LMFDB - Embedded newform 819.2.fy.a.344.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(50,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 7]))

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

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

chi := DirichletCharacter("819.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			344.14
Character	$\chi$	$=$	819.344
Dual form			819.2.fy.a.50.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.563544 + 2.10318i) q^{2} +(-1.71440 - 0.246659i) q^{3} +(-2.37372 - 1.37047i) q^{4} +(-0.775066 + 2.89259i) q^{5} +(1.48491 - 3.46668i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.14076 - 1.14076i) q^{8} +(2.87832 + 0.845744i) q^{9} +O(q^{10})$	\(q+(-0.563544 + 2.10318i) q^{2} +(-1.71440 - 0.246659i) q^{3} +(-2.37372 - 1.37047i) q^{4} +(-0.775066 + 2.89259i) q^{5} +(1.48491 - 3.46668i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.14076 - 1.14076i) q^{8} +(2.87832 + 0.845744i) q^{9} +(-5.64684 - 3.26020i) q^{10} +(-1.60810 - 0.430888i) q^{11} +(3.73146 + 2.93502i) q^{12} +(-2.85587 - 2.20091i) q^{13} +(1.88566 - 1.08868i) q^{14} +(2.04226 - 4.76787i) q^{15} +(-0.984577 - 1.70534i) q^{16} +(0.438522 + 0.759542i) q^{17} +(-3.40081 + 5.57700i) q^{18} +(0.110423 + 0.0295877i) q^{19} +(5.80398 - 5.80398i) q^{20} +(1.03785 + 1.38668i) q^{21} +(1.81247 - 3.13928i) q^{22} -4.42750 q^{23} +(-2.23710 + 1.67434i) q^{24} +(-3.43621 - 1.98389i) q^{25} +(6.23830 - 4.76610i) q^{26} +(-4.72597 - 2.15991i) q^{27} +(0.709405 + 2.64754i) q^{28} +(5.46881 - 3.15742i) q^{29} +(8.87676 + 6.98213i) q^{30} +(-6.55354 - 1.75602i) q^{31} +(7.25810 - 1.94480i) q^{32} +(2.65063 + 1.13536i) q^{33} +(-1.84458 + 0.494253i) q^{34} +(2.59342 - 1.49731i) q^{35} +(-5.67325 - 5.95220i) q^{36} +(7.53882 - 2.02002i) q^{37} +(-0.124456 + 0.215565i) q^{38} +(4.35323 + 4.47766i) q^{39} +(2.41559 + 4.18392i) q^{40} +(2.17756 + 2.17756i) q^{41} +(-3.50130 + 1.40132i) q^{42} +0.0653628i q^{43} +(3.22665 + 3.22665i) q^{44} +(-4.67728 + 7.67028i) q^{45} +(2.49509 - 9.31181i) q^{46} +(2.10694 + 7.86319i) q^{47} +(1.26732 + 3.16648i) q^{48} +1.00000i q^{49} +(6.10893 - 6.10893i) q^{50} +(-0.564453 - 1.41032i) q^{51} +(3.76277 + 9.13821i) q^{52} -1.23147i q^{53} +(7.20596 - 8.72235i) q^{54} +(2.49276 - 4.31759i) q^{55} -1.61328 q^{56} +(-0.182011 - 0.0779620i) q^{57} +(3.55869 + 13.2812i) q^{58} +(-1.26502 - 4.72111i) q^{59} +(-11.3819 + 8.51873i) q^{60} +6.24820 q^{61} +(7.38643 - 12.7937i) q^{62} +(-1.43725 - 2.63331i) q^{63} +12.4227i q^{64} +(8.57980 - 6.55502i) q^{65} +(-3.88162 + 4.93492i) q^{66} +(-3.88109 + 3.88109i) q^{67} -2.40392i q^{68} +(7.59049 + 1.09208i) q^{69} +(1.68760 + 6.29823i) q^{70} +(-0.779135 + 2.90777i) q^{71} +(4.24827 - 2.31869i) q^{72} +(0.741136 + 0.741136i) q^{73} +16.9938i q^{74} +(5.40168 + 4.24876i) q^{75} +(-0.221564 - 0.221564i) q^{76} +(0.832411 + 1.44178i) q^{77} +(-11.8705 + 6.63225i) q^{78} +(8.18837 - 14.1827i) q^{79} +(5.69595 - 1.52623i) q^{80} +(7.56943 + 4.86864i) q^{81} +(-5.80696 + 3.35265i) q^{82} +(9.52386 - 2.55191i) q^{83} +(-0.563163 - 4.71391i) q^{84} +(-2.53693 + 0.679767i) q^{85} +(-0.137470 - 0.0368349i) q^{86} +(-10.1545 + 4.06414i) q^{87} +(-2.32600 + 1.34291i) q^{88} +(-2.63978 - 9.85179i) q^{89} +(-13.4961 - 14.1597i) q^{90} +(0.463132 + 3.57568i) q^{91} +(10.5096 + 6.06774i) q^{92} +(10.8022 + 4.62700i) q^{93} -17.7250 q^{94} +(-0.171170 + 0.296476i) q^{95} +(-12.9230 + 1.54389i) q^{96} +(-8.02948 + 8.02948i) q^{97} +(-2.10318 - 0.563544i) q^{98} +(-4.26419 - 2.60027i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$1$

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 $

$2$	−0.563544	+	2.10318i	−0.398486	+	1.48717i	0.417275	+	0.908780i	$0.362985\pi$
$2$	−0.563544	+	2.10318i	−0.398486	+	1.48717i	−0.815761	+	0.578390i	$0.803681\pi$
$3$	−1.71440	−	0.246659i	−0.989808	−	0.142409i
$3$	−1.71440	−	0.246659i	−0.989808	−	0.142409i
$4$	−2.37372	−	1.37047i	−1.18686	−	0.685233i
$5$	−0.775066	+	2.89259i	−0.346620	+	1.29360i	0.544088	+	0.839028i	$0.316876\pi$
$5$	−0.775066	+	2.89259i	−0.346620	+	1.29360i	−0.890708	+	0.454576i	$0.849791\pi$
$6$	1.48491	−	3.46668i	0.606211	−	1.41526i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	1.14076	−	1.14076i	0.403321	−	0.403321i
$9$	2.87832	+	0.845744i	0.959439	+	0.281915i
$10$	−5.64684	−	3.26020i	−1.78569	−	1.03097i
$11$	−1.60810	−	0.430888i	−0.484859	−	0.129918i	0.00810527	−	0.999967i	$-0.497420\pi$
$11$	−1.60810	−	0.430888i	−0.484859	−	0.129918i	−0.492964	+	0.870050i	$0.664087\pi$
$12$	3.73146	+	2.93502i	1.07718	+	0.847268i
$13$	−2.85587	−	2.20091i	−0.792077	−	0.610421i
$13$	−2.85587	−	2.20091i	−0.792077	−	0.610421i
$14$	1.88566	−	1.08868i	0.503963	−	0.290963i
$15$	2.04226	−	4.76787i	0.527308	−	1.23106i
$16$	−0.984577	−	1.70534i	−0.246144	−	0.426334i
$17$	0.438522	+	0.759542i	0.106357	+	0.184216i	0.914292	−	0.405056i	$-0.132748\pi$
$17$	0.438522	+	0.759542i	0.106357	+	0.184216i	−0.807935	+	0.589272i	$0.799415\pi$
$18$	−3.40081	+	5.57700i	−0.801578	+	1.31451i
$19$	0.110423	+	0.0295877i	0.0253328	+	0.00678789i	0.271463	−	0.962449i	$-0.412492\pi$
$19$	0.110423	+	0.0295877i	0.0253328	+	0.00678789i	−0.246130	+	0.969237i	$0.579159\pi$
$20$	5.80398	−	5.80398i	1.29781	−	1.29781i
$21$	1.03785	+	1.38668i	0.226477	+	0.302598i
$22$	1.81247	−	3.13928i	0.386419	−	0.669297i
$23$	−4.42750			−0.923197			−0.461598	−	0.887089i	$-0.652724\pi$
$23$	−4.42750			−0.923197			−0.461598	+	0.887089i	$0.652724\pi$
$24$	−2.23710	+	1.67434i	−0.456646	+	0.341774i
$25$	−3.43621	−	1.98389i	−0.687241	−	0.396779i
$26$	6.23830	−	4.76610i	1.22343	−	0.934709i
$27$	−4.72597	−	2.15991i	−0.909514	−	0.415674i
$28$	0.709405	+	2.64754i	0.134065	+	0.500338i
$29$	5.46881	−	3.15742i	1.01553	−	0.586318i	0.102726	−	0.994710i	$-0.467244\pi$
$29$	5.46881	−	3.15742i	1.01553	−	0.586318i	0.912807	+	0.408392i	$0.133910\pi$
$30$	8.87676	+	6.98213i	1.62067	+	1.27476i
$31$	−6.55354	−	1.75602i	−1.17705	−	0.315390i	−0.383295	−	0.923626i	$-0.625211\pi$
$31$	−6.55354	−	1.75602i	−1.17705	−	0.315390i	−0.793756	+	0.608236i	$0.791877\pi$
$32$	7.25810	−	1.94480i	1.28306	−	0.343796i
$33$	2.65063	+	1.13536i	0.461416	+	0.197642i
$34$	−1.84458	+	0.494253i	−0.316342	+	0.0847637i
$35$	2.59342	−	1.49731i	0.438368	−	0.253092i
$36$	−5.67325	−	5.95220i	−0.945542	−	0.992033i
$37$	7.53882	−	2.02002i	1.23937	−	0.332089i	0.421151	−	0.906991i	$-0.361626\pi$
$37$	7.53882	−	2.02002i	1.23937	−	0.332089i	0.818223	+	0.574901i	$0.194960\pi$
$38$	−0.124456	+	0.215565i	−0.0201895	+	0.0349692i
$39$	4.35323	+	4.47766i	0.697075	+	0.716999i
$40$	2.41559	+	4.18392i	0.381938	+	0.661536i
$41$	2.17756	+	2.17756i	0.340079	+	0.340079i	0.856397	−	0.516318i	$-0.172698\pi$
$41$	2.17756	+	2.17756i	0.340079	+	0.340079i	−0.516318	+	0.856397i	$0.672698\pi$
$42$	−3.50130	+	1.40132i	−0.540262	+	0.216229i
$43$			0.0653628i			0.00996774i	0.999988	+	0.00498387i	$0.00158642\pi$
$43$			0.0653628i			0.00996774i	−0.999988	+	0.00498387i	$0.998414\pi$
$44$	3.22665	+	3.22665i	0.486435	+	0.486435i
$45$	−4.67728	+	7.67028i	−0.697247	+	1.14342i
$46$	2.49509	−	9.31181i	0.367881	−	1.37295i
$47$	2.10694	+	7.86319i	0.307328	+	1.14696i	0.930923	+	0.365216i	$0.119005\pi$
$47$	2.10694	+	7.86319i	0.307328	+	1.14696i	−0.623595	+	0.781748i	$0.714328\pi$
$48$	1.26732	+	3.16648i	0.182922	+	0.457042i
$49$			1.00000i			0.142857i
$50$	6.10893	−	6.10893i	0.863934	−	0.863934i
$51$	−0.564453	−	1.41032i	−0.0790392	−	0.197485i
$52$	3.76277	+	9.13821i	0.521802	+	1.26724i
$53$		−	1.23147i		−	0.169155i	−0.996417	−	0.0845775i	$-0.973046\pi$
$53$		−	1.23147i		−	0.169155i	0.996417	−	0.0845775i	$-0.0269541\pi$
$54$	7.20596	−	8.72235i	0.980607	−	1.18696i
$55$	2.49276	−	4.31759i	0.336124	−	0.582184i
$56$	−1.61328			−0.215584
$57$	−0.182011	−	0.0779620i	−0.0241079	−	0.0103263i
$58$	3.55869	+	13.2812i	0.467279	+	1.74391i
$59$	−1.26502	−	4.72111i	−0.164691	−	0.614637i	−0.998079	−	0.0619482i	$-0.980269\pi$
$59$	−1.26502	−	4.72111i	−0.164691	−	0.614637i	0.833388	−	0.552688i	$-0.186398\pi$
$60$	−11.3819	+	8.51873i	−1.46940	+	1.09976i
$61$	6.24820			0.799999			0.400000	−	0.916515i	$-0.369010\pi$
$61$	6.24820			0.799999			0.400000	+	0.916515i	$0.369010\pi$
$62$	7.38643	−	12.7937i	0.938077	−	1.62480i
$63$	−1.43725	−	2.63331i	−0.181076	−	0.331766i
$64$			12.4227i			1.55284i
$65$	8.57980	−	6.55502i	1.06419	−	0.813050i
$66$	−3.88162	+	4.93492i	−0.477794	+	0.607446i
$67$	−3.88109	+	3.88109i	−0.474151	+	0.474151i	−0.903255	−	0.429104i	$-0.858829\pi$
$67$	−3.88109	+	3.88109i	−0.474151	+	0.474151i	0.429104	+	0.903255i	$0.358829\pi$
$68$		−	2.40392i		−	0.291518i
$69$	7.59049	+	1.09208i	0.913788	+	0.131471i
$70$	1.68760	+	6.29823i	0.201707	+	0.752782i
$71$	−0.779135	+	2.90777i	−0.0924663	+	0.345089i	−0.996623	−	0.0821117i	$-0.973834\pi$
$71$	−0.779135	+	2.90777i	−0.0924663	+	0.345089i	0.904157	+	0.427201i	$0.140500\pi$
$72$	4.24827	−	2.31869i	0.500664	−	0.273260i
$73$	0.741136	+	0.741136i	0.0867434	+	0.0867434i	0.749147	−	0.662404i	$-0.230464\pi$
$73$	0.741136	+	0.741136i	0.0867434	+	0.0867434i	−0.662404	+	0.749147i	$0.730464\pi$
$74$			16.9938i			1.97549i
$75$	5.40168	+	4.24876i	0.623732	+	0.490604i
$76$	−0.221564	−	0.221564i	−0.0254151	−	0.0254151i
$77$	0.832411	+	1.44178i	0.0948621	+	0.164306i
$78$	−11.8705	+	6.63225i	−1.34407	+	0.750954i
$79$	8.18837	−	14.1827i	0.921263	−	1.59567i	0.123800	−	0.992307i	$-0.460492\pi$
$79$	8.18837	−	14.1827i	0.921263	−	1.59567i	0.797463	−	0.603368i	$-0.206175\pi$
$80$	5.69595	−	1.52623i	0.636827	−	0.170637i
$81$	7.56943	+	4.86864i	0.841048	+	0.540960i
$82$	−5.80696	+	3.35265i	−0.641271	+	0.370238i
$83$	9.52386	−	2.55191i	1.04538	−	0.280109i	0.305039	−	0.952340i	$-0.401331\pi$
$83$	9.52386	−	2.55191i	1.04538	−	0.280109i	0.740341	+	0.672231i	$0.234664\pi$
$84$	−0.563163	−	4.71391i	−0.0614462	−	0.514330i
$85$	−2.53693	+	0.679767i	−0.275168	+	0.0737311i
$86$	−0.137470	−	0.0368349i	−0.0148237	−	0.00397201i
$87$	−10.1545	+	4.06414i	−1.08868	+	0.435722i
$88$	−2.32600	+	1.34291i	−0.247952	+	0.143155i
$89$	−2.63978	−	9.85179i	−0.279816	−	1.04429i	−0.952545	−	0.304398i	$-0.901545\pi$
$89$	−2.63978	−	9.85179i	−0.279816	−	1.04429i	0.672729	−	0.739889i	$-0.265122\pi$
$90$	−13.4961	−	14.1597i	−1.42261	−	1.49256i
$91$	0.463132	+	3.57568i	0.0485495	+	0.374833i
$92$	10.5096	+	6.06774i	1.09570	+	0.632605i
$93$	10.8022	+	4.62700i	1.12014	+	0.479798i
$94$	−17.7250			−1.82820
$95$	−0.171170	+	0.296476i	−0.0175617	+	0.0304177i
$96$	−12.9230	+	1.54389i	−1.31895	+	0.157572i
$97$	−8.02948	+	8.02948i	−0.815270	+	0.815270i	−0.985418	−	0.170149i	$-0.945575\pi$
$97$	−8.02948	+	8.02948i	−0.815270	+	0.815270i	0.170149	+	0.985418i	$0.445575\pi$
$98$	−2.10318	−	0.563544i	−0.212453	−	0.0569266i
$99$	−4.26419	−	2.60027i	−0.428567	−	0.261337i
$100$	5.43772	+	9.41841i	0.543772	+	0.941841i
$101$	−3.18060	−	5.50897i	−0.316482	−	0.548163i	0.663269	−	0.748381i	$-0.269168\pi$
$101$	−3.18060	−	5.50897i	−0.316482	−	0.548163i	−0.979751	+	0.200218i	$0.935835\pi$
$102$	3.28425	−	0.392364i	0.325189	−	0.0388498i
$103$	−11.1554	+	6.44056i	−1.09917	+	0.634608i	−0.936004	−	0.351991i	$-0.885505\pi$
$103$	−11.1554	+	6.44056i	−1.09917	+	0.634608i	−0.163169	+	0.986598i	$0.552172\pi$
$104$	−5.76859	+	0.747163i	−0.565656	+	0.0732654i
$105$	−4.81548	+	1.92730i	−0.469943	+	0.188085i
$106$	2.58999	+	0.693986i	0.251562	+	0.0674059i
$107$	−10.6455	−	6.14621i	−1.02914	−	0.594176i	−0.112405	−	0.993663i	$-0.535855\pi$
$107$	−10.6455	−	6.14621i	−1.02914	−	0.594176i	−0.916739	+	0.399486i	$0.869189\pi$
$108$	8.25804	+	11.6038i	0.794630	+	1.11658i
$109$	9.19135	−	9.19135i	0.880372	−	0.880372i	−0.113200	−	0.993572i	$-0.536110\pi$
$109$	9.19135	−	9.19135i	0.880372	−	0.880372i	0.993572	+	0.113200i	$0.0361101\pi$
$110$	7.67587	+	7.67587i	0.731865	+	0.731865i
$111$	−13.4228	+	1.60360i	−1.27403	+	0.152207i
$112$	−0.509655	+	1.90206i	−0.0481578	+	0.179728i
$113$	−7.99176	−	4.61405i	−0.751802	−	0.434053i	0.0745428	−	0.997218i	$-0.476250\pi$
$113$	−7.99176	−	4.61405i	−0.751802	−	0.434053i	−0.826345	+	0.563165i	$0.809584\pi$
$114$	0.266539	−	0.338866i	0.0249637	−	0.0317377i
$115$	3.43160	−	12.8069i	0.319999	−	1.19425i
$116$	−17.3085			−1.60706
$117$	−6.35871	−	8.75025i	−0.587863	−	0.808961i
$118$	10.6422			0.979696
$119$	0.226996	−	0.847159i	0.0208087	−	0.0776590i
$120$	−3.10928	−	7.76874i	−0.283837	−	0.709185i
$121$	−7.12597	−	4.11418i	−0.647816	−	0.374017i
$122$	−3.52114	+	13.1411i	−0.318789	+	1.18974i
$123$	−3.19610	−	4.27033i	−0.288182	−	0.385043i
$124$	13.1497	+	13.1497i	1.18088	+	1.18088i
$125$	−2.18573	+	2.18573i	−0.195497	+	0.195497i
$126$	6.34827	−	1.53880i	0.565549	−	0.137087i
$127$	−9.66065	−	5.57758i	−0.857244	−	0.494930i	0.00584412	−	0.999983i	$-0.498140\pi$
$127$	−9.66065	−	5.57758i	−0.857244	−	0.494930i	−0.863089	+	0.505053i	$0.831473\pi$
$128$	−11.6110	−	3.11116i	−1.02628	−	0.274990i
$129$	0.0161224	−	0.112058i	0.00141949	−	0.00986615i
$130$	8.95125	+	21.7389i	0.785077	+	1.90663i
$131$	−16.7910	+	9.69431i	−1.46704	+	0.846996i	−0.999320	−	0.0368811i	$-0.988258\pi$
$131$	−16.7910	+	9.69431i	−1.46704	+	0.846996i	−0.467720	+	0.883877i	$0.654924\pi$
$132$	−4.73587	−	6.32764i	−0.412205	−	0.550750i
$133$	−0.0571591	−	0.0990025i	−0.00495632	−	0.00858461i
$134$	−5.97546	−	10.3498i	−0.516201	−	0.894086i
$135$	9.91066	−	11.9962i	0.852974	−	1.03247i
$136$	1.36671	+	0.366208i	0.117194	+	0.0314021i
$137$	13.9052	−	13.9052i	1.18800	−	1.18800i	0.210383	−	0.977619i	$-0.432529\pi$
$137$	13.9052	−	13.9052i	1.18800	−	1.18800i	0.977619	−	0.210383i	$-0.0674711\pi$
$138$	−6.57442	+	15.3487i	−0.559652	+	1.30657i
$139$	8.89085	−	15.3994i	0.754112	−	1.30616i	−0.191703	−	0.981453i	$-0.561401\pi$
$139$	8.89085	−	15.3994i	0.754112	−	1.30616i	0.945815	−	0.324707i	$-0.105266\pi$
$140$	−8.20807			−0.693708
$141$	−1.67260	−	14.0003i	−0.140858	−	1.17904i
$142$	−5.67648	−	3.27732i	−0.476360	−	0.275026i
$143$	3.64417	+	4.76983i	0.304741	+	0.398873i
$144$	−1.39165	−	5.74121i	−0.115971	−	0.478434i
$145$	4.89442	+	18.2662i	0.406459	+	1.51693i
$146$	−1.97640	+	1.14108i	−0.163568	+	0.0944361i
$147$	0.246659	−	1.71440i	0.0203441	−	0.141401i
$148$	−20.6634	−	5.53674i	−1.69852	−	0.455117i
$149$	4.54029	−	1.21657i	0.371955	−	0.0996651i	−0.0679988	−	0.997685i	$-0.521661\pi$
$149$	4.54029	−	1.21657i	0.371955	−	0.0996651i	0.439954	+	0.898020i	$0.354995\pi$
$150$	−11.9800	+	8.96632i	−0.978160	+	0.732097i
$151$	−6.09949	+	1.63435i	−0.496370	+	0.133002i	−0.498315	−	0.866996i	$-0.666048\pi$
$151$	−6.09949	+	1.63435i	−0.496370	+	0.133002i	0.00194492	+	0.999998i	$0.499381\pi$
$152$	0.159719	−	0.0922138i	0.0129549	−	0.00747953i
$153$	0.619827	+	2.55708i	0.0501101	+	0.206728i
$154$	−3.50142	+	0.938201i	−0.282152	+	0.0756024i
$155$	10.1589	−	17.5957i	0.815980	−	1.41332i
$156$	−4.19686	−	16.5946i	−0.336018	−	1.32863i
$157$	−8.81631	−	15.2703i	−0.703618	−	1.21870i	−0.967188	−	0.254062i	$-0.918233\pi$
$157$	−8.81631	−	15.2703i	−0.703618	−	1.21870i	0.263570	−	0.964640i	$-0.415100\pi$
$158$	25.2141	+	25.2141i	2.00593	+	2.00593i
$159$	−0.303753	+	2.11122i	−0.0240892	+	0.167431i
$160$			22.5020i			1.77894i
$161$	3.13071	+	3.13071i	0.246735	+	0.246735i
$162$	−14.5053	+	13.1762i	−1.13965	+	1.03522i
$163$	1.42810	−	5.32975i	0.111858	−	0.417458i	−0.887175	−	0.461433i	$-0.847335\pi$
$163$	1.42810	−	5.32975i	0.111858	−	0.417458i	0.999033	+	0.0439747i	$0.0140021\pi$
$164$	−2.18464	−	8.15320i	−0.170592	−	0.636658i
$165$	−5.33856	+	6.78720i	−0.415606	+	0.528383i
$166$			21.4685i			1.66628i
$167$	0.302751	−	0.302751i	0.0234276	−	0.0234276i	−0.695296	−	0.718724i	$-0.744727\pi$
$167$	0.302751	−	0.302751i	0.0234276	−	0.0234276i	0.718724	+	0.695296i	$0.244727\pi$
$168$	2.76581	+	0.397931i	0.213387	+	0.0307011i
$169$	3.31203	+	12.5710i	0.254771	+	0.967001i
$170$		−	5.71868i		−	0.438603i
$171$	0.292809	+	0.178552i	0.0223916	+	0.0136543i
$172$	0.0895776	−	0.155153i	0.00683022	−	0.0118303i
$173$	−18.2583			−1.38815			−0.694076	−	0.719901i	$-0.744187\pi$
$173$	−18.2583			−1.38815			−0.694076	+	0.719901i	$0.744187\pi$
$174$	−2.82508	−	23.6471i	−0.214169	−	1.79268i
$175$	1.02694	+	3.83259i	0.0776293	+	0.289717i
$176$	0.848485	+	3.16659i	0.0639569	+	0.238691i
$177$	1.00424	+	8.40589i	0.0754832	+	0.631826i
$178$	22.2077			1.66454
$179$	1.89163	−	3.27641i	0.141387	−	0.244890i	−0.786632	−	0.617422i	$-0.788177\pi$
$179$	1.89163	−	3.27641i	0.141387	−	0.244890i	0.928019	+	0.372532i	$0.121510\pi$
$180$	21.6144	−	11.7970i	1.61104	−	0.879298i
$181$		−	13.3627i		−	0.993240i	−0.867968	−	0.496620i	$-0.834574\pi$
$181$		−	13.3627i		−	0.993240i	0.867968	−	0.496620i	$-0.165426\pi$
$182$	−7.78129	−	1.04101i	−0.576787	−	0.0771646i
$183$	−10.7119	−	1.54118i	−0.791846	−	0.113927i
$184$	−5.05073	+	5.05073i	−0.372344	+	0.372344i
$185$			23.3723i			1.71837i
$186$	−15.8189	+	20.1115i	−1.15990	+	1.47465i
$187$	−0.377907	−	1.41037i	−0.0276353	−	0.103136i
$188$	5.77497	−	21.5525i	0.421183	−	1.57188i
$189$	1.81448	+	4.86905i	0.131984	+	0.354171i
$190$	−0.527078	−	0.527078i	−0.0382383	−	0.0382383i
$191$		−	10.2559i		−	0.742093i	−0.928614	−	0.371046i	$-0.878999\pi$
$191$		−	10.2559i		−	0.742093i	0.928614	−	0.371046i	$-0.121001\pi$
$192$	3.06418	−	21.2975i	0.221138	−	1.53702i
$193$	13.2036	+	13.2036i	0.950418	+	0.950418i	0.998828	−	0.0484096i	$-0.0154153\pi$
$193$	13.2036	+	13.2036i	0.950418	+	0.950418i	−0.0484096	+	0.998828i	$0.515415\pi$
$194$	−12.3624	−	21.4124i	−0.887571	−	1.53732i
$195$	−16.3261	+	9.12161i	−1.16913	+	0.653212i
$196$	1.37047	−	2.37372i	0.0978904	−	0.169551i
$197$	21.8280	−	5.84879i	1.55518	−	0.416709i	0.624046	−	0.781388i	$-0.285488\pi$
$197$	21.8280	−	5.84879i	1.55518	−	0.416709i	0.931133	+	0.364679i	$0.118821\pi$
$198$	7.87188	−	7.50297i	0.559430	−	0.533213i
$199$	19.0591	−	11.0038i	1.35107	−	0.780038i	0.362667	−	0.931919i	$-0.381866\pi$
$199$	19.0591	−	11.0038i	1.35107	−	0.780038i	0.988399	+	0.151881i	$0.0485330\pi$
$200$	−6.18305	+	1.65674i	−0.437208	+	0.117149i
$201$	7.61105	−	5.69643i	0.536842	−	0.401795i
$202$	13.3787	−	3.58482i	0.941325	−	0.252227i
$203$	−6.09967	−	1.63440i	−0.428113	−	0.114712i
$204$	−0.592949	+	4.12127i	−0.0415147	+	0.288547i
$205$	−7.98655	+	4.61104i	−0.557805	+	0.322049i
$206$	−7.25909	−	27.0913i	−0.505764	−	1.88754i
$207$	−12.7437	−	3.74453i	−0.885752	−	0.260263i
$208$	−0.941459	+	7.03719i	−0.0652785	+	0.487941i
$209$	−0.164822	−	0.0951598i	−0.0114009	−	0.00658234i
$210$	−1.33971	−	11.2139i	−0.0924487	−	0.773835i
$211$	16.1424			1.11129			0.555643	−	0.831421i	$-0.312472\pi$
$211$	16.1424			1.11129			0.555643	+	0.831421i	$0.312472\pi$
$212$	−1.68768	+	2.92315i	−0.115911	+	0.200763i
$213$	2.05298	−	4.79290i	0.140668	−	0.328404i
$214$	18.9258	−	18.9258i	1.29374	−	1.29374i
$215$	−0.189068	−	0.0506605i	−0.0128943	−	0.00345502i
$216$	−7.85515	+	2.92727i	−0.534476	+	0.199176i
$217$	3.39236	+	5.87575i	0.230289	+	0.398872i
$218$	14.1513	+	24.5108i	0.958447	+	1.66008i
$219$	−1.08779	−	1.45341i	−0.0735063	−	0.0982123i
$220$	−11.8342	+	6.83249i	−0.797863	+	0.460646i
$221$	0.419318	−	3.13430i	0.0282064	−	0.210836i
$222$	4.19169	−	29.1342i	0.281328	−	1.95536i
$223$	−26.1678	−	7.01163i	−1.75232	−	0.469533i	−0.767203	−	0.641404i	$-0.778352\pi$
$223$	−26.1678	−	7.01163i	−1.75232	−	0.469533i	−0.985119	+	0.171871i	$0.945019\pi$
$224$	−6.50744	−	3.75707i	−0.434796	−	0.251030i
$225$	−8.21263	−	8.61643i	−0.547509	−	0.574429i
$226$	14.2079	−	14.2079i	0.945093	−	0.945093i
$227$	−0.509102	−	0.509102i	−0.0337903	−	0.0337903i	0.690010	−	0.723800i	$-0.257606\pi$
$227$	−0.509102	−	0.509102i	−0.0337903	−	0.0337903i	−0.723800	+	0.690010i	$0.757606\pi$
$228$	0.325198	+	0.434499i	0.0215367	+	0.0287754i
$229$	−2.44737	+	9.13370i	−0.161727	+	0.603572i	0.836708	+	0.547649i	$0.184477\pi$
$229$	−2.44737	+	9.13370i	−0.161727	+	0.603572i	−0.998435	+	0.0559233i	$0.982190\pi$
$230$	25.0014	+	14.4345i	1.64854	+	0.951785i
$231$	−1.07146	−	2.67710i	−0.0704966	−	0.176141i
$232$	2.63675	−	9.84049i	0.173111	−	0.646060i
$233$	−26.6077			−1.74313			−0.871565	−	0.490279i	$-0.836895\pi$
$233$	−26.6077			−1.74313			−0.871565	+	0.490279i	$0.836895\pi$
$234$	21.9867	−	8.44234i	1.43732	−	0.551893i
$235$	−24.3780			−1.59024
$236$	−3.46733	+	12.9403i	−0.225704	+	0.842339i
$237$	−17.5364	+	22.2950i	−1.13911	+	1.44822i
$238$	1.65380	+	0.954824i	0.107200	+	0.0618920i
$239$	2.56301	−	9.56527i	0.165787	−	0.618726i	−0.832151	−	0.554549i	$-0.812891\pi$
$239$	2.56301	−	9.56527i	0.165787	−	0.618726i	0.997939	−	0.0641775i	$-0.0204424\pi$
$240$	−10.1416	+	1.21160i	−0.654636	+	0.0782083i
$241$	−7.25437	−	7.25437i	−0.467295	−	0.467295i	0.433742	−	0.901037i	$-0.357193\pi$
$241$	−7.25437	−	7.25437i	−0.467295	−	0.467295i	−0.901037	+	0.433742i	$0.857193\pi$
$242$	12.6687	−	12.6687i	0.814372	−	0.814372i
$243$	−11.7761	−	10.2139i	−0.755439	−	0.655219i
$244$	−14.8314	−	8.56294i	−0.949486	−	0.548186i
$245$	−2.89259	−	0.775066i	−0.184801	−	0.0495172i
$246$	10.7824	−	4.31543i	0.687460	−	0.275142i
$247$	−0.250234	−	0.327529i	−0.0159220	−	0.0208402i
$248$	−9.47924	+	5.47284i	−0.601932	+	0.347526i
$249$	−16.9571	+	2.02584i	−1.07462	+	0.128382i
$250$	−3.36522	−	5.82873i	−0.212835	−	0.368641i
$251$	−2.35889	−	4.08572i	−0.148892	−	0.257888i	0.781926	−	0.623371i	$-0.214237\pi$
$251$	−2.35889	−	4.08572i	−0.148892	−	0.257888i	−0.930818	+	0.365483i	$0.880904\pi$
$252$	−0.197245	+	8.22043i	−0.0124252	+	0.517838i
$253$	7.11984	+	1.90775i	0.447620	+	0.119939i
$254$	17.1748	−	17.1748i	1.07765	−	1.07765i
$255$	4.51697	−	0.539635i	0.282864	−	0.0337932i
$256$	0.663896	−	1.14990i	0.0414935	−	0.0718688i
$257$	−12.5234			−0.781188			−0.390594	−	0.920563i	$-0.627730\pi$
$257$	−12.5234			−0.781188			−0.390594	+	0.920563i	$0.627730\pi$
$258$	0.226592	+	0.0970577i	0.0141070	+	0.00604255i
$259$	−6.75912	−	3.90238i	−0.419991	−	0.242482i
$260$	−29.3495	+	3.80142i	−1.82018	+	0.235754i
$261$	18.4114	−	4.46284i	1.13963	−	0.276243i
$262$	−10.9263	−	40.7777i	−0.675032	−	2.51925i
$263$	−10.7230	+	6.19091i	−0.661206	+	0.381748i	−0.792736	−	0.609565i	$-0.791344\pi$
$263$	−10.7230	+	6.19091i	−0.661206	+	0.381748i	0.131530	+	0.991312i	$0.458011\pi$
$264$	4.31893	−	1.72856i	0.265811	−	0.106386i
$265$	3.56213	+	0.954469i	0.218820	+	0.0586325i
$266$	0.240431	−	0.0644234i	0.0147418	−	0.00395005i
$267$	2.09560	+	17.5410i	0.128248	+	1.07349i
$268$	14.5315	−	3.89371i	0.887654	−	0.237846i
$269$	−3.06396	+	1.76898i	−0.186813	+	0.107856i	−0.590490	−	0.807045i	$-0.701065\pi$
$269$	−3.06396	+	1.76898i	−0.186813	+	0.107856i	0.403677	+	0.914902i	$0.367732\pi$
$270$	19.6451	+	27.6043i	1.19556	+	1.67994i
$271$	−1.83335	+	0.491244i	−0.111368	+	0.0298409i	−0.314073	−	0.949399i	$-0.601694\pi$
$271$	−1.83335	+	0.491244i	−0.111368	+	0.0298409i	0.202705	+	0.979240i	$0.435027\pi$
$272$	0.863517	−	1.49566i	0.0523584	−	0.0906875i
$273$	0.0879825	−	6.24438i	0.00532494	−	0.377927i
$274$	21.4089	+	37.0813i	1.29336	+	2.24016i
$275$	4.67091	+	4.67091i	0.281667	+	0.281667i
$276$	−16.5210	−	12.9948i	−0.994448	−	0.782195i
$277$			3.76754i			0.226369i	0.993574	+	0.113185i	$0.0361052\pi$
$277$			3.76754i			0.226369i	−0.993574	+	0.113185i	$0.963895\pi$
$278$	27.3773	+	27.3773i	1.64198	+	1.64198i
$279$	−17.3780	−	10.5970i	−1.04040	−	0.634426i
$280$	1.25040	−	4.66656i	0.0747258	−	0.278880i
$281$	3.61832	+	13.5037i	0.215851	+	0.805566i	0.985865	+	0.167540i	$0.0535822\pi$
$281$	3.61832	+	13.5037i	0.215851	+	0.805566i	−0.770015	+	0.638026i	$0.779751\pi$
$282$	30.3877	+	4.37204i	1.80956	+	0.260351i
$283$		−	18.0131i		−	1.07077i	−0.844608	−	0.535385i	$-0.820166\pi$
$283$		−	18.0131i		−	1.07077i	0.844608	−	0.535385i	$-0.179834\pi$
$284$	5.83445	−	5.83445i	0.346211	−	0.346211i
$285$	0.366582	−	0.466056i	0.0217145	−	0.0276068i
$286$	−12.0854	+	4.97633i	−0.714627	+	0.294257i
$287$		−	3.07954i		−	0.181780i
$288$	22.5359	+	0.540737i	1.32794	+	0.0318632i
$289$	8.11540	−	14.0563i	0.477376	−	0.826840i
$290$	−41.1753			−2.41790
$291$	15.7463	−	11.7852i	0.923062	−	0.690859i
$292$	−0.743545	−	2.77495i	−0.0435127	−	0.162392i
$293$	3.96080	+	14.7819i	0.231392	+	0.863568i	0.979742	+	0.200264i	$0.0641799\pi$
$293$	3.96080	+	14.7819i	0.231392	+	0.863568i	−0.748350	+	0.663305i	$0.769153\pi$
$294$	3.46668	+	1.48491i	0.202181	+	0.0866015i
$295$	14.6367			0.852182
$296$	6.29564	−	10.9044i	0.365927	−	0.633803i
$297$	6.66913	+	5.50970i	0.386982	+	0.319705i
$298$			10.2346i			0.592876i
$299$	12.6444	+	9.74450i	0.731243	+	0.563539i
$300$	−6.99928	−	17.4882i	−0.404103	−	1.00968i
$301$	0.0462185	−	0.0462185i	0.00266399	−	0.00266399i
$302$		−	13.7493i		−	0.791186i
$303$	4.09398	+	10.2291i	0.235193	+	0.587646i
$304$	−0.0582628	−	0.217440i	−0.00334160	−	0.0124710i
$305$	−4.84277	+	18.0735i	−0.277296	+	1.03488i
$306$	−5.72729	−	0.137423i	−0.327408	−	0.00785596i
$307$	−18.7538	−	18.7538i	−1.07034	−	1.07034i	−0.997332	−	0.0730043i	$-0.976741\pi$
$307$	−18.7538	−	18.7538i	−1.07034	−	1.07034i	−0.0730043	−	0.997332i	$-0.523259\pi$
$308$		−	4.56317i		−	0.260011i
$309$	20.7134	−	8.29011i	1.17834	−	0.471608i
$310$	31.2818	+	31.2818i	1.77669	+	1.77669i
$311$	9.90355	+	17.1534i	0.561579	+	0.972683i	0.997359	+	0.0726297i	$0.0231391\pi$
$311$	9.90355	+	17.1534i	0.561579	+	0.972683i	−0.435780	+	0.900053i	$0.643528\pi$
$312$	10.0739	+	0.141941i	0.570325	+	0.00803581i
$313$	−13.1664	+	22.8048i	−0.744207	+	1.28901i	0.206357	+	0.978477i	$0.433839\pi$
$313$	−13.1664	+	22.8048i	−0.744207	+	1.28901i	−0.950564	+	0.310528i	$0.899494\pi$
$314$	37.0845	−	9.93676i	2.09280	−	0.560764i
$315$	8.73104	−	2.11637i	0.491938	−	0.119244i
$316$	−38.8737	+	22.4438i	−2.18682	+	1.26256i
$317$	−11.1864	+	2.99738i	−0.628290	+	0.168350i	−0.558894	−	0.829239i	$-0.688774\pi$
$317$	−11.1864	+	2.99738i	−0.628290	+	0.168350i	−0.0693965	+	0.997589i	$0.522107\pi$
$318$	−4.26910	−	1.82861i	−0.239399	−	0.102544i
$319$	−10.1549	+	2.72099i	−0.568563	+	0.152346i
$320$	−35.9339	−	9.62845i	−2.00876	−	0.538247i
$321$	16.7347	+	13.1629i	0.934039	+	0.734680i
$322$	−8.34874	+	4.82015i	−0.465257	+	0.268616i
$323$	0.0259497	+	0.0968457i	0.00144388	+	0.00538864i
$324$	−11.2954	−	21.9304i	−0.627521	−	1.21836i
$325$	5.44701	+	13.2285i	0.302146	+	0.733786i
$326$	10.4046	+	6.00710i	0.576258	+	0.332703i
$327$	−18.0248	+	13.4905i	−0.996772	+	0.746027i
$328$	4.96817			0.274321
$329$	4.07029	−	7.04994i	0.224402	−	0.388676i
$330$	−11.2662	−	15.0528i	−0.620182	−	0.828630i
$331$	13.9213	−	13.9213i	0.765185	−	0.765185i	−0.212070	−	0.977254i	$-0.568020\pi$
$331$	13.9213	−	13.9213i	0.765185	−	0.765185i	0.977254	+	0.212070i	$0.0680205\pi$
$332$	−26.1043	−	6.99462i	−1.43266	−	0.383880i
$333$	23.4075	+	0.561651i	1.28272	+	0.0307783i
$334$	0.466125	+	0.807353i	0.0255052	+	0.0441764i
$335$	−8.21830	−	14.2345i	−0.449014	−	0.777714i
$336$	1.34291	−	3.13517i	0.0732618	−	0.171038i
$337$	−17.4846	+	10.0948i	−0.952448	+	0.549896i	−0.893841	−	0.448385i	$-0.851999\pi$
$337$	−17.4846	+	10.0948i	−0.952448	+	0.549896i	−0.0586077	+	0.998281i	$0.518666\pi$
$338$	−28.3055	−	0.118546i	−1.53962	−	0.00644804i
$339$	12.5630	+	9.88155i	0.682326	+	0.536692i
$340$	6.95354	+	1.86320i	0.377109	+	0.101046i
$341$	9.78208	+	5.64768i	0.529729	+	0.305839i
$342$	−0.540538	+	0.515206i	−0.0292289	+	0.0278592i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	0.0745635	+	0.0745635i	0.00402020	+	0.00402020i
$345$	−9.04208	+	21.1097i	−0.486809	+	1.13651i
$346$	10.2894	−	38.4004i	0.553159	−	2.06442i
$347$	14.5084	+	8.37642i	0.778851	+	0.449670i	0.836023	−	0.548695i	$-0.184875\pi$
$347$	14.5084	+	8.37642i	0.778851	+	0.449670i	−0.0571720	+	0.998364i	$0.518208\pi$
$348$	29.6737	+	4.26931i	1.59068	+	0.228859i
$349$	2.44309	−	9.11775i	0.130776	−	0.488062i	−0.869204	−	0.494454i	$-0.835368\pi$
$349$	2.44309	−	9.11775i	0.130776	−	0.488062i	0.999980	+	0.00639220i	$0.00203471\pi$
$350$	−8.63934			−0.461792
$351$	8.74303	+	16.5698i	0.466668	+	0.884432i
$352$	−12.5097			−0.666770
$353$	−4.59301	+	17.1413i	−0.244461	+	0.912342i	0.729192	+	0.684309i	$0.239896\pi$
$353$	−4.59301	+	17.1413i	−0.244461	+	0.912342i	−0.973653	+	0.228033i	$0.926771\pi$
$354$	−18.2450	−	2.62500i	−0.969711	−	0.139517i
$355$	−7.80710	−	4.50743i	−0.414358	−	0.239230i
$356$	−7.23546	+	27.0031i	−0.383478	+	1.43116i
$357$	−0.598120	+	1.39638i	−0.0316559	+	0.0739041i
$358$	5.82484	+	5.82484i	0.307852	+	0.307852i
$359$	−22.8272	+	22.8272i	−1.20478	+	1.20478i	−0.232078	+	0.972697i	$0.574553\pi$
$359$	−22.8272	+	22.8272i	−1.20478	+	1.20478i	−0.972697	+	0.232078i	$0.925447\pi$
$360$	3.41431	+	14.0856i	0.179950	+	0.742378i
$361$	−16.4432	−	9.49347i	−0.865430	−	0.499656i
$362$	28.1041	+	7.53046i	1.47712	+	0.395792i
$363$	11.2020	+	8.81103i	0.587950	+	0.462459i
$364$	3.80101	−	9.12237i	0.199227	−	0.478142i
$365$	−2.71823	+	1.56937i	−0.142279	+	0.0821446i
$366$	9.27799	−	21.6605i	0.484968	−	1.13221i
$367$	2.91002	+	5.04030i	0.151902	+	0.263102i	0.931927	−	0.362647i	$-0.118127\pi$
$367$	2.91002	+	5.04030i	0.151902	+	0.263102i	−0.780025	+	0.625749i	$0.784794\pi$
$368$	4.35921	+	7.55038i	0.227240	+	0.393591i
$369$	4.42606	+	8.10939i	0.230412	+	0.422158i
$370$	−49.1561	−	13.1713i	−2.55551	−	0.684746i
$371$	−0.870779	+	0.870779i	−0.0452086	+	0.0452086i
$372$	−19.3003	−	25.7873i	−1.00067	−	1.33701i
$373$	6.66113	−	11.5374i	0.344900	−	0.597385i	−0.640435	−	0.768012i	$-0.721246\pi$
$373$	6.66113	−	11.5374i	0.344900	−	0.597385i	0.985336	+	0.170627i	$0.0545794\pi$
$374$	3.17922			0.164394
$375$	4.28634	−	3.20808i	0.221346	−	0.165664i
$376$	11.3736	+	6.56652i	0.586546	+	0.338643i
$377$	−22.5674	−	3.01915i	−1.16228	−	0.155494i
$378$	−11.2630	+	1.07225i	−0.579307	+	0.0551506i
$379$	2.65919	+	9.92423i	0.136593	+	0.509773i	0.999986	+	0.00524117i	$0.00166832\pi$
$379$	2.65919	+	9.92423i	0.136593	+	0.509773i	−0.863393	+	0.504532i	$0.831665\pi$
$380$	0.812619	−	0.469166i	0.0416865	−	0.0240677i
$381$	15.1864	+	11.9451i	0.778025	+	0.611965i
$382$	21.5700	+	5.77967i	1.10362	+	0.295714i
$383$	−0.882876	+	0.236566i	−0.0451128	+	0.0120880i	−0.281305	−	0.959618i	$-0.590767\pi$
$383$	−0.882876	+	0.236566i	−0.0451128	+	0.0120880i	0.236192	+	0.971706i	$0.424101\pi$
$384$	19.1385	+	8.19773i	0.976657	+	0.418339i
$385$	−4.81564	+	1.29035i	−0.245428	+	0.0657622i
$386$	−35.2104	+	20.3287i	−1.79216	+	1.03470i
$387$	−0.0552802	+	0.188135i	−0.00281005	+	0.00956344i
$388$	30.0638	−	8.05558i	1.52626	−	0.408960i
$389$	−1.56916	+	2.71787i	−0.0795598	+	0.137802i	−0.903060	−	0.429514i	$-0.858685\pi$
$389$	−1.56916	+	2.71787i	−0.0795598	+	0.137802i	0.823500	+	0.567316i	$0.192018\pi$
$390$	−9.98391	−	39.4770i	−0.505555	−	1.99900i
$391$	−1.94155	−	3.36287i	−0.0981886	−	0.170068i
$392$	1.14076	+	1.14076i	0.0576172	+	0.0576172i
$393$	31.1777	−	12.4782i	1.57271	−	0.629444i
$394$			49.2041i			2.47887i
$395$	34.6781	+	34.6781i	1.74484	+	1.74484i
$396$	6.55840	+	12.0162i	0.329572	+	0.603838i
$397$	4.98685	−	18.6112i	0.250283	−	0.934068i	−0.720371	−	0.693589i	$-0.756029\pi$
$397$	4.98685	−	18.6112i	0.250283	−	0.934068i	0.970654	−	0.240480i	$-0.0773047\pi$
$398$	12.4022	+	46.2858i	0.621669	+	2.32010i
$399$	0.0735736	+	0.183828i	0.00368329	+	0.00920293i
$400$			7.81319i			0.390659i
$401$	−21.1882	+	21.1882i	−1.05809	+	1.05809i	−0.0598821	+	0.998205i	$0.519072\pi$
$401$	−21.1882	+	21.1882i	−1.05809	+	1.05809i	−0.998205	+	0.0598821i	$0.980928\pi$
$402$	7.69143	+	19.2176i	0.383614	+	0.958485i
$403$	14.8513	+	19.4387i	0.739794	+	0.968310i
$404$			17.4356i			0.867456i
$405$	−19.9498	+	18.1217i	−0.991313	+	0.900476i
$406$	6.87487	−	11.9076i	0.341194	−	0.590965i
$407$	−12.9935			−0.644066
$408$	−2.25275	−	0.964937i	−0.111528	−	0.0477715i
$409$	3.12901	+	11.6776i	0.154720	+	0.577422i	0.999129	+	0.0417236i	$0.0132849\pi$
$409$	3.12901	+	11.6776i	0.154720	+	0.577422i	−0.844409	+	0.535698i	$0.820048\pi$
$410$	−5.19705	−	19.3957i	−0.256664	−	0.957883i
$411$	−27.2689	+	20.4092i	−1.34508	+	1.00671i
$412$	35.3063			1.73942
$413$	−2.44383	+	4.23283i	−0.120253	+	0.208284i
$414$	15.0571	−	24.6921i	0.740015	−	1.21355i
$415$			29.5265i			1.44940i
$416$	−25.0085	−	10.4203i	−1.22614	−	0.510897i
$417$	−19.0409	+	24.2077i	−0.932435	+	1.18546i
$418$	0.293022	−	0.293022i	0.0143322	−	0.0143322i
$419$		−	2.39407i		−	0.116958i	−0.998289	−	0.0584790i	$-0.981375\pi$
$419$		−	2.39407i		−	0.116958i	0.998289	−	0.0584790i	$-0.0186251\pi$
$420$	14.0719	+	2.02460i	0.686638	+	0.0987902i
$421$	−8.37172	−	31.2437i	−0.408013	−	1.52272i	−0.798431	−	0.602087i	$-0.794336\pi$
$421$	−8.37172	−	31.2437i	−0.408013	−	1.52272i	0.390418	−	0.920638i	$-0.372330\pi$
$422$	−9.09694	+	33.9502i	−0.442832	+	1.65267i
$423$	−0.585817	+	24.4147i	−0.0284834	+	1.18708i
$424$	−1.40481	−	1.40481i	−0.0682237	−	0.0682237i
$425$		−	3.47992i		−	0.168801i
$426$	8.92336	+	7.01878i	0.432338	+	0.340061i
$427$	−4.41814	−	4.41814i	−0.213809	−	0.213809i
$428$	16.8463	+	29.1787i	0.814299	+	1.41041i
$429$	−5.07104	−	9.07625i	−0.244832	−	0.438205i
$430$	0.213096	−	0.369093i	0.0102764	−	0.0177993i
$431$	32.3475	−	8.66748i	1.55812	−	0.417498i	0.626054	−	0.779780i	$-0.284669\pi$
$431$	32.3475	−	8.66748i	1.55812	−	0.417498i	0.932069	+	0.362282i	$0.118002\pi$
$432$	0.969715	+	10.1860i	0.0466554	+	0.490073i
$433$	32.6280	−	18.8378i	1.56800	−	0.905286i	0.571600	−	0.820533i	$-0.306323\pi$
$433$	32.6280	−	18.8378i	1.56800	−	0.905286i	0.996402	−	0.0847536i	$-0.0270103\pi$
$434$	−14.2695	+	3.82350i	−0.684957	+	0.183534i
$435$	−3.88545	−	32.5228i	−0.186293	−	1.55935i
$436$	−34.4141	+	9.22123i	−1.64814	+	0.441617i
$437$	−0.488897	−	0.131000i	−0.0233871	−	0.00626656i
$438$	3.66980	−	1.46876i	0.175350	−	0.0701801i
$439$	−16.3961	+	9.46632i	−0.782545	+	0.451803i	−0.837332	−	0.546695i	$-0.815886\pi$
$439$	−16.3961	+	9.46632i	−0.782545	+	0.451803i	0.0547863	+	0.998498i	$0.482552\pi$
$440$	−2.08170	−	7.76900i	−0.0992410	−	0.370372i
$441$	−0.845744	+	2.87832i	−0.0402735	+	0.137063i
$442$	6.35568	+	2.64822i	0.302309	+	0.125963i
$443$	7.96778	+	4.60020i	0.378561	+	0.218562i	0.677192	−	0.735806i	$-0.263197\pi$
$443$	7.96778	+	4.60020i	0.378561	+	0.218562i	−0.298631	+	0.954369i	$0.596530\pi$
$444$	34.0596	+	14.5890i	1.61640	+	0.692363i
$445$	30.5432			1.44788
$446$	29.4934	−	51.0840i	1.39655	−	2.41890i
$447$	−8.08394	+	0.965775i	−0.382357	+	0.0456796i
$448$	8.78420	−	8.78420i	0.415015	−	0.415015i
$449$	10.8963	+	2.91965i	0.514228	+	0.137787i	0.506595	−	0.862184i	$-0.330904\pi$
$449$	10.8963	+	2.91965i	0.514228	+	0.137787i	0.00763260	+	0.999971i	$0.497570\pi$
$450$	22.7501	−	12.4169i	1.07245	−	0.585336i
$451$	−2.56345	−	4.44002i	−0.120708	−	0.209072i
$452$	12.6468	+	21.9049i	0.594855	+	1.03032i
$453$	10.8601	−	1.29744i	0.510251	−	0.0609589i
$454$	1.35763	−	0.783830i	0.0637169	−	0.0367870i
$455$	−10.7019	−	1.43174i	−0.501714	−	0.0671211i
$456$	−0.296567	+	0.118695i	−0.0138880	+	0.00555840i
$457$	6.60893	+	1.77086i	0.309153	+	0.0828373i	0.410060	−	0.912059i	$-0.365508\pi$
$457$	6.60893	+	1.77086i	0.309153	+	0.0828373i	−0.100907	+	0.994896i	$0.532174\pi$
$458$	−17.8306	−	10.2945i	−0.833168	−	0.481030i
$459$	−0.431902	−	4.53674i	−0.0201595	−	0.211757i
$460$	−25.6971	+	25.6971i	−1.19813	+	1.19813i
$461$	−28.8513	−	28.8513i	−1.34374	−	1.34374i	−0.892306	−	0.451432i	$-0.850913\pi$
$461$	−28.8513	−	28.8513i	−1.34374	−	1.34374i	−0.451432	−	0.892306i	$-0.649087\pi$
$462$	6.23423	−	0.744794i	0.290043	−	0.0346509i
$463$	9.79736	−	36.5642i	0.455322	−	1.69928i	−0.231818	−	0.972759i	$-0.574468\pi$
$463$	9.79736	−	36.5642i	0.455322	−	1.69928i	0.687140	−	0.726525i	$-0.258866\pi$
$464$	−10.7689	−	6.21745i	−0.499935	−	0.288638i
$465$	−21.7565	+	27.6602i	−1.00893	+	1.28271i
$466$	14.9946	−	55.9608i	0.694613	−	2.59233i
$467$	35.8726			1.65998			0.829992	−	0.557776i	$-0.188345\pi$
$467$	35.8726			1.65998			0.829992	+	0.557776i	$0.188345\pi$
$468$	3.10186	+	29.4850i	0.143384	+	1.36294i
$469$	5.48870			0.253444
$470$	13.7381	−	51.2712i	0.633690	−	2.36496i
$471$	11.3481	+	28.3540i	0.522893	+	1.30648i
$472$	−6.82876	−	3.94259i	−0.314319	−	0.181472i
$473$	0.0281640	−	0.105110i	0.00129498	−	0.00483295i
$474$	−37.0078	−	49.4464i	−1.69982	−	2.27115i
$475$	−0.320737	−	0.320737i	−0.0147164	−	0.0147164i
$476$	−1.69983	+	1.69983i	−0.0779114	+	0.0779114i
$477$	1.04151	−	3.54455i	0.0476873	−	0.162294i
$478$	18.6731	+	10.7809i	0.854087	+	0.493107i
$479$	29.9634	+	8.02866i	1.36906	+	0.366839i	0.867136	−	0.498072i	$-0.165958\pi$
$479$	29.9634	+	8.02866i	1.36906	+	0.366839i	0.501926	+	0.864911i	$0.332625\pi$
$480$	5.55034	−	38.5774i	0.253337	−	1.76081i
$481$	−25.9758	−	10.8233i	−1.18439	−	0.493500i
$482$	19.3454	−	11.1691i	0.881158	−	0.508737i
$483$	−4.59507	−	6.13951i	−0.209083	−	0.279357i
$484$	11.2767	+	19.5318i	0.512577	+	0.887810i
$485$	−17.0026	−	29.4493i	−0.772047	−	1.33723i
$486$	28.1179	−	19.0113i	1.27545	−	0.862370i
$487$	5.19379	+	1.39167i	0.235353	+	0.0630627i	0.374568	−	0.927200i	$-0.377791\pi$
$487$	5.19379	+	1.39167i	0.235353	+	0.0630627i	−0.139215	+	0.990262i	$0.544458\pi$
$488$	7.12771	−	7.12771i	0.322656	−	0.322656i
$489$	−3.76297	+	8.78506i	−0.170167	+	0.397274i
$490$	3.26020	−	5.64684i	0.147281	−	0.255098i
$491$	−20.2830			−0.915361			−0.457680	−	0.889117i	$-0.651320\pi$
$491$	−20.2830			−0.915361			−0.457680	+	0.889117i	$0.651320\pi$
$492$	1.73429	+	14.5167i	0.0781876	+	0.654463i
$493$	4.79639	+	2.76920i	0.216018	+	0.124718i
$494$	0.829870	−	0.341709i	0.0373376	−	0.0153742i
$495$	10.8265	−	10.3192i	0.486617	−	0.463812i
$496$	3.45787	+	12.9049i	0.155263	+	0.579449i
$497$	2.60704	−	1.50517i	0.116942	−	0.0675163i
$498$	5.29540	−	36.8055i	0.237293	−	1.64929i
$499$	−29.8871	−	8.00823i	−1.33793	−	0.358498i	−0.482265	−	0.876026i	$-0.660186\pi$
$499$	−29.8871	−	8.00823i	−1.33793	−	0.358498i	−0.855666	+	0.517528i	$0.826852\pi$
$500$	8.18377	−	2.19283i	0.365989	−	0.0980665i
$501$	−0.593712	+	0.444359i	−0.0265251	+	0.0198525i
$502$	9.92233	−	2.65868i	0.442855	−	0.118663i
$503$	−13.9822	+	8.07265i	−0.623438	+	0.359942i	−0.778206	−	0.628009i	$-0.783870\pi$
$503$	−13.9822	+	8.07265i	−0.623438	+	0.359942i	0.154769	+	0.987951i	$0.450537\pi$
$504$	−4.64354	−	1.36442i	−0.206840	−	0.0607763i
$505$	18.4004	−	4.93036i	0.818805	−	0.219398i
$506$	−8.02469	+	13.8992i	−0.356741	+	0.617893i
$507$	−2.57738	−	22.3687i	−0.114465	−	0.993427i
$508$	15.2878	+	26.4792i	0.678285	+	1.17482i
$509$	0.0582470	+	0.0582470i	0.00258175	+	0.00258175i	0.708396	−	0.705815i	$-0.249419\pi$
$509$	0.0582470	+	0.0582470i	0.00258175	+	0.00258175i	−0.705815	+	0.708396i	$0.749419\pi$
$510$	−1.41057	+	9.80409i	−0.0624609	+	0.434132i
$511$		−	1.04812i		−	0.0463663i
$512$	−14.9554	−	14.9554i	−0.660941	−	0.660941i
$513$	−0.457949	−	0.378334i	−0.0202189	−	0.0167039i
$514$	7.05749	−	26.3389i	0.311293	−	1.16176i
$515$	−9.98373	−	37.2598i	−0.439936	−	1.64186i
$516$	−0.191841	+	0.243899i	−0.00844535	+	0.0107370i
$517$		−	13.5526i		−	0.596043i
$518$	12.0165	−	12.0165i	0.527973	−	0.527973i
$519$	31.3020	+	4.50358i	1.37400	+	0.197685i
$520$	2.30980	−	17.2652i	0.101292	−	0.757131i
$521$			29.7978i			1.30546i	0.757589	+	0.652732i	$0.226377\pi$
$521$			29.7978i			1.30546i	−0.757589	+	0.652732i	$0.773623\pi$
$522$	−0.989467	+	41.2373i	−0.0433078	+	1.80491i
$523$	−2.83751	+	4.91472i	−0.124076	+	0.214906i	−0.921371	−	0.388684i	$-0.872930\pi$
$523$	−2.83751	+	4.91472i	−0.124076	+	0.214906i	0.797295	+	0.603589i	$0.206263\pi$
$524$	53.1429			2.32156
$525$	−0.815238	−	6.82389i	−0.0355799	−	0.297819i
$526$	−6.97770	−	26.0411i	−0.304242	−	1.13545i
$527$	−1.54010	−	5.74775i	−0.0670880	−	0.250376i
$528$	−0.673572	−	5.63808i	−0.0293134	−	0.245366i
$529$	−3.39727			−0.147707
$530$	−4.01483	+	6.95389i	−0.174393	+	0.302058i
$531$	0.351729	−	14.6588i	0.0152637	−	0.636136i
$532$			0.313339i			0.0135849i
$533$	−1.42624	−	11.0115i	−0.0617771	−	0.476960i
$534$	−38.0728	−	5.47773i	−1.64757	−	0.237045i
$535$	26.0295	−	26.0295i	1.12535	−	1.12535i
$536$			8.85482i			0.382470i
$537$	−4.05117	+	5.15047i	−0.174821	+	0.222259i
$538$	−1.99379	−	7.44094i	−0.0859586	−	0.320802i
$539$	0.430888	−	1.60810i	0.0185597	−	0.0692656i
$540$	−39.9655	+	14.8934i	−1.71984	+	0.640910i
$541$	14.7256	+	14.7256i	0.633101	+	0.633101i	0.948845	−	0.315743i	$-0.102254\pi$
$541$	14.7256	+	14.7256i	0.633101	+	0.633101i	−0.315743	+	0.948845i	$0.602254\pi$
$542$		−	4.13269i		−	0.177514i
$543$	−3.29603	+	22.9090i	−0.141446	+	0.983117i
$544$	4.66000	+	4.66000i	0.199796	+	0.199796i
$545$	19.4629	+	33.7107i	0.833698	+	1.44401i
$546$	13.0834	+	3.70403i	0.559920	+	0.158518i
$547$	−18.4674	+	31.9864i	−0.789608	+	1.36764i	0.136599	+	0.990626i	$0.456383\pi$
$547$	−18.4674	+	31.9864i	−0.789608	+	1.36764i	−0.926207	+	0.377015i	$0.876951\pi$
$548$	−52.0636	+	13.9504i	−2.22405	+	0.595932i
$549$	17.9843	+	5.28438i	0.767551	+	0.225532i
$550$	−12.4560	+	7.19148i	−0.531126	+	0.306646i
$551$	0.697303	−	0.186842i	0.0297061	−	0.00795973i
$552$	9.90476	−	7.41314i	0.421575	−	0.315524i
$553$	−15.8187	+	4.23861i	−0.672680	+	0.180244i
$554$	−7.92379	−	2.12317i	−0.336650	−	0.0902050i
$555$	5.76500	−	40.0695i	0.244711	−	1.70085i
$556$	−42.2087	+	24.3692i	−1.79005	+	1.03349i
$557$	−7.33692	−	27.3818i	−0.310875	−	1.16020i	−0.927769	−	0.373156i	$-0.878276\pi$
$557$	−7.33692	−	27.3818i	−0.310875	−	1.16020i	0.616894	−	0.787047i	$-0.288391\pi$
$558$	32.0807	−	30.5772i	1.35808	−	1.29444i
$559$	0.143857	−	0.186668i	0.00608452	−	0.00789522i
$560$	−5.10685	−	2.94844i	−0.215804	−	0.124594i
$561$	0.300003	+	2.51115i	0.0126661	+	0.106021i
$562$	−30.4398			−1.28403
$563$	17.6997	−	30.6568i	0.745954	−	1.29203i	−0.203793	−	0.979014i	$-0.565327\pi$
$563$	17.6997	−	30.6568i	0.745954	−	1.29203i	0.949748	−	0.313017i	$-0.101340\pi$
$564$	−15.2167	+	35.5251i	−0.640739	+	1.49587i
$565$	19.5407	−	19.5407i	0.822083	−	0.822083i
$566$	37.8848	+	10.1512i	1.59242	+	0.426687i
$567$	−1.90975	−	8.79505i	−0.0802019	−	0.369357i
$568$	2.42827	+	4.20589i	0.101888	+	0.176475i
$569$	−6.41099	−	11.1042i	−0.268763	−	0.465510i	0.699780	−	0.714358i	$-0.253281\pi$
$569$	−6.41099	−	11.1042i	−0.268763	−	0.465510i	−0.968543	+	0.248848i	$0.919948\pi$
$570$	0.773613	+	1.03363i	0.0324031	+	0.0432940i
$571$	15.7607	−	9.09946i	0.659566	−	0.380801i	−0.132546	−	0.991177i	$-0.542315\pi$
$571$	15.7607	−	9.09946i	0.659566	−	0.380801i	0.792112	+	0.610376i	$0.208982\pi$
$572$	−2.11335	−	16.3164i	−0.0883636	−	0.682224i
$573$	−2.52972	+	17.5827i	−0.105681	+	0.734529i
$574$	6.47682	+	1.73546i	0.270337	+	0.0724366i
$575$	15.2138	+	8.78369i	0.634459	+	0.366305i
$576$	−10.5065	+	35.7566i	−0.437769	+	1.48986i
$577$	−11.9771	+	11.9771i	−0.498614	+	0.498614i	−0.911006	−	0.412392i	$-0.864693\pi$
$577$	−11.9771	+	11.9771i	−0.498614	+	0.498614i	0.412392	+	0.911006i	$0.364693\pi$
$578$	24.9894	+	24.9894i	1.03942	+	1.03942i
$579$	−19.3795	−	25.8931i	−0.805383	−	1.07608i
$580$	13.4153	−	50.0665i	0.557039	−	2.07890i
$581$	−8.53886	−	4.92991i	−0.354252	−	0.204527i
$582$	15.9126	+	39.7586i	0.659597	+	1.64805i
$583$	−0.530624	+	1.98032i	−0.0219762	+	0.0820163i
$584$	1.69092			0.0699708
$585$	30.2393	−	11.6111i	1.25024	−	0.480060i
$586$	−33.3210			−1.37648
$587$	−7.50211	+	27.9983i	−0.309645	+	1.15561i	0.619227	+	0.785212i	$0.287446\pi$
$587$	−7.50211	+	27.9983i	−0.309645	+	1.15561i	−0.928872	+	0.370400i	$0.879221\pi$
$588$	−2.93502	+	3.73146i	−0.121038	+	0.153883i
$589$	−0.671705	−	0.387809i	−0.0276771	−	0.0159794i
$590$	−8.24843	+	30.7836i	−0.339583	+	1.26734i
$591$	−38.8645	+	4.64308i	−1.59867	+	0.190991i
$592$	−10.8674	−	10.8674i	−0.446646	−	0.446646i
$593$	−6.02126	+	6.02126i	−0.247264	+	0.247264i	−0.819847	−	0.572583i	$-0.805941\pi$
$593$	−6.02126	+	6.02126i	−0.247264	+	0.247264i	0.572583	+	0.819847i	$0.305941\pi$
$594$	−15.3462	+	10.9214i	−0.629663	+	0.448111i
$595$	2.27455	+	1.31321i	0.0932473	+	0.0538363i
$596$	−12.4446	−	3.33453i	−0.509752	−	0.136588i
$597$	−35.3891	+	14.1638i	−1.44838	+	0.579684i
$598$	−27.6201	+	21.1019i	−1.12947	+	0.862920i
$599$	13.9622	−	8.06108i	0.570480	−	0.329367i	−0.186861	−	0.982386i	$-0.559831\pi$
$599$	13.9622	−	8.06108i	0.570480	−	0.329367i	0.757341	+	0.653020i	$0.226498\pi$
$600$	11.0089	−	1.31521i	0.449435	−	0.0536932i
$601$	−9.95872	−	17.2490i	−0.406224	−	0.703601i	0.588239	−	0.808687i	$-0.299822\pi$
$601$	−9.95872	−	17.2490i	−0.406224	−	0.703601i	−0.994463	+	0.105086i	$0.966488\pi$
$602$	0.0711595	+	0.123252i	0.00290024	+	0.00502337i
$603$	−14.4534	+	7.88861i	−0.588589	+	0.321249i
$604$	16.7183	+	4.47966i	0.680258	+	0.182275i
$605$	17.4237	−	17.4237i	0.708376	−	0.708376i
$606$	−23.8207	+	2.84582i	−0.967651	+	0.115604i
$607$	19.0984	−	33.0794i	0.775181	−	1.34265i	−0.159512	−	0.987196i	$-0.550992\pi$
$607$	19.0984	−	33.0794i	0.775181	−	1.34265i	0.934693	−	0.355457i	$-0.115675\pi$
$608$	0.859003			0.0348372
$609$	10.0541	+	4.30655i	0.407413	+	0.174510i
$610$	−35.2825	−	20.3704i	−1.42855	−	0.824773i
$611$	11.2890	−	27.0934i	0.456704	−	1.09608i
$612$	2.03310	−	6.91924i	0.0821832	−	0.279694i
$613$	10.1596	+	37.9162i	0.410343	+	1.53142i	0.793984	+	0.607938i	$0.208003\pi$
$613$	10.1596	+	37.9162i	0.410343	+	1.53142i	−0.383641	+	0.923482i	$0.625330\pi$
$614$	50.0111	−	28.8739i	2.01829	−	1.16526i
$615$	14.8295	−	5.93520i	0.597983	−	0.239330i
$616$	2.59431	+	0.695144i	0.104528	+	0.0280081i
$617$	−36.0718	+	9.66541i	−1.45220	+	0.389115i	−0.896787	−	0.442463i	$-0.854105\pi$
$617$	−36.0718	+	9.66541i	−1.45220	+	0.389115i	−0.555409	+	0.831578i	$0.687438\pi$
$618$	5.76264	+	48.2357i	0.231808	+	1.94033i
$619$	−10.7529	+	2.88123i	−0.432196	+	0.115807i	−0.468357	−	0.883539i	$-0.655154\pi$
$619$	−10.7529	+	2.88123i	−0.432196	+	0.115807i	0.0361609	+	0.999346i	$0.488487\pi$
$620$	−48.2285	+	27.8448i	−1.93690	+	1.11827i
$621$	20.9242	+	9.56298i	0.839660	+	0.383749i
$622$	−41.6578	+	11.1622i	−1.67033	+	0.447563i
$623$	−5.09966	+	8.83287i	−0.204314	+	0.353882i
$624$	3.34982	−	11.8323i	0.134100	−	0.473672i
$625$	−14.5478	−	25.1975i	−0.581912	−	1.00790i
$626$	−40.5427	−	40.5427i	−1.62041	−	1.62041i
$627$	0.259098	+	0.203797i	0.0103474	+	0.00813885i
$628$			48.3298i			1.92857i
$629$	4.84023	+	4.84023i	0.192992	+	0.192992i
$630$	−0.469225	+	19.5556i	−0.0186944	+	0.779113i
$631$	−5.27938	+	19.7029i	−0.210169	+	0.784361i	0.777643	+	0.628706i	$0.216415\pi$
$631$	−5.27938	+	19.7029i	−0.210169	+	0.784361i	−0.987812	+	0.155654i	$0.950251\pi$
$632$	−6.83808	−	25.5200i	−0.272004	−	1.01513i
$633$	−27.6744	−	3.98166i	−1.09996	−	0.158257i
$634$		−	25.2161i		−	1.00146i
$635$	23.6213	−	23.6213i	0.937382	−	0.937382i
$636$	3.61438	−	4.59517i	0.143320	−	0.182210i
$637$	2.20091	−	2.85587i	0.0872031	−	0.113154i
$638$		−	22.8909i		−	0.906258i
$639$	−4.70183	+	7.71054i	−0.186002	+	0.305024i
$640$	17.9986	−	31.1745i	0.711457	−	1.23228i
$641$	−37.8500			−1.49499			−0.747493	−	0.664270i	$-0.768743\pi$
$641$	−37.8500			−1.49499			−0.747493	+	0.664270i	$0.768743\pi$
$642$	−37.1146	+	27.7781i	−1.46480	+	1.09631i
$643$	−11.3141	−	42.2249i	−0.446186	−	1.66519i	−0.712786	−	0.701381i	$-0.752567\pi$
$643$	−11.3141	−	42.2249i	−0.446186	−	1.66519i	0.266600	−	0.963807i	$-0.414100\pi$
$644$	−3.14089	−	11.7220i	−0.123768	−	0.461910i
$645$	0.311641	+	0.133488i	0.0122709	+	0.00525607i
$646$	−0.218307			−0.00858919
$647$	12.0617	−	20.8915i	0.474195	−	0.821330i	−0.525368	−	0.850875i	$-0.676072\pi$
$647$	12.0617	−	20.8915i	0.474195	−	0.821330i	0.999563	+	0.0295449i	$0.00940579\pi$
$648$	14.1889	−	3.08096i	0.557393	−	0.121032i
$649$			8.13708i			0.319408i
$650$	−30.8915	+	4.00116i	−1.21167	+	0.156938i
$651$	−4.36655	−	10.9101i	−0.171139	−	0.427602i
$652$	−10.6942	+	10.6942i	−0.418815	+	0.418815i
$653$			28.0282i			1.09683i	0.836207	+	0.548413i	$0.184768\pi$
$653$			28.0282i			1.09683i	−0.836207	+	0.548413i	$0.815232\pi$
$654$	−18.2151	−	45.5118i	−0.712269	−	1.77965i
$655$	−15.0275	−	56.0833i	−0.587172	−	2.19135i
$656$	1.56950	−	5.85746i	0.0612788	−	0.228696i
$657$	1.50641	+	2.76004i	0.0587708	+	0.107679i
$658$	12.5335	+	12.5335i	0.488606	+	0.488606i
$659$		−	26.8463i		−	1.04578i	−0.852399	−	0.522891i	$-0.824853\pi$
$659$		−	26.8463i		−	1.04578i	0.852399	−	0.522891i	$-0.175147\pi$
$660$	21.9739	−	8.79458i	0.855331	−	0.342329i
$661$	15.7368	+	15.7368i	0.612091	+	0.612091i	0.943491	−	0.331400i	$-0.107521\pi$
$661$	15.7368	+	15.7368i	0.612091	+	0.612091i	−0.331400	+	0.943491i	$0.607521\pi$
$662$	21.4337	+	37.1243i	0.833044	+	1.44287i
$663$	−1.49198	+	5.27001i	−0.0579438	+	0.204670i
$664$	7.95335	−	13.7756i	0.308650	−	0.534597i
$665$	0.330675	−	0.0886042i	0.0128230	−	0.00343592i
$666$	−14.3724	+	48.9136i	−0.556920	+	1.89537i
$667$	−24.2131	+	13.9795i	−0.937537	+	0.541287i
$668$	−1.13356	+	0.303735i	−0.0438586	+	0.0117519i
$669$	43.1325	+	18.4752i	1.66760	+	0.714294i
$670$	34.5691	−	9.26275i	1.33552	−	0.357851i
$671$	−10.0477	−	2.69227i	−0.387887	−	0.103934i
$672$	10.2296	+	8.04623i	0.394616	+	0.310390i
$673$	20.6236	−	11.9070i	0.794980	−	0.458982i	−0.0467326	−	0.998907i	$-0.514881\pi$
$673$	20.6236	−	11.9070i	0.794980	−	0.458982i	0.841713	+	0.539925i	$0.181548\pi$
$674$	−11.3777	−	42.4621i	−0.438252	−	1.63558i
$675$	11.9544	+	16.7977i	0.460125	+	0.646544i
$676$	9.36633	−	34.3791i	0.360244	−	1.32227i
$677$	35.2413	+	20.3465i	1.35443	+	0.781981i	0.988867	−	0.148805i	$-0.0475425\pi$
$677$	35.2413	+	20.3465i	1.35443	+	0.781981i	0.365565	+	0.930786i	$0.380876\pi$
$678$	−27.8624	+	20.8534i	−1.07005	+	0.800871i
$679$	11.3554			0.435780
$680$	−2.11858	+	3.66948i	−0.0812437	+	0.140718i
$681$	0.747229	+	0.998378i	0.0286339	+	0.0382579i
$682$	−17.3907	+	17.3907i	−0.665925	+	0.665925i
$683$	−12.6069	−	3.37802i	−0.482391	−	0.129256i	0.00942460	−	0.999956i	$-0.497000\pi$
$683$	−12.6069	−	3.37802i	−0.482391	−	0.129256i	−0.491816	+	0.870699i	$0.663667\pi$
$684$	−0.450345	−	0.825118i	−0.0172194	−	0.0315492i
$685$	29.4446	+	50.9995i	1.12502	+	1.94859i
$686$	1.08868	+	1.88566i	0.0415662	+	0.0719947i
$687$	6.44867	−	15.0551i	0.246032	−	0.574389i
$688$	0.111466	−	0.0643548i	0.00424959	−	0.00245350i
$689$	−2.71034	+	3.51691i	−0.103256	+	0.133984i
$690$	−39.3018	−	30.9134i	−1.49620	−	1.17685i
$691$	12.4403	+	3.33338i	0.473253	+	0.126808i	0.487559	−	0.873090i	$-0.337887\pi$
$691$	12.4403	+	3.33338i	0.473253	+	0.126808i	−0.0143063	+	0.999898i	$0.504554\pi$
$692$	43.3400	+	25.0224i	1.64754	+	0.951208i
$693$	1.17657	+	4.85391i	0.0446941	+	0.184385i
$694$	−25.7932	+	25.7932i	−0.979097	+	0.979097i
$695$	37.6531	+	37.6531i	1.42826	+	1.42826i
$696$	−6.94769	+	16.2201i	−0.263351	+	0.614822i
$697$	−0.699043	+	2.60886i	−0.0264781	+	0.0988177i
$698$	17.7994	+	10.2765i	0.673719	+	0.388972i
$699$	45.6162	+	6.56305i	1.72536	+	0.248237i
$700$	2.81477	−	10.5049i	0.106388	−	0.397047i
$701$	−13.2460			−0.500294			−0.250147	−	0.968208i	$-0.580479\pi$
$701$	−13.2460			−0.500294			−0.250147	+	0.968208i	$0.580479\pi$
$702$	−39.7764	+	9.05029i	−1.50126	+	0.341581i
$703$	0.892226			0.0336509
$704$	5.35281	−	19.9769i	0.201742	−	0.752910i
$705$	41.7936	+	6.01306i	1.57404	+	0.226465i
$706$	−33.4629	−	19.3198i	−1.25939	−	0.727111i
$707$	−1.64640	+	6.14446i	−0.0619193	+	0.231086i
$708$	9.13622	−	21.3295i	0.343360	−	0.801611i
$709$	−13.7602	−	13.7602i	−0.516776	−	0.516776i	0.399819	−	0.916594i	$-0.369073\pi$
$709$	−13.7602	−	13.7602i	−0.516776	−	0.516776i	−0.916594	+	0.399819i	$0.869073\pi$
$710$	13.8796	−	13.8796i	0.520891	−	0.520891i
$711$	35.5636	−	33.8970i	1.33374	−	1.27124i
$712$	−14.2499	−	8.22719i	−0.534038	−	0.308327i
$713$	29.0158	+	7.77476i	1.08665	+	0.291167i
$714$	−2.59976	−	2.04487i	−0.0972936	−	0.0765275i
$715$	−16.6216	+	6.84416i	−0.621613	+	0.255957i
$716$	−8.98041	+	5.18484i	−0.335614	+	0.193767i
$717$	−6.75338	+	15.7665i	−0.252209	+	0.588810i
$718$	−35.1455	−	60.8739i	−1.31162	−	2.27179i
$719$	12.4012	+	21.4795i	0.462486	+	0.801049i	0.999084	−	0.0427888i	$-0.0136242\pi$
$719$	12.4012	+	21.4795i	0.462486	+	0.801049i	−0.536598	+	0.843838i	$0.680291\pi$
$720$	17.6856	+	0.424355i	0.659102	+	0.0158148i
$721$	12.4422	+	3.33388i	0.463372	+	0.124160i
$722$	29.2329	−	29.2329i	1.08794	−	1.08794i
$723$	10.6475	+	14.2262i	0.395985	+	0.529079i
$724$	−18.3131	+	31.7192i	−0.680601	+	1.17884i
$725$	−25.0560			−0.930555
$726$	−24.8440	+	18.5943i	−0.922046	+	0.690098i
$727$	14.0053	+	8.08599i	0.519430	+	0.299893i	0.736701	−	0.676218i	$-0.236382\pi$
$727$	14.0053	+	8.08599i	0.519430	+	0.299893i	−0.217272	+	0.976111i	$0.569716\pi$
$728$	4.60733	+	3.55068i	0.170759	+	0.131597i
$729$	17.6696	+	20.4153i	0.654430	+	0.756123i
$730$	−1.76882	−	6.60132i	−0.0654670	−	0.244326i
$731$	−0.0496458	+	0.0286630i	−0.00183622	+	0.00106014i
$732$	23.3149	+	18.3386i	0.861742	+	0.677814i
$733$	−30.2768	−	8.11265i	−1.11830	−	0.299648i	−0.348105	−	0.937456i	$-0.613175\pi$
$733$	−30.2768	−	8.11265i	−1.11830	−	0.299648i	−0.770196	+	0.637808i	$0.779841\pi$
$734$	−12.2406	+	3.27985i	−0.451808	+	0.121062i
$735$	4.76787	+	2.04226i	0.175865	+	0.0753297i
$736$	−32.1352	+	8.61061i	−1.18452	+	0.317391i
$737$	7.91348	−	4.56885i	0.291497	−	0.168296i
$738$	−19.5498	+	4.73879i	−0.719636	+	0.174437i
$739$	−45.0063	+	12.0594i	−1.65558	+	0.443613i	−0.961169	−	0.275961i	$-0.911004\pi$
$739$	−45.0063	+	12.0594i	−1.65558	+	0.443613i	−0.694416	+	0.719574i	$0.744337\pi$
$740$	32.0310	−	55.4793i	1.17748	−	2.03946i
$741$	0.348213	+	0.623238i	0.0127919	+	0.0228952i
$742$	−1.34068	−	2.32212i	−0.0492179	−	0.0852478i
$743$	−5.85484	−	5.85484i	−0.214793	−	0.214793i	0.591507	−	0.806300i	$-0.298533\pi$
$743$	−5.85484	−	5.85484i	−0.214793	−	0.214793i	−0.806300	+	0.591507i	$0.798533\pi$
$744$	17.6011	−	7.04448i	0.645288	−	0.258263i
$745$			14.0761i			0.515709i
$746$	20.5114	+	20.5114i	0.750975	+	0.750975i
$747$	29.5710	+	0.709539i	1.08195	+	0.0259607i
$748$	−1.03582	+	3.86573i	−0.0378733	+	0.141345i
$749$	3.18151	+	11.8736i	0.116250	+	0.433851i
$750$	4.33161	+	10.8228i	0.158168	+	0.395193i
$751$		−	19.1225i		−	0.697791i	−0.937162	−	0.348896i	$-0.886557\pi$
$751$		−	19.1225i		−	0.697791i	0.937162	−	0.348896i	$-0.113443\pi$
$752$	11.3350	−	11.3350i	0.413343	−	0.413343i
$753$	3.03630	+	7.58639i	0.110649	+	0.276463i
$754$	19.0675	−	45.7618i	0.694399	−	1.66655i
$755$		−	18.9101i		−	0.688207i
$756$	2.36580	−	14.0444i	0.0860434	−	0.510791i
$757$	11.4661	−	19.8599i	0.416743	−	0.721820i	−0.578867	−	0.815422i	$-0.696505\pi$
$757$	11.4661	−	19.8599i	0.416743	−	0.721820i	0.995610	+	0.0936022i	$0.0298382\pi$
$758$	−22.3710			−0.812550
$759$	−11.7357	−	5.02682i	−0.425978	−	0.182462i
$760$	0.142944	+	0.533473i	0.00518511	+	0.0193511i
$761$	−3.89211	−	14.5256i	−0.141089	−	0.526551i	−0.999898	−	0.0142560i	$-0.995462\pi$
$761$	−3.89211	−	14.5256i	−0.141089	−	0.526551i	0.858809	−	0.512295i	$-0.171205\pi$
$762$	−33.6808	+	25.2082i	−1.22013	+	0.913196i
$763$	−12.9985			−0.470579
$764$	−14.0554	+	24.3447i	−0.508506	+	0.880759i
$765$	−7.87699	−	0.189004i	−0.284793	−	0.00683345i
$766$		−	1.99016i		−	0.0719074i
$767$	−6.77799	+	16.2671i	−0.244739	+	0.587371i
$768$	−1.42182	+	1.80763i	−0.0513053	+	0.0652273i
$769$	4.87516	−	4.87516i	0.175803	−	0.175803i	−0.613721	−	0.789523i	$-0.710328\pi$
$769$	4.87516	−	4.87516i	0.175803	−	0.175803i	0.789523	+	0.613721i	$0.210328\pi$
$770$		−	10.8553i		−	0.391198i
$771$	21.4701	+	3.08901i	0.773226	+	0.111248i
$772$	−13.2466	−	49.4368i	−0.476754	−	1.77927i
$773$	5.22961	−	19.5172i	0.188096	−	0.701983i	−0.805851	−	0.592119i	$-0.798292\pi$
$773$	5.22961	−	19.5172i	0.188096	−	0.701983i	0.993947	−	0.109865i	$-0.0350417\pi$
$774$	−0.364528	−	0.222287i	−0.0131027	−	0.00798993i
$775$	19.0356	+	19.0356i	0.683778	+	0.683778i
$776$			18.3195i			0.657630i
$777$	10.6253	+	8.35743i	0.381179	+	0.299821i
$778$	−4.83187	−	4.83187i	−0.173231	−	0.173231i
$779$	0.176024	+	0.304882i	0.00630671	+	0.0109235i
$780$	51.2543	+	0.722167i	1.83520	+	0.0258577i
$781$	2.50585	−	4.34025i	0.0896663	−	0.155307i
$782$	8.16686	−	2.18830i	0.292046	−	0.0782536i
$783$	−32.6652	+	3.10976i	−1.16736	+	0.111134i
$784$	1.70534	−	0.984577i	0.0609049	−	0.0351635i
$785$	51.0039	−	13.6665i	1.82041	−	0.487777i
$786$	8.67391	+	72.6042i	0.309388	+	2.58971i
$787$	16.9112	−	4.53135i	0.602820	−	0.161525i	0.0555143	−	0.998458i	$-0.482320\pi$
$787$	16.9112	−	4.53135i	0.602820	−	0.161525i	0.547306	+	0.836933i	$0.315653\pi$
$788$	−59.8290	−	16.0311i	−2.13132	−	0.571086i
$789$	19.9105	−	7.96875i	0.708831	−	0.283695i
$790$	−92.4767	+	53.3915i	−3.29017	+	1.89958i
$791$	2.38841	+	8.91365i	0.0849220	+	0.316933i
$792$	−7.83072	+	1.89814i	−0.278253	+	0.0674474i
$793$	−17.8441	−	13.7517i	−0.633661	−	0.488337i
$794$	36.3323	+	20.9764i	1.28938	+	0.744426i
$795$	−5.87147	−	2.51497i	−0.208240	−	0.0891968i
$796$	−60.3213			−2.13803
$797$	17.3843	−	30.1104i	0.615782	−	1.06657i	−0.374464	−	0.927241i	$-0.622173\pi$
$797$	17.3843	−	30.1104i	0.615782	−	1.06657i	0.990247	−	0.139325i	$-0.0444932\pi$
$798$	−0.428086	+	0.0511427i	−0.0151541	+	0.00181043i
$799$	−5.04849	+	5.04849i	−0.178603	+	0.178603i
$800$	−28.7986	−	7.71657i	−1.01818	−	0.272822i
$801$	0.733970	−	30.5892i	0.0259336	−	1.08081i
$802$	−32.6220	−	56.5030i	−1.15192	−	1.99519i
$803$	−0.872470	−	1.51116i	−0.0307888	−	0.0533278i
$804$	−25.8732	+	3.09103i	−0.912479	+	0.109012i
$805$	−11.4824	+	6.62935i	−0.404700	+	0.233654i
$806$	−49.2524	+	20.2803i	−1.73484	+	0.714342i
$807$	5.68918	−	2.27698i	0.200269	−	0.0801534i
$808$	−9.91274	−	2.65611i	−0.348729	−	0.0934417i
$809$	−43.6279	−	25.1886i	−1.53388	−	0.885583i	−0.999178	−	0.0405395i	$-0.987092\pi$
$809$	−43.6279	−	25.1886i	−1.53388	−	0.885583i	−0.534697	−	0.845044i	$-0.679574\pi$
$810$	−26.8706	−	52.1703i	−0.944136	−	1.83308i
$811$	−4.77657	+	4.77657i	−0.167728	+	0.167728i	−0.785980	−	0.618252i	$-0.787841\pi$
$811$	−4.77657	+	4.77657i	−0.167728	+	0.167728i	0.618252	+	0.785980i	$0.287841\pi$
$812$	12.2390	+	12.2390i	0.429504	+	0.429504i
$813$	3.26425	−	0.389975i	0.114482	−	0.0136770i
$814$	7.32243	−	27.3277i	0.256651	−	0.957835i
$815$	14.3099	+	8.26182i	0.501254	+	0.289399i
$816$	−1.84933	+	2.35115i	−0.0647395	+	0.0823069i
$817$	−0.00193394	+	0.00721756i	−6.76599e−5	+	0.000252510i
$818$	−26.3235			−0.920378
$819$	−1.69107	+	10.6836i	−0.0590908	+	0.373317i
$820$	25.2771			0.882714
$821$	−9.21627	+	34.3956i	−0.321650	+	1.20041i	0.595987	+	0.802994i	$0.296761\pi$
$821$	−9.21627	+	34.3956i	−0.321650	+	1.20041i	−0.917637	+	0.397420i	$0.869906\pi$
$822$	−27.5569	−	68.8528i	−0.961158	−	2.40152i
$823$	37.1078	+	21.4242i	1.29350	+	0.746800i	0.979272	−	0.202549i	$-0.0649226\pi$
$823$	37.1078	+	21.4242i	1.29350	+	0.746800i	0.314223	+	0.949349i	$0.398256\pi$
$824$	−5.37849	+	20.0728i	−0.187369	+	0.699269i
$825$	−6.85567	−	9.15992i	−0.238684	−	0.318908i
$826$	−7.52519	−	7.52519i	−0.261835	−	0.261835i
$827$	−11.1869	+	11.1869i	−0.389007	+	0.389007i	−0.874333	−	0.485326i	$-0.838701\pi$
$827$	−11.1869	+	11.1869i	−0.389007	+	0.389007i	0.485326	+	0.874333i	$0.338701\pi$
$828$	25.1183	+	26.3533i	0.872921	+	0.915841i
$829$	−0.195837	−	0.113067i	−0.00680170	−	0.00392696i	0.496595	−	0.867982i	$-0.334583\pi$
$829$	−0.195837	−	0.113067i	−0.00680170	−	0.00392696i	−0.503397	+	0.864055i	$0.667917\pi$
$830$	−62.0995	−	16.6395i	−2.15550	−	0.577565i
$831$	0.929298	−	6.45906i	0.0322370	−	0.224062i
$832$	27.3413	−	35.4778i	0.947888	−	1.22997i
$833$	−0.759542	+	0.438522i	−0.0263166	+	0.0151939i
$834$	−40.1827	−	53.6884i	−1.39141	−	1.85908i
$835$	0.641082	+	1.11039i	0.0221856	+	0.0384265i
$836$	0.260827	+	0.451765i	0.00902087	+	0.0156246i
$837$	27.1790	+	22.4539i	0.939445	+	0.776121i
$838$	5.03515	+	1.34916i	0.173936	+	0.0466061i
$839$	23.9014	−	23.9014i	0.825167	−	0.825167i	−0.161677	−	0.986844i	$-0.551690\pi$
$839$	23.9014	−	23.9014i	0.825167	−	0.825167i	0.986844	+	0.161677i	$0.0516903\pi$
$840$	−3.29474	+	7.69192i	−0.113679	+	0.265396i
$841$	5.43860	−	9.41993i	0.187538	−	0.324825i
$842$	70.4288			2.42714
$843$	−2.87241	−	24.0433i	−0.0989311	−	0.828095i
$844$	−38.3174	−	22.1226i	−1.31894	−	0.761490i
$845$	−38.9298	−	0.163041i	−1.33923	−	0.00560878i
$846$	−51.0183	−	14.9908i	−1.75404	−	0.515396i
$847$	2.12966	+	7.94799i	0.0731759	+	0.273096i
$848$	−2.10007	+	1.21247i	−0.0721166	+	0.0416365i
$849$	−4.44311	+	30.8817i	−0.152487	+	1.05986i
$850$	7.31889	+	1.96109i	0.251036	+	0.0672649i
$851$	−33.3781	+	8.94363i	−1.14419	+	0.306584i
$852$	−11.4417	+	8.56344i	−0.391986	+	0.293379i
$853$	10.8362	−	2.90356i	0.371026	−	0.0994161i	−0.0684878	−	0.997652i	$-0.521817\pi$
$853$	10.8362	−	2.90356i	0.371026	−	0.0994161i	0.439514	+	0.898236i	$0.355151\pi$
$854$	11.7819	−	6.80231i	0.403170	−	0.232770i
$855$	−0.743425	+	0.708585i	−0.0254246	+	0.0242331i
$856$	−19.1554	+	5.13268i	−0.654719	+	0.175431i
$857$	−22.4845	+	38.9444i	−0.768057	+	1.33031i	0.170558	+	0.985348i	$0.445443\pi$
$857$	−22.4845	+	38.9444i	−0.768057	+	1.33031i	−0.938615	+	0.344967i	$0.887890\pi$
$858$	21.9467	−	5.55042i	0.749248	−	0.189488i
$859$	24.9324	+	43.1842i	0.850683	+	1.47343i	0.880593	+	0.473873i	$0.157145\pi$
$859$	24.9324	+	43.1842i	0.850683	+	1.47343i	−0.0299102	+	0.999553i	$0.509522\pi$
$860$	0.379365	+	0.379365i	0.0129362	+	0.0129362i
$861$	−0.759598	+	5.27956i	−0.0258870	+	0.179927i
$862$			72.9169i			2.48356i
$863$	−21.8607	−	21.8607i	−0.744148	−	0.744148i	0.229225	−	0.973373i	$-0.426381\pi$
$863$	−21.8607	−	21.8607i	−0.744148	−	0.744148i	−0.973373	+	0.229225i	$0.926381\pi$
$864$	−38.5022	−	6.48574i	−1.30987	−	0.220649i
$865$	14.1514	−	52.8137i	0.481162	−	1.79572i
$866$	21.2319	+	79.2384i	0.721488	+	2.69263i
$867$	−17.3801	+	22.0963i	−0.590260	+	0.750430i
$868$		−	18.5965i		−	0.631206i
$869$	−19.2788	+	19.2788i	−0.653989	+	0.653989i
$870$	70.5909	+	10.1563i	2.39325	+	0.344330i
$871$	19.6258	−	2.54199i	0.664996	−	0.0861321i
$872$		−	20.9703i		−	0.710144i
$873$	−29.9023	+	16.3205i	−1.01204	+	0.552365i
$874$	0.551031	−	0.954413i	0.0186389	−	0.0322835i
$875$	3.09109			0.104498
$876$	0.590265	+	4.94077i	0.0199432	+	0.166933i
$877$	6.73490	+	25.1350i	0.227422	+	0.848749i	0.981420	+	0.191872i	$0.0614560\pi$
$877$	6.73490	+	25.1350i	0.227422	+	0.848749i	−0.753998	+	0.656876i	$0.771877\pi$
$878$	−10.6694	−	39.8187i	−0.360074	−	1.34381i
$879$	−3.14429	−	26.3190i	−0.106054	−	0.887719i
$880$	−9.81726			−0.330940
$881$	1.32517	−	2.29526i	0.0446461	−	0.0773294i	−0.842839	−	0.538166i	$-0.819117\pi$
$881$	1.32517	−	2.29526i	0.0446461	−	0.0773294i	0.887485	+	0.460837i	$0.152451\pi$
$882$	−5.57700	−	3.40081i	−0.187787	−	0.114511i
$883$			13.4754i			0.453483i	0.973955	+	0.226741i	$0.0728072\pi$
$883$			13.4754i			0.453483i	−0.973955	+	0.226741i	$0.927193\pi$
$884$	−5.29080	+	6.86528i	−0.177949	+	0.230905i
$885$	−25.0931	−	3.61028i	−0.843496	−	0.121358i
$886$	−14.1652	+	14.1652i	−0.475890	+	0.475890i
$887$		−	27.7253i		−	0.930926i	−0.885067	−	0.465463i	$-0.845888\pi$
$887$		−	27.7253i		−	0.930926i	0.885067	−	0.465463i	$-0.154112\pi$
$888$	−13.4829	+	17.1415i	−0.452456	+	0.575232i
$889$	2.88717	+	10.7751i	0.0968325	+	0.361384i
$890$	−17.2124	+	64.2377i	−0.576962	+	2.15325i
$891$	−10.0745	−	11.0908i	−0.337509	−	0.371556i
$892$	52.5056	+	52.5056i	1.75802	+	1.75802i
$893$			0.930616i			0.0311419i
$894$	2.52447	−	17.5462i	0.0844308	−	0.586833i
$895$	8.01115	+	8.01115i	0.267783	+	0.267783i
$896$	6.01030	+	10.4101i	0.200790	+	0.347779i
$897$	−19.2739	−	19.8248i	−0.643537	−	0.661931i
$898$	−12.2811	+	21.2715i	−0.409825	+	0.709838i
$899$	−41.3846	+	11.0890i	−1.38025	+	0.369838i
$900$	7.68593	+	31.7081i	0.256198	+	1.05694i
$901$	0.935351	−	0.540025i	0.0311611	−	0.0179908i
$902$	10.7828	−	2.88923i	0.359026	−	0.0962009i
$903$	−0.0906371	+	0.0678367i	−0.00301621	+	0.00225746i
$904$	−14.3802	+	3.85317i	−0.478280	+	0.128155i
$905$	38.6527	+	10.3570i	1.28486	+	0.344277i
$906$	−3.39140	+	23.5718i	−0.112672	+	0.783122i
$907$	−11.8680	+	6.85200i	−0.394071	+	0.227517i	−0.683922	−	0.729555i	$-0.739727\pi$
$907$	−11.8680	+	6.85200i	−0.394071	+	0.227517i	0.289852	+	0.957072i	$0.406394\pi$
$908$	0.510757	+	1.90617i	0.0169501	+	0.0632585i
$909$	−4.49561	−	18.5465i	−0.149110	−	0.615150i
$910$	9.04222	−	21.7012i	0.299747	−	0.719388i
$911$	−29.0112	−	16.7496i	−0.961183	−	0.554940i	−0.0646464	−	0.997908i	$-0.520592\pi$
$911$	−29.0112	−	16.7496i	−0.961183	−	0.554940i	−0.896537	+	0.442969i	$0.853925\pi$
$912$	0.0462521	+	0.387149i	0.00153156	+	0.0128198i
$913$	−16.4149			−0.543253
$914$	−7.44886	+	12.9018i	−0.246386	+	0.426753i
$915$	12.7604	−	29.7906i	0.421846	−	0.984846i
$916$	18.3268	−	18.3268i	0.605534	−	0.605534i
$917$	18.7280	+	5.01814i	0.618452	+	0.165714i
$918$	9.78496	+	1.64829i	0.322952	+	0.0544016i
$919$	13.2383	+	22.9293i	0.436690	+	0.756369i	0.997432	−	0.0716215i	$-0.0228174\pi$
$919$	13.2383	+	22.9293i	0.436690	+	0.756369i	−0.560742	+	0.827991i	$0.689484\pi$
$920$	−10.6950	−	18.5243i	−0.352604	−	0.610728i
$921$	27.5257	+	36.7773i	0.907002	+	1.21185i
$922$	76.9383	−	44.4203i	2.53383	−	1.46291i
$923$	8.62484	−	6.58943i	0.283890	−	0.216894i
$924$	−1.12555	+	7.82308i	−0.0370278	+	0.257360i
$925$	−29.9124	−	8.01501i	−0.983515	−	0.263532i
$926$	71.3798	+	41.2111i	2.34568	+	1.35428i
$927$	−37.5558	+	9.10339i	−1.23349	+	0.298995i
$928$	33.5526	−	33.5526i	1.10142	−	1.10142i
$929$	−5.62970	−	5.62970i	−0.184704	−	0.184704i	0.608698	−	0.793402i	$-0.291692\pi$
$929$	−5.62970	−	5.62970i	−0.184704	−	0.184704i	−0.793402	+	0.608698i	$0.791692\pi$
$930$	−45.9135	−	61.3454i	−1.50556	−	2.01160i
$931$	−0.0295877	+	0.110423i	−0.000969699	+	0.00361897i
$932$	63.1592	+	36.4650i	2.06885	+	1.19445i
$933$	−12.7476	−	31.8506i	−0.417336	−	1.04274i
$934$	−20.2158	+	75.4463i	−0.661480	+	2.46868i
$935$	4.37252			0.142997
$936$	−17.2357	−	2.72818i	−0.563368	−	0.0891732i
$937$	9.24801			0.302119			0.151060	−	0.988525i	$-0.451731\pi$
$937$	9.24801			0.302119			0.151060	+	0.988525i	$0.451731\pi$
$938$	−3.09312	+	11.5437i	−0.100994	+	0.376915i
$939$	28.1974	−	35.8489i	0.920188	−	1.16989i
$940$	57.8664	+	33.4092i	1.88739	+	1.08969i
$941$	9.44678	−	35.2559i	0.307956	−	1.14931i	−0.622414	−	0.782688i	$-0.713848\pi$
$941$	9.44678	−	35.2559i	0.307956	−	1.14931i	0.930371	−	0.366620i	$-0.119485\pi$
$942$	−66.0286	+	7.88833i	−2.15133	+	0.257016i
$943$	−9.64116	−	9.64116i	−0.313959	−	0.313959i
$944$	−6.80559	+	6.80559i	−0.221503	+	0.221503i
$945$	−15.4905	+	1.47471i	−0.503906	+	0.0479723i
$946$	0.205192	+	0.118468i	0.00667138	+	0.00385172i
$947$	−11.2143	−	3.00486i	−0.364415	−	0.0976448i	0.0719648	−	0.997407i	$-0.477073\pi$
$947$	−11.2143	−	3.00486i	−0.364415	−	0.0976448i	−0.436380	+	0.899762i	$0.643740\pi$
$948$	72.1810	−	28.8890i	2.34433	−	0.938270i
$949$	−0.485420	−	3.74776i	−0.0157574	−	0.121657i
$950$	0.855316	−	0.493817i	0.0277501	−	0.0160215i
$951$	19.9173	−	2.37948i	0.645861	−	0.0771600i
$952$	−0.707460	−	1.22536i	−0.0229289	−	0.0397140i
$953$	−14.1880	−	24.5743i	−0.459595	−	0.796041i	0.539345	−	0.842085i	$-0.318672\pi$
$953$	−14.1880	−	24.5743i	−0.459595	−	0.796041i	−0.998939	+	0.0460438i	$0.985339\pi$
$954$	6.86789	+	4.18798i	0.222356	+	0.135591i
$955$	29.6662	+	7.94902i	0.959974	+	0.257224i
$956$	−19.1927	+	19.1927i	−0.620737	+	0.620737i
$957$	18.0806	−	2.16006i	0.584464	−	0.0698249i
$958$	−33.7714	+	58.4937i	−1.09110	+	1.88985i
$959$	−19.6649			−0.635014
$960$	59.2300	+	25.3704i	1.91164	+	0.818826i
$961$	13.0186	+	7.51627i	0.419954	+	0.242460i
$962$	37.4018	−	48.5322i	1.20588	−	1.56474i
$963$	−25.4432	−	26.6942i	−0.819894	−	0.860207i
$964$	7.27795	+	27.1617i	0.234407	+	0.874819i
$965$	−48.4263	+	27.9590i	−1.55890	+	0.900031i
$966$	15.5020	−	6.20435i	0.498768	−	0.199622i
$967$	−16.7312	−	4.48310i	−0.538038	−	0.144167i	−0.0204405	−	0.999791i	$-0.506507\pi$
$967$	−16.7312	−	4.48310i	−0.538038	−	0.144167i	−0.517598	+	0.855624i	$0.673174\pi$
$968$	−12.8224	+	3.43574i	−0.412126	+	0.110429i
$969$	−0.0206003	−	0.172433i	−0.000661776	−	0.00553934i
$970$	71.5188	−	19.1634i	2.29633	−	0.615300i
$971$	−25.5006	+	14.7228i	−0.818355	+	0.472477i	−0.849849	−	0.527027i	$-0.823307\pi$
$971$	−25.5006	+	14.7228i	−0.818355	+	0.472477i	0.0314940	+	0.999504i	$0.489973\pi$
$972$	13.9554	+	40.3836i	0.447621	+	1.29530i
$973$	−17.1758	+	4.60224i	−0.550631	+	0.147541i
$974$	−5.85386	+	10.1392i	−0.187570	+	0.324880i
$975$	−6.07540	−	24.0225i	−0.194568	−	0.769336i
$976$	−6.15183	−	10.6553i	−0.196915	−	0.341067i
$977$	12.1275	+	12.1275i	0.387994	+	0.387994i	0.873971	−	0.485977i	$-0.161536\pi$
$977$	12.1275	+	12.1275i	0.387994	+	0.387994i	−0.485977	+	0.873971i	$0.661536\pi$
$978$	−16.3559	−	12.8650i	−0.523005	−	0.411376i
$979$			16.9801i			0.542685i
$980$	5.80398	+	5.80398i	0.185401	+	0.185401i
$981$	34.2292	−	18.6821i	1.09285	−	0.596474i
$982$	11.4304	−	42.6588i	0.364758	−	1.36130i
$983$	7.28272	+	27.1795i	0.232283	+	0.866891i	0.979355	+	0.202148i	$0.0647923\pi$
$983$	7.28272	+	27.1795i	0.232283	+	0.866891i	−0.747072	+	0.664743i	$0.768541\pi$
$984$	−8.51742	−	1.22545i	−0.271525	−	0.0390658i
$985$			67.6725i			2.15623i
$986$	−8.52708	+	8.52708i	−0.271558	+	0.271558i
$987$	−8.71703	+	11.0824i	−0.277466	+	0.352758i
$988$	0.145117	+	1.12040i	0.00461679	+	0.0356447i
$989$		−	0.289394i		−	0.00920219i
$990$	15.6018	+	28.5854i	0.495857	+	0.908504i
$991$	−8.03206	+	13.9119i	−0.255147	+	0.441927i	−0.964935	−	0.262488i	$-0.915457\pi$
$991$	−8.03206	+	13.9119i	−0.255147	+	0.441927i	0.709789	+	0.704415i	$0.248790\pi$
$992$	−50.9814			−1.61866
$993$	−27.3005	+	20.4328i	−0.866355	+	0.648417i
$994$	1.69646	+	6.33129i	0.0538086	+	0.200816i
$995$	17.0573	+	63.6589i	0.540754	+	2.01812i
$996$	43.0278	+	18.4304i	1.36339	+	0.583990i
$997$	−4.97841			−0.157668			−0.0788339	−	0.996888i	$-0.525120\pi$
$997$	−4.97841			−0.157668			−0.0788339	+	0.996888i	$0.525120\pi$
$998$	33.6854	−	58.3449i	1.06629	−	1.84687i
$999$	−39.9913	−	6.73658i	−1.26527	−	0.213136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fy.a.344.14	yes	336
9.5	odd	6		819.2.ew.a.617.71	yes	336
13.11	odd	12		819.2.ew.a.596.71	✓	336
117.50	even	12	inner	819.2.fy.a.50.14	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.596.71	✓	336	13.11	odd	12
819.2.ew.a.617.71	yes	336	9.5	odd	6
819.2.fy.a.50.14	yes	336	117.50	even	12	inner
819.2.fy.a.344.14	yes	336	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.563544 + 2.10318i) q^{2} +(-1.71440 - 0.246659i) q^{3} +(-2.37372 - 1.37047i) q^{4} +(-0.775066 + 2.89259i) q^{5} +(1.48491 - 3.46668i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.14076 - 1.14076i) q^{8} +(2.87832 + 0.845744i) q^{9} +O(q^{10})\)	\(q+(-0.563544 + 2.10318i) q^{2} +(-1.71440 - 0.246659i) q^{3} +(-2.37372 - 1.37047i) q^{4} +(-0.775066 + 2.89259i) q^{5} +(1.48491 - 3.46668i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.14076 - 1.14076i) q^{8} +(2.87832 + 0.845744i) q^{9} +(-5.64684 - 3.26020i) q^{10} +(-1.60810 - 0.430888i) q^{11} +(3.73146 + 2.93502i) q^{12} +(-2.85587 - 2.20091i) q^{13} +(1.88566 - 1.08868i) q^{14} +(2.04226 - 4.76787i) q^{15} +(-0.984577 - 1.70534i) q^{16} +(0.438522 + 0.759542i) q^{17} +(-3.40081 + 5.57700i) q^{18} +(0.110423 + 0.0295877i) q^{19} +(5.80398 - 5.80398i) q^{20} +(1.03785 + 1.38668i) q^{21} +(1.81247 - 3.13928i) q^{22} -4.42750 q^{23} +(-2.23710 + 1.67434i) q^{24} +(-3.43621 - 1.98389i) q^{25} +(6.23830 - 4.76610i) q^{26} +(-4.72597 - 2.15991i) q^{27} +(0.709405 + 2.64754i) q^{28} +(5.46881 - 3.15742i) q^{29} +(8.87676 + 6.98213i) q^{30} +(-6.55354 - 1.75602i) q^{31} +(7.25810 - 1.94480i) q^{32} +(2.65063 + 1.13536i) q^{33} +(-1.84458 + 0.494253i) q^{34} +(2.59342 - 1.49731i) q^{35} +(-5.67325 - 5.95220i) q^{36} +(7.53882 - 2.02002i) q^{37} +(-0.124456 + 0.215565i) q^{38} +(4.35323 + 4.47766i) q^{39} +(2.41559 + 4.18392i) q^{40} +(2.17756 + 2.17756i) q^{41} +(-3.50130 + 1.40132i) q^{42} +0.0653628i q^{43} +(3.22665 + 3.22665i) q^{44} +(-4.67728 + 7.67028i) q^{45} +(2.49509 - 9.31181i) q^{46} +(2.10694 + 7.86319i) q^{47} +(1.26732 + 3.16648i) q^{48} +1.00000i q^{49} +(6.10893 - 6.10893i) q^{50} +(-0.564453 - 1.41032i) q^{51} +(3.76277 + 9.13821i) q^{52} -1.23147i q^{53} +(7.20596 - 8.72235i) q^{54} +(2.49276 - 4.31759i) q^{55} -1.61328 q^{56} +(-0.182011 - 0.0779620i) q^{57} +(3.55869 + 13.2812i) q^{58} +(-1.26502 - 4.72111i) q^{59} +(-11.3819 + 8.51873i) q^{60} +6.24820 q^{61} +(7.38643 - 12.7937i) q^{62} +(-1.43725 - 2.63331i) q^{63} +12.4227i q^{64} +(8.57980 - 6.55502i) q^{65} +(-3.88162 + 4.93492i) q^{66} +(-3.88109 + 3.88109i) q^{67} -2.40392i q^{68} +(7.59049 + 1.09208i) q^{69} +(1.68760 + 6.29823i) q^{70} +(-0.779135 + 2.90777i) q^{71} +(4.24827 - 2.31869i) q^{72} +(0.741136 + 0.741136i) q^{73} +16.9938i q^{74} +(5.40168 + 4.24876i) q^{75} +(-0.221564 - 0.221564i) q^{76} +(0.832411 + 1.44178i) q^{77} +(-11.8705 + 6.63225i) q^{78} +(8.18837 - 14.1827i) q^{79} +(5.69595 - 1.52623i) q^{80} +(7.56943 + 4.86864i) q^{81} +(-5.80696 + 3.35265i) q^{82} +(9.52386 - 2.55191i) q^{83} +(-0.563163 - 4.71391i) q^{84} +(-2.53693 + 0.679767i) q^{85} +(-0.137470 - 0.0368349i) q^{86} +(-10.1545 + 4.06414i) q^{87} +(-2.32600 + 1.34291i) q^{88} +(-2.63978 - 9.85179i) q^{89} +(-13.4961 - 14.1597i) q^{90} +(0.463132 + 3.57568i) q^{91} +(10.5096 + 6.06774i) q^{92} +(10.8022 + 4.62700i) q^{93} -17.7250 q^{94} +(-0.171170 + 0.296476i) q^{95} +(-12.9230 + 1.54389i) q^{96} +(-8.02948 + 8.02948i) q^{97} +(-2.10318 - 0.563544i) q^{98} +(-4.26419 - 2.60027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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