LMFDB - Embedded newform 804.2.c.b.671.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.13
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36593 - 0.366392i) q^{2} +(-0.973809 - 1.43237i) q^{3} +(1.73151 + 1.00093i) q^{4} +2.42154i q^{5} +(0.805342 + 2.31331i) q^{6} -1.75439i q^{7} +(-1.99839 - 2.00161i) q^{8} +(-1.10339 + 2.78972i) q^{9} +O(q^{10})$	\(q+(-1.36593 - 0.366392i) q^{2} +(-0.973809 - 1.43237i) q^{3} +(1.73151 + 1.00093i) q^{4} +2.42154i q^{5} +(0.805342 + 2.31331i) q^{6} -1.75439i q^{7} +(-1.99839 - 2.00161i) q^{8} +(-1.10339 + 2.78972i) q^{9} +(0.887230 - 3.30764i) q^{10} +0.337759 q^{11} +(-0.252459 - 3.45489i) q^{12} -1.33945 q^{13} +(-0.642794 + 2.39637i) q^{14} +(3.46855 - 2.35811i) q^{15} +(1.99628 + 3.46624i) q^{16} -4.05920i q^{17} +(2.52928 - 3.40628i) q^{18} +1.16371i q^{19} +(-2.42378 + 4.19292i) q^{20} +(-2.51294 + 1.70844i) q^{21} +(-0.461354 - 0.123752i) q^{22} +1.81407 q^{23} +(-0.921002 + 4.81163i) q^{24} -0.863832 q^{25} +(1.82959 + 0.490764i) q^{26} +(5.07041 - 1.13618i) q^{27} +(1.75602 - 3.03775i) q^{28} +8.51104i q^{29} +(-5.60177 + 1.95016i) q^{30} +4.75899i q^{31} +(-1.45677 - 5.46606i) q^{32} +(-0.328913 - 0.483798i) q^{33} +(-1.48726 + 5.54458i) q^{34} +4.24832 q^{35} +(-4.70285 + 3.72602i) q^{36} +6.50846 q^{37} +(0.426373 - 1.58954i) q^{38} +(1.30437 + 1.91860i) q^{39} +(4.84696 - 4.83917i) q^{40} -0.0765846i q^{41} +(4.05846 - 1.41288i) q^{42} +9.26180i q^{43} +(0.584835 + 0.338073i) q^{44} +(-6.75540 - 2.67191i) q^{45} +(-2.47789 - 0.664660i) q^{46} -8.82365 q^{47} +(3.02096 - 6.23488i) q^{48} +3.92212 q^{49} +(1.17993 + 0.316501i) q^{50} +(-5.81430 + 3.95289i) q^{51} +(-2.31928 - 1.34069i) q^{52} -2.03937i q^{53} +(-7.34210 - 0.305820i) q^{54} +0.817896i q^{55} +(-3.51160 + 3.50596i) q^{56} +(1.66686 - 1.13323i) q^{57} +(3.11837 - 11.6255i) q^{58} +14.7468 q^{59} +(8.36614 - 0.611338i) q^{60} +10.1820 q^{61} +(1.74365 - 6.50044i) q^{62} +(4.89425 + 1.93578i) q^{63} +(-0.0128704 + 7.99999i) q^{64} -3.24353i q^{65} +(0.272011 + 0.781343i) q^{66} -1.00000i q^{67} +(4.06297 - 7.02857i) q^{68} +(-1.76656 - 2.59843i) q^{69} +(-5.80289 - 1.55655i) q^{70} +3.10054 q^{71} +(7.78893 - 3.36638i) q^{72} +11.7805 q^{73} +(-8.89008 - 2.38464i) q^{74} +(0.841207 + 1.23733i) q^{75} +(-1.16479 + 2.01498i) q^{76} -0.592561i q^{77} +(-1.07872 - 3.09857i) q^{78} -4.35094i q^{79} +(-8.39363 + 4.83407i) q^{80} +(-6.56505 - 6.15631i) q^{81} +(-0.0280600 + 0.104609i) q^{82} +8.52629 q^{83} +(-6.06122 + 0.442911i) q^{84} +9.82950 q^{85} +(3.39345 - 12.6509i) q^{86} +(12.1910 - 8.28812i) q^{87} +(-0.674975 - 0.676061i) q^{88} -0.230176i q^{89} +(8.24842 + 6.12475i) q^{90} +2.34992i q^{91} +(3.14109 + 1.81575i) q^{92} +(6.81666 - 4.63435i) q^{93} +(12.0525 + 3.23291i) q^{94} -2.81796 q^{95} +(-6.41082 + 7.40954i) q^{96} +0.733942 q^{97} +(-5.35732 - 1.43703i) q^{98} +(-0.372681 + 0.942252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.36593	−	0.366392i	−0.965856	−	0.259078i
$2$	−1.36593	−	0.366392i	−0.965856	−	0.259078i
$3$	−0.973809	−	1.43237i	−0.562229	−	0.826982i
$3$	−0.973809	−	1.43237i	−0.562229	−	0.826982i
$4$	1.73151	+	1.00093i	0.865757	+	0.500464i
$5$			2.42154i			1.08294i	0.840719	+	0.541472i	$0.182133\pi$
$5$			2.42154i			1.08294i	−0.840719	+	0.541472i	$0.817867\pi$
$6$	0.805342	+	2.31331i	0.328779	+	0.944407i
$7$		−	1.75439i		−	0.663097i	−0.943438	−	0.331549i	$-0.892429\pi$
$7$		−	1.75439i		−	0.663097i	0.943438	−	0.331549i	$-0.107571\pi$
$8$	−1.99839	−	2.00161i	−0.706538	−	0.707675i
$9$	−1.10339	+	2.78972i	−0.367798	+	0.929906i
$10$	0.887230	−	3.30764i	0.280567	−	1.04597i
$11$	0.337759			0.101838			0.0509191	−	0.998703i	$-0.483785\pi$
$11$	0.337759			0.101838			0.0509191	+	0.998703i	$0.483785\pi$
$12$	−0.252459	−	3.45489i	−0.0728786	−	0.997341i
$13$	−1.33945			−0.371497			−0.185748	−	0.982597i	$-0.559471\pi$
$13$	−1.33945			−0.371497			−0.185748	+	0.982597i	$0.559471\pi$
$14$	−0.642794	+	2.39637i	−0.171794	+	0.640457i
$15$	3.46855	−	2.35811i	0.895575	−	0.608862i
$16$	1.99628	+	3.46624i	0.499071	+	0.866561i
$17$		−	4.05920i		−	0.984501i	−0.870453	−	0.492251i	$-0.836174\pi$
$17$		−	4.05920i		−	0.984501i	0.870453	−	0.492251i	$-0.163826\pi$
$18$	2.52928	−	3.40628i	0.596158	−	0.802867i
$19$			1.16371i			0.266973i	0.991051	+	0.133486i	$0.0426172\pi$
$19$			1.16371i			0.266973i	−0.991051	+	0.133486i	$0.957383\pi$
$20$	−2.42378	+	4.19292i	−0.541975	+	0.937566i
$21$	−2.51294	+	1.70844i	−0.548369	+	0.372812i
$22$	−0.461354	−	0.123752i	−0.0983611	−	0.0263840i
$23$	1.81407			0.378259			0.189130	−	0.981952i	$-0.439433\pi$
$23$	1.81407			0.378259			0.189130	+	0.981952i	$0.439433\pi$
$24$	−0.921002	+	4.81163i	−0.187999	+	0.982169i
$25$	−0.863832			−0.172766
$26$	1.82959	+	0.490764i	0.358813	+	0.0962467i
$27$	5.07041	−	1.13618i	0.975802	−	0.218658i
$28$	1.75602	−	3.03775i	0.331856	−	0.574081i
$29$			8.51104i			1.58046i	0.612810	+	0.790230i	$0.290039\pi$
$29$			8.51104i			1.58046i	−0.612810	+	0.790230i	$0.709961\pi$
$30$	−5.60177	+	1.95016i	−1.02274	+	0.356049i
$31$			4.75899i			0.854740i	0.904077	+	0.427370i	$0.140560\pi$
$31$			4.75899i			0.854740i	−0.904077	+	0.427370i	$0.859440\pi$
$32$	−1.45677	−	5.46606i	−0.257524	−	0.966272i
$33$	−0.328913	−	0.483798i	−0.0572564	−	0.0842183i
$34$	−1.48726	+	5.54458i	−0.255063	+	0.950887i
$35$	4.24832			0.718097
$36$	−4.70285	+	3.72602i	−0.783808	+	0.621003i
$37$	6.50846			1.06998			0.534992	−	0.844857i	$-0.320315\pi$
$37$	6.50846			1.06998			0.534992	+	0.844857i	$0.320315\pi$
$38$	0.426373	−	1.58954i	0.0691668	−	0.257857i
$39$	1.30437	+	1.91860i	0.208866	+	0.307221i
$40$	4.84696	−	4.83917i	0.766372	−	0.765140i
$41$		−	0.0765846i		−	0.0119605i	−0.999982	−	0.00598026i	$-0.998096\pi$
$41$		−	0.0765846i		−	0.0119605i	0.999982	−	0.00598026i	$-0.00190359\pi$
$42$	4.05846	−	1.41288i	0.626233	−	0.218013i
$43$			9.26180i			1.41241i	0.708007	+	0.706206i	$0.249595\pi$
$43$			9.26180i			1.41241i	−0.708007	+	0.706206i	$0.750405\pi$
$44$	0.584835	+	0.338073i	0.0881671	+	0.0509664i
$45$	−6.75540	−	2.67191i	−1.00704	−	0.398304i
$46$	−2.47789	−	0.664660i	−0.365344	−	0.0979987i
$47$	−8.82365			−1.28706			−0.643531	−	0.765420i	$-0.722531\pi$
$47$	−8.82365			−1.28706			−0.643531	+	0.765420i	$0.722531\pi$
$48$	3.02096	−	6.23488i	0.436038	−	0.899928i
$49$	3.92212			0.560302
$50$	1.17993	+	0.316501i	0.166868	+	0.0447600i
$51$	−5.81430	+	3.95289i	−0.814165	+	0.553515i
$52$	−2.31928	−	1.34069i	−0.321626	−	0.185921i
$53$		−	2.03937i		−	0.280130i	−0.990142	−	0.140065i	$-0.955269\pi$
$53$		−	2.03937i		−	0.280130i	0.990142	−	0.140065i	$-0.0447311\pi$
$54$	−7.34210	−	0.305820i	−0.999134	−	0.0416169i
$55$			0.817896i			0.110285i
$56$	−3.51160	+	3.50596i	−0.469257	+	0.468503i
$57$	1.66686	−	1.13323i	0.220782	−	0.150100i
$58$	3.11837	−	11.6255i	0.409463	−	1.52650i
$59$	14.7468			1.91987			0.959933	−	0.280231i	$-0.0904110\pi$
$59$	14.7468			1.91987			0.959933	+	0.280231i	$0.0904110\pi$
$60$	8.36614	−	0.611338i	1.08006	−	0.0789234i
$61$	10.1820			1.30367			0.651835	−	0.758361i	$-0.273999\pi$
$61$	10.1820			1.30367			0.651835	+	0.758361i	$0.273999\pi$
$62$	1.74365	−	6.50044i	0.221444	−	0.825556i
$63$	4.89425	+	1.93578i	0.616618	+	0.243886i
$64$	−0.0128704	+	7.99999i	−0.00160880	+	0.999999i
$65$		−	3.24353i		−	0.402310i
$66$	0.272011	+	0.781343i	0.0334823	+	0.0961767i
$67$		−	1.00000i		−	0.122169i
$67$		−	1.00000i		−	0.122169i
$68$	4.06297	−	7.02857i	0.492708	−	0.852339i
$69$	−1.76656	−	2.59843i	−0.212668	−	0.312814i
$70$	−5.80289	−	1.55655i	−0.693578	−	0.186043i
$71$	3.10054			0.367966			0.183983	−	0.982929i	$-0.441101\pi$
$71$	3.10054			0.367966			0.183983	+	0.982929i	$0.441101\pi$
$72$	7.78893	−	3.36638i	0.917934	−	0.396732i
$73$	11.7805			1.37880			0.689401	−	0.724380i	$-0.257874\pi$
$73$	11.7805			1.37880			0.689401	+	0.724380i	$0.257874\pi$
$74$	−8.89008	−	2.38464i	−1.03345	−	0.277209i
$75$	0.841207	+	1.23733i	0.0971343	+	0.142875i
$76$	−1.16479	+	2.01498i	−0.133610	+	0.231134i
$77$		−	0.592561i		−	0.0675286i
$78$	−1.07872	−	3.09857i	−0.122140	−	0.350844i
$79$		−	4.35094i		−	0.489519i	−0.969584	−	0.244760i	$-0.921291\pi$
$79$		−	4.35094i		−	0.489519i	0.969584	−	0.244760i	$-0.0787091\pi$
$80$	−8.39363	+	4.83407i	−0.938437	+	0.540466i
$81$	−6.56505	−	6.15631i	−0.729450	−	0.684035i
$82$	−0.0280600	+	0.104609i	−0.00309871	+	0.0115521i
$83$	8.52629			0.935882			0.467941	−	0.883760i	$-0.344996\pi$
$83$	8.52629			0.935882			0.467941	+	0.883760i	$0.344996\pi$
$84$	−6.06122	+	0.442911i	−0.661334	+	0.0483256i
$85$	9.82950			1.06616
$86$	3.39345	−	12.6509i	0.365925	−	1.36419i
$87$	12.1910	−	8.28812i	1.30701	−	0.888580i
$88$	−0.674975	−	0.676061i	−0.0719525	−	0.0720684i
$89$		−	0.230176i		−	0.0243986i	−0.999926	−	0.0121993i	$-0.996117\pi$
$89$		−	0.230176i		−	0.0243986i	0.999926	−	0.0121993i	$-0.00388326\pi$
$90$	8.24842	+	6.12475i	0.869460	+	0.645605i
$91$			2.34992i			0.246338i
$92$	3.14109	+	1.81575i	0.327481	+	0.189305i
$93$	6.81666	−	4.63435i	0.706855	−	0.480559i
$94$	12.0525	+	3.23291i	1.24312	+	0.333449i
$95$	−2.81796			−0.289116
$96$	−6.41082	+	7.40954i	−0.654302	+	0.756233i
$97$	0.733942			0.0745205			0.0372603	−	0.999306i	$-0.488137\pi$
$97$	0.733942			0.0745205			0.0372603	+	0.999306i	$0.488137\pi$
$98$	−5.35732	−	1.43703i	−0.541172	−	0.145162i
$99$	−0.372681	+	0.942252i	−0.0374559	+	0.0946999i
$100$	−1.49574	−	0.864635i	−0.149574	−	0.0864635i
$101$		−	7.44649i		−	0.740953i	−0.928842	−	0.370477i	$-0.879194\pi$
$101$		−	7.44649i		−	0.740953i	0.928842	−	0.370477i	$-0.120806\pi$
$102$	9.39022	−	3.26905i	0.929770	−	0.323684i
$103$			5.90797i			0.582130i	0.956703	+	0.291065i	$0.0940096\pi$
$103$			5.90797i			0.582130i	−0.956703	+	0.291065i	$0.905990\pi$
$104$	2.67675	+	2.68106i	0.262477	+	0.262899i
$105$	−4.13705	−	6.08518i	−0.403735	−	0.593853i
$106$	−0.747210	+	2.78564i	−0.0725754	+	0.270565i
$107$	−2.90009			−0.280362			−0.140181	−	0.990126i	$-0.544768\pi$
$107$	−2.90009			−0.280362			−0.140181	+	0.990126i	$0.544768\pi$
$108$	9.91673	+	3.10781i	0.954238	+	0.299050i
$109$	−3.34202			−0.320107			−0.160054	−	0.987108i	$-0.551167\pi$
$109$	−3.34202			−0.320107			−0.160054	+	0.987108i	$0.551167\pi$
$110$	0.299670	−	1.11719i	0.0285724	−	0.106519i
$111$	−6.33799	−	9.32255i	−0.601575	−	0.884857i
$112$	6.08114	−	3.50226i	0.574614	−	0.330932i
$113$			6.51949i			0.613302i	0.951822	+	0.306651i	$0.0992084\pi$
$113$			6.51949i			0.613302i	−0.951822	+	0.306651i	$0.900792\pi$
$114$	−2.69202	+	0.937182i	−0.252131	+	0.0877751i
$115$			4.39283i			0.409634i
$116$	−8.51894	+	14.7370i	−0.790964	+	1.36829i
$117$	1.47794	−	3.73669i	0.136636	−	0.345457i
$118$	−20.1430	−	5.40309i	−1.85431	−	0.497395i
$119$	−7.12143			−0.652820
$120$	−11.6515	−	2.23024i	−1.06363	−	0.203592i
$121$	−10.8859			−0.989629
$122$	−13.9079	−	3.73060i	−1.25916	−	0.337752i
$123$	−0.109698	+	0.0745788i	−0.00989113	+	0.00672454i
$124$	−4.76341	+	8.24026i	−0.427767	+	0.739997i
$125$			10.0159i			0.895847i
$126$	−5.97594	−	4.43735i	−0.532379	−	0.395311i
$127$			13.5743i			1.20452i	0.798299	+	0.602262i	$0.205734\pi$
$127$			13.5743i			1.20452i	−0.798299	+	0.602262i	$0.794266\pi$
$128$	2.94871	−	10.9227i	0.260632	−	0.965438i
$129$	13.2664	−	9.01922i	1.16804	−	0.794098i
$130$	−1.18840	+	4.43042i	−0.104230	+	0.388574i
$131$	18.1110			1.58236			0.791182	−	0.611580i	$-0.209466\pi$
$131$	18.1110			1.58236			0.791182	+	0.611580i	$0.209466\pi$
$132$	−0.0852703	−	1.16692i	−0.00742183	−	0.101567i
$133$	2.04160			0.177029
$134$	−0.366392	+	1.36593i	−0.0316514	+	0.117998i
$135$	2.75130	+	12.2782i	0.236794	+	1.05674i
$136$	−8.12493	+	8.11187i	−0.696707	+	0.695587i
$137$			6.99766i			0.597850i	0.954277	+	0.298925i	$0.0966281\pi$
$137$			6.99766i			0.597850i	−0.954277	+	0.298925i	$0.903372\pi$
$138$	1.46095	+	4.19651i	0.124364	+	0.357231i
$139$		−	1.25579i		−	0.106515i	−0.998581	−	0.0532574i	$-0.983040\pi$
$139$		−	1.25579i		−	0.106515i	0.998581	−	0.0532574i	$-0.0169604\pi$
$140$	7.35602	+	4.25226i	0.621697	+	0.359382i
$141$	8.59255	+	12.6388i	0.723623	+	1.06438i
$142$	−4.23511	−	1.13601i	−0.355403	−	0.0953320i
$143$	−0.452412			−0.0378326
$144$	−11.8725	+	1.74444i	−0.989377	+	0.145370i
$145$	−20.6098			−1.71155
$146$	−16.0913	−	4.31628i	−1.33173	−	0.357218i
$147$	−3.81939	−	5.61794i	−0.315018	−	0.463360i
$148$	11.2695	+	6.51450i	0.926346	+	0.535489i
$149$		−	8.81368i		−	0.722045i	−0.932557	−	0.361022i	$-0.882428\pi$
$149$		−	8.81368i		−	0.722045i	0.932557	−	0.361022i	$-0.117572\pi$
$150$	−0.695680	−	1.99832i	−0.0568021	−	0.163162i
$151$			12.8312i			1.04419i	0.852887	+	0.522095i	$0.174849\pi$
$151$			12.8312i			1.04419i	−0.852887	+	0.522095i	$0.825151\pi$
$152$	2.32929	−	2.32554i	0.188930	−	0.188626i
$153$	11.3240	+	4.47890i	0.915494	+	0.362097i
$154$	−0.217109	+	0.809395i	−0.0174952	+	0.0652229i
$155$	−11.5241			−0.925635
$156$	0.338156	+	4.62766i	0.0270742	+	0.370509i
$157$	−18.8027			−1.50062			−0.750308	−	0.661089i	$-0.770095\pi$
$157$	−18.8027			−1.50062			−0.750308	+	0.661089i	$0.770095\pi$
$158$	−1.59415	+	5.94307i	−0.126824	+	0.472805i
$159$	−2.92115	+	1.98596i	−0.231662	+	0.157497i
$160$	13.2363	−	3.52763i	1.04642	−	0.278884i
$161$		−	3.18258i		−	0.250823i
$162$	6.71175	+	10.8145i	0.527325	+	0.849664i
$163$		−	8.64155i		−	0.676859i	−0.940992	−	0.338429i	$-0.890104\pi$
$163$		−	8.64155i		−	0.676859i	0.940992	−	0.338429i	$-0.109896\pi$
$164$	0.0766558	−	0.132607i	0.00598581	−	0.0103549i
$165$	1.17153	−	0.796474i	0.0912037	−	0.0620054i
$166$	−11.6463	−	3.12396i	−0.903928	−	0.242466i
$167$	13.8923			1.07502			0.537509	−	0.843258i	$-0.319365\pi$
$167$	13.8923			1.07502			0.537509	+	0.843258i	$0.319365\pi$
$168$	8.44147	+	1.61580i	0.651274	+	0.124661i
$169$	−11.2059			−0.861990
$170$	−13.4264	−	3.60145i	−1.02976	−	0.276218i
$171$	−3.24641	−	1.28403i	−0.248259	−	0.0981920i
$172$	−9.27040	+	16.0369i	−0.706861	+	1.22280i
$173$			13.4769i			1.02463i	0.858799	+	0.512313i	$0.171211\pi$
$173$			13.4769i			1.02463i	−0.858799	+	0.512313i	$0.828789\pi$
$174$	−19.6887	+	6.85430i	−1.49260	+	0.519623i
$175$			1.51550i			0.114561i
$176$	0.674263	+	1.17076i	0.0508245	+	0.0882490i
$177$	−14.3605	−	21.1229i	−1.07940	−	1.58769i
$178$	−0.0843346	+	0.314404i	−0.00632115	+	0.0235656i
$179$	−15.6492			−1.16967			−0.584837	−	0.811151i	$-0.698841\pi$
$179$	−15.6492			−1.16967			−0.584837	+	0.811151i	$0.698841\pi$
$180$	−9.02268	−	11.3881i	−0.672511	−	0.848820i
$181$	−1.47999			−0.110007			−0.0550033	−	0.998486i	$-0.517517\pi$
$181$	−1.47999			−0.110007			−0.0550033	+	0.998486i	$0.517517\pi$
$182$	0.860991	−	3.20982i	0.0638209	−	0.237928i
$183$	−9.91531	−	14.5844i	−0.732961	−	1.07811i
$184$	−3.62522	−	3.63105i	−0.267255	−	0.267685i
$185$			15.7605i			1.15873i
$186$	−11.0090	+	3.83261i	−0.807222	+	0.281021i
$187$		−	1.37103i		−	0.100260i
$188$	−15.2783	−	8.83185i	−1.11428	−	0.644129i
$189$	−1.99330	−	8.89548i	−0.144991	−	0.647051i
$190$	3.84913	+	1.03248i	0.279245	+	0.0749037i
$191$	−9.98074			−0.722181			−0.361090	−	0.932531i	$-0.617595\pi$
$191$	−9.98074			−0.722181			−0.361090	+	0.932531i	$0.617595\pi$
$192$	11.4715	−	7.77202i	0.827885	−	0.560898i
$193$	10.5987			0.762908			0.381454	−	0.924388i	$-0.375423\pi$
$193$	10.5987			0.762908			0.381454	+	0.924388i	$0.375423\pi$
$194$	−1.00251	−	0.268910i	−0.0719761	−	0.0193066i
$195$	−4.64595	+	3.15858i	−0.332703	+	0.226190i
$196$	6.79120	+	3.92576i	0.485086	+	0.280411i
$197$			0.207828i			0.0148071i	0.999973	+	0.00740355i	$0.00235665\pi$
$197$			0.207828i			0.0148071i	−0.999973	+	0.00740355i	$0.997643\pi$
$198$	0.854289	−	1.15050i	0.0607117	−	0.0817625i
$199$		−	5.84910i		−	0.414632i	−0.978274	−	0.207316i	$-0.933527\pi$
$199$		−	5.84910i		−	0.414632i	0.978274	−	0.207316i	$-0.0664728\pi$
$200$	1.72627	+	1.72905i	0.122066	+	0.122263i
$201$	−1.43237	+	0.973809i	−0.101032	+	0.0686872i
$202$	−2.72833	+	10.1714i	−0.191965	+	0.715655i
$203$	14.9317			1.04800
$204$	−14.0241	+	1.02478i	−0.981884	+	0.0717491i
$205$	0.185452			0.0129526
$206$	2.16463	−	8.06986i	0.150817	−	0.562254i
$207$	−2.00163	+	5.06074i	−0.139123	+	0.351746i
$208$	−2.67392	−	4.64286i	−0.185403	−	0.321925i
$209$			0.393053i			0.0271880i
$210$	3.42135	+	9.82769i	0.236095	+	0.678175i
$211$			4.93959i			0.340055i	0.985439	+	0.170028i	$0.0543857\pi$
$211$			4.93959i			0.340055i	−0.985439	+	0.170028i	$0.945614\pi$
$212$	2.04127	−	3.53121i	0.140195	−	0.242524i
$213$	−3.01933	−	4.44114i	−0.206881	−	0.304302i
$214$	3.96131	+	1.06257i	0.270790	+	0.0726357i
$215$	−22.4278			−1.52956
$216$	−12.4069	−	7.87845i	−0.844179	−	0.536061i
$217$	8.34913			0.566776
$218$	4.56495	+	1.22449i	0.309177	+	0.0829327i
$219$	−11.4719	−	16.8741i	−0.775202	−	1.14024i
$220$	−0.818655	+	1.41620i	−0.0551937	+	0.0954800i
$221$			5.43710i			0.365739i
$222$	5.24153	+	15.0561i	0.351789	+	1.01050i
$223$			11.8399i			0.792860i	0.918065	+	0.396430i	$0.129751\pi$
$223$			11.8399i			0.792860i	−0.918065	+	0.396430i	$0.870249\pi$
$224$	−9.58960	+	2.55575i	−0.640732	+	0.170763i
$225$	0.953147	−	2.40985i	0.0635431	−	0.160657i
$226$	2.38869	−	8.90515i	0.158893	−	0.592361i
$227$	21.9181			1.45475			0.727377	−	0.686239i	$-0.240739\pi$
$227$	21.9181			1.45475			0.727377	+	0.686239i	$0.240739\pi$
$228$	4.02048	−	0.293788i	0.266263	−	0.0194566i
$229$	−4.54827			−0.300558			−0.150279	−	0.988644i	$-0.548017\pi$
$229$	−4.54827			−0.300558			−0.150279	+	0.988644i	$0.548017\pi$
$230$	1.60950	−	6.00029i	0.106127	−	0.395647i
$231$	−0.848770	+	0.577041i	−0.0558449	+	0.0379665i
$232$	17.0358	−	17.0084i	1.11845	−	1.11666i
$233$		−	26.5742i		−	1.74093i	−0.492228	−	0.870466i	$-0.663817\pi$
$233$		−	26.5742i		−	1.74093i	0.492228	−	0.870466i	$-0.336183\pi$
$234$	−3.38785	+	4.56254i	−0.221471	+	0.298263i
$235$		−	21.3668i		−	1.39382i
$236$	25.5342	+	14.7605i	1.66214	+	0.960824i
$237$	−6.23218	+	4.23699i	−0.404824	+	0.275222i
$238$	9.72735	+	2.60923i	0.630530	+	0.169131i
$239$	−0.563864			−0.0364733			−0.0182366	−	0.999834i	$-0.505805\pi$
$239$	−0.563864			−0.0364733			−0.0182366	+	0.999834i	$0.505805\pi$
$240$	15.0980	+	7.31537i	0.974571	+	0.472205i
$241$	−20.6935			−1.33299			−0.666494	−	0.745510i	$-0.732206\pi$
$241$	−20.6935			−1.33299			−0.666494	+	0.745510i	$0.732206\pi$
$242$	14.8694	+	3.98851i	0.955839	+	0.256391i
$243$	−2.42504	+	15.3987i	−0.155567	+	0.987825i
$244$	17.6303	+	10.1914i	1.12866	+	0.652441i
$245$			9.49754i			0.606776i
$246$	0.177164	−	0.0616768i	0.0112956	−	0.00393237i
$247$		−	1.55873i		−	0.0991795i
$248$	9.52564	−	9.51032i	0.604879	−	0.603906i
$249$	−8.30298	−	12.2128i	−0.526180	−	0.773957i
$250$	3.66973	−	13.6810i	0.232094	−	0.865260i
$251$	6.57418			0.414959			0.207479	−	0.978239i	$-0.433474\pi$
$251$	6.57418			0.414959			0.207479	+	0.978239i	$0.433474\pi$
$252$	6.53689	+	8.25063i	0.411785	+	0.519741i
$253$	0.612718			0.0385213
$254$	4.97351	−	18.5415i	0.312065	−	1.16340i
$255$	−9.57206	−	14.0795i	−0.599425	−	0.881694i
$256$	−8.02970	+	13.8392i	−0.501857	+	0.864951i
$257$		−	9.06984i		−	0.565761i	−0.959155	−	0.282881i	$-0.908710\pi$
$257$		−	9.06984i		−	0.565761i	0.959155	−	0.282881i	$-0.0912900\pi$
$258$	−21.4255	+	7.45891i	−1.33389	+	0.464372i
$259$		−	11.4184i		−	0.709503i
$260$	3.24654	−	5.61621i	0.201342	−	0.348303i
$261$	−23.7434	−	9.39103i	−1.46968	−	0.581290i
$262$	−24.7383	−	6.63572i	−1.52834	−	0.409956i
$263$	−3.87258			−0.238794			−0.119397	−	0.992847i	$-0.538096\pi$
$263$	−3.87258			−0.238794			−0.119397	+	0.992847i	$0.538096\pi$
$264$	−0.311077	+	1.62517i	−0.0191455	+	0.100022i
$265$	4.93842			0.303365
$266$	−2.78867	−	0.748024i	−0.170984	−	0.0458643i
$267$	−0.329698	+	0.224148i	−0.0201772	+	0.0137176i
$268$	1.00093	−	1.73151i	0.0611415	−	0.105769i
$269$			23.0395i			1.40474i	0.711812	+	0.702370i	$0.247875\pi$
$269$			23.0395i			1.40474i	−0.711812	+	0.702370i	$0.752125\pi$
$270$	0.740555	−	17.7792i	0.0450687	−	1.08201i
$271$		−	0.600063i		−	0.0364512i	−0.999834	−	0.0182256i	$-0.994198\pi$
$271$		−	0.600063i		−	0.0364512i	0.999834	−	0.0182256i	$-0.00580172\pi$
$272$	14.0702	−	8.10332i	0.853131	−	0.491336i
$273$	3.36596	−	2.28837i	0.203717	−	0.138499i
$274$	2.56388	−	9.55829i	0.154890	−	0.577438i
$275$	−0.291767			−0.0175942
$276$	−0.457978	−	6.26741i	−0.0275670	−	0.377254i
$277$	5.70716			0.342910			0.171455	−	0.985192i	$-0.445153\pi$
$277$	5.70716			0.342910			0.171455	+	0.985192i	$0.445153\pi$
$278$	−0.460111	+	1.71532i	−0.0275956	+	0.102878i
$279$	−13.2762	−	5.25104i	−0.794828	−	0.314372i
$280$	−8.48980	−	8.50347i	−0.507362	−	0.508179i
$281$		−	13.7301i		−	0.819070i	−0.912294	−	0.409535i	$-0.865691\pi$
$281$		−	13.7301i		−	0.819070i	0.912294	−	0.409535i	$-0.134309\pi$
$282$	−7.10605	−	20.4119i	−0.423159	−	1.21551i
$283$		−	24.8048i		−	1.47449i	−0.675625	−	0.737245i	$-0.736126\pi$
$283$		−	24.8048i		−	1.47449i	0.675625	−	0.737245i	$-0.263874\pi$
$284$	5.36863	+	3.10342i	0.318570	+	0.184154i
$285$	2.74415	+	4.03637i	0.162550	+	0.239094i
$286$	0.617962	+	0.165760i	0.0365408	+	0.00980159i
$287$	−0.134359			−0.00793098
$288$	16.8562	+	1.96722i	0.993259	+	0.115920i
$289$	0.522866			0.0307568
$290$	28.1515	+	7.55125i	1.65311	+	0.443425i
$291$	−0.714719	−	1.05128i	−0.0418976	−	0.0616271i
$292$	20.3981	+	11.7914i	1.19371	+	0.690042i
$293$			14.2943i			0.835079i	0.908659	+	0.417540i	$0.137108\pi$
$293$			14.2943i			0.835079i	−0.908659	+	0.417540i	$0.862892\pi$
$294$	3.15864	+	9.07309i	0.184216	+	0.529153i
$295$			35.7098i			2.07911i
$296$	−13.0064	−	13.0274i	−0.755984	−	0.757201i
$297$	1.71258	−	0.383755i	0.0993739	−	0.0222677i
$298$	−3.22926	+	12.0388i	−0.187066	+	0.697392i
$299$	−2.42986			−0.140522
$300$	0.218082	+	2.98445i	0.0125910	+	0.172307i
$301$	16.2488			0.936566
$302$	4.70125	−	17.5265i	0.270527	−	1.00854i
$303$	−10.6662	+	7.25146i	−0.612755	+	0.416585i
$304$	−4.03369	+	2.32309i	−0.231348	+	0.133238i
$305$			24.6560i			1.41180i
$306$	−13.8268	−	10.2669i	−0.790424	−	0.586918i
$307$		−	20.1390i		−	1.14940i	−0.818366	−	0.574698i	$-0.805120\pi$
$307$		−	20.1390i		−	1.14940i	0.818366	−	0.574698i	$-0.194880\pi$
$308$	0.593111	−	1.02603i	0.0337957	−	0.0584634i
$309$	8.46243	−	5.75323i	0.481411	−	0.327290i
$310$	15.7410	+	4.22232i	0.894031	+	0.239812i
$311$	16.6924			0.946539			0.473270	−	0.880918i	$-0.343074\pi$
$311$	16.6924			0.946539			0.473270	+	0.880918i	$0.343074\pi$
$312$	1.23364	−	6.44494i	0.0698410	−	0.364873i
$313$	−28.8533			−1.63089			−0.815443	−	0.578838i	$-0.803507\pi$
$313$	−28.8533			−1.63089			−0.815443	+	0.578838i	$0.803507\pi$
$314$	25.6831	+	6.88914i	1.44938	+	0.388776i
$315$	−4.68756	+	11.8516i	−0.264114	+	0.667762i
$316$	4.35498	−	7.53372i	0.244987	−	0.423805i
$317$			34.8536i			1.95757i	0.204883	+	0.978786i	$0.434318\pi$
$317$			34.8536i			1.95757i	−0.204883	+	0.978786i	$0.565682\pi$
$318$	4.71772	−	1.64239i	0.264556	−	0.0921008i
$319$			2.87468i			0.160951i
$320$	−19.3723	−	0.0311662i	−1.08294	−	0.00174224i
$321$	2.82413	+	4.15402i	0.157628	+	0.231855i
$322$	−1.16607	+	4.34718i	−0.0649827	+	0.242259i
$323$	4.72372			0.262835
$324$	−5.20544	−	17.2309i	−0.289191	−	0.957271i
$325$	1.15706			0.0641822
$326$	−3.16619	+	11.8037i	−0.175359	+	0.653748i
$327$	3.25448	+	4.78702i	0.179973	+	0.264723i
$328$	−0.153292	+	0.153046i	−0.00846416	+	0.00845055i
$329$			15.4801i			0.853447i
$330$	−1.89205	+	0.658685i	−0.104154	+	0.0362594i
$331$			23.5479i			1.29431i	0.762360	+	0.647154i	$0.224041\pi$
$331$			23.5479i			1.29431i	−0.762360	+	0.647154i	$0.775959\pi$
$332$	14.7634	+	8.53421i	0.810246	+	0.468376i
$333$	−7.18139	+	18.1568i	−0.393538	+	0.994984i
$334$	−18.9759	−	5.09002i	−1.03831	−	0.278513i
$335$	2.42154			0.132303
$336$	−10.9384	−	5.29995i	−0.596740	−	0.289136i
$337$	−31.7590			−1.73002			−0.865010	−	0.501754i	$-0.832688\pi$
$337$	−31.7590			−1.73002			−0.865010	+	0.501754i	$0.832688\pi$
$338$	15.3064	+	4.10574i	0.832559	+	0.223323i
$339$	9.33835	−	6.34873i	0.507189	−	0.344816i
$340$	17.0199	+	9.83863i	0.923035	+	0.533575i
$341$			1.60739i			0.0870452i
$342$	3.96391	+	2.94335i	0.214344	+	0.159158i
$343$		−	19.1617i		−	1.03463i
$344$	18.5385	−	18.5087i	0.999528	−	0.997922i
$345$	6.29218	−	4.27778i	0.338760	−	0.230308i
$346$	4.93781	−	18.4084i	0.265458	−	0.989642i
$347$	−14.0740			−0.755533			−0.377766	−	0.925901i	$-0.623308\pi$
$347$	−14.0740			−0.755533			−0.377766	+	0.925901i	$0.623308\pi$
$348$	29.4047	−	2.14869i	1.57626	−	0.115182i
$349$	6.22850			0.333404			0.166702	−	0.986007i	$-0.446688\pi$
$349$	6.22850			0.333404			0.166702	+	0.986007i	$0.446688\pi$
$350$	0.555266	−	2.07006i	0.0296802	−	0.110649i
$351$	−6.79157	+	1.52186i	−0.362507	+	0.0812306i
$352$	−0.492039	−	1.84621i	−0.0262258	−	0.0984034i
$353$			14.8595i			0.790892i	0.918489	+	0.395446i	$0.129410\pi$
$353$			14.8595i			0.790892i	−0.918489	+	0.395446i	$0.870590\pi$
$354$	11.8762	+	34.1139i	0.631212	+	1.81313i
$355$			7.50807i			0.398487i
$356$	0.230390	−	0.398553i	0.0122106	−	0.0211233i
$357$	6.93491	+	10.2005i	0.367034	+	0.539870i
$358$	21.3756	+	5.73372i	1.12974	+	0.303037i
$359$	−11.2390			−0.593174			−0.296587	−	0.955006i	$-0.595848\pi$
$359$	−11.2390			−0.593174			−0.296587	+	0.955006i	$0.595848\pi$
$360$	8.15182	+	18.8612i	0.429638	+	0.994071i
$361$	17.6458			0.928726
$362$	2.02156	+	0.542255i	0.106251	+	0.0285003i
$363$	10.6008	+	15.5927i	0.556398	+	0.818405i
$364$	−2.35210	+	4.06892i	−0.123284	+	0.213269i
$365$			28.5269i			1.49317i
$366$	8.19998	+	23.5541i	0.428620	+	1.23120i
$367$		−	30.6588i		−	1.60038i	−0.599749	−	0.800188i	$-0.704733\pi$
$367$		−	30.6588i		−	1.60038i	0.599749	−	0.800188i	$-0.295267\pi$
$368$	3.62140	+	6.28801i	0.188778	+	0.327785i
$369$	0.213649	+	0.0845030i	0.0111221	+	0.00439905i
$370$	5.77450	−	21.5276i	0.300202	−	1.11917i
$371$	−3.57786			−0.185753
$372$	16.4418	−	1.20145i	0.852467	−	0.0622923i
$373$	32.8342			1.70009			0.850045	−	0.526711i	$-0.176575\pi$
$373$	32.8342			1.70009			0.850045	+	0.526711i	$0.176575\pi$
$374$	−0.502335	+	1.87273i	−0.0259751	+	0.0968366i
$375$	14.3465	−	9.75355i	0.740849	−	0.503671i
$376$	17.6331	+	17.6615i	0.909358	+	0.910822i
$377$		−	11.4001i		−	0.587136i
$378$	−0.536528	+	12.8809i	−0.0275960	+	0.662523i
$379$			20.9941i			1.07840i	0.842179	+	0.539198i	$0.181273\pi$
$379$			20.9941i			1.07840i	−0.842179	+	0.539198i	$0.818727\pi$
$380$	−4.87933	−	2.82057i	−0.250305	−	0.144692i
$381$	19.4435	−	13.2188i	0.996119	−	0.677217i
$382$	13.6330	+	3.65686i	0.697523	+	0.187101i
$383$	−29.2172			−1.49293			−0.746464	−	0.665425i	$-0.768250\pi$
$383$	−29.2172			−1.49293			−0.746464	+	0.665425i	$0.768250\pi$
$384$	−18.5169	+	6.41295i	−0.944934	+	0.327260i
$385$	1.43491			0.0731297
$386$	−14.4770	−	3.88326i	−0.736860	−	0.197653i
$387$	−25.8378	−	10.2194i	−1.31341	−	0.519482i
$388$	1.27083	+	0.734623i	0.0645167	+	0.0372949i
$389$		−	15.0341i		−	0.762259i	−0.924522	−	0.381129i	$-0.875535\pi$
$389$		−	15.0341i		−	0.762259i	0.924522	−	0.381129i	$-0.124465\pi$
$390$	7.50330	−	2.61215i	0.379944	−	0.132271i
$391$		−	7.36367i		−	0.372397i
$392$	−7.83792	−	7.85054i	−0.395875	−	0.396512i
$393$	−17.6366	−	25.9417i	−0.889651	−	1.30859i
$394$	0.0761463	−	0.283877i	0.00383620	−	0.0143015i
$395$	10.5360			0.530122
$396$	−1.58843	+	1.25850i	−0.0798216	+	0.0632418i
$397$	−14.3972			−0.722572			−0.361286	−	0.932455i	$-0.617662\pi$
$397$	−14.3972			−0.722572			−0.361286	+	0.932455i	$0.617662\pi$
$398$	−2.14306	+	7.98944i	−0.107422	+	0.400475i
$399$	−1.98812	−	2.92433i	−0.0995307	−	0.146400i
$400$	−1.72445	−	2.99425i	−0.0862227	−	0.149713i
$401$		−	8.28541i		−	0.413754i	−0.978367	−	0.206877i	$-0.933670\pi$
$401$		−	8.28541i		−	0.413754i	0.978367	−	0.206877i	$-0.0663300\pi$
$402$	2.31331	−	0.805342i	0.115378	−	0.0401668i
$403$		−	6.37444i		−	0.317533i
$404$	7.45341	−	12.8937i	0.370821	−	0.641486i
$405$	14.9077	−	15.8975i	0.740771	−	0.789953i
$406$	−20.3956	−	5.47084i	−1.01222	−	0.271513i
$407$	2.19829			0.108965
$408$	19.5314	+	3.73854i	0.966947	+	0.185085i
$409$	24.0722			1.19030			0.595148	−	0.803616i	$-0.297093\pi$
$409$	24.0722			1.19030			0.595148	+	0.803616i	$0.297093\pi$
$410$	−0.253314	−	0.0679482i	−0.0125103	−	0.00335572i
$411$	10.0233	−	6.81438i	0.494411	−	0.336129i
$412$	−5.91346	+	10.2297i	−0.291335	+	0.503983i
$413$		−	25.8716i		−	1.27306i
$414$	4.58830	−	6.17922i	0.225502	−	0.303692i
$415$			20.6467i			1.01351i
$416$	1.95128	+	7.32152i	0.0956693	+	0.358967i
$417$	−1.79876	+	1.22290i	−0.0880857	+	0.0598856i
$418$	0.144011	−	0.536881i	0.00704382	−	0.0262597i
$419$	−23.6806			−1.15687			−0.578436	−	0.815728i	$-0.696337\pi$
$419$	−23.6806			−1.15687			−0.578436	+	0.815728i	$0.696337\pi$
$420$	−1.07253	−	14.6775i	−0.0523339	−	0.716187i
$421$	35.4520			1.72782			0.863912	−	0.503643i	$-0.168007\pi$
$421$	35.4520			1.72782			0.863912	+	0.503643i	$0.168007\pi$
$422$	1.80982	−	6.74712i	0.0881009	−	0.328445i
$423$	9.73596	−	24.6155i	0.473379	−	1.19685i
$424$	−4.08203	+	4.07547i	−0.198241	+	0.197922i
$425$			3.50647i			0.170089i
$426$	2.49699	+	7.17253i	0.120980	+	0.347510i
$427$		−	17.8632i		−	0.864460i
$428$	−5.02155	−	2.90278i	−0.242726	−	0.140311i
$429$	0.440562	+	0.648023i	0.0212706	+	0.0312868i
$430$	30.6347	+	8.21735i	1.47734	+	0.396276i
$431$	−29.6967			−1.43044			−0.715221	−	0.698898i	$-0.753674\pi$
$431$	−29.6967			−1.43044			−0.715221	+	0.698898i	$0.753674\pi$
$432$	14.0603	+	15.3072i	0.676474	+	0.736466i
$433$	−4.86045			−0.233578			−0.116789	−	0.993157i	$-0.537260\pi$
$433$	−4.86045			−0.233578			−0.116789	+	0.993157i	$0.537260\pi$
$434$	−11.4043	−	3.05905i	−0.547424	−	0.146839i
$435$	20.0700	+	29.5209i	0.962282	+	1.41542i
$436$	−5.78675	−	3.34512i	−0.277135	−	0.160202i
$437$			2.11104i			0.100985i
$438$	9.48732	+	27.2520i	0.453322	+	1.30215i
$439$		−	18.1792i		−	0.867646i	−0.900998	−	0.433823i	$-0.857164\pi$
$439$		−	18.1792i		−	0.867646i	0.900998	−	0.433823i	$-0.142836\pi$
$440$	1.63711	−	1.63447i	0.0780460	−	0.0779205i
$441$	−4.32764	+	10.9416i	−0.206078	+	0.521028i
$442$	1.99211	−	7.42669i	0.0947550	−	0.353252i
$443$	20.6724			0.982177			0.491089	−	0.871110i	$-0.336599\pi$
$443$	20.6724			0.982177			0.491089	+	0.871110i	$0.336599\pi$
$444$	−1.64312	−	22.4860i	−0.0779789	−	1.06714i
$445$	0.557380			0.0264223
$446$	4.33805	−	16.1725i	0.205413	−	0.765789i
$447$	−12.6245	+	8.58284i	−0.597118	+	0.405954i
$448$	14.0351	+	0.0225797i	0.663096	+	0.00106679i
$449$		−	24.1650i		−	1.14042i	−0.821499	−	0.570209i	$-0.806862\pi$
$449$		−	24.1650i		−	1.14042i	0.821499	−	0.570209i	$-0.193138\pi$
$450$	−2.18488	+	2.94245i	−0.102996	+	0.138709i
$451$		−	0.0258672i		−	0.00121804i
$452$	−6.52554	+	11.2886i	−0.306936	+	0.530970i
$453$	18.3791	−	12.4952i	0.863526	−	0.587074i
$454$	−29.9385	−	8.03060i	−1.40508	−	0.376895i
$455$	−5.69041			−0.266771
$456$	−5.59932	−	1.07178i	−0.262212	−	0.0501906i
$457$	−21.5576			−1.00842			−0.504211	−	0.863581i	$-0.668217\pi$
$457$	−21.5576			−1.00842			−0.504211	+	0.863581i	$0.668217\pi$
$458$	6.21260	+	1.66645i	0.290296	+	0.0778679i
$459$	−4.61198	−	20.5818i	−0.215269	−	0.960678i
$460$	−4.39691	+	7.60625i	−0.205007	+	0.354643i
$461$			18.8531i			0.878077i	0.898468	+	0.439039i	$0.144681\pi$
$461$			18.8531i			0.878077i	−0.898468	+	0.439039i	$0.855319\pi$
$462$	1.37078	−	0.477214i	0.0637745	−	0.0222020i
$463$		−	4.38292i		−	0.203692i	−0.994800	−	0.101846i	$-0.967525\pi$
$463$		−	4.38292i		−	0.203692i	0.994800	−	0.101846i	$-0.0324748\pi$
$464$	−29.5013	+	16.9904i	−1.36957	+	0.788762i
$465$	11.2222	+	16.5068i	0.520419	+	0.765484i
$466$	−9.73656	+	36.2984i	−0.451037	+	1.68149i
$467$	−25.0496			−1.15916			−0.579579	−	0.814916i	$-0.696783\pi$
$467$	−25.0496			−1.15916			−0.579579	+	0.814916i	$0.696783\pi$
$468$	6.29924	−	4.99082i	0.291182	−	0.230701i
$469$	−1.75439			−0.0810102
$470$	−7.82861	+	29.1855i	−0.361107	+	1.34623i
$471$	18.3102	+	26.9324i	0.843689	+	1.24098i
$472$	−29.4698	−	29.5172i	−1.35646	−	1.35864i
$473$			3.12826i			0.143837i
$474$	10.0651	−	3.50400i	0.462305	−	0.160944i
$475$		−	1.00525i		−	0.0461239i
$476$	−12.3309	−	7.12804i	−0.565184	−	0.326713i
$477$	5.68928	+	2.25023i	0.260494	+	0.103031i
$478$	0.770197	+	0.206595i	0.0352280	+	0.00944943i
$479$	12.3441			0.564016			0.282008	−	0.959412i	$-0.408999\pi$
$479$	12.3441			0.564016			0.282008	+	0.959412i	$0.408999\pi$
$480$	−17.9425	−	15.5240i	−0.818958	−	0.708572i
$481$	−8.71776			−0.397496
$482$	28.2659	+	7.58194i	1.28748	+	0.345348i
$483$	−4.55865	+	3.09923i	−0.207426	+	0.141020i
$484$	−18.8491	−	10.8960i	−0.856778	−	0.495274i
$485$			1.77727i			0.0807015i
$486$	8.95438	−	20.1450i	0.406179	−	0.913794i
$487$		−	33.9623i		−	1.53898i	−0.638659	−	0.769490i	$-0.720511\pi$
$487$		−	33.9623i		−	1.53898i	0.638659	−	0.769490i	$-0.279489\pi$
$488$	−20.3476	−	20.3804i	−0.921092	−	0.922575i
$489$	−12.3779	+	8.41522i	−0.559750	+	0.380549i
$490$	3.47982	−	12.9730i	0.157202	−	0.586058i
$491$	−4.55227			−0.205441			−0.102721	−	0.994710i	$-0.532755\pi$
$491$	−4.55227			−0.205441			−0.102721	+	0.994710i	$0.532755\pi$
$492$	−0.264592	+	0.0193345i	−0.0119287	+	0.000871665i
$493$	34.5480			1.55597
$494$	−0.571105	+	2.12911i	−0.0256952	+	0.0957932i
$495$	−2.28170	−	0.902461i	−0.102555	−	0.0405626i
$496$	−16.4958	+	9.50030i	−0.740685	+	0.426576i
$497$		−	5.43956i		−	0.243997i
$498$	6.86658	+	19.7240i	0.307699	+	0.883853i
$499$		−	22.9604i		−	1.02785i	−0.857836	−	0.513923i	$-0.828192\pi$
$499$		−	22.9604i		−	1.02785i	0.857836	−	0.513923i	$-0.171808\pi$
$500$	−10.0252	+	17.3426i	−0.448340	+	0.775586i
$501$	−13.5284	−	19.8990i	−0.604406	−	0.889020i
$502$	−8.97985	−	2.40873i	−0.400790	−	0.107507i
$503$	2.01888			0.0900173			0.0450087	−	0.998987i	$-0.485668\pi$
$503$	2.01888			0.0900173			0.0450087	+	0.998987i	$0.485668\pi$
$504$	−5.90595	−	13.6648i	−0.263072	−	0.608680i
$505$	18.0319			0.802411
$506$	−0.836929	−	0.224495i	−0.0372060	−	0.00998001i
$507$	10.9124	+	16.0510i	0.484636	+	0.712850i
$508$	−13.5869	+	23.5041i	−0.602821	+	1.04282i
$509$			27.2643i			1.20847i	0.796807	+	0.604234i	$0.206521\pi$
$509$			27.2643i			1.20847i	−0.796807	+	0.604234i	$0.793479\pi$
$510$	7.91611	+	22.7387i	0.350531	+	1.00689i
$511$		−	20.6676i		−	0.914280i
$512$	16.0386	−	15.9613i	0.708811	−	0.705398i
$513$	1.32218	+	5.90048i	0.0583756	+	0.260512i
$514$	−3.32311	+	12.3887i	−0.146576	+	0.546444i
$515$	−14.3064			−0.630414
$516$	31.9985	−	2.33822i	1.40866	−	0.102935i
$517$	−2.98027			−0.131072
$518$	−4.18360	+	15.5967i	−0.183817	+	0.685278i
$519$	19.3039	−	13.1239i	0.847347	−	0.576074i
$520$	−6.49227	+	6.48183i	−0.284705	+	0.284247i
$521$		−	19.6443i		−	0.860631i	−0.902679	−	0.430316i	$-0.858402\pi$
$521$		−	19.6443i		−	0.860631i	0.902679	−	0.430316i	$-0.141598\pi$
$522$	28.9910	+	21.5268i	1.26890	+	0.942204i
$523$		−	23.6600i		−	1.03458i	−0.855810	−	0.517291i	$-0.826941\pi$
$523$		−	23.6600i		−	1.03458i	0.855810	−	0.517291i	$-0.173059\pi$
$524$	31.3594	+	18.1278i	1.36994	+	0.791917i
$525$	2.17076	−	1.47581i	0.0947398	−	0.0644095i
$526$	5.28967	+	1.41888i	0.230640	+	0.0618662i
$527$	19.3177			0.841493
$528$	1.02036	−	2.10589i	0.0444054	−	0.0916471i
$529$	−19.7092			−0.856920
$530$	−6.74552	−	1.80939i	−0.293007	−	0.0785951i
$531$	−16.2715	+	41.1393i	−0.706122	+	1.78529i
$532$	3.53505	+	2.04349i	0.153264	+	0.0885966i
$533$			0.102581i			0.00444329i
$534$	0.532470	−	0.185370i	0.0230422	−	0.00802176i
$535$		−	7.02267i		−	0.303617i
$536$	−2.00161	+	1.99839i	−0.0864563	+	0.0863173i
$537$	15.2393	+	22.4155i	0.657624	+	0.967298i
$538$	8.44146	−	31.4702i	0.363937	−	1.35678i
$539$	1.32473			0.0570602
$540$	−7.52568	+	24.0137i	−0.323854	+	1.03339i
$541$	20.6306			0.886978			0.443489	−	0.896280i	$-0.353741\pi$
$541$	20.6306			0.886978			0.443489	+	0.896280i	$0.353741\pi$
$542$	−0.219858	+	0.819642i	−0.00944371	+	0.0352067i
$543$	1.44122	+	2.11990i	0.0618489	+	0.0909735i
$544$	−22.1878	+	5.91335i	−0.951296	+	0.253533i
$545$		−	8.09281i		−	0.346658i
$546$	−5.43610	+	1.89249i	−0.232644	+	0.0809910i
$547$		−	30.6770i		−	1.31165i	−0.754912	−	0.655826i	$-0.772320\pi$
$547$		−	30.6770i		−	1.31165i	0.754912	−	0.655826i	$-0.227680\pi$
$548$	−7.00416	+	12.1165i	−0.299203	+	0.517593i
$549$	−11.2347	+	28.4049i	−0.479487	+	1.21229i
$550$	0.398533	+	0.106901i	0.0169935	+	0.00455828i
$551$	−9.90436			−0.421940
$552$	−1.67076	+	8.72862i	−0.0711123	+	0.371515i
$553$	−7.63325			−0.324599
$554$	−7.79556	−	2.09106i	−0.331202	−	0.0888404i
$555$	22.5749	−	15.3477i	0.958250	−	0.651472i
$556$	1.25696	−	2.17442i	0.0533068	−	0.0922159i
$557$		−	41.7157i		−	1.76755i	−0.467910	−	0.883776i	$-0.654993\pi$
$557$		−	41.7157i		−	1.76755i	0.467910	−	0.883776i	$-0.345007\pi$
$558$	16.2104	+	12.0368i	0.686243	+	0.509560i
$559$		−	12.4057i		−	0.524706i
$560$	8.48084	+	14.7257i	0.358381	+	0.622275i
$561$	−1.96383	+	1.33512i	−0.0829131	+	0.0563690i
$562$	−5.03060	+	18.7543i	−0.212203	+	0.791104i
$563$	37.7631			1.59152			0.795762	−	0.605610i	$-0.207071\pi$
$563$	37.7631			1.59152			0.795762	+	0.605610i	$0.207071\pi$
$564$	2.22761	+	30.4847i	0.0937993	+	1.28364i
$565$	−15.7872			−0.664171
$566$	−9.08826	+	33.8815i	−0.382008	+	1.42415i
$567$	−10.8006	+	11.5177i	−0.453581	+	0.483696i
$568$	−6.19609	−	6.20607i	−0.259982	−	0.260401i
$569$		−	3.56714i		−	0.149542i	−0.997201	−	0.0747712i	$-0.976177\pi$
$569$		−	3.56714i		−	0.149542i	0.997201	−	0.0747712i	$-0.0238226\pi$
$570$	−2.26942	−	6.51882i	−0.0950555	−	0.273043i
$571$		−	7.04923i		−	0.295001i	−0.989062	−	0.147501i	$-0.952877\pi$
$571$		−	7.04923i		−	0.295001i	0.989062	−	0.147501i	$-0.0471228\pi$
$572$	−0.783357	−	0.452832i	−0.0327538	−	0.0189339i
$573$	9.71933	+	14.2962i	0.406031	+	0.597230i
$574$	0.183525	+	0.0492281i	0.00766019	+	0.00205474i
$575$	−1.56705			−0.0653506
$576$	−22.3035	−	8.86304i	−0.929313	−	0.369293i
$577$	−31.1050			−1.29492			−0.647459	−	0.762100i	$-0.724168\pi$
$577$	−31.1050			−1.29492			−0.647459	+	0.762100i	$0.724168\pi$
$578$	−0.714197	−	0.191574i	−0.0297067	−	0.00796842i
$579$	−10.3211	−	15.1813i	−0.428929	−	0.630911i
$580$	−35.6861	−	20.6289i	−1.48179	−	0.856569i
$581$		−	14.9584i		−	0.620581i
$582$	0.591074	+	1.69784i	0.0245008	+	0.0703777i
$583$		−	0.688817i		−	0.0285279i
$584$	−23.5420	−	23.5799i	−0.974176	−	0.975745i
$585$	9.04853	+	3.57889i	0.374110	+	0.147969i
$586$	5.23730	−	19.5249i	0.216351	−	0.806567i
$587$	21.9550			0.906178			0.453089	−	0.891465i	$-0.350322\pi$
$587$	21.9550			0.906178			0.453089	+	0.891465i	$0.350322\pi$
$588$	−0.990173	−	13.5505i	−0.0408340	−	0.558812i
$589$	−5.53807			−0.228192
$590$	13.0838	−	48.7770i	0.538651	−	2.00812i
$591$	0.297687	−	0.202384i	0.0122452	−	0.00832498i
$592$	12.9927	+	22.5599i	0.533998	+	0.927206i
$593$			16.2319i			0.666564i	0.942827	+	0.333282i	$0.108156\pi$
$593$			16.2319i			0.666564i	−0.942827	+	0.333282i	$0.891844\pi$
$594$	−2.47986	−	0.103294i	−0.101750	−	0.00423819i
$595$		−	17.2448i		−	0.706967i
$596$	8.82186	−	15.2610i	0.361358	−	0.625115i
$597$	−8.37810	+	5.69590i	−0.342893	+	0.233118i
$598$	3.31901	+	0.890279i	0.135724	+	0.0364062i
$599$	14.6050			0.596743			0.298371	−	0.954450i	$-0.403557\pi$
$599$	14.6050			0.596743			0.298371	+	0.954450i	$0.403557\pi$
$600$	0.795592	−	4.15644i	0.0324799	−	0.169686i
$601$	31.2179			1.27341			0.636703	−	0.771109i	$-0.280298\pi$
$601$	31.2179			1.27341			0.636703	+	0.771109i	$0.280298\pi$
$602$	−22.1947	−	5.95343i	−0.904588	−	0.242644i
$603$	2.78972	+	1.10339i	0.113606	+	0.0449337i
$604$	−12.8431	+	22.2174i	−0.522580	+	0.904015i
$605$		−	26.3606i		−	1.07171i
$606$	17.2261	−	5.99697i	0.699761	−	0.243610i
$607$			34.1317i			1.38536i	0.721244	+	0.692681i	$0.243571\pi$
$607$			34.1317i			1.38536i	−0.721244	+	0.692681i	$0.756429\pi$
$608$	6.36089	−	1.69526i	0.257968	−	0.0687518i
$609$	−14.5406	−	21.3878i	−0.589215	−	0.866676i
$610$	9.03377	−	33.6784i	0.365767	−	1.36360i
$611$	11.8188			0.478139
$612$	15.1247	+	19.0898i	0.611378	+	0.771660i
$613$	38.0864			1.53829			0.769147	−	0.639072i	$-0.220681\pi$
$613$	38.0864			1.53829			0.769147	+	0.639072i	$0.220681\pi$
$614$	−7.37878	+	27.5085i	−0.297783	+	1.11015i
$615$	−0.180595	−	0.265637i	−0.00728230	−	0.0107115i
$616$	−1.18608	+	1.18417i	−0.0477883	+	0.0477115i
$617$			31.6358i			1.27361i	0.771025	+	0.636805i	$0.219744\pi$
$617$			31.6358i			1.27361i	−0.771025	+	0.636805i	$0.780256\pi$
$618$	−13.6670	+	4.75794i	−0.549767	+	0.191392i
$619$			7.59864i			0.305415i	0.988271	+	0.152708i	$0.0487993\pi$
$619$			7.59864i			0.305415i	−0.988271	+	0.152708i	$0.951201\pi$
$620$	−19.9541	−	11.5348i	−0.801375	−	0.463247i
$621$	9.19808	−	2.06111i	0.369106	−	0.0827093i
$622$	−22.8006	−	6.11596i	−0.914221	−	0.245228i
$623$	−0.403819			−0.0161787
$624$	−4.04643	+	8.35132i	−0.161987	+	0.334320i
$625$	−28.5730			−1.14292
$626$	39.4115	+	10.5716i	1.57520	+	0.422527i
$627$	0.562999	−	0.382758i	0.0224840	−	0.0152859i
$628$	−32.5571	−	18.8201i	−1.29917	−	0.751004i
$629$		−	26.4191i		−	1.05340i
$630$	10.7452	−	14.4709i	0.428099	−	0.576536i
$631$			24.2502i			0.965384i	0.875790	+	0.482692i	$0.160341\pi$
$631$			24.2502i			0.965384i	−0.875790	+	0.482692i	$0.839659\pi$
$632$	−8.70889	+	8.69489i	−0.346421	+	0.345864i
$633$	7.07534	−	4.81021i	0.281220	−	0.191189i
$634$	12.7701	−	47.6075i	0.507164	−	1.89073i
$635$	−32.8706			−1.30443
$636$	−7.04581	+	0.514858i	−0.279385	+	0.0204155i
$637$	−5.25348			−0.208151
$638$	1.05326	−	3.92661i	0.0416989	−	0.155456i
$639$	−3.42112	+	8.64963i	−0.135337	+	0.342174i
$640$	26.4497	+	7.14040i	1.04552	+	0.282249i
$641$		−	3.70656i		−	0.146400i	−0.997317	−	0.0732001i	$-0.976679\pi$
$641$		−	3.70656i		−	0.146400i	0.997317	−	0.0732001i	$-0.0233212\pi$
$642$	−2.33556	−	6.70882i	−0.0921773	−	0.264776i
$643$			3.33117i			0.131368i	0.997840	+	0.0656842i	$0.0209230\pi$
$643$			3.33117i			0.131368i	−0.997840	+	0.0656842i	$0.979077\pi$
$644$	3.18554	−	5.51069i	0.125528	−	0.217152i
$645$	21.8404	+	32.1250i	0.859963	+	1.26492i
$646$	−6.45226	−	1.73073i	−0.253861	−	0.0680948i
$647$	−5.05294			−0.198652			−0.0993258	−	0.995055i	$-0.531669\pi$
$647$	−5.05294			−0.198652			−0.0993258	+	0.995055i	$0.531669\pi$
$648$	0.797003	+	25.4434i	0.0313092	+	0.999510i
$649$	4.98085			0.195516
$650$	−1.58046	−	0.423938i	−0.0619908	−	0.0166282i
$651$	−8.13045	−	11.9591i	−0.318658	−	0.468713i
$652$	8.64958	−	14.9630i	0.338744	−	0.585995i
$653$			25.1373i			0.983700i	0.870680	+	0.491850i	$0.163679\pi$
$653$			25.1373i			0.983700i	−0.870680	+	0.491850i	$0.836321\pi$
$654$	−2.69147	−	7.73114i	−0.105245	−	0.302311i
$655$			43.8564i			1.71361i
$656$	0.265461	−	0.152885i	0.0103645	−	0.00596914i
$657$	−12.9985	+	32.8643i	−0.507121	+	1.28216i
$658$	5.67179	−	21.1447i	0.221109	−	0.824307i
$659$	−28.1599			−1.09695			−0.548477	−	0.836166i	$-0.684792\pi$
$659$	−28.1599			−1.09695			−0.548477	+	0.836166i	$0.684792\pi$
$660$	2.82574	−	0.206485i	0.109992	−	0.00803742i
$661$	−45.2959			−1.76181			−0.880904	−	0.473295i	$-0.843064\pi$
$661$	−45.2959			−1.76181			−0.880904	+	0.473295i	$0.843064\pi$
$662$	8.62774	−	32.1647i	0.335327	−	1.25011i
$663$	7.78797	−	5.29470i	0.302460	−	0.205629i
$664$	−17.0389	−	17.0663i	−0.661236	−	0.662301i
$665$			4.94380i			0.191712i
$666$	16.4617	−	22.1696i	0.637879	−	0.859055i
$667$			15.4396i			0.597824i
$668$	24.0547	+	13.9052i	0.930704	+	0.538008i
$669$	16.9592	−	11.5298i	0.655681	−	0.445769i
$670$	−3.30764	−	0.887230i	−0.127785	−	0.0342767i
$671$	3.43906			0.132763
$672$	12.9992	+	11.2471i	0.501456	+	0.433866i
$673$	−29.2754			−1.12848			−0.564242	−	0.825609i	$-0.690832\pi$
$673$	−29.2754			−1.12848			−0.564242	+	0.825609i	$0.690832\pi$
$674$	43.3804	+	11.6362i	1.67095	+	0.448210i
$675$	−4.37999	+	0.981468i	−0.168586	+	0.0377767i
$676$	−19.4031	−	11.2163i	−0.746274	−	0.431395i
$677$		−	21.5652i		−	0.828818i	−0.910091	−	0.414409i	$-0.863988\pi$
$677$		−	21.5652i		−	0.828818i	0.910091	−	0.414409i	$-0.136012\pi$
$678$	−15.0816	+	5.25041i	−0.579206	+	0.201641i
$679$		−	1.28762i		−	0.0494143i
$680$	−19.6432	−	19.6748i	−0.753282	−	0.754495i
$681$	−21.3440	−	31.3949i	−0.817904	−	1.20305i
$682$	0.588935	−	2.19558i	0.0225515	−	0.0840732i
$683$	5.80503			0.222123			0.111062	−	0.993814i	$-0.464575\pi$
$683$	5.80503			0.222123			0.111062	+	0.993814i	$0.464575\pi$
$684$	−4.33599	−	5.47274i	−0.165791	−	0.209255i
$685$	−16.9451			−0.647438
$686$	−7.02067	+	26.1734i	−0.268050	+	0.999306i
$687$	4.42914	+	6.51482i	0.168982	+	0.248556i
$688$	−32.1037	+	18.4892i	−1.22394	+	0.704893i
$689$			2.73164i			0.104067i
$690$	−10.1620	+	3.53773i	−0.386861	+	0.134679i
$691$			39.6635i			1.50887i	0.656374	+	0.754436i	$0.272089\pi$
$691$			39.6635i			1.50887i	−0.656374	+	0.754436i	$0.727911\pi$
$692$	−13.4894	+	23.3354i	−0.512789	+	0.887077i
$693$	1.65308	+	0.653828i	0.0627952	+	0.0248369i
$694$	19.2241	+	5.15660i	0.729736	+	0.195742i
$695$	3.04094			0.115349
$696$	−40.9520	−	7.83869i	−1.55228	−	0.297125i
$697$	−0.310873			−0.0117751
$698$	−8.50768	−	2.28207i	−0.322020	−	0.0863777i
$699$	−38.0642	+	25.8782i	−1.43972	+	0.978802i
$700$	−1.51691	+	2.62411i	−0.0573337	+	0.0991820i
$701$		−	43.4754i		−	1.64204i	−0.570896	−	0.821022i	$-0.693404\pi$
$701$		−	43.4754i		−	1.64204i	0.570896	−	0.821022i	$-0.306596\pi$
$702$	9.83439	+	0.409632i	0.371175	+	0.0154605i
$703$			7.57394i			0.285656i
$704$	−0.00434710	+	2.70207i	−0.000163838	+	0.101838i
$705$	−30.6052	+	20.8072i	−1.15266	+	0.783643i
$706$	5.44440	−	20.2970i	0.204903	−	0.763888i
$707$	−13.0640			−0.491324
$708$	−3.72295	−	50.9484i	−0.139917	−	1.91476i
$709$	−17.2998			−0.649706			−0.324853	−	0.945765i	$-0.605315\pi$
$709$	−17.2998			−0.649706			−0.324853	+	0.945765i	$0.605315\pi$
$710$	2.75089	−	10.2555i	0.103239	−	0.384881i
$711$	12.1379	+	4.80080i	0.455207	+	0.180044i
$712$	−0.460722	+	0.459982i	−0.0172663	+	0.0172385i
$713$			8.63314i			0.323314i
$714$	−5.73518	−	16.4741i	−0.214634	−	0.616528i
$715$		−	1.09553i		−	0.0409705i
$716$	−27.0967	−	15.6637i	−1.01265	−	0.585380i
$717$	0.549095	+	0.807664i	0.0205063	+	0.0301628i
$718$	15.3517	+	4.11789i	0.572921	+	0.153678i
$719$	15.7041			0.585662			0.292831	−	0.956164i	$-0.405403\pi$
$719$	15.7041			0.585662			0.292831	+	0.956164i	$0.405403\pi$
$720$	−4.22421	−	28.7497i	−0.157427	−	1.07144i
$721$	10.3649			0.386009
$722$	−24.1029	−	6.46527i	−0.897016	−	0.240612i
$723$	20.1515	+	29.6409i	0.749444	+	1.10236i
$724$	−2.56262	−	1.48136i	−0.0952390	−	0.0550544i
$725$		−	7.35211i		−	0.273051i
$726$	−8.76688	−	25.1826i	−0.325370	−	0.934612i
$727$			18.6188i			0.690534i	0.938505	+	0.345267i	$0.112212\pi$
$727$			18.6188i			0.690534i	−0.938505	+	0.345267i	$0.887788\pi$
$728$	4.70362	−	4.69606i	0.174328	−	0.174047i
$729$	24.4182	−	11.5218i	0.904378	−	0.426733i
$730$	10.4520	−	38.9656i	0.386846	−	1.44218i
$731$	37.5955			1.39052
$732$	−2.57053	−	35.1777i	−0.0950097	−	1.30020i
$733$	37.1929			1.37375			0.686875	−	0.726776i	$-0.258982\pi$
$733$	37.1929			1.37375			0.686875	+	0.726776i	$0.258982\pi$
$734$	−11.2331	+	41.8777i	−0.414622	+	1.54573i
$735$	13.6040	−	9.24879i	0.501792	−	0.341147i
$736$	−2.64269	−	9.91581i	−0.0974108	−	0.365502i
$737$		−	0.337759i		−	0.0124415i
$738$	−0.260868	−	0.193704i	−0.00960270	−	0.00713035i
$739$		−	47.8820i		−	1.76137i	−0.473703	−	0.880685i	$-0.657083\pi$
$739$		−	47.8820i		−	1.76137i	0.473703	−	0.880685i	$-0.342917\pi$
$740$	−15.7751	+	27.2895i	−0.579904	+	1.00318i
$741$	−2.23268	+	1.51790i	−0.0820197	+	0.0557616i
$742$	4.88709	+	1.31090i	0.179411	+	0.0481246i
$743$	9.47111			0.347461			0.173731	−	0.984793i	$-0.444418\pi$
$743$	9.47111			0.347461			0.173731	+	0.984793i	$0.444418\pi$
$744$	−22.8985	−	4.38304i	−0.839500	−	0.160690i
$745$	21.3426			0.781934
$746$	−44.8491	−	12.0302i	−1.64204	−	0.440456i
$747$	−9.40785	+	23.7859i	−0.344215	+	0.870282i
$748$	1.37231	−	2.37396i	0.0501765	−	0.0868007i
$749$			5.08789i			0.185907i
$750$	−23.1699	+	8.06620i	−0.846044	+	0.294536i
$751$			14.4388i			0.526880i	0.964676	+	0.263440i	$0.0848570\pi$
$751$			14.4388i			0.526880i	−0.964676	+	0.263440i	$0.915143\pi$
$752$	−17.6145	−	30.5849i	−0.642335	−	1.11532i
$753$	−6.40199	−	9.41669i	−0.233302	−	0.343163i
$754$	−4.17691	+	15.5717i	−0.152114	+	0.567089i
$755$	−31.0713			−1.13080
$756$	5.45232	−	17.3978i	0.198299	−	0.632752i
$757$	−44.9004			−1.63193			−0.815966	−	0.578100i	$-0.803794\pi$
$757$	−44.9004			−1.63193			−0.815966	+	0.578100i	$0.803794\pi$
$758$	7.69208	−	28.6765i	0.279389	−	1.04158i
$759$	−0.596670	−	0.877642i	−0.0216578	−	0.0318564i
$760$	5.63138	+	5.64045i	0.204272	+	0.204601i
$761$		−	2.80263i		−	0.101595i	−0.998709	−	0.0507976i	$-0.983824\pi$
$761$		−	2.80263i		−	0.101595i	0.998709	−	0.0507976i	$-0.0161763\pi$
$762$	−31.4016	+	10.9319i	−1.13756	+	0.396022i
$763$			5.86320i			0.212262i
$764$	−17.2818	−	9.99001i	−0.625233	−	0.361426i
$765$	−10.8458	+	27.4215i	−0.392131	+	0.991428i
$766$	39.9086	+	10.7049i	1.44195	+	0.386785i
$767$	−19.7526			−0.713224
$768$	27.6423	−	1.97520i	0.997457	−	0.0712740i
$769$	−35.1082			−1.26603			−0.633017	−	0.774138i	$-0.718184\pi$
$769$	−35.1082			−1.26603			−0.633017	+	0.774138i	$0.718184\pi$
$770$	−1.95998	−	0.525738i	−0.0706328	−	0.0189463i
$771$	−12.9914	+	8.83229i	−0.467874	+	0.318087i
$772$	18.3517	+	10.6085i	0.660493	+	0.381808i
$773$			10.8115i			0.388864i	0.980916	+	0.194432i	$0.0622863\pi$
$773$			10.8115i			0.388864i	−0.980916	+	0.194432i	$0.937714\pi$
$774$	31.5482	+	23.4257i	1.13398	+	0.842020i
$775$		−	4.11097i		−	0.147670i
$776$	−1.46670	−	1.46906i	−0.0526516	−	0.0527363i
$777$	−16.3554	+	11.1193i	−0.586746	+	0.398903i
$778$	−5.50837	+	20.5355i	−0.197484	+	0.736232i
$779$	0.0891221			0.00319313
$780$	−11.2060	+	0.818857i	−0.401240	+	0.0293198i
$781$	1.04724			0.0374730
$782$	−2.69799	+	10.0582i	−0.0964799	+	0.359682i
$783$	9.67006	+	43.1545i	0.345580	+	1.54222i
$784$	7.82966	+	13.5950i	0.279631	+	0.485536i
$785$		−	45.5313i		−	1.62508i
$786$	14.5855	+	41.8964i	0.520249	+	1.49440i
$787$			52.1256i			1.85808i	0.369984	+	0.929038i	$0.379363\pi$
$787$			52.1256i			1.85808i	−0.369984	+	0.929038i	$0.620637\pi$
$788$	−0.208021	+	0.359856i	−0.00741043	+	0.0128194i
$789$	3.77115	+	5.54699i	0.134257	+	0.197478i
$790$	−14.3914	−	3.86029i	−0.512022	−	0.137343i
$791$	11.4377			0.406679
$792$	2.63078	−	1.13703i	0.0934808	−	0.0404025i
$793$	−13.6383			−0.484309
$794$	19.6655	+	5.27500i	0.697901	+	0.187203i
$795$	−4.80907	−	7.07366i	−0.170560	−	0.250877i
$796$	5.85453	−	10.1278i	0.207508	−	0.358970i
$797$			3.59649i			0.127394i	0.997969	+	0.0636972i	$0.0202892\pi$
$797$			3.59649i			0.127394i	−0.997969	+	0.0636972i	$0.979711\pi$
$798$	1.64418	+	4.72285i	0.0582034	+	0.167187i
$799$			35.8170i			1.26711i
$800$	1.25841	+	4.72176i	0.0444915	+	0.166939i
$801$	0.642126	+	0.253975i	0.0226884	+	0.00897376i
$802$	−3.03571	+	11.3173i	−0.107195	+	0.399627i
$803$	3.97897			0.140415
$804$	−3.45489	+	0.252459i	−0.121845	+	0.00890354i
$805$	7.70674			0.271627
$806$	−2.33554	+	8.70702i	−0.0822659	+	0.306692i
$807$	33.0011	−	22.4360i	1.16169	−	0.789785i
$808$	−14.9050	+	14.8810i	−0.524354	+	0.523512i
$809$			32.6512i			1.14795i	0.818871	+	0.573977i	$0.194600\pi$
$809$			32.6512i			1.14795i	−0.818871	+	0.573977i	$0.805400\pi$
$810$	−26.1876	+	16.2527i	−0.920138	+	0.571063i
$811$			23.0323i			0.808774i	0.914588	+	0.404387i	$0.132515\pi$
$811$			23.0323i			0.808774i	−0.914588	+	0.404387i	$0.867485\pi$
$812$	25.8544	+	14.9456i	0.907312	+	0.524486i
$813$	−0.859515	+	0.584347i	−0.0301445	+	0.0204939i
$814$	−3.00270	−	0.805435i	−0.105245	−	0.0282305i
$815$	20.9258			0.733000
$816$	−25.3087	−	12.2627i	−0.885981	−	0.429280i
$817$	−10.7780			−0.377075
$818$	−32.8809	−	8.81987i	−1.14965	−	0.308380i
$819$	−6.55561	−	2.59289i	−0.229072	−	0.0906027i
$820$	0.321113	+	0.185625i	0.0112138	+	0.00648229i
$821$		−	8.07470i		−	0.281809i	−0.990023	−	0.140905i	$-0.954999\pi$
$821$		−	8.07470i		−	0.281809i	0.990023	−	0.140905i	$-0.0450011\pi$
$822$	−16.1878	+	5.63551i	−0.564614	+	0.196561i
$823$		−	32.4055i		−	1.12958i	−0.825233	−	0.564792i	$-0.808956\pi$
$823$		−	32.4055i		−	1.12958i	0.825233	−	0.564792i	$-0.191044\pi$
$824$	11.8254	−	11.8064i	0.411959	−	0.411297i
$825$	0.284125	+	0.417920i	0.00989198	+	0.0145501i
$826$	−9.47913	+	35.3387i	−0.329821	+	1.22959i
$827$	11.9691			0.416208			0.208104	−	0.978107i	$-0.433271\pi$
$827$	11.9691			0.416208			0.208104	+	0.978107i	$0.433271\pi$
$828$	−8.53129	+	6.75925i	−0.296483	+	0.234900i
$829$	55.5986			1.93102			0.965510	−	0.260365i	$-0.0838428\pi$
$829$	55.5986			1.93102			0.965510	+	0.260365i	$0.0838428\pi$
$830$	7.56478	−	28.2019i	0.262577	−	0.978902i
$831$	−5.55768	−	8.17479i	−0.192794	−	0.283580i
$832$	0.0172393	−	10.7156i	0.000597665	−	0.371496i
$833$		−	15.9207i		−	0.551618i
$834$	2.90504	−	1.01134i	0.100593	−	0.0350198i
$835$			33.6407i			1.16418i
$836$	−0.393418	+	0.680576i	−0.0136066	+	0.0235382i
$837$	5.40706	+	24.1301i	0.186895	+	0.834057i
$838$	32.3459	+	8.67636i	1.11737	+	0.299720i
$839$	18.0545			0.623309			0.311655	−	0.950195i	$-0.399117\pi$
$839$	18.0545			0.623309			0.311655	+	0.950195i	$0.399117\pi$
$840$	−3.91271	+	20.4413i	−0.135001	+	0.705292i
$841$	−43.4378			−1.49786
$842$	−48.4248	−	12.9893i	−1.66883	−	0.447641i
$843$	−19.6667	+	13.3705i	−0.677356	+	0.460504i
$844$	−4.94418	+	8.55297i	−0.170186	+	0.294405i
$845$		−	27.1354i		−	0.933487i
$846$	−22.3175	+	30.0558i	−0.767292	+	1.03334i
$847$			19.0981i			0.656220i
$848$	7.06897	−	4.07117i	0.242749	−	0.139805i
$849$	−35.5297	+	24.1551i	−1.21938	+	0.829001i
$850$	1.28474	−	4.78958i	0.0440663	−	0.164281i
$851$	11.8068			0.404731
$852$	−0.782759	−	10.7120i	−0.0268169	−	0.366988i
$853$	48.4263			1.65808			0.829042	−	0.559187i	$-0.188887\pi$
$853$	48.4263			1.65808			0.829042	+	0.559187i	$0.188887\pi$
$854$	−6.54492	+	24.3998i	−0.223963	+	0.834944i
$855$	3.10932	−	7.86131i	0.106336	−	0.268851i
$856$	5.79551	+	5.80484i	0.198087	+	0.198405i
$857$		−	43.2895i		−	1.47874i	−0.673299	−	0.739370i	$-0.735123\pi$
$857$		−	43.2895i		−	1.47874i	0.673299	−	0.739370i	$-0.264877\pi$
$858$	−0.364346	−	1.04657i	−0.0124386	−	0.0357293i
$859$			0.598378i			0.0204164i	0.999948	+	0.0102082i	$0.00324943\pi$
$859$			0.598378i			0.0204164i	−0.999948	+	0.0102082i	$0.996751\pi$
$860$	−38.8340	−	22.4486i	−1.32423	−	0.765491i
$861$	0.130840	+	0.192453i	0.00445902	+	0.00655878i
$862$	40.5636	+	10.8806i	1.38160	+	0.370596i
$863$	20.3469			0.692618			0.346309	−	0.938120i	$-0.387435\pi$
$863$	20.3469			0.692618			0.346309	+	0.938120i	$0.387435\pi$
$864$	−13.5969	−	26.0600i	−0.462575	−	0.886580i
$865$	−32.6347			−1.10961
$866$	6.63903	+	1.78083i	0.225603	+	0.0605151i
$867$	−0.509172	−	0.748940i	−0.0172924	−	0.0254353i
$868$	14.4566	+	8.35688i	0.490690	+	0.283651i
$869$		−	1.46957i		−	0.0498518i
$870$	−16.5979	−	47.6769i	−0.562722	−	1.61640i
$871$			1.33945i			0.0453856i
$872$	6.67865	+	6.68941i	0.226168	+	0.226532i
$873$	−0.809827	+	2.04749i	−0.0274085	+	0.0692971i
$874$	0.773469	−	2.88353i	0.0261630	−	0.0975370i
$875$	17.5718			0.594034
$876$	−2.97409	−	40.7003i	−0.100485	−	1.37514i
$877$	−39.1455			−1.32185			−0.660924	−	0.750453i	$-0.729836\pi$
$877$	−39.1455			−1.32185			−0.660924	+	0.750453i	$0.729836\pi$
$878$	−6.66071	+	24.8315i	−0.224788	+	0.838021i
$879$	20.4747	−	13.9199i	0.690596	−	0.469506i
$880$	−2.83503	+	1.63275i	−0.0955687	+	0.0550400i
$881$		−	52.0716i		−	1.75434i	−0.480183	−	0.877168i	$-0.659430\pi$
$881$		−	52.0716i		−	1.75434i	0.480183	−	0.877168i	$-0.340570\pi$
$882$	9.92015	−	13.3598i	0.334029	−	0.449848i
$883$		−	24.2954i		−	0.817606i	−0.912623	−	0.408803i	$-0.865946\pi$
$883$		−	24.2954i		−	0.817606i	0.912623	−	0.408803i	$-0.134054\pi$
$884$	−5.44215	+	9.41442i	−0.183039	+	0.316641i
$885$	51.1498	−	34.7745i	1.71938	−	1.16893i
$886$	−28.2370	−	7.57421i	−0.948642	−	0.254461i
$887$	−23.5018			−0.789112			−0.394556	−	0.918872i	$-0.629102\pi$
$887$	−23.5018			−0.789112			−0.394556	+	0.918872i	$0.629102\pi$
$888$	−5.99430	+	31.3163i	−0.201156	+	1.05090i
$889$	23.8146			0.798716
$890$	−0.761340	−	0.204219i	−0.0255202	−	0.00684544i
$891$	−2.21740	−	2.07935i	−0.0742858	−	0.0696609i
$892$	−11.8509	+	20.5010i	−0.396798	+	0.686424i
$893$		−	10.2681i		−	0.343610i
$894$	20.3888	−	7.09802i	0.681904	−	0.237393i
$895$		−	37.8950i		−	1.26669i
$896$	−19.1627	−	5.17319i	−0.640179	−	0.172824i
$897$	2.36621	+	3.48046i	0.0790056	+	0.116209i
$898$	−8.85387	+	33.0077i	−0.295457	+	1.10148i
$899$	−40.5040			−1.35088
$900$	4.06247	−	3.21865i	0.135416	−	0.107288i
$901$	−8.27824			−0.275788
$902$	−0.00947751	+	0.0353327i	−0.000315567	+	0.00117645i
$903$	−15.8232	−	23.2744i	−0.526564	−	0.774523i
$904$	13.0495	−	13.0285i	0.434019	−	0.433321i
$905$		−	3.58384i		−	0.119131i
$906$	−29.6827	+	10.3335i	−0.986140	+	0.343308i
$907$			43.2105i			1.43478i	0.696672	+	0.717390i	$0.254663\pi$
$907$			43.2105i			1.43478i	−0.696672	+	0.717390i	$0.745337\pi$
$908$	37.9514	+	21.9384i	1.25946	+	0.728052i
$909$	20.7736	+	8.21641i	0.689017	+	0.272521i
$910$	7.77269	+	2.08492i	0.257662	+	0.0691144i
$911$	32.6334			1.08119			0.540596	−	0.841282i	$-0.318199\pi$
$911$	32.6334			1.08119			0.540596	+	0.841282i	$0.318199\pi$
$912$	7.25558	+	3.51552i	0.240256	+	0.116410i
$913$	2.87983			0.0953085
$914$	29.4461	+	7.89852i	0.973990	+	0.261260i
$915$	35.3167	−	24.0103i	1.16753	−	0.793755i
$916$	−7.87539	−	4.55249i	−0.260210	−	0.150419i
$917$		−	31.7737i		−	1.04926i
$918$	−1.24139	+	29.8031i	−0.0409719	+	0.983649i
$919$			31.6193i			1.04303i	0.853243	+	0.521513i	$0.174632\pi$
$919$			31.6193i			1.04303i	−0.853243	+	0.521513i	$0.825368\pi$
$920$	8.79273	−	8.77859i	0.289888	−	0.289422i
$921$	−28.8466	+	19.6116i	−0.950529	+	0.646223i
$922$	6.90762	−	25.7520i	0.227490	−	0.848096i
$923$	−4.15302			−0.136698
$924$	−2.04723	+	0.149597i	−0.0673490	+	0.00492139i
$925$	−5.62222			−0.184857
$926$	−1.60587	+	5.98675i	−0.0527720	+	0.196737i
$927$	−16.4816	−	6.51882i	−0.541326	−	0.214106i
$928$	46.5219	−	12.3987i	1.52715	−	0.407006i
$929$			13.3308i			0.437370i	0.975796	+	0.218685i	$0.0701767\pi$
$929$			13.3308i			0.437370i	−0.975796	+	0.218685i	$0.929823\pi$
$930$	−9.28081	−	26.6588i	−0.304330	−	0.874176i
$931$			4.56419i			0.149585i
$932$	26.5989	−	46.0136i	0.871275	−	1.50722i
$933$	−16.2552	−	23.9098i	−0.532172	−	0.782771i
$934$	34.2160	+	9.17797i	1.11958	+	0.300312i
$935$	3.32000			0.108576
$936$	−10.4329	+	4.50911i	−0.341010	+	0.147385i
$937$	12.1995			0.398539			0.199269	−	0.979945i	$-0.436143\pi$
$937$	12.1995			0.398539			0.199269	+	0.979945i	$0.436143\pi$
$938$	2.39637	+	0.642794i	0.0782442	+	0.0209880i
$939$	28.0976	+	41.3288i	0.916931	+	1.34871i
$940$	21.3866	−	36.9969i	0.697555	−	1.20671i
$941$		−	16.5447i		−	0.539342i	−0.962953	−	0.269671i	$-0.913085\pi$
$941$		−	16.5447i		−	0.539342i	0.962953	−	0.269671i	$-0.0869150\pi$
$942$	−15.1426	−	43.4965i	−0.493371	−	1.41719i
$943$		−	0.138930i		−	0.00452418i
$944$	29.4387	+	51.1159i	0.958149	+	1.66368i
$945$	21.5407	−	4.82685i	0.700720	−	0.157017i
$946$	1.14617	−	4.27297i	0.0372651	−	0.138926i
$947$	−46.4875			−1.51064			−0.755321	−	0.655355i	$-0.772519\pi$
$947$	−46.4875			−1.51064			−0.755321	+	0.655355i	$0.772519\pi$
$948$	−15.0320	+	1.09843i	−0.488218	+	0.0356755i
$949$	−15.7794			−0.512221
$950$	−0.368314	+	1.37310i	−0.0119497	+	0.0445491i
$951$	49.9234	−	33.9407i	1.61888	−	1.10060i
$952$	14.2314	+	14.2543i	0.461242	+	0.461985i
$953$		−	27.7409i		−	0.898617i	−0.893377	−	0.449309i	$-0.851670\pi$
$953$		−	27.7409i		−	0.898617i	0.893377	−	0.449309i	$-0.148330\pi$
$954$	−6.94667	−	5.15816i	−0.224907	−	0.167002i
$955$		−	24.1687i		−	0.782081i
$956$	−0.976338	−	0.564387i	−0.0315770	−	0.0182536i
$957$	4.11762	−	2.79939i	0.133104	−	0.0904914i
$958$	−16.8611	−	4.52278i	−0.544759	−	0.146124i
$959$	12.2766			0.396433
$960$	18.8202	+	27.7787i	0.607420	+	0.896553i
$961$	8.35200			0.269419
$962$	11.9078	+	3.19411i	0.383924	+	0.102982i
$963$	3.19994	−	8.09043i	0.103117	−	0.260711i
$964$	−35.8312	−	20.7128i	−1.15404	−	0.667113i
$965$			25.6650i			0.826187i
$966$	7.36232	−	2.56307i	0.236879	−	0.0824653i
$967$		−	36.3700i		−	1.16958i	−0.811184	−	0.584791i	$-0.801177\pi$
$967$		−	36.3700i		−	1.16958i	0.811184	−	0.584791i	$-0.198823\pi$
$968$	21.7543	+	21.7893i	0.699210	+	0.700336i
$969$	−4.60000	−	6.76614i	−0.147773	−	0.217360i
$970$	0.651175	−	2.42762i	0.0209080	−	0.0779461i
$971$	52.5091			1.68510			0.842548	−	0.538621i	$-0.181055\pi$
$971$	52.5091			1.68510			0.842548	+	0.538621i	$0.181055\pi$
$972$	−19.6120	+	24.2357i	−0.629054	+	0.777361i
$973$	−2.20315			−0.0706296
$974$	−12.4435	+	46.3901i	−0.398716	+	1.48643i
$975$	−1.12676	−	1.65734i	−0.0360851	−	0.0530775i
$976$	20.3261	+	35.2933i	0.650624	+	1.12971i
$977$			26.6635i			0.853040i	0.904478	+	0.426520i	$0.140261\pi$
$977$			26.6635i			0.853040i	−0.904478	+	0.426520i	$0.859739\pi$
$978$	19.9906	−	6.95940i	0.639230	−	0.222537i
$979$		−	0.0777441i		−	0.00248471i
$980$	−9.50636	+	16.4451i	−0.303670	+	0.525320i
$981$	3.68756	−	9.32328i	0.117735	−	0.297669i
$982$	6.21807	+	1.66791i	0.198427	+	0.0532253i
$983$	44.2612			1.41171			0.705857	−	0.708354i	$-0.250562\pi$
$983$	44.2612			1.41171			0.705857	+	0.708354i	$0.250562\pi$
$984$	0.368497	+	0.0705346i	0.0117472	+	0.00224856i
$985$	−0.503262			−0.0160353
$986$	−47.1901	−	12.6581i	−1.50284	−	0.403117i
$987$	22.1733	−	15.0747i	0.705785	−	0.479832i
$988$	1.56018	−	2.69896i	0.0496358	−	0.0858654i
$989$			16.8015i			0.534258i
$990$	2.78598	+	2.06869i	0.0885442	+	0.0657473i
$991$			19.8598i			0.630867i	0.948948	+	0.315433i	$0.102150\pi$
$991$			19.8598i			0.630867i	−0.948948	+	0.315433i	$0.897850\pi$
$992$	26.0129	−	6.93278i	0.825911	−	0.220116i
$993$	33.7293	−	22.9311i	1.07037	−	0.727697i
$994$	−1.99301	+	7.43004i	−0.0632144	+	0.235667i
$995$	14.1638			0.449022
$996$	−2.15254	−	29.4574i	−0.0682058	−	0.933393i
$997$	−10.9554			−0.346961			−0.173480	−	0.984837i	$-0.555501\pi$
$997$	−10.9554			−0.346961			−0.173480	+	0.984837i	$0.555501\pi$
$998$	−8.41248	+	31.3622i	−0.266292	+	0.992752i
$999$	33.0006	−	7.39477i	1.04409	−	0.233960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.13	✓	128
3.2	odd	2	inner	804.2.c.b.671.116	yes	128
4.3	odd	2	inner	804.2.c.b.671.115	yes	128
12.11	even	2	inner	804.2.c.b.671.14	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.13	✓	128	1.1	even	1	trivial
804.2.c.b.671.14	yes	128	12.11	even	2	inner
804.2.c.b.671.115	yes	128	4.3	odd	2	inner
804.2.c.b.671.116	yes	128	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36593 - 0.366392i) q^{2} +(-0.973809 - 1.43237i) q^{3} +(1.73151 + 1.00093i) q^{4} +2.42154i q^{5} +(0.805342 + 2.31331i) q^{6} -1.75439i q^{7} +(-1.99839 - 2.00161i) q^{8} +(-1.10339 + 2.78972i) q^{9} +O(q^{10})\)	\(q+(-1.36593 - 0.366392i) q^{2} +(-0.973809 - 1.43237i) q^{3} +(1.73151 + 1.00093i) q^{4} +2.42154i q^{5} +(0.805342 + 2.31331i) q^{6} -1.75439i q^{7} +(-1.99839 - 2.00161i) q^{8} +(-1.10339 + 2.78972i) q^{9} +(0.887230 - 3.30764i) q^{10} +0.337759 q^{11} +(-0.252459 - 3.45489i) q^{12} -1.33945 q^{13} +(-0.642794 + 2.39637i) q^{14} +(3.46855 - 2.35811i) q^{15} +(1.99628 + 3.46624i) q^{16} -4.05920i q^{17} +(2.52928 - 3.40628i) q^{18} +1.16371i q^{19} +(-2.42378 + 4.19292i) q^{20} +(-2.51294 + 1.70844i) q^{21} +(-0.461354 - 0.123752i) q^{22} +1.81407 q^{23} +(-0.921002 + 4.81163i) q^{24} -0.863832 q^{25} +(1.82959 + 0.490764i) q^{26} +(5.07041 - 1.13618i) q^{27} +(1.75602 - 3.03775i) q^{28} +8.51104i q^{29} +(-5.60177 + 1.95016i) q^{30} +4.75899i q^{31} +(-1.45677 - 5.46606i) q^{32} +(-0.328913 - 0.483798i) q^{33} +(-1.48726 + 5.54458i) q^{34} +4.24832 q^{35} +(-4.70285 + 3.72602i) q^{36} +6.50846 q^{37} +(0.426373 - 1.58954i) q^{38} +(1.30437 + 1.91860i) q^{39} +(4.84696 - 4.83917i) q^{40} -0.0765846i q^{41} +(4.05846 - 1.41288i) q^{42} +9.26180i q^{43} +(0.584835 + 0.338073i) q^{44} +(-6.75540 - 2.67191i) q^{45} +(-2.47789 - 0.664660i) q^{46} -8.82365 q^{47} +(3.02096 - 6.23488i) q^{48} +3.92212 q^{49} +(1.17993 + 0.316501i) q^{50} +(-5.81430 + 3.95289i) q^{51} +(-2.31928 - 1.34069i) q^{52} -2.03937i q^{53} +(-7.34210 - 0.305820i) q^{54} +0.817896i q^{55} +(-3.51160 + 3.50596i) q^{56} +(1.66686 - 1.13323i) q^{57} +(3.11837 - 11.6255i) q^{58} +14.7468 q^{59} +(8.36614 - 0.611338i) q^{60} +10.1820 q^{61} +(1.74365 - 6.50044i) q^{62} +(4.89425 + 1.93578i) q^{63} +(-0.0128704 + 7.99999i) q^{64} -3.24353i q^{65} +(0.272011 + 0.781343i) q^{66} -1.00000i q^{67} +(4.06297 - 7.02857i) q^{68} +(-1.76656 - 2.59843i) q^{69} +(-5.80289 - 1.55655i) q^{70} +3.10054 q^{71} +(7.78893 - 3.36638i) q^{72} +11.7805 q^{73} +(-8.89008 - 2.38464i) q^{74} +(0.841207 + 1.23733i) q^{75} +(-1.16479 + 2.01498i) q^{76} -0.592561i q^{77} +(-1.07872 - 3.09857i) q^{78} -4.35094i q^{79} +(-8.39363 + 4.83407i) q^{80} +(-6.56505 - 6.15631i) q^{81} +(-0.0280600 + 0.104609i) q^{82} +8.52629 q^{83} +(-6.06122 + 0.442911i) q^{84} +9.82950 q^{85} +(3.39345 - 12.6509i) q^{86} +(12.1910 - 8.28812i) q^{87} +(-0.674975 - 0.676061i) q^{88} -0.230176i q^{89} +(8.24842 + 6.12475i) q^{90} +2.34992i q^{91} +(3.14109 + 1.81575i) q^{92} +(6.81666 - 4.63435i) q^{93} +(12.0525 + 3.23291i) q^{94} -2.81796 q^{95} +(-6.41082 + 7.40954i) q^{96} +0.733942 q^{97} +(-5.35732 - 1.43703i) q^{98} +(-0.372681 + 0.942252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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