LMFDB - Embedded newform 750.2.l.c.107.6

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			107.6
Character	$\chi$	$=$	750.107
Dual form			750.2.l.c.743.6

$q$-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	0.360507	−	0.932756i	$-0.382604\pi$
$7$	−1.51403	−	1.51403i	−0.572249	−	0.572249i	−0.932756	+	0.360507i	$0.882604\pi$
$8$	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	0.814881	−	0.579628i	$-0.196802\pi$
$13$	−0.479621	−	0.941310i	−0.133023	−	0.261072i	−0.947904	+	0.318556i	$0.896802\pi$
$14$	−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	0.576969	−	0.816766i	$-0.304235\pi$
$17$	5.68203	−	0.899945i	1.37809	−	0.218269i	0.801125	+	0.598497i	$0.204235\pi$
$18$	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	−0.952597	−	0.304235i	$-0.901599\pi$
$23$	−0.702799	+	1.37932i	−0.146544	+	0.287608i	0.806054	+	0.591843i	$0.201599\pi$
$24$	−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	−0.470109	−	0.882608i	$-0.655786\pi$
$37$	−0.197006	+	0.100380i	−0.0323876	+	0.0165023i	0.437722	+	0.899111i	$0.355786\pi$
$38$	−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	−0.597921	−	0.801555i	$-0.704006\pi$
$43$	1.33532	−	1.33532i	0.203634	−	0.203634i	0.801555	+	0.597921i	$0.204006\pi$
$44$	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	$0.164093\pi$
$47$	−0.752458	+	4.75083i	−0.109757	+	0.692980i	−0.979796	+	0.199998i	$0.935907\pi$
$48$	−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	0.554049	−	0.832484i	$-0.313082\pi$
$53$	5.99683	+	0.949805i	0.823728	+	0.130466i	0.269680	+	0.962950i	$0.413082\pi$
$54$	−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	0.972199	−	0.234158i	$-0.0752332\pi$
$67$	−0.202800	−	1.28043i	−0.0247759	−	0.156429i	−0.996975	+	0.0777287i	$0.975233\pi$
$68$	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	0.437615	−	0.899163i	$-0.355823\pi$
$73$	−0.278530	−	0.141918i	−0.0325994	−	0.0166102i	−0.470214	+	0.882552i	$0.655823\pi$
$74$	−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	$-0.913725\pi$
$83$	−1.18337	−	7.47149i	−0.129891	−	0.820102i	0.833601	−	0.552367i	$-0.186275\pi$
$84$	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	0.728584	−	0.684956i	$-0.240179\pi$
$97$	11.9156	+	1.88725i	1.20985	+	0.191621i	0.481262	+	0.876577i	$0.340179\pi$
$98$	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	$0.193335\pi$
$103$	−1.38199	+	8.72553i	−0.136171	+	0.859752i	−0.957318	+	0.289035i	$0.906665\pi$
$104$	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	−0.474831	−	0.880077i	$-0.657491\pi$
$107$	4.19190	−	4.19190i	0.405246	−	0.405246i	0.880077	+	0.474831i	$0.157491\pi$
$108$	−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	−0.0608066	−	0.998150i	$-0.519367\pi$
$113$	7.55774	−	3.85086i	0.710972	−	0.362258i	0.771779	+	0.635891i	$0.219367\pi$
$114$	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	$0.303594\pi$
$127$	−4.74807	+	9.31862i	−0.421323	+	0.826894i	−0.999936	+	0.0112913i	$0.996406\pi$
$128$	−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	$-0.978837\pi$
$137$	−5.44330	−	10.6831i	−0.465053	−	0.912717i	0.532738	−	0.846280i	$-0.321163\pi$
$138$	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	$-0.789114\pi$
$157$	−17.5864	−	17.5864i	−1.40355	−	1.40355i	−0.615104	−	0.788446i	$-0.710886\pi$
$158$	−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	0.852519	−	0.522696i	$-0.175074\pi$
$163$	−0.912200	−	1.79029i	−0.0714490	−	0.140227i	−0.923968	+	0.382469i	$0.875074\pi$
$164$	−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	−0.695179	−	0.718837i	$-0.744675\pi$
$167$	−14.6571	+	2.32146i	−1.13420	+	0.179640i	−0.439021	+	0.898477i	$0.644675\pi$
$168$	−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	−0.788126	−	0.615514i	$-0.788949\pi$
$173$	2.27656	−	4.46800i	0.173084	−	0.339696i	0.961210	+	0.275818i	$0.0889486\pi$
$174$	−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	−0.408309	−	0.912844i	$-0.633881\pi$
$193$	7.00922	−	7.00922i	0.504535	−	0.504535i	0.912844	+	0.408309i	$0.133881\pi$
$194$	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	$0.168465\pi$
$197$	−1.59685	+	10.0821i	−0.113771	+	0.718320i	−0.976957	+	0.213435i	$0.931535\pi$
$198$	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	0.805205	−	0.592996i	$-0.202055\pi$
$223$	11.9279	+	6.07755i	0.798748	+	0.406983i	−0.00645660	+	0.999979i	$0.502055\pi$
$224$	2.14116			0.143062
$225$		0			0
$226$	8.48225			0.564231
$227$	0.762629	+	0.388579i	0.0506175	+	0.0257909i	0.479116	−	0.877752i	$-0.340957\pi$
$227$	0.762629	+	0.388579i	0.0506175	+	0.0257909i	−0.428499	+	0.903542i	$0.640957\pi$
$228$	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	$0.00713710\pi$
$233$	0.852656	+	5.38346i	0.0558593	+	0.352682i	−0.943889	+	0.330262i	$0.892863\pi$
$234$	−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	−0.232792	−	0.972526i	$-0.574786\pi$
$257$	11.8588	−	11.8588i	0.739734	−	0.739734i	0.972526	+	0.232792i	$0.0747863\pi$
$258$	−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	0.301453	−	0.953481i	$-0.402529\pi$
$263$	20.2720	−	10.3291i	1.25002	−	0.636919i	0.948572	+	0.316562i	$0.102529\pi$
$264$	−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	$0.515560\pi$
$277$	−13.7839	+	27.0524i	−0.828193	+	1.62542i	−0.779328	+	0.626616i	$0.784440\pi$
$278$	−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	−0.0540343	−	0.998539i	$-0.517208\pi$
$283$	3.41737	−	0.541258i	0.203142	−	0.0321745i	0.257176	+	0.966365i	$0.417208\pi$
$284$	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	0.967744	−	0.251936i	$-0.0810673\pi$
$293$	12.2527	+	12.2527i	0.715808	+	0.715808i	−0.251936	+	0.967744i	$0.581067\pi$
$294$	−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	0.999215	−	0.0396263i	$-0.0126167\pi$
$307$	16.8133	+	16.8133i	0.959588	+	0.959588i	−0.0396263	+	0.999215i	$0.512617\pi$
$308$	−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	$-0.949981\pi$
$313$	−9.44284	−	18.5326i	−0.533741	−	1.04753i	0.453939	−	0.891033i	$-0.350019\pi$
$314$	−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	−0.150419	−	0.988622i	$-0.548062\pi$
$317$	0.214085	−	0.0339077i	0.0120242	−	0.00190445i	0.162444	+	0.986718i	$0.448062\pi$
$318$	−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	−0.610147	−	0.792288i	$-0.708890\pi$
$337$	−6.01777	+	3.06621i	−0.327809	+	0.167027i	0.282339	+	0.959315i	$0.408890\pi$
$338$	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	−0.960984	−	0.276603i	$-0.910791\pi$
$347$	0.716076	−	4.52113i	0.0384410	−	0.242707i	0.999425	+	0.0338958i	$0.0107914\pi$
$348$	−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	−0.135136	−	0.990827i	$-0.543147\pi$
$353$	−10.7063	−	1.69571i	−0.569840	−	0.0902538i	−0.434704	+	0.900573i	$0.643147\pi$
$354$	−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	$0.199028\pi$
$367$	4.22522	+	26.6770i	0.220555	+	1.39253i	−0.590254	+	0.807218i	$0.700972\pi$
$368$	−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	−0.289711	−	0.957114i	$-0.593559\pi$
$373$	−23.8387	−	12.1464i	−1.23432	−	0.628917i	−0.944609	+	0.328197i	$0.893559\pi$
$374$	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	$-0.916247\pi$
$383$	−2.49780	−	15.7705i	−0.127632	−	0.805836i	0.837952	−	0.545744i	$-0.183753\pi$
$384$	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	−0.386030	−	0.922486i	$-0.626154\pi$
$397$	−20.6866	−	3.27643i	−1.03823	−	0.164439i	−0.652200	+	0.758047i	$0.726154\pi$
$398$	−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	−0.540380	−	0.841421i	$-0.681720\pi$
$433$	−16.5283	+	2.61783i	−0.794299	+	0.125805i	−0.253919	+	0.967225i	$0.581720\pi$
$434$	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	0.985402	−	0.170243i	$-0.0544552\pi$
$443$	17.1571	+	17.1571i	0.815159	+	0.815159i	−0.170243	+	0.985402i	$0.554455\pi$
$444$	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	0.758908	−	0.651198i	$-0.225733\pi$
$457$	2.30257	+	2.30257i	0.107710	+	0.107710i	−0.651198	+	0.758908i	$0.725733\pi$
$458$	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	$0.0305245\pi$
$463$	10.4958	+	20.5992i	0.487783	+	0.957328i	−0.507623	+	0.861580i	$0.669476\pi$
$464$	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	−0.261726	−	0.965142i	$-0.584292\pi$
$467$	−4.58995	+	0.726976i	−0.212397	+	0.0336405i	0.0493288	+	0.998783i	$0.484292\pi$
$468$	−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	−0.456725	−	0.889608i	$-0.650978\pi$
$487$	−0.120793	+	0.0615473i	−0.00547367	+	0.00278898i	0.451252	+	0.892397i	$0.350978\pi$
$488$	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	−0.0894274	−	0.995993i	$-0.528504\pi$
$503$	−10.8159	−	1.71307i	−0.482257	−	0.0763820i	−0.392829	+	0.919611i	$0.628504\pi$
$504$	−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	−0.423488	−	0.905902i	$-0.639194\pi$
$523$	−32.1380	−	16.3751i	−1.40530	−	0.716035i	−0.981810	+	0.189867i	$0.939194\pi$
$524$	−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	−0.340098	−	0.940390i	$-0.610460\pi$
$547$	−22.3156	−	3.53445i	−0.954148	−	0.151122i	−0.614049	+	0.789268i	$0.710460\pi$
$548$	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	−0.782267	−	0.622943i	$-0.785937\pi$
$557$	−3.76017	+	3.76017i	−0.159323	+	0.159323i	0.622943	+	0.782267i	$0.285937\pi$
$558$	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	0.0650508	−	0.997882i	$-0.479279\pi$
$563$	21.6061	−	11.0089i	0.910590	−	0.463969i	0.845539	+	0.533913i	$0.179279\pi$
$564$	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	$-0.670324\pi$
$577$	11.6678	−	22.8994i	0.485739	−	0.953316i	0.995657	−	0.0930933i	$-0.0296755\pi$
$578$	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	0.985871	−	0.167506i	$-0.0535713\pi$
$587$	6.56280	+	12.8802i	0.270876	+	0.531623i	−0.714995	+	0.699129i	$0.753571\pi$
$588$	−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	$0.0385075\pi$
$593$	27.1124	+	27.1124i	1.11337	+	1.11337i	0.120680	+	0.992691i	$0.461492\pi$
$594$	−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	$-0.992268\pi$
$607$	−25.2285	−	25.2285i	−1.02399	−	1.02399i	−0.0242876	−	0.999705i	$-0.507732\pi$
$608$	−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	$0.0183184\pi$
$613$	11.3412	+	22.2583i	0.458065	+	0.899003i	−0.540280	+	0.841485i	$0.681682\pi$
$614$	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	−0.741661	−	0.670775i	$-0.765962\pi$
$617$	−30.7946	+	4.87738i	−1.23974	+	0.196356i	−0.498081	+	0.867131i	$0.665962\pi$
$618$	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	−0.965827	−	0.259188i	$-0.916545\pi$
$643$	−17.9186	+	17.9186i	−0.706639	+	0.706639i	0.259188	+	0.965827i	$0.416545\pi$
$644$	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	−0.955889	−	0.293730i	$-0.905103\pi$
$647$	1.11876	−	7.06356i	0.0439829	−	0.277697i	0.999871	+	0.0160323i	$0.00510347\pi$
$648$	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	−0.310470	−	0.950583i	$-0.600486\pi$
$653$	−22.9855	−	3.64054i	−0.899490	−	0.142465i	−0.589021	+	0.808118i	$0.700486\pi$
$654$	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	0.474380	−	0.880320i	$-0.342672\pi$
$673$	1.06415	+	0.542210i	0.0410198	+	0.0209006i	−0.433360	+	0.901221i	$0.642672\pi$
$674$	−6.75390			−0.260151
$675$		0			0
$676$	11.8839			0.457073
$677$	−30.6338	−	15.6087i	−1.17735	−	0.599892i	−0.247884	−	0.968790i	$-0.579735\pi$
$677$	−30.6338	−	15.6087i	−1.17735	−	0.599892i	−0.929470	+	0.368898i	$0.879735\pi$
$678$	−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	$-0.719070\pi$
$683$	−7.05008	−	44.5125i	−0.269764	−	1.70322i	0.365405	−	0.930849i	$-0.380930\pi$
$684$	−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	$-0.561161\pi$
$727$	19.2896	−	37.8579i	0.715411	−	1.40407i	0.906374	−	0.422476i	$-0.138839\pi$
$728$	−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	−0.902559	−	0.430565i	$-0.858314\pi$
$733$	−44.0735	+	6.98056i	−1.62789	+	0.257833i	−0.725333	+	0.688398i	$0.758314\pi$
$734$	−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	0.0824029	−	0.996599i	$-0.473741\pi$
$743$	−24.9192	−	24.9192i	−0.914196	−	0.914196i	−0.996599	+	0.0824029i	$0.973741\pi$
$744$	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	0.801176	−	0.598429i	$-0.204208\pi$
$757$	5.57829	+	5.57829i	0.202746	+	0.202746i	−0.598429	+	0.801176i	$0.704208\pi$
$758$	−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	$0.359936\pi$
$773$	−15.4685	+	30.3587i	−0.556364	+	1.09193i	−0.982325	+	0.187185i	$0.940064\pi$
$774$	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	−0.874863	−	0.484371i	$-0.839049\pi$
$787$	−27.9758	+	14.2544i	−0.997230	+	0.508114i	−0.122367	+	0.992485i	$0.539049\pi$
$788$	−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	$-0.890076\pi$
$797$	1.65300	−	10.4366i	0.0585523	−	0.369685i	0.999514	−	0.0311718i	$-0.00992392\pi$
$798$	−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	0.681715	−	0.731618i	$-0.261235\pi$
$823$	14.0722	+	7.17013i	0.490525	+	0.249935i	−0.191190	+	0.981553i	$0.561235\pi$
$824$	−8.83429			−0.307757
$825$		0			0
$826$	−15.5291			−0.540326
$827$	6.05244	+	3.08387i	0.210464	+	0.107237i	0.556045	−	0.831152i	$-0.312318\pi$
$827$	6.05244	+	3.08387i	0.210464	+	0.107237i	−0.345581	+	0.938389i	$0.612318\pi$
$828$	−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	$0.240360\pi$
$853$	−5.14470	+	32.4823i	−0.176151	+	1.11217i	−0.904345	+	0.426803i	$0.859640\pi$
$854$	−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	−0.907196	−	0.420708i	$-0.861782\pi$
$857$	−14.2417	+	14.2417i	−0.486489	+	0.486489i	0.420708	+	0.907196i	$0.361782\pi$
$858$	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	−0.0927901	−	0.995686i	$-0.529579\pi$
$863$	19.3357	−	9.85205i	0.658196	−	0.335368i	0.750986	+	0.660318i	$0.229579\pi$
$864$	−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	−0.825712	−	0.564092i	$-0.809226\pi$
$877$	3.43493	−	6.74142i	0.115989	−	0.227642i	0.941701	+	0.336450i	$0.109226\pi$
$878$	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	−0.614083	−	0.789241i	$-0.710474\pi$
$883$	−28.3550	+	4.49099i	−0.954222	+	0.151134i	−0.340139	+	0.940375i	$0.610474\pi$
$884$	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	0.779815	−	0.626010i	$-0.215313\pi$
$887$	−5.50981	−	10.8136i	−0.185001	−	0.363086i	−0.964816	+	0.262924i	$0.915313\pi$
$888$	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	0.945863	−	0.324567i	$-0.105219\pi$
$907$	18.7112	+	18.7112i	0.621295	+	0.621295i	−0.324567	+	0.945863i	$0.605219\pi$
$908$	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	$-0.284917\pi$
$937$	49.7213	−	25.3343i	1.62432	−	0.827634i	0.998878	−	0.0473659i	$-0.0150827\pi$
$938$	−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	$-0.855106\pi$
$947$	2.82795	−	17.8550i	0.0918962	−	0.580210i	0.990071	−	0.140571i	$-0.0448937\pi$
$948$	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	0.919667	−	0.392698i	$-0.128458\pi$
$953$	51.6458	+	8.17990i	1.67297	+	0.264973i	0.753305	+	0.657671i	$0.228458\pi$
$954$	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	$-0.883388\pi$
$967$	−4.86314	−	30.7047i	−0.156388	−	0.987395i	0.777254	−	0.629187i	$-0.216612\pi$
$968$	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	$0.0481174\pi$
$977$	52.8715	+	26.9394i	1.69151	+	0.861867i	0.702912	+	0.711276i	$0.251883\pi$
$978$	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	$0.157368\pi$
$983$	5.94792	+	37.5537i	0.189709	+	1.19778i	−0.690550	+	0.723284i	$0.742632\pi$
$984$	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	0.661863	−	0.749625i	$-0.269766\pi$
$997$	33.4599	+	5.29952i	1.05968	+	0.167838i	0.397822	+	0.917463i	$0.369766\pi$
$998$	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.c.107.6		80
3.2	odd	2	inner	750.2.l.c.107.5		80
5.2	odd	4		750.2.l.b.143.4		80
5.3	odd	4		150.2.l.a.83.7	yes	80
5.4	even	2		750.2.l.a.107.5		80
15.2	even	4		750.2.l.b.143.10		80
15.8	even	4		150.2.l.a.83.1	yes	80
15.14	odd	2		750.2.l.a.107.6		80
25.3	odd	20	inner	750.2.l.c.743.5		80
25.4	even	10		750.2.l.b.257.10		80
25.21	even	5		150.2.l.a.47.1	✓	80
25.22	odd	20		750.2.l.a.743.6		80
75.29	odd	10		750.2.l.b.257.4		80
75.47	even	20		750.2.l.a.743.5		80
75.53	even	20	inner	750.2.l.c.743.6		80
75.71	odd	10		150.2.l.a.47.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.1	✓	80	25.21	even	5
150.2.l.a.47.7	yes	80	75.71	odd	10
150.2.l.a.83.1	yes	80	15.8	even	4
150.2.l.a.83.7	yes	80	5.3	odd	4
750.2.l.a.107.5		80	5.4	even	2
750.2.l.a.107.6		80	15.14	odd	2
750.2.l.a.743.5		80	75.47	even	20
750.2.l.a.743.6		80	25.22	odd	20
750.2.l.b.143.4		80	5.2	odd	4
750.2.l.b.143.10		80	15.2	even	4
750.2.l.b.257.4		80	75.29	odd	10
750.2.l.b.257.10		80	25.4	even	10
750.2.l.c.107.5		80	3.2	odd	2	inner
750.2.l.c.107.6		80	1.1	even	1	trivial
750.2.l.c.743.5		80	25.3	odd	20	inner
750.2.l.c.743.6		80	75.53	even	20	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
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

Properties

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