61} +(1.26487 - 7.17342i) q^{62} +(8.79718 + 3.20191i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-7.80272 + 13.5147i) q^{65} +(3.24048 - 2.71909i) q^{66} +(-8.85581 + 7.43091i) q^{67} +(-2.48459 + 4.30343i) q^{68} +(3.14880 + 5.45389i) q^{69} +(6.45690 + 2.35012i) q^{70} +(1.21501 - 6.89068i) q^{71} +(-0.581920 - 3.30023i) q^{72} +(5.81312 - 2.11580i) q^{73} +(0.422069 + 0.354158i) q^{74} +2.64584 q^{75} +4.68915 q^{77} +(12.2485 + 10.2777i) q^{78} +(-5.55507 + 2.02188i) q^{79} +(-0.427114 - 2.42228i) q^{80} +(-1.35850 + 7.70442i) q^{81} +(2.45017 + 0.891788i) q^{82} +(-7.58866 - 13.1439i) q^{83} +(3.52015 - 6.09707i) q^{84} +(-9.36292 + 7.85643i) q^{85} +(-2.19953 + 1.84563i) q^{86} +(7.47449 - 12.9462i) q^{87} +(-0.839266 - 1.45365i) q^{88} +(6.48859 + 2.36166i) q^{89} +(1.43132 - 8.11741i) q^{90} +(3.07778 + 17.4550i) q^{91} +(2.34820 - 0.854675i) q^{92} +(-14.0622 - 11.7996i) q^{93} -0.745593 q^{94} -2.52015 q^{96} +(-11.0214 - 9.24803i) q^{97} +(0.755725 - 0.275062i) q^{98} +(-0.976770 - 5.53954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{7} + 12 q^{8}+O(q^{10}) \) 24 * q + 6 * q^7 + 12 * q^8	\( 24 q + 6 q^{7} + 12 q^{8} - 6 q^{11} + 6 q^{12} - 24 q^{18} - 12 q^{20} - 54 q^{26} - 12 q^{27} - 12 q^{30} + 78 q^{31} - 24 q^{37} - 36 q^{39} + 66 q^{45} - 30 q^{46} + 36 q^{49} + 18 q^{50} + 12 q^{56} - 12 q^{58} - 12 q^{64} - 12 q^{65} - 18 q^{68} - 60 q^{69} - 48 q^{75} + 24 q^{77} + 36 q^{83} + 12 q^{84} + 78 q^{87} + 6 q^{88} + 72 q^{94} + 12 q^{96}+O(q^{100}) \) 24 * q + 6 * q^7 + 12 * q^8 - 6 * q^11 + 6 * q^12 - 24 * q^18 - 12 * q^20 - 54 * q^26 - 12 * q^27 - 12 * q^30 + 78 * q^31 - 24 * q^37 - 36 * q^39 + 66 * q^45 - 30 * q^46 + 36 * q^49 + 18 * q^50 + 12 * q^56 - 12 * q^58 - 12 * q^64 - 12 * q^65 - 18 * q^68 - 60 * q^69 - 48 * q^75 + 24 * q^77 + 36 * q^83 + 12 * q^84 + 78 * q^87 + 6 * q^88 + 72 * q^94 + 12 * q^96

Introduction

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