LMFDB - Embedded newform 750.2.l.a.107.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.5
Character	$\chi$	$=$	750.107
Dual form			750.2.l.a.743.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(1.59860 - 0.666690i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.72703 - 0.131724i) q^{6} +(1.51403 + 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.11105 - 2.13154i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(1.59860 - 0.666690i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.72703 - 0.131724i) q^{6} +(1.51403 + 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.11105 - 2.13154i) q^{9} +(5.62798 - 1.82864i) q^{11} +(1.47900 + 0.901424i) q^{12} +(0.479621 + 0.941310i) q^{13} +(-0.661655 - 2.03636i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-5.68203 + 0.899945i) q^{17} +(-2.84866 + 0.940823i) q^{18} +(-3.16950 + 4.36244i) q^{19} +(3.42972 + 1.41094i) q^{21} +(-5.84476 - 0.925718i) q^{22} +(0.702799 - 1.37932i) q^{23} +(-0.908558 - 1.47463i) q^{24} -1.05646i q^{26} +(1.95364 - 4.81490i) q^{27} +(-0.334951 + 2.11480i) q^{28} +(3.67723 - 2.67167i) q^{29} +(8.62475 + 6.26624i) q^{31} +(0.707107 - 0.707107i) q^{32} +(7.77776 - 6.67539i) q^{33} +(5.47129 + 1.77773i) q^{34} +(2.96530 + 0.454984i) q^{36} +(0.197006 - 0.100380i) q^{37} +(4.80455 - 2.44804i) q^{38} +(1.39429 + 1.18502i) q^{39} +(-1.54235 - 0.501139i) q^{41} +(-2.41535 - 2.81421i) q^{42} +(-1.33532 + 1.33532i) q^{43} +(4.78745 + 3.47829i) q^{44} +(-1.25240 + 0.909919i) q^{46} +(0.752458 - 4.75083i) q^{47} +(0.140065 + 1.72638i) q^{48} -2.41543i q^{49} +(-8.48331 + 5.22681i) q^{51} +(-0.479621 + 0.941310i) q^{52} +(-5.99683 - 0.949805i) q^{53} +(-3.92663 + 3.40317i) q^{54} +(1.25854 - 1.73224i) q^{56} +(-2.15837 + 9.08688i) q^{57} +(-4.48935 + 0.711043i) q^{58} +(2.24119 - 6.89769i) q^{59} +(-1.30934 - 4.02973i) q^{61} +(-4.83989 - 9.49882i) q^{62} +(6.42341 - 0.0310298i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-9.96060 + 2.41679i) q^{66} +(0.202800 + 1.28043i) q^{67} +(-4.06788 - 4.06788i) q^{68} +(0.203915 - 2.67353i) q^{69} +(-2.39892 - 3.30183i) q^{71} +(-2.43554 - 1.75161i) q^{72} +(0.278530 + 0.141918i) q^{73} -0.221105 q^{74} -5.39228 q^{76} +(11.2895 + 5.75231i) q^{77} +(-0.704330 - 1.68885i) q^{78} +(-0.555462 - 0.764528i) q^{79} +(-0.0869513 - 8.99958i) q^{81} +(1.14673 + 1.14673i) q^{82} +(1.18337 + 7.47149i) q^{83} +(0.874463 + 3.60403i) q^{84} +(1.79600 - 0.583556i) q^{86} +(4.09725 - 6.72250i) q^{87} +(-2.68654 - 5.27263i) q^{88} +(2.67429 + 8.23061i) q^{89} +(-0.699010 + 2.15133i) q^{91} +(1.52899 - 0.242168i) q^{92} +(17.9652 + 4.26719i) q^{93} +(-2.82728 + 3.89142i) q^{94} +(0.658960 - 1.60180i) q^{96} +(-11.9156 - 1.88725i) q^{97} +(-1.09658 + 2.15217i) q^{98} +(7.98311 - 15.8566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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 $

$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$3$	1.59860	−	0.666690i	0.922953	−	0.384914i
$3$	1.59860	−	0.666690i	0.922953	−	0.384914i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	−1.72703	−	0.131724i	−0.705059	−	0.0537762i
$7$	1.51403	+	1.51403i	0.572249	+	0.572249i	0.932756	−	0.360507i	$-0.117396\pi$
$7$	1.51403	+	1.51403i	0.572249	+	0.572249i	−0.360507	+	0.932756i	$0.617396\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	2.11105	−	2.13154i	0.703683	−	0.710514i
$10$		0			0
$11$	5.62798	−	1.82864i	1.69690	−	0.551357i	0.708833	−	0.705376i	$-0.249222\pi$
$11$	5.62798	−	1.82864i	1.69690	−	0.551357i	0.988068	+	0.154020i	$0.0492219\pi$
$12$	1.47900	+	0.901424i	0.426950	+	0.260219i
$13$	0.479621	+	0.941310i	0.133023	+	0.261072i	0.947904	−	0.318556i	$-0.103198\pi$
$13$	0.479621	+	0.941310i	0.133023	+	0.261072i	−0.814881	+	0.579628i	$0.803198\pi$
$14$	−0.661655	−	2.03636i	−0.176835	−	0.544241i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−5.68203	+	0.899945i	−1.37809	+	0.218269i	−0.801125	−	0.598497i	$-0.795765\pi$
$17$	−5.68203	+	0.899945i	−1.37809	+	0.218269i	−0.576969	+	0.816766i	$0.695765\pi$
$18$	−2.84866	+	0.940823i	−0.671435	+	0.221754i
$19$	−3.16950	+	4.36244i	−0.727133	+	1.00081i	0.272123	+	0.962262i	$0.412274\pi$
$19$	−3.16950	+	4.36244i	−0.727133	+	1.00081i	−0.999257	+	0.0385508i	$0.987726\pi$
$20$		0			0
$21$	3.42972	+	1.41094i	0.748425	+	0.307892i
$22$	−5.84476	−	0.925718i	−1.24611	−	0.197364i
$23$	0.702799	−	1.37932i	0.146544	−	0.287608i	−0.806054	−	0.591843i	$-0.798401\pi$
$23$	0.702799	−	1.37932i	0.146544	−	0.287608i	0.952597	+	0.304235i	$0.0984007\pi$
$24$	−0.908558	−	1.47463i	−0.185459	−	0.301007i
$25$		0			0
$26$		−	1.05646i		−	0.207188i
$27$	1.95364	−	4.81490i	0.375979	−	0.926628i
$28$	−0.334951	+	2.11480i	−0.0632998	+	0.399659i
$29$	3.67723	−	2.67167i	0.682845	−	0.496116i	−0.191455	−	0.981501i	$-0.561321\pi$
$29$	3.67723	−	2.67167i	0.682845	−	0.496116i	0.874300	+	0.485386i	$0.161321\pi$
$30$		0			0
$31$	8.62475	+	6.26624i	1.54905	+	1.12545i	0.944324	+	0.329017i	$0.106718\pi$
$31$	8.62475	+	6.26624i	1.54905	+	1.12545i	0.604726	+	0.796433i	$0.293282\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	7.77776	−	6.67539i	1.35393	−	1.16204i
$34$	5.47129	+	1.77773i	0.938319	+	0.304878i
$35$		0			0
$36$	2.96530	+	0.454984i	0.494216	+	0.0758307i
$37$	0.197006	−	0.100380i	0.0323876	−	0.0165023i	−0.437722	−	0.899111i	$-0.644214\pi$
$37$	0.197006	−	0.100380i	0.0323876	−	0.0165023i	0.470109	+	0.882608i	$0.344214\pi$
$38$	4.80455	−	2.44804i	0.779402	−	0.397125i
$39$	1.39429	+	1.18502i	0.223264	+	0.189755i
$40$		0			0
$41$	−1.54235	−	0.501139i	−0.240874	−	0.0782648i	0.186092	−	0.982532i	$-0.440418\pi$
$41$	−1.54235	−	0.501139i	−0.240874	−	0.0782648i	−0.426966	+	0.904268i	$0.640418\pi$
$42$	−2.41535	−	2.81421i	−0.372696	−	0.434243i
$43$	−1.33532	+	1.33532i	−0.203634	+	0.203634i	−0.801555	−	0.597921i	$-0.795994\pi$
$43$	−1.33532	+	1.33532i	−0.203634	+	0.203634i	0.597921	+	0.801555i	$0.295994\pi$
$44$	4.78745	+	3.47829i	0.721735	+	0.524371i
$45$		0			0
$46$	−1.25240	+	0.909919i	−0.184656	+	0.134160i
$47$	0.752458	−	4.75083i	0.109757	−	0.692980i	−0.870039	−	0.492983i	$-0.835907\pi$
$47$	0.752458	−	4.75083i	0.109757	−	0.692980i	0.979796	−	0.199998i	$-0.0640935\pi$
$48$	0.140065	+	1.72638i	0.0202167	+	0.249181i
$49$		−	2.41543i		−	0.345062i
$50$		0			0
$51$	−8.48331	+	5.22681i	−1.18790	+	0.731899i
$52$	−0.479621	+	0.941310i	−0.0665115	+	0.130536i
$53$	−5.99683	−	0.949805i	−0.823728	−	0.130466i	−0.269680	−	0.962950i	$-0.586918\pi$
$53$	−5.99683	−	0.949805i	−0.823728	−	0.130466i	−0.554049	+	0.832484i	$0.686918\pi$
$54$	−3.92663	+	3.40317i	−0.534347	+	0.463113i
$55$		0			0
$56$	1.25854	−	1.73224i	0.168180	−	0.231480i
$57$	−2.15837	+	9.08688i	−0.285883	+	1.20359i
$58$	−4.48935	+	0.711043i	−0.589480	+	0.0933645i
$59$	2.24119	−	6.89769i	0.291779	−	0.898002i	−0.692506	−	0.721412i	$-0.743493\pi$
$59$	2.24119	−	6.89769i	0.291779	−	0.898002i	0.984285	−	0.176590i	$-0.0565066\pi$
$60$		0			0
$61$	−1.30934	−	4.02973i	−0.167644	−	0.515954i	0.831578	−	0.555408i	$-0.187438\pi$
$61$	−1.30934	−	4.02973i	−0.167644	−	0.515954i	−0.999221	+	0.0394543i	$0.987438\pi$
$62$	−4.83989	−	9.49882i	−0.614667	−	1.20635i
$63$	6.42341	−	0.0310298i	0.809273	−	0.00390939i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	−9.96060	+	2.41679i	−1.22607	+	0.297486i
$67$	0.202800	+	1.28043i	0.0247759	+	0.156429i	0.996975	−	0.0777287i	$-0.0247668\pi$
$67$	0.202800	+	1.28043i	0.0247759	+	0.156429i	−0.972199	+	0.234158i	$0.924767\pi$
$68$	−4.06788	−	4.06788i	−0.493303	−	0.493303i
$69$	0.203915	−	2.67353i	0.0245485	−	0.321855i
$70$		0			0
$71$	−2.39892	−	3.30183i	−0.284700	−	0.391856i	0.642584	−	0.766215i	$-0.277862\pi$
$71$	−2.39892	−	3.30183i	−0.284700	−	0.391856i	−0.927283	+	0.374360i	$0.877862\pi$
$72$	−2.43554	−	1.75161i	−0.287031	−	0.206429i
$73$	0.278530	+	0.141918i	0.0325994	+	0.0166102i	0.470214	−	0.882552i	$-0.344177\pi$
$73$	0.278530	+	0.141918i	0.0325994	+	0.0166102i	−0.437615	+	0.899163i	$0.644177\pi$
$74$	−0.221105			−0.0257030
$75$		0			0
$76$	−5.39228			−0.618537
$77$	11.2895	+	5.75231i	1.28656	+	0.655537i
$78$	−0.704330	−	1.68885i	−0.0797496	−	0.191225i
$79$	−0.555462	−	0.764528i	−0.0624944	−	0.0860162i	0.776626	−	0.629962i	$-0.216930\pi$
$79$	−0.555462	−	0.764528i	−0.0624944	−	0.0860162i	−0.839120	+	0.543946i	$0.816930\pi$
$80$		0			0
$81$	−0.0869513	−	8.99958i	−0.00966125	−	0.999953i
$82$	1.14673	+	1.14673i	0.126635	+	0.126635i
$83$	1.18337	+	7.47149i	0.129891	+	0.820102i	0.963493	+	0.267735i	$0.0862752\pi$
$83$	1.18337	+	7.47149i	0.129891	+	0.820102i	−0.833601	+	0.552367i	$0.813725\pi$
$84$	0.874463	+	3.60403i	0.0954117	+	0.393232i
$85$		0			0
$86$	1.79600	−	0.583556i	0.193668	−	0.0629264i
$87$	4.09725	−	6.72250i	0.439272	−	0.720728i
$88$	−2.68654	−	5.27263i	−0.286386	−	0.562064i
$89$	2.67429	+	8.23061i	0.283474	+	0.872443i	0.986852	+	0.161627i	$0.0516741\pi$
$89$	2.67429	+	8.23061i	0.283474	+	0.872443i	−0.703378	+	0.710816i	$0.748326\pi$
$90$		0			0
$91$	−0.699010	+	2.15133i	−0.0732762	+	0.225521i
$92$	1.52899	−	0.242168i	0.159408	−	0.0252477i
$93$	17.9652	+	4.26719i	1.86290	+	0.442487i
$94$	−2.82728	+	3.89142i	−0.291612	+	0.401369i
$95$		0			0
$96$	0.658960	−	1.60180i	0.0672548	−	0.163483i
$97$	−11.9156	−	1.88725i	−1.20985	−	0.191621i	−0.481262	−	0.876577i	$-0.659821\pi$
$97$	−11.9156	−	1.88725i	−1.20985	−	0.191621i	−0.728584	+	0.684956i	$0.759821\pi$
$98$	−1.09658	+	2.15217i	−0.110772	+	0.217402i
$99$	7.98311	−	15.8566i	0.802333	−	1.59365i
$100$		0			0
$101$		−	0.310282i		−	0.0308742i	−0.999881	−	0.0154371i	$-0.995086\pi$
$101$		−	0.310282i		−	0.0308742i	0.999881	−	0.0154371i	$-0.00491398\pi$
$102$	9.93161	−	0.805776i	0.983375	−	0.0797837i
$103$	1.38199	−	8.72553i	0.136171	−	0.859752i	−0.821147	−	0.570717i	$-0.806665\pi$
$103$	1.38199	−	8.72553i	0.136171	−	0.859752i	0.957318	−	0.289035i	$-0.0933345\pi$
$104$	0.854692	−	0.620970i	0.0838094	−	0.0608911i
$105$		0			0
$106$	4.91201	+	3.56879i	0.477097	+	0.346631i
$107$	−4.19190	+	4.19190i	−0.405246	+	0.405246i	−0.880077	−	0.474831i	$-0.842509\pi$
$107$	−4.19190	+	4.19190i	−0.405246	+	0.405246i	0.474831	+	0.880077i	$0.342509\pi$
$108$	5.04366	−	1.24960i	0.485326	−	0.120243i
$109$	−1.79521	−	0.583300i	−0.171950	−	0.0558700i	0.221777	−	0.975098i	$-0.428814\pi$
$109$	−1.79521	−	0.583300i	−0.171950	−	0.0558700i	−0.393727	+	0.919227i	$0.628814\pi$
$110$		0			0
$111$	0.248012	−	0.291809i	0.0235403	−	0.0276973i
$112$	−1.90779	+	0.972066i	−0.180269	+	0.0918516i
$113$	−7.55774	+	3.85086i	−0.710972	+	0.362258i	−0.771779	−	0.635891i	$-0.780633\pi$
$113$	−7.55774	+	3.85086i	−0.710972	+	0.362258i	0.0608066	+	0.998150i	$0.480633\pi$
$114$	6.04848	−	7.11659i	0.566492	−	0.666530i
$115$		0			0
$116$	4.32285	+	1.40458i	0.401366	+	0.130412i
$117$	3.01895	+	0.964817i	0.279102	+	0.0891974i
$118$	−5.12840	+	5.12840i	−0.472108	+	0.472108i
$119$	−9.96530	−	7.24021i	−0.913517	−	0.663709i
$120$		0			0
$121$	19.4311	−	14.1175i	1.76646	−	1.28341i
$122$	−0.662830	+	4.18494i	−0.0600098	+	0.378887i
$123$	−2.79970	+	0.227147i	−0.252441	+	0.0204811i
$124$			10.6608i			0.957366i
$125$		0			0
$126$	−5.73738	−	2.88852i	−0.511127	−	0.257330i
$127$	4.74807	−	9.31862i	0.421323	−	0.826894i	−0.578613	−	0.815602i	$-0.696406\pi$
$127$	4.74807	−	9.31862i	0.421323	−	0.826894i	0.999936	−	0.0112913i	$-0.00359421\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	−1.24440	+	3.02489i	−0.109563	+	0.266326i
$130$		0			0
$131$	−11.4805	+	15.8015i	−1.00306	+	1.38059i	−0.0796236	+	0.996825i	$0.525372\pi$
$131$	−11.4805	+	15.8015i	−1.00306	+	1.38059i	−0.923432	+	0.383762i	$0.874628\pi$
$132$	9.97216	+	2.36864i	0.867965	+	0.206164i
$133$	−11.4036	+	1.80615i	−0.988816	+	0.156613i
$134$	0.400605	−	1.23294i	0.0346070	−	0.106510i
$135$		0			0
$136$	1.77773	+	5.47129i	0.152439	+	0.469159i
$137$	5.44330	+	10.6831i	0.465053	+	0.912717i	0.997791	+	0.0664369i	$0.0211631\pi$
$137$	5.44330	+	10.6831i	0.465053	+	0.912717i	−0.532738	+	0.846280i	$0.678837\pi$
$138$	−1.39545	+	2.28956i	−0.118788	+	0.194900i
$139$	−22.1318	+	7.19107i	−1.87720	+	0.609939i	−0.888747	+	0.458399i	$0.848423\pi$
$139$	−22.1318	+	7.19107i	−1.87720	+	0.609939i	−0.988451	+	0.151540i	$0.951577\pi$
$140$		0			0
$141$	−1.96445	−	8.09634i	−0.165437	−	0.681835i
$142$	0.638455	+	4.03104i	0.0535779	+	0.338278i
$143$	4.42062	+	4.42062i	0.369671	+	0.369671i
$144$	1.37487	+	2.66641i	0.114572	+	0.222201i
$145$		0			0
$146$	−0.183742	−	0.252900i	−0.0152066	−	0.0209301i
$147$	−1.61035	−	3.86131i	−0.132819	−	0.318476i
$148$	0.197006	+	0.100380i	0.0161938	+	0.00825116i
$149$	−14.7140			−1.20542			−0.602711	−	0.797960i	$-0.705913\pi$
$149$	−14.7140			−1.20542			−0.602711	+	0.797960i	$0.705913\pi$
$150$		0			0
$151$	−8.54879			−0.695691			−0.347845	−	0.937552i	$-0.613087\pi$
$151$	−8.54879			−0.695691			−0.347845	+	0.937552i	$0.613087\pi$
$152$	4.80455	+	2.44804i	0.389701	+	0.198562i
$153$	−10.0768	+	14.0113i	−0.814658	+	1.13275i
$154$	−7.44757	−	10.2507i	−0.600142	−	0.826025i
$155$		0			0
$156$	−0.139161	+	1.82454i	−0.0111418	+	0.146080i
$157$	17.5864	+	17.5864i	1.40355	+	1.40355i	0.788446	+	0.615104i	$0.210886\pi$
$157$	17.5864	+	17.5864i	1.40355	+	1.40355i	0.615104	+	0.788446i	$0.289114\pi$
$158$	0.147832	+	0.933375i	0.0117609	+	0.0742553i
$159$	−10.2198	+	2.47967i	−0.810480	+	0.196651i
$160$		0			0
$161$	3.15239	−	1.02427i	0.248443	−	0.0807240i
$162$	−4.00825	+	8.05816i	−0.314918	+	0.633109i
$163$	0.912200	+	1.79029i	0.0714490	+	0.140227i	0.923968	−	0.382469i	$-0.124926\pi$
$163$	0.912200	+	1.79029i	0.0714490	+	0.140227i	−0.852519	+	0.522696i	$0.824926\pi$
$164$	−0.501139	−	1.54235i	−0.0391324	−	0.120437i
$165$		0			0
$166$	2.33760	−	7.19438i	0.181433	−	0.558392i
$167$	14.6571	−	2.32146i	1.13420	−	0.179640i	0.439021	−	0.898477i	$-0.355325\pi$
$167$	14.6571	−	2.32146i	1.13420	−	0.179640i	0.695179	+	0.718837i	$0.255325\pi$
$168$	0.857043	−	3.60821i	0.0661223	−	0.278379i
$169$	6.98518	−	9.61428i	0.537322	−	0.739560i
$170$		0			0
$171$	2.60777	+	15.9653i	0.199421	+	1.22089i
$172$	−1.86518	−	0.295415i	−0.142218	−	0.0225252i
$173$	−2.27656	+	4.46800i	−0.173084	+	0.339696i	−0.961210	−	0.275818i	$-0.911051\pi$
$173$	−2.27656	+	4.46800i	−0.173084	+	0.339696i	0.788126	+	0.615514i	$0.211051\pi$
$174$	−6.70263	+	4.12968i	−0.508125	+	0.313070i
$175$		0			0
$176$			5.91761i			0.446057i
$177$	−1.01585	−	12.5208i	−0.0763556	−	0.941123i
$178$	1.35381	−	8.54762i	0.101472	−	0.640672i
$179$	−2.56353	+	1.86252i	−0.191607	+	0.139211i	−0.679453	−	0.733719i	$-0.737783\pi$
$179$	−2.56353	+	1.86252i	−0.191607	+	0.139211i	0.487846	+	0.872930i	$0.337783\pi$
$180$		0			0
$181$	−5.04884	−	3.66820i	−0.375278	−	0.272655i	0.384118	−	0.923284i	$-0.374505\pi$
$181$	−5.04884	−	3.66820i	−0.375278	−	0.272655i	−0.759396	+	0.650629i	$0.774505\pi$
$182$	1.59951	−	1.59951i	0.118563	−	0.118563i
$183$	−4.77969	−	5.56901i	−0.353325	−	0.411673i
$184$	−1.47228	−	0.478373i	−0.108538	−	0.0352661i
$185$		0			0
$186$	−14.0698	−	11.9581i	−1.03165	−	0.876811i
$187$	−30.3327	+	15.4553i	−2.21815	+	1.13020i
$188$	4.28579	−	2.18372i	0.312573	−	0.159264i
$189$	10.2478	−	4.33203i	0.745416	−	0.315109i
$190$		0			0
$191$	−19.9806	−	6.49209i	−1.44574	−	0.469751i	−0.522062	−	0.852908i	$-0.674837\pi$
$191$	−19.9806	−	6.49209i	−1.44574	−	0.469751i	−0.923683	+	0.383157i	$0.874837\pi$
$192$	−1.31434	+	1.12805i	−0.0948544	+	0.0814103i
$193$	−7.00922	+	7.00922i	−0.504535	+	0.504535i	−0.912844	−	0.408309i	$-0.866119\pi$
$193$	−7.00922	+	7.00922i	−0.504535	+	0.504535i	0.408309	+	0.912844i	$0.366119\pi$
$194$	9.76009	+	7.09112i	0.700734	+	0.509113i
$195$		0			0
$196$	1.95413	−	1.41976i	0.139580	−	0.101411i
$197$	1.59685	−	10.0821i	0.113771	−	0.718320i	−0.863186	−	0.504885i	$-0.831535\pi$
$197$	1.59685	−	10.0821i	0.113771	−	0.718320i	0.976957	−	0.213435i	$-0.0684652\pi$
$198$	−14.3118	+	10.5041i	−1.01709	+	0.746495i
$199$			15.1147i			1.07146i	0.844391	+	0.535728i	$0.179963\pi$
$199$			15.1147i			1.07146i	−0.844391	+	0.535728i	$0.820037\pi$
$200$		0			0
$201$	1.17784	+	1.91169i	0.0830786	+	0.134840i
$202$	−0.140865	+	0.276463i	−0.00991123	+	0.0194519i
$203$	9.61241	+	1.52246i	0.674659	+	0.106856i
$204$	−9.21494	−	3.79090i	−0.645175	−	0.265416i
$205$		0			0
$206$	−5.19267	+	7.14709i	−0.361790	+	0.497962i
$207$	−1.45644	−	4.40986i	−0.101229	−	0.306506i
$208$	−1.04345	+	0.165266i	−0.0723503	+	0.0114592i
$209$	−9.86055	+	30.3476i	−0.682068	+	2.09919i
$210$		0			0
$211$	−1.22728	−	3.77719i	−0.0844897	−	0.260033i	0.899883	−	0.436132i	$-0.143652\pi$
$211$	−1.22728	−	3.77719i	−0.0844897	−	0.260033i	−0.984372	+	0.176099i	$0.943652\pi$
$212$	−2.75644	−	5.40982i	−0.189313	−	0.371548i
$213$	−6.03622	−	3.67898i	−0.413595	−	0.252079i
$214$	5.63809	−	1.83193i	0.385412	−	0.125228i
$215$		0			0
$216$	−5.06124	−	1.17637i	−0.344374	−	0.0800422i
$217$	3.57084	+	22.5454i	0.242404	+	1.53048i
$218$	1.33473	+	1.33473i	0.0903996	+	0.0903996i
$219$	0.539873	+	0.0411771i	0.0364812	+	0.00278249i
$220$		0			0
$221$	−3.57235	−	4.91692i	−0.240302	−	0.330748i
$222$	−0.353459	+	0.147409i	−0.0237226	+	0.00989342i
$223$	−11.9279	−	6.07755i	−0.798748	−	0.406983i	0.00645660	−	0.999979i	$-0.497945\pi$
$223$	−11.9279	−	6.07755i	−0.798748	−	0.406983i	−0.805205	+	0.592996i	$0.797945\pi$
$224$	2.14116			0.143062
$225$		0			0
$226$	8.48225			0.564231
$227$	−0.762629	−	0.388579i	−0.0506175	−	0.0257909i	0.428499	−	0.903542i	$-0.359043\pi$
$227$	−0.762629	−	0.388579i	−0.0506175	−	0.0257909i	−0.479116	+	0.877752i	$0.659043\pi$
$228$	−8.62010	+	3.59498i	−0.570880	+	0.238083i
$229$	9.72545	+	13.3859i	0.642676	+	0.884567i	0.998755	−	0.0498887i	$-0.0158867\pi$
$229$	9.72545	+	13.3859i	0.642676	+	0.884567i	−0.356079	+	0.934456i	$0.615887\pi$
$230$		0			0
$231$	21.8825	+	1.66902i	1.43976	+	0.109813i
$232$	−3.21402	−	3.21402i	−0.211011	−	0.211011i
$233$	−0.852656	−	5.38346i	−0.0558593	−	0.352682i	−0.999749	−	0.0224200i	$-0.992863\pi$
$233$	−0.852656	−	5.38346i	−0.0558593	−	0.352682i	0.943889	−	0.330262i	$-0.107137\pi$
$234$	−2.25188	−	2.23023i	−0.147210	−	0.145795i
$235$		0			0
$236$	6.89769	−	2.24119i	0.449001	−	0.145889i
$237$	−1.39767	−	0.851854i	−0.0907882	−	0.0553339i
$238$	5.59216	+	10.9752i	0.362486	+	0.711418i
$239$	2.69306	+	8.28837i	0.174199	+	0.536130i	0.999596	−	0.0284230i	$-0.00904853\pi$
$239$	2.69306	+	8.28837i	0.174199	+	0.536130i	−0.825397	+	0.564553i	$0.809049\pi$
$240$		0			0
$241$	−7.85699	+	24.1813i	−0.506113	+	1.55766i	0.292779	+	0.956180i	$0.405420\pi$
$241$	−7.85699	+	24.1813i	−0.506113	+	1.55766i	−0.798892	+	0.601475i	$0.794580\pi$
$242$	−23.7224	+	3.75726i	−1.52494	+	0.241526i
$243$	−6.13893	−	14.3288i	−0.393813	−	0.919191i
$244$	2.49051	−	3.42789i	0.159439	−	0.219448i
$245$		0			0
$246$	2.59768	+	1.06865i	0.165622	+	0.0681346i
$247$	−5.62657	−	0.891162i	−0.358010	−	0.0567033i
$248$	4.83989	−	9.49882i	0.307333	−	0.603176i
$249$	6.87290	+	11.1550i	0.435552	+	0.706918i
$250$		0			0
$251$		−	21.0935i		−	1.33141i	−0.746215	−	0.665706i	$-0.768131\pi$
$251$		−	21.0935i		−	1.33141i	0.746215	−	0.665706i	$-0.231869\pi$
$252$	3.80069	+	5.17841i	0.239421	+	0.326209i
$253$	1.43306	−	9.04796i	0.0900954	−	0.568840i
$254$	−8.46113	+	6.14737i	−0.530898	+	0.385720i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−11.8588	+	11.8588i	−0.739734	+	0.739734i	−0.972526	−	0.232792i	$-0.925214\pi$
$257$	−11.8588	+	11.8588i	−0.739734	+	0.739734i	0.232792	+	0.972526i	$0.425214\pi$
$258$	2.48204	−	2.13025i	0.154525	−	0.132623i
$259$	0.450251	+	0.146295i	0.0279772	+	0.00909035i
$260$		0			0
$261$	2.06804	−	13.4782i	0.128009	−	0.834279i
$262$	17.4029	−	8.86724i	1.07516	−	0.547820i
$263$	−20.2720	+	10.3291i	−1.25002	+	0.636919i	−0.948572	−	0.316562i	$-0.897471\pi$
$263$	−20.2720	+	10.3291i	−1.25002	+	0.636919i	−0.301453	+	0.953481i	$0.597471\pi$
$264$	−7.80992	−	6.63774i	−0.480667	−	0.408525i
$265$		0			0
$266$	10.9806	+	3.56783i	0.673266	+	0.218757i
$267$	9.76238	+	11.3745i	0.597448	+	0.696110i
$268$	−0.916684	+	0.916684i	−0.0559954	+	0.0559954i
$269$	−8.37684	−	6.08613i	−0.510745	−	0.371078i	0.302361	−	0.953193i	$-0.402225\pi$
$269$	−8.37684	−	6.08613i	−0.510745	−	0.371078i	−0.813106	+	0.582115i	$0.802225\pi$
$270$		0			0
$271$	−0.517312	+	0.375849i	−0.0314245	+	0.0228312i	−0.603387	−	0.797449i	$-0.706182\pi$
$271$	−0.517312	+	0.375849i	−0.0314245	+	0.0228312i	0.571962	+	0.820280i	$0.306182\pi$
$272$	0.899945	−	5.68203i	0.0545672	−	0.344524i
$273$	0.316834	+	3.90514i	0.0191757	+	0.236350i
$274$		−	11.9899i		−	0.724336i
$275$		0			0
$276$	2.28279	−	1.40649i	0.137408	−	0.0846608i
$277$	13.7839	−	27.0524i	0.828193	−	1.62542i	0.0488650	−	0.998805i	$-0.484440\pi$
$277$	13.7839	−	27.0524i	0.828193	−	1.62542i	0.779328	−	0.626616i	$-0.215560\pi$
$278$	22.9843	+	3.64035i	1.37851	+	0.218334i
$279$	31.5640	−	5.15567i	1.88969	−	0.308662i
$280$		0			0
$281$	−12.7646	+	17.5690i	−0.761473	+	1.04808i	0.235617	+	0.971846i	$0.424289\pi$
$281$	−12.7646	+	17.5690i	−0.761473	+	1.04808i	−0.997090	+	0.0762322i	$0.975711\pi$
$282$	−1.92532	+	8.10574i	−0.114651	+	0.482690i
$283$	−3.41737	+	0.541258i	−0.203142	+	0.0321745i	−0.257176	−	0.966365i	$-0.582792\pi$
$283$	−3.41737	+	0.541258i	−0.203142	+	0.0321745i	0.0540343	+	0.998539i	$0.482792\pi$
$284$	1.26119	−	3.88154i	0.0748378	−	0.230327i
$285$		0			0
$286$	−1.93188	−	5.94572i	−0.114235	−	0.351578i
$287$	−1.57642	−	3.09390i	−0.0930531	−	0.182627i
$288$	−0.0144920	−	2.99996i	−0.000853952	−	0.176775i
$289$	15.3076	−	4.97374i	0.900446	−	0.292573i
$290$		0			0
$291$	−20.3065	+	4.92706i	−1.19039	+	0.288830i
$292$	0.0489016	+	0.308752i	0.00286175	+	0.0180684i
$293$	−12.2527	−	12.2527i	−0.715808	−	0.715808i	0.251936	−	0.967744i	$-0.418933\pi$
$293$	−12.2527	−	12.2527i	−0.715808	−	0.715808i	−0.967744	+	0.251936i	$0.918933\pi$
$294$	−0.318171	+	4.17154i	−0.0185561	+	0.243289i
$295$		0			0
$296$	−0.129962	−	0.178878i	−0.00755391	−	0.0103971i
$297$	2.19034	−	30.6707i	0.127097	−	1.77969i
$298$	13.1103	+	6.68004i	0.759460	+	0.386964i
$299$	1.63544			0.0945802
$300$		0			0
$301$	−4.04342			−0.233059
$302$	7.61703	+	3.88107i	0.438311	+	0.223330i
$303$	−0.206862	−	0.496017i	−0.0118839	−	0.0284954i
$304$	−3.16950	−	4.36244i	−0.181783	−	0.250203i
$305$		0			0
$306$	15.3395	−	7.90942i	0.876899	−	0.452151i
$307$	−16.8133	−	16.8133i	−0.959588	−	0.959588i	0.0396263	−	0.999215i	$-0.487383\pi$
$307$	−16.8133	−	16.8133i	−0.959588	−	0.959588i	−0.999215	+	0.0396263i	$0.987383\pi$
$308$	1.98211	+	12.5146i	0.112941	+	0.713083i
$309$	−3.60798	−	14.8700i	−0.205251	−	0.845924i
$310$		0			0
$311$	−7.39905	+	2.40410i	−0.419562	+	0.136324i	−0.511187	−	0.859470i	$-0.670794\pi$
$311$	−7.39905	+	2.40410i	−0.419562	+	0.136324i	0.0916250	+	0.995794i	$0.470794\pi$
$312$	0.952316	−	1.56250i	0.0539143	−	0.0884590i
$313$	9.44284	+	18.5326i	0.533741	+	1.04753i	0.987679	+	0.156492i	$0.0500186\pi$
$313$	9.44284	+	18.5326i	0.533741	+	1.04753i	−0.453939	+	0.891033i	$0.649981\pi$
$314$	−7.68555	−	23.6537i	−0.433721	−	1.33486i
$315$		0			0
$316$	0.292024	−	0.898757i	0.0164276	−	0.0505590i
$317$	−0.214085	+	0.0339077i	−0.0120242	+	0.00190445i	−0.162444	−	0.986718i	$-0.551938\pi$
$317$	−0.214085	+	0.0339077i	−0.0120242	+	0.00190445i	0.150419	+	0.988622i	$0.451938\pi$
$318$	10.2316	+	2.43027i	0.573761	+	0.136283i
$319$	15.8099	−	21.7604i	0.885183	−	1.21835i
$320$		0			0
$321$	−3.90647	+	9.49587i	−0.218038	+	0.530008i
$322$	−3.27381	−	0.518520i	−0.182442	−	0.0288960i
$323$	14.0832	−	27.6399i	0.783612	−	1.53793i
$324$	7.22970	−	5.36017i	0.401650	−	0.297787i
$325$		0			0
$326$		−	2.00929i		−	0.111284i
$327$	−3.25871	+	0.264387i	−0.180207	+	0.0146207i
$328$	−0.253693	+	1.60175i	−0.0140078	+	0.0884421i
$329$	8.33214	−	6.05366i	0.459366	−	0.333749i
$330$		0			0
$331$	5.81535	+	4.22510i	0.319640	+	0.232232i	0.736022	−	0.676958i	$-0.236702\pi$
$331$	5.81535	+	4.22510i	0.319640	+	0.232232i	−0.416382	+	0.909190i	$0.636702\pi$
$332$	−5.34899	+	5.34899i	−0.293564	+	0.293564i
$333$	0.201926	−	0.631833i	0.0110655	−	0.0346243i
$334$	−14.1135	−	4.58575i	−0.772255	−	0.250921i
$335$		0			0
$336$	−2.40172	+	2.82585i	−0.131025	+	0.154163i
$337$	6.01777	−	3.06621i	0.327809	−	0.167027i	−0.282339	−	0.959315i	$-0.591110\pi$
$337$	6.01777	−	3.06621i	0.327809	−	0.167027i	0.610147	+	0.792288i	$0.291110\pi$
$338$	−10.5886	+	5.39518i	−0.575946	+	0.293459i
$339$	−9.51447	+	11.1947i	−0.516755	+	0.608010i
$340$		0			0
$341$	59.9987	+	19.4947i	3.24911	+	1.05570i
$342$	4.92454	−	15.4090i	0.266288	−	0.833226i
$343$	14.2552	−	14.2552i	0.769710	−	0.769710i
$344$	1.52777	+	1.10999i	0.0823718	+	0.0598466i
$345$		0			0
$346$	4.05686	−	2.94748i	0.218098	−	0.158458i
$347$	−0.716076	+	4.52113i	−0.0384410	+	0.242707i	−0.999425	−	0.0338958i	$-0.989209\pi$
$347$	−0.716076	+	4.52113i	−0.0384410	+	0.242707i	0.960984	+	0.276603i	$0.0892086\pi$
$348$	7.84692	−	0.636640i	0.420639	−	0.0341275i
$349$			9.78119i			0.523575i	0.965126	+	0.261787i	$0.0843120\pi$
$349$			9.78119i			0.523575i	−0.965126	+	0.261787i	$0.915688\pi$
$350$		0			0
$351$	5.46932	−	0.470345i	0.291931	−	0.0251052i
$352$	2.68654	−	5.27263i	0.143193	−	0.281032i
$353$	10.7063	+	1.69571i	0.569840	+	0.0902538i	0.434704	−	0.900573i	$-0.356853\pi$
$353$	10.7063	+	1.69571i	0.569840	+	0.0902538i	0.135136	+	0.990827i	$0.456853\pi$
$354$	−4.77921	+	11.6173i	−0.254012	+	0.617454i
$355$		0			0
$356$	−5.08679	+	7.00137i	−0.269600	+	0.371072i
$357$	−20.7575	−	4.93044i	−1.09860	−	0.260947i
$358$	3.12969	−	0.495694i	0.165409	−	0.0261982i
$359$	6.51044	−	20.0371i	0.343608	−	1.05752i	−0.618717	−	0.785614i	$-0.712347\pi$
$359$	6.51044	−	20.0371i	0.343608	−	1.05752i	0.962325	−	0.271902i	$-0.0876527\pi$
$360$		0			0
$361$	−3.11386	−	9.58347i	−0.163887	−	0.504393i
$362$	2.83323	+	5.56052i	0.148911	+	0.292254i
$363$	21.6505	−	35.5228i	1.13636	−	1.86446i
$364$	−2.15133	+	0.699010i	−0.112760	+	0.0366381i
$365$		0			0
$366$	1.73046	+	7.13196i	0.0904526	+	0.372793i
$367$	−4.22522	−	26.6770i	−0.220555	−	1.39253i	−0.810809	−	0.585311i	$-0.800972\pi$
$367$	−4.22522	−	26.6770i	−0.220555	−	1.39253i	0.590254	−	0.807218i	$-0.299028\pi$
$368$	1.09463	+	1.09463i	0.0570618	+	0.0570618i
$369$	−4.32417	+	2.22965i	−0.225107	+	0.116071i
$370$		0			0
$371$	−7.64135	−	10.5174i	−0.396719	−	0.546037i
$372$	7.10743	+	17.0423i	0.368503	+	0.883603i
$373$	23.8387	+	12.1464i	1.23432	+	0.628917i	0.944609	−	0.328197i	$-0.106441\pi$
$373$	23.8387	+	12.1464i	1.23432	+	0.628917i	0.289711	+	0.957114i	$0.406441\pi$
$374$	34.0432			1.76033
$375$		0			0
$376$	−4.81005			−0.248060
$377$	4.27854	+	2.18003i	0.220356	+	0.112277i
$378$	−11.0975	−	0.792528i	−0.570795	−	0.0407632i
$379$	−9.28018	−	12.7731i	−0.476691	−	0.656109i	0.501174	−	0.865347i	$-0.332902\pi$
$379$	−9.28018	−	12.7731i	−0.476691	−	0.656109i	−0.977865	+	0.209238i	$0.932902\pi$
$380$		0			0
$381$	1.37764	−	18.0622i	0.0705787	−	0.925357i
$382$	14.8555	+	14.8555i	0.760073	+	0.760073i
$383$	2.49780	+	15.7705i	0.127632	+	0.805836i	0.965584	+	0.260092i	$0.0837529\pi$
$383$	2.49780	+	15.7705i	0.127632	+	0.805836i	−0.837952	+	0.545744i	$0.816247\pi$
$384$	1.68321	−	0.408406i	0.0858961	−	0.0208414i
$385$		0			0
$386$	9.42739	−	3.06314i	0.479841	−	0.155910i
$387$	0.0273672	+	5.66521i	0.00139115	+	0.287979i
$388$	−5.47700	−	10.7492i	−0.278053	−	0.545709i
$389$	3.56490	+	10.9716i	0.180748	+	0.556284i	0.999849	−	0.0173647i	$-0.00552762\pi$
$389$	3.56490	+	10.9716i	0.180748	+	0.556284i	−0.819102	+	0.573648i	$0.805528\pi$
$390$		0			0
$391$	−2.75201	+	8.46982i	−0.139175	+	0.428337i
$392$	−2.38569	+	0.377857i	−0.120496	+	0.0190847i
$393$	−7.81799	+	32.9143i	−0.394365	+	1.66031i
$394$	−5.99998	+	8.25827i	−0.302275	+	0.416046i
$395$		0			0
$396$	17.5206	−	2.86183i	0.880446	−	0.143812i
$397$	20.6866	+	3.27643i	1.03823	+	0.164439i	0.652200	−	0.758047i	$-0.273846\pi$
$397$	20.6866	+	3.27643i	1.03823	+	0.164439i	0.386030	+	0.922486i	$0.373846\pi$
$398$	6.86195	−	13.4673i	0.343958	−	0.675057i
$399$	−17.0256	+	10.4900i	−0.852348	+	0.525155i
$400$		0			0
$401$		−	24.4394i		−	1.22045i	−0.792229	−	0.610223i	$-0.791080\pi$
$401$		−	24.4394i		−	1.22045i	0.792229	−	0.610223i	$-0.208920\pi$
$402$	−0.181579	−	2.23805i	−0.00905633	−	0.111624i
$403$	−1.76187	+	11.1240i	−0.0877648	+	0.554125i
$404$	0.251023	−	0.182379i	0.0124889	−	0.00907370i
$405$		0			0
$406$	−7.87354	−	5.72046i	−0.390757	−	0.283902i
$407$	0.925189	−	0.925189i	0.0458599	−	0.0458599i
$408$	6.48954	+	7.56121i	0.321280	+	0.374336i
$409$	9.31361	+	3.02618i	0.460528	+	0.149635i	0.530087	−	0.847943i	$-0.322159\pi$
$409$	9.31361	+	3.02618i	0.460528	+	0.149635i	−0.0695588	+	0.997578i	$0.522159\pi$
$410$		0			0
$411$	15.8240	+	13.4490i	0.780539	+	0.663389i
$412$	7.87141	−	4.01069i	0.387797	−	0.197592i
$413$	13.8365	−	7.05006i	0.680851	−	0.346911i
$414$	−0.704337	+	4.59042i	−0.0346163	+	0.225607i
$415$		0			0
$416$	1.00475	+	0.326463i	0.0492619	+	0.0160062i
$417$	−30.5858	+	26.2507i	−1.49779	+	1.28550i
$418$	22.5634	−	22.5634i	1.10361	−	1.10361i
$419$	−20.8723	−	15.1646i	−1.01968	−	0.740840i	−0.0534618	−	0.998570i	$-0.517026\pi$
$419$	−20.8723	−	15.1646i	−1.01968	−	0.740840i	−0.966217	+	0.257730i	$0.917026\pi$
$420$		0			0
$421$	−31.8859	+	23.1664i	−1.55402	+	1.12906i	−0.613316	+	0.789837i	$0.710165\pi$
$421$	−31.8859	+	23.1664i	−1.55402	+	1.12906i	−0.940705	+	0.339225i	$0.889835\pi$
$422$	−0.621291	+	3.92268i	−0.0302440	+	0.190953i
$423$	−8.53813	−	11.6331i	−0.415138	−	0.565623i
$424$			6.07158i			0.294862i
$425$		0			0
$426$	3.70809	+	6.01838i	0.179658	+	0.291591i
$427$	4.11875	−	8.08350i	0.199320	−	0.391188i
$428$	−5.85525	−	0.927381i	−0.283024	−	0.0448267i
$429$	10.0140	+	4.11962i	0.483480	+	0.198897i
$430$		0			0
$431$	3.61295	−	4.97279i	0.174030	−	0.239531i	−0.713088	−	0.701074i	$-0.752704\pi$
$431$	3.61295	−	4.97279i	0.174030	−	0.239531i	0.887118	+	0.461543i	$0.152704\pi$
$432$	3.97553	+	3.34591i	0.191273	+	0.160980i
$433$	16.5283	−	2.61783i	0.794299	−	0.125805i	0.253919	−	0.967225i	$-0.418280\pi$
$433$	16.5283	−	2.61783i	0.794299	−	0.125805i	0.540380	+	0.841421i	$0.318280\pi$
$434$	7.05375	−	21.7092i	0.338591	−	1.04208i
$435$		0			0
$436$	−0.583300	−	1.79521i	−0.0279350	−	0.0859752i
$437$	3.78968	+	7.43768i	0.181285	+	0.355792i
$438$	−0.462336	−	0.281786i	−0.0220913	−	0.0134643i
$439$	19.1311	−	6.21606i	0.913076	−	0.296676i	0.185453	−	0.982653i	$-0.440625\pi$
$439$	19.1311	−	6.21606i	0.913076	−	0.296676i	0.727623	+	0.685977i	$0.240625\pi$
$440$		0			0
$441$	−5.14860	−	5.09909i	−0.245171	−	0.242814i
$442$	0.950753	+	6.00282i	0.0452227	+	0.285525i
$443$	−17.1571	−	17.1571i	−0.815159	−	0.815159i	0.170243	−	0.985402i	$-0.445545\pi$
$443$	−17.1571	−	17.1571i	−0.815159	−	0.815159i	−0.985402	+	0.170243i	$0.945545\pi$
$444$	0.381856	+	0.0291249i	0.0181221	+	0.00138221i
$445$		0			0
$446$	7.86865	+	10.8303i	0.372591	+	0.512828i
$447$	−23.5219	+	9.80971i	−1.11255	+	0.463984i
$448$	−1.90779	−	0.972066i	−0.0901345	−	0.0459258i
$449$	15.9242			0.751511			0.375755	−	0.926719i	$-0.377383\pi$
$449$	15.9242			0.751511			0.375755	+	0.926719i	$0.377383\pi$
$450$		0			0
$451$	−9.59671			−0.451891
$452$	−7.55774	−	3.85086i	−0.355486	−	0.181129i
$453$	−13.6661	+	5.69940i	−0.642089	+	0.267781i
$454$	0.503096	+	0.692453i	0.0236115	+	0.0324984i
$455$		0			0
$456$	9.31265	+	0.710293i	0.436105	+	0.0332625i
$457$	−2.30257	−	2.30257i	−0.107710	−	0.107710i	0.651198	−	0.758908i	$-0.274267\pi$
$457$	−2.30257	−	2.30257i	−0.107710	−	0.107710i	−0.758908	+	0.651198i	$0.774267\pi$
$458$	−2.58835	−	16.3422i	−0.120946	−	0.763621i
$459$	−6.76752	+	29.1166i	−0.315881	+	1.35905i
$460$		0			0
$461$	−9.43135	+	3.06443i	−0.439262	+	0.142725i	−0.520295	−	0.853987i	$-0.674178\pi$
$461$	−9.43135	+	3.06443i	−0.439262	+	0.142725i	0.0810333	+	0.996711i	$0.474178\pi$
$462$	−18.7397	−	11.4215i	−0.871851	−	0.531379i
$463$	−10.4958	−	20.5992i	−0.487783	−	0.957328i	−0.995406	−	0.0957485i	$-0.969476\pi$
$463$	−10.4958	−	20.5992i	−0.487783	−	0.957328i	0.507623	−	0.861580i	$-0.330524\pi$
$464$	1.40458	+	4.32285i	0.0652059	+	0.200683i
$465$		0			0
$466$	−1.68432	+	5.18379i	−0.0780245	+	0.240135i
$467$	4.58995	−	0.726976i	0.212397	−	0.0336405i	−0.0493288	−	0.998783i	$-0.515708\pi$
$467$	4.58995	−	0.726976i	0.212397	−	0.0336405i	0.261726	+	0.965142i	$0.415708\pi$
$468$	0.993939	+	3.00948i	0.0459448	+	0.139113i
$469$	−1.63156	+	2.24565i	−0.0753383	+	0.103694i
$470$		0			0
$471$	39.8384	+	16.3890i	1.83566	+	0.755164i
$472$	−7.16336	−	1.13457i	−0.329721	−	0.0522226i
$473$	−5.07333	+	9.95697i	−0.233272	+	0.457822i
$474$	0.858596	+	1.39353i	0.0394366	+	0.0640072i
$475$		0			0
$476$		−	12.3178i		−	0.564585i
$477$	−14.6842	+	10.7774i	−0.672341	+	0.493464i
$478$	1.36331	−	8.60761i	0.0623564	−	0.393703i
$479$	12.7801	−	9.28530i	0.583939	−	0.424256i	−0.256203	−	0.966623i	$-0.582472\pi$
$479$	12.7801	−	9.28530i	0.583939	−	0.424256i	0.840142	+	0.542367i	$0.182472\pi$
$480$		0			0
$481$	0.188977	+	0.137300i	0.00861660	+	0.00626032i
$482$	17.9787	−	17.9787i	0.818908	−	0.818908i
$483$	4.35654	−	3.73907i	0.198229	−	0.170134i
$484$	22.8426	+	7.42201i	1.03830	+	0.337364i
$485$		0			0
$486$	−1.03529	+	15.5540i	−0.0469619	+	0.705546i
$487$	0.120793	−	0.0615473i	0.00547367	−	0.00278898i	−0.451252	−	0.892397i	$-0.649022\pi$
$487$	0.120793	−	0.0615473i	0.00547367	−	0.00278898i	0.456725	+	0.889608i	$0.349022\pi$
$488$	−3.77529	+	1.92361i	−0.170899	+	0.0870776i
$489$	2.65182	+	2.25381i	0.119919	+	0.101921i
$490$		0			0
$491$	−8.65368	−	2.81175i	−0.390535	−	0.126893i	0.107166	−	0.994241i	$-0.465822\pi$
$491$	−8.65368	−	2.81175i	−0.390535	−	0.126893i	−0.497701	+	0.867349i	$0.665822\pi$
$492$	−1.82939	−	2.13149i	−0.0824752	−	0.0960951i
$493$	−18.4898	+	18.4898i	−0.832738	+	0.832738i
$494$	4.60873	+	3.34844i	0.207357	+	0.150654i
$495$		0			0
$496$	−8.62475	+	6.26624i	−0.387263	+	0.281363i
$497$	1.36703	−	8.63111i	0.0613198	−	0.387158i
$498$	−1.05954	−	13.0594i	−0.0474792	−	0.585205i
$499$		−	27.5900i		−	1.23510i	−0.786532	−	0.617549i	$-0.788126\pi$
$499$		−	27.5900i		−	1.23510i	0.786532	−	0.617549i	$-0.211874\pi$
$500$		0			0
$501$	21.8831	−	13.4828i	0.977667	−	0.602368i
$502$	−9.57626	+	18.7945i	−0.427409	+	0.838838i
$503$	10.8159	+	1.71307i	0.482257	+	0.0763820i	0.392829	−	0.919611i	$-0.371496\pi$
$503$	10.8159	+	1.71307i	0.482257	+	0.0763820i	0.0894274	+	0.995993i	$0.471496\pi$
$504$	−1.03549	−	6.33947i	−0.0461244	−	0.282382i
$505$		0			0
$506$	−5.38455	+	7.41120i	−0.239372	+	0.329468i
$507$	4.75677	−	20.0263i	0.211256	−	0.889401i
$508$	10.3298	−	1.63607i	0.458309	−	0.0725891i
$509$	−2.83257	+	8.71775i	−0.125551	+	0.386407i	−0.994001	−	0.109370i	$-0.965117\pi$
$509$	−2.83257	+	8.71775i	−0.125551	+	0.386407i	0.868450	+	0.495777i	$0.165117\pi$
$510$		0			0
$511$	0.206834	+	0.636570i	0.00914980	+	0.0281602i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	14.8127	+	23.7835i	0.653995	+	1.05007i
$514$	15.9501	−	5.18250i	0.703529	−	0.228590i
$515$		0			0
$516$	−3.17862	+	0.771244i	−0.139931	+	0.0339521i
$517$	−4.45276	−	28.1136i	−0.195832	−	1.23643i
$518$	−0.334760	−	0.334760i	−0.0147085	−	0.0147085i
$519$	−0.660538	+	8.66031i	−0.0289944	+	0.380146i
$520$		0			0
$521$	−13.3932	−	18.4342i	−0.586767	−	0.807615i	0.407650	−	0.913138i	$-0.366348\pi$
$521$	−13.3932	−	18.4342i	−0.586767	−	0.807615i	−0.994417	+	0.105523i	$0.966348\pi$
$522$	−7.96161	+	11.0703i	−0.348470	+	0.484533i
$523$	32.1380	+	16.3751i	1.40530	+	0.716035i	0.981810	−	0.189867i	$-0.0608055\pi$
$523$	32.1380	+	16.3751i	1.40530	+	0.716035i	0.423488	+	0.905902i	$0.360806\pi$
$524$	−19.5318			−0.853250
$525$		0			0
$526$	22.7518			0.992025
$527$	−54.6453	−	27.8432i	−2.38039	−	1.21287i
$528$	3.94521	+	9.45990i	0.171693	+	0.411689i
$529$	12.1105	+	16.6686i	0.526542	+	0.724723i
$530$		0			0
$531$	−9.97144	−	19.3385i	−0.432724	−	0.839221i
$532$	−8.16406	−	8.16406i	−0.353957	−	0.353957i
$533$	−0.268016	−	1.69218i	−0.0116090	−	0.0732966i
$534$	−3.53442	−	14.5668i	−0.152949	−	0.630368i
$535$		0			0
$536$	1.23294	−	0.400605i	0.0532548	−	0.0173035i
$537$	−2.85634	+	4.68650i	−0.123260	+	0.202237i
$538$	4.70077	+	9.22579i	0.202665	+	0.397752i
$539$	−4.41696	−	13.5940i	−0.190252	−	0.585536i
$540$		0			0
$541$	10.6711	−	32.8422i	0.458786	−	1.41200i	−0.407847	−	0.913050i	$-0.633720\pi$
$541$	10.6711	−	32.8422i	0.458786	−	1.41200i	0.866633	−	0.498947i	$-0.166280\pi$
$542$	0.631560	−	0.100029i	0.0271278	−	0.00429663i
$543$	−10.5166	−	2.49797i	−0.451312	−	0.107198i
$544$	−3.38144	+	4.65416i	−0.144978	+	0.199545i
$545$		0			0
$546$	1.49060	−	3.62335i	0.0637917	−	0.155065i
$547$	22.3156	+	3.53445i	0.954148	+	0.151122i	0.614049	−	0.789268i	$-0.289540\pi$
$547$	22.3156	+	3.53445i	0.954148	+	0.151122i	0.340098	+	0.940390i	$0.389540\pi$
$548$	−5.44330	+	10.6831i	−0.232526	+	0.456359i
$549$	−11.3536	−	5.71604i	−0.484561	−	0.243955i
$550$		0			0
$551$			24.5096i			1.04414i
$552$	−2.67251	+	0.216828i	−0.113750	+	0.00922880i
$553$	0.316532	−	1.99850i	0.0134603	−	0.0849851i
$554$	−24.5631	+	17.8461i	−1.04358	+	0.758209i
$555$		0			0
$556$	−18.8265	−	13.6782i	−0.798420	−	0.580086i
$557$	3.76017	−	3.76017i	0.159323	−	0.159323i	−0.622943	−	0.782267i	$-0.714063\pi$
$557$	3.76017	−	3.76017i	0.159323	−	0.159323i	0.782267	+	0.622943i	$0.214063\pi$
$558$	−30.4644	−	9.73603i	−1.28966	−	0.412159i
$559$	−1.89740	−	0.616502i	−0.0802513	−	0.0260752i
$560$		0			0
$561$	−38.1860	+	44.9293i	−1.61221	+	1.89692i
$562$	19.3495	−	9.85907i	0.816210	−	0.415880i
$563$	−21.6061	+	11.0089i	−0.910590	+	0.463969i	−0.845539	−	0.533913i	$-0.820721\pi$
$563$	−21.6061	+	11.0089i	−0.910590	+	0.463969i	−0.0650508	+	0.997882i	$0.520721\pi$
$564$	5.39540	−	6.34819i	0.227187	−	0.267307i
$565$		0			0
$566$	3.29063	+	1.06919i	0.138315	+	0.0449414i
$567$	13.4940	−	13.7573i	0.566694	−	0.577751i
$568$	−2.88591	+	2.88591i	−0.121090	+	0.121090i
$569$	24.5934	+	17.8681i	1.03101	+	0.749071i	0.968510	−	0.248974i	$-0.0800934\pi$
$569$	24.5934	+	17.8681i	1.03101	+	0.749071i	0.0624977	+	0.998045i	$0.480093\pi$
$570$		0			0
$571$	4.57335	−	3.32274i	0.191389	−	0.139052i	−0.487964	−	0.872864i	$-0.662260\pi$
$571$	4.57335	−	3.32274i	0.191389	−	0.139052i	0.679353	+	0.733811i	$0.262260\pi$
$572$	−0.977982	+	6.17473i	−0.0408915	+	0.258179i
$573$	−36.2692	+	2.94261i	−1.51517	+	0.122929i
$574$			3.47236i			0.144934i
$575$		0			0
$576$	−1.34904	+	2.67957i	−0.0562101	+	0.111649i
$577$	−11.6678	+	22.8994i	−0.485739	+	0.953316i	0.509919	+	0.860223i	$0.329676\pi$
$577$	−11.6678	+	22.8994i	−0.485739	+	0.953316i	−0.995657	+	0.0930933i	$0.970324\pi$
$578$	−15.8972	−	2.51787i	−0.661236	−	0.104729i
$579$	−6.53197	+	15.8779i	−0.271459	+	0.659864i
$580$		0			0
$581$	−9.52039	+	13.1037i	−0.394972	+	0.543633i
$582$	20.3301	+	4.82891i	0.842708	+	0.200165i
$583$	−35.4869	+	5.62058i	−1.46972	+	0.232781i
$584$	0.0965991	−	0.297301i	0.00399730	−	0.0123024i
$585$		0			0
$586$	5.35461	+	16.4798i	0.221197	+	0.680773i
$587$	−6.56280	−	12.8802i	−0.270876	−	0.531623i	0.714995	−	0.699129i	$-0.246429\pi$
$587$	−6.56280	−	12.8802i	−0.270876	−	0.531623i	−0.985871	+	0.167506i	$0.946429\pi$
$588$	2.17733	−	3.57242i	0.0897916	−	0.147324i
$589$	−54.6723	+	17.7641i	−2.25273	+	0.731957i
$590$		0			0
$591$	−4.16892	−	17.1819i	−0.171486	−	0.706768i
$592$	0.0345885	+	0.218383i	0.00142158	+	0.00897549i
$593$	−27.1124	−	27.1124i	−1.11337	−	1.11337i	−0.992691	−	0.120680i	$-0.961492\pi$
$593$	−27.1124	−	27.1124i	−1.11337	−	1.11337i	−0.120680	−	0.992691i	$-0.538508\pi$
$594$	−15.8758	+	26.3334i	−0.651393	+	1.08047i
$595$		0			0
$596$	−8.64870	−	11.9039i	−0.354265	−	0.487603i
$597$	10.0769	+	24.1624i	0.412418	+	0.988903i
$598$	−1.45719	−	0.742476i	−0.0595890	−	0.0303621i
$599$	−22.2597			−0.909506			−0.454753	−	0.890618i	$-0.650272\pi$
$599$	−22.2597			−0.909506			−0.454753	+	0.890618i	$0.650272\pi$
$600$		0			0
$601$	−0.661317			−0.0269757			−0.0134878	−	0.999909i	$-0.504293\pi$
$601$	−0.661317			−0.0269757			−0.0134878	+	0.999909i	$0.504293\pi$
$602$	3.60272	+	1.83568i	0.146836	+	0.0748165i
$603$	3.15740	+	2.27076i	0.128579	+	0.0924727i
$604$	−5.02485	−	6.91612i	−0.204458	−	0.281413i
$605$		0			0
$606$	−0.0408716	+	0.535868i	−0.00166030	+	0.0217681i
$607$	25.2285	+	25.2285i	1.02399	+	1.02399i	0.999705	+	0.0242876i	$0.00773174\pi$
$607$	25.2285	+	25.2285i	1.02399	+	1.02399i	0.0242876	+	0.999705i	$0.492268\pi$
$608$	0.843538	+	5.32589i	0.0342100	+	0.215993i
$609$	16.3814	−	3.97470i	0.663809	−	0.161063i
$610$		0			0
$611$	4.83290	−	1.57031i	0.195518	−	0.0635278i
$612$	−17.2584	+	0.0833706i	−0.697628	+	0.00337006i
$613$	−11.3412	−	22.2583i	−0.458065	−	0.899003i	−0.998345	−	0.0575173i	$-0.981682\pi$
$613$	−11.3412	−	22.2583i	−0.458065	−	0.899003i	0.540280	−	0.841485i	$-0.318318\pi$
$614$	7.34770	+	22.6139i	0.296529	+	0.912623i
$615$		0			0
$616$	3.91542	−	12.0504i	0.157757	−	0.485525i
$617$	30.7946	−	4.87738i	1.23974	−	0.196356i	0.498081	−	0.867131i	$-0.334038\pi$
$617$	30.7946	−	4.87738i	1.23974	−	0.196356i	0.741661	+	0.670775i	$0.234038\pi$
$618$	−3.53610	+	14.8873i	−0.142243	+	0.598853i
$619$	−2.12975	+	2.93135i	−0.0856019	+	0.117821i	−0.849670	−	0.527314i	$-0.823199\pi$
$619$	−2.12975	+	2.93135i	−0.0856019	+	0.117821i	0.764068	+	0.645135i	$0.223199\pi$
$620$		0			0
$621$	−5.26827	−	6.07861i	−0.211408	−	0.243926i
$622$	7.68404	+	1.21703i	0.308102	+	0.0487985i
$623$	−8.41243	+	16.5103i	−0.337037	+	0.661472i
$624$	−1.55788	+	0.959853i	−0.0623651	+	0.0384249i
$625$		0			0
$626$		−	20.7996i		−	0.831321i
$627$	4.46940	+	55.0877i	0.178491	+	2.19999i
$628$	−3.89068	+	24.5648i	−0.155255	+	0.980241i
$629$	−1.02906	+	0.747655i	−0.0410312	+	0.0298109i
$630$		0			0
$631$	4.12680	+	2.99829i	0.164285	+	0.119360i	0.666890	−	0.745156i	$-0.267625\pi$
$631$	4.12680	+	2.99829i	0.164285	+	0.119360i	−0.502605	+	0.864516i	$0.667625\pi$
$632$	−0.668222	+	0.668222i	−0.0265805	+	0.0265805i
$633$	−4.48015	−	5.22000i	−0.178070	−	0.207477i
$634$	0.206145	+	0.0669805i	0.00818706	+	0.00266014i
$635$		0			0
$636$	−8.01312	−	6.81045i	−0.317741	−	0.270052i
$637$	2.27367	−	1.15849i	0.0900861	−	0.0459012i
$638$	−23.9657	+	12.2112i	−0.948813	+	0.483444i
$639$	−12.1022	−	1.85692i	−0.478757	−	0.0734587i
$640$		0			0
$641$	45.1681	+	14.6760i	1.78403	+	0.579668i	0.999198	−	0.0400355i	$-0.0127471\pi$
$641$	45.1681	+	14.6760i	1.78403	+	0.579668i	0.784836	+	0.619703i	$0.212747\pi$
$642$	7.79173	−	6.68738i	0.307515	−	0.263930i
$643$	17.9186	−	17.9186i	0.706639	−	0.706639i	−0.259188	−	0.965827i	$-0.583455\pi$
$643$	17.9186	−	17.9186i	0.706639	−	0.706639i	0.965827	+	0.259188i	$0.0834550\pi$
$644$	2.68158	+	1.94828i	0.105669	+	0.0767731i
$645$		0			0
$646$	−25.0965	+	18.2337i	−0.987409	+	0.717395i
$647$	−1.11876	+	7.06356i	−0.0439829	+	0.277697i	−0.999871	−	0.0160323i	$-0.994897\pi$
$647$	−1.11876	+	7.06356i	−0.0439829	+	0.277697i	0.955889	+	0.293730i	$0.0948965\pi$
$648$	−8.87518	+	1.49373i	−0.348650	+	0.0586791i
$649$		−	42.9184i		−	1.68469i
$650$		0			0
$651$	20.7391	+	33.6604i	0.812831	+	1.31926i
$652$	−0.912200	+	1.79029i	−0.0357245	+	0.0701133i
$653$	22.9855	+	3.64054i	0.899490	+	0.142465i	0.589021	−	0.808118i	$-0.299514\pi$
$653$	22.9855	+	3.64054i	0.899490	+	0.142465i	0.310470	+	0.950583i	$0.399514\pi$
$654$	3.02356	+	1.24385i	0.118231	+	0.0486385i
$655$		0			0
$656$	0.953223	−	1.31200i	0.0372171	−	0.0512250i
$657$	0.890494	−	0.294102i	0.0347415	−	0.0114740i
$658$	−10.1723	+	1.61113i	−0.396557	+	0.0628085i
$659$	−1.14382	+	3.52031i	−0.0445568	+	0.137132i	−0.970860	−	0.239647i	$-0.922968\pi$
$659$	−1.14382	+	3.52031i	−0.0445568	+	0.137132i	0.926303	+	0.376779i	$0.122968\pi$
$660$		0			0
$661$	−11.4157	−	35.1339i	−0.444019	−	1.36655i	−0.883556	−	0.468326i	$-0.844857\pi$
$661$	−11.4157	−	35.1339i	−0.444019	−	1.36655i	0.439537	−	0.898224i	$-0.355143\pi$
$662$	−3.26336	−	6.40470i	−0.126834	−	0.248926i
$663$	−8.98882	−	5.47854i	−0.349097	−	0.212769i
$664$	7.19438	−	2.33760i	0.279196	−	0.0907163i
$665$		0			0
$666$	−0.466764	+	0.471295i	−0.0180867	+	0.0182623i
$667$	−1.10073	−	6.94972i	−0.0426203	−	0.269094i
$668$	10.4933	+	10.4933i	0.405999	+	0.405999i
$669$	−23.1197	−	1.76338i	−0.893860	−	0.0681764i
$670$		0			0
$671$	−14.7379	−	20.2849i	−0.568949	−	0.783092i
$672$	3.42286	−	1.42749i	0.132040	−	0.0550667i
$673$	−1.06415	−	0.542210i	−0.0410198	−	0.0209006i	0.433360	−	0.901221i	$-0.357328\pi$
$673$	−1.06415	−	0.542210i	−0.0410198	−	0.0209006i	−0.474380	+	0.880320i	$0.657328\pi$
$674$	−6.75390			−0.260151
$675$		0			0
$676$	11.8839			0.457073
$677$	30.6338	+	15.6087i	1.17735	+	0.599892i	0.929470	−	0.368898i	$-0.120265\pi$
$677$	30.6338	+	15.6087i	1.17735	+	0.599892i	0.247884	+	0.968790i	$0.420265\pi$
$678$	13.5597	−	5.65503i	0.520758	−	0.217180i
$679$	−15.1832	−	20.8979i	−0.582679	−	0.801988i
$680$		0			0
$681$	−1.47820	−	0.112745i	−0.0566448	−	0.00432040i
$682$	−44.6088	−	44.6088i	−1.70816	−	1.70816i
$683$	7.05008	+	44.5125i	0.269764	+	1.70322i	0.635169	+	0.772373i	$0.280930\pi$
$683$	7.05008	+	44.5125i	0.269764	+	1.70322i	−0.365405	+	0.930849i	$0.619070\pi$
$684$	−11.3834	+	11.4939i	−0.435254	+	0.439479i
$685$		0			0
$686$	−19.1733	+	6.22977i	−0.732038	+	0.237854i
$687$	24.4714	+	14.9149i	0.933641	+	0.569039i
$688$	−0.857327	−	1.68260i	−0.0326853	−	0.0641485i
$689$	−1.98215	−	6.10043i	−0.0755138	−	0.232408i
$690$		0			0
$691$	1.10289	−	3.39434i	0.0419558	−	0.129127i	−0.927885	−	0.372867i	$-0.878375\pi$
$691$	1.10289	−	3.39434i	0.0419558	−	0.129127i	0.969840	+	0.243741i	$0.0783746\pi$
$692$	−4.95282	+	0.784450i	−0.188278	+	0.0298203i
$693$	36.0941	−	11.9207i	1.37110	−	0.452832i
$694$	2.69058	−	3.70326i	0.102133	−	0.140574i
$695$		0			0
$696$	−7.28069	−	2.99518i	−0.275974	−	0.113532i
$697$	9.21466	+	1.45946i	0.349030	+	0.0552809i
$698$	4.44057	−	8.71510i	0.168078	−	0.329871i
$699$	−4.95215	−	8.03754i	−0.187308	−	0.304008i
$700$		0			0
$701$			19.6139i			0.740807i	0.928871	+	0.370403i	$0.120781\pi$
$701$			19.6139i			0.740807i	−0.928871	+	0.370403i	$0.879219\pi$
$702$	−5.08674	−	2.06394i	−0.191986	−	0.0778984i
$703$	−0.186511	+	1.17758i	−0.00703438	+	0.0444133i
$704$	−4.78745	+	3.47829i	−0.180434	+	0.131093i
$705$		0			0
$706$	−8.76956	−	6.37146i	−0.330047	−	0.239793i
$707$	0.469776	−	0.469776i	0.0176677	−	0.0176677i
$708$	9.53246	−	8.18139i	0.358252	−	0.307476i
$709$	22.4237	+	7.28590i	0.842140	+	0.273628i	0.698150	−	0.715951i	$-0.254007\pi$
$709$	22.4237	+	7.28590i	0.842140	+	0.273628i	0.143990	+	0.989579i	$0.454007\pi$
$710$		0			0
$711$	−2.80223	−	0.429964i	−0.105092	−	0.0161249i
$712$	7.71092	−	3.92891i	0.288979	−	0.147242i
$713$	14.7046	−	7.49238i	0.550692	−	0.280592i
$714$	16.2567	+	13.8168i	0.608392	+	0.517080i
$715$		0			0
$716$	−3.01361	−	0.979183i	−0.112624	−	0.0365938i
$717$	9.83090	+	11.4544i	0.367142	+	0.427771i
$718$	−14.8975	+	14.8975i	−0.555969	+	0.555969i
$719$	30.2210	+	21.9569i	1.12705	+	0.818853i	0.985263	−	0.171044i	$-0.0547140\pi$
$719$	30.2210	+	21.9569i	1.12705	+	0.818853i	0.141791	+	0.989897i	$0.454714\pi$
$720$		0			0
$721$	15.3031	−	11.1183i	0.569916	−	0.414068i
$722$	−1.57634	+	9.95259i	−0.0586651	+	0.370397i
$723$	3.56127	+	43.8944i	0.132445	+	1.63245i
$724$		−	6.24071i		−	0.231934i
$725$		0			0
$726$	−35.4178	+	21.8219i	−1.31448	+	0.809886i
$727$	−19.2896	+	37.8579i	−0.715411	+	1.40407i	0.190964	+	0.981597i	$0.438839\pi$
$727$	−19.2896	+	37.8579i	−0.715411	+	1.40407i	−0.906374	+	0.422476i	$0.861161\pi$
$728$	2.23419	+	0.353862i	0.0828047	+	0.0131150i
$729$	−19.3666	−	18.8132i	−0.717280	−	0.696785i
$730$		0			0
$731$	6.38561	−	8.78903i	0.236180	−	0.325074i
$732$	1.69599	−	7.14023i	0.0626855	−	0.263911i
$733$	44.0735	−	6.98056i	1.62789	−	0.257833i	0.725333	−	0.688398i	$-0.241686\pi$
$733$	44.0735	−	6.98056i	1.62789	−	0.257833i	0.902559	+	0.430565i	$0.141686\pi$
$734$	−8.34641	+	25.6876i	−0.308072	+	0.948147i
$735$		0			0
$736$	−0.478373	−	1.47228i	−0.0176331	−	0.0542690i
$737$	3.48279	+	6.83537i	0.128290	+	0.251784i
$738$	4.86510	−	0.0235020i	0.179087	−	0.000865122i
$739$	8.01855	−	2.60538i	0.294967	−	0.0958406i	−0.157795	−	0.987472i	$-0.550439\pi$
$739$	8.01855	−	2.60538i	0.294967	−	0.0958406i	0.452762	+	0.891631i	$0.350439\pi$
$740$		0			0
$741$	−9.58877	+	2.32657i	−0.352252	+	0.0854687i
$742$	2.03368	+	12.8402i	0.0746589	+	0.471378i
$743$	24.9192	+	24.9192i	0.914196	+	0.914196i	0.996599	−	0.0824029i	$-0.0262594\pi$
$743$	24.9192	+	24.9192i	0.914196	+	0.914196i	−0.0824029	+	0.996599i	$0.526259\pi$
$744$	1.40428	−	18.4115i	0.0514834	−	0.674999i
$745$		0			0
$746$	−15.7261	−	21.6451i	−0.575772	−	0.792482i
$747$	18.4239	+	13.2503i	0.674097	+	0.484802i
$748$	−30.3327	−	15.4553i	−1.10907	−	0.565101i
$749$	−12.6933			−0.463804
$750$		0			0
$751$	−8.40064			−0.306544			−0.153272	−	0.988184i	$-0.548981\pi$
$751$	−8.40064			−0.306544			−0.153272	+	0.988184i	$0.548981\pi$
$752$	4.28579	+	2.18372i	0.156287	+	0.0796320i
$753$	−14.0628	−	33.7201i	−0.512478	−	1.22883i
$754$	−2.82250	−	3.88484i	−0.102789	−	0.141477i
$755$		0			0
$756$	9.52817	+	5.74432i	0.346536	+	0.208919i
$757$	−5.57829	−	5.57829i	−0.202746	−	0.202746i	0.598429	−	0.801176i	$-0.295792\pi$
$757$	−5.57829	−	5.57829i	−0.202746	−	0.202746i	−0.801176	+	0.598429i	$0.795792\pi$
$758$	2.46985	+	15.5940i	0.0897089	+	0.566400i
$759$	−3.74130	−	15.4195i	−0.135801	−	0.559691i
$760$		0			0
$761$	5.92036	−	1.92364i	0.214613	−	0.0697320i	−0.199737	−	0.979849i	$-0.564009\pi$
$761$	5.92036	−	1.92364i	0.214613	−	0.0697320i	0.414350	+	0.910118i	$0.364009\pi$
$762$	−9.42757	+	15.4681i	−0.341525	+	0.560352i
$763$	−1.83487	−	3.60114i	−0.0664268	−	0.130370i
$764$	−6.49209	−	19.9806i	−0.234875	−	0.722872i
$765$		0			0
$766$	4.93411	−	15.1856i	0.178276	−	0.548679i
$767$	7.56779	−	1.19862i	0.273257	−	0.0432796i
$768$	−1.68517	−	0.400270i	−0.0608082	−	0.0144435i
$769$	2.22958	−	3.06876i	0.0804008	−	0.110662i	−0.766922	−	0.641740i	$-0.778213\pi$
$769$	2.22958	−	3.06876i	0.0804008	−	0.110662i	0.847323	+	0.531078i	$0.178213\pi$
$770$		0			0
$771$	−11.0514	+	26.8637i	−0.398006	+	0.967473i
$772$	−9.79050	−	1.55066i	−0.352368	−	0.0558096i
$773$	15.4685	−	30.3587i	0.556364	−	1.09193i	−0.425960	−	0.904742i	$-0.640064\pi$
$773$	15.4685	−	30.3587i	0.556364	−	1.09193i	0.982325	−	0.187185i	$-0.0599363\pi$
$774$	2.54757	−	5.06017i	0.0915704	−	0.181884i
$775$		0			0
$776$			12.0641i			0.433077i
$777$	0.817305	−	0.0663100i	0.0293206	−	0.00237886i
$778$	1.80467	−	11.3942i	0.0647005	−	0.408503i
$779$	7.07466	−	5.14004i	0.253476	−	0.184161i
$780$		0			0
$781$	−19.5390	−	14.1959i	−0.699159	−	0.507969i
$782$	6.29727	−	6.29727i	0.225190	−	0.225190i
$783$	−5.67980	−	22.9250i	−0.202980	−	0.819272i
$784$	2.29721	+	0.746410i	0.0820433	+	0.0266575i
$785$		0			0
$786$	21.9087	−	25.7776i	0.781456	−	0.919455i
$787$	27.9758	−	14.2544i	0.997230	−	0.508114i	0.122367	−	0.992485i	$-0.460951\pi$
$787$	27.9758	−	14.2544i	0.997230	−	0.508114i	0.874863	+	0.484371i	$0.160951\pi$
$788$	9.09520	−	4.63424i	0.324003	−	0.165088i
$789$	−25.5205	+	30.0272i	−0.908554	+	1.06900i
$790$		0			0
$791$	−17.2729	−	5.61232i	−0.614155	−	0.199551i
$792$	−16.9103	−	5.40430i	−0.600880	−	0.192034i
$793$	3.16524	−	3.16524i	0.112401	−	0.112401i
$794$	−16.9444	−	12.3108i	−0.601334	−	0.436895i
$795$		0			0
$796$	−12.2281	+	8.88422i	−0.433413	+	0.314893i
$797$	−1.65300	+	10.4366i	−0.0585523	+	0.369685i	0.940962	+	0.338513i	$0.109924\pi$
$797$	−1.65300	+	10.4366i	−0.0585523	+	0.369685i	−0.999514	+	0.0311718i	$0.990076\pi$
$798$	19.9323	−	1.61716i	0.705596	−	0.0572467i
$799$			27.6716i			0.978949i
$800$		0			0
$801$	23.1894	+	11.6749i	0.819358	+	0.412511i
$802$	−11.0953	+	21.7757i	−0.391787	+	0.768926i
$803$	1.82708	+	0.289381i	0.0644762	+	0.0102120i
$804$	−0.854267	+	2.07656i	−0.0301277	+	0.0732345i
$805$		0			0
$806$	6.62002	−	9.11167i	0.233180	−	0.320945i
$807$	−17.4488	−	4.14454i	−0.614227	−	0.145895i
$808$	−0.306462	+	0.0485388i	−0.0107813	+	0.00170759i
$809$	4.15772	−	12.7961i	0.146178	−	0.449889i	−0.850983	−	0.525193i	$-0.823993\pi$
$809$	4.15772	−	12.7961i	0.146178	−	0.449889i	0.997161	+	0.0753048i	$0.0239930\pi$
$810$		0			0
$811$	6.32531	+	19.4673i	0.222112	+	0.683590i	0.998572	+	0.0534235i	$0.0170133\pi$
$811$	6.32531	+	19.4673i	0.222112	+	0.683590i	−0.776460	+	0.630166i	$0.782987\pi$
$812$	4.41834	+	8.67148i	0.155053	+	0.304309i
$813$	−0.576400	+	0.945720i	−0.0202152	+	0.0331678i
$814$	−1.24438	+	0.404322i	−0.0436154	+	0.0141715i
$815$		0			0
$816$	−2.34950	−	9.68328i	−0.0822490	−	0.338983i
$817$	−1.59296	−	10.0575i	−0.0557306	−	0.351869i
$818$	−6.92463	−	6.92463i	−0.242114	−	0.242114i
$819$	3.11001	+	6.03153i	0.108673	+	0.210759i
$820$		0			0
$821$	−11.1279	−	15.3163i	−0.388368	−	0.534543i	0.569409	−	0.822054i	$-0.307172\pi$
$821$	−11.1279	−	15.3163i	−0.388368	−	0.534543i	−0.957777	+	0.287512i	$0.907172\pi$
$822$	−7.99355	−	19.1671i	−0.278807	−	0.668528i
$823$	−14.0722	−	7.17013i	−0.490525	−	0.249935i	0.191190	−	0.981553i	$-0.438765\pi$
$823$	−14.0722	−	7.17013i	−0.490525	−	0.249935i	−0.681715	+	0.731618i	$0.738765\pi$
$824$	−8.83429			−0.307757
$825$		0			0
$826$	−15.5291			−0.540326
$827$	−6.05244	−	3.08387i	−0.210464	−	0.107237i	0.345581	−	0.938389i	$-0.387682\pi$
$827$	−6.05244	−	3.08387i	−0.210464	−	0.107237i	−0.556045	+	0.831152i	$0.687682\pi$
$828$	2.71158	−	3.77033i	0.0942338	−	0.131028i
$829$	−11.0240	−	15.1733i	−0.382880	−	0.526989i	0.573465	−	0.819230i	$-0.305599\pi$
$829$	−11.0240	−	15.1733i	−0.382880	−	0.526989i	−0.956345	+	0.292241i	$0.905599\pi$
$830$		0			0
$831$	3.99936	−	52.4356i	0.138736	−	1.81897i
$832$	−0.747028	−	0.747028i	−0.0258985	−	0.0258985i
$833$	2.17376	+	13.7246i	0.0753162	+	0.475528i
$834$	39.1697	−	9.50393i	1.35634	−	0.329094i
$835$		0			0
$836$	−30.3476	+	9.86055i	−1.04960	+	0.341034i
$837$	47.0210	−	29.2853i	1.62528	−	1.01225i
$838$	11.7128	+	22.9876i	0.404611	+	0.794093i
$839$	−5.00273	−	15.3968i	−0.172713	−	0.531557i	0.826808	−	0.562484i	$-0.190154\pi$
$839$	−5.00273	−	15.3968i	−0.172713	−	0.531557i	−0.999522	+	0.0309268i	$0.990154\pi$
$840$		0			0
$841$	−2.57725	+	7.93197i	−0.0888709	+	0.273516i
$842$	38.9278	−	6.16556i	1.34154	−	0.212479i
$843$	−8.69245	+	36.5959i	−0.299384	+	1.26043i
$844$	2.33443	−	3.21307i	0.0803545	−	0.110598i
$845$		0			0
$846$	2.32620	+	14.2414i	0.0799763	+	0.489631i
$847$	50.7935	+	8.04490i	1.74529	+	0.276426i
$848$	2.75644	−	5.40982i	0.0946566	−	0.185774i
$849$	−5.10216	+	3.14358i	−0.175106	+	0.107887i
$850$		0			0
$851$		−	0.342281i		−	0.0117332i
$852$	−0.571647	−	7.04585i	−0.0195843	−	0.241387i
$853$	5.14470	−	32.4823i	0.176151	−	1.11217i	−0.728194	−	0.685371i	$-0.759640\pi$
$853$	5.14470	−	32.4823i	0.176151	−	1.11217i	0.904345	−	0.426803i	$-0.140360\pi$
$854$	−7.33967	+	5.33258i	−0.251158	+	0.182477i
$855$		0			0
$856$	4.79605	+	3.48453i	0.163926	+	0.119099i
$857$	14.2417	−	14.2417i	0.486489	−	0.486489i	−0.420708	−	0.907196i	$-0.638218\pi$
$857$	14.2417	−	14.2417i	0.486489	−	0.486489i	0.907196	+	0.420708i	$0.138218\pi$
$858$	−7.05226	−	8.21687i	−0.240760	−	0.280519i
$859$	−29.9968	−	9.74655i	−1.02348	−	0.332548i	−0.251269	−	0.967917i	$-0.580848\pi$
$859$	−29.9968	−	9.74655i	−1.02348	−	0.332548i	−0.772208	+	0.635369i	$0.780848\pi$
$860$		0			0
$861$	−4.58274	−	3.89492i	−0.156179	−	0.132739i
$862$	−5.47676	+	2.79055i	−0.186539	+	0.0950465i
$863$	−19.3357	+	9.85205i	−0.658196	+	0.335368i	−0.750986	−	0.660318i	$-0.770421\pi$
$863$	−19.3357	+	9.85205i	−0.658196	+	0.335368i	0.0927901	+	0.995686i	$0.470421\pi$
$864$	−2.02321	−	4.78608i	−0.0688312	−	0.162826i
$865$		0			0
$866$	−15.9153	−	5.17119i	−0.540824	−	0.175724i
$867$	21.1548	−	18.1564i	0.718454	−	0.616625i
$868$	−16.1407	+	16.1407i	−0.547852	+	0.547852i
$869$	−4.52418	−	3.28701i	−0.153472	−	0.111504i
$870$		0			0
$871$	−1.10801	+	0.805017i	−0.0375435	+	0.0272770i
$872$	−0.295286	+	1.86436i	−0.00999963	+	0.0631352i
$873$	−29.1772	+	21.4146i	−0.987497	+	0.724773i
$874$		−	8.34750i		−	0.282358i
$875$		0			0
$876$	0.284016	+	0.460970i	0.00959602	+	0.0155747i
$877$	−3.43493	+	6.74142i	−0.115989	+	0.227642i	−0.941701	−	0.336450i	$-0.890774\pi$
$877$	−3.43493	+	6.74142i	−0.115989	+	0.227642i	0.825712	+	0.564092i	$0.190774\pi$
$878$	−19.8679	−	3.14677i	−0.670510	−	0.106198i
$879$	−27.7558	−	11.4184i	−0.936181	−	0.385132i
$880$		0			0
$881$	−18.8656	+	25.9662i	−0.635597	+	0.874825i	−0.998371	−	0.0570525i	$-0.981830\pi$
$881$	−18.8656	+	25.9662i	−0.635597	+	0.874825i	0.362774	+	0.931877i	$0.381830\pi$
$882$	2.27249	+	6.88074i	0.0765189	+	0.231687i
$883$	28.3550	−	4.49099i	0.954222	−	0.151134i	0.340139	−	0.940375i	$-0.389526\pi$
$883$	28.3550	−	4.49099i	0.954222	−	0.151134i	0.614083	+	0.789241i	$0.289526\pi$
$884$	1.87810	−	5.78018i	0.0631672	−	0.194409i
$885$		0			0
$886$	7.49794	+	23.0763i	0.251898	+	0.775263i
$887$	5.50981	+	10.8136i	0.185001	+	0.363086i	0.964816	−	0.262924i	$-0.0846870\pi$
$887$	5.50981	+	10.8136i	0.185001	+	0.363086i	−0.779815	+	0.626010i	$0.784687\pi$
$888$	−0.327014	−	0.199310i	−0.0109739	−	0.00668839i
$889$	21.2974	−	6.91994i	0.714291	−	0.232087i
$890$		0			0
$891$	−16.9464	−	50.4905i	−0.567725	−	1.69149i
$892$	−2.09418	−	13.2221i	−0.0701183	−	0.442710i
$893$	18.3403	+	18.3403i	0.613736	+	0.613736i
$894$	25.4117	+	1.93820i	0.849893	+	0.0648230i
$895$		0			0
$896$	1.25854	+	1.73224i	0.0420450	+	0.0578699i
$897$	2.61442	−	1.09034i	0.0872931	−	0.0364052i
$898$	−14.1886	−	7.22945i	−0.473479	−	0.241250i
$899$	48.4565			1.61611
$900$		0			0
$901$	34.9289			1.16365
$902$	8.55073	+	4.35682i	0.284708	+	0.145066i
$903$	−6.46382	+	2.69571i	−0.215102	+	0.0897076i
$904$	4.98574	+	6.86228i	0.165823	+	0.228236i
$905$		0			0
$906$	14.7641	+	1.12608i	0.490503	+	0.0374116i
$907$	−18.7112	−	18.7112i	−0.621295	−	0.621295i	0.324567	−	0.945863i	$-0.394781\pi$
$907$	−18.7112	−	18.7112i	−0.621295	−	0.621295i	−0.945863	+	0.324567i	$0.894781\pi$
$908$	−0.133895	−	0.845381i	−0.00444347	−	0.0280549i
$909$	−0.661379	−	0.655020i	−0.0219366	−	0.0217257i
$910$		0			0
$911$	37.0222	−	12.0293i	1.22660	−	0.398547i	0.377119	−	0.926165i	$-0.376915\pi$
$911$	37.0222	−	12.0293i	1.22660	−	0.398547i	0.849482	+	0.527618i	$0.176915\pi$
$912$	−7.97517	−	4.86073i	−0.264084	−	0.160955i
$913$	20.3226	+	39.8854i	0.672581	+	1.32002i
$914$	1.00626	+	3.09695i	0.0332842	+	0.102438i
$915$		0			0
$916$	−5.11297	+	15.7361i	−0.168937	+	0.519935i
$917$	−41.3058	+	6.54220i	−1.36404	+	0.216042i
$918$	19.2486	−	22.8707i	0.635297	−	0.754845i
$919$	−13.4831	+	18.5579i	−0.444766	+	0.612168i	−0.971263	−	0.238009i	$-0.923505\pi$
$919$	−13.4831	+	18.5579i	−0.444766	+	0.612168i	0.526497	+	0.850177i	$0.323505\pi$
$920$		0			0
$921$	−38.0871	−	15.6685i	−1.25501	−	0.516296i
$922$	9.79461	+	1.55131i	0.322568	+	0.0510898i
$923$	1.95747	−	3.84176i	0.0644311	−	0.126453i
$924$	11.5119	+	18.6843i	0.378715	+	0.614669i
$925$		0			0
$926$			23.1191i			0.759740i
$927$	−15.6814	−	21.3658i	−0.515045	−	0.701744i
$928$	0.711043	−	4.48935i	0.0233411	−	0.147370i
$929$	0.473139	−	0.343755i	0.0155232	−	0.0112782i	−0.579997	−	0.814619i	$-0.696946\pi$
$929$	0.473139	−	0.343755i	0.0155232	−	0.0112782i	0.595520	+	0.803341i	$0.296946\pi$
$930$		0			0
$931$	10.5372	+	7.65572i	0.345342	+	0.250906i
$932$	3.85413	−	3.85413i	0.126246	−	0.126246i
$933$	−10.2253	+	8.77606i	−0.334763	+	0.287315i
$934$	−4.41971	−	1.43605i	−0.144617	−	0.0469891i
$935$		0			0
$936$	0.480671	−	3.13271i	0.0157112	−	0.102396i
$937$	−49.7213	+	25.3343i	−1.62432	+	0.827634i	−0.625445	+	0.780268i	$0.715083\pi$
$937$	−49.7213	+	25.3343i	−1.62432	+	0.827634i	−0.998878	+	0.0473659i	$0.984917\pi$
$938$	2.47323	−	1.26017i	0.0807538	−	0.0411461i
$939$	27.4508	+	23.3308i	0.895824	+	0.761372i
$940$		0			0
$941$	12.5712	+	4.08462i	0.409808	+	0.133155i	0.506664	−	0.862144i	$-0.330879\pi$
$941$	12.5712	+	4.08462i	0.409808	+	0.133155i	−0.0968556	+	0.995298i	$0.530879\pi$
$942$	−28.0558	−	32.6889i	−0.914108	−	1.06506i
$943$	−1.77519	+	1.77519i	−0.0578082	+	0.0578082i
$944$	5.86752	+	4.26300i	0.190972	+	0.138749i
$945$		0			0
$946$	9.04074	−	6.56848i	0.293940	−	0.213560i
$947$	−2.82795	+	17.8550i	−0.0918962	+	0.580210i	0.898174	+	0.439639i	$0.144894\pi$
$947$	−2.82795	+	17.8550i	−0.0918962	+	0.580210i	−0.990071	+	0.140571i	$0.955106\pi$
$948$	−0.132363	−	1.63144i	−0.00429895	−	0.0529868i
$949$			0.330250i			0.0107204i
$950$		0			0
$951$	−0.319630	+	0.196933i	−0.0103647	+	0.00638600i
$952$	−5.59216	+	10.9752i	−0.181243	+	0.355709i
$953$	−51.6458	−	8.17990i	−1.67297	−	0.264973i	−0.753305	−	0.657671i	$-0.771542\pi$
$953$	−51.6458	−	8.17990i	−1.67297	−	0.264973i	−0.919667	+	0.392698i	$0.871542\pi$
$954$	17.9765	−	2.93629i	0.582011	−	0.0950658i
$955$		0			0
$956$	−5.12250	+	7.05051i	−0.165673	+	0.228030i
$957$	10.7662	−	45.3265i	0.348022	−	1.46520i
$958$	−15.6026	+	2.47121i	−0.504097	+	0.0798412i
$959$	−7.93318	+	24.4158i	−0.256176	+	0.788428i
$960$		0			0
$961$	25.5409	+	78.6068i	0.823900	+	2.53570i
$962$	−0.106047	−	0.208129i	−0.00341909	−	0.00671033i
$963$	0.0859123	+	17.7845i	0.00276849	+	0.573098i
$964$	−24.1813	+	7.85699i	−0.778828	+	0.253056i
$965$		0			0
$966$	−5.57920	+	1.35371i	−0.179508	+	0.0435549i
$967$	4.86314	+	30.7047i	0.156388	+	0.987395i	0.933642	+	0.358208i	$0.116612\pi$
$967$	4.86314	+	30.7047i	0.156388	+	0.987395i	−0.777254	+	0.629187i	$0.783388\pi$
$968$	−16.9834	−	16.9834i	−0.545867	−	0.545867i
$969$	4.08621	−	53.5743i	0.131268	−	1.72106i
$970$		0			0
$971$	25.2468	+	34.7493i	0.810210	+	1.11516i	0.991291	+	0.131690i	$0.0420404\pi$
$971$	25.2468	+	34.7493i	0.810210	+	1.11516i	−0.181081	+	0.983468i	$0.557960\pi$
$972$	7.98384	−	13.3887i	0.256082	−	0.429444i
$973$	−44.3957	−	22.6208i	−1.42326	−	0.725188i
$974$	−0.135570			−0.00434393
$975$		0			0
$976$	4.23711			0.135627
$977$	−52.8715	−	26.9394i	−1.69151	−	0.861867i	−0.988596	−	0.150590i	$-0.951883\pi$
$977$	−52.8715	−	26.9394i	−1.69151	−	0.861867i	−0.702912	−	0.711276i	$-0.748117\pi$
$978$	−1.33958	−	3.21206i	−0.0428349	−	0.102710i
$979$	30.1017	+	41.4314i	0.962054	+	1.32415i
$980$		0			0
$981$	−5.03311	+	2.59520i	−0.160695	+	0.0828584i
$982$	6.43398	+	6.43398i	0.205317	+	0.205317i
$983$	−5.94792	−	37.5537i	−0.189709	−	1.19778i	−0.880260	−	0.474492i	$-0.842632\pi$
$983$	−5.94792	−	37.5537i	−0.189709	−	1.19778i	0.690550	−	0.723284i	$-0.257368\pi$
$984$	0.662320	+	2.72970i	0.0211140	+	0.0870197i
$985$		0			0
$986$	24.8687	−	8.08033i	0.791981	−	0.257330i
$987$	9.28386	−	15.2323i	0.295508	−	0.484851i
$988$	−2.58625	−	5.07580i	−0.0822796	−	0.161483i
$989$	0.903372	+	2.78029i	0.0287255	+	0.0884081i
$990$		0			0
$991$	9.31171	−	28.6585i	0.295796	−	0.910367i	−0.687157	−	0.726509i	$-0.741141\pi$
$991$	9.31171	−	28.6585i	0.295796	−	0.910367i	0.982953	−	0.183858i	$-0.0588585\pi$
$992$	10.5295	−	1.66771i	0.334313	−	0.0529499i
$993$	12.1132	+	2.87721i	0.384402	+	0.0913054i
$994$	−5.13648	+	7.06976i	−0.162919	+	0.224239i
$995$		0			0
$996$	−4.98478	+	12.1170i	−0.157949	+	0.383943i
$997$	−33.4599	−	5.29952i	−1.05968	−	0.167838i	−0.397822	−	0.917463i	$-0.630234\pi$
$997$	−33.4599	−	5.29952i	−1.05968	−	0.167838i	−0.661863	+	0.749625i	$0.730234\pi$
$998$	−12.5256	+	24.5829i	−0.396491	+	0.778157i
$999$	−0.0984382	−	1.14467i	−0.00311445	−	0.0362158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.a.107.5		80
3.2	odd	2	inner	750.2.l.a.107.6		80
5.2	odd	4		150.2.l.a.83.7	yes	80
5.3	odd	4		750.2.l.b.143.4		80
5.4	even	2		750.2.l.c.107.6		80
15.2	even	4		150.2.l.a.83.1	yes	80
15.8	even	4		750.2.l.b.143.10		80
15.14	odd	2		750.2.l.c.107.5		80
25.3	odd	20	inner	750.2.l.a.743.6		80
25.4	even	10		150.2.l.a.47.1	✓	80
25.21	even	5		750.2.l.b.257.10		80
25.22	odd	20		750.2.l.c.743.5		80
75.29	odd	10		150.2.l.a.47.7	yes	80
75.47	even	20		750.2.l.c.743.6		80
75.53	even	20	inner	750.2.l.a.743.5		80
75.71	odd	10		750.2.l.b.257.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.1	✓	80	25.4	even	10
150.2.l.a.47.7	yes	80	75.29	odd	10
150.2.l.a.83.1	yes	80	15.2	even	4
150.2.l.a.83.7	yes	80	5.2	odd	4
750.2.l.a.107.5		80	1.1	even	1	trivial
750.2.l.a.107.6		80	3.2	odd	2	inner
750.2.l.a.743.5		80	75.53	even	20	inner
750.2.l.a.743.6		80	25.3	odd	20	inner
750.2.l.b.143.4		80	5.3	odd	4
750.2.l.b.143.10		80	15.8	even	4
750.2.l.b.257.4		80	75.71	odd	10
750.2.l.b.257.10		80	25.21	even	5
750.2.l.c.107.5		80	15.14	odd	2
750.2.l.c.107.6		80	5.4	even	2
750.2.l.c.743.5		80	25.22	odd	20
750.2.l.c.743.6		80	75.47	even	20

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(1.59860 - 0.666690i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.72703 - 0.131724i) q^{6} +(1.51403 + 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.11105 - 2.13154i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(1.59860 - 0.666690i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.72703 - 0.131724i) q^{6} +(1.51403 + 1.51403i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(2.11105 - 2.13154i) q^{9} +(5.62798 - 1.82864i) q^{11} +(1.47900 + 0.901424i) q^{12} +(0.479621 + 0.941310i) q^{13} +(-0.661655 - 2.03636i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-5.68203 + 0.899945i) q^{17} +(-2.84866 + 0.940823i) q^{18} +(-3.16950 + 4.36244i) q^{19} +(3.42972 + 1.41094i) q^{21} +(-5.84476 - 0.925718i) q^{22} +(0.702799 - 1.37932i) q^{23} +(-0.908558 - 1.47463i) q^{24} -1.05646i q^{26} +(1.95364 - 4.81490i) q^{27} +(-0.334951 + 2.11480i) q^{28} +(3.67723 - 2.67167i) q^{29} +(8.62475 + 6.26624i) q^{31} +(0.707107 - 0.707107i) q^{32} +(7.77776 - 6.67539i) q^{33} +(5.47129 + 1.77773i) q^{34} +(2.96530 + 0.454984i) q^{36} +(0.197006 - 0.100380i) q^{37} +(4.80455 - 2.44804i) q^{38} +(1.39429 + 1.18502i) q^{39} +(-1.54235 - 0.501139i) q^{41} +(-2.41535 - 2.81421i) q^{42} +(-1.33532 + 1.33532i) q^{43} +(4.78745 + 3.47829i) q^{44} +(-1.25240 + 0.909919i) q^{46} +(0.752458 - 4.75083i) q^{47} +(0.140065 + 1.72638i) q^{48} -2.41543i q^{49} +(-8.48331 + 5.22681i) q^{51} +(-0.479621 + 0.941310i) q^{52} +(-5.99683 - 0.949805i) q^{53} +(-3.92663 + 3.40317i) q^{54} +(1.25854 - 1.73224i) q^{56} +(-2.15837 + 9.08688i) q^{57} +(-4.48935 + 0.711043i) q^{58} +(2.24119 - 6.89769i) q^{59} +(-1.30934 - 4.02973i) q^{61} +(-4.83989 - 9.49882i) q^{62} +(6.42341 - 0.0310298i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-9.96060 + 2.41679i) q^{66} +(0.202800 + 1.28043i) q^{67} +(-4.06788 - 4.06788i) q^{68} +(0.203915 - 2.67353i) q^{69} +(-2.39892 - 3.30183i) q^{71} +(-2.43554 - 1.75161i) q^{72} +(0.278530 + 0.141918i) q^{73} -0.221105 q^{74} -5.39228 q^{76} +(11.2895 + 5.75231i) q^{77} +(-0.704330 - 1.68885i) q^{78} +(-0.555462 - 0.764528i) q^{79} +(-0.0869513 - 8.99958i) q^{81} +(1.14673 + 1.14673i) q^{82} +(1.18337 + 7.47149i) q^{83} +(0.874463 + 3.60403i) q^{84} +(1.79600 - 0.583556i) q^{86} +(4.09725 - 6.72250i) q^{87} +(-2.68654 - 5.27263i) q^{88} +(2.67429 + 8.23061i) q^{89} +(-0.699010 + 2.15133i) q^{91} +(1.52899 - 0.242168i) q^{92} +(17.9652 + 4.26719i) q^{93} +(-2.82728 + 3.89142i) q^{94} +(0.658960 - 1.60180i) q^{96} +(-11.9156 - 1.88725i) q^{97} +(-1.09658 + 2.15217i) q^{98} +(7.98311 - 15.8566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} - 16 q^{12} + 20 q^{16} + 8 q^{18} + 40 q^{19} - 4 q^{22} + 56 q^{27} - 4 q^{28} + 96 q^{33} + 40 q^{34} + 64 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} - 16 q^{48} + 64 q^{57} - 20 q^{58} - 4 q^{63} + 104 q^{67} - 140 q^{69} - 8 q^{72} + 60 q^{73} + 60 q^{78} - 80 q^{79} - 40 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 24 q^{88} - 12 q^{93} + 12 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 - 16 * q^12 + 20 * q^16 + 8 * q^18 + 40 * q^19 - 4 * q^22 + 56 * q^27 - 4 * q^28 + 96 * q^33 + 40 * q^34 + 64 * q^37 + 40 * q^39 + 4 * q^42 + 24 * q^43 - 16 * q^48 + 64 * q^57 - 20 * q^58 - 4 * q^63 + 104 * q^67 - 140 * q^69 - 8 * q^72 + 60 * q^73 + 60 * q^78 - 80 * q^79 - 40 * q^81 - 96 * q^82 - 60 * q^84 - 80 * q^87 - 24 * q^88 - 12 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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