LMFDB - Embedded newform 930.2.k.a.247.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(247,930)]

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([0, 1, 2]))

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

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

chi := DirichletCharacter("930.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.k (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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			247.8
Character	$\chi$	$=$	930.247
Dual form			930.2.k.a.433.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.14513 + 0.631187i) q^{5} -1.00000i q^{6} +(2.22289 + 2.22289i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.14513 + 0.631187i) q^{5} -1.00000i q^{6} +(2.22289 + 2.22289i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.07052 - 1.96316i) q^{10} +2.67302i q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.52933 + 1.52933i) q^{13} -3.14364i q^{14} +(1.07052 + 1.96316i) q^{15} -1.00000 q^{16} +(-1.08641 + 1.08641i) q^{17} +(0.707107 - 0.707107i) q^{18} +1.14871i q^{19} +(-0.631187 + 2.14513i) q^{20} +3.14364i q^{21} +(1.89011 - 1.89011i) q^{22} +(-4.52431 - 4.52431i) q^{23} +1.00000 q^{24} +(4.20321 + 2.70796i) q^{25} -2.16280i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.22289 + 2.22289i) q^{28} -3.21939 q^{29} +(0.631187 - 2.14513i) q^{30} +(-3.35197 - 4.44571i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.89011 + 1.89011i) q^{33} +1.53641 q^{34} +(3.36534 + 6.17145i) q^{35} -1.00000 q^{36} +(-0.0599165 + 0.0599165i) q^{37} +(0.812260 - 0.812260i) q^{38} +2.16280i q^{39} +(1.96316 - 1.07052i) q^{40} +1.16545 q^{41} +(2.22289 - 2.22289i) q^{42} +(-3.62140 - 3.62140i) q^{43} -2.67302 q^{44} +(-0.631187 + 2.14513i) q^{45} +6.39835i q^{46} +(0.927393 + 0.927393i) q^{47} +(-0.707107 - 0.707107i) q^{48} +2.88246i q^{49} +(-1.05730 - 4.88693i) q^{50} -1.53641 q^{51} +(-1.52933 + 1.52933i) q^{52} +(-4.04461 - 4.04461i) q^{53} +1.00000 q^{54} +(-1.68718 + 5.73400i) q^{55} +3.14364 q^{56} +(-0.812260 + 0.812260i) q^{57} +(2.27645 + 2.27645i) q^{58} -14.0638i q^{59} +(-1.96316 + 1.07052i) q^{60} +11.1372i q^{61} +(-0.773391 + 5.51379i) q^{62} +(-2.22289 + 2.22289i) q^{63} -1.00000i q^{64} +(2.31532 + 4.24591i) q^{65} +2.67302 q^{66} +(8.98751 + 8.98751i) q^{67} +(-1.08641 - 1.08641i) q^{68} -6.39835i q^{69} +(1.98422 - 6.74353i) q^{70} +9.67268 q^{71} +(0.707107 + 0.707107i) q^{72} +(6.81687 + 6.81687i) q^{73} +0.0847348 q^{74} +(1.05730 + 4.88693i) q^{75} -1.14871 q^{76} +(-5.94183 + 5.94183i) q^{77} +(1.52933 - 1.52933i) q^{78} +11.2284 q^{79} +(-2.14513 - 0.631187i) q^{80} -1.00000 q^{81} +(-0.824095 - 0.824095i) q^{82} +(-11.0672 - 11.0672i) q^{83} -3.14364 q^{84} +(-3.01622 + 1.64476i) q^{85} +5.12143i q^{86} +(-2.27645 - 2.27645i) q^{87} +(1.89011 + 1.89011i) q^{88} +10.3719 q^{89} +(1.96316 - 1.07052i) q^{90} +6.79905i q^{91} +(4.52431 - 4.52431i) q^{92} +(0.773391 - 5.51379i) q^{93} -1.31153i q^{94} +(-0.725051 + 2.46414i) q^{95} +1.00000i q^{96} +(-0.00703286 - 0.00703286i) q^{97} +(2.03821 - 2.03821i) q^{98} -2.67302 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7}+O(q^{10}) $ 32 * q - 4 * q^7	$ 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			1.00000i			0.500000i
$5$	2.14513	+	0.631187i	0.959333	+	0.282275i
$5$	2.14513	+	0.631187i	0.959333	+	0.282275i
$6$		−	1.00000i		−	0.408248i
$7$	2.22289	+	2.22289i	0.840173	+	0.840173i	0.988881	−	0.148708i	$-0.0475116\pi$
$7$	2.22289	+	2.22289i	0.840173	+	0.840173i	−0.148708	+	0.988881i	$0.547512\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	−1.07052	−	1.96316i	−0.338529	−	0.620804i
$11$			2.67302i			0.805947i	0.915212	+	0.402974i	$0.132023\pi$
$11$			2.67302i			0.805947i	−0.915212	+	0.402974i	$0.867977\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	1.52933	+	1.52933i	0.424159	+	0.424159i	0.886633	−	0.462474i	$-0.153038\pi$
$13$	1.52933	+	1.52933i	0.424159	+	0.424159i	−0.462474	+	0.886633i	$0.653038\pi$
$14$		−	3.14364i		−	0.840173i
$15$	1.07052	+	1.96316i	0.276408	+	0.506885i
$16$	−1.00000			−0.250000
$17$	−1.08641	+	1.08641i	−0.263492	+	0.263492i	−0.826471	−	0.562979i	$-0.809655\pi$
$17$	−1.08641	+	1.08641i	−0.263492	+	0.263492i	0.562979	+	0.826471i	$0.309655\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$			1.14871i			0.263532i	0.991281	+	0.131766i	$0.0420648\pi$
$19$			1.14871i			0.263532i	−0.991281	+	0.131766i	$0.957935\pi$
$20$	−0.631187	+	2.14513i	−0.141138	+	0.479667i
$21$			3.14364i			0.685998i
$22$	1.89011	−	1.89011i	0.402974	−	0.402974i
$23$	−4.52431	−	4.52431i	−0.943385	−	0.943385i	0.0550962	−	0.998481i	$-0.482453\pi$
$23$	−4.52431	−	4.52431i	−0.943385	−	0.943385i	−0.998481	+	0.0550962i	$0.982453\pi$
$24$	1.00000			0.204124
$25$	4.20321	+	2.70796i	0.840641	+	0.541593i
$26$		−	2.16280i		−	0.424159i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.22289	+	2.22289i	−0.420086	+	0.420086i
$29$	−3.21939			−0.597826			−0.298913	−	0.954280i	$-0.596624\pi$
$29$	−3.21939			−0.597826			−0.298913	+	0.954280i	$0.596624\pi$
$30$	0.631187	−	2.14513i	0.115238	−	0.391646i
$31$	−3.35197	−	4.44571i	−0.602031	−	0.798473i
$31$	−3.35197	−	4.44571i	−0.602031	−	0.798473i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.89011	+	1.89011i	−0.329027	+	0.329027i
$34$	1.53641			0.263492
$35$	3.36534	+	6.17145i	0.568846	+	1.04317i
$36$	−1.00000			−0.166667
$37$	−0.0599165	+	0.0599165i	−0.00985022	+	0.00985022i	−0.712015	−	0.702165i	$-0.752217\pi$
$37$	−0.0599165	+	0.0599165i	−0.00985022	+	0.00985022i	0.702165	+	0.712015i	$0.252217\pi$
$38$	0.812260	−	0.812260i	0.131766	−	0.131766i
$39$			2.16280i			0.346325i
$40$	1.96316	−	1.07052i	0.310402	−	0.169264i
$41$	1.16545			0.182012			0.0910060	−	0.995850i	$-0.470992\pi$
$41$	1.16545			0.182012			0.0910060	+	0.995850i	$0.470992\pi$
$42$	2.22289	−	2.22289i	0.342999	−	0.342999i
$43$	−3.62140	−	3.62140i	−0.552258	−	0.552258i	0.374834	−	0.927092i	$-0.377700\pi$
$43$	−3.62140	−	3.62140i	−0.552258	−	0.552258i	−0.927092	+	0.374834i	$0.877700\pi$
$44$	−2.67302			−0.402974
$45$	−0.631187	+	2.14513i	−0.0940918	+	0.319778i
$46$			6.39835i			0.943385i
$47$	0.927393	+	0.927393i	0.135274	+	0.135274i	0.771502	−	0.636227i	$-0.219506\pi$
$47$	0.927393	+	0.927393i	0.135274	+	0.135274i	−0.636227	+	0.771502i	$0.719506\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$			2.88246i			0.411780i
$50$	−1.05730	−	4.88693i	−0.149524	−	0.691117i
$51$	−1.53641			−0.215141
$52$	−1.52933	+	1.52933i	−0.212080	+	0.212080i
$53$	−4.04461	−	4.04461i	−0.555569	−	0.555569i	0.372473	−	0.928043i	$-0.378510\pi$
$53$	−4.04461	−	4.04461i	−0.555569	−	0.555569i	−0.928043	+	0.372473i	$0.878510\pi$
$54$	1.00000			0.136083
$55$	−1.68718	+	5.73400i	−0.227499	+	0.773172i
$56$	3.14364			0.420086
$57$	−0.812260	+	0.812260i	−0.107587	+	0.107587i
$58$	2.27645	+	2.27645i	0.298913	+	0.298913i
$59$		−	14.0638i		−	1.83095i	−0.402376	−	0.915474i	$-0.631816\pi$
$59$		−	14.0638i		−	1.83095i	0.402376	−	0.915474i	$-0.368184\pi$
$60$	−1.96316	+	1.07052i	−0.253442	+	0.138204i
$61$			11.1372i			1.42598i	0.701176	+	0.712988i	$0.252659\pi$
$61$			11.1372i			1.42598i	−0.701176	+	0.712988i	$0.747341\pi$
$62$	−0.773391	+	5.51379i	−0.0982207	+	0.700252i
$63$	−2.22289	+	2.22289i	−0.280058	+	0.280058i
$64$		−	1.00000i		−	0.125000i
$65$	2.31532	+	4.24591i	0.287180	+	0.526640i
$66$	2.67302			0.329027
$67$	8.98751	+	8.98751i	1.09800	+	1.09800i	0.994645	+	0.103354i	$0.0329575\pi$
$67$	8.98751	+	8.98751i	1.09800	+	1.09800i	0.103354	+	0.994645i	$0.467043\pi$
$68$	−1.08641	−	1.08641i	−0.131746	−	0.131746i
$69$		−	6.39835i		−	0.770270i
$70$	1.98422	−	6.74353i	0.237160	−	0.806006i
$71$	9.67268			1.14794			0.573968	−	0.818878i	$-0.305403\pi$
$71$	9.67268			1.14794			0.573968	+	0.818878i	$0.305403\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	6.81687	+	6.81687i	0.797855	+	0.797855i	0.982757	−	0.184902i	$-0.0591969\pi$
$73$	6.81687	+	6.81687i	0.797855	+	0.797855i	−0.184902	+	0.982757i	$0.559197\pi$
$74$	0.0847348			0.00985022
$75$	1.05730	+	4.88693i	0.122086	+	0.564295i
$76$	−1.14871			−0.131766
$77$	−5.94183	+	5.94183i	−0.677135	+	0.677135i
$78$	1.52933	−	1.52933i	0.173162	−	0.173162i
$79$	11.2284			1.26330			0.631648	−	0.775255i	$-0.282379\pi$
$79$	11.2284			1.26330			0.631648	+	0.775255i	$0.282379\pi$
$80$	−2.14513	−	0.631187i	−0.239833	−	0.0705689i
$81$	−1.00000			−0.111111
$82$	−0.824095	−	0.824095i	−0.0910060	−	0.0910060i
$83$	−11.0672	−	11.0672i	−1.21478	−	1.21478i	−0.969437	−	0.245342i	$-0.921100\pi$
$83$	−11.0672	−	11.0672i	−1.21478	−	1.21478i	−0.245342	−	0.969437i	$-0.578900\pi$
$84$	−3.14364			−0.342999
$85$	−3.01622	+	1.64476i	−0.327155	+	0.178400i
$86$			5.12143i			0.552258i
$87$	−2.27645	−	2.27645i	−0.244061	−	0.244061i
$88$	1.89011	+	1.89011i	0.201487	+	0.201487i
$89$	10.3719			1.09942			0.549711	−	0.835355i	$-0.314738\pi$
$89$	10.3719			1.09942			0.549711	+	0.835355i	$0.314738\pi$
$90$	1.96316	−	1.07052i	0.206935	−	0.112843i
$91$			6.79905i			0.712734i
$92$	4.52431	−	4.52431i	0.471692	−	0.471692i
$93$	0.773391	−	5.51379i	0.0801969	−	0.571753i
$94$		−	1.31153i		−	0.135274i
$95$	−0.725051	+	2.46414i	−0.0743886	+	0.252815i
$96$			1.00000i			0.102062i
$97$	−0.00703286	−	0.00703286i	−0.000714079	−	0.000714079i	0.706750	−	0.707464i	$-0.250161\pi$
$97$	−0.00703286	−	0.00703286i	−0.000714079	−	0.000714079i	−0.707464	+	0.706750i	$0.750161\pi$
$98$	2.03821	−	2.03821i	0.205890	−	0.205890i
$99$	−2.67302			−0.268649
$100$	−2.70796	+	4.20321i	−0.270796	+	0.420321i
$101$	17.4523			1.73657			0.868287	−	0.496063i	$-0.165221\pi$
$101$	17.4523			1.73657			0.868287	+	0.496063i	$0.165221\pi$
$102$	1.08641	+	1.08641i	0.107570	+	0.107570i
$103$	−5.69619	+	5.69619i	−0.561262	+	0.561262i	−0.929666	−	0.368404i	$-0.879904\pi$
$103$	−5.69619	+	5.69619i	−0.561262	+	0.561262i	0.368404	+	0.929666i	$0.379904\pi$
$104$	2.16280			0.212080
$105$	−1.98422	+	6.74353i	−0.193640	+	0.658101i
$106$			5.71994i			0.555569i
$107$	−1.93400	−	1.93400i	−0.186967	−	0.186967i	0.607416	−	0.794384i	$-0.292206\pi$
$107$	−1.93400	−	1.93400i	−0.186967	−	0.186967i	−0.794384	+	0.607416i	$0.792206\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	6.84356i		−	0.655495i	−0.944765	−	0.327747i	$-0.893711\pi$
$109$		−	6.84356i		−	0.655495i	0.944765	−	0.327747i	$-0.106289\pi$
$110$	5.24756	−	2.86153i	0.500336	−	0.272836i
$111$	−0.0847348			−0.00804267
$112$	−2.22289	−	2.22289i	−0.210043	−	0.210043i
$113$	1.96389	−	1.96389i	0.184748	−	0.184748i	−0.608673	−	0.793421i	$-0.708298\pi$
$113$	1.96389	−	1.96389i	0.184748	−	0.184748i	0.793421	+	0.608673i	$0.208298\pi$
$114$	1.14871			0.107587
$115$	−6.84957	−	12.5610i	−0.638726	−	1.17131i
$116$		−	3.21939i		−	0.298913i
$117$	−1.52933	+	1.52933i	−0.141386	+	0.141386i
$118$	−9.94460	+	9.94460i	−0.915474	+	0.915474i
$119$	−4.82992			−0.442758
$120$	2.14513	+	0.631187i	0.195823	+	0.0576192i
$121$	3.85494			0.350449
$122$	7.87522	−	7.87522i	0.712988	−	0.712988i
$123$	0.824095	+	0.824095i	0.0743061	+	0.0743061i
$124$	4.44571	−	3.35197i	0.399236	−	0.301016i
$125$	7.30721	+	8.46195i	0.653577	+	0.756860i
$126$	3.14364			0.280058
$127$	2.68648	−	2.68648i	0.238387	−	0.238387i	−0.577795	−	0.816182i	$-0.696087\pi$
$127$	2.68648	−	2.68648i	0.238387	−	0.238387i	0.816182	+	0.577795i	$0.196087\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		−	5.12143i		−	0.450916i
$130$	1.36513	−	4.63949i	0.119730	−	0.406910i
$131$	−2.03096			−0.177445			−0.0887227	−	0.996056i	$-0.528278\pi$
$131$	−2.03096			−0.177445			−0.0887227	+	0.996056i	$0.528278\pi$
$132$	−1.89011	−	1.89011i	−0.164513	−	0.164513i
$133$	−2.55345	+	2.55345i	−0.221412	+	0.221412i
$134$		−	12.7103i		−	1.09800i
$135$	−1.96316	+	1.07052i	−0.168962	+	0.0921359i
$136$			1.53641i			0.131746i
$137$	1.61024	−	1.61024i	0.137572	−	0.137572i	−0.634967	−	0.772539i	$-0.718986\pi$
$137$	1.61024	−	1.61024i	0.137572	−	0.137572i	0.772539	+	0.634967i	$0.218986\pi$
$138$	−4.52431	+	4.52431i	−0.385135	+	0.385135i
$139$	16.9812			1.44033			0.720164	−	0.693803i	$-0.244066\pi$
$139$	16.9812			1.44033			0.720164	+	0.693803i	$0.244066\pi$
$140$	−6.17145	+	3.36534i	−0.521583	+	0.284423i
$141$			1.31153i			0.110451i
$142$	−6.83962	−	6.83962i	−0.573968	−	0.573968i
$143$	−4.08793	+	4.08793i	−0.341850	+	0.341850i
$144$		−	1.00000i		−	0.0833333i
$145$	−6.90603	−	2.03204i	−0.573514	−	0.168752i
$146$		−	9.64051i		−	0.797855i
$147$	−2.03821	+	2.03821i	−0.168109	+	0.168109i
$148$	−0.0599165	−	0.0599165i	−0.00492511	−	0.00492511i
$149$		−	7.83496i		−	0.641865i	−0.947102	−	0.320933i	$-0.896004\pi$
$149$		−	7.83496i		−	0.641865i	0.947102	−	0.320933i	$-0.103996\pi$
$150$	2.70796	−	4.20321i	0.221104	−	0.343190i
$151$		−	8.02319i		−	0.652918i	−0.945211	−	0.326459i	$-0.894144\pi$
$151$		−	8.02319i		−	0.652918i	0.945211	−	0.326459i	$-0.105856\pi$
$152$	0.812260	+	0.812260i	0.0658830	+	0.0658830i
$153$	−1.08641	−	1.08641i	−0.0878308	−	0.0878308i
$154$	8.40302			0.677135
$155$	−4.38435	−	11.6524i	−0.352159	−	0.935940i
$156$	−2.16280			−0.173162
$157$	−2.98462	−	2.98462i	−0.238199	−	0.238199i	0.577905	−	0.816104i	$-0.303870\pi$
$157$	−2.98462	−	2.98462i	−0.238199	−	0.238199i	−0.816104	+	0.577905i	$0.803870\pi$
$158$	−7.93970	−	7.93970i	−0.631648	−	0.631648i
$159$		−	5.71994i		−	0.453621i
$160$	1.07052	+	1.96316i	0.0846322	+	0.155201i
$161$		−	20.1141i		−	1.58521i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−11.3820	+	11.3820i	−0.891505	+	0.891505i	−0.994665	−	0.103160i	$-0.967105\pi$
$163$	−11.3820	+	11.3820i	−0.891505	+	0.891505i	0.103160	+	0.994665i	$0.467105\pi$
$164$			1.16545i			0.0910060i
$165$	−5.24756	+	2.86153i	−0.408522	+	0.222770i
$166$			15.6513i			1.21478i
$167$	−13.0021	+	13.0021i	−1.00614	+	1.00614i	−0.00615431	+	0.999981i	$0.501959\pi$
$167$	−13.0021	+	13.0021i	−1.00614	+	1.00614i	−0.999981	+	0.00615431i	$0.998041\pi$
$168$	2.22289	+	2.22289i	0.171500	+	0.171500i
$169$		−	8.32231i		−	0.640178i
$170$	3.29581	+	0.969764i	0.252777	+	0.0743775i
$171$	−1.14871			−0.0878440
$172$	3.62140	−	3.62140i	0.276129	−	0.276129i
$173$	4.95930	−	4.95930i	0.377049	−	0.377049i	−0.492988	−	0.870036i	$-0.664095\pi$
$173$	4.95930	−	4.95930i	0.377049	−	0.377049i	0.870036	+	0.492988i	$0.164095\pi$
$174$			3.21939i			0.244061i
$175$	3.32376	+	15.3628i	0.251252	+	1.16132i
$176$		−	2.67302i		−	0.201487i
$177$	9.94460	−	9.94460i	0.747482	−	0.747482i
$178$	−7.33406	−	7.33406i	−0.549711	−	0.549711i
$179$	2.13033			0.159229			0.0796143	−	0.996826i	$-0.474631\pi$
$179$	2.13033			0.159229			0.0796143	+	0.996826i	$0.474631\pi$
$180$	−2.14513	−	0.631187i	−0.159889	−	0.0470459i
$181$			13.2230i			0.982857i	0.870918	+	0.491428i	$0.163525\pi$
$181$			13.2230i			0.982857i	−0.870918	+	0.491428i	$0.836475\pi$
$182$	4.80766	−	4.80766i	0.356367	−	0.356367i
$183$	−7.87522	+	7.87522i	−0.582153	+	0.582153i
$184$	−6.39835			−0.471692
$185$	−0.166348	+	0.0907105i	−0.0122301	+	0.00666917i
$186$	−4.44571	+	3.35197i	−0.325975	+	0.245778i
$187$	−2.90399	−	2.90399i	−0.212361	−	0.212361i
$188$	−0.927393	+	0.927393i	−0.0676371	+	0.0676371i
$189$	−3.14364			−0.228666
$190$	2.25510	−	1.22972i	0.163602	−	0.0892132i
$191$	−5.57211			−0.403184			−0.201592	−	0.979470i	$-0.564611\pi$
$191$	−5.57211			−0.403184			−0.201592	+	0.979470i	$0.564611\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	0.152111	−	0.152111i	0.0109492	−	0.0109492i	−0.701611	−	0.712560i	$-0.747536\pi$
$193$	0.152111	−	0.152111i	0.0109492	−	0.0109492i	0.712560	+	0.701611i	$0.247536\pi$
$194$			0.00994596i			0.000714079i
$195$	−1.36513	+	4.63949i	−0.0977590	+	0.332241i
$196$	−2.88246			−0.205890
$197$	3.02442	−	3.02442i	0.215481	−	0.215481i	−0.591110	−	0.806591i	$-0.701310\pi$
$197$	3.02442	−	3.02442i	0.215481	−	0.215481i	0.806591	+	0.591110i	$0.201310\pi$
$198$	1.89011	+	1.89011i	0.134325	+	0.134325i
$199$	5.34811			0.379118			0.189559	−	0.981869i	$-0.439294\pi$
$199$	5.34811			0.379118			0.189559	+	0.981869i	$0.439294\pi$
$200$	4.88693	−	1.05730i	0.345558	−	0.0747621i
$201$			12.7103i			0.896512i
$202$	−12.3407	−	12.3407i	−0.868287	−	0.868287i
$203$	−7.15635	−	7.15635i	−0.502277	−	0.502277i
$204$		−	1.53641i		−	0.107570i
$205$	2.50004	+	0.735615i	0.174610	+	0.0513775i
$206$	8.05562			0.561262
$207$	4.52431	−	4.52431i	0.314462	−	0.314462i
$208$	−1.52933	−	1.52933i	−0.106040	−	0.106040i
$209$	−3.07053			−0.212393
$210$	6.17145	−	3.36534i	0.425871	−	0.232230i
$211$	−9.45235			−0.650727			−0.325363	−	0.945589i	$-0.605487\pi$
$211$	−9.45235			−0.650727			−0.325363	+	0.945589i	$0.605487\pi$
$212$	4.04461	−	4.04461i	0.277785	−	0.277785i
$213$	6.83962	+	6.83962i	0.468643	+	0.468643i
$214$			2.73509i			0.186967i
$215$	−5.48260	−	10.0542i	−0.373910	−	0.685688i
$216$			1.00000i			0.0680414i
$217$	2.43126	−	17.3334i	0.165045	−	1.17666i
$218$	−4.83913	+	4.83913i	−0.327747	+	0.327747i
$219$			9.64051i			0.651446i
$220$	−5.73400	−	1.68718i	−0.386586	−	0.113750i
$221$	−3.32295			−0.223526
$222$	0.0599165	+	0.0599165i	0.00402134	+	0.00402134i
$223$	−19.9697	−	19.9697i	−1.33727	−	1.33727i	−0.898694	−	0.438576i	$-0.855483\pi$
$223$	−19.9697	−	19.9697i	−1.33727	−	1.33727i	−0.438576	−	0.898694i	$-0.644517\pi$
$224$			3.14364i			0.210043i
$225$	−2.70796	+	4.20321i	−0.180531	+	0.280214i
$226$	−2.77737			−0.184748
$227$	−12.0426	−	12.0426i	−0.799296	−	0.799296i	0.183688	−	0.982985i	$-0.441196\pi$
$227$	−12.0426	−	12.0426i	−0.799296	−	0.799296i	−0.982985	+	0.183688i	$0.941196\pi$
$228$	−0.812260	−	0.812260i	−0.0537933	−	0.0537933i
$229$	6.18101			0.408453			0.204226	−	0.978924i	$-0.434532\pi$
$229$	6.18101			0.408453			0.204226	+	0.978924i	$0.434532\pi$
$230$	−4.03855	+	13.7253i	−0.266294	+	0.905021i
$231$	−8.40302			−0.552878
$232$	−2.27645	+	2.27645i	−0.149456	+	0.149456i
$233$	−12.0314	+	12.0314i	−0.788203	+	0.788203i	−0.981199	−	0.192997i	$-0.938179\pi$
$233$	−12.0314	+	12.0314i	−0.788203	+	0.788203i	0.192997	+	0.981199i	$0.438179\pi$
$234$	2.16280			0.141386
$235$	1.40402	+	2.57474i	0.0915884	+	0.167958i
$236$	14.0638			0.915474
$237$	7.93970	+	7.93970i	0.515739	+	0.515739i
$238$	3.41527	+	3.41527i	0.221379	+	0.221379i
$239$	−1.04440			−0.0675569			−0.0337785	−	0.999429i	$-0.510754\pi$
$239$	−1.04440			−0.0675569			−0.0337785	+	0.999429i	$0.510754\pi$
$240$	−1.07052	−	1.96316i	−0.0691019	−	0.126721i
$241$			3.35439i			0.216075i	0.994147	+	0.108038i	$0.0344567\pi$
$241$			3.35439i			0.216075i	−0.994147	+	0.108038i	$0.965543\pi$
$242$	−2.72586	−	2.72586i	−0.175225	−	0.175225i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−11.1372			−0.712988
$245$	−1.81937	+	6.18327i	−0.116235	+	0.395035i
$246$		−	1.16545i		−	0.0743061i
$247$	−1.75675	+	1.75675i	−0.111780	+	0.111780i
$248$	−5.51379	−	0.773391i	−0.350126	−	0.0491104i
$249$		−	15.6513i		−	0.991863i
$250$	0.816528	−	11.1505i	0.0516418	−	0.705218i
$251$		−	16.3991i		−	1.03510i	−0.855652	−	0.517551i	$-0.826844\pi$
$251$		−	16.3991i		−	1.03510i	0.855652	−	0.517551i	$-0.173156\pi$
$252$	−2.22289	−	2.22289i	−0.140029	−	0.140029i
$253$	12.0936	−	12.0936i	0.760318	−	0.760318i
$254$	−3.79926			−0.238387
$255$	−3.29581	−	0.969764i	−0.206392	−	0.0607289i
$256$	1.00000			0.0625000
$257$	−17.2719	−	17.2719i	−1.07739	−	1.07739i	−0.996743	−	0.0806466i	$-0.974301\pi$
$257$	−17.2719	−	17.2719i	−1.07739	−	1.07739i	−0.0806466	−	0.996743i	$-0.525699\pi$
$258$	−3.62140	+	3.62140i	−0.225458	+	0.225458i
$259$	−0.266376			−0.0165518
$260$	−4.24591	+	2.31532i	−0.263320	+	0.143590i
$261$		−	3.21939i		−	0.199275i
$262$	1.43610	+	1.43610i	0.0887227	+	0.0887227i
$263$	17.8202	+	17.8202i	1.09884	+	1.09884i	0.994546	+	0.104295i	$0.0332585\pi$
$263$	17.8202	+	17.8202i	1.09884	+	1.09884i	0.104295	+	0.994546i	$0.466741\pi$
$264$			2.67302i			0.164513i
$265$	−6.12332	−	11.2291i	−0.376153	−	0.689800i
$266$	3.61113			0.221412
$267$	7.33406	+	7.33406i	0.448837	+	0.448837i
$268$	−8.98751	+	8.98751i	−0.548999	+	0.548999i
$269$	7.33116			0.446989			0.223494	−	0.974705i	$-0.428254\pi$
$269$	7.33116			0.446989			0.223494	+	0.974705i	$0.428254\pi$
$270$	2.14513	+	0.631187i	0.130549	+	0.0384128i
$271$		−	26.8896i		−	1.63343i	−0.577042	−	0.816715i	$-0.695793\pi$
$271$		−	26.8896i		−	1.63343i	0.577042	−	0.816715i	$-0.304207\pi$
$272$	1.08641	−	1.08641i	0.0658731	−	0.0658731i
$273$	−4.80766	+	4.80766i	−0.290973	+	0.290973i
$274$	−2.27723			−0.137572
$275$	−7.23845	+	11.2353i	−0.436495	+	0.677512i
$276$	6.39835			0.385135
$277$	−4.85874	+	4.85874i	−0.291933	+	0.291933i	−0.837844	−	0.545910i	$-0.816184\pi$
$277$	−4.85874	+	4.85874i	−0.291933	+	0.291933i	0.545910	+	0.837844i	$0.316184\pi$
$278$	−12.0075	−	12.0075i	−0.720164	−	0.720164i
$279$	4.44571	−	3.35197i	0.266158	−	0.200677i
$280$	6.74353	+	1.98422i	0.403003	+	0.118580i
$281$	−8.59702			−0.512855			−0.256428	−	0.966563i	$-0.582546\pi$
$281$	−8.59702			−0.512855			−0.256428	+	0.966563i	$0.582546\pi$
$282$	0.927393	−	0.927393i	0.0552254	−	0.0552254i
$283$	−6.30932	+	6.30932i	−0.375050	+	0.375050i	−0.869313	−	0.494262i	$-0.835438\pi$
$283$	−6.30932	+	6.30932i	−0.375050	+	0.375050i	0.494262	+	0.869313i	$0.335438\pi$
$284$			9.67268i			0.573968i
$285$	−2.25510	+	1.22972i	−0.133580	+	0.0728423i
$286$	5.78121			0.341850
$287$	2.59066	+	2.59066i	0.152922	+	0.152922i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$			14.6394i			0.861143i
$290$	3.44643	+	6.32017i	0.202381	+	0.371133i
$291$		−	0.00994596i		−	0.000583043i
$292$	−6.81687	+	6.81687i	−0.398927	+	0.398927i
$293$	−3.38013	+	3.38013i	−0.197469	+	0.197469i	−0.798914	−	0.601445i	$-0.794592\pi$
$293$	−3.38013	+	3.38013i	−0.197469	+	0.197469i	0.601445	+	0.798914i	$0.294592\pi$
$294$	2.88246			0.168109
$295$	8.87688	−	30.1687i	0.516832	−	1.75649i
$296$			0.0847348i			0.00492511i
$297$	−1.89011	−	1.89011i	−0.109676	−	0.109676i
$298$	−5.54016	+	5.54016i	−0.320933	+	0.320933i
$299$		−	13.8383i		−	0.800291i
$300$	−4.88693	+	1.05730i	−0.282147	+	0.0610430i
$301$		−	16.0999i		−	0.927984i
$302$	−5.67325	+	5.67325i	−0.326459	+	0.326459i
$303$	12.3407	+	12.3407i	0.708953	+	0.708953i
$304$		−	1.14871i		−	0.0658830i
$305$	−7.02968	+	23.8909i	−0.402518	+	1.36799i
$306$			1.53641i			0.0878308i
$307$	−8.86665	−	8.86665i	−0.506046	−	0.506046i	0.407264	−	0.913310i	$-0.366483\pi$
$307$	−8.86665	−	8.86665i	−0.506046	−	0.506046i	−0.913310	+	0.407264i	$0.866483\pi$
$308$	−5.94183	−	5.94183i	−0.338567	−	0.338567i
$309$	−8.05562			−0.458268
$310$	−5.13926	+	11.3397i	−0.291890	+	0.644050i
$311$	−33.0951			−1.87665			−0.938326	−	0.345753i	$-0.887624\pi$
$311$	−33.0951			−1.87665			−0.938326	+	0.345753i	$0.887624\pi$
$312$	1.52933	+	1.52933i	0.0865812	+	0.0865812i
$313$	−1.89769	−	1.89769i	−0.107264	−	0.107264i	0.651438	−	0.758702i	$-0.274166\pi$
$313$	−1.89769	−	1.89769i	−0.107264	−	0.107264i	−0.758702	+	0.651438i	$0.774166\pi$
$314$			4.22089i			0.238199i
$315$	−6.17145	+	3.36534i	−0.347722	+	0.189615i
$316$			11.2284i			0.631648i
$317$	−5.89898	−	5.89898i	−0.331320	−	0.331320i	0.521768	−	0.853088i	$-0.325273\pi$
$317$	−5.89898	−	5.89898i	−0.331320	−	0.331320i	−0.853088	+	0.521768i	$0.825273\pi$
$318$	−4.04461	+	4.04461i	−0.226810	+	0.226810i
$319$		−	8.60551i		−	0.481816i
$320$	0.631187	−	2.14513i	0.0352844	−	0.119917i
$321$		−	2.73509i		−	0.152658i
$322$	−14.2228	+	14.2228i	−0.792606	+	0.792606i
$323$	−1.24797	−	1.24797i	−0.0694387	−	0.0694387i
$324$		−	1.00000i		−	0.0555556i
$325$	2.28672	+	10.5694i	0.126844	+	0.586287i
$326$	16.0965			0.891505
$327$	4.83913	−	4.83913i	0.267605	−	0.267605i
$328$	0.824095	−	0.824095i	0.0455030	−	0.0455030i
$329$			4.12298i			0.227307i
$330$	5.73400	+	1.68718i	0.315646	+	0.0928761i
$331$		−	10.9403i		−	0.601334i	−0.953729	−	0.300667i	$-0.902791\pi$
$331$		−	10.9403i		−	0.601334i	0.953729	−	0.300667i	$-0.0972092\pi$
$332$	11.0672	−	11.0672i	0.607389	−	0.607389i
$333$	−0.0599165	−	0.0599165i	−0.00328341	−	0.00328341i
$334$	18.3878			1.00614
$335$	13.6066	+	24.9522i	0.743409	+	1.36328i
$336$		−	3.14364i		−	0.171500i
$337$	19.8371	−	19.8371i	1.08059	−	1.08059i	0.0841403	−	0.996454i	$-0.473186\pi$
$337$	19.8371	−	19.8371i	1.08059	−	1.08059i	0.996454	−	0.0841403i	$-0.0268144\pi$
$338$	−5.88476	+	5.88476i	−0.320089	+	0.320089i
$339$	2.77737			0.150846
$340$	−1.64476	−	3.01622i	−0.0891998	−	0.163577i
$341$	11.8835	−	8.95989i	0.643527	−	0.485205i
$342$	0.812260	+	0.812260i	0.0439220	+	0.0439220i
$343$	9.15283	−	9.15283i	0.494206	−	0.494206i
$344$	−5.12143			−0.276129
$345$	4.03855	−	13.7253i	0.217428	−	0.738946i
$346$	−7.01351			−0.377049
$347$	4.97180	−	4.97180i	0.266900	−	0.266900i	−0.560950	−	0.827850i	$-0.689564\pi$
$347$	4.97180	−	4.97180i	0.266900	−	0.266900i	0.827850	+	0.560950i	$0.189564\pi$
$348$	2.27645	−	2.27645i	0.122031	−	0.122031i
$349$			15.4583i			0.827464i	0.910399	+	0.413732i	$0.135775\pi$
$349$			15.4583i			0.827464i	−0.910399	+	0.413732i	$0.864225\pi$
$350$	8.51286	−	13.2134i	0.455031	−	0.706284i
$351$	−2.16280			−0.115442
$352$	−1.89011	+	1.89011i	−0.100743	+	0.100743i
$353$	17.3752	+	17.3752i	0.924787	+	0.924787i	0.997363	−	0.0725762i	$-0.0231221\pi$
$353$	17.3752	+	17.3752i	0.924787	+	0.924787i	−0.0725762	+	0.997363i	$0.523122\pi$
$354$	−14.0638			−0.747482
$355$	20.7492	+	6.10527i	1.10125	+	0.324034i
$356$			10.3719i			0.549711i
$357$	−3.41527	−	3.41527i	−0.180755	−	0.180755i
$358$	−1.50637	−	1.50637i	−0.0796143	−	0.0796143i
$359$		−	9.08492i		−	0.479484i	−0.970837	−	0.239742i	$-0.922937\pi$
$359$		−	9.08492i		−	0.479484i	0.970837	−	0.239742i	$-0.0770629\pi$
$360$	1.07052	+	1.96316i	0.0564215	+	0.103467i
$361$	17.6805			0.930551
$362$	9.35006	−	9.35006i	0.491428	−	0.491428i
$363$	2.72586	+	2.72586i	0.143070	+	0.143070i
$364$	−6.79905			−0.356367
$365$	10.3204	+	18.9258i	0.540194	+	0.990623i
$366$	11.1372			0.582153
$367$	−23.1394	+	23.1394i	−1.20787	+	1.20787i	−0.236149	+	0.971717i	$0.575885\pi$
$367$	−23.1394	+	23.1394i	−1.20787	+	1.20787i	−0.971717	+	0.236149i	$0.924115\pi$
$368$	4.52431	+	4.52431i	0.235846	+	0.235846i
$369$			1.16545i			0.0606707i
$370$	0.181768	+	0.0534835i	0.00944964	+	0.00278048i
$371$		−	17.9814i		−	0.933548i
$372$	5.51379	+	0.773391i	0.285877	+	0.0400985i
$373$	25.3213	−	25.3213i	1.31109	−	1.31109i	0.390473	−	0.920614i	$-0.372312\pi$
$373$	25.3213	−	25.3213i	1.31109	−	1.31109i	0.920614	−	0.390473i	$-0.127688\pi$
$374$			4.10687i			0.212361i
$375$	−0.816528	+	11.1505i	−0.0421653	+	0.575808i
$376$	1.31153			0.0676371
$377$	−4.92351	−	4.92351i	−0.253573	−	0.253573i
$378$	2.22289	+	2.22289i	0.114333	+	0.114333i
$379$		−	14.2663i		−	0.732809i	−0.930456	−	0.366405i	$-0.880589\pi$
$379$		−	14.2663i		−	0.732809i	0.930456	−	0.366405i	$-0.119411\pi$
$380$	−2.46414	−	0.725051i	−0.126408	−	0.0371943i
$381$	3.79926			0.194642
$382$	3.94008	+	3.94008i	0.201592	+	0.201592i
$383$	13.4685	+	13.4685i	0.688207	+	0.688207i	0.961835	−	0.273629i	$-0.0882239\pi$
$383$	13.4685	+	13.4685i	0.688207	+	0.688207i	−0.273629	+	0.961835i	$0.588224\pi$
$384$	−1.00000			−0.0510310
$385$	−16.4964	+	8.99562i	−0.840736	+	0.458459i
$386$	−0.215117			−0.0109492
$387$	3.62140	−	3.62140i	0.184086	−	0.184086i
$388$	0.00703286	−	0.00703286i	0.000357039	−	0.000357039i
$389$	11.5020			0.583176			0.291588	−	0.956544i	$-0.405816\pi$
$389$	11.5020			0.583176			0.291588	+	0.956544i	$0.405816\pi$
$390$	4.24591	−	2.31532i	0.215000	−	0.117241i
$391$	9.83050			0.497150
$392$	2.03821	+	2.03821i	0.102945	+	0.102945i
$393$	−1.43610	−	1.43610i	−0.0724418	−	0.0724418i
$394$	−4.27718			−0.215481
$395$	24.0865	+	7.08724i	1.21192	+	0.356598i
$396$		−	2.67302i		−	0.134325i
$397$	−4.96451	−	4.96451i	−0.249162	−	0.249162i	0.571465	−	0.820627i	$-0.306375\pi$
$397$	−4.96451	−	4.96451i	−0.249162	−	0.249162i	−0.820627	+	0.571465i	$0.806375\pi$
$398$	−3.78169	−	3.78169i	−0.189559	−	0.189559i
$399$	−3.61113			−0.180782
$400$	−4.20321	−	2.70796i	−0.210160	−	0.135398i
$401$			33.8284i			1.68931i	0.535310	+	0.844655i	$0.320195\pi$
$401$			33.8284i			1.68931i	−0.535310	+	0.844655i	$0.679805\pi$
$402$	8.98751	−	8.98751i	0.448256	−	0.448256i
$403$	1.67269	−	11.9252i	0.0833225	−	0.594037i
$404$			17.4523i			0.868287i
$405$	−2.14513	−	0.631187i	−0.106593	−	0.0313639i
$406$			10.1206i			0.502277i
$407$	−0.160158	−	0.160158i	−0.00793876	−	0.00793876i
$408$	−1.08641	+	1.08641i	−0.0537852	+	0.0537852i
$409$	34.2781			1.69494			0.847472	−	0.530840i	$-0.178123\pi$
$409$	34.2781			1.69494			0.847472	+	0.530840i	$0.178123\pi$
$410$	−1.24764	−	2.28795i	−0.0616164	−	0.112994i
$411$	2.27723			0.112327
$412$	−5.69619	−	5.69619i	−0.280631	−	0.280631i
$413$	31.2622	−	31.2622i	1.53831	−	1.53831i
$414$	−6.39835			−0.314462
$415$	−16.7551	−	30.7260i	−0.822475	−	1.50828i
$416$			2.16280i			0.106040i
$417$	12.0075	+	12.0075i	0.588012	+	0.588012i
$418$	2.17119	+	2.17119i	0.106196	+	0.106196i
$419$			34.7923i			1.69971i	0.527014	+	0.849857i	$0.323312\pi$
$419$			34.7923i			1.69971i	−0.527014	+	0.849857i	$0.676688\pi$
$420$	−6.74353	−	1.98422i	−0.329050	−	0.0968202i
$421$	−32.9709			−1.60690			−0.803451	−	0.595371i	$-0.797005\pi$
$421$	−32.9709			−1.60690			−0.803451	+	0.595371i	$0.797005\pi$
$422$	6.68382	+	6.68382i	0.325363	+	0.325363i
$423$	−0.927393	+	0.927393i	−0.0450914	+	0.0450914i
$424$	−5.71994			−0.277785
$425$	−7.50834	+	1.62444i	−0.364208	+	0.0787970i
$426$		−	9.67268i		−	0.468643i
$427$	−24.7568	+	24.7568i	−1.19807	+	1.19807i
$428$	1.93400	−	1.93400i	0.0934836	−	0.0934836i
$429$	−5.78121			−0.279119
$430$	−3.23258	+	10.9861i	−0.155889	+	0.529799i
$431$	5.91759			0.285040			0.142520	−	0.989792i	$-0.454479\pi$
$431$	5.91759			0.285040			0.142520	+	0.989792i	$0.454479\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−19.7039	−	19.7039i	−0.946909	−	0.946909i	0.0517508	−	0.998660i	$-0.483520\pi$
$433$	−19.7039	−	19.7039i	−0.946909	−	0.946909i	−0.998660	+	0.0517508i	$0.983520\pi$
$434$	−13.9757	+	10.5374i	−0.670855	+	0.505810i
$435$	−3.44643	−	6.32017i	−0.165244	−	0.303029i
$436$	6.84356			0.327747
$437$	5.19712	−	5.19712i	0.248612	−	0.248612i
$438$	6.81687	−	6.81687i	0.325723	−	0.325723i
$439$		−	10.4485i		−	0.498677i	−0.968416	−	0.249339i	$-0.919787\pi$
$439$		−	10.4485i		−	0.498677i	0.968416	−	0.249339i	$-0.0802132\pi$
$440$	2.86153	+	5.24756i	0.136418	+	0.250168i
$441$	−2.88246			−0.137260
$442$	2.34968	+	2.34968i	0.111763	+	0.111763i
$443$	−19.6130	+	19.6130i	−0.931843	+	0.931843i	−0.997821	−	0.0659782i	$-0.978983\pi$
$443$	−19.6130	+	19.6130i	−0.931843	+	0.931843i	0.0659782	+	0.997821i	$0.478983\pi$
$444$		−	0.0847348i		−	0.00402134i
$445$	22.2492	+	6.54662i	1.05471	+	0.310340i
$446$			28.2414i			1.33727i
$447$	5.54016	−	5.54016i	0.262040	−	0.262040i
$448$	2.22289	−	2.22289i	0.105022	−	0.105022i
$449$	28.0525			1.32388			0.661939	−	0.749558i	$-0.269734\pi$
$449$	28.0525			1.32388			0.661939	+	0.749558i	$0.269734\pi$
$450$	4.88693	−	1.05730i	0.230372	−	0.0498414i
$451$			3.11526i			0.146692i
$452$	1.96389	+	1.96389i	0.0923738	+	0.0923738i
$453$	5.67325	−	5.67325i	0.266553	−	0.266553i
$454$			17.0308i			0.799296i
$455$	−4.29147	+	14.5849i	−0.201187	+	0.683750i
$456$			1.14871i			0.0537933i
$457$	11.6151	−	11.6151i	0.543334	−	0.543334i	−0.381171	−	0.924505i	$-0.624479\pi$
$457$	11.6151	−	11.6151i	0.543334	−	0.543334i	0.924505	+	0.381171i	$0.124479\pi$
$458$	−4.37063	−	4.37063i	−0.204226	−	0.204226i
$459$		−	1.53641i		−	0.0717136i
$460$	12.5610	−	6.84957i	0.585657	−	0.319363i
$461$		−	8.00520i		−	0.372839i	−0.982470	−	0.186420i	$-0.940312\pi$
$461$		−	8.00520i		−	0.372839i	0.982470	−	0.186420i	$-0.0596884\pi$
$462$	5.94183	+	5.94183i	0.276439	+	0.276439i
$463$	−3.40769	−	3.40769i	−0.158369	−	0.158369i	0.623475	−	0.781843i	$-0.285720\pi$
$463$	−3.40769	−	3.40769i	−0.158369	−	0.158369i	−0.781843	+	0.623475i	$0.785720\pi$
$464$	3.21939			0.149456
$465$	5.13926	−	11.3397i	0.238328	−	0.525864i
$466$	17.0150			0.788203
$467$	5.12823	+	5.12823i	0.237306	+	0.237306i	0.815734	−	0.578428i	$-0.196333\pi$
$467$	5.12823	+	5.12823i	0.237306	+	0.237306i	−0.578428	+	0.815734i	$0.696333\pi$
$468$	−1.52933	−	1.52933i	−0.0706932	−	0.0706932i
$469$			39.9564i			1.84502i
$470$	0.827822	−	2.81341i	0.0381846	−	0.129773i
$471$		−	4.22089i		−	0.194488i
$472$	−9.94460	−	9.94460i	−0.457737	−	0.457737i
$473$	9.68008	−	9.68008i	0.445090	−	0.445090i
$474$		−	11.2284i		−	0.515739i
$475$	−3.11066	+	4.82826i	−0.142727	+	0.221536i
$476$		−	4.82992i		−	0.221379i
$477$	4.04461	−	4.04461i	0.185190	−	0.185190i
$478$	0.738506	+	0.738506i	0.0337785	+	0.0337785i
$479$		−	22.0955i		−	1.00957i	−0.863246	−	0.504784i	$-0.831572\pi$
$479$		−	22.0955i		−	1.00957i	0.863246	−	0.504784i	$-0.168428\pi$
$480$	−0.631187	+	2.14513i	−0.0288096	+	0.0979116i
$481$	−0.183264			−0.00835613
$482$	2.37191	−	2.37191i	0.108038	−	0.108038i
$483$	14.2228	−	14.2228i	0.647160	−	0.647160i
$484$			3.85494i			0.175225i
$485$	−0.0106474	−	0.0195255i	−0.000483473	−	0.000886606i
$486$			1.00000i			0.0453609i
$487$	14.1443	−	14.1443i	0.640940	−	0.640940i	−0.309846	−	0.950787i	$-0.600278\pi$
$487$	14.1443	−	14.1443i	0.640940	−	0.640940i	0.950787	+	0.309846i	$0.100278\pi$
$488$	7.87522	+	7.87522i	0.356494	+	0.356494i
$489$	−16.0965			−0.727911
$490$	5.65872	−	3.08574i	0.255635	−	0.139400i
$491$			40.6239i			1.83333i	0.399655	+	0.916665i	$0.369130\pi$
$491$			40.6239i			1.83333i	−0.399655	+	0.916665i	$0.630870\pi$
$492$	−0.824095	+	0.824095i	−0.0371531	+	0.0371531i
$493$	3.49757	−	3.49757i	0.157523	−	0.157523i
$494$	2.48443			0.111780
$495$	−5.73400	−	1.68718i	−0.257724	−	0.0758330i
$496$	3.35197	+	4.44571i	0.150508	+	0.199618i
$497$	21.5013	+	21.5013i	0.964464	+	0.964464i
$498$	−11.0672	+	11.0672i	−0.495931	+	0.495931i
$499$	5.80075			0.259677			0.129839	−	0.991535i	$-0.458554\pi$
$499$	5.80075			0.259677			0.129839	+	0.991535i	$0.458554\pi$
$500$	−8.46195	+	7.30721i	−0.378430	+	0.326788i
$501$	−18.3878			−0.821506
$502$	−11.5959	+	11.5959i	−0.517551	+	0.517551i
$503$	−14.5702	+	14.5702i	−0.649655	+	0.649655i	−0.952910	−	0.303254i	$-0.901927\pi$
$503$	−14.5702	+	14.5702i	−0.649655	+	0.649655i	0.303254	+	0.952910i	$0.401927\pi$
$504$			3.14364i			0.140029i
$505$	37.4376	+	11.0157i	1.66595	+	0.490192i
$506$	−17.1029			−0.760318
$507$	5.88476	−	5.88476i	0.261351	−	0.261351i
$508$	2.68648	+	2.68648i	0.119193	+	0.119193i
$509$	−43.5509			−1.93036			−0.965180	−	0.261588i	$-0.915754\pi$
$509$	−43.5509			−1.93036			−0.965180	+	0.261588i	$0.915754\pi$
$510$	1.64476	+	3.01622i	0.0728314	+	0.133560i
$511$			30.3063i			1.34067i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.812260	−	0.812260i	−0.0358622	−	0.0358622i
$514$			24.4261i			1.07739i
$515$	−15.8144	+	8.62373i	−0.696868	+	0.380007i
$516$	5.12143			0.225458
$517$	−2.47894	+	2.47894i	−0.109024	+	0.109024i
$518$	0.188356	+	0.188356i	0.00827589	+	0.00827589i
$519$	7.01351			0.307859
$520$	4.63949	+	1.36513i	0.203455	+	0.0598649i
$521$	12.4810			0.546802			0.273401	−	0.961900i	$-0.411851\pi$
$521$	12.4810			0.546802			0.273401	+	0.961900i	$0.411851\pi$
$522$	−2.27645	+	2.27645i	−0.0996376	+	0.0996376i
$523$	14.7547	+	14.7547i	0.645179	+	0.645179i	0.951824	−	0.306645i	$-0.0992063\pi$
$523$	14.7547	+	14.7547i	0.645179	+	0.645179i	−0.306645	+	0.951824i	$0.599206\pi$
$524$		−	2.03096i		−	0.0887227i
$525$	−8.51286	+	13.2134i	−0.371532	+	0.576678i
$526$		−	25.2016i		−	1.09884i
$527$	8.47145	+	1.18825i	0.369022	+	0.0517609i
$528$	1.89011	−	1.89011i	0.0822566	−	0.0822566i
$529$			17.9388i			0.779950i
$530$	−3.61035	+	12.2700i	−0.156824	+	0.532976i
$531$	14.0638			0.610316
$532$	−2.55345	−	2.55345i	−0.110706	−	0.110706i
$533$	1.78235	+	1.78235i	0.0772021	+	0.0772021i
$534$		−	10.3719i		−	0.448837i
$535$	−2.92798	−	5.36942i	−0.126588	−	0.232140i
$536$	12.7103			0.548999
$537$	1.50637	+	1.50637i	0.0650048	+	0.0650048i
$538$	−5.18391	−	5.18391i	−0.223494	−	0.223494i
$539$	−7.70489			−0.331873
$540$	−1.07052	−	1.96316i	−0.0460680	−	0.0844808i
$541$	13.5883			0.584206			0.292103	−	0.956387i	$-0.405645\pi$
$541$	13.5883			0.584206			0.292103	+	0.956387i	$0.405645\pi$
$542$	−19.0138	+	19.0138i	−0.816715	+	0.816715i
$543$	−9.35006	+	9.35006i	−0.401250	+	0.401250i
$544$	−1.53641			−0.0658731
$545$	4.31957	−	14.6804i	0.185030	−	0.628838i
$546$	6.79905			0.290973
$547$	−2.94844	−	2.94844i	−0.126066	−	0.126066i	0.641259	−	0.767325i	$-0.278413\pi$
$547$	−2.94844	−	2.94844i	−0.126066	−	0.126066i	−0.767325	+	0.641259i	$0.778413\pi$
$548$	1.61024	+	1.61024i	0.0687862	+	0.0687862i
$549$	−11.1372			−0.475326
$550$	13.0629	−	2.82618i	0.557004	−	0.120509i
$551$		−	3.69815i		−	0.157546i
$552$	−4.52431	−	4.52431i	−0.192568	−	0.192568i
$553$	24.9595	+	24.9595i	1.06139	+	1.06139i
$554$	6.87129			0.291933
$555$	−0.181768	−	0.0534835i	−0.00771560	−	0.00227025i
$556$			16.9812i			0.720164i
$557$	−3.32432	+	3.32432i	−0.140856	+	0.140856i	−0.774019	−	0.633163i	$-0.781756\pi$
$557$	−3.32432	+	3.32432i	−0.140856	+	0.140856i	0.633163	+	0.774019i	$0.281756\pi$
$558$	−5.51379	−	0.773391i	−0.233417	−	0.0327402i
$559$		−	11.0766i		−	0.468491i
$560$	−3.36534	−	6.17145i	−0.142211	−	0.260791i
$561$		−	4.10687i		−	0.173392i
$562$	6.07901	+	6.07901i	0.256428	+	0.256428i
$563$	5.69538	−	5.69538i	0.240032	−	0.240032i	−0.576831	−	0.816863i	$-0.695711\pi$
$563$	5.69538	−	5.69538i	0.240032	−	0.240032i	0.816863	+	0.576831i	$0.195711\pi$
$564$	−1.31153			−0.0552254
$565$	5.45240	−	2.97323i	0.229384	−	0.125085i
$566$	8.92273			0.375050
$567$	−2.22289	−	2.22289i	−0.0933525	−	0.0933525i
$568$	6.83962	−	6.83962i	0.286984	−	0.286984i
$569$	−24.2130			−1.01506			−0.507530	−	0.861634i	$-0.669441\pi$
$569$	−24.2130			−1.01506			−0.507530	+	0.861634i	$0.669441\pi$
$570$	2.46414	+	0.725051i	0.103211	+	0.0303690i
$571$			10.8131i			0.452514i	0.974068	+	0.226257i	$0.0726489\pi$
$571$			10.8131i			0.452514i	−0.974068	+	0.226257i	$0.927351\pi$
$572$	−4.08793	−	4.08793i	−0.170925	−	0.170925i
$573$	−3.94008	−	3.94008i	−0.164599	−	0.164599i
$574$		−	3.66374i		−	0.152922i
$575$	−6.76495	−	31.2683i	−0.282118	−	1.30398i
$576$	1.00000			0.0416667
$577$	10.6183	+	10.6183i	0.442046	+	0.442046i	0.892699	−	0.450653i	$-0.148809\pi$
$577$	10.6183	+	10.6183i	0.442046	+	0.442046i	−0.450653	+	0.892699i	$0.648809\pi$
$578$	10.3516	−	10.3516i	0.430572	−	0.430572i
$579$	0.215117			0.00893995
$580$	2.03204	−	6.90603i	0.0843758	−	0.286757i
$581$		−	49.2021i		−	2.04125i
$582$	−0.00703286	+	0.00703286i	−0.000291521	+	0.000291521i
$583$	10.8113	−	10.8113i	0.447760	−	0.447760i
$584$	9.64051			0.398927
$585$	−4.24591	+	2.31532i	−0.175547	+	0.0957268i
$586$	4.78022			0.197469
$587$	−28.5590	+	28.5590i	−1.17875	+	1.17875i	−0.198692	+	0.980062i	$0.563669\pi$
$587$	−28.5590	+	28.5590i	−1.17875	+	1.17875i	−0.980062	+	0.198692i	$0.936331\pi$
$588$	−2.03821	−	2.03821i	−0.0840543	−	0.0840543i
$589$	5.10683	−	3.85044i	0.210423	−	0.158654i
$590$	−27.6094	+	15.0556i	−1.13666	+	0.619829i
$591$	4.27718			0.175940
$592$	0.0599165	−	0.0599165i	0.00246255	−	0.00246255i
$593$	−4.31516	+	4.31516i	−0.177202	+	0.177202i	−0.790135	−	0.612933i	$-0.789990\pi$
$593$	−4.31516	+	4.31516i	−0.177202	+	0.177202i	0.612933	+	0.790135i	$0.289990\pi$
$594$			2.67302i			0.109676i
$595$	−10.3608	−	3.04859i	−0.424753	−	0.124980i
$596$	7.83496			0.320933
$597$	3.78169	+	3.78169i	0.154774	+	0.154774i
$598$	−9.78517	+	9.78517i	−0.400146	+	0.400146i
$599$		−	38.0234i		−	1.55360i	−0.629750	−	0.776798i	$-0.716843\pi$
$599$		−	38.0234i		−	1.55360i	0.629750	−	0.776798i	$-0.283157\pi$
$600$	4.20321	+	2.70796i	0.171595	+	0.110552i
$601$			20.2660i			0.826666i	0.910580	+	0.413333i	$0.135636\pi$
$601$			20.2660i			0.826666i	−0.910580	+	0.413333i	$0.864364\pi$
$602$	−11.3844	+	11.3844i	−0.463992	+	0.463992i
$603$	−8.98751	+	8.98751i	−0.366000	+	0.366000i
$604$	8.02319			0.326459
$605$	8.26937	+	2.43319i	0.336198	+	0.0989233i
$606$		−	17.4523i		−	0.708953i
$607$	−2.76294	−	2.76294i	−0.112144	−	0.112144i	0.648808	−	0.760952i	$-0.275268\pi$
$607$	−2.76294	−	2.76294i	−0.112144	−	0.112144i	−0.760952	+	0.648808i	$0.775268\pi$
$608$	−0.812260	+	0.812260i	−0.0329415	+	0.0329415i
$609$		−	10.1206i		−	0.410107i
$610$	21.8641	−	11.9227i	0.885253	−	0.482734i
$611$			2.83658i			0.114756i
$612$	1.08641	−	1.08641i	0.0439154	−	0.0439154i
$613$	−11.7466	−	11.7466i	−0.474440	−	0.474440i	0.428908	−	0.903348i	$-0.358898\pi$
$613$	−11.7466	−	11.7466i	−0.474440	−	0.474440i	−0.903348	+	0.428908i	$0.858898\pi$
$614$			12.5393i			0.506046i
$615$	1.24764	+	2.28795i	0.0503095	+	0.0922591i
$616$			8.40302i			0.338567i
$617$	−12.9202	−	12.9202i	−0.520149	−	0.520149i	0.397468	−	0.917616i	$-0.369889\pi$
$617$	−12.9202	−	12.9202i	−0.520149	−	0.520149i	−0.917616	+	0.397468i	$0.869889\pi$
$618$	5.69619	+	5.69619i	0.229134	+	0.229134i
$619$	−8.99233			−0.361432			−0.180716	−	0.983535i	$-0.557842\pi$
$619$	−8.99233			−0.361432			−0.180716	+	0.983535i	$0.557842\pi$
$620$	11.6524	−	4.38435i	0.467970	−	0.176080i
$621$	6.39835			0.256757
$622$	23.4018	+	23.4018i	0.938326	+	0.938326i
$623$	23.0556	+	23.0556i	0.923704	+	0.923704i
$624$		−	2.16280i		−	0.0865812i
$625$	10.3339	+	22.7643i	0.413355	+	0.910570i
$626$			2.68373i			0.107264i
$627$	−2.17119	−	2.17119i	−0.0867090	−	0.0867090i
$628$	2.98462	−	2.98462i	0.119099	−	0.119099i
$629$		−	0.130188i		−	0.00519092i
$630$	6.74353	+	1.98422i	0.268669	+	0.0790534i
$631$		−	27.4182i		−	1.09150i	−0.837947	−	0.545751i	$-0.816244\pi$
$631$		−	27.4182i		−	1.09150i	0.837947	−	0.545751i	$-0.183756\pi$
$632$	7.93970	−	7.93970i	0.315824	−	0.315824i
$633$	−6.68382	−	6.68382i	−0.265658	−	0.265658i
$634$			8.34242i			0.331320i
$635$	7.45854	−	4.06719i	0.295983	−	0.161402i
$636$	5.71994			0.226810
$637$	−4.40823	+	4.40823i	−0.174660	+	0.174660i
$638$	−6.08501	+	6.08501i	−0.240908	+	0.240908i
$639$			9.67268i			0.382645i
$640$	−1.96316	+	1.07052i	−0.0776006	+	0.0423161i
$641$			8.07077i			0.318776i	0.987216	+	0.159388i	$0.0509521\pi$
$641$			8.07077i			0.318776i	−0.987216	+	0.159388i	$0.949048\pi$
$642$	−1.93400	+	1.93400i	−0.0763290	+	0.0763290i
$643$	−9.88586	−	9.88586i	−0.389860	−	0.389860i	0.484777	−	0.874638i	$-0.338901\pi$
$643$	−9.88586	−	9.88586i	−0.389860	−	0.389860i	−0.874638	+	0.484777i	$0.838901\pi$
$644$	20.1141			0.792606
$645$	3.23258	−	10.9861i	0.127283	−	0.432579i
$646$			1.76489i			0.0694387i
$647$	19.4574	−	19.4574i	0.764948	−	0.764948i	−0.212264	−	0.977212i	$-0.568084\pi$
$647$	19.4574	−	19.4574i	0.764948	−	0.764948i	0.977212	+	0.212264i	$0.0680836\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	37.5928			1.47565
$650$	5.85677	−	9.09068i	0.229722	−	0.356566i
$651$	13.9757	−	10.5374i	0.547751	−	0.412992i
$652$	−11.3820	−	11.3820i	−0.445752	−	0.445752i
$653$	15.7449	−	15.7449i	0.616145	−	0.616145i	−0.328396	−	0.944540i	$-0.606508\pi$
$653$	15.7449	−	15.7449i	0.616145	−	0.616145i	0.944540	+	0.328396i	$0.106508\pi$
$654$	−6.84356			−0.267605
$655$	−4.35667	−	1.28191i	−0.170229	−	0.0500885i
$656$	−1.16545			−0.0455030
$657$	−6.81687	+	6.81687i	−0.265952	+	0.265952i
$658$	2.91539	−	2.91539i	0.113654	−	0.113654i
$659$		−	5.40837i		−	0.210680i	−0.994436	−	0.105340i	$-0.966407\pi$
$659$		−	5.40837i		−	0.210680i	0.994436	−	0.105340i	$-0.0335931\pi$
$660$	−2.86153	−	5.24756i	−0.111385	−	0.204261i
$661$	−41.9034			−1.62985			−0.814927	−	0.579563i	$-0.803223\pi$
$661$	−41.9034			−1.62985			−0.814927	+	0.579563i	$0.803223\pi$
$662$	−7.73596	+	7.73596i	−0.300667	+	0.300667i
$663$	−2.34968	−	2.34968i	−0.0912540	−	0.0912540i
$664$	−15.6513			−0.607389
$665$	−7.08921	+	3.86579i	−0.274908	+	0.149909i
$666$			0.0847348i			0.00328341i
$667$	14.5655	+	14.5655i	0.563980	+	0.563980i
$668$	−13.0021	−	13.0021i	−0.503068	−	0.503068i
$669$		−	28.2414i		−	1.09188i
$670$	8.02255	−	27.2652i	0.309938	−	1.05335i
$671$	−29.7701			−1.14926
$672$	−2.22289	+	2.22289i	−0.0857498	+	0.0857498i
$673$	−1.82316	−	1.82316i	−0.0702777	−	0.0702777i	0.671094	−	0.741372i	$-0.265825\pi$
$673$	−1.82316	−	1.82316i	−0.0702777	−	0.0702777i	−0.741372	+	0.671094i	$0.765825\pi$
$674$	−28.0539			−1.08059
$675$	−4.88693	+	1.05730i	−0.188098	+	0.0406953i
$676$	8.32231			0.320089
$677$	−13.8214	+	13.8214i	−0.531199	+	0.531199i	−0.920929	−	0.389730i	$-0.872568\pi$
$677$	−13.8214	+	13.8214i	−0.531199	+	0.531199i	0.389730	+	0.920929i	$0.372568\pi$
$678$	−1.96389	−	1.96389i	−0.0754229	−	0.0754229i
$679$		−	0.0312665i		−	0.00119990i
$680$	−0.969764	+	3.29581i	−0.0371887	+	0.126389i
$681$		−	17.0308i		−	0.652623i
$682$	−14.7385	−	2.06729i	−0.564366	−	0.0791607i
$683$	−29.0965	+	29.0965i	−1.11335	+	1.11335i	−0.120653	+	0.992695i	$0.538499\pi$
$683$	−29.0965	+	29.0965i	−1.11335	+	1.11335i	−0.992695	+	0.120653i	$0.961501\pi$
$684$		−	1.14871i		−	0.0439220i
$685$	4.47056	−	2.43783i	0.170811	−	0.0931445i
$686$	−12.9441			−0.494206
$687$	4.37063	+	4.37063i	0.166750	+	0.166750i
$688$	3.62140	+	3.62140i	0.138064	+	0.138064i
$689$		−	12.3711i		−	0.471300i
$690$	−12.5610	+	6.84957i	−0.478187	+	0.260759i
$691$	−29.6351			−1.12737			−0.563686	−	0.825989i	$-0.690617\pi$
$691$	−29.6351			−1.12737			−0.563686	+	0.825989i	$0.690617\pi$
$692$	4.95930	+	4.95930i	0.188524	+	0.188524i
$693$	−5.94183	−	5.94183i	−0.225712	−	0.225712i
$694$	−7.03119			−0.266900
$695$	36.4270	+	10.7183i	1.38176	+	0.406570i
$696$	−3.21939			−0.122031
$697$	−1.26615	+	1.26615i	−0.0479588	+	0.0479588i
$698$	10.9307	−	10.9307i	0.413732	−	0.413732i
$699$	−17.0150			−0.643565
$700$	−15.3628	+	3.32376i	−0.580658	+	0.125626i
$701$	−21.2913			−0.804162			−0.402081	−	0.915604i	$-0.631713\pi$
$701$	−21.2913			−0.804162			−0.402081	+	0.915604i	$0.631713\pi$
$702$	1.52933	+	1.52933i	0.0577208	+	0.0577208i
$703$	−0.0688267	−	0.0688267i	−0.00259585	−	0.00259585i
$704$	2.67302			0.100743
$705$	−0.827822	+	2.81341i	−0.0311776	+	0.105959i
$706$		−	24.5722i		−	0.924787i
$707$	38.7946	+	38.7946i	1.45902	+	1.45902i
$708$	9.94460	+	9.94460i	0.373741	+	0.373741i
$709$	−28.9151			−1.08593			−0.542965	−	0.839756i	$-0.682698\pi$
$709$	−28.9151			−1.08593			−0.542965	+	0.839756i	$0.682698\pi$
$710$	−10.3548	−	18.9890i	−0.388609	−	0.712644i
$711$			11.2284i			0.421099i
$712$	7.33406	−	7.33406i	0.274855	−	0.274855i
$713$	−4.94842	+	35.2791i	−0.185320	+	1.32121i
$714$			4.82992i			0.180755i
$715$	−11.3494	+	6.18891i	−0.424444	+	0.231452i
$716$			2.13033i			0.0796143i
$717$	−0.738506	−	0.738506i	−0.0275800	−	0.0275800i
$718$	−6.42401	+	6.42401i	−0.239742	+	0.239742i
$719$	−26.0039			−0.969780			−0.484890	−	0.874575i	$-0.661140\pi$
$719$	−26.0039			−0.969780			−0.484890	+	0.874575i	$0.661140\pi$
$720$	0.631187	−	2.14513i	0.0235230	−	0.0799444i
$721$	−25.3240			−0.943114
$722$	−12.5020	−	12.5020i	−0.465275	−	0.465275i
$723$	−2.37191	+	2.37191i	−0.0882124	+	0.0882124i
$724$	−13.2230			−0.491428
$725$	−13.5318	−	8.71799i	−0.502557	−	0.323778i
$726$		−	3.85494i		−	0.143070i
$727$	−31.7693	−	31.7693i	−1.17826	−	1.17826i	−0.980188	−	0.198070i	$-0.936533\pi$
$727$	−31.7693	−	31.7693i	−1.17826	−	1.17826i	−0.198070	−	0.980188i	$-0.563467\pi$
$728$	4.80766	+	4.80766i	0.178184	+	0.178184i
$729$		−	1.00000i		−	0.0370370i
$730$	6.08497	−	20.6802i	0.225215	−	0.765409i
$731$	7.86862			0.291031
$732$	−7.87522	−	7.87522i	−0.291076	−	0.291076i
$733$	−3.40202	+	3.40202i	−0.125657	+	0.125657i	−0.767138	−	0.641482i	$-0.778320\pi$
$733$	−3.40202	+	3.40202i	−0.125657	+	0.125657i	0.641482	+	0.767138i	$0.278320\pi$
$734$	32.7240			1.20787
$735$	−5.65872	+	3.08574i	−0.208725	+	0.113819i
$736$		−	6.39835i		−	0.235846i
$737$	−24.0238	+	24.0238i	−0.884929	+	0.884929i
$738$	0.824095	−	0.824095i	0.0303353	−	0.0303353i
$739$	−0.406595			−0.0149568			−0.00747841	−	0.999972i	$-0.502380\pi$
$739$	−0.406595			−0.0149568			−0.00747841	+	0.999972i	$0.502380\pi$
$740$	−0.0907105	−	0.166348i	−0.00333458	−	0.00611506i
$741$	−2.48443			−0.0912677
$742$	−12.7148	+	12.7148i	−0.466774	+	0.466774i
$743$	−23.1394	−	23.1394i	−0.848901	−	0.848901i	0.141095	−	0.989996i	$-0.454938\pi$
$743$	−23.1394	−	23.1394i	−0.848901	−	0.848901i	−0.989996	+	0.141095i	$0.954938\pi$
$744$	−3.35197	−	4.44571i	−0.122889	−	0.162988i
$745$	4.94533	−	16.8070i	0.181183	−	0.615763i
$746$	−35.8097			−1.31109
$747$	11.0672	−	11.0672i	0.404926	−	0.404926i
$748$	2.90399	−	2.90399i	0.106180	−	0.106180i
$749$		−	8.59815i		−	0.314169i
$750$	8.46195	−	7.30721i	0.308987	−	0.266822i
$751$	−30.1429			−1.09993			−0.549965	−	0.835188i	$-0.685359\pi$
$751$	−30.1429			−1.09993			−0.549965	+	0.835188i	$0.685359\pi$
$752$	−0.927393	−	0.927393i	−0.0338185	−	0.0338185i
$753$	11.5959	−	11.5959i	0.422579	−	0.422579i
$754$			6.96289i			0.253573i
$755$	5.06414	−	17.2108i	0.184303	−	0.626366i
$756$		−	3.14364i		−	0.114333i
$757$	8.49009	−	8.49009i	0.308578	−	0.308578i	−0.535780	−	0.844358i	$-0.679982\pi$
$757$	8.49009	−	8.49009i	0.308578	−	0.308578i	0.844358	+	0.535780i	$0.179982\pi$
$758$	−10.0878	+	10.0878i	−0.366405	+	0.366405i
$759$	17.1029			0.620797
$760$	1.22972	+	2.25510i	0.0446066	+	0.0818009i
$761$		−	11.3354i		−	0.410907i	−0.978667	−	0.205454i	$-0.934133\pi$
$761$		−	11.3354i		−	0.410907i	0.978667	−	0.205454i	$-0.0658670\pi$
$762$	−2.68648	−	2.68648i	−0.0973210	−	0.0973210i
$763$	15.2125	−	15.2125i	0.550729	−	0.550729i
$764$		−	5.57211i		−	0.201592i
$765$	−1.64476	−	3.01622i	−0.0594666	−	0.109052i
$766$		−	19.0473i		−	0.688207i
$767$	21.5081	−	21.5081i	0.776614	−	0.776614i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$			19.1884i			0.691952i	0.938243	+	0.345976i	$0.112452\pi$
$769$			19.1884i			0.691952i	−0.938243	+	0.345976i	$0.887548\pi$
$770$	18.0256	+	5.30388i	0.649598	+	0.191139i
$771$		−	24.4261i		−	0.879685i
$772$	0.152111	+	0.152111i	0.00547458	+	0.00547458i
$773$	35.1922	+	35.1922i	1.26578	+	1.26578i	0.948249	+	0.317528i	$0.102853\pi$
$773$	35.1922	+	35.1922i	1.26578	+	1.26578i	0.317528	+	0.948249i	$0.397147\pi$
$774$	−5.12143			−0.184086
$775$	−2.05020	−	27.7632i	−0.0736452	−	0.997285i
$776$	−0.00994596			−0.000357039
$777$	−0.188356	−	0.188356i	−0.00675723	−	0.00675723i
$778$	−8.13316	−	8.13316i	−0.291588	−	0.291588i
$779$			1.33876i			0.0479660i
$780$	−4.63949	−	1.36513i	−0.166120	−	0.0488795i
$781$			25.8553i			0.925175i
$782$	−6.95121	−	6.95121i	−0.248575	−	0.248575i
$783$	2.27645	−	2.27645i	0.0813538	−	0.0813538i
$784$		−	2.88246i		−	0.102945i
$785$	−4.51856	−	8.28627i	−0.161274	−	0.295750i
$786$			2.03096i			0.0724418i
$787$	−31.8945	+	31.8945i	−1.13692	+	1.13692i	−0.147917	+	0.989000i	$0.547257\pi$
$787$	−31.8945	+	31.8945i	−1.13692	+	1.13692i	−0.989000	+	0.147917i	$0.952743\pi$
$788$	3.02442	+	3.02442i	0.107741	+	0.107741i
$789$			25.2016i			0.897200i
$790$	−12.0203	−	22.0432i	−0.427662	−	0.784260i
$791$	8.73103			0.310440
$792$	−1.89011	+	1.89011i	−0.0671623	+	0.0671623i
$793$	−17.0325	+	17.0325i	−0.604842	+	0.604842i
$794$			7.02088i			0.249162i
$795$	3.61035	−	12.2700i	0.128046	−	0.435173i
$796$			5.34811i			0.189559i
$797$	3.57347	−	3.57347i	0.126579	−	0.126579i	−0.640979	−	0.767558i	$-0.721472\pi$
$797$	3.57347	−	3.57347i	0.126579	−	0.126579i	0.767558	+	0.640979i	$0.221472\pi$
$798$	2.55345	+	2.55345i	0.0903912	+	0.0903912i
$799$	−2.01505			−0.0712874
$800$	1.05730	+	4.88693i	0.0373811	+	0.172779i
$801$			10.3719i			0.366474i
$802$	23.9203	−	23.9203i	0.844655	−	0.844655i
$803$	−18.2217	+	18.2217i	−0.643029	+	0.643029i
$804$	−12.7103			−0.448256
$805$	12.6958	−	43.1474i	0.447467	−	1.52075i
$806$	−9.61516	+	7.24963i	−0.338680	+	0.255357i
$807$	5.18391	+	5.18391i	0.182482	+	0.182482i
$808$	12.3407	−	12.3407i	0.434143	−	0.434143i
$809$	−13.4491			−0.472847			−0.236423	−	0.971650i	$-0.575975\pi$
$809$	−13.4491			−0.472847			−0.236423	+	0.971650i	$0.575975\pi$
$810$	1.07052	+	1.96316i	0.0376143	+	0.0689783i
$811$	1.47233			0.0517005			0.0258502	−	0.999666i	$-0.491771\pi$
$811$	1.47233			0.0517005			0.0258502	+	0.999666i	$0.491771\pi$
$812$	7.15635	−	7.15635i	0.251138	−	0.251138i
$813$	19.0138	−	19.0138i	0.666845	−	0.666845i
$814$			0.226498i			0.00793876i
$815$	−31.6000	+	17.2317i	−1.10690	+	0.603600i
$816$	1.53641			0.0537852
$817$	4.15993	−	4.15993i	0.145538	−	0.145538i
$818$	−24.2383	−	24.2383i	−0.847472	−	0.847472i
$819$	−6.79905			−0.237578
$820$	−0.735615	+	2.50004i	−0.0256888	+	0.0873051i
$821$		−	29.3524i		−	1.02441i	−0.858864	−	0.512203i	$-0.828829\pi$
$821$		−	29.3524i		−	1.02441i	0.858864	−	0.512203i	$-0.171171\pi$
$822$	−1.61024	−	1.61024i	−0.0561637	−	0.0561637i
$823$	−21.2817	−	21.2817i	−0.741835	−	0.741835i	0.231096	−	0.972931i	$-0.425769\pi$
$823$	−21.2817	−	21.2817i	−0.741835	−	0.741835i	−0.972931	+	0.231096i	$0.925769\pi$
$824$			8.05562i			0.280631i
$825$	−13.0629	+	2.82618i	−0.454792	+	0.0983949i
$826$	−44.2114			−1.53831
$827$	26.8309	−	26.8309i	0.933001	−	0.933001i	−0.0648917	−	0.997892i	$-0.520670\pi$
$827$	26.8309	−	26.8309i	0.933001	−	0.933001i	0.997892	+	0.0648917i	$0.0206702\pi$
$828$	4.52431	+	4.52431i	0.157231	+	0.157231i
$829$	48.0544			1.66900			0.834500	−	0.551008i	$-0.185757\pi$
$829$	48.0544			1.66900			0.834500	+	0.551008i	$0.185757\pi$
$830$	−9.87892	+	33.5742i	−0.342902	+	1.16538i
$831$	−6.87129			−0.238363
$832$	1.52933	−	1.52933i	0.0530199	−	0.0530199i
$833$	−3.13153	−	3.13153i	−0.108501	−	0.108501i
$834$		−	16.9812i		−	0.588012i
$835$	−36.0981	+	19.6845i	−1.24923	+	0.681212i
$836$		−	3.07053i		−	0.106196i
$837$	5.51379	+	0.773391i	0.190584	+	0.0267323i
$838$	24.6019	−	24.6019i	0.849857	−	0.849857i
$839$		−	12.1137i		−	0.418213i	−0.977893	−	0.209106i	$-0.932945\pi$
$839$		−	12.1137i		−	0.418213i	0.977893	−	0.209106i	$-0.0670555\pi$
$840$	3.36534	+	6.17145i	0.116115	+	0.212935i
$841$	−18.6355			−0.642604
$842$	23.3139	+	23.3139i	0.803451	+	0.803451i
$843$	−6.07901	−	6.07901i	−0.209372	−	0.209372i
$844$		−	9.45235i		−	0.325363i
$845$	5.25293	−	17.8525i	0.180706	−	0.614144i
$846$	1.31153			0.0450914
$847$	8.56911	+	8.56911i	0.294438	+	0.294438i
$848$	4.04461	+	4.04461i	0.138892	+	0.138892i
$849$	−8.92273			−0.306227
$850$	6.45786	+	4.16055i	0.221503	+	0.142706i
$851$	0.542163			0.0185851
$852$	−6.83962	+	6.83962i	−0.234321	+	0.234321i
$853$	9.54558	−	9.54558i	0.326834	−	0.326834i	−0.524547	−	0.851381i	$-0.675765\pi$
$853$	9.54558	−	9.54558i	0.326834	−	0.326834i	0.851381	+	0.524547i	$0.175765\pi$
$854$	35.0114			1.19807
$855$	−2.46414	−	0.725051i	−0.0842717	−	0.0247962i
$856$	−2.73509			−0.0934836
$857$	−9.53176	−	9.53176i	−0.325599	−	0.325599i	0.525311	−	0.850910i	$-0.323949\pi$
$857$	−9.53176	−	9.53176i	−0.325599	−	0.325599i	−0.850910	+	0.525311i	$0.823949\pi$
$858$	4.08793	+	4.08793i	0.139560	+	0.139560i
$859$	−28.2158			−0.962712			−0.481356	−	0.876525i	$-0.659856\pi$
$859$	−28.2158			−0.962712			−0.481356	+	0.876525i	$0.659856\pi$
$860$	10.0542	−	5.48260i	0.342844	−	0.186955i
$861$			3.66374i			0.124860i
$862$	−4.18437	−	4.18437i	−0.142520	−	0.142520i
$863$	30.7405	+	30.7405i	1.04642	+	1.04642i	0.998869	+	0.0475493i	$0.0151411\pi$
$863$	30.7405	+	30.7405i	1.04642	+	1.04642i	0.0475493	+	0.998869i	$0.484859\pi$
$864$	−1.00000			−0.0340207
$865$	13.7686	−	7.50812i	0.468147	−	0.255284i
$866$			27.8655i			0.946909i
$867$	−10.3516	+	10.3516i	−0.351560	+	0.351560i
$868$	17.3334	+	2.43126i	0.588332	+	0.0825224i
$869$			30.0139i			1.01815i
$870$	−2.03204	+	6.90603i	−0.0688925	+	0.234136i
$871$			27.4897i			0.931453i
$872$	−4.83913	−	4.83913i	−0.163874	−	0.163874i
$873$	0.00703286	−	0.00703286i	0.000238026	−	0.000238026i
$874$	−7.34984			−0.248612
$875$	−2.56687	+	35.0531i	−0.0867760	+	1.18501i
$876$	−9.64051			−0.325723
$877$	14.0082	+	14.0082i	0.473023	+	0.473023i	0.902892	−	0.429868i	$-0.141440\pi$
$877$	14.0082	+	14.0082i	0.473023	+	0.473023i	−0.429868	+	0.902892i	$0.641440\pi$
$878$	−7.38817	+	7.38817i	−0.249339	+	0.249339i
$879$	−4.78022			−0.161233
$880$	1.68718	−	5.73400i	0.0568748	−	0.193293i
$881$		−	27.4992i		−	0.926473i	−0.886235	−	0.463236i	$-0.846688\pi$
$881$		−	27.4992i		−	0.926473i	0.886235	−	0.463236i	$-0.153312\pi$
$882$	2.03821	+	2.03821i	0.0686300	+	0.0686300i
$883$	−29.7520	−	29.7520i	−1.00123	−	1.00123i	−0.999999	−	0.00123425i	$-0.999607\pi$
$883$	−29.7520	−	29.7520i	−1.00123	−	1.00123i	−0.00123425	−	0.999999i	$-0.500393\pi$
$884$		−	3.32295i		−	0.111763i
$885$	27.6094	−	15.0556i	0.928080	−	0.506088i
$886$	27.7370			0.931843
$887$	8.59818	+	8.59818i	0.288699	+	0.288699i	0.836565	−	0.547867i	$-0.184560\pi$
$887$	8.59818	+	8.59818i	0.288699	+	0.288699i	−0.547867	+	0.836565i	$0.684560\pi$
$888$	−0.0599165	+	0.0599165i	−0.00201067	+	0.00201067i
$889$	11.9435			0.400572
$890$	−11.1034	−	20.3617i	−0.372186	−	0.682526i
$891$		−	2.67302i		−	0.0895497i
$892$	19.9697	−	19.9697i	0.668635	−	0.668635i
$893$	−1.06530	+	1.06530i	−0.0356491	+	0.0356491i
$894$	−7.83496			−0.262040
$895$	4.56985	+	1.34464i	0.152753	+	0.0449463i
$896$	−3.14364			−0.105022
$897$	9.78517	−	9.78517i	0.326717	−	0.326717i
$898$	−19.8361	−	19.8361i	−0.661939	−	0.661939i
$899$	10.7913	+	14.3125i	0.359910	+	0.477348i
$900$	−4.20321	−	2.70796i	−0.140107	−	0.0902654i
$901$	8.78818			0.292777
$902$	2.20282	−	2.20282i	0.0733460	−	0.0733460i
$903$	11.3844	−	11.3844i	0.378848	−	0.378848i
$904$		−	2.77737i		−	0.0923738i
$905$	−8.34618	+	28.3651i	−0.277436	+	0.942887i
$906$	−8.02319			−0.266553
$907$	6.77396	+	6.77396i	0.224926	+	0.224926i	0.810569	−	0.585643i	$-0.199158\pi$
$907$	6.77396	+	6.77396i	0.224926	+	0.224926i	−0.585643	+	0.810569i	$0.699158\pi$
$908$	12.0426	−	12.0426i	0.399648	−	0.399648i
$909$			17.4523i			0.578858i
$910$	13.3476	−	7.27854i	0.442469	−	0.241281i
$911$		−	12.5214i		−	0.414853i	−0.978251	−	0.207427i	$-0.933491\pi$
$911$		−	12.5214i		−	0.414853i	0.978251	−	0.207427i	$-0.0665088\pi$
$912$	0.812260	−	0.812260i	0.0268966	−	0.0268966i
$913$	29.5828	−	29.5828i	0.979047	−	0.979047i
$914$	−16.4263			−0.543334
$915$	−21.8641	+	11.9227i	−0.722806	+	0.394151i
$916$			6.18101i			0.204226i
$917$	−4.51459	−	4.51459i	−0.149085	−	0.149085i
$918$	−1.08641	+	1.08641i	−0.0358568	+	0.0358568i
$919$			37.5553i			1.23884i	0.785061	+	0.619418i	$0.212631\pi$
$919$			37.5553i			1.23884i	−0.785061	+	0.619418i	$0.787369\pi$
$920$	−13.7253	−	4.03855i	−0.452510	−	0.133147i
$921$		−	12.5393i		−	0.413185i
$922$	−5.66053	+	5.66053i	−0.186420	+	0.186420i
$923$	14.7927	+	14.7927i	0.486908	+	0.486908i
$924$		−	8.40302i		−	0.276439i
$925$	−0.414093	+	0.0895898i	−0.0136153	+	0.00294569i
$926$			4.81920i			0.158369i
$927$	−5.69619	−	5.69619i	−0.187087	−	0.187087i
$928$	−2.27645	−	2.27645i	−0.0747282	−	0.0747282i
$929$	12.9305			0.424235			0.212118	−	0.977244i	$-0.431964\pi$
$929$	12.9305			0.424235			0.212118	+	0.977244i	$0.431964\pi$
$930$	−11.6524	+	4.38435i	−0.382096	+	0.143768i
$931$	−3.31111			−0.108517
$932$	−12.0314	−	12.0314i	−0.394101	−	0.394101i
$933$	−23.4018	−	23.4018i	−0.766140	−	0.766140i
$934$		−	7.25241i		−	0.237306i
$935$	−4.39649	−	8.06242i	−0.143781	−	0.263669i
$936$			2.16280i			0.0706932i
$937$	35.0704	+	35.0704i	1.14570	+	1.14570i	0.987389	+	0.158312i	$0.0506052\pi$
$937$	35.0704	+	35.0704i	1.14570	+	1.14570i	0.158312	+	0.987389i	$0.449395\pi$
$938$	28.2535	−	28.2535i	0.922508	−	0.922508i
$939$		−	2.68373i		−	0.0875803i
$940$	−2.57474	+	1.40402i	−0.0839788	+	0.0457942i
$941$		−	19.0478i		−	0.620939i	−0.950583	−	0.310469i	$-0.899514\pi$
$941$		−	19.0478i		−	0.620939i	0.950583	−	0.310469i	$-0.100486\pi$
$942$	−2.98462	+	2.98462i	−0.0972442	+	0.0972442i
$943$	−5.27284	−	5.27284i	−0.171707	−	0.171707i
$944$			14.0638i			0.457737i
$945$	−6.74353	−	1.98422i	−0.219367	−	0.0645468i
$946$	−13.6897			−0.445090
$947$	−20.1665	+	20.1665i	−0.655322	+	0.655322i	−0.954270	−	0.298947i	$-0.903365\pi$
$947$	−20.1665	+	20.1665i	−0.655322	+	0.655322i	0.298947	+	0.954270i	$0.403365\pi$
$948$	−7.93970	+	7.93970i	−0.257869	+	0.257869i
$949$			20.8505i			0.676835i
$950$	5.61367	−	1.21453i	0.182131	−	0.0394044i
$951$		−	8.34242i		−	0.270521i
$952$	−3.41527	+	3.41527i	−0.110690	+	0.110690i
$953$	6.10111	+	6.10111i	0.197634	+	0.197634i	0.798985	−	0.601351i	$-0.205371\pi$
$953$	6.10111	+	6.10111i	0.197634	+	0.197634i	−0.601351	+	0.798985i	$0.705371\pi$
$954$	−5.71994			−0.185190
$955$	−11.9529	−	3.51705i	−0.386788	−	0.113809i
$956$		−	1.04440i		−	0.0337785i
$957$	6.08501	−	6.08501i	0.196701	−	0.196701i
$958$	−15.6238	+	15.6238i	−0.504784	+	0.504784i
$959$	7.15879			0.231169
$960$	1.96316	−	1.07052i	0.0633606	−	0.0345510i
$961$	−8.52863	+	29.8037i	−0.275117	+	0.961411i
$962$	0.129587	+	0.129587i	0.00417806	+	0.00417806i
$963$	1.93400	−	1.93400i	0.0623224	−	0.0623224i
$964$	−3.35439			−0.108038
$965$	0.422308	−	0.230287i	0.0135946	−	0.00741321i
$966$	−20.1141			−0.647160
$967$	−14.9179	+	14.9179i	−0.479726	+	0.479726i	−0.905044	−	0.425318i	$-0.860162\pi$
$967$	−14.9179	+	14.9179i	−0.479726	+	0.479726i	0.425318	+	0.905044i	$0.360162\pi$
$968$	2.72586	−	2.72586i	0.0876123	−	0.0876123i
$969$		−	1.76489i		−	0.0566965i
$970$	−0.00627776	+	0.0213354i	−0.000201567	+	0.000685039i
$971$	57.4871			1.84485			0.922425	−	0.386177i	$-0.126205\pi$
$971$	57.4871			1.84485			0.922425	+	0.386177i	$0.126205\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	37.7474	+	37.7474i	1.21013	+	1.21013i
$974$	−20.0031			−0.640940
$975$	−5.85677	+	9.09068i	−0.187567	+	0.291135i
$976$		−	11.1372i		−	0.356494i
$977$	−16.3344	−	16.3344i	−0.522585	−	0.522585i	0.395767	−	0.918351i	$-0.370479\pi$
$977$	−16.3344	−	16.3344i	−0.522585	−	0.522585i	−0.918351	+	0.395767i	$0.870479\pi$
$978$	11.3820	+	11.3820i	0.363955	+	0.363955i
$979$			27.7244i			0.886075i
$980$	−6.18327	−	1.81937i	−0.197517	−	0.0581177i
$981$	6.84356			0.218498
$982$	28.7254	−	28.7254i	0.916665	−	0.916665i
$983$	44.0455	+	44.0455i	1.40483	+	1.40483i	0.783721	+	0.621112i	$0.213319\pi$
$983$	44.0455	+	44.0455i	1.40483	+	1.40483i	0.621112	+	0.783721i	$0.286681\pi$
$984$	1.16545			0.0371531
$985$	8.39676	−	4.57881i	0.267543	−	0.145893i
$986$	−4.94631			−0.157523
$987$	−2.91539	+	2.91539i	−0.0927978	+	0.0927978i
$988$	−1.75675	−	1.75675i	−0.0558898	−	0.0558898i
$989$			32.7687i			1.04198i
$990$	2.86153	+	5.24756i	0.0909455	+	0.166779i
$991$		−	56.2864i		−	1.78800i	−0.448069	−	0.893999i	$-0.647888\pi$
$991$		−	56.2864i		−	1.78800i	0.448069	−	0.893999i	$-0.352112\pi$
$992$	0.773391	−	5.51379i	0.0245552	−	0.175063i
$993$	7.73596	−	7.73596i	0.245493	−	0.245493i
$994$		−	30.4074i		−	0.964464i
$995$	11.4724	+	3.37566i	0.363700	+	0.107016i
$996$	15.6513			0.495931
$997$	−37.9509	−	37.9509i	−1.20192	−	1.20192i	−0.973583	−	0.228335i	$-0.926672\pi$
$997$	−37.9509	−	37.9509i	−1.20192	−	1.20192i	−0.228335	−	0.973583i	$-0.573328\pi$
$998$	−4.10175	−	4.10175i	−0.129839	−	0.129839i
$999$		−	0.0847348i		−	0.00268089i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.k.a.247.8	✓	32
5.3	odd	4		930.2.k.b.433.8	yes	32
31.30	odd	2		930.2.k.b.247.8	yes	32
155.123	even	4	inner	930.2.k.a.433.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.k.a.247.8	✓	32	1.1	even	1	trivial
930.2.k.a.433.8	yes	32	155.123	even	4	inner
930.2.k.b.247.8	yes	32	31.30	odd	2
930.2.k.b.433.8	yes	32	5.3	odd	4

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.14513 + 0.631187i) q^{5} -1.00000i q^{6} +(2.22289 + 2.22289i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.14513 + 0.631187i) q^{5} -1.00000i q^{6} +(2.22289 + 2.22289i) q^{7} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.07052 - 1.96316i) q^{10} +2.67302i q^{11} +(-0.707107 + 0.707107i) q^{12} +(1.52933 + 1.52933i) q^{13} -3.14364i q^{14} +(1.07052 + 1.96316i) q^{15} -1.00000 q^{16} +(-1.08641 + 1.08641i) q^{17} +(0.707107 - 0.707107i) q^{18} +1.14871i q^{19} +(-0.631187 + 2.14513i) q^{20} +3.14364i q^{21} +(1.89011 - 1.89011i) q^{22} +(-4.52431 - 4.52431i) q^{23} +1.00000 q^{24} +(4.20321 + 2.70796i) q^{25} -2.16280i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.22289 + 2.22289i) q^{28} -3.21939 q^{29} +(0.631187 - 2.14513i) q^{30} +(-3.35197 - 4.44571i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.89011 + 1.89011i) q^{33} +1.53641 q^{34} +(3.36534 + 6.17145i) q^{35} -1.00000 q^{36} +(-0.0599165 + 0.0599165i) q^{37} +(0.812260 - 0.812260i) q^{38} +2.16280i q^{39} +(1.96316 - 1.07052i) q^{40} +1.16545 q^{41} +(2.22289 - 2.22289i) q^{42} +(-3.62140 - 3.62140i) q^{43} -2.67302 q^{44} +(-0.631187 + 2.14513i) q^{45} +6.39835i q^{46} +(0.927393 + 0.927393i) q^{47} +(-0.707107 - 0.707107i) q^{48} +2.88246i q^{49} +(-1.05730 - 4.88693i) q^{50} -1.53641 q^{51} +(-1.52933 + 1.52933i) q^{52} +(-4.04461 - 4.04461i) q^{53} +1.00000 q^{54} +(-1.68718 + 5.73400i) q^{55} +3.14364 q^{56} +(-0.812260 + 0.812260i) q^{57} +(2.27645 + 2.27645i) q^{58} -14.0638i q^{59} +(-1.96316 + 1.07052i) q^{60} +11.1372i q^{61} +(-0.773391 + 5.51379i) q^{62} +(-2.22289 + 2.22289i) q^{63} -1.00000i q^{64} +(2.31532 + 4.24591i) q^{65} +2.67302 q^{66} +(8.98751 + 8.98751i) q^{67} +(-1.08641 - 1.08641i) q^{68} -6.39835i q^{69} +(1.98422 - 6.74353i) q^{70} +9.67268 q^{71} +(0.707107 + 0.707107i) q^{72} +(6.81687 + 6.81687i) q^{73} +0.0847348 q^{74} +(1.05730 + 4.88693i) q^{75} -1.14871 q^{76} +(-5.94183 + 5.94183i) q^{77} +(1.52933 - 1.52933i) q^{78} +11.2284 q^{79} +(-2.14513 - 0.631187i) q^{80} -1.00000 q^{81} +(-0.824095 - 0.824095i) q^{82} +(-11.0672 - 11.0672i) q^{83} -3.14364 q^{84} +(-3.01622 + 1.64476i) q^{85} +5.12143i q^{86} +(-2.27645 - 2.27645i) q^{87} +(1.89011 + 1.89011i) q^{88} +10.3719 q^{89} +(1.96316 - 1.07052i) q^{90} +6.79905i q^{91} +(4.52431 - 4.52431i) q^{92} +(0.773391 - 5.51379i) q^{93} -1.31153i q^{94} +(-0.725051 + 2.46414i) q^{95} +1.00000i q^{96} +(-0.00703286 - 0.00703286i) q^{97} +(2.03821 - 2.03821i) q^{98} -2.67302 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7}+O(q^{10}) \) 32 * q - 4 * q^7	\( 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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