LMFDB - Embedded newform 750.2.l.a.407.8

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			407.8
Character	$\chi$	$=$	750.407
Dual form			750.2.l.a.293.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 - 0.987688i) q^{2} +(-0.582259 + 1.63125i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.52008 + 0.830274i) q^{6} +(0.104631 + 0.104631i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.32195 - 1.89962i) q^{9} +O(q^{10})$	\(q+(0.156434 - 0.987688i) q^{2} +(-0.582259 + 1.63125i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.52008 + 0.830274i) q^{6} +(0.104631 + 0.104631i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.32195 - 1.89962i) q^{9} +(-1.81255 - 2.49477i) q^{11} +(1.05784 - 1.37148i) q^{12} +(4.49023 - 0.711182i) q^{13} +(0.119711 - 0.0869753i) q^{14} +(0.809017 + 0.587785i) q^{16} +(3.30481 + 1.68388i) q^{17} +(-2.23946 + 1.99620i) q^{18} +(3.32698 - 1.08100i) q^{19} +(-0.231603 + 0.109757i) q^{21} +(-2.74760 + 1.39997i) q^{22} +(4.88306 + 0.773401i) q^{23} +(-1.18911 - 1.25937i) q^{24} -4.54620i q^{26} +(4.45073 - 2.68161i) q^{27} +(-0.0671775 - 0.131843i) q^{28} +(-0.509399 + 1.56777i) q^{29} +(2.45755 + 7.56355i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.12496 - 1.50413i) q^{33} +(2.18014 - 3.00070i) q^{34} +(1.62129 + 2.52417i) q^{36} +(1.31491 + 8.30199i) q^{37} +(-0.547238 - 3.45513i) q^{38} +(-1.45436 + 7.73877i) q^{39} +(1.27149 - 1.75005i) q^{41} +(0.0721755 + 0.245921i) q^{42} +(-2.77052 + 2.77052i) q^{43} +(0.952916 + 2.93277i) q^{44} +(1.52776 - 4.70196i) q^{46} +(2.43413 + 4.77725i) q^{47} +(-1.42988 + 0.977465i) q^{48} -6.97810i q^{49} +(-4.67109 + 4.41051i) q^{51} +(-4.49023 - 0.711182i) q^{52} +(10.2880 - 5.24200i) q^{53} +(-1.95235 - 4.81543i) q^{54} +(-0.140729 + 0.0457256i) q^{56} +(-0.173781 + 6.05656i) q^{57} +(1.46878 + 0.748381i) q^{58} +(-10.4207 - 7.57107i) q^{59} +(11.8153 - 8.58430i) q^{61} +(7.85487 - 1.24409i) q^{62} +(-0.0441891 - 0.441709i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.683889 - 5.29716i) q^{66} +(1.64885 - 3.23605i) q^{67} +(-2.62271 - 2.62271i) q^{68} +(-4.10482 + 7.51517i) q^{69} +(4.79465 + 1.55788i) q^{71} +(2.74672 - 1.20646i) q^{72} +(1.68322 - 10.6274i) q^{73} +8.40547 q^{74} -3.49819 q^{76} +(0.0713809 - 0.450681i) q^{77} +(7.41598 + 2.64706i) q^{78} +(-8.57556 - 2.78637i) q^{79} +(1.78290 + 8.82164i) q^{81} +(-1.52960 - 1.52960i) q^{82} +(-4.59112 + 9.01058i) q^{83} +(0.254184 - 0.0328164i) q^{84} +(2.30301 + 3.16982i) q^{86} +(-2.26082 - 1.74381i) q^{87} +(3.04574 - 0.482397i) q^{88} +(6.13326 - 4.45607i) q^{89} +(0.544231 + 0.395407i) q^{91} +(-4.40507 - 2.24450i) q^{92} +(-13.7690 - 0.395073i) q^{93} +(5.09921 - 1.65683i) q^{94} +(0.741748 + 1.56519i) q^{96} +(-8.26018 + 4.20877i) q^{97} +(-6.89219 - 1.09162i) q^{98} +(-0.530447 + 9.23588i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$3$	−0.582259	+	1.63125i	−0.336167	+	0.941802i
$3$	−0.582259	+	1.63125i	−0.336167	+	0.941802i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$		0			0
$5$		0			0
$6$	1.52008	+	0.830274i	0.620570	+	0.338958i
$7$	0.104631	+	0.104631i	0.0395470	+	0.0395470i	0.726604	−	0.687057i	$-0.241098\pi$
$7$	0.104631	+	0.104631i	0.0395470	+	0.0395470i	−0.687057	+	0.726604i	$0.741098\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	−2.32195	−	1.89962i	−0.773983	−	0.633206i
$10$		0			0
$11$	−1.81255	−	2.49477i	−0.546506	−	0.752200i	0.443027	−	0.896508i	$-0.353904\pi$
$11$	−1.81255	−	2.49477i	−0.546506	−	0.752200i	−0.989533	+	0.144308i	$0.953904\pi$
$12$	1.05784	−	1.37148i	0.305374	−	0.395913i
$13$	4.49023	−	0.711182i	1.24536	−	0.197246i	0.501252	−	0.865301i	$-0.332873\pi$
$13$	4.49023	−	0.711182i	1.24536	−	0.197246i	0.744112	+	0.668055i	$0.232873\pi$
$14$	0.119711	−	0.0869753i	0.0319942	−	0.0232451i
$15$		0			0
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	3.30481	+	1.68388i	0.801533	+	0.408402i	0.806241	−	0.591587i	$-0.201499\pi$
$17$	3.30481	+	1.68388i	0.801533	+	0.408402i	−0.00470771	+	0.999989i	$0.501499\pi$
$18$	−2.23946	+	1.99620i	−0.527847	+	0.470508i
$19$	3.32698	−	1.08100i	0.763262	−	0.247999i	0.0985837	−	0.995129i	$-0.468569\pi$
$19$	3.32698	−	1.08100i	0.763262	−	0.247999i	0.664678	+	0.747130i	$0.268569\pi$
$20$		0			0
$21$	−0.231603	+	0.109757i	−0.0505398	+	0.0239510i
$22$	−2.74760	+	1.39997i	−0.585790	+	0.298475i
$23$	4.88306	+	0.773401i	1.01819	+	0.161265i	0.643147	−	0.765743i	$-0.277628\pi$
$23$	4.88306	+	0.773401i	1.01819	+	0.161265i	0.375042	+	0.927008i	$0.377628\pi$
$24$	−1.18911	−	1.25937i	−0.242727	−	0.257067i
$25$		0			0
$26$		−	4.54620i		−	0.891583i
$27$	4.45073	−	2.68161i	0.856543	−	0.516076i
$28$	−0.0671775	−	0.131843i	−0.0126954	−	0.0249161i
$29$	−0.509399	+	1.56777i	−0.0945931	+	0.291128i	−0.987147	−	0.159812i	$-0.948911\pi$
$29$	−0.509399	+	1.56777i	−0.0945931	+	0.291128i	0.892554	+	0.450940i	$0.148911\pi$
$30$		0			0
$31$	2.45755	+	7.56355i	0.441388	+	1.35845i	0.886396	+	0.462927i	$0.153201\pi$
$31$	2.45755	+	7.56355i	0.441388	+	1.35845i	−0.445008	+	0.895527i	$0.646799\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	5.12496	−	1.50413i	0.892141	−	0.261835i
$34$	2.18014	−	3.00070i	0.373890	−	0.514616i
$35$		0			0
$36$	1.62129	+	2.52417i	0.270215	+	0.420694i
$37$	1.31491	+	8.30199i	0.216169	+	1.36484i	0.822110	+	0.569329i	$0.192797\pi$
$37$	1.31491	+	8.30199i	0.216169	+	1.36484i	−0.605941	+	0.795510i	$0.707203\pi$
$38$	−0.547238	−	3.45513i	−0.0887737	−	0.560495i
$39$	−1.45436	+	7.73877i	−0.232884	+	1.23919i
$40$		0			0
$41$	1.27149	−	1.75005i	0.198573	−	0.273312i	−0.698105	−	0.715995i	$-0.745973\pi$
$41$	1.27149	−	1.75005i	0.198573	−	0.273312i	0.896678	+	0.442683i	$0.145973\pi$
$42$	0.0721755	+	0.245921i	0.0111369	+	0.0379464i
$43$	−2.77052	+	2.77052i	−0.422501	+	0.422501i	−0.886064	−	0.463563i	$-0.846571\pi$
$43$	−2.77052	+	2.77052i	−0.422501	+	0.422501i	0.463563	+	0.886064i	$0.346571\pi$
$44$	0.952916	+	2.93277i	0.143657	+	0.442132i
$45$		0			0
$46$	1.52776	−	4.70196i	0.225256	−	0.693266i
$47$	2.43413	+	4.77725i	0.355054	+	0.696833i	0.997587	−	0.0694250i	$-0.0221165\pi$
$47$	2.43413	+	4.77725i	0.355054	+	0.696833i	−0.642533	+	0.766258i	$0.722116\pi$
$48$	−1.42988	+	0.977465i	−0.206386	+	0.141085i
$49$		−	6.97810i		−	0.996872i
$50$		0			0
$51$	−4.67109	+	4.41051i	−0.654083	+	0.617595i
$52$	−4.49023	−	0.711182i	−0.622682	−	0.0986232i
$53$	10.2880	−	5.24200i	1.41317	−	0.720045i	0.430013	−	0.902823i	$-0.358509\pi$
$53$	10.2880	−	5.24200i	1.41317	−	0.720045i	0.983154	+	0.182778i	$0.0585089\pi$
$54$	−1.95235	−	4.81543i	−0.265681	−	0.655297i
$55$		0			0
$56$	−0.140729	+	0.0457256i	−0.0188057	+	0.00611035i
$57$	−0.173781	+	6.05656i	−0.0230178	+	0.802211i
$58$	1.46878	+	0.748381i	0.192860	+	0.0982673i
$59$	−10.4207	−	7.57107i	−1.35666	−	0.985670i	−0.998650	−	0.0519515i	$-0.983456\pi$
$59$	−10.4207	−	7.57107i	−1.35666	−	0.985670i	−0.358009	−	0.933718i	$-0.616544\pi$
$60$		0			0
$61$	11.8153	−	8.58430i	1.51279	−	1.09911i	0.547871	−	0.836563i	$-0.315439\pi$
$61$	11.8153	−	8.58430i	1.51279	−	1.09911i	0.964920	−	0.262544i	$-0.0845614\pi$
$62$	7.85487	−	1.24409i	0.997570	−	0.158000i
$63$	−0.0441891	−	0.441709i	−0.00556730	−	0.0556501i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$		0			0
$66$	−0.683889	−	5.29716i	−0.0841809	−	0.652036i
$67$	1.64885	−	3.23605i	0.201439	−	0.395346i	−0.768083	−	0.640350i	$-0.778789\pi$
$67$	1.64885	−	3.23605i	0.201439	−	0.395346i	0.969522	+	0.245004i	$0.0787893\pi$
$68$	−2.62271	−	2.62271i	−0.318050	−	0.318050i
$69$	−4.10482	+	7.51517i	−0.494162	+	0.904720i
$70$		0			0
$71$	4.79465	+	1.55788i	0.569020	+	0.184886i	0.579376	−	0.815061i	$-0.303296\pi$
$71$	4.79465	+	1.55788i	0.569020	+	0.184886i	−0.0103558	+	0.999946i	$0.503296\pi$
$72$	2.74672	−	1.20646i	0.323704	−	0.142183i
$73$	1.68322	−	10.6274i	0.197006	−	1.24385i	−0.668791	−	0.743451i	$-0.733188\pi$
$73$	1.68322	−	10.6274i	0.197006	−	1.24385i	0.865797	−	0.500396i	$-0.166812\pi$
$74$	8.40547			0.977116
$75$		0			0
$76$	−3.49819			−0.401270
$77$	0.0713809	−	0.450681i	0.00813461	−	0.0513599i
$78$	7.41598	+	2.64706i	0.839694	+	0.299721i
$79$	−8.57556	−	2.78637i	−0.964826	−	0.313491i	−0.216100	−	0.976371i	$-0.569334\pi$
$79$	−8.57556	−	2.78637i	−0.964826	−	0.313491i	−0.748725	+	0.662880i	$0.769334\pi$
$80$		0			0
$81$	1.78290	+	8.82164i	0.198100	+	0.980182i
$82$	−1.52960	−	1.52960i	−0.168916	−	0.168916i
$83$	−4.59112	+	9.01058i	−0.503941	+	0.989039i	0.489206	+	0.872168i	$0.337286\pi$
$83$	−4.59112	+	9.01058i	−0.503941	+	0.989039i	−0.993147	+	0.116871i	$0.962714\pi$
$84$	0.254184	−	0.0328164i	0.0277338	−	0.00358056i
$85$		0			0
$86$	2.30301	+	3.16982i	0.248340	+	0.341810i
$87$	−2.26082	−	1.74381i	−0.242386	−	0.186956i
$88$	3.04574	−	0.482397i	0.324676	−	0.0514237i
$89$	6.13326	−	4.45607i	0.650124	−	0.472343i	−0.213189	−	0.977011i	$-0.568385\pi$
$89$	6.13326	−	4.45607i	0.650124	−	0.472343i	0.863314	+	0.504668i	$0.168385\pi$
$90$		0			0
$91$	0.544231	+	0.395407i	0.0570509	+	0.0414499i
$92$	−4.40507	−	2.24450i	−0.459261	−	0.234005i
$93$	−13.7690	−	0.395073i	−1.42778	−	0.0409672i
$94$	5.09921	−	1.65683i	0.525944	−	0.170889i
$95$		0			0
$96$	0.741748	+	1.56519i	0.0757044	+	0.159746i
$97$	−8.26018	+	4.20877i	−0.838694	+	0.427336i	−0.819913	−	0.572487i	$-0.805979\pi$
$97$	−8.26018	+	4.20877i	−0.838694	+	0.427336i	−0.0187810	+	0.999824i	$0.505979\pi$
$98$	−6.89219	−	1.09162i	−0.696217	−	0.110270i
$99$	−0.530447	+	9.23588i	−0.0533120	+	0.928241i
$100$		0			0
$101$			4.19074i			0.416994i	0.978023	+	0.208497i	$0.0668571\pi$
$101$			4.19074i			0.416994i	−0.978023	+	0.208497i	$0.933143\pi$
$102$	3.62549	+	5.30353i	0.358977	+	0.525128i
$103$	−7.94553	−	15.5940i	−0.782896	−	1.53652i	−0.842745	−	0.538312i	$-0.819062\pi$
$103$	−7.94553	−	15.5940i	−0.782896	−	1.53652i	0.0598493	−	0.998207i	$-0.480938\pi$
$104$	−1.40485	+	4.32369i	−0.137757	+	0.423973i
$105$		0			0
$106$	−3.56807	−	10.9814i	−0.346561	−	1.06661i
$107$	−0.457779	+	0.457779i	−0.0442552	+	0.0442552i	−0.728888	−	0.684633i	$-0.759963\pi$
$107$	−0.457779	+	0.457779i	−0.0442552	+	0.0442552i	0.684633	+	0.728888i	$0.259963\pi$
$108$	−5.06156	+	1.17501i	−0.487048	+	0.113065i
$109$	0.0442666	−	0.0609277i	0.00423997	−	0.00583582i	−0.806892	−	0.590699i	$-0.798852\pi$
$109$	0.0442666	−	0.0609277i	0.00423997	−	0.00583582i	0.811132	+	0.584864i	$0.198852\pi$
$110$		0			0
$111$	−14.3082	−	2.68897i	−1.35808	−	0.255225i
$112$	0.0231478	+	0.146149i	0.00218726	+	0.0138098i
$113$	2.67766	+	16.9061i	0.251893	+	1.59039i	0.711774	+	0.702408i	$0.247892\pi$
$113$	2.67766	+	16.9061i	0.251893	+	1.59039i	−0.459881	+	0.887980i	$0.652108\pi$
$114$	5.95481	+	1.11910i	0.557719	+	0.104813i
$115$		0			0
$116$	0.968935	−	1.33363i	0.0899634	−	0.123824i
$117$	−11.7770	−	6.87839i	−1.08879	−	0.635907i
$118$	−9.10802	+	9.10802i	−0.838461	+	0.838461i
$119$	0.169600	+	0.521974i	0.0155472	+	0.0478493i
$120$		0			0
$121$	0.460680	−	1.41783i	0.0418800	−	0.128893i
$122$	−6.63030	−	13.0127i	−0.600279	−	1.17811i
$123$	2.11443	+	3.09309i	0.190652	+	0.278895i
$124$		−	7.95279i		−	0.714181i
$125$		0			0
$126$	−0.443183	−	0.0254535i	−0.0394819	−	0.00226758i
$127$	−8.80705	−	1.39490i	−0.781499	−	0.123777i	−0.247078	−	0.968996i	$-0.579470\pi$
$127$	−8.80705	−	1.39490i	−0.781499	−	0.123777i	−0.534421	+	0.845218i	$0.679470\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$	−2.90625	−	6.13257i	−0.255881	−	0.539943i
$130$		0			0
$131$	−1.60573	+	0.521733i	−0.140293	+	0.0455840i	−0.378322	−	0.925674i	$-0.623499\pi$
$131$	−1.60573	+	0.521733i	−0.140293	+	0.0455840i	0.238029	+	0.971258i	$0.423499\pi$
$132$	−5.33893	−	0.153190i	−0.464694	−	0.0133335i
$133$	0.461214	+	0.235000i	0.0399923	+	0.0203771i
$134$	−2.93827	−	2.13478i	−0.253828	−	0.184417i
$135$		0			0
$136$	−3.00070	+	2.18014i	−0.257308	+	0.186945i
$137$	−14.4460	+	2.28802i	−1.23420	+	0.195479i	−0.739244	−	0.673438i	$-0.764817\pi$
$137$	−14.4460	+	2.28802i	−1.23420	+	0.195479i	−0.494959	+	0.868916i	$0.664817\pi$
$138$	6.78051	+	5.22991i	0.577196	+	0.445200i
$139$	10.4809	+	14.4257i	0.888977	+	1.22357i	0.973853	+	0.227180i	$0.0729505\pi$
$139$	10.4809	+	14.4257i	0.888977	+	1.22357i	−0.0848764	+	0.996391i	$0.527050\pi$
$140$		0			0
$141$	−9.21017	+	1.18908i	−0.775637	+	0.100138i
$142$	2.28874	−	4.49191i	0.192067	−	0.376953i
$143$	−9.91301	−	9.91301i	−0.828967	−	0.828967i
$144$	−0.761928	−	2.90163i	−0.0634940	−	0.241803i
$145$		0			0
$146$	−10.2333	−	3.32499i	−0.846912	−	0.275178i
$147$	11.3830	+	4.06306i	0.938856	+	0.335116i
$148$	1.31491	−	8.30199i	0.108085	−	0.682419i
$149$	15.4486			1.26560			0.632800	−	0.774316i	$-0.281906\pi$
$149$	15.4486			1.26560			0.632800	+	0.774316i	$0.281906\pi$
$150$		0			0
$151$	−7.09145			−0.577094			−0.288547	−	0.957466i	$-0.593172\pi$
$151$	−7.09145			−0.577094			−0.288547	+	0.957466i	$0.593172\pi$
$152$	−0.547238	+	3.45513i	−0.0443869	+	0.280248i
$153$	−4.47486	−	10.1878i	−0.361771	−	0.823632i
$154$	−0.433966	−	0.141004i	−0.0349700	−	0.0113624i
$155$		0			0
$156$	3.77459	−	6.91059i	0.302209	−	0.553290i
$157$	−5.10830	−	5.10830i	−0.407687	−	0.407687i	0.473244	−	0.880931i	$-0.343083\pi$
$157$	−5.10830	−	5.10830i	−0.407687	−	0.407687i	−0.880931	+	0.473244i	$0.843083\pi$
$158$	−4.09358	+	8.03409i	−0.325667	+	0.639158i
$159$	2.56073	+	19.8345i	0.203079	+	1.57298i
$160$		0			0
$161$	0.430000	+	0.591844i	0.0338887	+	0.0466439i
$162$	8.99193	−	0.380938i	0.706473	−	0.0299293i
$163$	2.11572	−	0.335098i	0.165716	−	0.0262469i	−0.0730249	−	0.997330i	$-0.523265\pi$
$163$	2.11572	−	0.335098i	0.165716	−	0.0262469i	0.238741	+	0.971083i	$0.423265\pi$
$164$	−1.75005	+	1.27149i	−0.136656	+	0.0992863i
$165$		0			0
$166$	8.18143	+	5.94416i	0.635002	+	0.461356i
$167$	3.73873	+	1.90498i	0.289312	+	0.147412i	0.592623	−	0.805480i	$-0.298092\pi$
$167$	3.73873	+	1.90498i	0.289312	+	0.147412i	−0.303312	+	0.952891i	$0.598092\pi$
$168$	0.00735081	−	0.256188i	0.000567128	−	0.0197654i
$169$	7.29261	−	2.36951i	0.560970	−	0.182270i
$170$		0			0
$171$	−9.77857	−	3.80996i	−0.747786	−	0.291355i
$172$	3.49106	−	1.77878i	0.266191	−	0.135631i
$173$	0.107360	+	0.0170042i	0.00816244	+	0.00129280i	0.160514	−	0.987034i	$-0.448685\pi$
$173$	0.107360	+	0.0170042i	0.00816244	+	0.00129280i	−0.152352	+	0.988326i	$0.548685\pi$
$174$	−2.07601	+	1.96020i	−0.157382	+	0.148602i
$175$		0			0
$176$		−	3.08370i		−	0.232443i
$177$	18.4178	−	12.5904i	1.38437	−	0.946354i
$178$	−3.44176	−	6.75483i	−0.257971	−	0.506296i
$179$	−0.495650	+	1.52545i	−0.0370466	+	0.114018i	−0.967870	−	0.251452i	$-0.919092\pi$
$179$	−0.495650	+	1.52545i	−0.0370466	+	0.114018i	0.930823	+	0.365470i	$0.119092\pi$
$180$		0			0
$181$	−3.90297	−	12.0121i	−0.290105	−	0.892852i	−0.984822	−	0.173568i	$-0.944470\pi$
$181$	−3.90297	−	12.0121i	−0.290105	−	0.892852i	0.694717	−	0.719284i	$-0.255530\pi$
$182$	0.475675	−	0.475675i	0.0352594	−	0.0352594i
$183$	7.12358	+	24.2719i	0.526591	+	1.79423i
$184$	−2.90597	+	3.99972i	−0.214231	+	0.294864i
$185$		0			0
$186$	−2.54415	+	13.5376i	−0.186546	+	0.992628i
$187$	−1.78924	−	11.2968i	−0.130843	−	0.826107i
$188$	−0.838744	−	5.29562i	−0.0611717	−	0.386223i
$189$	0.746267	+	0.185106i	0.0542829	+	0.0134645i
$190$		0			0
$191$	−12.2687	+	16.8865i	−0.887734	+	1.22186i	0.0864840	+	0.996253i	$0.472437\pi$
$191$	−12.2687	+	16.8865i	−0.887734	+	1.22186i	−0.974218	+	0.225608i	$0.927563\pi$
$192$	1.66195	−	0.487767i	0.119941	−	0.0352016i
$193$	4.75446	−	4.75446i	0.342233	−	0.342233i	−0.514973	−	0.857206i	$-0.672198\pi$
$193$	4.75446	−	4.75446i	0.342233	−	0.342233i	0.857206	+	0.514973i	$0.172198\pi$
$194$	2.86478	+	8.81688i	0.205679	+	0.633015i
$195$		0			0
$196$	−2.15635	+	6.63657i	−0.154025	+	0.474041i
$197$	1.96506	+	3.85665i	0.140005	+	0.274775i	0.950353	−	0.311174i	$-0.100722\pi$
$197$	1.96506	+	3.85665i	0.140005	+	0.274775i	−0.810348	+	0.585948i	$0.800722\pi$
$198$	9.03919	+	1.96873i	0.642387	+	0.139911i
$199$		−	0.610848i		−	0.0433019i	−0.999766	−	0.0216509i	$-0.993108\pi$
$199$		−	0.610848i		−	0.0433019i	0.999766	−	0.0216509i	$-0.00689224\pi$
$200$		0			0
$201$	4.31874	+	4.57390i	0.304621	+	0.322618i
$202$	4.13914	+	0.655576i	0.291229	+	0.0461261i
$203$	−0.217337	+	0.110739i	−0.0152541	+	0.00777235i
$204$	5.80539	−	2.75120i	0.406458	−	0.192622i
$205$		0			0
$206$	−16.6449	+	5.40827i	−1.15971	+	0.376812i
$207$	−9.86905	−	11.0718i	−0.685947	−	0.769540i
$208$	4.05069	+	2.06393i	0.280865	+	0.143108i
$209$	−8.72718	−	6.34067i	−0.603671	−	0.438593i
$210$		0			0
$211$	3.67523	−	2.67021i	0.253013	−	0.183825i	−0.454048	−	0.890977i	$-0.650020\pi$
$211$	3.67523	−	2.67021i	0.253013	−	0.183825i	0.707061	+	0.707152i	$0.250020\pi$
$212$	−11.4044	+	1.80627i	−0.783254	+	0.124055i
$213$	−5.33301	+	6.91418i	−0.365412	+	0.473752i
$214$	0.380531	+	0.523756i	0.0260125	+	0.0358032i
$215$		0			0
$216$	0.368742	+	5.18305i	0.0250897	+	0.352662i
$217$	−0.534249	+	1.04852i	−0.0362672	+	0.0711783i
$218$	−0.0532528	−	0.0532528i	−0.00360673	−	0.00360673i
$219$	16.3559	+	8.93367i	1.10523	+	0.603681i
$220$		0			0
$221$	16.0369	+	5.21070i	1.07876	+	0.350509i
$222$	−4.89416	+	13.7114i	−0.328475	+	0.920250i
$223$	−3.05224	+	19.2711i	−0.204393	+	1.29049i	0.645593	+	0.763681i	$0.276610\pi$
$223$	−3.05224	+	19.2711i	−0.204393	+	1.29049i	−0.849986	+	0.526805i	$0.823390\pi$
$224$	0.147971			0.00988675
$225$		0			0
$226$	17.1168			1.13859
$227$	−1.89042	+	11.9356i	−0.125471	+	0.792194i	0.842049	+	0.539401i	$0.181349\pi$
$227$	−1.89042	+	11.9356i	−0.125471	+	0.792194i	−0.967520	+	0.252793i	$0.918651\pi$
$228$	2.03685	−	5.70643i	0.134894	−	0.377917i
$229$	−5.88719	−	1.91287i	−0.389037	−	0.126406i	0.107966	−	0.994155i	$-0.465566\pi$
$229$	−5.88719	−	1.91287i	−0.389037	−	0.126406i	−0.497003	+	0.867749i	$0.665566\pi$
$230$		0			0
$231$	0.693611	+	0.378853i	0.0456363	+	0.0249267i
$232$	−1.16563	−	1.16563i	−0.0765274	−	0.0765274i
$233$	3.43912	−	6.74965i	0.225304	−	0.442184i	−0.750488	−	0.660884i	$-0.770182\pi$
$233$	3.43912	−	6.74965i	0.225304	−	0.442184i	0.975792	+	0.218700i	$0.0701816\pi$
$234$	−8.63604	+	10.5560i	−0.564556	+	0.690070i
$235$		0			0
$236$	7.57107	+	10.4207i	0.492835	+	0.678329i
$237$	9.53845	−	12.3665i	0.619589	−	0.803290i
$238$	0.542079	−	0.0858568i	0.0351377	−	0.00556527i
$239$	−13.6576	+	9.92281i	−0.883435	+	0.641853i	−0.934158	−	0.356859i	$-0.883848\pi$
$239$	−13.6576	+	9.92281i	−0.883435	+	0.641853i	0.0507228	+	0.998713i	$0.483848\pi$
$240$		0			0
$241$	−7.96740	−	5.78866i	−0.513225	−	0.372880i	0.300820	−	0.953681i	$-0.402740\pi$
$241$	−7.96740	−	5.78866i	−0.513225	−	0.372880i	−0.814046	+	0.580801i	$0.802740\pi$
$242$	−1.32830	−	0.676805i	−0.0853866	−	0.0435066i
$243$	−15.4284	−	2.22813i	−0.989732	−	0.142934i
$244$	−13.8897	+	4.51303i	−0.889196	+	0.288917i
$245$		0			0
$246$	3.38578	−	1.60454i	0.215869	−	0.102301i
$247$	14.1701	−	7.22003i	0.901622	−	0.459399i
$248$	−7.85487	−	1.24409i	−0.498785	−	0.0789998i
$249$	−12.0253	−	12.7357i	−0.762071	−	0.807095i
$250$		0			0
$251$		−	0.308302i		−	0.0194599i	−0.999953	−	0.00972993i	$-0.996903\pi$
$251$		−	0.308302i		−	0.0194599i	0.999953	−	0.00972993i	$-0.00309718\pi$
$252$	−0.0944693	+	0.433745i	−0.00595101	+	0.0273234i
$253$	−6.92136	−	13.5839i	−0.435142	−	0.854014i
$254$	−2.75545	+	8.48041i	−0.172892	+	0.532108i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	5.10907	−	5.10907i	0.318695	−	0.318695i	−0.529571	−	0.848266i	$-0.677647\pi$
$257$	5.10907	−	5.10907i	0.318695	−	0.318695i	0.848266	+	0.529571i	$0.177647\pi$
$258$	−6.51171	+	1.91112i	−0.405401	+	0.118981i
$259$	−0.731069	+	1.00623i	−0.0454264	+	0.0625241i
$260$		0			0
$261$	4.16097	−	2.67262i	0.257557	−	0.165431i
$262$	0.264118	+	1.66758i	0.0163173	+	0.103023i
$263$	−0.817350	−	5.16055i	−0.0504000	−	0.318213i	−0.999989	−	0.00471508i	$-0.998499\pi$
$263$	−0.817350	−	5.16055i	−0.0504000	−	0.318213i	0.949589	−	0.313498i	$-0.101501\pi$
$264$	−0.986496	+	5.24923i	−0.0607147	+	0.323068i
$265$		0			0
$266$	0.304257	−	0.418773i	0.0186552	−	0.0256766i
$267$	3.69782	+	12.5995i	0.226303	+	0.771075i
$268$	−2.56814	+	2.56814i	−0.156874	+	0.156874i
$269$	0.702217	+	2.16120i	0.0428149	+	0.131771i	0.970179	−	0.242389i	$-0.0779311\pi$
$269$	0.702217	+	2.16120i	0.0428149	+	0.131771i	−0.927364	+	0.374160i	$0.877931\pi$
$270$		0			0
$271$	−5.82840	+	17.9380i	−0.354050	+	1.08965i	0.602508	+	0.798113i	$0.294168\pi$
$271$	−5.82840	+	17.9380i	−0.354050	+	1.08965i	−0.956558	+	0.291541i	$0.905832\pi$
$272$	1.68388	+	3.30481i	0.102100	+	0.200383i
$273$	−0.961891	+	0.657547i	−0.0582163	+	0.0397966i
$274$			14.6260i			0.883592i
$275$		0			0
$276$	6.22623	−	5.87890i	0.374775	−	0.353868i
$277$	−16.3654	−	2.59202i	−0.983299	−	0.155739i	−0.355973	−	0.934496i	$-0.615851\pi$
$277$	−16.3654	−	2.59202i	−0.983299	−	0.155739i	−0.627326	+	0.778757i	$0.715851\pi$
$278$	15.8877	−	8.09517i	0.952878	−	0.485516i
$279$	8.66156	−	22.2306i	0.518554	−	1.33091i
$280$		0			0
$281$	23.8171	−	7.73865i	1.42081	−	0.461649i	0.504951	−	0.863148i	$-0.331511\pi$
$281$	23.8171	−	7.73865i	1.42081	−	0.461649i	0.915859	+	0.401499i	$0.131511\pi$
$282$	−0.266351	+	9.28279i	−0.0158610	+	0.552782i
$283$	23.8762	+	12.1655i	1.41929	+	0.723165i	0.984173	−	0.177209i	$-0.0567069\pi$
$283$	23.8762	+	12.1655i	1.41929	+	0.723165i	0.435117	+	0.900374i	$0.356707\pi$
$284$	−4.07857	−	2.96325i	−0.242019	−	0.175837i
$285$		0			0
$286$	−11.3417	+	8.24023i	−0.670649	+	0.487255i
$287$	0.316148	−	0.0500729i	0.0186616	−	0.00295571i
$288$	−2.98510	+	0.298633i	−0.175899	+	0.0175971i
$289$	−1.90607	−	2.62348i	−0.112122	−	0.154322i
$290$		0			0
$291$	−2.05599	−	15.9250i	−0.120525	−	0.933541i
$292$	−4.88489	+	9.58715i	−0.285867	+	0.561045i
$293$	−1.78525	−	1.78525i	−0.104296	−	0.104296i	0.653033	−	0.757329i	$-0.273496\pi$
$293$	−1.78525	−	1.78525i	−0.104296	−	0.104296i	−0.757329	+	0.653033i	$0.773496\pi$
$294$	5.79374	−	10.6073i	0.337898	−	0.618629i
$295$		0			0
$296$	−7.99408	−	2.59743i	−0.464646	−	0.150973i
$297$	−14.7572	−	6.24297i	−0.856298	−	0.362254i
$298$	2.41669	−	15.2584i	0.139995	−	0.883896i
$299$	22.4761			1.29983
$300$		0			0
$301$	−0.579767			−0.0334172
$302$	−1.10935	+	7.00414i	−0.0638357	+	0.403043i
$303$	−6.83614	−	2.44009i	−0.392726	−	0.140180i
$304$	3.32698	+	1.08100i	0.190815	+	0.0619997i
$305$		0			0
$306$	−10.7624	+	2.82605i	−0.615243	+	0.161554i
$307$	18.1356	+	18.1356i	1.03505	+	1.03505i	0.999363	+	0.0356889i	$0.0113625\pi$
$307$	18.1356	+	18.1356i	1.03505	+	1.03505i	0.0356889	+	0.999363i	$0.488637\pi$
$308$	−0.207155	+	0.406565i	−0.0118038	+	0.0231662i
$309$	30.0640	−	3.88141i	1.71028	−	0.220805i
$310$		0			0
$311$	−6.19053	−	8.52054i	−0.351033	−	0.483155i	0.596590	−	0.802546i	$-0.296522\pi$
$311$	−6.19053	−	8.52054i	−0.351033	−	0.483155i	−0.947623	+	0.319391i	$0.896522\pi$
$312$	−6.23503	−	4.80917i	−0.352989	−	0.272266i
$313$	−17.4862	+	2.76954i	−0.988377	+	0.156543i	−0.629633	−	0.776893i	$-0.716795\pi$
$313$	−17.4862	+	2.76954i	−0.988377	+	0.156543i	−0.358744	+	0.933436i	$0.616795\pi$
$314$	−5.84453	+	4.24630i	−0.329826	+	0.239632i
$315$		0			0
$316$	7.29480	+	5.29999i	0.410365	+	0.298147i
$317$	4.53776	+	2.31211i	0.254866	+	0.129861i	0.576756	−	0.816916i	$-0.304318\pi$
$317$	4.53776	+	2.31211i	0.254866	+	0.129861i	−0.321890	+	0.946777i	$0.604318\pi$
$318$	19.9909	+	0.573599i	1.12103	+	0.0321659i
$319$	4.83453	−	1.57084i	0.270682	−	0.0879499i
$320$		0			0
$321$	−0.480206	−	1.01330i	−0.0268025	−	0.0565568i
$322$	0.651824	−	0.332121i	0.0363248	−	0.0185084i
$323$	12.8153	+	2.02974i	0.713063	+	0.112938i
$324$	1.03040	−	8.94082i	0.0572445	−	0.496712i
$325$		0			0
$326$		−	2.14210i		−	0.118640i
$327$	0.0736137	+	0.107686i	0.00407085	+	0.00595502i
$328$	0.982063	+	1.92741i	0.0542254	+	0.106423i
$329$	−0.245164	+	0.754537i	−0.0135163	+	0.0415990i
$330$		0			0
$331$	−4.54014	−	13.9731i	−0.249548	−	0.768031i	−0.994855	−	0.101309i	$-0.967697\pi$
$331$	−4.54014	−	13.9731i	−0.249548	−	0.768031i	0.745307	−	0.666722i	$-0.232303\pi$
$332$	7.15083	−	7.15083i	0.392453	−	0.392453i
$333$	12.7175	−	21.7746i	0.696913	−	1.19324i
$334$	2.46639	−	3.39470i	0.134955	−	0.185750i
$335$		0			0
$336$	−0.251884	−	0.0473370i	−0.0137414	−	0.00258244i
$337$	3.87373	+	24.4578i	0.211015	+	1.33230i	0.834735	+	0.550651i	$0.185621\pi$
$337$	3.87373	+	24.4578i	0.211015	+	1.33230i	−0.623720	+	0.781648i	$0.714379\pi$
$338$	−1.19952	−	7.57350i	−0.0652455	−	0.411944i
$339$	−29.1371	−	5.47578i	−1.58251	−	0.297404i
$340$		0			0
$341$	14.4149	−	19.8403i	0.780608	−	1.07441i
$342$	−5.29276	+	9.06217i	−0.286200	+	0.490026i
$343$	1.46255	−	1.46255i	0.0789703	−	0.0789703i
$344$	−1.21076	−	3.72634i	−0.0652799	−	0.200911i
$345$		0			0
$346$	0.0335897	−	0.103378i	0.00180579	−	0.00555765i
$347$	−14.5067	−	28.4710i	−0.778760	−	1.52840i	−0.847516	−	0.530769i	$-0.821903\pi$
$347$	−14.5067	−	28.4710i	−0.778760	−	1.52840i	0.0687565	−	0.997633i	$-0.478097\pi$
$348$	1.61130	+	2.35709i	0.0863750	+	0.126353i
$349$		−	27.0969i		−	1.45047i	−0.688504	−	0.725233i	$-0.741732\pi$
$349$		−	27.0969i		−	1.45047i	0.688504	−	0.725233i	$-0.258268\pi$
$350$		0			0
$351$	18.0777	−	15.2063i	0.964914	−	0.811652i
$352$	−3.04574	−	0.482397i	−0.162338	−	0.0257118i
$353$	−5.52827	+	2.81680i	−0.294240	+	0.149923i	−0.594879	−	0.803815i	$-0.702800\pi$
$353$	−5.52827	+	2.81680i	−0.294240	+	0.149923i	0.300639	+	0.953738i	$0.402800\pi$
$354$	−9.55422	−	20.1607i	−0.507801	−	1.07153i
$355$		0			0
$356$	−7.21008	+	2.34270i	−0.382133	+	0.124163i
$357$	−0.950221	−	0.0272647i	−0.0502910	−	0.00144300i
$358$	1.42914	+	0.728181i	0.0755321	+	0.0384855i
$359$	−27.6886	−	20.1169i	−1.46135	−	1.06173i	−0.983009	−	0.183555i	$-0.941239\pi$
$359$	−27.6886	−	20.1169i	−1.46135	−	1.06173i	−0.478338	−	0.878176i	$-0.658761\pi$
$360$		0			0
$361$	−5.47109	+	3.97498i	−0.287952	+	0.209209i
$362$	−12.4748	+	1.97581i	−0.655659	+	0.103846i
$363$	2.04459	+	1.57702i	0.107313	+	0.0827723i
$364$	−0.395407	−	0.544231i	−0.0207250	−	0.0285255i
$365$		0			0
$366$	25.0875	−	3.23891i	1.31134	−	0.169301i
$367$	5.51668	−	10.8271i	0.287968	−	0.565170i	−0.701024	−	0.713138i	$-0.747273\pi$
$367$	5.51668	−	10.8271i	0.287968	−	0.565170i	0.988992	+	0.147968i	$0.0472733\pi$
$368$	3.49589	+	3.49589i	0.182236	+	0.182236i
$369$	−6.27675	+	1.64819i	−0.326755	+	0.0858013i
$370$		0			0
$371$	1.62493	+	0.527971i	0.0843621	+	0.0274109i
$372$	12.9730	+	4.63058i	0.672618	+	0.240084i
$373$	−4.00874	+	25.3102i	−0.207565	+	1.31051i	0.635249	+	0.772307i	$0.280897\pi$
$373$	−4.00874	+	25.3102i	−0.207565	+	1.31051i	−0.842814	+	0.538205i	$0.819103\pi$
$374$	−11.4377			−0.591427
$375$		0			0
$376$	−5.36163			−0.276505
$377$	−1.17235	+	7.40192i	−0.0603790	+	0.381218i
$378$	0.299568	−	0.708122i	0.0154081	−	0.0364219i
$379$	6.14399	+	1.99630i	0.315596	+	0.102543i	0.462532	−	0.886603i	$-0.346941\pi$
$379$	6.14399	+	1.99630i	0.315596	+	0.102543i	−0.146936	+	0.989146i	$0.546941\pi$
$380$		0			0
$381$	7.40341	−	13.5543i	0.379288	−	0.694408i
$382$	14.7593	+	14.7593i	0.755152	+	0.755152i
$383$	0.124507	−	0.244359i	0.00636200	−	0.0124861i	−0.887804	−	0.460222i	$-0.847770\pi$
$383$	0.124507	−	0.244359i	0.00636200	−	0.0124861i	0.894166	+	0.447736i	$0.147770\pi$
$384$	−0.221775	−	1.71779i	−0.0113174	−	0.0876608i
$385$		0			0
$386$	−3.95216	−	5.43968i	−0.201160	−	0.276873i
$387$	11.6959	−	1.17008i	0.594538	−	0.0594783i
$388$	9.15648	−	1.45024i	0.464850	−	0.0736250i
$389$	22.1354	−	16.0823i	1.12231	−	0.815407i	0.137754	−	0.990467i	$-0.456012\pi$
$389$	22.1354	−	16.0823i	1.12231	−	0.815407i	0.984558	+	0.175059i	$0.0560117\pi$
$390$		0			0
$391$	14.8353	+	10.7784i	0.750251	+	0.545089i
$392$	6.21754	+	3.16799i	0.314033	+	0.160008i
$393$	0.0838734	−	2.92313i	0.00423085	−	0.147452i
$394$	4.11657	−	1.33755i	0.207390	−	0.0673850i
$395$		0			0
$396$	3.35853	−	8.61993i	0.168772	−	0.433168i
$397$	1.05681	−	0.538470i	0.0530396	−	0.0270250i	−0.427270	−	0.904124i	$-0.640524\pi$
$397$	1.05681	−	0.538470i	0.0530396	−	0.0270250i	0.480309	+	0.877099i	$0.340524\pi$
$398$	−0.603327	−	0.0955577i	−0.0302421	−	0.00478987i
$399$	−0.651890	+	0.615524i	−0.0326353	+	0.0308147i
$400$		0			0
$401$			4.37934i			0.218694i	0.994004	+	0.109347i	$0.0348759\pi$
$401$			4.37934i			0.218694i	−0.994004	+	0.109347i	$0.965124\pi$
$402$	5.19319	−	3.55006i	0.259013	−	0.177061i
$403$	16.4140	+	32.2143i	0.817639	+	1.60471i
$404$	1.29501	−	3.98563i	0.0644291	−	0.198292i
$405$		0			0
$406$	0.0753765	+	0.231985i	0.00374087	+	0.0115132i
$407$	18.3282	−	18.3282i	0.908494	−	0.908494i
$408$	−1.80916	−	6.16430i	−0.0895669	−	0.305178i
$409$	−19.0597	+	26.2334i	−0.942440	+	1.29716i	0.0123647	+	0.999924i	$0.496064\pi$
$409$	−19.0597	+	26.2334i	−0.942440	+	1.29716i	−0.954805	+	0.297234i	$0.903936\pi$
$410$		0			0
$411$	4.67897	−	24.8972i	0.230797	−	1.22809i
$412$	2.73784	+	17.2861i	0.134884	+	0.851623i
$413$	−0.298159	−	1.88250i	−0.0146715	−	0.0926320i
$414$	−12.4793	+	8.01555i	−0.613324	+	0.393943i
$415$		0			0
$416$	2.67219	−	3.67795i	0.131015	−	0.180326i
$417$	−29.6345	+	8.69744i	−1.45121	+	0.425915i
$418$	−7.62783	+	7.62783i	−0.373089	+	0.373089i
$419$	−9.10066	−	28.0089i	−0.444596	−	1.36833i	−0.882926	−	0.469512i	$-0.844430\pi$
$419$	−9.10066	−	28.0089i	−0.444596	−	1.36833i	0.438330	−	0.898814i	$-0.355570\pi$
$420$		0			0
$421$	1.83346	−	5.64281i	0.0893574	−	0.275014i	−0.896385	−	0.443277i	$-0.853816\pi$
$421$	1.83346	−	5.64281i	0.0893574	−	0.275014i	0.985742	+	0.168263i	$0.0538158\pi$
$422$	−2.06240	−	4.04770i	−0.100396	−	0.197039i
$423$	3.42302	−	15.7164i	0.166433	−	0.764159i
$424$			11.5465i			0.560748i
$425$		0			0
$426$	5.99479	+	6.34897i	0.290448	+	0.307608i
$427$	2.13444	+	0.338062i	0.103293	+	0.0163600i
$428$	0.576835	−	0.293912i	0.0278824	−	0.0142068i
$429$	21.9425	−	10.3987i	1.05940	−	0.502052i
$430$		0			0
$431$	16.7496	−	5.44228i	0.806801	−	0.262146i	0.123559	−	0.992337i	$-0.460569\pi$
$431$	16.7496	−	5.44228i	0.806801	−	0.262146i	0.683242	+	0.730192i	$0.260569\pi$
$432$	5.17692	+	0.446605i	0.249075	+	0.0214873i
$433$	−8.08290	−	4.11844i	−0.388439	−	0.197920i	0.248854	−	0.968541i	$-0.419946\pi$
$433$	−8.08290	−	4.11844i	−0.388439	−	0.197920i	−0.637293	+	0.770621i	$0.719946\pi$
$434$	0.952038	+	0.691696i	0.0456993	+	0.0332025i
$435$		0			0
$436$	−0.0609277	+	0.0442666i	−0.00291791	+	0.00211998i
$437$	17.0819	−	2.70551i	0.817138	−	0.129422i
$438$	11.3823	−	14.7570i	0.543868	−	0.705118i
$439$	−16.9822	−	23.3740i	−0.810517	−	1.11558i	−0.991243	−	0.132048i	$-0.957845\pi$
$439$	−16.9822	−	23.3740i	−0.810517	−	1.11558i	0.180726	−	0.983533i	$-0.442155\pi$
$440$		0			0
$441$	−13.2557	+	16.2028i	−0.631226	+	0.771562i
$442$	7.65526	−	15.0243i	0.364124	−	0.714633i
$443$	−12.4501	−	12.4501i	−0.591523	−	0.591523i	0.346520	−	0.938043i	$-0.387363\pi$
$443$	−12.4501	−	12.4501i	−0.591523	−	0.591523i	−0.938043	+	0.346520i	$0.887363\pi$
$444$	12.7770	+	6.97884i	0.606369	+	0.331201i
$445$		0			0
$446$	18.5563	+	6.02932i	0.878668	+	0.285497i
$447$	−8.99509	+	25.2005i	−0.425453	+	1.19194i
$448$	0.0231478	−	0.146149i	0.00109363	−	0.00690491i
$449$	−12.8503			−0.606444			−0.303222	−	0.952920i	$-0.598062\pi$
$449$	−12.8503			−0.606444			−0.303222	+	0.952920i	$0.598062\pi$
$450$		0			0
$451$	−6.67060			−0.314106
$452$	2.67766	−	16.9061i	0.125946	−	0.795194i
$453$	4.12906	−	11.5679i	0.194000	−	0.543508i
$454$	11.4929	+	3.73428i	0.539390	+	0.175259i
$455$		0			0
$456$	−5.31754	−	2.90446i	−0.249017	−	0.136014i
$457$	−10.9813	−	10.9813i	−0.513683	−	0.513683i	0.401970	−	0.915653i	$-0.368326\pi$
$457$	−10.9813	−	10.9813i	−0.513683	−	0.513683i	−0.915653	+	0.401970i	$0.868326\pi$
$458$	−2.81027	+	5.51547i	−0.131316	+	0.257721i
$459$	19.2243	−	1.36769i	0.897314	−	0.0638384i
$460$		0			0
$461$	−6.59561	−	9.07808i	−0.307188	−	0.422808i	0.627314	−	0.778767i	$-0.284154\pi$
$461$	−6.59561	−	9.07808i	−0.307188	−	0.422808i	−0.934502	+	0.355958i	$0.884154\pi$
$462$	0.482694	−	0.625806i	0.0224569	−	0.0291151i
$463$	−1.27477	+	0.201904i	−0.0592438	+	0.00938330i	−0.185986	−	0.982552i	$-0.559548\pi$
$463$	−1.27477	+	0.201904i	−0.0592438	+	0.00938330i	0.126742	+	0.991936i	$0.459548\pi$
$464$	−1.33363	+	0.968935i	−0.0619120	+	0.0449817i
$465$		0			0
$466$	−6.12855	−	4.45265i	−0.283900	−	0.206265i
$467$	32.6024	+	16.6117i	1.50866	+	0.768700i	0.995954	−	0.0898651i	$-0.0286436\pi$
$467$	32.6024	+	16.6117i	1.50866	+	0.768700i	0.512705	+	0.858565i	$0.328644\pi$
$468$	9.07510	+	10.1810i	0.419497	+	0.470619i
$469$	0.511114	−	0.166071i	0.0236010	−	0.00766845i
$470$		0			0
$471$	11.3073	−	5.35856i	0.521011	−	0.246909i
$472$	11.4768	−	5.84771i	0.528261	−	0.269162i
$473$	11.9335	+	1.89008i	0.548704	+	0.0869062i
$474$	−10.7221	−	11.3556i	−0.492482	−	0.521578i
$475$		0			0
$476$		−	0.548836i		−	0.0251559i
$477$	−33.8461	−	7.37164i	−1.54970	−	0.337524i
$478$	7.66413	+	15.0417i	0.350549	+	0.687991i
$479$	−8.59259	+	26.4453i	−0.392605	+	1.20832i	0.538205	+	0.842814i	$0.319103\pi$
$479$	−8.59259	+	26.4453i	−0.392605	+	1.20832i	−0.930811	+	0.365502i	$0.880897\pi$
$480$		0			0
$481$	11.8084	+	36.3427i	0.538419	+	1.65708i
$482$	−6.96376	+	6.96376i	−0.317191	+	0.317191i
$483$	−1.21582	+	0.356831i	−0.0553216	+	0.0162364i
$484$	−0.876264	+	1.20607i	−0.0398302	+	0.0548216i
$485$		0			0
$486$	−4.61423	+	14.8899i	−0.209306	+	0.675419i
$487$	−1.49720	−	9.45297i	−0.0678448	−	0.428355i	−0.998109	−	0.0614653i	$-0.980423\pi$
$487$	−1.49720	−	9.45297i	−0.0678448	−	0.428355i	0.930264	−	0.366890i	$-0.119577\pi$
$488$	2.28464	+	14.4247i	0.103421	+	0.652974i
$489$	−0.685271	+	3.64638i	−0.0309890	+	0.164895i
$490$		0			0
$491$	−6.14271	+	8.45471i	−0.277216	+	0.381556i	−0.924809	−	0.380431i	$-0.875776\pi$
$491$	−6.14271	+	8.45471i	−0.277216	+	0.381556i	0.647593	+	0.761986i	$0.275776\pi$
$492$	−1.05513	−	3.59510i	−0.0475688	−	0.162080i
$493$	−4.32341	+	4.32341i	−0.194716	+	0.194716i
$494$	−4.91445	−	15.1251i	−0.221111	−	0.680511i
$495$		0			0
$496$	−2.45755	+	7.56355i	−0.110347	+	0.339613i
$497$	0.338668	+	0.664674i	0.0151913	+	0.0298147i
$498$	−14.4601	+	9.88492i	−0.647973	+	0.442954i
$499$			15.0118i			0.672022i	0.941858	+	0.336011i	$0.109078\pi$
$499$			15.0118i			0.672022i	−0.941858	+	0.336011i	$0.890922\pi$
$500$		0			0
$501$	−5.28441	+	4.98961i	−0.236090	+	0.222920i
$502$	−0.304507	−	0.0482291i	−0.0135908	−	0.00215257i
$503$	−9.89345	+	5.04097i	−0.441127	+	0.224766i	−0.660424	−	0.750893i	$-0.729624\pi$
$503$	−9.89345	+	5.04097i	−0.441127	+	0.224766i	0.219297	+	0.975658i	$0.429624\pi$
$504$	0.413627	+	0.161159i	0.0184244	+	0.00717859i
$505$		0			0
$506$	−14.4994	+	4.71115i	−0.644578	+	0.209436i
$507$	−0.380921	+	13.2757i	−0.0169173	+	0.589596i
$508$	7.94495	+	4.04816i	0.352500	+	0.179608i
$509$	31.3045	+	22.7440i	1.38755	+	1.00811i	0.996130	+	0.0878971i	$0.0280147\pi$
$509$	31.3045	+	22.7440i	1.38755	+	1.00811i	0.391416	+	0.920214i	$0.371985\pi$
$510$		0			0
$511$	1.28808	−	0.935846i	0.0569814	−	0.0413994i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	11.9087	−	13.7329i	0.525780	−	0.606322i
$514$	−4.24694	−	5.84540i	−0.187324	−	0.257830i
$515$		0			0
$516$	0.868940	+	6.73050i	0.0382529	+	0.296294i
$517$	7.50612	−	14.7316i	0.330119	−	0.647895i
$518$	0.879477	+	0.879477i	0.0386420	+	0.0386420i
$519$	−0.0902495	+	0.165230i	−0.00396151	+	0.00725281i
$520$		0			0
$521$	−20.0378	−	6.51069i	−0.877874	−	0.285239i	−0.164800	−	0.986327i	$-0.552698\pi$
$521$	−20.0378	−	6.51069i	−0.877874	−	0.285239i	−0.713074	+	0.701089i	$0.752698\pi$
$522$	−1.98880	−	4.52783i	−0.0870472	−	0.198178i
$523$	−1.81949	+	11.4878i	−0.0795606	+	0.502326i	0.915440	+	0.402455i	$0.131843\pi$
$523$	−1.81949	+	11.4878i	−0.0795606	+	0.502326i	−0.995000	+	0.0998710i	$0.968157\pi$
$524$	1.68836			0.0737565
$525$		0			0
$526$	−5.22487			−0.227815
$527$	−4.61442	+	29.1343i	−0.201007	+	1.26911i
$528$	5.03028	+	1.79551i	0.218915	+	0.0781396i
$529$	1.37184	+	0.445739i	0.0596454	+	0.0193800i
$530$		0			0
$531$	9.81416	+	37.3750i	0.425898	+	1.62194i
$532$	−0.366021	−	0.366021i	−0.0158690	−	0.0158690i
$533$	4.46465	−	8.76237i	0.193386	−	0.379541i
$534$	13.0228	−	1.68131i	0.563552	−	0.0727572i
$535$		0			0
$536$	2.13478	+	2.93827i	0.0922084	+	0.126914i
$537$	−2.19980	−	1.69674i	−0.0949283	−	0.0732196i
$538$	2.24445	−	0.355485i	0.0967649	−	0.0153261i
$539$	−17.4087	+	12.6482i	−0.749847	+	0.544796i
$540$		0			0
$541$	−13.9722	−	10.1514i	−0.600713	−	0.436443i	0.245419	−	0.969417i	$-0.421074\pi$
$541$	−13.9722	−	10.1514i	−0.600713	−	0.436443i	−0.846132	+	0.532974i	$0.821074\pi$
$542$	16.8054	+	8.56276i	0.721852	+	0.367802i
$543$	21.8673	+	0.627438i	0.938414	+	0.0269259i
$544$	3.52754	−	1.14617i	0.151242	−	0.0491415i
$545$		0			0
$546$	0.498979	+	1.05291i	0.0213543	+	0.0450604i
$547$	4.99544	−	2.54530i	0.213590	−	0.108829i	−0.343923	−	0.938998i	$-0.611756\pi$
$547$	4.99544	−	2.54530i	0.213590	−	0.108829i	0.557512	+	0.830169i	$0.311756\pi$
$548$	14.4460	+	2.28802i	0.617101	+	0.0977393i
$549$	−43.7414	−	2.51221i	−1.86684	−	0.107219i
$550$		0			0
$551$			5.76660i			0.245666i
$552$	−4.83252	−	7.06923i	−0.205686	−	0.300887i
$553$	−0.605732	−	1.18882i	−0.0257583	−	0.0505536i
$554$	−5.12021	+	15.7584i	−0.217537	+	0.669510i
$555$		0			0
$556$	−5.51012	−	16.9584i	−0.233681	−	0.719197i
$557$	−0.714899	+	0.714899i	−0.0302913	+	0.0302913i	−0.722090	−	0.691799i	$-0.756818\pi$
$557$	−0.714899	+	0.714899i	−0.0302913	+	0.0302913i	0.691799	+	0.722090i	$0.256818\pi$
$558$	−20.6019	−	12.0326i	−0.872149	−	0.509379i
$559$	−10.4699	+	14.4106i	−0.442830	+	0.609504i
$560$		0			0
$561$	19.4698	+	3.65898i	0.822015	+	0.154482i
$562$	−3.91756	−	24.7345i	−0.165252	−	1.04336i
$563$	−0.262374	−	1.65657i	−0.0110578	−	0.0698159i	0.981542	−	0.191245i	$-0.0612524\pi$
$563$	−0.262374	−	1.65657i	−0.0110578	−	0.0698159i	−0.992600	+	0.121429i	$0.961252\pi$
$564$	9.12684	+	1.71522i	0.384309	+	0.0722238i
$565$		0			0
$566$	15.7508	−	21.6791i	0.662055	−	0.911241i
$567$	−0.736474	+	1.10957i	−0.0309290	+	0.0465975i
$568$	−3.56480	+	3.56480i	−0.149576	+	0.149576i
$569$	3.81378	+	11.7376i	0.159882	+	0.492066i	0.998623	−	0.0524648i	$-0.0167077\pi$
$569$	3.81378	+	11.7376i	0.159882	+	0.492066i	−0.838741	+	0.544531i	$0.816708\pi$
$570$		0			0
$571$	−1.99738	+	6.14731i	−0.0835879	+	0.257257i	−0.984112	−	0.177549i	$-0.943183\pi$
$571$	−1.99738	+	6.14731i	−0.0835879	+	0.257257i	0.900524	+	0.434806i	$0.143183\pi$
$572$	6.36454	+	12.4911i	0.266115	+	0.522280i
$573$	−20.4024	−	29.8456i	−0.852325	−	1.24682i
$574$		−	0.320088i		−	0.0133602i
$575$		0			0
$576$	−0.172016	+	2.99506i	−0.00716735	+	0.124794i
$577$	32.3673	+	5.12648i	1.34747	+	0.213418i	0.788124	−	0.615516i	$-0.211053\pi$
$577$	32.3673	+	5.12648i	1.34747	+	0.213418i	0.559346	+	0.828935i	$0.311053\pi$
$578$	−2.88935	+	1.47220i	−0.120181	+	0.0612354i
$579$	4.98738	+	10.5240i	0.207268	+	0.437364i
$580$		0			0
$581$	−1.42317	+	0.462415i	−0.0590429	+	0.0191842i
$582$	−16.0506	−	0.460539i	−0.665318	−	0.0190900i
$583$	−31.7252	−	16.1648i	−1.31392	−	0.669477i
$584$	8.70495	+	6.32451i	0.360213	+	0.261710i
$585$		0			0
$586$	−2.04255	+	1.48400i	−0.0843770	+	0.0613035i
$587$	−25.8604	+	4.09589i	−1.06737	+	0.169056i	−0.665319	−	0.746559i	$-0.731704\pi$
$587$	−25.8604	+	4.09589i	−1.06737	+	0.169056i	−0.402056	+	0.915615i	$0.631704\pi$
$588$	−9.57035	−	7.38175i	−0.394675	−	0.304418i
$589$	16.3524	+	22.5072i	0.673790	+	0.927392i
$590$		0			0
$591$	−7.43533	+	0.959936i	−0.305849	+	0.0394865i
$592$	−3.81600	+	7.48933i	−0.156837	+	0.307810i
$593$	28.6751	+	28.6751i	1.17754	+	1.17754i	0.980368	+	0.197176i	$0.0631772\pi$
$593$	28.6751	+	28.6751i	1.17754	+	1.17754i	0.197176	+	0.980368i	$0.436823\pi$
$594$	−8.47463	+	13.5989i	−0.347718	+	0.557968i
$595$		0			0
$596$	−14.6925	−	4.77388i	−0.601828	−	0.195546i
$597$	0.996445	+	0.355672i	0.0407818	+	0.0145567i
$598$	3.51603	−	22.1994i	0.143781	−	0.907799i
$599$	23.8130			0.972971			0.486486	−	0.873689i	$-0.338279\pi$
$599$	23.8130			0.972971			0.486486	+	0.873689i	$0.338279\pi$
$600$		0			0
$601$	−24.9278			−1.01683			−0.508413	−	0.861113i	$-0.669768\pi$
$601$	−24.9278			−1.01683			−0.508413	+	0.861113i	$0.669768\pi$
$602$	−0.0906956	+	0.572630i	−0.00369648	+	0.0233386i
$603$	−9.97580	+	4.38175i	−0.406246	+	0.178439i
$604$	6.74437	+	2.19138i	0.274424	+	0.0891659i
$605$		0			0
$606$	−3.47946	+	6.37026i	−0.141343	+	0.258774i
$607$	12.2020	+	12.2020i	0.495265	+	0.495265i	0.909960	−	0.414695i	$-0.136112\pi$
$607$	12.2020	+	12.2020i	0.495265	+	0.495265i	−0.414695	+	0.909960i	$0.636112\pi$
$608$	1.58815	−	3.11691i	0.0644079	−	0.126408i
$609$	−0.0540962	−	0.419010i	−0.00219209	−	0.0169791i
$610$		0			0
$611$	14.3273	+	19.7198i	0.579620	+	0.797778i
$612$	1.10765	+	11.0719i	0.0447741	+	0.447557i
$613$	1.82779	−	0.289494i	0.0738239	−	0.0116926i	−0.119413	−	0.992845i	$-0.538101\pi$
$613$	1.82779	−	0.289494i	0.0738239	−	0.0116926i	0.193237	+	0.981152i	$0.438101\pi$
$614$	20.7493	−	15.0753i	0.837375	−	0.608388i
$615$		0			0
$616$	0.369154	+	0.268206i	0.0148736	+	0.0108063i
$617$	3.92556	+	2.00017i	0.158037	+	0.0805239i	0.531220	−	0.847234i	$-0.321734\pi$
$617$	3.92556	+	2.00017i	0.158037	+	0.0805239i	−0.373183	+	0.927758i	$0.621734\pi$
$618$	0.869429	−	30.3011i	0.0349736	−	1.21889i
$619$	4.50152	−	1.46263i	0.180931	−	0.0587882i	−0.217150	−	0.976138i	$-0.569676\pi$
$619$	4.50152	−	1.46263i	0.180931	−	0.0587882i	0.398082	+	0.917350i	$0.369676\pi$
$620$		0			0
$621$	23.8071	−	9.65226i	0.955347	−	0.387332i
$622$	−9.38405	+	4.78141i	−0.376266	+	0.191717i
$623$	1.10798	+	0.175486i	0.0443902	+	0.00703072i
$624$	−5.72534	+	5.40595i	−0.229197	+	0.216411i
$625$		0			0
$626$			17.7041i			0.707599i
$627$	15.4247	−	10.5443i	0.616002	−	0.421099i
$628$	3.27973	+	6.43684i	0.130876	+	0.256858i
$629$	−9.63406	+	29.6506i	−0.384135	+	1.18225i
$630$		0			0
$631$	9.68700	+	29.8135i	0.385633	+	1.18686i	0.936020	+	0.351947i	$0.114480\pi$
$631$	9.68700	+	29.8135i	0.385633	+	1.18686i	−0.550387	+	0.834910i	$0.685520\pi$
$632$	6.37589	−	6.37589i	0.253619	−	0.253619i
$633$	2.21585	+	7.54998i	0.0880720	+	0.300085i
$634$	2.99350	−	4.12020i	0.118887	−	0.163634i
$635$		0			0
$636$	3.69380	−	19.6551i	0.146469	−	0.779374i
$637$	−4.96270	−	31.3333i	−0.196629	−	1.24147i
$638$	−0.795208	−	5.02075i	−0.0314826	−	0.198773i
$639$	−8.17356	−	12.7253i	−0.323341	−	0.503405i
$640$		0			0
$641$	−17.3534	+	23.8849i	−0.685419	+	0.943398i	−0.999983	−	0.00583804i	$-0.998142\pi$
$641$	−17.3534	+	23.8849i	−0.685419	+	0.943398i	0.314564	+	0.949236i	$0.398142\pi$
$642$	−1.07594	+	0.315779i	−0.0424641	+	0.0124628i
$643$	23.8141	−	23.8141i	0.939135	−	0.939135i	−0.0591164	−	0.998251i	$-0.518828\pi$
$643$	23.8141	−	23.8141i	0.939135	−	0.939135i	0.998251	+	0.0591164i	$0.0188283\pi$
$644$	−0.226064	−	0.695754i	−0.00890818	−	0.0274166i
$645$		0			0
$646$	4.00951	−	12.3400i	0.157752	−	0.485511i
$647$	−16.4252	−	32.2362i	−0.645740	−	1.26734i	−0.949254	−	0.314509i	$-0.898160\pi$
$647$	−16.4252	−	32.2362i	−0.645740	−	1.26734i	0.303514	−	0.952827i	$-0.401840\pi$
$648$	−8.66955	−	2.41637i	−0.340572	−	0.0949239i
$649$			39.7202i			1.55915i
$650$		0			0
$651$	−1.39933	−	1.48200i	−0.0548441	−	0.0580843i
$652$	−2.11572	−	0.335098i	−0.0828581	−	0.0131234i
$653$	−14.2513	+	7.26139i	−0.557696	+	0.284160i	−0.710033	−	0.704168i	$-0.751320\pi$
$653$	−14.2513	+	7.26139i	−0.557696	+	0.284160i	0.152337	+	0.988329i	$0.451320\pi$
$654$	0.117875	−	0.0558617i	0.00460930	−	0.00218436i
$655$		0			0
$656$	2.05731	−	0.668459i	0.0803243	−	0.0260990i
$657$	−24.0964	+	21.4789i	−0.940091	+	0.837971i
$658$	0.706895	+	0.360181i	0.0275576	+	0.0140413i
$659$	−9.25834	−	6.72658i	−0.360654	−	0.262030i	0.392671	−	0.919679i	$-0.371551\pi$
$659$	−9.25834	−	6.72658i	−0.360654	−	0.262030i	−0.753325	+	0.657649i	$0.771551\pi$
$660$		0			0
$661$	5.86553	−	4.26156i	0.228143	−	0.165755i	−0.467842	−	0.883812i	$-0.654968\pi$
$661$	5.86553	−	4.26156i	0.228143	−	0.165755i	0.695984	+	0.718057i	$0.254968\pi$
$662$	−14.5113	+	2.29836i	−0.563998	+	0.0893285i
$663$	−17.8376	+	23.1262i	−0.692753	+	0.898146i
$664$	−5.94416	−	8.18143i	−0.230678	−	0.317501i
$665$		0			0
$666$	−19.5171	−	15.9672i	−0.756271	−	0.618716i
$667$	−3.69994	+	7.26155i	−0.143262	+	0.281168i
$668$	−2.96707	−	2.96707i	−0.114800	−	0.114800i
$669$	−29.6587	−	16.1997i	−1.14667	−	0.626317i
$670$		0			0
$671$	−42.8316	−	13.9168i	−1.65350	−	0.537254i
$672$	−0.0861576	+	0.241378i	−0.00332360	+	0.00931136i
$673$	−3.38928	+	21.3991i	−0.130647	+	0.824874i	0.832131	+	0.554580i	$0.187121\pi$
$673$	−3.38928	+	21.3991i	−0.130647	+	0.824874i	−0.962778	+	0.270294i	$0.912879\pi$
$674$	24.7626			0.953821
$675$		0			0
$676$	−7.66790			−0.294919
$677$	−0.271360	+	1.71330i	−0.0104292	+	0.0658476i	−0.992354	−	0.123424i	$-0.960613\pi$
$677$	−0.271360	+	1.71330i	−0.0104292	+	0.0658476i	0.981925	+	0.189271i	$0.0606126\pi$
$678$	−9.96641	+	27.9218i	−0.382758	+	1.07233i
$679$	−1.30465	−	0.423905i	−0.0500677	−	0.0162680i
$680$		0			0
$681$	−18.3692	−	10.0334i	−0.703911	−	0.384479i
$682$	−17.3411	−	17.3411i	−0.664025	−	0.664025i
$683$	5.65426	−	11.0971i	0.216354	−	0.424619i	−0.757165	−	0.653224i	$-0.773416\pi$
$683$	5.65426	−	11.0971i	0.216354	−	0.424619i	0.973519	+	0.228604i	$0.0734162\pi$
$684$	8.12263	+	6.64524i	0.310576	+	0.254087i
$685$		0			0
$686$	−1.21575	−	1.67334i	−0.0464176	−	0.0638883i
$687$	6.54823	−	8.48970i	0.249831	−	0.323902i
$688$	−3.86987	+	0.612927i	−0.147537	+	0.0233676i
$689$	42.4675	−	30.8544i	1.61788	−	1.17546i
$690$		0			0
$691$	−30.9813	−	22.5093i	−1.17859	−	0.856293i	−0.186574	−	0.982441i	$-0.559738\pi$
$691$	−30.9813	−	22.5093i	−1.17859	−	0.856293i	−0.992011	+	0.126148i	$0.959738\pi$
$692$	−0.0968510	−	0.0493481i	−0.00368172	−	0.00187593i
$693$	−1.02187	+	0.910863i	−0.0388175	+	0.0346008i
$694$	−30.3898	+	9.87425i	−1.15358	+	0.374821i
$695$		0			0
$696$	2.58013	−	1.22274i	0.0977997	−	0.0463477i
$697$	7.14889	−	3.64254i	0.270784	−	0.137971i
$698$	−26.7633	−	4.23889i	−1.01301	−	0.160445i
$699$	9.00790	+	9.54010i	0.340710	+	0.360840i
$700$		0			0
$701$		−	22.4631i		−	0.848418i	−0.905564	−	0.424209i	$-0.860552\pi$
$701$		−	22.4631i		−	0.848418i	0.905564	−	0.424209i	$-0.139448\pi$
$702$	−12.1911	−	20.2339i	−0.460124	−	0.763679i
$703$	13.3491	+	26.1991i	0.503472	+	0.988119i
$704$	−0.952916	+	2.93277i	−0.0359144	+	0.110533i
$705$		0			0
$706$	1.91730	+	5.90085i	0.0721587	+	0.222082i
$707$	−0.438483	+	0.438483i	−0.0164909	+	0.0164909i
$708$	−21.4071	+	6.28277i	−0.804527	+	0.236121i
$709$	23.3849	−	32.1865i	0.878238	−	1.20879i	−0.0986680	−	0.995120i	$-0.531458\pi$
$709$	23.3849	−	32.1865i	0.878238	−	1.20879i	0.976906	−	0.213670i	$-0.0685418\pi$
$710$		0			0
$711$	14.6190	+	22.7601i	0.548254	+	0.853570i
$712$	1.18595	+	7.48779i	0.0444453	+	0.280617i
$713$	6.15069	+	38.8339i	0.230345	+	1.45434i
$714$	−0.175576	+	0.934257i	−0.00657078	+	0.0349637i
$715$		0			0
$716$	0.942782	−	1.29763i	0.0352334	−	0.0484946i
$717$	−8.23433	−	28.0566i	−0.307517	−	1.04779i
$718$	−24.2007	+	24.2007i	−0.903162	+	0.903162i
$719$	−3.27225	−	10.0709i	−0.122034	−	0.375583i	0.871315	−	0.490724i	$-0.163268\pi$
$719$	−3.27225	−	10.0709i	−0.122034	−	0.375583i	−0.993349	+	0.115142i	$0.963268\pi$
$720$		0			0
$721$	0.800268	−	2.46297i	0.0298036	−	0.0917259i
$722$	3.07017	+	6.02555i	0.114260	+	0.224248i
$723$	14.0818	−	9.62632i	0.523709	−	0.358007i
$724$			12.6303i			0.469400i
$725$		0			0
$726$	1.87745	−	1.77272i	0.0696788	−	0.0657918i
$727$	−12.8632	−	2.03732i	−0.477068	−	0.0755602i	−0.0867303	−	0.996232i	$-0.527642\pi$
$727$	−12.8632	−	2.03732i	−0.477068	−	0.0755602i	−0.390338	+	0.920672i	$0.627642\pi$
$728$	−0.599386	+	0.305402i	−0.0222147	+	0.0113190i
$729$	12.6180	−	23.8702i	0.467332	−	0.884082i
$730$		0			0
$731$	−13.8213	+	4.49080i	−0.511198	+	0.166098i
$732$	0.725511	−	25.2853i	0.0268157	−	0.934571i
$733$	−38.5339	−	19.6340i	−1.42328	−	0.725199i	−0.438458	−	0.898752i	$-0.644475\pi$
$733$	−38.5339	−	19.6340i	−1.42328	−	0.725199i	−0.984824	+	0.173553i	$0.944475\pi$
$734$	−9.83080	−	7.14249i	−0.362861	−	0.263634i
$735$		0			0
$736$	3.99972	−	2.90597i	0.147432	−	0.107115i
$737$	−11.0618	+	1.75202i	−0.407467	+	0.0645364i
$738$	0.645996	+	6.45731i	0.0237794	+	0.237697i
$739$	7.30628	+	10.0562i	0.268766	+	0.369924i	0.921973	−	0.387255i	$-0.126577\pi$
$739$	7.30628	+	10.0562i	0.268766	+	0.369924i	−0.653207	+	0.757180i	$0.726577\pi$
$740$		0			0
$741$	3.52700	+	27.3189i	0.129568	+	1.00358i
$742$	0.775666	−	1.52233i	0.0284756	−	0.0558865i
$743$	5.87728	+	5.87728i	0.215616	+	0.215616i	0.806648	−	0.591032i	$-0.201279\pi$
$743$	5.87728	+	5.87728i	0.215616	+	0.215616i	−0.591032	+	0.806648i	$0.701279\pi$
$744$	6.60299	−	12.0889i	0.242077	−	0.443200i
$745$		0			0
$746$	24.3715	+	7.91878i	0.892304	+	0.289927i
$747$	27.7770	−	12.2007i	1.01631	−	0.446401i
$748$	−1.78924	+	11.2968i	−0.0654213	+	0.413054i
$749$	−0.0957962			−0.00350032
$750$		0			0
$751$	−30.0007			−1.09474			−0.547371	−	0.836890i	$-0.684371\pi$
$751$	−30.0007			−1.09474			−0.547371	+	0.836890i	$0.684371\pi$
$752$	−0.838744	+	5.29562i	−0.0305858	+	0.193111i
$753$	0.502918	+	0.179512i	0.0183273	+	0.00654177i
$754$	7.12739	+	2.31583i	0.259564	+	0.0843376i
$755$		0			0
$756$	−0.652541	−	0.406655i	−0.0237327	−	0.0147899i
$757$	−0.751496	−	0.751496i	−0.0273136	−	0.0273136i	0.693318	−	0.720632i	$-0.256148\pi$
$757$	−0.751496	−	0.751496i	−0.0273136	−	0.0273136i	−0.720632	+	0.693318i	$0.756148\pi$
$758$	2.93286	−	5.75606i	0.106526	−	0.209069i
$759$	26.1888	−	3.38110i	0.950593	−	0.122726i
$760$		0			0
$761$	−26.8487	−	36.9541i	−0.973266	−	1.33959i	−0.940380	−	0.340126i	$-0.889530\pi$
$761$	−26.8487	−	36.9541i	−0.973266	−	1.33959i	−0.0328857	−	0.999459i	$-0.510470\pi$
$762$	−12.2293	−	9.43262i	−0.443020	−	0.341708i
$763$	0.0110066	−	0.00174328i	0.000398467	−	6.31110e-5i
$764$	16.8865	−	12.2687i	0.610931	−	0.443867i
$765$		0			0
$766$	−0.221873	−	0.161200i	−0.00801659	−	0.00582440i
$767$	−52.1757	−	26.5848i	−1.88395	−	0.959922i
$768$	−1.73134	−	0.0496773i	−0.0624743	−	0.00179258i
$769$	−40.4186	+	13.1328i	−1.45753	+	0.473580i	−0.927315	−	0.374283i	$-0.877889\pi$
$769$	−40.4186	+	13.1328i	−1.45753	+	0.473580i	−0.530216	+	0.847863i	$0.677889\pi$
$770$		0			0
$771$	5.35937	+	11.3090i	0.193013	+	0.407283i
$772$	−5.99097	+	3.05255i	−0.215620	+	0.109864i
$773$	−45.3851	−	7.18830i	−1.63239	−	0.258545i	−0.728102	−	0.685469i	$-0.759597\pi$
$773$	−45.3851	−	7.18830i	−1.63239	−	0.258545i	−0.904288	+	0.426923i	$0.859597\pi$
$774$	0.673979	−	11.7350i	0.0242257	−	0.421805i
$775$		0			0
$776$		−	9.27062i		−	0.332796i
$777$	−1.21574	−	1.77844i	−0.0436144	−	0.0638012i
$778$	−12.4216	−	24.3788i	−0.445336	−	0.874021i
$779$	2.33840	−	7.19686i	0.0837819	−	0.257854i
$780$		0			0
$781$	−4.80402	−	14.7853i	−0.171901	−	0.529058i
$782$	12.9665	−	12.9665i	0.463681	−	0.463681i
$783$	1.93695	+	8.34373i	0.0692209	+	0.298181i
$784$	4.10163	−	5.64541i	0.146487	−	0.201622i
$785$		0			0
$786$	−2.87402	−	0.540119i	−0.102513	−	0.0192654i
$787$	3.38594	+	21.3780i	0.120696	+	0.762043i	0.971584	+	0.236696i	$0.0760644\pi$
$787$	3.38594	+	21.3780i	0.120696	+	0.762043i	−0.850888	+	0.525347i	$0.823936\pi$
$788$	−0.677114	−	4.27513i	−0.0241212	−	0.152295i
$789$	8.89405	+	1.67147i	0.316636	+	0.0595060i
$790$		0			0
$791$	−1.48874	+	2.04907i	−0.0529335	+	0.0728567i
$792$	−7.98841	−	4.66563i	−0.283856	−	0.165786i
$793$	46.9482	−	46.9482i	1.66718	−	1.66718i
$794$	−0.366520	−	1.12803i	−0.0130073	−	0.0400323i
$795$		0			0
$796$	−0.188762	+	0.580951i	−0.00669050	+	0.0205913i
$797$	10.1366	+	19.8941i	0.359055	+	0.704685i	0.997908	−	0.0646433i	$-0.0205910\pi$
$797$	10.1366	+	19.8941i	0.359055	+	0.704685i	−0.638853	+	0.769328i	$0.720591\pi$
$798$	0.505968	+	0.740153i	0.0179111	+	0.0262011i
$799$			19.8867i			0.703539i
$800$		0			0
$801$	−22.7060	−	1.30408i	−0.802276	−	0.0460773i
$802$	4.32542	+	0.685079i	0.152736	+	0.0241910i
$803$	−29.5639	+	15.0636i	−1.04329	+	0.531581i
$804$	−2.69396	−	5.68460i	−0.0950085	−	0.200481i
$805$		0			0
$806$	34.3854	−	11.1725i	1.21117	−	0.393534i
$807$	−3.93433	−	0.112888i	−0.138495	−	0.00397384i
$808$	−3.73397	−	1.90255i	−0.131361	−	0.0669316i
$809$	−10.1700	−	7.38891i	−0.357557	−	0.259780i	0.394476	−	0.918906i	$-0.370926\pi$
$809$	−10.1700	−	7.38891i	−0.357557	−	0.259780i	−0.752032	+	0.659126i	$0.770926\pi$
$810$		0			0
$811$	20.5014	−	14.8951i	0.719902	−	0.523039i	−0.166451	−	0.986050i	$-0.553231\pi$
$811$	20.5014	−	14.8951i	0.719902	−	0.523039i	0.886353	+	0.463010i	$0.153231\pi$
$812$	0.240920	−	0.0381580i	0.00845465	−	0.00133908i
$813$	−25.8677	−	19.9521i	−0.907219	−	0.699751i
$814$	−15.2354	−	20.9697i	−0.533999	−	0.734987i
$815$		0			0
$816$	−6.37142	+	0.822580i	−0.223044	+	0.0287961i
$817$	−6.22253	+	12.2124i	−0.217699	+	0.427258i
$818$	22.9288	+	22.9288i	0.801687	+	0.801687i
$819$	−0.512554	−	1.95195i	−0.0179101	−	0.0682065i
$820$		0			0
$821$	23.8661	+	7.75457i	0.832933	+	0.270636i	0.694280	−	0.719705i	$-0.255723\pi$
$821$	23.8661	+	7.75457i	0.832933	+	0.270636i	0.138653	+	0.990341i	$0.455723\pi$
$822$	−23.8587	−	8.51614i	−0.832169	−	0.297035i
$823$	6.78412	−	42.8332i	0.236479	−	1.49307i	−0.528454	−	0.848962i	$-0.677228\pi$
$823$	6.78412	−	42.8332i	0.236479	−	1.49307i	0.764933	−	0.644110i	$-0.222772\pi$
$824$	17.5015			0.609695
$825$		0			0
$826$	−1.90597			−0.0663172
$827$	−0.349392	+	2.20597i	−0.0121495	+	0.0767091i	−0.993018	−	0.117962i	$-0.962364\pi$
$827$	−0.349392	+	2.20597i	−0.0121495	+	0.0767091i	0.980869	+	0.194671i	$0.0623639\pi$
$828$	5.96467	+	13.5796i	0.207287	+	0.471923i
$829$	8.12669	+	2.64052i	0.282251	+	0.0917091i	0.446722	−	0.894673i	$-0.352591\pi$
$829$	8.12669	+	2.64052i	0.282251	+	0.0917091i	−0.164470	+	0.986382i	$0.552591\pi$
$830$		0			0
$831$	13.7571	−	25.1868i	0.477229	−	0.873719i
$832$	−3.21465	−	3.21465i	−0.111448	−	0.111448i
$833$	11.7503	−	23.0613i	0.407124	−	0.799026i
$834$	3.95450	+	30.6302i	0.136933	+	1.06064i
$835$		0			0
$836$	6.34067	+	8.72718i	0.219296	+	0.301836i
$837$	31.2203	+	27.0731i	1.07913	+	0.935784i
$838$	−29.0878	+	4.60705i	−1.00482	+	0.159148i
$839$	−0.581684	+	0.422618i	−0.0200819	+	0.0145904i	−0.597781	−	0.801659i	$-0.703951\pi$
$839$	−0.581684	+	0.422618i	−0.0200819	+	0.0145904i	0.577699	+	0.816250i	$0.303951\pi$
$840$		0			0
$841$	21.2631	+	15.4485i	0.733210	+	0.532708i
$842$	−5.28652	−	2.69362i	−0.182186	−	0.0928282i
$843$	−1.24406	+	43.3576i	−0.0428477	+	1.49331i
$844$	−4.32049	+	1.40381i	−0.148718	+	0.0483213i
$845$		0			0
$846$	−14.9875	−	5.83947i	−0.515280	−	0.200765i
$847$	0.196551	−	0.100148i	0.00675357	−	0.00344111i
$848$	11.4044	+	1.80627i	0.391627	+	0.0620276i
$849$	−33.7471	+	31.8645i	−1.15820	+	1.09359i
$850$		0			0
$851$			41.5561i			1.42452i
$852$	7.20859	−	4.92778i	0.246962	−	0.168823i
$853$	18.0934	+	35.5102i	0.619505	+	1.21585i	0.961152	+	0.276019i	$0.0890152\pi$
$853$	18.0934	+	35.5102i	0.619505	+	1.21585i	−0.341647	+	0.939828i	$0.610985\pi$
$854$	0.667799	−	2.05527i	0.0228516	−	0.0703300i
$855$		0			0
$856$	−0.200057	−	0.615712i	−0.00683780	−	0.0210446i
$857$	−24.3570	+	24.3570i	−0.832018	+	0.832018i	−0.987793	−	0.155774i	$-0.950213\pi$
$857$	−24.3570	+	24.3570i	−0.832018	+	0.832018i	0.155774	+	0.987793i	$0.450213\pi$
$858$	−6.83806	−	23.2991i	−0.233447	−	0.795418i
$859$	−12.1583	+	16.7344i	−0.414835	+	0.570971i	−0.964389	−	0.264487i	$-0.914797\pi$
$859$	−12.1583	+	16.7344i	−0.414835	+	0.570971i	0.549555	+	0.835458i	$0.314797\pi$
$860$		0			0
$861$	−0.102398	+	0.544871i	−0.00348973	+	0.0185692i
$862$	−2.75506	−	17.3948i	−0.0938378	−	0.592468i
$863$	−9.03734	−	57.0595i	−0.307634	−	1.94233i	−0.333731	−	0.942668i	$-0.608308\pi$
$863$	−9.03734	−	57.0595i	−0.307634	−	1.94233i	0.0260968	−	0.999659i	$-0.491692\pi$
$864$	1.25096	−	5.04332i	0.0425584	−	0.171577i
$865$		0			0
$866$	−5.33218	+	7.33912i	−0.181195	+	0.249393i
$867$	5.38937	−	1.58173i	0.183033	−	0.0537183i
$868$	0.832112	−	0.832112i	0.0282437	−	0.0282437i
$869$	8.59232	+	26.4445i	0.291475	+	0.897067i
$870$		0			0
$871$	5.10228	−	15.7032i	0.172884	−	0.532083i
$872$	0.0341904	+	0.0671024i	0.00115783	+	0.00227237i
$873$	27.1748	+	5.91864i	0.919727	+	0.200316i
$874$		−	17.2948i		−	0.585006i
$875$		0			0
$876$	−12.7948	−	13.5507i	−0.432295	−	0.457835i
$877$	39.1633	+	6.20286i	1.32245	+	0.209456i	0.777432	−	0.628967i	$-0.216522\pi$
$877$	39.1633	+	6.20286i	1.32245	+	0.209456i	0.545020	+	0.838423i	$0.316522\pi$
$878$	−25.7429	+	13.1166i	−0.868779	+	0.442665i
$879$	3.95167	−	1.87271i	0.133287	−	0.0631651i
$880$		0			0
$881$	−17.2013	+	5.58904i	−0.579526	+	0.188299i	−0.584088	−	0.811690i	$-0.698548\pi$
$881$	−17.2013	+	5.58904i	−0.579526	+	0.188299i	0.00456226	+	0.999990i	$0.498548\pi$
$882$	13.9297	+	15.6272i	0.469036	+	0.526196i
$883$	−43.8739	−	22.3549i	−1.47647	−	0.752301i	−0.484037	−	0.875048i	$-0.660830\pi$
$883$	−43.8739	−	22.3549i	−1.47647	−	0.752301i	−0.992438	+	0.122746i	$0.960830\pi$
$884$	−13.6418	−	9.91133i	−0.458823	−	0.333354i
$885$		0			0
$886$	−14.2445	+	10.3492i	−0.478552	+	0.347689i
$887$	−9.93256	+	1.57316i	−0.333503	+	0.0528216i	−0.320940	−	0.947099i	$-0.603999\pi$
$887$	−9.93256	+	1.57316i	−0.333503	+	0.0528216i	−0.0125625	+	0.999921i	$0.503999\pi$
$888$	8.89169	−	11.5280i	0.298385	−	0.386853i
$889$	−0.775544	−	1.06745i	−0.0260109	−	0.0358010i
$890$		0			0
$891$	18.7763	−	20.4376i	0.629031	−	0.684685i
$892$	8.85794	−	17.3847i	0.296586	−	0.582082i
$893$	13.2625	+	13.2625i	0.443813	+	0.443813i
$894$	23.4831	+	12.8266i	0.785393	+	0.428985i
$895$		0			0
$896$	−0.140729	−	0.0457256i	−0.00470143	−	0.00152759i
$897$	−13.0869	+	36.6641i	−0.436959	+	1.22418i
$898$	−2.01023	+	12.6921i	−0.0670823	+	0.423541i
$899$	−13.1098			−0.437236
$900$		0			0
$901$	42.8268			1.42677
$902$	−1.04351	+	6.58847i	−0.0347451	+	0.219372i
$903$	0.337575	−	0.945745i	0.0112338	−	0.0314724i
$904$	−16.2790	−	5.28938i	−0.541433	−	0.175922i
$905$		0			0
$906$	−10.7796	−	5.88784i	−0.358127	−	0.195610i
$907$	−22.2868	−	22.2868i	−0.740021	−	0.740021i	0.232561	−	0.972582i	$-0.425290\pi$
$907$	−22.2868	−	22.2868i	−0.740021	−	0.740021i	−0.972582	+	0.232561i	$0.925290\pi$
$908$	5.48620	−	10.7673i	0.182066	−	0.357324i
$909$	7.96080	−	9.73068i	0.264043	−	0.322746i
$910$		0			0
$911$	3.12524	+	4.30152i	0.103544	+	0.142516i	0.857645	−	0.514243i	$-0.171927\pi$
$911$	3.12524	+	4.30152i	0.103544	+	0.142516i	−0.754101	+	0.656759i	$0.771927\pi$
$912$	−3.70055	+	4.79771i	−0.122537	+	0.158868i
$913$	30.8009	−	4.87839i	1.01936	−	0.161451i
$914$	−12.5639	+	9.12823i	−0.415578	+	0.301935i
$915$		0			0
$916$	5.00795	+	3.63849i	0.165467	+	0.120219i
$917$	−0.222600	−	0.113420i	−0.00735089	−	0.00374546i
$918$	1.65649	−	19.2016i	0.0546723	−	0.633746i
$919$	21.4823	−	6.98001i	0.708635	−	0.230249i	0.0675461	−	0.997716i	$-0.478483\pi$
$919$	21.4823	−	6.98001i	0.708635	−	0.230249i	0.641089	+	0.767467i	$0.278483\pi$
$920$		0			0
$921$	−40.1432	+	19.0240i	−1.32276	+	0.626864i
$922$	−9.99809	+	5.09428i	−0.329270	+	0.167771i
$923$	22.6370	+	3.58534i	0.745105	+	0.118013i
$924$	−0.542592	−	0.574649i	−0.0178500	−	0.0189045i
$925$		0			0
$926$			1.29066i			0.0424139i
$927$	−11.1735	+	51.3019i	−0.366986	+	1.68498i
$928$	0.748381	+	1.46878i	0.0245668	+	0.0482151i
$929$	−14.5401	+	44.7499i	−0.477046	+	1.46820i	0.366132	+	0.930563i	$0.380682\pi$
$929$	−14.5401	+	44.7499i	−0.477046	+	1.46820i	−0.843178	+	0.537634i	$0.819318\pi$
$930$		0			0
$931$	−7.54334	−	23.2160i	−0.247223	−	0.760874i
$932$	−5.35655	+	5.35655i	−0.175460	+	0.175460i
$933$	17.5036	−	5.13714i	0.573043	−	0.168183i
$934$	21.5074	−	29.6023i	0.703743	−	0.968618i
$935$		0			0
$936$	11.4754	−	7.37071i	0.375084	−	0.240919i
$937$	5.23090	+	33.0266i	0.170886	+	1.07893i	0.912791	+	0.408427i	$0.133923\pi$
$937$	5.23090	+	33.0266i	0.170886	+	1.07893i	−0.741905	+	0.670505i	$0.766077\pi$
$938$	−0.0840705	−	0.530801i	−0.00274500	−	0.0173313i
$939$	5.66367	−	30.1369i	0.184827	−	0.983480i
$940$		0			0
$941$	−3.42075	+	4.70826i	−0.111513	+	0.153485i	−0.861126	−	0.508392i	$-0.830240\pi$
$941$	−3.42075	+	4.70826i	−0.111513	+	0.153485i	0.749612	+	0.661877i	$0.230240\pi$
$942$	−3.52374	−	12.0063i	−0.114810	−	0.391187i
$943$	7.56223	−	7.56223i	0.246260	−	0.246260i
$944$	−3.98035	−	12.2503i	−0.129549	−	0.398712i
$945$		0			0
$946$	3.73363	−	11.4909i	0.121391	−	0.373602i
$947$	−7.66387	−	15.0412i	−0.249042	−	0.488773i	0.732315	−	0.680966i	$-0.238440\pi$
$947$	−7.66387	−	15.0412i	−0.249042	−	0.488773i	−0.981357	+	0.192193i	$0.938440\pi$
$948$	−12.8931	+	8.81368i	−0.418747	+	0.286255i
$949$		−	48.9166i		−	1.58790i
$950$		0			0
$951$	−6.41377	+	6.05598i	−0.207981	+	0.196379i
$952$	−0.542079	−	0.0858568i	−0.0175689	−	0.00278264i
$953$	−15.8844	+	8.09351i	−0.514547	+	0.262175i	−0.691927	−	0.721968i	$-0.743238\pi$
$953$	−15.8844	+	8.09351i	−0.514547	+	0.262175i	0.177380	+	0.984142i	$0.443238\pi$
$954$	−12.5756	+	32.2762i	−0.407149	+	1.04498i
$955$		0			0
$956$	16.0554	−	5.21673i	0.519270	−	0.168721i
$957$	−0.252526	+	8.80096i	−0.00816301	+	0.284495i
$958$	24.7755	+	12.6238i	0.800460	+	0.407855i
$959$	−1.75090	−	1.27210i	−0.0565396	−	0.0410784i
$960$		0			0
$961$	−26.0882	+	18.9542i	−0.841556	+	0.611426i
$962$	37.7425	−	5.97782i	1.21687	−	0.192733i
$963$	1.93255	−	0.193334i	0.0622754	−	0.00623010i
$964$	5.78866	+	7.96740i	0.186440	+	0.256613i
$965$		0			0
$966$	0.162242	+	1.25667i	0.00522005	+	0.0404326i
$967$	−18.3163	+	35.9477i	−0.589011	+	1.15600i	0.383586	+	0.923505i	$0.374689\pi$
$967$	−18.3163	+	35.9477i	−0.589011	+	1.15600i	−0.972598	+	0.232495i	$0.925311\pi$
$968$	1.05415	+	1.05415i	0.0338816	+	0.0338816i
$969$	−10.7728	+	19.7231i	−0.346074	+	0.633598i
$970$		0			0
$971$	25.6210	+	8.32477i	0.822217	+	0.267155i	0.689764	−	0.724035i	$-0.257714\pi$
$971$	25.6210	+	8.32477i	0.822217	+	0.267155i	0.132454	+	0.991189i	$0.457714\pi$
$972$	13.9847	+	6.88671i	0.448561	+	0.220891i
$973$	−0.412752	+	2.60601i	−0.0132322	+	0.0835449i
$974$	−9.57080			−0.306668
$975$		0			0
$976$	14.6045			0.467478
$977$	1.79808	−	11.3526i	0.0575256	−	0.363202i	−0.942087	−	0.335369i	$-0.891139\pi$
$977$	1.79808	−	11.3526i	0.0575256	−	0.363202i	0.999613	−	0.0278335i	$-0.00886083\pi$
$978$	3.49429	+	1.24725i	0.111735	+	0.0398828i
$979$	−22.2337	−	7.22418i	−0.710593	−	0.230886i
$980$		0			0
$981$	−0.218524	+	0.0573814i	−0.00697694	+	0.00183205i
$982$	7.38969	+	7.38969i	0.235814	+	0.235814i
$983$	14.5645	−	28.5844i	0.464535	−	0.911702i	−0.533299	−	0.845927i	$-0.679048\pi$
$983$	14.5645	−	28.5844i	0.464535	−	0.911702i	0.997834	−	0.0657754i	$-0.0209521\pi$
$984$	−3.71590	+	0.479740i	−0.118458	+	0.0152935i
$985$		0			0
$986$	3.59385	+	4.94651i	0.114451	+	0.157529i
$987$	−1.08809	−	0.839259i	−0.0346343	−	0.0267139i
$988$	−15.7077	+	2.48785i	−0.499728	+	0.0791491i
$989$	−15.6713	+	11.3859i	−0.498320	+	0.362051i
$990$		0			0
$991$	12.7382	+	9.25484i	0.404642	+	0.293990i	0.771429	−	0.636315i	$-0.219542\pi$
$991$	12.7382	+	9.25484i	0.404642	+	0.293990i	−0.366787	+	0.930305i	$0.619542\pi$
$992$	7.08598	+	3.61049i	0.224980	+	0.114633i
$993$	25.4371	+	0.729868i	0.807223	+	0.0231617i
$994$	0.709470	−	0.230521i	0.0225030	−	0.00731167i
$995$		0			0
$996$	7.50116	+	15.8284i	0.237683	+	0.501543i
$997$	−8.15491	+	4.15513i	−0.258269	+	0.131594i	−0.578331	−	0.815802i	$-0.696296\pi$
$997$	−8.15491	+	4.15513i	−0.258269	+	0.131594i	0.320063	+	0.947396i	$0.396296\pi$
$998$	14.8270	+	2.34837i	0.469341	+	0.0743363i
$999$	28.1150	+	33.4238i	0.889518	+	1.05748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.a.407.8		80
3.2	odd	2	inner	750.2.l.a.407.5		80
5.2	odd	4		150.2.l.a.23.10	yes	80
5.3	odd	4		750.2.l.b.593.1		80
5.4	even	2		750.2.l.c.407.3		80
15.2	even	4		150.2.l.a.23.3	✓	80
15.8	even	4		750.2.l.b.593.8		80
15.14	odd	2		750.2.l.c.407.6		80
25.9	even	10		150.2.l.a.137.3	yes	80
25.12	odd	20		750.2.l.c.293.6		80
25.13	odd	20	inner	750.2.l.a.293.5		80
25.16	even	5		750.2.l.b.707.8		80
75.38	even	20	inner	750.2.l.a.293.8		80
75.41	odd	10		750.2.l.b.707.1		80
75.59	odd	10		150.2.l.a.137.10	yes	80
75.62	even	20		750.2.l.c.293.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.23.3	✓	80	15.2	even	4
150.2.l.a.23.10	yes	80	5.2	odd	4
150.2.l.a.137.3	yes	80	25.9	even	10
150.2.l.a.137.10	yes	80	75.59	odd	10
750.2.l.a.293.5		80	25.13	odd	20	inner
750.2.l.a.293.8		80	75.38	even	20	inner
750.2.l.a.407.5		80	3.2	odd	2	inner
750.2.l.a.407.8		80	1.1	even	1	trivial
750.2.l.b.593.1		80	5.3	odd	4
750.2.l.b.593.8		80	15.8	even	4
750.2.l.b.707.1		80	75.41	odd	10
750.2.l.b.707.8		80	25.16	even	5
750.2.l.c.293.3		80	75.62	even	20
750.2.l.c.293.6		80	25.12	odd	20
750.2.l.c.407.3		80	5.4	even	2
750.2.l.c.407.6		80	15.14	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(-0.582259 + 1.63125i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.52008 + 0.830274i) q^{6} +(0.104631 + 0.104631i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.32195 - 1.89962i) q^{9} +O(q^{10})\)	\(q+(0.156434 - 0.987688i) q^{2} +(-0.582259 + 1.63125i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.52008 + 0.830274i) q^{6} +(0.104631 + 0.104631i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.32195 - 1.89962i) q^{9} +(-1.81255 - 2.49477i) q^{11} +(1.05784 - 1.37148i) q^{12} +(4.49023 - 0.711182i) q^{13} +(0.119711 - 0.0869753i) q^{14} +(0.809017 + 0.587785i) q^{16} +(3.30481 + 1.68388i) q^{17} +(-2.23946 + 1.99620i) q^{18} +(3.32698 - 1.08100i) q^{19} +(-0.231603 + 0.109757i) q^{21} +(-2.74760 + 1.39997i) q^{22} +(4.88306 + 0.773401i) q^{23} +(-1.18911 - 1.25937i) q^{24} -4.54620i q^{26} +(4.45073 - 2.68161i) q^{27} +(-0.0671775 - 0.131843i) q^{28} +(-0.509399 + 1.56777i) q^{29} +(2.45755 + 7.56355i) q^{31} +(0.707107 - 0.707107i) q^{32} +(5.12496 - 1.50413i) q^{33} +(2.18014 - 3.00070i) q^{34} +(1.62129 + 2.52417i) q^{36} +(1.31491 + 8.30199i) q^{37} +(-0.547238 - 3.45513i) q^{38} +(-1.45436 + 7.73877i) q^{39} +(1.27149 - 1.75005i) q^{41} +(0.0721755 + 0.245921i) q^{42} +(-2.77052 + 2.77052i) q^{43} +(0.952916 + 2.93277i) q^{44} +(1.52776 - 4.70196i) q^{46} +(2.43413 + 4.77725i) q^{47} +(-1.42988 + 0.977465i) q^{48} -6.97810i q^{49} +(-4.67109 + 4.41051i) q^{51} +(-4.49023 - 0.711182i) q^{52} +(10.2880 - 5.24200i) q^{53} +(-1.95235 - 4.81543i) q^{54} +(-0.140729 + 0.0457256i) q^{56} +(-0.173781 + 6.05656i) q^{57} +(1.46878 + 0.748381i) q^{58} +(-10.4207 - 7.57107i) q^{59} +(11.8153 - 8.58430i) q^{61} +(7.85487 - 1.24409i) q^{62} +(-0.0441891 - 0.441709i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.683889 - 5.29716i) q^{66} +(1.64885 - 3.23605i) q^{67} +(-2.62271 - 2.62271i) q^{68} +(-4.10482 + 7.51517i) q^{69} +(4.79465 + 1.55788i) q^{71} +(2.74672 - 1.20646i) q^{72} +(1.68322 - 10.6274i) q^{73} +8.40547 q^{74} -3.49819 q^{76} +(0.0713809 - 0.450681i) q^{77} +(7.41598 + 2.64706i) q^{78} +(-8.57556 - 2.78637i) q^{79} +(1.78290 + 8.82164i) q^{81} +(-1.52960 - 1.52960i) q^{82} +(-4.59112 + 9.01058i) q^{83} +(0.254184 - 0.0328164i) q^{84} +(2.30301 + 3.16982i) q^{86} +(-2.26082 - 1.74381i) q^{87} +(3.04574 - 0.482397i) q^{88} +(6.13326 - 4.45607i) q^{89} +(0.544231 + 0.395407i) q^{91} +(-4.40507 - 2.24450i) q^{92} +(-13.7690 - 0.395073i) q^{93} +(5.09921 - 1.65683i) q^{94} +(0.741748 + 1.56519i) q^{96} +(-8.26018 + 4.20877i) q^{97} +(-6.89219 - 1.09162i) q^{98} +(-0.530447 + 9.23588i) 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

Related objects

Downloads

Learn more