LMFDB - Embedded newform 357.2.bl.a.10.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(10,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 9])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$357 = 3 \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$ , degree $16$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.17
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.17

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06738 - 0.140524i) q^{2} +(-0.442289 - 0.896873i) q^{3} +(-0.812294 + 0.217654i) q^{4} +(-2.05370 + 1.80104i) q^{5} +(-0.598123 - 0.895154i) q^{6} +(-0.418160 - 2.61250i) q^{7} +(-2.82573 + 1.17045i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-1.93899 + 2.21099i) q^{10} +(-1.62437 + 0.106467i) q^{11} +(0.554476 + 0.632259i) q^{12} +(-3.58990 - 3.58990i) q^{13} +(-0.813454 - 2.72977i) q^{14} +(2.52363 + 1.04532i) q^{15} +(-1.39509 + 0.805454i) q^{16} +(-3.46096 + 2.24093i) q^{17} +(-0.538296 + 0.932356i) q^{18} +(0.0797791 + 0.605982i) q^{19} +(1.27620 - 1.90997i) q^{20} +(-2.15813 + 1.53051i) q^{21} +(-1.71887 + 0.341904i) q^{22} +(2.88199 + 1.42124i) q^{23} +(2.29954 + 2.01664i) q^{24} +(0.321280 - 2.44037i) q^{25} +(-4.33627 - 3.32733i) q^{26} +(0.980785 + 0.195090i) q^{27} +(0.908288 + 2.03110i) q^{28} +(0.0592767 + 0.298004i) q^{29} +(2.84057 + 0.761129i) q^{30} +(-2.75512 + 1.35867i) q^{31} +(3.47711 - 2.66808i) q^{32} +(0.813930 + 1.40977i) q^{33} +(-3.37926 + 2.87828i) q^{34} +(5.56399 + 4.61215i) q^{35} +(0.321817 - 0.776935i) q^{36} +(0.441226 - 6.73180i) q^{37} +(0.170309 + 0.635604i) q^{38} +(-1.63191 + 4.80746i) q^{39} +(3.69514 - 7.49301i) q^{40} +(2.11733 - 10.6445i) q^{41} +(-2.08848 + 1.93691i) q^{42} +(3.59946 + 8.68987i) q^{43} +(1.29630 - 0.440033i) q^{44} +(-0.178653 - 2.72571i) q^{45} +(3.27590 + 1.11202i) q^{46} +(-0.122970 + 0.458931i) q^{47} +(1.33942 + 0.894973i) q^{48} +(-6.65028 + 2.18489i) q^{49} -2.64995i q^{50} +(3.54057 + 2.11290i) q^{51} +(3.69741 + 2.13470i) q^{52} +(6.67624 + 8.70065i) q^{53} +(1.07429 + 0.0704125i) q^{54} +(3.14422 - 3.14422i) q^{55} +(4.23941 + 6.89276i) q^{56} +(0.508204 - 0.339571i) q^{57} +(0.105148 + 0.309755i) q^{58} +(-6.53848 - 0.860807i) q^{59} +(-2.27745 - 0.299832i) q^{60} +(-2.28082 - 6.71907i) q^{61} +(-2.74984 + 1.83738i) q^{62} +(2.32719 + 1.25864i) q^{63} +(5.61464 - 5.61464i) q^{64} +(13.8381 + 0.907000i) q^{65} +(1.06688 + 1.39038i) q^{66} +(-9.18527 - 5.30312i) q^{67} +(2.32357 - 2.57359i) q^{68} -3.21338i q^{69} +(6.58702 + 4.14106i) q^{70} +(-5.90931 - 3.94848i) q^{71} +(0.791609 - 2.95433i) q^{72} +(-13.8613 - 4.70526i) q^{73} +(-0.475020 - 7.24741i) q^{74} +(-2.33080 + 0.791199i) q^{75} +(-0.196698 - 0.474872i) q^{76} +(0.957394 + 4.19915i) q^{77} +(-1.06631 + 5.36072i) q^{78} +(3.95195 - 8.01377i) q^{79} +(1.41443 - 4.16677i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(0.764193 - 11.6593i) q^{82} +(-4.06472 + 9.81309i) q^{83} +(1.41991 - 1.71295i) q^{84} +(3.07174 - 10.8355i) q^{85} +(5.06313 + 8.76960i) q^{86} +(0.241054 - 0.184968i) q^{87} +(4.46542 - 2.20210i) q^{88} +(-6.14547 - 1.64667i) q^{89} +(-0.573717 - 2.88427i) q^{90} +(-7.87746 + 10.8798i) q^{91} +(-2.65036 - 0.527190i) q^{92} +(2.43711 + 1.87006i) q^{93} +(-0.0667655 + 0.507135i) q^{94} +(-1.25524 - 1.10082i) q^{95} +(-3.93081 - 1.93846i) q^{96} +(15.6375 - 3.11049i) q^{97} +(-6.79137 + 3.26663i) q^{98} +(0.904390 - 1.35352i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100})$ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$ .

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	1.06738	−	0.140524i	0.754753	−	0.0993651i	0.256676	−	0.966498i	$-0.417373\pi$
$2$	1.06738	−	0.140524i	0.754753	−	0.0993651i	0.498078	+	0.867132i	$0.334039\pi$
$3$	−0.442289	−	0.896873i	−0.255355	−	0.517810i
$3$	−0.442289	−	0.896873i	−0.255355	−	0.517810i
$4$	−0.812294	+	0.217654i	−0.406147	+	0.108827i
$5$	−2.05370	+	1.80104i	−0.918441	+	0.805451i	−0.981283	−	0.192572i	$-0.938317\pi$
$5$	−2.05370	+	1.80104i	−0.918441	+	0.805451i	0.0628419	+	0.998023i	$0.479984\pi$
$6$	−0.598123	−	0.895154i	−0.244183	−	0.365445i
$7$	−0.418160	−	2.61250i	−0.158050	−	0.987431i
$7$	−0.418160	−	2.61250i	−0.158050	−	0.987431i
$8$	−2.82573	+	1.17045i	−0.999045	+	0.413818i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	−1.93899	+	2.21099i	−0.613162	+	0.699178i
$11$	−1.62437	+	0.106467i	−0.489767	+	0.0321010i	−0.308287	−	0.951293i	$-0.599756\pi$
$11$	−1.62437	+	0.106467i	−0.489767	+	0.0321010i	−0.181481	+	0.983395i	$0.558089\pi$
$12$	0.554476	+	0.632259i	0.160063	+	0.182517i
$13$	−3.58990	−	3.58990i	−0.995660	−	0.995660i	0.00433028	−	0.999991i	$-0.498622\pi$
$13$	−3.58990	−	3.58990i	−0.995660	−	0.995660i	−0.999991	+	0.00433028i	$0.998622\pi$
$14$	−0.813454	−	2.72977i	−0.217405	−	0.729562i
$15$	2.52363	+	1.04532i	0.651599	+	0.269901i
$16$	−1.39509	+	0.805454i	−0.348772	+	0.201364i
$17$	−3.46096	+	2.24093i	−0.839405	+	0.543506i
$17$	−3.46096	+	2.24093i	−0.839405	+	0.543506i
$18$	−0.538296	+	0.932356i	−0.126878	+	0.219759i
$19$	0.0797791	+	0.605982i	0.0183026	+	0.139022i	0.998156	−	0.0606941i	$-0.0193314\pi$
$19$	0.0797791	+	0.605982i	0.0183026	+	0.139022i	−0.979854	+	0.199716i	$0.935998\pi$
$20$	1.27620	−	1.90997i	0.285367	−	0.427082i
$21$	−2.15813	+	1.53051i	−0.470943	+	0.333986i
$22$	−1.71887	+	0.341904i	−0.366464	+	0.0728942i
$23$	2.88199	+	1.42124i	0.600936	+	0.296349i	0.717198	−	0.696870i	$-0.245424\pi$
$23$	2.88199	+	1.42124i	0.600936	+	0.296349i	−0.116261	+	0.993219i	$0.537091\pi$
$24$	2.29954	+	2.01664i	0.469391	+	0.411645i
$25$	0.321280	−	2.44037i	0.0642561	−	0.488073i
$26$	−4.33627	−	3.32733i	−0.850412	−	0.652544i
$27$	0.980785	+	0.195090i	0.188752	+	0.0375451i
$28$	0.908288	+	2.03110i	0.171650	+	0.383842i
$29$	0.0592767	+	0.298004i	0.0110074	+	0.0553380i	0.985899	−	0.167344i	$-0.0535189\pi$
$29$	0.0592767	+	0.298004i	0.0110074	+	0.0553380i	−0.974891	+	0.222682i	$0.928519\pi$
$30$	2.84057	+	0.761129i	0.518615	+	0.138963i
$31$	−2.75512	+	1.35867i	−0.494834	+	0.244025i	−0.672543	−	0.740058i	$-0.734798\pi$
$31$	−2.75512	+	1.35867i	−0.494834	+	0.244025i	0.177709	+	0.984083i	$0.443131\pi$
$32$	3.47711	−	2.66808i	0.614671	−	0.471654i
$33$	0.813930	+	1.40977i	0.141687	+	0.245409i
$34$	−3.37926	+	2.87828i	−0.579538	+	0.493620i
$35$	5.56399	+	4.61215i	0.940487	+	0.779596i
$36$	0.321817	−	0.776935i	0.0536362	−	0.129489i
$37$	0.441226	−	6.73180i	0.0725371	−	1.10670i	−0.794108	−	0.607777i	$-0.792062\pi$
$37$	0.441226	−	6.73180i	0.0725371	−	1.10670i	0.866645	−	0.498925i	$-0.166272\pi$
$38$	0.170309	+	0.635604i	0.0276278	+	0.103109i
$39$	−1.63191	+	4.80746i	−0.261315	+	0.769810i
$40$	3.69514	−	7.49301i	0.584254	−	1.18475i
$41$	2.11733	−	10.6445i	0.330672	−	1.66240i	−0.355287	−	0.934757i	$-0.615617\pi$
$41$	2.11733	−	10.6445i	0.330672	−	1.66240i	0.685958	−	0.727641i	$-0.259383\pi$
$42$	−2.08848	+	1.93691i	−0.322259	+	0.298872i
$43$	3.59946	+	8.68987i	0.548913	+	1.32519i	0.918288	+	0.395912i	$0.129572\pi$
$43$	3.59946	+	8.68987i	0.548913	+	1.32519i	−0.369376	+	0.929280i	$0.620428\pi$
$44$	1.29630	−	0.440033i	0.195424	−	0.0663375i
$45$	−0.178653	−	2.72571i	−0.0266320	−	0.406325i
$46$	3.27590	+	1.11202i	0.483005	+	0.163958i
$47$	−0.122970	+	0.458931i	−0.0179370	+	0.0669419i	−0.974314	−	0.225193i	$-0.927699\pi$
$47$	−0.122970	+	0.458931i	−0.0179370	+	0.0669419i	0.956377	+	0.292135i	$0.0943655\pi$
$48$	1.33942	+	0.894973i	0.193329	+	0.129178i
$49$	−6.65028	+	2.18489i	−0.950041	+	0.312126i
$50$		−	2.64995i		−	0.374760i
$51$	3.54057	+	2.11290i	0.495779	+	0.295865i
$52$	3.69741	+	2.13470i	0.512739	+	0.296030i
$53$	6.67624	+	8.70065i	0.917053	+	1.19513i	0.980377	+	0.197133i	$0.0631632\pi$
$53$	6.67624	+	8.70065i	0.917053	+	1.19513i	−0.0633241	+	0.997993i	$0.520170\pi$
$54$	1.07429	+	0.0704125i	0.146192	+	0.00958193i
$55$	3.14422	−	3.14422i	0.423966	−	0.423966i
$56$	4.23941	+	6.89276i	0.566516	+	0.921084i
$57$	0.508204	−	0.339571i	0.0673132	−	0.0449772i
$58$	0.105148	+	0.309755i	0.0138065	+	0.0406728i
$59$	−6.53848	−	0.860807i	−0.851237	−	0.112068i	−0.307732	−	0.951473i	$-0.599570\pi$
$59$	−6.53848	−	0.860807i	−0.851237	−	0.112068i	−0.543505	+	0.839406i	$0.682903\pi$
$60$	−2.27745	−	0.299832i	−0.294018	−	0.0387081i
$61$	−2.28082	−	6.71907i	−0.292029	−	0.860289i	−0.989609	−	0.143783i	$-0.954073\pi$
$61$	−2.28082	−	6.71907i	−0.292029	−	0.860289i	0.697580	−	0.716506i	$-0.254260\pi$
$62$	−2.74984	+	1.83738i	−0.349230	+	0.233348i
$63$	2.32719	+	1.25864i	0.293199	+	0.158574i
$64$	5.61464	−	5.61464i	0.701830	−	0.701830i
$65$	13.8381	+	0.907000i	1.71641	+	0.112500i
$66$	1.06688	+	1.39038i	0.131324	+	0.171145i
$67$	−9.18527	−	5.30312i	−1.12216	−	0.647879i	−0.180208	−	0.983628i	$-0.557677\pi$
$67$	−9.18527	−	5.30312i	−1.12216	−	0.647879i	−0.941951	+	0.335749i	$0.891010\pi$
$68$	2.32357	−	2.57359i	0.281774	−	0.312093i
$69$		−	3.21338i		−	0.386845i
$70$	6.58702	+	4.14106i	0.787300	+	0.494951i
$71$	−5.90931	−	3.94848i	−0.701306	−	0.468598i	0.153095	−	0.988211i	$-0.451076\pi$
$71$	−5.90931	−	3.94848i	−0.701306	−	0.468598i	−0.854401	+	0.519614i	$0.826076\pi$
$72$	0.791609	−	2.95433i	0.0932921	−	0.348171i
$73$	−13.8613	−	4.70526i	−1.62234	−	0.550709i	−0.645328	−	0.763906i	$-0.723279\pi$
$73$	−13.8613	−	4.70526i	−1.62234	−	0.550709i	−0.977009	+	0.213196i	$0.931613\pi$
$74$	−0.475020	−	7.24741i	−0.0552200	−	0.842494i
$75$	−2.33080	+	0.791199i	−0.269137	+	0.0913598i
$76$	−0.196698	−	0.474872i	−0.0225628	−	0.0544715i
$77$	0.957394	+	4.19915i	0.109105	+	0.478538i
$78$	−1.06631	+	5.36072i	−0.120736	+	0.606982i
$79$	3.95195	−	8.01377i	0.444629	−	0.901619i	−0.553025	−	0.833165i	$-0.686527\pi$
$79$	3.95195	−	8.01377i	0.444629	−	0.901619i	0.997654	−	0.0684545i	$-0.0218068\pi$
$80$	1.41443	−	4.16677i	0.158138	−	0.465859i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	0.764193	−	11.6593i	0.0843910	−	1.28756i
$83$	−4.06472	+	9.81309i	−0.446161	+	1.07713i	0.527588	+	0.849500i	$0.323097\pi$
$83$	−4.06472	+	9.81309i	−0.446161	+	1.07713i	−0.973748	+	0.227627i	$0.926903\pi$
$84$	1.41991	−	1.71295i	0.154925	−	0.186898i
$85$	3.07174	−	10.8355i	0.333177	−	1.17528i
$86$	5.06313	+	8.76960i	0.545971	+	0.945650i
$87$	0.241054	−	0.184968i	0.0258437	−	0.0198306i
$88$	4.46542	−	2.20210i	0.476016	−	0.234745i
$89$	−6.14547	−	1.64667i	−0.651418	−	0.174547i	−0.0820482	−	0.996628i	$-0.526146\pi$
$89$	−6.14547	−	1.64667i	−0.651418	−	0.174547i	−0.569370	+	0.822081i	$0.692813\pi$
$90$	−0.573717	−	2.88427i	−0.0604751	−	0.304029i
$91$	−7.87746	+	10.8798i	−0.825782	+	1.14051i
$92$	−2.65036	−	0.527190i	−0.276319	−	0.0549633i
$93$	2.43711	+	1.87006i	0.252717	+	0.193917i
$94$	−0.0667655	+	0.507135i	−0.00688634	+	0.0523069i
$95$	−1.25524	−	1.10082i	−0.128785	−	0.112942i
$96$	−3.93081	−	1.93846i	−0.401187	−	0.197843i
$97$	15.6375	−	3.11049i	1.58775	−	0.315823i	0.679313	−	0.733848i	$-0.262278\pi$
$97$	15.6375	−	3.11049i	1.58775	−	0.315823i	0.908435	+	0.418025i	$0.137278\pi$
$98$	−6.79137	+	3.26663i	−0.686032	+	0.329979i
$99$	0.904390	−	1.35352i	0.0908947	−	0.136033i
$100$	0.270180	+	2.05222i	0.0270180	+	0.205222i
$101$	−7.01890	+	12.1571i	−0.698406	+	1.20968i	0.270613	+	0.962688i	$0.412774\pi$
$101$	−7.01890	+	12.1571i	−0.698406	+	1.20968i	−0.969019	+	0.246987i	$0.920560\pi$
$102$	4.07606	+	1.75774i	0.403590	+	0.174042i
$103$	−3.28060	+	1.89405i	−0.323247	+	0.186627i	−0.652839	−	0.757497i	$-0.726422\pi$
$103$	−3.28060	+	1.89405i	−0.323247	+	0.186627i	0.329592	+	0.944123i	$0.393089\pi$
$104$	14.3459	+	5.94227i	1.40673	+	0.582687i
$105$	1.67562	−	7.03010i	0.163524	−	0.686067i
$106$	8.34875	+	8.34875i	0.810902	+	0.810902i
$107$	4.39512	+	5.01167i	0.424892	+	0.484496i	0.924190	−	0.381934i	$-0.124742\pi$
$107$	4.39512	+	5.01167i	0.424892	+	0.484496i	−0.499298	+	0.866431i	$0.666409\pi$
$108$	−0.839148	+	0.0550007i	−0.0807471	+	0.00529244i
$109$	−9.60222	+	10.9492i	−0.919726	+	1.04875i	0.0789281	+	0.996880i	$0.474850\pi$
$109$	−9.60222	+	10.9492i	−0.919726	+	1.04875i	−0.998654	+	0.0518661i	$0.983483\pi$
$110$	2.91425	−	3.79792i	0.277863	−	0.362118i
$111$	−6.23272	+	2.58168i	−0.591584	+	0.245042i
$112$	2.68762	+	3.30785i	0.253956	+	0.312563i
$113$	7.56453	+	11.3211i	0.711611	+	1.06500i	0.994386	+	0.105815i	$0.0337450\pi$
$113$	7.56453	+	11.3211i	0.711611	+	1.06500i	−0.282775	+	0.959186i	$0.591255\pi$
$114$	0.494730	−	0.433866i	0.0463357	−	0.0406353i
$115$	−8.47845	+	2.27179i	−0.790619	+	0.211846i
$116$	−0.113012	−	0.229165i	−0.0104929	−	0.0212775i
$117$	5.03346	−	0.662667i	0.465343	−	0.0612636i
$118$	−7.10002			−0.653610
$119$	7.30166	+	8.10467i	0.669342	+	0.742954i
$120$	−8.35460			−0.762667
$121$	−8.27864	+	1.08990i	−0.752603	+	0.0990821i
$122$	−3.37869	−	6.85131i	−0.305892	−	0.620288i
$123$	−10.4833	+	2.80898i	−0.945245	+	0.253278i
$124$	1.94224	−	1.70330i	0.174419	−	0.152961i
$125$	−3.85248	−	5.76564i	−0.344576	−	0.515694i
$126$	2.66087	+	1.01642i	0.237049	+	0.0905502i
$127$	9.07043	−	3.75710i	0.804871	−	0.333388i	0.0579651	−	0.998319i	$-0.481539\pi$
$127$	9.07043	−	3.75710i	0.804871	−	0.333388i	0.746905	+	0.664930i	$0.231539\pi$
$128$	−0.132177	+	0.172256i	−0.0116829	+	0.0152254i
$129$	6.20170	−	7.07169i	0.546030	−	0.622627i
$130$	14.8980	−	0.976469i	1.30664	−	0.0856420i
$131$	5.09400	+	5.80860i	0.445065	+	0.507499i	0.930257	−	0.366908i	$-0.119584\pi$
$131$	5.09400	+	5.80860i	0.445065	+	0.507499i	−0.485192	+	0.874408i	$0.661250\pi$
$132$	−0.967991	−	0.967991i	−0.0842528	−	0.0842528i
$133$	1.54977	−	0.461820i	0.134382	−	0.0400449i
$134$	−10.5494	−	4.36971i	−0.911330	−	0.377485i
$135$	−2.36560	+	1.36578i	−0.203599	+	0.117548i
$136$	7.15681	−	10.3832i	0.613691	−	0.890348i
$137$	6.56514	−	11.3712i	0.560898	−	0.971503i	−0.436521	−	0.899694i	$-0.643789\pi$
$137$	6.56514	−	11.3712i	0.560898	−	0.971503i	0.997418	−	0.0718092i	$-0.0228773\pi$
$138$	−0.451555	−	3.42990i	−0.0384389	−	0.291972i
$139$	−2.30819	+	3.45445i	−0.195778	+	0.293003i	−0.916350	−	0.400377i	$-0.868879\pi$
$139$	−2.30819	+	3.45445i	−0.195778	+	0.293003i	0.720572	+	0.693380i	$0.243879\pi$
$140$	−5.52345	−	2.53540i	−0.466817	−	0.214280i
$141$	0.465991	−	0.0926913i	0.0392435	−	0.00780602i
$142$	−6.86235	−	3.38413i	−0.575875	−	0.283990i
$143$	6.21356	+	5.44914i	0.519604	+	0.455680i
$144$	0.210266	−	1.59713i	0.0175221	−	0.133094i
$145$	−0.658455	−	0.505250i	−0.0546817	−	0.0419587i
$146$	−15.4565	−	3.07448i	−1.27919	−	0.254446i
$147$	4.90091	+	4.99811i	0.404220	+	0.412237i
$148$	1.10680	+	5.56424i	0.0909780	+	0.457378i
$149$	−9.57864	−	2.56659i	−0.784713	−	0.210263i	−0.155851	−	0.987781i	$-0.549812\pi$
$149$	−9.57864	−	2.56659i	−0.784713	−	0.210263i	−0.628861	+	0.777517i	$0.716479\pi$
$150$	−2.37667	+	1.17204i	−0.194054	+	0.0956970i
$151$	−8.06036	+	6.18493i	−0.655943	+	0.503323i	−0.882279	−	0.470727i	$-0.843992\pi$
$151$	−8.06036	+	6.18493i	−0.655943	+	0.503323i	0.226336	+	0.974049i	$0.427325\pi$
$152$	−0.934708	−	1.61896i	−0.0758148	−	0.131315i
$153$	0.329046	−	4.10995i	0.0266018	−	0.332270i
$154$	1.61198	+	4.34756i	0.129897	+	0.350337i
$155$	3.21114	−	7.75239i	0.257925	−	0.622687i
$156$	0.279232	−	4.26026i	0.0223565	−	0.341094i
$157$	−0.126558	−	0.472319i	−0.0101004	−	0.0376952i	0.960692	−	0.277617i	$-0.0895447\pi$
$157$	−0.126558	−	0.472319i	−0.0101004	−	0.0376952i	−0.970792	+	0.239922i	$0.922878\pi$
$158$	3.09212	−	9.10909i	0.245996	−	0.724681i
$159$	4.85055	−	9.83594i	0.384674	−	0.780041i
$160$	−2.33560	+	11.7418i	−0.184645	+	0.928274i
$161$	2.50785	−	8.12350i	0.197646	−	0.640221i
$162$	−0.411994	−	0.994642i	−0.0323693	−	0.0781464i
$163$	−3.20912	+	1.08935i	−0.251357	+	0.0853244i	−0.444274	−	0.895891i	$-0.646539\pi$
$163$	−3.20912	+	1.08935i	−0.251357	+	0.0853244i	0.192917	+	0.981215i	$0.438205\pi$
$164$	0.596927	+	9.10734i	0.0466121	+	0.711164i
$165$	−4.21062	−	1.42931i	−0.327796	−	0.111272i
$166$	−2.95964	+	11.0455i	−0.229712	+	0.857298i
$167$	−4.66260	−	3.11545i	−0.360803	−	0.241081i	0.361934	−	0.932204i	$-0.382116\pi$
$167$	−4.66260	−	3.11545i	−0.360803	−	0.241081i	−0.722737	+	0.691123i	$0.757116\pi$
$168$	4.30689	−	6.85081i	0.332284	−	0.528551i
$169$			12.7748i			0.982679i
$170$	1.75607	−	11.9973i	0.134685	−	0.920151i
$171$	−0.529324	−	0.305606i	−0.0404784	−	0.0233702i
$172$	−4.81520	−	6.27529i	−0.367156	−	0.478486i
$173$	−0.197046	−	0.0129151i	−0.0149811	−	0.000981916i	0.0579107	−	0.998322i	$-0.481556\pi$
$173$	−0.197046	−	0.0129151i	−0.0149811	−	0.000981916i	−0.0728919	+	0.997340i	$0.523223\pi$
$174$	0.231305	−	0.231305i	0.0175352	−	0.0175352i
$175$	−6.50980	+	0.181120i	−0.492095	+	0.0136914i
$176$	2.18039	−	1.45689i	0.164353	−	0.109817i
$177$	2.11986	+	6.24491i	0.159338	+	0.469396i
$178$	−6.79096	−	0.894046i	−0.509004	−	0.0670116i
$179$	−15.2629	−	2.00940i	−1.14080	−	0.150190i	−0.463641	−	0.886023i	$-0.653457\pi$
$179$	−15.2629	−	2.00940i	−1.14080	−	0.150190i	−0.677163	+	0.735833i	$0.736791\pi$
$180$	0.738379	+	2.17520i	0.0550355	+	0.162130i
$181$	−0.773096	+	0.516566i	−0.0574638	+	0.0383961i	−0.583970	−	0.811775i	$-0.698502\pi$
$181$	−0.773096	+	0.516566i	−0.0574638	+	0.0383961i	0.526507	+	0.850171i	$0.323502\pi$
$182$	−6.87940	+	12.7198i	−0.509935	+	0.942857i
$183$	−5.01737	+	5.01737i	−0.370895	+	0.370895i
$184$	−9.80721	−	0.642798i	−0.722997	−	0.0473877i
$185$	11.2181	+	14.6197i	0.824773	+	1.07487i
$186$	2.86412	+	1.65360i	0.210007	+	0.121248i
$187$	5.38330	−	4.00859i	0.393666	−	0.293137i
$188$		−	0.399552i		−	0.0291403i
$189$	0.0995475	−	2.64388i	0.00724101	−	0.192314i
$190$	−1.49451	−	0.998602i	−0.108423	−	0.0724462i
$191$	2.91687	−	10.8859i	0.211057	−	0.787677i	−0.776460	−	0.630167i	$-0.782987\pi$
$191$	2.91687	−	10.8859i	0.211057	−	0.787677i	0.987517	−	0.157510i	$-0.0503468\pi$
$192$	−7.51891	−	2.55233i	−0.542631	−	0.184198i
$193$	−0.999782	−	15.2537i	−0.0719659	−	1.09799i	−0.869247	−	0.494378i	$-0.835396\pi$
$193$	−0.999782	−	15.2537i	−0.0719659	−	1.09799i	0.797281	−	0.603608i	$-0.206271\pi$
$194$	16.2541	−	5.51752i	1.16698	−	0.396135i
$195$	−5.30699	−	12.8122i	−0.380042	−	0.917502i
$196$	4.92644	−	3.22223i	0.351888	−	0.230159i
$197$	0.121950	−	0.613082i	0.00868855	−	0.0436803i	−0.976198	−	0.216882i	$-0.930411\pi$
$197$	0.121950	−	0.613082i	0.00868855	−	0.0436803i	0.984886	+	0.173202i	$0.0554113\pi$
$198$	0.775129	−	1.57181i	0.0550860	−	0.111703i
$199$	6.87602	−	20.2561i	0.487428	−	1.43592i	−0.373709	−	0.927546i	$-0.621914\pi$
$199$	6.87602	−	20.2561i	0.487428	−	1.43592i	0.861138	−	0.508372i	$-0.169752\pi$
$200$	1.94849	+	7.27185i	0.137779	+	0.514198i
$201$	−0.693681	+	10.5835i	−0.0489285	+	0.746505i
$202$	−5.78349	+	13.9626i	−0.406925	+	0.982403i
$203$	0.753748	−	0.279474i	0.0529027	−	0.0196152i
$204$	−3.33587	−	0.945677i	−0.233557	−	0.0662106i
$205$	14.8229	+	25.6741i	1.03528	+	1.79315i
$206$	−3.23549	+	2.48268i	−0.225427	+	0.172977i
$207$	−2.88199	+	1.42124i	−0.200312	+	0.0987830i
$208$	7.89973	+	2.11673i	0.547748	+	0.146769i
$209$	−0.194108	−	0.975848i	−0.0134267	−	0.0675008i
$210$	0.800633	−	7.73926i	0.0552489	−	0.534060i
$211$	−13.2836	−	2.64227i	−0.914481	−	0.181902i	−0.284648	−	0.958632i	$-0.591877\pi$
$211$	−13.2836	−	2.64227i	−0.914481	−	0.181902i	−0.629833	+	0.776730i	$0.716877\pi$
$212$	−7.31680	−	5.61438i	−0.502520	−	0.385597i
$213$	−0.927658	+	7.04627i	−0.0635621	+	0.482802i
$214$	5.39553	+	4.73175i	0.368831	+	0.323456i
$215$	−23.0430	−	11.3636i	−1.57152	−	0.774989i
$216$	−2.99977	+	0.596692i	−0.204109	+	0.0405998i
$217$	4.70161	+	6.62959i	0.319166	+	0.450046i
$218$	−8.71061	+	13.0364i	−0.589957	+	0.882933i
$219$	1.91066	+	14.5129i	0.129110	+	0.980689i
$220$	−1.86968	+	3.23838i	−0.126054	+	0.218332i
$221$	20.4692	+	4.37977i	1.37691	+	0.294615i
$222$	−6.28991	+	3.63148i	−0.422151	+	0.243729i
$223$	24.3084	+	10.0689i	1.62781	+	0.674262i	0.994984	−	0.100030i	$-0.0318938\pi$
$223$	24.3084	+	10.0689i	1.62781	+	0.674262i	0.632829	+	0.774292i	$0.281894\pi$
$224$	−8.42433	−	7.96825i	−0.562874	−	0.532401i
$225$	1.74049	+	1.74049i	0.116033	+	0.116033i
$226$	9.66512	+	11.0210i	0.642914	+	0.733103i
$227$	−12.4476	+	0.815857i	−0.826174	+	0.0541503i	−0.472623	−	0.881265i	$-0.656693\pi$
$227$	−12.4476	+	0.815857i	−0.826174	+	0.0541503i	−0.353551	+	0.935415i	$0.615026\pi$
$228$	−0.338902	+	0.386444i	−0.0224443	+	0.0255929i
$229$	6.00315	−	7.82346i	0.396700	−	0.516989i	−0.551710	−	0.834036i	$-0.686025\pi$
$229$	6.00315	−	7.82346i	0.396700	−	0.516989i	0.948410	+	0.317047i	$0.102691\pi$
$230$	−8.73050	+	3.61629i	−0.575672	+	0.238451i
$231$	3.34266	−	2.71590i	0.219931	−	0.178693i
$232$	−0.516300	−	0.772698i	−0.0338968	−	0.0507301i
$233$	3.02947	−	2.65677i	0.198467	−	0.174051i	−0.554344	−	0.832288i	$-0.687031\pi$
$233$	3.02947	−	2.65677i	0.198467	−	0.174051i	0.752811	+	0.658237i	$0.228697\pi$
$234$	5.27950	−	1.41464i	0.345132	−	0.0924778i
$235$	−0.574011	−	1.16398i	−0.0374443	−	0.0759296i
$236$	5.49852	−	0.723894i	0.357923	−	0.0471215i
$237$	−8.93523			−0.580406
$238$	8.93256	+	7.62473i	0.579012	+	0.494238i
$239$	−16.2133			−1.04875			−0.524376	−	0.851487i	$-0.675701\pi$
$239$	−16.2133			−1.04875			−0.524376	+	0.851487i	$0.675701\pi$
$240$	−4.36265	+	0.574354i	−0.281608	+	0.0370744i
$241$	0.0981533	+	0.199035i	0.00632261	+	0.0128210i	0.900011	−	0.435867i	$-0.143558\pi$
$241$	0.0981533	+	0.199035i	0.00632261	+	0.0128210i	−0.893689	+	0.448688i	$0.851891\pi$
$242$	−8.68331	+	2.32669i	−0.558184	+	0.149565i
$243$	−0.751840	+	0.659346i	−0.0482305	+	0.0422971i
$244$	3.31512	+	4.96143i	0.212229	+	0.317623i
$245$	9.72259	−	16.4645i	0.621153	−	1.05188i
$246$	−10.7949	+	4.47140i	−0.688259	+	0.285086i
$247$	1.88902	−	2.46182i	0.120195	−	0.156642i
$248$	6.19494	−	7.06398i	0.393379	−	0.448563i
$249$	10.5989	−	0.694687i	0.671676	−	0.0440240i
$250$	−4.92227	−	5.61277i	−0.311312	−	0.354983i
$251$	−19.1998	−	19.1998i	−1.21188	−	1.21188i	−0.970407	−	0.241477i	$-0.922368\pi$
$251$	−19.1998	−	19.1998i	−1.21188	−	1.21188i	−0.241477	−	0.970407i	$-0.577632\pi$
$252$	−2.16431	−	0.515863i	−0.136339	−	0.0324963i
$253$	−4.83275	−	2.00179i	−0.303832	−	0.125851i
$254$	9.15365	−	5.28486i	0.574351	−	0.331602i
$255$	−11.0767	+	2.03747i	−0.693649	+	0.127591i
$256$	−8.05718	+	13.9554i	−0.503574	+	0.872215i
$257$	−0.723200	−	5.49325i	−0.0451120	−	0.342660i	−0.999085	−	0.0427673i	$-0.986383\pi$
$257$	−0.723200	−	5.49325i	−0.0451120	−	0.342660i	0.953973	−	0.299892i	$-0.0969508\pi$
$258$	5.62585	−	8.41968i	0.350250	−	0.524186i
$259$	−17.7713	+	1.66227i	−1.10426	+	0.103289i
$260$	−11.4381	+	2.27517i	−0.709358	+	0.141100i
$261$	−0.272508	−	0.134386i	−0.0168678	−	0.00831829i
$262$	6.25349	+	5.48416i	0.386342	+	0.338813i
$263$	0.546239	−	4.14910i	0.0336826	−	0.255844i	−0.966316	−	0.257357i	$-0.917148\pi$
$263$	0.546239	−	4.14910i	0.0336826	−	0.255844i	0.999999	+	0.00151295i	$0.000481587\pi$
$264$	−3.95001	−	3.03095i	−0.243106	−	0.186542i
$265$	−29.3812	−	5.84429i	−1.80487	−	0.359012i
$266$	1.58930	−	0.710717i	0.0974460	−	0.0435769i
$267$	1.24121	+	6.24001i	0.0759611	+	0.381882i
$268$	8.61538	+	2.30849i	0.526268	+	0.141013i
$269$	5.08747	−	2.50886i	0.310189	−	0.152968i	−0.280531	−	0.959845i	$-0.590511\pi$
$269$	5.08747	−	2.50886i	0.310189	−	0.152968i	0.590720	+	0.806877i	$0.298844\pi$
$270$	−2.33308	+	1.79023i	−0.141986	+	0.108950i
$271$	12.5445	+	21.7278i	0.762027	+	1.31987i	0.941804	+	0.336162i	$0.109129\pi$
$271$	12.5445	+	21.7278i	0.762027	+	1.31987i	−0.179777	+	0.983707i	$0.557538\pi$
$272$	3.02337	−	5.91394i	0.183319	−	0.358585i
$273$	13.2419	+	2.25308i	0.801435	+	0.136363i
$274$	5.40960	−	13.0599i	0.326806	−	0.788979i
$275$	−0.262061	+	3.99828i	−0.0158029	+	0.241105i
$276$	0.699403	+	2.61021i	0.0420991	+	0.157116i
$277$	7.47659	−	22.0253i	0.449225	−	1.32337i	−0.452771	−	0.891627i	$-0.649564\pi$
$277$	7.47659	−	22.0253i	0.449225	−	1.32337i	0.901995	−	0.431746i	$-0.142102\pi$
$278$	−1.97829	+	4.01158i	−0.118650	+	0.240598i
$279$	0.599301	−	3.01289i	0.0358792	−	0.180377i
$280$	−21.1206	−	6.52027i	−1.26220	−	0.389661i
$281$	2.62040	+	6.32620i	0.156320	+	0.377389i	0.982565	−	0.185922i	$-0.0595272\pi$
$281$	2.62040	+	6.32620i	0.156320	+	0.377389i	−0.826245	+	0.563311i	$0.809527\pi$
$282$	0.484365	−	0.164420i	0.0288435	−	0.00979105i
$283$	1.36394	+	20.8096i	0.0810776	+	1.23700i	0.823595	+	0.567178i	$0.191965\pi$
$283$	1.36394	+	20.8096i	0.0810776	+	1.23700i	−0.742518	+	0.669827i	$0.766368\pi$
$284$	5.65950	+	1.92114i	0.335829	+	0.113999i
$285$	−0.432114	+	1.61267i	−0.0255962	+	0.0955264i
$286$	7.39797	+	4.94317i	0.437451	+	0.292296i
$287$	−28.6942	−	1.08040i	−1.69377	−	0.0637738i
$288$			4.38280i			0.258259i
$289$	6.95645	−	15.5115i	0.409203	−	0.912443i
$290$	−0.773822	−	0.446767i	−0.0454404	−	0.0262350i
$291$	−9.70601	−	12.6491i	−0.568976	−	0.741505i
$292$	12.2835	+	0.805105i	0.718839	+	0.0471152i
$293$	10.5579	−	10.5579i	0.616800	−	0.616800i	−0.327909	−	0.944709i	$-0.606344\pi$
$293$	10.5579	−	10.5579i	0.616800	−	0.616800i	0.944709	+	0.327909i	$0.106344\pi$
$294$	5.93349	+	4.64620i	0.346048	+	0.270972i
$295$	14.9784	−	10.0082i	0.872076	−	0.582703i
$296$	6.63248	+	19.5387i	0.385505	+	1.13566i
$297$	−1.61393	−	0.212478i	−0.0936499	−	0.0123292i
$298$	−10.5847	−	1.39351i	−0.613157	−	0.0807237i
$299$	−5.24395	−	15.4482i	−0.303266	−	0.893391i
$300$	1.72109	−	1.14999i	0.0993669	−	0.0663948i
$301$	21.1971	−	13.0373i	1.22178	−	0.751460i
$302$	−7.73435	+	7.73435i	−0.445062	+	0.445062i
$303$	14.0077	+	0.918116i	0.804723	+	0.0527444i
$304$	−0.599390	−	0.781140i	−0.0343773	−	0.0448014i
$305$	16.7854	+	9.69108i	0.961132	+	0.554910i
$306$	−0.226327	−	4.43313i	−0.0129383	−	0.253425i
$307$			25.5492i			1.45817i	0.684424	+	0.729085i	$0.260054\pi$
$307$			25.5492i			1.45817i	−0.684424	+	0.729085i	$0.739946\pi$
$308$	−1.69165	−	3.20257i	−0.0963905	−	0.182483i
$309$	3.14970	+	2.10456i	0.179180	+	0.119724i
$310$	2.33812	−	8.72600i	0.132797	−	0.495603i
$311$	17.6970	+	6.00732i	1.00350	+	0.340644i	0.774358	−	0.632748i	$-0.218073\pi$
$311$	17.6970	+	6.00732i	1.00350	+	0.340644i	0.229147	+	0.973392i	$0.426406\pi$
$312$	−1.01557	−	15.4946i	−0.0574955	−	0.877212i
$313$	−22.4034	+	7.60495i	−1.26632	+	0.429857i	−0.872176	−	0.489193i	$-0.837292\pi$
$313$	−22.4034	+	7.60495i	−1.26632	+	0.429857i	−0.394142	+	0.919050i	$0.628958\pi$
$314$	−0.201457	−	0.486361i	−0.0113689	−	0.0274469i
$315$	−7.04621	+	1.60651i	−0.397009	+	0.0905168i
$316$	−1.46592	+	7.36969i	−0.0824646	+	0.414578i
$317$	5.65916	−	11.4756i	0.317850	−	0.644537i	−0.678048	−	0.735018i	$-0.737174\pi$
$317$	5.65916	−	11.4756i	0.317850	−	0.644537i	0.995898	+	0.0904811i	$0.0288405\pi$
$318$	3.79521	−	11.1803i	0.212825	−	0.626961i
$319$	−0.128015	−	0.477759i	−0.00716748	−	0.0267494i
$320$	−1.41856	+	21.6430i	−0.0792997	+	1.20988i
$321$	2.55092	−	6.15847i	0.142378	−	0.343732i
$322$	1.53529	−	9.02329i	0.0855586	−	0.502848i
$323$	−1.63408	−	1.91850i	−0.0909225	−	0.106748i
$324$	0.420474	+	0.728283i	0.0233597	+	0.0404602i
$325$	−9.91405	+	7.60732i	−0.549933	+	0.421978i
$326$	−3.27227	+	1.61371i	−0.181235	+	0.0893750i
$327$	14.0670	+	3.76925i	0.777908	+	0.208440i
$328$	6.47595	+	32.5568i	0.357574	+	1.79765i
$329$	1.25038	+	0.129352i	0.0689355	+	0.00713143i
$330$	−4.69519	−	0.933931i	−0.258462	−	0.0514112i
$331$	−11.7704	−	9.03173i	−0.646958	−	0.496429i	0.232381	−	0.972625i	$-0.425349\pi$
$331$	−11.7704	−	9.03173i	−0.646958	−	0.496429i	−0.879339	+	0.476196i	$0.842015\pi$
$332$	1.16589	−	8.85582i	0.0639866	−	0.486026i
$333$	5.07210	+	4.44811i	0.277949	+	0.243755i
$334$	−5.41457	−	2.67017i	−0.296272	−	0.146105i
$335$	28.4149	−	5.65208i	1.55247	−	0.308806i
$336$	1.77802	−	3.87348i	0.0969990	−	0.211315i
$337$	2.95414	−	4.42119i	0.160922	−	0.240837i	−0.742242	−	0.670132i	$-0.766238\pi$
$337$	2.95414	−	4.42119i	0.160922	−	0.240837i	0.903165	+	0.429294i	$0.141238\pi$
$338$	1.79516	+	13.6356i	0.0976440	+	0.741680i
$339$	6.80789	−	11.7916i	0.369754	−	0.640433i
$340$	−0.136765	+	9.47021i	−0.00741710	+	0.513594i
$341$	4.33069	−	2.50032i	0.234520	−	0.135400i
$342$	−0.607936	−	0.251815i	−0.0328734	−	0.0136166i
$343$	8.48889	+	16.4602i	0.458357	+	0.888768i
$344$	−20.3422	−	20.3422i	−1.09678	−	1.09678i
$345$	5.78743	+	6.59930i	0.311585	+	0.355294i
$346$	−0.212138	+	0.0139043i	−0.0114046	+	0.000747499i
$347$	−18.9863	+	21.6498i	−1.01924	+	1.16222i	−0.0325723	+	0.999469i	$0.510370\pi$
$347$	−18.9863	+	21.6498i	−1.01924	+	1.16222i	−0.986667	+	0.162751i	$0.947963\pi$
$348$	−0.155548	+	0.202714i	−0.00833826	+	0.0108666i
$349$	14.3944	−	5.96236i	0.770515	−	0.319158i	0.0374341	−	0.999299i	$-0.488082\pi$
$349$	14.3944	−	5.96236i	0.770515	−	0.319158i	0.733081	+	0.680141i	$0.238082\pi$
$350$	−6.92299	+	1.10810i	−0.370049	+	0.0592307i
$351$	−2.82057	−	4.22128i	−0.150551	−	0.225315i
$352$	−5.36406	+	4.70415i	−0.285905	+	0.250732i
$353$	20.1026	−	5.38648i	1.06995	−	0.286693i	0.319480	−	0.947593i	$-0.396492\pi$
$353$	20.1026	−	5.38648i	1.06995	−	0.286693i	0.750474	+	0.660899i	$0.229825\pi$
$354$	3.14026	+	6.36781i	0.166903	+	0.338445i
$355$	19.2473	−	2.53396i	1.02154	−	0.134488i
$356$	5.35033			0.283567
$357$	4.03942	−	10.1333i	0.213789	−	0.536309i
$358$	−16.5737			−0.875949
$359$	6.95585	−	0.915754i	0.367115	−	0.0483317i	0.0552881	−	0.998470i	$-0.482392\pi$
$359$	6.95585	−	0.915754i	0.367115	−	0.0483317i	0.311827	+	0.950139i	$0.399059\pi$
$360$	3.69514	+	7.49301i	0.194751	+	0.394916i
$361$	17.9917	−	4.82087i	0.946934	−	0.253730i
$362$	−0.752599	+	0.660012i	−0.0395557	+	0.0346895i
$363$	4.63905	+	6.94283i	0.243487	+	0.364404i
$364$	4.03079	−	10.5521i	0.211271	−	0.553082i
$365$	36.9412	−	15.3015i	1.93359	−	0.800919i
$366$	−4.65040	+	6.06051i	−0.243080	+	0.316788i
$367$	19.2295	−	21.9270i	1.00377	−	1.14458i	0.0142923	−	0.999898i	$-0.495450\pi$
$367$	19.2295	−	21.9270i	1.00377	−	1.14458i	0.989478	−	0.144683i	$-0.0462162\pi$
$368$	−5.16537	+	0.338556i	−0.269264	+	0.0176485i
$369$	7.15593	+	8.15978i	0.372523	+	0.424781i
$370$	14.0284	+	14.0284i	0.729304	+	0.729304i
$371$	19.9387	−	21.0799i	1.03516	−	1.09442i
$372$	−2.38668	−	0.988595i	−0.123744	−	0.0512562i
$373$	−3.90231	+	2.25300i	−0.202054	+	0.116656i	−0.597613	−	0.801784i	$-0.703884\pi$
$373$	−3.90231	+	2.25300i	−0.202054	+	0.116656i	0.395559	+	0.918441i	$0.370551\pi$
$374$	5.18274	−	5.03518i	0.267993	−	0.260363i
$375$	−3.46714	+	6.00526i	−0.179042	+	0.310110i
$376$	−0.189677	−	1.44074i	−0.00978187	−	0.0743007i
$377$	0.857009	−	1.28260i	0.0441382	−	0.0660575i
$378$	−0.265272	−	2.83602i	−0.0136441	−	0.145869i
$379$	26.0722	−	5.18609i	1.33924	−	0.266392i	0.527076	−	0.849818i	$-0.323288\pi$
$379$	26.0722	−	5.18609i	1.33924	−	0.266392i	0.812166	+	0.583427i	$0.198288\pi$
$380$	1.25922	+	0.620980i	0.0645968	+	0.0318556i
$381$	−7.38138	−	6.47330i	−0.378160	−	0.331637i
$382$	1.58369	−	12.0293i	0.0810286	−	0.615474i
$383$	17.2187	+	13.2124i	0.879834	+	0.675121i	0.946517	−	0.322654i	$-0.104575\pi$
$383$	17.2187	+	13.2124i	0.879834	+	0.675121i	−0.0666828	+	0.997774i	$0.521242\pi$
$384$	0.212952	+	0.0423587i	0.0108671	+	0.00216161i
$385$	−9.52905	−	6.89948i	−0.485646	−	0.351630i
$386$	−3.21066	−	16.1411i	−0.163418	−	0.821558i
$387$	−9.08535	−	2.43441i	−0.461834	−	0.123748i
$388$	−12.0252	+	5.93020i	−0.610489	+	0.301060i
$389$	−19.5716	+	15.0178i	−0.992318	+	0.761432i	−0.971181	−	0.238344i	$-0.923395\pi$
$389$	−19.5716	+	15.0178i	−0.992318	+	0.761432i	−0.0211374	+	0.999777i	$0.506729\pi$
$390$	−7.46501	−	12.9298i	−0.378005	−	0.654724i
$391$	−13.1593	+	1.53949i	−0.665497	+	0.0778555i
$392$	16.2346	−	13.9577i	0.819970	−	0.704972i
$393$	2.95655	−	7.13775i	0.149138	−	0.360052i
$394$	0.0440144	−	0.671529i	0.00221741	−	0.0338312i
$395$	6.31703	+	23.5755i	0.317844	+	1.18621i
$396$	−0.440033	+	1.29630i	−0.0221125	+	0.0651414i
$397$	2.35970	−	4.78499i	0.118430	−	0.240152i	−0.829583	−	0.558383i	$-0.811422\pi$
$397$	2.35970	−	4.78499i	0.118430	−	0.240152i	0.948013	+	0.318231i	$0.103089\pi$
$398$	4.49288	−	22.5873i	0.225208	−	1.13220i
$399$	−1.09964	−	1.18569i	−0.0550508	−	0.0593585i
$400$	1.51739	+	3.66330i	0.0758695	+	0.183165i
$401$	−35.1624	+	11.9360i	−1.75593	+	0.596057i	−0.998389	−	0.0567351i	$-0.981931\pi$
$401$	−35.1624	+	11.9360i	−1.75593	+	0.596057i	−0.757537	+	0.652792i	$0.773598\pi$
$402$	0.746812	+	11.3941i	0.0372476	+	0.568288i
$403$	14.7681	+	5.01310i	0.735652	+	0.249720i
$404$	3.05537	−	11.4028i	0.152011	−	0.567311i
$405$	2.27121	+	1.51757i	0.112857	+	0.0754089i
$406$	0.765265	−	0.404225i	0.0379794	−	0.0200613i
$407$			10.9819i			0.544355i
$408$	−12.4777	−	1.82640i	−0.617740	−	0.0904201i
$409$	5.24713	+	3.02943i	0.259454	+	0.149796i	0.624086	−	0.781356i	$-0.285472\pi$
$409$	5.24713	+	3.02943i	0.259454	+	0.149796i	−0.364631	+	0.931152i	$0.618805\pi$
$410$	19.4295	+	25.3211i	0.959556	+	1.25052i
$411$	−13.1022	−	0.858761i	−0.646282	−	0.0423596i
$412$	2.25256	−	2.25256i	0.110976	−	0.110976i
$413$	0.485276	+	17.4417i	0.0238789	+	0.858250i
$414$	−2.87647	+	1.92199i	−0.141371	+	0.0944608i
$415$	−9.32611	−	27.4738i	−0.457801	−	1.34864i
$416$	−22.0606	−	2.90434i	−1.08161	−	0.142397i
$417$	4.11909	+	0.542289i	0.201713	+	0.0265560i
$418$	−0.344317	−	1.01433i	−0.0168411	−	0.0496123i
$419$	−19.4006	+	12.9631i	−0.947782	+	0.633288i	−0.930394	−	0.366561i	$-0.880535\pi$
$419$	−19.4006	+	12.9631i	−0.947782	+	0.633288i	−0.0173883	+	0.999849i	$0.505535\pi$
$420$	0.169029	+	6.07521i	0.00824777	+	0.296440i
$421$	12.5359	−	12.5359i	0.610962	−	0.610962i	−0.332235	−	0.943197i	$-0.607803\pi$
$421$	12.5359	−	12.5359i	0.610962	−	0.610962i	0.943197	+	0.332235i	$0.107803\pi$
$422$	−14.5500	−	0.953657i	−0.708282	−	0.0464233i
$423$	−0.289235	−	0.376938i	−0.0140631	−	0.0183274i
$424$	−29.0489	−	16.7714i	−1.41074	−	0.814492i
$425$	4.35676	+	9.16597i	0.211334	+	0.444615i
$426$			7.65142i			0.370712i
$427$	−16.5998	+	8.76828i	−0.803321	+	0.424327i
$428$	−4.66093	−	3.11434i	−0.225295	−	0.150537i
$429$	2.13900	−	7.98286i	0.103272	−	0.385416i
$430$	−26.1926	−	8.89118i	−1.26312	−	0.428771i
$431$	0.331829	+	5.06273i	0.0159836	+	0.243863i	0.998373	+	0.0570184i	$0.0181594\pi$
$431$	0.331829	+	5.06273i	0.0159836	+	0.243863i	−0.982390	+	0.186844i	$0.940174\pi$
$432$	−1.52542	+	0.517809i	−0.0733917	+	0.0249131i
$433$	9.21964	+	22.2582i	0.443067	+	1.06966i	0.974867	+	0.222789i	$0.0715161\pi$
$433$	9.21964	+	22.2582i	0.443067	+	1.06966i	−0.531799	+	0.846870i	$0.678484\pi$
$434$	5.95003	+	6.41562i	0.285610	+	0.307960i
$435$	−0.161918	+	0.814017i	−0.00776337	+	0.0390291i
$436$	5.41669	−	10.9840i	0.259412	−	0.526036i
$437$	−0.631324	+	1.85982i	−0.0302003	+	0.0889672i
$438$	4.07880	+	15.2223i	0.194893	+	0.727349i
$439$	−0.640137	+	9.76660i	−0.0305521	+	0.466135i	0.954983	+	0.296661i	$0.0958733\pi$
$439$	−0.640137	+	9.76660i	−0.0305521	+	0.466135i	−0.985535	+	0.169473i	$0.945793\pi$
$440$	−5.20454	+	12.5649i	−0.248117	+	0.599007i
$441$	2.31505	−	6.60610i	0.110240	−	0.314576i
$442$	22.4640	+	1.79848i	1.06850	+	0.0855451i
$443$	−9.45853	−	16.3827i	−0.449388	−	0.778364i	0.548958	−	0.835850i	$-0.315025\pi$
$443$	−9.45853	−	16.3827i	−0.449388	−	0.778364i	−0.998346	+	0.0574864i	$0.981691\pi$
$444$	4.50089	−	3.45365i	0.213603	−	0.163903i
$445$	15.5866	−	7.68648i	0.738878	−	0.364374i
$446$	27.3613	+	7.33144i	1.29560	+	0.347154i
$447$	1.93462	+	9.72599i	0.0915044	+	0.460024i
$448$	−17.0161	−	12.3204i	−0.803933	−	0.582085i
$449$	2.60024	+	0.517221i	0.122713	+	0.0244092i	0.256065	−	0.966660i	$-0.417574\pi$
$449$	2.60024	+	0.517221i	0.122713	+	0.0244092i	−0.133352	+	0.991069i	$0.542574\pi$
$450$	2.10235	+	1.61319i	0.0991056	+	0.0760464i
$451$	−2.30604	+	17.5161i	−0.108587	+	0.824803i
$452$	−8.60870	−	7.54963i	−0.404919	−	0.355105i
$453$	9.11210	+	4.49359i	0.428124	+	0.211127i
$454$	−13.1717	+	2.62001i	−0.618177	+	0.122963i
$455$	−3.41703	−	36.5314i	−0.160193	−	1.71262i
$456$	−1.03859	+	1.55436i	−0.0486365	+	0.0727897i
$457$	−4.27812	−	32.4955i	−0.200122	−	1.52008i	−0.736696	−	0.676224i	$-0.763615\pi$
$457$	−4.27812	−	32.4955i	−0.200122	−	1.52008i	0.536574	−	0.843853i	$-0.319718\pi$
$458$	5.30828	−	9.19421i	0.248040	−	0.429617i
$459$	−3.83164	+	1.52267i	−0.178846	+	0.0710723i
$460$	6.39253	−	3.69073i	0.298053	−	0.172081i
$461$	23.7282	+	9.82853i	1.10513	+	0.457760i	0.859259	−	0.511542i	$-0.170925\pi$
$461$	23.7282	+	9.82853i	1.10513	+	0.457760i	0.245873	+	0.969302i	$0.420925\pi$
$462$	3.18625	−	3.36862i	0.148238	−	0.156723i
$463$	4.31762	+	4.31762i	0.200657	+	0.200657i	0.800281	−	0.599625i	$-0.204683\pi$
$463$	4.31762	+	4.31762i	0.200657	+	0.200657i	−0.599625	+	0.800281i	$0.704683\pi$
$464$	−0.322725	−	0.367997i	−0.0149821	−	0.0170838i
$465$	−8.37316	+	0.548806i	−0.388296	+	0.0254503i
$466$	2.86026	−	3.26150i	0.132499	−	0.151086i
$467$	−9.54396	+	12.4379i	−0.441642	+	0.575559i	−0.960140	−	0.279520i	$-0.909825\pi$
$467$	−9.54396	+	12.4379i	−0.441642	+	0.575559i	0.518498	+	0.855079i	$0.326491\pi$
$468$	−3.94442	+	1.63383i	−0.182331	+	0.0755238i
$469$	−10.0135	+	26.2141i	−0.462379	+	1.21045i
$470$	−0.776255	−	1.16175i	−0.0358060	−	0.0535874i
$471$	−0.367635	+	0.322407i	−0.0169397	+	0.0148557i
$472$	19.4835	−	5.22058i	0.896800	−	0.240297i
$473$	−6.77206	−	13.7324i	−0.311380	−	0.631415i
$474$	−9.53731	+	1.25561i	−0.438063	+	0.0576721i
$475$	1.50445			0.0690289
$476$	−7.69511	−	4.99414i	−0.352705	−	0.228906i
$477$	−10.9669			−0.502141
$478$	−17.3058	+	2.27835i	−0.791549	+	0.104209i
$479$	9.75062	+	19.7723i	0.445517	+	0.903419i	0.997574	+	0.0696129i	$0.0221764\pi$
$479$	9.75062	+	19.7723i	0.445517	+	0.903419i	−0.552057	+	0.833806i	$0.686157\pi$
$480$	11.5639	−	3.09855i	0.527819	−	0.141429i
$481$	−25.7505	+	22.5826i	−1.17412	+	1.02968i
$482$	0.132736	+	0.198654i	0.00604597	+	0.00904843i
$483$	−8.39494	+	1.34371i	−0.381983	+	0.0611408i
$484$	6.48747	−	2.68720i	0.294885	−	0.122145i
$485$	−26.5126	+	34.5518i	−1.20387	+	1.56892i
$486$	−0.709847	+	0.809425i	−0.0321993	+	0.0367163i
$487$	11.9020	−	0.780100i	0.539332	−	0.0353497i	0.206697	−	0.978405i	$-0.433729\pi$
$487$	11.9020	−	0.780100i	0.539332	−	0.0353497i	0.332636	+	0.943055i	$0.392062\pi$
$488$	14.3093	+	16.3167i	0.647753	+	0.738621i
$489$	2.39636	+	2.39636i	0.108367	+	0.108367i
$490$	8.06406	−	18.9402i	0.364297	−	0.855631i
$491$	20.1812	+	8.35933i	0.910766	+	0.377251i	0.788350	−	0.615227i	$-0.210936\pi$
$491$	20.1812	+	8.35933i	0.910766	+	0.377251i	0.122416	+	0.992479i	$0.460936\pi$
$492$	7.90411	−	4.56344i	0.356345	−	0.205736i
$493$	−0.872961	−	0.898545i	−0.0393162	−	0.0404684i
$494$	1.67036	−	2.89315i	0.0751531	−	0.130169i
$495$	0.580398	+	4.40856i	0.0260869	+	0.198150i
$496$	2.74928	−	4.11459i	0.123446	−	0.184750i
$497$	−7.84434	+	17.0892i	−0.351867	+	0.766553i
$498$	11.2154	−	2.23089i	0.502575	−	0.0999685i
$499$	−20.3479	−	10.0345i	−0.910899	−	0.449206i	−0.0744339	−	0.997226i	$-0.523715\pi$
$499$	−20.3479	−	10.0345i	−0.910899	−	0.449206i	−0.836465	+	0.548020i	$0.815382\pi$
$500$	4.38425	+	3.84489i	0.196070	+	0.171949i
$501$	−0.731947	+	5.55969i	−0.0327010	+	0.248389i
$502$	−23.1916	−	17.7955i	−1.03509	−	0.794254i
$503$	−3.67018	−	0.730043i	−0.163645	−	0.0325510i	0.112588	−	0.993642i	$-0.464086\pi$
$503$	−3.67018	−	0.730043i	−0.163645	−	0.0325510i	−0.276233	+	0.961091i	$0.589086\pi$
$504$	−8.04919	−	0.832695i	−0.358539	−	0.0370912i
$505$	−7.48075	−	37.6083i	−0.332889	−	1.67355i
$506$	−5.43968	−	1.45756i	−0.241823	−	0.0647964i
$507$	11.4574	−	5.65016i	0.508841	−	0.250932i
$508$	−6.55011	+	5.02608i	−0.290614	+	0.222996i
$509$	−10.5081	−	18.2005i	−0.465763	−	0.806725i	0.533473	−	0.845817i	$-0.320887\pi$
$509$	−10.5081	−	18.2005i	−0.465763	−	0.806725i	−0.999236	+	0.0390922i	$0.987553\pi$
$510$	−11.5367	+	3.73130i	−0.510855	+	0.165225i
$511$	−6.49626	+	38.1800i	−0.287378	+	1.68899i
$512$	−6.47284	+	15.6268i	−0.286062	+	0.690614i
$513$	−0.0399751	+	0.609903i	−0.00176494	+	0.0269279i
$514$	−1.54386	−	5.76177i	−0.0680968	−	0.254141i
$515$	3.32608	−	9.79831i	0.146565	−	0.431765i
$516$	−3.49843	+	7.09411i	−0.154010	+	0.312301i
$517$	0.150888	−	0.758568i	0.00663607	−	0.0333618i
$518$	−18.7352	+	4.27157i	−0.823177	+	0.187682i
$519$	0.0755681	+	0.182437i	0.00331707	+	0.00800812i
$520$	−40.1644	+	13.6340i	−1.76133	+	0.597890i
$521$	−2.58340	−	39.4150i	−0.113181	−	1.72680i	−0.556850	−	0.830613i	$-0.687990\pi$
$521$	−2.58340	−	39.4150i	−0.113181	−	1.72680i	0.443670	−	0.896190i	$-0.353676\pi$
$522$	−0.309755	−	0.105148i	−0.0135576	−	0.00460218i
$523$	−4.94967	+	18.4724i	−0.216434	+	0.807743i	0.769223	+	0.638981i	$0.220644\pi$
$523$	−4.94967	+	18.4724i	−0.216434	+	0.807743i	−0.985657	+	0.168762i	$0.946023\pi$
$524$	−5.40209	−	3.60956i	−0.235991	−	0.157684i
$525$	3.04165	+	5.75835i	0.132749	+	0.251315i
$526$		−	4.50543i		−	0.196446i
$527$	6.49065	−	10.8763i	0.282737	−	0.473781i
$528$	−2.27101	−	1.31117i	−0.0988329	−	0.0570612i
$529$	−7.71557	−	10.0551i	−0.335460	−	0.437180i
$530$	−32.1823	−	2.10934i	−1.39791	−	0.0916237i
$531$	4.66330	−	4.66330i	0.202370	−	0.202370i
$532$	−1.15835	+	0.712446i	−0.0502208	+	0.0308885i
$533$	−45.8139	+	30.6119i	−1.98442	+	1.32595i
$534$	2.20172	+	6.48605i	0.0952776	+	0.280679i
$535$	−18.0525	−	2.37665i	−0.780476	−	0.102752i
$536$	32.1621	+	4.23422i	1.38919	+	0.182891i
$537$	4.94844	+	14.5776i	0.213541	+	0.629071i
$538$	5.07772	−	3.39283i	0.218916	−	0.146275i
$539$	10.5699	−	4.25711i	0.455279	−	0.183367i
$540$	1.62430	−	1.62430i	0.0698986	−	0.0698986i
$541$	−43.8124	−	2.87162i	−1.88364	−	0.123460i	−0.920212	−	0.391419i	$-0.871984\pi$
$541$	−43.8124	−	2.87162i	−1.88364	−	0.123460i	−0.963430	+	0.267959i	$0.913651\pi$
$542$	16.4431	+	21.4291i	0.706291	+	0.920457i
$543$	0.805226	+	0.464897i	0.0345556	+	0.0199507i
$544$	−6.05514	+	17.0261i	−0.259612	+	0.729986i
$545$		−	39.7804i		−	1.70401i
$546$	14.4508	+	0.544101i	0.618435	+	0.0232854i
$547$	15.8054	+	10.5609i	0.675792	+	0.451549i	0.845522	−	0.533941i	$-0.179290\pi$
$547$	15.8054	+	10.5609i	0.675792	+	0.451549i	−0.169730	+	0.985491i	$0.554290\pi$
$548$	−2.85785	+	10.6656i	−0.122081	+	0.455614i
$549$	6.71907	+	2.28082i	0.286763	+	0.0973429i
$550$	0.282133	+	4.30451i	0.0120302	+	0.183545i
$551$	−0.175856	+	0.0596951i	−0.00749173	+	0.00254310i
$552$	3.76111	+	9.08012i	0.160083	+	0.386476i
$553$	−22.5885	−	6.97343i	−0.960560	−	0.296540i
$554$	4.88530	−	24.5601i	0.207556	−	1.04346i
$555$	8.15040	−	16.5274i	0.345965	−	0.701548i
$556$	1.12306	−	3.30842i	0.0476282	−	0.140308i
$557$	5.52358	+	20.6143i	0.234042	+	0.873455i	0.978579	+	0.205874i	$0.0660037\pi$
$557$	5.52358	+	20.6143i	0.234042	+	0.873455i	−0.744537	+	0.667581i	$0.767330\pi$
$558$	0.216301	−	3.30012i	0.00915676	−	0.139705i
$559$	18.2741	−	44.1175i	0.772911	−	1.86597i
$560$	−11.4771	−	1.95281i	−0.484997	−	0.0825213i
$561$	−5.97617	−	3.05518i	−0.252314	−	0.128990i
$562$	3.68595	+	6.38424i	0.155482	+	0.269303i
$563$	−15.5710	+	11.9481i	−0.656240	+	0.503551i	−0.882376	−	0.470545i	$-0.844057\pi$
$563$	−15.5710	+	11.9481i	−0.656240	+	0.503551i	0.226136	+	0.974096i	$0.427391\pi$
$564$	−0.358347	+	0.176717i	−0.0150891	+	0.00744113i
$565$	−35.9251	−	9.62609i	−1.51138	−	0.404973i
$566$	4.38008	+	22.0202i	0.184109	+	0.925577i
$567$	−2.41525	+	1.08008i	−0.101431	+	0.0453589i
$568$	21.3196	+	4.24073i	0.894551	+	0.177937i
$569$	10.2221	+	7.84369i	0.428533	+	0.328825i	0.800405	−	0.599459i	$-0.204618\pi$
$569$	10.2221	+	7.84369i	0.428533	+	0.328825i	−0.371873	+	0.928284i	$0.621284\pi$
$570$	−0.234613	+	1.78206i	−0.00982684	+	0.0746422i
$571$	−5.86217	−	5.14099i	−0.245324	−	0.215144i	0.527849	−	0.849338i	$-0.322999\pi$
$571$	−5.86217	−	5.14099i	−0.245324	−	0.215144i	−0.773174	+	0.634194i	$0.781332\pi$
$572$	−6.23326	−	3.07390i	−0.260626	−	0.128526i
$573$	−11.0534	+	2.19865i	−0.461762	+	0.0918501i
$574$	−30.7795	+	2.87902i	−1.28471	+	0.120168i
$575$	4.39427	−	6.57650i	0.183254	−	0.274259i
$576$	1.03642	+	7.87237i	0.0431841	+	0.328015i
$577$	−1.32489	+	2.29478i	−0.0551561	+	0.0955331i	−0.892285	−	0.451472i	$-0.850899\pi$
$577$	−1.32489	+	2.29478i	−0.0551561	+	0.0955331i	0.837129	+	0.547005i	$0.184232\pi$
$578$	5.24545	−	17.5343i	0.218182	−	0.729330i
$579$	−13.2385	+	7.64323i	−0.550171	+	0.317642i
$580$	0.644828	+	0.267097i	0.0267750	+	0.0110906i
$581$	27.3364	+	6.51562i	1.13410	+	0.270313i
$582$	−12.1375	−	12.1375i	−0.503116	−	0.503116i
$583$	−11.7711	−	13.4223i	−0.487507	−	0.555895i
$584$	44.6754	−	2.92818i	1.84868	−	0.121169i
$585$	−9.14370	+	10.4264i	−0.378046	+	0.431078i
$586$	9.78570	−	12.7530i	0.404243	−	0.526820i
$587$	−10.7831	+	4.46649i	−0.445065	+	0.184352i	−0.593949	−	0.804503i	$-0.702432\pi$
$587$	−10.7831	+	4.46649i	−0.445065	+	0.184352i	0.148884	+	0.988855i	$0.452432\pi$
$588$	−5.06884	−	2.99323i	−0.209035	−	0.123439i
$589$	−1.04313	−	1.56116i	−0.0429815	−	0.0643264i
$590$	14.5813	−	12.7874i	0.600302	−	0.526450i
$591$	−0.603793	+	0.161786i	−0.0248367	+	0.00665499i
$592$	4.80661	+	9.74684i	0.197550	+	0.400593i
$593$	−41.8548	+	5.51028i	−1.71877	+	0.226280i	−0.924472	−	0.381249i	$-0.875494\pi$
$593$	−41.8548	+	5.51028i	−1.71877	+	0.226280i	−0.794297	+	0.607530i	$0.792161\pi$
$594$	−1.75254			−0.0719077
$595$	−29.5923	−	3.49392i	−1.21316	−	0.143237i
$596$	8.33930			0.341591
$597$	−21.2083	+	2.79213i	−0.868000	+	0.114274i
$598$	−7.76813	−	15.7522i	−0.317663	−	0.644156i
$599$	−12.7155	+	3.40712i	−0.519542	+	0.139211i	−0.509055	−	0.860734i	$-0.670005\pi$
$599$	−12.7155	+	3.40712i	−0.519542	+	0.139211i	−0.0104875	+	0.999945i	$0.503338\pi$
$600$	5.66013	−	4.96380i	0.231074	−	0.202646i
$601$	−23.1576	−	34.6578i	−0.944618	−	1.41372i	−0.910133	−	0.414315i	$-0.864021\pi$
$601$	−23.1576	−	34.6578i	−0.944618	−	1.41372i	−0.0344847	−	0.999405i	$-0.510979\pi$
$602$	20.7934	−	16.8945i	0.847474	−	0.688569i
$603$	9.79889	−	4.05883i	0.399042	−	0.165288i
$604$	5.20121	−	6.77835i	0.211634	−	0.275807i
$605$	15.0388	−	17.1485i	0.611416	−	0.697186i
$606$	15.0806	−	0.988436i	0.612608	−	0.0401525i
$607$	25.2011	+	28.7363i	1.02288	+	1.16637i	0.985948	+	0.167054i	$0.0534254\pi$
$607$	25.2011	+	28.7363i	1.02288	+	1.16637i	0.0369326	+	0.999318i	$0.488241\pi$
$608$	1.89421	+	1.89421i	0.0768203	+	0.0768203i
$609$	−0.584027	−	0.552408i	−0.0236660	−	0.0223847i
$610$	19.2783	+	7.98534i	0.780556	+	0.323317i
$611$	2.08897	−	1.20607i	0.0845106	−	0.0487922i
$612$	0.627264	+	3.41011i	0.0253556	+	0.137846i
$613$	17.1481	−	29.7014i	0.692605	−	1.19963i	−0.278377	−	0.960472i	$-0.589796\pi$
$613$	17.1481	−	29.7014i	0.692605	−	1.19963i	0.970982	−	0.239155i	$-0.0768703\pi$
$614$	3.59026	+	27.2707i	0.144891	+	1.10056i
$615$	16.4704	−	24.6496i	0.664149	−	0.993969i
$616$	−7.62025	−	10.7451i	−0.307029	−	0.432931i
$617$	−4.90620	+	0.975904i	−0.197516	+	0.0392884i	−0.292857	−	0.956156i	$-0.594606\pi$
$617$	−4.90620	+	0.975904i	−0.197516	+	0.0392884i	0.0953407	+	0.995445i	$0.469606\pi$
$618$	3.65767	+	1.80376i	0.147133	+	0.0725580i
$619$	8.23043	+	7.21790i	0.330809	+	0.290112i	0.808596	−	0.588364i	$-0.200228\pi$
$619$	8.23043	+	7.21790i	0.330809	+	0.290112i	−0.477787	+	0.878476i	$0.658561\pi$
$620$	−0.921058	+	6.99613i	−0.0369906	+	0.280971i
$621$	2.54934	+	1.95618i	0.102302	+	0.0784988i
$622$	19.7336	+	3.92526i	0.791246	+	0.157389i
$623$	−1.73214	+	16.7436i	−0.0693966	+	0.670818i
$624$	−1.59553	−	8.02126i	−0.0638722	−	0.321107i
$625$	30.1837	+	8.08771i	1.20735	+	0.323508i
$626$	−22.8444	+	11.2656i	−0.913045	+	0.450264i
$627$	−0.789360	+	0.605697i	−0.0315240	+	0.0241892i
$628$	0.205604	+	0.356116i	0.00820449	+	0.0142106i
$629$	13.5584	+	24.2872i	0.540611	+	0.968396i
$630$	−7.29525	+	2.70492i	−0.290650	+	0.107767i
$631$	10.7863	−	26.0403i	0.429394	−	1.03665i	−0.550086	−	0.835108i	$-0.685405\pi$
$631$	10.7863	−	26.0403i	0.429394	−	1.03665i	0.979480	−	0.201541i	$-0.0645948\pi$
$632$	−1.78739	+	27.2703i	−0.0710985	+	1.08475i
$633$	3.50541	+	13.0824i	0.139327	+	0.519977i
$634$	4.42789	−	13.0441i	0.175854	−	0.518049i
$635$	−11.8612	+	24.0522i	−0.470698	+	0.954481i
$636$	−1.79924	+	9.04541i	−0.0713447	+	0.358674i
$637$	31.7174	+	16.0304i	1.25669	+	0.635146i
$638$	−0.203778	−	0.491963i	−0.00806763	−	0.0194770i
$639$	6.72990	−	2.28449i	0.266231	−	0.0903731i
$640$	−0.0387897	−	0.591817i	−0.00153330	−	0.0233936i
$641$	−30.0387	−	10.1968i	−1.18646	−	0.402747i	−0.342684	−	0.939451i	$-0.611336\pi$
$641$	−30.0387	−	10.1968i	−1.18646	−	0.402747i	−0.843771	+	0.536703i	$0.819670\pi$
$642$	1.85740	−	6.93190i	0.0733056	−	0.273580i
$643$	−27.7253	−	18.5255i	−1.09338	−	0.730573i	−0.128092	−	0.991762i	$-0.540885\pi$
$643$	−27.7253	−	18.5255i	−1.09338	−	0.730573i	−0.965288	+	0.261189i	$0.915885\pi$
$644$	−0.269006	+	7.14451i	−0.0106003	+	0.281533i
$645$			25.6926i			1.01165i
$646$	−2.01378	−	1.81815i	−0.0792311	−	0.0715340i
$647$	−30.4496	−	17.5801i	−1.19710	−	0.691146i	−0.237192	−	0.971463i	$-0.576227\pi$
$647$	−30.4496	−	17.5801i	−1.19710	−	0.691146i	−0.959907	+	0.280317i	$0.909560\pi$
$648$	1.86192	+	2.42651i	0.0731433	+	0.0953222i
$649$	10.7126	+	0.702140i	0.420506	+	0.0275614i
$650$	−9.51307	+	9.51307i	−0.373133	+	0.373133i
$651$	3.86643	−	7.14894i	0.151537	−	0.280189i
$652$	2.36965	−	1.58335i	0.0928025	−	0.0620086i
$653$	4.58955	+	13.5204i	0.179603	+	0.529093i	0.999027	−	0.0440939i	$-0.0140401\pi$
$653$	4.58955	+	13.5204i	0.179603	+	0.529093i	−0.819424	+	0.573187i	$0.805707\pi$
$654$	15.5446	+	2.04648i	0.607840	+	0.0800237i
$655$	−20.9231	−	2.75457i	−0.817532	−	0.107630i
$656$	5.61983	+	16.5555i	0.219417	+	0.646383i
$657$	12.1711	−	8.13249i	0.474841	−	0.317279i
$658$	1.35281	−	0.0376388i	0.0527379	−	0.00146731i
$659$	23.5269	−	23.5269i	0.916480	−	0.916480i	−0.0802916	−	0.996771i	$-0.525585\pi$
$659$	23.5269	−	23.5269i	0.916480	−	0.916480i	0.996771	+	0.0802916i	$0.0255851\pi$
$660$	3.73135	+	0.244566i	0.145243	+	0.00951971i
$661$	−10.2972	−	13.4196i	−0.400516	−	0.521962i	0.548941	−	0.835861i	$-0.315031\pi$
$661$	−10.2972	−	13.4196i	−0.400516	−	0.521962i	−0.949456	+	0.313899i	$0.898365\pi$
$662$	−13.8327	−	7.98629i	−0.537622	−	0.310396i
$663$	−5.12521	−	20.2954i	−0.199047	−	0.788209i
$664$		−	32.4867i		−	1.26073i
$665$	−2.35099	+	3.73963i	−0.0911675	+	0.145017i
$666$	6.03893	+	4.03508i	0.234004	+	0.156356i
$667$	−0.252701	+	0.943092i	−0.00978461	+	0.0365166i
$668$	4.46549	+	1.51583i	0.172775	+	0.0586493i
$669$	−1.72084	−	26.2549i	−0.0665315	−	1.01507i
$670$	29.5353	−	10.0259i	1.14105	−	0.387334i
$671$	4.42026	+	10.6715i	0.170642	+	0.411967i
$672$	−3.42052	+	11.0798i	−0.131949	+	0.427413i
$673$	−6.67519	+	33.5584i	−0.257310	+	1.29358i	0.608638	+	0.793448i	$0.291716\pi$
$673$	−6.67519	+	33.5584i	−0.257310	+	1.29358i	−0.865948	+	0.500134i	$0.833284\pi$
$674$	2.53192	−	5.13422i	0.0975258	−	0.197763i
$675$	0.791199	−	2.33080i	0.0304533	−	0.0897124i
$676$	−2.78049	−	10.3769i	−0.106942	−	0.399112i
$677$	−1.44952	+	22.1154i	−0.0557095	+	0.849963i	0.874981	+	0.484157i	$0.160874\pi$
$677$	−1.44952	+	22.1154i	−0.0557095	+	0.849963i	−0.930691	+	0.365807i	$0.880793\pi$
$678$	5.60963	−	13.5428i	0.215436	−	0.520109i
$679$	−14.6651	−	39.5523i	−0.562797	−	1.51788i
$680$	4.00259	+	34.2136i	0.153492	+	1.31203i
$681$	6.23714	+	10.8030i	0.239008	+	0.413973i
$682$	4.27114	−	3.27736i	0.163551	−	0.125497i
$683$	−18.7131	+	9.22829i	−0.716038	+	0.353111i	−0.763540	−	0.645760i	$-0.776541\pi$
$683$	−18.7131	+	9.22829i	−0.716038	+	0.353111i	0.0475023	+	0.998871i	$0.484874\pi$
$684$	0.496483	+	0.133032i	0.0189835	+	0.00508662i
$685$	6.99714	+	35.1770i	0.267347	+	1.34404i
$686$	11.3739	+	16.3765i	0.434259	+	0.625256i
$687$	−9.67178	−	1.92384i	−0.369001	−	0.0733989i
$688$	−12.0209	−	9.22392i	−0.458291	−	0.351659i
$689$	7.26743	−	55.2016i	0.276867	−	2.10301i
$690$	7.10475	+	6.23070i	0.270473	+	0.237199i
$691$	−4.18400	−	2.06332i	−0.159167	−	0.0784925i	0.360961	−	0.932581i	$-0.382449\pi$
$691$	−4.18400	−	2.06332i	−0.159167	−	0.0784925i	−0.520127	+	0.854089i	$0.674116\pi$
$692$	0.162870	−	0.0323969i	0.00619140	−	0.00123155i
$693$	−3.91424	−	1.79673i	−0.148690	−	0.0682522i
$694$	−17.2234	+	25.7766i	−0.653790	+	0.978466i
$695$	−1.48129	−	11.2515i	−0.0561887	−	0.426795i
$696$	−0.464658	+	0.804811i	−0.0176128	+	0.0305063i
$697$	16.5257	+	41.5851i	0.625956	+	1.57515i
$698$	14.5265	−	8.38687i	0.549835	−	0.317448i
$699$	−3.72269	−	1.54199i	−0.140805	−	0.0583233i
$700$	5.24845	−	1.56400i	0.198373	−	0.0591138i
$701$	22.3746	+	22.3746i	0.845077	+	0.845077i	0.989514	−	0.144437i	$-0.0461371\pi$
$701$	22.3746	+	22.3746i	0.845077	+	0.845077i	−0.144437	+	0.989514i	$0.546137\pi$
$702$	−3.60381	−	4.10936i	−0.136017	−	0.155098i
$703$	4.11455	−	0.269682i	0.155183	−	0.0101713i
$704$	−8.52250	+	9.71805i	−0.321204	+	0.366263i
$705$	−0.790062	+	1.02963i	−0.0297555	+	0.0387781i
$706$	20.7003	−	8.57432i	0.779064	−	0.322699i
$707$	34.6954	+	13.2532i	1.30485	+	0.498439i
$708$	−3.08118	−	4.61131i	−0.115798	−	0.173303i
$709$	−28.3011	+	24.8194i	−1.06287	+	0.932111i	−0.997835	−	0.0657724i	$-0.979049\pi$
$709$	−28.3011	+	24.8194i	−1.06287	+	0.932111i	−0.0650338	+	0.997883i	$0.520716\pi$
$710$	20.1881	−	5.40940i	0.757648	−	0.203011i
$711$	3.95195	+	8.01377i	0.148210	+	0.300540i
$712$	19.2928	−	2.53994i	0.723027	−	0.0951883i
$713$	−9.87122			−0.369680
$714$	2.88764	−	11.3837i	0.108067	−	0.426024i
$715$	−22.5749			−0.844253
$716$	12.8353	−	1.68980i	0.479679	−	0.0631509i
$717$	7.17097	+	14.5413i	0.267805	+	0.543054i
$718$	7.29586	−	1.95492i	0.272279	−	0.0729570i
$719$	12.7367	−	11.1698i	0.474998	−	0.416562i	−0.388086	−	0.921623i	$-0.626864\pi$
$719$	12.7367	−	11.1698i	0.474998	−	0.416562i	0.863083	+	0.505062i	$0.168530\pi$
$720$	2.44467	+	3.65871i	0.0911075	+	0.136352i
$721$	6.32003	+	7.77854i	0.235370	+	0.289688i
$722$	18.5266	−	7.67398i	0.689489	−	0.285596i
$723$	0.135097	−	0.176062i	0.00502432	−	0.00654782i
$724$	0.515549	−	0.587871i	0.0191602	−	0.0218480i
$725$	0.746284	−	0.0489140i	0.0277163	−	0.00181662i
$726$	5.92727	+	6.75876i	0.219982	+	0.250841i
$727$	4.40266	+	4.40266i	0.163286	+	0.163286i	0.784021	−	0.620735i	$-0.213166\pi$
$727$	4.40266	+	4.40266i	0.163286	+	0.163286i	−0.620735	+	0.784021i	$0.713166\pi$
$728$	9.52527	−	39.9635i	0.353030	−	1.48114i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	37.2801	−	21.5237i	1.37980	−	0.796628i
$731$	−31.9310	−	22.0091i	−1.18101	−	0.814036i
$732$	2.98353	−	5.16763i	0.110275	−	0.191001i
$733$	−3.73455	−	28.3668i	−0.137939	−	1.04775i	−0.910705	−	0.413058i	$-0.864461\pi$
$733$	−3.73455	−	28.3668i	−0.137939	−	1.04775i	0.772766	−	0.634692i	$-0.218873\pi$
$734$	17.4439	−	26.1067i	0.643867	−	0.963616i
$735$	−19.0668	−	1.43785i	−0.703289	−	0.0530358i
$736$	13.8130	−	2.74757i	0.509153	−	0.101277i
$737$	15.4849	+	7.63632i	0.570395	+	0.281288i
$738$	8.78475	+	7.70402i	0.323371	+	0.283589i
$739$	−4.50789	+	34.2408i	−0.165825	+	1.25957i	0.682812	+	0.730594i	$0.260757\pi$
$739$	−4.50789	+	34.2408i	−0.165825	+	1.25957i	−0.848637	+	0.528975i	$0.822577\pi$
$740$	−12.2945	−	9.43387i	−0.451953	−	0.346796i
$741$	−3.04343	−	0.605376i	−0.111803	−	0.0222390i
$742$	18.3200	−	25.3022i	0.672547	−	0.928873i
$743$	3.65366	+	18.3682i	0.134040	+	0.673863i	0.988115	+	0.153714i	$0.0491236\pi$
$743$	3.65366	+	18.3682i	0.134040	+	0.673863i	−0.854076	+	0.520149i	$0.825876\pi$
$744$	−9.07544	−	2.43176i	−0.332722	−	0.0891525i
$745$	24.2942	−	11.9806i	0.890069	−	0.438933i
$746$	−3.84866	+	2.95318i	−0.140909	+	0.108124i
$747$	−5.31081	−	9.19859i	−0.194312	−	0.336559i
$748$	−3.50034	+	4.42785i	−0.127985	+	0.161898i
$749$	11.2551	−	13.5779i	0.411253	−	0.496126i
$750$	−2.85688	+	6.89712i	−0.104318	+	0.251847i
$751$	−1.07288	+	16.3690i	−0.0391500	+	0.597314i	0.932542	+	0.361062i	$0.117586\pi$
$751$	−1.07288	+	16.3690i	−0.0391500	+	0.597314i	−0.971692	+	0.236252i	$0.924081\pi$
$752$	−0.198094	−	0.739295i	−0.00722373	−	0.0269593i
$753$	−8.72794	+	25.7117i	−0.318064	+	0.936986i
$754$	0.734520	−	1.48946i	0.0267496	−	0.0542429i
$755$	5.41420	−	27.2190i	0.197043	−	0.990602i
$756$	0.494588	+	2.16927i	0.0179880	+	0.0788957i
$757$	−8.93461	−	21.5701i	−0.324734	−	0.783977i	−0.998966	−	0.0454579i	$-0.985525\pi$
$757$	−8.93461	−	21.5701i	−0.324734	−	0.783977i	0.674232	−	0.738519i	$-0.264475\pi$
$758$	27.1003	−	9.19931i	0.984326	−	0.334134i
$759$	0.342119	+	5.21973i	0.0124181	+	0.189464i
$760$	4.83543	+	1.64141i	0.175399	+	0.0595401i
$761$	1.17168	−	4.37277i	0.0424734	−	0.158513i	−0.941432	−	0.337203i	$-0.890519\pi$
$761$	1.17168	−	4.37277i	0.0424734	−	0.158513i	0.983905	+	0.178690i	$0.0571859\pi$
$762$	−8.78841	−	5.87223i	−0.318370	−	0.212728i
$763$	32.6201	+	20.5072i	1.18093	+	0.742412i
$764$			9.47743i			0.342881i
$765$	6.72645	+	9.03323i	0.243195	+	0.326597i
$766$	20.2356	+	11.6830i	0.731141	+	0.422125i
$767$	20.3823	+	26.5627i	0.735962	+	0.959124i
$768$	16.0799	+	1.05393i	0.580232	+	0.0380304i
$769$	−24.5227	+	24.5227i	−0.884312	+	0.884312i	−0.993969	−	0.109658i	$-0.965025\pi$
$769$	−24.5227	+	24.5227i	−0.884312	+	0.884312i	0.109658	+	0.993969i	$0.465025\pi$
$770$	−11.1407	−	6.02532i	−0.401482	−	0.217138i
$771$	−4.60688	+	3.07822i	−0.165913	+	0.110859i
$772$	4.13214	+	12.1729i	0.148719	+	0.438112i
$773$	−36.6940	−	4.83086i	−1.31979	−	0.173754i	−0.562482	−	0.826810i	$-0.690153\pi$
$773$	−36.6940	−	4.83086i	−1.31979	−	0.173754i	−0.757310	+	0.653056i	$0.773487\pi$
$774$	−10.0396	−	1.32174i	−0.360867	−	0.0475090i
$775$	2.43050	+	7.16001i	0.0873060	+	0.257195i
$776$	−40.5466	+	27.0924i	−1.45554	+	0.972560i
$777$	9.35090	+	15.2034i	0.335462	+	0.545419i
$778$	−18.7800	+	18.7800i	−0.673295	+	0.673295i
$779$	6.61932	+	0.433853i	0.237162	+	0.0155444i
$780$	7.09946	+	9.25220i	0.254201	+	0.331282i
$781$	10.0193	+	5.78465i	0.358519	+	0.206991i
$782$	−13.8297	+	3.49242i	−0.494550	+	0.124889i
$783$			0.303842i			0.0108584i
$784$	7.51790	−	8.40460i	0.268496	−	0.300164i
$785$	1.11058	+	0.742064i	0.0396382	+	0.0264854i
$786$	2.15275	−	8.03417i	0.0767860	−	0.286569i
$787$	40.7876	+	13.8455i	1.45392	+	0.493539i	0.932941	−	0.360030i	$-0.117234\pi$
$787$	40.7876	+	13.8455i	1.45392	+	0.493539i	0.520979	+	0.853569i	$0.325567\pi$
$788$	0.0343805	+	0.524546i	0.00122476	+	0.0186862i
$789$	−3.96281	+	1.34519i	−0.141080	+	0.0478901i
$790$	10.0556	+	24.2764i	0.357762	+	0.863714i
$791$	26.4132	−	24.4963i	0.939145	−	0.870990i
$792$	−0.971331	+	4.88321i	−0.0345148	+	0.173517i
$793$	−15.9329	+	32.3087i	−0.565794	+	1.14732i
$794$	1.84629	−	5.43900i	0.0655225	−	0.193023i
$795$	7.75340	+	28.9361i	0.274985	+	1.02626i
$796$	−1.17654	+	17.9505i	−0.0417013	+	0.636239i
$797$	1.36571	−	3.29711i	0.0483759	−	0.116790i	−0.897844	−	0.440313i	$-0.854867\pi$
$797$	1.36571	−	3.29711i	0.0483759	−	0.116790i	0.946220	+	0.323523i	$0.104867\pi$
$798$	−1.34035	−	1.11105i	−0.0474479	−	0.0393309i
$799$	−0.602838	−	1.86391i	−0.0213269	−	0.0659403i
$800$	−5.39396	−	9.34262i	−0.190705	−	0.330311i
$801$	5.04752	−	3.87310i	0.178345	−	0.136849i
$802$	−35.8544	+	17.6814i	−1.26606	+	0.624354i
$803$	23.0168	+	6.16734i	0.812246	+	0.217641i
$804$	−1.74007	−	8.74792i	−0.0613675	−	0.308515i
$805$	9.48040	+	21.1999i	0.334140	+	0.747200i
$806$	16.4677	+	3.27562i	0.580049	+	0.115379i
$807$	−4.50026	−	3.45317i	−0.158417	−	0.121557i
$808$	5.60417	−	42.5679i	0.197154	−	1.49753i
$809$	−17.7214	−	15.5412i	−0.623050	−	0.546400i	0.288557	−	0.957463i	$-0.406824\pi$
$809$	−17.7214	−	15.5412i	−0.623050	−	0.546400i	−0.911607	+	0.411063i	$0.865158\pi$
$810$	2.63750	+	1.30067i	0.0926724	+	0.0457010i
$811$	31.8014	−	6.32569i	1.11670	−	0.222125i	0.397958	−	0.917404i	$-0.369719\pi$
$811$	31.8014	−	6.32569i	1.11670	−	0.222125i	0.718740	+	0.695279i	$0.244719\pi$
$812$	−0.551437	+	0.391071i	−0.0193516	+	0.0137239i
$813$	13.9388	−	20.8608i	0.488853	−	0.731621i
$814$	1.54322	+	11.7219i	0.0540899	+	0.410853i
$815$	4.62859	−	8.01695i	0.162132	−	0.280821i
$816$	−6.64125	−	0.0959100i	−0.232490	−	0.00335752i
$817$	−4.97874	+	2.87448i	−0.174184	+	0.100565i
$818$	6.02640	+	2.49622i	0.210708	+	0.0872782i
$819$	−3.83601	−	12.8728i	−0.134041	−	0.449812i
$820$	−17.6286	−	17.6286i	−0.615618	−	0.615618i
$821$	−25.8460	−	29.4717i	−0.902032	−	1.02857i	−0.999445	−	0.0333258i	$-0.989390\pi$
$821$	−25.8460	−	29.4717i	−0.902032	−	1.02857i	0.0974130	−	0.995244i	$-0.468943\pi$
$822$	−14.1057	+	0.924536i	−0.491993	+	0.0322469i
$823$	3.15484	−	3.59741i	0.109971	−	0.125398i	−0.694235	−	0.719748i	$-0.744257\pi$
$823$	3.15484	−	3.59741i	0.109971	−	0.125398i	0.804206	+	0.594350i	$0.202591\pi$
$824$	7.05317	−	9.19187i	0.245709	−	0.320214i
$825$	3.70185	−	1.53336i	0.128882	−	0.0533846i
$826$	2.96895	+	18.5488i	0.103303	+	0.645394i
$827$	−16.6867	−	24.9734i	−0.580254	−	0.868412i	0.418962	−	0.908004i	$-0.362394\pi$
$827$	−16.6867	−	24.9734i	−0.580254	−	0.868412i	−0.999216	+	0.0395923i	$0.987394\pi$
$828$	2.03168	−	1.78174i	0.0706059	−	0.0619197i
$829$	1.31178	−	0.351491i	0.0455600	−	0.0122078i	−0.235967	−	0.971761i	$-0.575826\pi$
$829$	1.31178	−	0.351491i	0.0455600	−	0.0122078i	0.281527	+	0.959553i	$0.409159\pi$
$830$	−13.8152	−	28.0146i	−0.479534	−	0.972399i
$831$	−23.0607	+	3.03600i	−0.799967	+	0.105318i
$832$	−40.3121			−1.39757
$833$	18.1202	−	22.4646i	0.627827	−	0.778353i
$834$	4.47285			0.154882
$835$	15.1866	−	1.99936i	0.525555	−	0.0691906i
$836$	0.370070	+	0.750427i	0.0127991	+	0.0259541i
$837$	−2.96724	+	0.795070i	−0.102563	+	0.0274816i
$838$	−18.8863	+	16.5628i	−0.652415	+	0.572153i
$839$	−13.3174	−	19.9309i	−0.459767	−	0.688091i	0.527067	−	0.849824i	$-0.323292\pi$
$839$	−13.3174	−	19.9309i	−0.459767	−	0.688091i	−0.986835	+	0.161733i	$0.948292\pi$
$840$	3.49356	+	21.8264i	0.120539	+	0.753081i
$841$	26.7072	−	11.0625i	0.920938	−	0.381465i
$842$	11.6190	−	15.1422i	0.400417	−	0.521834i
$843$	4.51482	−	5.14817i	0.155499	−	0.177312i
$844$	11.3653	−	0.744921i	0.391210	−	0.0256412i
$845$	−23.0080	−	26.2356i	−0.791500	−	0.902533i
$846$	−0.361693	−	0.361693i	−0.0124352	−	0.0124352i
$847$	6.30917	+	21.1722i	0.216786	+	0.727484i
$848$	−16.3219	−	6.76076i	−0.560497	−	0.232165i
$849$	18.0603	−	10.4271i	0.619829	−	0.357859i
$850$	5.93836	+	9.17137i	0.203684	+	0.314575i
$851$	10.8391	−	18.7739i	0.371560	−	0.643561i
$852$	−0.780113	−	5.92555i	−0.0267262	−	0.203006i
$853$	4.48015	−	6.70503i	0.153398	−	0.229576i	−0.746809	−	0.665038i	$-0.768415\pi$
$853$	4.48015	−	6.70503i	0.153398	−	0.229576i	0.900207	+	0.435463i	$0.143415\pi$
$854$	−16.4862	+	11.6918i	−0.564146	+	0.400084i
$855$	1.63748	−	0.325715i	0.0560006	−	0.0111392i
$856$	−18.2853	−	9.01733i	−0.624980	−	0.308206i
$857$	−32.8115	−	28.7749i	−1.12082	−	0.982933i	−0.120868	−	0.992669i	$-0.538568\pi$
$857$	−32.8115	−	28.7749i	−1.12082	−	0.982933i	−0.999953	+	0.00973544i	$0.996901\pi$
$858$	1.16135	−	8.82134i	0.0396479	−	0.301156i
$859$	18.3510	+	14.0812i	0.626126	+	0.480444i	0.872423	−	0.488751i	$-0.162547\pi$
$859$	18.3510	+	14.0812i	0.626126	+	0.480444i	−0.246297	+	0.969194i	$0.579214\pi$
$860$	21.1910	+	4.21516i	0.722608	+	0.143736i
$861$	11.7221	+	26.2129i	0.399490	+	0.893334i
$862$	1.06562	+	5.35723i	0.0362952	+	0.182468i
$863$	−36.5135	−	9.78377i	−1.24294	−	0.333044i	−0.423332	−	0.905975i	$-0.639140\pi$
$863$	−36.5135	−	9.78377i	−1.24294	−	0.333044i	−0.819604	+	0.572931i	$0.805806\pi$
$864$	3.93081	−	1.93846i	0.133729	−	0.0659478i
$865$	0.427933	−	0.328365i	0.0145502	−	0.0111647i
$866$	12.9687	+	22.4624i	0.440693	+	0.763303i
$867$	−16.9886	+	0.621530i	−0.576964	+	0.0211083i
$868$	−5.26204	−	4.36186i	−0.178605	−	0.148051i
$869$	−5.56625	+	13.4381i	−0.188822	+	0.455857i
$870$	−0.0584399	+	0.891620i	−0.00198130	+	0.0302288i
$871$	13.9366	+	52.0119i	0.472222	+	1.76236i
$872$	14.3177	−	42.1785i	0.484858	−	1.42834i
$873$	−7.05179	+	14.2996i	−0.238667	+	0.483969i
$874$	−0.412515	+	2.07385i	−0.0139535	+	0.0701492i
$875$	−13.4518	+	12.4755i	−0.454752	+	0.421750i
$876$	−4.71079	−	11.3729i	−0.159163	−	0.384253i
$877$	51.1172	−	17.3519i	1.72610	−	0.585933i	0.730787	−	0.682605i	$-0.239153\pi$
$877$	51.1172	−	17.3519i	1.72610	−	0.585933i	0.995316	+	0.0966718i	$0.0308197\pi$
$878$	0.689167	+	10.5147i	0.0232582	+	0.354852i
$879$	−14.1388	−	4.79946i	−0.476888	−	0.161882i
$880$	−1.85394	+	6.91899i	−0.0624962	+	0.233239i
$881$	0.0478231	+	0.0319543i	0.00161120	+	0.00107657i	0.556376	−	0.830931i	$-0.312192\pi$
$881$	0.0478231	+	0.0319543i	0.00161120	+	0.00107657i	−0.554764	+	0.832008i	$0.687192\pi$
$882$	1.54273	−	7.37655i	0.0519465	−	0.248381i
$883$			49.1041i			1.65248i	0.563316	+	0.826241i	$0.309525\pi$
$883$			49.1041i			1.65248i	−0.563316	+	0.826241i	$0.690475\pi$
$884$	−17.5803	+	0.897538i	−0.591290	+	0.0301875i
$885$	−15.6009	−	9.00718i	−0.524418	−	0.302773i
$886$	−12.3980	−	16.1574i	−0.416520	−	0.542819i
$887$	−40.2120	−	2.63563i	−1.35019	−	0.0884959i	−0.626930	−	0.779075i	$-0.715689\pi$
$887$	−40.2120	−	2.63563i	−1.35019	−	0.0884959i	−0.723257	+	0.690579i	$0.757356\pi$
$888$	14.5902	−	14.5902i	0.489616	−	0.489616i
$889$	−13.6083	−	22.1254i	−0.456408	−	0.742062i
$890$	15.5568	−	10.3947i	0.521464	−	0.348431i
$891$	0.523258	+	1.54147i	0.0175298	+	0.0516412i
$892$	−21.9371	−	2.88808i	−0.734509	−	0.0967000i
$893$	−0.287914	−	0.0379046i	−0.00963468	−	0.00126843i
$894$	3.43171	+	10.1095i	0.114774	+	0.338112i
$895$	34.9644	−	23.3625i	1.16873	−	0.780921i
$896$	0.505289	+	0.273280i	0.0168805	+	0.00912966i
$897$	−11.5357	+	11.5357i	−0.385166	+	0.385166i
$898$	2.84814	+	0.186677i	0.0950435	+	0.00622948i
$899$	−0.568205	−	0.740499i	−0.0189507	−	0.0246970i
$900$	−1.79261	−	1.03497i	−0.0597538	−	0.0344989i
$901$	−42.6038	−	15.1516i	−1.41934	−	0.504772i
$902$			19.0205i			0.633312i
$903$	−21.0681	−	13.2448i	−0.701102	−	0.440761i
$904$	−34.6261	−	23.1364i	−1.15165	−	0.769507i
$905$	0.657346	−	2.45325i	0.0218509	−	0.0815488i
$906$	10.3575	+	3.51591i	0.344107	+	0.116808i
$907$	0.464102	+	7.08083i	0.0154103	+	0.235115i	0.998615	+	0.0526099i	$0.0167540\pi$
$907$	0.464102	+	7.08083i	0.0154103	+	0.235115i	−0.983205	+	0.182505i	$0.941579\pi$
$908$	9.93351	−	3.37197i	0.329655	−	0.111903i
$909$	−5.37203	−	12.9692i	−0.178179	−	0.430162i
$910$	−8.78079	−	38.5128i	−0.291080	−	1.27669i
$911$	4.41050	−	22.1731i	0.146126	−	0.734627i	−0.836344	−	0.548206i	$-0.815311\pi$
$911$	4.41050	−	22.1731i	0.146126	−	0.734627i	0.982470	−	0.186421i	$-0.0596889\pi$
$912$	−0.435480	+	0.883065i	−0.0144202	+	0.0292412i
$913$	5.55785	−	16.3729i	0.183938	−	0.541864i
$914$	−9.13278	−	34.0840i	−0.302085	−	1.12740i
$915$	1.26765	−	19.3407i	0.0419074	−	0.639383i
$916$	−3.17352	+	7.66156i	−0.104856	+	0.253145i
$917$	13.0448	−	15.7370i	0.430778	−	0.519681i
$918$	−3.87585	+	2.16371i	−0.127922	+	0.0714131i
$919$	−3.83539	−	6.64309i	−0.126518	−	0.219135i	0.795807	−	0.605550i	$-0.207047\pi$
$919$	−3.83539	−	6.64309i	−0.126518	−	0.219135i	−0.922325	+	0.386415i	$0.873713\pi$
$920$	21.2987	−	16.3431i	0.702199	−	0.538816i
$921$	22.9144	−	11.3001i	0.755054	−	0.372352i
$922$	26.7082	+	7.15643i	0.879587	+	0.235685i
$923$	7.03921	+	35.3885i	0.231698	+	1.16483i
$924$	−2.12410	+	2.93365i	−0.0698777	+	0.0965100i
$925$	−16.2863	−	3.23955i	−0.535491	−	0.106516i
$926$	5.21528	+	4.00183i	0.171385	+	0.131508i
$927$	0.494447	−	3.75570i	0.0162398	−	0.123353i
$928$	1.00121	+	0.878037i	0.0328663	+	0.0288230i
$929$	29.3554	+	14.4765i	0.963120	+	0.474958i	0.854686	−	0.519145i	$-0.173750\pi$
$929$	29.3554	+	14.4765i	0.963120	+	0.474958i	0.108434	+	0.994104i	$0.465416\pi$
$930$	−8.86024	+	1.76241i	−0.290539	+	0.0577917i
$931$	−1.85456	−	3.85565i	−0.0607806	−	0.126364i
$932$	−1.88256	+	2.81746i	−0.0616654	+	0.0922889i
$933$	−2.43938	−	18.5289i	−0.0798617	−	0.606610i
$934$	−8.43923	+	14.6172i	−0.276140	+	0.478289i
$935$	−3.83603	+	17.9280i	−0.125451	+	0.586308i
$936$	−13.4476	+	7.76395i	−0.439547	+	0.253773i
$937$	−27.7703	−	11.5028i	−0.907217	−	0.375782i	−0.120226	−	0.992747i	$-0.538362\pi$
$937$	−27.7703	−	11.5028i	−0.907217	−	0.375782i	−0.786991	+	0.616965i	$0.788362\pi$
$938$	−7.00451	+	29.3875i	−0.228705	+	0.959537i
$939$	16.7295	+	16.7295i	0.545945	+	0.545945i
$940$	0.719610	+	0.820557i	0.0234711	+	0.0267636i
$941$	−32.7583	+	2.14709i	−1.06789	+	0.0699932i	−0.589197	−	0.807990i	$-0.700556\pi$
$941$	−32.7583	+	2.14709i	−1.06789	+	0.0699932i	−0.478692	+	0.877983i	$0.658889\pi$
$942$	−0.347101	+	0.395793i	−0.0113092	+	0.0128956i
$943$	21.2306	−	27.6682i	0.691363	−	0.901001i
$944$	9.81509	−	4.06554i	0.319454	−	0.132322i
$945$	4.55730	+	5.60901i	0.148249	+	0.182461i
$946$	−9.15809	−	13.7061i	−0.297755	−	0.445622i
$947$	−34.4426	+	30.2054i	−1.11923	+	0.981542i	−0.999936	−	0.0113163i	$-0.996398\pi$
$947$	−34.4426	+	30.2054i	−1.11923	+	0.981542i	−0.119298	+	0.992858i	$0.538064\pi$
$948$	7.25804	−	1.94478i	0.235730	−	0.0631637i
$949$	32.8691	+	66.6520i	1.06698	+	2.16362i
$950$	1.60582	−	0.211411i	0.0520998	−	0.00685907i
$951$	−12.7952			−0.414912
$952$	−30.1186	−	14.3553i	−0.976151	−	0.465259i
$953$	−21.1142			−0.683958			−0.341979	−	0.939708i	$-0.611097\pi$
$953$	−21.1142			−0.683958			−0.341979	+	0.939708i	$0.611097\pi$
$954$	−11.7059	+	1.54111i	−0.378993	+	0.0498953i
$955$	13.6156	+	27.6098i	0.440592	+	0.893431i
$956$	13.1700	−	3.52889i	0.425948	−	0.114132i
$957$	−0.371870	+	0.326121i	−0.0120208	+	0.0105420i
$958$	13.1861	+	19.7344i	0.426024	+	0.637590i
$959$	−32.4524	−	12.3964i	−1.04794	−	0.400302i
$960$	20.0384	−	8.30018i	0.646737	−	0.267887i
$961$	−13.1269	+	17.1073i	−0.423449	+	0.551850i
$962$	−24.3122	+	27.7228i	−0.783858	+	0.893818i
$963$	−6.65160	+	0.435969i	−0.214345	+	0.0140489i
$964$	−0.123050	−	0.140312i	−0.00396317	−	0.00451913i
$965$	29.5259	+	29.5259i	0.950471	+	0.950471i
$966$	−8.77178	+	2.61393i	−0.282227	+	0.0841019i
$967$	−37.4352	−	15.5062i	−1.20383	−	0.498644i	−0.311598	−	0.950214i	$-0.600864\pi$
$967$	−37.4352	−	15.5062i	−1.20383	−	0.498644i	−0.892236	+	0.451570i	$0.850864\pi$
$968$	22.1175	−	12.7695i	0.710883	−	0.410428i
$969$	−0.997916	+	2.31409i	−0.0320577	+	0.0743393i
$970$	−23.4437	+	40.6057i	−0.752731	+	1.30377i
$971$	−1.19301	−	9.06178i	−0.0382854	−	0.290806i	−0.999867	−	0.0162883i	$-0.994815\pi$
$971$	−1.19301	−	9.06178i	−0.0382854	−	0.290806i	0.961582	−	0.274518i	$-0.0885183\pi$
$972$	0.467206	−	0.699223i	0.0149856	−	0.0224276i
$973$	9.98994	+	4.58563i	0.320263	+	0.147008i
$974$	12.5944	−	2.50518i	0.403550	−	0.0802711i
$975$	11.2077	+	5.52701i	0.358933	+	0.177006i
$976$	8.59384	+	7.53660i	0.275082	+	0.241241i
$977$	0.639492	−	4.85742i	0.0204591	−	0.155403i	−0.978166	−	0.207826i	$-0.933361\pi$
$977$	0.639492	−	4.85742i	0.0204591	−	0.155403i	0.998625	+	0.0524234i	$0.0166945\pi$
$978$	2.89458	+	2.22109i	0.0925585	+	0.0710226i
$979$	10.1579	+	2.02052i	0.324646	+	0.0645762i
$980$	−4.31404	+	15.4902i	−0.137807	+	0.494816i
$981$	−2.84115	−	14.2834i	−0.0907109	−	0.456035i
$982$	22.7158	+	6.08667i	0.724889	+	0.194233i
$983$	50.2982	−	24.8043i	1.60426	−	0.791135i	0.604279	−	0.796772i	$-0.293461\pi$
$983$	50.2982	−	24.8043i	1.60426	−	0.791135i	0.999984	+	0.00563724i	$0.00179440\pi$
$984$	26.3351	−	20.2076i	0.839531	−	0.644195i
$985$	0.853740	+	1.47872i	0.0272024	+	0.0471160i
$986$	−1.05805	−	0.836419i	−0.0336952	−	0.0266370i
$987$	−0.437015	−	1.17864i	−0.0139103	−	0.0375165i
$988$	−0.998616	+	2.41087i	−0.0317702	+	0.0767000i
$989$	−1.97678	+	30.1598i	−0.0628579	+	0.959026i
$990$	1.23901	+	4.62405i	0.0393784	+	0.146962i
$991$	14.5985	−	43.0058i	0.463737	−	1.36612i	−0.423953	−	0.905684i	$-0.639358\pi$
$991$	14.5985	−	43.0058i	0.463737	−	1.36612i	0.887690	−	0.460441i	$-0.152309\pi$
$992$	−5.95479	+	12.0751i	−0.189065	+	0.383385i
$993$	−2.89441	+	14.5512i	−0.0918512	+	0.461767i
$994$	−5.97148	+	19.3430i	−0.189404	+	0.613522i
$995$	22.3609	+	53.9839i	0.708887	+	1.71141i
$996$	−8.45820	+	2.87117i	−0.268008	+	0.0909766i
$997$	3.02314	+	46.1242i	0.0957438	+	1.46077i	0.727770	+	0.685821i	$0.240557\pi$
$997$	3.02314	+	46.1242i	0.0957438	+	1.46077i	−0.632026	+	0.774947i	$0.717776\pi$
$998$	−23.1291	−	7.85127i	−0.732139	−	0.248528i
$999$	1.74606	−	6.51637i	0.0552428	−	0.206169i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.17	✓	384
7.5	odd	6	inner	357.2.bl.a.61.8	yes	384
17.12	odd	16	inner	357.2.bl.a.199.8	yes	384
119.12	even	48	inner	357.2.bl.a.250.17	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.17	✓	384	1.1	even	1	trivial
357.2.bl.a.61.8	yes	384	7.5	odd	6	inner
357.2.bl.a.199.8	yes	384	17.12	odd	16	inner
357.2.bl.a.250.17	yes	384	119.12	even	48	inner

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

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	357.2.bl.a.10.17

Level	$357$
Weight	$2$
Character	357.10
Analytic conductor	$2.851$
Analytic rank	$0$
Dimension	$384$
Inner twists	$4$