LMFDB - Embedded newform 465.2.i.f.346.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(211,465)] 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("465.211"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 13 x^{12} - 8 x^{11} + 114 x^{10} - 65 x^{9} + 491 x^{8} - 152 x^{7} + 1434 x^{6} + \cdots + 256 $ x^14 - x^13 + 13x^12 - 8x^11 + 114x^10 - 65x^9 + 491x^8 - 152x^7 + 1434x^6 - 552x^5 + 1745x^4 - 480x^3 + 1424x^2 - 512x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			346.1
Root			$-1.29670 + 2.24596i$ of defining polynomial
Character	$\chi$	$=$	465.346
Dual form			465.2.i.f.211.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.59341 q^{2} +(0.500000 - 0.866025i) q^{3} +4.72576 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.29670 + 2.24596i) q^{6} +(2.21228 - 3.83178i) q^{7} -7.06901 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.29670 + 2.24596i) q^{10} +(-0.481621 - 0.834192i) q^{11} +(2.36288 - 4.09263i) q^{12} +(-1.92003 - 3.32558i) q^{13} +(-5.73735 + 9.93738i) q^{14} -1.00000 q^{15} +8.88129 q^{16} +(0.310634 - 0.538033i) q^{17} +(1.29670 + 2.24596i) q^{18} +(-1.40678 + 2.43661i) q^{19} +(-2.36288 - 4.09263i) q^{20} +(-2.21228 - 3.83178i) q^{21} +(1.24904 + 2.16340i) q^{22} +3.94043 q^{23} +(-3.53450 + 6.12194i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(4.97941 + 8.62459i) q^{26} -1.00000 q^{27} +(10.4547 - 18.1081i) q^{28} +3.48987 q^{29} +2.59341 q^{30} +(-2.36544 + 5.04031i) q^{31} -8.89478 q^{32} -0.963242 q^{33} +(-0.805599 + 1.39534i) q^{34} -4.42456 q^{35} +(-2.36288 - 4.09263i) q^{36} +(-4.82190 + 8.35178i) q^{37} +(3.64834 - 6.31912i) q^{38} -3.84005 q^{39} +(3.53450 + 6.12194i) q^{40} +(-1.23956 - 2.14697i) q^{41} +(5.73735 + 9.93738i) q^{42} +(5.02233 - 8.69893i) q^{43} +(-2.27603 - 3.94219i) q^{44} +(-0.500000 + 0.866025i) q^{45} -10.2191 q^{46} -11.0922 q^{47} +(4.44064 - 7.69142i) q^{48} +(-6.28838 - 10.8918i) q^{49} +(1.29670 - 2.24596i) q^{50} +(-0.310634 - 0.538033i) q^{51} +(-9.07359 - 15.7159i) q^{52} +(-6.17742 - 10.6996i) q^{53} +2.59341 q^{54} +(-0.481621 + 0.834192i) q^{55} +(-15.6386 + 27.0869i) q^{56} +(1.40678 + 2.43661i) q^{57} -9.05067 q^{58} +(2.44457 - 4.23411i) q^{59} -4.72576 q^{60} +6.36130 q^{61} +(6.13454 - 13.0716i) q^{62} -4.42456 q^{63} +5.30522 q^{64} +(-1.92003 + 3.32558i) q^{65} +2.49808 q^{66} +(4.94073 + 8.55760i) q^{67} +(1.46798 - 2.54261i) q^{68} +(1.97022 - 3.41252i) q^{69} +11.4747 q^{70} +(-5.50746 - 9.53919i) q^{71} +(3.53450 + 6.12194i) q^{72} +(-5.44509 - 9.43118i) q^{73} +(12.5052 - 21.6596i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-6.64809 + 11.5148i) q^{76} -4.26193 q^{77} +9.95882 q^{78} +(-5.78565 + 10.0210i) q^{79} +(-4.44064 - 7.69142i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.21467 + 5.56798i) q^{82} +(6.44069 + 11.1556i) q^{83} +(-10.4547 - 18.1081i) q^{84} -0.621267 q^{85} +(-13.0249 + 22.5599i) q^{86} +(1.74494 - 3.02232i) q^{87} +(3.40458 + 5.89691i) q^{88} +5.82218 q^{89} +(1.29670 - 2.24596i) q^{90} -16.9906 q^{91} +18.6215 q^{92} +(3.18232 + 4.56868i) q^{93} +28.7665 q^{94} +2.81355 q^{95} +(-4.44739 + 7.70311i) q^{96} +3.81210 q^{97} +(16.3083 + 28.2469i) q^{98} +(-0.481621 + 0.834192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} + 7 q^{3} + 22 q^{4} - 7 q^{5} + q^{6} - 2 q^{7} + 6 q^{8} - 7 q^{9} - q^{10} + 11 q^{12} + 2 q^{13} - 14 q^{14} - 14 q^{15} + 30 q^{16} + 7 q^{17} - q^{18} - 4 q^{19} - 11 q^{20} + 2 q^{21}+ \cdots + 2 q^{98}+O(q^{100}) $ 14 * q + 2 * q^2 + 7 * q^3 + 22 * q^4 - 7 * q^5 + q^6 - 2 * q^7 + 6 * q^8 - 7 * q^9 - q^10 + 11 * q^12 + 2 * q^13 - 14 * q^14 - 14 * q^15 + 30 * q^16 + 7 * q^17 - q^18 - 4 * q^19 - 11 * q^20 + 2 * q^21 - 2 * q^22 - 22 * q^23 + 3 * q^24 - 7 * q^25 + 9 * q^26 - 14 * q^27 + 11 * q^28 - 32 * q^29 - 2 * q^30 + 15 * q^31 + 24 * q^32 - 6 * q^34 + 4 * q^35 - 11 * q^36 - 5 * q^37 - 4 * q^38 + 4 * q^39 - 3 * q^40 - 5 * q^41 + 14 * q^42 + 17 * q^43 - 18 * q^44 - 7 * q^45 - 60 * q^46 - 6 * q^47 + 15 * q^48 - 21 * q^49 - q^50 - 7 * q^51 + 3 * q^52 - 7 * q^53 - 2 * q^54 - 62 * q^56 + 4 * q^57 - 20 * q^58 + 6 * q^59 - 22 * q^60 + 36 * q^61 + 55 * q^62 + 4 * q^63 + 42 * q^64 + 2 * q^65 - 4 * q^66 + 7 * q^68 - 11 * q^69 + 28 * q^70 - 6 * q^71 - 3 * q^72 - 14 * q^73 - 18 * q^74 + 7 * q^75 - 8 * q^76 - 4 * q^77 + 18 * q^78 + 6 * q^79 - 15 * q^80 - 7 * q^81 + 12 * q^82 - q^83 - 11 * q^84 - 14 * q^85 - 53 * q^86 - 16 * q^87 - 21 * q^88 + 40 * q^89 - q^90 - 94 * q^91 + 46 * q^92 + 27 * q^93 + 104 * q^94 + 8 * q^95 + 12 * q^96 + 40 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.59341			−1.83382			−0.916908	−	0.399099i	$-0.869323\pi$
$2$	−2.59341			−1.83382			−0.916908	+	0.399099i	$0.869323\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	4.72576			2.36288
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.29670	+	2.24596i	−0.529377	+	0.916908i
$7$	2.21228	−	3.83178i	0.836164	−	1.44828i	−0.0569153	−	0.998379i	$-0.518127\pi$
$7$	2.21228	−	3.83178i	0.836164	−	1.44828i	0.893079	−	0.449899i	$-0.148540\pi$
$8$	−7.06901			−2.49927
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.29670	+	2.24596i	0.410054	+	0.710234i
$11$	−0.481621	−	0.834192i	−0.145214	−	0.251518i	0.784239	−	0.620459i	$-0.213054\pi$
$11$	−0.481621	−	0.834192i	−0.145214	−	0.251518i	−0.929453	+	0.368941i	$0.879720\pi$
$12$	2.36288	−	4.09263i	0.682105	−	1.18144i
$13$	−1.92003	−	3.32558i	−0.532520	−	0.922351i	−0.999279	−	0.0379668i	$-0.987912\pi$
$13$	−1.92003	−	3.32558i	−0.532520	−	0.922351i	0.466759	−	0.884384i	$-0.345421\pi$
$14$	−5.73735	+	9.93738i	−1.53337	+	2.65588i
$15$	−1.00000			−0.258199
$16$	8.88129			2.22032
$17$	0.310634	−	0.538033i	0.0753397	−	0.130492i	−0.825894	−	0.563825i	$-0.809329\pi$
$17$	0.310634	−	0.538033i	0.0753397	−	0.130492i	0.901234	+	0.433333i	$0.142663\pi$
$18$	1.29670	+	2.24596i	0.305636	+	0.529377i
$19$	−1.40678	+	2.43661i	−0.322737	+	0.558996i	−0.981052	−	0.193746i	$-0.937936\pi$
$19$	−1.40678	+	2.43661i	−0.322737	+	0.558996i	0.658315	+	0.752742i	$0.271269\pi$
$20$	−2.36288	−	4.09263i	−0.528356	−	0.915139i
$21$	−2.21228	−	3.83178i	−0.482759	−	0.836164i
$22$	1.24904	+	2.16340i	0.266296	+	0.461238i
$23$	3.94043			0.821637			0.410819	−	0.911717i	$-0.365243\pi$
$23$	3.94043			0.821637			0.410819	+	0.911717i	$0.365243\pi$
$24$	−3.53450	+	6.12194i	−0.721477	+	1.24964i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.97941	+	8.62459i	0.976543	+	1.69142i
$27$	−1.00000			−0.192450
$28$	10.4547	−	18.1081i	1.97575	−	3.42211i
$29$	3.48987			0.648053			0.324027	−	0.946048i	$-0.394963\pi$
$29$	3.48987			0.648053			0.324027	+	0.946048i	$0.394963\pi$
$30$	2.59341			0.473489
$31$	−2.36544	+	5.04031i	−0.424845	+	0.905266i
$31$	−2.36544	+	5.04031i	−0.424845	+	0.905266i
$32$	−8.89478			−1.57239
$33$	−0.963242			−0.167679
$34$	−0.805599	+	1.39534i	−0.138159	+	0.239299i
$35$	−4.42456			−0.747888
$36$	−2.36288	−	4.09263i	−0.393813	−	0.682105i
$37$	−4.82190	+	8.35178i	−0.792716	+	1.37302i	0.131564	+	0.991308i	$0.458000\pi$
$37$	−4.82190	+	8.35178i	−0.792716	+	1.37302i	−0.924279	+	0.381716i	$0.875333\pi$
$38$	3.64834	−	6.31912i	0.591839	−	1.02510i
$39$	−3.84005			−0.614901
$40$	3.53450	+	6.12194i	0.558854	+	0.967963i
$41$	−1.23956	−	2.14697i	−0.193586	−	0.335301i	0.752850	−	0.658192i	$-0.228679\pi$
$41$	−1.23956	−	2.14697i	−0.193586	−	0.335301i	−0.946436	+	0.322891i	$0.895345\pi$
$42$	5.73735	+	9.93738i	0.885292	+	1.53337i
$43$	5.02233	−	8.69893i	0.765898	−	1.32657i	−0.173872	−	0.984768i	$-0.555628\pi$
$43$	5.02233	−	8.69893i	0.765898	−	1.32657i	0.939770	−	0.341806i	$-0.111039\pi$
$44$	−2.27603	−	3.94219i	−0.343124	−	0.594308i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−10.2191			−1.50673
$47$	−11.0922			−1.61796			−0.808980	−	0.587836i	$-0.799980\pi$
$47$	−11.0922			−1.61796			−0.808980	+	0.587836i	$0.799980\pi$
$48$	4.44064	−	7.69142i	0.640952	−	1.11016i
$49$	−6.28838	−	10.8918i	−0.898340	−	1.55597i
$50$	1.29670	−	2.24596i	0.183382	−	0.317626i
$51$	−0.310634	−	0.538033i	−0.0434974	−	0.0753397i
$52$	−9.07359	−	15.7159i	−1.25828	−	2.17941i
$53$	−6.17742	−	10.6996i	−0.848534	−	1.46970i	−0.882517	−	0.470281i	$-0.844153\pi$
$53$	−6.17742	−	10.6996i	−0.848534	−	1.46970i	0.0339834	−	0.999422i	$-0.489181\pi$
$54$	2.59341			0.352918
$55$	−0.481621	+	0.834192i	−0.0649418	+	0.112482i
$56$	−15.6386	+	27.0869i	−2.08980	+	3.61964i
$57$	1.40678	+	2.43661i	0.186332	+	0.322737i
$58$	−9.05067			−1.18841
$59$	2.44457	−	4.23411i	0.318255	−	0.551235i	−0.661869	−	0.749620i	$-0.730236\pi$
$59$	2.44457	−	4.23411i	0.318255	−	0.551235i	0.980124	+	0.198385i	$0.0635697\pi$
$60$	−4.72576			−0.610093
$61$	6.36130			0.814481			0.407241	−	0.913321i	$-0.366491\pi$
$61$	6.36130			0.814481			0.407241	+	0.913321i	$0.366491\pi$
$62$	6.13454	−	13.0716i	0.779088	−	1.66009i
$63$	−4.42456			−0.557443
$64$	5.30522			0.663152
$65$	−1.92003	+	3.32558i	−0.238150	+	0.412488i
$66$	2.49808			0.307492
$67$	4.94073	+	8.55760i	0.603606	+	1.04548i	0.992270	+	0.124097i	$0.0396035\pi$
$67$	4.94073	+	8.55760i	0.603606	+	1.04548i	−0.388664	+	0.921380i	$0.627063\pi$
$68$	1.46798	−	2.54261i	0.178019	−	0.308337i
$69$	1.97022	−	3.41252i	0.237186	−	0.410819i
$70$	11.4747			1.37149
$71$	−5.50746	−	9.53919i	−0.653615	−	1.13209i	−0.982239	−	0.187633i	$-0.939918\pi$
$71$	−5.50746	−	9.53919i	−0.653615	−	1.13209i	0.328625	−	0.944461i	$-0.393415\pi$
$72$	3.53450	+	6.12194i	0.416545	+	0.721477i
$73$	−5.44509	−	9.43118i	−0.637300	−	1.10384i	−0.986023	−	0.166610i	$-0.946718\pi$
$73$	−5.44509	−	9.43118i	−0.637300	−	1.10384i	0.348723	−	0.937226i	$-0.386615\pi$
$74$	12.5052	−	21.6596i	1.45369	−	2.51787i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−6.64809	+	11.5148i	−0.762588	+	1.32084i
$77$	−4.26193			−0.485692
$78$	9.95882			1.12761
$79$	−5.78565	+	10.0210i	−0.650936	+	1.12745i	0.331960	+	0.943293i	$0.392290\pi$
$79$	−5.78565	+	10.0210i	−0.650936	+	1.12745i	−0.982896	+	0.184161i	$0.941043\pi$
$80$	−4.44064	−	7.69142i	−0.496479	−	0.859927i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.21467	+	5.56798i	0.355001	+	0.614880i
$83$	6.44069	+	11.1556i	0.706958	+	1.22449i	0.965980	+	0.258616i	$0.0832663\pi$
$83$	6.44069	+	11.1556i	0.706958	+	1.22449i	−0.259022	+	0.965871i	$0.583400\pi$
$84$	−10.4547	−	18.1081i	−1.14070	−	1.97575i
$85$	−0.621267			−0.0673859
$86$	−13.0249	+	22.5599i	−1.40452	+	2.43269i
$87$	1.74494	−	3.02232i	0.187077	−	0.324027i
$88$	3.40458	+	5.89691i	0.362930	+	0.628613i
$89$	5.82218			0.617150			0.308575	−	0.951200i	$-0.400148\pi$
$89$	5.82218			0.617150			0.308575	+	0.951200i	$0.400148\pi$
$90$	1.29670	−	2.24596i	0.136685	−	0.236745i
$91$	−16.9906			−1.78110
$92$	18.6215			1.94143
$93$	3.18232	+	4.56868i	0.329991	+	0.473750i
$94$	28.7665			2.96704
$95$	2.81355			0.288664
$96$	−4.44739	+	7.70311i	−0.453910	+	0.786195i
$97$	3.81210			0.387060			0.193530	−	0.981094i	$-0.438006\pi$
$97$	3.81210			0.387060			0.193530	+	0.981094i	$0.438006\pi$
$98$	16.3083	+	28.2469i	1.64739	+	2.85336i
$99$	−0.481621	+	0.834192i	−0.0484047	+	0.0838395i
$100$	−2.36288	+	4.09263i	−0.236288	+	0.409263i
$101$	15.5666			1.54893			0.774467	−	0.632614i	$-0.218018\pi$
$101$	15.5666			1.54893			0.774467	+	0.632614i	$0.218018\pi$
$102$	0.805599	+	1.39534i	0.0797662	+	0.138159i
$103$	−7.60873	−	13.1787i	−0.749711	−	1.29854i	−0.947961	−	0.318386i	$-0.896859\pi$
$103$	−7.60873	−	13.1787i	−0.749711	−	1.29854i	0.198251	−	0.980151i	$-0.436474\pi$
$104$	13.5727	+	23.5086i	1.33091	+	2.30521i
$105$	−2.21228	+	3.83178i	−0.215897	+	0.373944i
$106$	16.0206	+	27.7484i	1.55605	+	2.69516i
$107$	−3.68871	+	6.38902i	−0.356601	+	0.617650i	−0.987391	−	0.158303i	$-0.949398\pi$
$107$	−3.68871	+	6.38902i	−0.356601	+	0.617650i	0.630790	+	0.775954i	$0.282731\pi$
$108$	−4.72576			−0.454736
$109$	11.7903			1.12930			0.564652	−	0.825329i	$-0.309010\pi$
$109$	11.7903			1.12930			0.564652	+	0.825329i	$0.309010\pi$
$110$	1.24904	−	2.16340i	0.119091	−	0.206272i
$111$	4.82190	+	8.35178i	0.457675	+	0.792716i
$112$	19.6479	−	34.0312i	1.85655	−	3.21564i
$113$	−0.687741	−	1.19120i	−0.0646972	−	0.112059i	0.831862	−	0.554982i	$-0.187275\pi$
$113$	−0.687741	−	1.19120i	−0.0646972	−	0.112059i	−0.896560	+	0.442923i	$0.853941\pi$
$114$	−3.64834	−	6.31912i	−0.341699	−	0.591839i
$115$	−1.97022	−	3.41252i	−0.183724	−	0.318219i
$116$	16.4923			1.53127
$117$	−1.92003	+	3.32558i	−0.177507	+	0.307450i
$118$	−6.33976	+	10.9808i	−0.583622	+	1.01086i
$119$	−1.37442	−	2.38056i	−0.125993	−	0.218226i
$120$	7.06901			0.645309
$121$	5.03608	−	8.72275i	0.457826	−	0.792977i
$122$	−16.4974			−1.49361
$123$	−2.47911			−0.223534
$124$	−11.1785	+	23.8193i	−1.00386	+	2.13903i
$125$	1.00000			0.0894427
$126$	11.4747			1.02225
$127$	−1.70745	+	2.95739i	−0.151512	+	0.262426i	−0.931783	−	0.363015i	$-0.881747\pi$
$127$	−1.70745	+	2.95739i	−0.151512	+	0.262426i	0.780272	+	0.625441i	$0.215081\pi$
$128$	4.03098			0.356291
$129$	−5.02233	−	8.69893i	−0.442191	−	0.765898i
$130$	4.97941	−	8.62459i	0.436723	−	0.756427i
$131$	8.65598	−	14.9926i	0.756276	−	1.30991i	−0.188461	−	0.982081i	$-0.560350\pi$
$131$	8.65598	−	14.9926i	0.756276	−	1.30991i	0.944737	−	0.327828i	$-0.106317\pi$
$132$	−4.55205			−0.396205
$133$	6.22437	+	10.7809i	0.539721	+	0.934825i
$134$	−12.8133	−	22.1933i	−1.10690	−	1.91721i
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−2.19587	+	3.80336i	−0.188294	+	0.326135i
$137$	1.77438	+	3.07331i	0.151595	+	0.262571i	0.931814	−	0.362936i	$-0.118226\pi$
$137$	1.77438	+	3.07331i	0.151595	+	0.262571i	−0.780219	+	0.625507i	$0.784892\pi$
$138$	−5.10957	+	8.85004i	−0.434956	+	0.753366i
$139$	8.24779			0.699569			0.349784	−	0.936830i	$-0.386255\pi$
$139$	8.24779			0.699569			0.349784	+	0.936830i	$0.386255\pi$
$140$	−20.9094			−1.76717
$141$	−5.54609	+	9.60611i	−0.467065	+	0.808980i
$142$	14.2831	+	24.7390i	1.19861	+	2.07605i
$143$	−1.84945	+	3.20334i	−0.154659	+	0.267877i
$144$	−4.44064	−	7.69142i	−0.370054	−	0.640952i
$145$	−1.74494	−	3.02232i	−0.144909	−	0.250990i
$146$	14.1213	+	24.4589i	1.16869	+	2.02423i
$147$	−12.5768			−1.03731
$148$	−22.7872	+	39.4685i	−1.87309	+	3.24429i
$149$	−9.59007	+	16.6105i	−0.785649	+	1.36078i	0.142961	+	0.989728i	$0.454338\pi$
$149$	−9.59007	+	16.6105i	−0.785649	+	1.36078i	−0.928610	+	0.371056i	$0.878996\pi$
$150$	−1.29670	−	2.24596i	−0.105875	−	0.183382i
$151$	−6.46119			−0.525804			−0.262902	−	0.964823i	$-0.584680\pi$
$151$	−6.46119			−0.525804			−0.262902	+	0.964823i	$0.584680\pi$
$152$	9.94451	−	17.2244i	0.806606	−	1.39708i
$153$	−0.621267			−0.0502265
$154$	11.0529			0.890669
$155$	5.54775	−	0.471625i	0.445606	−	0.0378818i
$156$	−18.1472			−1.45294
$157$	−7.49258			−0.597973			−0.298986	−	0.954257i	$-0.596649\pi$
$157$	−7.49258			−0.597973			−0.298986	+	0.954257i	$0.596649\pi$
$158$	15.0045	−	25.9886i	1.19370	−	2.06754i
$159$	−12.3548			−0.979802
$160$	4.44739	+	7.70311i	0.351597	+	0.608984i
$161$	8.71735	−	15.0989i	0.687023	−	1.18996i
$162$	1.29670	−	2.24596i	0.101879	−	0.176459i
$163$	10.7983			0.845787			0.422893	−	0.906179i	$-0.361015\pi$
$163$	10.7983			0.845787			0.422893	+	0.906179i	$0.361015\pi$
$164$	−5.85785	−	10.1461i	−0.457421	−	0.792276i
$165$	0.481621	+	0.834192i	0.0374942	+	0.0649418i
$166$	−16.7033	−	28.9310i	−1.29643	−	2.24548i
$167$	1.70936	−	2.96070i	0.132274	−	0.229106i	−0.792278	−	0.610160i	$-0.791105\pi$
$167$	1.70936	−	2.96070i	0.132274	−	0.229106i	0.924553	+	0.381053i	$0.124439\pi$
$168$	15.6386	+	27.0869i	1.20655	+	2.08980i
$169$	−0.873009	+	1.51210i	−0.0671545	+	0.116315i
$170$	1.61120			0.123573
$171$	2.81355			0.215158
$172$	23.7343	−	41.1091i	1.80973	−	3.13454i
$173$	8.18946	+	14.1846i	0.622633	+	1.07843i	0.988993	+	0.147959i	$0.0472704\pi$
$173$	8.18946	+	14.1846i	0.622633	+	1.07843i	−0.366361	+	0.930473i	$0.619396\pi$
$174$	−4.52533	+	7.83811i	−0.343065	+	0.594205i
$175$	2.21228	+	3.83178i	0.167233	+	0.289656i
$176$	−4.27742	−	7.40870i	−0.322422	−	0.558452i
$177$	−2.44457	−	4.23411i	−0.183745	−	0.318255i
$178$	−15.0993			−1.13174
$179$	8.77618	−	15.2008i	0.655962	−	1.13616i	−0.325689	−	0.945477i	$-0.605596\pi$
$179$	8.77618	−	15.2008i	0.655962	−	1.13616i	0.981652	−	0.190683i	$-0.0610704\pi$
$180$	−2.36288	+	4.09263i	−0.176119	+	0.305046i
$181$	−1.70506	−	2.95324i	−0.126736	−	0.219513i	0.795674	−	0.605725i	$-0.207117\pi$
$181$	−1.70506	−	2.95324i	−0.126736	−	0.219513i	−0.922410	+	0.386212i	$0.873783\pi$
$182$	44.0634			3.26620
$183$	3.18065	−	5.50905i	0.235121	−	0.407241i
$184$	−27.8549			−2.05349
$185$	9.64381			0.709027
$186$	−8.25304	−	11.8485i	−0.605142	−	0.868771i
$187$	−0.598431			−0.0437616
$188$	−52.4190			−3.82305
$189$	−2.21228	+	3.83178i	−0.160920	+	0.278721i
$190$	−7.29669			−0.529357
$191$	9.75370	+	16.8939i	0.705753	+	1.22240i	0.966419	+	0.256971i	$0.0827244\pi$
$191$	9.75370	+	16.8939i	0.705753	+	1.22240i	−0.260666	+	0.965429i	$0.583942\pi$
$192$	2.65261	−	4.59445i	0.191436	−	0.331576i
$193$	−2.16047	+	3.74204i	−0.155514	+	0.269358i	−0.933246	−	0.359238i	$-0.883037\pi$
$193$	−2.16047	+	3.74204i	−0.155514	+	0.269358i	0.777732	+	0.628596i	$0.216370\pi$
$194$	−9.88632			−0.709796
$195$	1.92003	+	3.32558i	0.137496	+	0.238150i
$196$	−29.7174	−	51.4720i	−2.12267	−	3.67657i
$197$	2.59888	+	4.50140i	0.185163	+	0.320712i	0.943631	−	0.330998i	$-0.107385\pi$
$197$	2.59888	+	4.50140i	0.185163	+	0.320712i	−0.758469	+	0.651710i	$0.774052\pi$
$198$	1.24904	−	2.16340i	0.0887654	−	0.153746i
$199$	−11.9204	−	20.6467i	−0.845014	−	1.46361i	−0.885609	−	0.464431i	$-0.846259\pi$
$199$	−11.9204	−	20.6467i	−0.845014	−	1.46361i	0.0405956	−	0.999176i	$-0.487074\pi$
$200$	3.53450	−	6.12194i	0.249927	−	0.432886i
$201$	9.88146			0.696985
$202$	−40.3705			−2.84046
$203$	7.72059	−	13.3724i	0.541879	−	0.938562i
$204$	−1.46798	−	2.54261i	−0.102779	−	0.178019i
$205$	−1.23956	+	2.14697i	−0.0865744	+	0.149951i
$206$	19.7325	+	34.1778i	1.37483	+	2.38128i
$207$	−1.97022	−	3.41252i	−0.136940	−	0.237186i
$208$	−17.0523	−	29.5355i	−1.18237	−	2.04792i
$209$	2.71013			0.187464
$210$	5.73735	−	9.93738i	0.395915	−	0.685744i
$211$	7.49542	−	12.9824i	0.516006	−	0.893749i	−0.483821	−	0.875167i	$-0.660752\pi$
$211$	7.49542	−	12.9824i	0.516006	−	0.893749i	0.999827	−	0.0185818i	$-0.00591510\pi$
$212$	−29.1930	−	50.5637i	−2.00498	−	3.47273i
$213$	−11.0149			−0.754729
$214$	9.56631	−	16.5693i	0.653940	−	1.13266i
$215$	−10.0447			−0.685040
$216$	7.06901			0.480985
$217$	14.0804	+	20.2144i	0.955837	+	1.37224i
$218$	−30.5770			−2.07094
$219$	−10.8902			−0.735891
$220$	−2.27603	+	3.94219i	−0.153450	+	0.265783i
$221$	−2.38570			−0.160479
$222$	−12.5052	−	21.6596i	−0.839291	−	1.45369i
$223$	3.07507	−	5.32617i	0.205922	−	0.356667i	−0.744504	−	0.667618i	$-0.767314\pi$
$223$	3.07507	−	5.32617i	0.205922	−	0.356667i	0.950426	+	0.310951i	$0.100647\pi$
$224$	−19.6778	+	34.0829i	−1.31478	+	2.27726i
$225$	1.00000			0.0666667
$226$	1.78359	+	3.08927i	0.118643	+	0.205495i
$227$	−4.69279	−	8.12816i	−0.311472	−	0.539485i	0.667210	−	0.744870i	$-0.267489\pi$
$227$	−4.69279	−	8.12816i	−0.311472	−	0.539485i	−0.978681	+	0.205385i	$0.934155\pi$
$228$	6.64809	+	11.5148i	0.440280	+	0.762588i
$229$	6.34132	−	10.9835i	0.419046	−	0.725809i	−0.576798	−	0.816887i	$-0.695698\pi$
$229$	6.34132	−	10.9835i	0.419046	−	0.725809i	0.995844	+	0.0910781i	$0.0290313\pi$
$230$	5.10957	+	8.85004i	0.336915	+	0.583555i
$231$	−2.13096	+	3.69094i	−0.140207	+	0.242846i
$232$	−24.6699			−1.61966
$233$	−5.43152			−0.355830			−0.177915	−	0.984046i	$-0.556935\pi$
$233$	−5.43152			−0.355830			−0.177915	+	0.984046i	$0.556935\pi$
$234$	4.97941	−	8.62459i	0.325514	−	0.563807i
$235$	5.54609	+	9.60611i	0.361787	+	0.626633i
$236$	11.5524	−	20.0094i	0.751999	−	1.30250i
$237$	5.78565	+	10.0210i	0.375818	+	0.650936i
$238$	3.56442	+	6.17376i	0.231047	+	0.400186i
$239$	−1.46977	−	2.54571i	−0.0950713	−	0.164668i	0.814567	−	0.580069i	$-0.196975\pi$
$239$	−1.46977	−	2.54571i	−0.0950713	−	0.164668i	−0.909638	+	0.415401i	$0.863641\pi$
$240$	−8.88129			−0.573285
$241$	−2.49539	+	4.32215i	−0.160742	+	0.278414i	−0.935135	−	0.354291i	$-0.884722\pi$
$241$	−2.49539	+	4.32215i	−0.160742	+	0.278414i	0.774393	+	0.632705i	$0.218056\pi$
$242$	−13.0606	+	22.6216i	−0.839568	+	1.45417i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	30.0620			1.92452
$245$	−6.28838	+	10.8918i	−0.401750	+	0.695851i
$246$	6.42935			0.409920
$247$	10.8042			0.687454
$248$	16.7213	−	35.6300i	1.06180	−	2.26250i
$249$	12.8814			0.816325
$250$	−2.59341			−0.164021
$251$	−8.25532	+	14.2986i	−0.521071	+	0.902521i	0.478629	+	0.878017i	$0.341134\pi$
$251$	−8.25532	+	14.2986i	−0.521071	+	0.902521i	−0.999700	+	0.0245039i	$0.992199\pi$
$252$	−20.9094			−1.31717
$253$	−1.89780	−	3.28708i	−0.119313	−	0.206657i
$254$	4.42811	−	7.66971i	0.277844	−	0.481240i
$255$	−0.310634	+	0.538033i	−0.0194526	+	0.0336929i
$256$	−21.0644			−1.31652
$257$	14.3487	+	24.8527i	0.895048	+	1.55027i	0.833745	+	0.552150i	$0.186193\pi$
$257$	14.3487	+	24.8527i	0.895048	+	1.55027i	0.0613038	+	0.998119i	$0.480474\pi$
$258$	13.0249	+	22.5599i	0.810898	+	1.40452i
$259$	21.3348	+	36.9530i	1.32568	+	2.29615i
$260$	−9.07359	+	15.7159i	−0.562720	+	0.974660i
$261$	−1.74494	−	3.02232i	−0.108009	−	0.187077i
$262$	−22.4485	+	38.8819i	−1.38687	+	2.40213i
$263$	−6.41267			−0.395422			−0.197711	−	0.980260i	$-0.563351\pi$
$263$	−6.41267			−0.395422			−0.197711	+	0.980260i	$0.563351\pi$
$264$	6.80916			0.419075
$265$	−6.17742	+	10.6996i	−0.379476	+	0.657271i
$266$	−16.1423	−	27.9593i	−0.989749	−	1.71430i
$267$	2.91109	−	5.04216i	0.178156	−	0.308575i
$268$	23.3487	+	40.4412i	1.42625	+	2.47034i
$269$	9.91499	+	17.1733i	0.604528	+	1.04707i	0.992126	+	0.125244i	$0.0399714\pi$
$269$	9.91499	+	17.1733i	0.604528	+	1.04707i	−0.387598	+	0.921828i	$0.626695\pi$
$270$	−1.29670	−	2.24596i	−0.0789149	−	0.136685i
$271$	8.52245			0.517702			0.258851	−	0.965917i	$-0.416656\pi$
$271$	8.52245			0.517702			0.258851	+	0.965917i	$0.416656\pi$
$272$	2.75883	−	4.77843i	0.167278	−	0.289735i
$273$	−8.49528	+	14.7143i	−0.514158	+	0.890548i
$274$	−4.60168	−	7.97035i	−0.277998	−	0.481506i
$275$	0.963242			0.0580857
$276$	9.31077	−	16.1267i	0.560443	−	0.970715i
$277$	19.0938			1.14723			0.573617	−	0.819123i	$-0.305540\pi$
$277$	19.0938			1.14723			0.573617	+	0.819123i	$0.305540\pi$
$278$	−21.3899			−1.28288
$279$	5.54775	−	0.471625i	0.332135	−	0.0282354i
$280$	31.2773			1.86917
$281$	23.6060			1.40821			0.704107	−	0.710094i	$-0.251348\pi$
$281$	23.6060			1.40821			0.704107	+	0.710094i	$0.251348\pi$
$282$	14.3833	−	24.9126i	0.856511	−	1.48352i
$283$	−9.48602			−0.563885			−0.281943	−	0.959431i	$-0.590979\pi$
$283$	−9.48602			−0.563885			−0.281943	+	0.959431i	$0.590979\pi$
$284$	−26.0269	−	45.0799i	−1.54441	−	2.67500i
$285$	1.40678	−	2.43661i	0.0833302	−	0.144332i
$286$	4.79638	−	8.30757i	0.283616	−	0.491237i
$287$	−10.9690			−0.647479
$288$	4.44739	+	7.70311i	0.262065	+	0.453910i
$289$	8.30701	+	14.3882i	0.488648	+	0.846363i
$290$	4.52533	+	7.83811i	0.265737	+	0.460269i
$291$	1.90605	−	3.30137i	0.111734	−	0.193530i
$292$	−25.7322	−	44.5695i	−1.50586	−	2.60823i
$293$	0.598826	−	1.03720i	0.0349838	−	0.0605937i	−0.848003	−	0.529991i	$-0.822195\pi$
$293$	0.598826	−	1.03720i	0.0349838	−	0.0605937i	0.882987	+	0.469397i	$0.155529\pi$
$294$	32.6167			1.90224
$295$	−4.88913			−0.284656
$296$	34.0861	−	59.0388i	1.98121	−	3.43156i
$297$	0.481621	+	0.834192i	0.0279465	+	0.0484047i
$298$	24.8710	−	43.0778i	1.44074	−	2.49543i
$299$	−7.56574	−	13.1042i	−0.437538	−	0.757838i
$300$	2.36288	+	4.09263i	0.136421	+	0.236288i
$301$	−22.2216	−	38.4890i	−1.28083	−	2.21847i
$302$	16.7565			0.964228
$303$	7.78330	−	13.4811i	0.447139	−	0.774467i
$304$	−12.4940	+	21.6402i	−0.716579	+	1.24115i
$305$	−3.18065	−	5.50905i	−0.182124	−	0.315447i
$306$	1.61120			0.0921061
$307$	−14.2353	+	24.6562i	−0.812450	+	1.40720i	0.0986945	+	0.995118i	$0.468533\pi$
$307$	−14.2353	+	24.6562i	−0.812450	+	1.40720i	−0.911145	+	0.412087i	$0.864800\pi$
$308$	−20.1408			−1.14763
$309$	−15.2175			−0.865691
$310$	−14.3876	+	1.22311i	−0.817160	+	0.0694682i
$311$	−1.82318			−0.103383			−0.0516917	−	0.998663i	$-0.516461\pi$
$311$	−1.82318			−0.103383			−0.0516917	+	0.998663i	$0.516461\pi$
$312$	27.1454			1.53680
$313$	3.06397	−	5.30695i	0.173186	−	0.299966i	−0.766346	−	0.642428i	$-0.777927\pi$
$313$	3.06397	−	5.30695i	0.173186	−	0.299966i	0.939532	+	0.342461i	$0.111261\pi$
$314$	19.4313			1.09657
$315$	2.21228	+	3.83178i	0.124648	+	0.215897i
$316$	−27.3416	+	47.3570i	−1.53808	+	2.66404i
$317$	−5.29526	+	9.17167i	−0.297412	+	0.515132i	−0.975543	−	0.219809i	$-0.929457\pi$
$317$	−5.29526	+	9.17167i	−0.297412	+	0.515132i	0.678131	+	0.734941i	$0.262790\pi$
$318$	32.0411			1.79678
$319$	−1.68080	−	2.91123i	−0.0941066	−	0.162997i
$320$	−2.65261	−	4.59445i	−0.148285	−	0.256838i
$321$	3.68871	+	6.38902i	0.205883	+	0.356601i
$322$	−22.6076	+	39.1576i	−1.25987	+	2.18217i
$323$	0.873984	+	1.51378i	0.0486297	+	0.0842292i
$324$	−2.36288	+	4.09263i	−0.131271	+	0.227368i
$325$	3.84005			0.213008
$326$	−28.0043			−1.55102
$327$	5.89514	−	10.2107i	0.326002	−	0.564652i
$328$	8.76243	+	15.1770i	0.483824	+	0.838008i
$329$	−24.5390	+	42.5028i	−1.35288	+	2.34326i
$330$	−1.24904	−	2.16340i	−0.0687574	−	0.119091i
$331$	−0.107020	−	0.185365i	−0.00588237	−	0.0101886i	0.863069	−	0.505086i	$-0.168539\pi$
$331$	−0.107020	−	0.185365i	−0.00588237	−	0.0101886i	−0.868952	+	0.494897i	$0.835206\pi$
$332$	30.4372	+	52.7187i	1.67046	+	2.89332i
$333$	9.64381			0.528477
$334$	−4.43307	+	7.67831i	−0.242567	+	0.420138i
$335$	4.94073	−	8.55760i	0.269941	−	0.467551i
$336$	−19.6479	−	34.0312i	−1.07188	−	1.85655i
$337$	18.8172			1.02504			0.512520	−	0.858675i	$-0.328712\pi$
$337$	18.8172			1.02504			0.512520	+	0.858675i	$0.328712\pi$
$338$	2.26407	−	3.92148i	0.123149	−	0.213300i
$339$	−1.37548			−0.0747059
$340$	−2.93596			−0.159225
$341$	5.34383	−	0.454289i	0.289385	−	0.0246011i
$342$	−7.29669			−0.394560
$343$	−24.6747			−1.33231
$344$	−35.5029	+	61.4928i	−1.91419	+	3.31547i
$345$	−3.94043			−0.212146
$346$	−21.2386	−	36.7863i	−1.14179	−	1.97765i
$347$	12.8866	−	22.3203i	0.691791	−	1.19822i	−0.279459	−	0.960158i	$-0.590155\pi$
$347$	12.8866	−	22.3203i	0.691791	−	1.19822i	0.971250	−	0.238060i	$-0.0765115\pi$
$348$	8.24615	−	14.2828i	0.442040	−	0.765636i
$349$	34.5636			1.85015			0.925073	−	0.379789i	$-0.124004\pi$
$349$	34.5636			1.85015			0.925073	+	0.379789i	$0.124004\pi$
$350$	−5.73735	−	9.93738i	−0.306674	−	0.531175i
$351$	1.92003	+	3.32558i	0.102483	+	0.177507i
$352$	4.28392	+	7.41996i	0.228333	+	0.395485i
$353$	14.0365	−	24.3119i	0.747086	−	1.29399i	−0.202129	−	0.979359i	$-0.564786\pi$
$353$	14.0365	−	24.3119i	0.747086	−	1.29399i	0.949214	−	0.314631i	$-0.101881\pi$
$354$	6.33976	+	10.9808i	0.336954	+	0.583622i
$355$	−5.50746	+	9.53919i	−0.292305	+	0.506288i
$356$	27.5142			1.45825
$357$	−2.74884			−0.145484
$358$	−22.7602	+	39.4218i	−1.20291	+	2.08351i
$359$	−8.95144	−	15.5043i	−0.472439	−	0.818288i	0.527064	−	0.849826i	$-0.323293\pi$
$359$	−8.95144	−	15.5043i	−0.472439	−	0.818288i	−0.999503	+	0.0315378i	$0.989960\pi$
$360$	3.53450	−	6.12194i	0.186285	−	0.322654i
$361$	5.54196	+	9.59896i	0.291682	+	0.505208i
$362$	4.42190	+	7.65896i	0.232410	+	0.402546i
$363$	−5.03608	−	8.72275i	−0.264326	−	0.457826i
$364$	−80.2933			−4.20851
$365$	−5.44509	+	9.43118i	−0.285009	+	0.493650i
$366$	−8.24872	+	14.2872i	−0.431168	+	0.746804i
$367$	−1.25975	−	2.18196i	−0.0657586	−	0.113897i	0.831272	−	0.555866i	$-0.187613\pi$
$367$	−1.25975	−	2.18196i	−0.0657586	−	0.113897i	−0.897030	+	0.441969i	$0.854280\pi$
$368$	34.9961			1.82430
$369$	−1.23956	+	2.14697i	−0.0645287	+	0.111767i
$370$	−25.0103			−1.30022
$371$	−54.6648			−2.83805
$372$	15.0389	+	21.5905i	0.779729	+	1.11942i
$373$	13.8016			0.714618			0.357309	−	0.933986i	$-0.383694\pi$
$373$	13.8016			0.714618			0.357309	+	0.933986i	$0.383694\pi$
$374$	1.55197			0.0802507
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	78.4107			4.04372
$377$	−6.70065	−	11.6059i	−0.345101	−	0.597733i
$378$	5.73735	−	9.93738i	0.295097	−	0.511124i
$379$	−1.75209	+	3.03470i	−0.0899987	+	0.155882i	−0.907510	−	0.420030i	$-0.862020\pi$
$379$	−1.75209	+	3.03470i	−0.0899987	+	0.155882i	0.817512	+	0.575912i	$0.195353\pi$
$380$	13.2962			0.682079
$381$	1.70745	+	2.95739i	0.0874752	+	0.151512i
$382$	−25.2953	−	43.8128i	−1.29422	−	2.24166i
$383$	−8.69279	−	15.0564i	−0.444181	−	0.769344i	0.553814	−	0.832641i	$-0.313172\pi$
$383$	−8.69279	−	15.0564i	−0.444181	−	0.769344i	−0.997995	+	0.0632965i	$0.979839\pi$
$384$	2.01549	−	3.49093i	0.102852	−	0.178146i
$385$	2.13096	+	3.69094i	0.108604	+	0.188108i
$386$	5.60297	−	9.70463i	0.285184	−	0.493952i
$387$	−10.0447			−0.510599
$388$	18.0150			0.914576
$389$	12.3603	−	21.4087i	0.626693	−	1.08546i	−0.361518	−	0.932365i	$-0.617741\pi$
$389$	12.3603	−	21.4087i	0.626693	−	1.08546i	0.988211	−	0.153099i	$-0.0489253\pi$
$390$	−4.97941	−	8.62459i	−0.252142	−	0.436723i
$391$	1.22403	−	2.12008i	0.0619019	−	0.107217i
$392$	44.4526	+	76.9942i	2.24520	+	3.88879i
$393$	−8.65598	−	14.9926i	−0.436636	−	0.756276i
$394$	−6.73997	−	11.6740i	−0.339555	−	0.588126i
$395$	11.5713			0.582215
$396$	−2.27603	+	3.94219i	−0.114375	+	0.198103i
$397$	10.2469	−	17.7481i	0.514276	−	0.890752i	−0.485587	−	0.874188i	$-0.661394\pi$
$397$	10.2469	−	17.7481i	0.514276	−	0.890752i	0.999863	−	0.0165637i	$-0.00527263\pi$
$398$	30.9144	+	53.5453i	1.54960	+	2.68398i
$399$	12.4487			0.623217
$400$	−4.44064	+	7.69142i	−0.222032	+	0.384571i
$401$	−11.6496			−0.581752			−0.290876	−	0.956761i	$-0.593947\pi$
$401$	−11.6496			−0.581752			−0.290876	+	0.956761i	$0.593947\pi$
$402$	−25.6267			−1.27814
$403$	21.3037	−	1.81106i	1.06121	−	0.0902155i
$404$	73.5640			3.65995
$405$	1.00000			0.0496904
$406$	−20.0226	+	34.6802i	−0.993706	+	1.72115i
$407$	9.28932			0.460455
$408$	2.19587	+	3.80336i	0.108712	+	0.188294i
$409$	−8.32105	+	14.4125i	−0.411450	+	0.712652i	−0.995049	−	0.0993905i	$-0.968311\pi$
$409$	−8.32105	+	14.4125i	−0.411450	+	0.712652i	0.583599	+	0.812042i	$0.301644\pi$
$410$	3.21467	−	5.56798i	0.158761	−	0.274983i
$411$	3.54875			0.175047
$412$	−35.9570	−	62.2794i	−1.77148	−	3.06829i
$413$	−10.8161	−	18.7341i	−0.532227	−	0.921845i
$414$	5.10957	+	8.85004i	0.251122	+	0.434956i
$415$	6.44069	−	11.1556i	0.316161	−	0.547607i
$416$	17.0782	+	29.5804i	0.837329	+	1.45030i
$417$	4.12390	−	7.14280i	0.201948	−	0.349784i
$418$	−7.02848			−0.343774
$419$	−13.4617			−0.657649			−0.328824	−	0.944391i	$-0.606652\pi$
$419$	−13.4617			−0.657649			−0.328824	+	0.944391i	$0.606652\pi$
$420$	−10.4547	+	18.1081i	−0.510138	+	0.883584i
$421$	5.73305	+	9.92993i	0.279412	+	0.483955i	0.971239	−	0.238108i	$-0.0765272\pi$
$421$	5.73305	+	9.92993i	0.279412	+	0.483955i	−0.691827	+	0.722063i	$0.743194\pi$
$422$	−19.4387	+	33.6688i	−0.946260	+	1.63897i
$423$	5.54609	+	9.60611i	0.269660	+	0.467065i
$424$	43.6682	+	75.6355i	2.12071	+	3.67319i
$425$	0.310634	+	0.538033i	0.0150679	+	0.0260984i
$426$	28.5661			1.38403
$427$	14.0730	−	24.3751i	0.681040	−	1.17960i
$428$	−17.4319	+	30.1930i	−0.842604	+	1.45943i
$429$	1.84945	+	3.20334i	0.0892923	+	0.154659i
$430$	26.0499			1.25624
$431$	1.01183	−	1.75254i	0.0487380	−	0.0844167i	−0.840627	−	0.541614i	$-0.817813\pi$
$431$	1.01183	−	1.75254i	0.0487380	−	0.0844167i	0.889365	+	0.457197i	$0.151147\pi$
$432$	−8.88129			−0.427301
$433$	−15.7587			−0.757315			−0.378657	−	0.925537i	$-0.623614\pi$
$433$	−15.7587			−0.757315			−0.378657	+	0.925537i	$0.623614\pi$
$434$	−36.5161	−	52.4242i	−1.75283	−	2.51644i
$435$	−3.48987			−0.167327
$436$	55.7181			2.66841
$437$	−5.54331	+	9.60129i	−0.265172	+	0.459292i
$438$	28.2427			1.34949
$439$	−19.8077	−	34.3079i	−0.945370	−	1.63743i	−0.755008	−	0.655715i	$-0.772367\pi$
$439$	−19.8077	−	34.3079i	−0.945370	−	1.63743i	−0.190362	−	0.981714i	$-0.560966\pi$
$440$	3.40458	−	5.89691i	0.162307	−	0.281124i
$441$	−6.28838	+	10.8918i	−0.299447	+	0.518657i
$442$	6.18709			0.294290
$443$	7.80370	+	13.5164i	0.370765	+	0.642184i	0.989683	−	0.143272i	$-0.0457622\pi$
$443$	7.80370	+	13.5164i	0.370765	+	0.642184i	−0.618919	+	0.785455i	$0.712429\pi$
$444$	22.7872	+	39.4685i	1.08143	+	1.87309i
$445$	−2.91109	−	5.04216i	−0.137999	−	0.239021i
$446$	−7.97490	+	13.8129i	−0.377622	+	0.654061i
$447$	9.59007	+	16.6105i	0.453595	+	0.785649i
$448$	11.7366	−	20.3284i	0.554504	−	0.960429i
$449$	−11.0413			−0.521069			−0.260535	−	0.965465i	$-0.583899\pi$
$449$	−11.0413			−0.521069			−0.260535	+	0.965465i	$0.583899\pi$
$450$	−2.59341			−0.122254
$451$	−1.19399	+	2.06806i	−0.0562229	+	0.0973810i
$452$	−3.25010	−	5.62933i	−0.152872	−	0.264782i
$453$	−3.23059	+	5.59555i	−0.151787	+	0.262902i
$454$	12.1703	+	21.0796i	0.571182	+	0.989315i
$455$	8.49528	+	14.7143i	0.398265	+	0.689815i
$456$	−9.94451	−	17.2244i	−0.465694	−	0.806606i
$457$	12.5929			0.589073			0.294536	−	0.955640i	$-0.404835\pi$
$457$	12.5929			0.589073			0.294536	+	0.955640i	$0.404835\pi$
$458$	−16.4456	+	28.4846i	−0.768453	+	1.33100i
$459$	−0.310634	+	0.538033i	−0.0144991	+	0.0251132i
$460$	−9.31077	−	16.1267i	−0.434117	−	0.751913i
$461$	−36.3871			−1.69472			−0.847358	−	0.531022i	$-0.821808\pi$
$461$	−36.3871			−1.69472			−0.847358	+	0.531022i	$0.821808\pi$
$462$	5.52646	−	9.57210i	0.257114	−	0.445334i
$463$	5.94125			0.276114			0.138057	−	0.990424i	$-0.455914\pi$
$463$	5.94125			0.276114			0.138057	+	0.990424i	$0.455914\pi$
$464$	30.9946			1.43889
$465$	2.36544	−	5.04031i	0.109695	−	0.233739i
$466$	14.0861			0.652528
$467$	22.5706			1.04444			0.522222	−	0.852810i	$-0.325103\pi$
$467$	22.5706			1.04444			0.522222	+	0.852810i	$0.325103\pi$
$468$	−9.07359	+	15.7159i	−0.419427	+	0.726468i
$469$	43.7212			2.01886
$470$	−14.3833	−	24.9126i	−0.663451	−	1.14913i
$471$	−3.74629	+	6.48876i	−0.172620	+	0.298986i
$472$	−17.2807	+	29.9310i	−0.795406	+	1.37768i
$473$	−9.67544			−0.444877
$474$	−15.0045	−	25.9886i	−0.689181	−	1.19370i
$475$	−1.40678	−	2.43661i	−0.0645473	−	0.111799i
$476$	−6.49517	−	11.2500i	−0.297706	−	0.515641i
$477$	−6.17742	+	10.6996i	−0.282845	+	0.489901i
$478$	3.81170	+	6.60206i	0.174343	+	0.301971i
$479$	5.49826	−	9.52327i	0.251222	−	0.435129i	−0.712641	−	0.701529i	$-0.752501\pi$
$479$	5.49826	−	9.52327i	0.251222	−	0.435129i	0.963863	+	0.266400i	$0.0858343\pi$
$480$	8.89478			0.405989
$481$	37.0327			1.68855
$482$	6.47157	−	11.2091i	0.294772	−	0.510560i
$483$	−8.71735	−	15.0989i	−0.396653	−	0.687023i
$484$	23.7993	−	41.2216i	1.08179	−	1.87371i
$485$	−1.90605	−	3.30137i	−0.0865492	−	0.149908i
$486$	−1.29670	−	2.24596i	−0.0588197	−	0.101879i
$487$	−13.7570	−	23.8278i	−0.623389	−	1.07974i	−0.988850	−	0.148914i	$-0.952422\pi$
$487$	−13.7570	−	23.8278i	−0.623389	−	1.07974i	0.365461	−	0.930826i	$-0.380911\pi$
$488$	−44.9681			−2.03561
$489$	5.39914	−	9.35158i	0.244158	−	0.422893i
$490$	16.3083	−	28.2469i	0.736735	−	1.27606i
$491$	10.6927	+	18.5203i	0.482555	+	0.835810i	0.999799	−	0.0200281i	$-0.00637556\pi$
$491$	10.6927	+	18.5203i	0.482555	+	0.835810i	−0.517245	+	0.855838i	$0.673042\pi$
$492$	−11.7157			−0.528184
$493$	1.08407	−	1.87767i	0.0488241	−	0.0845659i
$494$	−28.0197			−1.26066
$495$	0.963242			0.0432945
$496$	−21.0081	+	44.7644i	−0.943293	+	2.00998i
$497$	−48.7362			−2.18612
$498$	−33.4067			−1.49699
$499$	−15.3609	+	26.6058i	−0.687646	+	1.19104i	0.284951	+	0.958542i	$0.408023\pi$
$499$	−15.3609	+	26.6058i	−0.687646	+	1.19104i	−0.972597	+	0.232496i	$0.925311\pi$
$500$	4.72576			0.211342
$501$	−1.70936	−	2.96070i	−0.0763687	−	0.132274i
$502$	21.4094	−	37.0822i	0.955548	−	1.65506i
$503$	−3.87149	+	6.70562i	−0.172621	+	0.298989i	−0.939336	−	0.343000i	$-0.888557\pi$
$503$	−3.87149	+	6.70562i	−0.172621	+	0.298989i	0.766714	+	0.641989i	$0.221890\pi$
$504$	31.2773			1.39320
$505$	−7.78330	−	13.4811i	−0.346352	−	0.599900i
$506$	4.92176	+	8.52473i	0.218799	+	0.378971i
$507$	0.873009	+	1.51210i	0.0387717	+	0.0671545i
$508$	−8.06899	+	13.9759i	−0.358004	+	0.620080i
$509$	0.520599	+	0.901704i	0.0230751	+	0.0399673i	0.877332	−	0.479883i	$-0.159321\pi$
$509$	0.520599	+	0.901704i	0.0230751	+	0.0399673i	−0.854257	+	0.519851i	$0.825988\pi$
$510$	0.805599	−	1.39534i	0.0356725	−	0.0617866i
$511$	−48.1843			−2.13155
$512$	46.5666			2.05797
$513$	1.40678	−	2.43661i	0.0621107	−	0.107579i
$514$	−37.2121	−	64.4532i	−1.64135	−	2.84291i
$515$	−7.60873	+	13.1787i	−0.335281	+	0.580723i
$516$	−23.7343	−	41.1091i	−1.04485	−	1.80973i
$517$	5.34223	+	9.25301i	0.234951	+	0.406947i
$518$	−55.3299	−	95.8341i	−2.43105	−	4.21071i
$519$	16.3789			0.718955
$520$	13.5727	−	23.5086i	0.595201	−	1.03092i
$521$	1.83163	−	3.17248i	0.0802453	−	0.138989i	−0.823110	−	0.567882i	$-0.807763\pi$
$521$	1.83163	−	3.17248i	0.0802453	−	0.138989i	0.903355	+	0.428893i	$0.141096\pi$
$522$	4.52533	+	7.83811i	0.198068	+	0.343065i
$523$	7.81241			0.341613			0.170806	−	0.985305i	$-0.445363\pi$
$523$	7.81241			0.341613			0.170806	+	0.985305i	$0.445363\pi$
$524$	40.9061	−	70.8514i	1.78699	−	3.09516i
$525$	4.42456			0.193104
$526$	16.6307			0.725131
$527$	1.97707	+	2.83837i	0.0861224	+	0.123641i
$528$	−8.55483			−0.372301
$529$	−7.47298			−0.324912
$530$	16.0206	−	27.7484i	0.695889	−	1.20531i
$531$	−4.88913			−0.212170
$532$	29.4149	+	50.9481i	1.27530	+	2.20888i
$533$	−4.75996	+	8.24450i	−0.206177	+	0.357109i
$534$	−7.54964	+	13.0764i	−0.326705	+	0.565870i
$535$	7.37741			0.318953
$536$	−34.9261	−	60.4937i	−1.50858	−	2.61293i
$537$	−8.77618	−	15.2008i	−0.378720	−	0.655962i
$538$	−25.7136	−	44.5373i	−1.10859	−	1.92014i
$539$	−6.05723	+	10.4914i	−0.260904	+	0.451898i
$540$	2.36288	+	4.09263i	0.101682	+	0.176119i
$541$	11.6389	−	20.1592i	0.500397	−	0.866714i	−0.499603	−	0.866255i	$-0.666521\pi$
$541$	11.6389	−	20.1592i	0.500397	−	0.866714i	1.00000		0.000458888i	$-0.000146069\pi$
$542$	−22.1022			−0.949370
$543$	−3.41011			−0.146342
$544$	−2.76302	+	4.78569i	−0.118463	+	0.205185i
$545$	−5.89514	−	10.2107i	−0.252520	−	0.437378i
$546$	22.0317	−	38.1601i	0.942871	−	1.63310i
$547$	22.1494	+	38.3639i	0.947041	+	1.64032i	0.751613	+	0.659605i	$0.229276\pi$
$547$	22.1494	+	38.3639i	0.947041	+	1.64032i	0.195428	+	0.980718i	$0.437390\pi$
$548$	8.38528	+	14.5237i	0.358201	+	0.620423i
$549$	−3.18065	−	5.50905i	−0.135747	−	0.235121i
$550$	−2.49808			−0.106518
$551$	−4.90947	+	8.50346i	−0.209151	+	0.362259i
$552$	−13.9275	+	24.1231i	−0.592793	+	1.02675i
$553$	25.5990	+	44.3387i	1.08858	+	1.88547i
$554$	−49.5180			−2.10382
$555$	4.82190	−	8.35178i	0.204678	−	0.354513i
$556$	38.9771			1.65300
$557$	−34.4620			−1.46020			−0.730101	−	0.683339i	$-0.760527\pi$
$557$	−34.4620			−1.46020			−0.730101	+	0.683339i	$0.760527\pi$
$558$	−14.3876	+	1.22311i	−0.609075	+	0.0517786i
$559$	−38.5720			−1.63142
$560$	−39.2958			−1.66055
$561$	−0.299215	+	0.518256i	−0.0126329	+	0.0218808i
$562$	−61.2199			−2.58240
$563$	−5.42379	−	9.39428i	−0.228586	−	0.395922i	0.728804	−	0.684723i	$-0.240077\pi$
$563$	−5.42379	−	9.39428i	−0.228586	−	0.395922i	−0.957389	+	0.288801i	$0.906743\pi$
$564$	−26.2095	+	45.3962i	−1.10362	+	1.91152i
$565$	−0.687741	+	1.19120i	−0.0289335	+	0.0501142i
$566$	24.6011			1.03406
$567$	2.21228	+	3.83178i	0.0929071	+	0.160920i
$568$	38.9322	+	67.4326i	1.63356	+	2.82941i
$569$	5.18554	+	8.98162i	0.217389	+	0.376529i	0.954009	−	0.299778i	$-0.0969126\pi$
$569$	5.18554	+	8.98162i	0.217389	+	0.376529i	−0.736620	+	0.676307i	$0.763579\pi$
$570$	−3.64834	+	6.31912i	−0.152812	+	0.264679i
$571$	−20.7409	−	35.9243i	−0.867981	−	1.50339i	−0.864057	−	0.503395i	$-0.832084\pi$
$571$	−20.7409	−	35.9243i	−0.867981	−	1.50339i	−0.00392444	−	0.999992i	$-0.501249\pi$
$572$	−8.74006	+	15.1382i	−0.365440	+	0.632961i
$573$	19.5074			0.814933
$574$	28.4471			1.18736
$575$	−1.97022	+	3.41252i	−0.0821637	+	0.142312i
$576$	−2.65261	−	4.59445i	−0.110525	−	0.191436i
$577$	6.09755	−	10.5613i	0.253844	−	0.439671i	−0.710737	−	0.703458i	$-0.751638\pi$
$577$	6.09755	−	10.5613i	0.253844	−	0.439671i	0.964581	+	0.263787i	$0.0849715\pi$
$578$	−21.5435	−	37.3144i	−0.896090	−	1.55207i
$579$	2.16047	+	3.74204i	0.0897859	+	0.155514i
$580$	−8.24615	−	14.2828i	−0.342403	−	0.593059i
$581$	56.9945			2.36453
$582$	−4.94316	+	8.56180i	−0.204900	+	0.354898i
$583$	−5.95035	+	10.3063i	−0.246438	+	0.426844i
$584$	38.4914	+	66.6690i	1.59278	+	2.75878i
$585$	3.84005			0.158767
$586$	−1.55300	+	2.68987i	−0.0641538	+	0.111118i
$587$	−44.4914			−1.83636			−0.918178	−	0.396169i	$-0.870340\pi$
$587$	−44.4914			−1.83636			−0.918178	+	0.396169i	$0.870340\pi$
$588$	−59.4348			−2.45105
$589$	−8.95361	−	12.8542i	−0.368927	−	0.529649i
$590$	12.6795			0.522007
$591$	5.19777			0.213808
$592$	−42.8247	+	74.1746i	−1.76008	+	3.04856i
$593$	21.0910			0.866102			0.433051	−	0.901369i	$-0.357437\pi$
$593$	21.0910			0.866102			0.433051	+	0.901369i	$0.357437\pi$
$594$	−1.24904	−	2.16340i	−0.0512487	−	0.0887654i
$595$	−1.37442	+	2.38056i	−0.0563456	+	0.0975935i
$596$	−45.3204	+	78.4972i	−1.85640	+	3.21537i
$597$	−23.8408			−0.975738
$598$	19.6210	+	33.9846i	0.802364	+	1.38974i
$599$	9.46479	+	16.3935i	0.386721	+	0.669820i	0.992006	−	0.126188i	$-0.0402744\pi$
$599$	9.46479	+	16.3935i	0.386721	+	0.669820i	−0.605286	+	0.796008i	$0.706941\pi$
$600$	−3.53450	−	6.12194i	−0.144295	−	0.249927i
$601$	21.9190	−	37.9649i	0.894095	−	1.54862i	0.0591751	−	0.998248i	$-0.481153\pi$
$601$	21.9190	−	37.9649i	0.894095	−	1.54862i	0.834920	−	0.550371i	$-0.185514\pi$
$602$	57.6297	+	99.8176i	2.34881	+	4.06826i
$603$	4.94073	−	8.55760i	0.201202	−	0.348492i
$604$	−30.5340			−1.24241
$605$	−10.0722			−0.409492
$606$	−20.1853	+	34.9619i	−0.819970	+	1.42023i
$607$	−9.81026	−	16.9919i	−0.398186	−	0.689678i	0.595316	−	0.803492i	$-0.297027\pi$
$607$	−9.81026	−	16.9919i	−0.398186	−	0.689678i	−0.993502	+	0.113813i	$0.963693\pi$
$608$	12.5130	−	21.6731i	0.507468	−	0.878960i
$609$	−7.72059	−	13.3724i	−0.312854	−	0.541879i
$610$	8.24872	+	14.2872i	0.333981	+	0.578472i
$611$	21.2973	+	36.8880i	0.861596	+	1.49233i
$612$	−2.93596			−0.118679
$613$	9.34862	−	16.1923i	0.377587	−	0.654000i	−0.613123	−	0.789987i	$-0.710087\pi$
$613$	9.34862	−	16.1923i	0.377587	−	0.654000i	0.990711	+	0.135987i	$0.0434205\pi$
$614$	36.9179	−	63.9436i	1.48988	−	2.58055i
$615$	1.23956	+	2.14697i	0.0499837	+	0.0865744i
$616$	30.1276			1.21387
$617$	−11.9405	+	20.6815i	−0.480705	+	0.832605i	−0.999755	−	0.0221385i	$-0.992953\pi$
$617$	−11.9405	+	20.6815i	−0.480705	+	0.832605i	0.519050	+	0.854744i	$0.326286\pi$
$618$	39.4651			1.58752
$619$	−4.88486			−0.196339			−0.0981695	−	0.995170i	$-0.531299\pi$
$619$	−4.88486			−0.196339			−0.0981695	+	0.995170i	$0.531299\pi$
$620$	26.2174	−	2.22878i	1.05291	−	0.0895102i
$621$	−3.94043			−0.158124
$622$	4.72826			0.189586
$623$	12.8803	−	22.3093i	0.516039	−	0.893805i
$624$	−34.1046			−1.36528
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.94611	+	13.7631i	−0.317591	+	0.550083i
$627$	1.35507	−	2.34704i	0.0541161	−	0.0937319i
$628$	−35.4081			−1.41294
$629$	2.99569	+	5.18869i	0.119446	+	0.206886i
$630$	−5.73735	−	9.93738i	−0.228581	−	0.395915i
$631$	−4.15100	−	7.18975i	−0.165249	−	0.286219i	0.771495	−	0.636236i	$-0.219509\pi$
$631$	−4.15100	−	7.18975i	−0.165249	−	0.286219i	−0.936744	+	0.350016i	$0.886176\pi$
$632$	40.8988	−	70.8387i	1.62687	−	2.81781i
$633$	−7.49542	−	12.9824i	−0.297916	−	0.516006i
$634$	13.7328	−	23.7859i	0.545398	−	0.944657i
$635$	3.41490			0.135516
$636$	−58.3860			−2.31515
$637$	−24.1477	+	41.8251i	−0.956768	+	1.65717i
$638$	4.35899	+	7.54999i	0.172574	+	0.298907i
$639$	−5.50746	+	9.53919i	−0.217872	+	0.377365i
$640$	−2.01549	−	3.49093i	−0.0796692	−	0.137991i
$641$	15.2825	+	26.4701i	0.603624	+	1.04551i	0.992267	+	0.124119i	$0.0396106\pi$
$641$	15.2825	+	26.4701i	0.603624	+	1.04551i	−0.388643	+	0.921388i	$0.627056\pi$
$642$	−9.56631	−	16.5693i	−0.377552	−	0.653940i
$643$	−3.89775			−0.153712			−0.0768561	−	0.997042i	$-0.524488\pi$
$643$	−3.89775			−0.153712			−0.0768561	+	0.997042i	$0.524488\pi$
$644$	41.1961	−	71.3537i	1.62335	−	2.81173i
$645$	−5.02233	+	8.69893i	−0.197754	+	0.342520i
$646$	−2.26660	−	3.92586i	−0.0891780	−	0.154461i
$647$	8.48458			0.333563			0.166782	−	0.985994i	$-0.446662\pi$
$647$	8.48458			0.333563			0.166782	+	0.985994i	$0.446662\pi$
$648$	3.53450	−	6.12194i	0.138848	−	0.240492i
$649$	−4.70942			−0.184861
$650$	−9.95882			−0.390617
$651$	24.5464	−	2.08673i	0.962049	−	0.0817855i
$652$	51.0301			1.99849
$653$	1.24418			0.0486884			0.0243442	−	0.999704i	$-0.492250\pi$
$653$	1.24418			0.0486884			0.0243442	+	0.999704i	$0.492250\pi$
$654$	−15.2885	+	26.4805i	−0.597828	+	1.03547i
$655$	−17.3120			−0.676434
$656$	−11.0089	−	19.0679i	−0.429824	−	0.744476i
$657$	−5.44509	+	9.43118i	−0.212433	+	0.367945i
$658$	63.6397	−	110.227i	2.48093	−	4.29710i
$659$	22.7205			0.885067			0.442533	−	0.896752i	$-0.354080\pi$
$659$	22.7205			0.885067			0.442533	+	0.896752i	$0.354080\pi$
$660$	2.27603	+	3.94219i	0.0885942	+	0.153450i
$661$	9.20293	+	15.9399i	0.357953	+	0.619992i	0.987619	−	0.156874i	$-0.0501416\pi$
$661$	9.20293	+	15.9399i	0.357953	+	0.619992i	−0.629666	+	0.776866i	$0.716808\pi$
$662$	0.277547	+	0.480726i	0.0107872	+	0.0186839i
$663$	−1.19285	+	2.06608i	−0.0463264	+	0.0802397i
$664$	−45.5293	−	78.8590i	−1.76688	−	3.06032i
$665$	6.22437	−	10.7809i	0.241371	−	0.418066i
$666$	−25.0103			−0.969130
$667$	13.7516			0.532465
$668$	8.07804	−	13.9916i	0.312549	−	0.541350i
$669$	−3.07507	−	5.32617i	−0.118889	−	0.205922i
$670$	−12.8133	+	22.1933i	−0.495022	+	0.857403i
$671$	−3.06374	−	5.30655i	−0.118274	−	0.204857i
$672$	19.6778	+	34.0829i	0.759086	+	1.31478i
$673$	23.4656	+	40.6436i	0.904532	+	1.56670i	0.821544	+	0.570145i	$0.193113\pi$
$673$	23.4656	+	40.6436i	0.904532	+	1.56670i	0.0829878	+	0.996551i	$0.473554\pi$
$674$	−48.8007			−1.87973
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−4.12563	+	7.14580i	−0.158678	+	0.274838i
$677$	−10.1036	−	17.4999i	−0.388312	−	0.672576i	0.603911	−	0.797052i	$-0.293608\pi$
$677$	−10.1036	−	17.4999i	−0.388312	−	0.672576i	−0.992223	+	0.124476i	$0.960275\pi$
$678$	3.56718			0.136997
$679$	8.43343	−	14.6071i	0.323645	−	0.560570i
$680$	4.39174			0.168416
$681$	−9.38559			−0.359656
$682$	−13.8587	+	1.17816i	−0.530678	+	0.0451139i
$683$	2.24311			0.0858303			0.0429151	−	0.999079i	$-0.486335\pi$
$683$	2.24311			0.0858303			0.0429151	+	0.999079i	$0.486335\pi$
$684$	13.2962			0.508392
$685$	1.77438	−	3.07331i	0.0677955	−	0.117425i
$686$	63.9917			2.44321
$687$	−6.34132	−	10.9835i	−0.241936	−	0.419046i
$688$	44.6048	−	77.2577i	1.70054	−	2.94542i
$689$	−23.7216	+	41.0870i	−0.903722	+	1.56529i
$690$	10.2191			0.389036
$691$	13.9518	+	24.1653i	0.530753	+	0.919291i	0.999356	+	0.0358824i	$0.0114242\pi$
$691$	13.9518	+	24.1653i	0.530753	+	0.919291i	−0.468603	+	0.883409i	$0.655242\pi$
$692$	38.7014	+	67.0328i	1.47121	+	2.54821i
$693$	2.13096	+	3.69094i	0.0809486	+	0.140207i
$694$	−33.4203	+	57.8857i	−1.26862	+	2.19731i
$695$	−4.12390	−	7.14280i	−0.156428	−	0.270942i
$696$	−12.3350	+	21.3648i	−0.467556	+	0.809830i
$697$	−1.54019			−0.0583389
$698$	−89.6374			−3.39283
$699$	−2.71576	+	4.70383i	−0.102719	+	0.177915i
$700$	10.4547	+	18.1081i	0.395151	+	0.684422i
$701$	13.9183	−	24.1073i	0.525688	−	0.910519i	−0.473864	−	0.880598i	$-0.657141\pi$
$701$	13.9183	−	24.1073i	0.525688	−	0.910519i	0.999552	−	0.0299208i	$-0.00952551\pi$
$702$	−4.97941	−	8.62459i	−0.187936	−	0.325514i
$703$	−13.5667	−	23.4982i	−0.511677	−	0.886250i
$704$	−2.55510	−	4.42557i	−0.0962991	−	0.166795i
$705$	11.0922			0.417756
$706$	−36.4023	+	63.0506i	−1.37002	+	2.37294i
$707$	34.4377	−	59.6479i	1.29516	−	2.24329i
$708$	−11.5524	−	20.0094i	−0.434167	−	0.751999i
$709$	17.5639			0.659624			0.329812	−	0.944047i	$-0.393015\pi$
$709$	17.5639			0.659624			0.329812	+	0.944047i	$0.393015\pi$
$710$	14.2831	−	24.7390i	0.536034	−	0.928438i
$711$	11.5713			0.433957
$712$	−41.1570			−1.54243
$713$	−9.32085	+	19.8610i	−0.349069	+	0.743800i
$714$	7.12885			0.266790
$715$	3.69890			0.138331
$716$	41.4741	−	71.8353i	1.54996	−	2.68461i
$717$	−2.93953			−0.109779
$718$	23.2147	+	40.2091i	0.866366	+	1.50059i
$719$	−13.3340	+	23.0952i	−0.497274	+	0.861304i	−0.999995	−	0.00314467i	$-0.998999\pi$
$719$	−13.3340	+	23.0952i	−0.497274	+	0.861304i	0.502721	+	0.864449i	$0.332332\pi$
$720$	−4.44064	+	7.69142i	−0.165493	+	0.286642i
$721$	−67.3306			−2.50752
$722$	−14.3726	−	24.8940i	−0.534891	−	0.926459i
$723$	2.49539	+	4.32215i	0.0928047	+	0.160742i
$724$	−8.05769	−	13.9563i	−0.299462	−	0.518683i
$725$	−1.74494	+	3.02232i	−0.0648053	+	0.112246i
$726$	13.0606	+	22.6216i	0.484725	+	0.839568i
$727$	−9.40054	+	16.2822i	−0.348647	+	0.603874i	−0.986009	−	0.166690i	$-0.946692\pi$
$727$	−9.40054	+	16.2822i	−0.348647	+	0.603874i	0.637363	+	0.770564i	$0.280025\pi$
$728$	120.106			4.45144
$729$	1.00000			0.0370370
$730$	14.1213	−	24.4589i	0.522654	−	0.905264i
$731$	−3.12021	−	5.40436i	−0.115405	−	0.199887i
$732$	15.0310	−	26.0345i	0.555562	−	0.962261i
$733$	−9.05544	−	15.6845i	−0.334470	−	0.579319i	0.648913	−	0.760863i	$-0.275224\pi$
$733$	−9.05544	−	15.6845i	−0.334470	−	0.579319i	−0.983383	+	0.181543i	$0.941891\pi$
$734$	3.26705	+	5.65870i	0.120589	+	0.208866i
$735$	6.28838	+	10.8918i	0.231950	+	0.401750i
$736$	−35.0493			−1.29193
$737$	4.75912	−	8.24304i	0.175304	−	0.303636i
$738$	3.21467	−	5.56798i	0.118334	−	0.204960i
$739$	−6.38322	−	11.0561i	−0.234811	−	0.406704i	0.724407	−	0.689372i	$-0.242114\pi$
$739$	−6.38322	−	11.0561i	−0.234811	−	0.406704i	−0.959218	+	0.282669i	$0.908780\pi$
$740$	45.5743			1.67534
$741$	5.40210	−	9.35671i	0.198451	−	0.343727i
$742$	141.768			5.20447
$743$	27.0956			0.994040			0.497020	−	0.867739i	$-0.334428\pi$
$743$	27.0956			0.994040			0.497020	+	0.867739i	$0.334428\pi$
$744$	−22.4958	−	32.2960i	−0.824736	−	1.18403i
$745$	19.1801			0.702706
$746$	−35.7931			−1.31048
$747$	6.44069	−	11.1556i	0.235653	−	0.408162i
$748$	−2.82804			−0.103403
$749$	16.3209	+	28.2686i	0.596353	+	1.03291i
$750$	−1.29670	+	2.24596i	−0.0473489	+	0.0820107i
$751$	−23.9161	+	41.4240i	−0.872712	+	1.51158i	−0.0135324	+	0.999908i	$0.504308\pi$
$751$	−23.9161	+	41.4240i	−0.872712	+	1.51158i	−0.859180	+	0.511674i	$0.829026\pi$
$752$	−98.5128			−3.59239
$753$	8.25532	+	14.2986i	0.300840	+	0.521071i
$754$	17.3775	+	30.0988i	0.632852	+	1.09613i
$755$	3.23059	+	5.59555i	0.117573	+	0.203643i
$756$	−10.4547	+	18.1081i	−0.380234	+	0.658585i
$757$	10.7977	+	18.7021i	0.392448	+	0.679740i	0.992772	−	0.120017i	$-0.0382949\pi$
$757$	10.7977	+	18.7021i	0.392448	+	0.679740i	−0.600324	+	0.799757i	$0.704962\pi$
$758$	4.54388	−	7.87022i	0.165041	−	0.285859i
$759$	−3.79559			−0.137771
$760$	−19.8890			−0.721450
$761$	5.19113	−	8.99130i	0.188178	−	0.325934i	−0.756465	−	0.654035i	$-0.773075\pi$
$761$	5.19113	−	8.99130i	0.188178	−	0.325934i	0.944643	+	0.328100i	$0.106408\pi$
$762$	−4.42811	−	7.66971i	−0.160413	−	0.277844i
$763$	26.0834	−	45.1778i	0.944284	−	1.63555i
$764$	46.0936	+	79.8365i	1.66761	+	2.88838i
$765$	0.310634	+	0.538033i	0.0112310	+	0.0194526i
$766$	22.5440	+	39.0473i	0.814546	+	1.41084i
$767$	−18.7745			−0.677909
$768$	−10.5322	+	18.2423i	−0.380048	+	0.658262i
$769$	−7.93960	+	13.7518i	−0.286309	+	0.495902i	−0.972926	−	0.231118i	$-0.925762\pi$
$769$	−7.93960	+	13.7518i	−0.286309	+	0.495902i	0.686617	+	0.727020i	$0.259095\pi$
$770$	−5.52646	−	9.57210i	−0.199160	−	0.344955i
$771$	28.6974			1.03351
$772$	−10.2098	+	17.6840i	−0.367460	+	0.636460i
$773$	10.1852			0.366337			0.183169	−	0.983082i	$-0.441365\pi$
$773$	10.1852			0.366337			0.183169	+	0.983082i	$0.441365\pi$
$774$	26.0499			0.936344
$775$	−3.18232	−	4.56868i	−0.114312	−	0.164112i
$776$	−26.9477			−0.967367
$777$	42.6696			1.53076
$778$	−32.0553	+	55.5215i	−1.14924	+	1.99054i
$779$	6.97511			0.249909
$780$	9.07359	+	15.7159i	0.324887	+	0.562720i
$781$	−5.30501	+	9.18855i	−0.189828	+	0.328792i
$782$	−3.17441	+	5.49824i	−0.113517	+	0.196617i
$783$	−3.48987			−0.124718
$784$	−55.8489	−	96.7332i	−1.99460	−	3.45476i
$785$	3.74629	+	6.48876i	0.133711	+	0.231594i
$786$	22.4485	+	38.8819i	0.800711	+	1.38687i
$787$	−19.3804	+	33.5678i	−0.690836	+	1.19656i	0.280729	+	0.959787i	$0.409424\pi$
$787$	−19.3804	+	33.5678i	−0.690836	+	1.19656i	−0.971564	+	0.236776i	$0.923909\pi$
$788$	12.2817	+	21.2725i	0.437518	+	0.757803i
$789$	−3.20633	+	5.55353i	−0.114149	+	0.197711i
$790$	−30.0091			−1.06767
$791$	−6.08590			−0.216390
$792$	3.40458	−	5.89691i	0.120977	−	0.209538i
$793$	−12.2139	−	21.1551i	−0.433727	−	0.751238i
$794$	−26.5743	+	46.0281i	−0.943087	+	1.63348i
$795$	6.17742	+	10.6996i	0.219090	+	0.379476i
$796$	−56.3329	−	97.5714i	−1.99667	−	3.45833i
$797$	−10.2670	−	17.7830i	−0.363678	−	0.629908i	0.624885	−	0.780716i	$-0.285146\pi$
$797$	−10.2670	−	17.7830i	−0.363678	−	0.629908i	−0.988563	+	0.150808i	$0.951812\pi$
$798$	−32.2847			−1.14286
$799$	−3.44560	+	5.96796i	−0.121897	+	0.211131i
$800$	4.44739	−	7.70311i	0.157239	−	0.272346i
$801$	−2.91109	−	5.04216i	−0.102858	−	0.178156i
$802$	30.2121			1.06683
$803$	−5.24494	+	9.08451i	−0.185090	+	0.320585i
$804$	46.6974			1.64689
$805$	−17.4347			−0.614492
$806$	−55.2491	+	4.69683i	−1.94607	+	0.165439i
$807$	19.8300			0.698048
$808$	−110.040			−3.87121
$809$	0.667820	−	1.15670i	0.0234793	−	0.0406673i	−0.854047	−	0.520196i	$-0.825859\pi$
$809$	0.667820	−	1.15670i	0.0234793	−	0.0406673i	0.877526	+	0.479528i	$0.159192\pi$
$810$	−2.59341			−0.0911230
$811$	−19.9324	−	34.5240i	−0.699922	−	1.21230i	−0.968493	−	0.249041i	$-0.919885\pi$
$811$	−19.9324	−	34.5240i	−0.699922	−	1.21230i	0.268571	−	0.963260i	$-0.413449\pi$
$812$	36.4856	−	63.1950i	1.28039	−	2.21771i
$813$	4.26122	−	7.38066i	0.149448	−	0.258851i
$814$	−24.0910			−0.844389
$815$	−5.39914	−	9.35158i	−0.189124	−	0.327572i
$816$	−2.75883	−	4.77843i	−0.0965782	−	0.167278i
$817$	14.1306	+	24.4749i	0.494367	+	0.856268i
$818$	21.5799	−	37.3774i	0.754523	−	1.30687i
$819$	8.49528	+	14.7143i	0.296849	+	0.514158i
$820$	−5.85785	+	10.1461i	−0.204565	+	0.354317i
$821$	−24.9402			−0.870417			−0.435209	−	0.900330i	$-0.643325\pi$
$821$	−24.9402			−0.870417			−0.435209	+	0.900330i	$0.643325\pi$
$822$	−9.20336			−0.321004
$823$	−10.6488	+	18.4443i	−0.371195	+	0.642929i	−0.989750	−	0.142813i	$-0.954385\pi$
$823$	−10.6488	+	18.4443i	−0.371195	+	0.642929i	0.618554	+	0.785742i	$0.287719\pi$
$824$	53.7862	+	93.1604i	1.87373	+	3.24540i
$825$	0.481621	−	0.834192i	0.0167679	−	0.0290428i
$826$	28.0506	+	48.5851i	0.976007	+	1.69049i
$827$	−24.4268	−	42.3085i	−0.849404	−	1.47121i	−0.881741	−	0.471734i	$-0.843628\pi$
$827$	−24.4268	−	42.3085i	−0.849404	−	1.47121i	0.0323369	−	0.999477i	$-0.489705\pi$
$828$	−9.31077	−	16.1267i	−0.323572	−	0.560443i
$829$	−14.4526			−0.501961			−0.250980	−	0.967992i	$-0.580753\pi$
$829$	−14.4526			−0.501961			−0.250980	+	0.967992i	$0.580753\pi$
$830$	−16.7033	+	28.9310i	−0.579781	+	1.00421i
$831$	9.54690	−	16.5357i	0.331178	−	0.573617i
$832$	−10.1862	−	17.6429i	−0.353142	−	0.611659i
$833$	−7.81353			−0.270723
$834$	−10.6949	+	18.5242i	−0.370336	+	0.641440i
$835$	−3.41873			−0.118310
$836$	12.8074			0.442954
$837$	2.36544	−	5.04031i	0.0817615	−	0.174219i
$838$	34.9117			1.20601
$839$	6.63663			0.229122			0.114561	−	0.993416i	$-0.463454\pi$
$839$	6.63663			0.229122			0.114561	+	0.993416i	$0.463454\pi$
$840$	15.6386	−	27.0869i	0.539584	−	0.934587i
$841$	−16.8208			−0.580027
$842$	−14.8681	−	25.7524i	−0.512390	−	0.887485i
$843$	11.8030	−	20.4434i	0.406516	−	0.704107i
$844$	35.4216	−	61.3519i	1.21926	−	2.11182i
$845$	1.74602			0.0600648
$846$	−14.3833	−	24.9126i	−0.494507	−	0.856511i
$847$	−22.2825	−	38.5944i	−0.765635	−	1.32612i
$848$	−54.8634	−	95.0262i	−1.88402	−	3.26321i
$849$	−4.74301	+	8.21513i	−0.162780	+	0.281943i
$850$	−0.805599	−	1.39534i	−0.0276318	−	0.0478597i
$851$	−19.0004	+	32.9096i	−0.651325	+	1.12813i
$852$	−52.0538			−1.78333
$853$	34.3737			1.17693			0.588466	−	0.808522i	$-0.299732\pi$
$853$	34.3737			1.17693			0.588466	+	0.808522i	$0.299732\pi$
$854$	−36.4970	+	63.2147i	−1.24890	+	2.16316i
$855$	−1.40678	−	2.43661i	−0.0481107	−	0.0833302i
$856$	26.0755	−	45.1640i	0.891241	−	1.54368i
$857$	−15.3024	−	26.5045i	−0.522719	−	0.905375i	−0.999651	−	0.0264350i	$-0.991584\pi$
$857$	−15.3024	−	26.5045i	−0.522719	−	0.905375i	0.476932	−	0.878940i	$-0.341749\pi$
$858$	−4.79638	−	8.30757i	−0.163746	−	0.283616i
$859$	22.6194	+	39.1780i	0.771766	+	1.33674i	0.936595	+	0.350415i	$0.113959\pi$
$859$	22.6194	+	39.1780i	0.771766	+	1.33674i	−0.164829	+	0.986322i	$0.552707\pi$
$860$	−47.4687			−1.61867
$861$	−5.48450	+	9.49943i	−0.186911	+	0.323740i
$862$	−2.62408	+	4.54504i	−0.0893765	+	0.154805i
$863$	6.80988	+	11.7951i	0.231811	+	0.401509i	0.958341	−	0.285626i	$-0.0922015\pi$
$863$	6.80988	+	11.7951i	0.231811	+	0.401509i	−0.726530	+	0.687135i	$0.758868\pi$
$864$	8.89478			0.302607
$865$	8.18946	−	14.1846i	0.278450	−	0.482289i
$866$	40.8687			1.38878
$867$	16.6140			0.564242
$868$	66.5404	+	95.5285i	2.25853	+	3.24245i
$869$	11.1460			0.378101
$870$	9.05067			0.306846
$871$	18.9727	−	32.8616i	0.642865	−	1.11347i
$872$	−83.3456			−2.82244
$873$	−1.90605	−	3.30137i	−0.0645099	−	0.111734i
$874$	14.3761	−	24.9001i	0.486277	−	0.842257i
$875$	2.21228	−	3.83178i	0.0747888	−	0.129538i
$876$	−51.4644			−1.73882
$877$	3.69025	+	6.39171i	0.124611	+	0.215833i	0.921581	−	0.388187i	$-0.126898\pi$
$877$	3.69025	+	6.39171i	0.124611	+	0.215833i	−0.796970	+	0.604019i	$0.793565\pi$
$878$	51.3694	+	88.9745i	1.73363	+	3.00274i
$879$	−0.598826	−	1.03720i	−0.0201979	−	0.0349838i
$880$	−4.27742	+	7.40870i	−0.144192	+	0.249747i
$881$	−4.12246	−	7.14032i	−0.138889	−	0.240563i	0.788187	−	0.615436i	$-0.211020\pi$
$881$	−4.12246	−	7.14032i	−0.138889	−	0.240563i	−0.927076	+	0.374872i	$0.877687\pi$
$882$	16.3083	−	28.2469i	0.549130	−	0.951121i
$883$	−49.6813			−1.67191			−0.835955	−	0.548799i	$-0.815085\pi$
$883$	−49.6813			−1.67191			−0.835955	+	0.548799i	$0.815085\pi$
$884$	−11.2742			−0.379194
$885$	−2.44457	+	4.23411i	−0.0821732	+	0.142328i
$886$	−20.2382	−	35.0535i	−0.679915	−	1.17765i
$887$	−7.95401	+	13.7768i	−0.267070	+	0.462578i	−0.968104	−	0.250550i	$-0.919389\pi$
$887$	−7.95401	+	13.7768i	−0.267070	+	0.462578i	0.701034	+	0.713128i	$0.252722\pi$
$888$	−34.0861	−	59.0388i	−1.14385	−	1.98121i
$889$	7.55471	+	13.0851i	0.253377	+	0.438862i
$890$	7.54964	+	13.0764i	0.253065	+	0.438321i
$891$	0.963242			0.0322698
$892$	14.5320	−	25.1702i	0.486568	−	0.842761i
$893$	15.6042	−	27.0273i	0.522175	−	0.904434i
$894$	−24.8710	−	43.0778i	−0.831809	−	1.44074i
$895$	−17.5524			−0.586711
$896$	8.91766	−	15.4458i	0.297918	−	0.516009i
$897$	−15.1315			−0.505225
$898$	28.6345			0.955545
$899$	−8.25508	+	17.5900i	−0.275322	+	0.586661i
$900$	4.72576			0.157525
$901$	−7.67565			−0.255713
$902$	3.09651	−	5.36331i	0.103102	−	0.178579i
$903$	−44.4432			−1.47898
$904$	4.86164	+	8.42061i	0.161696	+	0.280065i
$905$	−1.70506	+	2.95324i	−0.0566780	+	0.0981691i
$906$	8.37824	−	14.5115i	0.278349	−	0.482114i
$907$	48.1440			1.59860			0.799298	−	0.600934i	$-0.205205\pi$
$907$	48.1440			1.59860			0.799298	+	0.600934i	$0.205205\pi$
$908$	−22.1770	−	38.4117i	−0.735970	−	1.27474i
$909$	−7.78330	−	13.4811i	−0.258156	−	0.447139i
$910$	−22.0317	−	38.1601i	−0.730345	−	1.26499i
$911$	4.15724	−	7.20054i	0.137735	−	0.238565i	−0.788904	−	0.614517i	$-0.789351\pi$
$911$	4.15724	−	7.20054i	0.137735	−	0.238565i	0.926639	+	0.375952i	$0.122684\pi$
$912$	12.4940	+	21.6402i	0.413717	+	0.716579i
$913$	6.20395	−	10.7456i	0.205321	−	0.355626i
$914$	−32.6586			−1.08025
$915$	−6.36130			−0.210298
$916$	29.9675	−	51.9053i	0.990155	−	1.71500i
$917$	−38.2989	−	66.3357i	−1.26474	−	2.19060i
$918$	0.805599	−	1.39534i	0.0265887	−	0.0460530i
$919$	3.94756	+	6.83738i	0.130218	+	0.225544i	0.923761	−	0.382971i	$-0.125099\pi$
$919$	3.94756	+	6.83738i	0.130218	+	0.225544i	−0.793542	+	0.608515i	$0.791766\pi$
$920$	13.9275	+	24.1231i	0.459175	+	0.795315i
$921$	14.2353	+	24.6562i	0.469068	+	0.812450i
$922$	94.3666			3.10780
$923$	−21.1489	+	36.6310i	−0.696125	+	1.20572i
$924$	−10.0704	+	17.4425i	−0.331293	+	0.573815i
$925$	−4.82190	−	8.35178i	−0.158543	−	0.274605i
$926$	−15.4081			−0.506341
$927$	−7.60873	+	13.1787i	−0.249904	+	0.432846i
$928$	−31.0417			−1.01899
$929$	−34.6142			−1.13565			−0.567827	−	0.823148i	$-0.692216\pi$
$929$	−34.6142			−1.13565			−0.567827	+	0.823148i	$0.692216\pi$
$930$	−6.13454	+	13.0716i	−0.201160	+	0.428634i
$931$	35.3854			1.15971
$932$	−25.6680			−0.840785
$933$	−0.911592	+	1.57892i	−0.0298442	+	0.0516917i
$934$	−58.5348			−1.91532
$935$	0.299215	+	0.518256i	0.00978539	+	0.0169488i
$936$	13.5727	−	23.5086i	0.443637	−	0.768402i
$937$	8.22898	−	14.2530i	0.268829	−	0.465626i	−0.699731	−	0.714407i	$-0.746697\pi$
$937$	8.22898	−	14.2530i	0.268829	−	0.465626i	0.968560	+	0.248781i	$0.0800300\pi$
$938$	−113.387			−3.70221
$939$	−3.06397	−	5.30695i	−0.0999888	−	0.173186i
$940$	26.2095	+	45.3962i	0.854859	+	1.48066i
$941$	−13.3981	−	23.2062i	−0.436766	−	0.756501i	0.560672	−	0.828038i	$-0.310543\pi$
$941$	−13.3981	−	23.2062i	−0.436766	−	0.756501i	−0.997438	+	0.0715371i	$0.977210\pi$
$942$	9.71565	−	16.8280i	0.316553	−	0.548286i
$943$	−4.88439	−	8.46001i	−0.159058	−	0.275496i
$944$	21.7109	−	37.6044i	0.706629	−	1.22392i
$945$	4.42456			0.143931
$946$	25.0924			0.815823
$947$	30.0815	−	52.1028i	0.977519	−	1.69311i	0.306159	−	0.951980i	$-0.400956\pi$
$947$	30.0815	−	52.1028i	0.977519	−	1.69311i	0.671360	−	0.741132i	$-0.265711\pi$
$948$	27.3416	+	47.3570i	0.888013	+	1.53808i
$949$	−20.9095	+	36.2162i	−0.678750	+	1.17563i
$950$	3.64834	+	6.31912i	0.118368	+	0.205019i
$951$	5.29526	+	9.17167i	0.171711	+	0.297412i
$952$	9.71577	+	16.8282i	0.314890	+	0.545405i
$953$	6.97741			0.226021			0.113010	−	0.993594i	$-0.463951\pi$
$953$	6.97741			0.226021			0.113010	+	0.993594i	$0.463951\pi$
$954$	16.0206	−	27.7484i	0.518685	−	0.898388i
$955$	9.75370	−	16.8939i	0.315622	−	0.546674i
$956$	−6.94576	−	12.0304i	−0.224642	−	0.389091i
$957$	−3.36159			−0.108665
$958$	−14.2592	+	24.6977i	−0.460695	+	0.797947i
$959$	15.7017			0.507034
$960$	−5.30522			−0.171225
$961$	−19.8094	−	23.8451i	−0.639013	−	0.769196i
$962$	−96.0410			−3.09648
$963$	7.37741			0.237734
$964$	−11.7926	+	20.4254i	−0.379815	+	0.657859i
$965$	4.32093			0.139096
$966$	22.6076	+	39.1576i	0.727389	+	1.25987i
$967$	22.9446	−	39.7412i	0.737849	−	1.27799i	−0.215613	−	0.976479i	$-0.569175\pi$
$967$	22.9446	−	39.7412i	0.737849	−	1.27799i	0.953462	−	0.301513i	$-0.0974918\pi$
$968$	−35.6001	+	61.6612i	−1.14423	+	1.98186i
$969$	1.74797			0.0561528
$970$	4.94316	+	8.56180i	0.158715	+	0.274903i
$971$	18.0170	+	31.2064i	0.578194	+	1.00146i	0.995687	+	0.0927814i	$0.0295758\pi$
$971$	18.0170	+	31.2064i	0.578194	+	1.00146i	−0.417492	+	0.908680i	$0.637091\pi$
$972$	2.36288	+	4.09263i	0.0757894	+	0.131271i
$973$	18.2464	−	31.6038i	0.584954	−	1.01317i
$974$	35.6775	+	61.7952i	1.14318	+	1.98005i
$975$	1.92003	−	3.32558i	0.0614901	−	0.106504i
$976$	56.4966			1.80841
$977$	11.7887			0.377153			0.188576	−	0.982059i	$-0.439613\pi$
$977$	11.7887			0.377153			0.188576	+	0.982059i	$0.439613\pi$
$978$	−14.0022	+	24.2525i	−0.447740	+	0.775508i
$979$	−2.80409	−	4.85682i	−0.0896190	−	0.155225i
$980$	−29.7174	+	51.4720i	−0.949287	+	1.64421i
$981$	−5.89514	−	10.2107i	−0.188217	−	0.326002i
$982$	−27.7305	−	48.0307i	−0.884917	−	1.53272i
$983$	−15.2488	−	26.4117i	−0.486361	−	0.842403i	0.513516	−	0.858080i	$-0.328343\pi$
$983$	−15.2488	−	26.4117i	−0.486361	−	0.842403i	−0.999877	+	0.0156775i	$0.995009\pi$
$984$	17.5249			0.558672
$985$	2.59888	−	4.50140i	0.0828074	−	0.143427i
$986$	−2.81144	+	4.86956i	−0.0895345	+	0.155078i
$987$	24.5390	+	42.5028i	0.781086	+	1.35288i
$988$	51.0580			1.62437
$989$	19.7902	−	34.2776i	0.629290	−	1.08996i
$990$	−2.49808			−0.0793942
$991$	3.23646			0.102810			0.0514048	−	0.998678i	$-0.483630\pi$
$991$	3.23646			0.102810			0.0514048	+	0.998678i	$0.483630\pi$
$992$	21.0401	−	44.8324i	0.668022	−	1.42343i
$993$	−0.214041			−0.00679237
$994$	126.393			4.00893
$995$	−11.9204	+	20.6467i	−0.377902	+	0.654545i
$996$	60.8743			1.92888
$997$	16.3801	+	28.3712i	0.518763	+	0.898524i	0.999762	+	0.0218030i	$0.00694067\pi$
$997$	16.3801	+	28.3712i	0.518763	+	0.898524i	−0.480999	+	0.876721i	$0.659726\pi$
$998$	39.8370	−	68.9996i	1.26102	−	2.18414i
$999$	4.82190	−	8.35178i	0.152558	−	0.264239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.i.f.346.1	yes	14
31.25	even	3	inner	465.2.i.f.211.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.i.f.211.1	✓	14	31.25	even	3	inner
465.2.i.f.346.1	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.59341 q^{2} +(0.500000 - 0.866025i) q^{3} +4.72576 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.29670 + 2.24596i) q^{6} +(2.21228 - 3.83178i) q^{7} -7.06901 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.29670 + 2.24596i) q^{10} +(-0.481621 - 0.834192i) q^{11} +(2.36288 - 4.09263i) q^{12} +(-1.92003 - 3.32558i) q^{13} +(-5.73735 + 9.93738i) q^{14} -1.00000 q^{15} +8.88129 q^{16} +(0.310634 - 0.538033i) q^{17} +(1.29670 + 2.24596i) q^{18} +(-1.40678 + 2.43661i) q^{19} +(-2.36288 - 4.09263i) q^{20} +(-2.21228 - 3.83178i) q^{21} +(1.24904 + 2.16340i) q^{22} +3.94043 q^{23} +(-3.53450 + 6.12194i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(4.97941 + 8.62459i) q^{26} -1.00000 q^{27} +(10.4547 - 18.1081i) q^{28} +3.48987 q^{29} +2.59341 q^{30} +(-2.36544 + 5.04031i) q^{31} -8.89478 q^{32} -0.963242 q^{33} +(-0.805599 + 1.39534i) q^{34} -4.42456 q^{35} +(-2.36288 - 4.09263i) q^{36} +(-4.82190 + 8.35178i) q^{37} +(3.64834 - 6.31912i) q^{38} -3.84005 q^{39} +(3.53450 + 6.12194i) q^{40} +(-1.23956 - 2.14697i) q^{41} +(5.73735 + 9.93738i) q^{42} +(5.02233 - 8.69893i) q^{43} +(-2.27603 - 3.94219i) q^{44} +(-0.500000 + 0.866025i) q^{45} -10.2191 q^{46} -11.0922 q^{47} +(4.44064 - 7.69142i) q^{48} +(-6.28838 - 10.8918i) q^{49} +(1.29670 - 2.24596i) q^{50} +(-0.310634 - 0.538033i) q^{51} +(-9.07359 - 15.7159i) q^{52} +(-6.17742 - 10.6996i) q^{53} +2.59341 q^{54} +(-0.481621 + 0.834192i) q^{55} +(-15.6386 + 27.0869i) q^{56} +(1.40678 + 2.43661i) q^{57} -9.05067 q^{58} +(2.44457 - 4.23411i) q^{59} -4.72576 q^{60} +6.36130 q^{61} +(6.13454 - 13.0716i) q^{62} -4.42456 q^{63} +5.30522 q^{64} +(-1.92003 + 3.32558i) q^{65} +2.49808 q^{66} +(4.94073 + 8.55760i) q^{67} +(1.46798 - 2.54261i) q^{68} +(1.97022 - 3.41252i) q^{69} +11.4747 q^{70} +(-5.50746 - 9.53919i) q^{71} +(3.53450 + 6.12194i) q^{72} +(-5.44509 - 9.43118i) q^{73} +(12.5052 - 21.6596i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-6.64809 + 11.5148i) q^{76} -4.26193 q^{77} +9.95882 q^{78} +(-5.78565 + 10.0210i) q^{79} +(-4.44064 - 7.69142i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.21467 + 5.56798i) q^{82} +(6.44069 + 11.1556i) q^{83} +(-10.4547 - 18.1081i) q^{84} -0.621267 q^{85} +(-13.0249 + 22.5599i) q^{86} +(1.74494 - 3.02232i) q^{87} +(3.40458 + 5.89691i) q^{88} +5.82218 q^{89} +(1.29670 - 2.24596i) q^{90} -16.9906 q^{91} +18.6215 q^{92} +(3.18232 + 4.56868i) q^{93} +28.7665 q^{94} +2.81355 q^{95} +(-4.44739 + 7.70311i) q^{96} +3.81210 q^{97} +(16.3083 + 28.2469i) q^{98} +(-0.481621 + 0.834192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} + 7 q^{3} + 22 q^{4} - 7 q^{5} + q^{6} - 2 q^{7} + 6 q^{8} - 7 q^{9} - q^{10} + 11 q^{12} + 2 q^{13} - 14 q^{14} - 14 q^{15} + 30 q^{16} + 7 q^{17} - q^{18} - 4 q^{19} - 11 q^{20} + 2 q^{21}+ \cdots + 2 q^{98}+O(q^{100}) \) 14 * q + 2 * q^2 + 7 * q^3 + 22 * q^4 - 7 * q^5 + q^6 - 2 * q^7 + 6 * q^8 - 7 * q^9 - q^10 + 11 * q^12 + 2 * q^13 - 14 * q^14 - 14 * q^15 + 30 * q^16 + 7 * q^17 - q^18 - 4 * q^19 - 11 * q^20 + 2 * q^21 - 2 * q^22 - 22 * q^23 + 3 * q^24 - 7 * q^25 + 9 * q^26 - 14 * q^27 + 11 * q^28 - 32 * q^29 - 2 * q^30 + 15 * q^31 + 24 * q^32 - 6 * q^34 + 4 * q^35 - 11 * q^36 - 5 * q^37 - 4 * q^38 + 4 * q^39 - 3 * q^40 - 5 * q^41 + 14 * q^42 + 17 * q^43 - 18 * q^44 - 7 * q^45 - 60 * q^46 - 6 * q^47 + 15 * q^48 - 21 * q^49 - q^50 - 7 * q^51 + 3 * q^52 - 7 * q^53 - 2 * q^54 - 62 * q^56 + 4 * q^57 - 20 * q^58 + 6 * q^59 - 22 * q^60 + 36 * q^61 + 55 * q^62 + 4 * q^63 + 42 * q^64 + 2 * q^65 - 4 * q^66 + 7 * q^68 - 11 * q^69 + 28 * q^70 - 6 * q^71 - 3 * q^72 - 14 * q^73 - 18 * q^74 + 7 * q^75 - 8 * q^76 - 4 * q^77 + 18 * q^78 + 6 * q^79 - 15 * q^80 - 7 * q^81 + 12 * q^82 - q^83 - 11 * q^84 - 14 * q^85 - 53 * q^86 - 16 * q^87 - 21 * q^88 + 40 * q^89 - q^90 - 94 * q^91 + 46 * q^92 + 27 * q^93 + 104 * q^94 + 8 * q^95 + 12 * q^96 + 40 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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