LMFDB - Embedded newform 285.2.i.f.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.i (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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$0.145349 - 0.251751i$ of defining polynomial
Character	$\chi$	$=$	285.121
Dual form			285.2.i.f.106.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.145349 + 0.251751i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.957748 - 1.65887i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.145349 + 0.251751i) q^{6} -0.486575 q^{7} +1.13822 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.145349 - 0.251751i) q^{10} +5.34764 q^{11} +1.91550 q^{12} +(1.24329 - 2.15344i) q^{13} +(-0.0707229 - 0.122496i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-1.75006 - 3.03119i) q^{16} +(1.70780 + 2.95800i) q^{17} -0.290697 q^{18} +(-2.46291 - 3.59640i) q^{19} -1.91550 q^{20} +(-0.243287 - 0.421386i) q^{21} +(0.777272 + 1.34627i) q^{22} +(-3.20619 + 5.55329i) q^{23} +(0.569112 + 0.985730i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.722840 q^{26} -1.00000 q^{27} +(-0.466016 + 0.807163i) q^{28} +(-1.38312 + 2.39564i) q^{29} +0.290697 q^{30} +4.83099 q^{31} +(1.64696 - 2.85262i) q^{32} +(2.67382 + 4.63119i) q^{33} +(-0.496454 + 0.859883i) q^{34} +(0.243287 + 0.421386i) q^{35} +(0.957748 + 1.65887i) q^{36} -6.31756 q^{37} +(0.547418 - 1.14277i) q^{38} +2.48657 q^{39} +(-0.569112 - 0.985730i) q^{40} +(-1.29070 - 2.23555i) q^{41} +(0.0707229 - 0.122496i) q^{42} +(1.24329 + 2.15344i) q^{43} +(5.12169 - 8.87102i) q^{44} +1.00000 q^{45} -1.86406 q^{46} +(-5.55533 + 9.62211i) q^{47} +(1.75006 - 3.03119i) q^{48} -6.76325 q^{49} -0.290697 q^{50} +(-1.70780 + 2.95800i) q^{51} +(-2.38151 - 4.12490i) q^{52} +(-1.49839 + 2.59529i) q^{53} +(-0.145349 - 0.251751i) q^{54} +(-2.67382 - 4.63119i) q^{55} -0.553831 q^{56} +(1.88312 - 3.93114i) q^{57} -0.804139 q^{58} +(-6.36659 - 11.0273i) q^{59} +(-0.957748 - 1.65887i) q^{60} +(-5.92742 + 10.2666i) q^{61} +(0.702178 + 1.21621i) q^{62} +(0.243287 - 0.421386i) q^{63} -6.04269 q^{64} -2.48657 q^{65} +(-0.777272 + 1.34627i) q^{66} +(7.58770 - 13.1423i) q^{67} +6.54258 q^{68} -6.41238 q^{69} +(-0.0707229 + 0.122496i) q^{70} +(4.96452 + 8.59879i) q^{71} +(-0.569112 + 0.985730i) q^{72} +(5.50642 + 9.53740i) q^{73} +(-0.918249 - 1.59045i) q^{74} -1.00000 q^{75} +(-8.32479 + 0.641189i) q^{76} -2.60202 q^{77} +(0.361420 + 0.625998i) q^{78} +(-4.06636 - 7.04314i) q^{79} +(-1.75006 + 3.03119i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.375202 - 0.649869i) q^{82} -5.86106 q^{83} -0.932031 q^{84} +(1.70780 - 2.95800i) q^{85} +(-0.361420 + 0.625998i) q^{86} -2.76624 q^{87} +6.08681 q^{88} +(3.25521 - 5.63820i) q^{89} +(0.145349 + 0.251751i) q^{90} +(-0.604952 + 1.04781i) q^{91} +(6.14145 + 10.6373i) q^{92} +(2.41550 + 4.18376i) q^{93} -3.22984 q^{94} +(-1.88312 + 3.93114i) q^{95} +3.29392 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-0.983028 - 1.70265i) q^{98} +(-2.67382 + 4.63119i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) $ 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.145349	+	0.251751i	0.102777	+	0.178015i	0.912828	−	0.408345i	$-0.133894\pi$
$2$	0.145349	+	0.251751i	0.102777	+	0.178015i	−0.810051	+	0.586360i	$0.800561\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.957748	−	1.65887i	0.478874	−	0.829434i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.145349	+	0.251751i	−0.0593383	+	0.102777i
$7$	−0.486575			−0.183908			−0.0919539	−	0.995763i	$-0.529311\pi$
$7$	−0.486575			−0.183908			−0.0919539	+	0.995763i	$0.529311\pi$
$8$	1.13822			0.402423
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.145349	−	0.251751i	0.0459633	−	0.0796107i
$11$	5.34764			1.61237			0.806187	−	0.591661i	$-0.201528\pi$
$11$	5.34764			1.61237			0.806187	+	0.591661i	$0.201528\pi$
$12$	1.91550			0.552956
$13$	1.24329	−	2.15344i	0.344826	−	0.597256i	−0.640496	−	0.767961i	$-0.721271\pi$
$13$	1.24329	−	2.15344i	0.344826	−	0.597256i	0.985322	+	0.170705i	$0.0546046\pi$
$14$	−0.0707229	−	0.122496i	−0.0189015	−	0.0327384i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−1.75006	−	3.03119i	−0.437514	−	0.757796i
$17$	1.70780	+	2.95800i	0.414203	+	0.717421i	0.995344	−	0.0963817i	$-0.0307270\pi$
$17$	1.70780	+	2.95800i	0.414203	+	0.717421i	−0.581141	+	0.813803i	$0.697394\pi$
$18$	−0.290697			−0.0685180
$19$	−2.46291	−	3.59640i	−0.565029	−	0.825071i
$19$	−2.46291	−	3.59640i	−0.565029	−	0.825071i
$20$	−1.91550			−0.428318
$21$	−0.243287	−	0.421386i	−0.0530896	−	0.0919539i
$22$	0.777272	+	1.34627i	0.165715	+	0.287027i
$23$	−3.20619	+	5.55329i	−0.668537	+	1.15794i	0.309776	+	0.950810i	$0.399746\pi$
$23$	−3.20619	+	5.55329i	−0.668537	+	1.15794i	−0.978313	+	0.207131i	$0.933587\pi$
$24$	0.569112	+	0.985730i	0.116169	+	0.201211i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.722840			0.141761
$27$	−1.00000			−0.192450
$28$	−0.466016	+	0.807163i	−0.0880687	+	0.152539i
$29$	−1.38312	+	2.39564i	−0.256839	+	0.444859i	−0.965393	−	0.260798i	$-0.916014\pi$
$29$	−1.38312	+	2.39564i	−0.256839	+	0.444859i	0.708554	+	0.705656i	$0.249348\pi$
$30$	0.290697			0.0530738
$31$	4.83099			0.867671			0.433836	−	0.900992i	$-0.357160\pi$
$31$	4.83099			0.867671			0.433836	+	0.900992i	$0.357160\pi$
$32$	1.64696	−	2.85262i	0.291144	−	0.504276i
$33$	2.67382	+	4.63119i	0.465452	+	0.806187i
$34$	−0.496454	+	0.859883i	−0.0851411	+	0.147469i
$35$	0.243287	+	0.421386i	0.0411231	+	0.0712272i
$36$	0.957748	+	1.65887i	0.159625	+	0.276478i
$37$	−6.31756			−1.03860			−0.519301	−	0.854592i	$-0.673808\pi$
$37$	−6.31756			−1.03860			−0.519301	+	0.854592i	$0.673808\pi$
$38$	0.547418	−	1.14277i	0.0888030	−	0.185382i
$39$	2.48657			0.398171
$40$	−0.569112	−	0.985730i	−0.0899845	−	0.155858i
$41$	−1.29070	−	2.23555i	−0.201573	−	0.349135i	0.747462	−	0.664304i	$-0.231272\pi$
$41$	−1.29070	−	2.23555i	−0.201573	−	0.349135i	−0.949035	+	0.315169i	$0.897939\pi$
$42$	0.0707229	−	0.122496i	0.0109128	−	0.0189015i
$43$	1.24329	+	2.15344i	0.189600	+	0.328396i	0.945117	−	0.326733i	$-0.105948\pi$
$43$	1.24329	+	2.15344i	0.189600	+	0.328396i	−0.755517	+	0.655129i	$0.772614\pi$
$44$	5.12169	−	8.87102i	0.772123	−	1.33736i
$45$	1.00000			0.149071
$46$	−1.86406			−0.274841
$47$	−5.55533	+	9.62211i	−0.810328	+	1.40353i	0.102306	+	0.994753i	$0.467378\pi$
$47$	−5.55533	+	9.62211i	−0.810328	+	1.40353i	−0.912634	+	0.408777i	$0.865956\pi$
$48$	1.75006	−	3.03119i	0.252599	−	0.437514i
$49$	−6.76325			−0.966178
$50$	−0.290697			−0.0411108
$51$	−1.70780	+	2.95800i	−0.239140	+	0.414203i
$52$	−2.38151	−	4.12490i	−0.330256	−	0.572020i
$53$	−1.49839	+	2.59529i	−0.205820	+	0.356490i	−0.950394	−	0.311050i	$-0.899319\pi$
$53$	−1.49839	+	2.59529i	−0.205820	+	0.356490i	0.744574	+	0.667540i	$0.232653\pi$
$54$	−0.145349	−	0.251751i	−0.0197794	−	0.0342590i
$55$	−2.67382	−	4.63119i	−0.360538	−	0.624470i
$56$	−0.553831			−0.0740087
$57$	1.88312	−	3.93114i	0.249426	−	0.520692i
$58$	−0.804139			−0.105589
$59$	−6.36659	−	11.0273i	−0.828859	−	1.43563i	−0.898934	−	0.438084i	$-0.855657\pi$
$59$	−6.36659	−	11.0273i	−0.828859	−	1.43563i	0.0700752	−	0.997542i	$-0.477676\pi$
$60$	−0.957748	−	1.65887i	−0.123645	−	0.214159i
$61$	−5.92742	+	10.2666i	−0.758929	+	1.31450i	0.184469	+	0.982838i	$0.440944\pi$
$61$	−5.92742	+	10.2666i	−0.758929	+	1.31450i	−0.943397	+	0.331664i	$0.892390\pi$
$62$	0.702178	+	1.21621i	0.0891767	+	0.154458i
$63$	0.243287	−	0.421386i	0.0306513	−	0.0530896i
$64$	−6.04269			−0.755336
$65$	−2.48657			−0.308422
$66$	−0.777272	+	1.34627i	−0.0956755	+	0.165715i
$67$	7.58770	−	13.1423i	0.926985	−	1.60559i	0.138649	−	0.990342i	$-0.455724\pi$
$67$	7.58770	−	13.1423i	0.926985	−	1.60559i	0.788336	−	0.615244i	$-0.210943\pi$
$68$	6.54258			0.793404
$69$	−6.41238			−0.771960
$70$	−0.0707229	+	0.122496i	−0.00845301	+	0.0146410i
$71$	4.96452	+	8.59879i	0.589180	+	1.02049i	0.994340	+	0.106244i	$0.0338823\pi$
$71$	4.96452	+	8.59879i	0.589180	+	1.02049i	−0.405160	+	0.914246i	$0.632784\pi$
$72$	−0.569112	+	0.985730i	−0.0670705	+	0.116169i
$73$	5.50642	+	9.53740i	0.644478	+	1.11627i	0.984422	+	0.175823i	$0.0562585\pi$
$73$	5.50642	+	9.53740i	0.644478	+	1.11627i	−0.339944	+	0.940446i	$0.610408\pi$
$74$	−0.918249	−	1.59045i	−0.106744	−	0.184887i
$75$	−1.00000			−0.115470
$76$	−8.32479	+	0.641189i	−0.954919	+	0.0735494i
$77$	−2.60202			−0.296528
$78$	0.361420	+	0.625998i	0.0409228	+	0.0708803i
$79$	−4.06636	−	7.04314i	−0.457501	−	0.792415i	0.541327	−	0.840812i	$-0.317922\pi$
$79$	−4.06636	−	7.04314i	−0.457501	−	0.792415i	−0.998828	+	0.0483971i	$0.984589\pi$
$80$	−1.75006	+	3.03119i	−0.195662	+	0.338897i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.375202	−	0.649869i	0.0414341	−	0.0717660i
$83$	−5.86106			−0.643335			−0.321668	−	0.946853i	$-0.604243\pi$
$83$	−5.86106			−0.643335			−0.321668	+	0.946853i	$0.604243\pi$
$84$	−0.932031			−0.101693
$85$	1.70780	−	2.95800i	0.185237	−	0.320840i
$86$	−0.361420	+	0.625998i	−0.0389729	+	0.0675031i
$87$	−2.76624			−0.296572
$88$	6.08681			0.648856
$89$	3.25521	−	5.63820i	0.345052	−	0.597647i	−0.640311	−	0.768116i	$-0.721195\pi$
$89$	3.25521	−	5.63820i	0.345052	−	0.597647i	0.985363	+	0.170468i	$0.0545280\pi$
$90$	0.145349	+	0.251751i	0.0153211	+	0.0265369i
$91$	−0.604952	+	1.04781i	−0.0634162	+	0.109840i
$92$	6.14145	+	10.6373i	0.640290	+	1.10901i
$93$	2.41550	+	4.18376i	0.250475	+	0.433836i
$94$	−3.22984			−0.333132
$95$	−1.88312	+	3.93114i	−0.193204	+	0.403326i
$96$	3.29392			0.336184
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−0.983028	−	1.70265i	−0.0993008	−	0.171994i
$99$	−2.67382	+	4.63119i	−0.268729	+	0.465452i
$100$	0.957748	+	1.65887i	0.0957748	+	0.165887i
$101$	−0.758324	+	1.31346i	−0.0754561	+	0.130694i	−0.901285	−	0.433228i	$-0.857375\pi$
$101$	−0.758324	+	1.31346i	−0.0754561	+	0.130694i	0.825828	+	0.563921i	$0.190708\pi$
$102$	−0.992907			−0.0983125
$103$	−9.15478			−0.902047			−0.451023	−	0.892512i	$-0.648941\pi$
$103$	−9.15478			−0.902047			−0.451023	+	0.892512i	$0.648941\pi$
$104$	1.41514	−	2.45109i	0.138766	−	0.240349i
$105$	−0.243287	+	0.421386i	−0.0237424	+	0.0411231i
$106$	−0.871155			−0.0846140
$107$	0.138936			0.0134315			0.00671574	−	0.999977i	$-0.497862\pi$
$107$	0.138936			0.0134315			0.00671574	+	0.999977i	$0.497862\pi$
$108$	−0.957748	+	1.65887i	−0.0921593	+	0.159625i
$109$	7.86497	+	13.6225i	0.753328	+	1.30480i	0.946201	+	0.323579i	$0.104886\pi$
$109$	7.86497	+	13.6225i	0.753328	+	1.30480i	−0.192873	+	0.981224i	$0.561781\pi$
$110$	0.777272	−	1.34627i	0.0741099	−	0.128362i
$111$	−3.15878	−	5.47117i	−0.299818	−	0.519301i
$112$	0.851533	+	1.47490i	0.0804623	+	0.139365i
$113$	14.8011			1.39237			0.696187	−	0.717860i	$-0.254878\pi$
$113$	14.8011			1.39237			0.696187	+	0.717860i	$0.254878\pi$
$114$	1.26338	−	0.0973074i	0.118326	−	0.00911367i
$115$	6.41238			0.597958
$116$	2.64936	+	4.58883i	0.245987	+	0.426062i
$117$	1.24329	+	2.15344i	0.114942	+	0.199085i
$118$	1.85075	−	3.20559i	0.170375	−	0.295099i
$119$	−0.830974	−	1.43929i	−0.0761752	−	0.131939i
$120$	0.569112	−	0.985730i	0.0519526	−	0.0899845i
$121$	17.5972			1.59975
$122$	−3.44617			−0.312002
$123$	1.29070	−	2.23555i	0.116378	−	0.201573i
$124$	4.62687	−	8.01397i	0.415505	−	0.719676i
$125$	1.00000			0.0894427
$126$	0.141446			0.0126010
$127$	4.91550	−	8.51389i	0.436180	−	0.755485i	−0.561211	−	0.827672i	$-0.689665\pi$
$127$	4.91550	−	8.51389i	0.436180	−	0.755485i	0.997391	+	0.0721871i	$0.0229979\pi$
$128$	−4.17222	−	7.22649i	−0.368775	−	0.638738i
$129$	−1.24329	+	2.15344i	−0.109465	+	0.189600i
$130$	−0.361420	−	0.625998i	−0.0316986	−	0.0549037i
$131$	−7.11459	−	12.3228i	−0.621605	−	1.07665i	−0.989187	−	0.146660i	$-0.953148\pi$
$131$	−7.11459	−	12.3228i	−0.621605	−	1.07665i	0.367582	−	0.929991i	$-0.380186\pi$
$132$	10.2434			0.891571
$133$	1.19839	+	1.74992i	0.103913	+	0.151737i
$134$	4.41145			0.381091
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	1.94386	+	3.36687i	0.166685	+	0.288707i
$137$	−3.29220	+	5.70225i	−0.281271	+	0.487176i	−0.971698	−	0.236226i	$-0.924089\pi$
$137$	−3.29220	+	5.70225i	−0.281271	+	0.487176i	0.690427	+	0.723402i	$0.257423\pi$
$138$	−0.932031	−	1.61433i	−0.0793398	−	0.137420i
$139$	−0.116878	+	0.202439i	−0.00991347	+	0.0171706i	−0.870940	−	0.491390i	$-0.836489\pi$
$139$	−0.116878	+	0.202439i	−0.00991347	+	0.0171706i	0.861026	+	0.508561i	$0.169822\pi$
$140$	0.932031			0.0787710
$141$	−11.1107			−0.935686
$142$	−1.44317	+	2.49965i	−0.121108	+	0.209766i
$143$	6.64865	−	11.5158i	0.555988	−	0.963000i
$144$	3.50011			0.291676
$145$	2.76624			0.229724
$146$	−1.60070	+	2.77250i	−0.132475	+	0.229453i
$147$	−3.38162	−	5.85714i	−0.278912	−	0.483089i
$148$	−6.05063	+	10.4800i	−0.497359	+	0.861451i
$149$	1.33650	+	2.31488i	0.109490	+	0.189642i	0.915564	−	0.402173i	$-0.131745\pi$
$149$	1.33650	+	2.31488i	0.109490	+	0.189642i	−0.806074	+	0.591815i	$0.798412\pi$
$150$	−0.145349	−	0.251751i	−0.0118677	−	0.0205554i
$151$	5.95266			0.484421			0.242210	−	0.970224i	$-0.422128\pi$
$151$	5.95266			0.484421			0.242210	+	0.970224i	$0.422128\pi$
$152$	−2.80334	−	4.09351i	−0.227381	−	0.332027i
$153$	−3.41561			−0.276135
$154$	−0.378201	−	0.655063i	−0.0304763	−	0.0527865i
$155$	−2.41550	−	4.18376i	−0.194017	−	0.336048i
$156$	2.38151	−	4.12490i	0.190673	−	0.330256i
$157$	3.60424	+	6.24273i	0.287650	+	0.498224i	0.973248	−	0.229756i	$-0.0737928\pi$
$157$	3.60424	+	6.24273i	0.287650	+	0.498224i	−0.685599	+	0.727980i	$0.740459\pi$
$158$	1.18208	−	2.04742i	0.0940411	−	0.162884i
$159$	−2.99678			−0.237660
$160$	−3.29392			−0.260407
$161$	1.56005	−	2.70209i	0.122949	−	0.212954i
$162$	0.145349	−	0.251751i	0.0114197	−	0.0197794i
$163$	14.1756			1.11032			0.555161	−	0.831743i	$-0.312657\pi$
$163$	14.1756			1.11032			0.555161	+	0.831743i	$0.312657\pi$
$164$	−4.94465			−0.386112
$165$	2.67382	−	4.63119i	0.208157	−	0.360538i
$166$	−0.851897	−	1.47553i	−0.0661201	−	0.114523i
$167$	−6.27817	+	10.8741i	−0.485819	+	0.841464i	−0.999867	−	0.0162977i	$-0.994812\pi$
$167$	−6.27817	+	10.8741i	−0.485819	+	0.841464i	0.514048	+	0.857762i	$0.328145\pi$
$168$	−0.276915	−	0.479631i	−0.0213645	−	0.0370044i
$169$	3.40847	+	5.90365i	0.262190	+	0.454127i
$170$	0.992907			0.0761525
$171$	4.34603	−	0.334738i	0.332349	−	0.0255981i
$172$	4.76302			0.363177
$173$	−1.09482	−	1.89628i	−0.0832376	−	0.144172i	0.821401	−	0.570351i	$-0.193193\pi$
$173$	−1.09482	−	1.89628i	−0.0832376	−	0.144172i	−0.904639	+	0.426179i	$0.859859\pi$
$174$	−0.402070	−	0.696405i	−0.0304808	−	0.0527943i
$175$	0.243287	−	0.421386i	0.0183908	−	0.0318538i
$176$	−9.35867	−	16.2097i	−0.705436	−	1.22185i
$177$	6.36659	−	11.0273i	0.478542	−	0.828859i
$178$	1.89256			0.141854
$179$	7.50421			0.560891			0.280445	−	0.959870i	$-0.409518\pi$
$179$	7.50421			0.560891			0.280445	+	0.959870i	$0.409518\pi$
$180$	0.957748	−	1.65887i	0.0713863	−	0.123645i
$181$	6.33260	−	10.9684i	0.470699	−	0.815274i	−0.528740	−	0.848784i	$-0.677335\pi$
$181$	6.33260	−	10.9684i	0.470699	−	0.815274i	0.999438	+	0.0335101i	$0.0106686\pi$
$182$	−0.351716			−0.0260709
$183$	−11.8548			−0.876335
$184$	−3.64936	+	6.32088i	−0.269035	+	0.465982i
$185$	3.15878	+	5.47117i	0.232238	+	0.402249i
$186$	−0.702178	+	1.21621i	−0.0514862	+	0.0891767i
$187$	9.13272	+	15.8183i	0.667850	+	1.15675i
$188$	10.6412	+	18.4311i	0.776090	+	1.34423i
$189$	0.486575			0.0353931
$190$	−1.26338	+	0.0973074i	−0.0916551	+	0.00705942i
$191$	8.15777			0.590276			0.295138	−	0.955455i	$-0.404634\pi$
$191$	8.15777			0.590276			0.295138	+	0.955455i	$0.404634\pi$
$192$	−3.02135	−	5.23312i	−0.218047	−	0.377668i
$193$	1.68252	+	2.91422i	0.121111	+	0.209770i	0.920206	−	0.391435i	$-0.128021\pi$
$193$	1.68252	+	2.91422i	0.121111	+	0.209770i	−0.799095	+	0.601204i	$0.794688\pi$
$194$	0.290697	−	0.503502i	0.0208708	−	0.0361494i
$195$	−1.24329	−	2.15344i	−0.0890336	−	0.154211i
$196$	−6.47748	+	11.2193i	−0.462677	+	0.801381i
$197$	3.83399			0.273160			0.136580	−	0.990629i	$-0.456389\pi$
$197$	3.83399			0.273160			0.136580	+	0.990629i	$0.456389\pi$
$198$	−1.55454			−0.110477
$199$	−6.34925	+	10.9972i	−0.450086	+	0.779572i	−0.998391	−	0.0567063i	$-0.981940\pi$
$199$	−6.34925	+	10.9972i	−0.450086	+	0.779572i	0.548305	+	0.836279i	$0.315273\pi$
$200$	−0.569112	+	0.985730i	−0.0402423	+	0.0697017i
$201$	15.1754			1.07039
$202$	−0.440885			−0.0310206
$203$	0.672992	−	1.16566i	0.0472348	−	0.0818130i
$204$	3.27129	+	5.66604i	0.229036	+	0.396702i
$205$	−1.29070	+	2.23555i	−0.0901462	+	0.156138i
$206$	−1.33063	−	2.30473i	−0.0927097	−	0.160578i
$207$	−3.20619	−	5.55329i	−0.222846	−	0.385980i
$208$	−8.70329			−0.603465
$209$	−13.1707	−	19.2323i	−0.911038	−	1.33032i
$210$	−0.141446			−0.00976069
$211$	4.57828	+	7.92982i	0.315182	+	0.545911i	0.979476	−	0.201560i	$-0.0646011\pi$
$211$	4.57828	+	7.92982i	0.315182	+	0.545911i	−0.664294	+	0.747471i	$0.731268\pi$
$212$	2.87016	+	4.97126i	0.197123	+	0.341427i
$213$	−4.96452	+	8.59879i	−0.340163	+	0.589180i
$214$	0.0201942	+	0.0349774i	0.00138045	+	0.00239100i
$215$	1.24329	−	2.15344i	0.0847915	−	0.146863i
$216$	−1.13822			−0.0774463
$217$	−2.35064			−0.159572
$218$	−2.28633	+	3.96003i	−0.154850	+	0.268207i
$219$	−5.50642	+	9.53740i	−0.372089	+	0.644478i
$220$	−10.2434			−0.690608
$221$	8.49316			0.571312
$222$	0.918249	−	1.59045i	0.0616288	−	0.106744i
$223$	−5.44877	−	9.43754i	−0.364876	−	0.631984i	0.623880	−	0.781520i	$-0.285555\pi$
$223$	−5.44877	−	9.43754i	−0.364876	−	0.631984i	−0.988756	+	0.149536i	$0.952222\pi$
$224$	−0.801369	+	1.38801i	−0.0535437	+	0.0927404i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	2.15133	+	3.72620i	0.143104	+	0.247863i
$227$	−24.6351			−1.63509			−0.817545	−	0.575864i	$-0.804666\pi$
$227$	−24.6351			−1.63509			−0.817545	+	0.575864i	$0.804666\pi$
$228$	−4.71768	−	6.88889i	−0.312436	−	0.456228i
$229$	17.1676			1.13447			0.567234	−	0.823557i	$-0.308013\pi$
$229$	17.1676			1.13447			0.567234	+	0.823557i	$0.308013\pi$
$230$	0.932031	+	1.61433i	0.0614563	+	0.106445i
$231$	−1.30101	−	2.25342i	−0.0856003	−	0.148264i
$232$	−1.57430	+	2.72677i	−0.103358	+	0.179021i
$233$	−14.2316	−	24.6498i	−0.932341	−	1.61486i	−0.779309	−	0.626640i	$-0.784430\pi$
$233$	−14.2316	−	24.6498i	−0.932341	−	1.61486i	−0.153032	−	0.988221i	$-0.548904\pi$
$234$	−0.361420	+	0.625998i	−0.0236268	+	0.0409228i
$235$	11.1107			0.724780
$236$	−24.3903			−1.58768
$237$	4.06636	−	7.04314i	0.264138	−	0.457501i
$238$	0.241562	−	0.418397i	0.0156581	−	0.0271207i
$239$	4.07741			0.263746			0.131873	−	0.991267i	$-0.457901\pi$
$239$	4.07741			0.263746			0.131873	+	0.991267i	$0.457901\pi$
$240$	−3.50011			−0.225931
$241$	6.33421	−	10.9712i	0.408023	−	0.706716i	−0.586646	−	0.809844i	$-0.699552\pi$
$241$	6.33421	−	10.9712i	0.408023	−	0.706716i	0.994668	+	0.103128i	$0.0328852\pi$
$242$	2.55773	+	4.43012i	0.164417	+	0.284779i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	11.3539	+	19.6656i	0.726862	+	1.25896i
$245$	3.38162	+	5.85714i	0.216044	+	0.374199i
$246$	0.750404			0.0478440
$247$	−10.8067	+	0.832351i	−0.687615	+	0.0529612i
$248$	5.49875			0.349171
$249$	−2.93053	−	5.07583i	−0.185715	−	0.321668i
$250$	0.145349	+	0.251751i	0.00919265	+	0.0159221i
$251$	5.81204	−	10.0668i	0.366853	−	0.635408i	−0.622219	−	0.782843i	$-0.713769\pi$
$251$	5.81204	−	10.0668i	0.366853	−	0.635408i	0.989072	+	0.147436i	$0.0471019\pi$
$252$	−0.466016	−	0.807163i	−0.0293562	−	0.0508465i
$253$	−17.1456	+	29.6970i	−1.07793	+	1.86703i
$254$	2.85784			0.179317
$255$	3.41561			0.213894
$256$	−4.82984	+	8.36553i	−0.301865	+	0.522845i
$257$	−5.27416	+	9.13512i	−0.328993	+	0.569833i	−0.982312	−	0.187250i	$-0.940043\pi$
$257$	−5.27416	+	9.13512i	−0.328993	+	0.569833i	0.653319	+	0.757083i	$0.273376\pi$
$258$	−0.722840			−0.0450021
$259$	3.07397			0.191007
$260$	−2.38151	+	4.12490i	−0.147695	+	0.255815i
$261$	−1.38312	−	2.39564i	−0.0856131	−	0.148286i
$262$	2.06819	−	3.58221i	0.127773	−	0.221310i
$263$	−11.8967	−	20.6058i	−0.733585	−	1.27061i	−0.955341	−	0.295504i	$-0.904512\pi$
$263$	−11.8967	−	20.6058i	−0.733585	−	1.27061i	0.221757	−	0.975102i	$-0.428821\pi$
$264$	3.04340	+	5.27133i	0.187309	+	0.324428i
$265$	2.99678			0.184091
$266$	−0.266360	+	0.556043i	−0.0163316	+	0.0340932i
$267$	6.51043			0.398432
$268$	−14.5342	−	25.1740i	−0.887818	−	1.53775i
$269$	2.11377	+	3.66115i	0.128879	+	0.223224i	0.923242	−	0.384218i	$-0.125529\pi$
$269$	2.11377	+	3.66115i	0.128879	+	0.223224i	−0.794364	+	0.607442i	$0.792196\pi$
$270$	−0.145349	+	0.251751i	−0.00884563	+	0.0153211i
$271$	−15.5736	−	26.9742i	−0.946027	−	1.63857i	−0.753682	−	0.657239i	$-0.771724\pi$
$271$	−15.5736	−	26.9742i	−0.946027	−	1.63857i	−0.192344	−	0.981328i	$-0.561609\pi$
$272$	5.97750	−	10.3533i	0.362439	−	0.627763i
$273$	−1.20990			−0.0732267
$274$	−1.91406			−0.115633
$275$	−2.67382	+	4.63119i	−0.161237	+	0.279271i
$276$	−6.14145	+	10.6373i	−0.369672	+	0.640290i
$277$	1.05393			0.0633243			0.0316621	−	0.999499i	$-0.489920\pi$
$277$	1.05393			0.0633243			0.0316621	+	0.999499i	$0.489920\pi$
$278$	−0.0679523			−0.00407551
$279$	−2.41550	+	4.18376i	−0.144612	+	0.250475i
$280$	0.276915	+	0.479631i	0.0165489	+	0.0286635i
$281$	−12.8177	+	22.2009i	−0.764638	+	1.32439i	0.175799	+	0.984426i	$0.443749\pi$
$281$	−12.8177	+	22.2009i	−0.764638	+	1.32439i	−0.940437	+	0.339967i	$0.889584\pi$
$282$	−1.61492	−	2.79712i	−0.0961670	−	0.166566i
$283$	−14.7056	−	25.4708i	−0.874157	−	1.51408i	−0.857658	−	0.514220i	$-0.828082\pi$
$283$	−14.7056	−	25.4708i	−0.874157	−	1.51408i	−0.0164983	−	0.999864i	$-0.505252\pi$
$284$	19.0190			1.12857
$285$	−4.34603	+	0.334738i	−0.257436	+	0.0198282i
$286$	3.86549			0.228571
$287$	0.628020	+	1.08776i	0.0370709	+	0.0642086i
$288$	1.64696	+	2.85262i	0.0970480	+	0.168092i
$289$	2.66681	−	4.61906i	0.156871	−	0.271709i
$290$	0.402070	+	0.696405i	0.0236103	+	0.0408943i
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	21.0950			1.23449
$293$	−10.8548			−0.634147			−0.317073	−	0.948401i	$-0.602700\pi$
$293$	−10.8548			−0.634147			−0.317073	+	0.948401i	$0.602700\pi$
$294$	0.983028	−	1.70265i	0.0573314	−	0.0993008i
$295$	−6.36659	+	11.0273i	−0.370677	+	0.642031i
$296$	−7.19080			−0.417957
$297$	−5.34764			−0.310301
$298$	−0.388516	+	0.672929i	−0.0225061	+	0.0389817i
$299$	7.97244	+	13.8087i	0.461058	+	0.798576i
$300$	−0.957748	+	1.65887i	−0.0552956	+	0.0957748i
$301$	−0.604952	−	1.04781i	−0.0348688	−	0.0603946i
$302$	0.865211	+	1.49859i	0.0497873	+	0.0862341i
$303$	−1.51665			−0.0871291
$304$	−6.59114	+	13.7594i	−0.378028	+	0.789157i
$305$	11.8548			0.678806
$306$	−0.496454	−	0.859883i	−0.0283804	−	0.0491562i
$307$	−16.8445	−	29.1756i	−0.961368	−	1.66514i	−0.719072	−	0.694936i	$-0.755433\pi$
$307$	−16.8445	−	29.1756i	−0.961368	−	1.66514i	−0.242296	−	0.970202i	$-0.577901\pi$
$308$	−2.49208	+	4.31641i	−0.142000	+	0.245950i
$309$	−4.57739	−	7.92827i	−0.260399	−	0.451023i
$310$	0.702178	−	1.21621i	0.0398810	−	0.0690759i
$311$	−11.7221			−0.664701			−0.332350	−	0.943156i	$-0.607842\pi$
$311$	−11.7221			−0.664701			−0.332350	+	0.943156i	$0.607842\pi$
$312$	2.83028			0.160233
$313$	−2.23928	+	3.87855i	−0.126572	+	0.219229i	−0.922346	−	0.386364i	$-0.873731\pi$
$313$	−2.23928	+	3.87855i	−0.126572	+	0.219229i	0.795775	+	0.605593i	$0.207064\pi$
$314$	−1.04774	+	1.81474i	−0.0591275	+	0.102412i
$315$	−0.486575			−0.0274154
$316$	−15.5782			−0.876341
$317$	−6.19367	+	10.7277i	−0.347871	+	0.602530i	−0.985871	−	0.167506i	$-0.946429\pi$
$317$	−6.19367	+	10.7277i	−0.347871	+	0.602530i	0.638000	+	0.770036i	$0.279762\pi$
$318$	−0.435577	−	0.754442i	−0.0244260	−	0.0423070i
$319$	−7.39644	+	12.8110i	−0.414121	+	0.717278i
$320$	3.02135	+	5.23312i	0.168898	+	0.292541i
$321$	0.0694682	+	0.120322i	0.00387733	+	0.00671574i
$322$	0.907005			0.0505454
$323$	6.43200	−	13.4272i	0.357886	−	0.747111i
$324$	−1.91550			−0.106416
$325$	1.24329	+	2.15344i	0.0689652	+	0.119451i
$326$	2.06041	+	3.56873i	0.114115	+	0.197654i
$327$	−7.86497	+	13.6225i	−0.434934	+	0.753328i
$328$	−1.46910	−	2.54456i	−0.0811176	−	0.140500i
$329$	2.70308	−	4.68188i	0.149026	−	0.258120i
$330$	1.55454			0.0855748
$331$	24.5058			1.34696			0.673480	−	0.739206i	$-0.264799\pi$
$331$	24.5058			1.34696			0.673480	+	0.739206i	$0.264799\pi$
$332$	−5.61342	+	9.72273i	−0.308076	+	0.533604i
$333$	3.15878	−	5.47117i	0.173100	−	0.299818i
$334$	−3.65009			−0.199724
$335$	−15.1754			−0.829121
$336$	−0.851533	+	1.47490i	−0.0464549	+	0.0804623i
$337$	−5.25038	−	9.09392i	−0.286006	−	0.495378i	0.686846	−	0.726803i	$-0.258995\pi$
$337$	−5.25038	−	9.09392i	−0.286006	−	0.495378i	−0.972853	+	0.231425i	$0.925661\pi$
$338$	−0.990834	+	1.71617i	−0.0538942	+	0.0933476i
$339$	7.40057	+	12.8182i	0.401944	+	0.696187i
$340$	−3.27129	−	5.66604i	−0.177411	−	0.307284i
$341$	25.8344			1.39901
$342$	0.715960	+	1.04546i	0.0387147	+	0.0565322i
$343$	6.69684			0.361596
$344$	1.41514	+	2.45109i	0.0762992	+	0.132154i
$345$	3.20619	+	5.55329i	0.172616	+	0.298979i
$346$	0.318261	−	0.551244i	0.0171098	−	0.0296351i
$347$	0.727562	+	1.26017i	0.0390576	+	0.0676497i	0.884893	−	0.465794i	$-0.154231\pi$
$347$	0.727562	+	1.26017i	0.0390576	+	0.0676497i	−0.845836	+	0.533443i	$0.820898\pi$
$348$	−2.64936	+	4.58883i	−0.142021	+	0.245987i
$349$	23.7332			1.27041			0.635204	−	0.772345i	$-0.280916\pi$
$349$	23.7332			1.27041			0.635204	+	0.772345i	$0.280916\pi$
$350$	0.141446			0.00756060
$351$	−1.24329	+	2.15344i	−0.0663618	+	0.114942i
$352$	8.80735	−	15.2548i	0.469433	−	0.813082i
$353$	−7.39055			−0.393359			−0.196680	−	0.980468i	$-0.563016\pi$
$353$	−7.39055			−0.393359			−0.196680	+	0.980468i	$0.563016\pi$
$354$	3.70150			0.196732
$355$	4.96452	−	8.59879i	0.263489	−	0.456377i
$356$	−6.23535	−	10.7999i	−0.330473	−	0.572395i
$357$	0.830974	−	1.43929i	0.0439798	−	0.0761752i
$358$	1.09073	+	1.88919i	0.0576467	+	0.0998469i
$359$	−1.17934	−	2.04268i	−0.0622433	−	0.107808i	0.833225	−	0.552935i	$-0.186492\pi$
$359$	−1.17934	−	2.04268i	−0.0622433	−	0.107808i	−0.895468	+	0.445126i	$0.853159\pi$
$360$	1.13822			0.0599896
$361$	−6.86820	+	17.7152i	−0.361484	+	0.932378i
$362$	3.68174			0.193508
$363$	8.79862	+	15.2397i	0.461808	+	0.799874i
$364$	1.15878	+	2.00707i	0.0607367	+	0.105199i
$365$	5.50642	−	9.53740i	0.288219	−	0.499210i
$366$	−1.72308	−	2.98447i	−0.0900671	−	0.156001i
$367$	11.0743	−	19.1812i	0.578073	−	1.00125i	−0.417628	−	0.908618i	$-0.637138\pi$
$367$	11.0743	−	19.1812i	0.578073	−	1.00125i	0.995700	−	0.0926329i	$-0.0295283\pi$
$368$	22.4441			1.16998
$369$	2.58139			0.134382
$370$	−0.918249	+	1.59045i	−0.0477375	+	0.0826838i
$371$	0.729078	−	1.26280i	0.0378518	−	0.0655613i
$372$	9.25374			0.479784
$373$	31.1738			1.61412			0.807060	−	0.590469i	$-0.201057\pi$
$373$	31.1738			1.61412			0.807060	+	0.590469i	$0.201057\pi$
$374$	−2.65485	+	4.59834i	−0.137279	+	0.237775i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−6.32321	+	10.9521i	−0.326094	+	0.564812i
$377$	3.43924	+	5.95693i	0.177130	+	0.306798i
$378$	0.0707229	+	0.122496i	0.00363759	+	0.00630050i
$379$	−26.0349			−1.33732			−0.668662	−	0.743567i	$-0.733132\pi$
$379$	−26.0349			−1.33732			−0.668662	+	0.743567i	$0.733132\pi$
$380$	4.71768	+	6.88889i	0.242012	+	0.353393i
$381$	9.83099			0.503657
$382$	1.18572	+	2.05373i	0.0606668	+	0.105078i
$383$	1.06647	+	1.84718i	0.0544941	+	0.0943865i	0.891986	−	0.452064i	$-0.149312\pi$
$383$	1.06647	+	1.84718i	0.0544941	+	0.0943865i	−0.837492	+	0.546450i	$0.815979\pi$
$384$	4.17222	−	7.22649i	0.212913	−	0.368775i
$385$	1.30101	+	2.25342i	0.0663057	+	0.114845i
$386$	−0.489105	+	0.847154i	−0.0248948	+	0.0431190i
$387$	−2.48657			−0.126400
$388$	−3.83099			−0.194489
$389$	6.52135	−	11.2953i	0.330645	−	0.572695i	−0.651993	−	0.758225i	$-0.726067\pi$
$389$	6.52135	−	11.2953i	0.330645	−	0.572695i	0.982639	+	0.185530i	$0.0594003\pi$
$390$	0.361420	−	0.625998i	0.0183012	−	0.0316986i
$391$	−21.9022			−1.10764
$392$	−7.69808			−0.388812
$393$	7.11459	−	12.3228i	0.358884	−	0.621605i
$394$	0.557265	+	0.965211i	0.0280746	+	0.0486266i
$395$	−4.06636	+	7.04314i	−0.204601	+	0.354379i
$396$	5.12169	+	8.87102i	0.257374	+	0.445786i
$397$	−0.0143214	−	0.0248054i	−0.000718770	−	0.00124495i	0.865666	−	0.500622i	$-0.166895\pi$
$397$	−0.0143214	−	0.0248054i	−0.000718770	−	0.00124495i	−0.866385	+	0.499377i	$0.833562\pi$
$398$	−3.69142			−0.185034
$399$	−0.916279	+	1.91279i	−0.0458713	+	0.0957594i
$400$	3.50011			0.175006
$401$	13.6596	+	23.6591i	0.682126	+	1.18148i	0.974331	+	0.225122i	$0.0722779\pi$
$401$	13.6596	+	23.6591i	0.682126	+	1.18148i	−0.292204	+	0.956356i	$0.594389\pi$
$402$	2.20572	+	3.82043i	0.110012	+	0.190546i
$403$	6.00631	−	10.4032i	0.299196	−	0.518222i
$404$	1.45257	+	2.51592i	0.0722679	+	0.125172i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	0.391274			0.0194186
$407$	−33.7841			−1.67461
$408$	−1.94386	+	3.36687i	−0.0962355	+	0.166685i
$409$	3.36958	−	5.83629i	0.166615	−	0.288586i	−0.770612	−	0.637304i	$-0.780050\pi$
$409$	3.36958	−	5.83629i	0.166615	−	0.288586i	0.937228	+	0.348718i	$0.113383\pi$
$410$	−0.750404			−0.0370598
$411$	−6.58439			−0.324784
$412$	−8.76796	+	15.1866i	−0.431967	+	0.748188i
$413$	3.09782	+	5.36558i	0.152434	+	0.264023i
$414$	0.932031	−	1.61433i	0.0458068	−	0.0793398i
$415$	2.93053	+	5.07583i	0.143854	+	0.249163i
$416$	−4.09529	−	7.09325i	−0.200788	−	0.347775i
$417$	−0.233756			−0.0114471
$418$	2.92739	−	6.11113i	0.143184	−	0.298905i
$419$	26.4076			1.29010			0.645048	−	0.764142i	$-0.276837\pi$
$419$	26.4076			1.29010			0.645048	+	0.764142i	$0.276837\pi$
$420$	0.466016	+	0.807163i	0.0227392	+	0.0393855i
$421$	−18.9448	−	32.8133i	−0.923311	−	1.59922i	−0.794255	−	0.607584i	$-0.792139\pi$
$421$	−18.9448	−	32.8133i	−0.923311	−	1.59922i	−0.129056	−	0.991637i	$-0.541195\pi$
$422$	−1.33089	+	2.30518i	−0.0647869	+	0.112214i
$423$	−5.55533	−	9.62211i	−0.270109	−	0.467843i
$424$	−1.70550	+	2.95401i	−0.0828265	+	0.143460i
$425$	−3.41561			−0.165681
$426$	−2.88634			−0.139844
$427$	2.88413	−	4.99546i	0.139573	−	0.241747i
$428$	0.133066	−	0.230477i	0.00643198	−	0.0111405i
$429$	13.2973			0.642000
$430$	0.722840			0.0348585
$431$	9.60285	−	16.6326i	0.462553	−	0.801165i	−0.536534	−	0.843879i	$-0.680267\pi$
$431$	9.60285	−	16.6326i	0.462553	−	0.801165i	0.999087	+	0.0427131i	$0.0136001\pi$
$432$	1.75006	+	3.03119i	0.0841996	+	0.145838i
$433$	−8.47562	+	14.6802i	−0.407312	+	0.705485i	−0.994588	−	0.103902i	$-0.966867\pi$
$433$	−8.47562	+	14.6802i	−0.407312	+	0.705485i	0.587275	+	0.809387i	$0.300201\pi$
$434$	−0.341662	−	0.591776i	−0.0164003	−	0.0284061i
$435$	1.38312	+	2.39564i	0.0663156	+	0.114862i
$436$	30.1306			1.44300
$437$	27.8684	−	2.14647i	1.33313	−	0.102680i
$438$	−3.20140			−0.152969
$439$	−5.55143	−	9.61536i	−0.264955	−	0.458916i	0.702597	−	0.711588i	$-0.252024\pi$
$439$	−5.55143	−	9.61536i	−0.264955	−	0.458916i	−0.967552	+	0.252672i	$0.918691\pi$
$440$	−3.04340	−	5.27133i	−0.145089	−	0.251301i
$441$	3.38162	−	5.85714i	0.161030	−	0.278912i
$442$	1.23447	+	2.13816i	0.0587177	+	0.101702i
$443$	6.94708	−	12.0327i	0.330066	−	0.571691i	−0.652459	−	0.757824i	$-0.726262\pi$
$443$	6.94708	−	12.0327i	0.330066	−	0.571691i	0.982524	+	0.186133i	$0.0595957\pi$
$444$	−12.1013			−0.574301
$445$	−6.51043			−0.308624
$446$	1.58394	−	2.74347i	0.0750018	−	0.129907i
$447$	−1.33650	+	2.31488i	−0.0632141	+	0.109490i
$448$	2.94022			0.138912
$449$	27.8675			1.31515			0.657573	−	0.753391i	$-0.271583\pi$
$449$	27.8675			1.31515			0.657573	+	0.753391i	$0.271583\pi$
$450$	0.145349	−	0.251751i	0.00685180	−	0.0118677i
$451$	−6.90218	−	11.9549i	−0.325011	−	0.562936i
$452$	14.1758	−	24.5531i	0.666772	−	1.15488i
$453$	2.97633	+	5.15516i	0.139840	+	0.242210i
$454$	−3.58068	−	6.20192i	−0.168050	−	0.291071i
$455$	1.20990			0.0567212
$456$	2.14341	−	4.47451i	0.100375	−	0.209538i
$457$	−36.5660			−1.71048			−0.855242	−	0.518229i	$-0.826591\pi$
$457$	−36.5660			−1.71048			−0.855242	+	0.518229i	$0.826591\pi$
$458$	2.49529	+	4.32197i	0.116597	+	0.201952i
$459$	−1.70780	−	2.95800i	−0.0797134	−	0.138068i
$460$	6.14145	−	10.6373i	0.286346	−	0.495966i
$461$	−10.9590	−	18.9816i	−0.510412	−	0.884059i	−0.999927	−	0.0120646i	$-0.996160\pi$
$461$	−10.9590	−	18.9816i	−0.510412	−	0.884059i	0.489515	−	0.871995i	$-0.337174\pi$
$462$	0.378201	−	0.655063i	0.0175955	−	0.0304763i
$463$	−14.0255			−0.651821			−0.325910	−	0.945401i	$-0.605671\pi$
$463$	−14.0255			−0.651821			−0.325910	+	0.945401i	$0.605671\pi$
$464$	9.68216			0.449483
$465$	2.41550	−	4.18376i	0.112016	−	0.194017i
$466$	4.13707	−	7.16562i	0.191646	−	0.331941i
$467$	33.9294			1.57007			0.785033	−	0.619453i	$-0.212646\pi$
$467$	33.9294			1.57007			0.785033	+	0.619453i	$0.212646\pi$
$468$	4.76302			0.220171
$469$	−3.69198	+	6.39470i	−0.170480	+	0.295280i
$470$	1.61492	+	2.79712i	0.0744906	+	0.129022i
$471$	−3.60424	+	6.24273i	−0.166075	+	0.287650i
$472$	−7.24660	−	12.5515i	−0.333552	−	0.577728i
$473$	6.64865	+	11.5158i	0.305705	+	0.529497i
$474$	2.36416			0.108589
$475$	4.34603	−	0.334738i	0.199409	−	0.0153588i
$476$	−3.18345			−0.145913
$477$	−1.49839	−	2.59529i	−0.0686065	−	0.118830i
$478$	0.592646	+	1.02649i	0.0271070	+	0.0469507i
$479$	−15.9748	+	27.6692i	−0.729909	+	1.26424i	0.227012	+	0.973892i	$0.427104\pi$
$479$	−15.9748	+	27.6692i	−0.729909	+	1.26424i	−0.956921	+	0.290348i	$0.906229\pi$
$480$	−1.64696	−	2.85262i	−0.0751731	−	0.130204i
$481$	−7.85455	+	13.6045i	−0.358137	+	0.620311i
$482$	3.68268			0.167741
$483$	3.12010			0.141970
$484$	16.8537	−	29.1915i	0.766078	−	1.32689i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	0.290697			0.0131863
$487$	37.6229			1.70486			0.852428	−	0.522844i	$-0.175129\pi$
$487$	37.6229			1.70486			0.852428	+	0.522844i	$0.175129\pi$
$488$	−6.74673	+	11.6857i	−0.305410	+	0.528986i
$489$	7.08781	+	12.2765i	0.320522	+	0.555161i
$490$	−0.983028	+	1.70265i	−0.0444087	+	0.0769181i
$491$	20.0421	+	34.7139i	0.904487	+	1.56662i	0.821604	+	0.570059i	$0.193080\pi$
$491$	20.0421	+	34.7139i	0.904487	+	1.56662i	0.0828838	+	0.996559i	$0.473587\pi$
$492$	−2.47232	−	4.28219i	−0.111461	−	0.193056i
$493$	−9.44840			−0.425535
$494$	−1.78029	−	2.59962i	−0.0800989	−	0.116963i
$495$	5.34764			0.240358
$496$	−8.45450	−	14.6436i	−0.379618	−	0.657518i
$497$	−2.41561	−	4.18395i	−0.108355	−	0.187676i
$498$	0.851897	−	1.47553i	0.0381744	−	0.0661201i
$499$	15.1533	+	26.2464i	0.678357	+	1.17495i	0.975475	+	0.220108i	$0.0706410\pi$
$499$	15.1533	+	26.2464i	0.678357	+	1.17495i	−0.297118	+	0.954841i	$0.596026\pi$
$500$	0.957748	−	1.65887i	0.0428318	−	0.0741868i
$501$	−12.5563			−0.560976
$502$	3.37909			0.150816
$503$	8.64393	−	14.9717i	0.385414	−	0.667556i	−0.606413	−	0.795150i	$-0.707392\pi$
$503$	8.64393	−	14.9717i	0.385414	−	0.667556i	0.991827	+	0.127594i	$0.0407254\pi$
$504$	0.276915	−	0.479631i	0.0123348	−	0.0213645i
$505$	1.51665			0.0674899
$506$	−9.96833			−0.443146
$507$	−3.40847	+	5.90365i	−0.151376	+	0.262190i
$508$	−9.41561	−	16.3083i	−0.417750	−	0.723564i
$509$	−2.80412	+	4.85688i	−0.124291	+	0.215278i	−0.921455	−	0.388484i	$-0.872999\pi$
$509$	−2.80412	+	4.85688i	−0.124291	+	0.215278i	0.797165	+	0.603762i	$0.206332\pi$
$510$	0.496454	+	0.859883i	0.0219833	+	0.0380763i
$511$	−2.67928	−	4.64066i	−0.118525	−	0.205291i
$512$	−19.4969			−0.861650
$513$	2.46291	+	3.59640i	0.108740	+	0.158785i
$514$	−3.06637			−0.135252
$515$	4.57739	+	7.92827i	0.201704	+	0.349361i
$516$	2.38151	+	4.12490i	0.104840	+	0.181588i
$517$	−29.7079	+	51.4556i	−1.30655	+	2.26301i
$518$	0.446797	+	0.773874i	0.0196311	+	0.0340021i
$519$	1.09482	−	1.89628i	0.0480573	−	0.0832376i
$520$	−2.83028			−0.124116
$521$	13.7128			0.600767			0.300384	−	0.953818i	$-0.402885\pi$
$521$	13.7128			0.600767			0.300384	+	0.953818i	$0.402885\pi$
$522$	0.402070	−	0.696405i	0.0175981	−	0.0304808i
$523$	17.6171	−	30.5137i	0.770341	−	1.33427i	−0.167035	−	0.985951i	$-0.553419\pi$
$523$	17.6171	−	30.5137i	0.770341	−	1.33427i	0.937376	−	0.348319i	$-0.113247\pi$
$524$	−27.2559			−1.19068
$525$	0.486575			0.0212359
$526$	3.45835	−	5.99004i	0.150791	−	0.261178i
$527$	8.25038	+	14.2901i	0.359392	+	0.622486i
$528$	9.35867	−	16.2097i	0.407284	−	0.705436i
$529$	−9.05934	−	15.6912i	−0.393884	−	0.682228i
$530$	0.435577	+	0.754442i	0.0189203	+	0.0327709i
$531$	12.7332			0.552573
$532$	4.05063	−	0.311986i	0.175617	−	0.0135263i
$533$	−6.41883			−0.278030
$534$	0.946281	+	1.63901i	0.0409496	+	0.0709268i
$535$	−0.0694682	−	0.120322i	−0.00300337	−	0.00520199i
$536$	8.63650	−	14.9589i	0.373040	−	0.646124i
$537$	3.75210	+	6.49883i	0.161915	+	0.280445i
$538$	−0.614466	+	1.06429i	−0.0264915	+	0.0458847i
$539$	−36.1674			−1.55784
$540$	1.91550			0.0824298
$541$	−15.1179	+	26.1849i	−0.649968	+	1.12578i	0.333162	+	0.942869i	$0.391884\pi$
$541$	−15.1179	+	26.1849i	−0.649968	+	1.12578i	−0.983130	+	0.182908i	$0.941449\pi$
$542$	4.52719	−	7.84133i	0.194460	−	0.336814i
$543$	12.6652			0.543516
$544$	11.2507			0.482371
$545$	7.86497	−	13.6225i	0.336899	−	0.583525i
$546$	−0.175858	−	0.304595i	−0.00752602	−	0.0130354i
$547$	−17.4766	+	30.2703i	−0.747244	+	1.29426i	0.201895	+	0.979407i	$0.435290\pi$
$547$	−17.4766	+	30.2703i	−0.747244	+	1.29426i	−0.949139	+	0.314858i	$0.898043\pi$
$548$	6.30619	+	10.9226i	0.269387	+	0.466592i
$549$	−5.92742	−	10.2666i	−0.252976	−	0.438168i
$550$	−1.55454			−0.0662860
$551$	12.0222	−	0.925967i	0.512162	−	0.0394475i
$552$	−7.29873			−0.310654
$553$	1.97859	+	3.42701i	0.0841380	+	0.145731i
$554$	0.153187	+	0.265327i	0.00650828	+	0.0112727i
$555$	−3.15878	+	5.47117i	−0.134083	+	0.232238i
$556$	0.223879	+	0.387771i	0.00949460	+	0.0164451i
$557$	−1.58139	+	2.73906i	−0.0670058	+	0.116058i	−0.897582	−	0.440848i	$-0.854678\pi$
$557$	−1.58139	+	2.73906i	−0.0670058	+	0.116058i	0.830576	+	0.556905i	$0.188011\pi$
$558$	−1.40436			−0.0594511
$559$	6.18305			0.261515
$560$	0.851533	−	1.47490i	0.0359838	−	0.0623258i
$561$	−9.13272	+	15.8183i	−0.385584	+	0.667850i
$562$	−7.45213			−0.314349
$563$	−29.0570			−1.22460			−0.612302	−	0.790624i	$-0.709756\pi$
$563$	−29.0570			−1.22460			−0.612302	+	0.790624i	$0.709756\pi$
$564$	−10.6412	+	18.4311i	−0.448076	+	0.776090i
$565$	−7.40057	−	12.8182i	−0.311344	−	0.539264i
$566$	4.27487	−	7.40430i	0.179686	−	0.311226i
$567$	0.243287	+	0.421386i	0.0102171	+	0.0176965i
$568$	5.65073	+	9.78735i	0.237099	+	0.410668i
$569$	−31.3398			−1.31383			−0.656916	−	0.753964i	$-0.728139\pi$
$569$	−31.3398			−1.31383			−0.656916	+	0.753964i	$0.728139\pi$
$570$	−0.715960	−	1.04546i	−0.0299882	−	0.0437897i
$571$	2.56556			0.107365			0.0536827	−	0.998558i	$-0.482904\pi$
$571$	2.56556			0.107365			0.0536827	+	0.998558i	$0.482904\pi$
$572$	−12.7355	−	22.0585i	−0.532496	−	0.922311i
$573$	4.07889	+	7.06484i	0.170398	+	0.295138i
$574$	−0.182564	+	0.316210i	−0.00762006	+	0.0131983i
$575$	−3.20619	−	5.55329i	−0.133707	−	0.231588i
$576$	3.02135	−	5.23312i	0.125889	−	0.218047i
$577$	3.12153			0.129951			0.0649755	−	0.997887i	$-0.479303\pi$
$577$	3.12153			0.129951			0.0649755	+	0.997887i	$0.479303\pi$
$578$	1.55047			0.0644911
$579$	−1.68252	+	2.91422i	−0.0699233	+	0.121111i
$580$	2.64936	−	4.58883i	0.110009	−	0.190541i
$581$	2.85184			0.118314
$582$	0.581394			0.0240996
$583$	−8.01284	+	13.8786i	−0.331858	+	0.574795i
$584$	6.26754	+	10.8557i	0.259353	+	0.449212i
$585$	1.24329	−	2.15344i	0.0514036	−	0.0890336i
$586$	−1.57774	−	2.73272i	−0.0651757	−	0.112888i
$587$	4.63985	+	8.03646i	0.191507	+	0.331700i	0.945750	−	0.324896i	$-0.105329\pi$
$587$	4.63985	+	8.03646i	0.191507	+	0.331700i	−0.754243	+	0.656596i	$0.771996\pi$
$588$	−12.9550			−0.534254
$589$	−11.8983	−	17.3742i	−0.490260	−	0.715891i
$590$	−3.70150			−0.152388
$591$	1.91699	+	3.32033i	0.0788546	+	0.136580i
$592$	11.0561	+	19.1497i	0.454403	+	0.787048i
$593$	−17.0224	+	29.4836i	−0.699025	+	1.21075i	0.269780	+	0.962922i	$0.413049\pi$
$593$	−17.0224	+	29.4836i	−0.699025	+	1.21075i	−0.968805	+	0.247825i	$0.920284\pi$
$594$	−0.777272	−	1.34627i	−0.0318918	−	0.0552383i
$595$	−0.830974	+	1.43929i	−0.0340666	+	0.0590051i
$596$	5.12010			0.209728
$597$	−12.6985			−0.519715
$598$	−2.31756	+	4.01414i	−0.0947723	+	0.164150i
$599$	−12.5366	+	21.7140i	−0.512231	+	0.887210i	0.487669	+	0.873029i	$0.337847\pi$
$599$	−12.5366	+	21.7140i	−0.512231	+	0.887210i	−0.999899	+	0.0141810i	$0.995486\pi$
$600$	−1.13822			−0.0464678
$601$	−26.0225			−1.06148			−0.530739	−	0.847535i	$-0.678086\pi$
$601$	−26.0225			−1.06148			−0.530739	+	0.847535i	$0.678086\pi$
$602$	0.175858	−	0.304595i	0.00716743	−	0.0124144i
$603$	7.58770	+	13.1423i	0.308995	+	0.535195i
$604$	5.70115	−	9.87468i	0.231976	−	0.401795i
$605$	−8.79862	−	15.2397i	−0.357715	−	0.619580i
$606$	−0.220443	−	0.381818i	−0.00895487	−	0.0155103i
$607$	−7.54650			−0.306303			−0.153151	−	0.988203i	$-0.548942\pi$
$607$	−7.54650			−0.306303			−0.153151	+	0.988203i	$0.548942\pi$
$608$	−14.3155	+	1.10260i	−0.580569	+	0.0447163i
$609$	1.34598			0.0545420
$610$	1.72308	+	2.98447i	0.0697657	+	0.120838i
$611$	13.8137	+	23.9261i	0.558844	+	0.967946i
$612$	−3.27129	+	5.66604i	−0.132234	+	0.229036i
$613$	19.1345	+	33.1419i	0.772836	+	1.33859i	0.936003	+	0.351992i	$0.114496\pi$
$613$	19.1345	+	33.1419i	0.772836	+	1.33859i	−0.163167	+	0.986598i	$0.552171\pi$
$614$	4.89666	−	8.48126i	0.197613	−	0.342276i
$615$	−2.58139			−0.104092
$616$	−2.96169			−0.119330
$617$	5.82540	−	10.0899i	0.234522	−	0.406203i	−0.724612	−	0.689157i	$-0.757981\pi$
$617$	5.82540	−	10.0899i	0.234522	−	0.406203i	0.959134	+	0.282954i	$0.0913143\pi$
$618$	1.33063	−	2.30473i	0.0535259	−	0.0927097i
$619$	−2.47710			−0.0995630			−0.0497815	−	0.998760i	$-0.515852\pi$
$619$	−2.47710			−0.0995630			−0.0497815	+	0.998760i	$0.515852\pi$
$620$	−9.25374			−0.371639
$621$	3.20619	−	5.55329i	0.128660	−	0.222846i
$622$	−1.70379	−	2.95106i	−0.0683159	−	0.118327i
$623$	−1.58390	+	2.74340i	−0.0634578	+	0.109912i
$624$	−4.35164	−	7.53727i	−0.174205	−	0.301732i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.30191			−0.0520346
$627$	10.0703	−	21.0223i	0.402167	−	0.839550i
$628$	13.8078			0.550991
$629$	−10.7892	−	18.6874i	−0.430192	−	0.745114i
$630$	−0.0707229	−	0.122496i	−0.00281767	−	0.00488035i
$631$	21.8279	−	37.8070i	0.868954	−	1.50507i	0.00588756	−	0.999983i	$-0.498126\pi$
$631$	21.8279	−	37.8070i	0.868954	−	1.50507i	0.863067	−	0.505090i	$-0.168541\pi$
$632$	−4.62842	−	8.01666i	−0.184109	−	0.318886i
$633$	−4.57828	+	7.92982i	−0.181970	+	0.315182i
$634$	−3.60096			−0.143012
$635$	−9.83099			−0.390131
$636$	−2.87016	+	4.97126i	−0.113809	+	0.197123i
$637$	−8.40866	+	14.5642i	−0.333163	+	0.577055i
$638$	−4.30025			−0.170248
$639$	−9.92903			−0.392786
$640$	−4.17222	+	7.22649i	−0.164921	+	0.285652i
$641$	−12.1163	−	20.9860i	−0.478564	−	0.828897i	0.521134	−	0.853475i	$-0.325509\pi$
$641$	−12.1163	−	20.9860i	−0.478564	−	0.828897i	−0.999698	+	0.0245776i	$0.992176\pi$
$642$	−0.0201942	+	0.0349774i	−0.000797002	+	0.00138045i
$643$	−4.15878	−	7.20322i	−0.164006	−	0.284067i	0.772296	−	0.635263i	$-0.219108\pi$
$643$	−4.15878	−	7.20322i	−0.164006	−	0.284067i	−0.936302	+	0.351196i	$0.885775\pi$
$644$	−2.98827	−	5.17584i	−0.117754	−	0.203957i
$645$	2.48657			0.0979088
$646$	4.31520	−	0.332364i	0.169779	−	0.0130767i
$647$	−10.9164			−0.429170			−0.214585	−	0.976705i	$-0.568840\pi$
$647$	−10.9164			−0.429170			−0.214585	+	0.976705i	$0.568840\pi$
$648$	−0.569112	−	0.985730i	−0.0223568	−	0.0387231i
$649$	−34.0462	−	58.9697i	−1.33643	−	2.31476i
$650$	−0.361420	+	0.625998i	−0.0141761	+	0.0245537i
$651$	−1.17532	−	2.03571i	−0.0460644	−	0.0797858i
$652$	13.5767	−	23.5155i	0.531704	−	0.920938i
$653$	−21.8452			−0.854868			−0.427434	−	0.904047i	$-0.640582\pi$
$653$	−21.8452			−0.854868			−0.427434	+	0.904047i	$0.640582\pi$
$654$	−4.57265			−0.178805
$655$	−7.11459	+	12.3228i	−0.277990	+	0.481493i
$656$	−4.51758	+	7.82469i	−0.176382	+	0.305503i
$657$	−11.0128			−0.429652
$658$	1.57156			0.0612657
$659$	13.2094	−	22.8794i	0.514566	−	0.891254i	−0.485291	−	0.874352i	$-0.661286\pi$
$659$	13.2094	−	22.8794i	0.514566	−	0.891254i	0.999857	−	0.0169015i	$-0.00538018\pi$
$660$	−5.12169	−	8.87102i	−0.199361	−	0.345304i
$661$	−9.30721	+	16.1206i	−0.362008	+	0.627017i	−0.988291	−	0.152579i	$-0.951242\pi$
$661$	−9.30721	+	16.1206i	−0.362008	+	0.627017i	0.626283	+	0.779596i	$0.284576\pi$
$662$	3.56188	+	6.16936i	0.138436	+	0.239779i
$663$	4.24658	+	7.35529i	0.164924	+	0.285656i
$664$	−6.67120			−0.258893
$665$	0.916279	−	1.91279i	0.0355318	−	0.0741749i
$666$	1.83650			0.0711629
$667$	−8.86911	−	15.3617i	−0.343413	−	0.594809i
$668$	12.0258	+	20.8293i	0.465292	+	0.805910i
$669$	5.44877	−	9.43754i	0.210661	−	0.364876i
$670$	−2.20572	−	3.82043i	−0.0852146	−	0.147596i
$671$	−31.6977	+	54.9020i	−1.22368	+	2.11947i
$672$	−1.60274			−0.0618269
$673$	5.98693			0.230779			0.115390	−	0.993320i	$-0.463188\pi$
$673$	5.98693			0.230779			0.115390	+	0.993320i	$0.463188\pi$
$674$	1.52627	−	2.64358i	0.0587898	−	0.101827i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	13.0578			0.502224
$677$	33.7287			1.29630			0.648150	−	0.761512i	$-0.275543\pi$
$677$	33.7287			1.29630			0.648150	+	0.761512i	$0.275543\pi$
$678$	−2.15133	+	3.72620i	−0.0826211	+	0.143104i
$679$	0.486575	+	0.842772i	0.0186730	+	0.0323426i
$680$	1.94386	−	3.36687i	0.0745437	−	0.129113i
$681$	−12.3176	−	21.3346i	−0.472010	−	0.817545i
$682$	3.75499	+	6.50384i	0.143786	+	0.249045i
$683$	11.4959			0.439880			0.219940	−	0.975513i	$-0.429414\pi$
$683$	11.4959			0.439880			0.219940	+	0.975513i	$0.429414\pi$
$684$	3.60711	−	7.53008i	0.137921	−	0.287920i
$685$	6.58439			0.251577
$686$	0.973377	+	1.68594i	0.0371637	+	0.0643694i
$687$	8.58381	+	14.8676i	0.327493	+	0.567234i
$688$	4.35164	−	7.53727i	0.165905	−	0.287356i
$689$	3.72586	+	6.45337i	0.141944	+	0.245854i
$690$	−0.932031	+	1.61433i	−0.0354818	+	0.0614563i
$691$	36.3039			1.38107			0.690533	−	0.723301i	$-0.257376\pi$
$691$	36.3039			1.38107			0.690533	+	0.723301i	$0.257376\pi$
$692$	−4.19424			−0.159441
$693$	1.30101	−	2.25342i	0.0494214	−	0.0856003i
$694$	−0.211500	+	0.366329i	−0.00802844	+	0.0139057i
$695$	0.233756			0.00886688
$696$	−3.14860			−0.119348
$697$	4.40851	−	7.63577i	0.166984	−	0.289225i
$698$	3.44958	+	5.97485i	0.130569	+	0.226152i
$699$	14.2316	−	24.6498i	0.538287	−	0.932341i
$700$	−0.466016	−	0.807163i	−0.0176137	−	0.0305079i
$701$	−6.76373	−	11.7151i	−0.255463	−	0.442474i	0.709558	−	0.704647i	$-0.248894\pi$
$701$	−6.76373	−	11.7151i	−0.255463	−	0.442474i	−0.965021	+	0.262172i	$0.915561\pi$
$702$	−0.722840			−0.0272818
$703$	15.5596	+	22.7205i	0.586840	+	0.856920i
$704$	−32.3141			−1.21788
$705$	5.55533	+	9.62211i	0.209226	+	0.362390i
$706$	−1.07421	−	1.86058i	−0.0404283	−	0.0700239i
$707$	0.368981	−	0.639094i	0.0138770	−	0.0240356i
$708$	−12.1952	−	21.1226i	−0.458322	−	0.793838i
$709$	0.496778	−	0.860444i	0.0186569	−	0.0323147i	−0.856546	−	0.516070i	$-0.827394\pi$
$709$	0.496778	−	0.860444i	0.0186569	−	0.0323147i	0.875203	+	0.483756i	$0.160728\pi$
$710$	2.88634			0.108322
$711$	8.13272			0.305001
$712$	3.70516	−	6.41753i	0.138857	−	0.240507i
$713$	−15.4891	+	26.8279i	−0.580071	+	1.00471i
$714$	0.483123			0.0180804
$715$	−13.2973			−0.497291
$716$	7.18714	−	12.4485i	0.268596	−	0.465222i
$717$	2.03871	+	3.53114i	0.0761369	+	0.131873i
$718$	0.342831	−	0.593801i	0.0127943	−	0.0221605i
$719$	0.700670	+	1.21360i	0.0261306	+	0.0452595i	0.878795	−	0.477200i	$-0.158348\pi$
$719$	0.700670	+	1.21360i	0.0261306	+	0.0452595i	−0.852664	+	0.522459i	$0.825015\pi$
$720$	−1.75006	−	3.03119i	−0.0652207	−	0.112966i
$721$	4.45448			0.165894
$722$	−5.45810	+	0.845801i	−0.203130	+	0.0314775i
$723$	12.6684			0.471144
$724$	−12.1301	−	21.0099i	−0.450810	−	0.780827i
$725$	−1.38312	−	2.39564i	−0.0513679	−	0.0889717i
$726$	−2.55773	+	4.43012i	−0.0949264	+	0.164417i
$727$	23.4834	+	40.6745i	0.870953	+	1.50853i	0.861013	+	0.508584i	$0.169831\pi$
$727$	23.4834	+	40.6745i	0.870953	+	1.50853i	0.00993990	+	0.999951i	$0.496836\pi$
$728$	−0.688570	+	1.19264i	−0.0255201	+	0.0442021i
$729$	1.00000			0.0370370
$730$	3.20140			0.118489
$731$	−4.24658	+	7.35529i	−0.157065	+	0.272045i
$732$	−11.3539	+	19.6656i	−0.419654	+	0.726862i
$733$	−21.6068			−0.798066			−0.399033	−	0.916937i	$-0.630654\pi$
$733$	−21.6068			−0.798066			−0.399033	+	0.916937i	$0.630654\pi$
$734$	6.43852			0.237650
$735$	−3.38162	+	5.85714i	−0.124733	+	0.216044i
$736$	10.5609	+	18.2921i	0.389281	+	0.674255i
$737$	40.5763	−	70.2802i	1.49465	−	2.58880i
$738$	0.375202	+	0.649869i	0.0138114	+	0.0239220i
$739$	15.4063	+	26.6845i	0.566729	+	0.981603i	0.996887	+	0.0788496i	$0.0251247\pi$
$739$	15.4063	+	26.6845i	0.566729	+	0.981603i	−0.430158	+	0.902754i	$0.641542\pi$
$740$	12.1013			0.444851
$741$	−6.12420	−	8.94272i	−0.224978	−	0.328519i
$742$	0.423882			0.0155612
$743$	−22.2143	−	38.4763i	−0.814964	−	1.41156i	−0.909354	−	0.416024i	$-0.863423\pi$
$743$	−22.2143	−	38.4763i	−0.814964	−	1.41156i	0.0943897	−	0.995535i	$-0.469910\pi$
$744$	2.74937	+	4.76205i	0.100797	+	0.174585i
$745$	1.33650	−	2.31488i	0.0489654	−	0.0848106i
$746$	4.53107	+	7.84805i	0.165894	+	0.287338i
$747$	2.93053	−	5.07583i	0.107223	−	0.185715i
$748$	34.9873			1.27926
$749$	−0.0676029			−0.00247016
$750$	−0.145349	+	0.251751i	−0.00530738	+	0.00919265i
$751$	−7.43935	+	12.8853i	−0.271466	+	0.470192i	−0.969237	−	0.246128i	$-0.920842\pi$
$751$	−7.43935	+	12.8853i	−0.271466	+	0.470192i	0.697772	+	0.716320i	$0.254175\pi$
$752$	38.8886			1.41812
$753$	11.6241			0.423605
$754$	−0.999776	+	1.73166i	−0.0364097	+	0.0630634i
$755$	−2.97633	−	5.15516i	−0.108320	−	0.187615i
$756$	0.466016	−	0.807163i	0.0169488	−	0.0293562i
$757$	−11.7204	−	20.3004i	−0.425986	−	0.737829i	0.570526	−	0.821279i	$-0.306739\pi$
$757$	−11.7204	−	20.3004i	−0.425986	−	0.737829i	−0.996512	+	0.0834503i	$0.973406\pi$
$758$	−3.78414	−	6.55432i	−0.137446	−	0.238063i
$759$	−34.2911			−1.24469
$760$	−2.14341	+	4.47451i	−0.0777498	+	0.162308i
$761$	36.3224			1.31669			0.658344	−	0.752717i	$-0.271257\pi$
$761$	36.3224			1.31669			0.658344	+	0.752717i	$0.271257\pi$
$762$	1.42892	+	2.47496i	0.0517643	+	0.0896585i
$763$	−3.82690	−	6.62838i	−0.138543	−	0.239963i
$764$	7.81309	−	13.5327i	0.282668	−	0.489595i
$765$	1.70780	+	2.95800i	0.0617458	+	0.106947i
$766$	−0.310020	+	0.536970i	−0.0112015	+	0.0194015i
$767$	−31.6620			−1.14325
$768$	−9.65968			−0.348564
$769$	−10.4052	+	18.0223i	−0.375220	+	0.649901i	−0.990360	−	0.138517i	$-0.955766\pi$
$769$	−10.4052	+	18.0223i	−0.375220	+	0.649901i	0.615140	+	0.788418i	$0.289100\pi$
$770$	−0.378201	+	0.655063i	−0.0136294	+	0.0236068i
$771$	−10.5483			−0.379889
$772$	6.44573			0.231987
$773$	−1.78351	+	3.08913i	−0.0641484	+	0.111108i	−0.896316	−	0.443416i	$-0.853766\pi$
$773$	−1.78351	+	3.08913i	−0.0641484	+	0.111108i	0.832168	+	0.554524i	$0.187100\pi$
$774$	−0.361420	−	0.625998i	−0.0129910	−	0.0225010i
$775$	−2.41550	+	4.18376i	−0.0867671	+	0.150285i
$776$	−1.13822	−	1.97146i	−0.0408598	−	0.0707713i
$777$	1.53698	+	2.66213i	0.0551390	+	0.0955035i
$778$	3.79147			0.135931
$779$	−4.86108	+	10.1478i	−0.174166	+	0.363583i
$780$	−4.76302			−0.170544
$781$	26.5484	+	45.9832i	0.949978	+	1.64541i
$782$	−3.18345	−	5.51390i	−0.113840	−	0.197177i
$783$	1.38312	−	2.39564i	0.0494287	−	0.0856131i
$784$	11.8361	+	20.5007i	0.422716	+	0.732166i
$785$	3.60424	−	6.24273i	0.128641	−	0.222812i
$786$	4.13639			0.147540
$787$	44.5660			1.58860			0.794302	−	0.607523i	$-0.207837\pi$
$787$	44.5660			1.58860			0.794302	+	0.607523i	$0.207837\pi$
$788$	3.67199	−	6.36008i	0.130809	−	0.226568i
$789$	11.8967	−	20.6058i	0.423535	−	0.733585i
$790$	−2.36416			−0.0841129
$791$	−7.20186			−0.256069
$792$	−3.04340	+	5.27133i	−0.108143	+	0.187309i
$793$	14.7390	+	25.5287i	0.523396	+	0.906549i
$794$	0.00416319	−	0.00721085i	0.000147746	−	0.000255904i
$795$	1.49839	+	2.59529i	0.0531424	+	0.0920453i
$796$	12.1620	+	21.0651i	0.431069	+	0.746634i
$797$	−44.7396			−1.58476			−0.792378	−	0.610030i	$-0.791157\pi$
$797$	−44.7396			−1.58476			−0.792378	+	0.610030i	$0.791157\pi$
$798$	−0.614727	+	0.0473473i	−0.0217611	+	0.00167608i
$799$	−37.9496			−1.34256
$800$	1.64696	+	2.85262i	0.0582288	+	0.100855i
$801$	3.25521	+	5.63820i	0.115017	+	0.199216i
$802$	−3.97080	+	6.87762i	−0.140214	+	0.242857i
$803$	29.4463	+	51.0026i	1.03914	+	1.79984i
$804$	14.5342	−	25.1740i	0.512582	−	0.887818i
$805$	−3.12010			−0.109969
$806$	3.49203			0.123002
$807$	−2.11377	+	3.66115i	−0.0744081	+	0.128879i
$808$	−0.863142	+	1.49501i	−0.0303652	+	0.0525941i
$809$	8.67442			0.304976			0.152488	−	0.988305i	$-0.451271\pi$
$809$	8.67442			0.304976			0.152488	+	0.988305i	$0.451271\pi$
$810$	−0.290697			−0.0102141
$811$	−13.3651	+	23.1490i	−0.469312	+	0.812872i	−0.999384	−	0.0350805i	$-0.988831\pi$
$811$	−13.3651	+	23.1490i	−0.469312	+	0.812872i	0.530073	+	0.847952i	$0.322165\pi$
$812$	−1.28911	−	2.23281i	−0.0452390	−	0.0783562i
$813$	15.5736	−	26.9742i	0.546189	−	0.946027i
$814$	−4.91046	−	8.50517i	−0.172112	−	0.298106i
$815$	−7.08781	−	12.2765i	−0.248275	−	0.430025i
$816$	11.9550			0.418509
$817$	4.68252	−	9.77507i	0.163821	−	0.341986i
$818$	1.95906			0.0684968
$819$	−0.604952	−	1.04781i	−0.0211387	−	0.0366134i
$820$	2.47232	+	4.28219i	0.0863373	+	0.149541i
$821$	4.72432	−	8.18275i	0.164880	−	0.285580i	−0.771733	−	0.635947i	$-0.780610\pi$
$821$	4.72432	−	8.18275i	0.164880	−	0.285580i	0.936613	+	0.350367i	$0.113943\pi$
$822$	−0.957032	−	1.65763i	−0.0333803	−	0.0578164i
$823$	9.73340	−	16.8587i	0.339285	−	0.587659i	−0.645014	−	0.764171i	$-0.723148\pi$
$823$	9.73340	−	16.8587i	0.339285	−	0.587659i	0.984298	+	0.176513i	$0.0564816\pi$
$824$	−10.4202			−0.363004
$825$	−5.34764			−0.186181
$826$	−0.900527	+	1.55976i	−0.0313333	+	0.0542709i
$827$	18.5009	−	32.0445i	0.643340	−	1.11430i	−0.341342	−	0.939939i	$-0.610882\pi$
$827$	18.5009	−	32.0445i	0.643340	−	1.11430i	0.984682	−	0.174358i	$-0.0557851\pi$
$828$	−12.2829			−0.426860
$829$	20.5418			0.713448			0.356724	−	0.934210i	$-0.383894\pi$
$829$	20.5418			0.713448			0.356724	+	0.934210i	$0.383894\pi$
$830$	−0.851897	+	1.47553i	−0.0295698	+	0.0512164i
$831$	0.526963	+	0.912727i	0.0182801	+	0.0316621i
$832$	−7.51280	+	13.0126i	−0.260459	+	0.451129i
$833$	−11.5503	−	20.0057i	−0.400194	−	0.693156i
$834$	−0.0339761	−	0.0588484i	−0.00117650	−	0.00203775i
$835$	12.5563			0.434530
$836$	−44.5180	+	3.42885i	−1.53969	+	0.118589i
$837$	−4.83099			−0.166983
$838$	3.83831	+	6.64814i	0.132592	+	0.229656i
$839$	23.8946	+	41.3866i	0.824932	+	1.42882i	0.901972	+	0.431795i	$0.142120\pi$
$839$	23.8946	+	41.3866i	0.824932	+	1.42882i	−0.0770401	+	0.997028i	$0.524547\pi$
$840$	−0.276915	+	0.479631i	−0.00955448	+	0.0165489i
$841$	10.6739	+	18.4878i	0.368067	+	0.637511i
$842$	5.50719	−	9.53873i	0.189790	−	0.328726i
$843$	−25.6354			−0.882928
$844$	17.5394			0.603730
$845$	3.40847	−	5.90365i	0.117255	−	0.203092i
$846$	1.61492	−	2.79712i	0.0555221	−	0.0961670i
$847$	−8.56237			−0.294206
$848$	10.4891			0.360196
$849$	14.7056	−	25.4708i	0.504695	−	0.874157i
$850$	−0.496454	−	0.859883i	−0.0170282	−	0.0294937i
$851$	20.2553	−	35.0833i	0.694344	−	1.20264i
$852$	9.50951	+	16.4709i	0.325790	+	0.564285i
$853$	−5.71632	−	9.90096i	−0.195723	−	0.339003i	0.751414	−	0.659831i	$-0.229372\pi$
$853$	−5.71632	−	9.90096i	−0.195723	−	0.339003i	−0.947137	+	0.320828i	$0.896039\pi$
$854$	1.67682			0.0573795
$855$	−2.46291	−	3.59640i	−0.0842296	−	0.122994i
$856$	0.158141			0.00540513
$857$	−2.78522	−	4.82414i	−0.0951412	−	0.164789i	0.814526	−	0.580127i	$-0.196997\pi$
$857$	−2.78522	−	4.82414i	−0.0951412	−	0.164789i	−0.909668	+	0.415337i	$0.863664\pi$
$858$	1.93274	+	3.34761i	0.0659828	+	0.114286i
$859$	8.50709	−	14.7347i	0.290258	−	0.502742i	−0.683612	−	0.729845i	$-0.739592\pi$
$859$	8.50709	−	14.7347i	0.290258	−	0.502742i	0.973871	+	0.227103i	$0.0729255\pi$
$860$	−2.38151	−	4.12490i	−0.0812088	−	0.140658i
$861$	−0.628020	+	1.08776i	−0.0214029	+	0.0370709i
$862$	5.58304			0.190159
$863$	46.8850			1.59598			0.797992	−	0.602668i	$-0.205896\pi$
$863$	46.8850			1.59598			0.797992	+	0.602668i	$0.205896\pi$
$864$	−1.64696	+	2.85262i	−0.0560307	+	0.0970480i
$865$	−1.09482	+	1.89628i	−0.0372250	+	0.0644756i
$866$	−4.92768			−0.167449
$867$	5.33363			0.181140
$868$	−2.25132	+	3.89939i	−0.0764147	+	0.132354i
$869$	−21.7454	−	37.6642i	−0.737662	−	1.27767i
$870$	−0.402070	+	0.696405i	−0.0136314	+	0.0236103i
$871$	−18.8674	−	32.6793i	−0.639297	−	1.10730i
$872$	8.95210	+	15.5055i	0.303156	+	0.525082i
$873$	2.00000			0.0676897
$874$	4.59101	+	6.70391i	0.155293	+	0.226763i
$875$	−0.486575			−0.0164492
$876$	10.5475	+	18.2688i	0.356368	+	0.617247i
$877$	14.8922	+	25.7940i	0.502873	+	0.871002i	0.999994	+	0.00332078i	$0.00105704\pi$
$877$	14.8922	+	25.7940i	0.502873	+	0.871002i	−0.497121	+	0.867681i	$0.665610\pi$
$878$	1.61379	−	2.79516i	0.0544626	−	0.0943321i
$879$	−5.42742	−	9.40057i	−0.183062	−	0.317073i
$880$	−9.35867	+	16.2097i	−0.315481	+	0.546428i
$881$	−20.4884			−0.690271			−0.345135	−	0.938553i	$-0.612167\pi$
$881$	−20.4884			−0.690271			−0.345135	+	0.938553i	$0.612167\pi$
$882$	1.96606			0.0662006
$883$	−15.7402	+	27.2628i	−0.529699	+	0.917466i	0.469701	+	0.882826i	$0.344362\pi$
$883$	−15.7402	+	27.2628i	−0.529699	+	0.917466i	−0.999400	+	0.0346401i	$0.988972\pi$
$884$	8.13430	−	14.0890i	0.273586	−	0.473865i
$885$	−12.7332			−0.428021
$886$	4.03900			0.135693
$887$	16.8051	−	29.1074i	0.564262	−	0.977330i	−0.432856	−	0.901463i	$-0.642494\pi$
$887$	16.8051	−	29.1074i	0.564262	−	0.977330i	0.997118	−	0.0758670i	$-0.0241724\pi$
$888$	−3.59540	−	6.22742i	−0.120654	−	0.208978i
$889$	−2.39175	+	4.14264i	−0.0802169	+	0.138940i
$890$	−0.946281	−	1.63901i	−0.0317194	−	0.0549397i
$891$	−2.67382	−	4.63119i	−0.0895763	−	0.155151i
$892$	−20.8742			−0.698919
$893$	48.2872	−	3.71916i	1.61587	−	0.124457i
$894$	−0.777031			−0.0259878
$895$	−3.75210	−	6.49883i	−0.125419	−	0.217232i
$896$	2.03009	+	3.51623i	0.0678207	+	0.117469i
$897$	−7.97244	+	13.8087i	−0.266192	+	0.461058i
$898$	4.05050	+	7.01567i	0.135167	+	0.234116i
$899$	−6.68185	+	11.5733i	−0.222852	+	0.385991i
$900$	−1.91550			−0.0638498
$901$	−10.2358			−0.341004
$902$	2.00644	−	3.47526i	0.0668073	−	0.115714i
$903$	0.604952	−	1.04781i	0.0201315	−	0.0348688i
$904$	16.8470			0.560323
$905$	−12.6652			−0.421006
$906$	−0.865211	+	1.49859i	−0.0287447	+	0.0497873i
$907$	−10.9747	−	19.0088i	−0.364410	−	0.631176i	0.624272	−	0.781207i	$-0.285396\pi$
$907$	−10.9747	−	19.0088i	−0.364410	−	0.631176i	−0.988681	+	0.150031i	$0.952063\pi$
$908$	−23.5942	+	40.8664i	−0.783002	+	1.35620i
$909$	−0.758324	−	1.31346i	−0.0251520	−	0.0435646i
$910$	0.175858	+	0.304595i	0.00582963	+	0.0100972i
$911$	21.2865			0.705253			0.352626	−	0.935764i	$-0.385289\pi$
$911$	21.2865			0.705253			0.352626	+	0.935764i	$0.385289\pi$
$912$	−15.2116	+	1.17162i	−0.503706	+	0.0387962i
$913$	−31.3428			−1.03730
$914$	−5.31481	−	9.20552i	−0.175798	−	0.304492i
$915$	5.92742	+	10.2666i	0.195955	+	0.339403i
$916$	16.4422	−	28.4788i	0.543267	−	0.940966i
$917$	3.46178	+	5.99598i	0.114318	+	0.198005i
$918$	0.496454	−	0.859883i	0.0163854	−	0.0283804i
$919$	−2.61948			−0.0864087			−0.0432043	−	0.999066i	$-0.513757\pi$
$919$	−2.61948			−0.0864087			−0.0432043	+	0.999066i	$0.513757\pi$
$920$	7.29873			0.240632
$921$	16.8445	−	29.1756i	0.555046	−	0.961368i
$922$	3.18575	−	5.51789i	0.104917	−	0.181722i
$923$	24.6893			0.812658
$924$	−4.98417			−0.163967
$925$	3.15878	−	5.47117i	0.103860	−	0.179891i
$926$	−2.03859	−	3.53094i	−0.0669921	−	0.116034i
$927$	4.57739	−	7.92827i	0.150341	−	0.260399i
$928$	4.55589	+	7.89104i	0.149554	+	0.259036i
$929$	−1.91237	−	3.31232i	−0.0627428	−	0.108674i	0.832948	−	0.553352i	$-0.186651\pi$
$929$	−1.91237	−	3.31232i	−0.0627428	−	0.108674i	−0.895691	+	0.444678i	$0.853318\pi$
$930$	1.40436			0.0460506
$931$	16.6572	+	24.3233i	0.545919	+	0.797165i
$932$	−54.5210			−1.78589
$933$	−5.86106	−	10.1517i	−0.191883	−	0.332350i
$934$	4.93160	+	8.54177i	0.161367	+	0.279495i
$935$	9.13272	−	15.8183i	0.298672	−	0.517315i
$936$	1.41514	+	2.45109i	0.0462553	+	0.0801165i
$937$	3.69584	−	6.40138i	0.120738	−	0.209124i	−0.799321	−	0.600904i	$-0.794807\pi$
$937$	3.69584	−	6.40138i	0.120738	−	0.209124i	0.920059	+	0.391780i	$0.128141\pi$
$938$	−2.14650			−0.0700856
$939$	−4.47856			−0.146152
$940$	10.6412	−	18.4311i	0.347078	−	0.601157i
$941$	−24.3057	+	42.0988i	−0.792344	+	1.37238i	0.132168	+	0.991227i	$0.457806\pi$
$941$	−24.3057	+	42.0988i	−0.792344	+	1.37238i	−0.924512	+	0.381153i	$0.875527\pi$
$942$	−2.09548			−0.0682746
$943$	16.5529			0.539036
$944$	−22.2838	+	38.5966i	−0.725275	+	1.25621i
$945$	−0.243287	−	0.421386i	−0.00791413	−	0.0137077i
$946$	−1.93274	+	3.34761i	−0.0628389	+	0.108840i
$947$	18.0103	+	31.1948i	0.585257	+	1.01370i	0.994843	+	0.101424i	$0.0323398\pi$
$947$	18.0103	+	31.1948i	0.585257	+	1.01370i	−0.409586	+	0.912271i	$0.634327\pi$
$948$	−7.78909	−	13.4911i	−0.252978	−	0.438170i
$949$	27.3843			0.888930
$950$	0.715960	+	1.04546i	0.0232288	+	0.0339193i
$951$	−12.3873			−0.401687
$952$	−0.945834	−	1.63823i	−0.0306546	−	0.0530954i
$953$	−5.60605	−	9.70996i	−0.181598	−	0.314537i	0.760827	−	0.648955i	$-0.224794\pi$
$953$	−5.60605	−	9.70996i	−0.181598	−	0.314537i	−0.942425	+	0.334418i	$0.891460\pi$
$954$	0.435577	−	0.754442i	0.0141023	−	0.0244260i
$955$	−4.07889	−	7.06484i	−0.131990	−	0.228613i
$956$	3.90513	−	6.76389i	0.126301	−	0.218760i
$957$	−14.7929			−0.478186
$958$	−9.28769			−0.300072
$959$	1.60190	−	2.77457i	0.0517280	−	0.0895955i
$960$	−3.02135	+	5.23312i	−0.0975135	+	0.168898i
$961$	−7.66153			−0.247146
$962$	−4.56659			−0.147233
$963$	−0.0694682	+	0.120322i	−0.00223858	+	0.00387733i
$964$	−12.1332	−	21.0152i	−0.390783	−	0.676855i
$965$	1.68252	−	2.91422i	0.0541623	−	0.0938119i
$966$	0.453503	+	0.785490i	0.0145912	+	0.0252727i
$967$	5.02307	+	8.70021i	0.161531	+	0.279780i	0.935418	−	0.353544i	$-0.115023\pi$
$967$	5.02307	+	8.70021i	0.161531	+	0.279780i	−0.773887	+	0.633324i	$0.781690\pi$
$968$	20.0296			0.643775
$969$	14.8443	−	1.14333i	0.476868	−	0.0367292i
$970$	−0.581394			−0.0186674
$971$	18.9495	+	32.8214i	0.608117	+	1.05329i	0.991551	+	0.129721i	$0.0414082\pi$
$971$	18.9495	+	32.8214i	0.608117	+	1.05329i	−0.383434	+	0.923568i	$0.625258\pi$
$972$	−0.957748	−	1.65887i	−0.0307198	−	0.0532082i
$973$	0.0568699	−	0.0985016i	0.00182317	−	0.00315782i
$974$	5.46844	+	9.47161i	0.175220	+	0.303490i
$975$	−1.24329	+	2.15344i	−0.0398171	+	0.0689652i
$976$	41.4933			1.32817
$977$	44.6435			1.42827			0.714135	−	0.700008i	$-0.246820\pi$
$977$	44.6435			1.42827			0.714135	+	0.700008i	$0.246820\pi$
$978$	−2.06041	+	3.56873i	−0.0658846	+	0.114115i
$979$	17.4077	−	30.1510i	0.556353	−	0.963631i
$980$	12.9550			0.413831
$981$	−15.7299			−0.502219
$982$	−5.82618	+	10.0912i	−0.185921	+	0.322025i
$983$	6.25454	+	10.8332i	0.199489	+	0.345525i	0.948363	−	0.317188i	$-0.102738\pi$
$983$	6.25454	+	10.8332i	0.199489	+	0.345525i	−0.748874	+	0.662712i	$0.769405\pi$
$984$	1.46910	−	2.54456i	0.0468333	−	0.0811176i
$985$	−1.91699	−	3.32033i	−0.0610805	−	0.105795i
$986$	−1.37331	−	2.37865i	−0.0437352	−	0.0757515i
$987$	5.40616			0.172080
$988$	−8.96935	+	18.7241i	−0.285353	+	0.595693i
$989$	−15.9449			−0.507017
$990$	0.777272	+	1.34627i	0.0247033	+	0.0427874i
$991$	−25.1503	−	43.5617i	−0.798927	−	1.38378i	−0.920315	−	0.391177i	$-0.872068\pi$
$991$	−25.1503	−	43.5617i	−0.798927	−	1.38378i	0.121388	−	0.992605i	$-0.461265\pi$
$992$	7.95645	−	13.7810i	0.252617	−	0.437546i
$993$	12.2529	+	21.2226i	0.388834	+	0.673480i
$994$	0.702210	−	1.21626i	0.0222728	−	0.0385775i
$995$	12.6985			0.402569
$996$	−11.2268			−0.355736
$997$	−6.46875	+	11.2042i	−0.204867	+	0.354841i	−0.950090	−	0.311975i	$-0.899010\pi$
$997$	−6.46875	+	11.2042i	−0.204867	+	0.354841i	0.745223	+	0.666815i	$0.232343\pi$
$998$	−4.40504	+	7.62975i	−0.139439	+	0.241515i
$999$	6.31756			0.199879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.i.f.121.3	yes	10
3.2	odd	2		855.2.k.i.406.3		10
19.7	even	3		5415.2.a.y.1.3		5
19.11	even	3	inner	285.2.i.f.106.3	✓	10
19.12	odd	6		5415.2.a.z.1.3		5
57.11	odd	6		855.2.k.i.676.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.3	✓	10	19.11	even	3	inner
285.2.i.f.121.3	yes	10	1.1	even	1	trivial
855.2.k.i.406.3		10	3.2	odd	2
855.2.k.i.676.3		10	57.11	odd	6
5415.2.a.y.1.3		5	19.7	even	3
5415.2.a.z.1.3		5	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.145349 + 0.251751i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.957748 - 1.65887i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.145349 + 0.251751i) q^{6} -0.486575 q^{7} +1.13822 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.145349 - 0.251751i) q^{10} +5.34764 q^{11} +1.91550 q^{12} +(1.24329 - 2.15344i) q^{13} +(-0.0707229 - 0.122496i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-1.75006 - 3.03119i) q^{16} +(1.70780 + 2.95800i) q^{17} -0.290697 q^{18} +(-2.46291 - 3.59640i) q^{19} -1.91550 q^{20} +(-0.243287 - 0.421386i) q^{21} +(0.777272 + 1.34627i) q^{22} +(-3.20619 + 5.55329i) q^{23} +(0.569112 + 0.985730i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.722840 q^{26} -1.00000 q^{27} +(-0.466016 + 0.807163i) q^{28} +(-1.38312 + 2.39564i) q^{29} +0.290697 q^{30} +4.83099 q^{31} +(1.64696 - 2.85262i) q^{32} +(2.67382 + 4.63119i) q^{33} +(-0.496454 + 0.859883i) q^{34} +(0.243287 + 0.421386i) q^{35} +(0.957748 + 1.65887i) q^{36} -6.31756 q^{37} +(0.547418 - 1.14277i) q^{38} +2.48657 q^{39} +(-0.569112 - 0.985730i) q^{40} +(-1.29070 - 2.23555i) q^{41} +(0.0707229 - 0.122496i) q^{42} +(1.24329 + 2.15344i) q^{43} +(5.12169 - 8.87102i) q^{44} +1.00000 q^{45} -1.86406 q^{46} +(-5.55533 + 9.62211i) q^{47} +(1.75006 - 3.03119i) q^{48} -6.76325 q^{49} -0.290697 q^{50} +(-1.70780 + 2.95800i) q^{51} +(-2.38151 - 4.12490i) q^{52} +(-1.49839 + 2.59529i) q^{53} +(-0.145349 - 0.251751i) q^{54} +(-2.67382 - 4.63119i) q^{55} -0.553831 q^{56} +(1.88312 - 3.93114i) q^{57} -0.804139 q^{58} +(-6.36659 - 11.0273i) q^{59} +(-0.957748 - 1.65887i) q^{60} +(-5.92742 + 10.2666i) q^{61} +(0.702178 + 1.21621i) q^{62} +(0.243287 - 0.421386i) q^{63} -6.04269 q^{64} -2.48657 q^{65} +(-0.777272 + 1.34627i) q^{66} +(7.58770 - 13.1423i) q^{67} +6.54258 q^{68} -6.41238 q^{69} +(-0.0707229 + 0.122496i) q^{70} +(4.96452 + 8.59879i) q^{71} +(-0.569112 + 0.985730i) q^{72} +(5.50642 + 9.53740i) q^{73} +(-0.918249 - 1.59045i) q^{74} -1.00000 q^{75} +(-8.32479 + 0.641189i) q^{76} -2.60202 q^{77} +(0.361420 + 0.625998i) q^{78} +(-4.06636 - 7.04314i) q^{79} +(-1.75006 + 3.03119i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.375202 - 0.649869i) q^{82} -5.86106 q^{83} -0.932031 q^{84} +(1.70780 - 2.95800i) q^{85} +(-0.361420 + 0.625998i) q^{86} -2.76624 q^{87} +6.08681 q^{88} +(3.25521 - 5.63820i) q^{89} +(0.145349 + 0.251751i) q^{90} +(-0.604952 + 1.04781i) q^{91} +(6.14145 + 10.6373i) q^{92} +(2.41550 + 4.18376i) q^{93} -3.22984 q^{94} +(-1.88312 + 3.93114i) q^{95} +3.29392 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-0.983028 - 1.70265i) q^{98} +(-2.67382 + 4.63119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

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Database

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