LMFDB - Embedded newform 833.2.l.e.246.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(246,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("833.246");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.l (of order $8$, 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			246.8
Character	$\chi$	$=$	833.246
Dual form			833.2.l.e.491.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.911810 - 0.911810i) q^{2} +(0.494163 - 1.19301i) q^{3} +0.337205i q^{4} +(-1.81755 - 0.752852i) q^{5} +(-0.637220 - 1.53839i) q^{6} +(2.13109 + 2.13109i) q^{8} +(0.942233 + 0.942233i) q^{9} +(-2.34371 + 0.970799i) q^{10} +(-1.99290 - 4.81128i) q^{11} +(0.402290 + 0.166634i) q^{12} -5.16091i q^{13} +(-1.79633 + 1.79633i) q^{15} +3.21188 q^{16} +(-4.12126 + 0.123465i) q^{17} +1.71827 q^{18} +(3.90171 - 3.90171i) q^{19} +(0.253865 - 0.612885i) q^{20} +(-6.20411 - 2.56983i) q^{22} +(-2.97594 - 7.18456i) q^{23} +(3.59552 - 1.48931i) q^{24} +(-0.798847 - 0.798847i) q^{25} +(-4.70577 - 4.70577i) q^{26} +(5.16876 - 2.14097i) q^{27} +(7.69521 + 3.18746i) q^{29} +3.27582i q^{30} +(-0.0970729 + 0.234355i) q^{31} +(-1.33355 + 1.33355i) q^{32} -6.72474 q^{33} +(-3.64523 + 3.87038i) q^{34} +(-0.317725 + 0.317725i) q^{36} +(-2.04782 + 4.94387i) q^{37} -7.11524i q^{38} +(-6.15704 - 2.55033i) q^{39} +(-2.26895 - 5.47774i) q^{40} +(-1.02603 + 0.424996i) q^{41} +(4.27537 + 4.27537i) q^{43} +(1.62239 - 0.672014i) q^{44} +(-1.00319 - 2.42191i) q^{45} +(-9.26445 - 3.83746i) q^{46} +2.71665i q^{47} +(1.58719 - 3.83182i) q^{48} -1.45679 q^{50} +(-1.88928 + 4.97773i) q^{51} +1.74028 q^{52} +(-0.174043 + 0.174043i) q^{53} +(2.76077 - 6.66508i) q^{54} +10.2451i q^{55} +(-2.72672 - 6.58288i) q^{57} +(9.92293 - 4.11021i) q^{58} +(-0.517389 - 0.517389i) q^{59} +(-0.605730 - 0.605730i) q^{60} +(-3.03505 + 1.25716i) q^{61} +(0.125175 + 0.302199i) q^{62} +8.85565i q^{64} +(-3.88540 + 9.38019i) q^{65} +(-6.13169 + 6.13169i) q^{66} +4.76074 q^{67} +(-0.0416328 - 1.38971i) q^{68} -10.0419 q^{69} +(2.78096 - 6.71384i) q^{71} +4.01596i q^{72} +(-1.53071 - 0.634043i) q^{73} +(2.64065 + 6.37509i) q^{74} +(-1.34780 + 0.558276i) q^{75} +(1.31568 + 1.31568i) q^{76} +(-7.93947 + 3.28864i) q^{78} +(0.268839 + 0.649035i) q^{79} +(-5.83775 - 2.41807i) q^{80} -3.22684i q^{81} +(-0.548029 + 1.32306i) q^{82} +(-9.59255 + 9.59255i) q^{83} +(7.58352 + 2.87829i) q^{85} +7.79665 q^{86} +(7.60537 - 7.60537i) q^{87} +(6.00621 - 14.5003i) q^{88} +17.4796i q^{89} +(-3.12304 - 1.29361i) q^{90} +(2.42267 - 1.00350i) q^{92} +(0.231619 + 0.231619i) q^{93} +(2.47707 + 2.47707i) q^{94} +(-10.0289 + 4.15413i) q^{95} +(0.931951 + 2.24993i) q^{96} +(5.18677 + 2.14843i) q^{97} +(2.65557 - 6.41111i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} + 8 q^{5} + 12 q^{6} + 20 q^{10} - 12 q^{12} - 8 q^{15} - 64 q^{16} - 16 q^{17} + 24 q^{18} - 8 q^{19} - 20 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{27} + 8 q^{29} + 36 q^{31} + 72 q^{33} - 8 q^{34}+ \cdots - 16 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 + 8 * q^5 + 12 * q^6 + 20 * q^10 - 12 * q^12 - 8 * q^15 - 64 * q^16 - 16 * q^17 + 24 * q^18 - 8 * q^19 - 20 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^27 + 8 * q^29 + 36 * q^31 + 72 * q^33 - 8 * q^34 - 16 * q^37 + 8 * q^39 - 80 * q^40 + 16 * q^41 - 32 * q^43 + 32 * q^44 + 36 * q^45 + 64 * q^46 - 112 * q^48 - 96 * q^50 + 8 * q^51 - 112 * q^52 + 100 * q^54 - 16 * q^57 + 80 * q^58 - 72 * q^60 - 96 * q^61 + 80 * q^62 - 8 * q^65 - 32 * q^67 + 116 * q^68 + 48 * q^69 - 16 * q^71 - 16 * q^73 - 80 * q^74 + 48 * q^75 + 16 * q^76 - 32 * q^78 - 16 * q^79 + 84 * q^80 + 40 * q^82 + 8 * q^83 + 16 * q^85 + 120 * q^86 + 48 * q^87 + 48 * q^88 + 72 * q^90 + 136 * q^92 - 16 * q^93 - 16 * q^94 + 16 * q^95 - 220 * q^96 - 8 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	0.911810	−	0.911810i	0.644747	−	0.644747i	−0.306972	−	0.951719i	$-0.599316\pi$
$2$	0.911810	−	0.911810i	0.644747	−	0.644747i	0.951719	+	0.306972i	$0.0993157\pi$
$3$	0.494163	−	1.19301i	0.285305	−	0.688787i	−0.714638	−	0.699495i	$-0.753408\pi$
$3$	0.494163	−	1.19301i	0.285305	−	0.688787i	0.999943	+	0.0107075i	$0.00340836\pi$
$4$			0.337205i			0.168602i
$5$	−1.81755	−	0.752852i	−0.812831	−	0.336686i	−0.0627482	−	0.998029i	$-0.519987\pi$
$5$	−1.81755	−	0.752852i	−0.812831	−	0.336686i	−0.750083	+	0.661344i	$0.769987\pi$
$6$	−0.637220	−	1.53839i	−0.260144	−	0.628043i
$7$		0			0
$7$		0			0
$8$	2.13109	+	2.13109i	0.753453	+	0.753453i
$9$	0.942233	+	0.942233i	0.314078	+	0.314078i
$10$	−2.34371	+	0.970799i	−0.741148	+	0.306993i
$11$	−1.99290	−	4.81128i	−0.600881	−	1.45065i	−0.872676	−	0.488299i	$-0.837617\pi$
$11$	−1.99290	−	4.81128i	−0.600881	−	1.45065i	0.271796	−	0.962355i	$-0.412383\pi$
$12$	0.402290	+	0.166634i	0.116131	+	0.0481031i
$13$		−	5.16091i		−	1.43138i	−0.698419	−	0.715689i	$-0.746113\pi$
$13$		−	5.16091i		−	1.43138i	0.698419	−	0.715689i	$-0.253887\pi$
$14$		0			0
$15$	−1.79633	+	1.79633i	−0.463810	+	0.463810i
$16$	3.21188			0.802971
$17$	−4.12126	+	0.123465i	−0.999552	+	0.0299446i
$17$	−4.12126	+	0.123465i	−0.999552	+	0.0299446i
$18$	1.71827			0.405001
$19$	3.90171	−	3.90171i	0.895114	−	0.895114i	−0.0998854	−	0.994999i	$-0.531848\pi$
$19$	3.90171	−	3.90171i	0.895114	−	0.895114i	0.994999	+	0.0998854i	$0.0318476\pi$
$20$	0.253865	−	0.612885i	0.0567660	−	0.137045i
$21$		0			0
$22$	−6.20411	−	2.56983i	−1.32272	−	0.547889i
$23$	−2.97594	−	7.18456i	−0.620527	−	1.49809i	−0.851086	−	0.525027i	$-0.824055\pi$
$23$	−2.97594	−	7.18456i	−0.620527	−	1.49809i	0.230559	−	0.973058i	$-0.425945\pi$
$24$	3.59552	−	1.48931i	0.733933	−	0.304005i
$25$	−0.798847	−	0.798847i	−0.159769	−	0.159769i
$26$	−4.70577	−	4.70577i	−0.922877	−	0.922877i
$27$	5.16876	−	2.14097i	0.994728	−	0.412030i
$28$		0			0
$29$	7.69521	+	3.18746i	1.42896	+	0.591896i	0.957096	−	0.289772i	$-0.0935796\pi$
$29$	7.69521	+	3.18746i	1.42896	+	0.591896i	0.471869	+	0.881669i	$0.343580\pi$
$30$			3.27582i			0.598080i
$31$	−0.0970729	+	0.234355i	−0.0174348	+	0.0420913i	−0.932357	−	0.361538i	$-0.882252\pi$
$31$	−0.0970729	+	0.234355i	−0.0174348	+	0.0420913i	0.914922	+	0.403630i	$0.132252\pi$
$32$	−1.33355	+	1.33355i	−0.235740	+	0.235740i
$33$	−6.72474			−1.17063
$34$	−3.64523	+	3.87038i	−0.625151	+	0.663765i
$35$		0			0
$36$	−0.317725	+	0.317725i	−0.0529542	+	0.0529542i
$37$	−2.04782	+	4.94387i	−0.336659	+	0.812767i	0.661373	+	0.750057i	$0.269974\pi$
$37$	−2.04782	+	4.94387i	−0.336659	+	0.812767i	−0.998032	+	0.0627097i	$0.980026\pi$
$38$		−	7.11524i		−	1.15424i
$39$	−6.15704	−	2.55033i	−0.985916	−	0.408380i
$40$	−2.26895	−	5.47774i	−0.358753	−	0.866107i
$41$	−1.02603	+	0.424996i	−0.160239	+	0.0663732i	−0.461361	−	0.887212i	$-0.652639\pi$
$41$	−1.02603	+	0.424996i	−0.160239	+	0.0663732i	0.301122	+	0.953586i	$0.402639\pi$
$42$		0			0
$43$	4.27537	+	4.27537i	0.651988	+	0.651988i	0.953471	−	0.301483i	$-0.0974818\pi$
$43$	4.27537	+	4.27537i	0.651988	+	0.651988i	−0.301483	+	0.953471i	$0.597482\pi$
$44$	1.62239	−	0.672014i	0.244584	−	0.101310i
$45$	−1.00319	−	2.42191i	−0.149547	−	0.361038i
$46$	−9.26445	−	3.83746i	−1.36597	−	0.565803i
$47$			2.71665i			0.396265i	0.980175	+	0.198132i	$0.0634876\pi$
$47$			2.71665i			0.396265i	−0.980175	+	0.198132i	$0.936512\pi$
$48$	1.58719	−	3.83182i	0.229092	−	0.553076i
$49$		0			0
$50$	−1.45679			−0.206022
$51$	−1.88928	+	4.97773i	−0.264552	+	0.697022i
$52$	1.74028			0.241334
$53$	−0.174043	+	0.174043i	−0.0239066	+	0.0239066i	−0.718959	−	0.695052i	$-0.755381\pi$
$53$	−0.174043	+	0.174043i	−0.0239066	+	0.0239066i	0.695052	+	0.718959i	$0.255381\pi$
$54$	2.76077	−	6.66508i	0.375693	−	0.907003i
$55$			10.2451i			1.38145i
$56$		0			0
$57$	−2.72672	−	6.58288i	−0.361163	−	0.871923i
$58$	9.92293	−	4.11021i	1.30294	−	0.539697i
$59$	−0.517389	−	0.517389i	−0.0673583	−	0.0673583i	0.672625	−	0.739983i	$-0.265167\pi$
$59$	−0.517389	−	0.517389i	−0.0673583	−	0.0673583i	−0.739983	+	0.672625i	$0.765167\pi$
$60$	−0.605730	−	0.605730i	−0.0781994	−	0.0781994i
$61$	−3.03505	+	1.25716i	−0.388599	+	0.160963i	−0.568424	−	0.822736i	$-0.692447\pi$
$61$	−3.03505	+	1.25716i	−0.388599	+	0.160963i	0.179825	+	0.983699i	$0.442447\pi$
$62$	0.125175	+	0.302199i	0.0158972	+	0.0383793i
$63$		0			0
$64$			8.85565i			1.10696i
$65$	−3.88540	+	9.38019i	−0.481925	+	1.16347i
$66$	−6.13169	+	6.13169i	−0.754758	+	0.754758i
$67$	4.76074			0.581616			0.290808	−	0.956781i	$-0.406076\pi$
$67$	4.76074			0.581616			0.290808	+	0.956781i	$0.406076\pi$
$68$	−0.0416328	−	1.38971i	−0.00504872	−	0.168527i
$69$	−10.0419			−1.20890
$70$		0			0
$71$	2.78096	−	6.71384i	0.330040	−	0.796787i	−0.668548	−	0.743669i	$-0.733084\pi$
$71$	2.78096	−	6.71384i	0.330040	−	0.796787i	0.998588	−	0.0531180i	$-0.0169159\pi$
$72$			4.01596i			0.473285i
$73$	−1.53071	−	0.634043i	−0.179157	−	0.0742091i	0.291302	−	0.956631i	$-0.405912\pi$
$73$	−1.53071	−	0.634043i	−0.179157	−	0.0742091i	−0.470459	+	0.882422i	$0.655912\pi$
$74$	2.64065	+	6.37509i	0.306969	+	0.741089i
$75$	−1.34780	+	0.558276i	−0.155630	+	0.0644641i
$76$	1.31568	+	1.31568i	0.150918	+	0.150918i
$77$		0			0
$78$	−7.93947	+	3.28864i	−0.898968	+	0.372365i
$79$	0.268839	+	0.649035i	0.0302468	+	0.0730221i	0.938281	−	0.345873i	$-0.112417\pi$
$79$	0.268839	+	0.649035i	0.0302468	+	0.0730221i	−0.908034	+	0.418896i	$0.862417\pi$
$80$	−5.83775	−	2.41807i	−0.652680	−	0.270349i
$81$		−	3.22684i		−	0.358538i
$82$	−0.548029	+	1.32306i	−0.0605197	+	0.146108i
$83$	−9.59255	+	9.59255i	−1.05292	+	1.05292i	−0.0543997	+	0.998519i	$0.517325\pi$
$83$	−9.59255	+	9.59255i	−1.05292	+	1.05292i	−0.998519	+	0.0543997i	$0.982675\pi$
$84$		0			0
$85$	7.58352	+	2.87829i	0.822549	+	0.312195i
$86$	7.79665			0.840735
$87$	7.60537	−	7.60537i	0.815382	−	0.815382i
$88$	6.00621	−	14.5003i	0.640264	−	1.54574i
$89$			17.4796i			1.85283i	0.376502	+	0.926416i	$0.377127\pi$
$89$			17.4796i			1.85283i	−0.376502	+	0.926416i	$0.622873\pi$
$90$	−3.12304	−	1.29361i	−0.329198	−	0.136358i
$91$		0			0
$92$	2.42267	−	1.00350i	0.252581	−	0.104622i
$93$	0.231619	+	0.231619i	0.0240177	+	0.0240177i
$94$	2.47707	+	2.47707i	0.255491	+	0.255491i
$95$	−10.0289	+	4.15413i	−1.02895	+	0.426204i
$96$	0.931951	+	2.24993i	0.0951169	+	0.229632i
$97$	5.18677	+	2.14843i	0.526637	+	0.218140i	0.630129	−	0.776490i	$-0.283002\pi$
$97$	5.18677	+	2.14843i	0.526637	+	0.218140i	−0.103493	+	0.994630i	$0.533002\pi$
$98$		0			0
$99$	2.65557	−	6.41111i	0.266895	−	0.644341i
$100$	0.269375	−	0.269375i	0.0269375	−	0.0269375i
$101$	11.7207			1.16626			0.583128	−	0.812380i	$-0.301828\pi$
$101$	11.7207			1.16626			0.583128	+	0.812380i	$0.301828\pi$
$102$	2.81608	+	6.26141i	0.278834	+	0.619972i
$103$	15.5823			1.53537			0.767685	−	0.640827i	$-0.221408\pi$
$103$	15.5823			1.53537			0.767685	+	0.640827i	$0.221408\pi$
$104$	10.9983	−	10.9983i	1.07848	−	1.07848i
$105$		0			0
$106$			0.317388i			0.0308274i
$107$	−0.719744	−	0.298128i	−0.0695803	−	0.0288211i	0.347622	−	0.937635i	$-0.386989\pi$
$107$	−0.719744	−	0.298128i	−0.0695803	−	0.0288211i	−0.417202	+	0.908814i	$0.636989\pi$
$108$	0.721945	+	1.74293i	0.0694692	+	0.167714i
$109$	16.3303	−	6.76422i	1.56416	−	0.647895i	0.578351	−	0.815788i	$-0.303696\pi$
$109$	16.3303	−	6.76422i	1.56416	−	0.647895i	0.985805	+	0.167893i	$0.0536965\pi$
$110$	9.34156	+	9.34156i	0.890683	+	0.890683i
$111$	4.88615	+	4.88615i	0.463773	+	0.463773i
$112$		0			0
$113$	−4.96006	−	11.9746i	−0.466603	−	1.12648i	−0.965636	−	0.259897i	$-0.916312\pi$
$113$	−4.96006	−	11.9746i	−0.466603	−	1.12648i	0.499033	−	0.866583i	$-0.333688\pi$
$114$	−8.48858	−	3.51609i	−0.795029	−	0.329312i
$115$			15.2987i			1.42661i
$116$	−1.07483	+	2.59486i	−0.0997952	+	0.240927i
$117$	4.86278	−	4.86278i	0.449564	−	0.449564i
$118$	−0.943520			−0.0868581
$119$		0			0
$120$	−7.65626			−0.698918
$121$	−11.3986	+	11.3986i	−1.03623	+	1.03623i
$122$	−1.62110	+	3.91369i	−0.146768	+	0.354328i
$123$			1.43409i			0.129307i
$124$	−0.0790255	−	0.0327334i	−0.00709670	−	0.00293955i
$125$	4.61479	+	11.1411i	0.412759	+	0.996489i
$126$		0			0
$127$	2.64110	+	2.64110i	0.234360	+	0.234360i	0.814510	−	0.580150i	$-0.197006\pi$
$127$	2.64110	+	2.64110i	0.234360	+	0.234360i	−0.580150	+	0.814510i	$0.697006\pi$
$128$	5.40758	+	5.40758i	0.477967	+	0.477967i
$129$	7.21331	−	2.98785i	0.635097	−	0.263066i
$130$	5.01020	+	12.0957i	0.439424	+	1.06086i
$131$	−15.3896	−	6.37456i	−1.34459	−	0.556948i	−0.409810	−	0.912171i	$-0.634405\pi$
$131$	−15.3896	−	6.37456i	−1.34459	−	0.556948i	−0.934782	+	0.355223i	$0.884405\pi$
$132$		−	2.26761i		−	0.197370i
$133$		0			0
$134$	4.34089	−	4.34089i	0.374995	−	0.374995i
$135$	−11.0063			−0.947271
$136$	−9.04587	−	8.51964i	−0.775677	−	0.730553i
$137$	−14.2015			−1.21332			−0.606660	−	0.794961i	$-0.707491\pi$
$137$	−14.2015			−1.21332			−0.606660	+	0.794961i	$0.707491\pi$
$138$	−9.15630	+	9.15630i	−0.779436	+	0.779436i
$139$	1.45887	−	3.52201i	0.123739	−	0.298733i	−0.849856	−	0.527016i	$-0.823311\pi$
$139$	1.45887	−	3.52201i	0.123739	−	0.298733i	0.973595	+	0.228282i	$0.0733109\pi$
$140$		0			0
$141$	3.24101	+	1.34247i	0.272942	+	0.113056i
$142$	−3.58604	−	8.65746i	−0.300934	−	0.726518i
$143$	−24.8306	+	10.2852i	−2.07644	+	0.860088i
$144$	3.02634	+	3.02634i	0.252195	+	0.252195i
$145$	−11.5867	−	11.5867i	−0.962224	−	0.962224i
$146$	−1.97385	+	0.817594i	−0.163357	+	0.0676646i
$147$		0			0
$148$	−1.66710	−	0.690534i	−0.137034	−	0.0567615i
$149$		−	18.4611i		−	1.51239i	−0.654346	−	0.756195i	$-0.727056\pi$
$149$		−	18.4611i		−	1.51239i	0.654346	−	0.756195i	$-0.272944\pi$
$150$	−0.719893	+	1.73798i	−0.0587790	+	0.141905i
$151$	3.95696	−	3.95696i	0.322013	−	0.322013i	−0.527526	−	0.849539i	$-0.676880\pi$
$151$	3.95696	−	3.95696i	0.322013	−	0.322013i	0.849539	+	0.527526i	$0.176880\pi$
$152$	16.6298			1.34885
$153$	−3.99952	−	3.76685i	−0.323342	−	0.304532i
$154$		0			0
$155$	0.352869	−	0.352869i	0.0283431	−	0.0283431i
$156$	0.859984	−	2.07618i	0.0688538	−	0.166228i
$157$			8.36719i			0.667774i	0.942613	+	0.333887i	$0.108360\pi$
$157$			8.36719i			0.667774i	−0.942613	+	0.333887i	$0.891640\pi$
$158$	0.836927	+	0.346666i	0.0665823	+	0.0275793i
$159$	0.121630	+	0.293641i	0.00964589	+	0.0232872i
$160$	3.42774	−	1.41982i	0.270987	−	0.112246i
$161$		0			0
$162$	−2.94226	−	2.94226i	−0.231166	−	0.231166i
$163$	−3.58651	+	1.48558i	−0.280917	+	0.116360i	−0.518694	−	0.854960i	$-0.673581\pi$
$163$	−3.58651	+	1.48558i	−0.280917	+	0.116360i	0.237776	+	0.971320i	$0.423581\pi$
$164$	−0.143311	−	0.345982i	−0.0111907	−	0.0270167i
$165$	12.2225	+	5.06273i	0.951522	+	0.394133i
$166$			17.4932i			1.35773i
$167$	2.95726	−	7.13946i	0.228840	−	0.552468i	−0.767197	−	0.641411i	$-0.778349\pi$
$167$	2.95726	−	7.13946i	0.228840	−	0.552468i	0.996037	+	0.0889438i	$0.0283492\pi$
$168$		0			0
$169$	−13.6350			−1.04885
$170$	9.53919	−	4.29028i	0.731623	−	0.329049i
$171$	7.35264			0.562270
$172$	−1.44168	+	1.44168i	−0.109927	+	0.109927i
$173$	−3.34115	+	8.06626i	−0.254023	+	0.613266i	−0.998522	−	0.0543581i	$-0.982689\pi$
$173$	−3.34115	+	8.06626i	−0.254023	+	0.613266i	0.744498	+	0.667624i	$0.232689\pi$
$174$		−	13.8693i		−	1.05143i
$175$		0			0
$176$	−6.40095	−	15.4533i	−0.482490	−	1.16483i
$177$	−0.872927	+	0.361578i	−0.0656132	+	0.0271779i
$178$	15.9381	+	15.9381i	1.19461	+	1.19461i
$179$	4.68148	+	4.68148i	0.349910	+	0.349910i	0.860076	−	0.510166i	$-0.170416\pi$
$179$	4.68148	+	4.68148i	0.349910	+	0.349910i	−0.510166	+	0.860076i	$0.670416\pi$
$180$	0.816681	−	0.338280i	0.0608718	−	0.0252139i
$181$	−0.843106	−	2.03544i	−0.0626676	−	0.151293i	0.889444	−	0.457045i	$-0.151092\pi$
$181$	−0.843106	−	2.03544i	−0.0626676	−	0.151293i	−0.952111	+	0.305752i	$0.901092\pi$
$182$		0			0
$183$			4.24211i			0.313586i
$184$	8.96893	−	21.6529i	0.661199	−	1.59627i
$185$	7.44401	−	7.44401i	0.547294	−	0.547294i
$186$	0.422385			0.0309707
$187$	8.80726	+	19.5825i	0.644050	+	1.43201i
$188$	−0.916069			−0.0668112
$189$		0			0
$190$	−5.35672	+	12.9323i	−0.388617	+	0.938205i
$191$		−	2.41526i		−	0.174762i	−0.996175	−	0.0873809i	$-0.972150\pi$
$191$		−	2.41526i		−	0.174762i	0.996175	−	0.0873809i	$-0.0278497\pi$
$192$	10.5649	+	4.37613i	0.762457	+	0.315820i
$193$	6.75000	+	16.2959i	0.485876	+	1.17301i	0.956777	+	0.290822i	$0.0939287\pi$
$193$	6.75000	+	16.2959i	0.485876	+	1.17301i	−0.470901	+	0.882186i	$0.656071\pi$
$194$	6.68831	−	2.77039i	0.480192	−	0.198902i
$195$	9.27068	+	9.27068i	0.663888	+	0.663888i
$196$		0			0
$197$	−9.59101	+	3.97272i	−0.683331	+	0.283045i	−0.697219	−	0.716859i	$-0.745579\pi$
$197$	−9.59101	+	3.97272i	−0.683331	+	0.283045i	0.0138876	+	0.999904i	$0.495579\pi$
$198$	−3.42434	−	8.26709i	−0.243357	−	0.587517i
$199$	5.82609	+	2.41325i	0.413000	+	0.171070i	0.579502	−	0.814971i	$-0.303247\pi$
$199$	5.82609	+	2.41325i	0.413000	+	0.171070i	−0.166502	+	0.986041i	$0.553247\pi$
$200$		−	3.40482i		−	0.240757i
$201$	2.35258	−	5.67963i	0.165938	−	0.400610i
$202$	10.6871	−	10.6871i	0.751941	−	0.751941i
$203$		0			0
$204$	−1.67851	−	0.637073i	−0.117520	−	0.0446041i
$205$	2.18482			0.152594
$206$	14.2081	−	14.2081i	0.989926	−	0.989926i
$207$	3.96550	−	9.57356i	0.275621	−	0.665409i
$208$		−	16.5762i		−	1.14936i
$209$	−26.5479	−	10.9965i	−1.83636	−	0.760644i
$210$		0			0
$211$	16.1575	−	6.69266i	1.11233	−	0.460742i	0.250590	−	0.968093i	$-0.419375\pi$
$211$	16.1575	−	6.69266i	1.11233	−	0.460742i	0.861739	+	0.507351i	$0.169375\pi$
$212$	−0.0586880	−	0.0586880i	−0.00403071	−	0.00403071i
$213$	−6.63546	−	6.63546i	−0.454655	−	0.454655i
$214$	−0.928106	+	0.384434i	−0.0634440	+	0.0262794i
$215$	−4.55196	−	10.9894i	−0.310441	−	0.749471i
$216$	15.5777	+	6.45248i	1.05993	+	0.439036i
$217$		0			0
$218$	8.72242	−	21.0578i	0.590757	−	1.42621i
$219$	−1.51284	+	1.51284i	−0.102229	+	0.102229i
$220$	−3.45469			−0.232915
$221$	0.637190	+	21.2694i	0.0428620	+	1.43074i
$222$	8.91049			0.598033
$223$	−17.9143	+	17.9143i	−1.19963	+	1.19963i	−0.225355	+	0.974277i	$0.572354\pi$
$223$	−17.9143	+	17.9143i	−1.19963	+	1.19963i	−0.974277	+	0.225355i	$0.927646\pi$
$224$		0			0
$225$		−	1.50540i		−	0.100360i
$226$	−15.4412	−	6.39597i	−1.02714	−	0.425453i
$227$	1.41304	+	3.41139i	0.0937870	+	0.226422i	0.963810	−	0.266588i	$-0.0858965\pi$
$227$	1.41304	+	3.41139i	0.0937870	+	0.226422i	−0.870023	+	0.493010i	$0.835896\pi$
$228$	2.21978	−	0.919462i	0.147008	−	0.0608929i
$229$	7.12679	+	7.12679i	0.470952	+	0.470952i	0.902223	−	0.431271i	$-0.141935\pi$
$229$	7.12679	+	7.12679i	0.470952	+	0.470952i	−0.431271	+	0.902223i	$0.641935\pi$
$230$	13.9495	+	13.9495i	0.919805	+	0.919805i
$231$		0			0
$232$	9.60640	+	23.1919i	0.630691	+	1.52262i
$233$	16.1640	+	6.69534i	1.05894	+	0.438626i	0.843074	−	0.537797i	$-0.180743\pi$
$233$	16.1640	+	6.69534i	1.05894	+	0.438626i	0.215863	+	0.976424i	$0.430743\pi$
$234$		−	8.86786i		−	0.579710i
$235$	2.04524	−	4.93764i	0.133417	−	0.322096i
$236$	0.174466	−	0.174466i	0.0113568	−	0.0113568i
$237$	0.907158			0.0589263
$238$		0			0
$239$	16.1180			1.04259			0.521295	−	0.853377i	$-0.325449\pi$
$239$	16.1180			1.04259			0.521295	+	0.853377i	$0.325449\pi$
$240$	−5.76960	+	5.76960i	−0.372426	+	0.372426i
$241$	1.98106	−	4.78270i	0.127611	−	0.308081i	−0.847142	−	0.531367i	$-0.821679\pi$
$241$	1.98106	−	4.78270i	0.127611	−	0.308081i	0.974753	+	0.223286i	$0.0716785\pi$
$242$			20.7867i			1.33622i
$243$	11.6566	+	4.82833i	0.747772	+	0.309737i
$244$	−0.423921	−	1.02343i	−0.0271387	−	0.0655187i
$245$		0			0
$246$	1.30761	+	1.30761i	0.0833705	+	0.0833705i
$247$	−20.1364	−	20.1364i	−1.28125	−	1.28125i
$248$	−0.706301	+	0.292559i	−0.0448502	+	0.0185775i
$249$	6.70377	+	16.1843i	0.424834	+	1.02564i
$250$	14.3664	+	5.95074i	0.908609	+	0.376358i
$251$		−	27.2069i		−	1.71728i	−0.512578	−	0.858641i	$-0.671309\pi$
$251$		−	27.2069i		−	1.71728i	0.512578	−	0.858641i	$-0.328691\pi$
$252$		0			0
$253$	−28.6362	+	28.6362i	−1.80034	+	1.80034i
$254$	4.81637			0.302206
$255$	7.18134	−	7.62491i	0.449713	−	0.477490i
$256$	−7.84993			−0.490621
$257$	4.11539	−	4.11539i	0.256711	−	0.256711i	−0.567004	−	0.823715i	$-0.691898\pi$
$257$	4.11539	−	4.11539i	0.256711	−	0.256711i	0.823715	+	0.567004i	$0.191898\pi$
$258$	3.85282	−	9.30152i	0.239866	−	0.579088i
$259$		0			0
$260$	−3.16304	−	1.31018i	−0.196164	−	0.0812537i
$261$	4.24735	+	10.2540i	0.262904	+	0.634707i
$262$	−19.8447	+	8.21996i	−1.22601	+	0.507831i
$263$	13.7795	+	13.7795i	0.849681	+	0.849681i	0.990093	−	0.140412i	$-0.0448428\pi$
$263$	13.7795	+	13.7795i	0.849681	+	0.849681i	−0.140412	+	0.990093i	$0.544843\pi$
$264$	−14.3310	−	14.3310i	−0.882012	−	0.882012i
$265$	0.447359	−	0.185302i	0.0274810	−	0.0113830i
$266$		0			0
$267$	20.8534	+	8.63776i	1.27621	+	0.528622i
$268$			1.60534i			0.0980619i
$269$	−4.08537	+	9.86295i	−0.249089	+	0.601355i	−0.998127	−	0.0611723i	$-0.980516\pi$
$269$	−4.08537	+	9.86295i	−0.249089	+	0.601355i	0.749038	+	0.662527i	$0.230516\pi$
$270$	−10.0356	+	10.0356i	−0.610750	+	0.610750i
$271$	19.7525			1.19988			0.599939	−	0.800046i	$-0.295192\pi$
$271$	19.7525			1.19988			0.599939	+	0.800046i	$0.295192\pi$
$272$	−13.2370	+	0.396554i	−0.802611	+	0.0240446i
$273$		0			0
$274$	−12.9491	+	12.9491i	−0.782285	+	0.782285i
$275$	−2.25145	+	5.43549i	−0.135768	+	0.327773i
$276$		−	3.38617i		−	0.203824i
$277$	−13.3441	−	5.52729i	−0.801767	−	0.332103i	−0.0561032	−	0.998425i	$-0.517868\pi$
$277$	−13.3441	−	5.52729i	−0.801767	−	0.332103i	−0.745664	+	0.666322i	$0.767868\pi$
$278$	−1.88120	−	4.54162i	−0.112827	−	0.272388i
$279$	−0.312282	+	0.129351i	−0.0186958	+	0.00774407i
$280$		0			0
$281$	−14.0732	−	14.0732i	−0.839539	−	0.839539i	0.149259	−	0.988798i	$-0.452311\pi$
$281$	−14.0732	−	14.0732i	−0.839539	−	0.839539i	−0.988798	+	0.149259i	$0.952311\pi$
$282$	4.17926	−	1.73111i	0.248871	−	0.103086i
$283$	9.27408	+	22.3896i	0.551287	+	1.33092i	0.916513	+	0.400006i	$0.130992\pi$
$283$	9.27408	+	22.3896i	0.551287	+	1.33092i	−0.365226	+	0.930919i	$0.619008\pi$
$284$	2.26394	+	0.937755i	0.134340	+	0.0556455i
$285$			14.0175i			0.830325i
$286$	−13.2626	+	32.0189i	−0.784237	+	1.89332i
$287$		0			0
$288$	−2.51302			−0.148081
$289$	16.9695	−	1.01766i	0.998207	−	0.0598623i
$290$	−21.1298			−1.24078
$291$	5.12622	−	5.12622i	0.300504	−	0.300504i
$292$	0.213802	−	0.516164i	0.0125118	−	0.0302062i
$293$		−	2.54471i		−	0.148664i	−0.997234	−	0.0743318i	$-0.976318\pi$
$293$		−	2.54471i		−	0.148664i	0.997234	−	0.0743318i	$-0.0236824\pi$
$294$		0			0
$295$	0.550861	+	1.32989i	0.0320723	+	0.0774295i
$296$	−14.8999	+	6.17174i	−0.866039	+	0.358725i
$297$	−20.6016	−	20.6016i	−1.19543	−	1.19543i
$298$	−16.8330	−	16.8330i	−0.975109	−	0.975109i
$299$	−37.0789	+	15.3586i	−2.14433	+	0.888209i
$300$	−0.188253	−	0.454484i	−0.0108688	−	0.0262396i
$301$		0			0
$302$		−	7.21599i		−	0.415234i
$303$	5.79195	−	13.9830i	0.332739	−	0.803303i
$304$	12.5318	−	12.5318i	0.718750	−	0.718750i
$305$	6.46281			0.370059
$306$	−7.08145	+	0.212146i	−0.404820	+	0.0121276i
$307$	−12.1457			−0.693192			−0.346596	−	0.938015i	$-0.612662\pi$
$307$	−12.1457			−0.693192			−0.346596	+	0.938015i	$0.612662\pi$
$308$		0			0
$309$	7.70020	−	18.5899i	0.438049	−	1.05754i
$310$		−	0.643499i		−	0.0365483i
$311$	9.22788	+	3.82231i	0.523265	+	0.216744i	0.628651	−	0.777688i	$-0.283608\pi$
$311$	9.22788	+	3.82231i	0.523265	+	0.216744i	−0.105385	+	0.994431i	$0.533608\pi$
$312$	−7.68622	−	18.5562i	−0.435146	−	1.05054i
$313$	−12.8720	+	5.33174i	−0.727567	+	0.301368i	−0.715552	−	0.698560i	$-0.753825\pi$
$313$	−12.8720	+	5.33174i	−0.727567	+	0.301368i	−0.0120150	+	0.999928i	$0.503825\pi$
$314$	7.62929	+	7.62929i	0.430546	+	0.430546i
$315$		0			0
$316$	−0.218858	+	0.0906538i	−0.0123117	+	0.00509967i
$317$	2.56268	+	6.18686i	0.143935	+	0.347489i	0.979363	−	0.202111i	$-0.0647802\pi$
$317$	2.56268	+	6.18686i	0.143935	+	0.347489i	−0.835428	+	0.549600i	$0.814780\pi$
$318$	0.378648	+	0.156841i	0.0212335	+	0.00879522i
$319$		−	43.3761i		−	2.42859i
$320$	6.66699	−	16.0955i	0.372696	−	0.899768i
$321$	−0.711342	+	0.711342i	−0.0397032	+	0.0397032i
$322$		0			0
$323$	−15.5982	+	16.5617i	−0.867908	+	0.921516i
$324$	1.08811			0.0604503
$325$	−4.12278	+	4.12278i	−0.228691	+	0.228691i
$326$	−1.91565	+	4.62478i	−0.106098	+	0.256143i
$327$		−	22.8249i		−	1.26222i
$328$	−3.09226	−	1.28086i	−0.170742	−	0.0707235i
$329$		0			0
$330$	15.7609	−	6.52837i	0.867607	−	0.359375i
$331$	7.68099	+	7.68099i	0.422185	+	0.422185i	0.885955	−	0.463770i	$-0.153504\pi$
$331$	7.68099	+	7.68099i	0.422185	+	0.422185i	−0.463770	+	0.885955i	$0.653504\pi$
$332$	−3.23465	−	3.23465i	−0.177525	−	0.177525i
$333$	−6.58780	+	2.72876i	−0.361009	+	0.149535i
$334$	−3.81337	−	9.20629i	−0.208658	−	0.503746i
$335$	−8.65286	−	3.58413i	−0.472756	−	0.195822i
$336$		0			0
$337$	6.71009	−	16.1996i	0.365522	−	0.882447i	−0.628950	−	0.777445i	$-0.716515\pi$
$337$	6.71009	−	16.1996i	0.365522	−	0.882447i	0.994472	−	0.105002i	$-0.0334849\pi$
$338$	−12.4325	+	12.4325i	−0.676240	+	0.676240i
$339$	−16.7370			−0.909029
$340$	−0.970575	+	2.55720i	−0.0526368	+	0.138684i
$341$	1.32100			0.0715362
$342$	6.70421	−	6.70421i	0.362522	−	0.362522i
$343$		0			0
$344$			18.2224i			0.982485i
$345$	18.2516	+	7.56006i	0.982633	+	0.407020i
$346$	4.30840	+	10.4014i	0.231621	+	0.559182i
$347$	−19.1326	+	7.92496i	−1.02709	+	0.425434i	−0.831661	−	0.555284i	$-0.812610\pi$
$347$	−19.1326	+	7.92496i	−1.02709	+	0.425434i	−0.195428	+	0.980718i	$0.562610\pi$
$348$	2.56457	+	2.56457i	0.137475	+	0.137475i
$349$	17.4028	+	17.4028i	0.931551	+	0.931551i	0.997803	−	0.0662519i	$-0.0211041\pi$
$349$	17.4028	+	17.4028i	0.931551	+	0.931551i	−0.0662519	+	0.997803i	$0.521104\pi$
$350$		0			0
$351$	−11.0494	−	26.6755i	−0.589771	−	1.42383i
$352$	9.07368	+	3.75844i	0.483629	+	0.200326i
$353$		−	7.71424i		−	0.410588i	−0.978700	−	0.205294i	$-0.934185\pi$
$353$		−	7.71424i		−	0.410588i	0.978700	−	0.205294i	$-0.0658150\pi$
$354$	−0.466253	+	1.12563i	−0.0247811	+	0.0598268i
$355$	−10.1091	+	10.1091i	−0.536533	+	0.536533i
$356$	−5.89420			−0.312392
$357$		0			0
$358$	8.53724			0.451207
$359$	−13.5669	+	13.5669i	−0.716032	+	0.716032i	−0.967790	−	0.251758i	$-0.918991\pi$
$359$	−13.5669	+	13.5669i	−0.716032	+	0.716032i	0.251758	+	0.967790i	$0.418991\pi$
$360$	3.02342	−	7.29919i	0.159348	−	0.384701i
$361$		−	11.4467i		−	0.602457i
$362$	−2.62469	−	1.08718i	−0.137950	−	0.0571410i
$363$	7.96591	+	19.2314i	0.418102	+	1.00939i
$364$		0			0
$365$	2.30480	+	2.30480i	0.120639	+	0.120639i
$366$	3.86800	+	3.86800i	0.202183	+	0.202183i
$367$	0.252634	−	0.104645i	0.0131874	−	0.00546240i	−0.376080	−	0.926587i	$-0.622728\pi$
$367$	0.252634	−	0.104645i	0.0131874	−	0.00546240i	0.389267	+	0.921125i	$0.372728\pi$
$368$	−9.55838	−	23.0760i	−0.498265	−	1.20292i
$369$	−1.36720	−	0.566315i	−0.0711738	−	0.0294812i
$370$		−	13.5750i		−	0.705733i
$371$		0			0
$372$	−0.0781030	+	0.0781030i	−0.00404945	+	0.00404945i
$373$	−3.39033			−0.175544			−0.0877722	−	0.996141i	$-0.527975\pi$
$373$	−3.39033			−0.175544			−0.0877722	+	0.996141i	$0.527975\pi$
$374$	25.8860	+	9.82493i	1.33853	+	0.508035i
$375$	15.5719			0.804131
$376$	−5.78943	+	5.78943i	−0.298567	+	0.298567i
$377$	16.4502	−	39.7143i	0.847228	−	2.04539i
$378$		0			0
$379$	−7.80725	−	3.23387i	−0.401032	−	0.166113i	0.173046	−	0.984914i	$-0.444639\pi$
$379$	−7.80725	−	3.23387i	−0.401032	−	0.166113i	−0.574077	+	0.818801i	$0.694639\pi$
$380$	−1.40079	−	3.38181i	−0.0718591	−	0.173483i
$381$	4.45601	−	1.84574i	0.228288	−	0.0945601i
$382$	−2.20225	−	2.20225i	−0.112677	−	0.112677i
$383$	−10.1289	−	10.1289i	−0.517560	−	0.517560i	0.399272	−	0.916832i	$-0.369263\pi$
$383$	−10.1289	−	10.1289i	−0.517560	−	0.517560i	−0.916832	+	0.399272i	$0.869263\pi$
$384$	9.12354	−	3.77910i	0.465584	−	0.192851i
$385$		0			0
$386$	21.0135	+	8.70409i	1.06956	+	0.443026i
$387$			8.05679i			0.409550i
$388$	−0.724461	+	1.74900i	−0.0367789	+	0.0887922i
$389$	4.55909	−	4.55909i	0.231155	−	0.231155i	−0.582020	−	0.813175i	$-0.697737\pi$
$389$	4.55909	−	4.55909i	0.231155	−	0.231155i	0.813175	+	0.582020i	$0.197737\pi$
$390$	16.9062			0.856079
$391$	13.1517	+	29.2420i	0.665108	+	1.47883i
$392$		0			0
$393$	−15.2099	+	15.2099i	−0.767238	+	0.767238i
$394$	−5.12281	+	12.3675i	−0.258083	+	0.623068i
$395$		−	1.38205i		−	0.0695383i
$396$	2.16186	+	0.895471i	0.108637	+	0.0449991i
$397$	−9.67322	−	23.3532i	−0.485485	−	1.17206i	−0.956969	−	0.290190i	$-0.906281\pi$
$397$	−9.67322	−	23.3532i	−0.485485	−	1.17206i	0.471484	−	0.881875i	$-0.343719\pi$
$398$	7.51271	−	3.11187i	0.376578	−	0.155984i
$399$		0			0
$400$	−2.56580	−	2.56580i	−0.128290	−	0.128290i
$401$	−28.3575	+	11.7460i	−1.41610	+	0.586570i	−0.953879	−	0.300193i	$-0.902949\pi$
$401$	−28.3575	+	11.7460i	−1.41610	+	0.586570i	−0.462226	+	0.886762i	$0.652949\pi$
$402$	−3.03364	−	7.32385i	−0.151304	−	0.365280i
$403$	1.20948	+	0.500984i	0.0602487	+	0.0249558i
$404$			3.95229i			0.196634i
$405$	−2.42933	+	5.86493i	−0.120715	+	0.291431i
$406$		0			0
$407$	27.8674			1.38134
$408$	−14.6342	+	6.58177i	−0.724501	+	0.325846i
$409$	2.49639			0.123438			0.0617192	−	0.998094i	$-0.480342\pi$
$409$	2.49639			0.123438			0.0617192	+	0.998094i	$0.480342\pi$
$410$	1.99214	−	1.99214i	0.0983846	−	0.0983846i
$411$	−7.01788	+	16.9427i	−0.346166	+	0.835720i
$412$			5.25443i			0.258867i
$413$		0			0
$414$	−5.11349	−	12.3451i	−0.251314	−	0.606726i
$415$	24.6567	−	10.2131i	1.21035	−	0.501343i
$416$	6.88231	+	6.88231i	0.337433	+	0.337433i
$417$	−3.48090	−	3.48090i	−0.170460	−	0.170460i
$418$	−34.2334	+	14.1799i	−1.67441	+	0.693563i
$419$	7.13648	+	17.2290i	0.348640	+	0.841691i	0.996781	+	0.0801711i	$0.0255467\pi$
$419$	7.13648	+	17.2290i	0.348640	+	0.841691i	−0.648141	+	0.761520i	$0.724453\pi$
$420$		0			0
$421$		−	26.6441i		−	1.29856i	−0.760551	−	0.649278i	$-0.775071\pi$
$421$		−	26.6441i		−	1.29856i	0.760551	−	0.649278i	$-0.224929\pi$
$422$	8.63015	−	20.8350i	0.420109	−	1.01423i
$423$	−2.55972	+	2.55972i	−0.124458	+	0.124458i
$424$	−0.741800			−0.0360250
$425$	3.39088	+	3.19362i	0.164482	+	0.154914i
$426$	−12.1006			−0.586274
$427$		0			0
$428$	0.100530	−	0.242701i	0.00485931	−	0.0117314i
$429$			34.7058i			1.67561i
$430$	−14.1708	−	5.86973i	−0.683376	−	0.283063i
$431$	−8.69373	−	20.9885i	−0.418762	−	1.01098i	−0.982707	−	0.185168i	$-0.940717\pi$
$431$	−8.69373	−	20.9885i	−0.418762	−	1.01098i	0.563945	−	0.825813i	$-0.309283\pi$
$432$	16.6015	−	6.87655i	0.798738	−	0.330848i
$433$	−27.9303	−	27.9303i	−1.34224	−	1.34224i	−0.893824	−	0.448418i	$-0.851987\pi$
$433$	−27.9303	−	27.9303i	−1.34224	−	1.34224i	−0.448418	−	0.893824i	$-0.648013\pi$
$434$		0			0
$435$	−19.5488	+	8.09739i	−0.937295	+	0.388240i
$436$	2.28093	+	5.50664i	0.109237	+	0.263720i
$437$	−39.6434	−	16.4208i	−1.89640	−	0.785514i
$438$			2.75885i			0.131823i
$439$	12.8588	−	31.0440i	0.613719	−	1.48165i	−0.245166	−	0.969481i	$-0.578843\pi$
$439$	12.8588	−	31.0440i	0.613719	−	1.48165i	0.858885	−	0.512168i	$-0.171157\pi$
$440$	−21.8331	+	21.8331i	−1.04085	+	1.04085i
$441$		0			0
$442$	19.9747	+	18.8127i	0.950099	+	0.894828i
$443$	20.6306			0.980190			0.490095	−	0.871669i	$-0.336962\pi$
$443$	20.6306			0.980190			0.490095	+	0.871669i	$0.336962\pi$
$444$	−1.64763	+	1.64763i	−0.0781933	+	0.0781933i
$445$	13.1595	−	31.7699i	0.623822	−	1.50604i
$446$			32.6689i			1.54692i
$447$	−22.0243	−	9.12278i	−1.04172	−	0.431493i
$448$		0			0
$449$	12.3940	−	5.13378i	0.584911	−	0.242278i	−0.0705488	−	0.997508i	$-0.522475\pi$
$449$	12.3940	−	5.13378i	0.584911	−	0.242278i	0.655459	+	0.755230i	$0.272475\pi$
$450$	−1.37264	−	1.37264i	−0.0647068	−	0.0647068i
$451$	4.08954	+	4.08954i	0.192569	+	0.192569i
$452$	4.03791	−	1.67256i	0.189927	−	0.0786704i
$453$	−2.76533	−	6.67609i	−0.129926	−	0.313670i
$454$	4.39897	+	1.82211i	0.206454	+	0.0855159i
$455$		0			0
$456$	8.21781	−	19.8396i	0.384834	−	0.929072i
$457$	1.51750	−	1.51750i	0.0709854	−	0.0709854i	−0.670723	−	0.741708i	$-0.734016\pi$
$457$	1.51750	−	1.51750i	0.0709854	−	0.0709854i	0.741708	+	0.670723i	$0.234016\pi$
$458$	12.9966			0.607289
$459$	−21.0374	+	9.46165i	−0.981944	+	0.441632i
$460$	−5.15880			−0.240530
$461$	9.22332	−	9.22332i	0.429573	−	0.429573i	−0.458910	−	0.888483i	$-0.651760\pi$
$461$	9.22332	−	9.22332i	0.429573	−	0.429573i	0.888483	+	0.458910i	$0.151760\pi$
$462$		0			0
$463$			31.6409i			1.47048i	0.677809	+	0.735238i	$0.262929\pi$
$463$			31.6409i			1.47048i	−0.677809	+	0.735238i	$0.737071\pi$
$464$	24.7161	+	10.2377i	1.14742	+	0.475276i
$465$	−0.246603	−	0.595352i	−0.0114359	−	0.0276088i
$466$	20.8434	−	8.63360i	0.965550	−	0.399944i
$467$	−17.7755	−	17.7755i	−0.822553	−	0.822553i	0.163921	−	0.986474i	$-0.447586\pi$
$467$	−17.7755	−	17.7755i	−0.822553	−	0.822553i	−0.986474	+	0.163921i	$0.947586\pi$
$468$	1.63975	+	1.63975i	0.0757976	+	0.0757976i
$469$		0			0
$470$	−2.63732	−	6.36706i	−0.121651	−	0.293691i
$471$	9.98218	+	4.13475i	0.459955	+	0.190519i
$472$		−	2.20520i		−	0.101503i
$473$	12.0496	−	29.0904i	0.554042	−	1.33758i
$474$	0.827156	−	0.827156i	0.0379925	−	0.0379925i
$475$	−6.23374			−0.286024
$476$		0			0
$477$	−0.327978			−0.0150171
$478$	14.6966	−	14.6966i	0.672207	−	0.672207i
$479$	0.806697	−	1.94754i	0.0368589	−	0.0889853i	−0.904378	−	0.426732i	$-0.859665\pi$
$479$	0.806697	−	1.94754i	0.0368589	−	0.0889853i	0.941237	+	0.337747i	$0.109665\pi$
$480$		−	4.79097i		−	0.218677i
$481$	25.5149	+	10.5686i	1.16338	+	0.481887i
$482$	−2.55456	−	6.16726i	−0.116357	−	0.280911i
$483$		0			0
$484$	−3.84365	−	3.84365i	−0.174711	−	0.174711i
$485$	−7.80974	−	7.80974i	−0.354622	−	0.354622i
$486$	15.0311	−	6.22610i	0.681826	−	0.282422i
$487$	1.54161	+	3.72177i	0.0698569	+	0.168650i	0.954952	−	0.296761i	$-0.0959066\pi$
$487$	1.54161	+	3.72177i	0.0698569	+	0.168650i	−0.885095	+	0.465411i	$0.845907\pi$
$488$	−9.14708	−	3.78885i	−0.414069	−	0.171513i
$489$			5.01288i			0.226690i
$490$		0			0
$491$	5.16257	−	5.16257i	0.232984	−	0.232984i	−0.580953	−	0.813937i	$-0.697320\pi$
$491$	5.16257	−	5.16257i	0.232984	−	0.232984i	0.813937	+	0.580953i	$0.197320\pi$
$492$	−0.483581			−0.0218015
$493$	−32.1075	−	12.1863i	−1.44605	−	0.548841i
$494$	−36.7211			−1.65216
$495$	−9.65324	+	9.65324i	−0.433881	+	0.433881i
$496$	−0.311787	+	0.752720i	−0.0139996	+	0.0337981i
$497$		0			0
$498$	20.8696	+	8.64447i	0.935189	+	0.387368i
$499$	−2.49764	−	6.02983i	−0.111810	−	0.269932i	0.858063	−	0.513544i	$-0.171668\pi$
$499$	−2.49764	−	6.02983i	−0.111810	−	0.269932i	−0.969873	+	0.243612i	$0.921668\pi$
$500$	−3.75683	+	1.55613i	−0.168010	+	0.0695922i
$501$	−7.05611	−	7.05611i	−0.315244	−	0.315244i
$502$	−24.8075	−	24.8075i	−1.10721	−	1.10721i
$503$	16.5032	−	6.83583i	0.735839	−	0.304795i	0.0168901	−	0.999857i	$-0.494623\pi$
$503$	16.5032	−	6.83583i	0.735839	−	0.304795i	0.718949	+	0.695063i	$0.244623\pi$
$504$		0			0
$505$	−21.3030	−	8.82398i	−0.947970	−	0.392662i
$506$			52.2215i			2.32153i
$507$	−6.73791	+	16.2667i	−0.299241	+	0.722431i
$508$	−0.890592	+	0.890592i	−0.0395137	+	0.0395137i
$509$	−9.72487			−0.431047			−0.215524	−	0.976499i	$-0.569146\pi$
$509$	−9.72487			−0.431047			−0.215524	+	0.976499i	$0.569146\pi$
$510$	−0.404448	−	13.5005i	−0.0179092	−	0.597812i
$511$		0			0
$512$	−17.9728	+	17.9728i	−0.794293	+	0.794293i
$513$	11.8136	−	28.5204i	0.521581	−	1.25921i
$514$		−	7.50492i		−	0.331028i
$515$	−28.3216	−	11.7312i	−1.24800	−	0.516937i
$516$	1.00752	+	2.43236i	0.0443535	+	0.107079i
$517$	13.0706	−	5.41401i	0.574843	−	0.238108i
$518$		0			0
$519$	7.97209	+	7.97209i	0.349936	+	0.349936i
$520$	−28.2701	+	11.7099i	−1.23973	+	0.513512i
$521$	−3.50365	−	8.45855i	−0.153498	−	0.370576i	0.828360	−	0.560196i	$-0.189274\pi$
$521$	−3.50365	−	8.45855i	−0.153498	−	0.370576i	−0.981857	+	0.189620i	$0.939274\pi$
$522$	13.2225	+	5.47693i	0.578732	+	0.239719i
$523$			0.446252i			0.0195133i	0.999952	+	0.00975663i	$0.00310568\pi$
$523$			0.446252i			0.0195133i	−0.999952	+	0.00975663i	$0.996894\pi$
$524$	2.14953	−	5.18943i	0.0939028	−	0.226701i
$525$		0			0
$526$	25.1286			1.09566
$527$	0.371128	−	0.977821i	0.0161666	−	0.0425945i
$528$	−21.5991			−0.939979
$529$	−26.4983	+	26.4983i	−1.15210	+	1.15210i
$530$	0.238946	−	0.576867i	0.0103792	−	0.0250575i
$531$		−	0.975001i		−	0.0423114i
$532$		0			0
$533$	2.19336	+	5.29525i	0.0950051	+	0.229363i
$534$	26.8903	−	11.1383i	1.16366	−	0.482003i
$535$	1.08372	+	1.08372i	0.0468534	+	0.0468534i
$536$	10.1455	+	10.1455i	0.438221	+	0.438221i
$537$	7.89849	−	3.27166i	0.340845	−	0.141183i
$538$	5.26806	+	12.7182i	0.227122	+	0.548321i
$539$		0			0
$540$		−	3.71137i		−	0.159712i
$541$	−3.73591	+	9.01929i	−0.160619	+	0.387769i	−0.983616	−	0.180277i	$-0.942301\pi$
$541$	−3.73591	+	9.01929i	−0.160619	+	0.387769i	0.822997	+	0.568046i	$0.192301\pi$
$542$	18.0105	−	18.0105i	0.773617	−	0.773617i
$543$	−2.84494			−0.122088
$544$	5.33124	−	5.66053i	0.228575	−	0.242693i
$545$	−34.7735			−1.48953
$546$		0			0
$547$	−14.4352	+	34.8496i	−0.617204	+	1.49006i	0.237732	+	0.971331i	$0.423596\pi$
$547$	−14.4352	+	34.8496i	−0.617204	+	1.49006i	−0.854937	+	0.518732i	$0.826404\pi$
$548$		−	4.78883i		−	0.204569i
$549$	−4.04427	−	1.67519i	−0.172605	−	0.0714954i
$550$	2.90324	+	7.00904i	0.123794	+	0.298866i
$551$	42.4610	−	17.5879i	1.80890	−	0.749271i
$552$	−21.4001	−	21.4001i	−0.910851	−	0.910851i
$553$		0			0
$554$	−17.2071	+	7.12741i	−0.731059	+	0.302815i
$555$	−5.20226	−	12.5594i	−0.220824	−	0.533115i
$556$	1.18764	+	0.491937i	0.0503672	+	0.0208628i
$557$			42.3653i			1.79508i	0.440937	+	0.897538i	$0.354646\pi$
$557$			42.3653i			1.79508i	−0.440937	+	0.897538i	$0.645354\pi$
$558$	−0.166798	+	0.402686i	−0.00706112	+	0.0170470i
$559$	22.0648	−	22.0648i	0.933242	−	0.933242i
$560$		0			0
$561$	27.7144	−	0.830267i	1.17010	−	0.0350539i
$562$	−25.6642			−1.08258
$563$	11.1395	−	11.1395i	0.469472	−	0.469472i	−0.432271	−	0.901744i	$-0.642288\pi$
$563$	11.1395	−	11.1395i	0.469472	−	0.469472i	0.901744	+	0.432271i	$0.142288\pi$
$564$	−0.452687	+	1.09288i	−0.0190616	+	0.0460187i
$565$			25.4986i			1.07274i
$566$	28.8713	+	11.9589i	1.21355	+	0.502669i
$567$		0			0
$568$	20.2343	−	8.38130i	0.849011	−	0.351672i
$569$	−28.6461	−	28.6461i	−1.20091	−	1.20091i	−0.973891	−	0.227017i	$-0.927103\pi$
$569$	−28.6461	−	28.6461i	−1.20091	−	1.20091i	−0.227017	−	0.973891i	$-0.572897\pi$
$570$	12.7813	+	12.7813i	0.535350	+	0.535350i
$571$	−25.2202	+	10.4465i	−1.05543	+	0.437175i	−0.841828	−	0.539746i	$-0.818520\pi$
$571$	−25.2202	+	10.4465i	−1.05543	+	0.437175i	−0.213605	+	0.976920i	$0.568520\pi$
$572$	−3.46820	−	8.37298i	−0.145013	−	0.350092i
$573$	−2.88144	−	1.19353i	−0.120374	−	0.0498604i
$574$		0			0
$575$	−3.36204	+	8.11669i	−0.140207	+	0.338489i
$576$	−8.34408	+	8.34408i	−0.347670	+	0.347670i
$577$	−16.9612			−0.706106			−0.353053	−	0.935603i	$-0.614856\pi$
$577$	−16.9612			−0.706106			−0.353053	+	0.935603i	$0.614856\pi$
$578$	14.5451	−	16.4009i	0.604995	−	0.682187i
$579$	22.7769			0.946576
$580$	3.90709	−	3.90709i	0.162233	−	0.162233i
$581$		0			0
$582$		−	9.34827i		−	0.387498i
$583$	1.18422	+	0.490519i	0.0490452	+	0.0203152i
$584$	−1.91089	−	4.61328i	−0.0790730	−	0.190899i
$585$	−12.4993	+	5.17737i	−0.516781	+	0.214058i
$586$	−2.32029	−	2.32029i	−0.0958505	−	0.0958505i
$587$	15.2431	+	15.2431i	0.629148	+	0.629148i	0.947854	−	0.318705i	$-0.103248\pi$
$587$	15.2431	+	15.2431i	0.629148	+	0.629148i	−0.318705	+	0.947854i	$0.603248\pi$
$588$		0			0
$589$	0.535634	+	1.29313i	0.0220704	+	0.0532827i
$590$	1.71489	+	0.710331i	0.0706010	+	0.0292439i
$591$			13.4054i			0.551424i
$592$	−6.57735	+	15.8791i	−0.270328	+	0.652628i
$593$	23.3609	−	23.3609i	0.959317	−	0.959317i	−0.0398870	−	0.999204i	$-0.512700\pi$
$593$	23.3609	−	23.3609i	0.959317	−	0.959317i	0.999204	+	0.0398870i	$0.0126998\pi$
$594$	−37.5695			−1.54149
$595$		0			0
$596$	6.22516			0.254993
$597$	5.75807	−	5.75807i	0.235662	−	0.235662i
$598$	−19.8048	+	47.8130i	−0.809878	+	1.95522i
$599$		−	6.52919i		−	0.266776i	−0.991064	−	0.133388i	$-0.957414\pi$
$599$		−	6.52919i		−	0.266776i	0.991064	−	0.133388i	$-0.0425856\pi$
$600$	−4.06201	−	1.68254i	−0.165831	−	0.0686893i
$601$	11.7442	+	28.3531i	0.479057	+	1.15655i	0.960052	+	0.279822i	$0.0902754\pi$
$601$	11.7442	+	28.3531i	0.479057	+	1.15655i	−0.480995	+	0.876723i	$0.659725\pi$
$602$		0			0
$603$	4.48572	+	4.48572i	0.182673	+	0.182673i
$604$	1.33431	+	1.33431i	0.0542921	+	0.0542921i
$605$	29.2989	−	12.1360i	1.19117	−	0.493398i
$606$	−7.46869	−	18.0310i	−0.303395	−	0.732460i
$607$	−9.04054	−	3.74472i	−0.366944	−	0.151993i	0.191589	−	0.981475i	$-0.438636\pi$
$607$	−9.04054	−	3.74472i	−0.366944	−	0.151993i	−0.558534	+	0.829482i	$0.688636\pi$
$608$			10.4062i			0.422028i
$609$		0			0
$610$	5.89285	−	5.89285i	0.238595	−	0.238595i
$611$	14.0204			0.567205
$612$	1.27020	−	1.34866i	0.0513448	−	0.0545162i
$613$	35.1221			1.41857			0.709285	−	0.704922i	$-0.249018\pi$
$613$	35.1221			1.41857			0.709285	+	0.704922i	$0.249018\pi$
$614$	−11.0746	+	11.0746i	−0.446933	+	0.446933i
$615$	1.07966	−	2.60652i	0.0435359	−	0.105105i
$616$		0			0
$617$	−27.2075	−	11.2697i	−1.09533	−	0.453701i	−0.239469	−	0.970904i	$-0.576973\pi$
$617$	−27.2075	−	11.2697i	−1.09533	−	0.453701i	−0.855863	+	0.517203i	$0.826973\pi$
$618$	−9.92936	−	23.9716i	−0.399418	−	0.964279i
$619$	34.0064	−	14.0859i	1.36683	−	0.566160i	0.425904	−	0.904768i	$-0.359956\pi$
$619$	34.0064	−	14.0859i	1.36683	−	0.566160i	0.940928	+	0.338608i	$0.109956\pi$
$620$	0.118989	+	0.118989i	0.00477872	+	0.00477872i
$621$	−30.7639	−	30.7639i	−1.23451	−	1.23451i
$622$	11.8993	−	4.92885i	0.477118	−	0.197629i
$623$		0			0
$624$	−19.7757	−	8.19136i	−0.791662	−	0.327917i
$625$		−	18.0750i		−	0.722999i
$626$	−6.87525	+	16.5983i	−0.274790	+	0.663403i
$627$	−26.2380	+	26.2380i	−1.04784	+	1.04784i
$628$	−2.82146			−0.112588
$629$	7.82919	−	20.6278i	0.312170	−	0.822484i
$630$		0			0
$631$	−29.7270	+	29.7270i	−1.18341	+	1.18341i	−0.204557	+	0.978855i	$0.565575\pi$
$631$	−29.7270	+	29.7270i	−1.18341	+	1.18341i	−0.978855	+	0.204557i	$0.934425\pi$
$632$	−0.810230	+	1.95607i	−0.0322292	+	0.0778082i
$633$		−	22.5834i		−	0.897611i
$634$	7.97792	+	3.30456i	0.316844	+	0.131241i
$635$	−2.81197	−	6.78869i	−0.111589	−	0.269401i
$636$	−0.0990171	+	0.0410142i	−0.00392629	+	0.00162632i
$637$		0			0
$638$	−39.5507	−	39.5507i	−1.56583	−	1.56583i
$639$	8.94632	−	3.70569i	0.353911	−	0.146595i
$640$	−5.75741	−	13.8996i	−0.227582	−	0.549431i
$641$	30.6623	+	12.7008i	1.21109	+	0.501649i	0.894566	−	0.446935i	$-0.147485\pi$
$641$	30.6623	+	12.7008i	1.21109	+	0.501649i	0.316523	+	0.948585i	$0.397485\pi$
$642$			1.29722i			0.0511971i
$643$	−1.50720	+	3.63871i	−0.0594383	+	0.143497i	−0.950808	−	0.309779i	$-0.899745\pi$
$643$	−1.50720	+	3.63871i	−0.0594383	+	0.143497i	0.891370	+	0.453276i	$0.149745\pi$
$644$		0			0
$645$	−15.3599			−0.604797
$646$	0.878480	+	29.3237i	0.0345633	+	1.15373i
$647$	46.4460			1.82598			0.912991	−	0.407981i	$-0.133767\pi$
$647$	46.4460			1.82598			0.912991	+	0.407981i	$0.133767\pi$
$648$	6.87667	−	6.87667i	0.270141	−	0.270141i
$649$	−1.45820	+	3.52040i	−0.0572393	+	0.138188i
$650$			7.51838i			0.294895i
$651$		0			0
$652$	−0.500945	−	1.20939i	−0.0196185	−	0.0473633i
$653$	23.3310	−	9.66403i	0.913014	−	0.378183i	0.123804	−	0.992307i	$-0.460491\pi$
$653$	23.3310	−	9.66403i	0.913014	−	0.378183i	0.789210	+	0.614124i	$0.210491\pi$
$654$	−20.8120	−	20.8120i	−0.813812	−	0.813812i
$655$	23.1721	+	23.1721i	0.905409	+	0.905409i
$656$	−3.29549	+	1.36504i	−0.128667	+	0.0532957i
$657$	−0.844873	−	2.03970i	−0.0329617	−	0.0795765i
$658$		0			0
$659$			24.0570i			0.937128i	0.883429	+	0.468564i	$0.155229\pi$
$659$			24.0570i			0.937128i	−0.883429	+	0.468564i	$0.844771\pi$
$660$	−1.70718	+	4.12149i	−0.0664518	+	0.160429i
$661$	−6.87300	+	6.87300i	−0.267329	+	0.267329i	−0.828023	−	0.560694i	$-0.810534\pi$
$661$	−6.87300	+	6.87300i	−0.267329	+	0.267329i	0.560694	+	0.828023i	$0.310534\pi$
$662$	14.0072			0.544405
$663$	25.6896	+	9.75039i	0.997702	+	0.378674i
$664$	−40.8851			−1.58665
$665$		0			0
$666$	−3.51871	+	8.49493i	−0.136347	+	0.329172i
$667$		−	64.7724i		−	2.50800i
$668$	2.40746	+	0.997202i	0.0931474	+	0.0385829i
$669$	12.5195	+	30.2246i	0.484030	+	1.16855i
$670$	−11.1578	+	4.62171i	−0.431064	+	0.178552i
$671$	12.0971	+	12.0971i	0.467003	+	0.467003i
$672$		0			0
$673$	−27.4854	+	11.3848i	−1.05948	+	0.438853i	−0.843268	−	0.537493i	$-0.819372\pi$
$673$	−27.4854	+	11.3848i	−1.05948	+	0.438853i	−0.216216	+	0.976346i	$0.569372\pi$
$674$	−8.65262	−	20.8893i	−0.333286	−	0.804624i
$675$	−5.83936	−	2.41874i	−0.224757	−	0.0930974i
$676$		−	4.59778i		−	0.176838i
$677$	8.98949	−	21.7026i	0.345494	−	0.834097i	−0.651646	−	0.758523i	$-0.725921\pi$
$677$	8.98949	−	21.7026i	0.345494	−	0.834097i	0.997140	−	0.0755736i	$-0.0240788\pi$
$678$	−15.2610	+	15.2610i	−0.586094	+	0.586094i
$679$		0			0
$680$	10.0273	+	22.2950i	0.384528	+	0.854976i
$681$	4.76811			0.182714
$682$	1.20450	−	1.20450i	0.0461228	−	0.0461228i
$683$	−5.27273	+	12.7295i	−0.201755	+	0.487080i	−0.992080	−	0.125608i	$-0.959912\pi$
$683$	−5.27273	+	12.7295i	−0.201755	+	0.487080i	0.790325	+	0.612688i	$0.209912\pi$
$684$			2.47934i			0.0948001i
$685$	25.8120	+	10.6917i	0.986225	+	0.408508i
$686$		0			0
$687$	12.0242	−	4.98057i	0.458751	−	0.190021i
$688$	13.7320	+	13.7320i	0.523527	+	0.523527i
$689$	0.898219	+	0.898219i	0.0342194	+	0.0342194i
$690$	23.5353	−	9.74865i	0.895975	−	0.371125i
$691$	16.5029	+	39.8416i	0.627800	+	1.51564i	0.842350	+	0.538931i	$0.181172\pi$
$691$	16.5029	+	39.8416i	0.627800	+	1.51564i	−0.214549	+	0.976713i	$0.568828\pi$
$692$	−2.71998	−	1.12665i	−0.103398	−	0.0428289i
$693$		0			0
$694$	−10.2192	+	24.6713i	−0.387915	+	0.936510i
$695$	−5.30311	+	5.30311i	−0.201158	+	0.201158i
$696$	32.4154			1.22870
$697$	4.17606	−	1.87819i	0.158180	−	0.0711417i
$698$	31.7361			1.20123
$699$	15.9753	−	15.9753i	0.604240	−	0.604240i
$700$		0			0
$701$		−	28.6852i		−	1.08343i	−0.840564	−	0.541713i	$-0.817776\pi$
$701$		−	28.6852i		−	1.08343i	0.840564	−	0.541713i	$-0.182224\pi$
$702$	−34.3979	−	14.2481i	−1.29827	−	0.537759i
$703$	11.2996	+	27.2795i	0.426171	+	1.02887i
$704$	42.6070	−	17.6484i	1.60581	−	0.665149i
$705$	−4.88000	−	4.88000i	−0.183792	−	0.183792i
$706$	−7.03392	−	7.03392i	−0.264725	−	0.264725i
$707$		0			0
$708$	−0.121926	−	0.294355i	−0.00458225	−	0.0110625i
$709$	−9.01194	−	3.73287i	−0.338450	−	0.140191i	0.206984	−	0.978344i	$-0.433635\pi$
$709$	−9.01194	−	3.73287i	−0.338450	−	0.140191i	−0.545434	+	0.838154i	$0.683635\pi$
$710$			18.4351i			0.691857i
$711$	−0.358233	+	0.864851i	−0.0134348	+	0.0324344i
$712$	−37.2505	+	37.2505i	−1.39602	+	1.39602i
$713$	1.97262			0.0738752
$714$		0			0
$715$	52.8739			1.97737
$716$	−1.57862	+	1.57862i	−0.0589957	+	0.0589957i
$717$	7.96494	−	19.2291i	0.297456	−	0.718123i
$718$			24.7408i			0.923319i
$719$	7.16194	+	2.96657i	0.267095	+	0.110635i	0.512212	−	0.858859i	$-0.328826\pi$
$719$	7.16194	+	2.96657i	0.267095	+	0.110635i	−0.245117	+	0.969494i	$0.578826\pi$
$720$	−3.22213	−	7.77890i	−0.120082	−	0.289903i
$721$		0			0
$722$	−10.4372	−	10.4372i	−0.388432	−	0.388432i
$723$	−4.72686	−	4.72686i	−0.175794	−	0.175794i
$724$	0.686360	−	0.284300i	0.0255084	−	0.0105659i
$725$	−3.60100	−	8.69359i	−0.133738	−	0.322872i
$726$	24.7988	+	10.2720i	0.920370	+	0.381230i
$727$		−	37.9746i		−	1.40840i	−0.710001	−	0.704201i	$-0.751306\pi$
$727$		−	37.9746i		−	1.40840i	0.710001	−	0.704201i	$-0.248694\pi$
$728$		0			0
$729$	18.3657	−	18.3657i	0.680211	−	0.680211i
$730$	4.20309			0.155563
$731$	−18.1478	−	17.0920i	−0.671219	−	0.632172i
$732$	−1.43046			−0.0528713
$733$	−21.8508	+	21.8508i	−0.807076	+	0.807076i	−0.984190	−	0.177114i	$-0.943324\pi$
$733$	−21.8508	+	21.8508i	−0.807076	+	0.807076i	0.177114	+	0.984190i	$0.443324\pi$
$734$	0.134939	−	0.325771i	0.00498067	−	0.0120244i
$735$		0			0
$736$	13.5495	+	5.61239i	0.499441	+	0.206875i
$737$	−9.48765	−	22.9052i	−0.349482	−	0.843724i
$738$	−1.76300	+	0.730259i	−0.0648970	+	0.0268812i
$739$	11.4178	+	11.4178i	0.420009	+	0.420009i	0.885207	−	0.465198i	$-0.154017\pi$
$739$	11.4178	+	11.4178i	0.420009	+	0.420009i	−0.465198	+	0.885207i	$0.654017\pi$
$740$	2.51015	+	2.51015i	0.0922751	+	0.0922751i
$741$	−33.9736	+	14.0723i	−1.24805	+	0.516960i
$742$		0			0
$743$	−4.51047	−	1.86830i	−0.165473	−	0.0685412i	0.298409	−	0.954438i	$-0.403544\pi$
$743$	−4.51047	−	1.86830i	−0.165473	−	0.0685412i	−0.463882	+	0.885897i	$0.653544\pi$
$744$			0.987199i			0.0361925i
$745$	−13.8985	+	33.5538i	−0.509200	+	1.22932i
$746$	−3.09133	+	3.09133i	−0.113182	+	0.113182i
$747$	−18.0768			−0.661397
$748$	−6.60330	+	2.96985i	−0.241440	+	0.108588i
$749$		0			0
$750$	14.1986	−	14.1986i	0.518461	−	0.518461i
$751$	−1.43111	+	3.45501i	−0.0522221	+	0.126075i	−0.947837	−	0.318754i	$-0.896736\pi$
$751$	−1.43111	+	3.45501i	−0.0522221	+	0.126075i	0.895615	+	0.444829i	$0.146736\pi$
$752$			8.72558i			0.318189i
$753$	−32.4582	−	13.4446i	−1.18284	−	0.489949i
$754$	−21.2124	−	51.2113i	−0.772511	−	1.86501i
$755$	−10.1710	+	4.21295i	−0.370159	+	0.153325i
$756$		0			0
$757$	−32.5314	−	32.5314i	−1.18238	−	1.18238i	−0.979127	−	0.203248i	$-0.934850\pi$
$757$	−32.5314	−	32.5314i	−1.18238	−	1.18238i	−0.203248	−	0.979127i	$-0.565150\pi$
$758$	−10.0674	+	4.17006i	−0.365665	+	0.151463i
$759$	20.0124	+	48.3143i	0.726406	+	1.75370i
$760$	−30.2254	−	12.5198i	−1.09639	−	0.454139i
$761$			23.2046i			0.841166i	0.907254	+	0.420583i	$0.138174\pi$
$761$			23.2046i			0.841166i	−0.907254	+	0.420583i	$0.861826\pi$
$762$	2.38007	−	5.74600i	0.0862209	−	0.208156i
$763$		0			0
$764$	0.814436			0.0294652
$765$	4.43342	+	9.85747i	0.160291	+	0.356398i
$766$	−18.4712			−0.667391
$767$	−2.67020	+	2.67020i	−0.0964152	+	0.0964152i
$768$	−3.87914	+	9.36508i	−0.139977	+	0.337933i
$769$		−	23.3712i		−	0.842787i	−0.906878	−	0.421393i	$-0.861541\pi$
$769$		−	23.3712i		−	0.842787i	0.906878	−	0.421393i	$-0.138459\pi$
$770$		0			0
$771$	−2.87605	−	6.94340i	−0.103578	−	0.250060i
$772$	−5.49507	+	2.27613i	−0.197772	+	0.0819198i
$773$	−19.8492	−	19.8492i	−0.713924	−	0.713924i	0.253429	−	0.967354i	$-0.418441\pi$
$773$	−19.8492	−	19.8492i	−0.713924	−	0.713924i	−0.967354	+	0.253429i	$0.918441\pi$
$774$	7.34626	+	7.34626i	0.264056	+	0.264056i
$775$	0.264760	−	0.109667i	0.00951046	−	0.00393936i
$776$	6.47496	+	15.6319i	0.232438	+	0.561154i
$777$		0			0
$778$		−	8.31406i		−	0.298073i
$779$	−2.34506	+	5.66148i	−0.0840206	+	0.202844i
$780$	−3.12612	+	3.12612i	−0.111933	+	0.111933i
$781$	−37.8443			−1.35418
$782$	38.6550	+	14.6713i	1.38230	+	0.524646i
$783$	46.5989			1.66531
$784$		0			0
$785$	6.29926	−	15.2078i	0.224830	−	0.542788i
$786$			27.7371i			0.989348i
$787$	46.3580	+	19.2021i	1.65248	+	0.684481i	0.997467	−	0.0711337i	$-0.0226617\pi$
$787$	46.3580	+	19.2021i	1.65248	+	0.684481i	0.655016	+	0.755615i	$0.272662\pi$
$788$	−1.33962	−	3.23413i	−0.0477220	−	0.115211i
$789$	23.2485	−	9.62984i	0.827668	−	0.342831i
$790$	−1.26016	−	1.26016i	−0.0448346	−	0.0448346i
$791$		0			0
$792$	19.3219	−	8.00339i	0.686574	−	0.284388i
$793$	6.48809	+	15.6636i	0.230399	+	0.556232i
$794$	−30.1139	−	12.4736i	−1.06870	−	0.442670i
$795$		−	0.625275i		−	0.0221762i
$796$	−0.813758	+	1.96458i	−0.0288429	+	0.0696329i
$797$	33.3423	−	33.3423i	1.18105	−	1.18105i	0.201572	−	0.979474i	$-0.435395\pi$
$797$	33.3423	−	33.3423i	1.18105	−	1.18105i	0.979474	−	0.201572i	$-0.0646049\pi$
$798$		0			0
$799$	−0.335411	−	11.1960i	−0.0118660	−	0.396087i
$800$	2.13060			0.0753280
$801$	−16.4698	+	16.4698i	−0.581933	+	0.581933i
$802$	−15.1465	+	36.5668i	−0.534840	+	1.29122i
$803$			8.62827i			0.304485i
$804$	1.91520	+	0.793301i	0.0675438	+	0.0279776i
$805$		0			0
$806$	1.55962	−	0.646016i	0.0549353	−	0.0227550i
$807$	9.74781	+	9.74781i	0.343139	+	0.343139i
$808$	24.9779	+	24.9779i	0.878720	+	0.878720i
$809$	10.8044	−	4.47534i	0.379863	−	0.157344i	−0.184578	−	0.982818i	$-0.559092\pi$
$809$	10.8044	−	4.47534i	0.379863	−	0.157344i	0.564441	+	0.825473i	$0.309092\pi$
$810$	3.13261	+	7.56279i	0.110069	+	0.265729i
$811$	−10.9405	−	4.53170i	−0.384173	−	0.159130i	0.182234	−	0.983255i	$-0.441667\pi$
$811$	−10.9405	−	4.53170i	−0.384173	−	0.159130i	−0.566407	+	0.824126i	$0.691667\pi$
$812$		0			0
$813$	9.76094	−	23.5650i	0.342331	−	0.826460i
$814$	25.4098	−	25.4098i	0.890612	−	0.890612i
$815$	7.63707			0.267515
$816$	−6.06814	+	15.9879i	−0.212427	+	0.559688i
$817$	33.3625			1.16721
$818$	2.27623	−	2.27623i	0.0795866	−	0.0795866i
$819$		0			0
$820$			0.736730i			0.0257277i
$821$	−12.6058	−	5.22149i	−0.439945	−	0.182231i	0.151705	−	0.988426i	$-0.451523\pi$
$821$	−12.6058	−	5.22149i	−0.439945	−	0.182231i	−0.591651	+	0.806194i	$0.701523\pi$
$822$	9.04951	+	21.8475i	0.315638	+	0.762018i
$823$	11.1123	−	4.60288i	0.387352	−	0.160446i	−0.180504	−	0.983574i	$-0.557773\pi$
$823$	11.1123	−	4.60288i	0.387352	−	0.160446i	0.567856	+	0.823128i	$0.307773\pi$
$824$	33.2073	+	33.2073i	1.15683	+	1.15683i
$825$	5.37204	+	5.37204i	0.187030	+	0.187030i
$826$		0			0
$827$	8.37419	+	20.2171i	0.291199	+	0.703017i	0.999997	−	0.00239456i	$-0.000762214\pi$
$827$	8.37419	+	20.2171i	0.291199	+	0.703017i	−0.708798	+	0.705412i	$0.750762\pi$
$828$	3.22825	+	1.33719i	0.112189	+	0.0464704i
$829$		−	40.0808i		−	1.39206i	−0.718010	−	0.696032i	$-0.754947\pi$
$829$		−	40.0808i		−	1.39206i	0.718010	−	0.696032i	$-0.245053\pi$
$830$	13.1698	−	31.7946i	0.457129	−	1.10361i
$831$	−13.1883	+	13.1883i	−0.457497	+	0.457497i
$832$	45.7032			1.58447
$833$		0			0
$834$	−6.34783			−0.219808
$835$	−10.7499	+	10.7499i	−0.372016	+	0.372016i
$836$	3.70807	−	8.95208i	0.128246	−	0.309614i
$837$			1.41915i			0.0490531i
$838$	22.2167	+	9.20245i	0.767463	+	0.317893i
$839$	11.1852	+	27.0035i	0.386157	+	0.932265i	0.990746	+	0.135728i	$0.0433372\pi$
$839$	11.1852	+	27.0035i	0.386157	+	0.932265i	−0.604589	+	0.796537i	$0.706663\pi$
$840$		0			0
$841$	28.5502	+	28.5502i	0.984491	+	0.984491i
$842$	−24.2944	−	24.2944i	−0.837240	−	0.837240i
$843$	−23.7440	+	9.83511i	−0.817788	+	0.338739i
$844$	2.25680	+	5.44839i	0.0776822	+	0.187541i
$845$	24.7822	+	10.2651i	0.852534	+	0.353131i
$846$			4.66796i			0.160488i
$847$		0			0
$848$	−0.559005	+	0.559005i	−0.0191963	+	0.0191963i
$849$	31.2941			1.07401
$850$	6.00382	−	0.179862i	0.205929	−	0.00616923i
$851$	41.6137			1.42650
$852$	2.23751	−	2.23751i	0.0766558	−	0.0766558i
$853$	−20.8765	+	50.4004i	−0.714799	+	1.72568i	−0.0271541	+	0.999631i	$0.508644\pi$
$853$	−20.8765	+	50.4004i	−0.714799	+	1.72568i	−0.687645	+	0.726047i	$0.741356\pi$
$854$		0			0
$855$	−13.3638	−	5.53545i	−0.457031	−	0.189308i
$856$	−0.898501	−	2.16917i	−0.0307101	−	0.0741408i
$857$	−8.53309	+	3.53452i	−0.291485	+	0.120737i	−0.523634	−	0.851943i	$-0.675424\pi$
$857$	−8.53309	+	3.53452i	−0.291485	+	0.120737i	0.232150	+	0.972680i	$0.425424\pi$
$858$	31.6451	+	31.6451i	1.08034	+	1.08034i
$859$	32.2226	+	32.2226i	1.09942	+	1.09942i	0.994478	+	0.104944i	$0.0334664\pi$
$859$	32.2226	+	32.2226i	1.09942	+	1.09942i	0.104944	+	0.994478i	$0.466534\pi$
$860$	3.70568	−	1.53494i	0.126363	−	0.0523411i
$861$		0			0
$862$	−27.0646	−	11.2105i	−0.921823	−	0.381831i
$863$			40.8966i			1.39214i	0.717976	+	0.696068i	$0.245069\pi$
$863$			40.8966i			1.39214i	−0.717976	+	0.696068i	$0.754931\pi$
$864$	−4.03770	+	9.74786i	−0.137365	+	0.331629i
$865$	12.1454	−	12.1454i	0.412956	−	0.412956i
$866$	−50.9342			−1.73081
$867$	7.17162	−	20.7478i	0.243561	−	0.704631i
$868$		0			0
$869$	2.58692	−	2.58692i	0.0877552	−	0.0877552i
$870$	−10.4415	+	25.2081i	−0.354001	+	0.854635i
$871$		−	24.5697i		−	0.832513i
$872$	49.2164	+	20.3861i	1.66668	+	0.690360i
$873$	2.86282	+	6.91146i	0.0968919	+	0.233918i
$874$	−51.1199	+	21.1745i	−1.72916	+	0.716240i
$875$		0			0
$876$	−0.510138	−	0.510138i	−0.0172360	−	0.0172360i
$877$	−19.9637	+	8.26922i	−0.674125	+	0.279232i	−0.693369	−	0.720583i	$-0.743874\pi$
$877$	−19.9637	+	8.26922i	−0.674125	+	0.279232i	0.0192434	+	0.999815i	$0.493874\pi$
$878$	−16.5814	−	40.0310i	−0.559595	−	1.35098i
$879$	−3.03588	−	1.25750i	−0.102398	−	0.0424145i
$880$			32.9060i			1.10926i
$881$	−5.21642	+	12.5936i	−0.175746	+	0.424288i	−0.987066	−	0.160314i	$-0.948749\pi$
$881$	−5.21642	+	12.5936i	−0.175746	+	0.424288i	0.811320	+	0.584602i	$0.198749\pi$
$882$		0			0
$883$	−2.21538			−0.0745534			−0.0372767	−	0.999305i	$-0.511868\pi$
$883$	−2.21538			−0.0745534			−0.0372767	+	0.999305i	$0.511868\pi$
$884$	−7.17215	+	0.214863i	−0.241226	+	0.00722664i
$885$	1.85880			0.0624829
$886$	18.8112	−	18.8112i	0.631975	−	0.631975i
$887$	2.00493	−	4.84033i	0.0673189	−	0.162522i	−0.886639	−	0.462461i	$-0.846966\pi$
$887$	2.00493	−	4.84033i	0.0673189	−	0.162522i	0.953958	+	0.299939i	$0.0969664\pi$
$888$			20.8256i			0.698863i
$889$		0			0
$890$	−16.9692	−	40.9672i	−0.568807	−	1.37322i
$891$	−15.5252	+	6.43075i	−0.520114	+	0.215438i
$892$	−6.04079	−	6.04079i	−0.202261	−	0.202261i
$893$	10.5996	+	10.5996i	0.354702	+	0.354702i
$894$	−28.4003	+	11.7638i	−0.949846	+	0.393439i
$895$	−4.98434	−	12.0333i	−0.166608	−	0.402228i
$896$		0			0
$897$			51.8253i			1.73040i
$898$	6.61998	−	15.9820i	0.220911	−	0.533327i
$899$	−1.49399	+	1.49399i	−0.0498274	+	0.0498274i
$900$	0.507628			0.0169209
$901$	0.695787	−	0.738763i	0.0231800	−	0.0246118i
$902$	7.45777			0.248317
$903$		0			0
$904$	14.9487	−	36.0893i	0.497186	−	1.20031i
$905$			4.33424i			0.144075i
$906$	−8.60878	−	3.56587i	−0.286008	−	0.118468i
$907$	−11.1928	−	27.0217i	−0.371650	−	0.897242i	−0.993471	−	0.114083i	$-0.963607\pi$
$907$	−11.1928	−	27.0217i	−0.371650	−	0.897242i	0.621821	−	0.783159i	$-0.286393\pi$
$908$	−1.15034	+	0.476485i	−0.0381753	+	0.0158127i
$909$	11.0437	+	11.0437i	0.366295	+	0.366295i
$910$		0			0
$911$	5.54275	−	2.29588i	0.183639	−	0.0760659i	−0.288969	−	0.957338i	$-0.593312\pi$
$911$	5.54275	−	2.29588i	0.183639	−	0.0760659i	0.472608	+	0.881273i	$0.343312\pi$
$912$	−8.75790	−	21.1434i	−0.290003	−	0.700129i
$913$	65.2693	+	27.0354i	2.16010	+	0.894743i
$914$		−	2.76734i		−	0.0915353i
$915$	3.19368	−	7.71023i	0.105580	−	0.254892i
$916$	−2.40319	+	2.40319i	−0.0794036	+	0.0794036i
$917$		0			0
$918$	−10.5549	+	27.8094i	−0.348365	+	0.917846i
$919$	−8.82028			−0.290954			−0.145477	−	0.989362i	$-0.546472\pi$
$919$	−8.82028			−0.290954			−0.145477	+	0.989362i	$0.546472\pi$
$920$	−32.6029	+	32.6029i	−1.07489	+	1.07489i
$921$	−6.00195	+	14.4900i	−0.197771	+	0.477462i
$922$		−	16.8198i		−	0.553932i
$923$	−34.6495	−	14.3523i	−1.14050	−	0.472412i
$924$		0			0
$925$	5.58529	−	2.31350i	0.183643	−	0.0760675i
$926$	28.8504	+	28.8504i	0.948085	+	0.948085i
$927$	14.6822	+	14.6822i	0.482226	+	0.482226i
$928$	−14.5125	+	6.01129i	−0.476397	+	0.197330i
$929$	−14.5106	−	35.0317i	−0.476077	−	1.14935i	−0.961434	−	0.275036i	$-0.911310\pi$
$929$	−14.5106	−	35.0317i	−0.476077	−	1.14935i	0.485357	−	0.874316i	$-0.338690\pi$
$930$	−0.767704	−	0.317993i	−0.0251740	−	0.0104274i
$931$		0			0
$932$	−2.25770	+	5.45057i	−0.0739534	+	0.178539i
$933$	9.12015	−	9.12015i	0.298580	−	0.298580i
$934$	−32.4158			−1.06068
$935$	−1.26490	−	42.2226i	−0.0413668	−	1.38083i
$936$	20.7260			0.677451
$937$	−33.3927	+	33.3927i	−1.09089	+	1.09089i	−0.0954591	+	0.995433i	$0.530432\pi$
$937$	−33.3927	+	33.3927i	−1.09089	+	1.09089i	−0.995433	+	0.0954591i	$0.969568\pi$
$938$		0			0
$939$			17.9912i			0.587121i
$940$	1.66500	+	0.689665i	0.0543062	+	0.0224944i
$941$	2.64544	+	6.38665i	0.0862387	+	0.208199i	0.961115	−	0.276147i	$-0.0890577\pi$
$941$	2.64544	+	6.38665i	0.0862387	+	0.208199i	−0.874877	+	0.484346i	$0.839058\pi$
$942$	12.8720	−	5.33174i	0.419391	−	0.173718i
$943$	6.10682	+	6.10682i	0.198865	+	0.198865i
$944$	−1.66179	−	1.66179i	−0.0540867	−	0.0540867i
$945$		0			0
$946$	−15.5379	−	37.5119i	−0.505181	−	1.21962i
$947$	−19.3686	−	8.02274i	−0.629395	−	0.260704i	0.0451010	−	0.998982i	$-0.485639\pi$
$947$	−19.3686	−	8.02274i	−0.629395	−	0.260704i	−0.674496	+	0.738278i	$0.735639\pi$
$948$			0.305898i			0.00993511i
$949$	−3.27224	+	7.89988i	−0.106221	+	0.256441i
$950$	−5.68399	+	5.68399i	−0.184413	+	0.184413i
$951$	8.64740			0.280411
$952$		0			0
$953$	−19.2737			−0.624335			−0.312167	−	0.950027i	$-0.601055\pi$
$953$	−19.2737			−0.624335			−0.312167	+	0.950027i	$0.601055\pi$
$954$	−0.299053	+	0.299053i	−0.00968221	+	0.00968221i
$955$	−1.81833	+	4.38984i	−0.0588398	+	0.142052i
$956$			5.43508i			0.175783i
$957$	−51.7483	−	21.4348i	−1.67278	−	0.692890i
$958$	−1.04023	−	2.51134i	−0.0336083	−	0.0811377i
$959$		0			0
$960$	−15.9076	−	15.9076i	−0.513417	−	0.513417i
$961$	21.8748	+	21.8748i	0.705639	+	0.705639i
$962$	32.9013	−	13.6282i	1.06078	−	0.439389i
$963$	−0.397261	−	0.959072i	−0.0128015	−	0.0309057i
$964$	1.61275	+	0.668022i	0.0519431	+	0.0215156i
$965$		−	34.7004i		−	1.11704i
$966$		0			0
$967$	−3.11479	+	3.11479i	−0.100165	+	0.100165i	−0.755413	−	0.655248i	$-0.772564\pi$
$967$	−3.11479	+	3.11479i	−0.100165	+	0.100165i	0.655248	+	0.755413i	$0.272564\pi$
$968$	−48.5827			−1.56151
$969$	12.0503	+	26.7931i	0.387110	+	0.860718i
$970$	−14.2420			−0.457283
$971$	−14.7431	+	14.7431i	−0.473129	+	0.473129i	−0.902926	−	0.429797i	$-0.858585\pi$
$971$	−14.7431	+	14.7431i	−0.473129	+	0.473129i	0.429797	+	0.902926i	$0.358585\pi$
$972$	−1.62813	+	3.93066i	−0.0522224	+	0.126076i
$973$		0			0
$974$	4.79920	+	1.98789i	0.153776	+	0.0636963i
$975$	2.88121	+	6.95586i	0.0922726	+	0.222766i
$976$	−9.74824	+	4.03785i	−0.312034	+	0.129249i
$977$	−27.6208	−	27.6208i	−0.883667	−	0.883667i	0.110239	−	0.993905i	$-0.464838\pi$
$977$	−27.6208	−	27.6208i	−0.883667	−	0.883667i	−0.993905	+	0.110239i	$0.964838\pi$
$978$	4.57079	+	4.57079i	0.146158	+	0.146158i
$979$	84.0991	−	34.8350i	2.68782	−	1.11333i
$980$		0			0
$981$	21.7604	+	9.01345i	0.694756	+	0.287777i
$982$		−	9.41457i		−	0.300431i
$983$	6.82144	−	16.4684i	0.217570	−	0.525261i	−0.776979	−	0.629526i	$-0.783249\pi$
$983$	6.82144	−	16.4684i	0.217570	−	0.525261i	0.994550	+	0.104265i	$0.0332491\pi$
$984$	−3.05616	+	3.05616i	−0.0974269	+	0.0974269i
$985$	20.4230			0.650730
$986$	−40.3875	+	18.1644i	−1.28620	+	0.578471i
$987$		0			0
$988$	6.79008	−	6.79008i	0.216021	−	0.216021i
$989$	17.9934	−	43.4399i	0.572157	−	1.38131i
$990$			17.6038i			0.559487i
$991$	28.7675	+	11.9159i	0.913828	+	0.378520i	0.789521	−	0.613724i	$-0.210329\pi$
$991$	28.7675	+	11.9159i	0.913828	+	0.378520i	0.124307	+	0.992244i	$0.460329\pi$
$992$	−0.183072	−	0.441974i	−0.00581253	−	0.0140327i
$993$	12.9592	−	5.36787i	0.411247	−	0.170344i
$994$		0			0
$995$	−8.77237	−	8.77237i	−0.278103	−	0.278103i
$996$	−5.45743	+	2.26054i	−0.172925	+	0.0716281i
$997$	−1.80376	−	4.35467i	−0.0571258	−	0.137914i	0.892740	−	0.450573i	$-0.148780\pi$
$997$	−1.80376	−	4.35467i	−0.0571258	−	0.137914i	−0.949865	+	0.312659i	$0.898780\pi$
$998$	−7.77543	−	3.22069i	−0.246127	−	0.101949i
$999$			29.9380i			0.947196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.l.e.246.8	yes	40
7.2	even	3		833.2.v.g.263.3		80
7.3	odd	6		833.2.v.h.569.8		80
7.4	even	3		833.2.v.g.569.8		80
7.5	odd	6		833.2.v.h.263.3		80
7.6	odd	2		833.2.l.d.246.8	✓	40
17.15	even	8	inner	833.2.l.e.491.8	yes	40
119.32	even	24		833.2.v.g.814.3		80
119.66	odd	24		833.2.v.h.814.3		80
119.83	odd	8		833.2.l.d.491.8	yes	40
119.100	even	24		833.2.v.g.508.8		80
119.117	odd	24		833.2.v.h.508.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.l.d.246.8	✓	40	7.6	odd	2
833.2.l.d.491.8	yes	40	119.83	odd	8
833.2.l.e.246.8	yes	40	1.1	even	1	trivial
833.2.l.e.491.8	yes	40	17.15	even	8	inner
833.2.v.g.263.3		80	7.2	even	3
833.2.v.g.508.8		80	119.100	even	24
833.2.v.g.569.8		80	7.4	even	3
833.2.v.g.814.3		80	119.32	even	24
833.2.v.h.263.3		80	7.5	odd	6
833.2.v.h.508.8		80	119.117	odd	24
833.2.v.h.569.8		80	7.3	odd	6
833.2.v.h.814.3		80	119.66	odd	24

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.911810 - 0.911810i) q^{2} +(0.494163 - 1.19301i) q^{3} +0.337205i q^{4} +(-1.81755 - 0.752852i) q^{5} +(-0.637220 - 1.53839i) q^{6} +(2.13109 + 2.13109i) q^{8} +(0.942233 + 0.942233i) q^{9} +(-2.34371 + 0.970799i) q^{10} +(-1.99290 - 4.81128i) q^{11} +(0.402290 + 0.166634i) q^{12} -5.16091i q^{13} +(-1.79633 + 1.79633i) q^{15} +3.21188 q^{16} +(-4.12126 + 0.123465i) q^{17} +1.71827 q^{18} +(3.90171 - 3.90171i) q^{19} +(0.253865 - 0.612885i) q^{20} +(-6.20411 - 2.56983i) q^{22} +(-2.97594 - 7.18456i) q^{23} +(3.59552 - 1.48931i) q^{24} +(-0.798847 - 0.798847i) q^{25} +(-4.70577 - 4.70577i) q^{26} +(5.16876 - 2.14097i) q^{27} +(7.69521 + 3.18746i) q^{29} +3.27582i q^{30} +(-0.0970729 + 0.234355i) q^{31} +(-1.33355 + 1.33355i) q^{32} -6.72474 q^{33} +(-3.64523 + 3.87038i) q^{34} +(-0.317725 + 0.317725i) q^{36} +(-2.04782 + 4.94387i) q^{37} -7.11524i q^{38} +(-6.15704 - 2.55033i) q^{39} +(-2.26895 - 5.47774i) q^{40} +(-1.02603 + 0.424996i) q^{41} +(4.27537 + 4.27537i) q^{43} +(1.62239 - 0.672014i) q^{44} +(-1.00319 - 2.42191i) q^{45} +(-9.26445 - 3.83746i) q^{46} +2.71665i q^{47} +(1.58719 - 3.83182i) q^{48} -1.45679 q^{50} +(-1.88928 + 4.97773i) q^{51} +1.74028 q^{52} +(-0.174043 + 0.174043i) q^{53} +(2.76077 - 6.66508i) q^{54} +10.2451i q^{55} +(-2.72672 - 6.58288i) q^{57} +(9.92293 - 4.11021i) q^{58} +(-0.517389 - 0.517389i) q^{59} +(-0.605730 - 0.605730i) q^{60} +(-3.03505 + 1.25716i) q^{61} +(0.125175 + 0.302199i) q^{62} +8.85565i q^{64} +(-3.88540 + 9.38019i) q^{65} +(-6.13169 + 6.13169i) q^{66} +4.76074 q^{67} +(-0.0416328 - 1.38971i) q^{68} -10.0419 q^{69} +(2.78096 - 6.71384i) q^{71} +4.01596i q^{72} +(-1.53071 - 0.634043i) q^{73} +(2.64065 + 6.37509i) q^{74} +(-1.34780 + 0.558276i) q^{75} +(1.31568 + 1.31568i) q^{76} +(-7.93947 + 3.28864i) q^{78} +(0.268839 + 0.649035i) q^{79} +(-5.83775 - 2.41807i) q^{80} -3.22684i q^{81} +(-0.548029 + 1.32306i) q^{82} +(-9.59255 + 9.59255i) q^{83} +(7.58352 + 2.87829i) q^{85} +7.79665 q^{86} +(7.60537 - 7.60537i) q^{87} +(6.00621 - 14.5003i) q^{88} +17.4796i q^{89} +(-3.12304 - 1.29361i) q^{90} +(2.42267 - 1.00350i) q^{92} +(0.231619 + 0.231619i) q^{93} +(2.47707 + 2.47707i) q^{94} +(-10.0289 + 4.15413i) q^{95} +(0.931951 + 2.24993i) q^{96} +(5.18677 + 2.14843i) q^{97} +(2.65557 - 6.41111i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} + 8 q^{5} + 12 q^{6} + 20 q^{10} - 12 q^{12} - 8 q^{15} - 64 q^{16} - 16 q^{17} + 24 q^{18} - 8 q^{19} - 20 q^{20} - 8 q^{23} - 12 q^{24} - 8 q^{27} + 8 q^{29} + 36 q^{31} + 72 q^{33} - 8 q^{34}+ \cdots - 16 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 + 8 * q^5 + 12 * q^6 + 20 * q^10 - 12 * q^12 - 8 * q^15 - 64 * q^16 - 16 * q^17 + 24 * q^18 - 8 * q^19 - 20 * q^20 - 8 * q^23 - 12 * q^24 - 8 * q^27 + 8 * q^29 + 36 * q^31 + 72 * q^33 - 8 * q^34 - 16 * q^37 + 8 * q^39 - 80 * q^40 + 16 * q^41 - 32 * q^43 + 32 * q^44 + 36 * q^45 + 64 * q^46 - 112 * q^48 - 96 * q^50 + 8 * q^51 - 112 * q^52 + 100 * q^54 - 16 * q^57 + 80 * q^58 - 72 * q^60 - 96 * q^61 + 80 * q^62 - 8 * q^65 - 32 * q^67 + 116 * q^68 + 48 * q^69 - 16 * q^71 - 16 * q^73 - 80 * q^74 + 48 * q^75 + 16 * q^76 - 32 * q^78 - 16 * q^79 + 84 * q^80 + 40 * q^82 + 8 * q^83 + 16 * q^85 + 120 * q^86 + 48 * q^87 + 48 * q^88 + 72 * q^90 + 136 * q^92 - 16 * q^93 - 16 * q^94 + 16 * q^95 - 220 * q^96 - 8 * q^97 - 16 * q^99

Introduction

L-functions

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