LMFDB - Embedded newform 804.2.l.a.431.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(431,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("804.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.l (of order $6$, degree $2$, 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:	$264$
Relative dimension:	$132$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.15
Character	$\chi$	$=$	804.431
Dual form			804.2.l.a.707.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31532 + 0.519539i) q^{2} +(-1.71904 - 0.211862i) q^{3} +(1.46016 - 1.36673i) q^{4} -0.428467i q^{5} +(2.37117 - 0.614444i) q^{6} +(-1.49589 + 0.863651i) q^{7} +(-1.21051 + 2.55630i) q^{8} +(2.91023 + 0.728399i) q^{9} +O(q^{10})$	\(q+(-1.31532 + 0.519539i) q^{2} +(-1.71904 - 0.211862i) q^{3} +(1.46016 - 1.36673i) q^{4} -0.428467i q^{5} +(2.37117 - 0.614444i) q^{6} +(-1.49589 + 0.863651i) q^{7} +(-1.21051 + 2.55630i) q^{8} +(2.91023 + 0.728399i) q^{9} +(0.222606 + 0.563574i) q^{10} +(0.446229 + 0.772892i) q^{11} +(-2.79963 + 2.04011i) q^{12} +(0.771200 - 1.33576i) q^{13} +(1.51888 - 1.91315i) q^{14} +(-0.0907757 + 0.736554i) q^{15} +(0.264123 - 3.99127i) q^{16} +(-3.15202 - 1.81982i) q^{17} +(-4.20633 + 0.553897i) q^{18} +(-1.83250 - 1.05799i) q^{19} +(-0.585597 - 0.625630i) q^{20} +(2.75447 - 1.16773i) q^{21} +(-0.988484 - 0.784770i) q^{22} +(-0.721633 + 1.24991i) q^{23} +(2.62251 - 4.13793i) q^{24} +4.81642 q^{25} +(-0.320400 + 2.15762i) q^{26} +(-4.84849 - 1.86872i) q^{27} +(-1.00386 + 3.30554i) q^{28} +(4.96095 - 2.86421i) q^{29} +(-0.263269 - 1.01597i) q^{30} +(-3.28865 + 1.89870i) q^{31} +(1.72621 + 5.38704i) q^{32} +(-0.603342 - 1.42317i) q^{33} +(5.09140 + 0.756056i) q^{34} +(0.370046 + 0.640939i) q^{35} +(5.24492 - 2.91391i) q^{36} +(-3.53404 + 6.12114i) q^{37} +(2.95999 + 0.439549i) q^{38} +(-1.60872 + 2.13284i) q^{39} +(1.09529 + 0.518666i) q^{40} +(-1.69847 + 0.980611i) q^{41} +(-3.01634 + 2.96701i) q^{42} +7.20118i q^{43} +(1.70790 + 0.518671i) q^{44} +(0.312095 - 1.24694i) q^{45} +(0.299807 - 2.01895i) q^{46} +(3.46092 + 5.99449i) q^{47} +(-1.29964 + 6.80521i) q^{48} +(-2.00821 + 3.47833i) q^{49} +(-6.33515 + 2.50232i) q^{50} +(5.03292 + 3.79615i) q^{51} +(-0.699540 - 3.00444i) q^{52} -3.02402i q^{53} +(7.34822 - 0.0610151i) q^{54} +(0.331159 - 0.191195i) q^{55} +(-0.396955 - 4.86940i) q^{56} +(2.92599 + 2.20697i) q^{57} +(-5.03720 + 6.34477i) q^{58} +2.75041 q^{59} +(0.874121 + 1.19955i) q^{60} +(-3.08756 + 5.34781i) q^{61} +(3.33919 - 4.20599i) q^{62} +(-4.98246 + 1.42382i) q^{63} +(-5.06931 - 6.18887i) q^{64} +(-0.572328 - 0.330434i) q^{65} +(1.53299 + 1.55848i) q^{66} +(-8.18423 - 0.135500i) q^{67} +(-7.08965 + 1.65072i) q^{68} +(1.50533 - 1.99576i) q^{69} +(-0.819724 - 0.650789i) q^{70} +(3.56341 + 6.17200i) q^{71} +(-5.38488 + 6.55767i) q^{72} +(-4.31639 + 7.47620i) q^{73} +(1.46824 - 9.88736i) q^{74} +(-8.27963 - 1.02041i) q^{75} +(-4.12172 + 0.959683i) q^{76} +(-1.33502 - 0.770773i) q^{77} +(1.00790 - 3.64117i) q^{78} +(-3.94775 + 2.27923i) q^{79} +(-1.71013 - 0.113168i) q^{80} +(7.93887 + 4.23962i) q^{81} +(1.72457 - 2.17224i) q^{82} +(-0.478190 + 0.828249i) q^{83} +(2.42599 - 5.46968i) q^{84} +(-0.779734 + 1.35054i) q^{85} +(-3.74130 - 9.47190i) q^{86} +(-9.13491 + 3.87267i) q^{87} +(-2.51591 + 0.205098i) q^{88} +8.42318i q^{89} +(0.237327 + 1.80227i) q^{90} +2.66419i q^{91} +(0.654579 + 2.81133i) q^{92} +(6.05560 - 2.56722i) q^{93} +(-7.66661 - 6.08662i) q^{94} +(-0.453315 + 0.785164i) q^{95} +(-1.82613 - 9.62628i) q^{96} +(-8.69282 + 15.0564i) q^{97} +(0.834325 - 5.61847i) q^{98} +(0.735656 + 2.57433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.31532	+	0.519539i	−0.930075	+	0.367370i
$2$	−1.31532	+	0.519539i	−0.930075	+	0.367370i
$3$	−1.71904	−	0.211862i	−0.992491	−	0.122318i
$3$	−1.71904	−	0.211862i	−0.992491	−	0.122318i
$4$	1.46016	−	1.36673i	0.730079	−	0.683363i
$5$		−	0.428467i		−	0.191616i	−0.995400	−	0.0958082i	$-0.969456\pi$
$5$		−	0.428467i		−	0.191616i	0.995400	−	0.0958082i	$-0.0305435\pi$
$6$	2.37117	−	0.614444i	0.968027	−	0.250846i
$7$	−1.49589	+	0.863651i	−0.565393	+	0.326430i	−0.755307	−	0.655371i	$-0.772512\pi$
$7$	−1.49589	+	0.863651i	−0.565393	+	0.326430i	0.189914	+	0.981801i	$0.439179\pi$
$8$	−1.21051	+	2.55630i	−0.427982	+	0.903787i
$9$	2.91023	+	0.728399i	0.970076	+	0.242800i
$10$	0.222606	+	0.563574i	0.0703941	+	0.178218i
$11$	0.446229	+	0.772892i	0.134543	+	0.233036i	0.925423	−	0.378936i	$-0.123710\pi$
$11$	0.446229	+	0.772892i	0.134543	+	0.233036i	−0.790880	+	0.611972i	$0.790377\pi$
$12$	−2.79963	+	2.04011i	−0.808185	+	0.588929i
$13$	0.771200	−	1.33576i	0.213892	−	0.370472i	−0.739037	−	0.673665i	$-0.764719\pi$
$13$	0.771200	−	1.33576i	0.213892	−	0.370472i	0.952929	+	0.303192i	$0.0980525\pi$
$14$	1.51888	−	1.91315i	0.405937	−	0.511312i
$15$	−0.0907757	+	0.736554i	−0.0234382	+	0.190178i
$16$	0.264123	−	3.99127i	0.0660308	−	0.997818i
$17$	−3.15202	−	1.81982i	−0.764478	−	0.441371i	0.0664235	−	0.997792i	$-0.478841\pi$
$17$	−3.15202	−	1.81982i	−0.764478	−	0.441371i	−0.830901	+	0.556420i	$0.812175\pi$
$18$	−4.20633	+	0.553897i	−0.991441	+	0.130555i
$19$	−1.83250	−	1.05799i	−0.420403	−	0.242720i	0.274847	−	0.961488i	$-0.411373\pi$
$19$	−1.83250	−	1.05799i	−0.420403	−	0.242720i	−0.695250	+	0.718768i	$0.744706\pi$
$20$	−0.585597	−	0.625630i	−0.130943	−	0.139895i
$21$	2.75447	−	1.16773i	0.601075	−	0.254820i
$22$	−0.988484	−	0.784770i	−0.210746	−	0.167314i
$23$	−0.721633	+	1.24991i	−0.150471	+	0.260623i	−0.931401	−	0.363996i	$-0.881412\pi$
$23$	−0.721633	+	1.24991i	−0.150471	+	0.260623i	0.780930	+	0.624619i	$0.214746\pi$
$24$	2.62251	−	4.13793i	0.535318	−	0.844651i
$25$	4.81642			0.963283
$26$	−0.320400	+	2.15762i	−0.0628356	+	0.423145i
$27$	−4.84849	−	1.86872i	−0.933093	−	0.359635i
$28$	−1.00386	+	3.30554i	−0.189711	+	0.624688i
$29$	4.96095	−	2.86421i	0.921226	−	0.531870i	0.0371999	−	0.999308i	$-0.488156\pi$
$29$	4.96095	−	2.86421i	0.921226	−	0.531870i	0.884026	+	0.467438i	$0.154823\pi$
$30$	−0.263269	−	1.01597i	−0.0480662	−	0.185490i
$31$	−3.28865	+	1.89870i	−0.590659	+	0.341017i	−0.765358	−	0.643605i	$-0.777438\pi$
$31$	−3.28865	+	1.89870i	−0.590659	+	0.341017i	0.174699	+	0.984622i	$0.444105\pi$
$32$	1.72621	+	5.38704i	0.305154	+	0.952303i
$33$	−0.603342	−	1.42317i	−0.105028	−	0.247743i
$34$	5.09140	+	0.756056i	0.873168	+	0.129663i
$35$	0.370046	+	0.640939i	0.0625492	+	0.108338i
$36$	5.24492	−	2.91391i	0.874153	−	0.485651i
$37$	−3.53404	+	6.12114i	−0.580993	+	1.00631i	0.414369	+	0.910109i	$0.364002\pi$
$37$	−3.53404	+	6.12114i	−0.580993	+	1.00631i	−0.995362	+	0.0962006i	$0.969331\pi$
$38$	2.95999	+	0.439549i	0.480174	+	0.0713043i
$39$	−1.60872	+	2.13284i	−0.257602	+	0.341528i
$40$	1.09529	+	0.518666i	0.173180	+	0.0820083i
$41$	−1.69847	+	0.980611i	−0.265256	+	0.153146i	−0.626730	−	0.779237i	$-0.715607\pi$
$41$	−1.69847	+	0.980611i	−0.265256	+	0.153146i	0.361474	+	0.932382i	$0.382274\pi$
$42$	−3.01634	+	2.96701i	−0.465432	+	0.457819i
$43$			7.20118i			1.09817i	0.835766	+	0.549085i	$0.185024\pi$
$43$			7.20118i			1.09817i	−0.835766	+	0.549085i	$0.814976\pi$
$44$	1.70790	+	0.518671i	0.257475	+	0.0781927i
$45$	0.312095	−	1.24694i	0.0465244	−	0.185883i
$46$	0.299807	−	2.01895i	0.0442042	−	0.297678i
$47$	3.46092	+	5.99449i	0.504828	+	0.874387i	0.999984	+	0.00558335i	$0.00177724\pi$
$47$	3.46092	+	5.99449i	0.504828	+	0.874387i	−0.495157	+	0.868804i	$0.664889\pi$
$48$	−1.29964	+	6.80521i	−0.187586	+	0.982248i
$49$	−2.00821	+	3.47833i	−0.286888	+	0.496904i
$50$	−6.33515	+	2.50232i	−0.895926	+	0.353881i
$51$	5.03292	+	3.79615i	0.704749	+	0.531567i
$52$	−0.699540	−	3.00444i	−0.0970087	−	0.416640i
$53$		−	3.02402i		−	0.415381i	−0.978195	−	0.207690i	$-0.933405\pi$
$53$		−	3.02402i		−	0.415381i	0.978195	−	0.207690i	$-0.0665946\pi$
$54$	7.34822	−	0.0610151i	0.999966	−	0.00830311i
$55$	0.331159	−	0.191195i	0.0446535	−	0.0257807i
$56$	−0.396955	−	4.86940i	−0.0530454	−	0.650701i
$57$	2.92599	+	2.20697i	0.387557	+	0.292320i
$58$	−5.03720	+	6.34477i	−0.661416	+	0.833109i
$59$	2.75041			0.358073			0.179037	−	0.983842i	$-0.442702\pi$
$59$	2.75041			0.358073			0.179037	+	0.983842i	$0.442702\pi$
$60$	0.874121	+	1.19955i	0.112849	+	0.154861i
$61$	−3.08756	+	5.34781i	−0.395322	+	0.684717i	−0.993142	−	0.116913i	$-0.962700\pi$
$61$	−3.08756	+	5.34781i	−0.395322	+	0.684717i	0.597821	+	0.801630i	$0.296033\pi$
$62$	3.33919	−	4.20599i	0.424078	−	0.534162i
$63$	−4.98246	+	1.42382i	−0.627731	+	0.179385i
$64$	−5.06931	−	6.18887i	−0.633664	−	0.773609i
$65$	−0.572328	−	0.330434i	−0.0709886	−	0.0409853i
$66$	1.53299	+	1.55848i	0.188698	+	0.191835i
$67$	−8.18423	−	0.135500i	−0.999863	−	0.0165539i
$67$	−8.18423	−	0.135500i	−0.999863	−	0.0165539i
$68$	−7.08965	+	1.65072i	−0.859746	+	0.200180i
$69$	1.50533	−	1.99576i	0.181220	−	0.240261i
$70$	−0.819724	−	0.650789i	−0.0979758	−	0.0777842i
$71$	3.56341	+	6.17200i	0.422899	+	0.732482i	0.996222	−	0.0868476i	$-0.0276793\pi$
$71$	3.56341	+	6.17200i	0.422899	+	0.732482i	−0.573323	+	0.819329i	$0.694346\pi$
$72$	−5.38488	+	6.55767i	−0.634614	+	0.772829i
$73$	−4.31639	+	7.47620i	−0.505195	+	0.875023i	0.494787	+	0.869014i	$0.335246\pi$
$73$	−4.31639	+	7.47620i	−0.505195	+	0.875023i	−0.999982	+	0.00600884i	$0.998087\pi$
$74$	1.46824	−	9.88736i	0.170680	−	1.14938i
$75$	−8.27963	−	1.02041i	−0.956050	−	0.117827i
$76$	−4.12172	+	0.959683i	−0.472793	+	0.110083i
$77$	−1.33502	−	0.770773i	−0.152139	−	0.0878378i
$78$	1.00790	−	3.64117i	0.114122	−	0.412281i
$79$	−3.94775	+	2.27923i	−0.444156	+	0.256434i	−0.705359	−	0.708850i	$-0.749214\pi$
$79$	−3.94775	+	2.27923i	−0.444156	+	0.256434i	0.261203	+	0.965284i	$0.415881\pi$
$80$	−1.71013	−	0.113168i	−0.191198	−	0.0126526i
$81$	7.93887	+	4.23962i	0.882097	+	0.471068i
$82$	1.72457	−	2.17224i	0.190447	−	0.239884i
$83$	−0.478190	+	0.828249i	−0.0524881	+	0.0909121i	−0.891076	−	0.453855i	$-0.850049\pi$
$83$	−0.478190	+	0.828249i	−0.0524881	+	0.0909121i	0.838588	+	0.544767i	$0.183382\pi$
$84$	2.42599	−	5.46968i	0.264698	−	0.596792i
$85$	−0.779734	+	1.35054i	−0.0845740	+	0.146486i
$86$	−3.74130	−	9.47190i	−0.403434	−	1.02138i
$87$	−9.13491	+	3.87267i	−0.979366	+	0.415193i
$88$	−2.51591	+	0.205098i	−0.268197	+	0.0218635i
$89$			8.42318i			0.892855i	0.894820	+	0.446428i	$0.147304\pi$
$89$			8.42318i			0.892855i	−0.894820	+	0.446428i	$0.852696\pi$
$90$	0.237327	+	1.80227i	0.0250164	+	0.189976i
$91$			2.66419i			0.279283i
$92$	0.654579	+	2.81133i	0.0682446	+	0.293102i
$93$	6.05560	−	2.56722i	0.627936	−	0.266208i
$94$	−7.66661	−	6.08662i	−0.790751	−	0.627787i
$95$	−0.453315	+	0.785164i	−0.0465091	+	0.0805561i
$96$	−1.82613	−	9.62628i	−0.186379	−	0.982478i
$97$	−8.69282	+	15.0564i	−0.882622	+	1.52875i	−0.0342077	+	0.999415i	$0.510891\pi$
$97$	−8.69282	+	15.0564i	−0.882622	+	1.52875i	−0.848415	+	0.529332i	$0.822443\pi$
$98$	0.834325	−	5.61847i	0.0842795	−	0.567552i
$99$	0.735656	+	2.57433i	0.0739362	+	0.258729i
$100$	7.03273	−	6.58272i	0.703273	−	0.658272i
$101$	−9.63547	+	5.56304i	−0.958765	+	0.553543i	−0.895793	−	0.444472i	$-0.853391\pi$
$101$	−9.63547	+	5.56304i	−0.958765	+	0.553543i	−0.0629725	+	0.998015i	$0.520058\pi$
$102$	−8.59217	−	2.37837i	−0.850751	−	0.235493i
$103$	−6.69655	+	3.86625i	−0.659831	+	0.380953i	−0.792212	−	0.610245i	$-0.791071\pi$
$103$	−6.69655	+	3.86625i	−0.659831	+	0.380953i	0.132382	+	0.991199i	$0.457737\pi$
$104$	2.48104	+	3.58837i	0.243286	+	0.351869i
$105$	−0.500336	−	1.18020i	−0.0488278	−	0.115176i
$106$	1.57110	+	3.97756i	0.152598	+	0.386335i
$107$	8.14496			0.787403			0.393701	−	0.919238i	$-0.371194\pi$
$107$	8.14496			0.787403			0.393701	+	0.919238i	$0.371194\pi$
$108$	−9.63359	+	3.89794i	−0.926993	+	0.375080i
$109$	13.5356			1.29648			0.648239	−	0.761437i	$-0.275506\pi$
$109$	13.5356			1.29648			0.648239	+	0.761437i	$0.275506\pi$
$110$	−0.336248	+	0.423533i	−0.0320600	+	0.0403823i
$111$	7.37201	−	9.77379i	0.699721	−	0.927687i
$112$	3.05197	+	6.19860i	0.288384	+	0.585713i
$113$	−16.4569	+	9.50142i	−1.54814	+	0.893818i	−0.549855	+	0.835260i	$0.685317\pi$
$113$	−16.4569	+	9.50142i	−1.54814	+	0.893818i	−0.998284	+	0.0585578i	$0.981350\pi$
$114$	−4.99524	−	1.38271i	−0.467847	−	0.129503i
$115$	0.535544	+	0.309196i	0.0499397	+	0.0288327i
$116$	3.32919	−	10.9625i	0.309108	−	1.01784i
$117$	3.21733	−	3.32562i	0.297442	−	0.307454i
$118$	−3.61768	+	1.42895i	−0.333035	+	0.131545i
$119$	6.28676			0.576307
$120$	−1.77297	−	1.12366i	−0.161849	−	0.102576i
$121$	5.10176	−	8.83651i	0.463796	−	0.803319i
$122$	1.28275	−	8.63822i	0.116134	−	0.782067i
$123$	3.12750	−	1.32587i	0.281997	−	0.119550i
$124$	−2.20694	+	7.26709i	−0.198189	+	0.652604i
$125$		−	4.20601i		−	0.376197i
$126$	5.81382	−	4.46137i	0.517936	−	0.397450i
$127$	8.17538	−	4.72006i	0.725447	−	0.418837i	−0.0913070	−	0.995823i	$-0.529104\pi$
$127$	8.17538	−	4.72006i	0.725447	−	0.418837i	0.816754	+	0.576986i	$0.195771\pi$
$128$	9.88315	+	5.50667i	0.873555	+	0.486725i
$129$	1.52565	−	12.3792i	0.134326	−	1.08992i
$130$	0.924471	+	0.137281i	0.0810815	+	0.0120403i
$131$	−0.0675095			−0.00589833			−0.00294917	−	0.999996i	$-0.500939\pi$
$131$	−0.0675095			−0.00589833			−0.00294917	+	0.999996i	$0.500939\pi$
$132$	−2.82606	−	1.25346i	−0.245977	−	0.109099i
$133$	3.65494			0.316924
$134$	10.8353	−	4.07380i	0.936029	−	0.351923i
$135$	−0.800684	+	2.07742i	−0.0689119	+	0.178796i
$136$	8.46757	−	5.85458i	0.726088	−	0.502027i
$137$			8.52468i			0.728313i	0.931338	+	0.364156i	$0.118643\pi$
$137$			8.52468i			0.728313i	−0.931338	+	0.364156i	$0.881357\pi$
$138$	−0.943119	+	3.40715i	−0.0802837	+	0.290035i
$139$		−	5.28312i		−	0.448108i	−0.974577	−	0.224054i	$-0.928071\pi$
$139$		−	5.28312i		−	0.448108i	0.974577	−	0.224054i	$-0.0719292\pi$
$140$	1.41631	+	0.430121i	0.119700	+	0.0363518i
$141$	−4.67948	−	11.0380i	−0.394083	−	0.929571i
$142$	−7.89363	−	6.26686i	−0.662419	−	0.525903i
$143$	1.37653			0.115111
$144$	3.67590	−	11.4231i	0.306325	−	0.951927i
$145$	−1.22722	−	2.12561i	−0.101915	−	0.176522i
$146$	1.79327	−	12.0762i	0.148412	−	0.999430i
$147$	4.18913	−	5.55394i	0.345514	−	0.458081i
$148$	3.20566	+	13.7679i	0.263504	+	1.13171i
$149$			0.475662i			0.0389678i	0.999810	+	0.0194839i	$0.00620230\pi$
$149$			0.475662i			0.0389678i	−0.999810	+	0.0194839i	$0.993798\pi$
$150$	11.4206	−	2.95942i	0.932484	−	0.241636i
$151$	−0.576409	−	0.332790i	−0.0469075	−	0.0270821i	0.476363	−	0.879249i	$-0.341955\pi$
$151$	−0.576409	−	0.332790i	−0.0469075	−	0.0270821i	−0.523270	+	0.852167i	$0.675288\pi$
$152$	4.92280	−	3.40369i	0.399292	−	0.276076i
$153$	−7.84755	−	7.59202i	−0.634437	−	0.613779i
$154$	2.15643	+	0.320223i	0.173770	+	0.0258043i
$155$	0.813532	+	1.40908i	0.0653445	+	0.113180i
$156$	0.566016	+	5.31296i	0.0453176	+	0.425378i
$157$	2.19931	−	3.80931i	0.175524	−	0.304016i	−0.764819	−	0.644246i	$-0.777171\pi$
$157$	2.19931	−	3.80931i	0.175524	−	0.304016i	0.940342	+	0.340229i	$0.110505\pi$
$158$	4.00842	−	5.04894i	0.318893	−	0.401672i
$159$	−0.640673	+	5.19842i	−0.0508087	+	0.412262i
$160$	2.30817	−	0.739626i	0.182477	−	0.0584726i
$161$		−	2.49296i		−	0.196473i
$162$	−12.6448	−	1.45192i	−0.993472	−	0.114073i
$163$	16.6603	−	9.61884i	1.30494	−	0.753405i	0.323690	−	0.946163i	$-0.395076\pi$
$163$	16.6603	−	9.61884i	1.30494	−	0.753405i	0.981246	+	0.192758i	$0.0617431\pi$
$164$	−1.13981	+	3.75319i	−0.0890039	+	0.293075i
$165$	−0.609784	+	0.258512i	−0.0474716	+	0.0201252i
$166$	0.198667	−	1.33785i	0.0154195	−	0.103838i
$167$	−6.57208	−	11.3832i	−0.508563	−	0.880857i	−0.999951	−	0.00991607i	$-0.996844\pi$
$167$	−6.57208	−	11.3832i	−0.508563	−	0.880857i	0.491388	−	0.870941i	$-0.336490\pi$
$168$	−0.349254	+	8.45481i	−0.0269455	+	0.652303i
$169$	5.31050	+	9.19806i	0.408500	+	0.707543i
$170$	0.323945	−	2.18150i	0.0248455	−	0.167313i
$171$	−4.56234	−	4.41379i	−0.348891	−	0.337531i
$172$	9.84204	+	10.5149i	0.750449	+	0.801751i
$173$	12.8506	+	7.41930i	0.977013	+	0.564079i	0.901367	−	0.433056i	$-0.142565\pi$
$173$	12.8506	+	7.41930i	0.977013	+	0.564079i	0.0756459	+	0.997135i	$0.475898\pi$
$174$	10.0034	−	9.83976i	0.758354	−	0.745950i
$175$	−7.20482	+	4.15970i	−0.544633	+	0.314444i
$176$	3.20268	−	1.57688i	0.241411	−	0.118862i
$177$	−4.72808	−	0.582706i	−0.355384	−	0.0437989i
$178$	−4.37617	−	11.0792i	−0.328008	−	0.830422i
$179$	−2.64524			−0.197714			−0.0988572	−	0.995102i	$-0.531519\pi$
$179$	−2.64524			−0.197714			−0.0988572	+	0.995102i	$0.531519\pi$
$180$	−1.24851	−	2.24727i	−0.0930587	−	0.167502i
$181$	−0.972575	−	1.68455i	−0.0722910	−	0.125212i	0.827614	−	0.561298i	$-0.189698\pi$
$181$	−0.972575	−	1.68455i	−0.0722910	−	0.125212i	−0.899905	+	0.436086i	$0.856364\pi$
$182$	−1.38415	−	3.50428i	−0.102600	−	0.259754i
$183$	6.44065	−	8.53899i	0.476106	−	0.631220i
$184$	−2.32158	−	3.35774i	−0.171149	−	0.247536i
$185$	2.62271	+	1.51422i	0.192825	+	0.111328i
$186$	−6.63131	+	6.52284i	−0.486231	+	0.478278i
$187$		−	3.24823i		−	0.237534i
$188$	13.2463	+	4.02278i	0.966087	+	0.293391i
$189$	8.86672	−	1.39202i	0.644959	−	0.101255i
$190$	0.188333	−	1.26826i	0.0136631	−	0.0920093i
$191$	4.65474	−	8.06224i	0.336805	−	0.583363i	−0.647025	−	0.762469i	$-0.723987\pi$
$191$	4.65474	−	8.06224i	0.336805	−	0.583363i	0.983830	+	0.179106i	$0.0573204\pi$
$192$	7.40319	+	11.7129i	0.534279	+	0.845308i
$193$	−0.841401			−0.0605654			−0.0302827	−	0.999541i	$-0.509641\pi$
$193$	−0.841401			−0.0605654			−0.0302827	+	0.999541i	$0.509641\pi$
$194$	3.61149	−	24.3203i	0.259290	−	1.74610i
$195$	0.913852	+	0.689285i	0.0654423	+	0.0493607i
$196$	1.82161	+	7.82358i	0.130115	+	0.558827i
$197$	10.5327	−	6.08108i	0.750426	−	0.433259i	−0.0754216	−	0.997152i	$-0.524030\pi$
$197$	10.5327	−	6.08108i	0.750426	−	0.433259i	0.825848	+	0.563893i	$0.190697\pi$
$198$	−2.30509	−	3.00387i	−0.163816	−	0.213476i
$199$	−10.9090	−	6.29831i	−0.773317	−	0.446475i	0.0607393	−	0.998154i	$-0.480654\pi$
$199$	−10.9090	−	6.29831i	−0.773317	−	0.446475i	−0.834057	+	0.551679i	$0.813988\pi$
$200$	−5.83034	+	12.3122i	−0.412267	+	0.870603i
$201$	14.0404	+	1.96685i	0.990330	+	0.138731i
$202$	9.78356	−	12.3232i	0.688369	−	0.867058i
$203$	−4.94735	+	8.56907i	−0.347236	+	0.601431i
$204$	12.5371	−	1.33564i	0.877776	−	0.0935137i
$205$	0.420160	+	0.727738i	0.0293452	+	0.0508275i
$206$	6.79947	−	8.56450i	0.473741	−	0.596717i
$207$	−3.01055	+	3.11188i	−0.209248	+	0.216290i
$208$	−5.12768	−	3.43087i	−0.355540	−	0.237888i
$209$		−	1.88843i		−	0.130625i
$210$	1.27127	+	1.29240i	0.0877256	+	0.0891844i
$211$	7.19086	+	4.15164i	0.495039	+	0.285811i	0.726663	−	0.686995i	$-0.241070\pi$
$211$	7.19086	+	4.15164i	0.495039	+	0.285811i	−0.231624	+	0.972806i	$0.574404\pi$
$212$	−4.13300	−	4.41554i	−0.283856	−	0.303261i
$213$	−4.81805	−	11.3649i	−0.330127	−	0.778710i
$214$	−10.7133	+	4.23162i	−0.732343	+	0.289268i
$215$	3.08547			0.210427
$216$	10.6462	−	10.1321i	0.724380	−	0.689401i
$217$	3.27963	−	5.68049i	0.222636	−	0.385617i
$218$	−17.8037	+	7.03229i	−1.20582	+	0.476287i
$219$	9.00398	−	11.9374i	0.608433	−	0.806658i
$220$	0.222234	−	0.731778i	0.0149830	−	0.0493364i
$221$	−4.86168	+	2.80689i	−0.327032	+	0.188812i
$222$	−4.61872	+	16.6858i	−0.309988	+	1.11987i
$223$		−	8.31619i		−	0.556893i	−0.960452	−	0.278446i	$-0.910181\pi$
$223$		−	8.31619i		−	0.556893i	0.960452	−	0.278446i	$-0.0898195\pi$
$224$	−7.23475	−	6.56756i	−0.483392	−	0.438814i
$225$	14.0169	+	3.50827i	0.934458	+	0.233885i
$226$	16.7099	−	21.0475i	1.11152	−	1.40006i
$227$	−11.4109	−	19.7642i	−0.757368	−	1.31180i	−0.944189	−	0.329405i	$-0.893152\pi$
$227$	−11.4109	−	19.7642i	−0.757368	−	1.31180i	0.186821	−	0.982394i	$-0.440182\pi$
$228$	7.28873	−	0.776505i	0.482708	−	0.0514253i
$229$	−4.44161	+	7.69309i	−0.293510	+	0.508374i	−0.974637	−	0.223791i	$-0.928157\pi$
$229$	−4.44161	+	7.69309i	−0.293510	+	0.508374i	0.681127	+	0.732165i	$0.261490\pi$
$230$	−0.865053	−	0.128458i	−0.0570399	−	0.00847024i
$231$	2.13166	+	1.60783i	0.140253	+	0.105788i
$232$	1.31646	+	16.1488i	0.0864298	+	1.06022i
$233$	−17.0094	+	9.82040i	−1.11432	+	0.643355i	−0.939946	−	0.341323i	$-0.889125\pi$
$233$	−17.0094	+	9.82040i	−1.11432	+	0.643355i	−0.174378	+	0.984679i	$0.555792\pi$
$234$	−2.50405	+	6.04580i	−0.163695	+	0.395226i
$235$	2.56844	−	1.48289i	0.167547	−	0.0967332i
$236$	4.01603	−	3.75906i	0.261422	−	0.244694i
$237$	7.26924	−	3.08173i	0.472188	−	0.200180i
$238$	−8.26913	+	3.26622i	−0.536008	+	0.211718i
$239$	12.9717	+	22.4676i	0.839070	+	1.45331i	0.890674	+	0.454643i	$0.150233\pi$
$239$	12.9717	+	22.4676i	0.839070	+	1.45331i	−0.0516040	+	0.998668i	$0.516433\pi$
$240$	2.91581	+	0.556851i	0.188215	+	0.0359446i
$241$	−11.9228			−0.768012			−0.384006	−	0.923331i	$-0.625456\pi$
$241$	−11.9228			−0.768012			−0.384006	+	0.923331i	$0.625456\pi$
$242$	−2.11956	+	14.2734i	−0.136250	+	0.917531i
$243$	−12.7491	−	8.97003i	−0.817853	−	0.575428i
$244$	2.80066	+	12.0285i	0.179294	+	0.770046i
$245$	1.49035	+	0.860453i	0.0952149	+	0.0549723i
$246$	−3.42483	+	3.36881i	−0.218359	+	0.214788i
$247$	−2.82644	+	1.63185i	−0.179842	+	0.103832i
$248$	−0.872690	−	10.7052i	−0.0554159	−	0.679779i
$249$	0.997504	−	1.32249i	0.0632142	−	0.0838092i
$250$	2.18519	+	5.53227i	0.138203	+	0.349892i
$251$	−0.592255	+	1.02582i	−0.0373828	+	0.0647489i	−0.884111	−	0.467276i	$-0.845235\pi$
$251$	−0.592255	+	1.02582i	−0.0373828	+	0.0647489i	0.846729	+	0.532025i	$0.178569\pi$
$252$	−5.32921	+	8.88866i	−0.335709	+	0.559933i
$253$	−1.28806			−0.0809794
$254$	−8.30102	+	10.4558i	−0.520852	+	0.656057i
$255$	1.62652	−	2.15644i	0.101857	−	0.135042i
$256$	−15.8605	−	2.10837i	−0.991280	−	0.131773i
$257$	−8.62666	+	4.98060i	−0.538116	+	0.310682i	−0.744315	−	0.667829i	$-0.767224\pi$
$257$	−8.62666	+	4.98060i	−0.538116	+	0.310682i	0.206199	+	0.978510i	$0.433891\pi$
$258$	4.42473	+	17.0752i	0.275472	+	1.06306i
$259$		−	12.2087i		−	0.758613i
$260$	−1.28730	+	0.299730i	−0.0798351	+	0.0185885i
$261$	16.5238	−	4.72195i	1.02280	−	0.292281i
$262$	0.0887969	−	0.0350738i	0.00548589	−	0.00216687i
$263$	−19.1630			−1.18164			−0.590821	−	0.806803i	$-0.701196\pi$
$263$	−19.1630			−1.18164			−0.590821	+	0.806803i	$0.701196\pi$
$264$	4.36841	+	0.180452i	0.268857	+	0.0111060i
$265$	−1.29569			−0.0795937
$266$	−4.80744	+	1.89889i	−0.294763	+	0.116428i
$267$	1.78455	−	14.4798i	0.109213	−	0.886150i
$268$	−12.1355	+	10.9877i	−0.741291	+	0.671183i
$269$		−	5.82725i		−	0.355294i	−0.984094	−	0.177647i	$-0.943152\pi$
$269$		−	5.82725i		−	0.355294i	0.984094	−	0.177647i	$-0.0568484\pi$
$270$	−0.0261430	−	3.14847i	−0.00159101	−	0.191610i
$271$			24.8684i			1.51065i	0.655351	+	0.755324i	$0.272521\pi$
$271$			24.8684i			1.51065i	−0.655351	+	0.755324i	$0.727479\pi$
$272$	−8.09592	+	12.0999i	−0.490887	+	0.733665i
$273$	0.564440	−	4.57986i	0.0341614	−	0.277186i
$274$	−4.42891	−	11.2127i	−0.267560	−	0.677385i
$275$	2.14923	+	3.72257i	0.129603	+	0.224479i
$276$	−0.529637	−	4.97149i	−0.0318804	−	0.299249i
$277$	−13.9789			−0.839912			−0.419956	−	0.907544i	$-0.637955\pi$
$277$	−13.9789			−0.839912			−0.419956	+	0.907544i	$0.637955\pi$
$278$	2.74479	+	6.94901i	0.164621	+	0.416774i
$279$	−10.9537	+	3.13021i	−0.655783	+	0.187401i
$280$	−2.08638	+	0.170082i	−0.124685	+	0.0101644i
$281$	−5.68345	−	3.28134i	−0.339046	−	0.195748i	0.320804	−	0.947146i	$-0.396047\pi$
$281$	−5.68345	−	3.28134i	−0.339046	−	0.195748i	−0.659850	+	0.751397i	$0.729380\pi$
$282$	11.8897	+	12.0874i	0.708023	+	0.719796i
$283$		−	0.0629846i		−	0.00374404i	−0.999998	−	0.00187202i	$-0.999404\pi$
$283$		−	0.0629846i		−	0.00374404i	0.999998	−	0.00187202i	$-0.000595883\pi$
$284$	13.6386	+	4.14190i	0.809300	+	0.245776i
$285$	0.945614	−	1.25369i	0.0560134	−	0.0742623i
$286$	−1.81058	+	0.715160i	−0.107062	+	0.0422883i
$287$	1.69381	−	2.93377i	0.0999826	−	0.173175i
$288$	1.09977	+	16.9349i	0.0648043	+	0.997898i
$289$	−1.87651	−	3.25020i	−0.110383	−	0.191188i
$290$	2.71853	+	2.15827i	0.159637	+	0.126738i
$291$	18.1332	−	24.0410i	1.06299	−	1.40931i
$292$	3.91531	+	16.8157i	0.229126	+	0.984067i
$293$			0.610284i			0.0356532i	0.999841	+	0.0178266i	$0.00567468\pi$
$293$			0.610284i			0.0356532i	−0.999841	+	0.0178266i	$0.994325\pi$
$294$	−2.62458	+	9.48165i	−0.153069	+	0.552981i
$295$		−	1.17846i		−	0.0686127i
$296$	−11.3694	−	16.4438i	−0.660836	−	0.955776i
$297$	−0.719225	−	4.58124i	−0.0417337	−	0.265830i
$298$	−0.247125	−	0.625650i	−0.0143156	−	0.0362429i
$299$	1.11305	+	1.92785i	0.0643692	+	0.111491i
$300$	−13.4842	+	9.82602i	−0.778511	+	0.567306i
$301$	−6.21931	−	10.7722i	−0.358475	−	0.620897i
$302$	0.931062	+	0.138260i	0.0535766	+	0.00795595i
$303$	17.7424	−	7.52173i	1.01927	−	0.432112i
$304$	−4.70673	+	7.03454i	−0.269950	+	0.403459i
$305$	2.29136	+	1.32292i	0.131203	+	0.0757501i
$306$	14.2664	+	5.90887i	0.815558	+	0.337787i
$307$	16.9580	+	9.79073i	0.967847	+	0.558787i	0.898579	−	0.438811i	$-0.144600\pi$
$307$	16.9580	+	9.79073i	0.967847	+	0.558787i	0.0692677	+	0.997598i	$0.477934\pi$
$308$	−3.00277	+	0.699153i	−0.171099	+	0.0398379i
$309$	12.3308	−	5.22752i	0.701473	−	0.297383i
$310$	−1.80213	−	1.43073i	−0.102354	−	0.0812603i
$311$	−0.887087			−0.0503021			−0.0251510	−	0.999684i	$-0.508007\pi$
$311$	−0.887087			−0.0503021			−0.0251510	+	0.999684i	$0.508007\pi$
$312$	−3.50479	−	6.69421i	−0.198420	−	0.378985i
$313$	−0.578659			−0.0327078			−0.0163539	−	0.999866i	$-0.505206\pi$
$313$	−0.578659			−0.0327078			−0.0163539	+	0.999866i	$0.505206\pi$
$314$	−0.913717	+	6.15311i	−0.0515640	+	0.347240i
$315$	0.610061	+	2.13482i	0.0343730	+	0.120284i
$316$	−2.64925	+	8.72353i	−0.149032	+	0.490737i
$317$	−5.17033	−	2.98509i	−0.290395	−	0.167659i	0.347725	−	0.937596i	$-0.386954\pi$
$317$	−5.17033	−	2.98509i	−0.290395	−	0.167659i	−0.638120	+	0.769937i	$0.720288\pi$
$318$	−1.85809	−	7.17047i	−0.104197	−	0.402100i
$319$	4.42745	+	2.55619i	0.247889	+	0.143119i
$320$	−2.65173	+	2.17203i	−0.148236	+	0.121420i
$321$	−14.0015	−	1.72560i	−0.781490	−	0.0963137i
$322$	1.29519	+	3.27905i	0.0721781	+	0.182734i
$323$	3.85071	+	6.66963i	0.214259	+	0.371108i
$324$	17.3864	−	4.65975i	0.965911	−	0.258875i
$325$	3.71442	−	6.43356i	0.206039	−	0.356870i
$326$	−16.9164	+	21.3076i	−0.936911	+	1.18012i
$327$	−23.2683	−	2.86768i	−1.28674	−	0.158583i
$328$	−0.450713	−	5.52884i	−0.0248865	−	0.305279i
$329$	−10.3543	−	5.97806i	−0.570851	−	0.329581i
$330$	0.667756	−	0.656834i	0.0367588	−	0.0361575i
$331$	−3.22672	+	1.86295i	−0.177357	+	0.102397i	−0.586050	−	0.810275i	$-0.699318\pi$
$331$	−3.22672	+	1.86295i	−0.177357	+	0.102397i	0.408693	+	0.912672i	$0.365985\pi$
$332$	0.433756	+	1.86293i	0.0238055	+	0.102241i
$333$	−14.7435	+	15.2397i	−0.807939	+	0.835132i
$334$	14.5584	+	11.5581i	0.796602	+	0.632432i
$335$	−0.0580573	+	3.50668i	−0.00317201	+	0.191590i
$336$	−3.93322	−	11.3023i	−0.214575	−	0.616589i
$337$	9.09033	−	15.7449i	0.495182	−	0.857680i	−0.504803	−	0.863235i	$-0.668435\pi$
$337$	9.09033	−	15.7449i	0.495182	−	0.857680i	0.999985	+	0.00555444i	$0.00176804\pi$
$338$	−11.7638	−	9.33942i	−0.639866	−	0.507997i
$339$	30.3032	−	12.8468i	1.64584	−	0.697741i
$340$	0.707281	+	3.03768i	0.0383577	+	0.164741i
$341$	−2.93498	−	1.69451i	−0.158938	−	0.0917631i
$342$	8.29409	+	3.43525i	0.448493	+	0.185757i
$343$		−	19.0287i		−	1.02745i
$344$	−18.4084	−	8.71714i	−0.992513	−	0.469997i
$345$	−0.855117	−	0.644983i	−0.0460379	−	0.0347247i
$346$	−20.7573	−	3.08239i	−1.11592	−	0.165711i
$347$	−6.32213	−	10.9503i	−0.339390	−	0.587840i	0.644928	−	0.764243i	$-0.276887\pi$
$347$	−6.32213	−	10.9503i	−0.339390	−	0.587840i	−0.984318	+	0.176403i	$0.943554\pi$
$348$	−8.04555	+	18.1396i	−0.431287	+	0.972386i
$349$	18.5994			0.995603			0.497801	−	0.867291i	$-0.334141\pi$
$349$	18.5994			0.995603			0.497801	+	0.867291i	$0.334141\pi$
$350$	7.31555	−	9.21455i	0.391032	−	0.492538i
$351$	−6.23531	+	5.03526i	−0.332816	+	0.268762i
$352$	−3.39331	+	3.73803i	−0.180864	+	0.199238i
$353$	20.0623	+	11.5830i	1.06781	+	0.616499i	0.927582	−	0.373620i	$-0.121884\pi$
$353$	20.0623	+	11.5830i	1.06781	+	0.616499i	0.140226	+	0.990120i	$0.455217\pi$
$354$	6.52170	−	1.68997i	0.346624	−	0.0898211i
$355$	2.64450	−	1.52680i	0.140356	−	0.0810343i
$356$	11.5122	+	12.2992i	0.610144	+	0.651855i
$357$	−10.8072	−	1.33192i	−0.571979	−	0.0704928i
$358$	3.47935	−	1.37431i	0.183889	−	0.0726343i
$359$	7.94201			0.419163			0.209581	−	0.977791i	$-0.432790\pi$
$359$	7.94201			0.419163			0.209581	+	0.977791i	$0.432790\pi$
$360$	2.80975	+	2.30724i	0.148087	+	0.121602i
$361$	−7.26131	−	12.5770i	−0.382174	−	0.661945i
$362$	2.15444	+	1.71044i	0.113235	+	0.0898987i
$363$	−10.6423	+	14.1095i	−0.558574	+	0.740556i
$364$	3.64122	+	3.89014i	0.190852	+	0.203899i
$365$	3.20331	+	1.84943i	0.167669	+	0.0968036i
$366$	−4.03520	+	14.5777i	−0.210923	+	0.761989i
$367$	19.3682	−	11.1822i	1.01101	−	0.583708i	0.0995247	−	0.995035i	$-0.468268\pi$
$367$	19.3682	−	11.1822i	1.01101	−	0.583708i	0.911488	+	0.411327i	$0.134934\pi$
$368$	4.79811	+	3.21036i	0.250119	+	0.167352i
$369$	−5.65721	+	1.61664i	−0.294503	+	0.0841590i
$370$	−4.23641	−	0.629093i	−0.220241	−	0.0327050i
$371$	2.61170	+	4.52359i	0.135593	+	0.234853i
$372$	5.33345	−	12.0249i	0.276527	−	0.623461i
$373$	−8.72796	−	15.1173i	−0.451916	−	0.782742i	0.546589	−	0.837401i	$-0.315926\pi$
$373$	−8.72796	−	15.1173i	−0.451916	−	0.782742i	−0.998505	+	0.0546590i	$0.982593\pi$
$374$	1.68758	+	4.27248i	0.0872628	+	0.220925i
$375$	−0.891092	+	7.23032i	−0.0460158	+	0.373372i
$376$	−19.5132	+	1.59072i	−1.00632	+	0.0820354i
$377$		−	8.83551i		−	0.455052i
$378$	−10.9394	+	6.43757i	−0.562663	+	0.331113i
$379$	−12.7368	−	7.35362i	−0.654247	−	0.377730i	0.135834	−	0.990732i	$-0.456629\pi$
$379$	−12.7368	−	7.35362i	−0.654247	−	0.377730i	−0.790082	+	0.613002i	$0.789962\pi$
$380$	0.411193	+	1.76602i	0.0210937	+	0.0905949i
$381$	−15.0538	+	6.38194i	−0.771231	+	0.326957i
$382$	−1.93384	+	13.0228i	−0.0989438	+	0.666303i
$383$	−10.2194	+	17.7006i	−0.522189	+	0.904458i	0.477478	+	0.878644i	$0.341551\pi$
$383$	−10.2194	+	17.7006i	−0.522189	+	0.904458i	−0.999667	+	0.0258141i	$0.991782\pi$
$384$	−15.8229	−	11.5601i	−0.807460	−	0.589922i
$385$	−0.330251	+	0.572012i	−0.0168312	+	0.0291524i
$386$	1.10672	−	0.437141i	0.0563303	−	0.0222499i
$387$	−5.24533	+	20.9571i	−0.266635	+	1.06531i
$388$	7.88508	+	33.8654i	0.400305	+	1.71926i
$389$	3.40385	+	1.96521i	0.172582	+	0.0996403i	0.583803	−	0.811895i	$-0.301564\pi$
$389$	3.40385	+	1.96521i	0.172582	+	0.0996403i	−0.411221	+	0.911536i	$0.634897\pi$
$390$	−1.56012	−	0.431852i	−0.0789999	−	0.0218677i
$391$	4.54921	−	2.62649i	0.230063	−	0.132827i
$392$	−6.46066	−	9.34415i	−0.326313	−	0.471951i
$393$	0.116052	+	0.0143027i	0.00585404	+	0.000721474i
$394$	−10.6946	+	13.4708i	−0.538787	+	0.678647i
$395$	0.976577	+	1.69148i	0.0491369	+	0.0851076i
$396$	4.59257	+	2.75348i	0.230785	+	0.138368i
$397$	−24.0843			−1.20876			−0.604378	−	0.796698i	$-0.706578\pi$
$397$	−24.0843			−1.20876			−0.604378	+	0.796698i	$0.706578\pi$
$398$	17.6211	+	2.61667i	0.883265	+	0.131162i
$399$	−6.28301	−	0.774342i	−0.314544	−	0.0387656i
$400$	1.27213	−	19.2236i	0.0636063	−	0.961181i
$401$			28.6652i			1.43147i	0.698370	+	0.715737i	$0.253909\pi$
$401$			28.6652i			1.43147i	−0.698370	+	0.715737i	$0.746091\pi$
$402$	−19.4895	+	4.70746i	−0.972047	+	0.234787i
$403$			5.85712i			0.291764i
$404$	−6.46616	+	21.2920i	−0.321704	+	1.05931i
$405$	1.81654	−	3.40155i	0.0902644	−	0.169024i
$406$	2.05541	−	13.8414i	0.102008	−	0.686940i
$407$	−6.30798			−0.312675
$408$	−15.7965	+	8.27034i	−0.782043	+	0.409443i
$409$	−16.9460	−	29.3513i	−0.837926	−	1.45133i	−0.891626	−	0.452773i	$-0.850435\pi$
$409$	−16.9460	−	29.3513i	−0.837926	−	1.45133i	0.0536999	−	0.998557i	$-0.482899\pi$
$410$	−0.930735	−	0.738923i	−0.0459657	−	0.0364928i
$411$	1.80605	−	14.6543i	0.0890859	−	0.722844i
$412$	−4.49391	+	14.7977i	−0.221399	+	0.729030i
$413$	−4.11431	+	2.37540i	−0.202452	+	0.116886i
$414$	2.34311	−	5.65722i	0.115157	−	0.278037i
$415$	0.354878	+	0.204889i	0.0174203	+	0.0100576i
$416$	8.52703	+	1.84868i	0.418072	+	0.0906390i
$417$	−1.11929	+	9.08191i	−0.0548118	+	0.444743i
$418$	0.981112	+	2.48390i	0.0479878	+	0.121491i
$419$	−13.2641	+	22.9740i	−0.647992	+	1.12235i	0.335610	+	0.942001i	$0.391058\pi$
$419$	−13.2641	+	22.9740i	−0.647992	+	1.12235i	−0.983602	+	0.180354i	$0.942276\pi$
$420$	−2.34358	−	1.03946i	−0.114355	−	0.0507204i
$421$	8.54659	−	14.8031i	0.416535	−	0.721460i	−0.579053	−	0.815290i	$-0.696578\pi$
$421$	8.54659	−	14.8031i	0.416535	−	0.721460i	0.995588	+	0.0938298i	$0.0299110\pi$
$422$	−11.6153	−	1.72483i	−0.565422	−	0.0839633i
$423$	5.70570	+	19.9663i	0.277421	+	0.970794i
$424$	7.73029	+	3.66062i	0.375416	+	0.177775i
$425$	−15.1814	−	8.76501i	−0.736408	−	0.425166i
$426$	12.2418	+	12.4454i	0.593117	+	0.602980i
$427$		−	10.6663i		−	0.516179i
$428$	11.8929	−	11.1319i	0.574866	−	0.538082i
$429$	−2.36631	−	0.291633i	−0.114247	−	0.0140802i
$430$	−4.05840	+	1.60302i	−0.195713	+	0.0773047i
$431$	−16.1118	−	27.9065i	−0.776080	−	1.34421i	−0.934186	−	0.356787i	$-0.883872\pi$
$431$	−16.1118	−	27.9065i	−0.776080	−	1.34421i	0.158106	−	0.987422i	$-0.449461\pi$
$432$	−8.73915	+	18.8581i	−0.420463	+	0.907310i
$433$	−1.07163	−	1.85612i	−0.0514992	−	0.0891992i	0.839127	−	0.543936i	$-0.183067\pi$
$433$	−1.07163	−	1.85612i	−0.0514992	−	0.0891992i	−0.890626	+	0.454737i	$0.849733\pi$
$434$	−1.36255	+	9.17559i	−0.0654043	+	0.440443i
$435$	1.65931	+	3.91401i	0.0795578	+	0.187663i
$436$	19.7642	−	18.4995i	0.946531	−	0.885965i
$437$	2.64478	−	1.52696i	0.126517	−	0.0730446i
$438$	−5.64119	+	20.3795i	−0.269546	+	0.973772i
$439$	20.4924	+	11.8313i	0.978051	+	0.564678i	0.901681	−	0.432402i	$-0.142334\pi$
$439$	20.4924	+	11.8313i	0.978051	+	0.564678i	0.0763698	+	0.997080i	$0.475667\pi$
$440$	0.0878778	+	1.07798i	0.00418941	+	0.0513909i
$441$	−8.37797	+	8.65995i	−0.398951	+	0.412378i
$442$	4.93639	−	6.21780i	0.234800	−	0.295751i
$443$	20.5083	+	35.5214i	0.974378	+	1.68767i	0.681971	+	0.731379i	$0.261123\pi$
$443$	20.5083	+	35.5214i	0.974378	+	1.68767i	0.292407	+	0.956294i	$0.405544\pi$
$444$	−2.59378	−	24.3468i	−0.123096	−	1.15545i
$445$	3.60906			0.171086
$446$	4.32058	+	10.9385i	0.204586	+	0.517952i
$447$	0.100775	−	0.817684i	0.00476647	−	0.0386751i
$448$	12.9281	+	4.87974i	0.610797	+	0.230546i
$449$	−11.2486	+	6.49439i	−0.530855	+	0.306489i	−0.741365	−	0.671102i	$-0.765821\pi$
$449$	−11.2486	+	6.49439i	−0.530855	+	0.306489i	0.210510	+	0.977592i	$0.432488\pi$
$450$	−20.2594	+	2.66780i	−0.955039	+	0.125761i
$451$	−1.51581	−	0.875155i	−0.0713769	−	0.0412095i
$452$	−11.0439	+	36.3657i	−0.519461	+	1.71050i
$453$	0.920367	+	0.694200i	0.0432426	+	0.0326163i
$454$	25.2773	+	20.0680i	1.18632	+	0.941838i
$455$	1.14152			0.0535152
$456$	−9.18363	+	4.80814i	−0.430063	+	0.225162i
$457$	0.683811	+	1.18440i	0.0319873	+	0.0554037i	0.881576	−	0.472042i	$-0.156483\pi$
$457$	0.683811	+	1.18440i	0.0319873	+	0.0554037i	−0.849589	+	0.527446i	$0.823150\pi$
$458$	1.84530	−	12.4265i	0.0862250	−	0.580653i
$459$	11.8818	+	14.7136i	0.554597	+	0.686773i
$460$	1.20456	−	0.280466i	0.0561631	−	0.0130768i
$461$		−	38.4680i		−	1.79163i	−0.444423	−	0.895817i	$-0.646591\pi$
$461$		−	38.4680i		−	1.79163i	0.444423	−	0.895817i	$-0.353409\pi$
$462$	−3.63916	−	1.00734i	−0.169309	−	0.0468658i
$463$	24.5061	+	14.1486i	1.13889	+	0.657540i	0.946156	−	0.323711i	$-0.104930\pi$
$463$	24.5061	+	14.1486i	1.13889	+	0.657540i	0.192737	+	0.981251i	$0.438264\pi$
$464$	−10.1215	−	20.5570i	−0.469880	−	0.954335i
$465$	−1.09997	−	2.59463i	−0.0510098	−	0.120323i
$466$	17.2708	−	21.7541i	0.800056	−	1.00774i
$467$	10.9011	−	18.8812i	0.504441	−	0.873717i	−0.495546	−	0.868582i	$-0.665032\pi$
$467$	10.9011	−	18.8812i	0.504441	−	0.873717i	0.999987	−	0.00513529i	$-0.00163462\pi$
$468$	0.152606	−	9.25314i	0.00705420	−	0.427727i
$469$	12.3597	−	6.86563i	0.570719	−	0.317025i
$470$	−2.60792	+	3.28489i	−0.120294	+	0.151521i
$471$	−4.58776	+	6.08243i	−0.211393	+	0.280264i
$472$	−3.32941	+	7.03087i	−0.153249	+	0.323622i
$473$	−5.56574	+	3.21338i	−0.255913	+	0.147751i
$474$	−7.96033	+	7.83013i	−0.365630	+	0.359650i
$475$	−8.82606	−	5.09573i	−0.404967	−	0.233808i
$476$	9.17967	−	8.59228i	0.420749	−	0.393826i
$477$	2.20269	−	8.80058i	0.100854	−	0.402951i
$478$	−28.7348	−	22.8129i	−1.31430	−	1.04344i
$479$	−2.28621	+	3.95984i	−0.104460	+	0.180930i	−0.913517	−	0.406800i	$-0.866645\pi$
$479$	−2.28621	+	3.95984i	−0.104460	+	0.180930i	0.809058	+	0.587729i	$0.199978\pi$
$480$	−4.12455	+	0.782438i	−0.188259	+	0.0357132i
$481$	5.45091	+	9.44125i	0.248540	+	0.430484i
$482$	15.6823	−	6.19434i	0.714309	−	0.282144i
$483$	−0.528162	+	4.28551i	−0.0240322	+	0.194997i
$484$	−4.62770	−	19.8754i	−0.210350	−	0.903427i
$485$	6.45118	+	3.72459i	0.292933	+	0.169125i
$486$	21.4294	+	5.17486i	0.972059	+	0.234737i
$487$	−9.38134	−	5.41632i	−0.425109	−	0.245437i	0.272152	−	0.962254i	$-0.412265\pi$
$487$	−9.38134	−	5.41632i	−0.425109	−	0.245437i	−0.697261	+	0.716817i	$0.745598\pi$
$488$	−9.93306	−	14.3663i	−0.449648	−	0.650333i
$489$	−30.6777	+	13.0055i	−1.38729	+	0.588130i
$490$	−2.40733	−	0.357481i	−0.108752	−	0.0161493i
$491$	27.4213			1.23751			0.618754	−	0.785585i	$-0.287638\pi$
$491$	27.4213			1.23751			0.618754	+	0.785585i	$0.287638\pi$
$492$	2.75453	−	6.21042i	0.124184	−	0.279987i
$493$	−20.8494			−0.939009
$494$	2.86988	−	3.61485i	0.129122	−	0.162640i
$495$	1.10301	−	0.315205i	0.0495768	−	0.0141674i
$496$	6.70963	+	13.6274i	0.301271	+	0.611888i
$497$	−10.6609	−	6.15508i	−0.478207	−	0.276093i
$498$	−0.624957	+	2.25774i	−0.0280050	+	0.101172i
$499$	3.37870	+	1.95069i	0.151251	+	0.0873250i	0.573716	−	0.819055i	$-0.305501\pi$
$499$	3.37870	+	1.95069i	0.151251	+	0.0873250i	−0.422464	+	0.906380i	$0.638835\pi$
$500$	−5.74846	−	6.14144i	−0.257079	−	0.274654i
$501$	8.88605	+	20.9606i	0.396999	+	0.936449i
$502$	0.246056	−	1.65698i	0.0109820	−	0.0739546i
$503$	12.5873	+	21.8018i	0.561239	+	0.972094i	0.997389	+	0.0722199i	$0.0230083\pi$
$503$	12.5873	+	21.8018i	0.561239	+	0.972094i	−0.436150	+	0.899874i	$0.643658\pi$
$504$	2.39163	−	14.4602i	0.106532	−	0.644109i
$505$	2.38358	+	4.12848i	0.106068	+	0.183715i
$506$	1.69421	−	0.669196i	0.0753169	−	0.0297494i
$507$	−7.18028	−	16.9370i	−0.318887	−	0.752197i
$508$	5.48632	−	18.0655i	0.243416	−	0.801528i
$509$			35.2268i			1.56140i	0.624905	+	0.780701i	$0.285138\pi$
$509$			35.2268i			1.56140i	−0.624905	+	0.780701i	$0.714862\pi$
$510$	−1.01905	+	3.68146i	−0.0451244	+	0.163018i
$511$		−	14.9114i		−	0.659642i
$512$	21.9571	−	5.46694i	0.970374	−	0.241607i
$513$	6.90776	+	8.55408i	0.304985	+	0.377672i
$514$	8.75924	−	11.0330i	0.386353	−	0.486645i
$515$	1.65656	+	2.86925i	0.0729969	+	0.126434i
$516$	−14.6912	−	20.1607i	−0.646745	−	0.887524i
$517$	−3.08873	+	5.34984i	−0.135842	+	0.235286i
$518$	6.34291	+	16.0584i	0.278692	+	0.705567i
$519$	−20.5189	−	15.4766i	−0.900679	−	0.679349i
$520$	1.53750	−	1.06305i	0.0674238	−	0.0466177i
$521$		−	14.7026i		−	0.644133i	−0.946717	−	0.322067i	$-0.895622\pi$
$521$		−	14.7026i		−	0.644133i	0.946717	−	0.322067i	$-0.104378\pi$
$522$	−19.2809	+	14.7957i	−0.843903	+	0.647588i
$523$	13.7368	+	7.93092i	0.600667	+	0.346795i	0.769304	−	0.638883i	$-0.220603\pi$
$523$	13.7368	+	7.93092i	0.600667	+	0.346795i	−0.168637	+	0.985678i	$0.553937\pi$
$524$	−0.0985746	+	0.0922670i	−0.00430625	+	0.00403070i
$525$	13.2667	−	5.62429i	0.579006	−	0.245464i
$526$	25.2056	−	9.95594i	1.09902	−	0.434099i
$527$	13.8212			0.602061
$528$	−5.83963	+	2.03221i	−0.254137	+	0.0884405i
$529$	10.4585	+	18.1146i	0.454717	+	0.787593i
$530$	1.70426	−	0.673163i	0.0740282	−	0.0292403i
$531$	8.00433	+	2.00340i	0.347358	+	0.0869400i
$532$	5.33680	−	4.99530i	0.231379	−	0.216574i
$533$			3.02499i			0.131027i
$534$	5.17557	+	19.9728i	0.223969	+	0.864308i
$535$		−	3.48985i		−	0.150879i
$536$	10.2535	−	20.7573i	0.442884	−	0.896579i
$537$	4.54728	+	0.560424i	0.196230	+	0.0241841i
$538$	3.02748	+	7.66472i	0.130524	+	0.330450i
$539$	−3.58449			−0.154395
$540$	1.67014	+	4.12768i	0.0718714	+	0.177627i
$541$	25.4434			1.09390			0.546950	−	0.837166i	$-0.315789\pi$
$541$	25.4434			1.09390			0.546950	+	0.837166i	$0.315789\pi$
$542$	−12.9201	−	32.7100i	−0.554966	−	1.40502i
$543$	1.31501	+	3.10187i	0.0564325	+	0.133114i
$544$	4.36238	−	20.1215i	0.187036	−	0.862701i
$545$		−	5.79957i		−	0.248426i
$546$	1.63700	+	6.31726i	0.0700570	+	0.270354i
$547$	4.42136	−	2.55267i	0.189044	−	0.109144i	−0.402491	−	0.915424i	$-0.631856\pi$
$547$	4.42136	−	2.55267i	0.189044	−	0.109144i	0.591535	+	0.806279i	$0.298522\pi$
$548$	11.6509	+	12.4474i	0.497702	+	0.531726i
$549$	−12.8808	+	13.3144i	−0.549741	+	0.568244i
$550$	−4.76095	−	3.77978i	−0.203008	−	0.161170i
$551$	−12.1212			−0.516382
$552$	3.27953	+	6.26396i	0.139586	+	0.266612i
$553$	3.93693	−	6.81896i	0.167415	−	0.289972i
$554$	18.3868	−	7.26260i	0.781181	−	0.308558i
$555$	−4.18775	−	3.15867i	−0.177760	−	0.134078i
$556$	−7.22057	−	7.71418i	−0.306220	−	0.327154i
$557$	17.9585	−	10.3684i	0.760927	−	0.439322i	−0.0687012	−	0.997637i	$-0.521886\pi$
$557$	17.9585	−	10.3684i	0.760927	−	0.439322i	0.829629	+	0.558316i	$0.188552\pi$
$558$	12.7815	−	9.80814i	0.541082	−	0.415212i
$559$	9.61903	+	5.55355i	0.406842	+	0.234890i
$560$	2.65590	−	1.30767i	0.112232	−	0.0552591i
$561$	−0.688175	+	5.58385i	−0.0290548	+	0.235750i
$562$	9.18036	+	1.36325i	0.387250	+	0.0575054i
$563$	−12.1252			−0.511016			−0.255508	−	0.966807i	$-0.582243\pi$
$563$	−12.1252			−0.511016			−0.255508	+	0.966807i	$0.582243\pi$
$564$	−21.9188	−	9.72172i	−0.922946	−	0.409358i
$565$	4.07105	+	7.05126i	0.171270	+	0.296649i
$566$	0.0327229	+	0.0828451i	0.00137545	+	0.00348224i
$567$	−15.5372	+	0.514426i	−0.652502	+	0.0216039i
$568$	−20.0910	+	1.63783i	−0.843001	+	0.0687218i
$569$	−24.4036	+	14.0894i	−1.02305	+	0.590659i	−0.914986	−	0.403485i	$-0.867799\pi$
$569$	−24.4036	+	14.0894i	−1.02305	+	0.590659i	−0.108065	+	0.994144i	$0.534466\pi$
$570$	−0.592448	+	2.14030i	−0.0248149	+	0.0896471i
$571$	−26.8044	+	15.4755i	−1.12173	+	0.647631i	−0.941842	−	0.336056i	$-0.890907\pi$
$571$	−26.8044	+	15.4755i	−1.12173	+	0.647631i	−0.179888	+	0.983687i	$0.557574\pi$
$572$	2.00995	−	1.88134i	0.0840402	−	0.0786626i
$573$	−9.70978	+	12.8732i	−0.405632	+	0.537785i
$574$	−0.703705	+	4.73886i	−0.0293721	+	0.197796i
$575$	−3.47569	+	6.02006i	−0.144946	+	0.251054i
$576$	−10.2449	−	21.7035i	−0.426870	−	0.904313i
$577$	−1.60430	−	2.77873i	−0.0667878	−	0.115680i	0.830698	−	0.556724i	$-0.187942\pi$
$577$	−1.60430	−	2.77873i	−0.0667878	−	0.115680i	−0.897486	+	0.441044i	$0.854608\pi$
$578$	4.15682	+	3.30015i	0.172901	+	0.137268i
$579$	1.44641	+	0.178260i	0.0601106	+	0.00740825i
$580$	−4.69705	−	1.42645i	−0.195035	−	0.0592301i
$581$		−	1.65196i		−	0.0685347i
$582$	−11.3609	+	41.0426i	−0.470923	+	1.70127i
$583$	2.33724	−	1.34941i	0.0967985	−	0.0558867i
$584$	−13.8863	−	20.0840i	−0.574621	−	0.831082i
$585$	−1.42492	−	1.37852i	−0.0589131	−	0.0569949i
$586$	−0.317066	−	0.802721i	−0.0130979	−	0.0331601i
$587$	−5.67704	+	9.83293i	−0.234317	+	0.405848i	−0.959074	−	0.283156i	$-0.908619\pi$
$587$	−5.67704	+	9.83293i	−0.234317	+	0.405848i	0.724757	+	0.689004i	$0.241952\pi$
$588$	−1.47391	−	13.8350i	−0.0607831	−	0.570546i
$589$	8.03525			0.331087
$590$	0.612257	+	1.55006i	0.0252062	+	0.0638149i
$591$	−19.3946	+	8.22216i	−0.797787	+	0.338215i
$592$	23.4977	+	15.7221i	0.965750	+	0.646173i
$593$	6.03806	+	3.48608i	0.247954	+	0.143156i	0.618827	−	0.785527i	$-0.287608\pi$
$593$	6.03806	+	3.48608i	0.247954	+	0.143156i	−0.370873	+	0.928683i	$0.620942\pi$
$594$	3.32615	+	5.65215i	0.136474	+	0.231911i
$595$		−	2.69367i		−	0.110430i
$596$	0.650100	+	0.694542i	0.0266291	+	0.0284495i
$597$	17.4187	+	13.1383i	0.712898	+	0.537713i
$598$	−2.46561	−	1.95748i	−0.100826	−	0.0800474i
$599$	3.69925	+	6.40729i	0.151147	+	0.261795i	0.931649	−	0.363358i	$-0.118370\pi$
$599$	3.69925	+	6.40729i	0.151147	+	0.261795i	−0.780502	+	0.625153i	$0.785037\pi$
$600$	12.6311	−	19.9300i	0.515662	−	0.813638i
$601$	−15.3607	+	26.6055i	−0.626576	+	1.08526i	0.361657	+	0.932311i	$0.382211\pi$
$601$	−15.3607	+	26.6055i	−0.626576	+	1.08526i	−0.988234	+	0.152951i	$0.951122\pi$
$602$	13.7770	+	10.9377i	0.561508	+	0.445788i
$603$	−23.7193	−	6.35572i	−0.965924	−	0.258825i
$604$	−1.29648	+	0.301867i	−0.0527530	+	0.0122828i
$605$	−3.78615	−	2.18594i	−0.153929	−	0.0888710i
$606$	−19.4292	+	19.1114i	−0.789257	+	0.776347i
$607$	41.7546	−	24.1070i	1.69477	−	0.978475i	0.744201	−	0.667956i	$-0.232831\pi$
$607$	41.7546	−	24.1070i	1.69477	−	0.978475i	0.950567	−	0.310519i	$-0.100503\pi$
$608$	2.53616	−	11.6980i	0.102855	−	0.474418i
$609$	10.3202	−	13.6825i	0.418195	−	0.554441i
$610$	−3.70119	−	0.549615i	−0.149857	−	0.0222533i
$611$	10.6763			0.431915
$612$	−21.8349	−	0.360108i	−0.882623	−	0.0145565i
$613$	15.4991	−	26.8452i	0.626002	−	1.08427i	−0.362344	−	0.932044i	$-0.618023\pi$
$613$	15.4991	−	26.8452i	0.626002	−	1.08427i	0.988346	−	0.152223i	$-0.0486432\pi$
$614$	−27.3920	−	4.06762i	−1.10545	−	0.164156i
$615$	−0.568094	−	1.34003i	−0.0229078	−	0.0540352i
$616$	3.58638	−	2.47967i	0.144500	−	0.0999088i
$617$			41.1617i			1.65711i	0.559910	+	0.828553i	$0.310836\pi$
$617$			41.1617i			1.65711i	−0.559910	+	0.828553i	$0.689164\pi$
$618$	−13.5031	+	13.2822i	−0.543173	+	0.534289i
$619$	−21.8833	−	12.6343i	−0.879564	−	0.507817i	−0.00904952	−	0.999959i	$-0.502881\pi$
$619$	−21.8833	−	12.6343i	−0.879564	−	0.507817i	−0.870515	+	0.492142i	$0.836214\pi$
$620$	3.11371	+	0.945603i	0.125050	+	0.0379763i
$621$	5.83455	−	4.71163i	0.234133	−	0.189071i
$622$	1.16681	−	0.460877i	0.0467847	−	0.0184795i
$623$	−7.27469	−	12.6001i	−0.291454	−	0.504814i
$624$	8.08784	+	6.98418i	0.323773	+	0.279591i
$625$	22.2799			0.891198
$626$	0.761125	−	0.300636i	0.0304207	−	0.0120158i
$627$	−0.400085	+	3.24629i	−0.0159779	+	0.129644i
$628$	−1.99495	−	8.56805i	−0.0796071	−	0.341902i
$629$	22.2788	−	12.8627i	0.888313	−	0.512867i
$630$	−1.91155	−	2.49103i	−0.0761580	−	0.0992451i
$631$	−41.1188	−	23.7399i	−1.63691	−	0.945072i	−0.981887	−	0.189466i	$-0.939324\pi$
$631$	−41.1188	−	23.7399i	−1.63691	−	0.945072i	−0.655026	−	0.755606i	$-0.727342\pi$
$632$	−1.04759	−	12.8507i	−0.0416709	−	0.511172i
$633$	−11.4818	−	8.66033i	−0.456362	−	0.344217i
$634$	8.35153	+	1.24018i	0.331682	+	0.0492536i
$635$	−2.02239	−	3.50288i	−0.0802561	−	0.139008i
$636$	6.16933	+	8.46614i	0.244630	+	0.335704i
$637$	3.09747	+	5.36497i	0.122726	+	0.212568i
$638$	−7.15157	−	1.06198i	−0.283133	−	0.0420444i
$639$	5.87465	+	20.5575i	0.232398	+	0.813243i
$640$	2.35943	−	4.23461i	0.0932645	−	0.167387i
$641$	−7.53876	+	4.35250i	−0.297763	+	0.171914i	−0.641438	−	0.767175i	$-0.721662\pi$
$641$	−7.53876	+	4.35250i	−0.297763	+	0.171914i	0.343675	+	0.939089i	$0.388328\pi$
$642$	19.3131	−	5.00462i	0.762227	−	0.197517i
$643$			38.8649i			1.53268i	0.642434	+	0.766341i	$0.277925\pi$
$643$			38.8649i			1.53268i	−0.642434	+	0.766341i	$0.722075\pi$
$644$	−3.40719	−	3.64011i	−0.134262	−	0.143441i
$645$	−5.30406	−	0.653693i	−0.208847	−	0.0257391i
$646$	−8.53007	−	6.77213i	−0.335611	−	0.266446i
$647$	17.9102	−	31.0214i	0.704123	−	1.21958i	−0.262885	−	0.964827i	$-0.584674\pi$
$647$	17.9102	−	31.0214i	0.704123	−	1.21958i	0.967007	−	0.254749i	$-0.0819928\pi$
$648$	−20.4478	+	15.1620i	−0.803267	+	0.595619i
$649$	1.22731	+	2.12577i	0.0481763	+	0.0834438i
$650$	−1.54318	+	10.3920i	−0.0605285	+	0.407608i
$651$	−6.84132	+	9.07019i	−0.268132	+	0.355489i
$652$	11.1804	−	36.8151i	0.437858	−	1.44179i
$653$	−39.0142	−	22.5248i	−1.52674	−	0.881465i	−0.999496	−	0.0317531i	$-0.989891\pi$
$653$	−39.0142	−	22.5248i	−1.52674	−	0.881465i	−0.527247	−	0.849712i	$-0.676776\pi$
$654$	32.0953	−	8.31689i	1.25503	−	0.325216i
$655$			0.0289256i			0.00113022i
$656$	3.46528	+	7.03805i	0.135296	+	0.274790i
$657$	−18.0073	+	18.6134i	−0.702533	+	0.726178i
$658$	16.7251	+	2.48362i	0.652013	+	0.0968218i
$659$	−20.3892	−	35.3152i	−0.794252	−	1.37568i	−0.923313	−	0.384048i	$-0.874530\pi$
$659$	−20.3892	−	35.3152i	−0.794252	−	1.37568i	0.129061	−	0.991637i	$-0.458804\pi$
$660$	−0.537065	+	1.21088i	−0.0209052	+	0.0471333i
$661$	32.0036			1.24480			0.622398	−	0.782701i	$-0.286158\pi$
$661$	32.0036			1.24480			0.622398	+	0.782701i	$0.286158\pi$
$662$	3.27631	−	4.12679i	0.127338	−	0.160392i
$663$	8.95211	−	3.79517i	0.347671	−	0.147392i
$664$	−1.53839	−	2.22500i	−0.0597013	−	0.0863468i
$665$		−	1.56602i		−	0.0607278i
$666$	11.4749	−	27.7050i	0.444642	−	1.07355i
$667$			8.26763i			0.320124i
$668$	−25.1540	−	7.63901i	−0.973236	−	0.295562i
$669$	−1.76188	+	14.2959i	−0.0681182	+	0.552711i
$670$	−1.74549	−	4.64258i	−0.0674342	−	0.179358i
$671$	−5.51104			−0.212751
$672$	11.0454	+	12.8227i	0.426087	+	0.494646i
$673$	−5.51760			−0.212688			−0.106344	−	0.994329i	$-0.533914\pi$
$673$	−5.51760			−0.212688			−0.106344	+	0.994329i	$0.533914\pi$
$674$	−3.77664	+	25.4325i	−0.145471	+	0.979622i
$675$	−23.3524	−	9.00051i	−0.898833	−	0.346430i
$676$	20.3254	+	6.17262i	0.781746	+	0.237409i
$677$	36.1164	−	20.8518i	1.38806	−	0.801400i	0.394968	−	0.918695i	$-0.370756\pi$
$677$	36.1164	−	20.8518i	1.38806	−	0.801400i	0.993097	+	0.117295i	$0.0374224\pi$
$678$	−33.1841	+	32.6414i	−1.27443	+	1.25358i
$679$		−	30.0303i		−	1.15246i
$680$	−2.50850	−	3.62808i	−0.0961965	−	0.139130i
$681$	15.4286	+	36.3932i	0.591223	+	1.39459i
$682$	4.74082	+	0.703997i	0.181536	+	0.0269574i
$683$	−10.7405	+	18.6031i	−0.410973	+	0.711826i	−0.994996	−	0.0999107i	$-0.968144\pi$
$683$	−10.7405	+	18.6031i	−0.410973	+	0.711826i	0.584023	+	0.811737i	$0.301478\pi$
$684$	−12.6942	−	0.209356i	−0.485374	−	0.00800493i
$685$	3.65255			0.139557
$686$	9.88616	+	25.0289i	0.377455	+	0.955609i
$687$	9.26520	−	12.2838i	0.353489	−	0.468655i
$688$	28.7419	+	1.90200i	1.09577	+	0.0725130i
$689$	−4.03935	−	2.33212i	−0.153887	−	0.0888467i
$690$	1.45985	+	0.404096i	0.0555755	+	0.0153837i
$691$	−30.0192	+	17.3316i	−1.14199	+	0.659326i	−0.946921	−	0.321465i	$-0.895825\pi$
$691$	−30.0192	+	17.3316i	−1.14199	+	0.659326i	−0.195064	+	0.980791i	$0.562491\pi$
$692$	28.9040	−	6.72989i	1.09877	−	0.255832i
$693$	−3.32378	−	3.21555i	−0.126260	−	0.122149i
$694$	14.0047	+	11.1185i	0.531613	+	0.422054i
$695$	−2.26364			−0.0858648
$696$	1.15826	−	28.0395i	0.0439038	−	1.06283i
$697$	7.13815			0.270377
$698$	−24.4642	+	9.66311i	−0.925985	+	0.365754i
$699$	31.3205	−	13.2781i	1.18465	−	0.502222i
$700$	−4.83500	+	15.9208i	−0.182746	+	0.601751i
$701$	21.4561	−	12.3877i	0.810386	−	0.467877i	−0.0367037	−	0.999326i	$-0.511686\pi$
$701$	21.4561	−	12.3877i	0.810386	−	0.467877i	0.847090	+	0.531449i	$0.178352\pi$
$702$	5.58544	−	9.86249i	0.210809	−	0.372236i
$703$	12.9522	−	7.47798i	0.488503	−	0.282037i
$704$	2.52125	−	6.67968i	0.0950233	−	0.251750i
$705$	−4.72944	+	2.00500i	−0.178121	+	0.0755128i
$706$	−32.4062	−	4.81222i	−1.21962	−	0.181110i
$707$	9.60906	−	16.6434i	0.361386	−	0.625939i
$708$	−7.70014	+	5.61114i	−0.289389	+	0.210880i
$709$	−5.84623	+	10.1260i	−0.219560	+	0.380289i	−0.954673	−	0.297655i	$-0.903795\pi$
$709$	−5.84623	+	10.1260i	−0.219560	+	0.380289i	0.735114	+	0.677944i	$0.237129\pi$
$710$	−2.68514	+	3.38216i	−0.100772	+	0.126930i
$711$	−13.1490	+	3.75756i	−0.493128	+	0.140919i
$712$	−21.5321	−	10.1964i	−0.806951	−	0.382125i
$713$		−	5.48067i		−	0.205253i
$714$	14.9070	−	3.86287i	0.557880	−	0.144564i
$715$		−	0.589797i		−	0.0220572i
$716$	−3.86247	+	3.61532i	−0.144347	+	0.135111i
$717$	−17.5389	−	41.3711i	−0.655002	−	1.54503i
$718$	−10.4463	+	4.12618i	−0.389853	+	0.153988i
$719$	17.9357	−	31.0655i	0.668888	−	1.15855i	−0.309328	−	0.950955i	$-0.600104\pi$
$719$	17.9357	−	31.0655i	0.668888	−	1.15855i	0.978216	−	0.207592i	$-0.0665626\pi$
$720$	−4.89444	−	1.57500i	−0.182405	−	0.0586968i
$721$	6.67819	−	11.5670i	0.248709	−	0.430776i
$722$	16.0852	+	12.7702i	0.598629	+	0.475259i
$723$	20.4958	+	2.52597i	0.762245	+	0.0939420i
$724$	−3.72243	−	1.13047i	−0.138343	−	0.0420134i
$725$	23.8940	−	13.7952i	0.887401	−	0.512341i
$726$	6.66761	−	24.0876i	0.247458	−	0.893976i
$727$	25.4201	+	14.6763i	0.942781	+	0.544315i	0.890831	−	0.454335i	$-0.150123\pi$
$727$	25.4201	+	14.6763i	0.942781	+	0.544315i	0.0519497	+	0.998650i	$0.483456\pi$
$728$	−6.81046	−	3.22504i	−0.252413	−	0.119528i
$729$	20.0158	+	18.1209i	0.741326	+	0.671145i
$730$	−5.17424	−	0.768358i	−0.191507	−	0.0284382i
$731$	13.1049	−	22.6983i	0.484701	−	0.839527i
$732$	−2.26609	−	21.2709i	−0.0837571	−	0.786194i
$733$	0.763565	+	1.32253i	0.0282029	+	0.0488489i	0.879782	−	0.475377i	$-0.157688\pi$
$733$	0.763565	+	1.32253i	0.0282029	+	0.0488489i	−0.851579	+	0.524226i	$0.824355\pi$
$734$	−19.6659	+	24.7708i	−0.725881	+	0.914308i
$735$	−2.37968	−	1.79491i	−0.0877758	−	0.0662061i
$736$	−7.97898	−	1.72986i	−0.294109	−	0.0637636i
$737$	−3.54732	−	6.38599i	−0.130667	−	0.235231i
$738$	6.60116	−	5.06555i	0.242992	−	0.186466i
$739$	25.2376	+	14.5710i	0.928382	+	0.536001i	0.886299	−	0.463113i	$-0.153268\pi$
$739$	25.2376	+	14.5710i	0.928382	+	0.536001i	0.0420823	+	0.999114i	$0.486601\pi$
$740$	5.89910	−	1.37352i	0.216855	−	0.0504916i
$741$	5.20450	−	2.20640i	0.191192	−	0.0810542i
$742$	−5.78541	−	4.59311i	−0.212389	−	0.168618i
$743$	−0.511436	+	0.885832i	−0.0187627	+	0.0324980i	−0.875254	−	0.483663i	$-0.839306\pi$
$743$	−0.511436	+	0.885832i	−0.0187627	+	0.0324980i	0.856492	+	0.516161i	$0.172639\pi$
$744$	−0.767821	+	18.5876i	−0.0281497	+	0.681453i
$745$	0.203806			0.00746686
$746$	19.3341	+	15.3496i	0.707872	+	0.561989i
$747$	−1.99494	+	2.06208i	−0.0729909	+	0.0754476i
$748$	−4.43944	−	4.74293i	−0.162322	−	0.173419i
$749$	−12.1839	+	7.03440i	−0.445192	+	0.257031i
$750$	−2.58436	−	9.97318i	−0.0943675	−	0.364169i
$751$			46.6478i			1.70220i	0.525002	+	0.851101i	$0.324065\pi$
$751$			46.6478i			1.70220i	−0.525002	+	0.851101i	$0.675935\pi$
$752$	24.8398	−	12.2302i	0.905813	−	0.445989i
$753$	1.23544	−	1.63795i	0.0450220	−	0.0596901i
$754$	4.59039	+	11.6216i	0.167172	+	0.423232i
$755$	−0.142590	+	0.246972i	−0.00518937	+	0.00898825i
$756$	11.0443	−	14.1509i	0.401678	−	0.514665i
$757$	−18.4222	−	31.9081i	−0.669565	−	1.15972i	−0.978026	−	0.208484i	$-0.933147\pi$
$757$	−18.4222	−	31.9081i	−0.669565	−	1.15972i	0.308461	−	0.951237i	$-0.400186\pi$
$758$	20.5736	+	3.05511i	0.747266	+	0.110966i
$759$	2.21423	+	0.272889i	0.0803713	+	0.00990526i
$760$	−1.45837	−	2.10926i	−0.0529006	−	0.0765109i
$761$			17.7964i			0.645120i	0.946549	+	0.322560i	$0.104543\pi$
$761$			17.7964i			0.645120i	−0.946549	+	0.322560i	$0.895457\pi$
$762$	16.4850	−	16.2154i	0.597189	−	0.587421i
$763$	−20.2478	+	11.6901i	−0.733019	+	0.423209i
$764$	−4.22222	−	18.1339i	−0.152754	−	0.656061i
$765$	−3.25293	+	3.36242i	−0.117610	+	0.121569i
$766$	4.24573	−	28.5914i	0.153405	−	1.03305i
$767$	2.12112	−	3.67388i	0.0765891	−	0.132656i
$768$	26.8182	+	6.98461i	0.967718	+	0.252036i
$769$	3.03025	+	5.24855i	0.109274	+	0.189268i	0.915476	−	0.402372i	$-0.131814\pi$
$769$	3.03025	+	5.24855i	0.109274	+	0.189268i	−0.806203	+	0.591640i	$0.798481\pi$
$770$	0.137205	−	0.923960i	0.00494452	−	0.0332972i
$771$	15.8848	−	6.73422i	0.572078	−	0.242527i
$772$	−1.22858	+	1.14996i	−0.0442175	+	0.0413881i
$773$	25.2845	−	14.5980i	0.909419	−	0.525053i	0.0291747	−	0.999574i	$-0.490712\pi$
$773$	25.2845	−	14.5980i	0.909419	−	0.525053i	0.880244	+	0.474521i	$0.157379\pi$
$774$	−3.98872	−	30.2905i	−0.143371	−	1.08877i
$775$	−15.8395	+	9.14494i	−0.568972	+	0.328496i
$776$	−27.9659	−	40.4474i	−1.00392	−	1.45198i
$777$	−2.58656	+	20.9873i	−0.0927923	+	0.752917i
$778$	−5.49818	−	0.816461i	−0.197119	−	0.0292715i
$779$	4.14991			0.148686
$780$	2.27643	−	0.242519i	0.0815093	−	0.00868359i
$781$	−3.18019	+	5.50826i	−0.113796	+	0.197101i
$782$	−4.61912	+	5.81817i	−0.165179	+	0.208057i
$783$	−29.4055	+	4.61648i	−1.05087	+	0.164980i
$784$	13.3525	+	8.93403i	0.476876	+	0.319072i
$785$	−1.63217	−	0.942332i	−0.0582545	−	0.0336333i
$786$	−0.160077	+	0.0414809i	−0.00570975	+	0.00147957i
$787$	−32.8291	−	18.9539i	−1.17023	−	0.675632i	−0.216496	−	0.976284i	$-0.569463\pi$
$787$	−32.8291	−	18.9539i	−1.17023	−	0.675632i	−0.953734	+	0.300651i	$0.902796\pi$
$788$	7.06829	−	23.2747i	0.251798	−	0.829127i
$789$	32.9421	+	4.05990i	1.17277	+	0.144536i
$790$	−2.16331	−	1.71748i	−0.0769670	−	0.0611051i
$791$	16.4118	−	28.4261i	0.583537	−	1.01072i
$792$	−7.47126	−	1.23570i	−0.265480	−	0.0439088i
$793$	4.76225	+	8.24846i	0.169113	+	0.292911i
$794$	31.6787	−	12.5127i	1.12423	−	0.444060i
$795$	2.22735	+	0.274507i	0.0789961	+	0.00973577i
$796$	−24.5369	+	5.71307i	−0.869687	+	0.202494i
$797$	39.8062	−	22.9821i	1.41001	−	0.814068i	0.414619	−	0.909995i	$-0.363915\pi$
$797$	39.8062	−	22.9821i	1.41001	−	0.814068i	0.995388	+	0.0959275i	$0.0305817\pi$
$798$	8.66650	−	2.24576i	0.306791	−	0.0794990i
$799$		−	25.1930i		−	0.891266i
$800$	8.31416	+	25.9462i	0.293950	+	0.917337i
$801$	−6.13543	+	24.5134i	−0.216785	+	0.866138i
$802$	−14.8927	−	37.7041i	−0.525880	−	1.33138i
$803$	−7.70439			−0.271882
$804$	23.1893	−	16.3174i	0.817823	−	0.575470i
$805$	−1.06815			−0.0376474
$806$	−3.04300	−	7.70401i	−0.107185	−	0.271362i
$807$	−1.23457	+	10.0173i	−0.0434589	+	0.352626i
$808$	−2.55691	−	31.3653i	−0.0899518	−	1.10343i
$809$		−	31.1562i		−	1.09539i	−0.836676	−	0.547697i	$-0.815504\pi$
$809$		−	31.1562i		−	1.09539i	0.836676	−	0.547697i	$-0.184496\pi$
$810$	−0.622099	+	5.41790i	−0.0218583	+	0.190366i
$811$	−28.3598	+	16.3735i	−0.995846	+	0.574952i	−0.907017	−	0.421095i	$-0.861646\pi$
$811$	−28.3598	+	16.3735i	−0.995846	+	0.574952i	−0.0888296	+	0.996047i	$0.528313\pi$
$812$	4.48764	+	19.2739i	0.157485	+	0.676380i
$813$	5.26866	−	42.7499i	0.184780	−	1.49930i
$814$	8.29704	−	3.27724i	0.290811	−	0.114867i
$815$	−4.12136	−	7.13840i	−0.144365	−	0.250047i
$816$	16.4808	−	19.0851i	0.576942	−	0.668111i
$817$	7.61879	−	13.1961i	0.266548	−	0.461674i
$818$	37.5387	+	29.8024i	1.31251	+	1.04202i
$819$	−1.94059	+	7.75341i	−0.0678098	+	0.270926i
$820$	1.60812	+	0.488370i	0.0561579	+	0.0170546i
$821$	25.8556	+	14.9277i	0.902366	+	0.520981i	0.877967	−	0.478721i	$-0.158900\pi$
$821$	25.8556	+	14.9277i	0.902366	+	0.520981i	0.0243988	+	0.999702i	$0.492233\pi$
$822$	5.23794	+	20.2135i	0.182694	+	0.705026i
$823$	−5.30949	−	3.06544i	−0.185077	−	0.106854i	0.404599	−	0.914494i	$-0.367411\pi$
$823$	−5.30949	−	3.06544i	−0.185077	−	0.106854i	−0.589676	+	0.807640i	$0.700745\pi$
$824$	−1.77702	−	21.7985i	−0.0619056	−	0.759388i
$825$	−2.90595	−	6.85460i	−0.101172	−	0.238647i
$826$	4.17754	−	5.26196i	0.145355	−	0.183087i
$827$	5.94975	−	10.3053i	0.206893	−	0.358349i	−0.743841	−	0.668356i	$-0.766998\pi$
$827$	5.94975	−	10.3053i	0.206893	−	0.358349i	0.950734	+	0.310007i	$0.100331\pi$
$828$	−0.142797	+	8.65842i	−0.00496255	+	0.300901i
$829$	−32.2179			−1.11897			−0.559487	−	0.828839i	$-0.689002\pi$
$829$	−32.2179			−1.11897			−0.559487	+	0.828839i	$0.689002\pi$
$830$	−0.573227	−	0.0851223i	−0.0198970	−	0.00295464i
$831$	24.0304	+	2.96160i	0.833605	+	0.102737i
$832$	−12.1763	+	1.99851i	−0.422136	+	0.0692859i
$833$	12.6599	−	7.30917i	0.438638	−	0.253248i
$834$	−3.24618	−	12.5272i	−0.112406	−	0.433781i
$835$	−4.87732	+	2.81592i	−0.168787	+	0.0974490i
$836$	−2.58096	−	2.75740i	−0.0892644	−	0.0953668i
$837$	19.4931	−	3.06030i	0.673781	−	0.105779i
$838$	5.51064	−	37.1095i	0.190362	−	1.28193i
$839$	−4.72749	−	8.18825i	−0.163211	−	0.282690i	0.772807	−	0.634641i	$-0.218852\pi$
$839$	−4.72749	−	8.18825i	−0.163211	−	0.282690i	−0.936019	+	0.351951i	$0.885518\pi$
$840$	3.62261	+	0.149644i	0.124992	+	0.00516320i
$841$	1.90737	−	3.30366i	0.0657713	−	0.113919i
$842$	−3.55073	+	23.9112i	−0.122366	+	0.824034i
$843$	9.07491	+	6.84487i	0.312556	+	0.235750i
$844$	16.1739	−	3.76587i	0.556730	−	0.129627i
$845$	3.94107	−	2.27538i	0.135577	−	0.0782753i
$846$	−17.8781	−	23.2978i	−0.614662	−	0.800995i
$847$			17.6246i			0.605587i
$848$	−12.0697	−	0.798713i	−0.414474	−	0.0274279i
$849$	−0.0133440	+	0.108273i	−0.000457965	+	0.00371593i
$850$	24.5223	+	3.64148i	0.841108	+	0.124902i
$851$	−5.10057	−	8.83444i	−0.174845	−	0.302841i
$852$	−22.5678	−	10.0096i	−0.773160	−	0.342923i
$853$	−13.6580	+	23.6563i	−0.467640	+	0.809976i	−0.999316	−	0.0369713i	$-0.988229\pi$
$853$	−13.6580	+	23.6563i	−0.467640	+	0.809976i	0.531676	+	0.846948i	$0.321562\pi$
$854$	5.54156	+	14.0296i	0.189628	+	0.480085i
$855$	−1.89116	+	1.95481i	−0.0646764	+	0.0668532i
$856$	−9.85959	+	20.8209i	−0.336994	+	0.711645i
$857$		−	17.3716i		−	0.593404i	−0.954970	−	0.296702i	$-0.904113\pi$
$857$		−	17.3716i		−	0.593404i	0.954970	−	0.296702i	$-0.0958867\pi$
$858$	3.26399	−	0.845800i	0.111431	−	0.0288751i
$859$	−11.0406	+	6.37427i	−0.376699	+	0.217487i	−0.676381	−	0.736552i	$-0.736453\pi$
$859$	−11.0406	+	6.37427i	−0.376699	+	0.217487i	0.299682	+	0.954039i	$0.403119\pi$
$860$	4.50528	−	4.21699i	0.153629	−	0.143798i
$861$	−3.53329	+	4.68443i	−0.120414	+	0.159645i
$862$	35.6908	+	28.3354i	1.21563	+	0.965107i
$863$	4.26365			0.145136			0.0725682	−	0.997363i	$-0.476881\pi$
$863$	4.26365			0.145136			0.0725682	+	0.997363i	$0.476881\pi$
$864$	1.69731	−	29.3448i	0.0577435	−	0.998331i
$865$	3.17893	−	5.50606i	0.108087	−	0.187212i
$866$	2.37387	+	1.88464i	0.0806672	+	0.0640427i
$867$	2.53720	+	5.98480i	0.0861680	+	0.203255i
$868$	−2.97489	−	12.7768i	−0.100974	−	0.433672i
$869$	−3.52320	−	2.03412i	−0.119516	−	0.0690029i
$870$	−4.21601	−	4.28612i	−0.142936	−	0.145313i
$871$	−6.49267	+	10.8276i	−0.219996	+	0.366881i
$872$	−16.3851	+	34.6011i	−0.554868	+	1.17174i
$873$	−36.2652	+	37.4858i	−1.22739	+	1.26870i
$874$	−2.68543	+	3.38252i	−0.0908359	+	0.114415i
$875$	3.63253	+	6.29172i	0.122802	+	0.212699i
$876$	−3.16798	−	29.7365i	−0.107036	−	1.00470i
$877$	5.67046	−	9.82153i	0.191478	−	0.331650i	−0.754262	−	0.656573i	$-0.772005\pi$
$877$	5.67046	−	9.82153i	0.191478	−	0.331650i	0.945740	+	0.324924i	$0.105339\pi$
$878$	−33.1010	−	4.91540i	−1.11711	−	0.165887i
$879$	0.129296	−	1.04911i	0.00436103	−	0.0353854i
$880$	−0.675643	−	1.37224i	−0.0227759	−	0.0462583i
$881$	23.8564	+	13.7735i	0.803741	+	0.464040i	0.844778	−	0.535117i	$-0.179733\pi$
$881$	23.8564	+	13.7735i	0.803741	+	0.464040i	−0.0410364	+	0.999158i	$0.513066\pi$
$882$	6.52057	−	15.7433i	0.219559	−	0.530105i
$883$	−48.1318	+	27.7889i	−1.61976	+	0.935171i	−0.632783	+	0.774329i	$0.718088\pi$
$883$	−48.1318	+	27.7889i	−1.61976	+	0.935171i	−0.986980	+	0.160842i	$0.948579\pi$
$884$	−3.26257	+	10.7431i	−0.109732	+	0.361329i
$885$	−0.249671	+	2.02583i	−0.00839258	+	0.0680974i
$886$	−45.4298	−	36.0673i	−1.52624	−	1.21171i
$887$	−6.22000	+	10.7734i	−0.208847	+	0.361734i	−0.951352	−	0.308107i	$-0.900304\pi$
$887$	−6.22000	+	10.7734i	−0.208847	+	0.361734i	0.742504	+	0.669841i	$0.233638\pi$
$888$	16.0608	+	30.6764i	0.538965	+	1.02943i
$889$	−8.15296	+	14.1213i	−0.273442	+	0.473615i
$890$	−4.74708	+	1.87505i	−0.159122	+	0.0628517i
$891$	0.265793	+	8.02773i	0.00890439	+	0.268939i
$892$	−11.3659	−	12.1429i	−0.380560	−	0.406576i
$893$		−	14.6465i		−	0.490127i
$894$	0.292268	+	1.12788i	0.00977490	+	0.0377218i
$895$			1.13340i			0.0378853i
$896$	−19.5399	+	0.298236i	−0.652783	+	0.00996336i
$897$	−1.50494	−	3.54988i	−0.0502485	−	0.118527i
$898$	11.4215	−	14.3863i	0.381140	−	0.480078i
$899$	−10.8766	+	18.8388i	−0.362754	+	0.628308i
$900$	25.2617	−	14.0346i	0.842057	−	0.467820i
$901$	−5.50317	+	9.53177i	−0.183337	+	0.317549i
$902$	2.44846	+	0.363589i	0.0815250	+	0.0121062i
$903$	8.40907	+	19.8355i	0.279836	+	0.660083i
$904$	−4.36708	−	53.5704i	−0.145247	−	1.78173i
$905$	−0.721775	+	0.416717i	−0.0239926	+	0.0138521i
$906$	−1.57125	−	0.434931i	−0.0522012	−	0.0144496i
$907$	−26.1649	+	15.1063i	−0.868792	+	0.501597i	−0.866947	−	0.498401i	$-0.833921\pi$
$907$	−26.1649	+	15.1063i	−0.868792	+	0.501597i	−0.00184547	+	0.999998i	$0.500587\pi$
$908$	−43.6740	−	13.2634i	−1.44937	−	0.440160i
$909$	−32.0935	+	9.17126i	−1.06448	+	0.304192i
$910$	−1.50147	+	0.593064i	−0.0497732	+	0.0196599i
$911$	−42.9862			−1.42420			−0.712098	−	0.702080i	$-0.752255\pi$
$911$	−42.9862			−1.42420			−0.712098	+	0.702080i	$0.752255\pi$
$912$	9.58144	−	11.0955i	0.317273	−	0.367409i
$913$	−0.853529			−0.0282477
$914$	−1.51477	−	1.20260i	−0.0501043	−	0.0397784i
$915$	−3.65868	−	2.75961i	−0.120952	−	0.0912298i
$916$	4.02889	+	17.3036i	0.133118	+	0.571727i
$917$	0.100987	−	0.0583047i	0.00333487	−	0.00192539i
$918$	−23.2728	−	13.1801i	−0.768116	−	0.435009i
$919$	5.58187	+	3.22269i	0.184129	+	0.106307i	0.589231	−	0.807965i	$-0.299431\pi$
$919$	5.58187	+	3.22269i	0.184129	+	0.106307i	−0.405102	+	0.914271i	$0.632764\pi$
$920$	−1.43868	+	0.994722i	−0.0474319	+	0.0327950i
$921$	−27.0774	−	20.4235i	−0.892229	−	0.672976i
$922$	19.9856	+	50.5979i	0.658192	+	1.66635i
$923$	10.9924			0.361819
$924$	5.31003	−	0.565703i	0.174687	−	0.0186103i
$925$	−17.0214	+	29.4820i	−0.559661	+	0.969361i
$926$	−39.5842	−	5.87812i	−1.30082	−	0.193167i
$927$	−22.3047	+	6.37393i	−0.732581	+	0.209347i
$928$	23.9933	+	21.7806i	0.787617	+	0.714984i
$929$			23.1643i			0.759996i	0.924987	+	0.379998i	$0.124075\pi$
$929$			23.1643i			0.759996i	−0.924987	+	0.379998i	$0.875925\pi$
$930$	2.79483	+	2.84130i	0.0916459	+	0.0931698i
$931$	7.36008	−	4.24934i	0.241217	−	0.139267i
$932$	−11.4147	+	37.5865i	−0.373900	+	1.23119i
$933$	1.52494	+	0.187940i	0.0499244	+	0.00615287i
$934$	−4.52891	+	30.4984i	−0.148191	+	0.997938i
$935$	−1.39176			−0.0455154
$936$	4.60664	+	12.2502i	0.150573	+	0.400409i
$937$	18.4473			0.602648			0.301324	−	0.953522i	$-0.402571\pi$
$937$	18.4473			0.602648			0.301324	+	0.953522i	$0.402571\pi$
$938$	−12.6901	+	15.4519i	−0.414346	+	0.504522i
$939$	0.994741	+	0.122596i	0.0324622	+	0.00400076i
$940$	1.72363	−	5.67562i	0.0562186	−	0.185118i
$941$			4.59708i			0.149861i	0.997189	+	0.0749303i	$0.0238734\pi$
$941$			4.59708i			0.149861i	−0.997189	+	0.0749303i	$0.976127\pi$
$942$	2.87433	−	10.3839i	0.0936506	−	0.338325i
$943$		−	2.83057i		−	0.0921760i
$944$	0.726447	−	10.9776i	0.0236438	−	0.357292i
$945$	−0.596435	−	3.79910i	−0.0194020	−	0.123585i
$946$	5.65128	−	7.11826i	0.183739	−	0.231435i
$947$	38.7669			1.25976			0.629878	−	0.776694i	$-0.283105\pi$
$947$	38.7669			1.25976			0.629878	+	0.776694i	$0.283105\pi$
$948$	6.40236	−	14.4349i	0.207939	−	0.468823i
$949$	6.65759	+	11.5313i	0.216115	+	0.374321i
$950$	14.2566	+	2.11705i	0.462544	+	0.0686863i
$951$	8.25560	+	6.22690i	0.267706	+	0.201921i
$952$	−7.61022	+	16.0708i	−0.246649	+	0.520859i
$953$			14.5075i			0.469945i	0.972002	+	0.234972i	$0.0755000\pi$
$953$			14.5075i			0.469945i	−0.972002	+	0.234972i	$0.924500\pi$
$954$	1.67499	+	12.7200i	0.0542300	+	0.411825i
$955$	−3.45441	−	1.99440i	−0.111782	−	0.0645373i
$956$	49.6478	+	15.0776i	1.60573	+	0.487643i
$957$	−7.06942	−	5.33221i	−0.228522	−	0.172366i
$958$	0.949822	−	6.39625i	0.0306873	−	0.206653i
$959$	−7.36235	−	12.7520i	−0.237743	−	0.411782i
$960$	5.01861	−	3.17202i	0.161975	−	0.102377i
$961$	−8.28985	+	14.3584i	−0.267415	+	0.463176i
$962$	−12.0748	−	9.58635i	−0.389308	−	0.309076i
$963$	23.7037	+	5.93278i	0.763841	+	0.191181i
$964$	−17.4091	+	16.2951i	−0.560710	+	0.524831i
$965$			0.360513i			0.0116053i
$966$	−1.53178	−	5.91123i	−0.0492844	−	0.190191i
$967$	35.7875	−	20.6619i	1.15085	−	0.664443i	0.201754	−	0.979436i	$-0.435336\pi$
$967$	35.7875	−	20.6619i	1.15085	−	0.664443i	0.949094	+	0.314994i	$0.102002\pi$
$968$	16.4130	+	23.7383i	0.527533	+	0.762979i
$969$	−5.20651	−	12.2812i	−0.167257	−	0.394529i
$970$	−10.4205	−	1.54740i	−0.334581	−	0.0496842i
$971$	−28.0068	−	48.5092i	−0.898782	−	1.55674i	−0.829053	−	0.559170i	$-0.811120\pi$
$971$	−28.0068	−	48.5092i	−0.898782	−	1.55674i	−0.0697288	−	0.997566i	$-0.522213\pi$
$972$	−30.8752	+	4.32681i	−0.990323	+	0.138782i
$973$	4.56277	+	7.90295i	0.146276	+	0.253357i
$974$	15.1535	+	2.25024i	0.485549	+	0.0721025i
$975$	−7.74828	+	10.2726i	−0.248143	+	0.328988i
$976$	20.5291	+	13.7358i	0.657119	+	0.439671i
$977$	−1.82619	−	1.05435i	−0.0584251	−	0.0337318i	0.470503	−	0.882398i	$-0.344073\pi$
$977$	−1.82619	−	1.05435i	−0.0584251	−	0.0337318i	−0.528928	+	0.848667i	$0.677406\pi$
$978$	33.5942	−	33.0448i	1.07423	−	1.05665i
$979$	−6.51021	+	3.75867i	−0.208067	+	0.120128i
$980$	3.35215	−	0.780500i	0.107080	−	0.0249322i
$981$	39.3918	+	9.85933i	1.25768	+	0.314784i
$982$	−36.0679	+	14.2465i	−1.15097	+	0.454623i
$983$	−27.8825			−0.889313			−0.444656	−	0.895701i	$-0.646674\pi$
$983$	−27.8825			−0.889313			−0.444656	+	0.895701i	$0.646674\pi$
$984$	−0.396552	+	9.59980i	−0.0126416	+	0.306031i
$985$	−2.60554	−	4.51293i	−0.0830195	−	0.143794i
$986$	27.4237	−	10.8321i	0.873348	−	0.344963i
$987$	16.5330	+	12.4702i	0.526251	+	0.396932i
$988$	−1.89676	+	6.24572i	−0.0603441	+	0.198703i
$989$	−9.00080	−	5.19661i	−0.286209	−	0.165243i
$990$	−1.28706	+	0.987656i	−0.0409055	+	0.0313898i
$991$			20.5001i			0.651209i	0.945506	+	0.325604i	$0.105568\pi$
$991$			20.5001i			0.651209i	−0.945506	+	0.325604i	$0.894432\pi$
$992$	−15.9053	−	14.4385i	−0.504994	−	0.458423i
$993$	5.94157	−	2.51887i	0.188550	−	0.0799341i
$994$	17.2204	+	2.55717i	0.546197	+	0.0811085i
$995$	−2.69862	+	4.67414i	−0.0855519	+	0.148180i
$996$	−0.350964	−	3.29435i	−0.0111207	−	0.104386i
$997$	13.6023			0.430789			0.215394	−	0.976527i	$-0.430896\pi$
$997$	13.6023			0.430789			0.215394	+	0.976527i	$0.430896\pi$
$998$	−5.45755	−	0.810428i	−0.172756	−	0.0256536i
$999$	28.5735	−	23.0742i	0.904025	−	0.730036i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.l.a.431.15	✓	264
3.2	odd	2	inner	804.2.l.a.431.118	yes	264
4.3	odd	2	inner	804.2.l.a.431.61	yes	264
12.11	even	2	inner	804.2.l.a.431.72	yes	264
67.37	even	3	inner	804.2.l.a.707.72	yes	264
201.104	odd	6	inner	804.2.l.a.707.61	yes	264
268.171	odd	6	inner	804.2.l.a.707.118	yes	264
804.707	even	6	inner	804.2.l.a.707.15	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.l.a.431.15	✓	264	1.1	even	1	trivial
804.2.l.a.431.61	yes	264	4.3	odd	2	inner
804.2.l.a.431.72	yes	264	12.11	even	2	inner
804.2.l.a.431.118	yes	264	3.2	odd	2	inner
804.2.l.a.707.15	yes	264	804.707	even	6	inner
804.2.l.a.707.61	yes	264	201.104	odd	6	inner
804.2.l.a.707.72	yes	264	67.37	even	3	inner
804.2.l.a.707.118	yes	264	268.171	odd	6	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.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31532 + 0.519539i) q^{2} +(-1.71904 - 0.211862i) q^{3} +(1.46016 - 1.36673i) q^{4} -0.428467i q^{5} +(2.37117 - 0.614444i) q^{6} +(-1.49589 + 0.863651i) q^{7} +(-1.21051 + 2.55630i) q^{8} +(2.91023 + 0.728399i) q^{9} +O(q^{10})\)	\(q+(-1.31532 + 0.519539i) q^{2} +(-1.71904 - 0.211862i) q^{3} +(1.46016 - 1.36673i) q^{4} -0.428467i q^{5} +(2.37117 - 0.614444i) q^{6} +(-1.49589 + 0.863651i) q^{7} +(-1.21051 + 2.55630i) q^{8} +(2.91023 + 0.728399i) q^{9} +(0.222606 + 0.563574i) q^{10} +(0.446229 + 0.772892i) q^{11} +(-2.79963 + 2.04011i) q^{12} +(0.771200 - 1.33576i) q^{13} +(1.51888 - 1.91315i) q^{14} +(-0.0907757 + 0.736554i) q^{15} +(0.264123 - 3.99127i) q^{16} +(-3.15202 - 1.81982i) q^{17} +(-4.20633 + 0.553897i) q^{18} +(-1.83250 - 1.05799i) q^{19} +(-0.585597 - 0.625630i) q^{20} +(2.75447 - 1.16773i) q^{21} +(-0.988484 - 0.784770i) q^{22} +(-0.721633 + 1.24991i) q^{23} +(2.62251 - 4.13793i) q^{24} +4.81642 q^{25} +(-0.320400 + 2.15762i) q^{26} +(-4.84849 - 1.86872i) q^{27} +(-1.00386 + 3.30554i) q^{28} +(4.96095 - 2.86421i) q^{29} +(-0.263269 - 1.01597i) q^{30} +(-3.28865 + 1.89870i) q^{31} +(1.72621 + 5.38704i) q^{32} +(-0.603342 - 1.42317i) q^{33} +(5.09140 + 0.756056i) q^{34} +(0.370046 + 0.640939i) q^{35} +(5.24492 - 2.91391i) q^{36} +(-3.53404 + 6.12114i) q^{37} +(2.95999 + 0.439549i) q^{38} +(-1.60872 + 2.13284i) q^{39} +(1.09529 + 0.518666i) q^{40} +(-1.69847 + 0.980611i) q^{41} +(-3.01634 + 2.96701i) q^{42} +7.20118i q^{43} +(1.70790 + 0.518671i) q^{44} +(0.312095 - 1.24694i) q^{45} +(0.299807 - 2.01895i) q^{46} +(3.46092 + 5.99449i) q^{47} +(-1.29964 + 6.80521i) q^{48} +(-2.00821 + 3.47833i) q^{49} +(-6.33515 + 2.50232i) q^{50} +(5.03292 + 3.79615i) q^{51} +(-0.699540 - 3.00444i) q^{52} -3.02402i q^{53} +(7.34822 - 0.0610151i) q^{54} +(0.331159 - 0.191195i) q^{55} +(-0.396955 - 4.86940i) q^{56} +(2.92599 + 2.20697i) q^{57} +(-5.03720 + 6.34477i) q^{58} +2.75041 q^{59} +(0.874121 + 1.19955i) q^{60} +(-3.08756 + 5.34781i) q^{61} +(3.33919 - 4.20599i) q^{62} +(-4.98246 + 1.42382i) q^{63} +(-5.06931 - 6.18887i) q^{64} +(-0.572328 - 0.330434i) q^{65} +(1.53299 + 1.55848i) q^{66} +(-8.18423 - 0.135500i) q^{67} +(-7.08965 + 1.65072i) q^{68} +(1.50533 - 1.99576i) q^{69} +(-0.819724 - 0.650789i) q^{70} +(3.56341 + 6.17200i) q^{71} +(-5.38488 + 6.55767i) q^{72} +(-4.31639 + 7.47620i) q^{73} +(1.46824 - 9.88736i) q^{74} +(-8.27963 - 1.02041i) q^{75} +(-4.12172 + 0.959683i) q^{76} +(-1.33502 - 0.770773i) q^{77} +(1.00790 - 3.64117i) q^{78} +(-3.94775 + 2.27923i) q^{79} +(-1.71013 - 0.113168i) q^{80} +(7.93887 + 4.23962i) q^{81} +(1.72457 - 2.17224i) q^{82} +(-0.478190 + 0.828249i) q^{83} +(2.42599 - 5.46968i) q^{84} +(-0.779734 + 1.35054i) q^{85} +(-3.74130 - 9.47190i) q^{86} +(-9.13491 + 3.87267i) q^{87} +(-2.51591 + 0.205098i) q^{88} +8.42318i q^{89} +(0.237327 + 1.80227i) q^{90} +2.66419i q^{91} +(0.654579 + 2.81133i) q^{92} +(6.05560 - 2.56722i) q^{93} +(-7.66661 - 6.08662i) q^{94} +(-0.453315 + 0.785164i) q^{95} +(-1.82613 - 9.62628i) q^{96} +(-8.69282 + 15.0564i) q^{97} +(0.834325 - 5.61847i) q^{98} +(0.735656 + 2.57433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

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