LMFDB - Embedded newform 1155.2.q.h.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(331,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1155.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 9x^{10} + 61x^{8} - 2x^{7} + 164x^{6} - 36x^{5} + 328x^{4} - 40x^{3} + 164x^{2} + 16x + 64 $ x^12 + 9x^10 + 61x^8 - 2x^7 + 164x^6 - 36x^5 + 328x^4 - 40x^3 + 164x^2 + 16*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.1
Root			$-1.16512 + 2.01805i$ of defining polynomial
Character	$\chi$	$=$	1155.331
Dual form			1155.2.q.h.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16512 + 2.01805i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.71503 - 2.97052i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.33025 q^{6} +(-1.60347 - 2.10449i) q^{7} +3.33238 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.16512 + 2.01805i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.71503 - 2.97052i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.33025 q^{6} +(-1.60347 - 2.10449i) q^{7} +3.33238 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.16512 + 2.01805i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.71503 + 2.97052i) q^{12} -6.56567 q^{13} +(6.11522 - 0.783901i) q^{14} -1.00000 q^{15} +(-0.452585 + 0.783901i) q^{16} +(1.27775 + 2.21312i) q^{17} +(-1.16512 - 2.01805i) q^{18} +(1.19422 - 2.06845i) q^{19} -3.43006 q^{20} +(-1.02081 + 2.44089i) q^{21} +2.33025 q^{22} +(1.85935 - 3.22048i) q^{23} +(-1.66619 - 2.88593i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(7.64982 - 13.2499i) q^{26} +1.00000 q^{27} +(-3.50142 + 8.37240i) q^{28} -4.34552 q^{29} +(1.16512 - 2.01805i) q^{30} +(4.63958 + 8.03599i) q^{31} +(2.27775 + 3.94518i) q^{32} +(-0.500000 + 0.866025i) q^{33} -5.95494 q^{34} +(-2.62428 + 0.336402i) q^{35} +3.43006 q^{36} +(-3.49343 + 6.05080i) q^{37} +(2.78283 + 4.82001i) q^{38} +(3.28283 + 5.68603i) q^{39} +(1.66619 - 2.88593i) q^{40} +5.85125 q^{41} +(-3.73649 - 4.90398i) q^{42} -0.577059 q^{43} +(-1.71503 + 2.97052i) q^{44} +(0.500000 + 0.866025i) q^{45} +(4.33274 + 7.50452i) q^{46} +(-0.610040 + 1.05662i) q^{47} +0.905171 q^{48} +(-1.85776 + 6.74898i) q^{49} +2.33025 q^{50} +(1.27775 - 2.21312i) q^{51} +(11.2603 + 19.5034i) q^{52} +(-0.857818 - 1.48578i) q^{53} +(-1.16512 + 2.01805i) q^{54} -1.00000 q^{55} +(-5.34338 - 7.01297i) q^{56} -2.38844 q^{57} +(5.06307 - 8.76950i) q^{58} +(5.88478 + 10.1927i) q^{59} +(1.71503 + 2.97052i) q^{60} +(-5.05392 + 8.75364i) q^{61} -21.6228 q^{62} +(2.62428 - 0.336402i) q^{63} -12.4258 q^{64} +(-3.28283 + 5.68603i) q^{65} +(-1.16512 - 2.01805i) q^{66} +(6.05184 + 10.4821i) q^{67} +(4.38275 - 7.59114i) q^{68} -3.71869 q^{69} +(2.37873 - 5.68788i) q^{70} +1.12615 q^{71} +(-1.66619 + 2.88593i) q^{72} +(-3.83339 - 6.63963i) q^{73} +(-8.14056 - 14.0999i) q^{74} +(-0.500000 + 0.866025i) q^{75} -8.19250 q^{76} +(-1.02081 + 2.44089i) q^{77} -15.2996 q^{78} +(-0.372163 + 0.644604i) q^{79} +(0.452585 + 0.783901i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.81743 + 11.8081i) q^{82} -12.9061 q^{83} +(9.00142 - 1.15388i) q^{84} +2.55550 q^{85} +(0.672346 - 1.16454i) q^{86} +(2.17276 + 3.76333i) q^{87} +(-1.66619 - 2.88593i) q^{88} +(8.03826 - 13.9227i) q^{89} -2.33025 q^{90} +(10.5279 + 13.8174i) q^{91} -12.7553 q^{92} +(4.63958 - 8.03599i) q^{93} +(-1.42154 - 2.46219i) q^{94} +(-1.19422 - 2.06845i) q^{95} +(2.27775 - 3.94518i) q^{96} -4.43219 q^{97} +(-11.4553 - 11.6125i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 6 q^{4} + 6 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 6 * q^4 + 6 * q^5 - 2 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} - 6 q^{4} + 6 q^{5} - 2 q^{7} - 6 q^{9} - 6 q^{11} - 6 q^{12} - 8 q^{13} - 2 q^{14} - 12 q^{15} + 2 q^{16} - 2 q^{17} + 13 q^{19} - 12 q^{20} + q^{21} + 7 q^{23} - 6 q^{25} + 26 q^{26} + 12 q^{27} - 40 q^{28} + 6 q^{29} + 15 q^{31} + 10 q^{32} - 6 q^{33} - 28 q^{34} - q^{35} + 12 q^{36} + 11 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{41} + 4 q^{42} - 8 q^{43} - 6 q^{44} + 6 q^{45} + 16 q^{46} + 19 q^{47} - 4 q^{48} - 2 q^{51} + 16 q^{52} + q^{53} - 12 q^{55} - 18 q^{56} - 26 q^{57} + 22 q^{59} + 6 q^{60} + 14 q^{61} - 4 q^{62} + q^{63} - 20 q^{64} - 4 q^{65} + 21 q^{67} + 14 q^{68} - 14 q^{69} + 2 q^{70} + 16 q^{71} + 11 q^{73} - 20 q^{74} - 6 q^{75} + q^{77} - 52 q^{78} + 13 q^{79} - 2 q^{80} - 6 q^{81} + 6 q^{82} - 20 q^{83} + 44 q^{84} - 4 q^{85} - 36 q^{86} - 3 q^{87} + 28 q^{89} + 2 q^{91} + 12 q^{92} + 15 q^{93} + 14 q^{94} - 13 q^{95} + 10 q^{96} - 12 q^{97} - 36 q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 - 6 * q^4 + 6 * q^5 - 2 * q^7 - 6 * q^9 - 6 * q^11 - 6 * q^12 - 8 * q^13 - 2 * q^14 - 12 * q^15 + 2 * q^16 - 2 * q^17 + 13 * q^19 - 12 * q^20 + q^21 + 7 * q^23 - 6 * q^25 + 26 * q^26 + 12 * q^27 - 40 * q^28 + 6 * q^29 + 15 * q^31 + 10 * q^32 - 6 * q^33 - 28 * q^34 - q^35 + 12 * q^36 + 11 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^41 + 4 * q^42 - 8 * q^43 - 6 * q^44 + 6 * q^45 + 16 * q^46 + 19 * q^47 - 4 * q^48 - 2 * q^51 + 16 * q^52 + q^53 - 12 * q^55 - 18 * q^56 - 26 * q^57 + 22 * q^59 + 6 * q^60 + 14 * q^61 - 4 * q^62 + q^63 - 20 * q^64 - 4 * q^65 + 21 * q^67 + 14 * q^68 - 14 * q^69 + 2 * q^70 + 16 * q^71 + 11 * q^73 - 20 * q^74 - 6 * q^75 + q^77 - 52 * q^78 + 13 * q^79 - 2 * q^80 - 6 * q^81 + 6 * q^82 - 20 * q^83 + 44 * q^84 - 4 * q^85 - 36 * q^86 - 3 * q^87 + 28 * q^89 + 2 * q^91 + 12 * q^92 + 15 * q^93 + 14 * q^94 - 13 * q^95 + 10 * q^96 - 12 * q^97 - 36 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.16512	+	2.01805i	−0.823867	+	1.42698i	0.0789150	+	0.996881i	$0.474854\pi$
$2$	−1.16512	+	2.01805i	−0.823867	+	1.42698i	−0.902782	+	0.430098i	$0.858479\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.71503	−	2.97052i	−0.857514	−	1.48526i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	2.33025			0.951320
$7$	−1.60347	−	2.10449i	−0.606055	−	0.795422i
$7$	−1.60347	−	2.10449i	−0.606055	−	0.795422i
$8$	3.33238			1.17818
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.16512	+	2.01805i	0.368445	+	0.638165i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.71503	+	2.97052i	−0.495086	+	0.857514i
$13$	−6.56567			−1.82099			−0.910494	−	0.413522i	$-0.864299\pi$
$13$	−6.56567			−1.82099			−0.910494	+	0.413522i	$0.864299\pi$
$14$	6.11522	−	0.783901i	1.63436	−	0.209506i
$15$	−1.00000			−0.258199
$16$	−0.452585	+	0.783901i	−0.113146	+	0.195975i
$17$	1.27775	+	2.21312i	0.309899	+	0.536762i	0.978340	−	0.207004i	$-0.0663713\pi$
$17$	1.27775	+	2.21312i	0.309899	+	0.536762i	−0.668441	+	0.743765i	$0.733038\pi$
$18$	−1.16512	−	2.01805i	−0.274622	−	0.475660i
$19$	1.19422	−	2.06845i	0.273973	−	0.474536i	−0.695902	−	0.718136i	$-0.744995\pi$
$19$	1.19422	−	2.06845i	0.273973	−	0.474536i	0.969876	+	0.243601i	$0.0783287\pi$
$20$	−3.43006			−0.766984
$21$	−1.02081	+	2.44089i	−0.222758	+	0.532646i
$22$	2.33025			0.496811
$23$	1.85935	−	3.22048i	0.387700	−	0.671517i	−0.604439	−	0.796651i	$-0.706603\pi$
$23$	1.85935	−	3.22048i	0.387700	−	0.671517i	0.992140	+	0.125134i	$0.0399362\pi$
$24$	−1.66619	−	2.88593i	−0.340110	−	0.589088i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	7.64982	−	13.2499i	1.50025	−	2.59851i
$27$	1.00000			0.192450
$28$	−3.50142	+	8.37240i	−0.661706	+	1.58223i
$29$	−4.34552			−0.806943			−0.403472	−	0.914992i	$-0.632197\pi$
$29$	−4.34552			−0.806943			−0.403472	+	0.914992i	$0.632197\pi$
$30$	1.16512	−	2.01805i	0.212722	−	0.368445i
$31$	4.63958	+	8.03599i	0.833294	+	1.44331i	0.895412	+	0.445238i	$0.146881\pi$
$31$	4.63958	+	8.03599i	0.833294	+	1.44331i	−0.0621183	+	0.998069i	$0.519786\pi$
$32$	2.27775	+	3.94518i	0.402653	+	0.697415i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	−5.95494			−1.02126
$35$	−2.62428	+	0.336402i	−0.443584	+	0.0568624i
$36$	3.43006			0.571676
$37$	−3.49343	+	6.05080i	−0.574316	+	0.994745i	0.421799	+	0.906689i	$0.361399\pi$
$37$	−3.49343	+	6.05080i	−0.574316	+	0.994745i	−0.996116	+	0.0880557i	$0.971935\pi$
$38$	2.78283	+	4.82001i	0.451435	+	0.781909i
$39$	3.28283	+	5.68603i	0.525674	+	0.910494i
$40$	1.66619	−	2.88593i	0.263448	−	0.456306i
$41$	5.85125			0.913811			0.456906	−	0.889515i	$-0.348958\pi$
$41$	5.85125			0.913811			0.456906	+	0.889515i	$0.348958\pi$
$42$	−3.73649	−	4.90398i	−0.576552	−	0.756701i
$43$	−0.577059			−0.0880007			−0.0440004	−	0.999032i	$-0.514010\pi$
$43$	−0.577059			−0.0880007			−0.0440004	+	0.999032i	$0.514010\pi$
$44$	−1.71503	+	2.97052i	−0.258550	+	0.447822i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	4.33274	+	7.50452i	0.638827	+	1.10648i
$47$	−0.610040	+	1.05662i	−0.0889835	+	0.154124i	−0.907082	−	0.420955i	$-0.861695\pi$
$47$	−0.610040	+	1.05662i	−0.0889835	+	0.154124i	0.818098	+	0.575079i	$0.195029\pi$
$48$	0.905171			0.130650
$49$	−1.85776	+	6.74898i	−0.265394	+	0.964140i
$50$	2.33025			0.329547
$51$	1.27775	−	2.21312i	0.178921	−	0.309899i
$52$	11.2603	+	19.5034i	1.56152	+	2.70464i
$53$	−0.857818	−	1.48578i	−0.117830	−	0.204088i	0.801077	−	0.598561i	$-0.204261\pi$
$53$	−0.857818	−	1.48578i	−0.117830	−	0.204088i	−0.918908	+	0.394473i	$0.870927\pi$
$54$	−1.16512	+	2.01805i	−0.158553	+	0.274622i
$55$	−1.00000			−0.134840
$56$	−5.34338	−	7.01297i	−0.714040	−	0.937147i
$57$	−2.38844			−0.316357
$58$	5.06307	−	8.76950i	0.664814	−	1.15149i
$59$	5.88478	+	10.1927i	0.766133	+	1.32698i	0.939646	+	0.342149i	$0.111155\pi$
$59$	5.88478	+	10.1927i	0.766133	+	1.32698i	−0.173513	+	0.984832i	$0.555512\pi$
$60$	1.71503	+	2.97052i	0.221409	+	0.383492i
$61$	−5.05392	+	8.75364i	−0.647088	+	1.12079i	0.336727	+	0.941602i	$0.390680\pi$
$61$	−5.05392	+	8.75364i	−0.647088	+	1.12079i	−0.983815	+	0.179187i	$0.942653\pi$
$62$	−21.6228			−2.74609
$63$	2.62428	−	0.336402i	0.330628	−	0.0423827i
$64$	−12.4258			−1.55322
$65$	−3.28283	+	5.68603i	−0.407185	+	0.705266i
$66$	−1.16512	−	2.01805i	−0.143417	−	0.248405i
$67$	6.05184	+	10.4821i	0.739350	+	1.28059i	0.952788	+	0.303636i	$0.0982006\pi$
$67$	6.05184	+	10.4821i	0.739350	+	1.28059i	−0.213438	+	0.976957i	$0.568466\pi$
$68$	4.38275	−	7.59114i	0.531486	−	0.920561i
$69$	−3.71869			−0.447678
$70$	2.37873	−	5.68788i	0.284313	−	0.679832i
$71$	1.12615			0.133649			0.0668245	−	0.997765i	$-0.478713\pi$
$71$	1.12615			0.133649			0.0668245	+	0.997765i	$0.478713\pi$
$72$	−1.66619	+	2.88593i	−0.196363	+	0.340110i
$73$	−3.83339	−	6.63963i	−0.448664	−	0.777110i	0.549635	−	0.835405i	$-0.314767\pi$
$73$	−3.83339	−	6.63963i	−0.448664	−	0.777110i	−0.998299	+	0.0582954i	$0.981433\pi$
$74$	−8.14056	−	14.0999i	−0.946321	−	1.63908i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−8.19250			−0.939744
$77$	−1.02081	+	2.44089i	−0.116332	+	0.278165i
$78$	−15.2996			−1.73234
$79$	−0.372163	+	0.644604i	−0.0418716	+	0.0725237i	−0.886202	−	0.463300i	$-0.846665\pi$
$79$	−0.372163	+	0.644604i	−0.0418716	+	0.0725237i	0.844330	+	0.535823i	$0.179999\pi$
$80$	0.452585	+	0.783901i	0.0506006	+	0.0876428i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.81743	+	11.8081i	−0.752859	+	1.30399i
$83$	−12.9061			−1.41663			−0.708313	−	0.705898i	$-0.750544\pi$
$83$	−12.9061			−1.41663			−0.708313	+	0.705898i	$0.750544\pi$
$84$	9.00142	−	1.15388i	0.982135	−	0.125898i
$85$	2.55550			0.277183
$86$	0.672346	−	1.16454i	0.0725009	−	0.125575i
$87$	2.17276	+	3.76333i	0.232944	+	0.403472i
$88$	−1.66619	−	2.88593i	−0.177617	−	0.307641i
$89$	8.03826	−	13.9227i	0.852054	−	1.47580i	−0.0272977	−	0.999627i	$-0.508690\pi$
$89$	8.03826	−	13.9227i	0.852054	−	1.47580i	0.879352	−	0.476173i	$-0.157976\pi$
$90$	−2.33025			−0.245630
$91$	10.5279	+	13.8174i	1.10362	+	1.44845i
$92$	−12.7553			−1.32983
$93$	4.63958	−	8.03599i	0.481102	−	0.833294i
$94$	−1.42154	−	2.46219i	−0.146621	−	0.253955i
$95$	−1.19422	−	2.06845i	−0.122525	−	0.212219i
$96$	2.27775	−	3.94518i	0.232472	−	0.402653i
$97$	−4.43219			−0.450021			−0.225010	−	0.974356i	$-0.572242\pi$
$97$	−4.43219			−0.450021			−0.225010	+	0.974356i	$0.572242\pi$
$98$	−11.4553	−	11.6125i	−1.15716	−	1.17303i
$99$	1.00000			0.100504
$100$	−1.71503	+	2.97052i	−0.171503	+	0.297052i
$101$	−5.27118	−	9.12995i	−0.524502	−	0.908464i	−0.999593	−	0.0285272i	$-0.990918\pi$
$101$	−5.27118	−	9.12995i	−0.524502	−	0.908464i	0.475091	−	0.879937i	$-0.342415\pi$
$102$	2.97747	+	5.15713i	0.294813	+	0.510632i
$103$	−2.96541	+	5.13625i	−0.292191	+	0.506089i	−0.974328	−	0.225135i	$-0.927718\pi$
$103$	−2.96541	+	5.13625i	−0.292191	+	0.506089i	0.682137	+	0.731225i	$0.261051\pi$
$104$	−21.8793			−2.14544
$105$	1.60347	+	2.10449i	0.156483	+	0.205377i
$106$	3.99786			0.388306
$107$	−8.39232	+	14.5359i	−0.811317	+	1.40524i	0.100626	+	0.994924i	$0.467915\pi$
$107$	−8.39232	+	14.5359i	−0.811317	+	1.40524i	−0.911943	+	0.410317i	$0.865418\pi$
$108$	−1.71503	−	2.97052i	−0.165029	−	0.285838i
$109$	8.28442	+	14.3490i	0.793504	+	1.37439i	0.923785	+	0.382912i	$0.125079\pi$
$109$	8.28442	+	14.3490i	0.793504	+	1.37439i	−0.130281	+	0.991477i	$0.541588\pi$
$110$	1.16512	−	2.01805i	0.111090	−	0.192414i
$111$	6.98686			0.663163
$112$	2.37542	−	0.304502i	0.224456	−	0.0287727i
$113$	17.2975			1.62721			0.813606	−	0.581417i	$-0.197502\pi$
$113$	17.2975			1.62721			0.813606	+	0.581417i	$0.197502\pi$
$114$	2.78283	−	4.82001i	0.260636	−	0.451435i
$115$	−1.85935	−	3.22048i	−0.173385	−	0.300311i
$116$	7.45269	+	12.9084i	0.691965	+	1.19852i
$117$	3.28283	−	5.68603i	0.303498	−	0.525674i
$118$	−27.4260			−2.52477
$119$	2.60867	−	6.23769i	0.239136	−	0.571808i
$120$	−3.33238			−0.304204
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−11.7769	−	20.3982i	−1.06623	−	1.84676i
$123$	−2.92562	−	5.06733i	−0.263795	−	0.456906i
$124$	15.9140	−	27.5639i	1.42912	−	2.47531i
$125$	−1.00000			−0.0894427
$126$	−2.37873	+	5.68788i	−0.211914	+	0.506717i
$127$	−6.96467			−0.618015			−0.309007	−	0.951060i	$-0.599997\pi$
$127$	−6.96467			−0.618015			−0.309007	+	0.951060i	$0.599997\pi$
$128$	9.92208	−	17.1855i	0.876996	−	1.51900i
$129$	0.288530	+	0.499748i	0.0254036	+	0.0440004i
$130$	−7.64982	−	13.2499i	−0.670933	−	1.16209i
$131$	7.80481	−	13.5183i	0.681910	−	1.18110i	−0.292488	−	0.956269i	$-0.594483\pi$
$131$	7.80481	−	13.5183i	0.681910	−	1.18110i	0.974397	−	0.224833i	$-0.0721837\pi$
$132$	3.43006			0.298548
$133$	−6.26794	+	0.803478i	−0.543499	+	0.0696704i
$134$	−28.2046			−2.43651
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	4.25795	+	7.37498i	0.365116	+	0.632400i
$137$	−1.11869	−	1.93762i	−0.0955757	−	0.165542i	0.814273	−	0.580482i	$-0.197136\pi$
$137$	−1.11869	−	1.93762i	−0.0955757	−	0.165542i	−0.909849	+	0.414940i	$0.863803\pi$
$138$	4.33274	−	7.50452i	0.368827	−	0.638827i
$139$	−12.3721			−1.04939			−0.524693	−	0.851292i	$-0.675820\pi$
$139$	−12.3721			−1.04939			−0.524693	+	0.851292i	$0.675820\pi$
$140$	5.50000	+	7.21852i	0.464835	+	0.610076i
$141$	1.22008			0.102749
$142$	−1.31210	+	2.27262i	−0.110109	+	0.190714i
$143$	3.28283	+	5.68603i	0.274524	+	0.475490i
$144$	−0.452585	−	0.783901i	−0.0377154	−	0.0653251i
$145$	−2.17276	+	3.76333i	−0.180438	+	0.312528i
$146$	17.8655			1.47856
$147$	6.77367	−	1.76563i	0.558683	−	0.145626i
$148$	23.9653			1.96994
$149$	−1.69522	+	2.93620i	−0.138878	+	0.240543i	−0.927072	−	0.374883i	$-0.877683\pi$
$149$	−1.69522	+	2.93620i	−0.138878	+	0.240543i	0.788194	+	0.615426i	$0.211016\pi$
$150$	−1.16512	−	2.01805i	−0.0951320	−	0.164773i
$151$	0.460315	+	0.797288i	0.0374599	+	0.0648824i	0.884148	−	0.467208i	$-0.154740\pi$
$151$	0.460315	+	0.797288i	0.0374599	+	0.0648824i	−0.846688	+	0.532090i	$0.821407\pi$
$152$	3.97961	−	6.89288i	0.322789	−	0.559086i
$153$	−2.55550			−0.206600
$154$	−3.73649	−	4.90398i	−0.301095	−	0.395174i
$155$	9.27917			0.745321
$156$	11.2603	−	19.5034i	0.901546	−	1.56152i
$157$	−9.81237	−	16.9955i	−0.783113	−	1.35639i	−0.930120	−	0.367256i	$-0.880297\pi$
$157$	−9.81237	−	16.9955i	−0.783113	−	1.35639i	0.147007	−	0.989135i	$-0.453036\pi$
$158$	−0.867231	−	1.50209i	−0.0689932	−	0.119500i
$159$	−0.857818	+	1.48578i	−0.0680294	+	0.117830i
$160$	4.55550			0.360144
$161$	−9.75888	+	1.25098i	−0.769108	+	0.0985908i
$162$	2.33025			0.183082
$163$	−5.09803	+	8.83005i	−0.399309	+	0.691623i	−0.993641	−	0.112597i	$-0.964083\pi$
$163$	−5.09803	+	8.83005i	−0.399309	+	0.691623i	0.594332	+	0.804220i	$0.297416\pi$
$164$	−10.0351	−	17.3812i	−0.783606	−	1.35725i
$165$	0.500000	+	0.866025i	0.0389249	+	0.0674200i
$166$	15.0372	−	26.0452i	1.16711	−	2.02150i
$167$	0.708129			0.0547967			0.0273983	−	0.999625i	$-0.491278\pi$
$167$	0.708129			0.0547967			0.0273983	+	0.999625i	$0.491278\pi$
$168$	−3.40172	+	8.13399i	−0.262448	+	0.627551i
$169$	30.1080			2.31600
$170$	−2.97747	+	5.15713i	−0.228362	+	0.395534i
$171$	1.19422	+	2.06845i	0.0913244	+	0.158179i
$172$	0.989673	+	1.71416i	0.0754618	+	0.130704i
$173$	−6.76671	+	11.7203i	−0.514464	+	0.891077i	0.485395	+	0.874295i	$0.338676\pi$
$173$	−6.76671	+	11.7203i	−0.514464	+	0.891077i	−0.999859	+	0.0167825i	$0.994658\pi$
$174$	−10.1261			−0.767661
$175$	−1.02081	+	2.44089i	−0.0771657	+	0.184514i
$176$	0.905171			0.0682298
$177$	5.88478	−	10.1927i	0.442327	−	0.766133i
$178$	18.7311	+	32.4433i	1.40396	+	2.43173i
$179$	6.98764	+	12.1029i	0.522281	+	0.904617i	0.999664	+	0.0259216i	$0.00825204\pi$
$179$	6.98764	+	12.1029i	0.522281	+	0.904617i	−0.477383	+	0.878695i	$0.658415\pi$
$180$	1.71503	−	2.97052i	0.127831	−	0.221409i
$181$	−9.94639			−0.739309			−0.369655	−	0.929169i	$-0.620524\pi$
$181$	−9.94639			−0.739309			−0.369655	+	0.929169i	$0.620524\pi$
$182$	−40.1505	+	5.14683i	−2.97615	+	0.381509i
$183$	10.1078			0.747193
$184$	6.19606	−	10.7319i	0.456779	−	0.791165i
$185$	3.49343	+	6.05080i	0.256842	+	0.444863i
$186$	10.8114	+	18.7259i	0.792729	+	1.37305i
$187$	1.27775	−	2.21312i	0.0934382	−	0.161840i
$188$	4.18494			0.305218
$189$	−1.60347	−	2.10449i	−0.116635	−	0.153079i
$190$	5.56567			0.403776
$191$	−6.24144	+	10.8105i	−0.451615	+	0.782220i	−0.998487	−	0.0549966i	$-0.982485\pi$
$191$	−6.24144	+	10.8105i	−0.451615	+	0.782220i	0.546872	+	0.837216i	$0.315819\pi$
$192$	6.21289	+	10.7610i	0.448377	+	0.776611i
$193$	−0.859332	−	1.48841i	−0.0618561	−	0.107138i	0.833439	−	0.552611i	$-0.186369\pi$
$193$	−0.859332	−	1.48841i	−0.0618561	−	0.107138i	−0.895295	+	0.445474i	$0.853035\pi$
$194$	5.16405	−	8.94440i	0.370757	−	0.642171i
$195$	6.56567			0.470177
$196$	23.2341	−	6.05620i	1.65958	−	0.432585i
$197$	0.0590259			0.00420542			0.00210271	−	0.999998i	$-0.499331\pi$
$197$	0.0590259			0.00420542			0.00210271	+	0.999998i	$0.499331\pi$
$198$	−1.16512	+	2.01805i	−0.0828018	+	0.143417i
$199$	−10.6909	−	18.5171i	−0.757856	−	1.31265i	−0.943942	−	0.330112i	$-0.892913\pi$
$199$	−10.6909	−	18.5171i	−0.757856	−	1.31265i	0.186085	−	0.982534i	$-0.440420\pi$
$200$	−1.66619	−	2.88593i	−0.117818	−	0.204066i
$201$	6.05184	−	10.4821i	0.426864	−	0.739350i
$202$	24.5663			1.72848
$203$	6.96792	+	9.14511i	0.489052	+	0.641861i
$204$	−8.76550			−0.613707
$205$	2.92562	−	5.06733i	0.204334	−	0.353918i
$206$	−6.91015	−	11.9687i	−0.481453	−	0.833901i
$207$	1.85935	+	3.22048i	0.129233	+	0.223839i
$208$	2.97152	−	5.14683i	0.206038	−	0.356869i
$209$	−2.38844			−0.165212
$210$	−6.11522	+	0.783901i	−0.421990	+	0.0540943i
$211$	16.1643			1.11280			0.556398	−	0.830916i	$-0.312183\pi$
$211$	16.1643			1.11280			0.556398	+	0.830916i	$0.312183\pi$
$212$	−2.94236	+	5.09633i	−0.202082	+	0.350017i
$213$	−0.563073	−	0.975271i	−0.0385811	−	0.0668245i
$214$	−19.5562	−	33.8723i	−1.33683	−	2.31546i
$215$	−0.288530	+	0.499748i	−0.0196776	+	0.0340825i
$216$	3.33238			0.226740
$217$	9.47223	−	22.6494i	0.643017	−	1.53754i
$218$	−38.6095			−2.61497
$219$	−3.83339	+	6.63963i	−0.259037	+	0.448664i
$220$	1.71503	+	2.97052i	0.115627	+	0.200272i
$221$	−8.38927	−	14.5306i	−0.564323	−	0.977437i
$222$	−8.14056	+	14.0999i	−0.546358	+	0.946321i
$223$	−9.06835			−0.607262			−0.303631	−	0.952790i	$-0.598199\pi$
$223$	−9.06835			−0.607262			−0.303631	+	0.952790i	$0.598199\pi$
$224$	4.65028	−	11.1195i	0.310710	−	0.742951i
$225$	1.00000			0.0666667
$226$	−20.1537	+	34.9073i	−1.34061	+	2.32200i
$227$	6.65868	+	11.5332i	0.441952	+	0.765483i	0.997834	−	0.0657776i	$-0.0209528\pi$
$227$	6.65868	+	11.5332i	0.441952	+	0.765483i	−0.555882	+	0.831261i	$0.687619\pi$
$228$	4.09625	+	7.09491i	0.271281	+	0.469872i
$229$	−8.97166	+	15.5394i	−0.592864	+	1.02687i	0.400981	+	0.916087i	$0.368669\pi$
$229$	−8.97166	+	15.5394i	−0.592864	+	1.02687i	−0.993845	+	0.110784i	$0.964664\pi$
$230$	8.66547			0.571384
$231$	2.62428	−	0.336402i	0.172665	−	0.0221336i
$232$	−14.4809			−0.950721
$233$	−4.33046	+	7.50057i	−0.283698	+	0.491379i	−0.972293	−	0.233768i	$-0.924895\pi$
$233$	−4.33046	+	7.50057i	−0.283698	+	0.491379i	0.688595	+	0.725146i	$0.258228\pi$
$234$	7.64982	+	13.2499i	0.500084	+	0.866171i
$235$	0.610040	+	1.05662i	0.0397946	+	0.0689263i
$236$	20.1851	−	34.9616i	1.31394	−	2.27581i
$237$	0.744325			0.0483491
$238$	9.54858	+	12.5321i	0.618942	+	0.812336i
$239$	−5.89784			−0.381499			−0.190750	−	0.981639i	$-0.561092\pi$
$239$	−5.89784			−0.381499			−0.190750	+	0.981639i	$0.561092\pi$
$240$	0.452585	−	0.783901i	0.0292143	−	0.0506006i
$241$	−12.8722	−	22.2953i	−0.829170	−	1.43616i	−0.898690	−	0.438584i	$-0.855480\pi$
$241$	−12.8722	−	22.2953i	−0.829170	−	1.43616i	0.0695205	−	0.997581i	$-0.477853\pi$
$242$	−1.16512	−	2.01805i	−0.0748970	−	0.129725i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	34.6704			2.21955
$245$	4.91591	+	4.98335i	0.314066	+	0.318375i
$246$	13.6349			0.869327
$247$	−7.84086	+	13.5808i	−0.498902	+	0.864124i
$248$	15.4609	+	26.7790i	0.981767	+	1.70047i
$249$	6.45304	+	11.1770i	0.408945	+	0.708313i
$250$	1.16512	−	2.01805i	0.0736889	−	0.127633i
$251$	−20.9817			−1.32435			−0.662176	−	0.749348i	$-0.730367\pi$
$251$	−20.9817			−1.32435			−0.662176	+	0.749348i	$0.730367\pi$
$252$	−5.50000	−	7.21852i	−0.346467	−	0.454724i
$253$	−3.71869			−0.233792
$254$	8.11471	−	14.0551i	0.509162	−	0.881895i
$255$	−1.27775	−	2.21312i	−0.0800157	−	0.138591i
$256$	10.6951	+	18.5245i	0.668445	+	1.15778i
$257$	6.87262	−	11.9037i	0.428702	−	0.742534i	−0.568056	−	0.822990i	$-0.692304\pi$
$257$	6.87262	−	11.9037i	0.428702	−	0.742534i	0.996758	+	0.0804559i	$0.0256376\pi$
$258$	−1.34469			−0.0837168
$259$	18.3355	−	2.35040i	1.13931	−	0.146046i
$260$	22.5206			1.39667
$261$	2.17276	−	3.76333i	0.134491	−	0.232944i
$262$	18.1872	+	31.5011i	1.12361	+	1.94614i
$263$	13.2124	+	22.8846i	0.814713	+	1.41112i	0.909534	+	0.415630i	$0.136439\pi$
$263$	13.2124	+	22.8846i	0.814713	+	1.41112i	−0.0948205	+	0.995494i	$0.530228\pi$
$264$	−1.66619	+	2.88593i	−0.102547	+	0.177617i
$265$	−1.71564			−0.105391
$266$	5.68147	−	13.5852i	0.348353	−	0.832962i
$267$	−16.0765			−0.983867
$268$	20.7582	−	35.9542i	1.26801	−	2.19625i
$269$	10.7518	+	18.6226i	0.655546	+	1.13544i	0.981757	+	0.190142i	$0.0608950\pi$
$269$	10.7518	+	18.6226i	0.655546	+	1.13544i	−0.326210	+	0.945297i	$0.605772\pi$
$270$	1.16512	+	2.01805i	0.0709072	+	0.122815i
$271$	−6.49818	+	11.2552i	−0.394736	+	0.683704i	−0.993068	−	0.117545i	$-0.962497\pi$
$271$	−6.49818	+	11.2552i	−0.394736	+	0.683704i	0.598331	+	0.801249i	$0.295831\pi$
$272$	−2.31316			−0.140256
$273$	6.70227	−	16.0261i	0.405640	−	0.969943i
$274$	5.21363			0.314967
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	6.37766	+	11.0464i	0.383890	+	0.664917i
$277$	7.59172	+	13.1492i	0.456142	+	0.790062i	0.998753	−	0.0499226i	$-0.0158975\pi$
$277$	7.59172	+	13.1492i	0.456142	+	0.790062i	−0.542611	+	0.839984i	$0.682564\pi$
$278$	14.4150	−	24.9675i	0.864554	−	1.49745i
$279$	−9.27917			−0.555529
$280$	−8.74510	+	1.12102i	−0.522620	+	0.0669939i
$281$	9.45336			0.563940			0.281970	−	0.959423i	$-0.409012\pi$
$281$	9.45336			0.563940			0.281970	+	0.959423i	$0.409012\pi$
$282$	−1.42154	+	2.46219i	−0.0846518	+	0.146621i
$283$	9.09011	+	15.7445i	0.540351	+	0.935915i	0.998884	+	0.0472377i	$0.0150418\pi$
$283$	9.09011	+	15.7445i	0.540351	+	0.935915i	−0.458533	+	0.888677i	$0.651625\pi$
$284$	−1.93137	−	3.34524i	−0.114606	−	0.198503i
$285$	−1.19422	+	2.06845i	−0.0707396	+	0.122525i
$286$	−15.2996			−0.904686
$287$	−9.38231	−	12.3139i	−0.553820	−	0.726866i
$288$	−4.55550			−0.268435
$289$	5.23472	−	9.06680i	0.307925	−	0.533341i
$290$	−5.06307	−	8.76950i	−0.297314	−	0.514963i
$291$	2.21610	+	3.83839i	0.129910	+	0.225010i
$292$	−13.1487	+	22.7743i	−0.769472	+	1.33276i
$293$	28.7950			1.68222			0.841112	−	0.540862i	$-0.181902\pi$
$293$	28.7950			1.68222			0.841112	+	0.540862i	$0.181902\pi$
$294$	−4.32903	+	15.7268i	−0.252474	+	0.917206i
$295$	11.7696			0.685250
$296$	−11.6414	+	20.1636i	−0.676646	+	1.17198i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	−3.95027	−	6.84208i	−0.228833	−	0.396351i
$299$	−12.2078	+	21.1446i	−0.705998	+	1.22282i
$300$	3.43006			0.198034
$301$	0.925298	+	1.21442i	0.0533333	+	0.0699977i
$302$	−2.14529			−0.123448
$303$	−5.27118	+	9.12995i	−0.302821	+	0.524502i
$304$	1.08097	+	1.87230i	0.0619982	+	0.107384i
$305$	5.05392	+	8.75364i	0.289387	+	0.501232i
$306$	2.97747	−	5.15713i	0.170211	−	0.294813i
$307$	−25.7537			−1.46984			−0.734920	−	0.678154i	$-0.762780\pi$
$307$	−25.7537			−1.46984			−0.734920	+	0.678154i	$0.762780\pi$
$308$	9.00142	−	1.15388i	0.512903	−	0.0657483i
$309$	5.93083			0.337393
$310$	−10.8114	+	18.7259i	−0.614045	+	1.06356i
$311$	3.47750	+	6.02320i	0.197191	+	0.341544i	0.947616	−	0.319410i	$-0.103485\pi$
$311$	3.47750	+	6.02320i	0.197191	+	0.341544i	−0.750426	+	0.660955i	$0.770152\pi$
$312$	10.9397	+	18.9481i	0.619336	+	1.07272i
$313$	7.97224	−	13.8083i	0.450618	−	0.780493i	−0.547807	−	0.836605i	$-0.684537\pi$
$313$	7.97224	−	13.8083i	0.450618	−	0.780493i	0.998424	+	0.0561122i	$0.0178705\pi$
$314$	45.7305			2.58072
$315$	1.02081	−	2.44089i	0.0575159	−	0.137529i
$316$	2.55308			0.143622
$317$	−3.05779	+	5.29625i	−0.171743	+	0.297467i	−0.939029	−	0.343837i	$-0.888273\pi$
$317$	−3.05779	+	5.29625i	−0.171743	+	0.297467i	0.767287	+	0.641304i	$0.221606\pi$
$318$	−1.99893	−	3.46225i	−0.112094	−	0.194153i
$319$	2.17276	+	3.76333i	0.121651	+	0.210706i
$320$	−6.21289	+	10.7610i	−0.347311	+	0.601560i
$321$	16.7846			0.936828
$322$	8.84577	−	21.1515i	0.492955	−	1.17873i
$323$	6.10366			0.339617
$324$	−1.71503	+	2.97052i	−0.0952793	+	0.165029i
$325$	3.28283	+	5.68603i	0.182099	+	0.315404i
$326$	−11.8797	−	20.5762i	−0.657955	−	1.13961i
$327$	8.28442	−	14.3490i	0.458130	−	0.793504i
$328$	19.4986			1.07663
$329$	3.20183	−	0.410438i	0.176523	−	0.0226282i
$330$	−2.33025			−0.128276
$331$	−1.10750	+	1.91825i	−0.0608737	+	0.105436i	−0.894856	−	0.446355i	$-0.852722\pi$
$331$	−1.10750	+	1.91825i	−0.0608737	+	0.105436i	0.833982	+	0.551791i	$0.186055\pi$
$332$	22.1343	+	38.3377i	1.21478	+	2.10406i
$333$	−3.49343	−	6.05080i	−0.191439	−	0.331582i
$334$	−0.825059	+	1.42904i	−0.0451452	+	0.0781938i
$335$	12.1037			0.661295
$336$	−1.45142	−	1.90492i	−0.0791812	−	0.103922i
$337$	−12.9876			−0.707480			−0.353740	−	0.935344i	$-0.615090\pi$
$337$	−12.9876			−0.707480			−0.353740	+	0.935344i	$0.615090\pi$
$338$	−35.0795	+	60.7595i	−1.90807	+	3.30488i
$339$	−8.64875	−	14.9801i	−0.469735	−	0.813606i
$340$	−4.38275	−	7.59114i	−0.237688	−	0.411687i
$341$	4.63958	−	8.03599i	0.251248	−	0.435173i
$342$	−5.56567			−0.300957
$343$	17.1820	−	6.91217i	0.927742	−	0.373222i
$344$	−1.92298			−0.103680
$345$	−1.85935	+	3.22048i	−0.100104	+	0.173385i
$346$	−15.7681	−	27.3112i	−0.847699	−	1.46826i
$347$	2.93144	+	5.07741i	0.157368	+	0.272570i	0.933919	−	0.357485i	$-0.116366\pi$
$347$	2.93144	+	5.07741i	0.157368	+	0.272570i	−0.776551	+	0.630055i	$0.783032\pi$
$348$	7.45269	−	12.9084i	0.399506	−	0.691965i
$349$	9.96125			0.533213			0.266607	−	0.963805i	$-0.414098\pi$
$349$	9.96125			0.533213			0.266607	+	0.963805i	$0.414098\pi$
$350$	−3.73649	−	4.90398i	−0.199724	−	0.262129i
$351$	−6.56567			−0.350449
$352$	2.27775	−	3.94518i	0.121404	−	0.210279i
$353$	−3.45653	−	5.98689i	−0.183973	−	0.318650i	0.759257	−	0.650791i	$-0.225562\pi$
$353$	−3.45653	−	5.98689i	−0.183973	−	0.318650i	−0.943230	+	0.332141i	$0.892229\pi$
$354$	13.7130	+	23.7516i	0.728837	+	1.26238i
$355$	0.563073	−	0.975271i	0.0298848	−	0.0517620i
$356$	−55.1434			−2.92259
$357$	−6.70633	+	0.859675i	−0.354937	+	0.0454988i
$358$	−32.5659			−1.72116
$359$	−2.54804	+	4.41333i	−0.134480	+	0.232926i	−0.925399	−	0.378995i	$-0.876270\pi$
$359$	−2.54804	+	4.41333i	−0.134480	+	0.232926i	0.790919	+	0.611921i	$0.209603\pi$
$360$	1.66619	+	2.88593i	0.0878160	+	0.152102i
$361$	6.64767	+	11.5141i	0.349877	+	0.606005i
$362$	11.5888	−	20.0724i	0.609093	−	1.05498i
$363$	1.00000			0.0524864
$364$	22.9892	−	54.9704i	1.20496	−	2.88123i
$365$	−7.66678			−0.401298
$366$	−11.7769	+	20.3982i	−0.615588	+	1.06623i
$367$	7.83395	+	13.5688i	0.408929	+	0.708286i	0.994770	−	0.102140i	$-0.0325691\pi$
$367$	7.83395	+	13.5688i	0.408929	+	0.708286i	−0.585841	+	0.810426i	$0.699236\pi$
$368$	1.68303	+	2.91509i	0.0877338	+	0.151959i
$369$	−2.92562	+	5.06733i	−0.152302	+	0.263795i
$370$	−16.2811			−0.846415
$371$	−1.75133	+	4.18768i	−0.0909246	+	0.217414i
$372$	−31.8281			−1.65021
$373$	11.0271	−	19.0995i	0.570962	−	0.988936i	−0.425505	−	0.904956i	$-0.639904\pi$
$373$	11.0271	−	19.0995i	0.570962	−	0.988936i	0.996467	−	0.0839797i	$-0.0267631\pi$
$374$	2.97747	+	5.15713i	0.153961	+	0.266669i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−2.03289	+	3.52107i	−0.104838	+	0.181585i
$377$	28.5312			1.46943
$378$	6.11522	−	0.783901i	0.314533	−	0.0403195i
$379$	7.40055			0.380141			0.190070	−	0.981770i	$-0.439128\pi$
$379$	7.40055			0.380141			0.190070	+	0.981770i	$0.439128\pi$
$380$	−4.09625	+	7.09491i	−0.210133	+	0.363961i
$381$	3.48234	+	6.03158i	0.178406	+	0.309007i
$382$	−14.5441	−	25.1911i	−0.744141	−	1.28889i
$383$	8.40005	−	14.5493i	0.429223	−	0.743435i	−0.567582	−	0.823317i	$-0.692121\pi$
$383$	8.40005	−	14.5493i	0.429223	−	0.743435i	0.996804	+	0.0798816i	$0.0254542\pi$
$384$	−19.8442			−1.01267
$385$	1.60347	+	2.10449i	0.0817205	+	0.107255i
$386$	4.00491			0.203845
$387$	0.288530	−	0.499748i	0.0146668	−	0.0254036i
$388$	7.60133	+	13.1659i	0.385899	+	0.668397i
$389$	8.98127	+	15.5560i	0.455369	+	0.788722i	0.998709	−	0.0507906i	$-0.0161741\pi$
$389$	8.98127	+	15.5560i	0.455369	+	0.788722i	−0.543341	+	0.839512i	$0.682841\pi$
$390$	−7.64982	+	13.2499i	−0.387363	+	0.670933i
$391$	9.50310			0.480593
$392$	−6.19076	+	22.4902i	−0.312680	+	1.13593i
$393$	−15.6096			−0.787402
$394$	−0.0687725	+	0.119117i	−0.00346471	+	0.00600105i
$395$	0.372163	+	0.644604i	0.0187255	+	0.0324336i
$396$	−1.71503	−	2.97052i	−0.0861834	−	0.149274i
$397$	0.221618	−	0.383854i	0.0111227	−	0.0192651i	−0.860410	−	0.509602i	$-0.829793\pi$
$397$	0.221618	−	0.383854i	0.0111227	−	0.0192651i	0.871533	+	0.490337i	$0.163126\pi$
$398$	49.8248			2.49749
$399$	3.82980	+	5.02646i	0.191730	+	0.251638i
$400$	0.905171			0.0452585
$401$	−14.8143	+	25.6592i	−0.739793	+	1.28136i	0.212795	+	0.977097i	$0.431743\pi$
$401$	−14.8143	+	25.6592i	−0.739793	+	1.28136i	−0.952588	+	0.304262i	$0.901590\pi$
$402$	14.1023	+	24.4259i	0.703359	+	1.21825i
$403$	−30.4620	−	52.7617i	−1.51742	−	2.62825i
$404$	−18.0804	+	31.3162i	−0.899535	+	1.55804i
$405$	−1.00000			−0.0496904
$406$	−26.5738	+	3.40646i	−1.31884	+	0.169060i
$407$	6.98686			0.346326
$408$	4.25795	−	7.37498i	0.210800	−	0.365116i
$409$	−4.49593	−	7.78718i	−0.222310	−	0.385051i	0.733199	−	0.680014i	$-0.238026\pi$
$409$	−4.49593	−	7.78718i	−0.222310	−	0.385051i	−0.955509	+	0.294962i	$0.904693\pi$
$410$	6.81743	+	11.8081i	0.336689	+	0.583162i
$411$	−1.11869	+	1.93762i	−0.0551807	+	0.0955757i
$412$	20.3431			1.00223
$413$	12.0144	−	28.7282i	0.591192	−	1.41362i
$414$	−8.66547			−0.425885
$415$	−6.45304	+	11.1770i	−0.316767	+	0.548657i
$416$	−14.9549	−	25.9027i	−0.733226	−	1.26998i
$417$	6.18604	+	10.7145i	0.302932	+	0.524693i
$418$	2.78283	−	4.82001i	0.136113	−	0.235754i
$419$	16.4514			0.803704			0.401852	−	0.915705i	$-0.368367\pi$
$419$	16.4514			0.803704			0.401852	+	0.915705i	$0.368367\pi$
$420$	3.50142	−	8.37240i	0.170852	−	0.408531i
$421$	−28.4904			−1.38854			−0.694268	−	0.719717i	$-0.744272\pi$
$421$	−28.4904			−1.38854			−0.694268	+	0.719717i	$0.744272\pi$
$422$	−18.8334	+	32.6204i	−0.916797	+	1.58794i
$423$	−0.610040	−	1.05662i	−0.0296612	−	0.0513746i
$424$	−2.85858	−	4.95121i	−0.138825	−	0.240452i
$425$	1.27775	−	2.21312i	0.0619799	−	0.107352i
$426$	2.62420			0.127143
$427$	26.5258	−	3.40030i	1.28367	−	0.164552i
$428$	57.5723			2.78286
$429$	3.28283	−	5.68603i	0.158497	−	0.274524i
$430$	−0.672346	−	1.16454i	−0.0324234	−	0.0561589i
$431$	−13.8344	−	23.9619i	−0.666379	−	1.15420i	−0.978910	−	0.204294i	$-0.934510\pi$
$431$	−13.8344	−	23.9619i	−0.666379	−	1.15420i	0.312531	−	0.949908i	$-0.398823\pi$
$432$	−0.452585	+	0.783901i	−0.0217750	+	0.0377154i
$433$	−31.9507			−1.53545			−0.767727	−	0.640777i	$-0.778612\pi$
$433$	−31.9507			−1.53545			−0.767727	+	0.640777i	$0.778612\pi$
$434$	34.6715	+	45.5049i	1.66428	+	2.18430i
$435$	4.34552			0.208352
$436$	28.4160	−	49.2180i	1.36088	−	2.35711i
$437$	−4.44094	−	7.69194i	−0.212439	−	0.367955i
$438$	−8.93275	−	15.4720i	−0.426823	−	0.739280i
$439$	−17.0448	+	29.5224i	−0.813503	+	1.40903i	0.0968954	+	0.995295i	$0.469109\pi$
$439$	−17.0448	+	29.5224i	−0.813503	+	1.40903i	−0.910398	+	0.413733i	$0.864225\pi$
$440$	−3.33238			−0.158865
$441$	−4.91591	−	4.98335i	−0.234091	−	0.237303i
$442$	39.0982			1.85971
$443$	20.5709	−	35.6298i	0.977353	−	1.69283i	0.305412	−	0.952220i	$-0.401206\pi$
$443$	20.5709	−	35.6298i	0.977353	−	1.69283i	0.671941	−	0.740605i	$-0.265461\pi$
$444$	−11.9827	−	20.7546i	−0.568672	−	0.984968i
$445$	−8.03826	−	13.9227i	−0.381050	−	0.659998i
$446$	10.5658	−	18.3004i	0.500303	−	0.866550i
$447$	3.39043			0.160362
$448$	19.9244	+	26.1499i	0.941339	+	1.23547i
$449$	−32.0369			−1.51191			−0.755957	−	0.654621i	$-0.772828\pi$
$449$	−32.0369			−1.51191			−0.755957	+	0.654621i	$0.772828\pi$
$450$	−1.16512	+	2.01805i	−0.0549245	+	0.0951320i
$451$	−2.92562	−	5.06733i	−0.137762	−	0.238611i
$452$	−29.6657	−	51.3825i	−1.39536	−	2.41683i
$453$	0.460315	−	0.797288i	0.0216275	−	0.0374599i
$454$	−31.0327			−1.45644
$455$	17.2301	−	2.20871i	0.807761	−	0.103546i
$456$	−7.95921			−0.372724
$457$	10.7819	−	18.6748i	0.504357	−	0.873571i	−0.495631	−	0.868533i	$-0.665063\pi$
$457$	10.7819	−	18.6748i	0.504357	−	0.873571i	0.999987	−	0.00503788i	$-0.00160361\pi$
$458$	−20.9062	−	36.2106i	−0.976882	−	1.69201i
$459$	1.27775	+	2.21312i	0.0596402	+	0.103300i
$460$	−6.37766	+	11.0464i	−0.297360	+	0.515043i
$461$	−23.9259			−1.11434			−0.557171	−	0.830398i	$-0.688113\pi$
$461$	−23.9259			−1.11434			−0.557171	+	0.830398i	$0.688113\pi$
$462$	−2.37873	+	5.68788i	−0.110669	+	0.264624i
$463$	−15.7595			−0.732407			−0.366203	−	0.930535i	$-0.619343\pi$
$463$	−15.7595			−0.732407			−0.366203	+	0.930535i	$0.619343\pi$
$464$	1.96672	−	3.40646i	0.0913027	−	0.158141i
$465$	−4.63958	−	8.03599i	−0.215156	−	0.372660i
$466$	−10.0910	−	17.4782i	−0.467458	−	0.809661i
$467$	−0.209846	+	0.363463i	−0.00971050	+	0.0168191i	−0.870840	−	0.491567i	$-0.836424\pi$
$467$	−0.209846	+	0.363463i	−0.00971050	+	0.0168191i	0.861129	+	0.508386i	$0.169758\pi$
$468$	−22.5206			−1.04102
$469$	12.3555	−	29.5438i	0.570525	−	1.36421i
$470$	−2.84309			−0.131142
$471$	−9.81237	+	16.9955i	−0.452130	+	0.783113i
$472$	19.6103	+	33.9661i	0.902639	+	1.56342i
$473$	0.288530	+	0.499748i	0.0132666	+	0.0229784i
$474$	−0.867231	+	1.50209i	−0.0398332	+	0.0689932i
$475$	−2.38844			−0.109589
$476$	−23.0031	+	2.94873i	−1.05435	+	0.135155i
$477$	1.71564			0.0785536
$478$	6.87171	−	11.9022i	0.314305	−	0.544392i
$479$	−15.9645	−	27.6514i	−0.729439	−	1.26342i	−0.957121	−	0.289689i	$-0.906448\pi$
$479$	−15.9645	−	27.6514i	−0.729439	−	1.26342i	0.227682	−	0.973736i	$-0.426885\pi$
$480$	−2.27775	−	3.94518i	−0.103965	−	0.180072i
$481$	22.9367	−	39.7275i	1.04582	−	1.81142i
$482$	59.9907			2.73250
$483$	5.96282	+	7.82595i	0.271318	+	0.356093i
$484$	3.43006			0.155912
$485$	−2.21610	+	3.83839i	−0.100628	+	0.174292i
$486$	−1.16512	−	2.01805i	−0.0528511	−	0.0915408i
$487$	−4.50884	−	7.80954i	−0.204315	−	0.353884i	0.745599	−	0.666395i	$-0.232163\pi$
$487$	−4.50884	−	7.80954i	−0.204315	−	0.353884i	−0.949914	+	0.312511i	$0.898830\pi$
$488$	−16.8416	+	29.1705i	−0.762383	+	1.32049i
$489$	10.1961			0.461082
$490$	−15.7843	+	4.11435i	−0.713063	+	0.185867i
$491$	26.8024			1.20957			0.604787	−	0.796388i	$-0.293258\pi$
$491$	26.8024			1.20957			0.604787	+	0.796388i	$0.293258\pi$
$492$	−10.0351	+	17.3812i	−0.452415	+	0.783606i
$493$	−5.55248	−	9.61718i	−0.250071	−	0.433136i
$494$	−18.2712	−	31.6466i	−0.822058	−	1.42385i
$495$	0.500000	−	0.866025i	0.0224733	−	0.0389249i
$496$	−8.39923			−0.377137
$497$	−1.80574	−	2.36996i	−0.0809987	−	0.106307i
$498$	−30.0744			−1.34767
$499$	6.74371	−	11.6805i	0.301890	−	0.522889i	−0.674674	−	0.738116i	$-0.735716\pi$
$499$	6.74371	−	11.6805i	0.301890	−	0.522889i	0.976564	+	0.215227i	$0.0690491\pi$
$500$	1.71503	+	2.97052i	0.0766984	+	0.132845i
$501$	−0.354065	−	0.613258i	−0.0158184	−	0.0273983i
$502$	24.4463	−	42.3422i	1.09109	−	1.88982i
$503$	0.989318			0.0441115			0.0220557	−	0.999757i	$-0.492979\pi$
$503$	0.989318			0.0441115			0.0220557	+	0.999757i	$0.492979\pi$
$504$	8.74510	−	1.12102i	0.389538	−	0.0499343i
$505$	−10.5424			−0.469129
$506$	4.33274	−	7.50452i	0.192614	−	0.333617i
$507$	−15.0540	−	26.0743i	−0.668571	−	1.15800i
$508$	11.9446	+	20.6887i	0.529956	+	0.917911i
$509$	6.82082	−	11.8140i	0.302328	−	0.523647i	−0.674335	−	0.738425i	$-0.735570\pi$
$509$	6.82082	−	11.8140i	0.302328	−	0.523647i	0.976663	+	0.214779i	$0.0689030\pi$
$510$	5.95494			0.263689
$511$	−7.82630	+	18.7138i	−0.346215	+	0.827849i
$512$	−10.1563			−0.448847
$513$	1.19422	−	2.06845i	0.0527262	−	0.0913244i
$514$	16.0149	+	27.7386i	0.706387	+	1.22350i
$515$	2.96541	+	5.13625i	0.130672	+	0.226330i
$516$	0.989673	−	1.71416i	0.0435679	−	0.0754618i
$517$	1.22008			0.0536591
$518$	−16.6199	+	39.7404i	−0.730235	+	1.74609i
$519$	13.5334			0.594051
$520$	−10.9397	+	18.9481i	−0.479736	+	0.830927i
$521$	−15.1607	−	26.2592i	−0.664204	−	1.15043i	−0.979501	−	0.201441i	$-0.935437\pi$
$521$	−15.1607	−	26.2592i	−0.664204	−	1.15043i	0.315297	−	0.948993i	$-0.397896\pi$
$522$	5.06307	+	8.76950i	0.221605	+	0.383830i
$523$	4.78322	−	8.28479i	0.209156	−	0.362268i	−0.742293	−	0.670075i	$-0.766262\pi$
$523$	4.78322	−	8.28479i	0.209156	−	0.362268i	0.951449	+	0.307807i	$0.0995951\pi$
$524$	−53.5419			−2.33899
$525$	2.62428	−	0.336402i	0.114533	−	0.0146818i
$526$	−61.5765			−2.68486
$527$	−11.8564	+	20.5360i	−0.516475	+	0.894560i
$528$	−0.452585	−	0.783901i	−0.0196963	−	0.0341149i
$529$	4.58567	+	7.94260i	0.199377	+	0.345331i
$530$	1.99893	−	3.46225i	0.0868279	−	0.150390i
$531$	−11.7696			−0.510755
$532$	13.1364	+	17.2410i	0.569537	+	0.747493i
$533$	−38.4173			−1.66404
$534$	18.7311	−	32.4433i	0.810576	−	1.40396i
$535$	8.39232	+	14.5359i	0.362832	+	0.628443i
$536$	20.1671	+	34.9304i	0.871085	+	1.50876i
$537$	6.98764	−	12.1029i	0.301539	−	0.522281i
$538$	−50.1085			−2.16033
$539$	6.77367	−	1.76563i	0.291762	−	0.0760509i
$540$	−3.43006			−0.147606
$541$	−11.3900	+	19.7281i	−0.489695	+	0.848176i	−0.999930	−	0.0118589i	$-0.996225\pi$
$541$	−11.3900	+	19.7281i	−0.489695	+	0.848176i	0.510235	+	0.860035i	$0.329558\pi$
$542$	−15.1424	−	26.2274i	−0.650421	−	1.12656i
$543$	4.97320	+	8.61383i	0.213420	+	0.369655i
$544$	−5.82078	+	10.0819i	−0.249564	+	0.432257i
$545$	16.5688			0.709731
$546$	24.5325	+	32.1979i	1.04990	+	1.37794i
$547$	−41.7796			−1.78637			−0.893184	−	0.449691i	$-0.851534\pi$
$547$	−41.7796			−1.78637			−0.893184	+	0.449691i	$0.851534\pi$
$548$	−3.83715	+	6.64614i	−0.163915	+	0.283909i
$549$	−5.05392	−	8.75364i	−0.215696	−	0.373596i
$550$	−1.16512	−	2.01805i	−0.0496811	−	0.0860501i
$551$	−5.18952	+	8.98851i	−0.221081	+	0.382923i
$552$	−12.3921			−0.527443
$553$	1.95332	−	0.250393i	0.0830634	−	0.0106478i
$554$	−35.3812			−1.50320
$555$	3.49343	−	6.05080i	0.148288	−	0.256842i
$556$	21.2184	+	36.7514i	0.899863	+	1.55861i
$557$	7.32912	+	12.6944i	0.310545	+	0.537879i	0.978480	−	0.206340i	$-0.0661552\pi$
$557$	7.32912	+	12.6944i	0.310545	+	0.537879i	−0.667936	+	0.744219i	$0.732822\pi$
$558$	10.8114	−	18.7259i	0.457682	−	0.792729i
$559$	3.78878			0.160248
$560$	0.924004	−	2.20942i	0.0390463	−	0.0933652i
$561$	−2.55550			−0.107893
$562$	−11.0143	+	19.0774i	−0.464612	+	0.804731i
$563$	−5.25892	−	9.10871i	−0.221637	−	0.383886i	0.733668	−	0.679508i	$-0.237807\pi$
$563$	−5.25892	−	9.10871i	−0.221637	−	0.383886i	−0.955305	+	0.295621i	$0.904473\pi$
$564$	−2.09247	−	3.62427i	−0.0881090	−	0.152609i
$565$	8.64875	−	14.9801i	0.363855	−	0.630216i
$566$	−42.3644			−1.78071
$567$	−1.02081	+	2.44089i	−0.0428698	+	0.102508i
$568$	3.75275			0.157462
$569$	2.50344	−	4.33609i	0.104950	−	0.181779i	−0.808768	−	0.588128i	$-0.799865\pi$
$569$	2.50344	−	4.33609i	0.104950	−	0.181779i	0.913718	+	0.406350i	$0.133198\pi$
$570$	−2.78283	−	4.82001i	−0.116560	−	0.201888i
$571$	4.26835	+	7.39299i	0.178625	+	0.309387i	0.941410	−	0.337265i	$-0.109502\pi$
$571$	4.26835	+	7.39299i	0.178625	+	0.309387i	−0.762785	+	0.646652i	$0.776169\pi$
$572$	11.2603	−	19.5034i	0.470817	−	0.815479i
$573$	12.4829			0.521480
$574$	35.7817	−	4.58680i	1.49350	−	0.191449i
$575$	−3.71869			−0.155080
$576$	6.21289	−	10.7610i	0.258870	−	0.448377i
$577$	−3.57975	−	6.20030i	−0.149027	−	0.258122i	0.781841	−	0.623478i	$-0.214281\pi$
$577$	−3.57975	−	6.20030i	−0.149027	−	0.258122i	−0.930868	+	0.365356i	$0.880947\pi$
$578$	12.1982	+	21.1279i	0.507378	+	0.878804i
$579$	−0.859332	+	1.48841i	−0.0357126	+	0.0618561i
$580$	14.9054			0.618912
$581$	20.6945	+	27.1607i	0.858554	+	1.12682i
$582$	−10.3281			−0.428114
$583$	−0.857818	+	1.48578i	−0.0355272	+	0.0615349i
$584$	−12.7743	−	22.1258i	−0.528606	−	0.915572i
$585$	−3.28283	−	5.68603i	−0.135728	−	0.235089i
$586$	−33.5498	+	58.1099i	−1.38593	+	2.40050i
$587$	29.4112			1.21393			0.606964	−	0.794729i	$-0.292387\pi$
$587$	29.4112			1.21393			0.606964	+	0.794729i	$0.292387\pi$
$588$	−16.8618	−	17.0932i	−0.695371	−	0.704911i
$589$	22.1628			0.913201
$590$	−13.7130	+	23.7516i	−0.564555	+	0.977838i
$591$	−0.0295129	−	0.0511179i	−0.00121400	−	0.00210271i
$592$	−3.16215	−	5.47700i	−0.129964	−	0.225104i
$593$	−0.772727	+	1.33840i	−0.0317321	+	0.0549616i	−0.881455	−	0.472267i	$-0.843436\pi$
$593$	−0.772727	+	1.33840i	−0.0317321	+	0.0549616i	0.849723	+	0.527229i	$0.176769\pi$
$594$	2.33025			0.0956112
$595$	−4.09767	−	5.37802i	−0.167988	−	0.220477i
$596$	11.6294			0.476358
$597$	−10.6909	+	18.5171i	−0.437549	+	0.757856i
$598$	−28.4473	−	49.2722i	−1.16330	−	2.01489i
$599$	−5.26067	−	9.11175i	−0.214945	−	0.372296i	0.738310	−	0.674461i	$-0.235624\pi$
$599$	−5.26067	−	9.11175i	−0.214945	−	0.372296i	−0.953256	+	0.302165i	$0.902291\pi$
$600$	−1.66619	+	2.88593i	−0.0680220	+	0.117818i
$601$	−35.8037			−1.46046			−0.730232	−	0.683199i	$-0.760588\pi$
$601$	−35.8037			−1.46046			−0.730232	+	0.683199i	$0.760588\pi$
$602$	−3.52884	+	0.452357i	−0.143825	+	0.0184367i
$603$	−12.1037			−0.492900
$604$	1.57890	−	2.73474i	0.0642447	−	0.111275i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	−12.2832	−	21.2750i	−0.498969	−	0.864240i
$607$	−0.282003	+	0.488444i	−0.0114462	+	0.0198253i	−0.871692	−	0.490055i	$-0.836977\pi$
$607$	−0.282003	+	0.488444i	−0.0114462	+	0.0198253i	0.860246	+	0.509880i	$0.170310\pi$
$608$	10.8805			0.441264
$609$	4.43593	−	10.6069i	0.179753	−	0.429815i
$610$	−23.5538			−0.953664
$611$	4.00532	−	6.93742i	0.162038	−	0.280658i
$612$	4.38275	+	7.59114i	0.177162	+	0.306854i
$613$	6.82819	+	11.8268i	0.275788	+	0.477679i	0.970334	−	0.241770i	$-0.0777279\pi$
$613$	6.82819	+	11.8268i	0.275788	+	0.477679i	−0.694546	+	0.719449i	$0.744395\pi$
$614$	30.0062	−	51.9723i	1.21095	−	2.09743i
$615$	−5.85125			−0.235945
$616$	−3.40172	+	8.13399i	−0.137059	+	0.327728i
$617$	−26.4948			−1.06664			−0.533320	−	0.845913i	$-0.679056\pi$
$617$	−26.4948			−1.06664			−0.533320	+	0.845913i	$0.679056\pi$
$618$	−6.91015	+	11.9687i	−0.277967	+	0.481453i
$619$	−6.10828	−	10.5799i	−0.245513	−	0.425240i	0.716763	−	0.697317i	$-0.245623\pi$
$619$	−6.10828	−	10.5799i	−0.245513	−	0.425240i	−0.962276	+	0.272076i	$0.912290\pi$
$620$	−15.9140	−	27.5639i	−0.639123	−	1.10699i
$621$	1.85935	−	3.22048i	0.0746130	−	0.129233i
$622$	−16.2069			−0.649836
$623$	−42.1893	+	5.40818i	−1.69028	+	0.216674i
$624$	−5.94305			−0.237912
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	18.5773	+	32.1768i	0.742498	+	1.28604i
$627$	1.19422	+	2.06845i	0.0476926	+	0.0826061i
$628$	−33.6570	+	58.2956i	−1.34306	+	2.32625i
$629$	−17.8549			−0.711921
$630$	3.73649	+	4.90398i	0.148865	+	0.195379i
$631$	−15.4089			−0.613417			−0.306709	−	0.951803i	$-0.599228\pi$
$631$	−15.4089			−0.613417			−0.306709	+	0.951803i	$0.599228\pi$
$632$	−1.24019	+	2.14807i	−0.0493321	+	0.0854456i
$633$	−8.08215	−	13.9987i	−0.321237	−	0.556398i
$634$	−7.12541	−	12.3416i	−0.282986	−	0.490147i
$635$	−3.48234	+	6.03158i	−0.138192	+	0.239356i
$636$	5.88473			0.233345
$637$	12.1974	−	44.3116i	0.483279	−	1.75569i
$638$	−10.1261			−0.400898
$639$	−0.563073	+	0.975271i	−0.0222748	+	0.0385811i
$640$	−9.92208	−	17.1855i	−0.392204	−	0.679318i
$641$	6.95746	+	12.0507i	0.274803	+	0.475973i	0.970085	−	0.242764i	$-0.0780539\pi$
$641$	6.95746	+	12.0507i	0.274803	+	0.475973i	−0.695282	+	0.718737i	$0.744721\pi$
$642$	−19.5562	+	33.8723i	−0.771822	+	1.33683i
$643$	−16.1658			−0.637519			−0.318759	−	0.947836i	$-0.603266\pi$
$643$	−16.1658			−0.637519			−0.318759	+	0.947836i	$0.603266\pi$
$644$	20.4528	+	26.8434i	0.805953	+	1.05778i
$645$	0.577059			0.0227217
$646$	−7.11152	+	12.3175i	−0.279799	+	0.484626i
$647$	14.8425	+	25.7080i	0.583519	+	1.01068i	0.995058	+	0.0992922i	$0.0316579\pi$
$647$	14.8425	+	25.7080i	0.583519	+	1.01068i	−0.411540	+	0.911392i	$0.635009\pi$
$648$	−1.66619	−	2.88593i	−0.0654542	−	0.113370i
$649$	5.88478	−	10.1927i	0.230998	−	0.400100i
$650$	−15.2996			−0.600101
$651$	−24.3511	+	3.12153i	−0.954395	+	0.122343i
$652$	34.9731			1.36965
$653$	0.155150	−	0.268728i	0.00607149	−	0.0105161i	−0.862974	−	0.505249i	$-0.831401\pi$
$653$	0.155150	−	0.268728i	0.00607149	−	0.0105161i	0.869045	+	0.494733i	$0.164734\pi$
$654$	19.3048	+	33.4368i	0.754876	+	1.30748i
$655$	−7.80481	−	13.5183i	−0.304959	−	0.528205i
$656$	−2.64819	+	4.58680i	−0.103394	+	0.179084i
$657$	7.66678			0.299110
$658$	−2.90224	+	6.93968i	−0.113141	+	0.270537i
$659$	22.0773			0.860008			0.430004	−	0.902827i	$-0.358512\pi$
$659$	22.0773			0.860008			0.430004	+	0.902827i	$0.358512\pi$
$660$	1.71503	−	2.97052i	0.0667574	−	0.115627i
$661$	−22.2299	−	38.5032i	−0.864641	−	1.49760i	−0.867403	−	0.497606i	$-0.834212\pi$
$661$	−22.2299	−	38.5032i	−0.864641	−	1.49760i	0.00276183	−	0.999996i	$-0.499121\pi$
$662$	−2.58075	−	4.46999i	−0.100304	−	0.173731i
$663$	−8.38927	+	14.5306i	−0.325812	+	0.564323i
$664$	−43.0080			−1.66904
$665$	−2.43814	+	5.82993i	−0.0945469	+	0.226075i
$666$	16.2811			0.630880
$667$	−8.07983	+	13.9947i	−0.312852	+	0.541876i
$668$	−1.21446	−	2.10351i	−0.0469889	−	0.0813872i
$669$	4.53417	+	7.85342i	0.175301	+	0.303631i
$670$	−14.1023	+	24.4259i	−0.544819	+	0.943655i
$671$	10.1078			0.390209
$672$	−11.9549	+	1.53248i	−0.461170	+	0.0591167i
$673$	−5.27727			−0.203424			−0.101712	−	0.994814i	$-0.532432\pi$
$673$	−5.27727			−0.203424			−0.101712	+	0.994814i	$0.532432\pi$
$674$	15.1322	−	26.2097i	0.582869	−	1.00956i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−51.6360	−	89.4362i	−1.98600	−	3.43985i
$677$	−23.5956	+	40.8688i	−0.906853	+	1.57072i	−0.0884428	+	0.996081i	$0.528189\pi$
$677$	−23.5956	+	40.8688i	−0.906853	+	1.57072i	−0.818410	+	0.574634i	$0.805144\pi$
$678$	40.3074			1.54800
$679$	7.10690	+	9.32750i	0.272738	+	0.357957i
$680$	8.51590			0.326570
$681$	6.65868	−	11.5332i	0.255161	−	0.441952i
$682$	10.8114	+	18.7259i	0.413989	+	0.717050i
$683$	8.49512	+	14.7140i	0.325057	+	0.563015i	0.981524	−	0.191340i	$-0.0612833\pi$
$683$	8.49512	+	14.7140i	0.325057	+	0.563015i	−0.656467	+	0.754355i	$0.727950\pi$
$684$	4.09625	−	7.09491i	0.156624	−	0.271281i
$685$	−2.23737			−0.0854855
$686$	−6.07005	+	42.7278i	−0.231756	+	1.63135i
$687$	17.9433			0.684580
$688$	0.261169	−	0.452357i	0.00995696	−	0.0172460i
$689$	5.63215	+	9.75517i	0.214568	+	0.371642i
$690$	−4.33274	−	7.50452i	−0.164944	−	0.285692i
$691$	−5.81784	+	10.0768i	−0.221321	+	0.383340i	−0.955209	−	0.295931i	$-0.904370\pi$
$691$	−5.81784	+	10.0768i	−0.221321	+	0.383340i	0.733888	+	0.679270i	$0.237704\pi$
$692$	46.4204			1.76464
$693$	−1.60347	−	2.10449i	−0.0609109	−	0.0799430i
$694$	−13.6620			−0.518602
$695$	−6.18604	+	10.7145i	−0.234650	+	0.406425i
$696$	7.24047	+	12.5409i	0.274449	+	0.475360i
$697$	7.47642	+	12.9495i	0.283190	+	0.490499i
$698$	−11.6061	+	20.1023i	−0.439297	+	0.760885i
$699$	8.66091			0.327586
$700$	9.00142	−	1.15388i	0.340222	−	0.0436125i
$701$	6.31631			0.238564			0.119282	−	0.992860i	$-0.461941\pi$
$701$	6.31631			0.238564			0.119282	+	0.992860i	$0.461941\pi$
$702$	7.64982	−	13.2499i	0.288724	−	0.500084i
$703$	8.34386	+	14.4520i	0.314695	+	0.545067i
$704$	6.21289	+	10.7610i	0.234157	+	0.405572i
$705$	0.610040	−	1.05662i	0.0229754	−	0.0397946i
$706$	16.1091			0.606276
$707$	−10.7617	+	25.7328i	−0.404735	+	0.967780i
$708$	−40.3702			−1.51721
$709$	−8.48268	+	14.6924i	−0.318574	+	0.551786i	−0.980191	−	0.198056i	$-0.936537\pi$
$709$	−8.48268	+	14.6924i	−0.318574	+	0.551786i	0.661617	+	0.749842i	$0.269870\pi$
$710$	1.31210	+	2.27262i	0.0492422	+	0.0852901i
$711$	−0.372163	−	0.644604i	−0.0139572	−	0.0241746i
$712$	26.7866	−	46.3957i	1.00387	−	1.73875i
$713$	34.5064			1.29227
$714$	6.07884	−	14.5354i	0.227495	−	0.543973i
$715$	6.56567			0.245542
$716$	23.9680	−	41.5138i	0.895726	−	1.55144i
$717$	2.94892	+	5.10768i	0.110129	+	0.190750i
$718$	−5.93755	−	10.2841i	−0.221588	−	0.383801i
$719$	4.76647	−	8.25577i	0.177759	−	0.307888i	−0.763353	−	0.645981i	$-0.776448\pi$
$719$	4.76647	−	8.25577i	0.177759	−	0.307888i	0.941113	+	0.338093i	$0.109782\pi$
$720$	−0.905171			−0.0337337
$721$	15.5641	−	1.99514i	0.579639	−	0.0743031i
$722$	−30.9814			−1.15301
$723$	−12.8722	+	22.2953i	−0.478721	+	0.829170i
$724$	17.0583	+	29.5459i	0.633968	+	1.09806i
$725$	2.17276	+	3.76333i	0.0806943	+	0.139767i
$726$	−1.16512	+	2.01805i	−0.0432418	+	0.0748970i
$727$	45.7753			1.69771			0.848855	−	0.528625i	$-0.177292\pi$
$727$	45.7753			1.69771			0.848855	+	0.528625i	$0.177292\pi$
$728$	35.0829	+	46.0448i	1.30026	+	1.70653i
$729$	1.00000			0.0370370
$730$	8.93275	−	15.4720i	0.330616	−	0.572644i
$731$	−0.737336	−	1.27710i	−0.0272714	−	0.0472354i
$732$	−17.3352	−	30.0255i	−0.640728	−	1.10977i
$733$	−3.27485	+	5.67221i	−0.120959	+	0.209508i	−0.920146	−	0.391575i	$-0.871930\pi$
$733$	−3.27485	+	5.67221i	−0.120959	+	0.209508i	0.799187	+	0.601083i	$0.205264\pi$
$734$	−36.5101			−1.34761
$735$	1.85776	−	6.74898i	0.0685244	−	0.248940i
$736$	16.9405			0.624435
$737$	6.05184	−	10.4821i	0.222923	−	0.386113i
$738$	−6.81743	−	11.8081i	−0.250953	−	0.434663i
$739$	10.3270	+	17.8868i	0.379884	+	0.657978i	0.991045	−	0.133528i	$-0.0426306\pi$
$739$	10.3270	+	17.8868i	0.379884	+	0.657978i	−0.611161	+	0.791506i	$0.709297\pi$
$740$	11.9827	−	20.7546i	0.440491	−	0.762953i
$741$	15.6817			0.576083
$742$	−6.41045	−	8.41345i	−0.235335	−	0.308868i
$743$	39.7387			1.45787			0.728936	−	0.684582i	$-0.240015\pi$
$743$	39.7387			1.45787			0.728936	+	0.684582i	$0.240015\pi$
$744$	15.4609	−	26.7790i	0.566823	−	0.981767i
$745$	1.69522	+	2.93620i	0.0621079	+	0.107574i
$746$	25.6959	+	44.5066i	0.940794	+	1.62950i
$747$	6.45304	−	11.1770i	0.236104	−	0.408945i
$748$	−8.76550			−0.320498
$749$	44.0476	−	5.64640i	1.60946	−	0.206315i
$750$	−2.33025			−0.0850886
$751$	−21.2623	+	36.8274i	−0.775873	+	1.34385i	0.158429	+	0.987370i	$0.449357\pi$
$751$	−21.2623	+	36.8274i	−0.775873	+	1.34385i	−0.934302	+	0.356481i	$0.883976\pi$
$752$	−0.552191	−	0.956422i	−0.0201363	−	0.0348771i
$753$	10.4908	+	18.1707i	0.382308	+	0.662176i
$754$	−33.2424	+	57.5776i	−1.21062	+	2.09685i
$755$	0.920629			0.0335051
$756$	−3.50142	+	8.37240i	−0.127345	+	0.304501i
$757$	−37.5157			−1.36353			−0.681767	−	0.731570i	$-0.738788\pi$
$757$	−37.5157			−1.36353			−0.681767	+	0.731570i	$0.738788\pi$
$758$	−8.62256	+	14.9347i	−0.313185	+	0.542453i
$759$	1.85935	+	3.22048i	0.0674900	+	0.116896i
$760$	−3.97961	−	6.89288i	−0.144356	−	0.250031i
$761$	−22.4966	+	38.9653i	−0.815501	+	1.41249i	0.0934663	+	0.995622i	$0.470205\pi$
$761$	−22.4966	+	38.9653i	−0.815501	+	1.41249i	−0.908967	+	0.416867i	$0.863128\pi$
$762$	−16.2294			−0.587930
$763$	16.9136	−	40.4428i	0.612312	−	1.46413i
$764$	42.8170			1.54906
$765$	−1.27775	+	2.21312i	−0.0461971	+	0.0800157i
$766$	19.5742	+	33.9035i	0.707245	+	1.22498i
$767$	−38.6375	−	66.9221i	−1.39512	−	2.41642i
$768$	10.6951	−	18.5245i	0.385927	−	0.668445i
$769$	0.330307			0.0119112			0.00595559	−	0.999982i	$-0.498104\pi$
$769$	0.330307			0.0119112			0.00595559	+	0.999982i	$0.498104\pi$
$770$	−6.11522	+	0.783901i	−0.220377	+	0.0282498i
$771$	−13.7452			−0.495023
$772$	−2.94756	+	5.10532i	−0.106085	+	0.183744i
$773$	−3.84785	−	6.66467i	−0.138398	−	0.239712i	0.788493	−	0.615044i	$-0.210862\pi$
$773$	−3.84785	−	6.66467i	−0.138398	−	0.239712i	−0.926890	+	0.375333i	$0.877528\pi$
$774$	0.672346	+	1.16454i	0.0241670	+	0.0418584i
$775$	4.63958	−	8.03599i	0.166659	−	0.288661i
$776$	−14.7698			−0.530204
$777$	−11.2032	−	14.7038i	−0.401914	−	0.527495i
$778$	−41.8572			−1.50065
$779$	6.98769	−	12.1030i	0.250360	−	0.433636i
$780$	−11.2603	−	19.5034i	−0.403183	−	0.698334i
$781$	−0.563073	−	0.975271i	−0.0201483	−	0.0348980i
$782$	−11.0723	+	19.1778i	−0.395944	+	0.685796i
$783$	−4.34552			−0.155296
$784$	−4.44974	−	4.51079i	−0.158919	−	0.161100i
$785$	−19.6247			−0.700437
$786$	18.1872	−	31.5011i	0.648714	−	1.12361i
$787$	13.5195	+	23.4165i	0.481919	+	0.834709i	0.999785	−	0.0207535i	$-0.00660652\pi$
$787$	13.5195	+	23.4165i	0.481919	+	0.834709i	−0.517865	+	0.855462i	$0.673273\pi$
$788$	−0.101231	−	0.175337i	−0.00360621	−	0.00624613i
$789$	13.2124	−	22.8846i	0.470375	−	0.814713i
$790$	−1.73446			−0.0617094
$791$	−27.7360	−	36.4024i	−0.986180	−	1.29432i
$792$	3.33238			0.118411
$793$	33.1823	−	57.4735i	1.17834	−	2.04094i
$794$	0.516425	+	0.894474i	0.0183272	+	0.0317437i
$795$	0.857818	+	1.48578i	0.0304237	+	0.0526954i
$796$	−36.6703	+	63.5148i	−1.29974	+	2.25122i
$797$	−13.7899			−0.488465			−0.244232	−	0.969717i	$-0.578536\pi$
$797$	−13.7899			−0.488465			−0.244232	+	0.969717i	$0.578536\pi$
$798$	−14.6059	+	1.87230i	−0.517042	+	0.0662788i
$799$	−3.11791			−0.110304
$800$	2.27775	−	3.94518i	0.0805306	−	0.139483i
$801$	8.03826	+	13.9227i	0.284018	+	0.491934i
$802$	−34.5211	−	59.7923i	−1.21898	−	2.11134i
$803$	−3.83339	+	6.63963i	−0.135277	+	0.234307i
$804$	−41.5163			−1.46417
$805$	−3.79606	+	9.07693i	−0.133794	+	0.319920i
$806$	141.968			5.00060
$807$	10.7518	−	18.6226i	0.378480	−	0.655546i
$808$	−17.5656	−	30.4245i	−0.617955	−	1.07033i
$809$	−12.1582	−	21.0586i	−0.427460	−	0.740382i	0.569187	−	0.822208i	$-0.307258\pi$
$809$	−12.1582	−	21.0586i	−0.427460	−	0.740382i	−0.996647	+	0.0818264i	$0.973925\pi$
$810$	1.16512	−	2.01805i	0.0409383	−	0.0709072i
$811$	25.5442			0.896978			0.448489	−	0.893788i	$-0.351962\pi$
$811$	25.5442			0.896978			0.448489	+	0.893788i	$0.351962\pi$
$812$	15.2155	−	36.3824i	0.533959	−	1.27677i
$813$	12.9964			0.455802
$814$	−8.14056	+	14.0999i	−0.285326	+	0.494200i
$815$	5.09803	+	8.83005i	0.178576	+	0.309303i
$816$	1.15658	+	2.00326i	0.0404884	+	0.0701280i
$817$	−0.689137	+	1.19362i	−0.0241098	+	0.0417595i
$818$	20.9533			0.732614
$819$	−17.2301	+	2.20871i	−0.602070	+	0.0771784i
$820$	−20.0701			−0.700878
$821$	−16.2600	+	28.1632i	−0.567478	+	0.982901i	0.429336	+	0.903145i	$0.358747\pi$
$821$	−16.2600	+	28.1632i	−0.567478	+	0.982901i	−0.996814	+	0.0797562i	$0.974586\pi$
$822$	−2.60681	−	4.51513i	−0.0909231	−	0.157483i
$823$	23.4197	+	40.5641i	0.816359	+	1.41398i	0.908348	+	0.418216i	$0.137344\pi$
$823$	23.4197	+	40.5641i	0.816359	+	1.41398i	−0.0919884	+	0.995760i	$0.529322\pi$
$824$	−9.88190	+	17.1160i	−0.344252	+	0.596262i
$825$	1.00000			0.0348155
$826$	43.9768	+	57.7177i	1.53015	+	2.00826i
$827$	36.2843			1.26173			0.630864	−	0.775893i	$-0.282701\pi$
$827$	36.2843			1.26173			0.630864	+	0.775893i	$0.282701\pi$
$828$	6.37766	−	11.0464i	0.221639	−	0.383890i
$829$	19.2797	+	33.3934i	0.669612	+	1.15980i	0.978013	+	0.208545i	$0.0668727\pi$
$829$	19.2797	+	33.3934i	0.669612	+	1.15980i	−0.308401	+	0.951256i	$0.599794\pi$
$830$	−15.0372	−	26.0452i	−0.521948	−	0.904041i
$831$	7.59172	−	13.1492i	0.263354	−	0.456142i
$832$	81.5835			2.82840
$833$	−17.3101	+	4.51205i	−0.599759	+	0.156333i
$834$	−28.8300			−0.998301
$835$	0.354065	−	0.613258i	0.0122529	−	0.0212227i
$836$	4.09625	+	7.09491i	0.141672	+	0.245383i
$837$	4.63958	+	8.03599i	0.160367	+	0.277765i
$838$	−19.1679	+	33.1998i	−0.662145	+	1.14687i
$839$	−40.9551			−1.41393			−0.706964	−	0.707249i	$-0.749936\pi$
$839$	−40.9551			−1.41393			−0.706964	+	0.707249i	$0.749936\pi$
$840$	5.34338	+	7.01297i	0.184364	+	0.241970i
$841$	−10.1164			−0.348843
$842$	33.1948	−	57.4951i	1.14397	−	1.98141i
$843$	−4.72668	−	8.18685i	−0.162796	−	0.281970i
$844$	−27.7222	−	48.0163i	−0.954239	−	1.65279i
$845$	15.0540	−	26.0743i	0.517873	−	0.896982i
$846$	2.84309			0.0977474
$847$	2.62428	−	0.336402i	0.0901712	−	0.0115589i
$848$	1.55294			0.0533283
$849$	9.09011	−	15.7445i	0.311972	−	0.540351i
$850$	2.97747	+	5.15713i	0.102126	+	0.176888i
$851$	12.9910	+	22.5011i	0.445325	+	0.771326i
$852$	−1.93137	+	3.34524i	−0.0661677	+	0.114606i
$853$	55.8708			1.91298			0.956489	−	0.291768i	$-0.0942436\pi$
$853$	55.8708			1.91298			0.956489	+	0.291768i	$0.0942436\pi$
$854$	−24.0438	+	57.4922i	−0.822763	+	1.96734i
$855$	2.38844			0.0816831
$856$	−27.9665	+	48.4393i	−0.955874	+	1.65562i
$857$	−3.04891	−	5.28087i	−0.104149	−	0.180391i	0.809241	−	0.587476i	$-0.199878\pi$
$857$	−3.04891	−	5.28087i	−0.104149	−	0.180391i	−0.913390	+	0.407085i	$0.866545\pi$
$858$	7.64982	+	13.2499i	0.261160	+	0.452343i
$859$	−13.9519	+	24.1653i	−0.476031	+	0.824510i	−0.999623	−	0.0274593i	$-0.991258\pi$
$859$	−13.9519	+	24.1653i	−0.476031	+	0.824510i	0.523592	+	0.851969i	$0.324592\pi$
$860$	1.97935			0.0674951
$861$	−5.97299	+	14.2823i	−0.203559	+	0.486738i
$862$	64.4751			2.19603
$863$	15.2615	−	26.4337i	0.519507	−	0.899813i	−0.480236	−	0.877140i	$-0.659449\pi$
$863$	15.2615	−	26.4337i	0.519507	−	0.899813i	0.999743	−	0.0226736i	$-0.00721785\pi$
$864$	2.27775	+	3.94518i	0.0774906	+	0.134218i
$865$	6.76671	+	11.7203i	0.230075	+	0.398502i
$866$	37.2266	−	64.4783i	1.26501	−	2.19106i
$867$	−10.4694			−0.355561
$868$	−83.5257	+	10.7070i	−2.83505	+	0.363420i
$869$	0.744325			0.0252495
$870$	−5.06307	+	8.76950i	−0.171654	+	0.297314i
$871$	−39.7344	−	68.8220i	−1.34635	−	2.33194i
$872$	27.6069	+	47.8165i	0.934887	+	1.61927i
$873$	2.21610	−	3.83839i	0.0750035	−	0.129910i
$874$	20.6970			0.700086
$875$	1.60347	+	2.10449i	0.0542072	+	0.0711447i
$876$	26.2975			0.888510
$877$	18.0631	−	31.2862i	0.609947	−	1.05646i	−0.381302	−	0.924451i	$-0.624524\pi$
$877$	18.0631	−	31.2862i	0.609947	−	1.05646i	0.991249	−	0.132008i	$-0.0421426\pi$
$878$	−39.7186	−	68.7945i	−1.34044	−	2.32170i
$879$	−14.3975	−	24.9372i	−0.485616	−	0.841112i
$880$	0.452585	−	0.783901i	0.0152567	−	0.0264253i
$881$	−42.0321			−1.41610			−0.708048	−	0.706164i	$-0.750424\pi$
$881$	−42.0321			−1.41610			−0.708048	+	0.706164i	$0.750424\pi$
$882$	15.7843	−	4.11435i	0.531486	−	0.138537i
$883$	−37.1106			−1.24887			−0.624436	−	0.781076i	$-0.714671\pi$
$883$	−37.1106			−1.24887			−0.624436	+	0.781076i	$0.714671\pi$
$884$	−28.7757	+	49.8409i	−0.967830	+	1.67633i
$885$	−5.88478	−	10.1927i	−0.197815	−	0.342625i
$886$	47.9353	+	83.0264i	1.61042	+	2.78933i
$887$	−13.9045	+	24.0834i	−0.466869	+	0.808641i	−0.999284	−	0.0378427i	$-0.987951\pi$
$887$	−13.9045	+	24.0834i	−0.466869	+	0.808641i	0.532415	+	0.846484i	$0.321285\pi$
$888$	23.2829			0.781323
$889$	11.1677	+	14.6571i	0.374551	+	0.491583i
$890$	37.4623			1.25574
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	15.5525	+	26.9377i	0.520735	+	0.901940i
$893$	1.45705	+	2.52368i	0.0487582	+	0.0844517i
$894$	−3.95027	+	6.84208i	−0.132117	+	0.228833i
$895$	13.9753			0.467142
$896$	−52.0766	+	6.67562i	−1.73976	+	0.223017i
$897$	24.4157			0.815216
$898$	37.3269	−	64.6522i	1.24562	−	2.15747i
$899$	−20.1614	−	34.9206i	−0.672421	−	1.16467i
$900$	−1.71503	−	2.97052i	−0.0571676	−	0.0990172i
$901$	2.19215	−	3.79692i	0.0730312	−	0.126494i
$902$	13.6349			0.453991
$903$	0.589065	−	1.40854i	0.0196029	−	0.0468733i
$904$	57.6419			1.91714
$905$	−4.97320	+	8.61383i	−0.165315	+	0.286333i
$906$	1.07265	+	1.85788i	0.0356363	+	0.0617239i
$907$	−7.49181	−	12.9762i	−0.248761	−	0.430867i	0.714421	−	0.699716i	$-0.246690\pi$
$907$	−7.49181	−	12.9762i	−0.248761	−	0.430867i	−0.963182	+	0.268849i	$0.913357\pi$
$908$	22.8396	−	39.5594i	0.757960	−	1.31283i
$909$	10.5424			0.349668
$910$	−15.6180	+	37.3448i	−0.517730	+	1.23797i
$911$	−24.1417			−0.799851			−0.399925	−	0.916548i	$-0.630964\pi$
$911$	−24.1417			−0.799851			−0.399925	+	0.916548i	$0.630964\pi$
$912$	1.08097	−	1.87230i	0.0357947	−	0.0619982i
$913$	6.45304	+	11.1770i	0.213565	+	0.369905i
$914$	25.1245	+	43.5170i	0.831046	+	1.43941i
$915$	5.05392	−	8.75364i	0.167077	−	0.289387i
$916$	61.5466			2.03356
$917$	−40.9640	+	5.25112i	−1.35275	+	0.173407i
$918$	−5.95494			−0.196542
$919$	13.6668	−	23.6715i	0.450825	−	0.780851i	−0.547613	−	0.836732i	$-0.684463\pi$
$919$	13.6668	−	23.6715i	0.450825	−	0.780851i	0.998437	+	0.0558807i	$0.0177967\pi$
$920$	−6.19606	−	10.7319i	−0.204278	−	0.353820i
$921$	12.8768	+	22.3033i	0.424306	+	0.734920i
$922$	27.8767	−	48.2838i	0.918070	−	1.59014i
$923$	−7.39390			−0.243373
$924$	−5.50000	−	7.21852i	−0.180937	−	0.237472i
$925$	6.98686			0.229727
$926$	18.3618	−	31.8036i	0.603406	−	1.04513i
$927$	−2.96541	−	5.13625i	−0.0973970	−	0.168696i
$928$	−9.89800	−	17.1438i	−0.324918	−	0.562774i
$929$	4.76244	−	8.24879i	0.156251	−	0.270634i	−0.777263	−	0.629176i	$-0.783393\pi$
$929$	4.76244	−	8.24879i	0.156251	−	0.270634i	0.933514	+	0.358542i	$0.116726\pi$
$930$	21.6228			0.709038
$931$	11.7414	+	11.9025i	0.384808	+	0.390087i
$932$	29.7074			0.973099
$933$	3.47750	−	6.02320i	0.113848	−	0.197191i
$934$	−0.488992	−	0.846959i	−0.0160003	−	0.0277134i
$935$	−1.27775	−	2.21312i	−0.0417868	−	0.0723769i
$936$	10.9397	−	18.9481i	0.357574	−	0.619336i
$937$	9.95761			0.325301			0.162650	−	0.986684i	$-0.447996\pi$
$937$	9.95761			0.325301			0.162650	+	0.986684i	$0.447996\pi$
$938$	45.2253	+	59.3563i	1.47666	+	1.93805i
$939$	−15.9445			−0.520328
$940$	2.09247	−	3.62427i	0.0682489	−	0.118211i
$941$	−10.6309	−	18.4132i	−0.346556	−	0.600253i	0.639079	−	0.769141i	$-0.279316\pi$
$941$	−10.6309	−	18.4132i	−0.346556	−	0.600253i	−0.985635	+	0.168888i	$0.945982\pi$
$942$	−22.8653	−	39.6038i	−0.744991	−	1.29036i
$943$	10.8795	−	18.8438i	0.354285	−	0.613640i
$944$	−10.6535			−0.346741
$945$	−2.62428	+	0.336402i	−0.0853678	+	0.0109432i
$946$	−1.34469			−0.0437197
$947$	4.80819	−	8.32803i	0.156245	−	0.270625i	−0.777267	−	0.629172i	$-0.783394\pi$
$947$	4.80819	−	8.32803i	0.156245	−	0.270625i	0.933512	+	0.358547i	$0.116728\pi$
$948$	−1.27654	−	2.21103i	−0.0414600	−	0.0718109i
$949$	25.1688	+	43.5936i	0.817013	+	1.41511i
$950$	2.78283	−	4.82001i	0.0902870	−	0.156382i
$951$	6.11558			0.198311
$952$	8.69308	−	20.7864i	0.281744	−	0.673691i
$953$	−16.6598			−0.539665			−0.269833	−	0.962907i	$-0.586968\pi$
$953$	−16.6598			−0.539665			−0.269833	+	0.962907i	$0.586968\pi$
$954$	−1.99893	+	3.46225i	−0.0647177	+	0.112094i
$955$	6.24144	+	10.8105i	0.201968	+	0.349819i
$956$	10.1150	+	17.5196i	0.327141	+	0.566625i
$957$	2.17276	−	3.76333i	0.0702354	−	0.121651i
$958$	74.4027			2.40384
$959$	−2.28392	+	5.46118i	−0.0737516	+	0.176351i
$960$	12.4258			0.401040
$961$	−27.5515	+	47.7205i	−0.888757	+	1.53937i
$962$	53.4482	+	92.5750i	1.72324	+	2.98474i
$963$	−8.39232	−	14.5359i	−0.270439	−	0.468414i
$964$	−44.1523	+	76.4740i	−1.42205	+	2.46306i
$965$	−1.71866			−0.0553257
$966$	−22.7406	+	2.91509i	−0.731667	+	0.0937914i
$967$	8.39085			0.269831			0.134916	−	0.990857i	$-0.456924\pi$
$967$	8.39085			0.269831			0.134916	+	0.990857i	$0.456924\pi$
$968$	−1.66619	+	2.88593i	−0.0535534	+	0.0927573i
$969$	−3.05183	−	5.28592i	−0.0980389	−	0.169808i
$970$	−5.16405	−	8.94440i	−0.165808	−	0.287187i
$971$	−23.9270	+	41.4428i	−0.767855	+	1.32996i	0.170869	+	0.985294i	$0.445343\pi$
$971$	−23.9270	+	41.4428i	−0.767855	+	1.32996i	−0.938724	+	0.344670i	$0.887991\pi$
$972$	3.43006			0.110019
$973$	19.8383	+	26.0369i	0.635986	+	0.834705i
$974$	21.0134			0.673314
$975$	3.28283	−	5.68603i	0.105135	−	0.182099i
$976$	−4.57466	−	7.92354i	−0.146431	−	0.253626i
$977$	−13.7822	−	23.8714i	−0.440931	−	0.763715i	0.556828	−	0.830628i	$-0.312018\pi$
$977$	−13.7822	−	23.8714i	−0.440931	−	0.763715i	−0.997759	+	0.0669132i	$0.978685\pi$
$978$	−11.8797	+	20.5762i	−0.379870	+	0.657955i
$979$	−16.0765			−0.513808
$980$	6.37221	−	23.1494i	0.203553	−	0.739480i
$981$	−16.5688			−0.529002
$982$	−31.2281	+	54.0886i	−0.996528	+	1.72604i
$983$	−7.32652	−	12.6899i	−0.233680	−	0.404745i	0.725209	−	0.688529i	$-0.241743\pi$
$983$	−7.32652	−	12.6899i	−0.233680	−	0.404745i	−0.958888	+	0.283784i	$0.908410\pi$
$984$	−9.74930	−	16.8863i	−0.310796	−	0.538315i
$985$	0.0295129	−	0.0511179i	0.000940360	−	0.00162875i
$986$	25.8773			0.824102
$987$	−1.95636	−	2.56765i	−0.0622718	−	0.0817291i
$988$	53.7892			1.71126
$989$	−1.07295	+	1.85841i	−0.0341179	+	0.0590940i
$990$	1.16512	+	2.01805i	0.0370301	+	0.0641380i
$991$	−23.5251	−	40.7467i	−0.747301	−	1.29436i	−0.949112	−	0.314939i	$-0.898016\pi$
$991$	−23.5251	−	40.7467i	−0.747301	−	1.29436i	0.201811	−	0.979424i	$-0.435317\pi$
$992$	−21.1356	+	36.6079i	−0.671056	+	1.16230i
$993$	2.21500			0.0702909
$994$	6.88663	−	0.882787i	0.218431	−	0.0280003i
$995$	−21.3818			−0.677847
$996$	22.1343	−	38.3377i	0.701352	−	1.21478i
$997$	−4.93494	−	8.54756i	−0.156291	−	0.270704i	0.777237	−	0.629208i	$-0.216620\pi$
$997$	−4.93494	−	8.54756i	−0.156291	−	0.270704i	−0.933528	+	0.358504i	$0.883287\pi$
$998$	15.7145	+	27.2184i	0.497435	+	0.861582i
$999$	−3.49343	+	6.05080i	−0.110527	+	0.191439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.q.h.331.1	✓	12
7.2	even	3		8085.2.a.bz.1.6		6
7.4	even	3	inner	1155.2.q.h.991.1	yes	12
7.5	odd	6		8085.2.a.bx.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.h.331.1	✓	12	1.1	even	1	trivial
1155.2.q.h.991.1	yes	12	7.4	even	3	inner
8085.2.a.bx.1.6		6	7.5	odd	6
8085.2.a.bz.1.6		6	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16512 + 2.01805i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.71503 - 2.97052i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.33025 q^{6} +(-1.60347 - 2.10449i) q^{7} +3.33238 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.16512 + 2.01805i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.71503 - 2.97052i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.33025 q^{6} +(-1.60347 - 2.10449i) q^{7} +3.33238 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.16512 + 2.01805i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.71503 + 2.97052i) q^{12} -6.56567 q^{13} +(6.11522 - 0.783901i) q^{14} -1.00000 q^{15} +(-0.452585 + 0.783901i) q^{16} +(1.27775 + 2.21312i) q^{17} +(-1.16512 - 2.01805i) q^{18} +(1.19422 - 2.06845i) q^{19} -3.43006 q^{20} +(-1.02081 + 2.44089i) q^{21} +2.33025 q^{22} +(1.85935 - 3.22048i) q^{23} +(-1.66619 - 2.88593i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(7.64982 - 13.2499i) q^{26} +1.00000 q^{27} +(-3.50142 + 8.37240i) q^{28} -4.34552 q^{29} +(1.16512 - 2.01805i) q^{30} +(4.63958 + 8.03599i) q^{31} +(2.27775 + 3.94518i) q^{32} +(-0.500000 + 0.866025i) q^{33} -5.95494 q^{34} +(-2.62428 + 0.336402i) q^{35} +3.43006 q^{36} +(-3.49343 + 6.05080i) q^{37} +(2.78283 + 4.82001i) q^{38} +(3.28283 + 5.68603i) q^{39} +(1.66619 - 2.88593i) q^{40} +5.85125 q^{41} +(-3.73649 - 4.90398i) q^{42} -0.577059 q^{43} +(-1.71503 + 2.97052i) q^{44} +(0.500000 + 0.866025i) q^{45} +(4.33274 + 7.50452i) q^{46} +(-0.610040 + 1.05662i) q^{47} +0.905171 q^{48} +(-1.85776 + 6.74898i) q^{49} +2.33025 q^{50} +(1.27775 - 2.21312i) q^{51} +(11.2603 + 19.5034i) q^{52} +(-0.857818 - 1.48578i) q^{53} +(-1.16512 + 2.01805i) q^{54} -1.00000 q^{55} +(-5.34338 - 7.01297i) q^{56} -2.38844 q^{57} +(5.06307 - 8.76950i) q^{58} +(5.88478 + 10.1927i) q^{59} +(1.71503 + 2.97052i) q^{60} +(-5.05392 + 8.75364i) q^{61} -21.6228 q^{62} +(2.62428 - 0.336402i) q^{63} -12.4258 q^{64} +(-3.28283 + 5.68603i) q^{65} +(-1.16512 - 2.01805i) q^{66} +(6.05184 + 10.4821i) q^{67} +(4.38275 - 7.59114i) q^{68} -3.71869 q^{69} +(2.37873 - 5.68788i) q^{70} +1.12615 q^{71} +(-1.66619 + 2.88593i) q^{72} +(-3.83339 - 6.63963i) q^{73} +(-8.14056 - 14.0999i) q^{74} +(-0.500000 + 0.866025i) q^{75} -8.19250 q^{76} +(-1.02081 + 2.44089i) q^{77} -15.2996 q^{78} +(-0.372163 + 0.644604i) q^{79} +(0.452585 + 0.783901i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.81743 + 11.8081i) q^{82} -12.9061 q^{83} +(9.00142 - 1.15388i) q^{84} +2.55550 q^{85} +(0.672346 - 1.16454i) q^{86} +(2.17276 + 3.76333i) q^{87} +(-1.66619 - 2.88593i) q^{88} +(8.03826 - 13.9227i) q^{89} -2.33025 q^{90} +(10.5279 + 13.8174i) q^{91} -12.7553 q^{92} +(4.63958 - 8.03599i) q^{93} +(-1.42154 - 2.46219i) q^{94} +(-1.19422 - 2.06845i) q^{95} +(2.27775 - 3.94518i) q^{96} -4.43219 q^{97} +(-11.4553 - 11.6125i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 6 q^{4} + 6 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 6 * q^4 + 6 * q^5 - 2 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} - 6 q^{4} + 6 q^{5} - 2 q^{7} - 6 q^{9} - 6 q^{11} - 6 q^{12} - 8 q^{13} - 2 q^{14} - 12 q^{15} + 2 q^{16} - 2 q^{17} + 13 q^{19} - 12 q^{20} + q^{21} + 7 q^{23} - 6 q^{25} + 26 q^{26} + 12 q^{27} - 40 q^{28} + 6 q^{29} + 15 q^{31} + 10 q^{32} - 6 q^{33} - 28 q^{34} - q^{35} + 12 q^{36} + 11 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{41} + 4 q^{42} - 8 q^{43} - 6 q^{44} + 6 q^{45} + 16 q^{46} + 19 q^{47} - 4 q^{48} - 2 q^{51} + 16 q^{52} + q^{53} - 12 q^{55} - 18 q^{56} - 26 q^{57} + 22 q^{59} + 6 q^{60} + 14 q^{61} - 4 q^{62} + q^{63} - 20 q^{64} - 4 q^{65} + 21 q^{67} + 14 q^{68} - 14 q^{69} + 2 q^{70} + 16 q^{71} + 11 q^{73} - 20 q^{74} - 6 q^{75} + q^{77} - 52 q^{78} + 13 q^{79} - 2 q^{80} - 6 q^{81} + 6 q^{82} - 20 q^{83} + 44 q^{84} - 4 q^{85} - 36 q^{86} - 3 q^{87} + 28 q^{89} + 2 q^{91} + 12 q^{92} + 15 q^{93} + 14 q^{94} - 13 q^{95} + 10 q^{96} - 12 q^{97} - 36 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 - 6 * q^4 + 6 * q^5 - 2 * q^7 - 6 * q^9 - 6 * q^11 - 6 * q^12 - 8 * q^13 - 2 * q^14 - 12 * q^15 + 2 * q^16 - 2 * q^17 + 13 * q^19 - 12 * q^20 + q^21 + 7 * q^23 - 6 * q^25 + 26 * q^26 + 12 * q^27 - 40 * q^28 + 6 * q^29 + 15 * q^31 + 10 * q^32 - 6 * q^33 - 28 * q^34 - q^35 + 12 * q^36 + 11 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^41 + 4 * q^42 - 8 * q^43 - 6 * q^44 + 6 * q^45 + 16 * q^46 + 19 * q^47 - 4 * q^48 - 2 * q^51 + 16 * q^52 + q^53 - 12 * q^55 - 18 * q^56 - 26 * q^57 + 22 * q^59 + 6 * q^60 + 14 * q^61 - 4 * q^62 + q^63 - 20 * q^64 - 4 * q^65 + 21 * q^67 + 14 * q^68 - 14 * q^69 + 2 * q^70 + 16 * q^71 + 11 * q^73 - 20 * q^74 - 6 * q^75 + q^77 - 52 * q^78 + 13 * q^79 - 2 * q^80 - 6 * q^81 + 6 * q^82 - 20 * q^83 + 44 * q^84 - 4 * q^85 - 36 * q^86 - 3 * q^87 + 28 * q^89 + 2 * q^91 + 12 * q^92 + 15 * q^93 + 14 * q^94 - 13 * q^95 + 10 * q^96 - 12 * q^97 - 36 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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