LMFDB - Embedded newform 930.2.j.g.497.15

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			497.15
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.516967 + 1.65310i) q^{3} -1.00000i q^{4} +(0.633448 + 2.14447i) q^{5} +(0.803369 + 1.53447i) q^{6} +(-2.44874 - 2.44874i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46549 - 1.70920i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.516967 + 1.65310i) q^{3} -1.00000i q^{4} +(0.633448 + 2.14447i) q^{5} +(0.803369 + 1.53447i) q^{6} +(-2.44874 - 2.44874i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46549 - 1.70920i) q^{9} +(1.96428 + 1.06845i) q^{10} -6.26953i q^{11} +(1.65310 + 0.516967i) q^{12} +(2.06590 - 2.06590i) q^{13} -3.46304 q^{14} +(-3.87250 - 0.0614640i) q^{15} -1.00000 q^{16} +(-5.14726 + 5.14726i) q^{17} +(-2.95195 + 0.534780i) q^{18} -3.95225i q^{19} +(2.14447 - 0.633448i) q^{20} +(5.31393 - 2.78210i) q^{21} +(-4.43322 - 4.43322i) q^{22} +(-0.977633 - 0.977633i) q^{23} +(1.53447 - 0.803369i) q^{24} +(-4.19749 + 2.71682i) q^{25} -2.92162i q^{26} +(4.10005 - 3.19211i) q^{27} +(-2.44874 + 2.44874i) q^{28} +7.01894 q^{29} +(-2.78173 + 2.69481i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(10.3642 + 3.24114i) q^{33} +7.27932i q^{34} +(3.70009 - 6.80239i) q^{35} +(-1.70920 + 2.46549i) q^{36} +(-6.92538 - 6.92538i) q^{37} +(-2.79466 - 2.79466i) q^{38} +(2.34714 + 4.48314i) q^{39} +(1.06845 - 1.96428i) q^{40} -7.39856i q^{41} +(1.79028 - 5.72476i) q^{42} +(-1.60599 + 1.60599i) q^{43} -6.26953 q^{44} +(2.10356 - 6.36985i) q^{45} -1.38258 q^{46} +(7.18779 - 7.18779i) q^{47} +(0.516967 - 1.65310i) q^{48} +4.99265i q^{49} +(-1.04699 + 4.88915i) q^{50} +(-5.84798 - 11.1699i) q^{51} +(-2.06590 - 2.06590i) q^{52} +(4.50085 + 4.50085i) q^{53} +(0.642014 - 5.15634i) q^{54} +(13.4448 - 3.97142i) q^{55} +3.46304i q^{56} +(6.53347 + 2.04318i) q^{57} +(4.96314 - 4.96314i) q^{58} -1.19798 q^{59} +(-0.0614640 + 3.87250i) q^{60} -7.46744 q^{61} +(0.707107 - 0.707107i) q^{62} +(1.85197 + 10.2227i) q^{63} +1.00000i q^{64} +(5.73890 + 3.12162i) q^{65} +(9.62040 - 5.03674i) q^{66} +(-4.48628 - 4.48628i) q^{67} +(5.14726 + 5.14726i) q^{68} +(2.12153 - 1.11072i) q^{69} +(-2.19366 - 7.42638i) q^{70} +3.67991i q^{71} +(0.534780 + 2.95195i) q^{72} +(-1.34025 + 1.34025i) q^{73} -9.79397 q^{74} +(-2.32122 - 8.34338i) q^{75} -3.95225 q^{76} +(-15.3524 + 15.3524i) q^{77} +(4.82974 + 1.51038i) q^{78} +2.94015i q^{79} +(-0.633448 - 2.14447i) q^{80} +(3.15729 + 8.42802i) q^{81} +(-5.23157 - 5.23157i) q^{82} +(7.44922 + 7.44922i) q^{83} +(-2.78210 - 5.31393i) q^{84} +(-14.2987 - 7.77761i) q^{85} +2.27121i q^{86} +(-3.62856 + 11.6030i) q^{87} +(-4.43322 + 4.43322i) q^{88} -3.81775 q^{89} +(-3.01673 - 5.99161i) q^{90} -10.1177 q^{91} +(-0.977633 + 0.977633i) q^{92} +(-0.516967 + 1.65310i) q^{93} -10.1651i q^{94} +(8.47547 - 2.50354i) q^{95} +(-0.803369 - 1.53447i) q^{96} +(5.39673 + 5.39673i) q^{97} +(3.53034 + 3.53034i) q^{98} +(-10.7159 + 15.4575i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 - 8 * q^7	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * 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
$3$	−0.516967	+	1.65310i	−0.298471	+	0.954419i
$3$	−0.516967	+	1.65310i	−0.298471	+	0.954419i
$4$		−	1.00000i		−	0.500000i
$5$	0.633448	+	2.14447i	0.283287	+	0.959035i
$5$	0.633448	+	2.14447i	0.283287	+	0.959035i
$6$	0.803369	+	1.53447i	0.327974	+	0.626445i
$7$	−2.44874	−	2.44874i	−0.925536	−	0.925536i	0.0718770	−	0.997414i	$-0.477101\pi$
$7$	−2.44874	−	2.44874i	−0.925536	−	0.925536i	−0.997414	+	0.0718770i	$0.977101\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.46549	−	1.70920i	−0.821830	−	0.569732i
$10$	1.96428	+	1.06845i	0.621161	+	0.337874i
$11$		−	6.26953i		−	1.89033i	−0.326589	−	0.945166i	$-0.605899\pi$
$11$		−	6.26953i		−	1.89033i	0.326589	−	0.945166i	$-0.394101\pi$
$12$	1.65310	+	0.516967i	0.477209	+	0.149235i
$13$	2.06590	−	2.06590i	0.572977	−	0.572977i	−0.359982	−	0.932959i	$-0.617217\pi$
$13$	2.06590	−	2.06590i	0.572977	−	0.572977i	0.932959	+	0.359982i	$0.117217\pi$
$14$	−3.46304			−0.925536
$15$	−3.87250	−	0.0614640i	−0.999874	−	0.0158699i
$16$	−1.00000			−0.250000
$17$	−5.14726	+	5.14726i	−1.24839	+	1.24839i	−0.291965	+	0.956429i	$0.594309\pi$
$17$	−5.14726	+	5.14726i	−1.24839	+	1.24839i	−0.956429	+	0.291965i	$0.905691\pi$
$18$	−2.95195	+	0.534780i	−0.695781	+	0.126049i
$19$		−	3.95225i		−	0.906708i	−0.891331	−	0.453354i	$-0.850227\pi$
$19$		−	3.95225i		−	0.906708i	0.891331	−	0.453354i	$-0.149773\pi$
$20$	2.14447	−	0.633448i	0.479518	−	0.141643i
$21$	5.31393	−	2.78210i	1.15960	−	0.607104i
$22$	−4.43322	−	4.43322i	−0.945166	−	0.945166i
$23$	−0.977633	−	0.977633i	−0.203851	−	0.203851i	0.597797	−	0.801648i	$-0.296043\pi$
$23$	−0.977633	−	0.977633i	−0.203851	−	0.203851i	−0.801648	+	0.597797i	$0.796043\pi$
$24$	1.53447	−	0.803369i	0.313222	−	0.163987i
$25$	−4.19749	+	2.71682i	−0.839497	+	0.543364i
$26$		−	2.92162i		−	0.572977i
$27$	4.10005	−	3.19211i	0.789056	−	0.614322i
$28$	−2.44874	+	2.44874i	−0.462768	+	0.462768i
$29$	7.01894			1.30338			0.651692	−	0.758484i	$-0.274059\pi$
$29$	7.01894			1.30338			0.651692	+	0.758484i	$0.274059\pi$
$30$	−2.78173	+	2.69481i	−0.507872	+	0.492002i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	10.3642	+	3.24114i	1.80417	+	0.564209i
$34$			7.27932i			1.24839i
$35$	3.70009	−	6.80239i	0.625430	−	1.14981i
$36$	−1.70920	+	2.46549i	−0.284866	+	0.410915i
$37$	−6.92538	−	6.92538i	−1.13853	−	1.13853i	−0.988715	−	0.149811i	$-0.952134\pi$
$37$	−6.92538	−	6.92538i	−1.13853	−	1.13853i	−0.149811	−	0.988715i	$-0.547866\pi$
$38$	−2.79466	−	2.79466i	−0.453354	−	0.453354i
$39$	2.34714	+	4.48314i	0.375843	+	0.717878i
$40$	1.06845	−	1.96428i	0.168937	−	0.310580i
$41$		−	7.39856i		−	1.15546i	−0.816228	−	0.577730i	$-0.803939\pi$
$41$		−	7.39856i		−	1.15546i	0.816228	−	0.577730i	$-0.196061\pi$
$42$	1.79028	−	5.72476i	0.276246	−	0.883349i
$43$	−1.60599	+	1.60599i	−0.244911	+	0.244911i	−0.818878	−	0.573967i	$-0.805404\pi$
$43$	−1.60599	+	1.60599i	−0.244911	+	0.244911i	0.573967	+	0.818878i	$0.305404\pi$
$44$	−6.26953			−0.945166
$45$	2.10356	−	6.36985i	0.313580	−	0.949562i
$46$	−1.38258			−0.203851
$47$	7.18779	−	7.18779i	1.04845	−	1.04845i	0.0496812	−	0.998765i	$-0.484179\pi$
$47$	7.18779	−	7.18779i	1.04845	−	1.04845i	0.998765	−	0.0496812i	$-0.0158205\pi$
$48$	0.516967	−	1.65310i	0.0746177	−	0.238605i
$49$			4.99265i			0.713236i
$50$	−1.04699	+	4.88915i	−0.148067	+	0.691431i
$51$	−5.84798	−	11.1699i	−0.818881	−	1.56410i
$52$	−2.06590	−	2.06590i	−0.286489	−	0.286489i
$53$	4.50085	+	4.50085i	0.618239	+	0.618239i	0.945079	−	0.326841i	$-0.105984\pi$
$53$	4.50085	+	4.50085i	0.618239	+	0.618239i	−0.326841	+	0.945079i	$0.605984\pi$
$54$	0.642014	−	5.15634i	0.0873670	−	0.701689i
$55$	13.4448	−	3.97142i	1.81290	−	0.535506i
$56$			3.46304i			0.462768i
$57$	6.53347	+	2.04318i	0.865379	+	0.270626i
$58$	4.96314	−	4.96314i	0.651692	−	0.651692i
$59$	−1.19798			−0.155964			−0.0779822	−	0.996955i	$-0.524848\pi$
$59$	−1.19798			−0.155964			−0.0779822	+	0.996955i	$0.524848\pi$
$60$	−0.0614640	+	3.87250i	−0.00793497	+	0.499937i
$61$	−7.46744			−0.956107			−0.478054	−	0.878331i	$-0.658658\pi$
$61$	−7.46744			−0.956107			−0.478054	+	0.878331i	$0.658658\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	1.85197	+	10.2227i	0.233326	+	1.28794i
$64$			1.00000i			0.125000i
$65$	5.73890	+	3.12162i	0.711823	+	0.387189i
$66$	9.62040	−	5.03674i	1.18419	−	0.619980i
$67$	−4.48628	−	4.48628i	−0.548087	−	0.548087i	0.377800	−	0.925887i	$-0.376681\pi$
$67$	−4.48628	−	4.48628i	−0.548087	−	0.548087i	−0.925887	+	0.377800i	$0.876681\pi$
$68$	5.14726	+	5.14726i	0.624197	+	0.624197i
$69$	2.12153	−	1.11072i	0.255402	−	0.133715i
$70$	−2.19366	−	7.42638i	−0.262192	−	0.887622i
$71$			3.67991i			0.436725i	0.975868	+	0.218363i	$0.0700716\pi$
$71$			3.67991i			0.436725i	−0.975868	+	0.218363i	$0.929928\pi$
$72$	0.534780	+	2.95195i	0.0630245	+	0.347891i
$73$	−1.34025	+	1.34025i	−0.156864	+	0.156864i	−0.781175	−	0.624312i	$-0.785380\pi$
$73$	−1.34025	+	1.34025i	−0.156864	+	0.156864i	0.624312	+	0.781175i	$0.285380\pi$
$74$	−9.79397			−1.13853
$75$	−2.32122	−	8.34338i	−0.268031	−	0.963410i
$76$	−3.95225			−0.453354
$77$	−15.3524	+	15.3524i	−1.74957	+	1.74957i
$78$	4.82974	+	1.51038i	0.546860	+	0.171017i
$79$			2.94015i			0.330792i	0.986227	+	0.165396i	$0.0528903\pi$
$79$			2.94015i			0.330792i	−0.986227	+	0.165396i	$0.947110\pi$
$80$	−0.633448	−	2.14447i	−0.0708217	−	0.239759i
$81$	3.15729	+	8.42802i	0.350810	+	0.936447i
$82$	−5.23157	−	5.23157i	−0.577730	−	0.577730i
$83$	7.44922	+	7.44922i	0.817658	+	0.817658i	0.985768	−	0.168110i	$-0.0537664\pi$
$83$	7.44922	+	7.44922i	0.817658	+	0.817658i	−0.168110	+	0.985768i	$0.553766\pi$
$84$	−2.78210	−	5.31393i	−0.303552	−	0.579798i
$85$	−14.2987	−	7.77761i	−1.55091	−	0.843600i
$86$			2.27121i			0.244911i
$87$	−3.62856	+	11.6030i	−0.389022	+	1.24397i
$88$	−4.43322	+	4.43322i	−0.472583	+	0.472583i
$89$	−3.81775			−0.404680			−0.202340	−	0.979315i	$-0.564855\pi$
$89$	−3.81775			−0.404680			−0.202340	+	0.979315i	$0.564855\pi$
$90$	−3.01673	−	5.99161i	−0.317991	−	0.631571i
$91$	−10.1177			−1.06062
$92$	−0.977633	+	0.977633i	−0.101925	+	0.101925i
$93$	−0.516967	+	1.65310i	−0.0536070	+	0.171419i
$94$		−	10.1651i		−	1.04845i
$95$	8.47547	−	2.50354i	0.869565	−	0.256858i
$96$	−0.803369	−	1.53447i	−0.0819935	−	0.156611i
$97$	5.39673	+	5.39673i	0.547955	+	0.547955i	0.925849	−	0.377894i	$-0.123352\pi$
$97$	5.39673	+	5.39673i	0.547955	+	0.547955i	−0.377894	+	0.925849i	$0.623352\pi$
$98$	3.53034	+	3.53034i	0.356618	+	0.356618i
$99$	−10.7159	+	15.4575i	−1.07698	+	1.55353i
$100$	2.71682	+	4.19749i	0.271682	+	0.419749i
$101$		−	15.4674i		−	1.53907i	−0.638608	−	0.769533i	$-0.720489\pi$
$101$		−	15.4674i		−	1.53907i	0.638608	−	0.769533i	$-0.279511\pi$
$102$	−12.0335	−	3.76317i	−1.19149	−	0.372609i
$103$	−5.89381	+	5.89381i	−0.580734	+	0.580734i	−0.935105	−	0.354371i	$-0.884695\pi$
$103$	−5.89381	+	5.89381i	−0.580734	+	0.580734i	0.354371	+	0.935105i	$0.384695\pi$
$104$	−2.92162			−0.286489
$105$	9.33222	+	9.63324i	0.910732	+	0.940108i
$106$	6.36516			0.618239
$107$	−3.55096	+	3.55096i	−0.343284	+	0.343284i	−0.857601	−	0.514316i	$-0.828046\pi$
$107$	−3.55096	+	3.55096i	−0.343284	+	0.343284i	0.514316	+	0.857601i	$0.328046\pi$
$108$	−3.19211	−	4.10005i	−0.307161	−	0.394528i
$109$			6.22684i			0.596423i	0.954500	+	0.298211i	$0.0963901\pi$
$109$			6.22684i			0.596423i	−0.954500	+	0.298211i	$0.903610\pi$
$110$	6.69869	−	12.3151i	0.638695	−	1.17420i
$111$	15.0285	−	7.86817i	1.42645	−	0.746813i
$112$	2.44874	+	2.44874i	0.231384	+	0.231384i
$113$	−6.24503	−	6.24503i	−0.587483	−	0.587483i	0.349466	−	0.936949i	$-0.386363\pi$
$113$	−6.24503	−	6.24503i	−0.587483	−	0.587483i	−0.936949	+	0.349466i	$0.886363\pi$
$114$	6.06460	−	3.17511i	0.568002	−	0.297376i
$115$	1.47722	−	2.71578i	0.137752	−	0.253248i
$116$		−	7.01894i		−	0.651692i
$117$	−8.62449	+	1.56243i	−0.797334	+	0.144446i
$118$	−0.847103	+	0.847103i	−0.0779822	+	0.0779822i
$119$	25.2086			2.31087
$120$	2.69481	+	2.78173i	0.246001	+	0.253936i
$121$	−28.3069			−2.57336
$122$	−5.28027	+	5.28027i	−0.478054	+	0.478054i
$123$	12.2306	+	3.82481i	1.10279	+	0.344871i
$124$		−	1.00000i		−	0.0898027i
$125$	−8.48502	−	7.28041i	−0.758924	−	0.651180i
$126$	8.53809	+	5.91902i	0.760634	+	0.527308i
$127$	0.172396	+	0.172396i	0.0152977	+	0.0152977i	0.714714	−	0.699417i	$-0.246557\pi$
$127$	0.172396	+	0.172396i	0.0152977	+	0.0152977i	−0.699417	+	0.714714i	$0.746557\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−1.82462	−	3.48510i	−0.160649	−	0.306846i
$130$	6.26533	−	1.85070i	0.549506	−	0.162317i
$131$		−	6.61958i		−	0.578355i	−0.957275	−	0.289178i	$-0.906618\pi$
$131$		−	6.61958i		−	0.578355i	0.957275	−	0.289178i	$-0.0933818\pi$
$132$	3.24114	−	10.3642i	0.282105	−	0.902085i
$133$	−9.67802	+	9.67802i	−0.839191	+	0.839191i
$134$	−6.34456			−0.548087
$135$	9.44255	+	6.77040i	0.812685	+	0.582703i
$136$	7.27932			0.624197
$137$	6.49887	−	6.49887i	0.555236	−	0.555236i	−0.372711	−	0.927947i	$-0.621572\pi$
$137$	6.49887	−	6.49887i	0.555236	−	0.555236i	0.927947	+	0.372711i	$0.121572\pi$
$138$	0.714749	−	2.28555i	0.0608435	−	0.194559i
$139$		−	10.1101i		−	0.857530i	−0.903416	−	0.428765i	$-0.858949\pi$
$139$		−	10.1101i		−	0.857530i	0.903416	−	0.428765i	$-0.141051\pi$
$140$	−6.80239	−	3.70009i	−0.574907	−	0.312715i
$141$	8.16630	+	15.5980i	0.687726	+	1.31359i
$142$	2.60209	+	2.60209i	0.218363	+	0.218363i
$143$	−12.9522	−	12.9522i	−1.08312	−	1.08312i
$144$	2.46549	+	1.70920i	0.205458	+	0.142433i
$145$	4.44613	+	15.0519i	0.369231	+	1.24999i
$146$			1.89539i			0.156864i
$147$	−8.25336	−	2.58103i	−0.680725	−	0.212880i
$148$	−6.92538	+	6.92538i	−0.569263	+	0.569263i
$149$	−3.39989			−0.278530			−0.139265	−	0.990255i	$-0.544474\pi$
$149$	−3.39989			−0.278530			−0.139265	+	0.990255i	$0.544474\pi$
$150$	−7.54101	−	4.25831i	−0.615721	−	0.347690i
$151$	−0.992815			−0.0807942			−0.0403971	−	0.999184i	$-0.512862\pi$
$151$	−0.992815			−0.0807942			−0.0403971	+	0.999184i	$0.512862\pi$
$152$	−2.79466	+	2.79466i	−0.226677	+	0.226677i
$153$	21.4882	−	3.89284i	1.73722	−	0.314717i
$154$			21.7116i			1.74957i
$155$	0.633448	+	2.14447i	0.0508798	+	0.172248i
$156$	4.48314	−	2.34714i	0.358939	−	0.187922i
$157$	−3.99275	−	3.99275i	−0.318656	−	0.318656i	0.529595	−	0.848251i	$-0.322344\pi$
$157$	−3.99275	−	3.99275i	−0.318656	−	0.318656i	−0.848251	+	0.529595i	$0.822344\pi$
$158$	2.07900	+	2.07900i	0.165396	+	0.165396i
$159$	−9.76715	+	5.11357i	−0.774585	+	0.405533i
$160$	−1.96428	−	1.06845i	−0.155290	−	0.0844686i
$161$			4.78794i			0.377342i
$162$	8.19205	+	3.72697i	0.643628	+	0.292818i
$163$	−4.27466	+	4.27466i	−0.334817	+	0.334817i	−0.854412	−	0.519595i	$-0.826083\pi$
$163$	−4.27466	+	4.27466i	−0.334817	+	0.334817i	0.519595	+	0.854412i	$0.326083\pi$
$164$	−7.39856			−0.577730
$165$	−0.385350	+	24.2787i	−0.0299995	+	1.89009i
$166$	10.5348			0.817658
$167$	−5.03736	+	5.03736i	−0.389802	+	0.389802i	−0.874617	−	0.484815i	$-0.838887\pi$
$167$	−5.03736	+	5.03736i	−0.389802	+	0.389802i	0.484815	+	0.874617i	$0.338887\pi$
$168$	−5.72476	−	1.79028i	−0.441675	−	0.138123i
$169$			4.46412i			0.343394i
$170$	−15.6103	+	4.61108i	−1.19725	+	0.353653i
$171$	−6.75517	+	9.74423i	−0.516581	+	0.745160i
$172$	1.60599	+	1.60599i	0.122455	+	0.122455i
$173$	15.9853	+	15.9853i	1.21534	+	1.21534i	0.969246	+	0.246092i	$0.0791467\pi$
$173$	15.9853	+	15.9853i	1.21534	+	1.21534i	0.246092	+	0.969246i	$0.420853\pi$
$174$	5.63880	+	10.7703i	0.427476	+	0.816498i
$175$	16.9313	+	3.62577i	1.27989	+	0.274082i
$176$			6.26953i			0.472583i
$177$	0.619318	−	1.98039i	0.0465508	−	0.148855i
$178$	−2.69955	+	2.69955i	−0.202340	+	0.202340i
$179$	15.4996			1.15850			0.579248	−	0.815152i	$-0.303346\pi$
$179$	15.4996			1.15850			0.579248	+	0.815152i	$0.303346\pi$
$180$	−6.36985	−	2.10356i	−0.474781	−	0.156790i
$181$	4.19484			0.311800			0.155900	−	0.987773i	$-0.450172\pi$
$181$	4.19484			0.311800			0.155900	+	0.987773i	$0.450172\pi$
$182$	−7.15429	+	7.15429i	−0.530312	+	0.530312i
$183$	3.86042	−	12.3444i	0.285370	−	0.912527i
$184$			1.38258i			0.101925i
$185$	10.4644	−	19.2381i	0.769357	−	1.41442i
$186$	0.803369	+	1.53447i	0.0589059	+	0.112513i
$187$	32.2709	+	32.2709i	2.35988	+	2.35988i
$188$	−7.18779	−	7.18779i	−0.524223	−	0.524223i
$189$	−17.8566	−	2.22332i	−1.29888	−	0.161723i
$190$	4.22279	−	7.76333i	0.306353	−	0.563211i
$191$			21.7176i			1.57143i	0.618588	+	0.785716i	$0.287705\pi$
$191$			21.7176i			1.57143i	−0.618588	+	0.785716i	$0.712295\pi$
$192$	−1.65310	−	0.516967i	−0.119302	−	0.0373089i
$193$	−13.9466	+	13.9466i	−1.00390	+	1.00390i	−0.00390758	+	0.999992i	$0.501244\pi$
$193$	−13.9466	+	13.9466i	−1.00390	+	1.00390i	−0.999992	+	0.00390758i	$0.998756\pi$
$194$	7.63213			0.547955
$195$	−8.12717	+	7.87321i	−0.581998	+	0.563812i
$196$	4.99265			0.356618
$197$	3.81388	−	3.81388i	0.271728	−	0.271728i	−0.558068	−	0.829795i	$-0.688457\pi$
$197$	3.81388	−	3.81388i	0.271728	−	0.271728i	0.829795	+	0.558068i	$0.188457\pi$
$198$	3.35282	+	18.5073i	0.238274	+	1.31526i
$199$		−	19.9944i		−	1.41737i	−0.705526	−	0.708684i	$-0.749289\pi$
$199$		−	19.9944i		−	1.41737i	0.705526	−	0.708684i	$-0.250711\pi$
$200$	4.88915	+	1.04699i	0.345715	+	0.0740333i
$201$	9.73554	−	5.09702i	0.686692	−	0.359516i
$202$	−10.9371	−	10.9371i	−0.769533	−	0.769533i
$203$	−17.1875	−	17.1875i	−1.20633	−	1.20633i
$204$	−11.1699	+	5.84798i	−0.782050	+	0.409441i
$205$	15.8660	−	4.68660i	1.10813	−	0.327327i
$206$			8.33510i			0.580734i
$207$	0.739378	+	4.08131i	0.0513903	+	0.283671i
$208$	−2.06590	+	2.06590i	−0.143244	+	0.143244i
$209$	−24.7787			−1.71398
$210$	13.4106	+	0.212852i	0.925420	+	0.0146882i
$211$	9.96204			0.685815			0.342908	−	0.939369i	$-0.388588\pi$
$211$	9.96204			0.685815			0.342908	+	0.939369i	$0.388588\pi$
$212$	4.50085	−	4.50085i	0.309119	−	0.309119i
$213$	−6.08327	−	1.90239i	−0.416819	−	0.130350i
$214$			5.02181i			0.343284i
$215$	−4.46130	−	2.42668i	−0.304258	−	0.165498i
$216$	−5.15634	−	0.642014i	−0.350844	−	0.0436835i
$217$	−2.44874	−	2.44874i	−0.166231	−	0.166231i
$218$	4.40304	+	4.40304i	0.298211	+	0.298211i
$219$	−1.52270	−	2.90842i	−0.102895	−	0.196533i
$220$	−3.97142	−	13.4448i	−0.267753	−	0.906448i
$221$			21.2674i			1.43060i
$222$	5.06315	−	16.1904i	0.339817	−	1.08663i
$223$	6.64495	−	6.64495i	0.444979	−	0.444979i	−0.448702	−	0.893681i	$-0.648114\pi$
$223$	6.64495	−	6.64495i	0.444979	−	0.444979i	0.893681	+	0.448702i	$0.148114\pi$
$224$	3.46304			0.231384
$225$	14.9924	+	0.476038i	0.999496	+	0.0317359i
$226$	−8.83181			−0.587483
$227$	18.5718	−	18.5718i	1.23266	−	1.23266i	0.269716	−	0.962940i	$-0.413070\pi$
$227$	18.5718	−	18.5718i	1.23266	−	1.23266i	0.962940	−	0.269716i	$-0.0869298\pi$
$228$	2.04318	−	6.53347i	0.135313	−	0.432689i
$229$		−	24.0483i		−	1.58915i	−0.607163	−	0.794577i	$-0.707693\pi$
$229$		−	24.0483i		−	1.58915i	0.607163	−	0.794577i	$-0.292307\pi$
$230$	−0.875794	−	2.96490i	−0.0577482	−	0.195500i
$231$	−17.4424	−	33.3158i	−1.14763	−	2.19202i
$232$	−4.96314	−	4.96314i	−0.325846	−	0.325846i
$233$	1.15508	+	1.15508i	0.0756720	+	0.0756720i	0.743930	−	0.668258i	$-0.232960\pi$
$233$	1.15508	+	1.15508i	0.0756720	+	0.0756720i	−0.668258	+	0.743930i	$0.732960\pi$
$234$	−4.99363	+	7.20324i	−0.326444	+	0.470890i
$235$	19.9671	+	10.8609i	1.30251	+	0.708486i
$236$			1.19798i			0.0779822i
$237$	−4.86036	−	1.51996i	−0.315714	−	0.0987319i
$238$	17.8252	−	17.8252i	1.15543	−	1.15543i
$239$	14.9692			0.968279			0.484140	−	0.874991i	$-0.339133\pi$
$239$	14.9692			0.968279			0.484140	+	0.874991i	$0.339133\pi$
$240$	3.87250	+	0.0614640i	0.249969	+	0.00396749i
$241$	14.4611			0.931524			0.465762	−	0.884910i	$-0.345780\pi$
$241$	14.4611			0.931524			0.465762	+	0.884910i	$0.345780\pi$
$242$	−20.0160	+	20.0160i	−1.28668	+	1.28668i
$243$	−15.5646	+	0.862316i	−0.998469	+	0.0553176i
$244$			7.46744i			0.478054i
$245$	−10.7066	+	3.16259i	−0.684018	+	0.202050i
$246$	11.3529	−	5.94377i	0.723832	−	0.378961i
$247$	−8.16495	−	8.16495i	−0.519523	−	0.519523i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	−16.1653	+	8.46332i	−1.02444	+	0.536341i
$250$	−11.1478	+	0.851790i	−0.705052	+	0.0538719i
$251$		−	9.30186i		−	0.587128i	−0.955939	−	0.293564i	$-0.905159\pi$
$251$		−	9.30186i		−	0.587128i	0.955939	−	0.293564i	$-0.0948414\pi$
$252$	10.2227	−	1.85197i	0.643971	−	0.116663i
$253$	−6.12929	+	6.12929i	−0.385345	+	0.385345i
$254$	0.243805			0.0152977
$255$	20.2491	−	19.6164i	1.26805	−	1.22842i
$256$	1.00000			0.0625000
$257$	−9.78406	+	9.78406i	−0.610313	+	0.610313i	−0.943028	−	0.332715i	$-0.892035\pi$
$257$	−9.78406	+	9.78406i	−0.610313	+	0.610313i	0.332715	+	0.943028i	$0.392035\pi$
$258$	−3.75454	−	1.17414i	−0.233747	−	0.0730987i
$259$			33.9169i			2.10749i
$260$	3.12162	−	5.73890i	0.193594	−	0.355911i
$261$	−17.3051	−	11.9967i	−1.07116	−	0.742580i
$262$	−4.68075	−	4.68075i	−0.289178	−	0.289178i
$263$	0.447596	+	0.447596i	0.0275999	+	0.0275999i	0.720772	−	0.693172i	$-0.243787\pi$
$263$	0.447596	+	0.447596i	0.0275999	+	0.0275999i	−0.693172	+	0.720772i	$0.743787\pi$
$264$	−5.03674	−	9.62040i	−0.309990	−	0.592095i
$265$	−6.80087	+	12.5030i	−0.417774	+	0.768052i
$266$			13.6868i			0.839191i
$267$	1.97365	−	6.31112i	0.120785	−	0.386235i
$268$	−4.48628	+	4.48628i	−0.274043	+	0.274043i
$269$	6.06422			0.369742			0.184871	−	0.982763i	$-0.440813\pi$
$269$	6.06422			0.369742			0.184871	+	0.982763i	$0.440813\pi$
$270$	11.4643	−	1.88950i	0.697694	−	0.114991i
$271$	−5.93827			−0.360724			−0.180362	−	0.983600i	$-0.557727\pi$
$271$	−5.93827			−0.360724			−0.180362	+	0.983600i	$0.557727\pi$
$272$	5.14726	−	5.14726i	0.312098	−	0.312098i
$273$	5.23051	−	16.7256i	0.316565	−	1.01228i
$274$		−	9.19079i		−	0.555236i
$275$	17.0332	+	26.3162i	1.02714	+	1.58693i
$276$	−1.11072	−	2.12153i	−0.0668577	−	0.127701i
$277$	5.29723	+	5.29723i	0.318280	+	0.318280i	0.848106	−	0.529826i	$-0.177743\pi$
$277$	5.29723	+	5.29723i	0.318280	+	0.318280i	−0.529826	+	0.848106i	$0.677743\pi$
$278$	−7.14894	−	7.14894i	−0.428765	−	0.428765i
$279$	−2.46549	−	1.70920i	−0.147605	−	0.102327i
$280$	−7.42638	+	2.19366i	−0.443811	+	0.131096i
$281$			2.98650i			0.178159i	0.996024	+	0.0890797i	$0.0283926\pi$
$281$			2.98650i			0.178159i	−0.996024	+	0.0890797i	$0.971607\pi$
$282$	16.8039	+	5.25500i	1.00066	+	0.312931i
$283$	−20.6733	+	20.6733i	−1.22890	+	1.22890i	−0.264516	+	0.964381i	$0.585212\pi$
$283$	−20.6733	+	20.6733i	−1.22890	+	1.22890i	−0.964381	+	0.264516i	$0.914788\pi$
$284$	3.67991			0.218363
$285$	−0.242921	+	15.3051i	−0.0143894	+	0.906593i
$286$	−18.3172			−1.08312
$287$	−18.1171	+	18.1171i	−1.06942	+	1.06942i
$288$	2.95195	−	0.534780i	0.173945	−	0.0315122i
$289$		−	35.9886i		−	2.11697i
$290$	13.7872	+	7.49940i	0.809611	+	0.440380i
$291$	−11.7113	+	6.13142i	−0.686527	+	0.359430i
$292$	1.34025	+	1.34025i	0.0784319	+	0.0784319i
$293$	14.3597	+	14.3597i	0.838904	+	0.838904i	0.988715	−	0.149811i	$-0.0478665\pi$
$293$	14.3597	+	14.3597i	0.838904	+	0.838904i	−0.149811	+	0.988715i	$0.547866\pi$
$294$	−7.66107	+	4.01094i	−0.446803	+	0.233923i
$295$	−0.758861	−	2.56904i	−0.0441826	−	0.149575i
$296$			9.79397i			0.569263i
$297$	−20.0130	−	25.7054i	−1.16127	−	1.49158i
$298$	−2.40408	+	2.40408i	−0.139265	+	0.139265i
$299$	−4.03938			−0.233604
$300$	−8.34338	+	2.32122i	−0.481705	+	0.134016i
$301$	7.86528			0.453347
$302$	−0.702026	+	0.702026i	−0.0403971	+	0.0403971i
$303$	25.5692	+	7.99614i	1.46891	+	0.459366i
$304$			3.95225i			0.226677i
$305$	−4.73023	−	16.0137i	−0.270852	−	0.916940i
$306$	12.4418	−	17.9471i	0.711250	−	1.02597i
$307$	7.70450	+	7.70450i	0.439719	+	0.439719i	0.891917	−	0.452198i	$-0.149360\pi$
$307$	7.70450	+	7.70450i	0.439719	+	0.439719i	−0.452198	+	0.891917i	$0.649360\pi$
$308$	15.3524	+	15.3524i	0.874786	+	0.874786i
$309$	−6.69616	−	12.7900i	−0.380931	−	0.727596i
$310$	1.96428	+	1.06845i	0.111564	+	0.0606840i
$311$		−	28.6925i		−	1.62700i	−0.581562	−	0.813502i	$-0.697558\pi$
$311$		−	28.6925i		−	1.62700i	0.581562	−	0.813502i	$-0.302442\pi$
$312$	1.51038	−	4.82974i	0.0855085	−	0.273430i
$313$	23.1963	−	23.1963i	1.31113	−	1.31113i	0.390554	−	0.920580i	$-0.372283\pi$
$313$	23.1963	−	23.1963i	1.31113	−	1.31113i	0.920580	−	0.390554i	$-0.127717\pi$
$314$	−5.64660			−0.318656
$315$	−20.7492	+	10.4470i	−1.16908	+	0.588625i
$316$	2.94015			0.165396
$317$	5.33677	−	5.33677i	0.299743	−	0.299743i	−0.541170	−	0.840913i	$-0.682019\pi$
$317$	5.33677	−	5.33677i	0.299743	−	0.299743i	0.840913	+	0.541170i	$0.182019\pi$
$318$	−3.29058	+	10.5223i	−0.184526	+	0.590059i
$319$		−	44.0054i		−	2.46383i
$320$	−2.14447	+	0.633448i	−0.119879	+	0.0354108i
$321$	−4.03437	−	7.70582i	−0.225177	−	0.430097i
$322$	3.38558	+	3.38558i	0.188671	+	0.188671i
$323$	20.3432	+	20.3432i	1.13193	+	1.13193i
$324$	8.42802	−	3.15729i	0.468223	−	0.175405i
$325$	−3.05891	+	14.2843i	−0.169678	+	0.792348i
$326$			6.04528i			0.334817i
$327$	−10.2936	−	3.21907i	−0.569237	−	0.178015i
$328$	−5.23157	+	5.23157i	−0.288865	+	0.288865i
$329$	−35.2020			−1.94075
$330$	16.8952	+	17.4401i	0.930048	+	0.960047i
$331$	5.49366			0.301959			0.150979	−	0.988537i	$-0.451757\pi$
$331$	5.49366			0.301959			0.150979	+	0.988537i	$0.451757\pi$
$332$	7.44922	−	7.44922i	0.408829	−	0.408829i
$333$	5.23762	+	28.9113i	0.287020	+	1.58433i
$334$			7.12390i			0.389802i
$335$	6.77886	−	12.4625i	0.370369	−	0.680900i
$336$	−5.31393	+	2.78210i	−0.289899	+	0.151776i
$337$	7.30292	+	7.30292i	0.397815	+	0.397815i	0.877462	−	0.479646i	$-0.159235\pi$
$337$	7.30292	+	7.30292i	0.397815	+	0.397815i	−0.479646	+	0.877462i	$0.659235\pi$
$338$	3.15661	+	3.15661i	0.171697	+	0.171697i
$339$	13.5521	−	7.09520i	0.736051	−	0.385358i
$340$	−7.77761	+	14.2987i	−0.421800	+	0.775454i
$341$		−	6.26953i		−	0.339514i
$342$	2.11358	+	11.6668i	0.114290	+	0.630870i
$343$	−4.91548	+	4.91548i	−0.265411	+	0.265411i
$344$	2.27121			0.122455
$345$	3.72579	+	3.84597i	0.200590	+	0.207060i
$346$	22.6066			1.21534
$347$	13.4736	−	13.4736i	0.723303	−	0.723303i	−0.245974	−	0.969276i	$-0.579108\pi$
$347$	13.4736	−	13.4736i	0.723303	−	0.723303i	0.969276	+	0.245974i	$0.0791077\pi$
$348$	11.6030	+	3.62856i	0.621987	+	0.194511i
$349$		−	28.9757i		−	1.55103i	−0.631327	−	0.775517i	$-0.717489\pi$
$349$		−	28.9757i		−	1.55103i	0.631327	−	0.775517i	$-0.282511\pi$
$350$	14.5361	−	9.40846i	0.776985	−	0.502903i
$351$	1.87572	−	15.0649i	0.100119	−	0.804104i
$352$	4.43322	+	4.43322i	0.236292	+	0.236292i
$353$	6.55865	+	6.55865i	0.349082	+	0.349082i	0.859768	−	0.510686i	$-0.170608\pi$
$353$	6.55865	+	6.55865i	0.349082	+	0.349082i	−0.510686	+	0.859768i	$0.670608\pi$
$354$	−0.962423	−	1.83827i	−0.0511522	−	0.0977030i
$355$	−7.89146	+	2.33103i	−0.418835	+	0.123718i
$356$			3.81775i			0.202340i
$357$	−13.0320	+	41.6724i	−0.689727	+	2.20554i
$358$	10.9599	−	10.9599i	0.579248	−	0.579248i
$359$	−15.8792			−0.838073			−0.419037	−	0.907969i	$-0.637632\pi$
$359$	−15.8792			−0.838073			−0.419037	+	0.907969i	$0.637632\pi$
$360$	−5.99161	+	3.01673i	−0.315785	+	0.158995i
$361$	3.37975			0.177881
$362$	2.96620	−	2.96620i	0.155900	−	0.155900i
$363$	14.6337	−	46.7943i	0.768073	−	2.45606i
$364$			10.1177i			0.530312i
$365$	−3.72309	−	2.02514i	−0.194875	−	0.106001i
$366$	−5.99910	−	11.4586i	−0.313578	−	0.598948i
$367$	−12.9999	−	12.9999i	−0.678591	−	0.678591i	0.281090	−	0.959681i	$-0.409304\pi$
$367$	−12.9999	−	12.9999i	−0.678591	−	0.678591i	−0.959681	+	0.281090i	$0.909304\pi$
$368$	0.977633	+	0.977633i	0.0509626	+	0.0509626i
$369$	−12.6456	+	18.2411i	−0.658303	+	0.949592i
$370$	−6.20397	−	21.0028i	−0.322529	−	1.09189i
$371$		−	22.0428i		−	1.14441i
$372$	1.65310	+	0.516967i	0.0857093	+	0.0268035i
$373$	1.57385	−	1.57385i	0.0814908	−	0.0814908i	−0.665186	−	0.746677i	$-0.731648\pi$
$373$	1.57385	−	1.57385i	0.0814908	−	0.0814908i	0.746677	+	0.665186i	$0.231648\pi$
$374$	45.6379			2.35988
$375$	16.4217	−	10.2629i	0.848015	−	0.529973i
$376$	−10.1651			−0.524223
$377$	14.5004	−	14.5004i	0.746810	−	0.746810i
$378$	−14.1987	+	11.0544i	−0.730300	+	0.568577i
$379$		−	9.52834i		−	0.489438i	−0.969594	−	0.244719i	$-0.921304\pi$
$379$		−	9.52834i		−	0.489438i	0.969594	−	0.244719i	$-0.0786957\pi$
$380$	−2.50354	−	8.47547i	−0.128429	−	0.434782i
$381$	−0.374111	+	0.195865i	−0.0191663	+	0.0100345i
$382$	15.3567	+	15.3567i	0.785716	+	0.785716i
$383$	−1.47124	−	1.47124i	−0.0751768	−	0.0751768i	0.668519	−	0.743695i	$-0.266929\pi$
$383$	−1.47124	−	1.47124i	−0.0751768	−	0.0751768i	−0.743695	+	0.668519i	$0.766929\pi$
$384$	−1.53447	+	0.803369i	−0.0783056	+	0.0409967i
$385$	−42.6478	−	23.1978i	−2.17353	−	1.18227i
$386$			19.7235i			1.00390i
$387$	6.70449	−	1.21460i	0.340808	−	0.0617415i
$388$	5.39673	−	5.39673i	0.273978	−	0.273978i
$389$	−23.6658			−1.19990			−0.599951	−	0.800037i	$-0.704813\pi$
$389$	−23.6658			−1.19990			−0.599951	+	0.800037i	$0.704813\pi$
$390$	−0.179575	+	11.3140i	−0.00909312	+	0.572905i
$391$	10.0643			0.508972
$392$	3.53034	−	3.53034i	0.178309	−	0.178309i
$393$	10.9428	+	3.42210i	0.551993	+	0.172622i
$394$		−	5.39364i		−	0.271728i
$395$	−6.30505	+	1.86243i	−0.317242	+	0.0937091i
$396$	15.4575	+	10.7159i	0.776766	+	0.538492i
$397$	23.9139	+	23.9139i	1.20020	+	1.20020i	0.974105	+	0.226097i	$0.0725968\pi$
$397$	23.9139	+	23.9139i	1.20020	+	1.20020i	0.226097	+	0.974105i	$0.427403\pi$
$398$	−14.1382	−	14.1382i	−0.708684	−	0.708684i
$399$	−10.9955	−	21.0020i	−0.550466	−	1.05141i
$400$	4.19749	−	2.71682i	0.209874	−	0.135841i
$401$			16.0705i			0.802523i	0.915964	+	0.401262i	$0.131428\pi$
$401$			16.0705i			0.802523i	−0.915964	+	0.401262i	$0.868572\pi$
$402$	3.27993	−	10.4882i	0.163588	−	0.523104i
$403$	2.06590	−	2.06590i	0.102910	−	0.102910i
$404$	−15.4674			−0.769533
$405$	−16.0736	+	12.1094i	−0.798706	+	0.601722i
$406$	−24.3069			−1.20633
$407$	−43.4188	+	43.4188i	−2.15219	+	2.15219i
$408$	−3.76317	+	12.0335i	−0.186305	+	0.595745i
$409$			26.3636i			1.30359i	0.758393	+	0.651797i	$0.225985\pi$
$409$			26.3636i			1.30359i	−0.758393	+	0.651797i	$0.774015\pi$
$410$	7.90501	−	14.5329i	0.390400	−	0.717727i
$411$	7.38359	+	14.1030i	0.364206	+	0.695649i
$412$	5.89381	+	5.89381i	0.290367	+	0.290367i
$413$	2.93355	+	2.93355i	0.144351	+	0.144351i
$414$	3.40874	+	2.36310i	0.167531	+	0.116140i
$415$	−11.2559	+	20.6933i	−0.552531	+	1.01579i
$416$			2.92162i			0.143244i
$417$	16.7131	+	5.22660i	0.818443	+	0.255948i
$418$	−17.5212	+	17.5212i	−0.856990	+	0.856990i
$419$	8.03339			0.392457			0.196228	−	0.980558i	$-0.437131\pi$
$419$	8.03339			0.392457			0.196228	+	0.980558i	$0.437131\pi$
$420$	9.63324	−	9.33222i	0.470054	−	0.455366i
$421$	−9.22916			−0.449801			−0.224901	−	0.974382i	$-0.572206\pi$
$421$	−9.22916			−0.449801			−0.224901	+	0.974382i	$0.572206\pi$
$422$	7.04422	−	7.04422i	0.342908	−	0.342908i
$423$	−30.0068	+	5.43608i	−1.45898	+	0.264311i
$424$		−	6.36516i		−	0.309119i
$425$	7.62138	−	35.5897i	0.369691	−	1.72636i
$426$	−5.64672	+	2.95633i	−0.273584	+	0.143235i
$427$	18.2858	+	18.2858i	0.884912	+	0.884912i
$428$	3.55096	+	3.55096i	0.171642	+	0.171642i
$429$	28.1072	−	14.7155i	1.35703	−	0.710469i
$430$	−4.87053	+	1.43869i	−0.234878	+	0.0693799i
$431$			14.7050i			0.708316i	0.935186	+	0.354158i	$0.115233\pi$
$431$			14.7050i			0.708316i	−0.935186	+	0.354158i	$0.884767\pi$
$432$	−4.10005	+	3.19211i	−0.197264	+	0.153580i
$433$	22.5252	−	22.5252i	1.08249	−	1.08249i	0.0862166	−	0.996276i	$-0.472522\pi$
$433$	22.5252	−	22.5252i	1.08249	−	1.08249i	0.996276	−	0.0862166i	$-0.0274777\pi$
$434$	−3.46304			−0.166231
$435$	−27.1808	−	0.431412i	−1.30322	−	0.0206846i
$436$	6.22684			0.298211
$437$	−3.86385	+	3.86385i	−0.184833	+	0.184833i
$438$	−3.13328	−	0.979855i	−0.149714	−	0.0468193i
$439$		−	13.5046i		−	0.644538i	−0.946648	−	0.322269i	$-0.895555\pi$
$439$		−	13.5046i		−	0.644538i	0.946648	−	0.322269i	$-0.104445\pi$
$440$	−12.3151	−	6.69869i	−0.587101	−	0.319347i
$441$	8.53342	−	12.3093i	0.406353	−	0.586159i
$442$	15.0384	+	15.0384i	0.715302	+	0.715302i
$443$	−4.04923	−	4.04923i	−0.192385	−	0.192385i	0.604341	−	0.796726i	$-0.293436\pi$
$443$	−4.04923	−	4.04923i	−0.192385	−	0.192385i	−0.796726	+	0.604341i	$0.793436\pi$
$444$	−7.86817	−	15.0285i	−0.373407	−	0.713223i
$445$	−2.41835	−	8.18704i	−0.114641	−	0.388103i
$446$		−	9.39738i		−	0.444979i
$447$	1.75763	−	5.62036i	0.0831330	−	0.265834i
$448$	2.44874	−	2.44874i	0.115692	−	0.115692i
$449$	19.4044			0.915750			0.457875	−	0.889017i	$-0.348611\pi$
$449$	19.4044			0.915750			0.457875	+	0.889017i	$0.348611\pi$
$450$	10.9379	−	10.2646i	0.515616	−	0.483880i
$451$	−46.3854			−2.18421
$452$	−6.24503	+	6.24503i	−0.293742	+	0.293742i
$453$	0.513252	−	1.64122i	0.0241147	−	0.0771115i
$454$		−	26.2645i		−	1.23266i
$455$	−6.40904	−	21.6971i	−0.300460	−	1.01717i
$456$	−3.17511	−	6.06460i	−0.148688	−	0.284001i
$457$	−15.7048	−	15.7048i	−0.734641	−	0.734641i	0.236894	−	0.971535i	$-0.423871\pi$
$457$	−15.7048	−	15.7048i	−0.734641	−	0.734641i	−0.971535	+	0.236894i	$0.923871\pi$
$458$	−17.0047	−	17.0047i	−0.794577	−	0.794577i
$459$	−4.67343	+	37.5347i	−0.218137	+	1.75197i
$460$	−2.71578	−	1.47722i	−0.126624	−	0.0688759i
$461$			39.0740i			1.81986i	0.414767	+	0.909928i	$0.363863\pi$
$461$			39.0740i			1.81986i	−0.414767	+	0.909928i	$0.636137\pi$
$462$	−35.8915	−	11.2242i	−1.66982	−	0.522196i
$463$	12.1876	−	12.1876i	0.566406	−	0.566406i	−0.364714	−	0.931120i	$-0.618833\pi$
$463$	12.1876	−	12.1876i	0.566406	−	0.566406i	0.931120	+	0.364714i	$0.118833\pi$
$464$	−7.01894			−0.325846
$465$	−3.87250	−	0.0614640i	−0.179583	−	0.00285033i
$466$	1.63353			0.0756720
$467$	−2.32458	+	2.32458i	−0.107569	+	0.107569i	−0.758843	−	0.651274i	$-0.774235\pi$
$467$	−2.32458	+	2.32458i	−0.107569	+	0.107569i	0.651274	+	0.758843i	$0.274235\pi$
$468$	1.56243	+	8.62449i	0.0722232	+	0.398667i
$469$			21.9715i			1.01455i
$470$	21.7987	−	6.43904i	1.00550	−	0.297011i
$471$	8.66453	−	4.53630i	0.399241	−	0.209022i
$472$	0.847103	+	0.847103i	0.0389911	+	0.0389911i
$473$	10.0688	+	10.0688i	0.462963	+	0.462963i
$474$	−4.51157	+	2.36202i	−0.207223	+	0.108491i
$475$	10.7375	+	16.5895i	0.492672	+	0.761179i
$476$		−	25.2086i		−	1.15543i
$477$	−3.40396	−	18.7896i	−0.155857	−	0.860318i
$478$	10.5848	−	10.5848i	0.484140	−	0.484140i
$479$	12.5578			0.573783			0.286891	−	0.957963i	$-0.407378\pi$
$479$	12.5578			0.573783			0.286891	+	0.957963i	$0.407378\pi$
$480$	2.78173	−	2.69481i	0.126968	−	0.123001i
$481$	−28.6143			−1.30470
$482$	10.2256	−	10.2256i	0.465762	−	0.465762i
$483$	−7.91495	−	2.47520i	−0.360143	−	0.112626i
$484$			28.3069i			1.28668i
$485$	−8.15457	+	14.9917i	−0.370280	+	0.680737i
$486$	−10.3961	+	11.6156i	−0.471576	+	0.526893i
$487$	−7.00546	−	7.00546i	−0.317448	−	0.317448i	0.530338	−	0.847786i	$-0.322065\pi$
$487$	−7.00546	−	7.00546i	−0.317448	−	0.317448i	−0.847786	+	0.530338i	$0.822065\pi$
$488$	5.28027	+	5.28027i	0.239027	+	0.239027i
$489$	−4.85659	−	9.27630i	−0.219622	−	0.419489i
$490$	−5.33441	+	9.80698i	−0.240984	+	0.443034i
$491$			11.7494i			0.530241i	0.964215	+	0.265121i	$0.0854118\pi$
$491$			11.7494i			0.530241i	−0.964215	+	0.265121i	$0.914588\pi$
$492$	3.82481	−	12.2306i	0.172436	−	0.551397i
$493$	−36.1283	+	36.1283i	−1.62714	+	1.62714i
$494$	−11.5470			−0.519523
$495$	−39.9360	−	13.1883i	−1.79499	−	0.592770i
$496$	−1.00000			−0.0449013
$497$	9.01115	−	9.01115i	0.404205	−	0.404205i
$498$	−5.44614	+	17.4151i	−0.244047	+	0.780388i
$499$		−	26.7044i		−	1.19545i	−0.801701	−	0.597726i	$-0.796071\pi$
$499$		−	26.7044i		−	1.19545i	0.801701	−	0.597726i	$-0.203929\pi$
$500$	−7.28041	+	8.48502i	−0.325590	+	0.379462i
$501$	−5.72312	−	10.9314i	−0.255690	−	0.488379i
$502$	−6.57740	−	6.57740i	−0.293564	−	0.293564i
$503$	−23.1182	−	23.1182i	−1.03079	−	1.03079i	−0.999511	−	0.0312770i	$-0.990043\pi$
$503$	−23.1182	−	23.1182i	−1.03079	−	1.03079i	−0.0312770	−	0.999511i	$-0.509957\pi$
$504$	5.91902	−	8.53809i	0.263654	−	0.380317i
$505$	33.1694	−	9.79781i	1.47602	−	0.435997i
$506$			8.66813i			0.385345i
$507$	−7.37964	−	2.30780i	−0.327741	−	0.102493i
$508$	0.172396	−	0.172396i	0.00764884	−	0.00764884i
$509$	35.6347			1.57948			0.789740	−	0.613442i	$-0.210215\pi$
$509$	35.6347			1.57948			0.789740	+	0.613442i	$0.210215\pi$
$510$	0.447417	−	28.1892i	0.0198119	−	1.24824i
$511$	6.56382			0.290366
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−12.6160	−	16.2044i	−0.557010	−	0.715443i
$514$			13.8367i			0.610313i
$515$	−16.3725	−	8.90566i	−0.721459	−	0.392430i
$516$	−3.48510	+	1.82462i	−0.153423	+	0.0803243i
$517$	−45.0640	−	45.0640i	−1.98191	−	1.98191i
$518$	23.9829	+	23.9829i	1.05375	+	1.05375i
$519$	−34.6892	+	18.1614i	−1.52269	+	0.797199i
$520$	−1.85070	−	6.26533i	−0.0811585	−	0.274753i
$521$			27.6615i			1.21187i	0.795513	+	0.605936i	$0.207201\pi$
$521$			27.6615i			1.21187i	−0.795513	+	0.605936i	$0.792799\pi$
$522$	−20.7196	+	3.75359i	−0.906870	+	0.164290i
$523$	15.1994	−	15.1994i	0.664622	−	0.664622i	−0.291844	−	0.956466i	$-0.594269\pi$
$523$	15.1994	−	15.1994i	0.664622	−	0.664622i	0.956466	+	0.291844i	$0.0942687\pi$
$524$	−6.61958			−0.289178
$525$	−14.7467	+	26.1148i	−0.643599	+	1.13974i
$526$	0.632996			0.0275999
$527$	−5.14726	+	5.14726i	−0.224218	+	0.224218i
$528$	−10.3642	−	3.24114i	−0.451042	−	0.141052i
$529$		−	21.0885i		−	0.916890i
$530$	4.03200	+	13.6499i	0.175139	+	0.592913i
$531$	2.95362	+	2.04759i	0.128176	+	0.0888579i
$532$	9.67802	+	9.67802i	0.419595	+	0.419595i
$533$	−15.2847	−	15.2847i	−0.662053	−	0.662053i
$534$	−3.06706	−	5.85822i	−0.132725	−	0.253510i
$535$	−9.86427	−	5.36557i	−0.426469	−	0.231974i
$536$			6.34456i			0.274043i
$537$	−8.01278	+	25.6224i	−0.345777	+	1.10569i
$538$	4.28805	−	4.28805i	0.184871	−	0.184871i
$539$	31.3015			1.34825
$540$	6.77040	−	9.44255i	0.291352	−	0.406343i
$541$	−16.1694			−0.695179			−0.347589	−	0.937647i	$-0.613000\pi$
$541$	−16.1694			−0.695179			−0.347589	+	0.937647i	$0.613000\pi$
$542$	−4.19899	+	4.19899i	−0.180362	+	0.180362i
$543$	−2.16859	+	6.93449i	−0.0930631	+	0.297587i
$544$		−	7.27932i		−	0.312098i
$545$	−13.3533	+	3.94438i	−0.571991	+	0.168959i
$546$	−8.12824	−	15.5253i	−0.347857	−	0.664422i
$547$	−15.4445	−	15.4445i	−0.660360	−	0.660360i	0.295105	−	0.955465i	$-0.404645\pi$
$547$	−15.4445	−	15.4445i	−0.660360	−	0.660360i	−0.955465	+	0.295105i	$0.904645\pi$
$548$	−6.49887	−	6.49887i	−0.277618	−	0.277618i
$549$	18.4109	+	12.7633i	0.785758	+	0.544725i
$550$	30.6527	+	6.56413i	1.30703	+	0.279895i
$551$		−	27.7406i		−	1.18179i
$552$	−2.28555	−	0.714749i	−0.0972794	−	0.0304217i
$553$	7.19965	−	7.19965i	0.306160	−	0.306160i
$554$	7.49142			0.318280
$555$	26.3928	+	27.2442i	1.12031	+	1.15645i
$556$	−10.1101			−0.428765
$557$	−14.3040	+	14.3040i	−0.606079	+	0.606079i	−0.941919	−	0.335840i	$-0.890980\pi$
$557$	−14.3040	+	14.3040i	−0.606079	+	0.606079i	0.335840	+	0.941919i	$0.390980\pi$
$558$	−2.95195	+	0.534780i	−0.124966	+	0.0226391i
$559$			6.63561i			0.280657i
$560$	−3.70009	+	6.80239i	−0.156357	+	0.287454i
$561$	−70.0300	+	36.6641i	−2.95667	+	1.54796i
$562$	2.11177	+	2.11177i	0.0890797	+	0.0890797i
$563$	6.91953	+	6.91953i	0.291623	+	0.291623i	0.837721	−	0.546098i	$-0.183887\pi$
$563$	6.91953	+	6.91953i	0.291623	+	0.291623i	−0.546098	+	0.837721i	$0.683887\pi$
$564$	15.5980	−	8.16630i	0.656794	−	0.343863i
$565$	9.43636	−	17.3482i	0.396991	−	0.729843i
$566$			29.2364i			1.22890i
$567$	12.9066	−	28.3694i	0.542028	−	1.19140i
$568$	2.60209	−	2.60209i	0.109181	−	0.109181i
$569$	7.28785			0.305523			0.152761	−	0.988263i	$-0.451183\pi$
$569$	7.28785			0.305523			0.152761	+	0.988263i	$0.451183\pi$
$570$	10.6505	+	10.9941i	0.446102	+	0.460491i
$571$	36.3365			1.52063			0.760317	−	0.649552i	$-0.225044\pi$
$571$	36.3365			1.52063			0.760317	+	0.649552i	$0.225044\pi$
$572$	−12.9522	+	12.9522i	−0.541559	+	0.541559i
$573$	−35.9014	−	11.2273i	−1.49980	−	0.469027i
$574$			25.6215i			1.06942i
$575$	6.75965	+	1.44755i	0.281897	+	0.0603670i
$576$	1.70920	−	2.46549i	0.0712165	−	0.102729i
$577$	19.3897	+	19.3897i	0.807205	+	0.807205i	0.984210	−	0.177005i	$-0.0566408\pi$
$577$	19.3897	+	19.3897i	0.807205	+	0.807205i	−0.177005	+	0.984210i	$0.556641\pi$
$578$	−25.4478	−	25.4478i	−1.05849	−	1.05849i
$579$	−15.8452	−	30.2651i	−0.658506	−	1.25778i
$580$	15.0519	−	4.44613i	0.624996	−	0.184616i
$581$		−	36.4824i		−	1.51355i
$582$	−3.94556	+	12.6167i	−0.163549	+	0.522979i
$583$	28.2182	−	28.2182i	1.16868	−	1.16868i
$584$	1.89539			0.0784319
$585$	−8.81374	−	17.5052i	−0.364403	−	0.723752i
$586$	20.3077			0.838904
$587$	18.0841	−	18.0841i	0.746412	−	0.746412i	−0.227392	−	0.973803i	$-0.573020\pi$
$587$	18.0841	−	18.0841i	0.746412	−	0.746412i	0.973803	+	0.227392i	$0.0730197\pi$
$588$	−2.58103	+	8.25336i	−0.106440	+	0.340363i
$589$		−	3.95225i		−	0.162849i
$590$	−2.35318	−	1.27999i	−0.0968789	−	0.0526963i
$591$	4.33308	+	8.27638i	0.178239	+	0.340445i
$592$	6.92538	+	6.92538i	0.284631	+	0.284631i
$593$	26.9043	+	26.9043i	1.10483	+	1.10483i	0.993819	+	0.111009i	$0.0354082\pi$
$593$	26.9043	+	26.9043i	1.10483	+	1.10483i	0.111009	+	0.993819i	$0.464592\pi$
$594$	−32.3278	−	4.02512i	−1.32643	−	0.165153i
$595$	15.9683	+	54.0590i	0.654638	+	2.21620i
$596$			3.39989i			0.139265i
$597$	33.0528	+	10.3365i	1.35276	+	0.423043i
$598$	−2.85628	+	2.85628i	−0.116802	+	0.116802i
$599$	−41.6420			−1.70145			−0.850723	−	0.525614i	$-0.823836\pi$
$599$	−41.6420			−1.70145			−0.850723	+	0.525614i	$0.823836\pi$
$600$	−4.25831	+	7.54101i	−0.173845	+	0.307860i
$601$	36.7969			1.50098			0.750488	−	0.660884i	$-0.229819\pi$
$601$	36.7969			1.50098			0.750488	+	0.660884i	$0.229819\pi$
$602$	5.56160	−	5.56160i	0.226674	−	0.226674i
$603$	3.39295	+	18.7288i	0.138172	+	0.762697i
$604$			0.992815i			0.0403971i
$605$	−17.9310	−	60.7033i	−0.728998	−	2.46794i
$606$	23.7343	−	12.4260i	0.964139	−	0.504773i
$607$	−5.75906	−	5.75906i	−0.233753	−	0.233753i	0.580504	−	0.814257i	$-0.302855\pi$
$607$	−5.75906	−	5.75906i	−0.233753	−	0.233753i	−0.814257	+	0.580504i	$0.802855\pi$
$608$	2.79466	+	2.79466i	0.113338	+	0.113338i
$609$	37.2982	−	19.5274i	1.51140	−	0.791289i
$610$	−14.6682	−	7.97860i	−0.593896	−	0.323044i
$611$		−	29.6985i		−	1.20147i
$612$	−3.89284	−	21.4882i	−0.157359	−	0.868609i
$613$	−10.0746	+	10.0746i	−0.406907	+	0.406907i	−0.880659	−	0.473751i	$-0.842900\pi$
$613$	−10.0746	+	10.0746i	−0.406907	+	0.406907i	0.473751	+	0.880659i	$0.342900\pi$
$614$	10.8958			0.439719
$615$	−0.454745	+	28.6509i	−0.0183371	+	1.15531i
$616$	21.7116			0.874786
$617$	4.23104	−	4.23104i	0.170335	−	0.170335i	−0.616791	−	0.787127i	$-0.711568\pi$
$617$	4.23104	−	4.23104i	0.170335	−	0.170335i	0.787127	+	0.616791i	$0.211568\pi$
$618$	−13.7788	−	4.30897i	−0.554263	−	0.173332i
$619$			19.7569i			0.794096i	0.917798	+	0.397048i	$0.129965\pi$
$619$			19.7569i			0.794096i	−0.917798	+	0.397048i	$0.870035\pi$
$620$	2.14447	−	0.633448i	0.0861239	−	0.0254399i
$621$	−7.12906	−	0.887636i	−0.286079	−	0.0356196i
$622$	−20.2887	−	20.2887i	−0.813502	−	0.813502i
$623$	9.34867	+	9.34867i	0.374546	+	0.374546i
$624$	−2.34714	−	4.48314i	−0.0939608	−	0.179469i
$625$	10.2378	−	22.8076i	0.409511	−	0.912305i
$626$		−	32.8046i		−	1.31113i
$627$	12.8098	−	40.9617i	0.511573	−	1.63585i
$628$	−3.99275	+	3.99275i	−0.159328	+	0.159328i
$629$	71.2935			2.84266
$630$	−7.28471	+	22.0591i	−0.290230	+	0.878854i
$631$	−30.6221			−1.21905			−0.609523	−	0.792768i	$-0.708639\pi$
$631$	−30.6221			−1.21905			−0.609523	+	0.792768i	$0.708639\pi$
$632$	2.07900	−	2.07900i	0.0826981	−	0.0826981i
$633$	−5.15004	+	16.4683i	−0.204696	+	0.654555i
$634$		−	7.54733i		−	0.299743i
$635$	−0.260494	+	0.478902i	−0.0103374	+	0.0190046i
$636$	5.11357	+	9.76715i	0.202766	+	0.387293i
$637$	10.3143	+	10.3143i	0.408668	+	0.408668i
$638$	−31.1165	−	31.1165i	−1.23191	−	1.23191i
$639$	6.28970	−	9.07279i	0.248817	−	0.358914i
$640$	−1.06845	+	1.96428i	−0.0422343	+	0.0776451i
$641$		−	21.4403i		−	0.846843i	−0.905933	−	0.423421i	$-0.860829\pi$
$641$		−	21.4403i		−	0.846843i	0.905933	−	0.423421i	$-0.139171\pi$
$642$	−8.30157	−	2.59611i	−0.327637	−	0.102460i
$643$	26.8332	−	26.8332i	1.05820	−	1.05820i	0.0599994	−	0.998198i	$-0.480890\pi$
$643$	26.8332	−	26.8332i	1.05820	−	1.05820i	0.998198	−	0.0599994i	$-0.0191099\pi$
$644$	4.78794			0.188671
$645$	6.31789	−	6.12046i	0.248767	−	0.240993i
$646$	28.7697			1.13193
$647$	23.9941	−	23.9941i	0.943305	−	0.943305i	−0.0551715	−	0.998477i	$-0.517571\pi$
$647$	23.9941	−	23.9941i	0.943305	−	0.943305i	0.998477	+	0.0551715i	$0.0175706\pi$
$648$	3.72697	−	8.19205i	0.146409	−	0.321814i
$649$			7.51079i			0.294824i
$650$	7.93752	+	12.2635i	0.311335	+	0.481013i
$651$	5.31393	−	2.78210i	0.208269	−	0.109039i
$652$	4.27466	+	4.27466i	0.167408	+	0.167408i
$653$	−14.2311	−	14.2311i	−0.556904	−	0.556904i	0.371520	−	0.928425i	$-0.378837\pi$
$653$	−14.2311	−	14.2311i	−0.556904	−	0.556904i	−0.928425	+	0.371520i	$0.878837\pi$
$654$	−9.55490	+	5.00245i	−0.373626	+	0.195611i
$655$	14.1955	−	4.19316i	0.554663	−	0.163840i
$656$			7.39856i			0.288865i
$657$	5.59511	−	1.01362i	0.218286	−	0.0395450i
$658$	−24.8916	+	24.8916i	−0.970375	+	0.970375i
$659$	6.21784			0.242213			0.121106	−	0.992640i	$-0.461356\pi$
$659$	6.21784			0.242213			0.121106	+	0.992640i	$0.461356\pi$
$660$	24.2787	+	0.385350i	0.945047	+	0.0149997i
$661$	44.9074			1.74670			0.873349	−	0.487096i	$-0.161944\pi$
$661$	44.9074			1.74670			0.873349	+	0.487096i	$0.161944\pi$
$662$	3.88461	−	3.88461i	0.150979	−	0.150979i
$663$	−35.1572	−	10.9946i	−1.36539	−	0.426993i
$664$		−	10.5348i		−	0.408829i
$665$	−26.8847	−	14.6237i	−1.04255	−	0.567082i
$666$	24.1469	+	16.7398i	0.935675	+	0.648655i
$667$	−6.86194	−	6.86194i	−0.265696	−	0.265696i
$668$	5.03736	+	5.03736i	0.194901	+	0.194901i
$669$	7.54956	+	14.4200i	0.291883	+	0.557509i
$670$	−4.01895	−	13.6057i	−0.155266	−	0.525635i
$671$			46.8173i			1.80736i
$672$	−1.79028	+	5.72476i	−0.0690614	+	0.220837i
$673$	5.21190	−	5.21190i	0.200904	−	0.200904i	−0.599483	−	0.800387i	$-0.704627\pi$
$673$	5.21190	−	5.21190i	0.200904	−	0.200904i	0.800387	+	0.599483i	$0.204627\pi$
$674$	10.3279			0.397815
$675$	−8.53753	+	24.5379i	−0.328610	+	0.944466i
$676$	4.46412			0.171697
$677$	−16.0801	+	16.0801i	−0.618007	+	0.618007i	−0.945020	−	0.327013i	$-0.893958\pi$
$677$	−16.0801	+	16.0801i	−0.618007	+	0.618007i	0.327013	+	0.945020i	$0.393958\pi$
$678$	4.56575	−	14.5999i	0.175347	−	0.560705i
$679$		−	26.4304i		−	1.01431i
$680$	4.61108	+	15.6103i	0.176827	+	0.598627i
$681$	21.1001	+	40.3022i	0.808558	+	1.54438i
$682$	−4.43322	−	4.43322i	−0.169757	−	0.169757i
$683$	−14.5758	−	14.5758i	−0.557728	−	0.557728i	0.370932	−	0.928660i	$-0.379038\pi$
$683$	−14.5758	−	14.5758i	−0.557728	−	0.557728i	−0.928660	+	0.370932i	$0.879038\pi$
$684$	9.74423	+	6.75517i	0.372580	+	0.258290i
$685$	18.0533	+	9.81992i	0.689782	+	0.375200i
$686$			6.95154i			0.265411i
$687$	39.7542	+	12.4322i	1.51672	+	0.474316i
$688$	1.60599	−	1.60599i	0.0612277	−	0.0612277i
$689$	18.5966			0.708474
$690$	5.35404	+	0.0849790i	0.203825	+	0.00323510i
$691$	−28.2688			−1.07540			−0.537698	−	0.843138i	$-0.680706\pi$
$691$	−28.2688			−1.07540			−0.537698	+	0.843138i	$0.680706\pi$
$692$	15.9853	−	15.9853i	0.607669	−	0.607669i
$693$	64.0916	−	11.6109i	2.43464	−	0.441063i
$694$		−	19.0546i		−	0.723303i
$695$	21.6809	−	6.40425i	0.822402	−	0.242927i
$696$	10.7703	−	5.63880i	0.408249	−	0.213738i
$697$	38.0823	+	38.0823i	1.44247	+	1.44247i
$698$	−20.4889	−	20.4889i	−0.775517	−	0.775517i
$699$	−2.50661	+	1.31233i	−0.0948086	+	0.0496369i
$700$	3.62577	−	16.9313i	0.137041	−	0.639944i
$701$			26.8630i			1.01460i	0.861769	+	0.507300i	$0.169356\pi$
$701$			26.8630i			1.01460i	−0.861769	+	0.507300i	$0.830644\pi$
$702$	−9.32614	−	11.9788i	−0.351993	−	0.452111i
$703$	−27.3708	+	27.3708i	−1.03231	+	1.03231i
$704$	6.26953			0.236292
$705$	−28.2765	+	27.3929i	−1.06495	+	1.03168i
$706$	9.27534			0.349082
$707$	−37.8757	+	37.8757i	−1.42446	+	1.42446i
$708$	−1.98039	−	0.619318i	−0.0744276	−	0.0232754i
$709$			48.3302i			1.81508i	0.419969	+	0.907538i	$0.362041\pi$
$709$			48.3302i			1.81508i	−0.419969	+	0.907538i	$0.637959\pi$
$710$	−3.93181	+	7.22839i	−0.147558	+	0.271277i
$711$	5.02529	−	7.24890i	0.188463	−	0.271855i
$712$	2.69955	+	2.69955i	0.101170	+	0.101170i
$713$	−0.977633	−	0.977633i	−0.0366126	−	0.0366126i
$714$	20.2518	+	38.6818i	0.757904	+	1.44763i
$715$	19.5710	−	35.9802i	0.731916	−	1.34558i
$716$		−	15.4996i		−	0.579248i
$717$	−7.73860	+	24.7457i	−0.289003	+	0.924144i
$718$	−11.2283	+	11.2283i	−0.419037	+	0.419037i
$719$	35.1223			1.30984			0.654921	−	0.755698i	$-0.272702\pi$
$719$	35.1223			1.30984			0.654921	+	0.755698i	$0.272702\pi$
$720$	−2.10356	+	6.36985i	−0.0783950	+	0.237390i
$721$	28.8648			1.07498
$722$	2.38984	−	2.38984i	0.0889407	−	0.0889407i
$723$	−7.47593	+	23.9057i	−0.278033	+	0.889064i
$724$		−	4.19484i		−	0.155900i
$725$	−29.4619	+	19.0692i	−1.09419	+	0.708212i
$726$	−22.7409	−	43.4362i	−0.843995	−	1.61207i
$727$	−25.7841	−	25.7841i	−0.956278	−	0.956278i	0.0428056	−	0.999083i	$-0.486370\pi$
$727$	−25.7841	−	25.7841i	−0.956278	−	0.956278i	−0.999083	+	0.0428056i	$0.986370\pi$
$728$	7.15429	+	7.15429i	0.265156	+	0.265156i
$729$	6.62088	−	26.1756i	0.245218	−	0.969468i
$730$	−4.06461	+	1.20063i	−0.150438	+	0.0444374i
$731$		−	16.5329i		−	0.611490i
$732$	−12.3444	−	3.86042i	−0.456263	−	0.142685i
$733$	−15.1274	+	15.1274i	−0.558743	+	0.558743i	−0.928949	−	0.370207i	$-0.879287\pi$
$733$	−15.1274	+	15.1274i	−0.558743	+	0.558743i	0.370207	+	0.928949i	$0.379287\pi$
$734$	−18.3847			−0.678591
$735$	0.306868	−	19.3340i	0.0113190	−	0.713146i
$736$	1.38258			0.0509626
$737$	−28.1269	+	28.1269i	−1.03607	+	1.03607i
$738$	3.95660	+	21.8402i	0.145645	+	0.803948i
$739$		−	14.8005i		−	0.544446i	−0.962234	−	0.272223i	$-0.912241\pi$
$739$		−	14.8005i		−	0.544446i	0.962234	−	0.272223i	$-0.0877589\pi$
$740$	−19.2381	−	10.4644i	−0.707208	−	0.384678i
$741$	17.7185	−	9.27648i	0.650905	−	0.340780i
$742$	−15.5866	−	15.5866i	−0.572203	−	0.572203i
$743$	−3.04936	−	3.04936i	−0.111870	−	0.111870i	0.648956	−	0.760826i	$-0.275206\pi$
$743$	−3.04936	−	3.04936i	−0.111870	−	0.111870i	−0.760826	+	0.648956i	$0.775206\pi$
$744$	1.53447	−	0.803369i	0.0562564	−	0.0294529i
$745$	−2.15365	−	7.29095i	−0.0789038	−	0.267120i
$746$		−	2.22576i		−	0.0814908i
$747$	−5.63380	−	31.0982i	−0.206130	−	1.13782i
$748$	32.2709	−	32.2709i	1.17994	−	1.17994i
$749$	17.3907			0.635444
$750$	4.35497	−	18.8689i	0.159021	−	0.688994i
$751$	−4.27666			−0.156058			−0.0780288	−	0.996951i	$-0.524863\pi$
$751$	−4.27666			−0.156058			−0.0780288	+	0.996951i	$0.524863\pi$
$752$	−7.18779	+	7.18779i	−0.262112	+	0.262112i
$753$	15.3769	+	4.80875i	0.560366	+	0.175241i
$754$		−	20.5067i		−	0.746810i
$755$	−0.628897	−	2.12906i	−0.0228879	−	0.0774844i
$756$	−2.22332	+	17.8566i	−0.0808613	+	0.649438i
$757$	9.84883	+	9.84883i	0.357962	+	0.357962i	0.863061	−	0.505099i	$-0.168544\pi$
$757$	9.84883	+	9.84883i	0.357962	+	0.357962i	−0.505099	+	0.863061i	$0.668544\pi$
$758$	−6.73756	−	6.73756i	−0.244719	−	0.244719i
$759$	−6.96371	−	13.3010i	−0.252767	−	0.482795i
$760$	−7.76333	−	4.22279i	−0.281606	−	0.153177i
$761$		−	31.3688i		−	1.13712i	−0.822643	−	0.568559i	$-0.807501\pi$
$761$		−	31.3688i		−	1.13712i	0.822643	−	0.568559i	$-0.192499\pi$
$762$	−0.126039	+	0.403034i	−0.00456591	+	0.0146004i
$763$	15.2479	−	15.2479i	0.552011	−	0.552011i
$764$	21.7176			0.785716
$765$	21.9597	+	43.6149i	0.793956	+	1.57690i
$766$	−2.08065			−0.0751768
$767$	−2.47492	+	2.47492i	−0.0893640	+	0.0893640i
$768$	−0.516967	+	1.65310i	−0.0186544	+	0.0596512i
$769$			24.9613i			0.900126i	0.892997	+	0.450063i	$0.148598\pi$
$769$			24.9613i			0.900126i	−0.892997	+	0.450063i	$0.851402\pi$
$770$	−46.5599	+	13.7532i	−1.67790	+	0.495631i
$771$	−11.1160	−	21.2321i	−0.400333	−	0.764655i
$772$	13.9466	+	13.9466i	0.501950	+	0.501950i
$773$	−10.4377	−	10.4377i	−0.375416	−	0.375416i	0.494029	−	0.869445i	$-0.335524\pi$
$773$	−10.4377	−	10.4377i	−0.375416	−	0.375416i	−0.869445	+	0.494029i	$0.835524\pi$
$774$	3.88194	−	5.59964i	0.139534	−	0.201275i
$775$	−4.19749	+	2.71682i	−0.150778	+	0.0975910i
$776$		−	7.63213i		−	0.273978i
$777$	−56.0681	−	17.5339i	−2.01143	−	0.629025i
$778$	−16.7342	+	16.7342i	−0.599951	+	0.599951i
$779$	−29.2409			−1.04766
$780$	7.87321	+	8.12717i	0.281906	+	0.290999i
$781$	23.0713			0.825556
$782$	7.11651	−	7.11651i	0.254486	−	0.254486i
$783$	28.7780	−	22.4052i	1.02844	−	0.800697i
$784$		−	4.99265i		−	0.178309i
$785$	6.03312	−	11.0915i	0.215331	−	0.395873i
$786$	10.1575	−	5.31796i	0.362308	−	0.189685i
$787$	−30.1812	−	30.1812i	−1.07584	−	1.07584i	−0.996877	−	0.0789672i	$-0.974838\pi$
$787$	−30.1812	−	30.1812i	−1.07584	−	1.07584i	−0.0789672	−	0.996877i	$-0.525162\pi$
$788$	−3.81388	−	3.81388i	−0.135864	−	0.135864i
$789$	−0.971314	+	0.508529i	−0.0345797	+	0.0181041i
$790$	−3.14141	+	5.77528i	−0.111766	+	0.205475i
$791$			30.5849i			1.08747i
$792$	18.5073	−	3.35282i	0.657629	−	0.119137i
$793$	−15.4270	+	15.4270i	−0.547828	+	0.547828i
$794$	33.8193			1.20020
$795$	−17.1529	−	17.7062i	−0.608350	−	0.627973i
$796$	−19.9944			−0.708684
$797$	−12.9429	+	12.9429i	−0.458461	+	0.458461i	−0.898150	−	0.439689i	$-0.855089\pi$
$797$	−12.9429	+	12.9429i	−0.458461	+	0.458461i	0.439689	+	0.898150i	$0.355089\pi$
$798$	−22.6257	−	7.07562i	−0.800940	−	0.250474i
$799$			73.9948i			2.61775i
$800$	1.04699	−	4.88915i	0.0370167	−	0.172858i
$801$	9.41262	+	6.52528i	0.332579	+	0.230560i
$802$	11.3636	+	11.3636i	0.401262	+	0.401262i
$803$	8.40270	+	8.40270i	0.296525	+	0.296525i
$804$	−5.09702	−	9.73554i	−0.179758	−	0.343346i
$805$	−10.2676	+	3.03291i	−0.361885	+	0.106896i
$806$		−	2.92162i		−	0.102910i
$807$	−3.13500	+	10.0248i	−0.110357	+	0.352889i
$808$	−10.9371	+	10.9371i	−0.384766	+	0.384766i
$809$	−14.7277			−0.517799			−0.258900	−	0.965904i	$-0.583360\pi$
$809$	−14.7277			−0.517799			−0.258900	+	0.965904i	$0.583360\pi$
$810$	−2.80312	+	19.9284i	−0.0984918	+	0.700214i
$811$	22.4757			0.789229			0.394614	−	0.918847i	$-0.370878\pi$
$811$	22.4757			0.789229			0.394614	+	0.918847i	$0.370878\pi$
$812$	−17.1875	+	17.1875i	−0.603165	+	0.603165i
$813$	3.06989	−	9.81657i	0.107666	−	0.344282i
$814$			61.4035i			2.15219i
$815$	−11.8746	−	6.45909i	−0.415950	−	0.226252i
$816$	5.84798	+	11.1699i	0.204720	+	0.391025i
$817$	6.34725	+	6.34725i	0.222062	+	0.222062i
$818$	18.6419	+	18.6419i	0.651797	+	0.651797i
$819$	24.9451	+	17.2931i	0.871652	+	0.604271i
$820$	−4.68660	−	15.8660i	−0.163663	−	0.554064i
$821$		−	12.7346i		−	0.444441i	−0.974996	−	0.222221i	$-0.928669\pi$
$821$		−	12.7346i		−	0.444441i	0.974996	−	0.222221i	$-0.0713305\pi$
$822$	15.1933	+	4.75133i	0.529928	+	0.165722i
$823$	21.0730	−	21.0730i	0.734558	−	0.734558i	−0.236961	−	0.971519i	$-0.576151\pi$
$823$	21.0730	−	21.0730i	0.734558	−	0.734558i	0.971519	+	0.236961i	$0.0761514\pi$
$824$	8.33510			0.290367
$825$	−52.3090	+	14.5529i	−1.82117	+	0.506668i
$826$	4.14867			0.144351
$827$	28.4080	−	28.4080i	0.987842	−	0.987842i	−0.0120853	−	0.999927i	$-0.503847\pi$
$827$	28.4080	−	28.4080i	0.987842	−	0.987842i	0.999927	+	0.0120853i	$0.00384697\pi$
$828$	4.08131	−	0.739378i	0.141835	−	0.0256951i
$829$			16.5914i			0.576243i	0.957594	+	0.288121i	$0.0930307\pi$
$829$			16.5914i			0.576243i	−0.957594	+	0.288121i	$0.906969\pi$
$830$	6.67325	+	22.5915i	0.231632	+	0.784163i
$831$	−11.4954	+	6.01837i	−0.398769	+	0.208775i
$832$	2.06590	+	2.06590i	0.0716222	+	0.0716222i
$833$	−25.6985	−	25.6985i	−0.890399	−	0.890399i
$834$	15.5137	−	8.12216i	0.537195	−	0.281248i
$835$	−13.9934	−	7.61155i	−0.484260	−	0.263408i
$836$			24.7787i			0.856990i
$837$	4.10005	−	3.19211i	0.141719	−	0.110335i
$838$	5.68046	−	5.68046i	0.196228	−	0.196228i
$839$	4.77405			0.164818			0.0824092	−	0.996599i	$-0.473739\pi$
$839$	4.77405			0.164818			0.0824092	+	0.996599i	$0.473739\pi$
$840$	0.212852	−	13.4106i	0.00734411	−	0.462710i
$841$	20.2655			0.698810
$842$	−6.52600	+	6.52600i	−0.224901	+	0.224901i
$843$	−4.93698	−	1.54392i	−0.170039	−	0.0531754i
$844$		−	9.96204i		−	0.342908i
$845$	−9.57316	+	2.82779i	−0.329327	+	0.0972788i
$846$	−17.3741	+	25.0619i	−0.597334	+	0.861645i
$847$	69.3163	+	69.3163i	2.38174	+	2.38174i
$848$	−4.50085	−	4.50085i	−0.154560	−	0.154560i
$849$	−23.4876	−	44.8624i	−0.806093	−	1.53967i
$850$	−19.7766	−	30.5549i	−0.678332	−	1.04802i
$851$			13.5410i			0.464178i
$852$	−1.90239	+	6.08327i	−0.0651749	+	0.208409i
$853$	−19.0341	+	19.0341i	−0.651715	+	0.651715i	−0.953406	−	0.301690i	$-0.902449\pi$
$853$	−19.0341	+	19.0341i	−0.651715	+	0.651715i	0.301690	+	0.953406i	$0.402449\pi$
$854$	25.8600			0.884912
$855$	−25.1752	−	8.31378i	−0.860975	−	0.284325i
$856$	5.02181			0.171642
$857$	15.1375	−	15.1375i	0.517086	−	0.517086i	−0.399603	−	0.916689i	$-0.630852\pi$
$857$	15.1375	−	15.1375i	0.517086	−	0.517086i	0.916689	+	0.399603i	$0.130852\pi$
$858$	9.46938	−	30.2802i	0.323279	−	1.03375i
$859$			46.1064i			1.57313i	0.617507	+	0.786565i	$0.288143\pi$
$859$			46.1064i			1.57313i	−0.617507	+	0.786565i	$0.711857\pi$
$860$	−2.42668	+	4.46130i	−0.0827490	+	0.152129i
$861$	−20.5835	−	39.3154i	−0.701484	−	1.33987i
$862$	10.3980	+	10.3980i	0.354158	+	0.354158i
$863$	−14.8334	−	14.8334i	−0.504933	−	0.504933i	0.408034	−	0.912967i	$-0.366215\pi$
$863$	−14.8334	−	14.8334i	−0.504933	−	0.504933i	−0.912967	+	0.408034i	$0.866215\pi$
$864$	−0.642014	+	5.15634i	−0.0218417	+	0.175422i
$865$	−24.1541	+	44.4058i	−0.821263	+	1.50984i
$866$		−	31.8555i		−	1.08249i
$867$	59.4928	+	18.6049i	2.02048	+	0.631855i
$868$	−2.44874	+	2.44874i	−0.0831156	+	0.0831156i
$869$	18.4333			0.625308
$870$	−19.5248	+	18.9147i	−0.661952	+	0.641268i
$871$	−18.5364			−0.628083
$872$	4.40304	−	4.40304i	0.149106	−	0.149106i
$873$	−4.08151	−	22.5297i	−0.138138	−	0.762514i
$874$			5.46430i			0.184833i
$875$	2.94978	+	38.6054i	0.0997209	+	1.30510i
$876$	−2.90842	+	1.52270i	−0.0982665	+	0.0514473i
$877$	33.2810	+	33.2810i	1.12382	+	1.12382i	0.991162	+	0.132657i	$0.0423508\pi$
$877$	33.2810	+	33.2810i	1.12382	+	1.12382i	0.132657	+	0.991162i	$0.457649\pi$
$878$	−9.54917	−	9.54917i	−0.322269	−	0.322269i
$879$	−31.1616	+	16.3146i	−1.05105	+	0.550277i
$880$	−13.4448	+	3.97142i	−0.453224	+	0.133877i
$881$		−	52.6269i		−	1.77304i	−0.462686	−	0.886522i	$-0.653114\pi$
$881$		−	52.6269i		−	1.77304i	0.462686	−	0.886522i	$-0.346886\pi$
$882$	−2.66997	−	14.7381i	−0.0899026	−	0.496256i
$883$	−25.3525	+	25.3525i	−0.853179	+	0.853179i	−0.990523	−	0.137344i	$-0.956143\pi$
$883$	−25.3525	+	25.3525i	−0.853179	+	0.853179i	0.137344	+	0.990523i	$0.456143\pi$
$884$	21.2674			0.715302
$885$	4.63919	+	0.0736330i	0.155945	+	0.00247515i
$886$	−5.72648			−0.192385
$887$	−26.5043	+	26.5043i	−0.889927	+	0.889927i	−0.994516	−	0.104588i	$-0.966647\pi$
$887$	−26.5043	+	26.5043i	−0.889927	+	0.889927i	0.104588	+	0.994516i	$0.466647\pi$
$888$	−16.1904	−	5.06315i	−0.543315	−	0.169908i
$889$		−	0.844306i		−	0.0283171i
$890$	−7.49914	−	4.07908i	−0.251372	−	0.136731i
$891$	52.8397	−	19.7947i	1.77020	−	0.663148i
$892$	−6.64495	−	6.64495i	−0.222489	−	0.222489i
$893$	−28.4079	−	28.4079i	−0.950634	−	0.950634i
$894$	−2.73136	−	5.21703i	−0.0913505	−	0.174484i
$895$	9.81820	+	33.2384i	0.328186	+	1.11104i
$896$		−	3.46304i		−	0.115692i
$897$	2.08823	−	6.67751i	0.0697239	−	0.222956i
$898$	13.7210	−	13.7210i	0.457875	−	0.457875i
$899$	7.01894			0.234095
$900$	0.476038	−	14.9924i	0.0158679	−	0.499748i
$901$	−46.3341			−1.54361
$902$	−32.7995	+	32.7995i	−1.09210	+	1.09210i
$903$	−4.06609	+	13.0021i	−0.135311	+	0.432683i
$904$			8.83181i			0.293742i
$905$	2.65721	+	8.99569i	0.0883287	+	0.299027i
$906$	−0.797597	−	1.52345i	−0.0264984	−	0.0506131i
$907$	−33.2952	−	33.2952i	−1.10555	−	1.10555i	−0.993728	−	0.111822i	$-0.964331\pi$
$907$	−33.2952	−	33.2952i	−1.10555	−	1.10555i	−0.111822	−	0.993728i	$-0.535669\pi$
$908$	−18.5718	−	18.5718i	−0.616328	−	0.616328i
$909$	−26.4369	+	38.1348i	−0.876855	+	1.26485i
$910$	−19.8740	−	10.8103i	−0.658818	−	0.358357i
$911$			43.4861i			1.44076i	0.693581	+	0.720379i	$0.256032\pi$
$911$			43.4861i			1.44076i	−0.693581	+	0.720379i	$0.743968\pi$
$912$	−6.53347	−	2.04318i	−0.216345	−	0.0676565i
$913$	46.7031	−	46.7031i	1.54565	−	1.54565i
$914$	−22.2100			−0.734641
$915$	28.9176	+	0.458979i	0.955987	+	0.0151734i
$916$	−24.0483			−0.794577
$917$	−16.2096	+	16.2096i	−0.535289	+	0.535289i
$918$	23.2364	+	29.8456i	0.766915	+	0.985052i
$919$		−	25.6036i		−	0.844584i	−0.906460	−	0.422292i	$-0.861226\pi$
$919$		−	25.6036i		−	0.844584i	0.906460	−	0.422292i	$-0.138774\pi$
$920$	−2.96490	+	0.875794i	−0.0977499	+	0.0288741i
$921$	−16.7193	+	8.75335i	−0.550919	+	0.288433i
$922$	27.6295	+	27.6295i	0.909928	+	0.909928i
$923$	7.60233	+	7.60233i	0.250234	+	0.250234i
$924$	−33.3158	+	17.4424i	−1.09601	+	0.573814i
$925$	47.8842	+	10.2542i	1.57442	+	0.337155i
$926$		−	17.2359i		−	0.566406i
$927$	24.6048	−	4.45745i	0.808128	−	0.146402i
$928$	−4.96314	+	4.96314i	−0.162923	+	0.162923i
$929$	−25.5918			−0.839640			−0.419820	−	0.907607i	$-0.637907\pi$
$929$	−25.5918			−0.839640			−0.419820	+	0.907607i	$0.637907\pi$
$930$	−2.78173	+	2.69481i	−0.0912165	+	0.0883662i
$931$	19.7322			0.646696
$932$	1.15508	−	1.15508i	0.0378360	−	0.0378360i
$933$	47.4317	+	14.8331i	1.55284	+	0.485613i
$934$			3.28745i			0.107569i
$935$	−48.7619	+	89.6458i	−1.59469	+	2.93173i
$936$	7.20324	+	4.99363i	0.235445	+	0.163222i
$937$	7.38886	+	7.38886i	0.241384	+	0.241384i	0.817422	−	0.576039i	$-0.195402\pi$
$937$	7.38886	+	7.38886i	0.241384	+	0.241384i	−0.576039	+	0.817422i	$0.695402\pi$
$938$	15.5362	+	15.5362i	0.507274	+	0.507274i
$939$	26.3542	+	50.3376i	0.860036	+	1.64271i
$940$	10.8609	−	19.9671i	0.354243	−	0.651254i
$941$			15.2532i			0.497241i	0.968601	+	0.248620i	$0.0799772\pi$
$941$			15.2532i			0.497241i	−0.968601	+	0.248620i	$0.920023\pi$
$942$	2.91910	−	9.33440i	0.0951095	−	0.304131i
$943$	−7.23307	+	7.23307i	−0.235541	+	0.235541i
$944$	1.19798			0.0389911
$945$	−6.54340	−	39.7013i	−0.212857	−	1.29148i
$946$	14.2394			0.462963
$947$	19.1200	−	19.1200i	0.621318	−	0.621318i	−0.324550	−	0.945868i	$-0.605213\pi$
$947$	19.1200	−	19.1200i	0.621318	−	0.621318i	0.945868	+	0.324550i	$0.105213\pi$
$948$	−1.51996	+	4.86036i	−0.0493659	+	0.157857i
$949$			5.53762i			0.179759i
$950$	19.3231	+	4.13796i	0.626925	+	0.134253i
$951$	6.06329	+	11.5811i	0.196616	+	0.375544i
$952$	−17.8252	−	17.8252i	−0.577717	−	0.577717i
$953$	35.6226	+	35.6226i	1.15393	+	1.15393i	0.985757	+	0.168173i	$0.0537868\pi$
$953$	35.6226	+	35.6226i	1.15393	+	1.15393i	0.168173	+	0.985757i	$0.446213\pi$
$954$	−15.6932	−	10.8793i	−0.508087	−	0.352231i
$955$	−46.5727	+	13.7570i	−1.50706	+	0.445166i
$956$		−	14.9692i		−	0.484140i
$957$	72.7454	+	22.7493i	2.35153	+	0.735381i
$958$	8.87974	−	8.87974i	0.286891	−	0.286891i
$959$	−31.8281			−1.02778
$960$	0.0614640	−	3.87250i	0.00198374	−	0.124984i
$961$	1.00000			0.0322581
$962$	−20.2334	+	20.2334i	−0.652349	+	0.652349i
$963$	14.8241	−	2.68557i	0.477701	−	0.0865412i
$964$		−	14.4611i		−	0.465762i
$965$	−38.7426	−	21.0736i	−1.24717	−	0.678384i
$966$	−7.34695	+	3.84648i	−0.236384	+	0.123758i
$967$	−16.5723	−	16.5723i	−0.532931	−	0.532931i	0.388513	−	0.921443i	$-0.372989\pi$
$967$	−16.5723	−	16.5723i	−0.532931	−	0.532931i	−0.921443	+	0.388513i	$0.872989\pi$
$968$	20.0160	+	20.0160i	0.643340	+	0.643340i
$969$	−44.1462	+	23.1127i	−1.41818	+	0.742486i
$970$	4.83456	+	16.3669i	0.155228	+	0.525508i
$971$			32.2634i			1.03538i	0.855568	+	0.517691i	$0.173208\pi$
$971$			32.2634i			1.03538i	−0.855568	+	0.517691i	$0.826792\pi$
$972$	0.862316	+	15.5646i	0.0276588	+	0.499234i
$973$	−24.7571	+	24.7571i	−0.793676	+	0.793676i
$974$	−9.90721			−0.317448
$975$	−22.0320	−	12.4412i	−0.705588	−	0.398437i
$976$	7.46744			0.239027
$977$	0.431347	−	0.431347i	0.0138000	−	0.0138000i	−0.700173	−	0.713973i	$-0.746894\pi$
$977$	0.431347	−	0.431347i	0.0138000	−	0.0138000i	0.713973	+	0.700173i	$0.246894\pi$
$978$	−9.99346	−	3.12521i	−0.319556	−	0.0999331i
$979$			23.9355i			0.764981i
$980$	3.16259	+	10.7066i	0.101025	+	0.342009i
$981$	10.6429	−	15.3522i	0.339801	−	0.490158i
$982$	8.30806	+	8.30806i	0.265121	+	0.265121i
$983$	12.3131	+	12.3131i	0.392728	+	0.392728i	0.875659	−	0.482931i	$-0.160428\pi$
$983$	12.3131	+	12.3131i	0.392728	+	0.392728i	−0.482931	+	0.875659i	$0.660428\pi$
$984$	−5.94377	−	11.3529i	−0.189480	−	0.361916i
$985$	10.5946	+	5.76284i	0.337573	+	0.183619i
$986$			51.0931i			1.62714i
$987$	18.1983	−	58.1925i	0.579258	−	1.85229i
$988$	−8.16495	+	8.16495i	−0.259762	+	0.259762i
$989$	3.14013			0.0998503
$990$	−37.5645	+	18.9134i	−1.19388	+	0.601109i
$991$	−11.2672			−0.357916			−0.178958	−	0.983857i	$-0.557273\pi$
$991$	−11.2672			−0.357916			−0.178958	+	0.983857i	$0.557273\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	−2.84004	+	9.08158i	−0.0901260	+	0.288195i
$994$		−	12.7437i		−	0.404205i
$995$	42.8774	−	12.6654i	1.35931	−	0.401522i
$996$	8.46332	+	16.1653i	0.268171	+	0.512218i
$997$	−37.1843	−	37.1843i	−1.17764	−	1.17764i	−0.980344	−	0.197294i	$-0.936785\pi$
$997$	−37.1843	−	37.1843i	−1.17764	−	1.17764i	−0.197294	−	0.980344i	$-0.563215\pi$
$998$	−18.8828	−	18.8828i	−0.597726	−	0.597726i
$999$	−50.5010	−	6.28786i	−1.59778	−	0.198939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.15	yes	40
3.2	odd	2	inner	930.2.j.g.497.1	✓	40
5.3	odd	4	inner	930.2.j.g.683.1	yes	40
15.8	even	4	inner	930.2.j.g.683.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.1	✓	40	3.2	odd	2	inner
930.2.j.g.497.15	yes	40	1.1	even	1	trivial
930.2.j.g.683.1	yes	40	5.3	odd	4	inner
930.2.j.g.683.15	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.516967 + 1.65310i) q^{3} -1.00000i q^{4} +(0.633448 + 2.14447i) q^{5} +(0.803369 + 1.53447i) q^{6} +(-2.44874 - 2.44874i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46549 - 1.70920i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.516967 + 1.65310i) q^{3} -1.00000i q^{4} +(0.633448 + 2.14447i) q^{5} +(0.803369 + 1.53447i) q^{6} +(-2.44874 - 2.44874i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.46549 - 1.70920i) q^{9} +(1.96428 + 1.06845i) q^{10} -6.26953i q^{11} +(1.65310 + 0.516967i) q^{12} +(2.06590 - 2.06590i) q^{13} -3.46304 q^{14} +(-3.87250 - 0.0614640i) q^{15} -1.00000 q^{16} +(-5.14726 + 5.14726i) q^{17} +(-2.95195 + 0.534780i) q^{18} -3.95225i q^{19} +(2.14447 - 0.633448i) q^{20} +(5.31393 - 2.78210i) q^{21} +(-4.43322 - 4.43322i) q^{22} +(-0.977633 - 0.977633i) q^{23} +(1.53447 - 0.803369i) q^{24} +(-4.19749 + 2.71682i) q^{25} -2.92162i q^{26} +(4.10005 - 3.19211i) q^{27} +(-2.44874 + 2.44874i) q^{28} +7.01894 q^{29} +(-2.78173 + 2.69481i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(10.3642 + 3.24114i) q^{33} +7.27932i q^{34} +(3.70009 - 6.80239i) q^{35} +(-1.70920 + 2.46549i) q^{36} +(-6.92538 - 6.92538i) q^{37} +(-2.79466 - 2.79466i) q^{38} +(2.34714 + 4.48314i) q^{39} +(1.06845 - 1.96428i) q^{40} -7.39856i q^{41} +(1.79028 - 5.72476i) q^{42} +(-1.60599 + 1.60599i) q^{43} -6.26953 q^{44} +(2.10356 - 6.36985i) q^{45} -1.38258 q^{46} +(7.18779 - 7.18779i) q^{47} +(0.516967 - 1.65310i) q^{48} +4.99265i q^{49} +(-1.04699 + 4.88915i) q^{50} +(-5.84798 - 11.1699i) q^{51} +(-2.06590 - 2.06590i) q^{52} +(4.50085 + 4.50085i) q^{53} +(0.642014 - 5.15634i) q^{54} +(13.4448 - 3.97142i) q^{55} +3.46304i q^{56} +(6.53347 + 2.04318i) q^{57} +(4.96314 - 4.96314i) q^{58} -1.19798 q^{59} +(-0.0614640 + 3.87250i) q^{60} -7.46744 q^{61} +(0.707107 - 0.707107i) q^{62} +(1.85197 + 10.2227i) q^{63} +1.00000i q^{64} +(5.73890 + 3.12162i) q^{65} +(9.62040 - 5.03674i) q^{66} +(-4.48628 - 4.48628i) q^{67} +(5.14726 + 5.14726i) q^{68} +(2.12153 - 1.11072i) q^{69} +(-2.19366 - 7.42638i) q^{70} +3.67991i q^{71} +(0.534780 + 2.95195i) q^{72} +(-1.34025 + 1.34025i) q^{73} -9.79397 q^{74} +(-2.32122 - 8.34338i) q^{75} -3.95225 q^{76} +(-15.3524 + 15.3524i) q^{77} +(4.82974 + 1.51038i) q^{78} +2.94015i q^{79} +(-0.633448 - 2.14447i) q^{80} +(3.15729 + 8.42802i) q^{81} +(-5.23157 - 5.23157i) q^{82} +(7.44922 + 7.44922i) q^{83} +(-2.78210 - 5.31393i) q^{84} +(-14.2987 - 7.77761i) q^{85} +2.27121i q^{86} +(-3.62856 + 11.6030i) q^{87} +(-4.43322 + 4.43322i) q^{88} -3.81775 q^{89} +(-3.01673 - 5.99161i) q^{90} -10.1177 q^{91} +(-0.977633 + 0.977633i) q^{92} +(-0.516967 + 1.65310i) q^{93} -10.1651i q^{94} +(8.47547 - 2.50354i) q^{95} +(-0.803369 - 1.53447i) q^{96} +(5.39673 + 5.39673i) q^{97} +(3.53034 + 3.53034i) q^{98} +(-10.7159 + 15.4575i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 - 8 * q^7	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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