LMFDB - Embedded newform 455.2.j.g.326.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [455,2,Mod(261,455)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("455.261"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(455, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 455 = 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	455.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,1,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.63319329197$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 17 x^{18} - 12 x^{17} + 181 x^{16} - 114 x^{15} + 1154 x^{14} - 605 x^{13} + \cdots + 625 $ x^20 - x^19 + 17x^18 - 12x^17 + 181x^16 - 114x^15 + 1154x^14 - 605x^13 + 5287x^12 - 2528x^11 + 15737x^10 - 5902x^9 + 32767x^8 - 10275x^7 + 37264x^6 - 2882x^5 + 24959x^4 - 2550x^3 + 7231x^2 + 1475x + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			326.2
Root			$-1.16558 + 2.01884i$ of defining polynomial
Character	$\chi$	$=$	455.326
Dual form			455.2.j.g.261.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16558 - 2.01884i) q^{2} +(1.60462 - 2.77928i) q^{3} +(-1.71715 + 2.97419i) q^{4} +(0.500000 + 0.866025i) q^{5} -7.48124 q^{6} +(1.52339 - 2.16317i) q^{7} +3.34356 q^{8} +(-3.64960 - 6.32129i) q^{9} +(1.16558 - 2.01884i) q^{10} +(0.450686 - 0.780611i) q^{11} +(5.51073 + 9.54487i) q^{12} -1.00000 q^{13} +(-6.14272 - 0.554136i) q^{14} +3.20924 q^{15} +(-0.462893 - 0.801755i) q^{16} +(-0.907858 + 1.57246i) q^{17} +(-8.50779 + 14.7359i) q^{18} +(-2.04243 - 3.53760i) q^{19} -3.43429 q^{20} +(-3.56759 - 7.70498i) q^{21} -2.10124 q^{22} +(2.54900 + 4.41500i) q^{23} +(5.36515 - 9.29270i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.16558 + 2.01884i) q^{26} -13.7972 q^{27} +(3.81778 + 8.24531i) q^{28} -5.72225 q^{29} +(-3.74062 - 6.47894i) q^{30} +(1.01596 - 1.75969i) q^{31} +(2.26449 - 3.92221i) q^{32} +(-1.44636 - 2.50517i) q^{33} +4.23272 q^{34} +(2.63505 + 0.237709i) q^{35} +25.0676 q^{36} +(-0.889726 - 1.54105i) q^{37} +(-4.76123 + 8.24669i) q^{38} +(-1.60462 + 2.77928i) q^{39} +(1.67178 + 2.89561i) q^{40} +10.3700 q^{41} +(-11.3968 + 16.1832i) q^{42} +9.38071 q^{43} +(1.54779 + 2.68085i) q^{44} +(3.64960 - 6.32129i) q^{45} +(5.94212 - 10.2921i) q^{46} +(6.32232 + 10.9506i) q^{47} -2.97107 q^{48} +(-2.35858 - 6.59068i) q^{49} +2.33116 q^{50} +(2.91353 + 5.04638i) q^{51} +(1.71715 - 2.97419i) q^{52} +(-1.08714 + 1.88298i) q^{53} +(16.0817 + 27.8543i) q^{54} +0.901372 q^{55} +(5.09354 - 7.23269i) q^{56} -13.1093 q^{57} +(6.66974 + 11.5523i) q^{58} +(-0.333079 + 0.576910i) q^{59} +(-5.51073 + 9.54487i) q^{60} +(2.35694 + 4.08235i) q^{61} -4.73672 q^{62} +(-19.2338 - 1.73508i) q^{63} -12.4093 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-3.37169 + 5.83994i) q^{66} +(7.15443 - 12.3918i) q^{67} +(-3.11785 - 5.40028i) q^{68} +16.3607 q^{69} +(-2.59146 - 5.59682i) q^{70} -16.5124 q^{71} +(-12.2027 - 21.1357i) q^{72} +(7.65042 - 13.2509i) q^{73} +(-2.07409 + 3.59243i) q^{74} +(1.60462 + 2.77928i) q^{75} +14.0286 q^{76} +(-1.00202 - 2.16408i) q^{77} +7.48124 q^{78} +(1.94722 + 3.37268i) q^{79} +(0.462893 - 0.801755i) q^{80} +(-11.1904 + 19.3823i) q^{81} +(-12.0870 - 20.9353i) q^{82} +5.50843 q^{83} +(29.0421 + 2.61990i) q^{84} -1.81572 q^{85} +(-10.9340 - 18.9382i) q^{86} +(-9.18203 + 15.9037i) q^{87} +(1.50690 - 2.61002i) q^{88} +(-0.823877 - 1.42700i) q^{89} -17.0156 q^{90} +(-1.52339 + 2.16317i) q^{91} -17.5080 q^{92} +(-3.26045 - 5.64727i) q^{93} +(14.7383 - 25.5275i) q^{94} +(2.04243 - 3.53760i) q^{95} +(-7.26728 - 12.5873i) q^{96} -15.1306 q^{97} +(-10.5564 + 12.4436i) q^{98} -6.57930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 4 q^{3} - 13 q^{4} + 10 q^{5} - 18 q^{6} + q^{7} - 6 q^{8} - 14 q^{9} - q^{10} - 7 q^{11} + 7 q^{12} - 20 q^{13} + 3 q^{14} + 8 q^{15} - 7 q^{16} + 6 q^{17} + 5 q^{18} + 10 q^{19} - 26 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) $ 20 * q + q^2 + 4 * q^3 - 13 * q^4 + 10 * q^5 - 18 * q^6 + q^7 - 6 * q^8 - 14 * q^9 - q^10 - 7 * q^11 + 7 * q^12 - 20 * q^13 + 3 * q^14 + 8 * q^15 - 7 * q^16 + 6 * q^17 + 5 * q^18 + 10 * q^19 - 26 * q^20 + 16 * q^21 - 22 * q^22 - 7 * q^23 + 20 * q^24 - 10 * q^25 - q^26 - 32 * q^27 + 36 * q^28 + 6 * q^29 - 9 * q^30 + 26 * q^31 + 22 * q^32 + 18 * q^33 - 6 * q^34 + 2 * q^35 + 56 * q^36 + 2 * q^37 - 25 * q^38 - 4 * q^39 - 3 * q^40 - 38 * q^41 + 21 * q^42 - 2 * q^43 - 33 * q^44 + 14 * q^45 + 20 * q^46 + 31 * q^47 - 46 * q^48 - 25 * q^49 - 2 * q^50 - 34 * q^51 + 13 * q^52 + 22 * q^53 + 42 * q^54 - 14 * q^55 + 30 * q^56 - 46 * q^57 + 7 * q^58 - q^59 - 7 * q^60 + 14 * q^61 + 30 * q^62 - 17 * q^63 - 10 * q^64 - 10 * q^65 - 45 * q^66 + 26 * q^67 + 12 * q^68 - 2 * q^69 + 3 * q^70 + 14 * q^71 - 40 * q^72 + 30 * q^73 + 13 * q^74 + 4 * q^75 - 86 * q^76 - 25 * q^77 + 18 * q^78 - 10 * q^79 + 7 * q^80 - 22 * q^81 + 9 * q^82 - 40 * q^83 + 46 * q^84 + 12 * q^85 - 17 * q^86 + 52 * q^88 + q^89 + 10 * q^90 - q^91 + 30 * q^92 + 32 * q^93 + 22 * q^94 - 10 * q^95 - 22 * q^96 - 38 * q^97 - 26 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/455\mathbb{Z}\right)^\times$.

$n$	$66$	$92$	$106$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.16558	−	2.01884i	−0.824189	−	1.42754i	−0.902538	−	0.430610i	$-0.858298\pi$
$2$	−1.16558	−	2.01884i	−0.824189	−	1.42754i	0.0783494	−	0.996926i	$-0.475035\pi$
$3$	1.60462	−	2.77928i	0.926427	−	1.60462i	0.137177	−	0.990547i	$-0.456197\pi$
$3$	1.60462	−	2.77928i	0.926427	−	1.60462i	0.789250	−	0.614072i	$-0.210470\pi$
$4$	−1.71715	+	2.97419i	−0.858573	+	1.48709i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−7.48124			−3.05420
$7$	1.52339	−	2.16317i	0.575786	−	0.817600i
$7$	1.52339	−	2.16317i	0.575786	−	0.817600i
$8$	3.34356			1.18213
$9$	−3.64960	−	6.32129i	−1.21653	−	2.10710i
$10$	1.16558	−	2.01884i	0.368588	−	0.638414i
$11$	0.450686	−	0.780611i	0.135887	−	0.235363i	−0.790049	−	0.613044i	$-0.789945\pi$
$11$	0.450686	−	0.780611i	0.135887	−	0.235363i	0.925936	+	0.377681i	$0.123278\pi$
$12$	5.51073	+	9.54487i	1.59081	+	2.75537i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−6.14272	−	0.554136i	−1.64171	−	0.148099i
$15$	3.20924			0.828621
$16$	−0.462893	−	0.801755i	−0.115723	−	0.200439i
$17$	−0.907858	+	1.57246i	−0.220188	+	0.381377i	−0.954865	−	0.297040i	$-0.904000\pi$
$17$	−0.907858	+	1.57246i	−0.220188	+	0.381377i	0.734677	+	0.678417i	$0.237334\pi$
$18$	−8.50779	+	14.7359i	−2.00531	+	3.47329i
$19$	−2.04243	−	3.53760i	−0.468566	−	0.811580i	0.530789	−	0.847504i	$-0.321896\pi$
$19$	−2.04243	−	3.53760i	−0.468566	−	0.811580i	−0.999355	+	0.0359243i	$0.988562\pi$
$20$	−3.43429			−0.767931
$21$	−3.56759	−	7.70498i	−0.778513	−	1.68136i
$22$	−2.10124			−0.447986
$23$	2.54900	+	4.41500i	0.531503	+	0.920591i	0.999324	+	0.0367674i	$0.0117061\pi$
$23$	2.54900	+	4.41500i	0.531503	+	0.920591i	−0.467820	+	0.883824i	$0.654961\pi$
$24$	5.36515	−	9.29270i	1.09516	−	1.89687i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.16558	+	2.01884i	0.228589	+	0.395927i
$27$	−13.7972			−2.65526
$28$	3.81778	+	8.24531i	0.721493	+	1.55822i
$29$	−5.72225			−1.06260			−0.531298	−	0.847185i	$-0.678295\pi$
$29$	−5.72225			−1.06260			−0.531298	+	0.847185i	$0.678295\pi$
$30$	−3.74062	−	6.47894i	−0.682940	−	1.18289i
$31$	1.01596	−	1.75969i	0.182472	−	0.316050i	−0.760250	−	0.649631i	$-0.774924\pi$
$31$	1.01596	−	1.75969i	0.182472	−	0.316050i	0.942722	+	0.333580i	$0.108257\pi$
$32$	2.26449	−	3.92221i	0.400309	−	0.693355i
$33$	−1.44636	−	2.50517i	−0.251779	−	0.436093i
$34$	4.23272			0.725905
$35$	2.63505	+	0.237709i	0.445405	+	0.0401801i
$36$	25.0676			4.17793
$37$	−0.889726	−	1.54105i	−0.146270	−	0.253347i	0.783576	−	0.621296i	$-0.213394\pi$
$37$	−0.889726	−	1.54105i	−0.146270	−	0.253347i	−0.929846	+	0.367949i	$0.880060\pi$
$38$	−4.76123	+	8.24669i	−0.772373	+	1.33779i
$39$	−1.60462	+	2.77928i	−0.256945	+	0.445041i
$40$	1.67178	+	2.89561i	0.264332	+	0.457836i
$41$	10.3700			1.61952			0.809758	−	0.586764i	$-0.199598\pi$
$41$	10.3700			1.61952			0.809758	+	0.586764i	$0.199598\pi$
$42$	−11.3968	+	16.1832i	−1.75857	+	2.49712i
$43$	9.38071			1.43055			0.715273	−	0.698846i	$-0.246303\pi$
$43$	9.38071			1.43055			0.715273	+	0.698846i	$0.246303\pi$
$44$	1.54779	+	2.68085i	0.233338	+	0.404153i
$45$	3.64960	−	6.32129i	0.544050	−	0.942323i
$46$	5.94212	−	10.2921i	0.876118	−	1.51748i
$47$	6.32232	+	10.9506i	0.922205	+	1.59731i	0.795996	+	0.605302i	$0.206948\pi$
$47$	6.32232	+	10.9506i	0.922205	+	1.59731i	0.126209	+	0.992004i	$0.459719\pi$
$48$	−2.97107			−0.428837
$49$	−2.35858	−	6.59068i	−0.336940	−	0.941526i
$50$	2.33116			0.329675
$51$	2.91353	+	5.04638i	0.407976	+	0.706635i
$52$	1.71715	−	2.97419i	0.238125	−	0.412445i
$53$	−1.08714	+	1.88298i	−0.149330	+	0.258647i	−0.930980	−	0.365070i	$-0.881045\pi$
$53$	−1.08714	+	1.88298i	−0.149330	+	0.258647i	0.781650	+	0.623717i	$0.214378\pi$
$54$	16.0817	+	27.8543i	2.18844	+	3.79049i
$55$	0.901372			0.121541
$56$	5.09354	−	7.23269i	0.680653	−	0.966509i
$57$	−13.1093			−1.73637
$58$	6.66974	+	11.5523i	0.875779	+	1.51689i
$59$	−0.333079	+	0.576910i	−0.0433632	+	0.0751073i	−0.886892	−	0.461976i	$-0.847141\pi$
$59$	−0.333079	+	0.576910i	−0.0433632	+	0.0751073i	0.843529	+	0.537083i	$0.180474\pi$
$60$	−5.51073	+	9.54487i	−0.711432	+	1.23224i
$61$	2.35694	+	4.08235i	0.301776	+	0.522691i	0.976538	−	0.215344i	$-0.0690873\pi$
$61$	2.35694	+	4.08235i	0.301776	+	0.522691i	−0.674762	+	0.738035i	$0.735754\pi$
$62$	−4.73672			−0.601564
$63$	−19.2338	−	1.73508i	−2.42323	−	0.218600i
$64$	−12.4093			−1.55117
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	−3.37169	+	5.83994i	−0.415026	+	0.718846i
$67$	7.15443	−	12.3918i	0.874052	−	1.51390i	0.0162831	−	0.999867i	$-0.494817\pi$
$67$	7.15443	−	12.3918i	0.874052	−	1.51390i	0.857769	−	0.514035i	$-0.171850\pi$
$68$	−3.11785	−	5.40028i	−0.378095	−	0.654880i
$69$	16.3607			1.96960
$70$	−2.59146	−	5.59682i	−0.309739	−	0.668948i
$71$	−16.5124			−1.95966			−0.979830	−	0.199834i	$-0.935960\pi$
$71$	−16.5124			−1.95966			−0.979830	+	0.199834i	$0.935960\pi$
$72$	−12.2027	−	21.1357i	−1.43810	−	2.49086i
$73$	7.65042	−	13.2509i	0.895414	−	1.55090i	0.0621222	−	0.998069i	$-0.480213\pi$
$73$	7.65042	−	13.2509i	0.895414	−	1.55090i	0.833292	−	0.552834i	$-0.186454\pi$
$74$	−2.07409	+	3.59243i	−0.241108	+	0.417612i
$75$	1.60462	+	2.77928i	0.185285	+	0.320924i
$76$	14.0286			1.60919
$77$	−1.00202	−	2.16408i	−0.114191	−	0.246620i
$78$	7.48124			0.847083
$79$	1.94722	+	3.37268i	0.219079	+	0.379456i	0.954527	−	0.298126i	$-0.0963614\pi$
$79$	1.94722	+	3.37268i	0.219079	+	0.379456i	−0.735448	+	0.677582i	$0.763028\pi$
$80$	0.462893	−	0.801755i	0.0517530	−	0.0896389i
$81$	−11.1904	+	19.3823i	−1.24337	+	2.15359i
$82$	−12.0870	−	20.9353i	−1.33479	−	2.31192i
$83$	5.50843			0.604628			0.302314	−	0.953208i	$-0.402241\pi$
$83$	5.50843			0.604628			0.302314	+	0.953208i	$0.402241\pi$
$84$	29.0421	+	2.61990i	3.16875	+	0.285854i
$85$	−1.81572			−0.196942
$86$	−10.9340	−	18.9382i	−1.17904	−	2.04216i
$87$	−9.18203	+	15.9037i	−0.984417	+	1.70506i
$88$	1.50690	−	2.61002i	0.160636	−	0.278229i
$89$	−0.823877	−	1.42700i	−0.0873307	−	0.151261i	0.819051	−	0.573720i	$-0.194500\pi$
$89$	−0.823877	−	1.42700i	−0.0873307	−	0.151261i	−0.906382	+	0.422459i	$0.861167\pi$
$90$	−17.0156			−1.79360
$91$	−1.52339	+	2.16317i	−0.159694	+	0.226762i
$92$	−17.5080			−1.82534
$93$	−3.26045	−	5.64727i	−0.338093	−	0.585595i
$94$	14.7383	−	25.5275i	1.52014	−	2.63296i
$95$	2.04243	−	3.53760i	0.209549	−	0.362950i
$96$	−7.26728	−	12.5873i	−0.741713	−	1.28469i
$97$	−15.1306			−1.53628			−0.768139	−	0.640283i	$-0.778817\pi$
$97$	−15.1306			−1.53628			−0.768139	+	0.640283i	$0.778817\pi$
$98$	−10.5564	+	12.4436i	−1.06636	+	1.25699i
$99$	−6.57930			−0.661244
$100$	−1.71715	−	2.97419i	−0.171715	−	0.297419i
$101$	−3.72797	+	6.45703i	−0.370947	+	0.642498i	−0.989711	−	0.143078i	$-0.954300\pi$
$101$	−3.72797	+	6.45703i	−0.370947	+	0.642498i	0.618765	+	0.785576i	$0.287633\pi$
$102$	6.79190	−	11.7639i	0.672498	−	1.16480i
$103$	6.87775	+	11.9126i	0.677685	+	1.17378i	0.975676	+	0.219216i	$0.0703499\pi$
$103$	6.87775	+	11.9126i	0.677685	+	1.17378i	−0.297992	+	0.954568i	$0.596317\pi$
$104$	−3.34356			−0.327863
$105$	4.88891	−	6.94212i	0.477109	−	0.677481i
$106$	5.06858			0.492304
$107$	1.68776	+	2.92329i	0.163162	+	0.282605i	0.936001	−	0.351997i	$-0.114497\pi$
$107$	1.68776	+	2.92329i	0.163162	+	0.282605i	−0.772839	+	0.634602i	$0.781164\pi$
$108$	23.6917	−	41.0353i	2.27974	−	3.94862i
$109$	6.05541	−	10.4883i	0.580003	−	1.00460i	−0.415475	−	0.909605i	$-0.636385\pi$
$109$	6.05541	−	10.4883i	0.580003	−	1.00460i	0.995478	−	0.0949905i	$-0.0302821\pi$
$110$	−1.05062	−	1.81973i	−0.100173	−	0.173504i
$111$	−5.71068			−0.542034
$112$	−2.43949	−	0.220067i	−0.230511	−	0.0207944i
$113$	5.74150			0.540115			0.270058	−	0.962844i	$-0.412957\pi$
$113$	5.74150			0.540115			0.270058	+	0.962844i	$0.412957\pi$
$114$	15.2799	+	26.4656i	1.43109	+	2.47873i
$115$	−2.54900	+	4.41500i	−0.237696	+	0.411701i
$116$	9.82595	−	17.0190i	0.912316	−	1.58018i
$117$	3.64960	+	6.32129i	0.337406	+	0.584404i
$118$	1.55292			0.142958
$119$	2.01847	+	4.35931i	0.185032	+	0.399617i
$120$	10.7303			0.979537
$121$	5.09376	+	8.82266i	0.463069	+	0.802060i
$122$	5.49441	−	9.51659i	0.497440	−	0.861592i
$123$	16.6398	−	28.8210i	1.50036	−	2.59871i
$124$	3.48910	+	6.04330i	0.313331	+	0.542705i
$125$	−1.00000			−0.0894427
$126$	18.9156	+	40.8523i	1.68514	+	3.63941i
$127$	5.73807			0.509172			0.254586	−	0.967050i	$-0.418061\pi$
$127$	5.73807			0.509172			0.254586	+	0.967050i	$0.418061\pi$
$128$	9.93507	+	17.2080i	0.878144	+	1.52099i
$129$	15.0525	−	26.0716i	1.32530	−	2.29548i
$130$	−1.16558	+	2.01884i	−0.102228	+	0.177064i
$131$	−5.22618	−	9.05200i	−0.456613	−	0.790877i	0.542166	−	0.840271i	$-0.317604\pi$
$131$	−5.22618	−	9.05200i	−0.456613	−	0.790877i	−0.998779	+	0.0493940i	$0.984271\pi$
$132$	9.93444			0.864682
$133$	−10.7638	−	0.971007i	−0.933342	−	0.0841970i
$134$	−33.3562			−2.88154
$135$	−6.89858	−	11.9487i	−0.593735	−	1.02838i
$136$	−3.03548	+	5.25761i	−0.260290	+	0.450836i
$137$	2.19339	−	3.79906i	0.187394	−	0.324576i	−0.756987	−	0.653430i	$-0.773329\pi$
$137$	2.19339	−	3.79906i	0.187394	−	0.324576i	0.944381	+	0.328854i	$0.106663\pi$
$138$	−19.0697	−	33.0296i	−1.62332	−	2.81167i
$139$	−18.8692			−1.60046			−0.800231	−	0.599692i	$-0.795290\pi$
$139$	−18.8692			−1.60046			−0.800231	+	0.599692i	$0.795290\pi$
$140$	−5.23176	+	7.42895i	−0.442164	+	0.627861i
$141$	40.5796			3.41742
$142$	19.2465	+	33.3359i	1.61513	+	2.79749i
$143$	−0.450686	+	0.780611i	−0.0376883	+	0.0652780i
$144$	−3.37875	+	5.85217i	−0.281563	+	0.487681i
$145$	−2.86113	−	4.95562i	−0.237604	−	0.411542i
$146$	−35.6687			−2.95196
$147$	−22.1020	−	4.02037i	−1.82294	−	0.331594i
$148$	6.11116			0.502334
$149$	−2.42932	−	4.20771i	−0.199018	−	0.344709i	0.749192	−	0.662352i	$-0.230442\pi$
$149$	−2.42932	−	4.20771i	−0.199018	−	0.344709i	−0.948210	+	0.317643i	$0.897108\pi$
$150$	3.74062	−	6.47894i	0.305420	−	0.529003i
$151$	−0.700967	+	1.21411i	−0.0570439	+	0.0988030i	−0.893137	−	0.449784i	$-0.851501\pi$
$151$	−0.700967	+	1.21411i	−0.0570439	+	0.0988030i	0.836093	+	0.548587i	$0.184834\pi$
$152$	−6.82900	−	11.8282i	−0.553905	−	0.959392i
$153$	13.2533			1.07146
$154$	−3.20100	+	4.54533i	−0.257944	+	0.366273i
$155$	2.03192			0.163208
$156$	−5.51073	−	9.54487i	−0.441212	−	0.764201i
$157$	3.73007	−	6.46067i	0.297692	−	0.515617i	−0.677916	−	0.735140i	$-0.737117\pi$
$157$	3.73007	−	6.46067i	0.297692	−	0.515617i	0.975607	+	0.219522i	$0.0704499\pi$
$158$	4.53927	−	7.86224i	0.361125	−	0.625486i
$159$	3.48888	+	6.04292i	0.276686	+	0.479235i
$160$	4.52898			0.358047
$161$	13.4335	+	1.21184i	1.05871	+	0.0955063i
$162$	52.1730			4.09910
$163$	2.15383	+	3.73055i	0.168701	+	0.292199i	0.937963	−	0.346734i	$-0.112709\pi$
$163$	2.15383	+	3.73055i	0.168701	+	0.292199i	−0.769262	+	0.638933i	$0.779376\pi$
$164$	−17.8068	+	30.8422i	−1.39047	+	2.40837i
$165$	1.44636	−	2.50517i	0.112599	−	0.195027i
$166$	−6.42050	−	11.1206i	−0.498328	−	0.863129i
$167$	−15.9916			−1.23747			−0.618734	−	0.785601i	$-0.712354\pi$
$167$	−15.9916			−1.23747			−0.618734	+	0.785601i	$0.712354\pi$
$168$	−11.9285	−	25.7621i	−0.920302	−	1.98759i
$169$	1.00000			0.0769231
$170$	2.11636	+	3.66564i	0.162317	+	0.281142i
$171$	−14.9081	+	25.8216i	−1.14005	+	1.97463i
$172$	−16.1081	+	27.9000i	−1.22823	+	2.12735i
$173$	−2.37584	−	4.11508i	−0.180632	−	0.312864i	0.761464	−	0.648207i	$-0.224481\pi$
$173$	−2.37584	−	4.11508i	−0.180632	−	0.312864i	−0.942096	+	0.335343i	$0.891148\pi$
$174$	42.8095			3.24538
$175$	1.11166	+	2.40088i	0.0840339	+	0.181489i
$176$	−0.834478			−0.0629011
$177$	1.06893	+	1.85144i	0.0803457	+	0.139163i
$178$	−1.92059	+	3.32655i	−0.143954	+	0.249336i
$179$	−11.6053	+	20.1009i	−0.867418	+	1.50241i	−0.00279260	+	0.999996i	$0.500889\pi$
$179$	−11.6053	+	20.1009i	−0.867418	+	1.50241i	−0.864626	+	0.502417i	$0.832444\pi$
$180$	12.5338	+	21.7092i	0.934214	+	1.61811i
$181$	2.04014			0.151643			0.0758213	−	0.997121i	$-0.475842\pi$
$181$	2.04014			0.151643			0.0758213	+	0.997121i	$0.475842\pi$
$182$	6.14272	+	0.554136i	0.455329	+	0.0410753i
$183$	15.1280			1.11829
$184$	8.52275	+	14.7618i	0.628305	+	1.08826i
$185$	0.889726	−	1.54105i	0.0654140	−	0.113300i
$186$	−7.60063	+	13.1647i	−0.557305	+	0.965281i
$187$	0.818318	+	1.41737i	0.0598413	+	0.103648i
$188$	−43.4254			−3.16712
$189$	−21.0184	+	29.8456i	−1.52886	+	2.17094i
$190$	−9.52246			−0.690832
$191$	−2.09749	−	3.63295i	−0.151769	−	0.262871i	0.780109	−	0.625644i	$-0.215164\pi$
$191$	−2.09749	−	3.63295i	−0.151769	−	0.262871i	−0.931878	+	0.362772i	$0.881830\pi$
$192$	−19.9122	+	34.4890i	−1.43704	+	2.48903i
$193$	0.586423	−	1.01571i	0.0422116	−	0.0731127i	−0.844148	−	0.536111i	$-0.819893\pi$
$193$	0.586423	−	1.01571i	0.0422116	−	0.0731127i	0.886359	+	0.462998i	$0.153226\pi$
$194$	17.6359	+	30.5463i	1.26618	+	2.19309i
$195$	−3.20924			−0.229818
$196$	23.6519	+	4.30231i	1.68942	+	0.307308i
$197$	16.3473			1.16470			0.582350	−	0.812938i	$-0.302133\pi$
$197$	16.3473			1.16470			0.582350	+	0.812938i	$0.302133\pi$
$198$	7.66869	+	13.2826i	0.544990	+	0.943950i
$199$	4.19533	−	7.26653i	0.297399	−	0.515110i	−0.678141	−	0.734932i	$-0.737214\pi$
$199$	4.19533	−	7.26653i	0.297399	−	0.515110i	0.975540	+	0.219821i	$0.0705475\pi$
$200$	−1.67178	+	2.89561i	−0.118213	+	0.204751i
$201$	−22.9602	−	39.7683i	−1.61949	−	2.80504i
$202$	17.3810			1.22292
$203$	−8.71721	+	12.3782i	−0.611828	+	0.868779i
$204$	−20.0118			−1.40111
$205$	5.18498	+	8.98065i	0.362135	+	0.627236i
$206$	16.0331	−	27.7702i	1.11708	−	1.93484i
$207$	18.6057	−	32.2260i	1.29318	−	2.23986i
$208$	0.462893	+	0.801755i	0.0320959	+	0.0555917i
$209$	−3.68198			−0.254688
$210$	−19.7134	−	1.77835i	−1.36036	−	0.122718i
$211$	17.2392			1.18680			0.593398	−	0.804909i	$-0.297786\pi$
$211$	17.2392			1.18680			0.593398	+	0.804909i	$0.297786\pi$
$212$	−3.73355	−	6.46670i	−0.256421	−	0.444135i
$213$	−26.4961	+	45.8926i	−1.81548	+	3.14451i
$214$	3.93443	−	6.81464i	0.268952	−	0.465839i
$215$	4.69036	+	8.12393i	0.319880	+	0.554048i
$216$	−46.1317			−3.13886
$217$	−2.25881	−	4.87838i	−0.153338	−	0.331166i
$218$	−28.2322			−1.91213
$219$	−24.5520	−	42.5253i	−1.65907	−	2.87360i
$220$	−1.54779	+	2.68085i	−0.104352	+	0.180743i
$221$	0.907858	−	1.57246i	0.0610691	−	0.105775i
$222$	6.65625	+	11.5290i	0.446738	+	0.773773i
$223$	−0.0621872			−0.00416437			−0.00208218	−	0.999998i	$-0.500663\pi$
$223$	−0.0621872			−0.00416437			−0.00208218	+	0.999998i	$0.500663\pi$
$224$	−5.03470	−	10.8735i	−0.336395	−	0.726517i
$225$	7.29920			0.486613
$226$	−6.69217	−	11.5912i	−0.445157	−	0.771034i
$227$	−3.69954	+	6.40779i	−0.245547	+	0.425300i	−0.962285	−	0.272042i	$-0.912301\pi$
$227$	−3.69954	+	6.40779i	−0.245547	+	0.425300i	0.716738	+	0.697342i	$0.245634\pi$
$228$	22.5106	−	38.9895i	1.49080	−	2.58214i
$229$	−2.59589	−	4.49621i	−0.171541	−	0.297118i	0.767418	−	0.641147i	$-0.221541\pi$
$229$	−2.59589	−	4.49621i	−0.171541	−	0.297118i	−0.938959	+	0.344030i	$0.888208\pi$
$230$	11.8842			0.783624
$231$	−7.62246	−	0.687624i	−0.501521	−	0.0452423i
$232$	−19.1327			−1.25612
$233$	0.246030	+	0.426136i	0.0161179	+	0.0279171i	0.873972	−	0.485977i	$-0.161536\pi$
$233$	0.246030	+	0.426136i	0.0161179	+	0.0279171i	−0.857854	+	0.513894i	$0.828203\pi$
$234$	8.50779	−	14.7359i	0.556172	−	0.963318i
$235$	−6.32232	+	10.9506i	−0.412422	+	0.714337i
$236$	−1.14389	−	1.98128i	−0.0744610	−	0.128970i
$237$	12.4982			0.811843
$238$	6.44807	−	9.15608i	0.417966	−	0.593500i
$239$	25.2807			1.63527			0.817636	−	0.575736i	$-0.195284\pi$
$239$	25.2807			1.63527			0.817636	+	0.575736i	$0.195284\pi$
$240$	−1.48553	−	2.57302i	−0.0958908	−	0.166088i
$241$	−6.94862	+	12.0354i	−0.447600	+	0.775266i	−0.998229	−	0.0594838i	$-0.981055\pi$
$241$	−6.94862	+	12.0354i	−0.447600	+	0.775266i	0.550629	+	0.834750i	$0.314388\pi$
$242$	11.8744	−	20.5670i	0.763313	−	1.32210i
$243$	15.2168	+	26.3563i	0.976159	+	1.69076i
$244$	−16.1889			−1.03639
$245$	4.52841	−	5.33793i	0.289309	−	0.341028i
$246$	−77.5802			−4.94633
$247$	2.04243	+	3.53760i	0.129957	+	0.225092i
$248$	3.39693	−	5.88365i	0.215705	−	0.373612i
$249$	8.83892	−	15.3095i	0.560144	−	0.970198i
$250$	1.16558	+	2.01884i	0.0737177	+	0.127683i
$251$	9.45803			0.596986			0.298493	−	0.954412i	$-0.403516\pi$
$251$	9.45803			0.596986			0.298493	+	0.954412i	$0.403516\pi$
$252$	38.1877	−	54.2254i	2.40560	−	3.41588i
$253$	4.59520			0.288898
$254$	−6.68818	−	11.5843i	−0.419654	−	0.726861i
$255$	−2.91353	+	5.04638i	−0.182452	+	0.316017i
$256$	10.7509	−	18.6211i	0.671930	−	1.16382i
$257$	4.64742	+	8.04956i	0.289898	+	0.502118i	0.973785	−	0.227470i	$-0.0730453\pi$
$257$	4.64742	+	8.04956i	0.289898	+	0.502118i	−0.683887	+	0.729588i	$0.739712\pi$
$258$	−70.1793			−4.36917
$259$	−4.68895	−	0.422991i	−0.291357	−	0.0262834i
$260$	3.43429			0.212986
$261$	20.8839	+	36.1720i	1.29268	+	2.23899i
$262$	−12.1830	+	21.1016i	−0.752671	+	1.30366i
$263$	10.8244	−	18.7485i	0.667463	−	1.15608i	−0.311149	−	0.950361i	$-0.600714\pi$
$263$	10.8244	−	18.7485i	0.667463	−	1.15608i	0.978611	−	0.205718i	$-0.0659530\pi$
$264$	−4.83599	−	8.37618i	−0.297635	−	0.515519i
$265$	−2.17428			−0.133565
$266$	10.5858	+	22.8622i	0.649055	+	1.40177i
$267$	−5.28803			−0.323622
$268$	24.5704	+	42.5572i	1.50088	+	2.59959i
$269$	−4.47886	+	7.75762i	−0.273081	+	0.472990i	−0.969649	−	0.244500i	$-0.921376\pi$
$269$	−4.47886	+	7.75762i	−0.273081	+	0.472990i	0.696568	+	0.717491i	$0.254709\pi$
$270$	−16.0817	+	27.8543i	−0.978699	+	1.69516i
$271$	12.0882	+	20.9373i	0.734303	+	1.27185i	0.955028	+	0.296514i	$0.0958243\pi$
$271$	12.0882	+	20.9373i	0.734303	+	1.27185i	−0.220725	+	0.975336i	$0.570842\pi$
$272$	1.68097			0.101923
$273$	3.56759	+	7.70498i	0.215921	+	0.466327i
$274$	−10.2263			−0.617792
$275$	0.450686	+	0.780611i	0.0271774	+	0.0470726i
$276$	−28.0937	+	48.6597i	−1.69104	+	2.92897i
$277$	−8.34923	+	14.4613i	−0.501657	+	0.868895i	0.498341	+	0.866981i	$0.333943\pi$
$277$	−8.34923	+	14.4613i	−0.501657	+	0.868895i	−0.999998	+	0.00191405i	$0.999391\pi$
$278$	21.9935	+	38.0938i	1.31908	+	2.28472i
$279$	−14.8314			−0.887932
$280$	8.81046	+	0.794794i	0.526526	+	0.0474980i
$281$	0.945863			0.0564254			0.0282127	−	0.999602i	$-0.491018\pi$
$281$	0.945863			0.0564254			0.0282127	+	0.999602i	$0.491018\pi$
$282$	−47.2987	−	81.9238i	−2.81660	−	4.87849i
$283$	−10.6077	+	18.3731i	−0.630564	+	1.09217i	0.356873	+	0.934153i	$0.383843\pi$
$283$	−10.6077	+	18.3731i	−0.630564	+	1.09217i	−0.987437	+	0.158016i	$0.949490\pi$
$284$	28.3542	−	49.1109i	1.68251	−	2.91420i
$285$	−6.55465	−	11.3530i	−0.388264	−	0.672493i
$286$	2.10124			0.124249
$287$	15.7975	−	22.4320i	0.932495	−	1.32412i
$288$	−33.0579			−1.94796
$289$	6.85159	+	11.8673i	0.403035	+	0.698076i
$290$	−6.66974	+	11.5523i	−0.391660	+	0.678376i
$291$	−24.2788	+	42.0521i	−1.42325	+	2.46514i
$292$	26.2738	+	45.5075i	1.53756	+	2.66313i
$293$	−0.380451			−0.0222262			−0.0111131	−	0.999938i	$-0.503537\pi$
$293$	−0.380451			−0.0222262			−0.0111131	+	0.999938i	$0.503537\pi$
$294$	17.6451	+	49.3064i	1.02908	+	2.87561i
$295$	−0.666158			−0.0387852
$296$	−2.97486	−	5.15260i	−0.172910	−	0.299489i
$297$	−6.21819	+	10.7702i	−0.360816	+	0.624951i
$298$	−5.66313	+	9.80883i	−0.328056	+	0.568210i
$299$	−2.54900	−	4.41500i	−0.147413	−	0.255326i
$300$	−11.0215			−0.636324
$301$	14.2905	−	20.2920i	0.823688	−	1.16961i
$302$	3.26813			0.188060
$303$	11.9639	+	20.7221i	0.687310	+	1.19046i
$304$	−1.89086	+	3.27506i	−0.108448	+	0.187837i
$305$	−2.35694	+	4.08235i	−0.134958	+	0.233755i
$306$	−15.4477	−	26.7563i	−0.883088	−	1.52955i
$307$	−1.04030			−0.0593729			−0.0296864	−	0.999559i	$-0.509451\pi$
$307$	−1.04030			−0.0593729			−0.0296864	+	0.999559i	$0.509451\pi$
$308$	8.15700	+	0.735845i	0.464788	+	0.0419287i
$309$	44.1446			2.51130
$310$	−2.36836	−	4.10212i	−0.134514	−	0.232985i
$311$	8.95590	−	15.5121i	0.507842	−	0.879609i	−0.492116	−	0.870529i	$-0.663777\pi$
$311$	8.95590	−	15.5121i	0.507842	−	0.879609i	0.999959	−	0.00907953i	$-0.00289014\pi$
$312$	−5.36515	+	9.29270i	−0.303742	+	0.526096i
$313$	−5.20018	−	9.00697i	−0.293931	−	0.509104i	0.680804	−	0.732465i	$-0.261630\pi$
$313$	−5.20018	−	9.00697i	−0.293931	−	0.509104i	−0.974736	+	0.223361i	$0.928297\pi$
$314$	−17.3907			−0.981417
$315$	−8.11426	−	17.5245i	−0.457187	−	0.987392i
$316$	−13.3746			−0.752382
$317$	5.06740	+	8.77699i	0.284613	+	0.492965i	0.972515	−	0.232839i	$-0.0748015\pi$
$317$	5.06740	+	8.77699i	0.284613	+	0.492965i	−0.687902	+	0.725804i	$0.741468\pi$
$318$	8.13314	−	14.0870i	0.456084	−	0.789960i
$319$	−2.57894	+	4.46685i	−0.144393	+	0.250096i
$320$	−6.20466	−	10.7468i	−0.346851	−	0.600764i
$321$	10.8328			0.604630
$322$	−13.2113	−	28.5326i	−0.736236	−	1.59006i
$323$	7.41695			0.412690
$324$	−38.4310	−	66.5645i	−2.13506	−	3.69803i
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$	5.02093	−	8.69650i	0.278083	−	0.481654i
$327$	−19.4333	−	33.6594i	−1.07466	−	1.86137i
$328$	34.6726			1.91448
$329$	33.3193	+	3.00574i	1.83695	+	0.165712i
$330$	−6.74338			−0.371211
$331$	−4.85871	−	8.41553i	−0.267059	−	0.462559i	0.701042	−	0.713120i	$-0.252718\pi$
$331$	−4.85871	−	8.41553i	−0.267059	−	0.462559i	−0.968101	+	0.250560i	$0.919385\pi$
$332$	−9.45878	+	16.3831i	−0.519118	+	0.899138i
$333$	−6.49429	+	11.2484i	−0.355885	+	0.616411i
$334$	18.6395	+	32.2845i	1.01991	+	1.76653i
$335$	14.3089			0.781776
$336$	−4.52609	+	6.42692i	−0.246918	+	0.350617i
$337$	10.5702			0.575797			0.287899	−	0.957661i	$-0.407043\pi$
$337$	10.5702			0.575797			0.287899	+	0.957661i	$0.407043\pi$
$338$	−1.16558	−	2.01884i	−0.0633991	−	0.109810i
$339$	9.21292	−	15.9572i	0.500377	−	0.866679i
$340$	3.11785	−	5.40028i	0.169089	−	0.292871i
$341$	−0.915758	−	1.58614i	−0.0495911	−	0.0858942i
$342$	69.5063			3.75847
$343$	−17.8498	−	4.93815i	−0.963797	−	0.266635i
$344$	31.3650			1.69109
$345$	8.18035	+	14.1688i	0.440415	+	0.762821i
$346$	−5.53846	+	9.59290i	−0.297750	+	0.515718i
$347$	9.74281	−	16.8750i	0.523021	−	0.905899i	−0.476620	−	0.879110i	$-0.658138\pi$
$347$	9.74281	−	16.8750i	0.523021	−	0.905899i	0.999641	−	0.0267899i	$-0.00852850\pi$
$348$	−31.5338	−	54.6181i	−1.69039	−	2.92784i
$349$	12.7523			0.682617			0.341309	−	0.939951i	$-0.389130\pi$
$349$	12.7523			0.682617			0.341309	+	0.939951i	$0.389130\pi$
$350$	3.55126	−	5.04268i	0.189823	−	0.269543i
$351$	13.7972			0.736438
$352$	−2.04115	−	3.53537i	−0.108793	−	0.188436i
$353$	−16.1030	+	27.8912i	−0.857076	+	1.48450i	0.0176299	+	0.999845i	$0.494388\pi$
$353$	−16.1030	+	27.8912i	−0.857076	+	1.48450i	−0.874706	+	0.484654i	$0.838945\pi$
$354$	2.49184	−	4.31600i	0.132440	−	0.229393i
$355$	−8.25619	−	14.3001i	−0.438193	−	0.758973i
$356$	5.65887			0.299919
$357$	15.3546	+	1.38514i	0.812652	+	0.0733096i
$358$	54.1074			2.85966
$359$	16.7790	+	29.0622i	0.885564	+	1.53384i	0.845066	+	0.534662i	$0.179561\pi$
$359$	16.7790	+	29.0622i	0.885564	+	1.53384i	0.0404980	+	0.999180i	$0.487106\pi$
$360$	12.2027	−	21.1357i	0.643137	−	1.11395i
$361$	1.15695	−	2.00389i	0.0608920	−	0.105468i
$362$	−2.37795	−	4.11872i	−0.124982	−	0.216475i
$363$	32.6942			1.71600
$364$	−3.81778	−	8.24531i	−0.200106	−	0.432172i
$365$	15.3008			0.800882
$366$	−17.6329	−	30.5410i	−0.921684	−	1.59640i
$367$	2.00030	−	3.46462i	0.104415	−	0.180852i	−0.809084	−	0.587693i	$-0.800036\pi$
$367$	2.00030	−	3.46462i	0.104415	−	0.180852i	0.913499	+	0.406841i	$0.133370\pi$
$368$	2.35983	−	4.08735i	0.123015	−	0.213068i
$369$	−37.8462	−	65.5516i	−1.97020	−	3.41248i
$370$	−4.14818			−0.215654
$371$	2.41706	+	5.22017i	0.125488	+	0.271018i
$372$	22.3947			1.16111
$373$	−1.88335	−	3.26207i	−0.0975164	−	0.168903i	0.813140	−	0.582069i	$-0.197757\pi$
$373$	−1.88335	−	3.26207i	−0.0975164	−	0.168903i	−0.910656	+	0.413165i	$0.864423\pi$
$374$	1.90763	−	3.30411i	0.0986411	−	0.170851i
$375$	−1.60462	+	2.77928i	−0.0828621	+	0.143521i
$376$	21.1391	+	36.6139i	1.09016	+	1.88822i
$377$	5.72225			0.294711
$378$	84.7521	+	7.64551i	4.35918	+	0.393242i
$379$	−20.3320			−1.04438			−0.522191	−	0.852828i	$-0.674885\pi$
$379$	−20.3320			−1.04438			−0.522191	+	0.852828i	$0.674885\pi$
$380$	7.01431	+	12.1491i	0.359826	+	0.623238i
$381$	9.20742	−	15.9477i	0.471710	−	0.817026i
$382$	−4.88957	+	8.46899i	−0.250172	+	0.433311i
$383$	4.75254	+	8.23163i	0.242843	+	0.420617i	0.961523	−	0.274724i	$-0.0885866\pi$
$383$	4.75254	+	8.23163i	0.242843	+	0.420617i	−0.718680	+	0.695341i	$0.755253\pi$
$384$	63.7680			3.25415
$385$	1.37314	−	1.94982i	0.0699816	−	0.0993719i
$386$	−2.73409			−0.139161
$387$	−34.2359	−	59.2982i	−1.74031	−	3.01430i
$388$	25.9814	−	45.0012i	1.31901	−	2.28459i
$389$	−7.32916	+	12.6945i	−0.371603	+	0.643635i	−0.989812	−	0.142378i	$-0.954525\pi$
$389$	−7.32916	+	12.6945i	−0.371603	+	0.643635i	0.618209	+	0.786014i	$0.287858\pi$
$390$	3.74062	+	6.47894i	0.189414	+	0.328074i
$391$	−9.25652			−0.468123
$392$	−7.88607	−	22.0364i	−0.398307	−	1.11300i
$393$	−33.5441			−1.69208
$394$	−19.0541	−	33.0027i	−0.959932	−	1.66265i
$395$	−1.94722	+	3.37268i	−0.0979751	+	0.169698i
$396$	11.2976	−	19.5681i	0.567727	−	0.983332i
$397$	7.45342	+	12.9097i	0.374077	+	0.647920i	0.990188	−	0.139739i	$-0.0446264\pi$
$397$	7.45342	+	12.9097i	0.374077	+	0.647920i	−0.616112	+	0.787659i	$0.711293\pi$
$398$	−19.5600			−0.980452
$399$	−19.9705	+	28.3576i	−0.999777	+	1.41966i
$400$	0.925786			0.0462893
$401$	−10.2632	−	17.7765i	−0.512522	−	0.887714i	−0.999895	−	0.0145201i	$-0.995378\pi$
$401$	−10.2632	−	17.7765i	−0.512522	−	0.887714i	0.487372	−	0.873194i	$-0.337955\pi$
$402$	−53.5239	+	92.7062i	−2.66953	+	4.62376i
$403$	−1.01596	+	1.75969i	−0.0506085	+	0.0876566i
$404$	−12.8029	−	22.1753i	−0.636970	−	1.10326i
$405$	−22.3807			−1.11211
$406$	35.1502	+	3.17091i	1.74447	+	0.157370i
$407$	−1.60395			−0.0795048
$408$	9.74158	+	16.8729i	0.482280	+	0.835334i
$409$	−12.7256	+	22.0413i	−0.629239	+	1.08987i	0.358465	+	0.933543i	$0.383300\pi$
$409$	−12.7256	+	22.0413i	−0.629239	+	1.08987i	−0.987705	+	0.156331i	$0.950033\pi$
$410$	12.0870	−	20.9353i	0.596935	−	1.03392i
$411$	−7.03911	−	12.1921i	−0.347214	−	0.601392i
$412$	−47.2404			−2.32737
$413$	0.740544	+	1.59936i	0.0364398	+	0.0786995i
$414$	−86.7455			−4.26331
$415$	2.75421	+	4.77044i	0.135199	+	0.234172i
$416$	−2.26449	+	3.92221i	−0.111026	+	0.192302i
$417$	−30.2778	+	52.4427i	−1.48271	+	2.56813i
$418$	4.29164	+	7.43334i	0.209911	+	0.363576i
$419$	−22.3064			−1.08974			−0.544869	−	0.838521i	$-0.683421\pi$
$419$	−22.3064			−1.08974			−0.544869	+	0.838521i	$0.683421\pi$
$420$	12.2522	+	26.4612i	0.597844	+	1.29117i
$421$	−25.2622			−1.23120			−0.615601	−	0.788058i	$-0.711087\pi$
$421$	−25.2622			−1.23120			−0.615601	+	0.788058i	$0.711087\pi$
$422$	−20.0936	−	34.8032i	−0.978143	−	1.69419i
$423$	46.1479	−	79.9305i	2.24379	−	3.88635i
$424$	−3.63492	+	6.29586i	−0.176527	+	0.305754i
$425$	−0.907858	−	1.57246i	−0.0440376	−	0.0762753i
$426$	123.533			5.98520
$427$	12.4213	+	1.12053i	0.601111	+	0.0542264i
$428$	−11.5925			−0.560346
$429$	1.44636	+	2.50517i	0.0698308	+	0.120951i
$430$	10.9340	−	18.9382i	0.527282	−	0.913280i
$431$	11.0563	−	19.1501i	0.532565	−	0.922429i	−0.466712	−	0.884409i	$-0.654562\pi$
$431$	11.0563	−	19.1501i	0.532565	−	0.922429i	0.999277	−	0.0380200i	$-0.0121051\pi$
$432$	6.38661	+	11.0619i	0.307276	+	0.532218i
$433$	−23.6558			−1.13683			−0.568413	−	0.822743i	$-0.692443\pi$
$433$	−23.6558			−1.13683			−0.568413	+	0.822743i	$0.692443\pi$
$434$	−7.21586	+	10.2463i	−0.346373	+	0.491839i
$435$	−18.3641			−0.880490
$436$	20.7961	+	36.0198i	0.995951	+	1.72504i
$437$	10.4123	−	18.0347i	0.498089	−	0.862715i
$438$	−57.2346	+	99.1332i	−2.73477	+	4.73677i
$439$	−7.83532	−	13.5712i	−0.373959	−	0.647716i	0.616211	−	0.787581i	$-0.288667\pi$
$439$	−7.83532	−	13.5712i	−0.373959	−	0.647716i	−0.990171	+	0.139864i	$0.955333\pi$
$440$	3.01380			0.143677
$441$	−33.0538	+	38.9627i	−1.57399	+	1.85536i
$442$	−4.23272			−0.201330
$443$	1.98860	+	3.44436i	0.0944814	+	0.163647i	0.909392	−	0.415940i	$-0.136547\pi$
$443$	1.98860	+	3.44436i	0.0944814	+	0.163647i	−0.814911	+	0.579587i	$0.803214\pi$
$444$	9.80608	−	16.9846i	0.465376	−	0.806055i
$445$	0.823877	−	1.42700i	0.0390555	−	0.0676461i
$446$	0.0724841	+	0.125546i	0.00343222	+	0.00594478i
$447$	−15.5925			−0.737502
$448$	−18.9042	+	26.8434i	−0.893140	+	1.26823i
$449$	23.9806			1.13172			0.565858	−	0.824503i	$-0.308545\pi$
$449$	23.9806			1.13172			0.565858	+	0.824503i	$0.308545\pi$
$450$	−8.50779	−	14.7359i	−0.401061	−	0.694658i
$451$	4.67360	−	8.09491i	0.220071	−	0.381174i
$452$	−9.85900	+	17.0763i	−0.463728	+	0.803201i
$453$	2.24957	+	3.89637i	0.105694	+	0.183067i
$454$	17.2484			0.809508
$455$	−2.63505	−	0.237709i	−0.123533	−	0.0111440i
$456$	−43.8318			−2.05261
$457$	18.5123	+	32.0642i	0.865967	+	1.49990i	0.866084	+	0.499899i	$0.166630\pi$
$457$	18.5123	+	32.0642i	0.865967	+	1.49990i	−0.000116463		1.00000i	$0.500037\pi$
$458$	−6.05142	+	10.4814i	−0.282764	+	0.489762i
$459$	12.5259	−	21.6954i	0.584657	−	1.01266i
$460$	−8.75402	−	15.1624i	−0.408158	−	0.706951i
$461$	1.41759			0.0660239			0.0330119	−	0.999455i	$-0.489490\pi$
$461$	1.41759			0.0660239			0.0330119	+	0.999455i	$0.489490\pi$
$462$	7.49637	+	16.1900i	0.348763	+	0.753227i
$463$	12.6844			0.589495			0.294747	−	0.955575i	$-0.404764\pi$
$463$	12.6844			0.589495			0.294747	+	0.955575i	$0.404764\pi$
$464$	2.64879	+	4.58784i	0.122967	+	0.212985i
$465$	3.26045	−	5.64727i	0.151200	−	0.261886i
$466$	0.573534	−	0.993389i	0.0265684	−	0.0460179i
$467$	11.9015	+	20.6140i	0.550735	+	0.953901i	0.998222	+	0.0596102i	$0.0189858\pi$
$467$	11.9015	+	20.6140i	0.550735	+	0.953901i	−0.447487	+	0.894290i	$0.647681\pi$
$468$	−25.0676			−1.15875
$469$	−15.9066	−	34.3538i	−0.734500	−	1.58631i
$470$	29.4766			1.35966
$471$	−11.9707	−	20.7338i	−0.551579	−	0.955363i
$472$	−1.11367	+	1.92894i	−0.0512609	+	0.0887865i
$473$	4.22776	−	7.32269i	0.194392	−	0.336698i
$474$	−14.5676	−	25.2318i	−0.669111	−	1.15893i
$475$	4.08486			0.187426
$476$	−16.4314	−	1.48228i	−0.753132	−	0.0679402i
$477$	15.8705			0.726659
$478$	−29.4666	−	51.0377i	−1.34777	−	2.33441i
$479$	−20.6461	+	35.7600i	−0.943343	+	1.63392i	−0.184307	+	0.982869i	$0.559004\pi$
$479$	−20.6461	+	35.7600i	−0.943343	+	1.63392i	−0.759036	+	0.651049i	$0.774329\pi$
$480$	7.26728	−	12.5873i	0.331704	−	0.574529i
$481$	0.889726	+	1.54105i	0.0405680	+	0.0702659i
$482$	32.3967			1.47563
$483$	24.9237	−	35.3909i	1.13407	−	1.61034i
$484$	−34.9870			−1.59032
$485$	−7.56529	−	13.1035i	−0.343522	−	0.594998i
$486$	35.4728	−	61.4407i	1.60908	−	2.78701i
$487$	−14.8641	+	25.7453i	−0.673556	+	1.16663i	0.303333	+	0.952885i	$0.401901\pi$
$487$	−14.8641	+	25.7453i	−0.673556	+	1.16663i	−0.976889	+	0.213748i	$0.931433\pi$
$488$	7.88059	+	13.6496i	0.356738	+	0.617888i
$489$	13.8243			0.625158
$490$	−16.0547	−	2.92035i	−0.725275	−	0.131928i
$491$	−33.6558			−1.51886			−0.759432	−	0.650586i	$-0.774523\pi$
$491$	−33.6558			−1.51886			−0.759432	+	0.650586i	$0.774523\pi$
$492$	57.1461	+	98.9799i	2.57634	+	4.46236i
$493$	5.19499	−	8.99799i	0.233971	−	0.405249i
$494$	4.76123	−	8.24669i	0.214218	−	0.371036i
$495$	−3.28965	−	5.69784i	−0.147859	−	0.256099i
$496$	−1.88112			−0.0844649
$497$	−25.1548	+	35.7190i	−1.12835	+	1.60222i
$498$	−41.2098			−1.84666
$499$	−0.934128	−	1.61796i	−0.0418173	−	0.0724297i	0.844359	−	0.535777i	$-0.179981\pi$
$499$	−0.934128	−	1.61796i	−0.0418173	−	0.0724297i	−0.886177	+	0.463348i	$0.846648\pi$
$500$	1.71715	−	2.97419i	0.0767931	−	0.133010i
$501$	−25.6604	+	44.4452i	−1.14642	+	1.98566i
$502$	−11.0241	−	19.0943i	−0.492029	−	0.852219i
$503$	−29.0713			−1.29623			−0.648113	−	0.761544i	$-0.724442\pi$
$503$	−29.0713			−1.29623			−0.648113	+	0.761544i	$0.724442\pi$
$504$	−64.3093	−	5.80136i	−2.86457	−	0.258413i
$505$	−7.45593			−0.331785
$506$	−5.35606	−	9.27697i	−0.238106	−	0.412412i
$507$	1.60462	−	2.77928i	0.0712636	−	0.123432i
$508$	−9.85312	+	17.0661i	−0.437161	+	0.757186i
$509$	2.42337	+	4.19740i	0.107414	+	0.186047i	0.914722	−	0.404084i	$-0.132410\pi$
$509$	2.42337	+	4.19740i	0.107414	+	0.186047i	−0.807308	+	0.590131i	$0.799076\pi$
$510$	13.5838			0.601501
$511$	−17.0094	−	36.7354i	−0.752451	−	1.62508i
$512$	−10.3837			−0.458900
$513$	28.1797	+	48.8088i	1.24417	+	2.15496i
$514$	10.8339	−	18.7648i	0.477861	−	0.827680i
$515$	−6.87775	+	11.9126i	−0.303070	+	0.524932i
$516$	51.6946	+	89.5376i	2.27573	+	3.94167i
$517$	11.3975			0.501262
$518$	4.61138	+	9.95927i	0.202613	+	0.437585i
$519$	−15.2493			−0.669369
$520$	−1.67178	−	2.89561i	−0.0733125	−	0.126981i
$521$	−16.8364	+	29.1614i	−0.737614	+	1.27759i	0.215952	+	0.976404i	$0.430714\pi$
$521$	−16.8364	+	29.1614i	−0.737614	+	1.27759i	−0.953567	+	0.301182i	$0.902619\pi$
$522$	48.6837	−	84.3227i	2.13083	−	3.69071i
$523$	−13.1048	−	22.6982i	−0.573033	−	0.992522i	−0.996252	−	0.0864950i	$-0.972433\pi$
$523$	−13.1048	−	22.6982i	−0.573033	−	0.992522i	0.423219	−	0.906027i	$-0.360900\pi$
$524$	35.8965			1.56814
$525$	8.45650	+	0.762863i	0.369072	+	0.0332941i
$526$	−50.4669			−2.20046
$527$	1.84469	+	3.19510i	0.0803561	+	0.139181i
$528$	−1.33902	+	2.31925i	−0.0582733	+	0.100932i
$529$	−1.49481	+	2.58909i	−0.0649918	+	0.112569i
$530$	2.53429	+	4.38952i	0.110083	+	0.190669i
$531$	4.86242			0.211011
$532$	21.3710	−	30.3462i	0.926551	−	1.31568i
$533$	−10.3700			−0.449173
$534$	6.16362	+	10.6757i	0.266726	+	0.461982i
$535$	−1.68776	+	2.92329i	−0.0729682	+	0.126385i
$536$	23.9213	−	41.4329i	1.03324	−	1.78963i
$537$	37.2440	+	64.5086i	1.60720	+	2.78375i
$538$	20.8819			0.900281
$539$	−6.20774	−	1.12919i	−0.267386	−	0.0486378i
$540$	47.3835			2.03906
$541$	6.84491	+	11.8557i	0.294286	+	0.509718i	0.974818	−	0.223000i	$-0.0715849\pi$
$541$	6.84491	+	11.8557i	0.294286	+	0.509718i	−0.680533	+	0.732718i	$0.738252\pi$
$542$	28.1794	−	48.8081i	1.21041	−	2.09649i
$543$	3.27365	−	5.67013i	0.140486	−	0.243328i
$544$	4.11167	+	7.12161i	0.176286	+	0.305337i
$545$	12.1108			0.518771
$546$	11.3968	−	16.1832i	0.487739	−	0.692575i
$547$	26.2312			1.12157			0.560783	−	0.827963i	$-0.310500\pi$
$547$	26.2312			1.12157			0.560783	+	0.827963i	$0.310500\pi$
$548$	7.53275	+	13.0471i	0.321783	+	0.557345i
$549$	17.2038	−	29.7979i	0.734241	−	1.27174i
$550$	1.05062	−	1.81973i	0.0447986	−	0.0775934i
$551$	11.6873	+	20.2430i	0.497896	+	0.862381i
$552$	54.7030			2.32832
$553$	10.2620	+	0.925740i	0.436386	+	0.0393665i
$554$	38.9267			1.65384
$555$	−2.85534	−	4.94560i	−0.121202	−	0.209929i
$556$	32.4011	−	56.1204i	1.37411	−	2.38003i
$557$	2.85616	−	4.94702i	0.121019	−	0.209612i	−0.799151	−	0.601131i	$-0.794717\pi$
$557$	2.85616	−	4.94702i	0.121019	−	0.209612i	0.920170	+	0.391519i	$0.128050\pi$
$558$	17.2871	+	29.9422i	0.731823	+	1.26756i
$559$	−9.38071			−0.396762
$560$	−1.02916	−	2.22270i	−0.0434901	−	0.0939261i
$561$	5.25235			0.221754
$562$	−1.10248	−	1.90955i	−0.0465052	−	0.0805494i
$563$	−8.32630	+	14.4216i	−0.350912	+	0.607797i	−0.986409	−	0.164306i	$-0.947462\pi$
$563$	−8.32630	+	14.4216i	−0.350912	+	0.607797i	0.635498	+	0.772103i	$0.280795\pi$
$564$	−69.6812	+	120.691i	−2.93411	+	5.08202i
$565$	2.87075	+	4.97229i	0.120773	+	0.209186i
$566$	49.4566			2.07881
$567$	24.8799	+	53.7334i	1.04486	+	2.25659i
$568$	−55.2102			−2.31657
$569$	−14.8705	−	25.7564i	−0.623403	−	1.07977i	−0.988847	−	0.148933i	$-0.952416\pi$
$569$	−14.8705	−	25.7564i	−0.623403	−	1.07977i	0.365444	−	0.930833i	$-0.380917\pi$
$570$	−15.2799	+	26.4656i	−0.640005	+	1.10852i
$571$	−3.43094	+	5.94256i	−0.143580	+	0.248688i	−0.928842	−	0.370475i	$-0.879195\pi$
$571$	−3.43094	+	5.94256i	−0.143580	+	0.248688i	0.785262	+	0.619164i	$0.212528\pi$
$572$	−1.54779	−	2.68085i	−0.0647163	−	0.112092i
$573$	−13.4627			−0.562411
$574$	−63.6998	−	5.74637i	−2.65878	−	0.239849i
$575$	−5.09800			−0.212601
$576$	45.2891	+	78.4430i	1.88705	+	3.26846i
$577$	8.50664	−	14.7339i	0.354136	−	0.613382i	−0.632834	−	0.774288i	$-0.718108\pi$
$577$	8.50664	−	14.7339i	0.354136	−	0.613382i	0.986970	+	0.160906i	$0.0514416\pi$
$578$	15.9721	−	27.6645i	0.664353	−	1.15069i
$579$	−1.88197	−	3.25967i	−0.0782120	−	0.135467i
$580$	19.6519			0.816001
$581$	8.39147	−	11.9156i	0.348137	−	0.494344i
$582$	113.195			4.69210
$583$	0.979916	+	1.69726i	0.0405840	+	0.0702935i
$584$	25.5797	−	44.3053i	1.05849	−	1.83337i
$585$	−3.64960	+	6.32129i	−0.150892	+	0.261353i
$586$	0.443445	+	0.768069i	0.0183185	+	0.0317286i
$587$	−18.8520			−0.778104			−0.389052	−	0.921216i	$-0.627197\pi$
$587$	−18.8520			−0.778104			−0.389052	+	0.921216i	$0.627197\pi$
$588$	49.9097	−	58.8318i	2.05824	−	2.42618i
$589$	−8.30011			−0.342000
$590$	0.776460	+	1.34487i	0.0319663	+	0.0553673i
$591$	26.2312	−	45.4339i	1.07901	−	1.86890i
$592$	−0.823696	+	1.42668i	−0.0338537	+	0.0586363i
$593$	−14.0049	−	24.2572i	−0.575111	−	0.996122i	−0.996030	−	0.0890232i	$-0.971625\pi$
$593$	−14.0049	−	24.2572i	−0.575111	−	0.996122i	0.420918	−	0.907099i	$-0.361708\pi$
$594$	28.9911			1.18952
$595$	−2.76604	+	3.92770i	−0.113397	+	0.161020i
$596$	16.6860			0.683486
$597$	−13.4638	−	23.3200i	−0.551037	−	0.954424i
$598$	−5.94212	+	10.2921i	−0.242991	+	0.420874i
$599$	2.85373	−	4.94280i	0.116600	−	0.201957i	−0.801818	−	0.597568i	$-0.796134\pi$
$599$	2.85373	−	4.94280i	0.116600	−	0.201957i	0.918418	+	0.395611i	$0.129467\pi$
$600$	5.36515	+	9.29270i	0.219031	+	0.379373i
$601$	−28.6217			−1.16750			−0.583752	−	0.811932i	$-0.698416\pi$
$601$	−28.6217			−1.16750			−0.583752	+	0.811932i	$0.698416\pi$
$602$	−57.6231	−	5.19819i	−2.34854	−	0.211863i
$603$	−104.443			−4.25326
$604$	−2.40733	−	4.16961i	−0.0979528	−	0.169659i
$605$	−5.09376	+	8.82266i	−0.207091	+	0.358692i
$606$	27.8898	−	48.3066i	1.13295	−	1.96232i
$607$	17.2033	+	29.7970i	0.698261	+	1.20942i	0.969069	+	0.246790i	$0.0793759\pi$
$607$	17.2033	+	29.7970i	0.698261	+	1.20942i	−0.270808	+	0.962633i	$0.587291\pi$
$608$	−18.5002			−0.750284
$609$	20.4147	+	44.0898i	0.827244	+	1.78661i
$610$	10.9888			0.444924
$611$	−6.32232	−	10.9506i	−0.255774	−	0.443013i
$612$	−22.7578	+	39.4177i	−0.919931	+	1.59337i
$613$	15.5342	−	26.9060i	0.627420	−	1.08672i	−0.360647	−	0.932702i	$-0.617444\pi$
$613$	15.5342	−	26.9060i	0.627420	−	1.08672i	0.988067	−	0.154022i	$-0.0492225\pi$
$614$	1.21255	+	2.10019i	0.0489344	+	0.0847569i
$615$	33.2797			1.34197
$616$	−3.35033	−	7.23575i	−0.134989	−	0.291537i
$617$	20.0335			0.806518			0.403259	−	0.915086i	$-0.367877\pi$
$617$	20.0335			0.806518			0.403259	+	0.915086i	$0.367877\pi$
$618$	−51.4541	−	89.1210i	−2.06979	−	3.58497i
$619$	−10.8958	+	18.8721i	−0.437941	+	0.758536i	−0.997531	−	0.0702342i	$-0.977625\pi$
$619$	−10.8958	+	18.8721i	−0.437941	+	0.758536i	0.559590	+	0.828770i	$0.310959\pi$
$620$	−3.48910	+	6.04330i	−0.140126	+	0.242705i
$621$	−35.1690	−	60.9144i	−1.41128	−	2.44441i
$622$	−41.7552			−1.67423
$623$	−4.34191	−	0.391685i	−0.173955	−	0.0156925i
$624$	2.97107			0.118938
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−12.1224	+	20.9967i	−0.484510	+	0.839195i
$627$	−5.90818	+	10.2333i	−0.235950	+	0.408677i
$628$	12.8101	+	22.1878i	0.511181	+	0.885391i
$629$	3.23098			0.128828
$630$	−25.9213	+	36.8076i	−1.03273	+	1.46645i
$631$	−23.5386			−0.937057			−0.468529	−	0.883448i	$-0.655216\pi$
$631$	−23.5386			−0.937057			−0.468529	+	0.883448i	$0.655216\pi$
$632$	6.51064	+	11.2768i	0.258979	+	0.448566i
$633$	27.6623	−	47.9126i	1.09948	−	1.90435i
$634$	11.8129	−	20.4605i	0.469150	−	0.812592i
$635$	2.86904	+	4.96932i	0.113854	+	0.197201i
$636$	−23.9637			−0.950223
$637$	2.35858	+	6.59068i	0.0934504	+	0.261132i
$638$	12.0238			0.476028
$639$	60.2636	+	104.380i	2.38399	+	4.12919i
$640$	−9.93507	+	17.2080i	−0.392718	+	0.680208i
$641$	−12.0378	+	20.8501i	−0.475465	+	0.823529i	−0.999605	−	0.0281029i	$-0.991053\pi$
$641$	−12.0378	+	20.8501i	−0.475465	+	0.823529i	0.524140	+	0.851632i	$0.324387\pi$
$642$	−12.6265	−	21.8698i	−0.498329	−	0.863132i
$643$	8.34273			0.329005			0.164503	−	0.986377i	$-0.447398\pi$
$643$	8.34273			0.329005			0.164503	+	0.986377i	$0.447398\pi$
$644$	−26.6715	+	37.8728i	−1.05101	+	1.49240i
$645$	30.1049			1.18538
$646$	−8.64504	−	14.9736i	−0.340135	−	0.589130i
$647$	−10.5292	+	18.2372i	−0.413947	+	0.716978i	−0.995317	−	0.0966616i	$-0.969184\pi$
$647$	−10.5292	+	18.2372i	−0.413947	+	0.716978i	0.581370	+	0.813639i	$0.302517\pi$
$648$	−37.4157	+	64.8059i	−1.46983	+	2.54582i
$649$	0.300228	+	0.520011i	0.0117850	+	0.0204122i
$650$	−2.33116			−0.0914355
$651$	−17.1829	−	1.55008i	−0.673452	−	0.0607523i
$652$	−14.7938			−0.579370
$653$	3.47340	+	6.01610i	0.135924	+	0.235428i	0.925950	−	0.377646i	$-0.123266\pi$
$653$	3.47340	+	6.01610i	0.135924	+	0.235428i	−0.790026	+	0.613074i	$0.789933\pi$
$654$	−45.3020	+	78.4653i	−1.77145	+	3.06824i
$655$	5.22618	−	9.05200i	0.204204	−	0.353691i
$656$	−4.80019	−	8.31417i	−0.187416	−	0.324614i
$657$	−111.684			−4.35720
$658$	−32.7681	−	70.7697i	−1.27743	−	2.75889i
$659$	47.5865			1.85371			0.926853	−	0.375425i	$-0.122503\pi$
$659$	47.5865			1.85371			0.926853	+	0.375425i	$0.122503\pi$
$660$	4.96722	+	8.60348i	0.193349	+	0.334890i
$661$	−23.5828	+	40.8466i	−0.917264	+	1.58875i	−0.113711	+	0.993514i	$0.536274\pi$
$661$	−23.5828	+	40.8466i	−0.917264	+	1.58875i	−0.803553	+	0.595234i	$0.797060\pi$
$662$	−11.3264	+	19.6179i	−0.440214	+	0.762472i
$663$	−2.91353	−	5.04638i	−0.113152	−	0.195985i
$664$	18.4178			0.714748
$665$	−4.54099	−	9.80725i	−0.176092	−	0.380309i
$666$	30.2784			1.17326
$667$	−14.5860	−	25.2637i	−0.564773	−	0.978216i
$668$	27.4599	−	47.5620i	1.06246	−	1.84023i
$669$	−0.0997868	+	0.172836i	−0.00385798	+	0.00668222i
$670$	−16.6781	−	28.8873i	−0.644331	−	1.11601i
$671$	4.24897			0.164030
$672$	−38.2993	−	3.45499i	−1.47743	−	0.133279i
$673$	16.4016			0.632235			0.316118	−	0.948720i	$-0.397621\pi$
$673$	16.4016			0.632235			0.316118	+	0.948720i	$0.397621\pi$
$674$	−12.3204	−	21.3396i	−0.474566	−	0.821972i
$675$	6.89858	−	11.9487i	0.265526	−	0.459905i
$676$	−1.71715	+	2.97419i	−0.0660441	+	0.114392i
$677$	7.35487	+	12.7390i	0.282671	+	0.489600i	0.972042	−	0.234808i	$-0.0754463\pi$
$677$	7.35487	+	12.7390i	0.282671	+	0.489600i	−0.689371	+	0.724409i	$0.742113\pi$
$678$	−42.9535			−1.64962
$679$	−23.0497	+	32.7300i	−0.884568	+	1.25606i
$680$	−6.07096			−0.232811
$681$	11.8727	+	20.5641i	0.454963	+	0.788019i
$682$	−2.13477	+	3.69754i	−0.0817448	+	0.141586i
$683$	9.91744	−	17.1775i	0.379480	−	0.657279i	−0.611507	−	0.791239i	$-0.709436\pi$
$683$	9.91744	−	17.1775i	0.379480	−	0.657279i	0.990987	+	0.133960i	$0.0427695\pi$
$684$	−51.1989	−	88.6790i	−1.95764	−	3.39073i
$685$	4.38678			0.167610
$686$	10.8360	+	41.7917i	0.413719	+	1.59561i
$687$	−16.6616			−0.635681
$688$	−4.34227	−	7.52103i	−0.165547	−	0.286736i
$689$	1.08714	−	1.88298i	0.0414167	−	0.0717358i
$690$	19.0697	−	33.0296i	0.725970	−	1.25742i
$691$	2.21156	+	3.83054i	0.0841319	+	0.145721i	0.905021	−	0.425367i	$-0.139855\pi$
$691$	2.21156	+	3.83054i	0.0841319	+	0.145721i	−0.820889	+	0.571088i	$0.806522\pi$
$692$	16.3187			0.620343
$693$	−10.0228	+	14.2321i	−0.380735	+	0.540633i
$694$	−45.4240			−1.72427
$695$	−9.43458	−	16.3412i	−0.357874	−	0.619856i
$696$	−30.7007	+	53.1752i	−1.16371	+	2.01560i
$697$	−9.41446	+	16.3063i	−0.356598	+	0.617646i
$698$	−14.8639	−	25.7450i	−0.562605	−	0.974461i
$699$	1.57913			0.0597283
$700$	−9.04954	−	0.816361i	−0.342040	−	0.0308556i
$701$	17.4977			0.660879			0.330439	−	0.943827i	$-0.392803\pi$
$701$	17.4977			0.660879			0.330439	+	0.943827i	$0.392803\pi$
$702$	−16.0817	−	27.8543i	−0.606964	−	1.05129i
$703$	−3.63441	+	6.29498i	−0.137074	+	0.237420i
$704$	−5.59271	+	9.68686i	−0.210783	+	0.365087i
$705$	20.2898	+	35.1430i	0.764159	+	1.32356i
$706$	75.0772			2.82557
$707$	8.28849	+	17.9008i	0.311721	+	0.673228i
$708$	−7.34204			−0.275931
$709$	−6.13499	−	10.6261i	−0.230404	−	0.399072i	0.727523	−	0.686084i	$-0.240672\pi$
$709$	−6.13499	−	10.6261i	−0.230404	−	0.399072i	−0.957927	+	0.287011i	$0.907338\pi$
$710$	−19.2465	+	33.3359i	−0.722308	+	1.25107i
$711$	14.2131	−	24.6179i	0.533034	−	0.923242i
$712$	−2.75468	−	4.77125i	−0.103236	−	0.178810i
$713$	10.3587			0.387937
$714$	−15.1006	−	32.6130i	−0.565126	−	1.22051i
$715$	−0.901372			−0.0337094
$716$	−39.8559	−	69.0324i	−1.48948	−	2.57986i
$717$	40.5659	−	70.2621i	1.51496	−	2.62399i
$718$	39.1146	−	67.7484i	1.45974	−	2.52835i
$719$	−4.30624	−	7.45863i	−0.160596	−	0.278160i	0.774487	−	0.632590i	$-0.218008\pi$
$719$	−4.30624	−	7.45863i	−0.160596	−	0.278160i	−0.935082	+	0.354430i	$0.884675\pi$
$720$	−6.75750			−0.251837
$721$	36.2464	+	3.26980i	1.34989	+	0.121774i
$722$	−5.39405			−0.200746
$723$	22.2998	+	38.6243i	0.829338	+	1.43646i
$724$	−3.50322	+	6.06776i	−0.130196	+	0.225507i
$725$	2.86113	−	4.95562i	0.106260	−	0.184047i
$726$	−38.1077	−	66.0044i	−1.41431	−	2.44965i
$727$	−32.1671			−1.19301			−0.596506	−	0.802608i	$-0.703445\pi$
$727$	−32.1671			−1.19301			−0.596506	+	0.802608i	$0.703445\pi$
$728$	−5.09354	+	7.23269i	−0.188779	+	0.268061i
$729$	30.5265			1.13061
$730$	−17.8343	−	30.8900i	−0.660078	−	1.14329i
$731$	−8.51635	+	14.7508i	−0.314989	+	0.545576i
$732$	−25.9770	+	44.9934i	−0.960137	+	1.66301i
$733$	−5.09483	−	8.82451i	−0.188182	−	0.325941i	0.756462	−	0.654037i	$-0.226926\pi$
$733$	−5.09483	−	8.82451i	−0.188182	−	0.325941i	−0.944644	+	0.328097i	$0.893593\pi$
$734$	−9.32603			−0.344230
$735$	−7.56925	−	21.1511i	−0.279196	−	0.780169i
$736$	23.0887			0.851062
$737$	−6.44880	−	11.1696i	−0.237545	−	0.411439i
$738$	−88.2255	+	152.811i	−3.24763	+	5.62505i
$739$	−5.10193	+	8.83680i	−0.187677	+	0.325067i	−0.944475	−	0.328582i	$-0.893429\pi$
$739$	−5.10193	+	8.83680i	−0.187677	+	0.325067i	0.756798	+	0.653649i	$0.226763\pi$
$740$	3.05558	+	5.29242i	0.112325	+	0.194553i
$741$	13.1093			0.481582
$742$	7.72141	−	10.9642i	0.283462	−	0.402508i
$743$	1.13749			0.0417304			0.0208652	−	0.999782i	$-0.493358\pi$
$743$	1.13749			0.0417304			0.0208652	+	0.999782i	$0.493358\pi$
$744$	−10.9015	−	18.8820i	−0.399670	−	0.692249i
$745$	2.42932	−	4.20771i	0.0890035	−	0.154159i
$746$	−4.39040	+	7.60439i	−0.160744	+	0.278416i
$747$	−20.1036	−	34.8204i	−0.735551	−	1.27401i
$748$	−5.62069			−0.205513
$749$	8.89467	+	0.802390i	0.325004	+	0.0293187i
$750$	7.48124			0.273176
$751$	−4.92844	−	8.53631i	−0.179841	−	0.311495i	0.761985	−	0.647595i	$-0.224225\pi$
$751$	−4.92844	−	8.53631i	−0.179841	−	0.311495i	−0.941826	+	0.336101i	$0.890892\pi$
$752$	5.85311	−	10.1379i	0.213441	−	0.369691i
$753$	15.1765	−	26.2865i	0.553063	−	0.957934i
$754$	−6.66974	−	11.5523i	−0.242897	−	0.420711i
$755$	−1.40193			−0.0510216
$756$	−52.6745	−	113.762i	−1.91575	−	4.13748i
$757$	17.9256			0.651517			0.325759	−	0.945453i	$-0.394380\pi$
$757$	17.9256			0.651517			0.325759	+	0.945453i	$0.394380\pi$
$758$	23.6985	+	41.0470i	0.860768	+	1.49089i
$759$	7.37354	−	12.7713i	0.267642	−	0.463570i
$760$	6.82900	−	11.8282i	0.247714	−	0.429053i
$761$	−12.9813	−	22.4843i	−0.470573	−	0.815056i	0.528861	−	0.848708i	$-0.322619\pi$
$761$	−12.9813	−	22.4843i	−0.470573	−	0.815056i	−0.999434	+	0.0336528i	$0.989286\pi$
$762$	−42.9279			−1.55511
$763$	−13.4632	−	29.0766i	−0.487399	−	1.05264i
$764$	14.4068			0.521219
$765$	6.62664	+	11.4777i	0.239587	+	0.414976i
$766$	11.0789	−	19.1892i	0.400297	−	0.693335i
$767$	0.333079	−	0.576910i	0.0120268	−	0.0208310i
$768$	−34.5021	−	59.7594i	−1.24499	−	2.15638i
$769$	10.9599			0.395224			0.197612	−	0.980280i	$-0.436681\pi$
$769$	10.9599			0.395224			0.197612	+	0.980280i	$0.436681\pi$
$770$	−5.53688	−	0.499483i	−0.199535	−	0.0180001i
$771$	29.8293			1.07428
$772$	2.01395	+	3.48826i	0.0724835	+	0.125545i
$773$	8.18958	−	14.1848i	0.294559	−	0.510191i	−0.680323	−	0.732912i	$-0.738161\pi$
$773$	8.18958	−	14.1848i	0.294559	−	0.510191i	0.974882	+	0.222721i	$0.0714940\pi$
$774$	−79.8092	+	138.234i	−2.86868	+	4.96870i
$775$	1.01596	+	1.75969i	0.0364943	+	0.0632101i
$776$	−50.5901			−1.81608
$777$	−8.69958	+	12.3532i	−0.312096	+	0.443167i
$778$	34.1708			1.22508
$779$	−21.1799	−	36.6847i	−0.758850	−	1.31437i
$780$	5.51073	−	9.54487i	0.197316	−	0.341761i
$781$	−7.44190	+	12.8898i	−0.266292	+	0.461232i
$782$	10.7892	+	18.6875i	0.385821	+	0.668262i
$783$	78.9508			2.82147
$784$	−4.19234	+	4.94179i	−0.149726	+	0.176492i
$785$	7.46013			0.266264
$786$	39.0983	+	67.7202i	1.39459	+	2.41550i
$787$	14.7390	−	25.5287i	0.525388	−	0.909999i	−0.474175	−	0.880431i	$-0.657253\pi$
$787$	14.7390	−	25.5287i	0.525388	−	0.909999i	0.999563	−	0.0295681i	$-0.00941319\pi$
$788$	−28.0708	+	48.6200i	−0.999980	+	1.73202i
$789$	−34.7382	−	60.1682i	−1.23671	−	2.14205i
$790$	9.07854			0.323000
$791$	8.74653	−	12.4198i	0.310991	−	0.441598i
$792$	−21.9983			−0.781676
$793$	−2.35694	−	4.08235i	−0.0836975	−	0.144968i
$794$	17.3751	−	30.0946i	0.616619	−	1.06802i
$795$	−3.48888	+	6.04292i	−0.123738	+	0.214320i
$796$	14.4080	+	24.9554i	0.510678	+	0.884520i
$797$	−0.809099			−0.0286598			−0.0143299	−	0.999897i	$-0.504561\pi$
$797$	−0.809099			−0.0286598			−0.0143299	+	0.999897i	$0.504561\pi$
$798$	80.5267	+	7.26433i	2.85061	+	0.257155i
$799$	−22.9591			−0.812233
$800$	2.26449	+	3.92221i	0.0800617	+	0.138671i
$801$	−6.01364	+	10.4159i	−0.212482	+	0.368029i
$802$	−23.9252	+	41.4397i	−0.844830	+	1.46329i
$803$	−6.89587	−	11.9440i	−0.243350	−	0.421495i
$804$	157.704			5.56181
$805$	5.66726	+	12.2397i	0.199745	+	0.431392i
$806$	4.73672			0.166844
$807$	14.3737	+	24.8960i	0.505979	+	0.876382i
$808$	−12.4647	+	21.5895i	−0.438507	+	0.759516i
$809$	1.67445	−	2.90023i	0.0588705	−	0.101967i	−0.835088	−	0.550116i	$-0.814583\pi$
$809$	1.67445	−	2.90023i	0.0588705	−	0.101967i	0.893959	+	0.448150i	$0.147917\pi$
$810$	26.0865	+	45.1832i	0.916587	+	1.58757i
$811$	−38.7624			−1.36113			−0.680566	−	0.732687i	$-0.738266\pi$
$811$	−38.7624			−1.36113			−0.680566	+	0.732687i	$0.738266\pi$
$812$	−21.8463	−	47.1818i	−0.766655	−	1.65576i
$813$	77.5875			2.72111
$814$	1.86953	+	3.23812i	0.0655269	+	0.113496i
$815$	−2.15383	+	3.73055i	−0.0754455	+	0.130675i
$816$	2.69731	−	4.67187i	0.0944247	−	0.163548i
$817$	−19.1595	−	33.1852i	−0.670305	−	1.16100i
$818$	59.3306			2.07445
$819$	19.2338	+	1.73508i	0.672082	+	0.0606287i
$820$	−35.6135			−1.24368
$821$	−0.820826	−	1.42171i	−0.0286470	−	0.0496181i	0.851346	−	0.524604i	$-0.175787\pi$
$821$	−0.820826	−	1.42171i	−0.0286470	−	0.0496181i	−0.879993	+	0.474986i	$0.842453\pi$
$822$	−16.4093	+	28.4217i	−0.572339	+	0.991320i
$823$	−4.64213	+	8.04040i	−0.161814	+	0.280271i	−0.935519	−	0.353275i	$-0.885068\pi$
$823$	−4.64213	+	8.04040i	−0.161814	+	0.280271i	0.773705	+	0.633546i	$0.218401\pi$
$824$	22.9962	+	39.8306i	0.801110	+	1.38756i
$825$	2.89272			0.100711
$826$	2.36570	−	3.35922i	0.0823132	−	0.116882i
$827$	−50.0529			−1.74051			−0.870254	−	0.492602i	$-0.836046\pi$
$827$	−50.0529			−1.74051			−0.870254	+	0.492602i	$0.836046\pi$
$828$	63.8973	+	110.673i	2.22059	+	3.84617i
$829$	7.06768	−	12.2416i	0.245471	−	0.425168i	−0.716793	−	0.697286i	$-0.754391\pi$
$829$	7.06768	−	12.2416i	0.245471	−	0.425168i	0.962264	+	0.272118i	$0.0877242\pi$
$830$	6.42050	−	11.1206i	0.222859	−	0.386003i
$831$	26.7947	+	46.4097i	0.929497	+	1.60994i
$832$	12.4093			0.430216
$833$	12.5048	+	2.27464i	0.433266	+	0.0788115i
$834$	141.165			4.88813
$835$	−7.99580	−	13.8491i	−0.276706	−	0.479269i
$836$	6.32250	−	10.9509i	0.218668	−	0.378745i
$837$	−14.0174	+	24.2788i	−0.484511	+	0.839197i
$838$	25.9998	+	45.0330i	0.898149	+	1.55564i
$839$	−50.7636			−1.75255			−0.876276	−	0.481809i	$-0.839980\pi$
$839$	−50.7636			−1.75255			−0.876276	+	0.481809i	$0.839980\pi$
$840$	16.3464	−	23.2114i	0.564004	−	0.800870i
$841$	3.74418			0.129110
$842$	29.4450	+	51.0003i	1.01474	+	1.75759i
$843$	1.51775	−	2.62882i	0.0522740	−	0.0905413i
$844$	−29.6022	+	51.2726i	−1.01895	+	1.76487i
$845$	0.500000	+	0.866025i	0.0172005	+	0.0297922i
$846$	−215.156			−7.39721
$847$	26.8447	+	2.42166i	0.922393	+	0.0832094i
$848$	2.01292			0.0691238
$849$	34.0427	+	58.9637i	1.16834	+	2.02363i
$850$	−2.11636	+	3.66564i	−0.0725905	+	0.125730i
$851$	4.53582	−	7.85628i	0.155486	−	0.269310i
$852$	−90.9953	−	157.609i	−3.11745	−	5.39958i
$853$	21.4362			0.733962			0.366981	−	0.930228i	$-0.380391\pi$
$853$	21.4362			0.733962			0.366981	+	0.930228i	$0.380391\pi$
$854$	−12.2159	−	26.3828i	−0.418018	−	0.902800i
$855$	−29.8162			−1.01969
$856$	5.64313	+	9.77419i	0.192878	+	0.334075i
$857$	0.436493	−	0.756028i	0.0149103	−	0.0258254i	−0.858474	−	0.512857i	$-0.828587\pi$
$857$	0.436493	−	0.756028i	0.0149103	−	0.0258254i	0.873384	+	0.487032i	$0.161920\pi$
$858$	3.37169	−	5.83994i	0.115108	−	0.199372i
$859$	16.0962	+	27.8794i	0.549195	+	0.951234i	0.998330	+	0.0577698i	$0.0183989\pi$
$859$	16.0962	+	27.8794i	0.549195	+	0.951234i	−0.449135	+	0.893464i	$0.648268\pi$
$860$	−32.2161			−1.09856
$861$	−36.9958	−	79.9004i	−1.26081	−	2.72300i
$862$	−51.5481			−1.75574
$863$	−14.5939	−	25.2774i	−0.496782	−	0.860452i	0.503211	−	0.864164i	$-0.332152\pi$
$863$	−14.5939	−	25.2774i	−0.496782	−	0.860452i	−0.999993	+	0.00371138i	$0.998819\pi$
$864$	−31.2435	+	54.1153i	−1.06293	+	1.84104i
$865$	2.37584	−	4.11508i	0.0807811	−	0.139917i
$866$	27.5727	+	47.7574i	0.936959	+	1.62286i
$867$	43.9767			1.49353
$868$	18.3879	+	1.65878i	0.624127	+	0.0563027i
$869$	3.51033			0.119080
$870$	21.4048	+	37.0741i	0.725689	+	1.25693i
$871$	−7.15443	+	12.3918i	−0.242418	+	0.419881i
$872$	20.2467	−	35.0682i	0.685638	−	1.18756i
$873$	55.2206	+	95.6449i	1.86893	+	3.23709i
$874$	−48.5455			−1.64208
$875$	−1.52339	+	2.16317i	−0.0514999	+	0.0731284i
$876$	168.638			5.69774
$877$	−22.3034	−	38.6307i	−0.753133	−	1.30446i	−0.946297	−	0.323298i	$-0.895208\pi$
$877$	−22.3034	−	38.6307i	−0.753133	−	1.30446i	0.193164	−	0.981166i	$-0.438125\pi$
$878$	−18.2654	+	31.6365i	−0.616426	+	1.06768i
$879$	−0.610478	+	1.05738i	−0.0205909	+	0.0356645i
$880$	−0.417239	−	0.722679i	−0.0140651	−	0.0243615i
$881$	−12.5678			−0.423421			−0.211711	−	0.977332i	$-0.567903\pi$
$881$	−12.5678			−0.423421			−0.211711	+	0.977332i	$0.567903\pi$
$882$	117.186	+	21.3163i	3.94586	+	0.717756i
$883$	−29.7736			−1.00196			−0.500981	−	0.865458i	$-0.667027\pi$
$883$	−29.7736			−1.00196			−0.500981	+	0.865458i	$0.667027\pi$
$884$	3.11785	+	5.40028i	0.104865	+	0.181631i
$885$	−1.06893	+	1.85144i	−0.0359317	+	0.0622355i
$886$	4.63574	−	8.02935i	0.155741	−	0.269751i
$887$	14.7932	+	25.6226i	0.496708	+	0.860324i	0.999993	−	0.00379670i	$-0.00120853\pi$
$887$	14.7932	+	25.6226i	0.496708	+	0.860324i	−0.503284	+	0.864121i	$0.667875\pi$
$888$	−19.0940			−0.640754
$889$	8.74131	−	12.4124i	0.293174	−	0.416299i
$890$	−3.84117			−0.128756
$891$	10.0867	+	17.4707i	0.337917	+	0.585289i
$892$	0.106785	−	0.184956i	0.00357541	−	0.00619280i
$893$	25.8258	−	44.7316i	0.864227	−	1.49689i
$894$	18.1743	+	31.4789i	0.607841	+	1.05281i
$895$	−23.2105			−0.775843
$896$	52.3588	+	4.72330i	1.74919	+	0.157795i
$897$	−16.3607			−0.546268
$898$	−27.9513	−	48.4131i	−0.932747	−	1.61556i
$899$	−5.81358	+	10.0694i	−0.193894	+	0.335834i
$900$	−12.5338	+	21.7092i	−0.417793	+	0.723639i
$901$	−1.97393	−	3.41895i	−0.0657613	−	0.113902i
$902$	−21.7898			−0.725521
$903$	−33.4666	−	72.2782i	−1.11370	−	2.40527i
$904$	19.1971			0.638485
$905$	1.02007	+	1.76681i	0.0339083	+	0.0587309i
$906$	5.24410	−	9.08305i	0.174224	−	0.301764i
$907$	15.4069	−	26.6855i	0.511577	−	0.886077i	−0.488333	−	0.872657i	$-0.662395\pi$
$907$	15.4069	−	26.6855i	0.511577	−	0.886077i	0.999910	−	0.0134199i	$-0.00427181\pi$
$908$	−12.7053	−	22.0062i	−0.421640	−	0.730303i
$909$	54.4224			1.80508
$910$	2.59146	+	5.59682i	0.0859062	+	0.185533i
$911$	10.3932			0.344344			0.172172	−	0.985067i	$-0.444922\pi$
$911$	10.3932			0.344344			0.172172	+	0.985067i	$0.444922\pi$
$912$	6.06820	+	10.5104i	0.200938	+	0.348035i
$913$	2.48257	−	4.29994i	0.0821611	−	0.142307i
$914$	43.1550	−	74.7466i	1.42744	−	2.47240i
$915$	7.56399	+	13.1012i	0.250058	+	0.433113i
$916$	17.8301			0.589122
$917$	−27.5425	−	2.48462i	−0.909533	−	0.0820492i
$918$	−58.3995			−1.92747
$919$	24.5383	+	42.5017i	0.809445	+	1.40200i	0.913249	+	0.407403i	$0.133565\pi$
$919$	24.5383	+	42.5017i	0.809445	+	1.40200i	−0.103803	+	0.994598i	$0.533101\pi$
$920$	−8.52275	+	14.7618i	−0.280987	+	0.486683i
$921$	−1.66928	+	2.89128i	−0.0550046	+	0.0952708i
$922$	−1.65232	−	2.86189i	−0.0544161	−	0.0942515i
$923$	16.5124			0.543512
$924$	15.1340	−	21.4899i	0.497872	−	0.706964i
$925$	1.77945			0.0585080
$926$	−14.7847	−	25.6078i	−0.485855	−	0.841525i
$927$	50.2021	−	86.9525i	1.64885	−	2.85590i
$928$	−12.9580	+	22.4439i	−0.425366	+	0.736756i
$929$	10.0942	+	17.4836i	0.331180	+	0.573620i	0.982743	−	0.184974i	$-0.0592201\pi$
$929$	10.0942	+	17.4836i	0.331180	+	0.573620i	−0.651564	+	0.758594i	$0.725887\pi$
$930$	−15.2013			−0.498469
$931$	−18.4979	+	21.8047i	−0.606245	+	0.714621i
$932$	−1.68988			−0.0553537
$933$	−28.7416	−	49.7819i	−0.940958	−	1.62979i
$934$	27.7442	−	48.0544i	0.907819	−	1.57239i
$935$	−0.818318	+	1.41737i	−0.0267619	+	0.0463529i
$936$	12.2027	+	21.1357i	0.398857	+	0.690840i
$937$	30.6186			1.00027			0.500133	−	0.865948i	$-0.333284\pi$
$937$	30.6186			1.00027			0.500133	+	0.865948i	$0.333284\pi$
$938$	−50.8144	+	72.1550i	−1.65915	+	2.35594i
$939$	−33.3772			−1.08922
$940$	−21.7127	−	37.6075i	−0.708190	−	1.22662i
$941$	26.7189	−	46.2785i	0.871012	−	1.50864i	0.0100604	−	0.999949i	$-0.496798\pi$
$941$	26.7189	−	46.2785i	0.871012	−	1.50864i	0.860951	−	0.508687i	$-0.169869\pi$
$942$	−27.9055	+	48.3338i	−0.909211	+	1.57480i
$943$	26.4331	+	45.7834i	0.860779	+	1.49091i
$944$	0.616720			0.0200725
$945$	−36.3562	−	3.27970i	−1.18267	−	0.106689i
$946$	−19.7111			−0.640864
$947$	8.61196	+	14.9163i	0.279851	+	0.484716i	0.971347	−	0.237664i	$-0.0763816\pi$
$947$	8.61196	+	14.9163i	0.279851	+	0.484716i	−0.691497	+	0.722380i	$0.743048\pi$
$948$	−21.4612	+	37.1718i	−0.697026	+	1.20729i
$949$	−7.65042	+	13.2509i	−0.248343	+	0.430143i
$950$	−4.76123	−	8.24669i	−0.154475	−	0.267558i
$951$	32.5249			1.05469
$952$	6.74887	+	14.5756i	0.218732	+	0.472399i
$953$	−3.93429			−0.127444			−0.0637221	−	0.997968i	$-0.520297\pi$
$953$	−3.93429			−0.127444			−0.0637221	+	0.997968i	$0.520297\pi$
$954$	−18.4983	−	32.0400i	−0.598904	−	1.03733i
$955$	2.09749	−	3.63295i	0.0678731	−	0.117560i
$956$	−43.4107	+	75.1895i	−1.40400	+	2.43180i
$957$	8.27643	+	14.3352i	0.267539	+	0.463391i
$958$	96.2584			3.10997
$959$	−4.87663	−	10.5321i	−0.157474	−	0.340100i
$960$	−39.8245			−1.28533
$961$	13.4357	+	23.2712i	0.433408	+	0.750685i
$962$	2.07409	−	3.59243i	0.0668714	−	0.115825i
$963$	12.3193	−	21.3377i	0.396984	−	0.687596i
$964$	−23.8636	−	41.3330i	−0.768595	−	1.33125i
$965$	1.17285			0.0377552
$966$	−100.499	−	9.06606i	−3.23351	−	0.291696i
$967$	48.5386			1.56090			0.780449	−	0.625220i	$-0.214991\pi$
$967$	48.5386			1.56090			0.780449	+	0.625220i	$0.214991\pi$
$968$	17.0313	+	29.4991i	0.547408	+	0.948138i
$969$	11.9014	−	20.6138i	0.382327	−	0.662210i
$970$	−17.6359	+	30.5463i	−0.566254	+	0.980781i
$971$	−10.2831	−	17.8108i	−0.330000	−	0.571577i	0.652511	−	0.757779i	$-0.273715\pi$
$971$	−10.2831	−	17.8108i	−0.330000	−	0.571577i	−0.982511	+	0.186202i	$0.940382\pi$
$972$	−104.518			−3.35242
$973$	−28.7450	+	40.8171i	−0.921524	+	1.30854i
$974$	69.3010			2.22055
$975$	−1.60462	−	2.77928i	−0.0513889	−	0.0890082i
$976$	2.18203	−	3.77938i	0.0698450	−	0.120975i
$977$	−15.2593	+	26.4299i	−0.488188	+	0.845567i	−0.999908	−	0.0135859i	$-0.995675\pi$
$977$	−15.2593	+	26.4299i	−0.488188	+	0.845567i	0.511720	+	0.859153i	$0.329009\pi$
$978$	−16.1133	−	27.9091i	−0.515248	−	0.892435i
$979$	−1.48524			−0.0474684
$980$	8.10006	+	22.6343i	0.258747	+	0.723027i
$981$	−88.3993			−2.82237
$982$	39.2285	+	67.9457i	1.25183	+	2.16823i
$983$	−3.26711	+	5.65881i	−0.104205	+	0.180488i	−0.913413	−	0.407034i	$-0.866563\pi$
$983$	−3.26711	+	5.65881i	−0.104205	+	0.180488i	0.809208	+	0.587522i	$0.199896\pi$
$984$	55.6364	−	96.3650i	1.77362	−	3.07200i
$985$	8.17367	+	14.1572i	0.260435	+	0.451086i
$986$	−24.2207			−0.771344
$987$	61.8185	−	87.7805i	1.96770	−	2.79408i
$988$	−14.0286			−0.446310
$989$	23.9114	+	41.4158i	0.760340	+	1.31695i
$990$	−7.66869	+	13.2826i	−0.243727	+	0.422147i
$991$	−23.6245	+	40.9189i	−0.750458	+	1.29983i	0.197142	+	0.980375i	$0.436834\pi$
$991$	−23.6245	+	40.9189i	−0.750458	+	1.29983i	−0.947601	+	0.319457i	$0.896499\pi$
$992$	−4.60126	−	7.96961i	−0.146090	−	0.253035i
$993$	−31.1855			−0.989642
$994$	101.431	+	9.15011i	3.21719	+	0.290224i
$995$	8.39066			0.266002
$996$	30.3555	+	52.5772i	0.961849	+	1.66597i
$997$	16.5829	−	28.7224i	0.525186	−	0.909648i	−0.474384	−	0.880318i	$-0.657329\pi$
$997$	16.5829	−	28.7224i	0.525186	−	0.909648i	0.999570	−	0.0293303i	$-0.00933746\pi$
$998$	−2.17760	+	3.77171i	−0.0689307	+	0.119391i
$999$	12.2757	+	21.2621i	0.388386	+	0.672704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	455.2.j.g.326.2	yes	20
7.2	even	3	inner	455.2.j.g.261.2	✓	20
7.3	odd	6		3185.2.a.bc.1.9		10
7.4	even	3		3185.2.a.bb.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
455.2.j.g.261.2	✓	20	7.2	even	3	inner
455.2.j.g.326.2	yes	20	1.1	even	1	trivial
3185.2.a.bb.1.9		10	7.4	even	3
3185.2.a.bc.1.9		10	7.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 455 = 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	455.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16558 - 2.01884i) q^{2} +(1.60462 - 2.77928i) q^{3} +(-1.71715 + 2.97419i) q^{4} +(0.500000 + 0.866025i) q^{5} -7.48124 q^{6} +(1.52339 - 2.16317i) q^{7} +3.34356 q^{8} +(-3.64960 - 6.32129i) q^{9} +(1.16558 - 2.01884i) q^{10} +(0.450686 - 0.780611i) q^{11} +(5.51073 + 9.54487i) q^{12} -1.00000 q^{13} +(-6.14272 - 0.554136i) q^{14} +3.20924 q^{15} +(-0.462893 - 0.801755i) q^{16} +(-0.907858 + 1.57246i) q^{17} +(-8.50779 + 14.7359i) q^{18} +(-2.04243 - 3.53760i) q^{19} -3.43429 q^{20} +(-3.56759 - 7.70498i) q^{21} -2.10124 q^{22} +(2.54900 + 4.41500i) q^{23} +(5.36515 - 9.29270i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.16558 + 2.01884i) q^{26} -13.7972 q^{27} +(3.81778 + 8.24531i) q^{28} -5.72225 q^{29} +(-3.74062 - 6.47894i) q^{30} +(1.01596 - 1.75969i) q^{31} +(2.26449 - 3.92221i) q^{32} +(-1.44636 - 2.50517i) q^{33} +4.23272 q^{34} +(2.63505 + 0.237709i) q^{35} +25.0676 q^{36} +(-0.889726 - 1.54105i) q^{37} +(-4.76123 + 8.24669i) q^{38} +(-1.60462 + 2.77928i) q^{39} +(1.67178 + 2.89561i) q^{40} +10.3700 q^{41} +(-11.3968 + 16.1832i) q^{42} +9.38071 q^{43} +(1.54779 + 2.68085i) q^{44} +(3.64960 - 6.32129i) q^{45} +(5.94212 - 10.2921i) q^{46} +(6.32232 + 10.9506i) q^{47} -2.97107 q^{48} +(-2.35858 - 6.59068i) q^{49} +2.33116 q^{50} +(2.91353 + 5.04638i) q^{51} +(1.71715 - 2.97419i) q^{52} +(-1.08714 + 1.88298i) q^{53} +(16.0817 + 27.8543i) q^{54} +0.901372 q^{55} +(5.09354 - 7.23269i) q^{56} -13.1093 q^{57} +(6.66974 + 11.5523i) q^{58} +(-0.333079 + 0.576910i) q^{59} +(-5.51073 + 9.54487i) q^{60} +(2.35694 + 4.08235i) q^{61} -4.73672 q^{62} +(-19.2338 - 1.73508i) q^{63} -12.4093 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-3.37169 + 5.83994i) q^{66} +(7.15443 - 12.3918i) q^{67} +(-3.11785 - 5.40028i) q^{68} +16.3607 q^{69} +(-2.59146 - 5.59682i) q^{70} -16.5124 q^{71} +(-12.2027 - 21.1357i) q^{72} +(7.65042 - 13.2509i) q^{73} +(-2.07409 + 3.59243i) q^{74} +(1.60462 + 2.77928i) q^{75} +14.0286 q^{76} +(-1.00202 - 2.16408i) q^{77} +7.48124 q^{78} +(1.94722 + 3.37268i) q^{79} +(0.462893 - 0.801755i) q^{80} +(-11.1904 + 19.3823i) q^{81} +(-12.0870 - 20.9353i) q^{82} +5.50843 q^{83} +(29.0421 + 2.61990i) q^{84} -1.81572 q^{85} +(-10.9340 - 18.9382i) q^{86} +(-9.18203 + 15.9037i) q^{87} +(1.50690 - 2.61002i) q^{88} +(-0.823877 - 1.42700i) q^{89} -17.0156 q^{90} +(-1.52339 + 2.16317i) q^{91} -17.5080 q^{92} +(-3.26045 - 5.64727i) q^{93} +(14.7383 - 25.5275i) q^{94} +(2.04243 - 3.53760i) q^{95} +(-7.26728 - 12.5873i) q^{96} -15.1306 q^{97} +(-10.5564 + 12.4436i) q^{98} -6.57930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 4 q^{3} - 13 q^{4} + 10 q^{5} - 18 q^{6} + q^{7} - 6 q^{8} - 14 q^{9} - q^{10} - 7 q^{11} + 7 q^{12} - 20 q^{13} + 3 q^{14} + 8 q^{15} - 7 q^{16} + 6 q^{17} + 5 q^{18} + 10 q^{19} - 26 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) \) 20 * q + q^2 + 4 * q^3 - 13 * q^4 + 10 * q^5 - 18 * q^6 + q^7 - 6 * q^8 - 14 * q^9 - q^10 - 7 * q^11 + 7 * q^12 - 20 * q^13 + 3 * q^14 + 8 * q^15 - 7 * q^16 + 6 * q^17 + 5 * q^18 + 10 * q^19 - 26 * q^20 + 16 * q^21 - 22 * q^22 - 7 * q^23 + 20 * q^24 - 10 * q^25 - q^26 - 32 * q^27 + 36 * q^28 + 6 * q^29 - 9 * q^30 + 26 * q^31 + 22 * q^32 + 18 * q^33 - 6 * q^34 + 2 * q^35 + 56 * q^36 + 2 * q^37 - 25 * q^38 - 4 * q^39 - 3 * q^40 - 38 * q^41 + 21 * q^42 - 2 * q^43 - 33 * q^44 + 14 * q^45 + 20 * q^46 + 31 * q^47 - 46 * q^48 - 25 * q^49 - 2 * q^50 - 34 * q^51 + 13 * q^52 + 22 * q^53 + 42 * q^54 - 14 * q^55 + 30 * q^56 - 46 * q^57 + 7 * q^58 - q^59 - 7 * q^60 + 14 * q^61 + 30 * q^62 - 17 * q^63 - 10 * q^64 - 10 * q^65 - 45 * q^66 + 26 * q^67 + 12 * q^68 - 2 * q^69 + 3 * q^70 + 14 * q^71 - 40 * q^72 + 30 * q^73 + 13 * q^74 + 4 * q^75 - 86 * q^76 - 25 * q^77 + 18 * q^78 - 10 * q^79 + 7 * q^80 - 22 * q^81 + 9 * q^82 - 40 * q^83 + 46 * q^84 + 12 * q^85 - 17 * q^86 + 52 * q^88 + q^89 + 10 * q^90 - q^91 + 30 * q^92 + 32 * q^93 + 22 * q^94 - 10 * q^95 - 22 * q^96 - 38 * q^97 - 26 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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