LMFDB - Embedded newform 930.2.j.g.683.15

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			683.15
Character	$\chi$	$=$	930.683
Dual form			930.2.j.g.497.15

$q$-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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	−0.997414	−	0.0718770i	$-0.977101\pi$
$7$	−2.44874	+	2.44874i	−0.925536	+	0.925536i	0.0718770	+	0.997414i	$0.477101\pi$
$8$	−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	$0.394101\pi$
$11$			6.26953i			1.89033i	−0.326589	+	0.945166i	$0.605899\pi$
$12$	1.65310	−	0.516967i	0.477209	−	0.149235i
$13$	2.06590	+	2.06590i	0.572977	+	0.572977i	0.932959	−	0.359982i	$-0.117217\pi$
$13$	2.06590	+	2.06590i	0.572977	+	0.572977i	−0.359982	+	0.932959i	$0.617217\pi$
$14$	−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	−0.956429	−	0.291965i	$-0.905691\pi$
$17$	−5.14726	−	5.14726i	−1.24839	−	1.24839i	−0.291965	−	0.956429i	$-0.594309\pi$
$18$	−2.95195	−	0.534780i	−0.695781	−	0.126049i
$19$			3.95225i			0.906708i	0.891331	+	0.453354i	$0.149773\pi$
$19$			3.95225i			0.906708i	−0.891331	+	0.453354i	$0.850227\pi$
$20$	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	−0.801648	−	0.597797i	$-0.796043\pi$
$23$	−0.977633	+	0.977633i	−0.203851	+	0.203851i	0.597797	+	0.801648i	$0.296043\pi$
$24$	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	−0.149811	+	0.988715i	$0.547866\pi$
$37$	−6.92538	+	6.92538i	−1.13853	+	1.13853i	−0.988715	+	0.149811i	$0.952134\pi$
$38$	−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	$0.196061\pi$
$41$			7.39856i			1.15546i	−0.816228	+	0.577730i	$0.803939\pi$
$42$	1.79028	+	5.72476i	0.276246	+	0.883349i
$43$	−1.60599	−	1.60599i	−0.244911	−	0.244911i	0.573967	−	0.818878i	$-0.305404\pi$
$43$	−1.60599	−	1.60599i	−0.244911	−	0.244911i	−0.818878	+	0.573967i	$0.805404\pi$
$44$	−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	0.998765	+	0.0496812i	$0.0158205\pi$
$47$	7.18779	+	7.18779i	1.04845	+	1.04845i	0.0496812	+	0.998765i	$0.484179\pi$
$48$	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	−0.326841	−	0.945079i	$-0.605984\pi$
$53$	4.50085	−	4.50085i	0.618239	−	0.618239i	0.945079	+	0.326841i	$0.105984\pi$
$54$	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	−0.925887	−	0.377800i	$-0.876681\pi$
$67$	−4.48628	+	4.48628i	−0.548087	+	0.548087i	0.377800	+	0.925887i	$0.376681\pi$
$68$	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	$-0.929928\pi$
$71$		−	3.67991i		−	0.436725i	0.975868	−	0.218363i	$-0.0700716\pi$
$72$	0.534780	−	2.95195i	0.0630245	−	0.347891i
$73$	−1.34025	−	1.34025i	−0.156864	−	0.156864i	0.624312	−	0.781175i	$-0.285380\pi$
$73$	−1.34025	−	1.34025i	−0.156864	−	0.156864i	−0.781175	+	0.624312i	$0.785380\pi$
$74$	−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	$-0.947110\pi$
$79$		−	2.94015i		−	0.330792i	0.986227	−	0.165396i	$-0.0528903\pi$
$80$	−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	−0.168110	−	0.985768i	$-0.553766\pi$
$83$	7.44922	−	7.44922i	0.817658	−	0.817658i	0.985768	+	0.168110i	$0.0537664\pi$
$84$	−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	−0.377894	−	0.925849i	$-0.623352\pi$
$97$	5.39673	−	5.39673i	0.547955	−	0.547955i	0.925849	+	0.377894i	$0.123352\pi$
$98$	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	$0.279511\pi$
$101$			15.4674i			1.53907i	−0.638608	+	0.769533i	$0.720489\pi$
$102$	−12.0335	+	3.76317i	−1.19149	+	0.372609i
$103$	−5.89381	−	5.89381i	−0.580734	−	0.580734i	0.354371	−	0.935105i	$-0.384695\pi$
$103$	−5.89381	−	5.89381i	−0.580734	−	0.580734i	−0.935105	+	0.354371i	$0.884695\pi$
$104$	−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	0.514316	−	0.857601i	$-0.328046\pi$
$107$	−3.55096	−	3.55096i	−0.343284	−	0.343284i	−0.857601	+	0.514316i	$0.828046\pi$
$108$	−3.19211	+	4.10005i	−0.307161	+	0.394528i
$109$		−	6.22684i		−	0.596423i	−0.954500	−	0.298211i	$-0.903610\pi$
$109$		−	6.22684i		−	0.596423i	0.954500	−	0.298211i	$-0.0963901\pi$
$110$	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	−0.936949	−	0.349466i	$-0.886363\pi$
$113$	−6.24503	+	6.24503i	−0.587483	+	0.587483i	0.349466	+	0.936949i	$0.386363\pi$
$114$	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	−0.699417	−	0.714714i	$-0.746557\pi$
$127$	0.172396	−	0.172396i	0.0152977	−	0.0152977i	0.714714	+	0.699417i	$0.246557\pi$
$128$	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	$0.0933818\pi$
$131$			6.61958i			0.578355i	−0.957275	+	0.289178i	$0.906618\pi$
$132$	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	0.927947	−	0.372711i	$-0.121572\pi$
$137$	6.49887	+	6.49887i	0.555236	+	0.555236i	−0.372711	+	0.927947i	$0.621572\pi$
$138$	0.714749	+	2.28555i	0.0608435	+	0.194559i
$139$			10.1101i			0.857530i	0.903416	+	0.428765i	$0.141051\pi$
$139$			10.1101i			0.857530i	−0.903416	+	0.428765i	$0.858949\pi$
$140$	−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	−0.848251	−	0.529595i	$-0.822344\pi$
$157$	−3.99275	+	3.99275i	−0.318656	+	0.318656i	0.529595	+	0.848251i	$0.322344\pi$
$158$	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	0.519595	−	0.854412i	$-0.326083\pi$
$163$	−4.27466	−	4.27466i	−0.334817	−	0.334817i	−0.854412	+	0.519595i	$0.826083\pi$
$164$	−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	0.484815	−	0.874617i	$-0.338887\pi$
$167$	−5.03736	−	5.03736i	−0.389802	−	0.389802i	−0.874617	+	0.484815i	$0.838887\pi$
$168$	−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	0.246092	−	0.969246i	$-0.420853\pi$
$173$	15.9853	−	15.9853i	1.21534	−	1.21534i	0.969246	−	0.246092i	$-0.0791467\pi$
$174$	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	$-0.712295\pi$
$191$		−	21.7176i		−	1.57143i	0.618588	−	0.785716i	$-0.287705\pi$
$192$	−1.65310	+	0.516967i	−0.119302	+	0.0373089i
$193$	−13.9466	−	13.9466i	−1.00390	−	1.00390i	−0.999992	−	0.00390758i	$-0.998756\pi$
$193$	−13.9466	−	13.9466i	−1.00390	−	1.00390i	−0.00390758	−	0.999992i	$-0.501244\pi$
$194$	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	0.829795	−	0.558068i	$-0.188457\pi$
$197$	3.81388	+	3.81388i	0.271728	+	0.271728i	−0.558068	+	0.829795i	$0.688457\pi$
$198$	3.35282	−	18.5073i	0.238274	−	1.31526i
$199$			19.9944i			1.41737i	0.705526	+	0.708684i	$0.250711\pi$
$199$			19.9944i			1.41737i	−0.705526	+	0.708684i	$0.749289\pi$
$200$	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	0.893681	−	0.448702i	$-0.148114\pi$
$223$	6.64495	+	6.64495i	0.444979	+	0.444979i	−0.448702	+	0.893681i	$0.648114\pi$
$224$	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	0.962940	+	0.269716i	$0.0869298\pi$
$227$	18.5718	+	18.5718i	1.23266	+	1.23266i	0.269716	+	0.962940i	$0.413070\pi$
$228$	2.04318	+	6.53347i	0.135313	+	0.432689i
$229$			24.0483i			1.58915i	0.607163	+	0.794577i	$0.292307\pi$
$229$			24.0483i			1.58915i	−0.607163	+	0.794577i	$0.707693\pi$
$230$	−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	−0.668258	−	0.743930i	$-0.732960\pi$
$233$	1.15508	−	1.15508i	0.0756720	−	0.0756720i	0.743930	+	0.668258i	$0.232960\pi$
$234$	−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	$0.0948414\pi$
$251$			9.30186i			0.587128i	−0.955939	+	0.293564i	$0.905159\pi$
$252$	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	0.332715	−	0.943028i	$-0.392035\pi$
$257$	−9.78406	−	9.78406i	−0.610313	−	0.610313i	−0.943028	+	0.332715i	$0.892035\pi$
$258$	−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	−0.693172	−	0.720772i	$-0.743787\pi$
$263$	0.447596	−	0.447596i	0.0275999	−	0.0275999i	0.720772	+	0.693172i	$0.243787\pi$
$264$	−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	−0.529826	−	0.848106i	$-0.677743\pi$
$277$	5.29723	−	5.29723i	0.318280	−	0.318280i	0.848106	+	0.529826i	$0.177743\pi$
$278$	−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	$-0.971607\pi$
$281$		−	2.98650i		−	0.178159i	0.996024	−	0.0890797i	$-0.0283926\pi$
$282$	16.8039	−	5.25500i	1.00066	−	0.312931i
$283$	−20.6733	−	20.6733i	−1.22890	−	1.22890i	−0.964381	−	0.264516i	$-0.914788\pi$
$283$	−20.6733	−	20.6733i	−1.22890	−	1.22890i	−0.264516	−	0.964381i	$-0.585212\pi$
$284$	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	−0.149811	−	0.988715i	$-0.547866\pi$
$293$	14.3597	−	14.3597i	0.838904	−	0.838904i	0.988715	+	0.149811i	$0.0478665\pi$
$294$	−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	−0.452198	−	0.891917i	$-0.649360\pi$
$307$	7.70450	−	7.70450i	0.439719	−	0.439719i	0.891917	+	0.452198i	$0.149360\pi$
$308$	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	$0.302442\pi$
$311$			28.6925i			1.62700i	−0.581562	+	0.813502i	$0.697558\pi$
$312$	1.51038	+	4.82974i	0.0855085	+	0.273430i
$313$	23.1963	+	23.1963i	1.31113	+	1.31113i	0.920580	+	0.390554i	$0.127717\pi$
$313$	23.1963	+	23.1963i	1.31113	+	1.31113i	0.390554	+	0.920580i	$0.372283\pi$
$314$	−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	0.840913	−	0.541170i	$-0.182019\pi$
$317$	5.33677	+	5.33677i	0.299743	+	0.299743i	−0.541170	+	0.840913i	$0.682019\pi$
$318$	−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	−0.479646	−	0.877462i	$-0.659235\pi$
$337$	7.30292	−	7.30292i	0.397815	−	0.397815i	0.877462	+	0.479646i	$0.159235\pi$
$338$	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	0.969276	−	0.245974i	$-0.0791077\pi$
$347$	13.4736	+	13.4736i	0.723303	+	0.723303i	−0.245974	+	0.969276i	$0.579108\pi$
$348$	11.6030	−	3.62856i	0.621987	−	0.194511i
$349$			28.9757i			1.55103i	0.631327	+	0.775517i	$0.282511\pi$
$349$			28.9757i			1.55103i	−0.631327	+	0.775517i	$0.717489\pi$
$350$	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	−0.510686	−	0.859768i	$-0.670608\pi$
$353$	6.55865	−	6.55865i	0.349082	−	0.349082i	0.859768	+	0.510686i	$0.170608\pi$
$354$	−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	−0.959681	−	0.281090i	$-0.909304\pi$
$367$	−12.9999	+	12.9999i	−0.678591	+	0.678591i	0.281090	+	0.959681i	$0.409304\pi$
$368$	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	0.746677	−	0.665186i	$-0.231648\pi$
$373$	1.57385	+	1.57385i	0.0814908	+	0.0814908i	−0.665186	+	0.746677i	$0.731648\pi$
$374$	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	$0.0786957\pi$
$379$			9.52834i			0.489438i	−0.969594	+	0.244719i	$0.921304\pi$
$380$	−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	−0.743695	−	0.668519i	$-0.766929\pi$
$383$	−1.47124	+	1.47124i	−0.0751768	+	0.0751768i	0.668519	+	0.743695i	$0.266929\pi$
$384$	−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	0.226097	−	0.974105i	$-0.427403\pi$
$397$	23.9139	−	23.9139i	1.20020	−	1.20020i	0.974105	−	0.226097i	$-0.0725968\pi$
$398$	−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	$-0.868572\pi$
$401$		−	16.0705i		−	0.802523i	0.915964	−	0.401262i	$-0.131428\pi$
$402$	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	$-0.774015\pi$
$409$		−	26.3636i		−	1.30359i	0.758393	−	0.651797i	$-0.225985\pi$
$410$	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	$-0.884767\pi$
$431$		−	14.7050i		−	0.708316i	0.935186	−	0.354158i	$-0.115233\pi$
$432$	−4.10005	−	3.19211i	−0.197264	−	0.153580i
$433$	22.5252	+	22.5252i	1.08249	+	1.08249i	0.996276	+	0.0862166i	$0.0274777\pi$
$433$	22.5252	+	22.5252i	1.08249	+	1.08249i	0.0862166	+	0.996276i	$0.472522\pi$
$434$	−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	$0.104445\pi$
$439$			13.5046i			0.644538i	−0.946648	+	0.322269i	$0.895555\pi$
$440$	−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	−0.796726	−	0.604341i	$-0.793436\pi$
$443$	−4.04923	+	4.04923i	−0.192385	+	0.192385i	0.604341	+	0.796726i	$0.293436\pi$
$444$	−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	−0.971535	−	0.236894i	$-0.923871\pi$
$457$	−15.7048	+	15.7048i	−0.734641	+	0.734641i	0.236894	+	0.971535i	$0.423871\pi$
$458$	−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	$-0.636137\pi$
$461$		−	39.0740i		−	1.81986i	0.414767	−	0.909928i	$-0.363863\pi$
$462$	−35.8915	+	11.2242i	−1.66982	+	0.522196i
$463$	12.1876	+	12.1876i	0.566406	+	0.566406i	0.931120	−	0.364714i	$-0.118833\pi$
$463$	12.1876	+	12.1876i	0.566406	+	0.566406i	−0.364714	+	0.931120i	$0.618833\pi$
$464$	−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	0.651274	−	0.758843i	$-0.274235\pi$
$467$	−2.32458	−	2.32458i	−0.107569	−	0.107569i	−0.758843	+	0.651274i	$0.774235\pi$
$468$	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	−0.847786	−	0.530338i	$-0.822065\pi$
$487$	−7.00546	+	7.00546i	−0.317448	+	0.317448i	0.530338	+	0.847786i	$0.322065\pi$
$488$	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	$-0.914588\pi$
$491$		−	11.7494i		−	0.530241i	0.964215	−	0.265121i	$-0.0854118\pi$
$492$	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	$0.203929\pi$
$499$			26.7044i			1.19545i	−0.801701	+	0.597726i	$0.796071\pi$
$500$	−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	−0.0312770	+	0.999511i	$0.509957\pi$
$503$	−23.1182	+	23.1182i	−1.03079	+	1.03079i	−0.999511	+	0.0312770i	$0.990043\pi$
$504$	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	$-0.792799\pi$
$521$		−	27.6615i		−	1.21187i	0.795513	−	0.605936i	$-0.207201\pi$
$522$	−20.7196	−	3.75359i	−0.906870	−	0.164290i
$523$	15.1994	+	15.1994i	0.664622	+	0.664622i	0.956466	−	0.291844i	$-0.0942687\pi$
$523$	15.1994	+	15.1994i	0.664622	+	0.664622i	−0.291844	+	0.956466i	$0.594269\pi$
$524$	−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	−0.955465	−	0.295105i	$-0.904645\pi$
$547$	−15.4445	+	15.4445i	−0.660360	+	0.660360i	0.295105	+	0.955465i	$0.404645\pi$
$548$	−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	0.335840	−	0.941919i	$-0.390980\pi$
$557$	−14.3040	−	14.3040i	−0.606079	−	0.606079i	−0.941919	+	0.335840i	$0.890980\pi$
$558$	−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	−0.546098	−	0.837721i	$-0.683887\pi$
$563$	6.91953	−	6.91953i	0.291623	−	0.291623i	0.837721	+	0.546098i	$0.183887\pi$
$564$	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	−0.177005	−	0.984210i	$-0.556641\pi$
$577$	19.3897	−	19.3897i	0.807205	−	0.807205i	0.984210	+	0.177005i	$0.0566408\pi$
$578$	−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	0.973803	−	0.227392i	$-0.0730197\pi$
$587$	18.0841	+	18.0841i	0.746412	+	0.746412i	−0.227392	+	0.973803i	$0.573020\pi$
$588$	−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	0.111009	−	0.993819i	$-0.464592\pi$
$593$	26.9043	−	26.9043i	1.10483	−	1.10483i	0.993819	−	0.111009i	$-0.0354082\pi$
$594$	−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	−0.814257	−	0.580504i	$-0.802855\pi$
$607$	−5.75906	+	5.75906i	−0.233753	+	0.233753i	0.580504	+	0.814257i	$0.302855\pi$
$608$	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	0.473751	−	0.880659i	$-0.342900\pi$
$613$	−10.0746	−	10.0746i	−0.406907	−	0.406907i	−0.880659	+	0.473751i	$0.842900\pi$
$614$	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	0.787127	−	0.616791i	$-0.211568\pi$
$617$	4.23104	+	4.23104i	0.170335	+	0.170335i	−0.616791	+	0.787127i	$0.711568\pi$
$618$	−13.7788	+	4.30897i	−0.554263	+	0.173332i
$619$		−	19.7569i		−	0.794096i	−0.917798	−	0.397048i	$-0.870035\pi$
$619$		−	19.7569i		−	0.794096i	0.917798	−	0.397048i	$-0.129965\pi$
$620$	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	$0.139171\pi$
$641$			21.4403i			0.846843i	−0.905933	+	0.423421i	$0.860829\pi$
$642$	−8.30157	+	2.59611i	−0.327637	+	0.102460i
$643$	26.8332	+	26.8332i	1.05820	+	1.05820i	0.998198	+	0.0599994i	$0.0191099\pi$
$643$	26.8332	+	26.8332i	1.05820	+	1.05820i	0.0599994	+	0.998198i	$0.480890\pi$
$644$	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	0.998477	−	0.0551715i	$-0.0175706\pi$
$647$	23.9941	+	23.9941i	0.943305	+	0.943305i	−0.0551715	+	0.998477i	$0.517571\pi$
$648$	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	−0.928425	−	0.371520i	$-0.878837\pi$
$653$	−14.2311	+	14.2311i	−0.556904	+	0.556904i	0.371520	+	0.928425i	$0.378837\pi$
$654$	−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	0.800387	−	0.599483i	$-0.204627\pi$
$673$	5.21190	+	5.21190i	0.200904	+	0.200904i	−0.599483	+	0.800387i	$0.704627\pi$
$674$	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	0.327013	−	0.945020i	$-0.393958\pi$
$677$	−16.0801	−	16.0801i	−0.618007	−	0.618007i	−0.945020	+	0.327013i	$0.893958\pi$
$678$	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	−0.928660	−	0.370932i	$-0.879038\pi$
$683$	−14.5758	+	14.5758i	−0.557728	+	0.557728i	0.370932	+	0.928660i	$0.379038\pi$
$684$	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	$-0.830644\pi$
$701$		−	26.8630i		−	1.01460i	0.861769	−	0.507300i	$-0.169356\pi$
$702$	−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	$-0.637959\pi$
$709$		−	48.3302i		−	1.81508i	0.419969	−	0.907538i	$-0.362041\pi$
$710$	−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	−0.999083	−	0.0428056i	$-0.986370\pi$
$727$	−25.7841	+	25.7841i	−0.956278	+	0.956278i	0.0428056	+	0.999083i	$0.486370\pi$
$728$	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	0.370207	−	0.928949i	$-0.379287\pi$
$733$	−15.1274	−	15.1274i	−0.558743	−	0.558743i	−0.928949	+	0.370207i	$0.879287\pi$
$734$	−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	$0.0877589\pi$
$739$			14.8005i			0.544446i	−0.962234	+	0.272223i	$0.912241\pi$
$740$	−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	−0.760826	−	0.648956i	$-0.775206\pi$
$743$	−3.04936	+	3.04936i	−0.111870	+	0.111870i	0.648956	+	0.760826i	$0.275206\pi$
$744$	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	−0.505099	−	0.863061i	$-0.668544\pi$
$757$	9.84883	−	9.84883i	0.357962	−	0.357962i	0.863061	+	0.505099i	$0.168544\pi$
$758$	−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	$0.192499\pi$
$761$			31.3688i			1.13712i	−0.822643	+	0.568559i	$0.807501\pi$
$762$	−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	$-0.851402\pi$
$769$		−	24.9613i		−	0.900126i	0.892997	−	0.450063i	$-0.148598\pi$
$770$	−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	−0.869445	−	0.494029i	$-0.835524\pi$
$773$	−10.4377	+	10.4377i	−0.375416	+	0.375416i	0.494029	+	0.869445i	$0.335524\pi$
$774$	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	−0.0789672	+	0.996877i	$0.525162\pi$
$787$	−30.1812	+	30.1812i	−1.07584	+	1.07584i	−0.996877	+	0.0789672i	$0.974838\pi$
$788$	−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	0.439689	−	0.898150i	$-0.355089\pi$
$797$	−12.9429	−	12.9429i	−0.458461	−	0.458461i	−0.898150	+	0.439689i	$0.855089\pi$
$798$	−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	$0.0713305\pi$
$821$			12.7346i			0.444441i	−0.974996	+	0.222221i	$0.928669\pi$
$822$	15.1933	−	4.75133i	0.529928	−	0.165722i
$823$	21.0730	+	21.0730i	0.734558	+	0.734558i	0.971519	−	0.236961i	$-0.0761514\pi$
$823$	21.0730	+	21.0730i	0.734558	+	0.734558i	−0.236961	+	0.971519i	$0.576151\pi$
$824$	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	0.999927	−	0.0120853i	$-0.00384697\pi$
$827$	28.4080	+	28.4080i	0.987842	+	0.987842i	−0.0120853	+	0.999927i	$0.503847\pi$
$828$	4.08131	+	0.739378i	0.141835	+	0.0256951i
$829$		−	16.5914i		−	0.576243i	−0.957594	−	0.288121i	$-0.906969\pi$
$829$		−	16.5914i		−	0.576243i	0.957594	−	0.288121i	$-0.0930307\pi$
$830$	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	0.301690	−	0.953406i	$-0.402449\pi$
$853$	−19.0341	−	19.0341i	−0.651715	−	0.651715i	−0.953406	+	0.301690i	$0.902449\pi$
$854$	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	0.916689	−	0.399603i	$-0.130852\pi$
$857$	15.1375	+	15.1375i	0.517086	+	0.517086i	−0.399603	+	0.916689i	$0.630852\pi$
$858$	9.46938	+	30.2802i	0.323279	+	1.03375i
$859$		−	46.1064i		−	1.57313i	−0.617507	−	0.786565i	$-0.711857\pi$
$859$		−	46.1064i		−	1.57313i	0.617507	−	0.786565i	$-0.288143\pi$
$860$	−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	−0.912967	−	0.408034i	$-0.866215\pi$
$863$	−14.8334	+	14.8334i	−0.504933	+	0.504933i	0.408034	+	0.912967i	$0.366215\pi$
$864$	−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	0.132657	−	0.991162i	$-0.457649\pi$
$877$	33.2810	−	33.2810i	1.12382	−	1.12382i	0.991162	−	0.132657i	$-0.0423508\pi$
$878$	−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	$0.346886\pi$
$881$			52.6269i			1.77304i	−0.462686	+	0.886522i	$0.653114\pi$
$882$	−2.66997	+	14.7381i	−0.0899026	+	0.496256i
$883$	−25.3525	−	25.3525i	−0.853179	−	0.853179i	0.137344	−	0.990523i	$-0.456143\pi$
$883$	−25.3525	−	25.3525i	−0.853179	−	0.853179i	−0.990523	+	0.137344i	$0.956143\pi$
$884$	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	0.104588	−	0.994516i	$-0.466647\pi$
$887$	−26.5043	−	26.5043i	−0.889927	−	0.889927i	−0.994516	+	0.104588i	$0.966647\pi$
$888$	−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	−0.111822	+	0.993728i	$0.535669\pi$
$907$	−33.2952	+	33.2952i	−1.10555	+	1.10555i	−0.993728	+	0.111822i	$0.964331\pi$
$908$	−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	$-0.743968\pi$
$911$		−	43.4861i		−	1.44076i	0.693581	−	0.720379i	$-0.256032\pi$
$912$	−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	$0.138774\pi$
$919$			25.6036i			0.844584i	−0.906460	+	0.422292i	$0.861226\pi$
$920$	−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	−0.576039	−	0.817422i	$-0.695402\pi$
$937$	7.38886	−	7.38886i	0.241384	−	0.241384i	0.817422	+	0.576039i	$0.195402\pi$
$938$	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	$-0.920023\pi$
$941$		−	15.2532i		−	0.497241i	0.968601	−	0.248620i	$-0.0799772\pi$
$942$	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	0.945868	−	0.324550i	$-0.105213\pi$
$947$	19.1200	+	19.1200i	0.621318	+	0.621318i	−0.324550	+	0.945868i	$0.605213\pi$
$948$	−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	0.168173	−	0.985757i	$-0.446213\pi$
$953$	35.6226	−	35.6226i	1.15393	−	1.15393i	0.985757	−	0.168173i	$-0.0537868\pi$
$954$	−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	−0.921443	−	0.388513i	$-0.872989\pi$
$967$	−16.5723	+	16.5723i	−0.532931	+	0.532931i	0.388513	+	0.921443i	$0.372989\pi$
$968$	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	$-0.826792\pi$
$971$		−	32.2634i		−	1.03538i	0.855568	−	0.517691i	$-0.173208\pi$
$972$	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	0.713973	−	0.700173i	$-0.246894\pi$
$977$	0.431347	+	0.431347i	0.0138000	+	0.0138000i	−0.700173	+	0.713973i	$0.746894\pi$
$978$	−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	−0.482931	−	0.875659i	$-0.660428\pi$
$983$	12.3131	−	12.3131i	0.392728	−	0.392728i	0.875659	+	0.482931i	$0.160428\pi$
$984$	−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	−0.197294	+	0.980344i	$0.563215\pi$
$997$	−37.1843	+	37.1843i	−1.17764	+	1.17764i	−0.980344	+	0.197294i	$0.936785\pi$
$998$	−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.683.15	yes	40
3.2	odd	2	inner	930.2.j.g.683.1	yes	40
5.2	odd	4	inner	930.2.j.g.497.1	✓	40
15.2	even	4	inner	930.2.j.g.497.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.1	✓	40	5.2	odd	4	inner
930.2.j.g.497.15	yes	40	15.2	even	4	inner
930.2.j.g.683.1	yes	40	3.2	odd	2	inner
930.2.j.g.683.15	yes	40	1.1	even	1	trivial

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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