LMFDB - Embedded newform 930.2.z.c.349.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, 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:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.5
Character	$\chi$	$=$	930.349
Dual form			930.2.z.c.469.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.618034 - 2.14896i) q^{5} -1.00000 q^{6} +(-2.27036 + 3.12489i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.618034 - 2.14896i) q^{5} -1.00000 q^{6} +(-2.27036 + 3.12489i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(1.25185 - 1.85280i) q^{10} +(0.577324 + 0.419451i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(-5.71731 + 1.85767i) q^{13} +(-3.12489 + 2.27036i) q^{14} +(0.0762803 + 2.23477i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.61218 + 2.21897i) q^{17} +(0.951057 - 0.309017i) q^{18} +(-1.57448 + 4.84575i) q^{19} +(1.76313 - 1.37527i) q^{20} +(1.19360 - 3.67353i) q^{21} +(0.419451 + 0.577324i) q^{22} +(3.46516 + 4.76938i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(-4.23607 - 2.65626i) q^{25} -6.01153 q^{26} +(-0.587785 + 0.809017i) q^{27} +(-3.67353 + 1.19360i) q^{28} +(0.426380 - 1.31226i) q^{29} +(-0.618034 + 2.14896i) q^{30} +(5.03799 - 2.37036i) q^{31} +1.00000i q^{32} +(-0.678685 - 0.220518i) q^{33} +(0.847572 + 2.60856i) q^{34} +(5.31210 + 6.81021i) q^{35} +1.00000 q^{36} +5.40876i q^{37} +(-2.99484 + 4.12204i) q^{38} +(4.86343 - 3.53349i) q^{39} +(2.10182 - 0.763128i) q^{40} +(-3.08526 + 9.49545i) q^{41} +(2.27036 - 3.12489i) q^{42} +(-1.97763 - 0.642571i) q^{43} +(0.220518 + 0.678685i) q^{44} +(-0.763128 - 2.10182i) q^{45} +(1.82174 + 5.60674i) q^{46} +(0.107224 - 0.0348390i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(-2.44725 - 7.53186i) q^{49} +(-3.20791 - 3.83527i) q^{50} +(-2.21897 - 1.61218i) q^{51} +(-5.71731 - 1.85767i) q^{52} +(-5.59026 - 7.69434i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(1.25819 - 0.981413i) q^{55} -3.86257 q^{56} -5.09513i q^{57} +(0.811022 - 1.11628i) q^{58} +(1.63348 + 5.02734i) q^{59} +(-1.25185 + 1.85280i) q^{60} -3.71828 q^{61} +(5.52390 - 0.697525i) q^{62} +3.86257i q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.458561 + 13.4344i) q^{65} +(-0.577324 - 0.419451i) q^{66} +7.24886i q^{67} +2.74280i q^{68} +(-4.76938 - 3.46516i) q^{69} +(2.94764 + 8.11842i) q^{70} +(5.18958 - 3.77045i) q^{71} +(0.951057 + 0.309017i) q^{72} +(-1.79467 + 2.47015i) q^{73} +(-1.67140 + 5.14403i) q^{74} +(4.84957 + 1.21724i) q^{75} +(-4.12204 + 2.99484i) q^{76} +(-2.62147 + 0.851768i) q^{77} +(5.71731 - 1.85767i) q^{78} +(8.60658 - 6.25305i) q^{79} +(2.23477 - 0.0762803i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.86851 + 8.07731i) q^{82} +(-12.9090 - 4.19440i) q^{83} +(3.12489 - 2.27036i) q^{84} +(5.76487 - 2.09311i) q^{85} +(-1.68227 - 1.22224i) q^{86} +1.37979i q^{87} +0.713612i q^{88} +(-7.59311 - 5.51672i) q^{89} +(-0.0762803 - 2.23477i) q^{90} +(7.17537 - 22.0835i) q^{91} +5.89528i q^{92} +(-4.05893 + 3.81118i) q^{93} +0.112741 q^{94} +(9.44025 + 6.37834i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(10.3835 - 14.2917i) q^{97} -7.91947i q^{98} +0.713612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9	$ 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9 - 4 * q^11 - 4 * q^14 - 8 * q^16 - 16 * q^19 + 16 * q^20 - 4 * q^21 - 8 * q^24 - 64 * q^25 - 16 * q^26 + 4 * q^29 + 16 * q^30 - 24 * q^31 - 12 * q^34 + 32 * q^36 + 4 * q^39 - 48 * q^41 + 4 * q^44 + 16 * q^45 + 8 * q^46 - 28 * q^49 + 8 * q^51 - 8 * q^54 - 8 * q^55 - 16 * q^56 - 8 * q^59 + 32 * q^61 + 8 * q^64 - 8 * q^65 + 4 * q^66 - 12 * q^69 - 8 * q^70 + 32 * q^71 + 4 * q^74 - 24 * q^76 + 64 * q^79 + 24 * q^80 - 8 * q^81 + 4 * q^84 + 28 * q^85 + 84 * q^86 - 128 * q^89 - 28 * q^91 + 40 * q^94 + 8 * q^95 + 8 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	0.618034	−	2.14896i	0.276393	−	0.961045i
$5$	0.618034	−	2.14896i	0.276393	−	0.961045i
$6$	−1.00000			−0.408248
$7$	−2.27036	+	3.12489i	−0.858117	+	1.18110i	0.123899	+	0.992295i	$0.460460\pi$
$7$	−2.27036	+	3.12489i	−0.858117	+	1.18110i	−0.982015	+	0.188801i	$0.939540\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	1.25185	−	1.85280i	0.395870	−	0.585907i
$11$	0.577324	+	0.419451i	0.174070	+	0.126469i	0.671409	−	0.741087i	$-0.265689\pi$
$11$	0.577324	+	0.419451i	0.174070	+	0.126469i	−0.497339	+	0.867556i	$0.665689\pi$
$12$	−0.951057	−	0.309017i	−0.274546	−	0.0892055i
$13$	−5.71731	+	1.85767i	−1.58570	+	0.515224i	−0.963516	−	0.267650i	$-0.913753\pi$
$13$	−5.71731	+	1.85767i	−1.58570	+	0.515224i	−0.622180	+	0.782874i	$0.713753\pi$
$14$	−3.12489	+	2.27036i	−0.835161	+	0.606780i
$15$	0.0762803	+	2.23477i	0.0196955	+	0.577014i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.61218	+	2.21897i	0.391011	+	0.538180i	0.958460	−	0.285229i	$-0.0920695\pi$
$17$	1.61218	+	2.21897i	0.391011	+	0.538180i	−0.567449	+	0.823409i	$0.692070\pi$
$18$	0.951057	−	0.309017i	0.224166	−	0.0728360i
$19$	−1.57448	+	4.84575i	−0.361211	+	1.11169i	0.591109	+	0.806591i	$0.298690\pi$
$19$	−1.57448	+	4.84575i	−0.361211	+	1.11169i	−0.952320	+	0.305101i	$0.901310\pi$
$20$	1.76313	−	1.37527i	0.394247	−	0.307521i
$21$	1.19360	−	3.67353i	0.260465	−	0.801629i
$22$	0.419451	+	0.577324i	0.0894272	+	0.123086i
$23$	3.46516	+	4.76938i	0.722535	+	0.994484i	0.999436	+	0.0335859i	$0.0106927\pi$
$23$	3.46516	+	4.76938i	0.722535	+	0.994484i	−0.276901	+	0.960899i	$0.589307\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	−4.23607	−	2.65626i	−0.847214	−	0.531252i
$26$	−6.01153			−1.17896
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	−3.67353	+	1.19360i	−0.694231	+	0.225569i
$29$	0.426380	−	1.31226i	0.0791767	−	0.243681i	−0.903631	−	0.428311i	$-0.859109\pi$
$29$	0.426380	−	1.31226i	0.0791767	−	0.243681i	0.982808	+	0.184630i	$0.0591087\pi$
$30$	−0.618034	+	2.14896i	−0.112837	+	0.392345i
$31$	5.03799	−	2.37036i	0.904850	−	0.425730i
$31$	5.03799	−	2.37036i	0.904850	−	0.425730i
$32$			1.00000i			0.176777i
$33$	−0.678685	−	0.220518i	−0.118144	−	0.0383873i
$34$	0.847572	+	2.60856i	0.145357	+	0.447364i
$35$	5.31210	+	6.81021i	0.897909	+	1.15114i
$36$	1.00000			0.166667
$37$			5.40876i			0.889194i	0.895731	+	0.444597i	$0.146653\pi$
$37$			5.40876i			0.889194i	−0.895731	+	0.444597i	$0.853347\pi$
$38$	−2.99484	+	4.12204i	−0.485827	+	0.668684i
$39$	4.86343	−	3.53349i	0.778773	−	0.565811i
$40$	2.10182	−	0.763128i	0.332327	−	0.120661i
$41$	−3.08526	+	9.49545i	−0.481836	+	1.48294i	0.354675	+	0.934990i	$0.384592\pi$
$41$	−3.08526	+	9.49545i	−0.481836	+	1.48294i	−0.836511	+	0.547950i	$0.815408\pi$
$42$	2.27036	−	3.12489i	0.350325	−	0.482181i
$43$	−1.97763	−	0.642571i	−0.301586	−	0.0979912i	0.154315	−	0.988022i	$-0.450683\pi$
$43$	−1.97763	−	0.642571i	−0.301586	−	0.0979912i	−0.455901	+	0.890030i	$0.650683\pi$
$44$	0.220518	+	0.678685i	0.0332444	+	0.102316i
$45$	−0.763128	−	2.10182i	−0.113760	−	0.313320i
$46$	1.82174	+	5.60674i	0.268601	+	0.826669i
$47$	0.107224	−	0.0348390i	0.0156402	−	0.00508180i	−0.301186	−	0.953565i	$-0.597383\pi$
$47$	0.107224	−	0.0348390i	0.0156402	−	0.00508180i	0.316827	+	0.948483i	$0.397383\pi$
$48$	−0.587785	−	0.809017i	−0.0848395	−	0.116772i
$49$	−2.44725	−	7.53186i	−0.349607	−	1.07598i
$50$	−3.20791	−	3.83527i	−0.453667	−	0.542389i
$51$	−2.21897	−	1.61218i	−0.310718	−	0.225750i
$52$	−5.71731	−	1.85767i	−0.792848	−	0.257612i
$53$	−5.59026	−	7.69434i	−0.767882	−	1.05690i	−0.996517	−	0.0833864i	$-0.973426\pi$
$53$	−5.59026	−	7.69434i	−0.767882	−	1.05690i	0.228636	−	0.973512i	$-0.426574\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	1.25819	−	0.981413i	0.169654	−	0.132334i
$56$	−3.86257			−0.516158
$57$		−	5.09513i		−	0.674866i
$58$	0.811022	−	1.11628i	0.106492	−	0.146574i
$59$	1.63348	+	5.02734i	0.212661	+	0.654504i	0.999311	+	0.0371050i	$0.0118136\pi$
$59$	1.63348	+	5.02734i	0.212661	+	0.654504i	−0.786650	+	0.617399i	$0.788186\pi$
$60$	−1.25185	+	1.85280i	−0.161613	+	0.239196i
$61$	−3.71828			−0.476077			−0.238039	−	0.971256i	$-0.576504\pi$
$61$	−3.71828			−0.476077			−0.238039	+	0.971256i	$0.576504\pi$
$62$	5.52390	−	0.697525i	0.701536	−	0.0885858i
$63$			3.86257i			0.486638i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	0.458561	+	13.4344i	0.0568775	+	1.66633i
$66$	−0.577324	−	0.419451i	−0.0710637	−	0.0516308i
$67$			7.24886i			0.885589i	0.896623	+	0.442794i	$0.146013\pi$
$67$			7.24886i			0.885589i	−0.896623	+	0.442794i	$0.853987\pi$
$68$			2.74280i			0.332614i
$69$	−4.76938	−	3.46516i	−0.574166	−	0.417156i
$70$	2.94764	+	8.11842i	0.352310	+	0.970337i
$71$	5.18958	−	3.77045i	0.615890	−	0.447470i	−0.235594	−	0.971852i	$-0.575703\pi$
$71$	5.18958	−	3.77045i	0.615890	−	0.447470i	0.851483	+	0.524382i	$0.175703\pi$
$72$	0.951057	+	0.309017i	0.112083	+	0.0364180i
$73$	−1.79467	+	2.47015i	−0.210050	+	0.289110i	−0.901023	−	0.433771i	$-0.857183\pi$
$73$	−1.79467	+	2.47015i	−0.210050	+	0.289110i	0.690973	+	0.722881i	$0.257183\pi$
$74$	−1.67140	+	5.14403i	−0.194296	+	0.597982i
$75$	4.84957	+	1.21724i	0.559980	+	0.140555i
$76$	−4.12204	+	2.99484i	−0.472831	+	0.343532i
$77$	−2.62147	+	0.851768i	−0.298744	+	0.0970680i
$78$	5.71731	−	1.85767i	0.647358	−	0.210339i
$79$	8.60658	−	6.25305i	0.968316	−	0.703523i	0.0132488	−	0.999912i	$-0.495783\pi$
$79$	8.60658	−	6.25305i	0.968316	−	0.703523i	0.955067	+	0.296389i	$0.0957826\pi$
$80$	2.23477	−	0.0762803i	0.249854	−	0.00852839i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−5.86851	+	8.07731i	−0.648068	+	0.891990i
$83$	−12.9090	−	4.19440i	−1.41695	−	0.460395i	−0.502319	−	0.864682i	$-0.667520\pi$
$83$	−12.9090	−	4.19440i	−1.41695	−	0.460395i	−0.914632	+	0.404287i	$0.867520\pi$
$84$	3.12489	−	2.27036i	0.340953	−	0.247717i
$85$	5.76487	−	2.09311i	0.625288	−	0.227029i
$86$	−1.68227	−	1.22224i	−0.181404	−	0.131798i
$87$			1.37979i			0.147929i
$88$			0.713612i			0.0760713i
$89$	−7.59311	−	5.51672i	−0.804868	−	0.584771i	0.107470	−	0.994208i	$-0.465725\pi$
$89$	−7.59311	−	5.51672i	−0.804868	−	0.584771i	−0.912338	+	0.409438i	$0.865725\pi$
$90$	−0.0762803	−	2.23477i	−0.00804065	−	0.235565i
$91$	7.17537	−	22.0835i	0.752183	−	2.31498i
$92$			5.89528i			0.614625i
$93$	−4.05893	+	3.81118i	−0.420892	+	0.395201i
$94$	0.112741			0.0116284
$95$	9.44025	+	6.37834i	0.968549	+	0.654404i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	10.3835	−	14.2917i	1.05429	−	1.45110i	0.169253	−	0.985573i	$-0.445865\pi$
$97$	10.3835	−	14.2917i	1.05429	−	1.45110i	0.885033	−	0.465527i	$-0.154135\pi$
$98$		−	7.91947i		−	0.799987i
$99$	0.713612			0.0717207
$100$	−1.86574	−	4.63886i	−0.186574	−	0.463886i
$101$	1.77065	−	1.28645i	0.176186	−	0.128006i	−0.496197	−	0.868210i	$-0.665271\pi$
$101$	1.77065	−	1.28645i	0.176186	−	0.128006i	0.672383	+	0.740203i	$0.265271\pi$
$102$	−1.61218	−	2.21897i	−0.159629	−	0.219711i
$103$	4.22523	+	1.37286i	0.416324	+	0.135272i	0.509686	−	0.860360i	$-0.329761\pi$
$103$	4.22523	+	1.37286i	0.416324	+	0.135272i	−0.0933623	+	0.995632i	$0.529761\pi$
$104$	−4.86343	−	3.53349i	−0.476899	−	0.346487i
$105$	−7.15658	−	4.83537i	−0.698410	−	0.471883i
$106$	−2.93898	−	9.04524i	−0.285459	−	0.878551i
$107$	3.03552	+	4.17804i	0.293455	+	0.403906i	0.930133	−	0.367224i	$-0.119692\pi$
$107$	3.03552	+	4.17804i	0.293455	+	0.403906i	−0.636678	+	0.771130i	$0.719692\pi$
$108$	−0.951057	+	0.309017i	−0.0915155	+	0.0297352i
$109$	5.62723	+	17.3188i	0.538991	+	1.65884i	0.734865	+	0.678214i	$0.237246\pi$
$109$	5.62723	+	17.3188i	0.538991	+	1.65884i	−0.195874	+	0.980629i	$0.562754\pi$
$110$	1.49988	−	0.544577i	0.143008	−	0.0519234i
$111$	−1.67140	−	5.14403i	−0.158642	−	0.488250i
$112$	−3.67353	−	1.19360i	−0.347116	−	0.112785i
$113$	5.28909	−	7.27981i	0.497556	−	0.684827i	−0.484203	−	0.874956i	$-0.660890\pi$
$113$	5.28909	−	7.27981i	0.497556	−	0.684827i	0.981759	+	0.190128i	$0.0608905\pi$
$114$	1.57448	−	4.84575i	0.147464	−	0.453846i
$115$	12.3908	−	4.49885i	1.15545	−	0.419520i
$116$	1.11628	−	0.811022i	0.103644	−	0.0753015i
$117$	−3.53349	+	4.86343i	−0.326671	+	0.449625i
$118$			5.28606i			0.486621i
$119$	−10.5943			−0.971175
$120$	−1.76313	+	1.37527i	−0.160951	+	0.125545i
$121$	−3.24182	−	9.97730i	−0.294711	−	0.907028i
$122$	−3.53629	−	1.14901i	−0.320161	−	0.104027i
$123$		−	9.98411i		−	0.900236i
$124$	5.46909	+	1.04359i	0.491139	+	0.0937174i
$125$	−8.32624	+	7.46149i	−0.744721	+	0.667376i
$126$	−1.19360	+	3.67353i	−0.106334	+	0.327264i
$127$	0.362824	−	0.117889i	0.0321954	−	0.0104609i	−0.292875	−	0.956151i	$-0.594612\pi$
$127$	0.362824	−	0.117889i	0.0321954	−	0.0104609i	0.325070	+	0.945690i	$0.394612\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	2.07940			0.183081
$130$	−3.71533	+	12.9186i	−0.325856	+	1.13303i
$131$	−8.16791	−	5.93433i	−0.713634	−	0.518485i	0.170710	−	0.985321i	$-0.445394\pi$
$131$	−8.16791	−	5.93433i	−0.713634	−	0.518485i	−0.884344	+	0.466836i	$0.845394\pi$
$132$	−0.419451	−	0.577324i	−0.0365085	−	0.0502496i
$133$	−11.5678	−	15.9217i	−1.00305	−	1.38059i
$134$	−2.24002	+	6.89407i	−0.193508	+	0.595557i
$135$	1.37527	+	1.76313i	0.118365	+	0.151746i
$136$	−0.847572	+	2.60856i	−0.0726787	+	0.223682i
$137$	−6.79193	+	2.20683i	−0.580274	+	0.188542i	−0.584423	−	0.811449i	$-0.698679\pi$
$137$	−6.79193	+	2.20683i	−0.580274	+	0.188542i	0.00414932	+	0.999991i	$0.498679\pi$
$138$	−3.46516	−	4.76938i	−0.294974	−	0.405997i
$139$	2.95307	+	9.08863i	0.250476	+	0.770887i	0.994687	+	0.102943i	$0.0328258\pi$
$139$	2.95307	+	9.08863i	0.250476	+	0.770887i	−0.744211	+	0.667945i	$0.767174\pi$
$140$	0.294638	+	8.63195i	0.0249015	+	0.729533i
$141$	−0.0912098	+	0.0662678i	−0.00768125	+	0.00558075i
$142$	6.10071	−	1.98224i	0.511961	−	0.166346i
$143$	−4.07994	−	1.32565i	−0.341182	−	0.110857i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	−2.55648	−	1.72730i	−0.212304	−	0.143444i
$146$	−2.47015	+	1.79467i	−0.204431	+	0.148528i
$147$	4.65495	+	6.40699i	0.383934	+	0.528439i
$148$	−3.17919	+	4.37578i	−0.261328	+	0.359687i
$149$	5.71377			0.468090			0.234045	−	0.972226i	$-0.424804\pi$
$149$	5.71377			0.468090			0.234045	+	0.972226i	$0.424804\pi$
$150$	4.23607	+	2.65626i	0.345874	+	0.216883i
$151$	−3.56657	−	2.59126i	−0.290243	−	0.210874i	0.433130	−	0.901332i	$-0.357409\pi$
$151$	−3.56657	−	2.59126i	−0.290243	−	0.210874i	−0.723373	+	0.690458i	$0.757409\pi$
$152$	−4.84575	+	1.57448i	−0.393042	+	0.127707i
$153$	2.60856	+	0.847572i	0.210890	+	0.0685222i
$154$	−2.75638			−0.222115
$155$	−1.98017	−	12.2914i	−0.159051	−	0.987270i
$156$	6.01153			0.481308
$157$	18.4517	+	5.99534i	1.47261	+	0.478480i	0.931896	−	0.362727i	$-0.118154\pi$
$157$	18.4517	+	5.99534i	1.47261	+	0.478480i	0.540714	+	0.841207i	$0.318154\pi$
$158$	10.1176	−	3.28742i	0.804916	−	0.261533i
$159$	7.69434	+	5.59026i	0.610201	+	0.443337i
$160$	2.14896	+	0.618034i	0.169890	+	0.0488599i
$161$	−22.7709			−1.79460
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	−4.69656	−	6.46426i	−0.367863	−	0.506320i	0.584456	−	0.811426i	$-0.301308\pi$
$163$	−4.69656	−	6.46426i	−0.367863	−	0.506320i	−0.952318	+	0.305106i	$0.901308\pi$
$164$	−8.07731	+	5.86851i	−0.630732	+	0.458254i
$165$	−0.893336	+	1.32218i	−0.0695461	+	0.102932i
$166$	−10.9811	−	7.97823i	−0.852298	−	0.619231i
$167$	20.1534	+	6.54823i	1.55952	+	0.506717i	0.956678	−	0.291147i	$-0.0940370\pi$
$167$	20.1534	+	6.54823i	1.55952	+	0.506717i	0.602837	+	0.797865i	$0.294037\pi$
$168$	3.67353	−	1.19360i	0.283419	−	0.0920883i
$169$	18.7195	−	13.6005i	1.43996	−	1.04619i
$170$	6.12952	−	0.209222i	0.470113	−	0.0160466i
$171$	1.57448	+	4.84575i	0.120404	+	0.370564i
$172$	−1.22224	−	1.68227i	−0.0931952	−	0.128272i
$173$	5.08522	−	1.65229i	0.386622	−	0.125621i	−0.109255	−	0.994014i	$-0.534847\pi$
$173$	5.08522	−	1.65229i	0.386622	−	0.125621i	0.495877	+	0.868393i	$0.334847\pi$
$174$	−0.426380	+	1.31226i	−0.0323238	+	0.0994823i
$175$	17.9179	−	7.20655i	1.35447	−	0.544764i
$176$	−0.220518	+	0.678685i	−0.0166222	+	0.0511578i
$177$	−3.10707	−	4.27651i	−0.233542	−	0.321442i
$178$	−5.51672	−	7.59311i	−0.413495	−	0.569127i
$179$	8.36589	+	6.07818i	0.625296	+	0.454304i	0.854767	−	0.519011i	$-0.173700\pi$
$179$	8.36589	+	6.07818i	0.625296	+	0.454304i	−0.229471	+	0.973315i	$0.573700\pi$
$180$	0.618034	−	2.14896i	0.0460655	−	0.160174i
$181$	−12.7894			−0.950629			−0.475315	−	0.879816i	$-0.657666\pi$
$181$	−12.7894			−0.950629			−0.475315	+	0.879816i	$0.657666\pi$
$182$	13.6484	−	18.7854i	1.01168	−	1.39246i
$183$	3.53629	−	1.14901i	0.261410	−	0.0849374i
$184$	−1.82174	+	5.60674i	−0.134301	+	0.413335i
$185$	11.6232	+	3.34280i	0.854555	+	0.245767i
$186$	−5.03799	+	2.37036i	−0.369404	+	0.173804i
$187$			1.95730i			0.143132i
$188$	0.107224	+	0.0348390i	0.00782008	+	0.00254090i
$189$	−1.19360	−	3.67353i	−0.0868217	−	0.267210i
$190$	7.00720	+	8.98336i	0.508356	+	0.651721i
$191$	23.7296			1.71701			0.858505	−	0.512805i	$-0.171394\pi$
$191$	23.7296			1.71701			0.858505	+	0.512805i	$0.171394\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	15.9964	−	22.0172i	1.15145	−	1.58483i	0.412666	−	0.910882i	$-0.364598\pi$
$193$	15.9964	−	22.0172i	1.15145	−	1.58483i	0.738780	−	0.673947i	$-0.235402\pi$
$194$	14.2917	−	10.3835i	1.02608	−	0.745493i
$195$	−4.58757	−	12.6351i	−0.328523	−	0.904822i
$196$	2.44725	−	7.53186i	0.174804	−	0.537990i
$197$	2.05205	−	2.82440i	0.146202	−	0.201230i	−0.729635	−	0.683837i	$-0.760310\pi$
$197$	2.05205	−	2.82440i	0.146202	−	0.201230i	0.875837	+	0.482607i	$0.160310\pi$
$198$	0.678685	+	0.220518i	0.0482321	+	0.0156715i
$199$	5.56747	+	17.1349i	0.394667	+	1.21466i	0.929220	+	0.369526i	$0.120480\pi$
$199$	5.56747	+	17.1349i	0.394667	+	1.21466i	−0.534553	+	0.845135i	$0.679520\pi$
$200$	−0.340937	−	4.98836i	−0.0241079	−	0.352731i
$201$	−2.24002	−	6.89407i	−0.157999	−	0.486270i
$202$	2.08152	−	0.676326i	0.146455	−	0.0475861i
$203$	3.13263	+	4.31170i	0.219868	+	0.302622i
$204$	−0.847572	−	2.60856i	−0.0593419	−	0.182636i
$205$	18.4986	+	12.4986i	1.29200	+	0.872941i
$206$	3.59419	+	2.61133i	0.250419	+	0.181940i
$207$	5.60674	+	1.82174i	0.389696	+	0.126620i
$208$	−3.53349	−	4.86343i	−0.245004	−	0.337218i
$209$	−2.94154	+	2.13715i	−0.203471	+	0.147830i
$210$	−5.31210	−	6.81021i	−0.366570	−	0.469949i
$211$	−11.3398			−0.780665			−0.390332	−	0.920674i	$-0.627640\pi$
$211$	−11.3398			−0.780665			−0.390332	+	0.920674i	$0.627640\pi$
$212$		−	9.51072i		−	0.653199i
$213$	−3.77045	+	5.18958i	−0.258347	+	0.355584i
$214$	1.59587	+	4.91158i	0.109091	+	0.335749i
$215$	−2.60310	+	3.85272i	−0.177530	+	0.262753i
$216$	−1.00000			−0.0680414
$217$	−4.03095	+	21.1247i	−0.273639	+	1.43404i
$218$			18.2101i			1.23334i
$219$	0.943515	−	2.90384i	0.0637568	−	0.196223i
$220$	1.59476	−	0.0544345i	0.107518	−	0.00366997i
$221$	−13.3394	−	9.69167i	−0.897307	−	0.651932i
$222$		−	5.40876i		−	0.363012i
$223$		−	23.3341i		−	1.56257i	−0.624177	−	0.781283i	$-0.714566\pi$
$223$		−	23.3341i		−	1.56257i	0.624177	−	0.781283i	$-0.285434\pi$
$224$	−3.12489	−	2.27036i	−0.208790	−	0.151695i
$225$	−4.98836	+	0.340937i	−0.332558	+	0.0227291i
$226$	7.27981	−	5.28909i	0.484246	−	0.351825i
$227$	−0.584965	−	0.190066i	−0.0388255	−	0.0126152i	0.289540	−	0.957166i	$-0.406498\pi$
$227$	−0.584965	−	0.190066i	−0.0388255	−	0.0126152i	−0.328365	+	0.944551i	$0.606498\pi$
$228$	2.99484	−	4.12204i	0.198338	−	0.272989i
$229$	1.40399	−	4.32104i	0.0927783	−	0.285542i	−0.893890	−	0.448286i	$-0.852035\pi$
$229$	1.40399	−	4.32104i	0.0927783	−	0.285542i	0.986668	+	0.162744i	$0.0520345\pi$
$230$	13.1746	−	0.449693i	0.868705	−	0.0296519i
$231$	2.22996	−	1.62016i	0.146720	−	0.106599i
$232$	1.31226	−	0.426380i	0.0861542	−	0.0279932i
$233$	14.1119	−	4.58524i	0.924501	−	0.300389i	0.192189	−	0.981358i	$-0.438441\pi$
$233$	14.1119	−	4.58524i	0.924501	−	0.300389i	0.732312	+	0.680969i	$0.238441\pi$
$234$	−4.86343	+	3.53349i	−0.317933	+	0.230992i
$235$	−0.00859995	−	0.251951i	−0.000560999	−	0.0164355i
$236$	−1.63348	+	5.02734i	−0.106331	+	0.327252i
$237$	−6.25305	+	8.60658i	−0.406179	+	0.559057i
$238$	−10.0758	−	3.27381i	−0.653114	−	0.212210i
$239$	−5.12906	+	3.72648i	−0.331771	+	0.241046i	−0.741182	−	0.671304i	$-0.765734\pi$
$239$	−5.12906	+	3.72648i	−0.331771	+	0.241046i	0.409410	+	0.912350i	$0.365734\pi$
$240$	−2.10182	+	0.763128i	−0.135672	+	0.0492597i
$241$	−15.5065	−	11.2661i	−0.998860	−	0.725715i	−0.0370168	−	0.999315i	$-0.511786\pi$
$241$	−15.5065	−	11.2661i	−0.998860	−	0.725715i	−0.961844	+	0.273600i	$0.911786\pi$
$242$		−	10.4908i		−	0.674371i
$243$			1.00000i			0.0641500i
$244$	−3.00815	−	2.18555i	−0.192577	−	0.139916i
$245$	−17.6982	+	0.604099i	−1.13069	+	0.0385945i
$246$	3.08526	−	9.49545i	0.196709	−	0.605408i
$247$		−	30.6295i		−	1.94891i
$248$	4.87892	+	2.68256i	0.309812	+	0.170343i
$249$	13.5734			0.860177
$250$	−10.2244	+	4.52335i	−0.646651	+	0.286081i
$251$	1.19371	+	3.67386i	0.0753462	+	0.231892i	0.981636	−	0.190766i	$-0.0610972\pi$
$251$	1.19371	+	3.67386i	0.0753462	+	0.231892i	−0.906289	+	0.422658i	$0.861097\pi$
$252$	−2.27036	+	3.12489i	−0.143019	+	0.196849i
$253$			4.20694i			0.264488i
$254$	0.381496			0.0239372
$255$	−4.83591	+	3.77211i	−0.302836	+	0.236218i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	12.4791	+	17.1760i	0.778424	+	1.07141i	0.995454	+	0.0952443i	$0.0303632\pi$
$257$	12.4791	+	17.1760i	0.778424	+	1.07141i	−0.217029	+	0.976165i	$0.569637\pi$
$258$	1.97763	+	0.642571i	0.123122	+	0.0400047i
$259$	−16.9018	−	12.2798i	−1.05022	−	0.763032i
$260$	−7.52554	+	11.1382i	−0.466714	+	0.690760i
$261$	−0.426380	−	1.31226i	−0.0263922	−	0.0812270i
$262$	−5.93433	−	8.16791i	−0.366624	−	0.504615i
$263$	25.0980	−	8.15484i	1.54761	−	0.502849i	0.594147	−	0.804357i	$-0.297490\pi$
$263$	25.0980	−	8.15484i	1.54761	−	0.502849i	0.953464	+	0.301508i	$0.0974899\pi$
$264$	−0.220518	−	0.678685i	−0.0135720	−	0.0417702i
$265$	−19.9898	+	7.25790i	−1.22796	+	0.445849i
$266$	−6.08155	−	18.7171i	−0.372884	−	1.14762i
$267$	8.92623	+	2.90031i	0.546277	+	0.177496i
$268$	−4.26077	+	5.86445i	−0.260268	+	0.358228i
$269$	−3.38102	+	10.4057i	−0.206144	+	0.634447i	0.793520	+	0.608544i	$0.208246\pi$
$269$	−3.38102	+	10.4057i	−0.206144	+	0.634447i	−0.999664	+	0.0259027i	$0.991754\pi$
$270$	0.763128	+	2.10182i	0.0464425	+	0.127913i
$271$	−24.6545	+	17.9125i	−1.49765	+	1.08811i	−0.526349	+	0.850269i	$0.676440\pi$
$271$	−24.6545	+	17.9125i	−1.49765	+	1.08811i	−0.971304	+	0.237840i	$0.923560\pi$
$272$	−1.61218	+	2.21897i	−0.0977527	+	0.134545i
$273$			23.2200i			1.40534i
$274$	−7.14146			−0.431431
$275$	−1.33141	−	3.31035i	−0.0802873	−	0.199621i
$276$	−1.82174	−	5.60674i	−0.109656	−	0.337486i
$277$	2.64908	+	0.860739i	0.159168	+	0.0517168i	0.387517	−	0.921862i	$-0.373333\pi$
$277$	2.64908	+	0.860739i	0.159168	+	0.0517168i	−0.228349	+	0.973579i	$0.573333\pi$
$278$			9.55635i			0.573152i
$279$	2.68256	−	4.87892i	0.160600	−	0.292093i
$280$	−2.38720	+	8.30052i	−0.142663	+	0.496051i
$281$	−9.73723	+	29.9681i	−0.580875	+	1.78775i	0.0343661	+	0.999409i	$0.489059\pi$
$281$	−9.73723	+	29.9681i	−0.580875	+	1.78775i	−0.615241	+	0.788339i	$0.710941\pi$
$282$	−0.107224	+	0.0348390i	−0.00638507	+	0.00207463i
$283$	−5.28715	+	7.27714i	−0.314288	+	0.432581i	−0.936713	−	0.350099i	$-0.886148\pi$
$283$	−5.28715	+	7.27714i	−0.314288	+	0.432581i	0.622424	+	0.782680i	$0.286148\pi$
$284$	6.41467			0.380641
$285$	−10.9492	−	3.14896i	−0.648576	−	0.186528i
$286$	−3.47060	−	2.52154i	−0.205221	−	0.149102i
$287$	−22.6675	−	31.1992i	−1.33802	−	1.84163i
$288$	0.587785	+	0.809017i	0.0346356	+	0.0476718i
$289$	2.92857	−	9.01320i	0.172269	−	0.530188i
$290$	−1.89760	−	2.43275i	−0.111431	−	0.142856i
$291$	−5.45894	+	16.8009i	−0.320008	+	0.984885i
$292$	−2.90384	+	0.943515i	−0.169934	+	0.0552150i
$293$	17.7617	+	24.4468i	1.03765	+	1.42820i	0.899048	+	0.437850i	$0.144260\pi$
$293$	17.7617	+	24.4468i	1.03765	+	1.42820i	0.138599	+	0.990349i	$0.455740\pi$
$294$	2.44725	+	7.53186i	0.142727	+	0.439267i
$295$	11.8131	−	0.403222i	0.687786	−	0.0234765i
$296$	−4.37578	+	3.17919i	−0.254337	+	0.184787i
$297$	−0.678685	+	0.220518i	−0.0393813	+	0.0127958i
$298$	5.43412	+	1.76565i	0.314790	+	0.102282i
$299$	−28.6713	−	20.8309i	−1.65810	−	1.20468i
$300$	3.20791	+	3.83527i	0.185209	+	0.221430i
$301$	6.49790	−	4.72100i	0.374533	−	0.272114i
$302$	−2.59126	−	3.56657i	−0.149110	−	0.205233i
$303$	−1.28645	+	1.77065i	−0.0739046	+	0.101721i
$304$	−5.09513			−0.292226
$305$	−2.29802	+	7.99044i	−0.131584	+	0.457531i
$306$	2.21897	+	1.61218i	0.126850	+	0.0921621i
$307$	−16.2438	+	5.27793i	−0.927082	+	0.301227i	−0.733369	−	0.679831i	$-0.762053\pi$
$307$	−16.2438	+	5.27793i	−0.927082	+	0.301227i	−0.193713	+	0.981058i	$0.562053\pi$
$308$	−2.62147	−	0.851768i	−0.149372	−	0.0485340i
$309$	−4.44267			−0.252734
$310$	1.91500	−	12.3017i	0.108765	−	0.698692i
$311$	−16.4174			−0.930945			−0.465473	−	0.885062i	$-0.654116\pi$
$311$	−16.4174			−0.930945			−0.465473	+	0.885062i	$0.654116\pi$
$312$	5.71731	+	1.85767i	0.323679	+	0.105170i
$313$	−21.2421	+	6.90198i	−1.20067	+	0.390123i	−0.840009	−	0.542572i	$-0.817450\pi$
$313$	−21.2421	+	6.90198i	−1.20067	+	0.390123i	−0.360666	+	0.932695i	$0.617450\pi$
$314$	15.6960	+	11.4038i	0.885776	+	0.643554i
$315$	8.30052	+	2.38720i	0.467681	+	0.134504i
$316$	10.6383			0.598452
$317$	−15.6685	+	21.5659i	−0.880032	+	1.21126i	0.0963799	+	0.995345i	$0.469274\pi$
$317$	−15.6685	+	21.5659i	−0.880032	+	1.21126i	−0.976412	+	0.215916i	$0.930726\pi$
$318$	5.59026	+	7.69434i	0.313486	+	0.431477i
$319$	0.796588	−	0.578755i	0.0446004	−	0.0324041i
$320$	1.85280	+	1.25185i	0.103575	+	0.0699806i
$321$	−4.17804	−	3.03552i	−0.233195	−	0.169426i
$322$	−21.6565	−	7.03661i	−1.20687	−	0.392135i
$323$	−13.2909	+	4.31849i	−0.739528	+	0.240287i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	29.1534	+	7.31747i	1.61714	+	0.405900i
$326$	−2.46913	−	7.59919i	−0.136752	−	0.420880i
$327$	−10.7036	−	14.7323i	−0.591912	−	0.814697i
$328$	−9.49545	+	3.08526i	−0.524298	+	0.170355i
$329$	−0.134568	+	0.414159i	−0.00741899	+	0.0228333i
$330$	−1.25819	+	0.981413i	−0.0692610	+	0.0540250i
$331$	1.62738	−	5.00856i	0.0894490	−	0.275296i	−0.896318	−	0.443411i	$-0.853768\pi$
$331$	1.62738	−	5.00856i	0.0894490	−	0.275296i	0.985767	+	0.168116i	$0.0537682\pi$
$332$	−7.97823	−	10.9811i	−0.437862	−	0.602666i
$333$	3.17919	+	4.37578i	0.174218	+	0.239791i
$334$	17.1435	+	12.4555i	0.938050	+	0.681533i
$335$	15.5775	+	4.48004i	0.851090	+	0.244771i
$336$	3.86257			0.210721
$337$	9.27900	−	12.7715i	0.505460	−	0.695705i	−0.477686	−	0.878531i	$-0.658524\pi$
$337$	9.27900	−	12.7715i	0.505460	−	0.695705i	0.983145	+	0.182825i	$0.0585243\pi$
$338$	22.0061	−	7.15020i	1.19697	−	0.388920i
$339$	−2.78064	+	8.55793i	−0.151024	+	0.464803i
$340$	5.89417	+	1.69514i	0.319656	+	0.0919321i
$341$	3.90281	+	0.744720i	0.211349	+	0.0403289i
$342$			5.09513i			0.275513i
$343$	3.37770	+	1.09748i	0.182379	+	0.0592584i
$344$	−0.642571	−	1.97763i	−0.0346451	−	0.106627i
$345$	−10.3941	+	8.10763i	−0.559601	+	0.436500i
$346$	5.34692			0.287452
$347$		−	7.51102i		−	0.403212i	−0.979467	−	0.201606i	$-0.935384\pi$
$347$		−	7.51102i		−	0.403212i	0.979467	−	0.201606i	$-0.0646161\pi$
$348$	−0.811022	+	1.11628i	−0.0434754	+	0.0598387i
$349$	5.76568	−	4.18901i	0.308630	−	0.224233i	−0.422679	−	0.906280i	$-0.638910\pi$
$349$	5.76568	−	4.18901i	0.308630	−	0.224233i	0.731308	+	0.682047i	$0.238910\pi$
$350$	19.2679	−	1.31689i	1.02991	−	0.0703910i
$351$	1.85767	−	5.71731i	0.0991549	−	0.305167i
$352$	−0.419451	+	0.577324i	−0.0223568	+	0.0307715i
$353$	−10.9085	−	3.54437i	−0.580599	−	0.188648i	0.00396998	−	0.999992i	$-0.498736\pi$
$353$	−10.9085	−	3.54437i	−0.580599	−	0.188648i	−0.584569	+	0.811344i	$0.698736\pi$
$354$	−1.63348	−	5.02734i	−0.0868186	−	0.267200i
$355$	−4.89521	−	13.4825i	−0.259811	−	0.715575i
$356$	−2.90031	−	8.92623i	−0.153716	−	0.473089i
$357$	10.0758	−	3.27381i	0.533265	−	0.173268i
$358$	6.07818	+	8.36589i	0.321242	+	0.442151i
$359$	−1.42767	−	4.39392i	−0.0753495	−	0.231902i	0.906287	−	0.422663i	$-0.138905\pi$
$359$	−1.42767	−	4.39392i	−0.0753495	−	0.231902i	−0.981637	+	0.190761i	$0.938905\pi$
$360$	1.25185	−	1.85280i	0.0659783	−	0.0976512i
$361$	−5.63101	−	4.09117i	−0.296369	−	0.215325i
$362$	−12.1635	−	3.95214i	−0.639297	−	0.207720i
$363$	6.16631	+	8.48720i	0.323647	+	0.445463i
$364$	18.7854	−	13.6484i	0.984621	−	0.715369i
$365$	4.19910	+	5.38332i	0.219791	+	0.281776i
$366$	3.71828			0.194358
$367$			12.4724i			0.651052i	0.945533	+	0.325526i	$0.105541\pi$
$367$			12.4724i			0.651052i	−0.945533	+	0.325526i	$0.894459\pi$
$368$	−3.46516	+	4.76938i	−0.180634	+	0.248621i
$369$	3.08526	+	9.49545i	0.160612	+	0.494313i
$370$	10.0213	+	6.77096i	0.520985	+	0.352005i
$371$	36.7359			1.90723
$372$	−5.52390	+	0.697525i	−0.286401	+	0.0361650i
$373$		−	11.8584i		−	0.614006i	−0.951708	−	0.307003i	$-0.900674\pi$
$373$		−	11.8584i		−	0.614006i	0.951708	−	0.307003i	$-0.0993262\pi$
$374$	−0.604838	+	1.86150i	−0.0312754	+	0.0962558i
$375$	5.61300	−	9.66924i	0.289854	−	0.499318i
$376$	0.0912098	+	0.0662678i	0.00470378	+	0.00341750i
$377$			8.29468i			0.427198i
$378$		−	3.86257i		−	0.198669i
$379$	−1.83554	−	1.33359i	−0.0942851	−	0.0685022i	0.539644	−	0.841893i	$-0.318559\pi$
$379$	−1.83554	−	1.33359i	−0.0942851	−	0.0685022i	−0.633929	+	0.773391i	$0.718559\pi$
$380$	3.88823	+	10.7090i	0.199462	+	0.549361i
$381$	−0.308637	+	0.224238i	−0.0158119	+	0.0114880i
$382$	22.5681	+	7.33284i	1.15469	+	0.375181i
$383$	−15.2998	+	21.0584i	−0.781783	+	1.07603i	0.213300	+	0.976987i	$0.431579\pi$
$383$	−15.2998	+	21.0584i	−0.781783	+	1.07603i	−0.995083	+	0.0990450i	$0.968421\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$	0.210257	+	6.15986i	0.0107157	+	0.313936i
$386$	22.0172	−	15.9964i	1.12064	−	0.814195i
$387$	−1.97763	+	0.642571i	−0.100529	+	0.0326637i
$388$	16.8009	−	5.45894i	0.852935	−	0.277135i
$389$	−13.4033	+	9.73809i	−0.679576	+	0.493741i	−0.873217	−	0.487332i	$-0.837970\pi$
$389$	−13.4033	+	9.73809i	−0.679576	+	0.493741i	0.193641	+	0.981072i	$0.437970\pi$
$390$	−0.458561	−	13.4344i	−0.0232202	−	0.680276i
$391$	−4.99667	+	15.3782i	−0.252693	+	0.777708i
$392$	4.65495	−	6.40699i	0.235110	−	0.323602i
$393$	9.60196	+	3.11986i	0.484355	+	0.157376i
$394$	2.82440	−	2.05205i	0.142291	−	0.103381i
$395$	−8.11840	−	22.3598i	−0.408481	−	1.12504i
$396$	0.577324	+	0.419451i	0.0290116	+	0.0210782i
$397$		−	30.2940i		−	1.52041i	−0.649682	−	0.760206i	$-0.725098\pi$
$397$		−	30.2940i		−	1.52041i	0.649682	−	0.760206i	$-0.274902\pi$
$398$			18.0167i			0.903096i
$399$	15.9217	+	11.5678i	0.797082	+	0.579114i
$400$	1.21724	−	4.84957i	0.0608619	−	0.242479i
$401$	9.27979	−	28.5603i	0.463411	−	1.42623i	−0.397560	−	0.917576i	$-0.630143\pi$
$401$	9.27979	−	28.5603i	0.463411	−	1.42623i	0.860970	−	0.508655i	$-0.169857\pi$
$402$		−	7.24886i		−	0.361540i
$403$	−24.4004	+	22.9110i	−1.21547	+	1.14128i
$404$	2.18864			0.108889
$405$	−1.85280	−	1.25185i	−0.0920664	−	0.0622050i
$406$	1.64692	+	5.06871i	0.0817354	+	0.251556i
$407$	−2.26871	+	3.12261i	−0.112456	+	0.154782i
$408$		−	2.74280i		−	0.135789i
$409$	−20.9703			−1.03691			−0.518457	−	0.855104i	$-0.673493\pi$
$409$	−20.9703			−1.03691			−0.518457	+	0.855104i	$0.673493\pi$
$410$	13.7309	+	17.6033i	0.678120	+	0.869363i
$411$	5.77756	−	4.19765i	0.284986	−	0.207055i
$412$	2.61133	+	3.59419i	0.128651	+	0.177073i
$413$	−19.4185	−	6.30945i	−0.955521	−	0.310467i
$414$	4.76938	+	3.46516i	0.234402	+	0.170303i
$415$	−16.9918	+	25.1487i	−0.834096	+	1.23450i
$416$	−1.85767	−	5.71731i	−0.0910796	−	0.280314i
$417$	−5.61708	−	7.73125i	−0.275070	−	0.378601i
$418$	−3.45799	+	1.12357i	−0.169136	+	0.0549555i
$419$	6.16793	+	18.9829i	0.301323	+	0.927378i	0.981024	+	0.193888i	$0.0621098\pi$
$419$	6.16793	+	18.9829i	0.301323	+	0.927378i	−0.679700	+	0.733490i	$0.737890\pi$
$420$	−2.94764	−	8.11842i	−0.143830	−	0.396138i
$421$	4.81669	+	14.8243i	0.234751	+	0.722490i	0.997154	+	0.0753877i	$0.0240194\pi$
$421$	4.81669	+	14.8243i	0.234751	+	0.722490i	−0.762403	+	0.647102i	$0.775981\pi$
$422$	−10.7848	−	3.50419i	−0.524996	−	0.170582i
$423$	0.0662678	−	0.0912098i	0.00322205	−	0.00443477i
$424$	2.93898	−	9.04524i	0.142729	−	0.439275i
$425$	−0.935123	−	13.6821i	−0.0453601	−	0.663679i
$426$	−5.18958	+	3.77045i	−0.251436	+	0.182679i
$427$	8.44185	−	11.6192i	0.408530	−	0.562293i
$428$			5.16434i			0.249628i
$429$	4.28990			0.207118
$430$	−3.66625	+	2.85975i	−0.176802	+	0.137909i
$431$	4.93376	+	15.1846i	0.237651	+	0.731415i	0.996759	+	0.0804495i	$0.0256356\pi$
$431$	4.93376	+	15.1846i	0.237651	+	0.731415i	−0.759108	+	0.650965i	$0.774364\pi$
$432$	−0.951057	−	0.309017i	−0.0457577	−	0.0148676i
$433$			1.91905i			0.0922238i	0.998936	+	0.0461119i	$0.0146831\pi$
$433$			1.91905i			0.0922238i	−0.998936	+	0.0461119i	$0.985317\pi$
$434$	−10.3616	+	18.8452i	−0.497371	+	0.904598i
$435$	2.96512	+	0.852759i	0.142167	+	0.0408867i
$436$	−5.62723	+	17.3188i	−0.269495	+	0.829421i
$437$	−28.5671	+	9.28200i	−1.36655	+	0.444018i
$438$	1.79467	−	2.47015i	0.0857527	−	0.118028i
$439$	26.0351			1.24259			0.621294	−	0.783578i	$-0.286607\pi$
$439$	26.0351			1.24259			0.621294	+	0.783578i	$0.286607\pi$
$440$	1.53352	+	0.441036i	0.0731079	+	0.0210256i
$441$	−6.40699	−	4.65495i	−0.305095	−	0.221664i
$442$	−9.69167	−	13.3394i	−0.460986	−	0.634492i
$443$	18.0638	+	24.8626i	0.858236	+	1.18126i	0.981987	+	0.188947i	$0.0605074\pi$
$443$	18.0638	+	24.8626i	0.858236	+	1.18126i	−0.123752	+	0.992313i	$0.539493\pi$
$444$	1.67140	−	5.14403i	0.0793210	−	0.244125i
$445$	−16.5480	+	12.9078i	−0.784451	+	0.611887i
$446$	7.21063	−	22.1920i	0.341433	−	1.05082i
$447$	−5.43412	+	1.76565i	−0.257025	+	0.0835125i
$448$	−2.27036	−	3.12489i	−0.107265	−	0.147637i
$449$	4.62753	+	14.2421i	0.218387	+	0.672126i	0.998896	+	0.0469810i	$0.0149600\pi$
$449$	4.62753	+	14.2421i	0.218387	+	0.672126i	−0.780509	+	0.625145i	$0.785040\pi$
$450$	−4.84957	−	1.21724i	−0.228611	−	0.0573812i
$451$	−5.76407	+	4.18784i	−0.271419	+	0.197198i
$452$	8.55793	−	2.78064i	0.402531	−	0.130790i
$453$	4.19275	+	1.36231i	0.196993	+	0.0640068i
$454$	−0.497601	−	0.361528i	−0.0233536	−	0.0169673i
$455$	−43.0220	−	29.0680i	−2.01690	−	1.36273i
$456$	4.12204	−	2.99484i	0.193032	−	0.140246i
$457$	16.6711	+	22.9458i	0.779842	+	1.07336i	0.995299	+	0.0968473i	$0.0308759\pi$
$457$	16.6711	+	22.9458i	0.779842	+	1.07336i	−0.215457	+	0.976513i	$0.569124\pi$
$458$	2.67055	−	3.67569i	0.124786	−	0.171754i
$459$	−2.74280			−0.128023
$460$	12.6687	+	3.64348i	0.590682	+	0.169878i
$461$	14.2500	+	10.3532i	0.663688	+	0.482198i	0.867906	−	0.496728i	$-0.165465\pi$
$461$	14.2500	+	10.3532i	0.663688	+	0.482198i	−0.204218	+	0.978925i	$0.565465\pi$
$462$	2.62147	−	0.851768i	0.121962	−	0.0396278i
$463$	−20.9786	−	6.81636i	−0.974959	−	0.316783i	−0.222143	−	0.975014i	$-0.571305\pi$
$463$	−20.9786	−	6.81636i	−0.974959	−	0.316783i	−0.752816	+	0.658231i	$0.771305\pi$
$464$	1.37979			0.0640553
$465$	5.68151	+	11.0779i	0.263474	+	0.513727i
$466$	14.8381			0.687363
$467$	20.9006	+	6.79103i	0.967166	+	0.314251i	0.749671	−	0.661810i	$-0.230212\pi$
$467$	20.9006	+	6.79103i	0.967166	+	0.314251i	0.217494	+	0.976062i	$0.430212\pi$
$468$	−5.71731	+	1.85767i	−0.264283	+	0.0858707i
$469$	−22.6519	−	16.4575i	−1.04597	−	0.759939i
$470$	0.0696781	−	0.242277i	0.00321401	−	0.0111754i
$471$	−19.4013			−0.893965
$472$	−3.10707	+	4.27651i	−0.143014	+	0.196842i
$473$	−0.872207	−	1.20049i	−0.0401041	−	0.0551986i
$474$	−8.60658	+	6.25305i	−0.395313	+	0.287212i
$475$	19.5412	−	16.3447i	0.896612	−	0.749947i
$476$	−8.57095	−	6.22716i	−0.392849	−	0.285421i
$477$	−9.04524	−	2.93898i	−0.414153	−	0.134566i
$478$	−6.02957	+	1.95913i	−0.275786	+	0.0896084i
$479$	14.7026	−	10.6820i	0.671777	−	0.488075i	−0.198843	−	0.980031i	$-0.563718\pi$
$479$	14.7026	−	10.6820i	0.671777	−	0.488075i	0.870620	+	0.491957i	$0.163718\pi$
$480$	−2.23477	+	0.0762803i	−0.102003	+	0.00348170i
$481$	−10.0477	−	30.9235i	−0.458134	−	1.40999i
$482$	−11.2661	−	15.5065i	−0.513158	−	0.706301i
$483$	21.6565	−	7.03661i	0.985403	−	0.320177i
$484$	3.24182	−	9.97730i	0.147356	−	0.453514i
$485$	−24.2949	−	31.1465i	−1.10317	−	1.41429i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	20.7784	+	28.5990i	0.941560	+	1.29595i	0.955176	+	0.296038i	$0.0956656\pi$
$487$	20.7784	+	28.5990i	0.941560	+	1.29595i	−0.0136165	+	0.999907i	$0.504334\pi$
$488$	−2.18555	−	3.00815i	−0.0989352	−	0.136173i
$489$	6.46426	+	4.69656i	0.292324	+	0.212386i
$490$	−17.0186	−	4.89450i	−0.768824	−	0.221111i
$491$	2.14984			0.0970211			0.0485106	−	0.998823i	$-0.484553\pi$
$491$	2.14984			0.0970211			0.0485106	+	0.998823i	$0.484553\pi$
$492$	5.86851	−	8.07731i	0.264573	−	0.364153i
$493$	3.59927	−	1.16947i	0.162103	−	0.0526705i
$494$	9.46504	−	29.1304i	0.425852	−	1.31064i
$495$	0.441036	−	1.53352i	0.0198231	−	0.0689268i
$496$	3.81118	+	4.05893i	0.171127	+	0.182251i
$497$			24.7771i			1.11141i
$498$	12.9090	+	4.19440i	0.578468	+	0.187956i
$499$	−6.35220	−	19.5500i	−0.284363	−	0.875180i	−0.986589	−	0.163226i	$-0.947810\pi$
$499$	−6.35220	−	19.5500i	−0.284363	−	0.875180i	0.702225	−	0.711955i	$-0.252190\pi$
$500$	−11.1218	+	1.14243i	−0.497383	+	0.0510910i
$501$	−21.1905			−0.946722
$502$			3.86292i			0.172411i
$503$	−7.79542	+	10.7295i	−0.347580	+	0.478403i	−0.946636	−	0.322304i	$-0.895543\pi$
$503$	−7.79542	+	10.7295i	−0.347580	+	0.478403i	0.599056	+	0.800707i	$0.295543\pi$
$504$	−3.12489	+	2.27036i	−0.139194	+	0.101130i
$505$	−1.67021	−	4.60012i	−0.0743234	−	0.204703i
$506$	−1.30002	+	4.00104i	−0.0577928	+	0.177868i
$507$	−13.6005	+	18.7195i	−0.604019	+	0.831361i
$508$	0.362824	+	0.117889i	0.0160977	+	0.00523046i
$509$	−2.65424	−	8.16891i	−0.117647	−	0.362081i	0.874843	−	0.484407i	$-0.160965\pi$
$509$	−2.65424	−	8.16891i	−0.117647	−	0.362081i	−0.992490	+	0.122326i	$0.960965\pi$
$510$	−5.76487	+	2.09311i	−0.255273	+	0.0926844i
$511$	−3.64439	−	11.2163i	−0.161219	−	0.496180i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−2.99484	−	4.12204i	−0.132225	−	0.181993i
$514$	6.56065	+	20.1916i	0.289378	+	0.890613i
$515$	5.56156	−	8.23138i	0.245071	−	0.362718i
$516$	1.68227	+	1.22224i	0.0740579	+	0.0538062i
$517$	0.0765160	+	0.0248616i	0.00336517	+	0.00109341i
$518$	−12.2798	−	16.9018i	−0.539545	−	0.742620i
$519$	−4.32575	+	3.14284i	−0.189879	+	0.137955i
$520$	−10.5991	+	8.26751i	−0.464801	+	0.362554i
$521$	−15.1220			−0.662508			−0.331254	−	0.943542i	$-0.607472\pi$
$521$	−15.1220			−0.662508			−0.331254	+	0.943542i	$0.607472\pi$
$522$		−	1.37979i		−	0.0603919i
$523$	15.2186	−	20.9467i	0.665465	−	0.915934i	−0.334182	−	0.942509i	$-0.608460\pi$
$523$	15.2186	−	20.9467i	0.665465	−	0.915934i	0.999647	+	0.0265748i	$0.00846000\pi$
$524$	−3.11986	−	9.60196i	−0.136292	−	0.419463i
$525$	−14.8140	+	12.3908i	−0.646537	+	0.540778i
$526$	26.3896			1.15064
$527$	13.3819	+	7.35772i	0.582926	+	0.320507i
$528$		−	0.713612i		−	0.0310560i
$529$	−3.63228	+	11.1790i	−0.157925	+	0.486044i
$530$	−21.2542	+	0.725480i	−0.923225	+	0.0315129i
$531$	4.27651	+	3.10707i	0.185585	+	0.134835i
$532$		−	19.6803i		−	0.853249i
$533$		−	60.0198i		−	2.59975i
$534$	7.59311	+	5.51672i	0.328586	+	0.238732i
$535$	10.8545	−	3.94105i	0.469281	−	0.170386i
$536$	−5.86445	+	4.26077i	−0.253306	+	0.184037i
$537$	−9.83470	−	3.19549i	−0.424398	−	0.137895i
$538$	−6.43107	+	8.85161i	−0.277263	+	0.381620i
$539$	1.74639	−	5.37483i	0.0752222	−	0.231510i
$540$	0.0762803	+	2.23477i	0.00328258	+	0.0961690i
$541$	−1.61203	+	1.17121i	−0.0693066	+	0.0503542i	−0.621899	−	0.783097i	$-0.713639\pi$
$541$	−1.61203	+	1.17121i	−0.0693066	+	0.0503542i	0.552592	+	0.833452i	$0.313639\pi$
$542$	−28.9831	+	9.41718i	−1.24493	+	0.404502i
$543$	12.1635	−	3.95214i	0.521984	−	0.169603i
$544$	−2.21897	+	1.61218i	−0.0951377	+	0.0691216i
$545$	40.6953	−	1.38907i	1.74320	−	0.0595012i
$546$	−7.17537	+	22.0835i	−0.307078	+	0.945088i
$547$	−14.9469	+	20.5726i	−0.639082	+	0.879621i	−0.998566	−	0.0535305i	$-0.982953\pi$
$547$	−14.9469	+	20.5726i	−0.639082	+	0.879621i	0.359484	+	0.933151i	$0.382953\pi$
$548$	−6.79193	−	2.20683i	−0.290137	−	0.0942712i
$549$	−3.00815	+	2.18555i	−0.128385	+	0.0932770i
$550$	−0.243297	−	3.55976i	−0.0103742	−	0.151788i
$551$	5.68757	+	4.13226i	0.242299	+	0.176040i
$552$		−	5.89528i		−	0.250920i
$553$			41.0913i			1.74738i
$554$	2.25344	+	1.63722i	0.0957397	+	0.0695590i
$555$	−12.0873	+	0.412581i	−0.513078	+	0.0175131i
$556$	−2.95307	+	9.08863i	−0.125238	+	0.385444i
$557$			26.0597i			1.10418i	0.833784	+	0.552091i	$0.186170\pi$
$557$			26.0597i			1.10418i	−0.833784	+	0.552091i	$0.813830\pi$
$558$	4.05893	−	3.81118i	0.171828	−	0.161340i
$559$	12.5004			0.528711
$560$	−4.83537	+	7.15658i	−0.204331	+	0.302421i
$561$	−0.604838	−	1.86150i	−0.0255363	−	0.0785926i
$562$	−18.5213	+	25.4924i	−0.781275	+	1.07533i
$563$			43.1490i			1.81851i	0.416237	+	0.909256i	$0.363349\pi$
$563$			43.1490i			1.81851i	−0.416237	+	0.909256i	$0.636651\pi$
$564$	−0.112741			−0.00474727
$565$	−12.3752	−	15.8652i	−0.520628	−	0.667455i
$566$	−7.27714	+	5.28715i	−0.305881	+	0.222235i
$567$	2.27036	+	3.12489i	0.0953463	+	0.131233i
$568$	6.10071	+	1.98224i	0.255980	+	0.0831730i
$569$	−21.0839	−	15.3184i	−0.883884	−	0.642179i	0.0503920	−	0.998730i	$-0.483953\pi$
$569$	−21.0839	−	15.3184i	−0.883884	−	0.642179i	−0.934276	+	0.356550i	$0.883953\pi$
$570$	−9.44025	−	6.37834i	−0.395409	−	0.267159i
$571$	10.5842	+	32.5748i	0.442935	+	1.36321i	0.884733	+	0.466099i	$0.154341\pi$
$571$	10.5842	+	32.5748i	0.442935	+	1.36321i	−0.441797	+	0.897115i	$0.645659\pi$
$572$	−2.52154	−	3.47060i	−0.105431	−	0.145113i
$573$	−22.5681	+	7.33284i	−0.942798	+	0.306334i
$574$	−11.9170	−	36.6769i	−0.497407	−	1.53086i
$575$	−2.00992	−	29.4078i	−0.0838194	−	1.22639i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	21.9035	+	7.11689i	0.911856	+	0.296280i	0.727122	−	0.686508i	$-0.240857\pi$
$577$	21.9035	+	7.11689i	0.911856	+	0.296280i	0.184735	+	0.982788i	$0.440857\pi$
$578$	5.57046	−	7.66709i	0.231701	−	0.318909i
$579$	−8.40980	+	25.8827i	−0.349499	+	1.07565i
$580$	−1.05296	−	2.90007i	−0.0437217	−	0.120419i
$581$	42.4153	−	30.8165i	1.75968	−	1.27848i
$582$	−10.3835	+	14.2917i	−0.430410	+	0.592409i
$583$		−	6.78697i		−	0.281087i
$584$	−3.05328			−0.126346
$585$	8.26751	+	10.5991i	0.341820	+	0.438219i
$586$	9.33786	+	28.7390i	0.385743	+	1.18720i
$587$	24.8981	+	8.08989i	1.02766	+	0.333905i	0.773863	−	0.633353i	$-0.218322\pi$
$587$	24.8981	+	8.08989i	1.02766	+	0.333905i	0.253792	+	0.967259i	$0.418322\pi$
$588$			7.91947i			0.326593i
$589$	3.55398	+	28.1450i	0.146439	+	1.15969i
$590$	11.3595	+	3.26696i	0.467665	+	0.134499i
$591$	−1.07882	+	3.32028i	−0.0443769	+	0.136578i
$592$	−5.14403	+	1.67140i	−0.211418	+	0.0686940i
$593$	16.3356	−	22.4840i	0.670822	−	0.923307i	−0.328957	−	0.944345i	$-0.606697\pi$
$593$	16.3356	−	22.4840i	0.670822	−	0.923307i	0.999779	+	0.0210379i	$0.00669707\pi$
$594$	−0.713612			−0.0292799
$595$	−6.54762	+	22.7667i	−0.268426	+	0.933343i
$596$	4.62254	+	3.35847i	0.189347	+	0.137568i
$597$	−10.5900	−	14.5758i	−0.433418	−	0.596549i
$598$	−20.8309	−	28.6713i	−0.851839	−	1.17246i
$599$	6.49635	−	19.9937i	0.265434	−	0.816921i	−0.726159	−	0.687526i	$-0.758697\pi$
$599$	6.49635	−	19.9937i	0.265434	−	0.816921i	0.991593	−	0.129395i	$-0.0413035\pi$
$600$	1.86574	+	4.63886i	0.0761685	+	0.189381i
$601$	−5.35768	+	16.4893i	−0.218544	+	0.672611i	0.780338	+	0.625357i	$0.215047\pi$
$601$	−5.35768	+	16.4893i	−0.218544	+	0.672611i	−0.998883	+	0.0472533i	$0.984953\pi$
$602$	7.63874	−	2.48198i	0.311332	−	0.101158i
$603$	4.26077	+	5.86445i	0.173512	+	0.238819i
$604$	−1.36231	−	4.19275i	−0.0554315	−	0.170601i
$605$	−23.4444	+	0.800238i	−0.953150	+	0.0325343i
$606$	−1.77065	+	1.28645i	−0.0719275	+	0.0522584i
$607$	−10.5654	+	3.43290i	−0.428835	+	0.139337i	−0.515479	−	0.856902i	$-0.672386\pi$
$607$	−10.5654	+	3.43290i	−0.428835	+	0.139337i	0.0866434	+	0.996239i	$0.472386\pi$
$608$	−4.84575	−	1.57448i	−0.196521	−	0.0638536i
$609$	−4.31170	−	3.13263i	−0.174719	−	0.126941i
$610$	−4.65473	+	6.88923i	−0.188465	+	0.278937i
$611$	−0.548311	+	0.398371i	−0.0221823	+	0.0161164i
$612$	1.61218	+	2.21897i	0.0651684	+	0.0896967i
$613$	0.922962	−	1.27035i	0.0372781	−	0.0513089i	−0.789971	−	0.613144i	$-0.789904\pi$
$613$	0.922962	−	1.27035i	0.0372781	−	0.0513089i	0.827249	+	0.561835i	$0.189904\pi$
$614$	−17.0797			−0.689282
$615$	−21.4555	−	6.17052i	−0.865167	−	0.248819i
$616$	−2.22996	−	1.62016i	−0.0898475	−	0.0652781i
$617$	−36.6149	+	11.8969i	−1.47406	+	0.478951i	−0.932332	−	0.361604i	$-0.882229\pi$
$617$	−36.6149	+	11.8969i	−1.47406	+	0.478951i	−0.541727	+	0.840555i	$0.682229\pi$
$618$	−4.22523	−	1.37286i	−0.169964	−	0.0552245i
$619$	−25.9310			−1.04225			−0.521127	−	0.853479i	$-0.674488\pi$
$619$	−25.9310			−1.04225			−0.521127	+	0.853479i	$0.674488\pi$
$620$	5.62272	−	11.1079i	0.225814	−	0.446103i
$621$	−5.89528			−0.236569
$622$	−15.6139	−	5.07325i	−0.626059	−	0.203419i
$623$	34.4782	−	11.2027i	1.38134	−	0.448825i
$624$	4.86343	+	3.53349i	0.194693	+	0.141453i
$625$	10.8885	+	22.5042i	0.435542	+	0.900169i
$626$	−22.3353			−0.892697
$627$	2.13715	−	2.94154i	0.0853497	−	0.117474i
$628$	11.4038	+	15.6960i	0.455061	+	0.626338i
$629$	−12.0019	+	8.71988i	−0.478547	+	0.347684i
$630$	7.15658	+	4.83537i	0.285125	+	0.192646i
$631$	37.9871	+	27.5993i	1.51224	+	1.09871i	0.965170	+	0.261624i	$0.0842582\pi$
$631$	37.9871	+	27.5993i	1.51224	+	1.09871i	0.547073	+	0.837085i	$0.315742\pi$
$632$	10.1176	+	3.28742i	0.402458	+	0.130767i
$633$	10.7848	−	3.50419i	0.428657	−	0.139279i
$634$	−21.5659	+	15.6685i	−0.856490	+	0.622277i
$635$	−0.0291006	−	0.852554i	−0.00115482	−	0.0338326i
$636$	2.93898	+	9.04524i	0.116538	+	0.358667i
$637$	27.9834	+	38.5158i	1.10874	+	1.52605i
$638$	0.936446	−	0.304270i	0.0370742	−	0.0120462i
$639$	1.98224	−	6.10071i	0.0784163	−	0.241341i
$640$	1.37527	+	1.76313i	0.0543625	+	0.0696937i
$641$	2.01592	−	6.20437i	0.0796241	−	0.245058i	−0.903318	−	0.428971i	$-0.858876\pi$
$641$	2.01592	−	6.20437i	0.0796241	−	0.245058i	0.982943	+	0.183913i	$0.0588764\pi$
$642$	−3.03552	−	4.17804i	−0.119802	−	0.164894i
$643$	10.6226	+	14.6208i	0.418916	+	0.576589i	0.965365	−	0.260904i	$-0.0840206\pi$
$643$	10.6226	+	14.6208i	0.418916	+	0.576589i	−0.546448	+	0.837493i	$0.684021\pi$
$644$	−18.4221	−	13.3844i	−0.725932	−	0.527420i
$645$	1.28514	−	4.46856i	0.0506024	−	0.175949i
$646$	−13.9749			−0.549836
$647$	22.1471	−	30.4828i	0.870692	−	1.19840i	−0.108221	−	0.994127i	$-0.534516\pi$
$647$	22.1471	−	30.4828i	0.870692	−	1.19840i	0.978913	−	0.204277i	$-0.0654844\pi$
$648$	0.951057	−	0.309017i	0.0373610	−	0.0121393i
$649$	−1.16567	+	3.58757i	−0.0457567	+	0.140824i
$650$	25.4653	+	15.9682i	0.998830	+	0.626325i
$651$	−2.69424	−	21.3365i	−0.105596	−	0.836242i
$652$		−	7.99026i		−	0.312923i
$653$	8.80334	+	2.86038i	0.344501	+	0.111935i	0.476157	−	0.879360i	$-0.342029\pi$
$653$	8.80334	+	2.86038i	0.344501	+	0.111935i	−0.131656	+	0.991295i	$0.542029\pi$
$654$	−5.62723	−	17.3188i	−0.220042	−	0.677220i
$655$	−17.8007	+	13.8849i	−0.695531	+	0.542528i
$656$	−9.98411			−0.389814
$657$			3.05328i			0.119120i
$658$	−0.255964	+	0.352304i	−0.00997852	+	0.0137343i
$659$	8.03410	−	5.83711i	0.312964	−	0.227382i	−0.420203	−	0.907430i	$-0.638041\pi$
$659$	8.03410	−	5.83711i	0.312964	−	0.227382i	0.733167	+	0.680048i	$0.238041\pi$
$660$	−1.49988	+	0.544577i	−0.0583828	+	0.0211976i
$661$	11.5718	−	35.6144i	0.450091	−	1.38524i	−0.426712	−	0.904388i	$-0.640328\pi$
$661$	11.5718	−	35.6144i	0.450091	−	1.38524i	0.876803	−	0.480850i	$-0.159672\pi$
$662$	3.09546	−	4.26054i	0.120309	−	0.165591i
$663$	15.6814	+	5.09521i	0.609017	+	0.197882i
$664$	−4.19440	−	12.9090i	−0.162774	−	0.500968i
$665$	−41.3644	+	15.0186i	−1.60404	+	0.582396i
$666$	1.67140	+	5.14403i	0.0647653	+	0.199327i
$667$	7.73615	−	2.51363i	0.299545	−	0.0973280i
$668$	12.4555	+	17.1435i	0.481917	+	0.663301i
$669$	7.21063	+	22.1920i	0.278779	+	0.857994i
$670$	13.4307	+	9.07449i	0.518873	+	0.350578i
$671$	−2.14665	−	1.55963i	−0.0828706	−	0.0602090i
$672$	3.67353	+	1.19360i	0.141709	+	0.0460441i
$673$	−22.7896	−	31.3672i	−0.878474	−	1.20912i	−0.976841	−	0.213966i	$-0.931362\pi$
$673$	−22.7896	−	31.3672i	−0.878474	−	1.20912i	0.0983671	−	0.995150i	$-0.468638\pi$
$674$	12.7715	−	9.27900i	0.491938	−	0.357414i
$675$	4.63886	−	1.86574i	0.178550	−	0.0718123i
$676$	23.1385			0.889944
$677$		−	31.8223i		−	1.22303i	−0.791233	−	0.611514i	$-0.790561\pi$
$677$		−	31.8223i		−	1.22303i	0.791233	−	0.611514i	$-0.209439\pi$
$678$	−5.28909	+	7.27981i	−0.203126	+	0.279579i
$679$	21.0855	+	64.8946i	0.809189	+	2.49043i
$680$	5.08186	+	3.43358i	0.194881	+	0.131672i
$681$	0.615068			0.0235695
$682$	3.48166	+	1.91430i	0.133320	+	0.0733025i
$683$		−	24.9851i		−	0.956027i	−0.878353	−	0.478013i	$-0.841357\pi$
$683$		−	24.9851i		−	0.956027i	0.878353	−	0.478013i	$-0.158643\pi$
$684$	−1.57448	+	4.84575i	−0.0602018	+	0.185282i
$685$	0.544753	+	15.9595i	0.0208139	+	0.609781i
$686$	2.87324	+	2.08753i	0.109701	+	0.0797024i
$687$			4.54341i			0.173342i
$688$		−	2.07940i		−	0.0792765i
$689$	46.2548	+	33.6061i	1.76217	+	1.28029i
$690$	−12.3908	+	4.49885i	−0.471710	+	0.171268i
$691$	−21.9846	+	15.9728i	−0.836334	+	0.607632i	−0.921344	−	0.388748i	$-0.872908\pi$
$691$	−21.9846	+	15.9728i	−0.836334	+	0.607632i	0.0850103	+	0.996380i	$0.472908\pi$
$692$	5.08522	+	1.65229i	0.193311	+	0.0628106i
$693$	−1.62016	+	2.22996i	−0.0615447	+	0.0847091i
$694$	2.32103	−	7.14340i	0.0881052	−	0.271160i
$695$	21.3562	−	0.728961i	0.810087	−	0.0276511i
$696$	−1.11628	+	0.811022i	−0.0423124	+	0.0307417i
$697$	−26.0441	+	8.46225i	−0.986492	+	0.320531i
$698$	6.77796	−	2.20229i	0.256550	−	0.0833580i
$699$	−12.0043	+	8.72164i	−0.454044	+	0.329883i
$700$	18.7318	+	4.70167i	0.707996	+	0.177707i
$701$	14.1504	−	43.5505i	0.534453	−	1.64488i	−0.210374	−	0.977621i	$-0.567468\pi$
$701$	14.1504	−	43.5505i	0.534453	−	1.64488i	0.744828	−	0.667257i	$-0.232532\pi$
$702$	3.53349	−	4.86343i	0.133363	−	0.183558i
$703$	−26.2095	−	8.51598i	−0.988510	−	0.321186i
$704$	−0.577324	+	0.419451i	−0.0217587	+	0.0158086i
$705$	0.0860361	+	0.236962i	0.00324031	+	0.00892451i
$706$	−9.27929	−	6.74180i	−0.349231	−	0.253731i
$707$			8.45377i			0.317937i
$708$		−	5.28606i		−	0.198662i
$709$	−27.5907	−	20.0458i	−1.03619	−	0.752837i	−0.0666524	−	0.997776i	$-0.521232\pi$
$709$	−27.5907	−	20.0458i	−1.03619	−	0.752837i	−0.969538	+	0.244940i	$0.921232\pi$
$710$	−0.489313	−	14.3353i	−0.0183636	−	0.537994i
$711$	3.28742	−	10.1176i	0.123288	−	0.379441i
$712$		−	9.38560i		−	0.351740i
$713$	28.7626	+	15.8144i	1.07717	+	0.592255i
$714$	10.5943			0.396481
$715$	−5.37032	+	7.94833i	−0.200839	+	0.297251i
$716$	3.19549	+	9.83470i	0.119421	+	0.367540i
$717$	3.72648	−	5.12906i	0.139168	−	0.191548i
$718$		−	4.62004i		−	0.172418i
$719$	−2.32233			−0.0866085			−0.0433042	−	0.999062i	$-0.513788\pi$
$719$	−2.32233			−0.0866085			−0.0433042	+	0.999062i	$0.513788\pi$
$720$	1.76313	−	1.37527i	0.0657079	−	0.0512535i
$721$	−13.8828	+	10.0865i	−0.517024	+	0.375640i
$722$	−4.09117	−	5.63101i	−0.152258	−	0.209564i
$723$	18.2290	+	5.92295i	0.677942	+	0.220277i
$724$	−10.3468	−	7.51743i	−0.384538	−	0.279383i
$725$	−5.29188	+	4.42625i	−0.196536	+	0.164387i
$726$	3.24182	+	9.97730i	0.120315	+	0.370292i
$727$	−2.21486	−	3.04850i	−0.0821448	−	0.113063i	0.765967	−	0.642880i	$-0.222261\pi$
$727$	−2.21486	−	3.04850i	−0.0821448	−	0.113063i	−0.848112	+	0.529817i	$0.822261\pi$
$728$	22.0835	−	7.17537i	0.818470	−	0.265937i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	2.33004	+	6.41743i	0.0862387	+	0.237520i
$731$	−1.76245	−	5.42425i	−0.0651864	−	0.200623i
$732$	3.53629	+	1.14901i	0.130705	+	0.0424687i
$733$	17.0998	−	23.5358i	0.631594	−	0.869314i	−0.366539	−	0.930403i	$-0.619457\pi$
$733$	17.0998	−	23.5358i	0.631594	−	0.869314i	0.998132	+	0.0610886i	$0.0194572\pi$
$734$	−3.85417	+	11.8619i	−0.142260	+	0.437832i
$735$	16.6453	−	6.04357i	0.613970	−	0.222920i
$736$	−4.76938	+	3.46516i	−0.175802	+	0.127727i
$737$	−3.04054	+	4.18494i	−0.112000	+	0.154154i
$738$			9.98411i			0.367520i
$739$	32.7851			1.20602			0.603010	−	0.797734i	$-0.293968\pi$
$739$	32.7851			1.20602			0.603010	+	0.797734i	$0.293968\pi$
$740$	7.43853	+	9.53633i	0.273446	+	0.350562i
$741$	9.46504	+	29.1304i	0.347707	+	1.07013i
$742$	34.9379	+	11.3520i	1.28261	+	0.416745i
$743$			20.1748i			0.740141i	0.929004	+	0.370071i	$0.120667\pi$
$743$			20.1748i			0.740141i	−0.929004	+	0.370071i	$0.879333\pi$
$744$	−5.46909	−	1.04359i	−0.200506	−	0.0382600i
$745$	3.53131	−	12.2787i	0.129377	−	0.449856i
$746$	3.66446	−	11.2780i	0.134165	−	0.412918i
$747$	−12.9090	+	4.19440i	−0.472317	+	0.153465i
$748$	−1.15047	+	1.58349i	−0.0420653	+	0.0578980i
$749$	−19.9476			−0.728871
$750$	8.32624	−	7.46149i	0.304031	−	0.272455i
$751$	23.5919	+	17.1405i	0.860881	+	0.625467i	0.928125	−	0.372270i	$-0.121420\pi$
$751$	23.5919	+	17.1405i	0.860881	+	0.625467i	−0.0672434	+	0.997737i	$0.521420\pi$
$752$	0.0662678	+	0.0912098i	0.00241654	+	0.00332608i
$753$	−2.27057	−	3.12517i	−0.0827442	−	0.113888i
$754$	−2.56320	+	7.88871i	−0.0933461	+	0.287290i
$755$	−7.77278	+	6.06292i	−0.282880	+	0.220652i
$756$	1.19360	−	3.67353i	0.0434108	−	0.133605i
$757$	48.0509	−	15.6127i	1.74644	−	0.567452i	0.750782	−	0.660550i	$-0.229677\pi$
$757$	48.0509	−	15.6127i	1.74644	−	0.567452i	0.995657	+	0.0930976i	$0.0296768\pi$
$758$	−1.33359	−	1.83554i	−0.0484383	−	0.0666697i
$759$	−1.30002	−	4.00104i	−0.0471876	−	0.145229i
$760$	0.388658	+	11.3864i	0.0140981	+	0.413029i
$761$	16.0118	−	11.6333i	0.580428	−	0.421706i	−0.258450	−	0.966025i	$-0.583212\pi$
$761$	16.0118	−	11.6333i	0.580428	−	0.421706i	0.838878	+	0.544319i	$0.183212\pi$
$762$	−0.362824	+	0.117889i	−0.0131437	+	0.00427066i
$763$	−66.8952	−	21.7356i	−2.42177	−	0.786881i
$764$	19.1976	+	13.9479i	0.694545	+	0.504617i
$765$	3.43358	−	5.08186i	0.124141	−	0.183735i
$766$	−21.0584	+	15.2998i	−0.760869	+	0.552804i
$767$	−18.6782	−	25.7084i	−0.674432	−	0.928277i
$768$	0.587785	−	0.809017i	0.0212099	−	0.0291929i
$769$	−17.0785			−0.615865			−0.307933	−	0.951408i	$-0.599637\pi$
$769$	−17.0785			−0.615865			−0.307933	+	0.951408i	$0.599637\pi$
$770$	−1.70354	+	5.92335i	−0.0613912	+	0.213463i
$771$	−17.1760	−	12.4791i	−0.618578	−	0.449424i
$772$	25.8827	−	8.40980i	0.931539	−	0.302675i
$773$	−31.2898	−	10.1667i	−1.12541	−	0.365669i	−0.313583	−	0.949561i	$-0.601529\pi$
$773$	−31.2898	−	10.1667i	−1.12541	−	0.365669i	−0.811832	+	0.583891i	$0.801529\pi$
$774$	−2.07940			−0.0747426
$775$	−27.6376	−	3.34120i	−0.992772	−	0.120020i
$776$	17.6655			0.634154
$777$	19.8692	+	6.45590i	0.712804	+	0.231604i
$778$	−15.7566	+	5.11962i	−0.564900	+	0.183547i
$779$	−41.1549	−	29.9008i	−1.47453	−	1.07131i
$780$	3.71533	−	12.9186i	0.133030	−	0.462558i
$781$	4.57759			0.163799
$782$	−9.50424	+	13.0815i	−0.339871	+	0.467792i
$783$	0.811022	+	1.11628i	0.0289836	+	0.0398925i
$784$	6.40699	−	4.65495i	0.228821	−	0.166248i
$785$	24.2875	−	35.9468i	0.866860	−	1.28299i
$786$	8.16791	+	5.93433i	0.291340	+	0.211671i
$787$	−37.7691	−	12.2719i	−1.34632	−	0.437447i	−0.454870	−	0.890558i	$-0.650314\pi$
$787$	−37.7691	−	12.2719i	−1.34632	−	0.437447i	−0.891454	+	0.453111i	$0.850314\pi$
$788$	3.32028	−	1.07882i	0.118280	−	0.0384315i
$789$	−21.3497	+	15.5114i	−0.760068	+	0.552222i
$790$	−0.811494	−	23.7742i	−0.0288717	−	0.845847i
$791$	10.7404	+	33.0556i	0.381886	+	1.17532i
$792$	0.419451	+	0.577324i	0.0149045	+	0.0205143i
$793$	21.2586	−	6.90732i	0.754913	−	0.245286i
$794$	9.36136	−	28.8113i	0.332222	−	1.02247i
$795$	16.7686	−	13.0799i	0.594722	−	0.463895i
$796$	−5.56747	+	17.1349i	−0.197334	+	0.607331i
$797$	−26.6547	−	36.6871i	−0.944159	−	1.29952i	−0.954074	−	0.299572i	$-0.903156\pi$
$797$	−26.6547	−	36.6871i	−0.944159	−	1.29952i	0.00991482	−	0.999951i	$-0.496844\pi$
$798$	11.5678	+	15.9217i	0.409495	+	0.563622i
$799$	0.250170	+	0.181759i	0.00885039	+	0.00643018i
$800$	2.65626	−	4.23607i	0.0939130	−	0.149768i
$801$	−9.38560			−0.331624
$802$	17.6512	−	24.2948i	0.623286	−	0.857879i
$803$	−2.07221	+	0.673303i	−0.0731269	+	0.0237604i
$804$	2.24002	−	6.89407i	0.0789994	−	0.243135i
$805$	−14.0732	+	48.9339i	−0.496016	+	1.72469i
$806$	−30.2861	+	14.2495i	−1.06678	+	0.501918i
$807$		−	10.9412i		−	0.385148i
$808$	2.08152	+	0.676326i	0.0732276	+	0.0237931i
$809$	−11.8523	−	36.4776i	−0.416705	−	1.28249i	−0.910717	−	0.413031i	$-0.864470\pi$
$809$	−11.8523	−	36.4776i	−0.416705	−	1.28249i	0.494012	−	0.869455i	$-0.335530\pi$
$810$	−1.37527	−	1.76313i	−0.0483222	−	0.0619500i
$811$	−4.90658			−0.172293			−0.0861467	−	0.996282i	$-0.527455\pi$
$811$	−4.90658			−0.172293			−0.0861467	+	0.996282i	$0.527455\pi$
$812$			5.32955i			0.187031i
$813$	17.9125	−	24.6545i	0.628220	−	0.864671i
$814$	−3.12261	+	2.26871i	−0.109447	+	0.0795181i
$815$	−16.7941	+	6.09759i	−0.588271	+	0.213589i
$816$	0.847572	−	2.60856i	0.0296710	−	0.0913178i
$817$	6.22748	−	8.57139i	0.217872	−	0.299875i
$818$	−19.9439	−	6.48018i	−0.697323	−	0.226574i
$819$	−7.17537	−	22.0835i	−0.250728	−	0.771661i
$820$	7.61915	+	20.9848i	0.266072	+	0.732820i
$821$	7.13726	+	21.9662i	0.249092	+	0.766626i	0.994936	+	0.100506i	$0.0320462\pi$
$821$	7.13726	+	21.9662i	0.249092	+	0.766626i	−0.745844	+	0.666120i	$0.767954\pi$
$822$	6.79193	−	2.20683i	0.236896	−	0.0769721i
$823$	−4.47823	−	6.16376i	−0.156101	−	0.214855i	0.723802	−	0.690008i	$-0.242393\pi$
$823$	−4.47823	−	6.16376i	−0.156101	−	0.214855i	−0.879903	+	0.475153i	$0.842393\pi$
$824$	1.37286	+	4.22523i	0.0478258	+	0.147193i
$825$	2.28920	+	2.73690i	0.0796998	+	0.0952865i
$826$	−16.5183	−	12.0013i	−0.574747	−	0.417578i
$827$	17.5795	+	5.71193i	0.611299	+	0.198623i	0.598273	−	0.801292i	$-0.295854\pi$
$827$	17.5795	+	5.71193i	0.611299	+	0.198623i	0.0130257	+	0.999915i	$0.495854\pi$
$828$	3.46516	+	4.76938i	0.120423	+	0.165747i
$829$	−29.7950	+	21.6474i	−1.03482	+	0.751844i	−0.969269	−	0.246005i	$-0.920882\pi$
$829$	−29.7950	+	21.6474i	−1.03482	+	0.751844i	−0.0655556	+	0.997849i	$0.520882\pi$
$830$	−23.9316	+	18.6671i	−0.830678	+	0.647945i
$831$	−2.78541			−0.0966248
$832$		−	6.01153i		−	0.208412i
$833$	12.7676	−	17.5731i	0.442371	−	0.608872i
$834$	−2.95307	−	9.08863i	−0.102257	−	0.314713i
$835$	26.5274	−	39.2618i	0.918017	−	1.35871i
$836$	−3.63594			−0.125752
$837$	−1.04359	+	5.46909i	−0.0360718	+	0.189039i
$838$			19.9599i			0.689502i
$839$	8.30417	−	25.5576i	0.286692	−	0.882346i	−0.699195	−	0.714931i	$-0.746458\pi$
$839$	8.30417	−	25.5576i	0.286692	−	0.882346i	0.985886	−	0.167415i	$-0.0535420\pi$
$840$	−0.294638	−	8.63195i	−0.0101660	−	0.297831i
$841$	21.9213	+	15.9267i	0.755906	+	0.549198i
$842$			15.5871i			0.537169i
$843$		−	31.5104i		−	1.08527i
$844$	−9.17410	−	6.66537i	−0.315786	−	0.229432i
$845$	−17.6577	−	48.6330i	−0.607442	−	1.67303i
$846$	0.0912098	−	0.0662678i	0.00313586	−	0.00227833i
$847$	38.5381	+	12.5218i	1.32418	+	0.430253i
$848$	5.59026	−	7.69434i	0.191970	−	0.264225i
$849$	2.77962	−	8.55479i	0.0953963	−	0.293600i
$850$	3.33864	−	13.3014i	0.114515	−	0.456235i
$851$	−25.7964	+	18.7422i	−0.884290	+	0.642474i
$852$	−6.10071	+	1.98224i	−0.209007	+	0.0679105i
$853$	44.4268	−	14.4352i	1.52115	−	0.494250i	0.575045	−	0.818122i	$-0.304985\pi$
$853$	44.4268	−	14.4352i	1.52115	−	0.494250i	0.946101	+	0.323871i	$0.104985\pi$
$854$	11.6192	−	8.44185i	0.397601	−	0.288874i
$855$	11.3864	−	0.388658i	0.389407	−	0.0132918i
$856$	−1.59587	+	4.91158i	−0.0545457	+	0.167874i
$857$	−18.0583	+	24.8552i	−0.616861	+	0.849036i	−0.997120	−	0.0758439i	$-0.975835\pi$
$857$	−18.0583	+	24.8552i	−0.616861	+	0.849036i	0.380259	+	0.924880i	$0.375835\pi$
$858$	4.07994	+	1.32565i	0.139287	+	0.0452570i
$859$	19.0663	−	13.8524i	0.650532	−	0.472639i	−0.212920	−	0.977070i	$-0.568297\pi$
$859$	19.0663	−	13.8524i	0.650532	−	0.472639i	0.863453	+	0.504430i	$0.168297\pi$
$860$	−4.37053	+	1.58685i	−0.149034	+	0.0541112i
$861$	31.1992	+	22.6675i	1.06327	+	0.772508i
$862$			15.9660i			0.543804i
$863$			40.5447i			1.38016i	0.723734	+	0.690079i	$0.242424\pi$
$863$			40.5447i			1.38016i	−0.723734	+	0.690079i	$0.757576\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−0.407864	−	11.9491i	−0.0138678	−	0.406282i
$866$	−0.593020	+	1.82513i	−0.0201516	+	0.0620204i
$867$			9.47704i			0.321857i
$868$	−15.6779	+	14.7209i	−0.532143	+	0.499661i
$869$	7.59163			0.257528
$870$	2.55648	+	1.72730i	0.0866729	+	0.0585608i
$871$	−13.4660	−	41.4440i	−0.456277	−	1.40427i
$872$	−10.7036	+	14.7323i	−0.362470	+	0.498898i
$873$		−	17.6655i		−	0.597886i
$874$	−30.0372			−1.01602
$875$	−4.41271	−	42.9588i	−0.149177	−	1.45227i
$876$	2.47015	−	1.79467i	0.0834587	−	0.0606363i
$877$	10.2462	+	14.1027i	0.345990	+	0.476214i	0.946179	−	0.323644i	$-0.104908\pi$
$877$	10.2462	+	14.1027i	0.345990	+	0.476214i	−0.600189	+	0.799858i	$0.704908\pi$
$878$	24.7609	+	8.04529i	0.835639	+	0.271515i
$879$	−24.4468	−	17.7617i	−0.824571	−	0.599086i
$880$	1.32218	+	0.893336i	0.0445707	+	0.0301143i
$881$	12.7866	+	39.3531i	0.430791	+	1.32584i	0.897339	+	0.441342i	$0.145497\pi$
$881$	12.7866	+	39.3531i	0.430791	+	1.32584i	−0.466548	+	0.884496i	$0.654503\pi$
$882$	−4.65495	−	6.40699i	−0.156740	−	0.215734i
$883$	−6.53259	+	2.12257i	−0.219839	+	0.0714300i	−0.416866	−	0.908968i	$-0.636871\pi$
$883$	−6.53259	+	2.12257i	−0.219839	+	0.0714300i	0.197027	+	0.980398i	$0.436871\pi$
$884$	−5.09521	−	15.6814i	−0.171370	−	0.527424i
$885$	−11.1103	+	4.03394i	−0.373470	+	0.135599i
$886$	9.49669	+	29.2278i	0.319047	+	0.981927i
$887$	1.15881	+	0.376519i	0.0389089	+	0.0126423i	0.328407	−	0.944536i	$-0.393488\pi$
$887$	1.15881	+	0.376519i	0.0389089	+	0.0126423i	−0.289498	+	0.957179i	$0.593488\pi$
$888$	3.17919	−	4.37578i	0.106687	−	0.146841i
$889$	−0.455354	+	1.40143i	−0.0152721	+	0.0470026i
$890$	−19.7268	+	7.16241i	−0.661244	+	0.240084i
$891$	0.577324	−	0.419451i	0.0193411	−	0.0140521i
$892$	13.7154	−	18.8777i	0.459227	−	0.632071i
$893$			0.574432i			0.0192226i
$894$	−5.71377			−0.191097
$895$	18.2322	−	14.2215i	0.609434	−	0.475371i
$896$	−1.19360	−	3.67353i	−0.0398754	−	0.122724i
$897$	33.7051	+	10.9515i	1.12538	+	0.365659i
$898$			14.9750i			0.499723i
$899$	−0.962441	−	7.62184i	−0.0320992	−	0.254203i
$900$	−4.23607	−	2.65626i	−0.141202	−	0.0885421i
$901$	8.06103	−	24.8093i	0.268552	−	0.826517i
$902$	−6.77607	+	2.20168i	−0.225618	+	0.0733078i
$903$	−4.72100	+	6.49790i	−0.157105	+	0.216237i
$904$	8.99834			0.299280
$905$	−7.90429	+	27.4839i	−0.262747	+	0.913597i
$906$	3.56657	+	2.59126i	0.118491	+	0.0860889i
$907$	−29.3407	−	40.3841i	−0.974243	−	1.34093i	−0.939874	−	0.341522i	$-0.889058\pi$
$907$	−29.3407	−	40.3841i	−0.974243	−	1.34093i	−0.0343696	−	0.999409i	$-0.510942\pi$
$908$	−0.361528	−	0.497601i	−0.0119977	−	0.0165135i
$909$	0.676326	−	2.08152i	0.0224323	−	0.0690396i
$910$	−31.9339	−	40.9398i	−1.05860	−	1.35714i
$911$	3.40707	−	10.4859i	0.112881	−	0.347413i	−0.878618	−	0.477525i	$-0.841534\pi$
$911$	3.40707	−	10.4859i	0.112881	−	0.347413i	0.991499	+	0.130113i	$0.0415339\pi$
$912$	4.84575	−	1.57448i	0.160459	−	0.0521363i
$913$	−5.69336	−	7.83624i	−0.188423	−	0.259342i
$914$	8.76453	+	26.9744i	0.289905	+	0.892235i
$915$	−0.283631	−	8.30949i	−0.00937656	−	0.274703i
$916$	3.67569	−	2.67055i	0.121448	−	0.0882374i
$917$	37.0883	−	12.0507i	1.22476	−	0.397949i
$918$	−2.60856	−	0.847572i	−0.0860953	−	0.0279741i
$919$	38.4319	+	27.9224i	1.26775	+	0.921075i	0.999111	−	0.0421649i	$-0.0134255\pi$
$919$	38.4319	+	27.9224i	1.26775	+	0.921075i	0.268641	+	0.963240i	$0.413425\pi$
$920$	10.9228	+	7.38001i	0.360113	+	0.243312i
$921$	13.8178	−	10.0392i	0.455312	−	0.330803i
$922$	10.3532	+	14.2500i	0.340965	+	0.469298i
$923$	−22.6662	+	31.1973i	−0.746066	+	1.02687i
$924$	2.75638			0.0906782
$925$	14.3671	−	22.9119i	0.472387	−	0.753337i
$926$	−17.8455	−	12.9655i	−0.586438	−	0.426073i
$927$	4.22523	−	1.37286i	0.138775	−	0.0450906i
$928$	1.31226	+	0.426380i	0.0430771	+	0.0139966i
$929$	21.4705			0.704425			0.352212	−	0.935920i	$-0.385429\pi$
$929$	21.4705			0.704425			0.352212	+	0.935920i	$0.385429\pi$
$930$	1.98017	+	12.2914i	0.0649323	+	0.403051i
$931$	40.3507			1.32244
$932$	14.1119	+	4.58524i	0.462251	+	0.150194i
$933$	15.6139	−	5.07325i	0.511175	−	0.166091i
$934$	17.7791	+	12.9173i	0.581751	+	0.422667i
$935$	4.20615	+	1.20968i	0.137556	+	0.0395606i
$936$	−6.01153			−0.196493
$937$	17.7704	−	24.4588i	0.580533	−	0.799035i	−0.413221	−	0.910631i	$-0.635596\pi$
$937$	17.7704	−	24.4588i	0.580533	−	0.799035i	0.993754	+	0.111596i	$0.0355963\pi$
$938$	−16.4575	−	22.6519i	−0.537358	−	0.739609i
$939$	18.0696	−	13.1283i	0.589680	−	0.428427i
$940$	0.141136	−	0.208887i	0.00460333	−	0.00681316i
$941$	24.7143	+	17.9560i	0.805662	+	0.585348i	0.912570	−	0.408921i	$-0.134095\pi$
$941$	24.7143	+	17.9560i	0.805662	+	0.585348i	−0.106907	+	0.994269i	$0.534095\pi$
$942$	−18.4517	−	5.99534i	−0.601190	−	0.195339i
$943$	−55.9783	+	18.1885i	−1.82290	+	0.592298i
$944$	−4.27651	+	3.10707i	−0.139189	+	0.101126i
$945$	−8.63195	+	0.294638i	−0.280797	+	0.00958458i
$946$	−0.458546	−	1.41126i	−0.0149086	−	0.0458841i
$947$	−32.1233	−	44.2139i	−1.04387	−	1.43676i	−0.894008	−	0.448051i	$-0.852118\pi$
$947$	−32.1233	−	44.2139i	−1.04387	−	1.43676i	−0.149858	−	0.988708i	$-0.547882\pi$
$948$	−10.1176	+	3.28742i	−0.328606	+	0.106770i
$949$	5.67197	−	17.4565i	0.184120	−	0.566663i
$950$	23.6356	−	9.50618i	0.766839	−	0.308421i
$951$	8.23743	−	25.3522i	0.267117	−	0.822102i
$952$	−6.22716	−	8.57095i	−0.201823	−	0.277786i
$953$	8.09252	+	11.1384i	0.262142	+	0.360808i	0.919717	−	0.392581i	$-0.128418\pi$
$953$	8.09252	+	11.1384i	0.262142	+	0.360808i	−0.657575	+	0.753389i	$0.728418\pi$
$954$	−7.69434	−	5.59026i	−0.249113	−	0.180991i
$955$	14.6657	−	50.9939i	0.474570	−	1.65012i
$956$	−6.33987			−0.205046
$957$	−0.578755	+	0.796588i	−0.0187085	+	0.0257500i
$958$	17.2839	−	5.61588i	0.558417	−	0.181441i
$959$	8.52405	−	26.2343i	0.275256	−	0.847151i
$960$	−2.14896	−	0.618034i	−0.0693574	−	0.0199470i
$961$	19.7627	−	23.8838i	0.637508	−	0.770444i
$962$		−	32.5149i		−	1.04832i
$963$	4.91158	+	1.59587i	0.158273	+	0.0514261i
$964$	−5.92295	−	18.2290i	−0.190765	−	0.587115i
$965$	−37.4277	−	47.9830i	−1.20484	−	1.54463i
$966$	22.7709			0.732643
$967$			47.2655i			1.51996i	0.649949	+	0.759978i	$0.274790\pi$
$967$			47.2655i			1.51996i	−0.649949	+	0.759978i	$0.725210\pi$
$968$	6.16631	−	8.48720i	0.198193	−	0.272789i
$969$	11.3059	−	8.21425i	0.363199	−	0.263880i
$970$	−13.4810	−	37.1296i	−0.432850	−	1.19216i
$971$	−11.4249	+	35.1623i	−0.366643	+	1.12841i	0.582303	+	0.812972i	$0.302152\pi$
$971$	−11.4249	+	35.1623i	−0.366643	+	1.12841i	−0.948946	+	0.315439i	$0.897848\pi$
$972$	−0.587785	+	0.809017i	−0.0188532	+	0.0259492i
$973$	−35.1055	−	11.4065i	−1.12543	−	0.365674i
$974$	10.9239	+	33.6202i	0.350023	+	1.07726i
$975$	−29.9877	+	2.04956i	−0.960375	+	0.0656383i
$976$	−1.14901	−	3.53629i	−0.0367790	−	0.113194i
$977$	−37.3675	+	12.1414i	−1.19549	+	0.388439i	−0.838101	−	0.545515i	$-0.816334\pi$
$977$	−37.3675	+	12.1414i	−1.19549	+	0.388439i	−0.357392	+	0.933955i	$0.616334\pi$
$978$	4.69656	+	6.46426i	0.150179	+	0.206704i
$979$	−2.06970	−	6.36987i	−0.0661477	−	0.203582i
$980$	−14.6732	−	9.91400i	−0.468718	−	0.316691i
$981$	14.7323	+	10.7036i	0.470365	+	0.341740i
$982$	2.04462	+	0.664339i	0.0652466	+	0.0211999i
$983$	−17.2504	−	23.7431i	−0.550202	−	0.757289i	0.439837	−	0.898078i	$-0.355036\pi$
$983$	−17.2504	−	23.7431i	−0.550202	−	0.757289i	−0.990040	+	0.140789i	$0.955036\pi$
$984$	8.07731	−	5.86851i	0.257495	−	0.187081i
$985$	−4.80129	−	6.15534i	−0.152982	−	0.196126i
$986$	3.78450			0.120523
$987$		−	0.435472i		−	0.0138612i
$988$	18.0036	−	24.7798i	0.572770	−	0.788351i
$989$	−3.78814	−	11.6587i	−0.120456	−	0.370725i
$990$	0.893336	−	1.32218i	0.0283921	−	0.0420217i
$991$	15.8626			0.503891			0.251946	−	0.967741i	$-0.418930\pi$
$991$	15.8626			0.503891			0.251946	+	0.967741i	$0.418930\pi$
$992$	2.37036	+	5.03799i	0.0752591	+	0.159956i
$993$			5.26632i			0.167122i
$994$	−7.65656	+	23.5645i	−0.242851	+	0.747419i
$995$	40.2631	−	1.37432i	1.27643	−	0.0435688i
$996$	10.9811	+	7.97823i	0.347949	+	0.252800i
$997$			8.65572i			0.274129i	0.990562	+	0.137065i	$0.0437668\pi$
$997$			8.65572i			0.274129i	−0.990562	+	0.137065i	$0.956233\pi$
$998$		−	20.5561i		−	0.650693i
$999$	−4.37578	−	3.17919i	−0.138443	−	0.100585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.c.349.5	yes	32
5.4	even	2	inner	930.2.z.c.349.4	✓	32
31.4	even	5	inner	930.2.z.c.469.2	yes	32
155.4	even	10	inner	930.2.z.c.469.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.c.349.4	✓	32	5.4	even	2	inner
930.2.z.c.349.5	yes	32	1.1	even	1	trivial
930.2.z.c.469.2	yes	32	31.4	even	5	inner
930.2.z.c.469.7	yes	32	155.4	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.618034 - 2.14896i) q^{5} -1.00000 q^{6} +(-2.27036 + 3.12489i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.618034 - 2.14896i) q^{5} -1.00000 q^{6} +(-2.27036 + 3.12489i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(1.25185 - 1.85280i) q^{10} +(0.577324 + 0.419451i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(-5.71731 + 1.85767i) q^{13} +(-3.12489 + 2.27036i) q^{14} +(0.0762803 + 2.23477i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.61218 + 2.21897i) q^{17} +(0.951057 - 0.309017i) q^{18} +(-1.57448 + 4.84575i) q^{19} +(1.76313 - 1.37527i) q^{20} +(1.19360 - 3.67353i) q^{21} +(0.419451 + 0.577324i) q^{22} +(3.46516 + 4.76938i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(-4.23607 - 2.65626i) q^{25} -6.01153 q^{26} +(-0.587785 + 0.809017i) q^{27} +(-3.67353 + 1.19360i) q^{28} +(0.426380 - 1.31226i) q^{29} +(-0.618034 + 2.14896i) q^{30} +(5.03799 - 2.37036i) q^{31} +1.00000i q^{32} +(-0.678685 - 0.220518i) q^{33} +(0.847572 + 2.60856i) q^{34} +(5.31210 + 6.81021i) q^{35} +1.00000 q^{36} +5.40876i q^{37} +(-2.99484 + 4.12204i) q^{38} +(4.86343 - 3.53349i) q^{39} +(2.10182 - 0.763128i) q^{40} +(-3.08526 + 9.49545i) q^{41} +(2.27036 - 3.12489i) q^{42} +(-1.97763 - 0.642571i) q^{43} +(0.220518 + 0.678685i) q^{44} +(-0.763128 - 2.10182i) q^{45} +(1.82174 + 5.60674i) q^{46} +(0.107224 - 0.0348390i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(-2.44725 - 7.53186i) q^{49} +(-3.20791 - 3.83527i) q^{50} +(-2.21897 - 1.61218i) q^{51} +(-5.71731 - 1.85767i) q^{52} +(-5.59026 - 7.69434i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(1.25819 - 0.981413i) q^{55} -3.86257 q^{56} -5.09513i q^{57} +(0.811022 - 1.11628i) q^{58} +(1.63348 + 5.02734i) q^{59} +(-1.25185 + 1.85280i) q^{60} -3.71828 q^{61} +(5.52390 - 0.697525i) q^{62} +3.86257i q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.458561 + 13.4344i) q^{65} +(-0.577324 - 0.419451i) q^{66} +7.24886i q^{67} +2.74280i q^{68} +(-4.76938 - 3.46516i) q^{69} +(2.94764 + 8.11842i) q^{70} +(5.18958 - 3.77045i) q^{71} +(0.951057 + 0.309017i) q^{72} +(-1.79467 + 2.47015i) q^{73} +(-1.67140 + 5.14403i) q^{74} +(4.84957 + 1.21724i) q^{75} +(-4.12204 + 2.99484i) q^{76} +(-2.62147 + 0.851768i) q^{77} +(5.71731 - 1.85767i) q^{78} +(8.60658 - 6.25305i) q^{79} +(2.23477 - 0.0762803i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.86851 + 8.07731i) q^{82} +(-12.9090 - 4.19440i) q^{83} +(3.12489 - 2.27036i) q^{84} +(5.76487 - 2.09311i) q^{85} +(-1.68227 - 1.22224i) q^{86} +1.37979i q^{87} +0.713612i q^{88} +(-7.59311 - 5.51672i) q^{89} +(-0.0762803 - 2.23477i) q^{90} +(7.17537 - 22.0835i) q^{91} +5.89528i q^{92} +(-4.05893 + 3.81118i) q^{93} +0.112741 q^{94} +(9.44025 + 6.37834i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(10.3835 - 14.2917i) q^{97} -7.91947i q^{98} +0.713612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9	\( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9 - 4 * q^11 - 4 * q^14 - 8 * q^16 - 16 * q^19 + 16 * q^20 - 4 * q^21 - 8 * q^24 - 64 * q^25 - 16 * q^26 + 4 * q^29 + 16 * q^30 - 24 * q^31 - 12 * q^34 + 32 * q^36 + 4 * q^39 - 48 * q^41 + 4 * q^44 + 16 * q^45 + 8 * q^46 - 28 * q^49 + 8 * q^51 - 8 * q^54 - 8 * q^55 - 16 * q^56 - 8 * q^59 + 32 * q^61 + 8 * q^64 - 8 * q^65 + 4 * q^66 - 12 * q^69 - 8 * q^70 + 32 * q^71 + 4 * q^74 - 24 * q^76 + 64 * q^79 + 24 * q^80 - 8 * q^81 + 4 * q^84 + 28 * q^85 + 84 * q^86 - 128 * q^89 - 28 * q^91 + 40 * q^94 + 8 * q^95 + 8 * q^96 - 16 * q^99

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