LMFDB - Embedded newform 930.2.j.h.497.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.17
Character	$\chi$	$=$	930.497
Dual form			930.2.j.h.683.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.10591 - 1.33303i) q^{3} -1.00000i q^{4} +(0.368595 + 2.20548i) q^{5} +(-0.160600 - 1.72459i) q^{6} +(-2.86656 - 2.86656i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.553937 - 2.94842i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.10591 - 1.33303i) q^{3} -1.00000i q^{4} +(0.368595 + 2.20548i) q^{5} +(-0.160600 - 1.72459i) q^{6} +(-2.86656 - 2.86656i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.553937 - 2.94842i) q^{9} +(1.82015 + 1.29887i) q^{10} +0.0722722i q^{11} +(-1.33303 - 1.10591i) q^{12} +(2.91767 - 2.91767i) q^{13} -4.05393 q^{14} +(3.34760 + 1.94771i) q^{15} -1.00000 q^{16} +(4.16969 - 4.16969i) q^{17} +(-2.47654 - 1.69315i) q^{18} +3.12636i q^{19} +(2.20548 - 0.368595i) q^{20} +(-6.99136 + 0.651060i) q^{21} +(0.0511042 + 0.0511042i) q^{22} +(-1.55408 - 1.55408i) q^{23} +(-1.72459 + 0.160600i) q^{24} +(-4.72828 + 1.62586i) q^{25} -4.12620i q^{26} +(-4.54293 - 2.52226i) q^{27} +(-2.86656 + 2.86656i) q^{28} -3.03469 q^{29} +(3.74435 - 0.989874i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.0963410 + 0.0799264i) q^{33} -5.89683i q^{34} +(5.26554 - 7.37874i) q^{35} +(-2.94842 + 0.553937i) q^{36} +(-5.90545 - 5.90545i) q^{37} +(2.21067 + 2.21067i) q^{38} +(-0.662667 - 7.11600i) q^{39} +(1.29887 - 1.82015i) q^{40} +1.90694i q^{41} +(-4.48327 + 5.40401i) q^{42} +(-0.388846 + 0.388846i) q^{43} +0.0722722 q^{44} +(6.29849 - 2.30847i) q^{45} -2.19780 q^{46} +(2.00099 - 2.00099i) q^{47} +(-1.10591 + 1.33303i) q^{48} +9.43435i q^{49} +(-2.19374 + 4.49305i) q^{50} +(-0.947029 - 10.1696i) q^{51} +(-2.91767 - 2.91767i) q^{52} +(6.68933 + 6.68933i) q^{53} +(-4.99584 + 1.42883i) q^{54} +(-0.159395 + 0.0266392i) q^{55} +4.05393i q^{56} +(4.16753 + 3.45747i) q^{57} +(-2.14585 + 2.14585i) q^{58} +2.33823 q^{59} +(1.94771 - 3.34760i) q^{60} +12.8123 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-6.86392 + 10.0397i) q^{63} +1.00000i q^{64} +(7.51029 + 5.35941i) q^{65} +(0.124640 - 0.0116069i) q^{66} +(7.43129 + 7.43129i) q^{67} +(-4.16969 - 4.16969i) q^{68} +(-3.79031 + 0.352967i) q^{69} +(-1.49426 - 8.94086i) q^{70} -5.69625i q^{71} +(-1.69315 + 2.47654i) q^{72} +(6.06642 - 6.06642i) q^{73} -8.35157 q^{74} +(-3.06172 + 8.10098i) q^{75} +3.12636 q^{76} +(0.207173 - 0.207173i) q^{77} +(-5.50035 - 4.56320i) q^{78} -7.62446i q^{79} +(-0.368595 - 2.20548i) q^{80} +(-8.38631 + 3.26647i) q^{81} +(1.34841 + 1.34841i) q^{82} +(0.153300 + 0.153300i) q^{83} +(0.651060 + 6.99136i) q^{84} +(10.7331 + 7.65924i) q^{85} +0.549911i q^{86} +(-3.35608 + 4.04533i) q^{87} +(0.0511042 - 0.0511042i) q^{88} +13.6113 q^{89} +(2.82137 - 6.08604i) q^{90} -16.7273 q^{91} +(-1.55408 + 1.55408i) q^{92} +(-1.10591 + 1.33303i) q^{93} -2.82982i q^{94} +(-6.89512 + 1.15236i) q^{95} +(0.160600 + 1.72459i) q^{96} +(-2.66031 - 2.66031i) q^{97} +(6.67109 + 6.67109i) q^{98} +(0.213089 - 0.0400343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.10591	−	1.33303i	0.638496	−	0.769625i
$3$	1.10591	−	1.33303i	0.638496	−	0.769625i
$4$		−	1.00000i		−	0.500000i
$5$	0.368595	+	2.20548i	0.164841	+	0.986320i
$5$	0.368595	+	2.20548i	0.164841	+	0.986320i
$6$	−0.160600	−	1.72459i	−0.0655646	−	0.704061i
$7$	−2.86656	−	2.86656i	−1.08346	−	1.08346i	−0.996184	−	0.0872740i	$-0.972184\pi$
$7$	−2.86656	−	2.86656i	−1.08346	−	1.08346i	−0.0872740	−	0.996184i	$-0.527816\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.553937	−	2.94842i	−0.184646	−	0.982805i
$10$	1.82015	+	1.29887i	0.575580	+	0.410740i
$11$			0.0722722i			0.0217909i	0.999941	+	0.0108954i	$0.00346820\pi$
$11$			0.0722722i			0.0217909i	−0.999941	+	0.0108954i	$0.996532\pi$
$12$	−1.33303	−	1.10591i	−0.384813	−	0.319248i
$13$	2.91767	−	2.91767i	0.809215	−	0.809215i	−0.175300	−	0.984515i	$-0.556090\pi$
$13$	2.91767	−	2.91767i	0.809215	−	0.809215i	0.984515	+	0.175300i	$0.0560896\pi$
$14$	−4.05393			−1.08346
$15$	3.34760	+	1.94771i	0.864347	+	0.502896i
$16$	−1.00000			−0.250000
$17$	4.16969	−	4.16969i	1.01130	−	1.01130i	0.0113627	−	0.999935i	$-0.496383\pi$
$17$	4.16969	−	4.16969i	1.01130	−	1.01130i	0.999935	−	0.0113627i	$-0.00361694\pi$
$18$	−2.47654	−	1.69315i	−0.583725	−	0.399080i
$19$			3.12636i			0.717236i	0.933484	+	0.358618i	$0.116752\pi$
$19$			3.12636i			0.717236i	−0.933484	+	0.358618i	$0.883248\pi$
$20$	2.20548	−	0.368595i	0.493160	−	0.0824203i
$21$	−6.99136	+	0.651060i	−1.52564	+	0.142073i
$22$	0.0511042	+	0.0511042i	0.0108954	+	0.0108954i
$23$	−1.55408	−	1.55408i	−0.324049	−	0.324049i	0.526269	−	0.850318i	$-0.323590\pi$
$23$	−1.55408	−	1.55408i	−0.324049	−	0.324049i	−0.850318	+	0.526269i	$0.823590\pi$
$24$	−1.72459	+	0.160600i	−0.352030	+	0.0327823i
$25$	−4.72828	+	1.62586i	−0.945655	+	0.325171i
$26$		−	4.12620i		−	0.809215i
$27$	−4.54293	−	2.52226i	−0.874287	−	0.485409i
$28$	−2.86656	+	2.86656i	−0.541729	+	0.541729i
$29$	−3.03469			−0.563527			−0.281764	−	0.959484i	$-0.590919\pi$
$29$	−3.03469			−0.563527			−0.281764	+	0.959484i	$0.590919\pi$
$30$	3.74435	−	0.989874i	0.683621	−	0.180725i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.0963410	+	0.0799264i	0.0167708	+	0.0139134i
$34$		−	5.89683i		−	1.01130i
$35$	5.26554	−	7.37874i	0.890039	−	1.24723i
$36$	−2.94842	+	0.553937i	−0.491403	+	0.0923228i
$37$	−5.90545	−	5.90545i	−0.970851	−	0.970851i	0.0287364	−	0.999587i	$-0.490852\pi$
$37$	−5.90545	−	5.90545i	−0.970851	−	0.970851i	−0.999587	+	0.0287364i	$0.990852\pi$
$38$	2.21067	+	2.21067i	0.358618	+	0.358618i
$39$	−0.662667	−	7.11600i	−0.106112	−	1.13947i
$40$	1.29887	−	1.82015i	0.205370	−	0.287790i
$41$			1.90694i			0.297814i	0.988851	+	0.148907i	$0.0475755\pi$
$41$			1.90694i			0.297814i	−0.988851	+	0.148907i	$0.952425\pi$
$42$	−4.48327	+	5.40401i	−0.691784	+	0.833857i
$43$	−0.388846	+	0.388846i	−0.0592984	+	0.0592984i	−0.736134	−	0.676836i	$-0.763351\pi$
$43$	−0.388846	+	0.388846i	−0.0592984	+	0.0592984i	0.676836	+	0.736134i	$0.263351\pi$
$44$	0.0722722			0.0108954
$45$	6.29849	−	2.30847i	0.938923	−	0.344126i
$46$	−2.19780			−0.324049
$47$	2.00099	−	2.00099i	0.291874	−	0.291874i	−0.545946	−	0.837820i	$-0.683830\pi$
$47$	2.00099	−	2.00099i	0.291874	−	0.291874i	0.837820	+	0.545946i	$0.183830\pi$
$48$	−1.10591	+	1.33303i	−0.159624	+	0.192406i
$49$			9.43435i			1.34776i
$50$	−2.19374	+	4.49305i	−0.310242	+	0.635413i
$51$	−0.947029	−	10.1696i	−0.132611	−	1.42403i
$52$	−2.91767	−	2.91767i	−0.404607	−	0.404607i
$53$	6.68933	+	6.68933i	0.918851	+	0.918851i	0.996946	−	0.0780952i	$-0.0248838\pi$
$53$	6.68933	+	6.68933i	0.918851	+	0.918851i	−0.0780952	+	0.996946i	$0.524884\pi$
$54$	−4.99584	+	1.42883i	−0.679848	+	0.194439i
$55$	−0.159395	+	0.0266392i	−0.0214928	+	0.00359203i
$56$			4.05393i			0.541729i
$57$	4.16753	+	3.45747i	0.552003	+	0.457953i
$58$	−2.14585	+	2.14585i	−0.281764	+	0.281764i
$59$	2.33823			0.304411			0.152206	−	0.988349i	$-0.451362\pi$
$59$	2.33823			0.304411			0.152206	+	0.988349i	$0.451362\pi$
$60$	1.94771	−	3.34760i	0.251448	−	0.432173i
$61$	12.8123			1.64045			0.820224	−	0.572043i	$-0.193849\pi$
$61$	12.8123			1.64045			0.820224	+	0.572043i	$0.193849\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	−6.86392	+	10.0397i	−0.864773	+	1.26488i
$64$			1.00000i			0.125000i
$65$	7.51029	+	5.35941i	0.931536	+	0.664753i
$66$	0.124640	−	0.0116069i	0.0153421	−	0.00142871i
$67$	7.43129	+	7.43129i	0.907876	+	0.907876i	0.996101	−	0.0882246i	$-0.0281193\pi$
$67$	7.43129	+	7.43129i	0.907876	+	0.907876i	−0.0882246	+	0.996101i	$0.528119\pi$
$68$	−4.16969	−	4.16969i	−0.505649	−	0.505649i
$69$	−3.79031	+	0.352967i	−0.456300	+	0.0424922i
$70$	−1.49426	−	8.94086i	−0.178598	−	1.06864i
$71$		−	5.69625i		−	0.676020i	−0.941142	−	0.338010i	$-0.890246\pi$
$71$		−	5.69625i		−	0.676020i	0.941142	−	0.338010i	$-0.109754\pi$
$72$	−1.69315	+	2.47654i	−0.199540	+	0.291863i
$73$	6.06642	−	6.06642i	0.710021	−	0.710021i	−0.256518	−	0.966539i	$-0.582575\pi$
$73$	6.06642	−	6.06642i	0.710021	−	0.710021i	0.966539	+	0.256518i	$0.0825754\pi$
$74$	−8.35157			−0.970851
$75$	−3.06172	+	8.10098i	−0.353537	+	0.935421i
$76$	3.12636			0.358618
$77$	0.207173	−	0.207173i	0.0236095	−	0.0236095i
$78$	−5.50035	−	4.56320i	−0.622792	−	0.516680i
$79$		−	7.62446i		−	0.857819i	−0.903348	−	0.428909i	$-0.858898\pi$
$79$		−	7.62446i		−	0.857819i	0.903348	−	0.428909i	$-0.141102\pi$
$80$	−0.368595	−	2.20548i	−0.0412102	−	0.246580i
$81$	−8.38631	+	3.26647i	−0.931812	+	0.362941i
$82$	1.34841	+	1.34841i	0.148907	+	0.148907i
$83$	0.153300	+	0.153300i	0.0168269	+	0.0168269i	0.715470	−	0.698643i	$-0.246213\pi$
$83$	0.153300	+	0.153300i	0.0168269	+	0.0168269i	−0.698643	+	0.715470i	$0.746213\pi$
$84$	0.651060	+	6.99136i	0.0710365	+	0.762820i
$85$	10.7331	+	7.65924i	1.16417	+	0.830761i
$86$			0.549911i			0.0592984i
$87$	−3.35608	+	4.04533i	−0.359810	+	0.433705i
$88$	0.0511042	−	0.0511042i	0.00544772	−	0.00544772i
$89$	13.6113			1.44280			0.721398	−	0.692521i	$-0.243500\pi$
$89$	13.6113			1.44280			0.721398	+	0.692521i	$0.243500\pi$
$90$	2.82137	−	6.08604i	0.297399	−	0.641525i
$91$	−16.7273			−1.75350
$92$	−1.55408	+	1.55408i	−0.162024	+	0.162024i
$93$	−1.10591	+	1.33303i	−0.114677	+	0.138229i
$94$		−	2.82982i		−	0.291874i
$95$	−6.89512	+	1.15236i	−0.707425	+	0.118230i
$96$	0.160600	+	1.72459i	0.0163911	+	0.176015i
$97$	−2.66031	−	2.66031i	−0.270113	−	0.270113i	0.559033	−	0.829146i	$-0.311173\pi$
$97$	−2.66031	−	2.66031i	−0.270113	−	0.270113i	−0.829146	+	0.559033i	$0.811173\pi$
$98$	6.67109	+	6.67109i	0.673882	+	0.673882i
$99$	0.213089	−	0.0400343i	0.0214162	−	0.00402360i
$100$	1.62586	+	4.72828i	0.162586	+	0.472828i
$101$			13.9690i			1.38997i	0.719026	+	0.694983i	$0.244588\pi$
$101$			13.9690i			1.38997i	−0.719026	+	0.694983i	$0.755412\pi$
$102$	−7.86065	−	6.52135i	−0.778320	−	0.645710i
$103$	9.62776	−	9.62776i	0.948652	−	0.948652i	−0.0500930	−	0.998745i	$-0.515952\pi$
$103$	9.62776	−	9.62776i	0.948652	−	0.948652i	0.998745	+	0.0500930i	$0.0159518\pi$
$104$	−4.12620			−0.404607
$105$	−4.01288	−	15.1793i	−0.391617	−	1.48135i
$106$	9.46015			0.918851
$107$	−13.2804	+	13.2804i	−1.28386	+	1.28386i	−0.345411	+	0.938451i	$0.612261\pi$
$107$	−13.2804	+	13.2804i	−1.28386	+	1.28386i	−0.938451	+	0.345411i	$0.887739\pi$
$108$	−2.52226	+	4.54293i	−0.242705	+	0.437144i
$109$			12.0047i			1.14984i	0.818210	+	0.574920i	$0.194967\pi$
$109$			12.0047i			1.14984i	−0.818210	+	0.574920i	$0.805033\pi$
$110$	−0.0938725	+	0.131546i	−0.00895039	+	0.0125424i
$111$	−14.4030	+	1.34126i	−1.36708	+	0.127307i
$112$	2.86656	+	2.86656i	0.270865	+	0.270865i
$113$	14.5548	+	14.5548i	1.36920	+	1.36920i	0.861578	+	0.507625i	$0.169476\pi$
$113$	14.5548	+	14.5548i	1.36920	+	1.36920i	0.507625	+	0.861578i	$0.330524\pi$
$114$	5.39169	−	0.502093i	0.504978	−	0.0470253i
$115$	2.85467	−	4.00032i	0.266199	−	0.373032i
$116$			3.03469i			0.281764i
$117$	−10.2187	−	6.98629i	−0.944719	−	0.645882i
$118$	1.65338	−	1.65338i	0.152206	−	0.152206i
$119$	−23.9053			−2.19140
$120$	−0.989874	−	3.74435i	−0.0903627	−	0.341811i
$121$	10.9948			0.999525
$122$	9.05967	−	9.05967i	0.820224	−	0.820224i
$123$	2.54201	+	2.10890i	0.229205	+	0.190153i
$124$			1.00000i			0.0898027i
$125$	−5.32861	−	9.82883i	−0.476605	−	0.879117i
$126$	2.24562	+	11.9527i	0.200056	+	1.06483i
$127$	−2.77146	−	2.77146i	−0.245928	−	0.245928i	0.573369	−	0.819297i	$-0.305636\pi$
$127$	−2.77146	−	2.77146i	−0.245928	−	0.245928i	−0.819297	+	0.573369i	$0.805636\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	0.0883156	+	0.948371i	0.00777575	+	0.0834994i
$130$	9.10025	−	1.52090i	0.798145	−	0.133391i
$131$			15.2844i			1.33540i	0.744429	+	0.667702i	$0.232722\pi$
$131$			15.2844i			1.33540i	−0.744429	+	0.667702i	$0.767278\pi$
$132$	0.0799264	−	0.0963410i	0.00695670	−	0.00838541i
$133$	8.96191	−	8.96191i	0.777096	−	0.777096i
$134$	10.5094			0.907876
$135$	3.88829	−	10.9490i	0.334651	−	0.942342i
$136$	−5.89683			−0.505649
$137$	3.94097	−	3.94097i	0.336699	−	0.336699i	−0.518424	−	0.855124i	$-0.673481\pi$
$137$	3.94097	−	3.94097i	0.336699	−	0.336699i	0.855124	+	0.518424i	$0.173481\pi$
$138$	−2.43057	+	2.92974i	−0.206904	+	0.249396i
$139$			10.9204i			0.926258i	0.886291	+	0.463129i	$0.153273\pi$
$139$			10.9204i			0.926258i	−0.886291	+	0.463129i	$0.846727\pi$
$140$	−7.37874	−	5.26554i	−0.623617	−	0.445019i
$141$	−0.454469	−	4.88028i	−0.0382732	−	0.410994i
$142$	−4.02786	−	4.02786i	−0.338010	−	0.338010i
$143$	0.210866	+	0.210866i	0.0176335	+	0.0176335i
$144$	0.553937	+	2.94842i	0.0461614	+	0.245701i
$145$	−1.11857	−	6.69294i	−0.0928922	−	0.555818i
$146$		−	8.57922i		−	0.710021i
$147$	12.5763	+	10.4335i	1.03727	+	0.860542i
$148$	−5.90545	+	5.90545i	−0.485425	+	0.485425i
$149$	−11.2480			−0.921468			−0.460734	−	0.887538i	$-0.652414\pi$
$149$	−11.2480			−0.921468			−0.460734	+	0.887538i	$0.652414\pi$
$150$	3.56329	+	7.89322i	0.290942	+	0.644479i
$151$	−11.8924			−0.967789			−0.483895	−	0.875126i	$-0.660778\pi$
$151$	−11.8924			−0.967789			−0.483895	+	0.875126i	$0.660778\pi$
$152$	2.21067	−	2.21067i	0.179309	−	0.179309i
$153$	−14.6037	−	9.98423i	−1.18064	−	0.807177i
$154$		−	0.292987i		−	0.0236095i
$155$	−0.368595	−	2.20548i	−0.0296063	−	0.177148i
$156$	−7.11600	+	0.662667i	−0.569736	+	0.0530558i
$157$	−0.977475	−	0.977475i	−0.0780110	−	0.0780110i	0.667025	−	0.745036i	$-0.267568\pi$
$157$	−0.977475	−	0.977475i	−0.0780110	−	0.0780110i	−0.745036	+	0.667025i	$0.767568\pi$
$158$	−5.39131	−	5.39131i	−0.428909	−	0.428909i
$159$	16.3149	−	1.51930i	1.29385	−	0.120488i
$160$	−1.82015	−	1.29887i	−0.143895	−	0.102685i
$161$			8.90974i			0.702186i
$162$	−3.62027	+	8.23976i	−0.284435	+	0.647377i
$163$	12.3528	−	12.3528i	0.967547	−	0.967547i	−0.0319424	−	0.999490i	$-0.510169\pi$
$163$	12.3528	−	12.3528i	0.967547	−	0.967547i	0.999490	+	0.0319424i	$0.0101693\pi$
$164$	1.90694			0.148907
$165$	−0.140765	+	0.241939i	−0.0109586	+	0.0188349i
$166$	0.216799			0.0168269
$167$	7.76866	−	7.76866i	0.601157	−	0.601157i	−0.339463	−	0.940620i	$-0.610245\pi$
$167$	7.76866	−	7.76866i	0.601157	−	0.601157i	0.940620	+	0.339463i	$0.110245\pi$
$168$	5.40401	+	4.48327i	0.416928	+	0.345892i
$169$		−	4.02554i		−	0.309657i
$170$	13.0053	−	2.17354i	0.997464	−	0.166703i
$171$	9.21781	−	1.73181i	0.704904	−	0.132435i
$172$	0.388846	+	0.388846i	0.0296492	+	0.0296492i
$173$	13.1245	+	13.1245i	0.997840	+	0.997840i	0.999998	−	0.00215773i	$-0.000686827\pi$
$173$	13.1245	+	13.1245i	0.997840	+	0.997840i	−0.00215773	+	0.999998i	$0.500687\pi$
$174$	0.487370	+	5.23359i	0.0369474	+	0.396757i
$175$	18.2145	+	8.89327i	1.37689	+	0.672268i
$176$		−	0.0722722i		−	0.00544772i
$177$	2.58586	−	3.11692i	0.194365	−	0.234282i
$178$	9.62465	−	9.62465i	0.721398	−	0.721398i
$179$	−16.8729			−1.26114			−0.630572	−	0.776131i	$-0.717179\pi$
$179$	−16.8729			−1.26114			−0.630572	+	0.776131i	$0.717179\pi$
$180$	−2.30847	−	6.29849i	−0.172063	−	0.469462i
$181$	16.8141			1.24978			0.624889	−	0.780713i	$-0.285144\pi$
$181$	16.8141			1.24978			0.624889	+	0.780713i	$0.285144\pi$
$182$	−11.8280	+	11.8280i	−0.876751	+	0.876751i
$183$	14.1692	−	17.0792i	1.04742	−	1.26253i
$184$			2.19780i			0.162024i
$185$	10.8476	−	15.2011i	0.797534	−	1.11761i
$186$	0.160600	+	1.72459i	0.0117757	+	0.126453i
$187$	0.301353	+	0.301353i	0.0220371	+	0.0220371i
$188$	−2.00099	−	2.00099i	−0.145937	−	0.145937i
$189$	5.79237	+	20.2528i	0.421333	+	1.47317i
$190$	−4.06075	+	5.69043i	−0.294598	+	0.412827i
$191$		−	17.7533i		−	1.28459i	−0.766459	−	0.642293i	$-0.777983\pi$
$191$		−	17.7533i		−	1.28459i	0.766459	−	0.642293i	$-0.222017\pi$
$192$	1.33303	+	1.10591i	0.0962031	+	0.0798120i
$193$	−4.22668	+	4.22668i	−0.304243	+	0.304243i	−0.842671	−	0.538428i	$-0.819018\pi$
$193$	−4.22668	+	4.22668i	−0.304243	+	0.304243i	0.538428	+	0.842671i	$0.319018\pi$
$194$	−3.76224			−0.270113
$195$	15.4499	−	4.08442i	1.10639	−	0.292491i
$196$	9.43435			0.673882
$197$	−6.01897	+	6.01897i	−0.428834	+	0.428834i	−0.888231	−	0.459397i	$-0.848066\pi$
$197$	−6.01897	+	6.01897i	−0.428834	+	0.428834i	0.459397	+	0.888231i	$0.348066\pi$
$198$	0.122368	−	0.178985i	0.00869631	−	0.0127199i
$199$		−	7.41699i		−	0.525777i	−0.964826	−	0.262888i	$-0.915325\pi$
$199$		−	7.41699i		−	0.525777i	0.964826	−	0.262888i	$-0.0846751\pi$
$200$	4.49305	+	2.19374i	0.317707	+	0.155121i
$201$	18.1244	−	1.68781i	1.27840	−	0.119049i
$202$	9.87756	+	9.87756i	0.694983	+	0.694983i
$203$	8.69912	+	8.69912i	0.610558	+	0.610558i
$204$	−10.1696	+	0.947029i	−0.712015	+	0.0663053i
$205$	−4.20571	+	0.702888i	−0.293740	+	0.0490918i
$206$		−	13.6157i		−	0.948652i
$207$	−3.72122	+	5.44294i	−0.258642	+	0.378311i
$208$	−2.91767	+	2.91767i	−0.202304	+	0.202304i
$209$	−0.225949			−0.0156292
$210$	−13.5709	−	7.89587i	−0.936484	−	0.544867i
$211$	−2.53992			−0.174855			−0.0874275	−	0.996171i	$-0.527865\pi$
$211$	−2.53992			−0.174855			−0.0874275	+	0.996171i	$0.527865\pi$
$212$	6.68933	−	6.68933i	0.459425	−	0.459425i
$213$	−7.59327	−	6.29952i	−0.520282	−	0.431636i
$214$			18.7813i			1.28386i
$215$	−1.00092	−	0.714265i	−0.0682620	−	0.0487125i
$216$	1.42883	+	4.99584i	0.0972195	+	0.339924i
$217$	2.86656	+	2.86656i	0.194595	+	0.194595i
$218$	8.48859	+	8.48859i	0.574920	+	0.574920i
$219$	−1.37782	−	14.7956i	−0.0931044	−	0.999796i
$220$	0.0266392	+	0.159395i	0.00179601	+	0.0107464i
$221$		−	24.3315i		−	1.63671i
$222$	−9.23607	+	11.1329i	−0.619884	+	0.747191i
$223$	−3.72524	+	3.72524i	−0.249461	+	0.249461i	−0.820749	−	0.571289i	$-0.806444\pi$
$223$	−3.72524	+	3.72524i	−0.249461	+	0.249461i	0.571289	+	0.820749i	$0.306444\pi$
$224$	4.05393			0.270865
$225$	7.41287	+	13.0403i	0.494191	+	0.869353i
$226$	20.5836			1.36920
$227$	−15.0376	+	15.0376i	−0.998082	+	0.998082i	−0.999998	−	0.00191666i	$-0.999390\pi$
$227$	−15.0376	+	15.0376i	−0.998082	+	0.998082i	0.00191666	+	0.999998i	$0.499390\pi$
$228$	3.45747	−	4.16753i	0.228976	−	0.276002i
$229$			1.28766i			0.0850909i	0.999095	+	0.0425455i	$0.0135467\pi$
$229$			1.28766i			0.0850909i	−0.999095	+	0.0425455i	$0.986453\pi$
$230$	−0.810099	−	4.84721i	−0.0534164	−	0.319616i
$231$	−0.0470536	−	0.505281i	−0.00309590	−	0.0332451i
$232$	2.14585	+	2.14585i	0.140882	+	0.140882i
$233$	18.5176	+	18.5176i	1.21313	+	1.21313i	0.969993	+	0.243132i	$0.0781748\pi$
$233$	18.5176	+	18.5176i	1.21313	+	1.21313i	0.243132	+	0.969993i	$0.421825\pi$
$234$	−12.1658	+	2.28566i	−0.795300	+	0.149418i
$235$	5.15069	+	3.67558i	0.335994	+	0.239768i
$236$		−	2.33823i		−	0.152206i
$237$	−10.1636	−	8.43195i	−0.660199	−	0.547714i
$238$	−16.9036	+	16.9036i	−1.09570	+	1.09570i
$239$	7.72147			0.499460			0.249730	−	0.968315i	$-0.419658\pi$
$239$	7.72147			0.499460			0.249730	+	0.968315i	$0.419658\pi$
$240$	−3.34760	−	1.94771i	−0.216087	−	0.125724i
$241$	−21.8089			−1.40483			−0.702417	−	0.711766i	$-0.747896\pi$
$241$	−21.8089			−1.40483			−0.702417	+	0.711766i	$0.747896\pi$
$242$	7.77448	−	7.77448i	0.499763	−	0.499763i
$243$	−4.92018	+	14.7916i	−0.315629	+	0.948883i
$244$		−	12.8123i		−	0.820224i
$245$	−20.8073	+	3.47745i	−1.32933	+	0.222166i
$246$	3.28869	−	0.306254i	0.209679	−	0.0195260i
$247$	9.12168	+	9.12168i	0.580398	+	0.580398i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	0.373890	−	0.0348179i	0.0236943	−	0.00220650i
$250$	−10.7179	−	3.18214i	−0.677861	−	0.201256i
$251$		−	25.7679i		−	1.62646i	−0.581944	−	0.813229i	$-0.697708\pi$
$251$		−	25.7679i		−	1.62646i	0.581944	−	0.813229i	$-0.302292\pi$
$252$	10.0397	+	6.86392i	0.632442	+	0.432386i
$253$	0.112317	−	0.112317i	0.00706131	−	0.00706131i
$254$	−3.91944			−0.245928
$255$	22.0798	−	5.83712i	1.38269	−	0.365535i
$256$	1.00000			0.0625000
$257$	−1.33326	+	1.33326i	−0.0831666	+	0.0831666i	−0.747466	−	0.664300i	$-0.768730\pi$
$257$	−1.33326	+	1.33326i	−0.0831666	+	0.0831666i	0.664300	+	0.747466i	$0.268730\pi$
$258$	0.733048	+	0.608151i	0.0456376	+	0.0378618i
$259$			33.8567i			2.10375i
$260$	5.35941	−	7.51029i	0.332377	−	0.465768i
$261$	1.68103	+	8.94752i	0.104053	+	0.553838i
$262$	10.8077	+	10.8077i	0.667702	+	0.667702i
$263$	−16.4679	−	16.4679i	−1.01546	−	1.01546i	−0.999879	−	0.0155767i	$-0.995042\pi$
$263$	−16.4679	−	16.4679i	−1.01546	−	1.01546i	−0.0155767	−	0.999879i	$-0.504958\pi$
$264$	−0.0116069	−	0.124640i	−0.000714355	−	0.00767106i
$265$	−12.2875	+	17.2188i	−0.754817	+	1.05775i
$266$		−	12.6740i		−	0.777096i
$267$	15.0529	−	18.1443i	0.921220	−	1.11041i
$268$	7.43129	−	7.43129i	0.453938	−	0.453938i
$269$	−30.4001			−1.85353			−0.926764	−	0.375643i	$-0.877422\pi$
$269$	−30.4001			−1.85353			−0.926764	+	0.375643i	$0.877422\pi$
$270$	−4.99269	−	10.4916i	−0.303846	−	0.638497i
$271$	12.4459			0.756036			0.378018	−	0.925798i	$-0.376606\pi$
$271$	12.4459			0.756036			0.378018	+	0.925798i	$0.376606\pi$
$272$	−4.16969	+	4.16969i	−0.252825	+	0.252825i
$273$	−18.4989	+	22.2980i	−1.11960	+	1.34954i
$274$		−	5.57337i		−	0.336699i
$275$	−0.117504	−	0.341723i	−0.00708577	−	0.0206067i
$276$	0.352967	+	3.79031i	0.0212461	+	0.228150i
$277$	−1.07651	−	1.07651i	−0.0646812	−	0.0646812i	0.674026	−	0.738707i	$-0.264563\pi$
$277$	−1.07651	−	1.07651i	−0.0646812	−	0.0646812i	−0.738707	+	0.674026i	$0.764563\pi$
$278$	7.72190	+	7.72190i	0.463129	+	0.463129i
$279$	0.553937	+	2.94842i	0.0331633	+	0.176517i
$280$	−8.94086	+	1.49426i	−0.534318	+	0.0892990i
$281$		−	28.3035i		−	1.68844i	−0.535993	−	0.844222i	$-0.680063\pi$
$281$		−	28.3035i		−	1.68844i	0.535993	−	0.844222i	$-0.319937\pi$
$282$	−3.77224	−	3.12952i	−0.224634	−	0.186360i
$283$	−9.27422	+	9.27422i	−0.551295	+	0.551295i	−0.926814	−	0.375520i	$-0.877464\pi$
$283$	−9.27422	+	9.27422i	−0.551295	+	0.551295i	0.375520	+	0.926814i	$0.377464\pi$
$284$	−5.69625			−0.338010
$285$	−6.08924	+	10.4658i	−0.360695	+	0.619941i
$286$	0.298210			0.0176335
$287$	5.46636	−	5.46636i	0.322669	−	0.322669i
$288$	2.47654	+	1.69315i	0.145931	+	0.0997699i
$289$		−	17.7726i		−	1.04545i
$290$	−5.52357	−	3.94167i	−0.324355	−	0.231463i
$291$	−6.48832	+	0.604215i	−0.380352	+	0.0354197i
$292$	−6.06642	−	6.06642i	−0.355011	−	0.355011i
$293$	−8.37669	−	8.37669i	−0.489371	−	0.489371i	0.418736	−	0.908108i	$-0.362473\pi$
$293$	−8.37669	−	8.37669i	−0.489371	−	0.489371i	−0.908108	+	0.418736i	$0.862473\pi$
$294$	16.2704	−	1.51515i	0.948907	−	0.0883655i
$295$	0.861858	+	5.15691i	0.0501793	+	0.300247i
$296$			8.35157i			0.485425i
$297$	0.182289	−	0.328328i	0.0105775	−	0.0190515i
$298$	−7.95351	+	7.95351i	−0.460734	+	0.460734i
$299$	−9.06858			−0.524450
$300$	8.10098	+	3.06172i	0.467710	+	0.176769i
$301$	2.22930			0.128495
$302$	−8.40919	+	8.40919i	−0.483895	+	0.483895i
$303$	18.6211	+	15.4484i	1.06975	+	0.887488i
$304$		−	3.12636i		−	0.179309i
$305$	4.72255	+	28.2573i	0.270412	+	1.61801i
$306$	−17.3863	+	3.26647i	−0.993909	+	0.186732i
$307$	−10.4197	−	10.4197i	−0.594684	−	0.594684i	0.344209	−	0.938893i	$-0.388147\pi$
$307$	−10.4197	−	10.4197i	−0.594684	−	0.594684i	−0.938893	+	0.344209i	$0.888147\pi$
$308$	−0.207173	−	0.207173i	−0.0118048	−	0.0118048i
$309$	−2.18668	−	23.4815i	−0.124396	−	1.33582i
$310$	−1.82015	−	1.29887i	−0.103377	−	0.0737710i
$311$			1.14021i			0.0646554i	0.999477	+	0.0323277i	$0.0102920\pi$
$311$			1.14021i			0.0646554i	−0.999477	+	0.0323277i	$0.989708\pi$
$312$	−4.56320	+	5.50035i	−0.258340	+	0.311396i
$313$	9.62782	−	9.62782i	0.544197	−	0.544197i	−0.380560	−	0.924756i	$-0.624269\pi$
$313$	9.62782	−	9.62782i	0.544197	−	0.544197i	0.924756	+	0.380560i	$0.124269\pi$
$314$	−1.38236			−0.0780110
$315$	−24.6724	−	11.4376i	−1.39013	−	0.644438i
$316$	−7.62446			−0.428909
$317$	−20.6739	+	20.6739i	−1.16116	+	1.16116i	−0.176938	+	0.984222i	$0.556619\pi$
$317$	−20.6739	+	20.6739i	−1.16116	+	1.16116i	−0.984222	+	0.176938i	$0.943381\pi$
$318$	10.4620	−	12.6107i	0.586683	−	0.707171i
$319$		−	0.219324i		−	0.0122798i
$320$	−2.20548	+	0.368595i	−0.123290	+	0.0206051i
$321$	3.01627	+	32.3900i	0.168352	+	1.80783i
$322$	6.30014	+	6.30014i	0.351093	+	0.351093i
$323$	13.0360	+	13.0360i	0.725340	+	0.725340i
$324$	3.26647	+	8.38631i	0.181471	+	0.465906i
$325$	−9.05182	+	18.5392i	−0.502105	+	1.02837i
$326$		−	17.4695i		−	0.967547i
$327$	16.0026	+	13.2761i	0.884945	+	0.734168i
$328$	1.34841	−	1.34841i	0.0744535	−	0.0744535i
$329$	−11.4719			−0.632466
$330$	0.0715404	+	0.270612i	0.00393817	+	0.0148967i
$331$	4.84875			0.266512			0.133256	−	0.991082i	$-0.457457\pi$
$331$	4.84875			0.266512			0.133256	+	0.991082i	$0.457457\pi$
$332$	0.153300	−	0.153300i	0.00841345	−	0.00841345i
$333$	−14.1405	+	20.6830i	−0.774894	+	1.13342i
$334$		−	10.9865i		−	0.601157i
$335$	−13.6504	+	19.1287i	−0.745802	+	1.04511i
$336$	6.99136	−	0.651060i	0.381410	−	0.0355182i
$337$	−1.86250	−	1.86250i	−0.101457	−	0.101457i	0.654556	−	0.756013i	$-0.272855\pi$
$337$	−1.86250	−	1.86250i	−0.101457	−	0.101457i	−0.756013	+	0.654556i	$0.772855\pi$
$338$	−2.84649	−	2.84649i	−0.154829	−	0.154829i
$339$	35.4983	−	3.30573i	1.92800	−	0.179542i
$340$	7.65924	−	10.7331i	0.415380	−	0.582083i
$341$		−	0.0722722i		−	0.00391376i
$342$	5.29340	−	7.74255i	0.286235	−	0.418669i
$343$	6.97821	−	6.97821i	0.376788	−	0.376788i
$344$	0.549911			0.0296492
$345$	−2.17555	−	8.22935i	−0.117128	−	0.443053i
$346$	18.5609			0.997840
$347$	16.5685	−	16.5685i	0.889444	−	0.889444i	−0.105026	−	0.994470i	$-0.533492\pi$
$347$	16.5685	−	16.5685i	0.889444	−	0.889444i	0.994470	+	0.105026i	$0.0334924\pi$
$348$	4.04533	+	3.35608i	0.216852	+	0.179905i
$349$		−	30.9903i		−	1.65888i	−0.558599	−	0.829438i	$-0.688661\pi$
$349$		−	30.9903i		−	1.65888i	0.558599	−	0.829438i	$-0.311339\pi$
$350$	19.1681	−	6.59111i	1.02458	−	0.352310i
$351$	−20.6139	+	5.89563i	−1.10029	+	0.314686i
$352$	−0.0511042	−	0.0511042i	−0.00272386	−	0.00272386i
$353$	6.53675	+	6.53675i	0.347916	+	0.347916i	0.859333	−	0.511417i	$-0.170879\pi$
$353$	6.53675	+	6.53675i	0.347916	+	0.347916i	−0.511417	+	0.859333i	$0.670879\pi$
$354$	−0.375518	−	4.03248i	−0.0199586	−	0.214324i
$355$	12.5630	−	2.09961i	0.666772	−	0.111436i
$356$		−	13.6113i		−	0.721398i
$357$	−26.4371	+	31.8665i	−1.39920	+	1.68656i
$358$	−11.9310	+	11.9310i	−0.630572	+	0.630572i
$359$	−19.5683			−1.03278			−0.516388	−	0.856355i	$-0.672724\pi$
$359$	−19.5683			−1.03278			−0.516388	+	0.856355i	$0.672724\pi$
$360$	−6.08604	−	2.82137i	−0.320762	−	0.148699i
$361$	9.22587			0.485572
$362$	11.8893	−	11.8893i	0.624889	−	0.624889i
$363$	12.1592	−	14.6564i	0.638193	−	0.769260i
$364$			16.7273i			0.876751i
$365$	15.6154	+	11.1433i	0.817348	+	0.583268i
$366$	−2.05765	−	22.0960i	−0.107555	−	1.15497i
$367$	22.2509	+	22.2509i	1.16149	+	1.16149i	0.984150	+	0.177336i	$0.0567479\pi$
$367$	22.2509	+	22.2509i	1.16149	+	1.16149i	0.177336	+	0.984150i	$0.443252\pi$
$368$	1.55408	+	1.55408i	0.0810121	+	0.0810121i
$369$	5.62245	−	1.05632i	0.292693	−	0.0549900i
$370$	−3.07835	−	18.4192i	−0.160036	−	0.957570i
$371$		−	38.3508i		−	1.99107i
$372$	1.33303	+	1.10591i	0.0691144	+	0.0573386i
$373$	14.3722	−	14.3722i	0.744164	−	0.744164i	−0.229213	−	0.973376i	$-0.573615\pi$
$373$	14.3722	−	14.3722i	0.744164	−	0.744164i	0.973376	+	0.229213i	$0.0736152\pi$
$374$	0.426177			0.0220371
$375$	−18.9951	−	3.76658i	−0.980901	−	0.194505i
$376$	−2.82982			−0.145937
$377$	−8.85420	+	8.85420i	−0.456015	+	0.456015i
$378$	18.4167	+	10.2251i	0.947254	+	0.525921i
$379$			27.6521i			1.42039i	0.704005	+	0.710195i	$0.251393\pi$
$379$			27.6521i			1.42039i	−0.704005	+	0.710195i	$0.748607\pi$
$380$	1.15236	+	6.89512i	0.0591149	+	0.353712i
$381$	−6.75943	+	0.629461i	−0.346296	+	0.0322483i
$382$	−12.5535	−	12.5535i	−0.642293	−	0.642293i
$383$	−8.40290	−	8.40290i	−0.429368	−	0.429368i	0.459045	−	0.888413i	$-0.348192\pi$
$383$	−8.40290	−	8.40290i	−0.429368	−	0.429368i	−0.888413	+	0.459045i	$0.848192\pi$
$384$	1.72459	−	0.160600i	0.0880076	−	0.00819557i
$385$	0.533278	+	0.380552i	0.0271784	+	0.0193947i
$386$			5.97743i			0.304243i
$387$	1.36188	+	0.931083i	0.0692280	+	0.0473296i
$388$	−2.66031	+	2.66031i	−0.135057	+	0.135057i
$389$	18.8733			0.956913			0.478457	−	0.878111i	$-0.341196\pi$
$389$	18.8733			0.956913			0.478457	+	0.878111i	$0.341196\pi$
$390$	8.03664	−	13.8129i	0.406951	−	0.699442i
$391$	−12.9601			−0.655419
$392$	6.67109	−	6.67109i	0.336941	−	0.336941i
$393$	20.3746	+	16.9031i	1.02776	+	0.852650i
$394$			8.51211i			0.428834i
$395$	16.8156	−	2.81034i	0.846084	−	0.141403i
$396$	−0.0400343	−	0.213089i	−0.00201180	−	0.0107081i
$397$	−11.7617	−	11.7617i	−0.590303	−	0.590303i	0.347410	−	0.937713i	$-0.387061\pi$
$397$	−11.7617	−	11.7617i	−0.590303	−	0.590303i	−0.937713	+	0.347410i	$0.887061\pi$
$398$	−5.24461	−	5.24461i	−0.262888	−	0.262888i
$399$	−2.03545	−	21.8575i	−0.101900	−	1.09424i
$400$	4.72828	−	1.62586i	0.236414	−	0.0812928i
$401$			12.7272i			0.635567i	0.948163	+	0.317783i	$0.102938\pi$
$401$			12.7272i			0.635567i	−0.948163	+	0.317783i	$0.897062\pi$
$402$	11.6225	−	14.0094i	0.579675	−	0.698724i
$403$	−2.91767	+	2.91767i	−0.145339	+	0.145339i
$404$	13.9690			0.694983
$405$	−10.2953	−	17.2918i	−0.511577	−	0.859237i
$406$	12.3024			0.610558
$407$	0.426800	−	0.426800i	0.0211557	−	0.0211557i
$408$	−6.52135	+	7.86065i	−0.322855	+	0.389160i
$409$		−	18.7099i		−	0.925144i	−0.886582	−	0.462572i	$-0.846927\pi$
$409$		−	18.7099i		−	0.925144i	0.886582	−	0.462572i	$-0.153073\pi$
$410$	−2.47687	+	3.47091i	−0.122324	+	0.171416i
$411$	−0.895081	−	9.61177i	−0.0441511	−	0.474114i
$412$	−9.62776	−	9.62776i	−0.474326	−	0.474326i
$413$	−6.70267	−	6.70267i	−0.329817	−	0.329817i
$414$	1.21745	+	6.48004i	0.0598342	+	0.318477i
$415$	−0.281595	+	0.394606i	−0.0138229	+	0.0193705i
$416$			4.12620i			0.202304i
$417$	14.5572	+	12.0770i	0.712871	+	0.591412i
$418$	−0.159770	+	0.159770i	−0.00781461	+	0.00781461i
$419$	−4.40881			−0.215384			−0.107692	−	0.994184i	$-0.534346\pi$
$419$	−4.40881			−0.215384			−0.107692	+	0.994184i	$0.534346\pi$
$420$	−15.1793	+	4.01288i	−0.740675	+	0.195808i
$421$	−22.3290			−1.08825			−0.544124	−	0.839005i	$-0.683138\pi$
$421$	−22.3290			−1.08825			−0.544124	+	0.839005i	$0.683138\pi$
$422$	−1.79599	+	1.79599i	−0.0874275	+	0.0874275i
$423$	−7.00816	−	4.79132i	−0.340748	−	0.232962i
$424$		−	9.46015i		−	0.459425i
$425$	−12.9361	+	26.4948i	−0.627494	+	1.28518i
$426$	−9.82369	+	0.914816i	−0.475959	+	0.0443230i
$427$	−36.7273	−	36.7273i	−1.77736	−	1.77736i
$428$	13.2804	+	13.2804i	0.641931	+	0.641931i
$429$	0.514289	−	0.0478924i	0.0248301	−	0.00231227i
$430$	−1.21282	+	0.202694i	−0.0584873	+	0.00977479i
$431$		−	12.2320i		−	0.589194i	−0.955622	−	0.294597i	$-0.904815\pi$
$431$		−	12.2320i		−	0.589194i	0.955622	−	0.294597i	$-0.0951853\pi$
$432$	4.54293	+	2.52226i	0.218572	+	0.121352i
$433$	−5.46824	+	5.46824i	−0.262787	+	0.262787i	−0.826185	−	0.563399i	$-0.809494\pi$
$433$	−5.46824	+	5.46824i	−0.262787	+	0.262787i	0.563399	+	0.826185i	$0.309494\pi$
$434$	4.05393			0.194595
$435$	−10.1589	−	5.91068i	−0.487083	−	0.283396i
$436$	12.0047			0.574920
$437$	4.85862	−	4.85862i	0.232419	−	0.232419i
$438$	−11.4364	−	9.48782i	−0.546450	−	0.453346i
$439$		−	33.1668i		−	1.58296i	−0.611192	−	0.791482i	$-0.709310\pi$
$439$		−	33.1668i		−	1.58296i	0.611192	−	0.791482i	$-0.290690\pi$
$440$	0.131546	+	0.0938725i	0.00627121	+	0.00447519i
$441$	27.8164	−	5.22603i	1.32459	−	0.248859i
$442$	−17.2050	−	17.2050i	−0.818357	−	0.818357i
$443$	12.0207	+	12.0207i	0.571122	+	0.571122i	0.932442	−	0.361320i	$-0.117674\pi$
$443$	12.0207	+	12.0207i	0.571122	+	0.571122i	−0.361320	+	0.932442i	$0.617674\pi$
$444$	1.34126	+	14.4030i	0.0636534	+	0.683538i
$445$	5.01706	+	30.0195i	0.237831	+	1.42306i
$446$			5.26828i			0.249461i
$447$	−12.4392	+	14.9939i	−0.588354	+	0.709185i
$448$	2.86656	−	2.86656i	0.135432	−	0.135432i
$449$	−2.93274			−0.138404			−0.0692022	−	0.997603i	$-0.522045\pi$
$449$	−2.93274			−0.138404			−0.0692022	+	0.997603i	$0.522045\pi$
$450$	14.4626	+	3.97920i	0.681772	+	0.187581i
$451$	−0.137819			−0.00648963
$452$	14.5548	−	14.5548i	0.684602	−	0.684602i
$453$	−13.1519	+	15.8529i	−0.617930	+	0.744835i
$454$			21.2664i			0.998082i
$455$	−6.16561	−	36.8918i	−0.289048	−	1.72951i
$456$	−0.502093	−	5.39169i	−0.0235126	−	0.252489i
$457$	−3.36381	−	3.36381i	−0.157352	−	0.157352i	0.624040	−	0.781392i	$-0.285490\pi$
$457$	−3.36381	−	3.36381i	−0.157352	−	0.157352i	−0.781392	+	0.624040i	$0.785490\pi$
$458$	0.910513	+	0.910513i	0.0425455	+	0.0425455i
$459$	−29.4596	+	8.42556i	−1.37506	+	0.393271i
$460$	−4.00032	−	2.85467i	−0.186516	−	0.133100i
$461$			29.5785i			1.37761i	0.724947	+	0.688804i	$0.241864\pi$
$461$			29.5785i			1.37761i	−0.724947	+	0.688804i	$0.758136\pi$
$462$	−0.390560	−	0.324016i	−0.0181705	−	0.0150746i
$463$	3.99421	−	3.99421i	0.185627	−	0.185627i	−0.608176	−	0.793803i	$-0.708098\pi$
$463$	3.99421	−	3.99421i	0.185627	−	0.185627i	0.793803	+	0.608176i	$0.208098\pi$
$464$	3.03469			0.140882
$465$	−3.34760	−	1.94771i	−0.155241	−	0.0903228i
$466$	26.1878			1.21313
$467$	10.7098	−	10.7098i	0.495590	−	0.495590i	−0.414472	−	0.910062i	$-0.636034\pi$
$467$	10.7098	−	10.7098i	0.495590	−	0.495590i	0.910062	+	0.414472i	$0.136034\pi$
$468$	−6.98629	+	10.2187i	−0.322941	+	0.472359i
$469$		−	42.6045i		−	1.96729i
$470$	6.24111	−	1.04306i	0.287881	−	0.0481127i
$471$	−2.38400	+	0.222006i	−0.109849	+	0.0102295i
$472$	−1.65338	−	1.65338i	−0.0761028	−	0.0761028i
$473$	−0.0281028	−	0.0281028i	−0.00129217	−	0.00129217i
$474$	−13.1491	+	1.22449i	−0.603956	+	0.0562425i
$475$	−5.08301	−	14.7823i	−0.233225	−	0.678258i
$476$			23.9053i			1.09570i
$477$	16.0175	−	23.4284i	0.733389	−	1.07271i
$478$	5.45990	−	5.45990i	0.249730	−	0.249730i
$479$	−34.0257			−1.55468			−0.777338	−	0.629084i	$-0.783430\pi$
$479$	−34.0257			−1.55468			−0.777338	+	0.629084i	$0.783430\pi$
$480$	−3.74435	+	0.989874i	−0.170905	+	0.0451814i
$481$	−34.4603			−1.57125
$482$	−15.4212	+	15.4212i	−0.702417	+	0.702417i
$483$	11.8770	+	9.85335i	0.540420	+	0.448343i
$484$		−	10.9948i		−	0.499763i
$485$	4.88668	−	6.84783i	0.221892	−	0.310944i
$486$	6.98016	+	13.9383i	0.316627	+	0.632256i
$487$	−18.7416	−	18.7416i	−0.849261	−	0.849261i	0.140780	−	0.990041i	$-0.455039\pi$
$487$	−18.7416	−	18.7416i	−0.849261	−	0.849261i	−0.990041	+	0.140780i	$0.955039\pi$
$488$	−9.05967	−	9.05967i	−0.410112	−	0.410112i
$489$	−2.80560	−	30.1277i	−0.126874	−	1.36242i
$490$	−12.2540	+	17.1719i	−0.553580	+	0.775747i
$491$			35.1520i			1.58639i	0.608970	+	0.793193i	$0.291583\pi$
$491$			35.1520i			1.58639i	−0.608970	+	0.793193i	$0.708417\pi$
$492$	2.10890	−	2.54201i	0.0950765	−	0.114603i
$493$	−12.6537	+	12.6537i	−0.569894	+	0.569894i
$494$	12.9000			0.580398
$495$	0.166838	+	0.455206i	0.00749881	+	0.0204600i
$496$	1.00000			0.0449013
$497$	−16.3286	+	16.3286i	−0.732440	+	0.732440i
$498$	0.239760	−	0.289000i	0.0107439	−	0.0129504i
$499$			24.5578i			1.09936i	0.835376	+	0.549679i	$0.185250\pi$
$499$			24.5578i			1.09936i	−0.835376	+	0.549679i	$0.814750\pi$
$500$	−9.82883	+	5.32861i	−0.439559	+	0.238303i
$501$	−1.76444	−	18.9473i	−0.0788292	−	0.846502i
$502$	−18.2207	−	18.2207i	−0.813229	−	0.813229i
$503$	−9.22718	−	9.22718i	−0.411420	−	0.411420i	0.470813	−	0.882233i	$-0.343961\pi$
$503$	−9.22718	−	9.22718i	−0.411420	−	0.411420i	−0.882233	+	0.470813i	$0.843961\pi$
$504$	11.9527	−	2.24562i	0.532414	−	0.100028i
$505$	−30.8083	+	5.14890i	−1.37095	+	0.229123i
$506$		−	0.158840i		−	0.00706131i
$507$	−5.36617	−	4.45188i	−0.238320	−	0.197715i
$508$	−2.77146	+	2.77146i	−0.122964	+	0.122964i
$509$	14.7415			0.653406			0.326703	−	0.945127i	$-0.394062\pi$
$509$	14.7415			0.653406			0.326703	+	0.945127i	$0.394062\pi$
$510$	11.4853	−	19.7402i	0.508578	−	0.874112i
$511$	−34.7795			−1.53856
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	7.88550	−	14.2028i	0.348153	−	0.627071i
$514$			1.88552i			0.0831666i
$515$	24.7826	+	17.6851i	1.09205	+	0.779298i
$516$	0.948371	−	0.0883156i	0.0417497	−	0.00388788i
$517$	0.144616	+	0.144616i	0.00636019	+	0.00636019i
$518$	23.9403	+	23.9403i	1.05188	+	1.05188i
$519$	32.0099	−	2.98087i	1.40508	−	0.130846i
$520$	−1.52090	−	9.10025i	−0.0666957	−	0.399072i
$521$		−	16.5929i		−	0.726948i	−0.931604	−	0.363474i	$-0.881591\pi$
$521$		−	16.5929i		−	0.726948i	0.931604	−	0.363474i	$-0.118409\pi$
$522$	7.51552	+	5.13819i	0.328945	+	0.224892i
$523$	−0.437151	+	0.437151i	−0.0191153	+	0.0191153i	−0.716600	−	0.697485i	$-0.754303\pi$
$523$	−0.437151	+	0.437151i	−0.0191153	+	0.0191153i	0.697485	+	0.716600i	$0.254303\pi$
$524$	15.2844			0.667702
$525$	31.9986	−	14.4453i	1.39653	−	0.630447i
$526$	−23.2892			−1.01546
$527$	−4.16969	+	4.16969i	−0.181635	+	0.181635i
$528$	−0.0963410	−	0.0799264i	−0.00419271	−	0.00347835i
$529$		−	18.1697i		−	0.789985i
$530$	3.48696	+	20.8642i	0.151464	+	0.906281i
$531$	−1.29523	−	6.89406i	−0.0562082	−	0.299177i
$532$	−8.96191	−	8.96191i	−0.388548	−	0.388548i
$533$	5.56381	+	5.56381i	0.240995	+	0.240995i
$534$	−2.18597	−	23.4739i	−0.0945963	−	1.01582i
$535$	−34.1847	−	24.3945i	−1.47793	−	1.05467i
$536$		−	10.5094i		−	0.453938i
$537$	−18.6599	+	22.4921i	−0.805235	+	0.970607i
$538$	−21.4961	+	21.4961i	−0.926764	+	0.926764i
$539$	−0.681841			−0.0293690
$540$	−10.9490	−	3.88829i	−0.471171	−	0.167325i
$541$	16.9164			0.727292			0.363646	−	0.931537i	$-0.381532\pi$
$541$	16.9164			0.727292			0.363646	+	0.931537i	$0.381532\pi$
$542$	8.80059	−	8.80059i	0.378018	−	0.378018i
$543$	18.5948	−	22.4136i	0.797979	−	0.961861i
$544$			5.89683i			0.252825i
$545$	−26.4761	+	4.42486i	−1.13411	+	0.189540i
$546$	2.68640	+	28.8478i	0.114968	+	1.23457i
$547$	−2.12387	−	2.12387i	−0.0908099	−	0.0908099i	0.660243	−	0.751052i	$-0.270453\pi$
$547$	−2.12387	−	2.12387i	−0.0908099	−	0.0908099i	−0.751052	+	0.660243i	$0.770453\pi$
$548$	−3.94097	−	3.94097i	−0.168350	−	0.168350i
$549$	−7.09721	−	37.7760i	−0.302901	−	1.61224i
$550$	−0.324723	−	0.158547i	−0.0138462	−	0.00676045i
$551$		−	9.48753i		−	0.404182i
$552$	2.92974	+	2.43057i	0.124698	+	0.103452i
$553$	−21.8560	+	21.8560i	−0.929411	+	0.929411i
$554$	−1.52242			−0.0646812
$555$	−8.26700	−	31.2712i	−0.350915	−	1.32739i
$556$	10.9204			0.463129
$557$	−13.9923	+	13.9923i	−0.592873	+	0.592873i	−0.938406	−	0.345534i	$-0.887698\pi$
$557$	−13.9923	+	13.9923i	−0.592873	+	0.592873i	0.345534	+	0.938406i	$0.387698\pi$
$558$	2.47654	+	1.69315i	0.104840	+	0.0716768i
$559$			2.26904i			0.0959704i
$560$	−5.26554	+	7.37874i	−0.222510	+	0.311809i
$561$	0.734980	−	0.0684439i	0.0310309	−	0.00288970i
$562$	−20.0136	−	20.0136i	−0.844222	−	0.844222i
$563$	−13.4923	−	13.4923i	−0.568632	−	0.568632i	0.363113	−	0.931745i	$-0.381714\pi$
$563$	−13.4923	−	13.4923i	−0.568632	−	0.568632i	−0.931745	+	0.363113i	$0.881714\pi$
$564$	−4.88028	+	0.454469i	−0.205497	+	0.0191366i
$565$	−26.7355	+	37.4652i	−1.12477	+	1.57617i
$566$			13.1157i			0.551295i
$567$	33.4034	+	14.6763i	1.40281	+	0.616348i
$568$	−4.02786	+	4.02786i	−0.169005	+	0.169005i
$569$	7.22021			0.302687			0.151343	−	0.988481i	$-0.451640\pi$
$569$	7.22021			0.302687			0.151343	+	0.988481i	$0.451640\pi$
$570$	3.09470	+	11.7062i	0.129623	+	0.490318i
$571$	34.6113			1.44844			0.724220	−	0.689569i	$-0.242200\pi$
$571$	34.6113			1.44844			0.724220	+	0.689569i	$0.242200\pi$
$572$	0.210866	−	0.210866i	0.00881676	−	0.00881676i
$573$	−23.6657	−	19.6335i	−0.988650	−	0.820203i
$574$		−	7.73060i		−	0.322669i
$575$	9.87484	+	4.82141i	0.411809	+	0.201067i
$576$	2.94842	−	0.553937i	0.122851	−	0.0230807i
$577$	21.1679	+	21.1679i	0.881230	+	0.881230i	0.993660	−	0.112429i	$-0.0358632\pi$
$577$	21.1679	+	21.1679i	0.881230	+	0.881230i	−0.112429	+	0.993660i	$0.535863\pi$
$578$	−12.5671	−	12.5671i	−0.522724	−	0.522724i
$579$	0.959973	+	10.3086i	0.0398951	+	0.428411i
$580$	−6.69294	+	1.11857i	−0.277909	+	0.0464461i
$581$		−	0.878889i		−	0.0364625i
$582$	−4.16069	+	5.01518i	−0.172466	+	0.207886i
$583$	−0.483453	+	0.483453i	−0.0200226	+	0.0200226i
$584$	−8.57922			−0.355011
$585$	11.6416	−	25.1122i	0.481319	−	1.03826i
$586$	−11.8464			−0.489371
$587$	2.92963	−	2.92963i	0.120919	−	0.120919i	−0.644058	−	0.764977i	$-0.722750\pi$
$587$	2.92963	−	2.92963i	0.120919	−	0.120919i	0.764977	+	0.644058i	$0.222750\pi$
$588$	10.4335	−	12.5763i	0.430271	−	0.518637i
$589$		−	3.12636i		−	0.128819i
$590$	4.25591	+	3.03706i	0.175213	+	0.125034i
$591$	1.36704	+	14.6799i	0.0562326	+	0.603850i
$592$	5.90545	+	5.90545i	0.242713	+	0.242713i
$593$	−0.395154	−	0.395154i	−0.0162270	−	0.0162270i	0.698947	−	0.715174i	$-0.253652\pi$
$593$	−0.395154	−	0.395154i	−0.0162270	−	0.0162270i	−0.715174	+	0.698947i	$0.753652\pi$
$594$	−0.103265	−	0.361061i	−0.00423700	−	0.0148145i
$595$	−8.81139	−	52.7227i	−0.361232	−	2.16142i
$596$			11.2480i			0.460734i
$597$	−9.88707	−	8.20251i	−0.404651	−	0.335706i
$598$	−6.41246	+	6.41246i	−0.262225	+	0.262225i
$599$	14.1461			0.577993			0.288997	−	0.957330i	$-0.406678\pi$
$599$	14.1461			0.577993			0.288997	+	0.957330i	$0.406678\pi$
$600$	7.89322	−	3.56329i	0.322239	−	0.145471i
$601$	23.2224			0.947262			0.473631	−	0.880723i	$-0.342943\pi$
$601$	23.2224			0.947262			0.473631	+	0.880723i	$0.342943\pi$
$602$	1.57635	−	1.57635i	0.0642474	−	0.0642474i
$603$	17.7941	−	26.0270i	0.724630	−	1.05990i
$604$			11.8924i			0.483895i
$605$	4.05262	+	24.2487i	0.164762	+	0.985852i
$606$	24.0908	−	2.24341i	0.978620	−	0.0911325i
$607$	34.6439	+	34.6439i	1.40615	+	1.40615i	0.778459	+	0.627695i	$0.216001\pi$
$607$	34.6439	+	34.6439i	1.40615	+	1.40615i	0.627695	+	0.778459i	$0.283999\pi$
$608$	−2.21067	−	2.21067i	−0.0896546	−	0.0896546i
$609$	21.2166	−	1.97576i	0.859740	−	0.0800620i
$610$	23.3203	+	16.6416i	0.944209	+	0.673797i
$611$		−	11.6764i		−	0.472377i
$612$	−9.98423	+	14.6037i	−0.403589	+	0.590320i
$613$	−9.06737	+	9.06737i	−0.366228	+	0.366228i	−0.866099	−	0.499872i	$-0.833380\pi$
$613$	−9.06737	+	9.06737i	−0.366228	+	0.366228i	0.499872	+	0.866099i	$0.333380\pi$
$614$	−14.7357			−0.594684
$615$	−3.71416	+	6.38367i	−0.149769	+	0.257415i
$616$	−0.292987			−0.0118048
$617$	−0.624644	+	0.624644i	−0.0251472	+	0.0251472i	−0.719569	−	0.694421i	$-0.755660\pi$
$617$	−0.624644	+	0.624644i	−0.0251472	+	0.0251472i	0.694421	+	0.719569i	$0.255660\pi$
$618$	−18.1501	−	15.0577i	−0.730106	−	0.605710i
$619$			26.1921i			1.05275i	0.850253	+	0.526374i	$0.176449\pi$
$619$			26.1921i			1.05275i	−0.850253	+	0.526374i	$0.823551\pi$
$620$	−2.20548	+	0.368595i	−0.0885742	+	0.0148031i
$621$	3.14028	+	10.9799i	0.126015	+	0.440608i
$622$	0.806250	+	0.806250i	0.0323277	+	0.0323277i
$623$	−39.0177	−	39.0177i	−1.56321	−	1.56321i
$624$	0.662667	+	7.11600i	0.0265279	+	0.284868i
$625$	19.7132	−	15.3750i	0.788527	−	0.615000i
$626$		−	13.6158i		−	0.544197i
$627$	−0.249879	+	0.301197i	−0.00997920	+	0.0120286i
$628$	−0.977475	+	0.977475i	−0.0390055	+	0.0390055i
$629$	−49.2478			−1.96364
$630$	−25.5336	+	9.35836i	−1.01728	+	0.372846i
$631$	−44.9178			−1.78815			−0.894075	−	0.447917i	$-0.852166\pi$
$631$	−44.9178			−1.78815			−0.894075	+	0.447917i	$0.852166\pi$
$632$	−5.39131	+	5.39131i	−0.214455	+	0.214455i
$633$	−2.80891	+	3.38578i	−0.111644	+	0.134573i
$634$			29.2373i			1.16116i
$635$	5.09086	−	7.13395i	0.202024	−	0.283102i
$636$	−1.51930	−	16.3149i	−0.0602440	−	0.646927i
$637$	27.5263	+	27.5263i	1.09063	+	1.09063i
$638$	−0.155085	−	0.155085i	−0.00613988	−	0.00613988i
$639$	−16.7949	+	3.15536i	−0.664396	+	0.124824i
$640$	−1.29887	+	1.82015i	−0.0513425	+	0.0719476i
$641$			38.6006i			1.52463i	0.647204	+	0.762317i	$0.275938\pi$
$641$			38.6006i			1.52463i	−0.647204	+	0.762317i	$0.724062\pi$
$642$	25.0360	+	20.7704i	0.988093	+	0.819741i
$643$	1.94839	−	1.94839i	0.0768371	−	0.0768371i	−0.667644	−	0.744481i	$-0.732697\pi$
$643$	1.94839	−	1.94839i	0.0768371	−	0.0768371i	0.744481	+	0.667644i	$0.232697\pi$
$644$	8.90974			0.351093
$645$	−2.05906	+	0.544343i	−0.0810754	+	0.0214335i
$646$	18.4356			0.725340
$647$	−11.6947	+	11.6947i	−0.459767	+	0.459767i	−0.898579	−	0.438812i	$-0.855399\pi$
$647$	−11.6947	+	11.6947i	−0.459767	+	0.459767i	0.438812	+	0.898579i	$0.355399\pi$
$648$	8.23976	+	3.62027i	0.323688	+	0.142218i
$649$			0.168989i			0.00663339i
$650$	6.70861	+	19.5098i	0.263133	+	0.765238i
$651$	6.99136	−	0.651060i	0.274013	−	0.0255171i
$652$	−12.3528	−	12.3528i	−0.483774	−	0.483774i
$653$	−12.5022	−	12.5022i	−0.489247	−	0.489247i	0.418821	−	0.908069i	$-0.362443\pi$
$653$	−12.5022	−	12.5022i	−0.489247	−	0.489247i	−0.908069	+	0.418821i	$0.862443\pi$
$654$	20.7031	−	1.92795i	0.809556	−	0.0753887i
$655$	−33.7094	+	5.63375i	−1.31714	+	0.220129i
$656$		−	1.90694i		−	0.0744535i
$657$	−21.2468	−	14.5259i	−0.828915	−	0.566710i
$658$	−8.11186	+	8.11186i	−0.316233	+	0.316233i
$659$	2.94693			0.114796			0.0573981	−	0.998351i	$-0.481720\pi$
$659$	2.94693			0.114796			0.0573981	+	0.998351i	$0.481720\pi$
$660$	0.241939	+	0.140765i	0.00941745	+	0.00547928i
$661$	−8.85216			−0.344309			−0.172154	−	0.985070i	$-0.555073\pi$
$661$	−8.85216			−0.344309			−0.172154	+	0.985070i	$0.555073\pi$
$662$	3.42859	−	3.42859i	0.133256	−	0.133256i
$663$	−32.4346	−	26.9084i	−1.25966	−	1.04504i
$664$		−	0.216799i		−	0.00841345i
$665$	23.0686	+	16.4620i	0.894562	+	0.638368i
$666$	4.62625	+	24.6239i	0.179263	+	0.954157i
$667$	4.71615	+	4.71615i	0.182610	+	0.182610i
$668$	−7.76866	−	7.76866i	−0.300578	−	0.300578i
$669$	0.846085	+	9.08563i	0.0327115	+	0.351271i
$670$	3.87372	+	23.1783i	0.149655	+	0.895457i
$671$			0.925974i			0.0357468i
$672$	4.48327	−	5.40401i	0.172946	−	0.208464i
$673$	10.7486	−	10.7486i	0.414327	−	0.414327i	−0.468916	−	0.883243i	$-0.655355\pi$
$673$	10.7486	−	10.7486i	0.414327	−	0.414327i	0.883243	+	0.468916i	$0.155355\pi$
$674$	−2.63397			−0.101457
$675$	25.5811	+	4.53979i	0.984615	+	0.174737i
$676$	−4.02554			−0.154829
$677$	17.0622	−	17.0622i	0.655753	−	0.655753i	−0.298619	−	0.954372i	$-0.596526\pi$
$677$	17.0622	−	17.0622i	0.655753	−	0.655753i	0.954372	+	0.298619i	$0.0965260\pi$
$678$	22.7636	−	27.4386i	0.874231	−	1.05377i
$679$			15.2519i			0.585313i
$680$	−2.17354	−	13.0053i	−0.0833515	−	0.498732i
$681$	3.41538	+	36.6758i	0.130878	+	1.40542i
$682$	−0.0511042	−	0.0511042i	−0.00195688	−	0.00195688i
$683$	6.31969	+	6.31969i	0.241816	+	0.241816i	0.817601	−	0.575785i	$-0.195303\pi$
$683$	6.31969	+	6.31969i	0.241816	+	0.241816i	−0.575785	+	0.817601i	$0.695303\pi$
$684$	−1.73181	−	9.21781i	−0.0662173	−	0.352452i
$685$	10.1443	+	7.23910i	0.387595	+	0.276592i
$686$		−	9.86867i		−	0.376788i
$687$	1.71649	+	1.42403i	0.0654881	+	0.0543302i
$688$	0.388846	−	0.388846i	0.0148246	−	0.0148246i
$689$	39.0345			1.48710
$690$	−7.35737	−	4.28068i	−0.280090	−	0.162963i
$691$	1.88357			0.0716545			0.0358272	−	0.999358i	$-0.488593\pi$
$691$	1.88357			0.0716545			0.0358272	+	0.999358i	$0.488593\pi$
$692$	13.1245	−	13.1245i	0.498920	−	0.498920i
$693$	−0.725592	−	0.496071i	−0.0275630	−	0.0188442i
$694$		−	23.4314i		−	0.889444i
$695$	−24.0848	+	4.02521i	−0.913587	+	0.152685i
$696$	5.23359	−	0.487370i	0.198379	−	0.0184737i
$697$	7.95134	+	7.95134i	0.301179	+	0.301179i
$698$	−21.9135	−	21.9135i	−0.829438	−	0.829438i
$699$	45.1631	−	4.20575i	1.70823	−	0.159076i
$700$	8.89327	−	18.2145i	0.336134	−	0.688444i
$701$		−	25.8155i		−	0.975039i	−0.873112	−	0.487520i	$-0.837902\pi$
$701$		−	25.8155i		−	0.975039i	0.873112	−	0.487520i	$-0.162098\pi$
$702$	−10.4074	+	18.7450i	−0.392800	+	0.707486i
$703$	18.4626	−	18.4626i	0.696329	−	0.696329i
$704$	−0.0722722			−0.00272386
$705$	10.5958	−	2.80117i	0.399063	−	0.105498i
$706$	9.24436			0.347916
$707$	40.0430	−	40.0430i	1.50597	−	1.50597i
$708$	−3.11692	−	2.58586i	−0.117141	−	0.0971826i
$709$		−	1.46369i		−	0.0549702i	−0.999622	−	0.0274851i	$-0.991250\pi$
$709$		−	1.46369i		−	0.0549702i	0.999622	−	0.0274851i	$-0.00874988\pi$
$710$	7.39870	−	10.3680i	0.277668	−	0.389104i
$711$	−22.4801	+	4.22347i	−0.843069	+	0.158393i
$712$	−9.62465	−	9.62465i	−0.360699	−	0.360699i
$713$	1.55408	+	1.55408i	0.0582008	+	0.0582008i
$714$	3.83919	+	41.2269i	0.143678	+	1.54288i
$715$	−0.387337	+	0.542785i	−0.0144856	+	0.0202990i
$716$			16.8729i			0.630572i
$717$	8.53923	−	10.2929i	0.318903	−	0.384397i
$718$	−13.8369	+	13.8369i	−0.516388	+	0.516388i
$719$	2.98907			0.111474			0.0557368	−	0.998445i	$-0.482249\pi$
$719$	2.98907			0.111474			0.0557368	+	0.998445i	$0.482249\pi$
$720$	−6.29849	+	2.30847i	−0.234731	+	0.0860315i
$721$	−55.1971			−2.05565
$722$	6.52367	−	6.52367i	0.242786	−	0.242786i
$723$	−24.1186	+	29.0719i	−0.896980	+	1.08119i
$724$		−	16.8141i		−	0.624889i
$725$	14.3488	−	4.93397i	0.532902	−	0.183243i
$726$	−1.76576	−	18.9615i	−0.0655334	−	0.703726i
$727$	21.9220	+	21.9220i	0.813043	+	0.813043i	0.985089	−	0.172046i	$-0.0550379\pi$
$727$	21.9220	+	21.9220i	0.813043	+	0.813043i	−0.172046	+	0.985089i	$0.555038\pi$
$728$	11.8280	+	11.8280i	0.438375	+	0.438375i
$729$	14.2764	+	22.9169i	0.528756	+	0.848774i
$730$	18.9213	−	3.16226i	0.700308	−	0.117040i
$731$			3.24273i			0.119937i
$732$	−17.0792	−	14.1692i	−0.631265	−	0.523710i
$733$	−17.9804	+	17.9804i	−0.664122	+	0.664122i	−0.956349	−	0.292227i	$-0.905604\pi$
$733$	−17.9804	+	17.9804i	−0.664122	+	0.664122i	0.292227	+	0.956349i	$0.405604\pi$
$734$	31.4675			1.16149
$735$	−18.3754	+	31.5824i	−0.677785	+	1.16494i
$736$	2.19780			0.0810121
$737$	−0.537076	+	0.537076i	−0.0197834	+	0.0197834i
$738$	3.22874	−	4.72261i	0.118851	−	0.173842i
$739$		−	22.6850i		−	0.834481i	−0.908796	−	0.417241i	$-0.862997\pi$
$739$		−	22.6850i		−	0.834481i	0.908796	−	0.417241i	$-0.137003\pi$
$740$	−15.2011	−	10.8476i	−0.558803	−	0.398767i
$741$	22.2472	−	2.07174i	0.817271	−	0.0761071i
$742$	−27.1181	−	27.1181i	−0.995537	−	0.995537i
$743$	−0.287185	−	0.287185i	−0.0105358	−	0.0105358i	0.701819	−	0.712355i	$-0.252371\pi$
$743$	−0.287185	−	0.287185i	−0.0105358	−	0.0105358i	−0.712355	+	0.701819i	$0.752371\pi$
$744$	1.72459	−	0.160600i	0.0632265	−	0.00588787i
$745$	−4.14594	−	24.8071i	−0.151895	−	0.908863i
$746$		−	20.3253i		−	0.744164i
$747$	0.367074	−	0.536912i	0.0134305	−	0.0196446i
$748$	0.301353	−	0.301353i	0.0110185	−	0.0110185i
$749$	76.1380			2.78202
$750$	−16.0949	+	10.7682i	−0.587703	+	0.393198i
$751$	1.98580			0.0724630			0.0362315	−	0.999343i	$-0.488465\pi$
$751$	1.98580			0.0724630			0.0362315	+	0.999343i	$0.488465\pi$
$752$	−2.00099	+	2.00099i	−0.0729685	+	0.0729685i
$753$	−34.3494	−	28.4970i	−1.25176	−	1.03849i
$754$			12.5217i			0.456015i
$755$	−4.38348	−	26.2284i	−0.159531	−	0.954550i
$756$	20.2528	−	5.79237i	0.736587	−	0.210666i
$757$	33.4398	+	33.4398i	1.21539	+	1.21539i	0.969228	+	0.246163i	$0.0791699\pi$
$757$	33.4398	+	33.4398i	1.21539	+	1.21539i	0.246163	+	0.969228i	$0.420830\pi$
$758$	19.5530	+	19.5530i	0.710195	+	0.710195i
$759$	−0.0255097	−	0.273934i	−0.000925943	−	0.00994318i
$760$	5.69043	+	4.06075i	0.206414	+	0.147299i
$761$			39.8343i			1.44399i	0.691897	+	0.721996i	$0.256775\pi$
$761$			39.8343i			1.44399i	−0.691897	+	0.721996i	$0.743225\pi$
$762$	−4.33454	+	5.22473i	−0.157024	+	0.189272i
$763$	34.4121	−	34.4121i	1.24580	−	1.24580i
$764$	−17.7533			−0.642293
$765$	16.6372	−	35.8883i	0.601518	−	1.29755i
$766$	−11.8835			−0.429368
$767$	6.82216	−	6.82216i	0.246334	−	0.246334i
$768$	1.10591	−	1.33303i	0.0399060	−	0.0481016i
$769$			1.26340i			0.0455593i	0.999741	+	0.0227797i	$0.00725162\pi$
$769$			1.26340i			0.0455593i	−0.999741	+	0.0227797i	$0.992748\pi$
$770$	0.646176	−	0.107993i	0.0232866	−	0.00389181i
$771$	0.302814	+	3.25174i	0.0109056	+	0.117109i
$772$	4.22668	+	4.22668i	0.152122	+	0.152122i
$773$	−14.8407	−	14.8407i	−0.533782	−	0.533782i	0.387914	−	0.921696i	$-0.373196\pi$
$773$	−14.8407	−	14.8407i	−0.533782	−	0.533782i	−0.921696	+	0.387914i	$0.873196\pi$
$774$	1.62137	−	0.304616i	0.0582788	−	0.0109492i
$775$	4.72828	−	1.62586i	0.169845	−	0.0584025i
$776$			3.76224i			0.135057i
$777$	45.1320	+	37.4424i	1.61910	+	1.34324i
$778$	13.3454	−	13.3454i	0.478457	−	0.478457i
$779$	−5.96178			−0.213603
$780$	−4.08442	−	15.4499i	−0.146246	−	0.553197i
$781$	0.411681			0.0147311
$782$	−9.16416	+	9.16416i	−0.327710	+	0.327710i
$783$	13.7864	+	7.65427i	0.492685	+	0.273541i
$784$		−	9.43435i		−	0.336941i
$785$	1.79551	−	2.51609i	0.0640844	−	0.0898032i
$786$	26.3593	−	2.45467i	0.940205	−	0.0875552i
$787$	36.6649	+	36.6649i	1.30696	+	1.30696i	0.923596	+	0.383367i	$0.125236\pi$
$787$	36.6649	+	36.6649i	1.30696	+	1.30696i	0.383367	+	0.923596i	$0.374764\pi$
$788$	6.01897	+	6.01897i	0.214417	+	0.214417i
$789$	−40.1642	+	3.74023i	−1.42988	+	0.133156i
$790$	9.90321	−	13.8776i	0.352340	−	0.493744i
$791$		−	83.4446i		−	2.96695i
$792$	−0.178985	−	0.122368i	−0.00635995	−	0.00434815i
$793$	37.3820	−	37.3820i	1.32747	−	1.32747i
$794$	−16.6336			−0.590303
$795$	9.36435	+	35.4221i	0.332119	+	1.25629i
$796$	−7.41699			−0.262888
$797$	8.54415	−	8.54415i	0.302649	−	0.302649i	−0.539400	−	0.842049i	$-0.681349\pi$
$797$	8.54415	−	8.54415i	0.302649	−	0.302649i	0.842049	+	0.539400i	$0.181349\pi$
$798$	−16.8949	−	14.0163i	−0.598072	−	0.496173i
$799$		−	16.6870i		−	0.590343i
$800$	2.19374	−	4.49305i	0.0775605	−	0.158853i
$801$	−7.53981	−	40.1318i	−0.266406	−	1.41799i
$802$	8.99950	+	8.99950i	0.317783	+	0.317783i
$803$	0.438434	+	0.438434i	0.0154720	+	0.0154720i
$804$	−1.68781	−	18.1244i	−0.0595245	−	0.639200i
$805$	−19.6503	+	3.28409i	−0.692580	+	0.115749i
$806$			4.12620i			0.145339i
$807$	−33.6197	+	40.5243i	−1.18347	+	1.42652i
$808$	9.87756	−	9.87756i	0.347491	−	0.347491i
$809$	−22.9717			−0.807641			−0.403820	−	0.914838i	$-0.632318\pi$
$809$	−22.9717			−0.807641			−0.403820	+	0.914838i	$0.632318\pi$
$810$	−19.5070	−	4.94730i	−0.685407	−	0.173830i
$811$	−36.5655			−1.28399			−0.641994	−	0.766710i	$-0.721892\pi$
$811$	−36.5655			−1.28399			−0.641994	+	0.766710i	$0.721892\pi$
$812$	8.69912	−	8.69912i	0.305279	−	0.305279i
$813$	13.7640	−	16.5908i	0.482726	−	0.581864i
$814$		−	0.603587i		−	0.0211557i
$815$	31.7971	+	22.6907i	1.11380	+	0.794820i
$816$	0.947029	+	10.1696i	0.0331527	+	0.356008i
$817$	−1.21567	−	1.21567i	−0.0425310	−	0.0425310i
$818$	−13.2299	−	13.2299i	−0.462572	−	0.462572i
$819$	9.26589	+	49.3191i	0.323776	+	1.72335i
$820$	0.702888	+	4.20571i	0.0245459	+	0.146870i
$821$			37.4440i			1.30680i	0.757011	+	0.653402i	$0.226659\pi$
$821$			37.4440i			1.30680i	−0.757011	+	0.653402i	$0.773341\pi$
$822$	−7.42946	−	6.16363i	−0.259132	−	0.214981i
$823$	−3.41342	+	3.41342i	−0.118984	+	0.118984i	−0.764092	−	0.645108i	$-0.776813\pi$
$823$	−3.41342	+	3.41342i	−0.118984	+	0.118984i	0.645108	+	0.764092i	$0.276813\pi$
$824$	−13.6157			−0.474326
$825$	−0.585476	−	0.221277i	−0.0203837	−	0.00770389i
$826$	−9.47900			−0.329817
$827$	25.9363	−	25.9363i	0.901894	−	0.901894i	−0.0937057	−	0.995600i	$-0.529871\pi$
$827$	25.9363	−	25.9363i	0.901894	−	0.901894i	0.995600	+	0.0937057i	$0.0298713\pi$
$828$	5.44294	+	3.72122i	0.189155	+	0.129321i
$829$			21.0807i			0.732164i	0.930583	+	0.366082i	$0.119301\pi$
$829$			21.0807i			0.732164i	−0.930583	+	0.366082i	$0.880699\pi$
$830$	0.0799111	+	0.478146i	0.00277376	+	0.0165967i
$831$	−2.62554	+	0.244499i	−0.0910790	+	0.00848159i
$832$	2.91767	+	2.91767i	0.101152	+	0.101152i
$833$	39.3383	+	39.3383i	1.36299	+	1.36299i
$834$	18.8332	−	1.75382i	0.652142	−	0.0607297i
$835$	19.9971	+	14.2701i	0.692028	+	0.493838i
$836$			0.225949i			0.00781461i
$837$	4.54293	+	2.52226i	0.157027	+	0.0871821i
$838$	−3.11750	+	3.11750i	−0.107692	+	0.107692i
$839$	18.2647			0.630569			0.315285	−	0.948997i	$-0.397900\pi$
$839$	18.2647			0.630569			0.315285	+	0.948997i	$0.397900\pi$
$840$	−7.89587	+	13.5709i	−0.272433	+	0.468242i
$841$	−19.7907			−0.682437
$842$	−15.7890	+	15.7890i	−0.544124	+	0.544124i
$843$	−37.7294	−	31.3010i	−1.29947	−	1.07807i
$844$			2.53992i			0.0874275i
$845$	8.87825	−	1.48379i	0.305421	−	0.0510441i
$846$	−8.34349	+	1.56754i	−0.286855	+	0.0538933i
$847$	−31.5172	−	31.5172i	−1.08294	−	1.08294i
$848$	−6.68933	−	6.68933i	−0.229713	−	0.229713i
$849$	2.10638	+	22.6192i	0.0722908	+	0.776290i
$850$	9.58740	+	27.8818i	0.328845	+	0.956339i
$851$			18.3551i			0.629205i
$852$	−6.29952	+	7.59327i	−0.215818	+	0.260141i
$853$	−22.0588	+	22.0588i	−0.755279	+	0.755279i	−0.975459	−	0.220180i	$-0.929335\pi$
$853$	−22.0588	+	22.0588i	−0.755279	+	0.755279i	0.220180	+	0.975459i	$0.429335\pi$
$854$	−51.9402			−1.77736
$855$	7.21710	+	19.6914i	0.246820	+	0.673430i
$856$	18.7813			0.641931
$857$	−29.4683	+	29.4683i	−1.00662	+	1.00662i	−0.00663960	+	0.999978i	$0.502113\pi$
$857$	−29.4683	+	29.4683i	−1.00662	+	1.00662i	−0.999978	+	0.00663960i	$0.997887\pi$
$858$	0.329793	−	0.397523i	0.0112589	−	0.0135712i
$859$			53.9577i			1.84101i	0.390729	+	0.920506i	$0.372223\pi$
$859$			53.9577i			1.84101i	−0.390729	+	0.920506i	$0.627777\pi$
$860$	−0.714265	+	1.00092i	−0.0243562	+	0.0341310i
$861$	−1.24153	−	13.3321i	−0.0423113	−	0.454357i
$862$	−8.64931	−	8.64931i	−0.294597	−	0.294597i
$863$	13.6856	+	13.6856i	0.465864	+	0.465864i	0.900572	−	0.434708i	$-0.143148\pi$
$863$	13.6856	+	13.6856i	0.465864	+	0.465864i	−0.434708	+	0.900572i	$0.643148\pi$
$864$	4.99584	−	1.42883i	0.169962	−	0.0486097i
$865$	−24.1083	+	33.7835i	−0.819705	+	1.14867i
$866$			7.73325i			0.262787i
$867$	−23.6914	−	19.6549i	−0.804603	−	0.667514i
$868$	2.86656	−	2.86656i	0.0972974	−	0.0972974i
$869$	0.551037			0.0186926
$870$	−11.3629	+	3.00396i	−0.385239	+	0.101844i
$871$	43.3640			1.46933
$872$	8.48859	−	8.48859i	0.287460	−	0.287460i
$873$	−6.37005	+	9.31733i	−0.215593	+	0.315344i
$874$		−	6.87113i		−	0.232419i
$875$	−12.9002	+	43.4497i	−0.436105	+	1.46887i
$876$	−14.7956	+	1.37782i	−0.499898	+	0.0465522i
$877$	−36.5887	−	36.5887i	−1.23551	−	1.23551i	−0.961816	−	0.273696i	$-0.911754\pi$
$877$	−36.5887	−	36.5887i	−1.23551	−	1.23551i	−0.273696	−	0.961816i	$-0.588246\pi$
$878$	−23.4525	−	23.4525i	−0.791482	−	0.791482i
$879$	−20.4302	+	1.90253i	−0.689094	+	0.0641708i
$880$	0.159395	−	0.0266392i	0.00537320	−	0.000898006i
$881$		−	1.05931i		−	0.0356889i	−0.999841	−	0.0178445i	$-0.994320\pi$
$881$		−	1.05931i		−	0.0356889i	0.999841	−	0.0178445i	$-0.00568037\pi$
$882$	15.9738	−	23.3645i	0.537865	−	0.786724i
$883$	−10.1350	+	10.1350i	−0.341069	+	0.341069i	−0.856769	−	0.515700i	$-0.827532\pi$
$883$	−10.1350	+	10.1350i	−0.341069	+	0.341069i	0.515700	+	0.856769i	$0.327532\pi$
$884$	−24.3315			−0.818357
$885$	7.82745	+	4.55418i	0.263117	+	0.153087i
$886$	16.9999			0.571122
$887$	−10.5215	+	10.5215i	−0.353278	+	0.353278i	−0.861328	−	0.508050i	$-0.830367\pi$
$887$	−10.5215	+	10.5215i	−0.353278	+	0.353278i	0.508050	+	0.861328i	$0.330367\pi$
$888$	11.1329	+	9.23607i	0.373596	+	0.309942i
$889$			15.8891i			0.532905i
$890$	24.7746	+	17.6794i	0.830445	+	0.592614i
$891$	−0.236075	−	0.606097i	−0.00790882	−	0.0203050i
$892$	3.72524	+	3.72524i	0.124730	+	0.124730i
$893$	6.25581	+	6.25581i	0.209343	+	0.209343i
$894$	1.80642	+	19.3981i	0.0604157	+	0.648770i
$895$	−6.21928	−	37.2129i	−0.207888	−	1.24389i
$896$		−	4.05393i		−	0.135432i
$897$	−10.0290	+	12.0887i	−0.334859	+	0.403630i
$898$	−2.07376	+	2.07376i	−0.0692022	+	0.0692022i
$899$	3.03469			0.101212
$900$	13.0403	−	7.41287i	0.434677	−	0.247096i
$901$	55.7849			1.85846
$902$	−0.0974526	+	0.0974526i	−0.00324482	+	0.00324482i
$903$	2.46540	−	2.97173i	0.0820434	−	0.0988928i
$904$		−	20.5836i		−	0.684602i
$905$	6.19757	+	37.0830i	0.206014	+	1.23268i
$906$	1.90992	+	20.5095i	0.0634527	+	0.681382i
$907$	−20.3221	−	20.3221i	−0.674786	−	0.674786i	0.284030	−	0.958815i	$-0.408329\pi$
$907$	−20.3221	−	20.3221i	−0.674786	−	0.674786i	−0.958815	+	0.284030i	$0.908329\pi$
$908$	15.0376	+	15.0376i	0.499041	+	0.499041i
$909$	41.1864	−	7.73794i	1.36607	−	0.256651i
$910$	−30.4462	−	21.7267i	−1.00928	−	0.720233i
$911$			38.8464i			1.28704i	0.765429	+	0.643520i	$0.222527\pi$
$911$			38.8464i			1.28704i	−0.765429	+	0.643520i	$0.777473\pi$
$912$	−4.16753	−	3.45747i	−0.138001	−	0.114488i
$913$	−0.0110794	+	0.0110794i	−0.000366673	+	0.000366673i
$914$	−4.75714			−0.157352
$915$	42.8905	+	24.9546i	1.41792	+	0.824974i
$916$	1.28766			0.0425455
$917$	43.8137	−	43.8137i	1.44685	−	1.44685i
$918$	−14.8733	+	26.7889i	−0.490893	+	0.884165i
$919$			0.402327i			0.0132715i	0.999978	+	0.00663577i	$0.00211225\pi$
$919$			0.402327i			0.0132715i	−0.999978	+	0.00663577i	$0.997888\pi$
$920$	−4.84721	+	0.810099i	−0.159808	+	0.0267082i
$921$	−25.4130	+	2.36655i	−0.837387	+	0.0779804i
$922$	20.9152	+	20.9152i	0.688804	+	0.688804i
$923$	−16.6197	−	16.6197i	−0.547046	−	0.547046i
$924$	−0.505281	+	0.0470536i	−0.0166225	+	0.00154795i
$925$	37.5240	+	18.3212i	1.23378	+	0.602397i
$926$		−	5.64867i		−	0.185627i
$927$	−33.7198	−	23.0535i	−1.10750	−	0.757175i
$928$	2.14585	−	2.14585i	0.0704409	−	0.0704409i
$929$	−29.8543			−0.979489			−0.489745	−	0.871866i	$-0.662910\pi$
$929$	−29.8543			−0.979489			−0.489745	+	0.871866i	$0.662910\pi$
$930$	−3.74435	+	0.989874i	−0.122782	+	0.0324592i
$931$	−29.4952			−0.966665
$932$	18.5176	−	18.5176i	0.606563	−	0.606563i
$933$	1.51993	+	1.26097i	0.0497604	+	0.0412822i
$934$		−	15.1459i		−	0.495590i
$935$	−0.553550	+	0.775704i	−0.0181030	+	0.0253682i
$936$	2.28566	+	12.1658i	0.0747090	+	0.397650i
$937$	22.7912	+	22.7912i	0.744558	+	0.744558i	0.973451	−	0.228894i	$-0.0735109\pi$
$937$	22.7912	+	22.7912i	0.744558	+	0.744558i	−0.228894	+	0.973451i	$0.573511\pi$
$938$	−30.1259	−	30.1259i	−0.983646	−	0.983646i
$939$	−2.18669	−	23.4817i	−0.0713600	−	0.766295i
$940$	3.67558	−	5.15069i	0.119884	−	0.167997i
$941$			27.9112i			0.909880i	0.890522	+	0.454940i	$0.150339\pi$
$941$			27.9112i			0.909880i	−0.890522	+	0.454940i	$0.849661\pi$
$942$	−1.52876	+	1.84272i	−0.0498097	+	0.0600392i
$943$	2.96354	−	2.96354i	0.0965062	−	0.0965062i
$944$	−2.33823			−0.0761028
$945$	−42.5321	+	20.2400i	−1.38357	+	0.658408i
$946$	−0.0397433			−0.00129217
$947$	42.8165	−	42.8165i	1.39135	−	1.39135i	0.569043	−	0.822308i	$-0.307314\pi$
$947$	42.8165	−	42.8165i	1.39135	−	1.39135i	0.822308	−	0.569043i	$-0.192686\pi$
$948$	−8.43195	+	10.1636i	−0.273857	+	0.330099i
$949$		−	35.3996i		−	1.14912i
$950$	−14.0469	−	6.85843i	−0.455741	−	0.222517i
$951$	4.69550	+	50.4223i	0.152262	+	1.63505i
$952$	16.9036	+	16.9036i	0.547850	+	0.547850i
$953$	−37.2483	−	37.2483i	−1.20659	−	1.20659i	−0.972124	−	0.234467i	$-0.924666\pi$
$953$	−37.2483	−	37.2483i	−1.20659	−	1.20659i	−0.234467	−	0.972124i	$-0.575334\pi$
$954$	−5.24033	−	27.8924i	−0.169662	−	0.903051i
$955$	39.1546	−	6.54379i	1.26701	−	0.211752i
$956$		−	7.72147i		−	0.249730i
$957$	−0.292365	−	0.242552i	−0.00945082	−	0.00784058i
$958$	−24.0598	+	24.0598i	−0.777338	+	0.777338i
$959$	−22.5940			−0.729600
$960$	−1.94771	+	3.34760i	−0.0628620	+	0.108043i
$961$	1.00000			0.0322581
$962$	−24.3671	+	24.3671i	−0.785627	+	0.785627i
$963$	46.5126	+	31.7996i	1.49885	+	1.02473i
$964$			21.8089i			0.702417i
$965$	−10.8798	−	7.76392i	−0.350233	−	0.249930i
$966$	15.3656	−	1.43090i	0.494382	−	0.0460385i
$967$	27.2787	+	27.2787i	0.877225	+	0.877225i	0.993247	−	0.116022i	$-0.0370142\pi$
$967$	27.2787	+	27.2787i	0.877225	+	0.877225i	−0.116022	+	0.993247i	$0.537014\pi$
$968$	−7.77448	−	7.77448i	−0.249881	−	0.249881i
$969$	31.7939	−	2.96076i	1.02137	−	0.0951132i
$970$	−1.38674	−	8.29755i	−0.0445256	−	0.266418i
$971$			39.9374i			1.28165i	0.767686	+	0.640826i	$0.221408\pi$
$971$			39.9374i			1.28165i	−0.767686	+	0.640826i	$0.778592\pi$
$972$	14.7916	+	4.92018i	0.474441	+	0.157815i
$973$	31.3040	−	31.3040i	1.00356	−	1.00356i
$974$	−26.5046			−0.849261
$975$	14.7029	+	32.5690i	0.470869	+	1.04304i
$976$	−12.8123			−0.410112
$977$	36.0641	−	36.0641i	1.15379	−	1.15379i	0.168007	−	0.985786i	$-0.446267\pi$
$977$	36.0641	−	36.0641i	1.15379	−	1.15379i	0.985786	−	0.168007i	$-0.0537331\pi$
$978$	−23.2874	−	19.3197i	−0.744649	−	0.617775i
$979$			0.983720i			0.0314398i
$980$	3.47745	+	20.8073i	0.111083	+	0.664663i
$981$	35.3948	−	6.64983i	1.13007	−	0.212313i
$982$	24.8562	+	24.8562i	0.793193	+	0.793193i
$983$	18.5071	+	18.5071i	0.590286	+	0.590286i	0.937709	−	0.347423i	$-0.112943\pi$
$983$	18.5071	+	18.5071i	0.590286	+	0.590286i	−0.347423	+	0.937709i	$0.612943\pi$
$984$	−0.306254	−	3.28869i	−0.00976302	−	0.104840i
$985$	−15.4933	−	11.0562i	−0.493657	−	0.352278i
$986$			17.8950i			0.569894i
$987$	−12.6869	+	15.2924i	−0.403827	+	0.486762i
$988$	9.12168	−	9.12168i	0.290199	−	0.290199i
$989$	1.20860			0.0384311
$990$	0.439852	+	0.203907i	0.0139794	+	0.00648059i
$991$	−16.0869			−0.511019			−0.255509	−	0.966807i	$-0.582243\pi$
$991$	−16.0869			−0.511019			−0.255509	+	0.966807i	$0.582243\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	5.36227	−	6.46353i	0.170167	−	0.205114i
$994$			23.0922i			0.732440i
$995$	16.3580	−	2.73386i	0.518584	−	0.0866693i
$996$	−0.0348179	−	0.373890i	−0.00110325	−	0.0118472i
$997$	−9.40355	−	9.40355i	−0.297814	−	0.297814i	0.542343	−	0.840157i	$-0.317537\pi$
$997$	−9.40355	−	9.40355i	−0.297814	−	0.297814i	−0.840157	+	0.542343i	$0.817537\pi$
$998$	17.3650	+	17.3650i	0.549679	+	0.549679i
$999$	11.9330	+	41.7231i	0.377542	+	1.32006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.497.17	yes	40
3.2	odd	2	inner	930.2.j.h.497.9	✓	40
5.3	odd	4	inner	930.2.j.h.683.9	yes	40
15.8	even	4	inner	930.2.j.h.683.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.9	✓	40	3.2	odd	2	inner
930.2.j.h.497.17	yes	40	1.1	even	1	trivial
930.2.j.h.683.9	yes	40	5.3	odd	4	inner
930.2.j.h.683.17	yes	40	15.8	even	4	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.10591 - 1.33303i) q^{3} -1.00000i q^{4} +(0.368595 + 2.20548i) q^{5} +(-0.160600 - 1.72459i) q^{6} +(-2.86656 - 2.86656i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.553937 - 2.94842i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.10591 - 1.33303i) q^{3} -1.00000i q^{4} +(0.368595 + 2.20548i) q^{5} +(-0.160600 - 1.72459i) q^{6} +(-2.86656 - 2.86656i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.553937 - 2.94842i) q^{9} +(1.82015 + 1.29887i) q^{10} +0.0722722i q^{11} +(-1.33303 - 1.10591i) q^{12} +(2.91767 - 2.91767i) q^{13} -4.05393 q^{14} +(3.34760 + 1.94771i) q^{15} -1.00000 q^{16} +(4.16969 - 4.16969i) q^{17} +(-2.47654 - 1.69315i) q^{18} +3.12636i q^{19} +(2.20548 - 0.368595i) q^{20} +(-6.99136 + 0.651060i) q^{21} +(0.0511042 + 0.0511042i) q^{22} +(-1.55408 - 1.55408i) q^{23} +(-1.72459 + 0.160600i) q^{24} +(-4.72828 + 1.62586i) q^{25} -4.12620i q^{26} +(-4.54293 - 2.52226i) q^{27} +(-2.86656 + 2.86656i) q^{28} -3.03469 q^{29} +(3.74435 - 0.989874i) q^{30} -1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.0963410 + 0.0799264i) q^{33} -5.89683i q^{34} +(5.26554 - 7.37874i) q^{35} +(-2.94842 + 0.553937i) q^{36} +(-5.90545 - 5.90545i) q^{37} +(2.21067 + 2.21067i) q^{38} +(-0.662667 - 7.11600i) q^{39} +(1.29887 - 1.82015i) q^{40} +1.90694i q^{41} +(-4.48327 + 5.40401i) q^{42} +(-0.388846 + 0.388846i) q^{43} +0.0722722 q^{44} +(6.29849 - 2.30847i) q^{45} -2.19780 q^{46} +(2.00099 - 2.00099i) q^{47} +(-1.10591 + 1.33303i) q^{48} +9.43435i q^{49} +(-2.19374 + 4.49305i) q^{50} +(-0.947029 - 10.1696i) q^{51} +(-2.91767 - 2.91767i) q^{52} +(6.68933 + 6.68933i) q^{53} +(-4.99584 + 1.42883i) q^{54} +(-0.159395 + 0.0266392i) q^{55} +4.05393i q^{56} +(4.16753 + 3.45747i) q^{57} +(-2.14585 + 2.14585i) q^{58} +2.33823 q^{59} +(1.94771 - 3.34760i) q^{60} +12.8123 q^{61} +(-0.707107 + 0.707107i) q^{62} +(-6.86392 + 10.0397i) q^{63} +1.00000i q^{64} +(7.51029 + 5.35941i) q^{65} +(0.124640 - 0.0116069i) q^{66} +(7.43129 + 7.43129i) q^{67} +(-4.16969 - 4.16969i) q^{68} +(-3.79031 + 0.352967i) q^{69} +(-1.49426 - 8.94086i) q^{70} -5.69625i q^{71} +(-1.69315 + 2.47654i) q^{72} +(6.06642 - 6.06642i) q^{73} -8.35157 q^{74} +(-3.06172 + 8.10098i) q^{75} +3.12636 q^{76} +(0.207173 - 0.207173i) q^{77} +(-5.50035 - 4.56320i) q^{78} -7.62446i q^{79} +(-0.368595 - 2.20548i) q^{80} +(-8.38631 + 3.26647i) q^{81} +(1.34841 + 1.34841i) q^{82} +(0.153300 + 0.153300i) q^{83} +(0.651060 + 6.99136i) q^{84} +(10.7331 + 7.65924i) q^{85} +0.549911i q^{86} +(-3.35608 + 4.04533i) q^{87} +(0.0511042 - 0.0511042i) q^{88} +13.6113 q^{89} +(2.82137 - 6.08604i) q^{90} -16.7273 q^{91} +(-1.55408 + 1.55408i) q^{92} +(-1.10591 + 1.33303i) q^{93} -2.82982i q^{94} +(-6.89512 + 1.15236i) q^{95} +(0.160600 + 1.72459i) q^{96} +(-2.66031 - 2.66031i) q^{97} +(6.67109 + 6.67109i) q^{98} +(0.213089 - 0.0400343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42} - 16 q^{43} + 76 q^{45} - 8 q^{46} + 4 q^{48} + 16 q^{51} - 24 q^{52} - 48 q^{55} + 56 q^{57} - 56 q^{58} + 12 q^{60} + 128 q^{61} - 24 q^{63} + 16 q^{66} + 8 q^{67} + 32 q^{70} + 248 q^{73} - 8 q^{75} + 56 q^{76} + 8 q^{78} + 40 q^{81} - 8 q^{82} - 48 q^{85} + 12 q^{87} + 16 q^{88} + 16 q^{90} - 192 q^{91} + 4 q^{93} - 8 q^{96} + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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