LMFDB - Embedded newform 930.2.i.n.211.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(211,930)] 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("930.211"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-6,3,6,-3,-3,-4,-6,-3,3,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3636603.4
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 4x^{3} + 12x^{2} - 16x + 64 $ x^6 - x^5 + 3x^4 + 4x^3 + 12x^2 - 16x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.3
Root			$1.34370 - 1.48137i$ of defining polynomial
Character	$\chi$	$=$	930.211
Dual form			930.2.i.n.811.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.954758 + 1.65369i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(3.18740 - 5.52074i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.90952 - 5.03943i) q^{13} +(-0.954758 - 1.65369i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-3.45476 - 5.98382i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.22212 - 2.11677i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.954758 + 1.65369i) q^{21} +(-3.18740 + 5.52074i) q^{22} -0.909516 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.90952 + 5.03943i) q^{26} -1.00000 q^{27} +(0.954758 + 1.65369i) q^{28} +5.46528 q^{29} +1.00000 q^{30} +(4.42004 + 3.38574i) q^{31} -1.00000 q^{32} +6.37480 q^{33} +(3.45476 + 5.98382i) q^{34} -1.90952 q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.45476 + 7.71587i) q^{37} +(1.22212 + 2.11677i) q^{38} +5.81903 q^{39} +(0.500000 - 0.866025i) q^{40} +(3.59692 - 6.23004i) q^{41} +(0.954758 - 1.65369i) q^{42} +(0.232642 + 0.402947i) q^{43} +(3.18740 - 5.52074i) q^{44} +(-0.500000 - 0.866025i) q^{45} +0.909516 q^{46} -8.72855 q^{47} +(0.500000 + 0.866025i) q^{48} +(1.67687 - 2.90443i) q^{49} +(0.500000 + 0.866025i) q^{50} +(3.45476 - 5.98382i) q^{51} +(2.90952 - 5.03943i) q^{52} +(-3.64216 + 6.30840i) q^{53} +1.00000 q^{54} +(3.18740 + 5.52074i) q^{55} +(-0.954758 - 1.65369i) q^{56} +(1.22212 - 2.11677i) q^{57} -5.46528 q^{58} +(2.86427 + 4.96107i) q^{59} -1.00000 q^{60} -4.44423 q^{61} +(-4.42004 - 3.38574i) q^{62} -1.90952 q^{63} +1.00000 q^{64} +(2.90952 + 5.03943i) q^{65} -6.37480 q^{66} +(-4.45476 + 7.71587i) q^{67} +(-3.45476 - 5.98382i) q^{68} +(-0.454758 - 0.787664i) q^{69} +1.90952 q^{70} +(4.90952 - 8.50353i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-4.45476 - 7.71587i) q^{74} +(0.500000 - 0.866025i) q^{75} +(-1.22212 - 2.11677i) q^{76} +12.1728 q^{77} -5.81903 q^{78} +(0.232642 + 0.402947i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.59692 + 6.23004i) q^{82} +(6.32956 - 10.9631i) q^{83} +(-0.954758 + 1.65369i) q^{84} +6.90952 q^{85} +(-0.232642 - 0.402947i) q^{86} +(2.73264 + 4.73307i) q^{87} +(-3.18740 + 5.52074i) q^{88} -15.8190 q^{89} +(0.500000 + 0.866025i) q^{90} +11.1115 q^{91} -0.909516 q^{92} +(-0.722116 + 5.52074i) q^{93} +8.72855 q^{94} +2.44423 q^{95} +(-0.500000 - 0.866025i) q^{96} +18.1728 q^{97} +(-1.67687 + 2.90443i) q^{98} +(3.18740 + 5.52074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 6 q^{16} - 11 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20}+ \cdots + 5 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 6 * q^16 - 11 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 14 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 - 6 * q^27 - 4 * q^28 + 24 * q^29 + 6 * q^30 + 8 * q^31 - 6 * q^32 + 10 * q^33 + 11 * q^34 + 8 * q^35 - 3 * q^36 + 17 * q^37 + 2 * q^38 - 4 * q^39 + 3 * q^40 - 12 * q^41 - 4 * q^42 - 3 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 + 6 * q^47 + 3 * q^48 - 5 * q^49 + 3 * q^50 + 11 * q^51 - 2 * q^52 + 2 * q^53 + 6 * q^54 + 5 * q^55 + 4 * q^56 + 2 * q^57 - 24 * q^58 - 12 * q^59 - 6 * q^60 - 16 * q^61 - 8 * q^62 + 8 * q^63 + 6 * q^64 - 2 * q^65 - 10 * q^66 - 17 * q^67 - 11 * q^68 + 7 * q^69 - 8 * q^70 + 10 * q^71 + 3 * q^72 + 6 * q^73 - 17 * q^74 + 3 * q^75 - 2 * q^76 + 4 * q^77 + 4 * q^78 - 3 * q^79 - 3 * q^80 - 3 * q^81 + 12 * q^82 + 4 * q^84 + 22 * q^85 + 3 * q^86 + 12 * q^87 - 5 * q^88 - 56 * q^89 + 3 * q^90 + 88 * q^91 + 14 * q^92 + q^93 - 6 * q^94 + 4 * q^95 - 3 * q^96 + 40 * q^97 + 5 * q^98 + 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	0.954758	+	1.65369i	0.360865	+	0.625036i	0.988103	−	0.153791i	$-0.0491483\pi$
$7$	0.954758	+	1.65369i	0.360865	+	0.625036i	−0.627239	+	0.778827i	$0.715815\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	3.18740	−	5.52074i	0.961037	−	1.66457i	0.241132	−	0.970492i	$-0.422481\pi$
$11$	3.18740	−	5.52074i	0.961037	−	1.66457i	0.719905	−	0.694073i	$-0.244185\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	2.90952	−	5.03943i	0.806955	−	1.39769i	−0.108009	−	0.994150i	$-0.534448\pi$
$13$	2.90952	−	5.03943i	0.806955	−	1.39769i	0.914964	−	0.403536i	$-0.132219\pi$
$14$	−0.954758	−	1.65369i	−0.255170	−	0.441967i
$15$	−1.00000			−0.258199
$16$	1.00000			0.250000
$17$	−3.45476	−	5.98382i	−0.837902	−	1.45129i	−0.891646	−	0.452734i	$-0.850449\pi$
$17$	−3.45476	−	5.98382i	−0.837902	−	1.45129i	0.0537438	−	0.998555i	$-0.482885\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.22212	−	2.11677i	−0.280373	−	0.485620i	0.691104	−	0.722756i	$-0.257125\pi$
$19$	−1.22212	−	2.11677i	−0.280373	−	0.485620i	−0.971477	+	0.237136i	$0.923791\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−0.954758	+	1.65369i	−0.208345	+	0.360865i
$22$	−3.18740	+	5.52074i	−0.679556	+	1.17703i
$23$	−0.909516			−0.189647			−0.0948236	−	0.995494i	$-0.530229\pi$
$23$	−0.909516			−0.189647			−0.0948236	+	0.995494i	$0.530229\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.90952	+	5.03943i	−0.570603	+	0.988313i
$27$	−1.00000			−0.192450
$28$	0.954758	+	1.65369i	0.180432	+	0.312518i
$29$	5.46528			1.01488			0.507439	−	0.861688i	$-0.330592\pi$
$29$	5.46528			1.01488			0.507439	+	0.861688i	$0.330592\pi$
$30$	1.00000			0.182574
$31$	4.42004	+	3.38574i	0.793863	+	0.608097i
$31$	4.42004	+	3.38574i	0.793863	+	0.608097i
$32$	−1.00000			−0.176777
$33$	6.37480			1.10971
$34$	3.45476	+	5.98382i	0.592486	+	1.02622i
$35$	−1.90952			−0.322767
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.45476	+	7.71587i	0.732358	+	1.26848i	0.955873	+	0.293780i	$0.0949134\pi$
$37$	4.45476	+	7.71587i	0.732358	+	1.26848i	−0.223515	+	0.974700i	$0.571753\pi$
$38$	1.22212	+	2.11677i	0.198253	+	0.343385i
$39$	5.81903			0.931791
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	3.59692	−	6.23004i	0.561744	−	0.972969i	−0.435601	−	0.900140i	$-0.643464\pi$
$41$	3.59692	−	6.23004i	0.561744	−	0.972969i	0.997344	−	0.0728288i	$-0.0232027\pi$
$42$	0.954758	−	1.65369i	0.147322	−	0.255170i
$43$	0.232642	+	0.402947i	0.0354775	+	0.0614488i	0.883219	−	0.468961i	$-0.155371\pi$
$43$	0.232642	+	0.402947i	0.0354775	+	0.0614488i	−0.847741	+	0.530410i	$0.822038\pi$
$44$	3.18740	−	5.52074i	0.480519	−	0.832283i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	0.909516			0.134101
$47$	−8.72855			−1.27319			−0.636595	−	0.771198i	$-0.719658\pi$
$47$	−8.72855			−1.27319			−0.636595	+	0.771198i	$0.719658\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	1.67687	−	2.90443i	0.239553	−	0.414919i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	3.45476	−	5.98382i	0.483763	−	0.837902i
$52$	2.90952	−	5.03943i	0.403477	−	0.698843i
$53$	−3.64216	+	6.30840i	−0.500289	+	0.866526i	0.499711	+	0.866192i	$0.333439\pi$
$53$	−3.64216	+	6.30840i	−0.500289	+	0.866526i	−1.00000		0.000333526i	$0.999894\pi$
$54$	1.00000			0.136083
$55$	3.18740	+	5.52074i	0.429789	+	0.744416i
$56$	−0.954758	−	1.65369i	−0.127585	−	0.220984i
$57$	1.22212	−	2.11677i	0.161873	−	0.280373i
$58$	−5.46528			−0.717627
$59$	2.86427	+	4.96107i	0.372897	+	0.645876i	0.990010	−	0.140998i	$-0.0450312\pi$
$59$	2.86427	+	4.96107i	0.372897	+	0.645876i	−0.617113	+	0.786874i	$0.711698\pi$
$60$	−1.00000			−0.129099
$61$	−4.44423			−0.569026			−0.284513	−	0.958672i	$-0.591832\pi$
$61$	−4.44423			−0.569026			−0.284513	+	0.958672i	$0.591832\pi$
$62$	−4.42004	−	3.38574i	−0.561346	−	0.429989i
$63$	−1.90952			−0.240576
$64$	1.00000			0.125000
$65$	2.90952	+	5.03943i	0.360881	+	0.625064i
$66$	−6.37480			−0.784684
$67$	−4.45476	+	7.71587i	−0.544235	+	0.942643i	0.454419	+	0.890788i	$0.349847\pi$
$67$	−4.45476	+	7.71587i	−0.544235	+	0.942643i	−0.998655	+	0.0518553i	$0.983487\pi$
$68$	−3.45476	−	5.98382i	−0.418951	−	0.725644i
$69$	−0.454758	−	0.787664i	−0.0547464	−	0.0948236i
$70$	1.90952			0.228231
$71$	4.90952	−	8.50353i	0.582652	−	1.00918i	−0.412511	−	0.910952i	$-0.635348\pi$
$71$	4.90952	−	8.50353i	0.582652	−	1.00918i	0.995164	−	0.0982310i	$-0.0313184\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	−4.45476	−	7.71587i	−0.517855	−	0.896951i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−1.22212	−	2.11677i	−0.140186	−	0.242810i
$77$	12.1728			1.38722
$78$	−5.81903			−0.658876
$79$	0.232642	+	0.402947i	0.0261742	+	0.0453351i	0.878816	−	0.477161i	$-0.158334\pi$
$79$	0.232642	+	0.402947i	0.0261742	+	0.0453351i	−0.852642	+	0.522496i	$0.825001\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.59692	+	6.23004i	−0.397213	+	0.687993i
$83$	6.32956	−	10.9631i	0.694759	−	1.20336i	−0.275503	−	0.961300i	$-0.588844\pi$
$83$	6.32956	−	10.9631i	0.694759	−	1.20336i	0.970262	−	0.242058i	$-0.0778224\pi$
$84$	−0.954758	+	1.65369i	−0.104173	+	0.180432i
$85$	6.90952			0.749442
$86$	−0.232642	−	0.402947i	−0.0250864	−	0.0434509i
$87$	2.73264	+	4.73307i	0.292970	+	0.507439i
$88$	−3.18740	+	5.52074i	−0.339778	+	0.588513i
$89$	−15.8190			−1.67681			−0.838407	−	0.545045i	$-0.816513\pi$
$89$	−15.8190			−1.67681			−0.838407	+	0.545045i	$0.816513\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	11.1115			1.16481
$92$	−0.909516			−0.0948236
$93$	−0.722116	+	5.52074i	−0.0748800	+	0.572474i
$94$	8.72855			0.900281
$95$	2.44423			0.250773
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	18.1728			1.84517			0.922583	−	0.385798i	$-0.126074\pi$
$97$	18.1728			1.84517			0.922583	+	0.385798i	$0.126074\pi$
$98$	−1.67687	+	2.90443i	−0.169390	+	0.293392i
$99$	3.18740	+	5.52074i	0.320346	+	0.554855i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	1.93057			0.192099			0.0960493	−	0.995377i	$-0.469379\pi$
$101$	1.93057			0.192099			0.0960493	+	0.995377i	$0.469379\pi$
$102$	−3.45476	+	5.98382i	−0.342072	+	0.592486i
$103$	1.86427	−	3.22902i	0.183692	−	0.318165i	−0.759443	−	0.650574i	$-0.774528\pi$
$103$	1.86427	−	3.22902i	0.183692	−	0.318165i	0.943135	+	0.332410i	$0.107862\pi$
$104$	−2.90952	+	5.03943i	−0.285302	+	0.494157i
$105$	−0.954758	−	1.65369i	−0.0931748	−	0.161384i
$106$	3.64216	−	6.30840i	0.353758	−	0.612726i
$107$	0.954758	+	1.65369i	0.0922999	+	0.159868i	0.908479	−	0.417932i	$-0.137245\pi$
$107$	0.954758	+	1.65369i	0.0922999	+	0.159868i	−0.816179	+	0.577800i	$0.803911\pi$
$108$	−1.00000			−0.0962250
$109$	−2.44423			−0.234115			−0.117058	−	0.993125i	$-0.537346\pi$
$109$	−2.44423			−0.234115			−0.117058	+	0.993125i	$0.537346\pi$
$110$	−3.18740	−	5.52074i	−0.303907	−	0.526382i
$111$	−4.45476	+	7.71587i	−0.422827	+	0.732358i
$112$	0.954758	+	1.65369i	0.0902161	+	0.156259i
$113$	−4.67687	+	8.10058i	−0.439963	+	0.762039i	−0.997686	−	0.0679884i	$-0.978342\pi$
$113$	−4.67687	+	8.10058i	−0.439963	+	0.762039i	0.557723	+	0.830027i	$0.311675\pi$
$114$	−1.22212	+	2.11677i	−0.114462	+	0.198253i
$115$	0.454758	−	0.787664i	0.0424064	−	0.0734500i
$116$	5.46528			0.507439
$117$	2.90952	+	5.03943i	0.268985	+	0.465895i
$118$	−2.86427	−	4.96107i	−0.263678	−	0.456703i
$119$	6.59692	−	11.4262i	0.604738	−	1.04744i
$120$	1.00000			0.0912871
$121$	−14.8190	−	25.6673i	−1.34718	−	2.33339i
$122$	4.44423			0.402362
$123$	7.19383			0.648646
$124$	4.42004	+	3.38574i	0.396931	+	0.304048i
$125$	1.00000			0.0894427
$126$	1.90952			0.170113
$127$	7.32956	+	12.6952i	0.650393	+	1.12651i	0.983028	+	0.183458i	$0.0587291\pi$
$127$	7.32956	+	12.6952i	0.650393	+	1.12651i	−0.332635	+	0.943056i	$0.607938\pi$
$128$	−1.00000			−0.0883883
$129$	−0.232642	+	0.402947i	−0.0204829	+	0.0354775i
$130$	−2.90952	−	5.03943i	−0.255181	−	0.441987i
$131$	−1.14216	−	1.97827i	−0.0997908	−	0.172843i	0.811807	−	0.583926i	$-0.198484\pi$
$131$	−1.14216	−	1.97827i	−0.0997908	−	0.172843i	−0.911598	+	0.411083i	$0.865151\pi$
$132$	6.37480			0.554855
$133$	2.33365	−	4.04200i	0.202353	−	0.350486i
$134$	4.45476	−	7.71587i	0.384832	−	0.666549i
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	3.45476	+	5.98382i	0.296243	+	0.513108i
$137$	−9.73907	+	16.8686i	−0.832065	+	1.44118i	0.0643326	+	0.997929i	$0.479508\pi$
$137$	−9.73907	+	16.8686i	−0.832065	+	1.44118i	−0.896398	+	0.443251i	$0.853825\pi$
$138$	0.454758	+	0.787664i	0.0387116	+	0.0670504i
$139$	11.3748			0.964798			0.482399	−	0.875952i	$-0.339766\pi$
$139$	11.3748			0.964798			0.482399	+	0.875952i	$0.339766\pi$
$140$	−1.90952			−0.161384
$141$	−4.36427	−	7.55914i	−0.367538	−	0.636595i
$142$	−4.90952	+	8.50353i	−0.411997	+	0.713600i
$143$	−18.5476	−	32.1254i	−1.55103	−	2.68646i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.73264	+	4.73307i	−0.226934	+	0.393060i
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$	3.35375			0.276613
$148$	4.45476	+	7.71587i	0.366179	+	0.634240i
$149$	3.35784	+	5.81595i	0.275085	+	0.476461i	0.970157	−	0.242479i	$-0.0779606\pi$
$149$	3.35784	+	5.81595i	0.275085	+	0.476461i	−0.695071	+	0.718941i	$0.744627\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−4.55577			−0.370743			−0.185372	−	0.982669i	$-0.559349\pi$
$151$	−4.55577			−0.370743			−0.185372	+	0.982669i	$0.559349\pi$
$152$	1.22212	+	2.11677i	0.0991267	+	0.171693i
$153$	6.90952			0.558601
$154$	−12.1728			−0.980911
$155$	−5.14216	+	2.13500i	−0.413028	+	0.171487i
$156$	5.81903			0.465895
$157$	−17.9434			−1.43204			−0.716021	−	0.698079i	$-0.754038\pi$
$157$	−17.9434			−1.43204			−0.716021	+	0.698079i	$0.754038\pi$
$158$	−0.232642	−	0.402947i	−0.0185080	−	0.0320567i
$159$	−7.28432			−0.577684
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−0.868368	−	1.50406i	−0.0684370	−	0.118536i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	5.79798			0.454133			0.227066	−	0.973879i	$-0.427087\pi$
$163$	5.79798			0.454133			0.227066	+	0.973879i	$0.427087\pi$
$164$	3.59692	−	6.23004i	0.280872	−	0.486484i
$165$	−3.18740	+	5.52074i	−0.248139	+	0.429789i
$166$	−6.32956	+	10.9631i	−0.491269	+	0.850903i
$167$	8.06220	+	13.9641i	0.623872	+	1.08058i	0.988758	+	0.149525i	$0.0477745\pi$
$167$	8.06220	+	13.9641i	0.623872	+	1.08058i	−0.364886	+	0.931052i	$0.618892\pi$
$168$	0.954758	−	1.65369i	0.0736612	−	0.127585i
$169$	−10.4306	−	18.0663i	−0.802351	−	1.38971i
$170$	−6.90952			−0.529936
$171$	2.44423			0.186915
$172$	0.232642	+	0.402947i	0.0177388	+	0.0307244i
$173$	0.732642	−	1.26897i	0.0557017	−	0.0964782i	−0.836830	−	0.547463i	$-0.815594\pi$
$173$	0.732642	−	1.26897i	0.0557017	−	0.0964782i	0.892532	+	0.450985i	$0.148927\pi$
$174$	−2.73264	−	4.73307i	−0.207161	−	0.358813i
$175$	0.954758	−	1.65369i	0.0721729	−	0.125007i
$176$	3.18740	−	5.52074i	0.240259	−	0.416141i
$177$	−2.86427	+	4.96107i	−0.215292	+	0.372897i
$178$	15.8190			1.18569
$179$	8.00643	+	13.8675i	0.598429	+	1.03651i	0.993053	+	0.117667i	$0.0375414\pi$
$179$	8.00643	+	13.8675i	0.598429	+	1.03651i	−0.394624	+	0.918843i	$0.629125\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	1.46528	−	2.53794i	0.108914	−	0.188644i	−0.806417	−	0.591348i	$-0.798596\pi$
$181$	1.46528	−	2.53794i	0.108914	−	0.188644i	0.915330	+	0.402704i	$0.131929\pi$
$182$	−11.1115			−0.823642
$183$	−2.22212	−	3.84882i	−0.164264	−	0.284513i
$184$	0.909516			0.0670504
$185$	−8.90952			−0.655041
$186$	0.722116	−	5.52074i	0.0529481	−	0.404800i
$187$	−44.0468			−3.22102
$188$	−8.72855			−0.636595
$189$	−0.954758	−	1.65369i	−0.0694484	−	0.120288i
$190$	−2.44423			−0.177323
$191$	0.222116	−	0.384717i	0.0160718	−	0.0278371i	−0.857878	−	0.513854i	$-0.828217\pi$
$191$	0.222116	−	0.384717i	0.0160718	−	0.0278371i	0.873949	+	0.486017i	$0.161551\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−8.73264	−	15.1254i	−0.628589	−	1.08875i	−0.987835	−	0.155506i	$-0.950299\pi$
$193$	−8.73264	−	15.1254i	−0.628589	−	1.08875i	0.359246	−	0.933243i	$-0.383034\pi$
$194$	−18.1728			−1.30473
$195$	−2.90952	+	5.03943i	−0.208355	+	0.360881i
$196$	1.67687	−	2.90443i	0.119777	−	0.207459i
$197$	5.28432	−	9.15270i	0.376492	−	0.652103i	−0.614057	−	0.789261i	$-0.710464\pi$
$197$	5.28432	−	9.15270i	0.376492	−	0.652103i	0.990549	+	0.137158i	$0.0437969\pi$
$198$	−3.18740	−	5.52074i	−0.226519	−	0.392342i
$199$	4.32956	−	7.49901i	0.306914	−	0.531591i	−0.670772	−	0.741664i	$-0.734037\pi$
$199$	4.32956	−	7.49901i	0.306914	−	0.531591i	0.977686	+	0.210073i	$0.0673702\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−8.90952			−0.628429
$202$	−1.93057			−0.135834
$203$	5.21802	+	9.03788i	0.366233	+	0.634335i
$204$	3.45476	−	5.98382i	0.241881	−	0.418951i
$205$	3.59692	+	6.23004i	0.251219	+	0.435125i
$206$	−1.86427	+	3.22902i	−0.129890	+	0.224976i
$207$	0.454758	−	0.787664i	0.0316079	−	0.0547464i
$208$	2.90952	−	5.03943i	0.201739	−	0.349422i
$209$	−15.5815			−1.07779
$210$	0.954758	+	1.65369i	0.0658846	+	0.114115i
$211$	5.22212	+	9.04497i	0.359505	+	0.622681i	0.987878	−	0.155231i	$-0.0496121\pi$
$211$	5.22212	+	9.04497i	0.359505	+	0.622681i	−0.628373	+	0.777912i	$0.716279\pi$
$212$	−3.64216	+	6.30840i	−0.250144	+	0.433263i
$213$	9.81903			0.672789
$214$	−0.954758	−	1.65369i	−0.0652659	−	0.113044i
$215$	−0.465283			−0.0317320
$216$	1.00000			0.0680414
$217$	−1.37889	+	10.5419i	−0.0936053	+	0.715633i
$218$	2.44423			0.165544
$219$	2.00000			0.135147
$220$	3.18740	+	5.52074i	0.214894	+	0.372208i
$221$	−40.2067			−2.70459
$222$	4.45476	−	7.71587i	0.298984	−	0.517855i
$223$	7.42004	+	12.8519i	0.496883	+	0.860626i	0.999994	−	0.00359581i	$-0.00114458\pi$
$223$	7.42004	+	12.8519i	0.496883	+	0.860626i	−0.503111	+	0.864222i	$0.667811\pi$
$224$	−0.954758	−	1.65369i	−0.0637925	−	0.110492i
$225$	1.00000			0.0666667
$226$	4.67687	−	8.10058i	0.311101	−	0.538843i
$227$	−1.48947	+	2.57985i	−0.0988599	+	0.171230i	−0.911213	−	0.411935i	$-0.864853\pi$
$227$	−1.48947	+	2.57985i	−0.0988599	+	0.171230i	0.812353	+	0.583166i	$0.198186\pi$
$228$	1.22212	−	2.11677i	0.0809366	−	0.140186i
$229$	3.75683	+	6.50703i	0.248259	+	0.429996i	0.963043	−	0.269349i	$-0.0868084\pi$
$229$	3.75683	+	6.50703i	0.248259	+	0.429996i	−0.714784	+	0.699345i	$0.753475\pi$
$230$	−0.454758	+	0.787664i	−0.0299859	+	0.0519370i
$231$	6.08639	+	10.5419i	0.400455	+	0.693609i
$232$	−5.46528			−0.358813
$233$	12.9095			0.845731			0.422865	−	0.906193i	$-0.361024\pi$
$233$	12.9095			0.845731			0.422865	+	0.906193i	$0.361024\pi$
$234$	−2.90952	−	5.03943i	−0.190201	−	0.329438i
$235$	4.36427	−	7.55914i	0.284694	−	0.493104i
$236$	2.86427	+	4.96107i	0.186448	+	0.322938i
$237$	−0.232642	+	0.402947i	−0.0151117	+	0.0261742i
$238$	−6.59692	+	11.4262i	−0.427615	+	0.740650i
$239$	6.46528	−	11.1982i	0.418204	−	0.724351i	−0.577555	−	0.816352i	$-0.695993\pi$
$239$	6.46528	−	11.1982i	0.418204	−	0.724351i	0.995759	+	0.0920008i	$0.0293262\pi$
$240$	−1.00000			−0.0645497
$241$	5.35784	+	9.28006i	0.345129	+	0.597781i	0.985377	−	0.170387i	$-0.0545018\pi$
$241$	5.35784	+	9.28006i	0.345129	+	0.597781i	−0.640248	+	0.768168i	$0.721169\pi$
$242$	14.8190	+	25.6673i	0.952603	+	1.64996i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.44423			−0.284513
$245$	1.67687	+	2.90443i	0.107132	+	0.185557i
$246$	−7.19383			−0.458662
$247$	−14.2231			−0.904992
$248$	−4.42004	−	3.38574i	−0.280673	−	0.214995i
$249$	12.6591			0.802239
$250$	−1.00000			−0.0632456
$251$	−1.76736	−	3.06115i	−0.111555	−	0.193218i	0.804843	−	0.593488i	$-0.202250\pi$
$251$	−1.76736	−	3.06115i	−0.111555	−	0.193218i	−0.916397	+	0.400270i	$0.868916\pi$
$252$	−1.90952			−0.120288
$253$	−2.89899	+	5.02120i	−0.182258	+	0.315680i
$254$	−7.32956	−	12.6952i	−0.459897	−	0.796566i
$255$	3.45476	+	5.98382i	0.216345	+	0.374721i
$256$	1.00000			0.0625000
$257$	−12.2948	+	21.2953i	−0.766931	+	1.32836i	0.172289	+	0.985047i	$0.444884\pi$
$257$	−12.2948	+	21.2953i	−0.766931	+	1.32836i	−0.939220	+	0.343317i	$0.888449\pi$
$258$	0.232642	−	0.402947i	0.0144836	−	0.0250864i
$259$	−8.50643	+	14.7336i	−0.528564	+	0.915500i
$260$	2.90952	+	5.03943i	0.180441	+	0.312532i
$261$	−2.73264	+	4.73307i	−0.169146	+	0.292970i
$262$	1.14216	+	1.97827i	0.0705627	+	0.122218i
$263$	−1.53472			−0.0946347			−0.0473173	−	0.998880i	$-0.515067\pi$
$263$	−1.53472			−0.0946347			−0.0473173	+	0.998880i	$0.515067\pi$
$264$	−6.37480			−0.392342
$265$	−3.64216	−	6.30840i	−0.223736	−	0.387522i
$266$	−2.33365	+	4.04200i	−0.143085	+	0.247831i
$267$	−7.90952	−	13.6997i	−0.484055	−	0.838407i
$268$	−4.45476	+	7.71587i	−0.272118	+	0.471322i
$269$	7.96119	−	13.7892i	0.485402	−	0.840741i	−0.514457	−	0.857516i	$-0.672006\pi$
$269$	7.96119	−	13.7892i	0.485402	−	0.840741i	0.999859	+	0.0167747i	$0.00533982\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	16.4781			1.00098			0.500488	−	0.865743i	$-0.333154\pi$
$271$	16.4781			1.00098			0.500488	+	0.865743i	$0.333154\pi$
$272$	−3.45476	−	5.98382i	−0.209475	−	0.362822i
$273$	5.55577	+	9.62287i	0.336250	+	0.582403i
$274$	9.73907	−	16.8686i	0.588359	−	1.01907i
$275$	−6.37480			−0.384415
$276$	−0.454758	−	0.787664i	−0.0273732	−	0.0474118i
$277$	−25.6591			−1.54171			−0.770853	−	0.637013i	$-0.780170\pi$
$277$	−25.6591			−1.54171			−0.770853	+	0.637013i	$0.780170\pi$
$278$	−11.3748			−0.682215
$279$	−5.14216	+	2.13500i	−0.307853	+	0.127819i
$280$	1.90952			0.114115
$281$	−31.1373			−1.85749			−0.928747	−	0.370715i	$-0.879113\pi$
$281$	−31.1373			−1.85749			−0.928747	+	0.370715i	$0.879113\pi$
$282$	4.36427	+	7.55914i	0.259889	+	0.450140i
$283$	−16.9918			−1.01006			−0.505029	−	0.863102i	$-0.668518\pi$
$283$	−16.9918			−1.01006			−0.505029	+	0.863102i	$0.668518\pi$
$284$	4.90952	−	8.50353i	0.291326	−	0.504592i
$285$	1.22212	+	2.11677i	0.0723919	+	0.125386i
$286$	18.5476	+	32.1254i	1.09674	+	1.89961i
$287$	13.7367			0.810854
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−15.3707	+	26.6228i	−0.904159	+	1.56605i
$290$	2.73264	−	4.73307i	0.160466	−	0.277936i
$291$	9.08639	+	15.7381i	0.532654	+	0.922583i
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	−13.4612	−	23.3155i	−0.786411	−	1.36210i	−0.928152	−	0.372200i	$-0.878603\pi$
$293$	−13.4612	−	23.3155i	−0.786411	−	1.36210i	0.141741	−	0.989904i	$-0.454730\pi$
$294$	−3.35375			−0.195595
$295$	−5.72855			−0.333529
$296$	−4.45476	−	7.71587i	−0.258928	−	0.448476i
$297$	−3.18740	+	5.52074i	−0.184952	+	0.320346i
$298$	−3.35784	−	5.81595i	−0.194515	−	0.336909i
$299$	−2.64625	+	4.58344i	−0.153037	+	0.265067i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	−0.444233	+	0.769434i	−0.0256052	+	0.0443494i
$302$	4.55577			0.262155
$303$	0.965283	+	1.67192i	0.0554541	+	0.0960493i
$304$	−1.22212	−	2.11677i	−0.0700932	−	0.121405i
$305$	2.22212	−	3.84882i	0.127238	−	0.220383i
$306$	−6.90952			−0.394991
$307$	−9.97171	−	17.2715i	−0.569116	−	0.985738i	−0.996654	−	0.0817401i	$-0.973952\pi$
$307$	−9.97171	−	17.2715i	−0.569116	−	0.985738i	0.427538	−	0.903997i	$-0.359381\pi$
$308$	12.1728			0.693609
$309$	3.72855			0.212110
$310$	5.14216	−	2.13500i	0.292055	−	0.121260i
$311$	24.5686			1.39316			0.696580	−	0.717480i	$-0.254704\pi$
$311$	24.5686			1.39316			0.696580	+	0.717480i	$0.254704\pi$
$312$	−5.81903			−0.329438
$313$	−11.9265	−	20.6573i	−0.674124	−	1.16762i	−0.976724	−	0.214500i	$-0.931188\pi$
$313$	−11.9265	−	20.6573i	−0.674124	−	1.16762i	0.302600	−	0.953118i	$-0.402145\pi$
$314$	17.9434			1.01261
$315$	0.954758	−	1.65369i	0.0537945	−	0.0931748i
$316$	0.232642	+	0.402947i	0.0130871	+	0.0226675i
$317$	7.55167	+	13.0799i	0.424144	+	0.734639i	0.996340	−	0.0854776i	$-0.0272416\pi$
$317$	7.55167	+	13.0799i	0.424144	+	0.734639i	−0.572196	+	0.820117i	$0.693908\pi$
$318$	7.28432			0.408484
$319$	17.4200	−	30.1724i	0.975335	−	1.68933i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−0.954758	+	1.65369i	−0.0532894	+	0.0922999i
$322$	0.868368	+	1.50406i	0.0483922	+	0.0838178i
$323$	−8.44423	+	14.6258i	−0.469850	+	0.813804i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−5.81903			−0.322782
$326$	−5.79798			−0.321121
$327$	−1.22212	−	2.11677i	−0.0675832	−	0.117058i
$328$	−3.59692	+	6.23004i	−0.198606	+	0.343996i
$329$	−8.33365	−	14.4343i	−0.459449	−	0.795789i
$330$	3.18740	−	5.52074i	0.175461	−	0.303907i
$331$	−0.0621987	+	0.107731i	−0.00341875	+	0.00592145i	−0.867730	−	0.497036i	$-0.834422\pi$
$331$	−0.0621987	+	0.107731i	−0.00341875	+	0.00592145i	0.864311	+	0.502958i	$0.167755\pi$
$332$	6.32956	−	10.9631i	0.347380	−	0.601679i
$333$	−8.90952			−0.488238
$334$	−8.06220	−	13.9641i	−0.441144	−	0.764084i
$335$	−4.45476	−	7.71587i	−0.243389	−	0.421563i
$336$	−0.954758	+	1.65369i	−0.0520863	+	0.0902161i
$337$	−11.4653			−0.624554			−0.312277	−	0.949991i	$-0.601092\pi$
$337$	−11.4653			−0.624554			−0.312277	+	0.949991i	$0.601092\pi$
$338$	10.4306	+	18.0663i	0.567348	+	0.982676i
$339$	−9.35375			−0.508026
$340$	6.90952			0.374721
$341$	32.7802	−	13.6102i	1.77515	−	0.737033i
$342$	−2.44423			−0.132169
$343$	19.7706			1.06751
$344$	−0.232642	−	0.402947i	−0.0125432	−	0.0217254i
$345$	0.909516			0.0489667
$346$	−0.732642	+	1.26897i	−0.0393871	+	0.0682204i
$347$	−2.48947	−	4.31190i	−0.133642	−	0.231475i	0.791436	−	0.611252i	$-0.209334\pi$
$347$	−2.48947	−	4.31190i	−0.133642	−	0.231475i	−0.925078	+	0.379777i	$0.876001\pi$
$348$	2.73264	+	4.73307i	0.146485	+	0.253719i
$349$	−26.1244			−1.39841			−0.699203	−	0.714923i	$-0.746462\pi$
$349$	−26.1244			−1.39841			−0.699203	+	0.714923i	$0.746462\pi$
$350$	−0.954758	+	1.65369i	−0.0510340	+	0.0883934i
$351$	−2.90952	+	5.03943i	−0.155298	+	0.268985i
$352$	−3.18740	+	5.52074i	−0.169889	+	0.294256i
$353$	14.4054	+	24.9509i	0.766723	+	1.32800i	0.939331	+	0.343013i	$0.111447\pi$
$353$	14.4054	+	24.9509i	0.766723	+	1.32800i	−0.172607	+	0.984991i	$0.555219\pi$
$354$	2.86427	−	4.96107i	0.152234	−	0.263678i
$355$	4.90952	+	8.50353i	0.260570	+	0.451321i
$356$	−15.8190			−0.838407
$357$	13.1938			0.698292
$358$	−8.00643	−	13.8675i	−0.423153	−	0.732923i
$359$	−3.31260	+	5.73759i	−0.174832	+	0.302819i	−0.940103	−	0.340890i	$-0.889272\pi$
$359$	−3.31260	+	5.73759i	−0.174832	+	0.302819i	0.765271	+	0.643708i	$0.222605\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	6.51286	−	11.2806i	0.342782	−	0.593716i
$362$	−1.46528	+	2.53794i	−0.0770136	+	0.133391i
$363$	14.8190	−	25.6673i	0.777797	−	1.34718i
$364$	11.1115			0.582403
$365$	1.00000	+	1.73205i	0.0523424	+	0.0906597i
$366$	2.22212	+	3.84882i	0.116152	+	0.201181i
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	−0.361874	−	0.932227i	$-0.617863\pi$
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	0.988269	−	0.152721i	$-0.0488036\pi$
$368$	−0.909516			−0.0474118
$369$	3.59692	+	6.23004i	0.187248	+	0.324323i
$370$	8.90952			0.463184
$371$	−13.9095			−0.722146
$372$	−0.722116	+	5.52074i	−0.0374400	+	0.286237i
$373$	−27.4360			−1.42058			−0.710292	−	0.703907i	$-0.751437\pi$
$373$	−27.4360			−1.42058			−0.710292	+	0.703907i	$0.751437\pi$
$374$	44.0468			2.27760
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	8.72855			0.450140
$377$	15.9013	−	27.5419i	0.818960	−	1.41848i
$378$	0.954758	+	1.65369i	0.0491075	+	0.0850566i
$379$	−9.26326	−	16.0444i	−0.475822	−	0.824148i	0.523794	−	0.851845i	$-0.324516\pi$
$379$	−9.26326	−	16.0444i	−0.475822	−	0.824148i	−0.999616	+	0.0276969i	$0.991183\pi$
$380$	2.44423			0.125386
$381$	−7.32956	+	12.6952i	−0.375505	+	0.650393i
$382$	−0.222116	+	0.384717i	−0.0113645	+	0.0196838i
$383$	−1.36427	+	2.36299i	−0.0697111	+	0.120743i	−0.898774	−	0.438412i	$-0.855541\pi$
$383$	−1.36427	+	2.36299i	−0.0697111	+	0.120743i	0.829063	+	0.559155i	$0.188874\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−6.08639	+	10.5419i	−0.310191	+	0.537267i
$386$	8.73264	+	15.1254i	0.444480	+	0.769862i
$387$	−0.465283			−0.0236517
$388$	18.1728			0.922583
$389$	8.87071	+	15.3645i	0.449763	+	0.779012i	0.998370	−	0.0570682i	$-0.0181753\pi$
$389$	8.87071	+	15.3645i	0.449763	+	0.779012i	−0.548608	+	0.836080i	$0.684842\pi$
$390$	2.90952	−	5.03943i	0.147329	−	0.255181i
$391$	3.14216	+	5.44238i	0.158906	+	0.275233i
$392$	−1.67687	+	2.90443i	−0.0846949	+	0.146696i
$393$	1.14216	−	1.97827i	0.0576142	−	0.0997908i
$394$	−5.28432	+	9.15270i	−0.266220	+	0.461106i
$395$	−0.465283			−0.0234109
$396$	3.18740	+	5.52074i	0.160173	+	0.277428i
$397$	5.85784	+	10.1461i	0.293997	+	0.509217i	0.974751	−	0.223295i	$-0.0716812\pi$
$397$	5.85784	+	10.1461i	0.293997	+	0.509217i	−0.680754	+	0.732512i	$0.738348\pi$
$398$	−4.32956	+	7.49901i	−0.217021	+	0.375892i
$399$	4.66730			0.233657
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	14.7075			0.734457			0.367229	−	0.930131i	$-0.380307\pi$
$401$	14.7075			0.734457			0.367229	+	0.930131i	$0.380307\pi$
$402$	8.90952			0.444366
$403$	29.9224	−	12.4236i	1.49054	−	0.618865i
$404$	1.93057			0.0960493
$405$	1.00000			0.0496904
$406$	−5.21802	−	9.03788i	−0.258966	−	0.448542i
$407$	56.7964			2.81529
$408$	−3.45476	+	5.98382i	−0.171036	+	0.296243i
$409$	11.6938	+	20.2543i	0.578223	+	1.00151i	0.995683	+	0.0928161i	$0.0295869\pi$
$409$	11.6938	+	20.2543i	0.578223	+	1.00151i	−0.417461	+	0.908695i	$0.637080\pi$
$410$	−3.59692	−	6.23004i	−0.177639	−	0.307680i
$411$	−19.4781			−0.960786
$412$	1.86427	−	3.22902i	0.0918462	−	0.159082i
$413$	−5.46938	+	9.47324i	−0.269130	+	0.466148i
$414$	−0.454758	+	0.787664i	−0.0223501	+	0.0387116i
$415$	6.32956	+	10.9631i	0.310706	+	0.538158i
$416$	−2.90952	+	5.03943i	−0.142651	+	0.247078i
$417$	5.68740	+	9.85087i	0.278513	+	0.482399i
$418$	15.5815			0.762116
$419$	−14.3748			−0.702255			−0.351127	−	0.936328i	$-0.614202\pi$
$419$	−14.3748			−0.702255			−0.351127	+	0.936328i	$0.614202\pi$
$420$	−0.954758	−	1.65369i	−0.0465874	−	0.0806918i
$421$	7.15268	−	12.3888i	0.348600	−	0.603794i	−0.637401	−	0.770533i	$-0.719990\pi$
$421$	7.15268	−	12.3888i	0.348600	−	0.603794i	0.986001	+	0.166739i	$0.0533237\pi$
$422$	−5.22212	−	9.04497i	−0.254209	−	0.440302i
$423$	4.36427	−	7.55914i	0.212198	−	0.367538i
$424$	3.64216	−	6.30840i	0.176879	−	0.306363i
$425$	−3.45476	+	5.98382i	−0.167580	+	0.290258i
$426$	−9.81903			−0.475734
$427$	−4.24317	−	7.34938i	−0.205341	−	0.355661i
$428$	0.954758	+	1.65369i	0.0461500	+	0.0799341i
$429$	18.5476	−	32.1254i	0.895486	−	1.55103i
$430$	0.465283			0.0224379
$431$	11.3255	+	19.6163i	0.545528	+	0.944883i	0.998573	+	0.0533953i	$0.0170043\pi$
$431$	11.3255	+	19.6163i	0.545528	+	0.944883i	−0.453045	+	0.891488i	$0.649662\pi$
$432$	−1.00000			−0.0481125
$433$	26.5686			1.27681			0.638403	−	0.769702i	$-0.279595\pi$
$433$	26.5686			1.27681			0.638403	+	0.769702i	$0.279595\pi$
$434$	1.37889	−	10.5419i	0.0661890	−	0.506029i
$435$	−5.46528			−0.262040
$436$	−2.44423			−0.117058
$437$	1.11153	+	1.92523i	0.0531719	+	0.0920964i
$438$	−2.00000			−0.0955637
$439$	3.91595	−	6.78262i	0.186898	−	0.323717i	−0.757316	−	0.653048i	$-0.773490\pi$
$439$	3.91595	−	6.78262i	0.186898	−	0.323717i	0.944214	+	0.329331i	$0.106823\pi$
$440$	−3.18740	−	5.52074i	−0.151953	−	0.263191i
$441$	1.67687	+	2.90443i	0.0798512	+	0.138306i
$442$	40.2067			1.91244
$443$	9.35375	−	16.2012i	0.444410	−	0.769741i	−0.553601	−	0.832782i	$-0.686747\pi$
$443$	9.35375	−	16.2012i	0.444410	−	0.769741i	0.998011	+	0.0630414i	$0.0200800\pi$
$444$	−4.45476	+	7.71587i	−0.211413	+	0.366179i
$445$	7.90952	−	13.6997i	0.374947	−	0.649427i
$446$	−7.42004	−	12.8519i	−0.351349	−	0.608555i
$447$	−3.35784	+	5.81595i	−0.158820	+	0.275085i
$448$	0.954758	+	1.65369i	0.0451081	+	0.0781295i
$449$	−14.8885			−0.702630			−0.351315	−	0.936257i	$-0.614265\pi$
$449$	−14.8885			−0.702630			−0.351315	+	0.936257i	$0.614265\pi$
$450$	−1.00000			−0.0471405
$451$	−22.9296	−	39.7153i	−1.07971	−	1.87012i
$452$	−4.67687	+	8.10058i	−0.219982	+	0.381019i
$453$	−2.27788	−	3.94541i	−0.107024	−	0.185372i
$454$	1.48947	−	2.57985i	0.0699045	−	0.121078i
$455$	−5.55577	+	9.62287i	−0.260458	+	0.451127i
$456$	−1.22212	+	2.11677i	−0.0572308	+	0.0991267i
$457$	−14.2067			−0.664561			−0.332281	−	0.943181i	$-0.607818\pi$
$457$	−14.2067			−0.664561			−0.332281	+	0.943181i	$0.607818\pi$
$458$	−3.75683	−	6.50703i	−0.175545	−	0.304053i
$459$	3.45476	+	5.98382i	0.161254	+	0.279301i
$460$	0.454758	−	0.787664i	0.0212032	−	0.0367250i
$461$	22.6802			1.05632			0.528160	−	0.849145i	$-0.322882\pi$
$461$	22.6802			1.05632			0.528160	+	0.849145i	$0.322882\pi$
$462$	−6.08639	−	10.5419i	−0.283165	−	0.490455i
$463$	−22.6170			−1.05110			−0.525551	−	0.850762i	$-0.676141\pi$
$463$	−22.6170			−1.05110			−0.525551	+	0.850762i	$0.676141\pi$
$464$	5.46528			0.253719
$465$	−4.42004	−	3.38574i	−0.204974	−	0.157010i
$466$	−12.9095			−0.598022
$467$	35.5897			1.64689			0.823447	−	0.567393i	$-0.192048\pi$
$467$	35.5897			1.64689			0.823447	+	0.567393i	$0.192048\pi$
$468$	2.90952	+	5.03943i	0.134492	+	0.232948i
$469$	−17.0129			−0.785581
$470$	−4.36427	+	7.55914i	−0.201309	+	0.348677i
$471$	−8.97171	−	15.5395i	−0.413395	−	0.716021i
$472$	−2.86427	−	4.96107i	−0.131839	−	0.228352i
$473$	2.96609			0.136381
$474$	0.232642	−	0.402947i	0.0106856	−	0.0185080i
$475$	−1.22212	+	2.11677i	−0.0560745	+	0.0971240i
$476$	6.59692	−	11.4262i	0.302369	−	0.523719i
$477$	−3.64216	−	6.30840i	−0.166763	−	0.288842i
$478$	−6.46528	+	11.1982i	−0.295715	+	0.512194i
$479$	1.24317	+	2.15323i	0.0568017	+	0.0983835i	0.893028	−	0.450001i	$-0.148576\pi$
$479$	1.24317	+	2.15323i	0.0568017	+	0.0983835i	−0.836226	+	0.548384i	$0.815243\pi$
$480$	1.00000			0.0456435
$481$	51.8448			2.36392
$482$	−5.35784	−	9.28006i	−0.244043	−	0.422695i
$483$	0.868368	−	1.50406i	0.0395121	−	0.0684370i
$484$	−14.8190	−	25.6673i	−0.673592	−	1.16670i
$485$	−9.08639	+	15.7381i	−0.412592	+	0.714630i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	4.51053	−	7.81246i	0.204391	−	0.354016i	−0.745547	−	0.666453i	$-0.767812\pi$
$487$	4.51053	−	7.81246i	0.204391	−	0.354016i	0.949939	+	0.312436i	$0.101145\pi$
$488$	4.44423			0.201181
$489$	2.89899	+	5.02120i	0.131097	+	0.227066i
$490$	−1.67687	−	2.90443i	−0.0757535	−	0.131209i
$491$	−9.07587	+	15.7199i	−0.409588	+	0.709427i	−0.994844	−	0.101422i	$-0.967661\pi$
$491$	−9.07587	+	15.7199i	−0.409588	+	0.709427i	0.585255	+	0.810849i	$0.300994\pi$
$492$	7.19383			0.324323
$493$	−18.8812	−	32.7033i	−0.850368	−	1.47288i
$494$	14.2231			0.639926
$495$	−6.37480			−0.286526
$496$	4.42004	+	3.38574i	0.198466	+	0.152024i
$497$	18.7496			0.841034
$498$	−12.6591			−0.567268
$499$	15.5759	+	26.9782i	0.697271	+	1.20771i	0.969409	+	0.245451i	$0.0789361\pi$
$499$	15.5759	+	26.9782i	0.697271	+	1.20771i	−0.272137	+	0.962258i	$0.587731\pi$
$500$	1.00000			0.0447214
$501$	−8.06220	+	13.9641i	−0.360192	+	0.623872i
$502$	1.76736	+	3.06115i	0.0788811	+	0.136626i
$503$	13.4370	+	23.2736i	0.599126	+	1.03772i	0.992950	+	0.118531i	$0.0378185\pi$
$503$	13.4370	+	23.2736i	0.599126	+	1.03772i	−0.393824	+	0.919186i	$0.628848\pi$
$504$	1.90952			0.0850566
$505$	−0.965283	+	1.67192i	−0.0429545	+	0.0743994i
$506$	2.89899	−	5.02120i	0.128876	−	0.223220i
$507$	10.4306	−	18.0663i	0.463238	−	0.802351i
$508$	7.32956	+	12.6952i	0.325197	+	0.563257i
$509$	−18.8877	+	32.7144i	−0.837181	+	1.45004i	0.0550614	+	0.998483i	$0.482465\pi$
$509$	−18.8877	+	32.7144i	−0.837181	+	1.45004i	−0.892242	+	0.451557i	$0.850869\pi$
$510$	−3.45476	−	5.98382i	−0.152979	−	0.264968i
$511$	3.81903			0.168944
$512$	−1.00000			−0.0441942
$513$	1.22212	+	2.11677i	0.0539578	+	0.0934576i
$514$	12.2948	−	21.2953i	0.542302	−	0.939295i
$515$	1.86427	+	3.22902i	0.0821497	+	0.142287i
$516$	−0.232642	+	0.402947i	−0.0102415	+	0.0177388i
$517$	−27.8214	+	48.1880i	−1.22358	+	2.11931i
$518$	8.50643	−	14.7336i	0.373751	−	0.647356i
$519$	1.46528			0.0643188
$520$	−2.90952	−	5.03943i	−0.127591	−	0.220994i
$521$	19.1938	+	33.2447i	0.840897	+	1.45648i	0.889137	+	0.457641i	$0.151305\pi$
$521$	19.1938	+	33.2447i	0.840897	+	1.45648i	−0.0482403	+	0.998836i	$0.515361\pi$
$522$	2.73264	−	4.73307i	0.119604	−	0.207161i
$523$	17.0339			0.744841			0.372421	−	0.928064i	$-0.378528\pi$
$523$	17.0339			0.744841			0.372421	+	0.928064i	$0.378528\pi$
$524$	−1.14216	−	1.97827i	−0.0498954	−	0.0864213i
$525$	1.90952			0.0833381
$526$	1.53472			0.0669168
$527$	4.98947	−	38.1456i	0.217345	−	1.66165i
$528$	6.37480			0.277428
$529$	−22.1728			−0.964034
$530$	3.64216	+	6.30840i	0.158205	+	0.274019i
$531$	−5.72855			−0.248598
$532$	2.33365	−	4.04200i	0.101177	−	0.175243i
$533$	−20.9306	−	36.2528i	−0.906603	−	1.57028i
$534$	7.90952	+	13.6997i	0.342278	+	0.592843i
$535$	−1.90952			−0.0825556
$536$	4.45476	−	7.71587i	0.192416	−	0.333275i
$537$	−8.00643	+	13.8675i	−0.345503	+	0.598429i
$538$	−7.96119	+	13.7892i	−0.343231	+	0.594494i
$539$	−10.6897	−	18.5152i	−0.460440	−	0.797505i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	2.97171	+	5.14716i	0.127764	+	0.221294i	0.922810	−	0.385255i	$-0.125887\pi$
$541$	2.97171	+	5.14716i	0.127764	+	0.221294i	−0.795046	+	0.606549i	$0.792553\pi$
$542$	−16.4781			−0.707797
$543$	2.93057			0.125763
$544$	3.45476	+	5.98382i	0.148122	+	0.256554i
$545$	1.22212	−	2.11677i	0.0523497	−	0.0906724i
$546$	−5.55577	−	9.62287i	−0.237765	−	0.411821i
$547$	4.42647	−	7.66688i	0.189262	−	0.327812i	−0.755742	−	0.654869i	$-0.772724\pi$
$547$	4.42647	−	7.66688i	0.189262	−	0.327812i	0.945005	+	0.327057i	$0.106057\pi$
$548$	−9.73907	+	16.8686i	−0.416033	+	0.720590i
$549$	2.22212	−	3.84882i	0.0948376	−	0.164264i
$550$	6.37480			0.271822
$551$	−6.67921	−	11.5687i	−0.284544	−	0.492845i
$552$	0.454758	+	0.787664i	0.0193558	+	0.0335252i
$553$	−0.444233	+	0.769434i	−0.0188907	+	0.0327197i
$554$	25.6591			1.09015
$555$	−4.45476	−	7.71587i	−0.189094	−	0.327520i
$556$	11.3748			0.482399
$557$	−9.42318			−0.399273			−0.199637	−	0.979870i	$-0.563976\pi$
$557$	−9.42318			−0.399273			−0.199637	+	0.979870i	$0.563976\pi$
$558$	5.14216	−	2.13500i	0.217685	−	0.0903817i
$559$	2.70750			0.114515
$560$	−1.90952			−0.0806918
$561$	−22.0234	−	38.1456i	−0.929828	−	1.61051i
$562$	31.1373			1.31345
$563$	−19.5023	+	33.7790i	−0.821926	+	1.42362i	0.0823209	+	0.996606i	$0.473767\pi$
$563$	−19.5023	+	33.7790i	−0.821926	+	1.42362i	−0.904246	+	0.427011i	$0.859567\pi$
$564$	−4.36427	−	7.55914i	−0.183769	−	0.318297i
$565$	−4.67687	−	8.10058i	−0.196758	−	0.340794i
$566$	16.9918			0.714219
$567$	0.954758	−	1.65369i	0.0400961	−	0.0694484i
$568$	−4.90952	+	8.50353i	−0.205999	+	0.356800i
$569$	−22.5897	+	39.1265i	−0.947009	+	1.64027i	−0.195330	+	0.980738i	$0.562578\pi$
$569$	−22.5897	+	39.1265i	−0.947009	+	1.64027i	−0.751679	+	0.659530i	$0.770756\pi$
$570$	−1.22212	−	2.11677i	−0.0511888	−	0.0886616i
$571$	−5.46528	+	9.46615i	−0.228715	+	0.396146i	−0.957428	−	0.288674i	$-0.906786\pi$
$571$	−5.46528	+	9.46615i	−0.228715	+	0.396146i	0.728713	+	0.684820i	$0.240119\pi$
$572$	−18.5476	−	32.1254i	−0.775513	−	1.34323i
$573$	0.444233			0.0185581
$574$	−13.7367			−0.573360
$575$	0.454758	+	0.787664i	0.0189647	+	0.0328479i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−2.71568	−	4.70370i	−0.113055	−	0.195818i	0.803945	−	0.594703i	$-0.202730\pi$
$577$	−2.71568	−	4.70370i	−0.113055	−	0.195818i	−0.917001	+	0.398885i	$0.869397\pi$
$578$	15.3707	−	26.6228i	0.639337	−	1.10736i
$579$	8.73264	−	15.1254i	0.362916	−	0.628589i
$580$	−2.73264	+	4.73307i	−0.113467	+	0.196530i
$581$	24.1728			1.00286
$582$	−9.08639	−	15.7381i	−0.376643	−	0.652365i
$583$	23.2180	+	40.2148i	0.961592	+	1.66553i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$	−5.81903			−0.240587
$586$	13.4612	+	23.3155i	0.556077	+	0.963153i
$587$	−39.9095			−1.64724			−0.823621	−	0.567141i	$-0.808050\pi$
$587$	−39.9095			−1.64724			−0.823621	+	0.567141i	$0.808050\pi$
$588$	3.35375			0.138306
$589$	1.76502	−	13.4940i	0.0727264	−	0.556009i
$590$	5.72855			0.235841
$591$	10.5686			0.434735
$592$	4.45476	+	7.71587i	0.183089	+	0.317120i
$593$	43.5394			1.78795			0.893974	−	0.448118i	$-0.147906\pi$
$593$	43.5394			1.78795			0.893974	+	0.448118i	$0.147906\pi$
$594$	3.18740	−	5.52074i	0.130781	−	0.226519i
$595$	6.59692	+	11.4262i	0.270447	+	0.468428i
$596$	3.35784	+	5.81595i	0.137543	+	0.238231i
$597$	8.65911			0.354394
$598$	2.64625	−	4.58344i	0.108213	−	0.187431i
$599$	−6.28432	+	10.8848i	−0.256770	+	0.444739i	−0.965375	−	0.260867i	$-0.915992\pi$
$599$	−6.28432	+	10.8848i	−0.256770	+	0.444739i	0.708605	+	0.705606i	$0.249325\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	1.41361	+	2.44844i	0.0576623	+	0.0998741i	0.893416	−	0.449231i	$-0.148302\pi$
$601$	1.41361	+	2.44844i	0.0576623	+	0.0998741i	−0.835753	+	0.549105i	$0.814969\pi$
$602$	0.444233	−	0.769434i	0.0181056	−	0.0313598i
$603$	−4.45476	−	7.71587i	−0.181412	−	0.314214i
$604$	−4.55577			−0.185372
$605$	29.6381			1.20496
$606$	−0.965283	−	1.67192i	−0.0392119	−	0.0679171i
$607$	4.93057	−	8.53999i	0.200126	−	0.346628i	−0.748443	−	0.663199i	$-0.769198\pi$
$607$	4.93057	−	8.53999i	0.200126	−	0.346628i	0.948569	+	0.316571i	$0.102532\pi$
$608$	1.22212	+	2.11677i	0.0495634	+	0.0858463i
$609$	−5.21802	+	9.03788i	−0.211445	+	0.366233i
$610$	−2.22212	+	3.84882i	−0.0899709	+	0.155834i
$611$	−25.3958	+	43.9869i	−1.02741	+	1.77952i
$612$	6.90952			0.279301
$613$	−19.4781	−	33.7371i	−0.786715	−	1.36263i	−0.927969	−	0.372657i	$-0.878447\pi$
$613$	−19.4781	−	33.7371i	−0.786715	−	1.36263i	0.141254	−	0.989973i	$-0.454886\pi$
$614$	9.97171	+	17.2715i	0.402426	+	0.697022i
$615$	−3.59692	+	6.23004i	−0.145042	+	0.251219i
$616$	−12.1728			−0.490455
$617$	−18.2738	−	31.6511i	−0.735675	−	1.27423i	−0.954427	−	0.298446i	$-0.903532\pi$
$617$	−18.2738	−	31.6511i	−0.735675	−	1.27423i	0.218751	−	0.975781i	$-0.429802\pi$
$618$	−3.72855			−0.149984
$619$	−45.6802			−1.83604			−0.918020	−	0.396533i	$-0.870213\pi$
$619$	−45.6802			−1.83604			−0.918020	+	0.396533i	$0.870213\pi$
$620$	−5.14216	+	2.13500i	−0.206514	+	0.0857436i
$621$	0.909516			0.0364976
$622$	−24.5686			−0.985112
$623$	−15.1033	−	26.1598i	−0.605103	−	1.04807i
$624$	5.81903			0.232948
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	11.9265	+	20.6573i	0.476678	+	0.825630i
$627$	−7.79075	−	13.4940i	−0.311132	−	0.538897i
$628$	−17.9434			−0.716021
$629$	30.7802	−	53.3129i	1.22729	−	2.12572i
$630$	−0.954758	+	1.65369i	−0.0380385	+	0.0658846i
$631$	9.16635	−	15.8766i	0.364907	−	0.632037i	−0.623855	−	0.781540i	$-0.714434\pi$
$631$	9.16635	−	15.8766i	0.364907	−	0.632037i	0.988761	+	0.149504i	$0.0477676\pi$
$632$	−0.232642	−	0.402947i	−0.00925399	−	0.0160284i
$633$	−5.22212	+	9.04497i	−0.207560	+	0.359505i
$634$	−7.55167	−	13.0799i	−0.299915	−	0.519468i
$635$	−14.6591			−0.581729
$636$	−7.28432			−0.288842
$637$	−9.75779	−	16.9010i	−0.386618	−	0.669641i
$638$	−17.4200	+	30.1724i	−0.689666	+	1.19454i
$639$	4.90952	+	8.50353i	0.194217	+	0.336394i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−6.86837	+	11.8964i	−0.271284	+	0.469878i	−0.969191	−	0.246311i	$-0.920782\pi$
$641$	−6.86837	+	11.8964i	−0.271284	+	0.469878i	0.697907	+	0.716189i	$0.254115\pi$
$642$	0.954758	−	1.65369i	0.0376813	−	0.0652659i
$643$	40.6509			1.60312			0.801558	−	0.597917i	$-0.204005\pi$
$643$	40.6509			1.60312			0.801558	+	0.597917i	$0.204005\pi$
$644$	−0.868368	−	1.50406i	−0.0342185	−	0.0592681i
$645$	−0.232642	−	0.402947i	−0.00916025	−	0.0158660i
$646$	8.44423	−	14.6258i	0.332234	−	0.575446i
$647$	30.6930			1.20667			0.603334	−	0.797489i	$-0.293839\pi$
$647$	30.6930			1.20667			0.603334	+	0.797489i	$0.293839\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	36.5183			1.43347
$650$	5.81903			0.228241
$651$	−9.81903	+	4.07681i	−0.384838	+	0.159783i
$652$	5.79798			0.227066
$653$	−15.6463			−0.612285			−0.306143	−	0.951986i	$-0.599038\pi$
$653$	−15.6463			−0.612285			−0.306143	+	0.951986i	$0.599038\pi$
$654$	1.22212	+	2.11677i	0.0477885	+	0.0827722i
$655$	2.28432			0.0892556
$656$	3.59692	−	6.23004i	0.140436	−	0.243242i
$657$	1.00000	+	1.73205i	0.0390137	+	0.0675737i
$658$	8.33365	+	14.4343i	0.324880	+	0.562708i
$659$	27.8319			1.08418			0.542088	−	0.840321i	$-0.317634\pi$
$659$	27.8319			1.08418			0.542088	+	0.840321i	$0.317634\pi$
$660$	−3.18740	+	5.52074i	−0.124069	+	0.214894i
$661$	0.0411483	−	0.0712710i	0.00160048	−	0.00277212i	−0.865224	−	0.501385i	$-0.832824\pi$
$661$	0.0411483	−	0.0712710i	0.00160048	−	0.00277212i	0.866825	+	0.498613i	$0.166157\pi$
$662$	0.0621987	−	0.107731i	0.00241742	−	0.00418710i
$663$	−20.1033	−	34.8200i	−0.780749	−	1.35230i
$664$	−6.32956	+	10.9631i	−0.245634	+	0.425451i
$665$	2.33365	+	4.04200i	0.0904951	+	0.156742i
$666$	8.90952			0.345237
$667$	−4.97076			−0.192469
$668$	8.06220	+	13.9641i	0.311936	+	0.540289i
$669$	−7.42004	+	12.8519i	−0.286875	+	0.496883i
$670$	4.45476	+	7.71587i	0.172102	+	0.298090i
$671$	−14.1655	+	24.5354i	−0.546855	+	0.947180i
$672$	0.954758	−	1.65369i	0.0368306	−	0.0637925i
$673$	−4.73264	+	8.19718i	−0.182430	+	0.315978i	−0.942707	−	0.333620i	$-0.891730\pi$
$673$	−4.73264	+	8.19718i	−0.182430	+	0.315978i	0.760278	+	0.649598i	$0.225063\pi$
$674$	11.4653			0.441626
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−10.4306	−	18.0663i	−0.401176	−	0.694857i
$677$	−7.39176	+	12.8029i	−0.284088	+	0.492055i	−0.972388	−	0.233371i	$-0.925024\pi$
$677$	−7.39176	+	12.8029i	−0.284088	+	0.492055i	0.688299	+	0.725427i	$0.258358\pi$
$678$	9.35375			0.359229
$679$	17.3506	+	30.0521i	0.665855	+	1.15330i
$680$	−6.90952			−0.264968
$681$	−2.97895			−0.114154
$682$	−32.7802	+	13.6102i	−1.25522	+	0.521161i
$683$	11.5219			0.440871			0.220436	−	0.975401i	$-0.429252\pi$
$683$	11.5219			0.440871			0.220436	+	0.975401i	$0.429252\pi$
$684$	2.44423			0.0934576
$685$	−9.73907	−	16.8686i	−0.372111	−	0.644515i
$686$	−19.7706			−0.754847
$687$	−3.75683	+	6.50703i	−0.143332	+	0.248259i
$688$	0.232642	+	0.402947i	0.00886938	+	0.0153622i
$689$	21.1938	+	36.7088i	0.807421	+	1.39849i
$690$	−0.909516			−0.0346247
$691$	5.86837	−	10.1643i	0.223243	−	0.386669i	−0.732548	−	0.680716i	$-0.761669\pi$
$691$	5.86837	−	10.1643i	0.223243	−	0.386669i	0.955791	+	0.294047i	$0.0950023\pi$
$692$	0.732642	−	1.26897i	0.0278509	−	0.0482391i
$693$	−6.08639	+	10.5419i	−0.231203	+	0.400455i
$694$	2.48947	+	4.31190i	0.0944992	+	0.163677i
$695$	−5.68740	+	9.85087i	−0.215735	+	0.373665i
$696$	−2.73264	−	4.73307i	−0.103581	−	0.179407i
$697$	−49.7059			−1.88274
$698$	26.1244			0.988823
$699$	6.45476	+	11.1800i	0.244141	+	0.422865i
$700$	0.954758	−	1.65369i	0.0360865	−	0.0625036i
$701$	−6.68097	−	11.5718i	−0.252337	−	0.437060i	0.711832	−	0.702350i	$-0.247866\pi$
$701$	−6.68097	−	11.5718i	−0.252337	−	0.437060i	−0.964169	+	0.265290i	$0.914532\pi$
$702$	2.90952	−	5.03943i	0.109813	−	0.190201i
$703$	10.8885	−	18.8594i	0.410666	−	0.711295i
$704$	3.18740	−	5.52074i	0.120130	−	0.208071i
$705$	8.72855			0.328736
$706$	−14.4054	−	24.9509i	−0.542155	−	0.939040i
$707$	1.84322	+	3.19256i	0.0693216	+	0.120068i
$708$	−2.86427	+	4.96107i	−0.107646	+	0.186448i
$709$	−24.1665			−0.907592			−0.453796	−	0.891106i	$-0.649930\pi$
$709$	−24.1665			−0.907592			−0.453796	+	0.891106i	$0.649930\pi$
$710$	−4.90952	−	8.50353i	−0.184251	−	0.319132i
$711$	−0.465283			−0.0174495
$712$	15.8190			0.592843
$713$	−4.02010	−	3.07938i	−0.150554	−	0.115324i
$714$	−13.1938			−0.493767
$715$	37.0952			1.38728
$716$	8.00643	+	13.8675i	0.299214	+	0.518255i
$717$	12.9306			0.482901
$718$	3.31260	−	5.73759i	0.123625	−	0.214125i
$719$	−5.84732	−	10.1279i	−0.218068	−	0.377705i	0.736149	−	0.676819i	$-0.236642\pi$
$719$	−5.84732	−	10.1279i	−0.218068	−	0.377705i	−0.954217	+	0.299114i	$0.903309\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	7.11972			0.265152
$722$	−6.51286	+	11.2806i	−0.242384	+	0.419821i
$723$	−5.35784	+	9.28006i	−0.199260	+	0.345129i
$724$	1.46528	−	2.53794i	0.0544568	−	0.0943220i
$725$	−2.73264	−	4.73307i	−0.101488	−	0.175782i
$726$	−14.8190	+	25.6673i	−0.549986	+	0.952603i
$727$	11.8771	+	20.5718i	0.440499	+	0.762966i	0.997726	−	0.0673936i	$-0.0214683\pi$
$727$	11.8771	+	20.5718i	0.440499	+	0.762966i	−0.557228	+	0.830360i	$0.688135\pi$
$728$	−11.1115			−0.411821
$729$	1.00000			0.0370370
$730$	−1.00000	−	1.73205i	−0.0370117	−	0.0641061i
$731$	1.60744	−	2.78417i	0.0594533	−	0.102976i
$732$	−2.22212	−	3.84882i	−0.0821318	−	0.142256i
$733$	−24.0645	+	41.6810i	−0.888844	+	1.53952i	−0.0476004	+	0.998866i	$0.515157\pi$
$733$	−24.0645	+	41.6810i	−0.888844	+	1.53952i	−0.841244	+	0.540656i	$0.818176\pi$
$734$	−12.0000	+	20.7846i	−0.442928	+	0.767174i
$735$	−1.67687	+	2.90443i	−0.0618524	+	0.107132i
$736$	0.909516			0.0335252
$737$	28.3982	+	49.1871i	1.04606	+	1.81183i
$738$	−3.59692	−	6.23004i	−0.132404	−	0.229331i
$739$	2.49357	−	4.31899i	0.0917274	−	0.158877i	−0.816511	−	0.577330i	$-0.804094\pi$
$739$	2.49357	−	4.31899i	0.0917274	−	0.158877i	0.908238	+	0.418454i	$0.137428\pi$
$740$	−8.90952			−0.327520
$741$	−7.11153	−	12.3175i	−0.261249	−	0.452496i
$742$	13.9095			0.510634
$743$	−28.2843			−1.03765			−0.518825	−	0.854880i	$-0.673631\pi$
$743$	−28.2843			−1.03765			−0.518825	+	0.854880i	$0.673631\pi$
$744$	0.722116	−	5.52074i	0.0264741	−	0.202400i
$745$	−6.71568			−0.246044
$746$	27.4360			1.00450
$747$	6.32956	+	10.9631i	0.231586	+	0.401119i
$748$	−44.0468			−1.61051
$749$	−1.82313	+	3.15775i	−0.0666156	+	0.115382i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	2.74317	+	4.75130i	0.100100	+	0.173378i	0.911726	−	0.410800i	$-0.134751\pi$
$751$	2.74317	+	4.75130i	0.100100	+	0.173378i	−0.811626	+	0.584177i	$0.801417\pi$
$752$	−8.72855			−0.318297
$753$	1.76736	−	3.06115i	0.0644061	−	0.111555i
$754$	−15.9013	+	27.5419i	−0.579092	+	1.00302i
$755$	2.27788	−	3.94541i	0.0829007	−	0.143588i
$756$	−0.954758	−	1.65369i	−0.0347242	−	0.0601441i
$757$	1.12111	−	1.94181i	0.0407473	−	0.0705765i	−0.844932	−	0.534873i	$-0.820359\pi$
$757$	1.12111	−	1.94181i	0.0407473	−	0.0705765i	0.885680	+	0.464297i	$0.153693\pi$
$758$	9.26326	+	16.0444i	0.336457	+	0.582760i
$759$	−5.79798			−0.210453
$760$	−2.44423			−0.0886616
$761$	−11.9717	−	20.7356i	−0.433974	−	0.751666i	0.563237	−	0.826295i	$-0.309556\pi$
$761$	−11.9717	−	20.7356i	−0.433974	−	0.751666i	−0.997211	+	0.0746298i	$0.976222\pi$
$762$	7.32956	−	12.6952i	0.265522	−	0.459897i
$763$	−2.33365	−	4.04200i	−0.0844838	−	0.146330i
$764$	0.222116	−	0.384717i	0.00803589	−	0.0139186i
$765$	−3.45476	+	5.98382i	−0.124907	+	0.216345i
$766$	1.36427	−	2.36299i	0.0492932	−	0.0853784i
$767$	33.3346			1.20364
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−6.73264	−	11.6613i	−0.242785	−	0.420516i	0.718721	−	0.695298i	$-0.244728\pi$
$769$	−6.73264	−	11.6613i	−0.242785	−	0.420516i	−0.961507	+	0.274782i	$0.911394\pi$
$770$	6.08639	−	10.5419i	0.219338	−	0.379905i
$771$	−24.5897			−0.885576
$772$	−8.73264	−	15.1254i	−0.314295	−	0.544374i
$773$	−2.36194			−0.0849529			−0.0424765	−	0.999097i	$-0.513525\pi$
$773$	−2.36194			−0.0849529			−0.0424765	+	0.999097i	$0.513525\pi$
$774$	0.465283			0.0167243
$775$	0.722116	−	5.52074i	0.0259392	−	0.198311i
$776$	−18.1728			−0.652365
$777$	−17.0129			−0.610333
$778$	−8.87071	−	15.3645i	−0.318030	−	0.550844i
$779$	−17.5834			−0.629991
$780$	−2.90952	+	5.03943i	−0.104177	+	0.180441i
$781$	−31.2972	−	54.2083i	−1.11990	−	1.93973i
$782$	−3.14216	−	5.44238i	−0.112363	−	0.194619i
$783$	−5.46528			−0.195313
$784$	1.67687	−	2.90443i	0.0598884	−	0.103730i
$785$	8.97171	−	15.5395i	0.320214	−	0.554627i
$786$	−1.14216	+	1.97827i	−0.0407394	+	0.0705627i
$787$	4.19149	+	7.25988i	0.149411	+	0.258787i	0.931010	−	0.364994i	$-0.118929\pi$
$787$	4.19149	+	7.25988i	0.149411	+	0.258787i	−0.781599	+	0.623781i	$0.785596\pi$
$788$	5.28432	−	9.15270i	0.188246	−	0.326052i
$789$	−0.767358	−	1.32910i	−0.0273187	−	0.0473173i
$790$	0.465283			0.0165540
$791$	−17.8611			−0.635069
$792$	−3.18740	−	5.52074i	−0.113259	−	0.196171i
$793$	−12.9306	+	22.3964i	−0.459178	+	0.795319i
$794$	−5.85784	−	10.1461i	−0.207887	−	0.360071i
$795$	3.64216	−	6.30840i	0.129174	−	0.223736i
$796$	4.32956	−	7.49901i	0.153457	−	0.265795i
$797$	4.08639	−	7.07784i	0.144747	−	0.250710i	−0.784531	−	0.620089i	$-0.787096\pi$
$797$	4.08639	−	7.07784i	0.144747	−	0.250710i	0.929279	+	0.369379i	$0.120430\pi$
$798$	−4.66730			−0.165221
$799$	30.1550	+	52.2300i	1.06681	+	1.84777i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	7.90952	−	13.6997i	0.279469	−	0.484055i
$802$	−14.7075			−0.519340
$803$	−6.37480	−	11.0415i	−0.224962	−	0.389645i
$804$	−8.90952			−0.314214
$805$	1.73674			0.0612119
$806$	−29.9224	+	12.4236i	−1.05397	+	0.437603i
$807$	15.9224			0.560494
$808$	−1.93057			−0.0679171
$809$	8.11058	+	14.0479i	0.285153	+	0.493899i	0.972646	−	0.232291i	$-0.0746223\pi$
$809$	8.11058	+	14.0479i	0.285153	+	0.493899i	−0.687493	+	0.726191i	$0.741289\pi$
$810$	−1.00000			−0.0351364
$811$	−19.2843	+	33.4014i	−0.677164	+	1.17288i	0.298667	+	0.954357i	$0.403458\pi$
$811$	−19.2843	+	33.4014i	−0.677164	+	1.17288i	−0.975831	+	0.218525i	$0.929875\pi$
$812$	5.21802	+	9.03788i	0.183117	+	0.317167i
$813$	8.23907	+	14.2705i	0.288957	+	0.500488i
$814$	−56.7964			−1.99071
$815$	−2.89899	+	5.02120i	−0.101547	+	0.175885i
$816$	3.45476	−	5.98382i	0.120941	−	0.209475i
$817$	0.568630	−	0.984896i	0.0198939	−	0.0344572i
$818$	−11.6938	−	20.2543i	−0.408865	−	0.708175i
$819$	−5.55577	+	9.62287i	−0.194134	+	0.336250i
$820$	3.59692	+	6.23004i	0.125610	+	0.217562i
$821$	−29.3877			−1.02564			−0.512818	−	0.858497i	$-0.671399\pi$
$821$	−29.3877			−1.02564			−0.512818	+	0.858497i	$0.671399\pi$
$822$	19.4781			0.679378
$823$	19.5928	+	33.9358i	0.682963	+	1.18293i	0.974072	+	0.226237i	$0.0726423\pi$
$823$	19.5928	+	33.9358i	0.682963	+	1.18293i	−0.291110	+	0.956690i	$0.594024\pi$
$824$	−1.86427	+	3.22902i	−0.0649451	+	0.112488i
$825$	−3.18740	−	5.52074i	−0.110971	−	0.192207i
$826$	5.46938	−	9.47324i	0.190304	−	0.329616i
$827$	0.180968	−	0.313446i	0.00629288	−	0.0108996i	−0.862862	−	0.505440i	$-0.831330\pi$
$827$	0.180968	−	0.313446i	0.00629288	−	0.0108996i	0.869155	+	0.494540i	$0.164664\pi$
$828$	0.454758	−	0.787664i	0.0158039	−	0.0273732i
$829$	37.4005			1.29897			0.649487	−	0.760373i	$-0.274984\pi$
$829$	37.4005			1.29897			0.649487	+	0.760373i	$0.274984\pi$
$830$	−6.32956	−	10.9631i	−0.219702	−	0.380535i
$831$	−12.8296	−	22.2214i	−0.445052	−	0.770853i
$832$	2.90952	−	5.03943i	0.100869	−	0.174711i
$833$	−23.1728			−0.802889
$834$	−5.68740	−	9.85087i	−0.196939	−	0.341108i
$835$	−16.1244			−0.558008
$836$	−15.5815			−0.538897
$837$	−4.42004	−	3.38574i	−0.152779	−	0.117028i
$838$	14.3748			0.496569
$839$	49.4005			1.70550			0.852748	−	0.522323i	$-0.174934\pi$
$839$	49.4005			1.70550			0.852748	+	0.522323i	$0.174934\pi$
$840$	0.954758	+	1.65369i	0.0329423	+	0.0570577i
$841$	0.869320			0.0299766
$842$	−7.15268	+	12.3888i	−0.246498	+	0.426947i
$843$	−15.5686	−	26.9657i	−0.536212	−	0.928747i
$844$	5.22212	+	9.04497i	0.179753	+	0.311341i
$845$	20.8611			0.717645
$846$	−4.36427	+	7.55914i	−0.150047	+	0.259889i
$847$	28.2972	−	49.0122i	0.972303	−	1.68408i
$848$	−3.64216	+	6.30840i	−0.125072	+	0.216631i
$849$	−8.49591	−	14.7153i	−0.291579	−	0.505029i
$850$	3.45476	−	5.98382i	0.118497	−	0.205243i
$851$	−4.05167	−	7.01770i	−0.138890	−	0.240564i
$852$	9.81903			0.336394
$853$	11.5960			0.397038			0.198519	−	0.980097i	$-0.436387\pi$
$853$	11.5960			0.397038			0.198519	+	0.980097i	$0.436387\pi$
$854$	4.24317	+	7.34938i	0.145198	+	0.251491i
$855$	−1.22212	+	2.11677i	−0.0417955	+	0.0723919i
$856$	−0.954758	−	1.65369i	−0.0326330	−	0.0565219i
$857$	23.5298	−	40.7548i	0.803763	−	1.39216i	−0.113359	−	0.993554i	$-0.536161\pi$
$857$	23.5298	−	40.7548i	0.803763	−	1.39216i	0.917123	−	0.398605i	$-0.130506\pi$
$858$	−18.5476	+	32.1254i	−0.633204	+	1.09674i
$859$	1.31260	−	2.27349i	0.0447853	−	0.0775705i	−0.842764	−	0.538284i	$-0.819073\pi$
$859$	1.31260	−	2.27349i	0.0447853	−	0.0775705i	0.887549	+	0.460713i	$0.152406\pi$
$860$	−0.465283			−0.0158660
$861$	6.86837	+	11.8964i	0.234073	+	0.405427i
$862$	−11.3255	−	19.6163i	−0.385747	−	0.668133i
$863$	−15.8497	+	27.4524i	−0.539529	+	0.934491i	0.459401	+	0.888229i	$0.348064\pi$
$863$	−15.8497	+	27.4524i	−0.539529	+	0.934491i	−0.998929	+	0.0462618i	$0.985269\pi$
$864$	1.00000			0.0340207
$865$	0.732642	+	1.26897i	0.0249106	+	0.0431464i
$866$	−26.5686			−0.902839
$867$	−30.7414			−1.04403
$868$	−1.37889	+	10.5419i	−0.0468027	+	0.357817i
$869$	2.96609			0.100618
$870$	5.46528			0.185290
$871$	25.9224	+	44.8989i	0.878346	+	1.52134i
$872$	2.44423			0.0827722
$873$	−9.08639	+	15.7381i	−0.307528	+	0.532654i
$874$	−1.11153	−	1.92523i	−0.0375982	−	0.0651220i
$875$	0.954758	+	1.65369i	0.0322767	+	0.0559049i
$876$	2.00000			0.0675737
$877$	15.8085	−	27.3811i	0.533815	−	0.924595i	−0.465404	−	0.885098i	$-0.654091\pi$
$877$	15.8085	−	27.3811i	0.533815	−	0.924595i	0.999220	−	0.0394971i	$-0.0125756\pi$
$878$	−3.91595	+	6.78262i	−0.132157	+	0.228902i
$879$	13.4612	−	23.3155i	0.454035	−	0.786411i
$880$	3.18740	+	5.52074i	0.107447	+	0.186104i
$881$	−26.9507	+	46.6799i	−0.907991	+	1.57269i	−0.0911397	+	0.995838i	$0.529051\pi$
$881$	−26.9507	+	46.6799i	−0.907991	+	1.57269i	−0.816851	+	0.576848i	$0.804282\pi$
$882$	−1.67687	−	2.90443i	−0.0564633	−	0.0977973i
$883$	−44.5055			−1.49773			−0.748864	−	0.662723i	$-0.769401\pi$
$883$	−44.5055			−1.49773			−0.748864	+	0.662723i	$0.769401\pi$
$884$	−40.2067			−1.35230
$885$	−2.86427	−	4.96107i	−0.0962815	−	0.166764i
$886$	−9.35375	+	16.2012i	−0.314245	+	0.544289i
$887$	−16.0645	−	27.8246i	−0.539394	−	0.934258i	−0.998937	−	0.0461026i	$-0.985320\pi$
$887$	−16.0645	−	27.8246i	−0.539394	−	0.934258i	0.459542	−	0.888156i	$-0.348013\pi$
$888$	4.45476	−	7.71587i	0.149492	−	0.258928i
$889$	−13.9959	+	24.2416i	−0.469408	+	0.813038i
$890$	−7.90952	+	13.6997i	−0.265128	+	0.459214i
$891$	−6.37480			−0.213564
$892$	7.42004	+	12.8519i	0.248441	+	0.430313i
$893$	10.6673	+	18.4763i	0.356968	+	0.618286i
$894$	3.35784	−	5.81595i	0.112303	−	0.194515i
$895$	−16.0129			−0.535251
$896$	−0.954758	−	1.65369i	−0.0318962	−	0.0552459i
$897$	−5.29250			−0.176712
$898$	14.8885			0.496835
$899$	24.1568	+	18.5040i	0.805674	+	0.617144i
$900$	1.00000			0.0333333
$901$	50.3311			1.67677
$902$	22.9296	+	39.7153i	0.763473	+	1.32237i
$903$	−0.888466			−0.0295663
$904$	4.67687	−	8.10058i	0.155551	−	0.269421i
$905$	1.46528	+	2.53794i	0.0487077	+	0.0843641i
$906$	2.27788	+	3.94541i	0.0756776	+	0.131077i
$907$	24.3619			0.808925			0.404462	−	0.914555i	$-0.367459\pi$
$907$	24.3619			0.808925			0.404462	+	0.914555i	$0.367459\pi$
$908$	−1.48947	+	2.57985i	−0.0494300	+	0.0856152i
$909$	−0.965283	+	1.67192i	−0.0320164	+	0.0554541i
$910$	5.55577	−	9.62287i	0.184172	−	0.318995i
$911$	−11.7084	−	20.2796i	−0.387918	−	0.671894i	0.604251	−	0.796794i	$-0.293472\pi$
$911$	−11.7084	−	20.2796i	−0.387918	−	0.671894i	−0.992169	+	0.124900i	$0.960139\pi$
$912$	1.22212	−	2.11677i	0.0404683	−	0.0700932i
$913$	−40.3497	−	69.8877i	−1.33538	−	2.31294i
$914$	14.2067			0.469916
$915$	4.44423			0.146922
$916$	3.75683	+	6.50703i	0.124129	+	0.214998i
$917$	2.18097	−	3.77755i	0.0720219	−	0.124746i
$918$	−3.45476	−	5.98382i	−0.114024	−	0.197495i
$919$	−4.11797	+	7.13253i	−0.135839	+	0.235280i	−0.925918	−	0.377725i	$-0.876706\pi$
$919$	−4.11797	+	7.13253i	−0.135839	+	0.235280i	0.790079	+	0.613006i	$0.210040\pi$
$920$	−0.454758	+	0.787664i	−0.0149929	+	0.0259685i
$921$	9.97171	−	17.2715i	0.328579	−	0.569116i
$922$	−22.6802			−0.746931
$923$	−28.5686	−	49.4823i	−0.940348	−	1.62873i
$924$	6.08639	+	10.5419i	0.200228	+	0.346804i
$925$	4.45476	−	7.71587i	0.146472	−	0.253696i
$926$	22.6170			0.743241
$927$	1.86427	+	3.22902i	0.0612308	+	0.106055i
$928$	−5.46528			−0.179407
$929$	−34.8062			−1.14195			−0.570977	−	0.820966i	$-0.693435\pi$
$929$	−34.8062			−1.14195			−0.570977	+	0.820966i	$0.693435\pi$
$930$	4.42004	+	3.38574i	0.144939	+	0.111023i
$931$	−8.19734			−0.268657
$932$	12.9095			0.422865
$933$	12.2843	+	21.2771i	0.402170	+	0.696580i
$934$	−35.5897			−1.16453
$935$	22.0234	−	38.1456i	0.720242	−	1.24750i
$936$	−2.90952	−	5.03943i	−0.0951005	−	0.164719i
$937$	11.8885	+	20.5914i	0.388379	+	0.672693i	0.992232	−	0.124404i	$-0.0397017\pi$
$937$	11.8885	+	20.5914i	0.388379	+	0.672693i	−0.603852	+	0.797096i	$0.706368\pi$
$938$	17.0129			0.555490
$939$	11.9265	−	20.6573i	0.389206	−	0.674124i
$940$	4.36427	−	7.55914i	0.142347	−	0.246552i
$941$	−6.59048	+	11.4151i	−0.214844	+	0.372120i	−0.953224	−	0.302264i	$-0.902258\pi$
$941$	−6.59048	+	11.4151i	−0.214844	+	0.372120i	0.738381	+	0.674384i	$0.235591\pi$
$942$	8.97171	+	15.5395i	0.292314	+	0.506303i
$943$	−3.27145	+	5.66632i	−0.106533	+	0.184521i
$944$	2.86427	+	4.96107i	0.0932242	+	0.161469i
$945$	1.90952			0.0621166
$946$	−2.96609			−0.0964358
$947$	−24.7285	−	42.8311i	−0.803570	−	1.39182i	−0.917252	−	0.398307i	$-0.869598\pi$
$947$	−24.7285	−	42.8311i	−0.803570	−	1.39182i	0.113682	−	0.993517i	$-0.463735\pi$
$948$	−0.232642	+	0.402947i	−0.00755585	+	0.0130871i
$949$	−5.81903	−	10.0789i	−0.188894	−	0.327174i
$950$	1.22212	−	2.11677i	0.0396507	−	0.0686770i
$951$	−7.55167	+	13.0799i	−0.244880	+	0.424144i
$952$	−6.59692	+	11.4262i	−0.213807	+	0.370325i
$953$	36.4442			1.18054			0.590272	−	0.807204i	$-0.299020\pi$
$953$	36.4442			1.18054			0.590272	+	0.807204i	$0.299020\pi$
$954$	3.64216	+	6.30840i	0.117919	+	0.204242i
$955$	0.222116	+	0.384717i	0.00718752	+	0.0124491i
$956$	6.46528	−	11.1982i	0.209102	−	0.362176i
$957$	34.8401			1.12622
$958$	−1.24317	−	2.15323i	−0.0401649	−	0.0695676i
$959$	−37.1938			−1.20105
$960$	−1.00000			−0.0322749
$961$	8.07353	+	29.9302i	0.260436	+	0.965491i
$962$	−51.8448			−1.67154
$963$	−1.90952			−0.0615333
$964$	5.35784	+	9.28006i	0.172564	+	0.298890i
$965$	17.4653			0.562227
$966$	−0.868368	+	1.50406i	−0.0279393	+	0.0483922i
$967$	−29.2761	−	50.7077i	−0.941457	−	1.63065i	−0.762695	−	0.646759i	$-0.776124\pi$
$967$	−29.2761	−	50.7077i	−0.941457	−	1.63065i	−0.178762	−	0.983892i	$-0.557209\pi$
$968$	14.8190	+	25.6673i	0.476302	+	0.824979i
$969$	−16.8885			−0.542536
$970$	9.08639	−	15.7381i	0.291746	−	0.505320i
$971$	17.0969	−	29.6127i	0.548666	−	0.950318i	−0.449700	−	0.893180i	$-0.648469\pi$
$971$	17.0969	−	29.6127i	0.548666	−	0.950318i	0.998366	−	0.0571380i	$-0.0181975\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	10.8602	+	18.8104i	0.348161	+	0.603033i
$974$	−4.51053	+	7.81246i	−0.144527	+	0.250327i
$975$	−2.90952	−	5.03943i	−0.0931791	−	0.161391i
$976$	−4.44423			−0.142256
$977$	−22.1810			−0.709632			−0.354816	−	0.934936i	$-0.615456\pi$
$977$	−22.1810			−0.709632			−0.354816	+	0.934936i	$0.615456\pi$
$978$	−2.89899	−	5.02120i	−0.0926995	−	0.160560i
$979$	−50.4216	+	87.3327i	−1.61148	+	2.79117i
$980$	1.67687	+	2.90443i	0.0535658	+	0.0927787i
$981$	1.22212	−	2.11677i	0.0390192	−	0.0675832i
$982$	9.07587	−	15.7199i	0.289622	−	0.501641i
$983$	4.53472	−	7.85436i	0.144635	−	0.250515i	−0.784602	−	0.620000i	$-0.787133\pi$
$983$	4.53472	−	7.85436i	0.144635	−	0.250515i	0.929237	+	0.369485i	$0.120466\pi$
$984$	−7.19383			−0.229331
$985$	5.28432	+	9.15270i	0.168372	+	0.291629i
$986$	18.8812	+	32.7033i	0.601301	+	1.04148i
$987$	8.33365	−	14.4343i	0.265263	−	0.459449i
$988$	−14.2231			−0.452496
$989$	−0.211591	−	0.366487i	−0.00672821	−	0.0116536i
$990$	6.37480			0.202604
$991$	34.3877			1.09236			0.546180	−	0.837668i	$-0.316081\pi$
$991$	34.3877			1.09236			0.546180	+	0.837668i	$0.316081\pi$
$992$	−4.42004	−	3.38574i	−0.140336	−	0.107497i
$993$	−0.124397			−0.00394763
$994$	−18.7496			−0.594701
$995$	4.32956	+	7.49901i	0.137256	+	0.237735i
$996$	12.6591			0.401119
$997$	−16.9296	+	29.3230i	−0.536166	+	0.928667i	0.462940	+	0.886390i	$0.346795\pi$
$997$	−16.9296	+	29.3230i	−0.536166	+	0.928667i	−0.999106	+	0.0422774i	$0.986539\pi$
$998$	−15.5759	−	26.9782i	−0.493045	−	0.853980i
$999$	−4.45476	−	7.71587i	−0.140942	−	0.244119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.n.211.3	✓	6
31.5	even	3	inner	930.2.i.n.811.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.n.211.3	✓	6	1.1	even	1	trivial
930.2.i.n.811.3	yes	6	31.5	even	3	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.954758 + 1.65369i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(3.18740 - 5.52074i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.90952 - 5.03943i) q^{13} +(-0.954758 - 1.65369i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-3.45476 - 5.98382i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.22212 - 2.11677i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.954758 + 1.65369i) q^{21} +(-3.18740 + 5.52074i) q^{22} -0.909516 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.90952 + 5.03943i) q^{26} -1.00000 q^{27} +(0.954758 + 1.65369i) q^{28} +5.46528 q^{29} +1.00000 q^{30} +(4.42004 + 3.38574i) q^{31} -1.00000 q^{32} +6.37480 q^{33} +(3.45476 + 5.98382i) q^{34} -1.90952 q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.45476 + 7.71587i) q^{37} +(1.22212 + 2.11677i) q^{38} +5.81903 q^{39} +(0.500000 - 0.866025i) q^{40} +(3.59692 - 6.23004i) q^{41} +(0.954758 - 1.65369i) q^{42} +(0.232642 + 0.402947i) q^{43} +(3.18740 - 5.52074i) q^{44} +(-0.500000 - 0.866025i) q^{45} +0.909516 q^{46} -8.72855 q^{47} +(0.500000 + 0.866025i) q^{48} +(1.67687 - 2.90443i) q^{49} +(0.500000 + 0.866025i) q^{50} +(3.45476 - 5.98382i) q^{51} +(2.90952 - 5.03943i) q^{52} +(-3.64216 + 6.30840i) q^{53} +1.00000 q^{54} +(3.18740 + 5.52074i) q^{55} +(-0.954758 - 1.65369i) q^{56} +(1.22212 - 2.11677i) q^{57} -5.46528 q^{58} +(2.86427 + 4.96107i) q^{59} -1.00000 q^{60} -4.44423 q^{61} +(-4.42004 - 3.38574i) q^{62} -1.90952 q^{63} +1.00000 q^{64} +(2.90952 + 5.03943i) q^{65} -6.37480 q^{66} +(-4.45476 + 7.71587i) q^{67} +(-3.45476 - 5.98382i) q^{68} +(-0.454758 - 0.787664i) q^{69} +1.90952 q^{70} +(4.90952 - 8.50353i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-4.45476 - 7.71587i) q^{74} +(0.500000 - 0.866025i) q^{75} +(-1.22212 - 2.11677i) q^{76} +12.1728 q^{77} -5.81903 q^{78} +(0.232642 + 0.402947i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.59692 + 6.23004i) q^{82} +(6.32956 - 10.9631i) q^{83} +(-0.954758 + 1.65369i) q^{84} +6.90952 q^{85} +(-0.232642 - 0.402947i) q^{86} +(2.73264 + 4.73307i) q^{87} +(-3.18740 + 5.52074i) q^{88} -15.8190 q^{89} +(0.500000 + 0.866025i) q^{90} +11.1115 q^{91} -0.909516 q^{92} +(-0.722116 + 5.52074i) q^{93} +8.72855 q^{94} +2.44423 q^{95} +(-0.500000 - 0.866025i) q^{96} +18.1728 q^{97} +(-1.67687 + 2.90443i) q^{98} +(3.18740 + 5.52074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 6 q^{16} - 11 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20}+ \cdots + 5 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 4 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 + 6 * q^16 - 11 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 14 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 - 6 * q^27 - 4 * q^28 + 24 * q^29 + 6 * q^30 + 8 * q^31 - 6 * q^32 + 10 * q^33 + 11 * q^34 + 8 * q^35 - 3 * q^36 + 17 * q^37 + 2 * q^38 - 4 * q^39 + 3 * q^40 - 12 * q^41 - 4 * q^42 - 3 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 + 6 * q^47 + 3 * q^48 - 5 * q^49 + 3 * q^50 + 11 * q^51 - 2 * q^52 + 2 * q^53 + 6 * q^54 + 5 * q^55 + 4 * q^56 + 2 * q^57 - 24 * q^58 - 12 * q^59 - 6 * q^60 - 16 * q^61 - 8 * q^62 + 8 * q^63 + 6 * q^64 - 2 * q^65 - 10 * q^66 - 17 * q^67 - 11 * q^68 + 7 * q^69 - 8 * q^70 + 10 * q^71 + 3 * q^72 + 6 * q^73 - 17 * q^74 + 3 * q^75 - 2 * q^76 + 4 * q^77 + 4 * q^78 - 3 * q^79 - 3 * q^80 - 3 * q^81 + 12 * q^82 + 4 * q^84 + 22 * q^85 + 3 * q^86 + 12 * q^87 - 5 * q^88 - 56 * q^89 + 3 * q^90 + 88 * q^91 + 14 * q^92 + q^93 - 6 * q^94 + 4 * q^95 - 3 * q^96 + 40 * q^97 + 5 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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