LMFDB - Embedded newform 315.2.r.b.184.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(184,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("315.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			184.8
Character	$\chi$	$=$	315.184
Dual form			315.2.r.b.214.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02504i q^{2} +(-0.248494 - 1.71413i) q^{3} -2.10077 q^{4} +(2.21568 - 0.301270i) q^{5} +(-3.47118 + 0.503210i) q^{6} +(-2.64524 + 0.0518041i) q^{7} +0.204070i q^{8} +(-2.87650 + 0.851904i) q^{9} +O(q^{10})$	\(q-2.02504i q^{2} +(-0.248494 - 1.71413i) q^{3} -2.10077 q^{4} +(2.21568 - 0.301270i) q^{5} +(-3.47118 + 0.503210i) q^{6} +(-2.64524 + 0.0518041i) q^{7} +0.204070i q^{8} +(-2.87650 + 0.851904i) q^{9} +(-0.610083 - 4.48683i) q^{10} +(0.561719 - 0.972925i) q^{11} +(0.522030 + 3.60100i) q^{12} +(-0.548992 - 0.316961i) q^{13} +(0.104905 + 5.35672i) q^{14} +(-1.06700 - 3.72310i) q^{15} -3.78830 q^{16} +(-2.94268 + 1.69895i) q^{17} +(1.72514 + 5.82502i) q^{18} +(2.80925 - 4.86576i) q^{19} +(-4.65464 + 0.632901i) q^{20} +(0.746127 + 4.52143i) q^{21} +(-1.97021 - 1.13750i) q^{22} +(4.61787 - 2.66613i) q^{23} +(0.349802 - 0.0507101i) q^{24} +(4.81847 - 1.33504i) q^{25} +(-0.641857 + 1.11173i) q^{26} +(2.17507 + 4.71901i) q^{27} +(5.55706 - 0.108829i) q^{28} +(3.75677 + 6.50691i) q^{29} +(-7.53942 + 2.16072i) q^{30} +4.41814 q^{31} +8.07958i q^{32} +(-1.80731 - 0.721094i) q^{33} +(3.44045 + 5.95903i) q^{34} +(-5.84541 + 0.911715i) q^{35} +(6.04288 - 1.78966i) q^{36} +(-5.02932 - 2.90368i) q^{37} +(-9.85334 - 5.68883i) q^{38} +(-0.406891 + 1.01981i) q^{39} +(0.0614801 + 0.452153i) q^{40} +(0.862448 - 1.49380i) q^{41} +(9.15605 - 1.51093i) q^{42} +(6.02776 - 3.48013i) q^{43} +(-1.18004 + 2.04390i) q^{44} +(-6.11675 + 2.75415i) q^{45} +(-5.39901 - 9.35136i) q^{46} +1.24361i q^{47} +(0.941370 + 6.49365i) q^{48} +(6.99463 - 0.274069i) q^{49} +(-2.70350 - 9.75758i) q^{50} +(3.64347 + 4.62196i) q^{51} +(1.15331 + 0.665862i) q^{52} +(2.46489 - 1.42310i) q^{53} +(9.55617 - 4.40460i) q^{54} +(0.951475 - 2.32492i) q^{55} +(-0.0105717 - 0.539814i) q^{56} +(-9.03864 - 3.60631i) q^{57} +(13.1767 - 7.60759i) q^{58} -3.61790 q^{59} +(2.24153 + 7.82140i) q^{60} -14.2788 q^{61} -8.94690i q^{62} +(7.56492 - 2.40251i) q^{63} +8.78485 q^{64} +(-1.31188 - 0.536888i) q^{65} +(-1.46024 + 3.65986i) q^{66} -10.5815i q^{67} +(6.18189 - 3.56912i) q^{68} +(-5.71761 - 7.25313i) q^{69} +(1.84626 + 11.8372i) q^{70} +14.8978 q^{71} +(-0.173848 - 0.587006i) q^{72} +(6.62219 - 3.82332i) q^{73} +(-5.88005 + 10.1845i) q^{74} +(-3.48579 - 7.92775i) q^{75} +(-5.90159 + 10.2219i) q^{76} +(-1.43548 + 2.60272i) q^{77} +(2.06515 + 0.823969i) q^{78} +0.655968 q^{79} +(-8.39366 + 1.14130i) q^{80} +(7.54852 - 4.90101i) q^{81} +(-3.02501 - 1.74649i) q^{82} +(-6.42026 + 3.70674i) q^{83} +(-1.56744 - 9.49849i) q^{84} +(-6.00818 + 4.65088i) q^{85} +(-7.04738 - 12.2064i) q^{86} +(10.2202 - 8.05653i) q^{87} +(0.198544 + 0.114630i) q^{88} +(0.545012 - 0.943989i) q^{89} +(5.57726 + 12.3866i) q^{90} +(1.46864 + 0.809998i) q^{91} +(-9.70110 + 5.60093i) q^{92} +(-1.09788 - 7.57328i) q^{93} +2.51836 q^{94} +(4.75848 - 11.6273i) q^{95} +(13.8495 - 2.00773i) q^{96} +(-16.2122 + 9.36013i) q^{97} +(-0.555000 - 14.1644i) q^{98} +(-0.786945 + 3.27715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.02504i		−	1.43192i	−0.698143	−	0.715959i	$-0.745990\pi$
$2$		−	2.02504i		−	1.43192i	0.698143	−	0.715959i	$-0.254010\pi$
$3$	−0.248494	−	1.71413i	−0.143468	−	0.989655i
$3$	−0.248494	−	1.71413i	−0.143468	−	0.989655i
$4$	−2.10077			−1.05039
$5$	2.21568	−	0.301270i	0.990882	−	0.134732i
$5$	2.21568	−	0.301270i	0.990882	−	0.134732i
$6$	−3.47118	+	0.503210i	−1.41710	+	0.205435i
$7$	−2.64524	+	0.0518041i	−0.999808	+	0.0195801i
$7$	−2.64524	+	0.0518041i	−0.999808	+	0.0195801i
$8$			0.204070i			0.0721495i
$9$	−2.87650	+	0.851904i	−0.958834	+	0.283968i
$10$	−0.610083	−	4.48683i	−0.192925	−	1.41886i
$11$	0.561719	−	0.972925i	0.169365	−	0.293348i	−0.768832	−	0.639451i	$-0.779162\pi$
$11$	0.561719	−	0.972925i	0.169365	−	0.293348i	0.938197	+	0.346103i	$0.112495\pi$
$12$	0.522030	+	3.60100i	0.150697	+	1.03952i
$13$	−0.548992	−	0.316961i	−0.152263	−	0.0879090i	0.421933	−	0.906627i	$-0.361352\pi$
$13$	−0.548992	−	0.316961i	−0.152263	−	0.0879090i	−0.574196	+	0.818718i	$0.694685\pi$
$14$	0.104905	+	5.35672i	0.0280371	+	1.43164i
$15$	−1.06700	−	3.72310i	−0.275498	−	0.961302i
$16$	−3.78830			−0.947075
$17$	−2.94268	+	1.69895i	−0.713704	+	0.412057i	−0.812431	−	0.583057i	$-0.801856\pi$
$17$	−2.94268	+	1.69895i	−0.713704	+	0.412057i	0.0987272	+	0.995115i	$0.468523\pi$
$18$	1.72514	+	5.82502i	0.406619	+	1.37297i
$19$	2.80925	−	4.86576i	0.644486	−	1.11628i	−0.339934	−	0.940449i	$-0.610405\pi$
$19$	2.80925	−	4.86576i	0.644486	−	1.11628i	0.984420	−	0.175833i	$-0.0562618\pi$
$20$	−4.65464	+	0.632901i	−1.04081	+	0.141521i
$21$	0.746127	+	4.52143i	0.162818	+	0.986656i
$22$	−1.97021	−	1.13750i	−0.420050	−	0.242516i
$23$	4.61787	−	2.66613i	0.962893	−	0.555926i	0.0658306	−	0.997831i	$-0.479030\pi$
$23$	4.61787	−	2.66613i	0.962893	−	0.555926i	0.897062	+	0.441904i	$0.145697\pi$
$24$	0.349802	−	0.0507101i	0.0714031	−	0.0103512i
$25$	4.81847	−	1.33504i	0.963694	−	0.267007i
$26$	−0.641857	+	1.11173i	−0.125878	+	0.218028i
$27$	2.17507	+	4.71901i	0.418593	+	0.908174i
$28$	5.55706	−	0.108829i	1.05019	−	0.0205667i
$29$	3.75677	+	6.50691i	0.697614	+	1.20830i	0.969291	+	0.245915i	$0.0790884\pi$
$29$	3.75677	+	6.50691i	0.697614	+	1.20830i	−0.271677	+	0.962388i	$0.587578\pi$
$30$	−7.53942	+	2.16072i	−1.37650	+	0.394491i
$31$	4.41814			0.793522			0.396761	−	0.917922i	$-0.370134\pi$
$31$	4.41814			0.793522			0.396761	+	0.917922i	$0.370134\pi$
$32$			8.07958i			1.42828i
$33$	−1.80731	−	0.721094i	−0.314612	−	0.125526i
$34$	3.44045	+	5.95903i	0.590032	+	1.02196i
$35$	−5.84541	+	0.911715i	−0.988054	+	0.154108i
$36$	6.04288	−	1.78966i	1.00715	−	0.298276i
$37$	−5.02932	−	2.90368i	−0.826814	−	0.477362i	0.0259463	−	0.999663i	$-0.491740\pi$
$37$	−5.02932	−	2.90368i	−0.826814	−	0.477362i	−0.852761	+	0.522302i	$0.825073\pi$
$38$	−9.85334	−	5.68883i	−1.59842	−	0.922850i
$39$	−0.406891	+	1.01981i	−0.0651547	+	0.163300i
$40$	0.0614801	+	0.452153i	0.00972086	+	0.0714916i
$41$	0.862448	−	1.49380i	0.134692	−	0.233293i	−0.790788	−	0.612090i	$-0.790329\pi$
$41$	0.862448	−	1.49380i	0.134692	−	0.233293i	0.925480	+	0.378797i	$0.123662\pi$
$42$	9.15605	−	1.51093i	1.41281	−	0.233142i
$43$	6.02776	−	3.48013i	0.919224	−	0.530714i	0.0358366	−	0.999358i	$-0.488590\pi$
$43$	6.02776	−	3.48013i	0.919224	−	0.530714i	0.883387	+	0.468643i	$0.155257\pi$
$44$	−1.18004	+	2.04390i	−0.177898	+	0.308129i
$45$	−6.11675	+	2.75415i	−0.911832	+	0.410565i
$46$	−5.39901	−	9.35136i	−0.796040	−	1.37878i
$47$			1.24361i			0.181400i	0.995878	+	0.0906999i	$0.0289104\pi$
$47$			1.24361i			0.181400i	−0.995878	+	0.0906999i	$0.971090\pi$
$48$	0.941370	+	6.49365i	0.135875	+	0.937277i
$49$	6.99463	−	0.274069i	0.999233	−	0.0391527i
$50$	−2.70350	−	9.75758i	−0.382332	−	1.37993i
$51$	3.64347	+	4.62196i	0.510188	+	0.647203i
$52$	1.15331	+	0.665862i	0.159935	+	0.0923385i
$53$	2.46489	−	1.42310i	0.338578	−	0.195478i	−0.321065	−	0.947057i	$-0.604041\pi$
$53$	2.46489	−	1.42310i	0.338578	−	0.195478i	0.659643	+	0.751579i	$0.270707\pi$
$54$	9.55617	−	4.40460i	1.30043	−	0.599390i
$55$	0.951475	−	2.32492i	0.128297	−	0.313492i
$56$	−0.0105717	−	0.539814i	−0.00141270	−	0.0721357i
$57$	−9.03864	−	3.60631i	−1.19720	−	0.477667i
$58$	13.1767	−	7.60759i	1.73019	−	0.998926i
$59$	−3.61790			−0.471010			−0.235505	−	0.971873i	$-0.575674\pi$
$59$	−3.61790			−0.471010			−0.235505	+	0.971873i	$0.575674\pi$
$60$	2.24153	+	7.82140i	0.289380	+	1.00974i
$61$	−14.2788			−1.82822			−0.914108	−	0.405470i	$-0.867108\pi$
$61$	−14.2788			−1.82822			−0.914108	+	0.405470i	$0.867108\pi$
$62$		−	8.94690i		−	1.13626i
$63$	7.56492	−	2.40251i	0.953090	−	0.302688i
$64$	8.78485			1.09811
$65$	−1.31188	−	0.536888i	−0.162719	−	0.0665928i
$66$	−1.46024	+	3.65986i	−0.179743	+	0.450498i
$67$		−	10.5815i		−	1.29274i	−0.763024	−	0.646370i	$-0.776286\pi$
$67$		−	10.5815i		−	1.29274i	0.763024	−	0.646370i	$-0.223714\pi$
$68$	6.18189	−	3.56912i	0.749665	−	0.432819i
$69$	−5.71761	−	7.25313i	−0.688320	−	0.873174i
$70$	1.84626	+	11.8372i	0.220670	+	1.41481i
$71$	14.8978			1.76804			0.884020	−	0.467448i	$-0.154827\pi$
$71$	14.8978			1.76804			0.884020	+	0.467448i	$0.154827\pi$
$72$	−0.173848	−	0.587006i	−0.0204882	−	0.0691794i
$73$	6.62219	−	3.82332i	0.775069	−	0.447486i	−0.0596112	−	0.998222i	$-0.518986\pi$
$73$	6.62219	−	3.82332i	0.775069	−	0.447486i	0.834680	+	0.550736i	$0.185653\pi$
$74$	−5.88005	+	10.1845i	−0.683542	+	1.18393i
$75$	−3.48579	−	7.92775i	−0.402505	−	0.915418i
$76$	−5.90159	+	10.2219i	−0.676959	+	1.17253i
$77$	−1.43548	+	2.60272i	−0.163588	+	0.296608i
$78$	2.06515	+	0.823969i	0.233832	+	0.0932962i
$79$	0.655968			0.0738022			0.0369011	−	0.999319i	$-0.488251\pi$
$79$	0.655968			0.0738022			0.0369011	+	0.999319i	$0.488251\pi$
$80$	−8.39366	+	1.14130i	−0.938439	+	0.127601i
$81$	7.54852	−	4.90101i	0.838724	−	0.544556i
$82$	−3.02501	−	1.74649i	−0.334056	−	0.192867i
$83$	−6.42026	+	3.70674i	−0.704715	+	0.406867i	−0.809101	−	0.587670i	$-0.800045\pi$
$83$	−6.42026	+	3.70674i	−0.704715	+	0.406867i	0.104386	+	0.994537i	$0.466712\pi$
$84$	−1.56744	−	9.49849i	−0.171022	−	1.03637i
$85$	−6.00818	+	4.65088i	−0.651679	+	0.504459i
$86$	−7.04738	−	12.2064i	−0.759939	−	1.31625i
$87$	10.2202	−	8.05653i	1.09572	−	0.863751i
$88$	0.198544	+	0.114630i	0.0211649	+	0.0122196i
$89$	0.545012	−	0.943989i	0.0577712	−	0.100063i	−0.835693	−	0.549196i	$-0.814934\pi$
$89$	0.545012	−	0.943989i	0.0577712	−	0.100063i	0.893465	+	0.449134i	$0.148267\pi$
$90$	5.57726	+	12.3866i	0.587894	+	1.30567i
$91$	1.46864	+	0.809998i	0.153955	+	0.0849108i
$92$	−9.70110	+	5.60093i	−1.01141	+	0.583938i
$93$	−1.09788	−	7.57328i	−0.113845	−	0.785313i
$94$	2.51836			0.259749
$95$	4.75848	−	11.6273i	0.488210	−	1.19294i
$96$	13.8495	−	2.00773i	1.41351	−	0.204913i
$97$	−16.2122	+	9.36013i	−1.64610	+	0.950377i	−0.667501	+	0.744609i	$0.732636\pi$
$97$	−16.2122	+	9.36013i	−1.64610	+	0.950377i	−0.978601	+	0.205769i	$0.934030\pi$
$98$	−0.555000	−	14.1644i	−0.0560635	−	1.43082i
$99$	−0.786945	+	3.27715i	−0.0790910	+	0.329366i
$100$	−10.1225	+	2.80461i	−1.01225	+	0.280461i
$101$	−0.376932	+	0.652865i	−0.0375061	+	0.0649625i	−0.884169	−	0.467167i	$-0.845275\pi$
$101$	−0.376932	+	0.652865i	−0.0375061	+	0.0649625i	0.846663	+	0.532129i	$0.178608\pi$
$102$	9.35963	−	7.37816i	0.926742	−	0.730547i
$103$	−11.1337	+	6.42804i	−1.09703	+	0.633373i	−0.935440	−	0.353484i	$-0.884997\pi$
$103$	−11.1337	+	6.42804i	−1.09703	+	0.633373i	−0.161594	+	0.986857i	$0.551663\pi$
$104$	0.0646820	−	0.112033i	0.00634259	−	0.0109857i
$105$	3.01535	+	9.79325i	0.294268	+	0.955723i
$106$	−2.88183	−	4.99148i	−0.279909	−	0.484816i
$107$	3.52076	+	2.03271i	0.340365	+	0.196510i	0.660433	−	0.750885i	$-0.270373\pi$
$107$	3.52076	+	2.03271i	0.340365	+	0.196510i	−0.320069	+	0.947394i	$0.603706\pi$
$108$	−4.56933	−	9.91357i	−0.439684	−	0.953934i
$109$	3.82783	+	6.63000i	0.366640	+	0.635039i	0.989038	−	0.147662i	$-0.0471748\pi$
$109$	3.82783	+	6.63000i	0.366640	+	0.635039i	−0.622398	+	0.782701i	$0.713841\pi$
$110$	−4.70805	−	1.92677i	−0.448895	−	0.183710i
$111$	−3.72753	+	9.34246i	−0.353802	+	0.886747i
$112$	10.0210	−	0.196250i	0.946893	−	0.0185438i
$113$	14.6728	+	8.47132i	1.38030	+	0.796915i	0.992194	−	0.124702i	$-0.0397974\pi$
$113$	14.6728	+	8.47132i	1.38030	+	0.796915i	0.388102	+	0.921616i	$0.373131\pi$
$114$	−7.30291	+	18.3036i	−0.683980	+	1.71429i
$115$	9.42850	−	7.29852i	0.879212	−	0.680590i
$116$	−7.89212	−	13.6696i	−0.732765	−	1.26919i
$117$	1.84920	+	0.444049i	0.170958	+	0.0410523i
$118$			7.32637i			0.674447i
$119$	7.69608	−	4.64659i	0.705499	−	0.425952i
$120$	0.759772	−	0.217742i	0.0693574	−	0.0198771i
$121$	4.86894	+	8.43326i	0.442631	+	0.766660i
$122$			28.9152i			2.61786i
$123$	−2.77489	−	1.10715i	−0.250204	−	0.0998282i
$124$	−9.28152			−0.833505
$125$	10.2740	−	4.40968i	0.918933	−	0.394413i
$126$	−4.86517	−	15.3192i	−0.433424	−	1.36475i
$127$			9.63027i			0.854548i	0.904122	+	0.427274i	$0.140526\pi$
$127$			9.63027i			0.854548i	−0.904122	+	0.427274i	$0.859474\pi$
$128$		−	1.63048i		−	0.144116i
$129$	−7.46326	−	9.46758i	−0.657103	−	0.833574i
$130$	−1.08722	+	2.65661i	−0.0953553	+	0.233000i
$131$	2.30991	+	4.00088i	0.201818	+	0.349558i	0.949114	−	0.314932i	$-0.101982\pi$
$131$	2.30991	+	4.00088i	0.201818	+	0.349558i	−0.747297	+	0.664491i	$0.768649\pi$
$132$	3.79674	+	1.51485i	0.330464	+	0.131851i
$133$	−7.17908	+	13.0167i	−0.622505	+	1.12869i
$134$	−21.4280			−1.85110
$135$	6.24096	+	9.80053i	0.537136	+	0.843496i
$136$	−0.346705	−	0.600511i	−0.0297297	−	0.0514934i
$137$	16.9160	+	9.76645i	1.44523	+	0.834404i	0.998192	−	0.0601106i	$-0.0191453\pi$
$137$	16.9160	+	9.76645i	1.44523	+	0.834404i	0.447039	+	0.894515i	$0.352479\pi$
$138$	−14.6878	+	11.5784i	−1.25031	+	0.985617i
$139$	2.28771	−	3.96243i	0.194041	−	0.336089i	−0.752545	−	0.658541i	$-0.771174\pi$
$139$	2.28771	−	3.96243i	0.194041	−	0.336089i	0.946586	+	0.322452i	$0.104507\pi$
$140$	12.2799	−	1.91531i	1.03784	−	0.161873i
$141$	2.13172	−	0.309031i	0.179523	−	0.0260251i
$142$		−	30.1685i		−	2.53169i
$143$	−0.616758	+	0.356085i	−0.0515759	+	0.0297773i
$144$	10.8970	−	3.22727i	0.908087	−	0.268939i
$145$	10.2841	+	13.2854i	0.854051	+	1.10330i
$146$	−7.74237	−	13.4102i	−0.640763	−	1.10983i
$147$	−2.20792	−	11.9216i	−0.182106	−	0.983279i
$148$	10.5655	+	6.09997i	0.868475	+	0.501414i
$149$	−9.22718	−	15.9819i	−0.755920	−	1.30929i	−0.944916	−	0.327314i	$-0.893857\pi$
$149$	−9.22718	−	15.9819i	−0.755920	−	1.30929i	0.188996	−	0.981978i	$-0.439477\pi$
$150$	−16.0540	+	7.05886i	−1.31080	+	0.576353i
$151$	2.41029	−	4.17474i	0.196147	−	0.339736i	−0.751129	−	0.660155i	$-0.770490\pi$
$151$	2.41029	−	4.17474i	0.196147	−	0.339736i	0.947276	+	0.320419i	$0.103824\pi$
$152$	0.992954	+	0.573282i	0.0805392	+	0.0464993i
$153$	7.01726	−	7.39392i	0.567312	−	0.597763i
$154$	5.27061	+	2.90690i	0.424718	+	0.234245i
$155$	9.78919	−	1.33106i	0.786287	−	0.106913i
$156$	0.854786	−	2.14238i	0.0684376	−	0.171528i
$157$			12.7151i			1.01478i	0.861717	+	0.507389i	$0.169389\pi$
$157$			12.7151i			1.01478i	−0.861717	+	0.507389i	$0.830611\pi$
$158$		−	1.32836i		−	0.105679i
$159$	−3.05190	−	3.87151i	−0.242031	−	0.307031i
$160$	2.43414	+	17.9018i	0.192435	+	1.41526i
$161$	−12.0773	+	7.29179i	−0.951823	+	0.574673i
$162$	−9.92472	−	15.2860i	−0.779759	−	1.20098i
$163$	−16.4285	−	9.48499i	−1.28678	−	0.742922i	−0.308700	−	0.951160i	$-0.599894\pi$
$163$	−16.4285	−	9.48499i	−1.28678	−	0.742922i	−0.978078	+	0.208238i	$0.933227\pi$
$164$	−1.81181	+	3.13814i	−0.141478	+	0.245048i
$165$	−4.22166	−	1.05323i	−0.328656	−	0.0819935i
$166$	7.50628	+	13.0013i	0.582600	+	1.00909i
$167$	−6.74599	−	3.89480i	−0.522020	−	0.301389i	0.215741	−	0.976451i	$-0.430783\pi$
$167$	−6.74599	−	3.89480i	−0.522020	−	0.301389i	−0.737761	+	0.675062i	$0.764117\pi$
$168$	−0.922686	+	0.152262i	−0.0711867	+	0.0117473i
$169$	−6.29907	−	10.9103i	−0.484544	−	0.839255i
$170$	9.41820	+	12.1668i	0.722343	+	0.933150i
$171$	−3.93564	+	16.3896i	−0.300966	+	1.25334i
$172$	−12.6629	+	7.31096i	−0.965541	+	0.557455i
$173$			19.8137i			1.50640i	0.657789	+	0.753202i	$0.271492\pi$
$173$			19.8137i			1.50640i	−0.657789	+	0.753202i	$0.728508\pi$
$174$	−16.3148	−	20.6962i	−1.23682	−	1.56898i
$175$	−12.6769	+	3.78112i	−0.958282	+	0.285825i
$176$	−2.12796	+	3.68573i	−0.160401	+	0.277822i
$177$	0.899026	+	6.20155i	0.0675750	+	0.466137i
$178$	−1.91161	−	1.10367i	−0.143281	−	0.0827236i
$179$	−1.05172	−	1.82164i	−0.0786096	−	0.136156i	0.824041	−	0.566531i	$-0.191715\pi$
$179$	−1.05172	−	1.82164i	−0.0786096	−	0.136156i	−0.902650	+	0.430375i	$0.858381\pi$
$180$	12.8499	−	5.78585i	0.957776	−	0.431252i
$181$	15.0111			1.11577			0.557885	−	0.829918i	$-0.311613\pi$
$181$	15.0111			1.11577			0.557885	+	0.829918i	$0.311613\pi$
$182$	1.64028	−	2.97404i	0.121585	−	0.220451i
$183$	3.54821	+	24.4758i	0.262291	+	1.80930i
$184$	0.544076	+	0.942367i	0.0401098	+	0.0694722i
$185$	−12.0181	−	4.91843i	−0.883592	−	0.361610i
$186$	−15.3362	+	2.22325i	−1.12450	+	0.163017i
$187$			3.81734i			0.279151i
$188$		−	2.61255i		−	0.190540i
$189$	−5.99806	−	12.3703i	−0.436294	−	0.899804i
$190$	−23.5457	−	9.63611i	−1.70819	−	0.699077i
$191$	13.0673			0.945515			0.472758	−	0.881193i	$-0.343259\pi$
$191$	13.0673			0.945515			0.472758	+	0.881193i	$0.343259\pi$
$192$	−2.18299	−	15.0584i	−0.157543	−	1.08675i
$193$			3.60816i			0.259721i	0.991532	+	0.129861i	$0.0414530\pi$
$193$			3.60816i			0.259721i	−0.991532	+	0.129861i	$0.958547\pi$
$194$	18.9546	+	32.8303i	1.36086	+	2.35708i
$195$	−0.594303	+	2.38215i	−0.0425589	+	0.170589i
$196$	−14.6941	+	0.575757i	−1.04958	+	0.0411255i
$197$			16.1792i			1.15272i	0.817196	+	0.576360i	$0.195528\pi$
$197$			16.1792i			1.15272i	−0.817196	+	0.576360i	$0.804472\pi$
$198$	6.63635	+	1.59359i	0.471625	+	0.113252i
$199$	−3.71908	−	6.44164i	−0.263639	−	0.456636i	0.703567	−	0.710629i	$-0.251589\pi$
$199$	−3.71908	−	6.44164i	−0.263639	−	0.456636i	−0.967206	+	0.253993i	$0.918256\pi$
$200$	0.272440	+	0.983304i	0.0192644	+	0.0695301i
$201$	−18.1381	+	2.62945i	−1.27937	+	0.185467i
$202$	1.32208	+	0.763301i	0.0930209	+	0.0537057i
$203$	−10.2747	−	17.0178i	−0.721139	−	1.19441i
$204$	−7.65411	−	9.70968i	−0.535895	−	0.679814i
$205$	1.46087	−	3.56962i	0.102032	−	0.249313i
$206$	13.0170	+	22.5461i	0.906938	+	1.57086i
$207$	−11.0120	+	11.6031i	−0.765389	+	0.806472i
$208$	2.07974	+	1.20074i	0.144204	+	0.0832564i
$209$	−3.15601	−	5.46638i	−0.218306	−	0.378117i
$210$	19.8317	−	6.10619i	1.36852	−	0.421367i
$211$	−9.62540	+	16.6717i	−0.662640	+	1.14773i	0.317279	+	0.948332i	$0.397231\pi$
$211$	−9.62540	+	16.6717i	−0.662640	+	1.14773i	−0.979919	+	0.199394i	$0.936103\pi$
$212$	−5.17817	+	2.98962i	−0.355638	+	0.205328i
$213$	−3.70201	−	25.5368i	−0.253658	−	1.74975i
$214$	4.11631	−	7.12966i	0.281385	−	0.487374i
$215$	12.3071	−	9.52683i	0.839338	−	0.649724i
$216$	−0.963007	+	0.443866i	−0.0655243	+	0.0302012i
$217$	−11.6871	+	0.228878i	−0.793370	+	0.0155373i
$218$	13.4260	−	7.75150i	0.909323	−	0.524998i
$219$	−8.19926	−	10.4012i	−0.554054	−	0.702850i
$220$	−1.99883	+	4.88413i	−0.134761	+	0.329288i
$221$	2.15401			0.144894
$222$	18.9188	+	7.54839i	1.26975	+	0.506615i
$223$	14.0757	−	8.12661i	0.942578	−	0.544198i	0.0518106	−	0.998657i	$-0.483501\pi$
$223$	14.0757	−	8.12661i	0.942578	−	0.544198i	0.890768	+	0.454459i	$0.150167\pi$
$224$	−0.418556	−	21.3725i	−0.0279659	−	1.42801i
$225$	−12.7230	+	7.94511i	−0.848201	+	0.529674i
$226$	17.1547	−	29.7129i	1.14112	−	1.97647i
$227$	−7.84040	−	4.52666i	−0.520386	−	0.300445i	0.216707	−	0.976237i	$-0.430468\pi$
$227$	−7.84040	−	4.52666i	−0.520386	−	0.300445i	−0.737093	+	0.675792i	$0.763802\pi$
$228$	18.9881	+	7.57604i	1.25752	+	0.501736i
$229$	−5.27212	−	9.13159i	−0.348392	−	0.603432i	0.637572	−	0.770391i	$-0.279939\pi$
$229$	−5.27212	−	9.13159i	−0.348392	−	0.603432i	−0.985964	+	0.166958i	$0.946605\pi$
$230$	−14.7798	−	19.0931i	−0.974549	−	1.25896i
$231$	4.81812	+	1.81384i	0.317009	+	0.119342i
$232$	−1.32786	+	0.766642i	−0.0871785	+	0.0503325i
$233$	4.92440	+	2.84311i	0.322608	+	0.186258i	0.652555	−	0.757742i	$-0.273697\pi$
$233$	4.92440	+	2.84311i	0.322608	+	0.186258i	−0.329946	+	0.944000i	$0.607031\pi$
$234$	0.899216	−	3.74469i	0.0587836	−	0.244798i
$235$	0.374664	+	2.75545i	0.0244404	+	0.179746i
$236$	7.60038			0.494743
$237$	−0.163004	−	1.12442i	−0.0105883	−	0.0730387i
$238$	−9.40952	−	15.5849i	−0.609929	−	1.01022i
$239$	−13.8595	+	24.0054i	−0.896496	+	1.55278i	−0.0645545	+	0.997914i	$0.520563\pi$
$239$	−13.8595	+	24.0054i	−0.896496	+	1.55278i	−0.831942	+	0.554863i	$0.812771\pi$
$240$	4.04212	+	14.1042i	0.260918	+	0.910424i
$241$	−1.99037	+	3.44741i	−0.128211	+	0.222067i	−0.922983	−	0.384840i	$-0.874257\pi$
$241$	−1.99037	+	3.44741i	−0.128211	+	0.222067i	0.794773	+	0.606907i	$0.207590\pi$
$242$	17.0777	−	9.85979i	1.09779	−	0.633811i
$243$	−10.2767	−	11.7213i	−0.659253	−	0.751921i
$244$	29.9966			1.92033
$245$	15.4153	−	2.71452i	0.984847	−	0.173425i
$246$	−2.24202	+	5.61926i	−0.142946	+	0.358271i
$247$	−3.08451	+	1.78084i	−0.196263	+	0.113312i
$248$			0.901609i			0.0572522i
$249$	7.94923	+	10.0841i	0.503762	+	0.639052i
$250$	−8.92976	−	20.8052i	−0.564767	−	1.31584i
$251$	−2.36861			−0.149505			−0.0747525	−	0.997202i	$-0.523817\pi$
$251$	−2.36861			−0.149505			−0.0747525	+	0.997202i	$0.523817\pi$
$252$	−15.8922	+	5.04713i	−1.00111	+	0.317939i
$253$		−	5.99046i		−	0.376617i
$254$	19.5016			1.22364
$255$	9.46522	+	9.14310i	0.592735	+	0.572563i
$256$	14.2679			0.891745
$257$	10.7177	−	6.18786i	0.668551	−	0.385988i	−0.126977	−	0.991906i	$-0.540527\pi$
$257$	10.7177	−	6.18786i	0.668551	−	0.385988i	0.795527	+	0.605918i	$0.207194\pi$
$258$	−19.1722	+	15.1134i	−1.19361	+	0.940918i
$259$	13.4542	+	7.42039i	0.836003	+	0.461081i
$260$	2.75596	+	1.12788i	0.170918	+	0.0699482i
$261$	−16.3496	−	15.5167i	−1.01202	−	0.960462i
$262$	8.10192	−	4.67765i	0.500538	−	0.288986i
$263$	10.4123	+	6.01153i	0.642049	+	0.370687i	0.785403	−	0.618984i	$-0.212456\pi$
$263$	10.4123	+	6.01153i	0.642049	+	0.370687i	−0.143355	+	0.989671i	$0.545789\pi$
$264$	0.147153	−	0.368816i	0.00905666	−	0.0226991i
$265$	5.03266	−	3.89574i	0.309154	−	0.239313i
$266$	26.3592	+	14.5379i	1.61619	+	0.891376i
$267$	−1.75355	−	0.699648i	−0.107316	−	0.0428177i
$268$			22.2294i			1.35788i
$269$	11.0425	+	19.1262i	0.673273	+	1.16614i	0.976970	+	0.213374i	$0.0684454\pi$
$269$	11.0425	+	19.1262i	0.673273	+	1.16614i	−0.303698	+	0.952769i	$0.598221\pi$
$270$	19.8464	−	12.6382i	1.20782	−	0.769134i
$271$	8.16999	−	14.1508i	0.496292	−	0.859603i	−0.503699	−	0.863879i	$-0.668028\pi$
$271$	8.16999	−	14.1508i	0.496292	−	0.859603i	0.999991	+	0.00427664i	$0.00136130\pi$
$272$	11.1477	−	6.43615i	0.675931	−	0.390249i
$273$	1.02350	−	2.71872i	0.0619448	−	0.164544i
$274$	19.7774	−	34.2555i	1.19480	−	2.06945i
$275$	1.40773	−	5.43793i	0.0848896	−	0.327919i
$276$	12.0114	+	15.2372i	0.723002	+	0.917170i
$277$	−12.5849	−	7.26589i	−0.756153	−	0.436565i	0.0717599	−	0.997422i	$-0.477138\pi$
$277$	−12.5849	−	7.26589i	−0.756153	−	0.436565i	−0.827913	+	0.560857i	$0.810472\pi$
$278$	−8.02406	−	4.63269i	−0.481251	−	0.277851i
$279$	−12.7088	+	3.76383i	−0.760856	+	0.225335i
$280$	−0.186053	−	1.19287i	−0.0111188	−	0.0712876i
$281$	−9.55682	−	16.5529i	−0.570112	−	0.987463i	−0.996554	−	0.0829479i	$-0.973566\pi$
$281$	−9.55682	−	16.5529i	−0.570112	−	0.987463i	0.426442	−	0.904515i	$-0.359767\pi$
$282$	−0.625799	−	4.31681i	−0.0372658	−	0.257062i
$283$			5.89481i			0.350410i	0.984532	+	0.175205i	$0.0560588\pi$
$283$			5.89481i			0.350410i	−0.984532	+	0.175205i	$0.943941\pi$
$284$	−31.2968			−1.85713
$285$	−21.1132	−	5.26735i	−1.25064	−	0.312011i
$286$	0.721086	+	1.24896i	0.0426387	+	0.0738524i
$287$	−2.20400	+	3.99615i	−0.130098	+	0.235886i
$288$	−6.88303	−	23.2409i	−0.405586	−	1.36948i
$289$	−2.72711	+	4.72349i	−0.160418	+	0.277852i
$290$	26.9035	−	20.8258i	1.57983	−	1.22293i
$291$	20.0732	+	25.4640i	1.17671	+	1.49272i
$292$	−13.9117	+	8.03193i	−0.814122	+	0.470033i
$293$	0.422648	+	0.244016i	0.0246913	+	0.0142556i	0.512295	−	0.858810i	$-0.328795\pi$
$293$	0.422648	+	0.244016i	0.0246913	+	0.0142556i	−0.487604	+	0.873065i	$0.662129\pi$
$294$	−24.1417	+	4.47111i	−1.40797	+	0.260761i
$295$	−8.01610	+	1.08996i	−0.466715	+	0.0634602i
$296$	0.592552	−	1.02633i	0.0344414	−	0.0596542i
$297$	5.81302	+	0.534576i	0.337306	+	0.0310192i
$298$	−32.3640	+	18.6854i	−1.87480	+	1.08241i
$299$	−3.38023			−0.195484
$300$	7.32286	+	16.6544i	0.422786	+	0.961543i
$301$	−15.7646	+	9.51805i	−0.908656	+	0.548611i
$302$	−8.45401	−	4.88092i	−0.486474	−	0.280866i
$303$	1.21276	+	0.483878i	0.0696714	+	0.0277981i
$304$	−10.6423	+	18.4329i	−0.610376	+	1.05720i
$305$	−31.6373	+	4.30179i	−1.81155	+	0.246320i
$306$	−14.9730	−	14.2102i	−0.855947	−	0.812344i
$307$		−	16.0075i		−	0.913598i	−0.889570	−	0.456799i	$-0.848996\pi$
$307$		−	16.0075i		−	0.913598i	0.889570	−	0.456799i	$-0.151004\pi$
$308$	3.01562	−	5.46773i	0.171831	−	0.311553i
$309$	13.7852	+	17.4873i	0.784210	+	0.994817i
$310$	−2.69544	−	19.8235i	−0.153090	−	1.12590i
$311$	2.37579			0.134718			0.0673592	−	0.997729i	$-0.478543\pi$
$311$	2.37579			0.134718			0.0673592	+	0.997729i	$0.478543\pi$
$312$	−0.208112	−	0.0830341i	−0.0117820	−	0.00470088i
$313$		−	5.43104i		−	0.306980i	−0.988150	−	0.153490i	$-0.950949\pi$
$313$		−	5.43104i		−	0.306980i	0.988150	−	0.153490i	$-0.0490513\pi$
$314$	25.7486			1.45308
$315$	16.0376	−	7.60227i	0.903618	−	0.428340i
$316$	−1.37804			−0.0775209
$317$		−	17.4269i		−	0.978794i	−0.872061	−	0.489397i	$-0.837217\pi$
$317$		−	17.4269i		−	0.978794i	0.872061	−	0.489397i	$-0.162783\pi$
$318$	−7.83995	+	6.18020i	−0.439642	+	0.346569i
$319$	8.44099			0.472605
$320$	19.4644	−	2.64661i	1.08809	−	0.147950i
$321$	2.60945	−	6.54016i	0.145645	−	0.365036i
$322$	14.7661	+	24.4569i	0.822885	+	1.36293i
$323$			19.0911i			1.06226i
$324$	−15.8577	+	10.2959i	−0.880985	+	0.571995i
$325$	−3.06846	−	0.794341i	−0.170207	−	0.0440621i
$326$	−19.2074	+	33.2683i	−1.06380	+	1.84256i
$327$	10.4135	−	8.20893i	0.575868	−	0.453955i
$328$	0.304840	+	0.175999i	0.0168320	+	0.00971794i
$329$	−0.0644244	−	3.28966i	−0.00355183	−	0.181365i
$330$	−2.13282	+	8.54901i	−0.117408	+	0.470607i
$331$	−14.0295			−0.771133			−0.385566	−	0.922680i	$-0.625994\pi$
$331$	−14.0295			−0.771133			−0.385566	+	0.922680i	$0.625994\pi$
$332$	13.4875	−	7.78701i	0.740223	−	0.427368i
$333$	16.9405	+	4.06794i	0.928333	+	0.222921i
$334$	−7.88711	+	13.6609i	−0.431563	+	0.747490i
$335$	−3.18790	−	23.4453i	−0.174174	−	1.28095i
$336$	−2.82655	−	17.1285i	−0.154201	−	0.934437i
$337$	−7.44981	−	4.30115i	−0.405817	−	0.234298i	0.283174	−	0.959069i	$-0.408613\pi$
$337$	−7.44981	−	4.30115i	−0.405817	−	0.234298i	−0.688991	+	0.724770i	$0.741946\pi$
$338$	−22.0938	+	12.7559i	−1.20174	+	0.693827i
$339$	10.8749	−	27.2561i	0.590642	−	1.48035i
$340$	12.6218	−	9.77044i	0.684515	−	0.529877i
$341$	2.48175	−	4.29852i	0.134394	−	0.232778i
$342$	33.1895	+	7.96982i	1.79468	+	0.430959i
$343$	−18.4883	+	1.08733i	−0.998275	+	0.0587103i
$344$	0.710188	+	1.23008i	0.0382908	+	0.0663216i
$345$	−14.8536	−	14.3481i	−0.799688	−	0.772473i
$346$	40.1234			2.15705
$347$		−	1.72808i		−	0.0927682i	−0.998924	−	0.0463841i	$-0.985230\pi$
$347$		−	1.72808i		−	0.0927682i	0.998924	−	0.0463841i	$-0.0147698\pi$
$348$	−21.4703	+	16.9249i	−1.15093	+	0.907272i
$349$	13.8154	+	23.9290i	0.739522	+	1.28089i	0.952711	+	0.303878i	$0.0982816\pi$
$349$	13.8154	+	23.9290i	0.739522	+	1.28089i	−0.213189	+	0.977011i	$0.568385\pi$
$350$	7.65690	+	25.6711i	0.409278	+	1.37218i
$351$	0.301645	−	3.28011i	0.0161006	−	0.175079i
$352$	7.86083	+	4.53845i	0.418984	+	0.241900i
$353$	11.6179	+	6.70761i	0.618359	+	0.357010i	0.776230	−	0.630450i	$-0.217130\pi$
$353$	11.6179	+	6.70761i	0.618359	+	0.357010i	−0.157871	+	0.987460i	$0.550463\pi$
$354$	12.5584	−	1.82056i	0.667470	−	0.0967617i
$355$	33.0087	−	4.48826i	1.75192	−	0.238212i
$356$	−1.14495	+	1.98311i	−0.0606821	+	0.105104i
$357$	−9.87731	−	12.0375i	−0.522763	−	0.637090i
$358$	−3.68889	+	2.12978i	−0.194964	+	0.112562i
$359$	−2.41265	+	4.17884i	−0.127335	+	0.220550i	−0.922643	−	0.385655i	$-0.873976\pi$
$359$	−2.41265	+	4.17884i	−0.127335	+	0.220550i	0.795308	+	0.606205i	$0.207309\pi$
$360$	−0.562038	−	1.24824i	−0.0296220	−	0.0657882i
$361$	−6.28375	−	10.8838i	−0.330724	−	0.572830i
$362$		−	30.3981i		−	1.59769i
$363$	13.2458	−	10.4416i	0.695225	−	0.548044i
$364$	−3.08527	−	1.70162i	−0.161712	−	0.0891892i
$365$	13.5208	−	10.4663i	0.707711	−	0.547833i
$366$	49.5644	−	7.18525i	2.59077	−	0.375579i
$367$	16.9429	+	9.78198i	0.884411	+	0.510615i	0.872110	−	0.489309i	$-0.162751\pi$
$367$	16.9429	+	9.78198i	0.884411	+	0.510615i	0.0123010	+	0.999924i	$0.496084\pi$
$368$	−17.4939	+	10.1001i	−0.911931	+	0.526504i
$369$	−1.20826	+	5.03165i	−0.0628993	+	0.261937i
$370$	−9.96001	+	24.3372i	−0.517796	+	1.26523i
$371$	−6.44650	+	3.89214i	−0.334686	+	0.202070i
$372$	2.30640	+	15.9098i	0.119581	+	0.824882i
$373$	−12.2712	+	7.08479i	−0.635380	+	0.366837i	−0.782833	−	0.622232i	$-0.786226\pi$
$373$	−12.2712	+	7.08479i	−0.635380	+	0.366837i	0.147453	+	0.989069i	$0.452893\pi$
$374$	7.73025			0.399722
$375$	−10.1118	−	16.5152i	−0.522171	−	0.852841i
$376$	−0.253784			−0.0130879
$377$		−	4.76299i		−	0.245306i
$378$	−25.0502	+	12.1463i	−1.28844	+	0.624737i
$379$	−0.716540			−0.0368062			−0.0184031	−	0.999831i	$-0.505858\pi$
$379$	−0.716540			−0.0368062			−0.0184031	+	0.999831i	$0.505858\pi$
$380$	−9.99650	+	24.4263i	−0.512809	+	1.25304i
$381$	16.5076	−	2.39307i	0.845708	−	0.122600i
$382$		−	26.4617i		−	1.35390i
$383$	−30.1973	+	17.4344i	−1.54301	+	0.890858i	−0.544364	+	0.838849i	$0.683229\pi$
$383$	−30.1973	+	17.4344i	−1.54301	+	0.890858i	−0.998647	+	0.0520087i	$0.983438\pi$
$384$	−2.79487	+	0.405166i	−0.142625	+	0.0206760i
$385$	−2.39644	+	6.19927i	−0.122134	+	0.315944i
$386$	7.30666			0.371899
$387$	−14.3741	+	15.1457i	−0.730677	+	0.769897i
$388$	34.0582	−	19.6635i	1.72904	−	0.998264i
$389$	0.0359340	−	0.0622394i	0.00182192	−	0.00315567i	−0.865113	−	0.501577i	$-0.832753\pi$
$389$	0.0359340	−	0.0622394i	0.00182192	−	0.00315567i	0.866935	+	0.498421i	$0.166087\pi$
$390$	4.82394	+	1.20348i	0.244270	+	0.0609408i
$391$	−9.05927	+	15.6911i	−0.458147	+	0.793533i
$392$	0.0559292	+	1.42739i	0.00282485	+	0.0720942i
$393$	6.28403	−	4.95368i	0.316988	−	0.249880i
$394$	32.7635			1.65060
$395$	1.45342	−	0.197624i	0.0731293	−	0.00994353i
$396$	1.65319	−	6.88455i	0.0830761	−	0.345962i
$397$	31.4580	+	18.1623i	1.57883	+	0.911539i	0.995023	+	0.0996484i	$0.0317718\pi$
$397$	31.4580	+	18.1623i	1.57883	+	0.911539i	0.583809	+	0.811891i	$0.301562\pi$
$398$	−13.0446	+	7.53128i	−0.653865	+	0.377509i
$399$	24.0962	+	9.07133i	1.20632	+	0.454135i
$400$	−18.2538	+	5.05752i	−0.912691	+	0.252876i
$401$	−4.21058	−	7.29294i	−0.210266	−	0.364192i	0.741532	−	0.670918i	$-0.234100\pi$
$401$	−4.21058	−	7.29294i	−0.210266	−	0.364192i	−0.951798	+	0.306726i	$0.900766\pi$
$402$	5.32473	+	36.7304i	0.265573	+	1.83195i
$403$	−2.42552	−	1.40038i	−0.120824	−	0.0697578i
$404$	0.791849	−	1.37152i	0.0393959	−	0.0682358i
$405$	15.2486	−	13.1332i	0.757708	−	0.652594i
$406$	−34.4616	+	20.8066i	−1.71030	+	1.03261i
$407$	−5.65012	+	3.26210i	−0.280066	+	0.161696i
$408$	−0.943201	+	0.743522i	−0.0466954	+	0.0368098i
$409$	−35.7574			−1.76809			−0.884046	−	0.467400i	$-0.845191\pi$
$409$	−35.7574			−1.76809			−0.884046	+	0.467400i	$0.845191\pi$
$410$	−7.22861	−	2.95831i	−0.356996	−	0.146101i
$411$	12.5375	−	31.4232i	0.618428	−	1.54999i
$412$	23.3893	−	13.5038i	1.15231	−	0.665287i
$413$	9.57022	−	0.187422i	0.470920	−	0.00922244i
$414$	23.4967	+	22.2998i	1.15480	+	1.09597i
$415$	−13.1085	+	10.1472i	−0.643471	+	0.498105i
$416$	2.56091	−	4.43562i	0.125559	−	0.217474i
$417$	−7.36061	−	2.93680i	−0.360451	−	0.143816i
$418$	−11.0696	+	6.39104i	−0.541432	+	0.312596i
$419$	−1.47887	+	2.56147i	−0.0722474	+	0.125136i	−0.899886	−	0.436125i	$-0.856350\pi$
$419$	−1.47887	+	2.56147i	−0.0722474	+	0.125136i	0.827639	+	0.561261i	$0.189684\pi$
$420$	−6.33457	−	20.5734i	−0.309095	−	1.00388i
$421$	−0.671309	−	1.16274i	−0.0327176	−	0.0566685i	0.849203	−	0.528067i	$-0.177083\pi$
$421$	−0.671309	−	1.16274i	−0.0327176	−	0.0566685i	−0.881921	+	0.471398i	$0.843750\pi$
$422$	33.7608	+	19.4918i	1.64345	+	0.948846i
$423$	−1.05944	−	3.57726i	−0.0515117	−	0.173932i
$424$	0.290412	+	0.503008i	0.0141037	+	0.0244282i
$425$	−11.9110	+	12.1149i	−0.577770	+	0.587661i
$426$	−51.7129	+	7.49671i	−2.50550	+	0.363217i
$427$	37.7710	−	0.739703i	1.82787	−	0.0357967i
$428$	−7.39631	−	4.27026i	−0.357514	−	0.206411i
$429$	0.763638	+	0.968719i	0.0368688	+	0.0467702i
$430$	−19.2922	−	24.9224i	−0.930351	−	1.20186i
$431$	−11.1165	−	19.2543i	−0.535461	−	0.927446i	−0.999141	−	0.0414430i	$-0.986804\pi$
$431$	−11.1165	−	19.2543i	−0.535461	−	0.927446i	0.463680	−	0.886003i	$-0.346529\pi$
$432$	−8.23982	−	17.8770i	−0.396438	−	0.860109i
$433$		−	16.2059i		−	0.778806i	−0.921067	−	0.389403i	$-0.872681\pi$
$433$		−	16.2059i		−	0.778806i	0.921067	−	0.389403i	$-0.127319\pi$
$434$	0.463487	+	23.6667i	0.0222481	+	1.13604i
$435$	20.2174	−	20.9297i	0.969352	−	1.00350i
$436$	−8.04141	−	13.9281i	−0.385113	−	0.667036i
$437$		−	29.9593i		−	1.43315i
$438$	−21.0629	+	16.6038i	−1.00642	+	0.793360i
$439$	−4.31878			−0.206124			−0.103062	−	0.994675i	$-0.532864\pi$
$439$	−4.31878			−0.206124			−0.103062	+	0.994675i	$0.532864\pi$
$440$	0.474445	+	0.194167i	0.0226183	+	0.00925655i
$441$	−19.8866	+	6.74712i	−0.946980	+	0.321291i
$442$		−	4.36194i		−	0.207476i
$443$		−	6.21872i		−	0.295460i	−0.989028	−	0.147730i	$-0.952803\pi$
$443$		−	6.21872i		−	0.295460i	0.989028	−	0.147730i	$-0.0471967\pi$
$444$	7.83070	−	19.6264i	0.371628	−	0.931427i
$445$	0.923177	−	2.25577i	0.0437628	−	0.106934i
$446$	−16.4567	−	28.5038i	−0.779246	−	1.34969i
$447$	−25.1023	+	19.7880i	−1.18730	+	0.935942i
$448$	−23.2381	+	0.455092i	−1.09790	+	0.0215011i
$449$	−24.9704			−1.17843			−0.589213	−	0.807977i	$-0.700562\pi$
$449$	−24.9704			−1.17843			−0.589213	+	0.807977i	$0.700562\pi$
$450$	16.0891	+	25.7646i	0.758449	+	1.21455i
$451$	−0.968906	−	1.67819i	−0.0456240	−	0.0790231i
$452$	−30.8241	−	17.7963i	−1.44985	−	0.837068i
$453$	−7.75501	−	3.09416i	−0.364362	−	0.145376i
$454$	−9.16665	+	15.8771i	−0.430212	+	0.745149i
$455$	3.49806	+	1.35224i	0.163991	+	0.0633939i
$456$	0.735938	−	1.84451i	0.0344635	−	0.0863772i
$457$			25.7394i			1.20404i	0.798481	+	0.602020i	$0.205637\pi$
$457$			25.7394i			1.20404i	−0.798481	+	0.602020i	$0.794363\pi$
$458$	−18.4918	+	10.6762i	−0.864065	+	0.498868i
$459$	−14.4179	−	10.1912i	−0.672971	−	0.475683i
$460$	−19.8071	+	15.3325i	−0.923512	+	0.714883i
$461$	−14.8794	−	25.7719i	−0.693004	−	1.20032i	−0.970849	−	0.239692i	$-0.922954\pi$
$461$	−14.8794	−	25.7719i	−0.693004	−	1.20032i	0.277845	−	0.960626i	$-0.410380\pi$
$462$	3.67310	−	9.75687i	0.170888	−	0.453931i
$463$	5.02677	+	2.90221i	0.233614	+	0.134877i	0.612238	−	0.790673i	$-0.290269\pi$
$463$	5.02677	+	2.90221i	0.233614	+	0.134877i	−0.378624	+	0.925550i	$0.623603\pi$
$464$	−14.2318	−	24.6501i	−0.660693	−	1.14435i
$465$	−4.71416	−	16.4492i	−0.218614	−	0.762814i
$466$	5.75739	−	9.97210i	0.266706	−	0.461949i
$467$	−20.2382	−	11.6845i	−0.936510	−	0.540694i	−0.0476455	−	0.998864i	$-0.515172\pi$
$467$	−20.2382	−	11.6845i	−0.936510	−	0.540694i	−0.888865	+	0.458170i	$0.848505\pi$
$468$	−3.88474	−	0.932846i	−0.179572	−	0.0431208i
$469$	0.548167	+	27.9907i	0.0253120	+	1.29249i
$470$	5.57989	−	0.758708i	0.257381	−	0.0349966i
$471$	21.7954	−	3.15964i	1.00428	−	0.145588i
$472$		−	0.738303i		−	0.0339831i
$473$		−	7.81941i		−	0.359537i
$474$	−2.27699	+	0.330090i	−0.104585	+	0.0151615i
$475$	7.04031	−	27.1960i	0.323032	−	1.24784i
$476$	−16.1677	+	9.76144i	−0.741046	+	0.447415i
$477$	−5.87790	+	6.19340i	−0.269131	+	0.283576i
$478$	48.6117	+	28.0660i	2.22345	+	1.28371i
$479$	−11.8495	+	20.5240i	−0.541419	+	0.937765i	0.457404	+	0.889259i	$0.348779\pi$
$479$	−11.8495	+	20.5240i	−0.541419	+	0.937765i	−0.998823	+	0.0485060i	$0.984554\pi$
$480$	30.0811	−	8.62092i	1.37301	−	0.393489i
$481$	1.84070	+	3.18819i	0.0839288	+	0.145369i
$482$	6.98114	+	4.03056i	0.317982	+	0.183587i
$483$	15.5002	+	18.8901i	0.705285	+	0.859529i
$484$	−10.2285	−	17.7164i	−0.464934	−	0.805289i
$485$	−33.1012	+	25.6233i	−1.50305	+	1.16349i
$486$	−23.7360	+	20.8108i	−1.07669	+	0.943996i
$487$	30.4975	−	17.6077i	1.38197	−	0.797883i	0.389581	−	0.920992i	$-0.372620\pi$
$487$	30.4975	−	17.6077i	1.38197	−	0.797883i	0.992393	+	0.123109i	$0.0392866\pi$
$488$		−	2.91388i		−	0.131905i
$489$	−12.1761	+	30.5176i	−0.550624	+	1.38005i
$490$	−5.49701	−	31.2165i	−0.248330	−	1.41022i
$491$	3.58013	−	6.20097i	0.161569	−	0.279846i	−0.773863	−	0.633354i	$-0.781678\pi$
$491$	3.58013	−	6.20097i	0.161569	−	0.279846i	0.935432	+	0.353508i	$0.115011\pi$
$492$	5.82942	+	2.32587i	0.262810	+	0.104858i
$493$	−22.1099	−	12.7652i	−0.995780	−	0.574914i
$494$	3.60627	+	6.24624i	0.162254	+	0.281032i
$495$	−0.756311	+	7.49820i	−0.0339936	+	0.337019i
$496$	−16.7372			−0.751525
$497$	−39.4083	+	0.771766i	−1.76770	+	0.0346185i
$498$	20.4206	−	16.0975i	0.915069	−	0.721346i
$499$	19.3222	+	33.4671i	0.864982	+	1.49819i	0.867065	+	0.498195i	$0.166003\pi$
$499$	19.3222	+	33.4671i	0.864982	+	1.49819i	−0.00208354	+	0.999998i	$0.500663\pi$
$500$	−21.5833	+	9.26373i	−0.965235	+	0.414287i
$501$	−4.99986	+	12.5314i	−0.223377	+	0.559860i
$502$			4.79651i			0.214079i
$503$			11.4806i			0.511893i	0.966691	+	0.255946i	$0.0823871\pi$
$503$			11.4806i			0.511893i	−0.966691	+	0.255946i	$0.917613\pi$
$504$	0.490279	+	1.54377i	0.0218388	+	0.0687650i
$505$	−0.638471	+	1.56010i	−0.0284116	+	0.0694235i
$506$	−12.1309			−0.539284
$507$	−17.1364	+	13.5086i	−0.761056	+	0.599938i
$508$		−	20.2310i		−	0.897606i
$509$	0.406115	+	0.703411i	0.0180007	+	0.0311781i	0.874885	−	0.484330i	$-0.160937\pi$
$509$	0.406115	+	0.703411i	0.0180007	+	0.0311781i	−0.856885	+	0.515508i	$0.827603\pi$
$510$	18.5151	−	19.1674i	0.819863	−	0.848748i
$511$	−17.3192	+	10.4567i	−0.766158	+	0.462576i
$512$		−	32.1540i		−	1.42102i
$513$	29.0719	+	2.67350i	1.28356	+	0.118038i
$514$	−12.5306	−	21.7037i	−0.552703	−	0.957309i
$515$	−22.7321	+	17.5967i	−1.00170	+	0.775404i
$516$	15.6786	+	19.8892i	0.690213	+	0.875575i
$517$	1.20994	+	0.698561i	0.0532132	+	0.0307227i
$518$	15.0266	−	27.2452i	0.660230	−	1.19709i
$519$	33.9632	−	4.92358i	1.49082	−	0.216121i
$520$	0.109563	−	0.267715i	0.00480463	−	0.0117401i
$521$	−16.7799	−	29.0636i	−0.735139	−	1.27330i	−0.954662	−	0.297691i	$-0.903784\pi$
$521$	−16.7799	−	29.0636i	−0.735139	−	1.27330i	0.219523	−	0.975607i	$-0.429550\pi$
$522$	−31.4220	+	33.1086i	−1.37530	+	1.44912i
$523$	−1.62974	−	0.940933i	−0.0712637	−	0.0411441i	0.463945	−	0.885864i	$-0.346434\pi$
$523$	−1.62974	−	0.940933i	−0.0712637	−	0.0411441i	−0.535208	+	0.844720i	$0.679767\pi$
$524$	−4.85259	−	8.40494i	−0.211986	−	0.367171i
$525$	9.63146	+	20.7903i	0.420352	+	0.907361i
$526$	12.1736	−	21.0852i	0.530793	−	0.919360i
$527$	−13.0012	+	7.50623i	−0.566340	+	0.326976i
$528$	6.84662	+	2.73172i	0.297961	+	0.118883i
$529$	2.71649	−	4.70510i	0.118108	−	0.204569i
$530$	−7.88901	−	10.1913i	−0.342677	−	0.442683i
$531$	10.4069	−	3.08210i	0.451620	−	0.133752i
$532$	15.0816	−	27.3450i	0.653871	−	1.18556i
$533$	−0.946954	+	0.546724i	−0.0410171	+	0.0236812i
$534$	−1.41681	+	3.55101i	−0.0613114	+	0.153667i
$535$	8.41327	+	3.44314i	0.363737	+	0.148860i
$536$	2.15937			0.0932705
$537$	−2.86118	+	2.25546i	−0.123469	+	0.0973304i
$538$	38.7312	−	22.3615i	1.66982	−	0.964071i
$539$	3.66237	−	6.95920i	0.157749	−	0.299754i
$540$	−13.1108	−	20.5887i	−0.564201	−	0.885997i
$541$	3.70888	−	6.42396i	0.159457	−	0.276188i	−0.775216	−	0.631696i	$-0.782359\pi$
$541$	3.70888	−	6.42396i	0.159457	−	0.276188i	0.934673	+	0.355509i	$0.115692\pi$
$542$	−28.6560	−	16.5445i	−1.23088	−	0.710649i
$543$	−3.73018	−	25.7311i	−0.160077	−	1.10423i
$544$	−13.7268	−	23.7756i	−0.588534	−	1.01937i
$545$	10.4787	+	13.5367i	0.448857	+	0.579850i
$546$	−5.50550	−	2.07262i	−0.235614	−	0.0886998i
$547$	21.0903	−	12.1765i	0.901757	−	0.520630i	0.0239874	−	0.999712i	$-0.492364\pi$
$547$	21.0903	−	12.1765i	0.901757	−	0.520630i	0.877770	+	0.479082i	$0.159031\pi$
$548$	−35.5367	−	20.5171i	−1.51805	−	0.876447i
$549$	41.0731	−	12.1642i	1.75296	−	0.519155i
$550$	−11.0120	−	2.85071i	−0.469553	−	0.121555i
$551$	42.2148			1.79841
$552$	1.48014	−	1.16679i	0.0629990	−	0.0496619i
$553$	−1.73520	+	0.0339819i	−0.0737881	+	0.00144506i
$554$	−14.7137	+	25.4849i	−0.625125	+	1.08275i
$555$	−5.44441	+	21.8229i	−0.231102	+	0.926330i
$556$	−4.80596	+	8.32416i	−0.203818	+	0.353023i
$557$	2.29777	−	1.32662i	0.0973597	−	0.0562106i	−0.450530	−	0.892761i	$-0.648765\pi$
$557$	2.29777	−	1.32662i	0.0973597	−	0.0562106i	0.547889	+	0.836551i	$0.315431\pi$
$558$	7.62190	+	25.7358i	0.322661	+	1.08948i
$559$	−4.41225			−0.186618
$560$	22.1441	−	3.45385i	0.935761	−	0.145952i
$561$	6.54342	−	0.948586i	0.276264	−	0.0400493i
$562$	−33.5202	+	19.3529i	−1.41396	+	0.816353i
$563$		−	0.370159i		−	0.0156003i	−0.999970	−	0.00780017i	$-0.997517\pi$
$563$		−	0.370159i		−	0.0156003i	0.999970	−	0.00780017i	$-0.00248289\pi$
$564$	−4.47826	+	0.649204i	−0.188569	+	0.0273364i
$565$	35.0623	+	14.3493i	1.47508	+	0.603678i
$566$	11.9372			0.501758
$567$	−19.7138	+	13.3554i	−0.827901	+	0.560874i
$568$			3.04018i			0.127563i
$569$	30.9217			1.29630			0.648152	−	0.761511i	$-0.275542\pi$
$569$	30.9217			1.29630			0.648152	+	0.761511i	$0.275542\pi$
$570$	−10.6666	+	42.7550i	−0.446774	+	1.79081i
$571$	−22.0954			−0.924663			−0.462332	−	0.886707i	$-0.652987\pi$
$571$	−22.0954			−0.924663			−0.462332	+	0.886707i	$0.652987\pi$
$572$	1.29567	−	0.748054i	0.0541746	−	0.0312777i
$573$	−3.24714	−	22.3990i	−0.135651	−	0.935734i
$574$	8.09236	+	4.46318i	0.337769	+	0.186290i
$575$	18.6917	−	19.0117i	0.779498	−	0.792843i
$576$	−25.2696	+	7.48385i	−1.05290	+	0.311827i
$577$	−33.0567	+	19.0853i	−1.37617	+	0.794531i	−0.991696	−	0.128605i	$-0.958950\pi$
$577$	−33.0567	+	19.0853i	−1.37617	+	0.794531i	−0.384473	+	0.923136i	$0.625617\pi$
$578$	9.56523	+	5.52249i	0.397861	+	0.229705i
$579$	6.18487	−	0.896607i	0.257034	−	0.0372617i
$580$	−21.6046	−	27.9097i	−0.897084	−	1.15889i
$581$	16.7911	−	10.1378i	0.696613	−	0.420588i
$582$	51.5655	−	40.6489i	2.13746	−	1.68495i
$583$		−	3.19753i		−	0.132428i
$584$	0.780224	+	1.35139i	0.0322859	+	0.0559208i
$585$	4.23100	+	0.426763i	0.174930	+	0.0176445i
$586$	0.494141	−	0.855877i	0.0204128	−	0.0353560i
$587$	−34.9116	+	20.1562i	−1.44095	+	0.831935i	−0.997913	−	0.0645662i	$-0.979434\pi$
$587$	−34.9116	+	20.1562i	−1.44095	+	0.831935i	−0.443041	+	0.896501i	$0.646100\pi$
$588$	4.63833	+	25.0446i	0.191282	+	1.03282i
$589$	12.4117	−	21.4976i	0.511414	−	0.885794i
$590$	2.20722	+	16.2329i	0.0908697	+	0.668298i
$591$	27.7333	−	4.02044i	1.14080	−	0.165379i
$592$	19.0525	+	11.0000i	0.783055	+	0.452097i
$593$	15.5991	+	9.00613i	0.640577	+	0.369838i	0.784837	−	0.619702i	$-0.212747\pi$
$593$	15.5991	+	9.00613i	0.640577	+	0.369838i	−0.144260	+	0.989540i	$0.546080\pi$
$594$	1.08254	−	11.7716i	0.0444170	−	0.482994i
$595$	15.6522	−	12.6140i	0.641677	−	0.517122i
$596$	19.3842	+	33.5744i	0.794008	+	1.37526i
$597$	−10.1177	+	7.97571i	−0.414088	+	0.326424i
$598$			6.84509i			0.279917i
$599$	40.6815			1.66220			0.831100	−	0.556123i	$-0.187712\pi$
$599$	40.6815			1.66220			0.831100	+	0.556123i	$0.187712\pi$
$600$	1.61781	−	0.711344i	0.0660469	−	0.0290405i
$601$	−15.5405	−	26.9169i	−0.633910	−	1.09796i	−0.986745	−	0.162278i	$-0.948116\pi$
$601$	−15.5405	−	26.9169i	−0.633910	−	1.09796i	0.352835	−	0.935685i	$-0.385218\pi$
$602$	19.2744	+	31.9239i	0.785566	+	1.30112i
$603$	9.01445	+	30.4378i	0.367097	+	1.23952i
$604$	−5.06347	+	8.77019i	−0.206030	+	0.356854i
$605$	13.3287	+	17.2185i	0.541889	+	0.700033i
$606$	0.979871	−	2.45589i	0.0398045	−	0.0997637i
$607$	−23.0164	+	13.2885i	−0.934209	+	0.539366i	−0.888140	−	0.459573i	$-0.848003\pi$
$607$	−23.0164	+	13.2885i	−0.934209	+	0.539366i	−0.0460684	+	0.998938i	$0.514669\pi$
$608$	39.3133	+	22.6975i	1.59437	+	0.920507i
$609$	−26.6175	+	21.8409i	−1.07860	+	0.885039i
$610$	8.71128	+	64.0667i	0.352709	+	2.59399i
$611$	0.394177	−	0.682734i	0.0159467	−	0.0276205i
$612$	−14.7417	+	15.5330i	−0.595897	+	0.627883i
$613$	5.88097	−	3.39538i	0.237530	−	0.137138i	−0.376511	−	0.926412i	$-0.622876\pi$
$613$	5.88097	−	3.39538i	0.237530	−	0.137138i	0.614041	+	0.789274i	$0.289543\pi$
$614$	−32.4158			−1.30820
$615$	−6.48182	−	1.61709i	−0.261372	−	0.0652075i
$616$	−0.531137	−	0.292938i	−0.0214001	−	0.0118028i
$617$	22.0280	+	12.7179i	0.886813	+	0.512002i	0.872899	−	0.487901i	$-0.162237\pi$
$617$	22.0280	+	12.7179i	0.886813	+	0.512002i	0.0139146	+	0.999903i	$0.495571\pi$
$618$	35.4124	−	27.9155i	1.42449	−	1.12292i
$619$	9.84856	−	17.0582i	0.395847	−	0.685627i	−0.597362	−	0.801972i	$-0.703784\pi$
$619$	9.84856	−	17.0582i	0.395847	−	0.685627i	0.993209	+	0.116345i	$0.0371177\pi$
$620$	−20.5649	+	2.79625i	−0.825905	+	0.112300i
$621$	22.6257	+	15.9928i	0.907938	+	0.641768i
$622$		−	4.81105i		−	0.192906i
$623$	−1.39279	+	2.52532i	−0.0558009	+	0.101175i
$624$	1.54142	−	3.86333i	0.0617064	−	0.154657i
$625$	21.4354	−	12.8657i	0.857414	−	0.514627i
$626$	−10.9980			−0.439570
$627$	−8.58584	+	6.76819i	−0.342885	+	0.270295i
$628$		−	26.7116i		−	1.06591i
$629$	19.7329			0.786801
$630$	−15.3949	−	32.4768i	−0.613347	−	1.29391i
$631$	11.2617			0.448322			0.224161	−	0.974552i	$-0.428036\pi$
$631$	11.2617			0.448322			0.224161	+	0.974552i	$0.428036\pi$
$632$			0.133863i			0.00532479i
$633$	30.9693	+	12.3564i	1.23092	+	0.491123i
$634$	−35.2902			−1.40155
$635$	2.90131	+	21.3376i	0.115135	+	0.846756i
$636$	6.41134	+	8.13316i	0.254226	+	0.322501i
$637$	−3.92686	−	2.06656i	−0.155588	−	0.0818801i
$638$		−	17.0933i		−	0.676731i
$639$	−42.8535	+	12.6915i	−1.69526	+	0.502067i
$640$	−0.491216	−	3.61263i	−0.0194170	−	0.142802i
$641$	7.93855	−	13.7500i	0.313554	−	0.543091i	−0.665575	−	0.746331i	$-0.731814\pi$
$641$	7.93855	−	13.7500i	0.313554	−	0.543091i	0.979129	+	0.203240i	$0.0651470\pi$
$642$	−13.2441	−	5.28423i	−0.522702	−	0.208552i
$643$	−5.93555	−	3.42689i	−0.234075	−	0.135143i	0.378375	−	0.925652i	$-0.376483\pi$
$643$	−5.93555	−	3.42689i	−0.234075	−	0.135143i	−0.612451	+	0.790509i	$0.709816\pi$
$644$	25.3716	−	15.3184i	0.999782	−	0.603629i
$645$	−19.3885	−	18.7287i	−0.763421	−	0.737441i
$646$	38.6603			1.52107
$647$	33.7260	−	19.4717i	1.32591	−	0.765513i	0.341244	−	0.939975i	$-0.389152\pi$
$647$	33.7260	−	19.4717i	1.32591	−	0.765513i	0.984664	+	0.174462i	$0.0558186\pi$
$648$	1.00015	+	1.54042i	0.0392895	+	0.0605135i
$649$	−2.03224	+	3.51994i	−0.0797724	+	0.138170i
$650$	−1.60857	+	6.21373i	−0.0630933	+	0.243723i
$651$	3.29650	+	19.9763i	0.129200	+	0.782933i
$652$	34.5125	+	19.9258i	1.35161	+	0.780355i
$653$	−15.1167	+	8.72765i	−0.591563	+	0.341539i	−0.765715	−	0.643180i	$-0.777615\pi$
$653$	−15.1167	+	8.72765i	−0.591563	+	0.341539i	0.174152	+	0.984719i	$0.444282\pi$
$654$	−16.6234	−	21.0877i	−0.650025	−	0.824595i
$655$	6.32336	+	8.16875i	0.247074	+	0.319180i
$656$	−3.26721	+	5.65897i	−0.127563	+	0.220946i
$657$	−15.7916	+	16.6393i	−0.616090	+	0.649159i
$658$	−6.66169	+	0.130462i	−0.259700	+	0.00508593i
$659$	−15.3956	−	26.6660i	−0.599727	−	1.03876i	−0.992861	−	0.119277i	$-0.961942\pi$
$659$	−15.3956	−	26.6660i	−0.599727	−	1.03876i	0.393134	−	0.919481i	$-0.371391\pi$
$660$	8.86874	+	2.21259i	0.345215	+	0.0861249i
$661$	−30.9829			−1.20510			−0.602548	−	0.798083i	$-0.705848\pi$
$661$	−30.9829			−1.20510			−0.602548	+	0.798083i	$0.705848\pi$
$662$			28.4103i			1.10420i
$663$	−0.535258	−	3.69225i	−0.0207877	−	0.143395i
$664$	−0.756432	−	1.31018i	−0.0293553	−	0.0508448i
$665$	−11.9850	+	31.0036i	−0.464759	+	1.20227i
$666$	8.23772	−	34.3051i	0.319205	−	1.32930i
$667$	34.6965	+	20.0321i	1.34346	+	0.775644i
$668$	14.1718	+	8.18209i	0.548323	+	0.316574i
$669$	−17.4278	−	22.1082i	−0.673798	−	0.854752i
$670$	−47.4775	+	6.45561i	−1.83422	+	0.249402i
$671$	−8.02068	+	13.8922i	−0.309635	+	0.536304i
$672$	−36.5312	+	6.02839i	−1.40922	+	0.232550i
$673$	−32.9962	+	19.0503i	−1.27191	+	0.734337i	−0.975347	−	0.220677i	$-0.929173\pi$
$673$	−32.9962	+	19.0503i	−1.27191	+	0.734337i	−0.296562	+	0.955014i	$0.595840\pi$
$674$	−8.70998	+	15.0861i	−0.335496	+	0.581096i
$675$	16.7806	+	19.8346i	0.645884	+	0.763435i
$676$	13.2329	+	22.9201i	0.508959	+	0.881542i
$677$		−	33.6327i		−	1.29261i	−0.763079	−	0.646305i	$-0.776313\pi$
$677$		−	33.6327i		−	1.29261i	0.763079	−	0.646305i	$-0.223687\pi$
$678$	−55.1946	−	22.0220i	−2.11974	−	0.845750i
$679$	42.4004	−	25.5997i	1.62718	−	0.982426i
$680$	−0.949103	−	1.22609i	−0.0363964	−	0.0470183i
$681$	−5.81100	+	14.5643i	−0.222678	+	0.558107i
$682$	−8.70467	−	5.02564i	−0.333319	−	0.192442i
$683$	−1.29390	+	0.747031i	−0.0495096	+	0.0285844i	−0.524550	−	0.851379i	$-0.675767\pi$
$683$	−1.29390	+	0.747031i	−0.0495096	+	0.0285844i	0.475041	+	0.879964i	$0.342433\pi$
$684$	8.26790	−	34.4308i	0.316131	−	1.31649i
$685$	40.4227	+	16.5430i	1.54447	+	0.632077i
$686$	2.20188	+	37.4395i	0.0840684	+	1.42945i
$687$	−14.3427	+	11.3063i	−0.547206	+	0.431361i
$688$	−22.8349	+	13.1838i	−0.870574	+	0.502626i
$689$	−1.80427			−0.0687372
$690$	−29.0553	+	30.0790i	−1.10612	+	1.14509i
$691$	−18.6323			−0.708806			−0.354403	−	0.935093i	$-0.615316\pi$
$691$	−18.6323			−0.708806			−0.354403	+	0.935093i	$0.615316\pi$
$692$		−	41.6240i		−	1.58231i
$693$	1.91189	−	8.70963i	0.0726268	−	0.330852i
$694$	−3.49943			−0.132836
$695$	3.87507	−	9.46869i	0.146990	−	0.359168i
$696$	1.64409	+	2.08563i	0.0623192	+	0.0790555i
$697$			5.86104i			0.222003i
$698$	48.4571	−	27.9767i	1.83413	−	1.05893i
$699$	3.64977	−	9.14758i	0.138047	−	0.345993i
$700$	26.6312	−	7.94327i	1.00657	−	0.300227i
$701$	48.0562			1.81506			0.907529	−	0.419989i	$-0.137966\pi$
$701$	48.0562			1.81506			0.907529	+	0.419989i	$0.137966\pi$
$702$	−6.64234	−	0.610841i	−0.250699	−	0.0230547i
$703$	−28.2572	+	16.3143i	−1.06574	+	0.615305i
$704$	4.93461	−	8.54700i	0.185980	−	0.322127i
$705$	4.63011	−	1.32694i	0.174380	−	0.0499753i
$706$	13.5832	−	23.5267i	0.511209	−	0.885440i
$707$	0.963256	−	1.74651i	0.0362270	−	0.0656844i
$708$	−1.88865	−	13.0281i	−0.0709798	−	0.489625i
$709$	18.8886			0.709377			0.354688	−	0.934985i	$-0.384587\pi$
$709$	18.8886			0.709377			0.354688	+	0.934985i	$0.384587\pi$
$710$	−9.08888	−	66.8438i	−0.341100	−	2.50860i
$711$	−1.88689	+	0.558822i	−0.0707641	+	0.0209575i
$712$	0.192639	+	0.111220i	0.00721947	+	0.00416816i
$713$	20.4024	−	11.7793i	0.764077	−	0.441140i
$714$	−24.3763	+	20.0019i	−0.912260	+	0.748553i
$715$	−1.25926	+	0.974782i	−0.0470936	+	0.0364548i
$716$	2.20943	+	3.82685i	0.0825704	+	0.143016i
$717$	44.5924	+	17.7918i	1.66533	+	0.664448i
$718$	8.46229	+	4.88571i	0.315810	+	0.182333i
$719$	−14.5678	+	25.2321i	−0.543287	+	0.941000i	0.455426	+	0.890274i	$0.349487\pi$
$719$	−14.5678	+	25.2321i	−0.543287	+	0.941000i	−0.998713	+	0.0507265i	$0.983846\pi$
$720$	23.1721	−	10.4335i	0.863572	−	0.388835i
$721$	29.1183	−	17.5805i	1.08442	−	0.654732i
$722$	−22.0400	+	12.7248i	−0.820245	+	0.473569i
$723$	6.40392	+	2.55509i	0.238164	+	0.0950247i
$724$	−31.5350			−1.17199
$725$	26.7889	+	26.3380i	0.994913	+	0.978167i
$726$	−21.1447	−	26.8233i	−0.784753	−	0.995505i
$727$	−9.08681	+	5.24627i	−0.337011	+	0.194573i	−0.658950	−	0.752187i	$-0.728999\pi$
$727$	−9.08681	+	5.24627i	−0.337011	+	0.194573i	0.321938	+	0.946761i	$0.395666\pi$
$728$	−0.165296	+	0.299704i	−0.00612628	+	0.0111078i
$729$	−17.5381	+	20.5284i	−0.649561	+	0.760310i
$730$	−21.1947	−	27.3801i	−0.784451	−	1.01338i
$731$	−11.8252	+	20.4818i	−0.437369	+	0.757546i
$732$	−7.45398	−	51.4181i	−0.275507	−	1.90047i
$733$	29.4743	−	17.0170i	1.08866	−	0.628537i	0.155439	−	0.987845i	$-0.450321\pi$
$733$	29.4743	−	17.0170i	1.08866	−	0.628537i	0.933219	+	0.359309i	$0.116987\pi$
$734$	19.8089	−	34.3100i	0.731159	−	1.26640i
$735$	−8.48367	−	25.7493i	−0.312925	−	0.949778i
$736$	21.5412	+	37.3105i	0.794019	+	1.37528i
$737$	−10.2950	−	5.94384i	−0.379222	−	0.218944i
$738$	10.1893	+	2.44676i	0.375073	+	0.0900665i
$739$	−10.6830	−	18.5035i	−0.392980	−	0.680662i	0.599861	−	0.800104i	$-0.295223\pi$
$739$	−10.6830	−	18.5035i	−0.392980	−	0.680662i	−0.992841	+	0.119443i	$0.961889\pi$
$740$	25.2474	+	10.3325i	0.928113	+	0.379831i
$741$	3.81908	+	4.84473i	0.140297	+	0.177975i
$742$	7.88174	+	13.0544i	0.289348	+	0.479242i
$743$	−4.99708	−	2.88507i	−0.183325	−	0.105843i	0.405529	−	0.914082i	$-0.367087\pi$
$743$	−4.99708	−	2.88507i	−0.183325	−	0.105843i	−0.588854	+	0.808239i	$0.700421\pi$
$744$	1.54548	−	0.224045i	0.0566599	−	0.00821387i
$745$	−25.2594	−	32.6310i	−0.925431	−	1.19551i
$746$	14.3470	+	24.8497i	0.525280	+	0.909811i
$747$	15.3101	−	16.1319i	0.560167	−	0.590234i
$748$		−	8.01936i		−	0.293217i
$749$	−9.41857	−	5.19463i	−0.344147	−	0.189808i
$750$	−33.4439	+	20.4768i	−1.22120	+	0.747705i
$751$	−10.3154	−	17.8667i	−0.376413	−	0.651966i	0.614125	−	0.789209i	$-0.289509\pi$
$751$	−10.3154	−	17.8667i	−0.376413	−	0.651966i	−0.990537	+	0.137243i	$0.956176\pi$
$752$		−	4.71118i		−	0.171799i
$753$	0.588585	+	4.06010i	0.0214492	+	0.147958i
$754$	−9.64523			−0.351258
$755$	4.08270	−	9.97604i	0.148585	−	0.363065i
$756$	12.6006	+	25.9871i	0.458278	+	0.945142i
$757$		−	25.2807i		−	0.918841i	−0.888219	−	0.459421i	$-0.848057\pi$
$757$		−	25.2807i		−	0.918841i	0.888219	−	0.459421i	$-0.151943\pi$
$758$			1.45102i			0.0527034i
$759$	−10.2684	+	1.48859i	−0.372721	+	0.0540325i
$760$	2.37278	+	0.971062i	0.0860698	+	0.0352241i
$761$	9.55109	+	16.5430i	0.346227	+	0.599682i	0.985576	−	0.169234i	$-0.0541295\pi$
$761$	9.55109	+	16.5430i	0.346227	+	0.599682i	−0.639349	+	0.768916i	$0.720796\pi$
$762$	−4.84605	−	33.4284i	−0.175554	−	1.21098i
$763$	−10.4690	−	17.3397i	−0.379004	−	0.627738i
$764$	−27.4514			−0.993156
$765$	13.3204	−	18.4967i	0.481602	−	0.668748i
$766$	35.3054	+	61.1507i	1.27563	+	2.20946i
$767$	1.98620	+	1.14673i	0.0717174	+	0.0414060i
$768$	−3.54549	−	24.4571i	−0.127937	−	0.882519i
$769$	−5.84875	+	10.1303i	−0.210911	+	0.365309i	−0.952000	−	0.306098i	$-0.900976\pi$
$769$	−5.84875	+	10.1303i	−0.210911	+	0.365309i	0.741089	+	0.671407i	$0.234310\pi$
$770$	12.5537	+	4.85289i	0.452406	+	0.174886i
$771$	−13.2701	−	16.8339i	−0.477911	−	0.606257i
$772$		−	7.57993i		−	0.272808i
$773$	25.1130	−	14.4990i	0.903253	−	0.521494i	0.0249991	−	0.999687i	$-0.492042\pi$
$773$	25.1130	−	14.4990i	0.903253	−	0.521494i	0.878254	+	0.478194i	$0.158708\pi$
$774$	30.6705	+	29.1081i	1.10243	+	1.04627i
$775$	21.2887	−	5.89838i	0.764713	−	0.211876i
$776$	−1.91012	−	3.30842i	−0.0685693	−	0.118765i
$777$	9.37625	−	24.9062i	0.336371	−	0.893505i
$778$	−0.126037	−	0.0727676i	−0.00451865	−	0.00260884i
$779$	−4.84566	−	8.39293i	−0.173614	−	0.300708i
$780$	1.24850	−	5.00436i	0.0447033	−	0.179185i
$781$	8.36836	−	14.4944i	0.299443	−	0.518651i
$782$	31.7751	+	18.3453i	1.13627	+	0.656028i
$783$	−22.5350	+	31.8812i	−0.805334	+	1.13934i
$784$	−26.4978	+	1.03826i	−0.946348	+	0.0370806i
$785$	3.83069	+	28.1727i	0.136723	+	1.00553i
$786$	−10.0314	−	12.7254i	−0.357808	−	0.453900i
$787$		−	39.0364i		−	1.39150i	−0.718285	−	0.695749i	$-0.755073\pi$
$787$		−	39.0364i		−	1.39150i	0.718285	−	0.695749i	$-0.244927\pi$
$788$		−	33.9888i		−	1.21080i
$789$	7.71717	−	19.3419i	0.274739	−	0.688588i
$790$	−0.400195	−	2.94322i	−0.0142383	−	0.104715i
$791$	−39.2519	−	21.6486i	−1.39564	−	0.769735i
$792$	−0.668767	−	0.160592i	−0.0237636	−	0.00570637i
$793$	7.83896	+	4.52583i	0.278370	+	0.160717i
$794$	36.7793	−	63.7036i	1.30525	−	2.26076i
$795$	−7.92840	−	7.65858i	−0.281191	−	0.271622i
$796$	7.81295	+	13.5324i	0.276923	+	0.479644i
$797$	28.5566	+	16.4872i	1.01153	+	0.584006i	0.911639	−	0.410993i	$-0.134818\pi$
$797$	28.5566	+	16.4872i	1.01153	+	0.584006i	0.0998894	+	0.994999i	$0.468151\pi$
$798$	18.3698	−	48.7957i	0.650283	−	1.72735i
$799$	−2.11284	−	3.65955i	−0.0747470	−	0.129466i
$800$	10.7865	+	38.9312i	0.381362	+	1.37643i
$801$	−0.763540	+	3.17968i	−0.0269784	+	0.112349i
$802$	−14.7685	+	8.52658i	−0.521493	+	0.301084i
$803$		−	8.59053i		−	0.303153i
$804$	38.1041	−	5.52387i	1.34383	−	0.194812i
$805$	−24.5626	+	19.7948i	−0.865717	+	0.697675i
$806$	−2.83581	+	4.91178i	−0.0998873	+	0.173010i
$807$	30.0408	−	23.6810i	1.05749	−	0.833612i
$808$	−0.133230	−	0.0769203i	−0.00468701	−	0.00270605i
$809$	−2.42987	−	4.20866i	−0.0854297	−	0.147969i	0.820145	−	0.572156i	$-0.193893\pi$
$809$	−2.42987	−	4.20866i	−0.0854297	−	0.147969i	−0.905574	+	0.424188i	$0.860560\pi$
$810$	−26.5952	−	30.8789i	−0.934461	−	1.08497i
$811$	−17.9161			−0.629121			−0.314560	−	0.949237i	$-0.601857\pi$
$811$	−17.9161			−0.629121			−0.314560	+	0.949237i	$0.601857\pi$
$812$	21.5847	+	35.7505i	0.757475	+	1.25460i
$813$	−26.2866	−	10.4880i	−0.921912	−	0.367832i
$814$	6.60587	+	11.4417i	0.231536	+	0.401031i
$815$	−39.2578	−	16.0663i	−1.37514	−	0.562777i
$816$	−13.8026	−	17.5093i	−0.483186	−	0.612950i
$817$		−	39.1061i		−	1.36815i
$818$			72.4101i			2.53176i
$819$	−4.91458	−	1.07882i	−0.171729	−	0.0376971i
$820$	−3.06896	+	7.49896i	−0.107173	+	0.261875i
$821$	24.9829			0.871911			0.435955	−	0.899968i	$-0.356411\pi$
$821$	24.9829			0.871911			0.435955	+	0.899968i	$0.356411\pi$
$822$	−63.6330	−	25.3888i	−2.21946	−	0.885537i
$823$		−	13.2989i		−	0.463571i	−0.972767	−	0.231785i	$-0.925543\pi$
$823$		−	13.2989i		−	0.463571i	0.972767	−	0.231785i	$-0.0744567\pi$
$824$	−1.31177	−	2.27205i	−0.0456976	−	0.0791505i
$825$	−9.67114	−	1.06175i	−0.336706	−	0.0369654i
$826$	−0.379536	−	19.3800i	−0.0132058	−	0.674318i
$827$		−	40.8288i		−	1.41976i	−0.704324	−	0.709878i	$-0.748750\pi$
$827$		−	40.8288i		−	1.41976i	0.704324	−	0.709878i	$-0.251250\pi$
$828$	23.1338	−	24.3755i	0.803954	−	0.847107i
$829$	3.37600	+	5.84741i	0.117253	+	0.203089i	0.918678	−	0.395007i	$-0.129258\pi$
$829$	3.37600	+	5.84741i	0.117253	+	0.203089i	−0.801425	+	0.598095i	$0.795924\pi$
$830$	20.5484	+	26.5452i	0.713245	+	0.921397i
$831$	−9.32743	+	23.3777i	−0.323565	+	0.810964i
$832$	−4.82281	−	2.78445i	−0.167201	−	0.0965335i
$833$	−20.1173	+	12.6901i	−0.697023	+	0.439685i
$834$	−5.94712	+	14.9055i	−0.205932	+	0.516135i
$835$	−16.1203	−	6.59726i	−0.557867	−	0.228308i
$836$	6.63007	+	11.4836i	0.229306	+	0.397169i
$837$	9.60977	+	20.8493i	0.332162	+	0.720656i
$838$	5.18707	+	2.99476i	0.179185	+	0.103452i
$839$	8.85315	+	15.3341i	0.305645	+	0.529392i	0.977405	−	0.211377i	$-0.0677947\pi$
$839$	8.85315	+	15.3341i	0.305645	+	0.529392i	−0.671760	+	0.740769i	$0.734461\pi$
$840$	−1.99850	+	0.615341i	−0.0689549	+	0.0212313i
$841$	−13.7266	+	23.7752i	−0.473332	+	0.819835i
$842$	−2.35459	+	1.35942i	−0.0811446	+	0.0468489i
$843$	−25.9990	+	20.4950i	−0.895455	+	0.705884i
$844$	20.2208	−	35.0234i	0.696028	−	1.20556i
$845$	−17.2437	−	22.2760i	−0.593201	−	0.766319i
$846$	−7.24408	+	2.14540i	−0.249057	+	0.0737605i
$847$	−13.3164	−	22.0558i	−0.457558	−	0.757846i
$848$	−9.33772	+	5.39114i	−0.320659	+	0.185132i
$849$	10.1045	−	1.46483i	0.346785	−	0.0502727i
$850$	24.5332	+	24.1203i	0.841482	+	0.827319i
$851$	−30.9663			−1.06151
$852$	7.77709	+	53.6469i	0.266439	+	1.83791i
$853$	41.0352	−	23.6917i	1.40502	−	0.811189i	0.410118	−	0.912033i	$-0.365488\pi$
$853$	41.0352	−	23.6917i	1.40502	−	0.811189i	0.994902	+	0.100844i	$0.0321542\pi$
$854$	−1.49792	−	76.4876i	−0.0512579	−	2.61735i
$855$	−3.78243	+	37.4997i	−0.129357	+	1.28246i
$856$	−0.414814	+	0.718480i	−0.0141781	+	0.0245571i
$857$	5.36340	+	3.09656i	0.183210	+	0.105777i	0.588800	−	0.808279i	$-0.299601\pi$
$857$	5.36340	+	3.09656i	0.183210	+	0.105777i	−0.405590	+	0.914055i	$0.632934\pi$
$858$	1.96169	−	1.54639i	0.0669711	−	0.0527931i
$859$	−14.0968	−	24.4164i	−0.480978	−	0.833078i	0.518784	−	0.854905i	$-0.326385\pi$
$859$	−14.0968	−	24.4164i	−0.480978	−	0.833078i	−0.999762	+	0.0218274i	$0.993052\pi$
$860$	−25.8545	+	20.0137i	−0.881630	+	0.682462i
$861$	7.39762	+	2.78493i	0.252110	+	0.0949101i
$862$	−38.9906	+	22.5112i	−1.32803	+	0.766736i
$863$	−38.9812	−	22.5058i	−1.32694	−	0.766107i	−0.342111	−	0.939659i	$-0.611142\pi$
$863$	−38.9812	−	22.5058i	−1.32694	−	0.766107i	−0.984825	+	0.173553i	$0.944475\pi$
$864$	−38.1276	+	17.5737i	−1.29713	+	0.597868i
$865$	5.96927	+	43.9007i	0.202961	+	1.49267i
$866$	−32.8176			−1.11519
$867$	8.77435	+	3.50086i	0.297993	+	0.118896i
$868$	24.5519	−	0.480821i	0.833345	−	0.0163201i
$869$	0.368470	−	0.638208i	0.0124995	−	0.0216497i
$870$	−42.3835	−	40.9411i	−1.43693	−	1.38803i
$871$	−3.35393	+	5.80917i	−0.113643	+	0.196836i
$872$	−1.35298	+	0.781144i	−0.0458177	+	0.0264529i
$873$	38.6605	−	40.7357i	1.30846	−	1.37869i
$874$	−60.6686			−2.05215
$875$	−26.9488	+	12.1969i	−0.911034	+	0.412331i
$876$	17.2248	+	21.8506i	0.581971	+	0.738265i
$877$	−4.66111	+	2.69109i	−0.157394	+	0.0908717i	−0.576629	−	0.817006i	$-0.695632\pi$
$877$	−4.66111	+	2.69109i	−0.157394	+	0.0908717i	0.419234	+	0.907878i	$0.362299\pi$
$878$			8.74569i			0.295153i
$879$	0.313250	−	0.785111i	0.0105657	−	0.0264811i
$880$	−3.60447	+	8.80749i	−0.121507	+	0.296900i
$881$	−7.66453			−0.258225			−0.129112	−	0.991630i	$-0.541213\pi$
$881$	−7.66453			−0.258225			−0.129112	+	0.991630i	$0.541213\pi$
$882$	13.6632	+	40.2711i	0.460062	+	1.35600i
$883$		−	12.8258i		−	0.431624i	−0.976435	−	0.215812i	$-0.930760\pi$
$883$		−	12.8258i		−	0.431624i	0.976435	−	0.215812i	$-0.0692398\pi$
$884$	−4.52508			−0.152195
$885$	3.86030	+	13.4698i	0.129763	+	0.452783i
$886$	−12.5931			−0.423075
$887$	−25.3248	+	14.6213i	−0.850323	+	0.490934i	−0.860760	−	0.509011i	$-0.830011\pi$
$887$	−25.3248	+	14.6213i	−0.850323	+	0.490934i	0.0104368	+	0.999946i	$0.496678\pi$
$888$	−1.90651	−	0.760676i	−0.0639784	−	0.0255266i
$889$	−0.498888	−	25.4744i	−0.0167322	−	0.854384i
$890$	−4.56802	−	1.86947i	−0.153120	−	0.0626647i
$891$	−0.528169	−	10.0971i	−0.0176943	−	0.338267i
$892$	−29.5698	+	17.0722i	−0.990072	+	0.571618i
$893$	6.05113	+	3.49362i	0.202493	+	0.116910i
$894$	40.0715	+	50.8330i	1.34019	+	1.70011i
$895$	−2.87909	−	3.71932i	−0.0962374	−	0.124323i
$896$	0.0844658	+	4.31303i	0.00282181	+	0.144088i
$897$	0.839968	+	5.79416i	0.0280457	+	0.193461i
$898$			50.5660i			1.68741i
$899$	16.5979	+	28.7485i	0.553572	+	0.958816i
$900$	26.7282	−	16.6909i	0.890939	−	0.556363i
$901$	−4.83557	+	8.37546i	−0.161096	+	0.279027i
$902$	−3.39841	+	1.96207i	−0.113155	+	0.0653298i
$903$	20.2326	+	24.6574i	0.673299	+	0.820548i
$904$	−1.72874	+	2.99426i	−0.0574970	+	0.0995877i
$905$	33.2599	−	4.52241i	1.10560	−	0.150330i
$906$	−6.26578	+	15.7042i	−0.208167	+	0.521736i
$907$	29.7274	+	17.1631i	0.987082	+	0.569892i	0.904401	−	0.426684i	$-0.140318\pi$
$907$	29.7274	+	17.1631i	0.987082	+	0.569892i	0.0826810	+	0.996576i	$0.473652\pi$
$908$	16.4709	+	9.50948i	0.546606	+	0.315583i
$909$	0.528067	−	2.19908i	0.0175149	−	0.0729388i
$910$	2.73833	−	7.08369i	0.0907749	−	0.234822i
$911$	−10.4416	−	18.0854i	−0.345947	−	0.599198i	0.639578	−	0.768726i	$-0.279109\pi$
$911$	−10.4416	−	18.0854i	−0.345947	−	0.599198i	−0.985525	+	0.169528i	$0.945776\pi$
$912$	34.2411	+	13.6618i	1.13383	+	0.452387i
$913$			8.32857i			0.275635i
$914$	52.1233			1.72409
$915$	15.2355	+	53.1616i	0.503671	+	1.75747i
$916$	11.0755	+	19.1834i	0.365946	+	0.633837i
$917$	−6.31753	−	10.4636i	−0.208623	−	0.345540i
$918$	−20.6375	+	29.1968i	−0.681139	+	0.963638i
$919$	−16.6733	+	28.8790i	−0.550001	+	0.952630i	0.448273	+	0.893897i	$0.352039\pi$
$919$	−16.6733	+	28.8790i	−0.550001	+	0.952630i	−0.998274	+	0.0587330i	$0.981294\pi$
$920$	1.48941	+	1.92407i	0.0491042	+	0.0634347i
$921$	−27.4390	+	3.97778i	−0.904146	+	0.131072i
$922$	−52.1891	+	30.1314i	−1.71876	+	0.992324i
$923$	−8.17876	−	4.72201i	−0.269207	−	0.155427i
$924$	−10.1218	−	3.81047i	−0.332982	−	0.125355i
$925$	−28.1101	−	7.27696i	−0.924256	−	0.239265i
$926$	5.87708	−	10.1794i	0.193133	−	0.334516i
$927$	26.5500	−	27.9751i	0.872016	−	0.918822i
$928$	−52.5731	+	30.3531i	−1.72580	+	0.996390i
$929$	−16.3990			−0.538035			−0.269017	−	0.963135i	$-0.586699\pi$
$929$	−16.3990			−0.538035			−0.269017	+	0.963135i	$0.586699\pi$
$930$	−33.3103	+	9.54635i	−1.09229	+	0.313037i
$931$	18.3161	−	34.8041i	0.600286	−	1.14066i
$932$	−10.3451	−	5.97272i	−0.338864	−	0.195643i
$933$	−0.590369	−	4.07241i	−0.0193278	−	0.133325i
$934$	−23.6616	+	40.9830i	−0.774230	+	1.34100i
$935$	1.15005	+	8.45800i	0.0376107	+	0.276606i
$936$	−0.0906169	+	0.377365i	−0.00296191	+	0.0123345i
$937$			26.6702i			0.871277i	0.900122	+	0.435639i	$0.143477\pi$
$937$			26.6702i			0.871277i	−0.900122	+	0.435639i	$0.856523\pi$
$938$	56.6822	−	1.11006i	1.85074	−	0.0362447i
$939$	−9.30952	+	1.34958i	−0.303805	+	0.0440419i
$940$	−0.787084	−	5.78858i	−0.0256718	−	0.188803i
$941$	30.7292			1.00174			0.500872	−	0.865521i	$-0.333013\pi$
$941$	30.7292			1.00174			0.500872	+	0.865521i	$0.333013\pi$
$942$	−6.39838	−	44.1365i	−0.208470	−	1.43805i
$943$		−	9.19759i		−	0.299515i
$944$	13.7057			0.446082
$945$	−17.0166	−	25.6015i	−0.553549	−	0.832817i
$946$	−15.8346			−0.514827
$947$			10.4517i			0.339634i	0.985476	+	0.169817i	$0.0543177\pi$
$947$			10.4517i			0.339634i	−0.985476	+	0.169817i	$0.945682\pi$
$948$	0.342435	+	2.36215i	0.0111218	+	0.0767189i
$949$	−4.84737			−0.157352
$950$	−55.0729	−	14.2569i	−1.78680	−	0.462555i
$951$	−29.8721	+	4.33049i	−0.968668	+	0.140426i
$952$	0.948228	+	1.57054i	0.0307323	+	0.0509014i
$953$		−	2.85127i		−	0.0923617i	−0.998933	−	0.0461808i	$-0.985295\pi$
$953$		−	2.85127i		−	0.0923617i	0.998933	−	0.0461808i	$-0.0147050\pi$
$954$	12.5419	+	11.9030i	0.406058	+	0.385373i
$955$	28.9529	−	3.93678i	0.936894	−	0.127391i
$956$	29.1157	−	50.4298i	0.941668	−	1.63102i
$957$	−2.09754	−	14.4690i	−0.0678037	−	0.467715i
$958$	41.5618	+	23.9957i	1.34280	+	0.775267i
$959$	−45.2529	−	24.9583i	−1.46129	−	0.805946i
$960$	−9.37344	−	32.7069i	−0.302527	−	1.05561i
$961$	−11.4800			−0.370323
$962$	6.45620	−	3.72749i	0.208156	−	0.120179i
$963$	−11.8591	−	2.84775i	−0.382155	−	0.0917674i
$964$	4.18131	−	7.24224i	0.134671	−	0.233257i
$965$	1.08703	+	7.99453i	0.0349928	+	0.257353i
$966$	38.2531	−	31.3885i	1.23077	−	1.00991i
$967$	22.3179	+	12.8853i	0.717696	+	0.414362i	0.813904	−	0.580999i	$-0.197338\pi$
$967$	22.3179	+	12.8853i	0.717696	+	0.414362i	−0.0962078	+	0.995361i	$0.530671\pi$
$968$	−1.72097	+	0.993604i	−0.0553141	+	0.0319356i
$969$	32.7247	−	4.74404i	1.05127	−	0.152400i
$970$	51.8882	+	67.0311i	1.66603	+	2.15224i
$971$	−18.7171	+	32.4190i	−0.600662	+	1.04038i	0.392059	+	0.919940i	$0.371763\pi$
$971$	−18.7171	+	32.4190i	−0.600662	+	1.04038i	−0.992721	+	0.120436i	$0.961571\pi$
$972$	21.5891	+	24.6238i	0.692471	+	0.789808i
$973$	−5.84628	+	10.6001i	−0.187423	+	0.339824i
$974$	−35.6563	−	61.7586i	−1.14250	−	1.97887i
$975$	−0.599113	+	5.45713i	−0.0191870	+	0.174768i
$976$	54.0925			1.73146
$977$			55.5331i			1.77666i	0.459204	+	0.888331i	$0.348135\pi$
$977$			55.5331i			1.77666i	−0.459204	+	0.888331i	$0.651865\pi$
$978$	61.7992	+	24.6571i	1.97612	+	0.788448i
$979$	−0.612287	−	1.06051i	−0.0195688	−	0.0338941i
$980$	−32.3840	+	5.70260i	−1.03447	+	0.182163i
$981$	−16.6589	−	15.8103i	−0.531877	−	0.504783i
$982$	−12.5572	−	7.24989i	−0.400716	−	0.231353i
$983$	−10.1730	−	5.87340i	−0.324469	−	0.187332i	0.328914	−	0.944360i	$-0.393317\pi$
$983$	−10.1730	−	5.87340i	−0.324469	−	0.187332i	−0.653383	+	0.757028i	$0.726651\pi$
$984$	0.225935	−	0.566271i	0.00720256	−	0.0180521i
$985$	4.87431	+	35.8479i	0.155309	+	1.14221i
$986$	−25.8499	+	44.7734i	−0.823229	+	1.42587i
$987$	−5.62291	+	0.927894i	−0.178979	+	0.0295352i
$988$	6.47985	−	3.74114i	0.206152	−	0.119022i
$989$	18.5569	−	32.1415i	0.590076	−	1.02204i
$990$	15.1841	+	1.53156i	0.482583	+	0.0486761i
$991$	−3.00927	−	5.21221i	−0.0955926	−	0.165571i	0.814263	−	0.580496i	$-0.197141\pi$
$991$	−3.00927	−	5.21221i	−0.0955926	−	0.165571i	−0.909856	+	0.414925i	$0.863808\pi$
$992$			35.6968i			1.13337i
$993$	3.48626	+	24.0485i	0.110633	+	0.763155i
$994$	1.56286	+	79.8032i	0.0495708	+	2.53120i
$995$	−10.1810	−	13.1522i	−0.322758	−	0.416952i
$996$	−16.6995	−	21.1843i	−0.529145	−	0.671251i
$997$	−12.9856	−	7.49722i	−0.411257	−	0.237439i	0.280073	−	0.959979i	$-0.409641\pi$
$997$	−12.9856	−	7.49722i	−0.411257	−	0.237439i	−0.691330	+	0.722540i	$0.742975\pi$
$998$	67.7721	−	39.1282i	2.14529	−	1.23858i
$999$	2.76337	−	30.0491i	0.0874291	−	0.950711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.r.b.184.8	✓	84
3.2	odd	2		945.2.r.b.604.35		84
5.4	even	2	inner	315.2.r.b.184.35	yes	84
7.4	even	3		315.2.bo.b.4.35	yes	84
9.2	odd	6		945.2.bo.b.289.35		84
9.7	even	3		315.2.bo.b.79.8	yes	84
15.14	odd	2		945.2.r.b.604.8		84
21.11	odd	6		945.2.bo.b.739.8		84
35.4	even	6		315.2.bo.b.4.8	yes	84
45.29	odd	6		945.2.bo.b.289.8		84
45.34	even	6		315.2.bo.b.79.35	yes	84
63.11	odd	6		945.2.r.b.424.35		84
63.25	even	3	inner	315.2.r.b.214.8	yes	84
105.74	odd	6		945.2.bo.b.739.35		84
315.74	odd	6		945.2.r.b.424.8		84
315.214	even	6	inner	315.2.r.b.214.35	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.8	✓	84	1.1	even	1	trivial
315.2.r.b.184.35	yes	84	5.4	even	2	inner
315.2.r.b.214.8	yes	84	63.25	even	3	inner
315.2.r.b.214.35	yes	84	315.214	even	6	inner
315.2.bo.b.4.8	yes	84	35.4	even	6
315.2.bo.b.4.35	yes	84	7.4	even	3
315.2.bo.b.79.8	yes	84	9.7	even	3
315.2.bo.b.79.35	yes	84	45.34	even	6
945.2.r.b.424.8		84	315.74	odd	6
945.2.r.b.424.35		84	63.11	odd	6
945.2.r.b.604.8		84	15.14	odd	2
945.2.r.b.604.35		84	3.2	odd	2
945.2.bo.b.289.8		84	45.29	odd	6
945.2.bo.b.289.35		84	9.2	odd	6
945.2.bo.b.739.8		84	21.11	odd	6
945.2.bo.b.739.35		84	105.74	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.02504i q^{2} +(-0.248494 - 1.71413i) q^{3} -2.10077 q^{4} +(2.21568 - 0.301270i) q^{5} +(-3.47118 + 0.503210i) q^{6} +(-2.64524 + 0.0518041i) q^{7} +0.204070i q^{8} +(-2.87650 + 0.851904i) q^{9} +O(q^{10})\)	\(q-2.02504i q^{2} +(-0.248494 - 1.71413i) q^{3} -2.10077 q^{4} +(2.21568 - 0.301270i) q^{5} +(-3.47118 + 0.503210i) q^{6} +(-2.64524 + 0.0518041i) q^{7} +0.204070i q^{8} +(-2.87650 + 0.851904i) q^{9} +(-0.610083 - 4.48683i) q^{10} +(0.561719 - 0.972925i) q^{11} +(0.522030 + 3.60100i) q^{12} +(-0.548992 - 0.316961i) q^{13} +(0.104905 + 5.35672i) q^{14} +(-1.06700 - 3.72310i) q^{15} -3.78830 q^{16} +(-2.94268 + 1.69895i) q^{17} +(1.72514 + 5.82502i) q^{18} +(2.80925 - 4.86576i) q^{19} +(-4.65464 + 0.632901i) q^{20} +(0.746127 + 4.52143i) q^{21} +(-1.97021 - 1.13750i) q^{22} +(4.61787 - 2.66613i) q^{23} +(0.349802 - 0.0507101i) q^{24} +(4.81847 - 1.33504i) q^{25} +(-0.641857 + 1.11173i) q^{26} +(2.17507 + 4.71901i) q^{27} +(5.55706 - 0.108829i) q^{28} +(3.75677 + 6.50691i) q^{29} +(-7.53942 + 2.16072i) q^{30} +4.41814 q^{31} +8.07958i q^{32} +(-1.80731 - 0.721094i) q^{33} +(3.44045 + 5.95903i) q^{34} +(-5.84541 + 0.911715i) q^{35} +(6.04288 - 1.78966i) q^{36} +(-5.02932 - 2.90368i) q^{37} +(-9.85334 - 5.68883i) q^{38} +(-0.406891 + 1.01981i) q^{39} +(0.0614801 + 0.452153i) q^{40} +(0.862448 - 1.49380i) q^{41} +(9.15605 - 1.51093i) q^{42} +(6.02776 - 3.48013i) q^{43} +(-1.18004 + 2.04390i) q^{44} +(-6.11675 + 2.75415i) q^{45} +(-5.39901 - 9.35136i) q^{46} +1.24361i q^{47} +(0.941370 + 6.49365i) q^{48} +(6.99463 - 0.274069i) q^{49} +(-2.70350 - 9.75758i) q^{50} +(3.64347 + 4.62196i) q^{51} +(1.15331 + 0.665862i) q^{52} +(2.46489 - 1.42310i) q^{53} +(9.55617 - 4.40460i) q^{54} +(0.951475 - 2.32492i) q^{55} +(-0.0105717 - 0.539814i) q^{56} +(-9.03864 - 3.60631i) q^{57} +(13.1767 - 7.60759i) q^{58} -3.61790 q^{59} +(2.24153 + 7.82140i) q^{60} -14.2788 q^{61} -8.94690i q^{62} +(7.56492 - 2.40251i) q^{63} +8.78485 q^{64} +(-1.31188 - 0.536888i) q^{65} +(-1.46024 + 3.65986i) q^{66} -10.5815i q^{67} +(6.18189 - 3.56912i) q^{68} +(-5.71761 - 7.25313i) q^{69} +(1.84626 + 11.8372i) q^{70} +14.8978 q^{71} +(-0.173848 - 0.587006i) q^{72} +(6.62219 - 3.82332i) q^{73} +(-5.88005 + 10.1845i) q^{74} +(-3.48579 - 7.92775i) q^{75} +(-5.90159 + 10.2219i) q^{76} +(-1.43548 + 2.60272i) q^{77} +(2.06515 + 0.823969i) q^{78} +0.655968 q^{79} +(-8.39366 + 1.14130i) q^{80} +(7.54852 - 4.90101i) q^{81} +(-3.02501 - 1.74649i) q^{82} +(-6.42026 + 3.70674i) q^{83} +(-1.56744 - 9.49849i) q^{84} +(-6.00818 + 4.65088i) q^{85} +(-7.04738 - 12.2064i) q^{86} +(10.2202 - 8.05653i) q^{87} +(0.198544 + 0.114630i) q^{88} +(0.545012 - 0.943989i) q^{89} +(5.57726 + 12.3866i) q^{90} +(1.46864 + 0.809998i) q^{91} +(-9.70110 + 5.60093i) q^{92} +(-1.09788 - 7.57328i) q^{93} +2.51836 q^{94} +(4.75848 - 11.6273i) q^{95} +(13.8495 - 2.00773i) q^{96} +(-16.2122 + 9.36013i) q^{97} +(-0.555000 - 14.1644i) q^{98} +(-0.786945 + 3.27715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

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