LMFDB - Embedded newform 375.2.g.d.76.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, not 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			76.4
Root			$-1.53767i$ of defining polynomial
Character	$\chi$	$=$	375.76
Dual form			375.2.g.d.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24400 + 0.903822i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.112618 + 0.346603i) q^{4} +(0.475167 - 1.46241i) q^{6} +1.68601 q^{7} +(0.777165 - 2.39187i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.24400 + 0.903822i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.112618 + 0.346603i) q^{4} +(0.475167 - 1.46241i) q^{6} +1.68601 q^{7} +(0.777165 - 2.39187i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(2.40891 + 1.75017i) q^{11} +(0.294838 - 0.214212i) q^{12} +(-0.188414 + 0.136890i) q^{13} +(2.09740 + 1.52385i) q^{14} +(3.71829 - 2.70150i) q^{16} +(2.30496 - 7.09394i) q^{17} -1.53767 q^{18} +(0.232853 - 0.716646i) q^{19} +(-0.521005 - 1.60349i) q^{21} +(1.41484 + 4.35444i) q^{22} +(-0.706046 - 0.512972i) q^{23} -2.51496 q^{24} -0.358112 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.189875 + 0.584375i) q^{28} +(2.12444 + 6.53835i) q^{29} +(-3.03433 + 9.33870i) q^{31} +2.03733 q^{32} +(0.920120 - 2.83184i) q^{33} +(9.27904 - 6.74162i) q^{34} +(-0.294838 - 0.214212i) q^{36} +(-8.19304 + 5.95259i) q^{37} +(0.937390 - 0.681054i) q^{38} +(0.188414 + 0.136890i) q^{39} +(-3.07210 + 2.23201i) q^{41} +(0.801135 - 2.46564i) q^{42} -5.27322 q^{43} +(-0.335328 + 1.03203i) q^{44} +(-0.414688 - 1.27628i) q^{46} +(-2.64749 - 8.14814i) q^{47} +(-3.71829 - 2.70150i) q^{48} -4.15738 q^{49} -7.45901 q^{51} +(-0.0686654 - 0.0498883i) q^{52} +(1.84754 + 5.68614i) q^{53} +(0.475167 + 1.46241i) q^{54} +(1.31031 - 4.03270i) q^{56} -0.753527 q^{57} +(-3.26669 + 10.0538i) q^{58} +(3.11564 - 2.26365i) q^{59} +(3.55679 + 2.58416i) q^{61} +(-12.2152 + 8.87488i) q^{62} +(-1.36401 + 0.991010i) q^{63} +(-4.90214 - 3.56161i) q^{64} +(3.70411 - 2.69119i) q^{66} +(0.554013 - 1.70508i) q^{67} +2.71836 q^{68} +(-0.269686 + 0.830007i) q^{69} +(-1.35179 - 4.16039i) q^{71} +(0.777165 + 2.39187i) q^{72} +(12.1780 + 8.84783i) q^{73} -15.5723 q^{74} +0.274615 q^{76} +(4.06143 + 2.95080i) q^{77} +(0.110663 + 0.340585i) q^{78} +(2.27926 + 7.01484i) q^{79} +(0.309017 - 0.951057i) q^{81} -5.83904 q^{82} +(1.34253 - 4.13188i) q^{83} +(0.497099 - 0.361163i) q^{84} +(-6.55991 - 4.76605i) q^{86} +(5.56185 - 4.04092i) q^{87} +(6.05830 - 4.40161i) q^{88} +(-9.79170 - 7.11409i) q^{89} +(-0.317667 + 0.230798i) q^{91} +(0.0982841 - 0.302487i) q^{92} +9.81929 q^{93} +(4.07098 - 12.5292i) q^{94} +(-0.629569 - 1.93761i) q^{96} +(2.92771 + 9.01055i) q^{97} +(-5.17180 - 3.75753i) q^{98} -2.97757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 - 6 * q^8 - 4 * q^9	$ 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9} - 6 q^{11} + 2 q^{12} - 8 q^{13} + 12 q^{14} - 10 q^{16} - 8 q^{17} + 8 q^{18} + 2 q^{19} + 4 q^{21} + 4 q^{22} - 2 q^{23} - 24 q^{24} + 12 q^{26} + 4 q^{27} - 28 q^{28} - 16 q^{29} + 6 q^{31} - 4 q^{32} - 4 q^{33} + 36 q^{34} - 2 q^{36} - 24 q^{37} + 38 q^{38} + 8 q^{39} - 14 q^{41} + 18 q^{42} + 40 q^{43} - 26 q^{44} + 16 q^{46} + 10 q^{47} + 10 q^{48} - 32 q^{51} - 48 q^{52} - 12 q^{53} + 2 q^{54} + 28 q^{57} - 44 q^{58} - 12 q^{59} - 28 q^{62} - 4 q^{63} - 8 q^{64} + 16 q^{66} + 12 q^{67} - 4 q^{68} + 12 q^{69} - 8 q^{71} - 6 q^{72} + 8 q^{73} + 52 q^{74} - 32 q^{76} - 18 q^{77} - 32 q^{78} + 20 q^{79} - 4 q^{81} + 32 q^{82} - 6 q^{83} - 12 q^{84} - 36 q^{86} - 14 q^{87} - 16 q^{88} - 18 q^{89} + 26 q^{91} + 36 q^{92} + 44 q^{93} + 38 q^{94} - 26 q^{96} - 8 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 - 6 * q^8 - 4 * q^9 - 6 * q^11 + 2 * q^12 - 8 * q^13 + 12 * q^14 - 10 * q^16 - 8 * q^17 + 8 * q^18 + 2 * q^19 + 4 * q^21 + 4 * q^22 - 2 * q^23 - 24 * q^24 + 12 * q^26 + 4 * q^27 - 28 * q^28 - 16 * q^29 + 6 * q^31 - 4 * q^32 - 4 * q^33 + 36 * q^34 - 2 * q^36 - 24 * q^37 + 38 * q^38 + 8 * q^39 - 14 * q^41 + 18 * q^42 + 40 * q^43 - 26 * q^44 + 16 * q^46 + 10 * q^47 + 10 * q^48 - 32 * q^51 - 48 * q^52 - 12 * q^53 + 2 * q^54 + 28 * q^57 - 44 * q^58 - 12 * q^59 - 28 * q^62 - 4 * q^63 - 8 * q^64 + 16 * q^66 + 12 * q^67 - 4 * q^68 + 12 * q^69 - 8 * q^71 - 6 * q^72 + 8 * q^73 + 52 * q^74 - 32 * q^76 - 18 * q^77 - 32 * q^78 + 20 * q^79 - 4 * q^81 + 32 * q^82 - 6 * q^83 - 12 * q^84 - 36 * q^86 - 14 * q^87 - 16 * q^88 - 18 * q^89 + 26 * q^91 + 36 * q^92 + 44 * q^93 + 38 * q^94 - 26 * q^96 - 8 * q^97 + 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	1.24400	+	0.903822i	0.879644	+	0.639099i	0.933157	−	0.359469i	$-0.117042\pi$
$2$	1.24400	+	0.903822i	0.879644	+	0.639099i	−0.0535136	+	0.998567i	$0.517042\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.112618	+	0.346603i	0.0563090	+	0.173301i
$5$		0			0
$5$		0			0
$6$	0.475167	−	1.46241i	0.193986	−	0.597028i
$7$	1.68601			0.637251			0.318625	−	0.947881i	$-0.396779\pi$
$7$	1.68601			0.637251			0.318625	+	0.947881i	$0.396779\pi$
$8$	0.777165	−	2.39187i	0.274769	−	0.845653i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	2.40891	+	1.75017i	0.726312	+	0.527697i	0.888395	−	0.459080i	$-0.151821\pi$
$11$	2.40891	+	1.75017i	0.726312	+	0.527697i	−0.162082	+	0.986777i	$0.551821\pi$
$12$	0.294838	−	0.214212i	0.0851123	−	0.0618377i
$13$	−0.188414	+	0.136890i	−0.0522565	+	0.0379666i	−0.613607	−	0.789612i	$-0.710282\pi$
$13$	−0.188414	+	0.136890i	−0.0522565	+	0.0379666i	0.561350	+	0.827578i	$0.310282\pi$
$14$	2.09740	+	1.52385i	0.560554	+	0.407266i
$15$		0			0
$16$	3.71829	−	2.70150i	0.929573	−	0.675375i
$17$	2.30496	−	7.09394i	0.559035	−	1.72053i	−0.126005	−	0.992030i	$-0.540216\pi$
$17$	2.30496	−	7.09394i	0.559035	−	1.72053i	0.685041	−	0.728505i	$-0.259784\pi$
$18$	−1.53767			−0.362433
$19$	0.232853	−	0.716646i	0.0534200	−	0.164410i	−0.920787	−	0.390065i	$-0.872452\pi$
$19$	0.232853	−	0.716646i	0.0534200	−	0.164410i	0.974207	+	0.225656i	$0.0724524\pi$
$20$		0			0
$21$	−0.521005	−	1.60349i	−0.113693	−	0.349910i
$22$	1.41484	+	4.35444i	0.301646	+	0.928370i
$23$	−0.706046	−	0.512972i	−0.147221	−	0.106962i	0.511737	−	0.859142i	$-0.329002\pi$
$23$	−0.706046	−	0.512972i	−0.147221	−	0.106962i	−0.658958	+	0.752180i	$0.729002\pi$
$24$	−2.51496			−0.513364
$25$		0			0
$26$	−0.358112			−0.0702315
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.189875	+	0.584375i	0.0358830	+	0.110436i
$29$	2.12444	+	6.53835i	0.394498	+	1.21414i	0.929352	+	0.369195i	$0.120367\pi$
$29$	2.12444	+	6.53835i	0.394498	+	1.21414i	−0.534854	+	0.844945i	$0.679633\pi$
$30$		0			0
$31$	−3.03433	+	9.33870i	−0.544981	+	1.67728i	0.176054	+	0.984381i	$0.443667\pi$
$31$	−3.03433	+	9.33870i	−0.544981	+	1.67728i	−0.721035	+	0.692899i	$0.756333\pi$
$32$	2.03733			0.360152
$33$	0.920120	−	2.83184i	0.160172	−	0.492960i
$34$	9.27904	−	6.74162i	1.59134	−	1.15618i
$35$		0			0
$36$	−0.294838	−	0.214212i	−0.0491396	−	0.0357020i
$37$	−8.19304	+	5.95259i	−1.34693	+	0.978600i	−0.347769	+	0.937580i	$0.613061\pi$
$37$	−8.19304	+	5.95259i	−1.34693	+	0.978600i	−0.999158	+	0.0410198i	$0.986939\pi$
$38$	0.937390	−	0.681054i	0.152065	−	0.110482i
$39$	0.188414	+	0.136890i	0.0301703	+	0.0219200i
$40$		0			0
$41$	−3.07210	+	2.23201i	−0.479781	+	0.348581i	−0.801241	−	0.598342i	$-0.795826\pi$
$41$	−3.07210	+	2.23201i	−0.479781	+	0.348581i	0.321460	+	0.946923i	$0.395826\pi$
$42$	0.801135	−	2.46564i	0.123618	−	0.380457i
$43$	−5.27322			−0.804159			−0.402079	−	0.915605i	$-0.631712\pi$
$43$	−5.27322			−0.804159			−0.402079	+	0.915605i	$0.631712\pi$
$44$	−0.335328	+	1.03203i	−0.0505526	+	0.155585i
$45$		0			0
$46$	−0.414688	−	1.27628i	−0.0611425	−	0.188177i
$47$	−2.64749	−	8.14814i	−0.386176	−	1.18853i	−0.935623	−	0.353000i	$-0.885161\pi$
$47$	−2.64749	−	8.14814i	−0.386176	−	1.18853i	0.549447	−	0.835529i	$-0.314839\pi$
$48$	−3.71829	−	2.70150i	−0.536689	−	0.389928i
$49$	−4.15738			−0.593911
$50$		0			0
$51$	−7.45901			−1.04447
$52$	−0.0686654	−	0.0498883i	−0.00952217	−	0.00691826i
$53$	1.84754	+	5.68614i	0.253779	+	0.781051i	0.994068	+	0.108762i	$0.0346887\pi$
$53$	1.84754	+	5.68614i	0.253779	+	0.781051i	−0.740289	+	0.672289i	$0.765311\pi$
$54$	0.475167	+	1.46241i	0.0646621	+	0.199009i
$55$		0			0
$56$	1.31031	−	4.03270i	0.175097	−	0.538893i
$57$	−0.753527			−0.0998070
$58$	−3.26669	+	10.0538i	−0.428937	+	1.32013i
$59$	3.11564	−	2.26365i	0.405622	−	0.294702i	−0.366205	−	0.930534i	$-0.619343\pi$
$59$	3.11564	−	2.26365i	0.405622	−	0.294702i	0.771827	+	0.635833i	$0.219343\pi$
$60$		0			0
$61$	3.55679	+	2.58416i	0.455400	+	0.330867i	0.791724	−	0.610879i	$-0.209184\pi$
$61$	3.55679	+	2.58416i	0.455400	+	0.330867i	−0.336324	+	0.941746i	$0.609184\pi$
$62$	−12.2152	+	8.87488i	−1.55134	+	1.12711i
$63$	−1.36401	+	0.991010i	−0.171849	+	0.124856i
$64$	−4.90214	−	3.56161i	−0.612768	−	0.445202i
$65$		0			0
$66$	3.70411	−	2.69119i	0.455944	−	0.331263i
$67$	0.554013	−	1.70508i	0.0676835	−	0.208308i	−0.911494	−	0.411312i	$-0.865070\pi$
$67$	0.554013	−	1.70508i	0.0676835	−	0.208308i	0.979178	+	0.203004i	$0.0650705\pi$
$68$	2.71836			0.329650
$69$	−0.269686	+	0.830007i	−0.0324663	+	0.0999211i
$70$		0			0
$71$	−1.35179	−	4.16039i	−0.160428	−	0.493748i	0.838242	−	0.545298i	$-0.183584\pi$
$71$	−1.35179	−	4.16039i	−0.160428	−	0.493748i	−0.998670	+	0.0515506i	$0.983584\pi$
$72$	0.777165	+	2.39187i	0.0915897	+	0.281884i
$73$	12.1780	+	8.84783i	1.42533	+	1.03556i	0.990863	+	0.134870i	$0.0430617\pi$
$73$	12.1780	+	8.84783i	1.42533	+	1.03556i	0.434463	+	0.900690i	$0.356938\pi$
$74$	−15.5723			−1.81024
$75$		0			0
$76$	0.274615			0.0315005
$77$	4.06143	+	2.95080i	0.462843	+	0.336275i
$78$	0.110663	+	0.340585i	0.0125301	+	0.0385636i
$79$	2.27926	+	7.01484i	0.256437	+	0.789232i	0.993543	+	0.113455i	$0.0361917\pi$
$79$	2.27926	+	7.01484i	0.256437	+	0.789232i	−0.737106	+	0.675777i	$0.763808\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−5.83904			−0.644814
$83$	1.34253	−	4.13188i	0.147362	−	0.453532i	−0.849946	−	0.526871i	$-0.823365\pi$
$83$	1.34253	−	4.13188i	0.147362	−	0.453532i	0.997307	+	0.0733383i	$0.0233653\pi$
$84$	0.497099	−	0.361163i	0.0542379	−	0.0394061i
$85$		0			0
$86$	−6.55991	−	4.76605i	−0.707373	−	0.513937i
$87$	5.56185	−	4.04092i	0.596293	−	0.433232i
$88$	6.05830	−	4.40161i	0.645817	−	0.469213i
$89$	−9.79170	−	7.11409i	−1.03792	−	0.754092i	−0.0680399	−	0.997683i	$-0.521675\pi$
$89$	−9.79170	−	7.11409i	−1.03792	−	0.754092i	−0.969878	+	0.243591i	$0.921675\pi$
$90$		0			0
$91$	−0.317667	+	0.230798i	−0.0333005	+	0.0241942i
$92$	0.0982841	−	0.302487i	0.0102468	−	0.0315365i
$93$	9.81929			1.01821
$94$	4.07098	−	12.5292i	0.419889	−	1.29229i
$95$		0			0
$96$	−0.629569	−	1.93761i	−0.0642551	−	0.197757i
$97$	2.92771	+	9.01055i	0.297264	+	0.914883i	0.982452	+	0.186517i	$0.0597199\pi$
$97$	2.92771	+	9.01055i	0.297264	+	0.914883i	−0.685188	+	0.728366i	$0.740280\pi$
$98$	−5.17180	−	3.75753i	−0.522430	−	0.379568i
$99$	−2.97757			−0.299257
$100$		0			0
$101$	−6.54468			−0.651220			−0.325610	−	0.945504i	$-0.605570\pi$
$101$	−6.54468			−0.651220			−0.325610	+	0.945504i	$0.605570\pi$
$102$	−9.27904	−	6.74162i	−0.918762	−	0.667520i
$103$	−0.216560	−	0.666504i	−0.0213383	−	0.0656726i	0.939820	−	0.341669i	$-0.110992\pi$
$103$	−0.216560	−	0.666504i	−0.0213383	−	0.0656726i	−0.961159	+	0.275996i	$0.910992\pi$
$104$	0.180995	+	0.557047i	0.0177481	+	0.0546229i
$105$		0			0
$106$	−2.84091	+	8.74342i	−0.275934	+	0.849236i
$107$	12.5288			1.21120			0.605602	−	0.795768i	$-0.292933\pi$
$107$	12.5288			1.21120			0.605602	+	0.795768i	$0.292933\pi$
$108$	−0.112618	+	0.346603i	−0.0108367	+	0.0333519i
$109$	−3.46541	+	2.51776i	−0.331926	+	0.241158i	−0.741247	−	0.671232i	$-0.765765\pi$
$109$	−3.46541	+	2.51776i	−0.331926	+	0.241158i	0.409322	+	0.912390i	$0.365765\pi$
$110$		0			0
$111$	8.19304	+	5.95259i	0.777649	+	0.564995i
$112$	6.26907	−	4.55474i	0.592371	−	0.430383i
$113$	−6.65628	+	4.83607i	−0.626170	+	0.454939i	−0.855071	−	0.518511i	$-0.826487\pi$
$113$	−6.65628	+	4.83607i	−0.626170	+	0.454939i	0.228901	+	0.973450i	$0.426487\pi$
$114$	−0.937390	−	0.681054i	−0.0877946	−	0.0637865i
$115$		0			0
$116$	−2.02696	+	1.47267i	−0.188198	+	0.136734i
$117$	0.0719676	−	0.221493i	0.00665340	−	0.0204771i
$118$	5.92180			0.545146
$119$	3.88618	−	11.9604i	0.356246	−	1.09641i
$120$		0			0
$121$	−0.659464	−	2.02962i	−0.0599512	−	0.184511i
$122$	2.08904	+	6.42940i	0.189133	+	0.582091i
$123$	3.07210	+	2.23201i	0.277002	+	0.201253i
$124$	−3.57854			−0.321362
$125$		0			0
$126$	−2.59253			−0.230961
$127$	−9.66627	−	7.02296i	−0.857743	−	0.623187i	0.0695269	−	0.997580i	$-0.477851\pi$
$127$	−9.66627	−	7.02296i	−0.857743	−	0.623187i	−0.927270	+	0.374393i	$0.877851\pi$
$128$	−4.13836	−	12.7366i	−0.365783	−	1.12576i
$129$	1.62951	+	5.01513i	0.143471	+	0.441558i
$130$		0			0
$131$	6.63068	−	20.4071i	0.579326	−	1.78298i	−0.0416276	−	0.999133i	$-0.513254\pi$
$131$	6.63068	−	20.4071i	0.579326	−	1.78298i	0.620953	−	0.783848i	$-0.286746\pi$
$132$	1.08514			0.0944497
$133$	0.392591	−	1.20827i	0.0340420	−	0.104770i
$134$	2.23028	−	1.62039i	0.192667	−	0.139981i
$135$		0			0
$136$	−15.1764	−	11.0263i	−1.30137	−	0.945500i
$137$	−8.10570	+	5.88914i	−0.692517	+	0.503143i	−0.877487	−	0.479601i	$-0.840781\pi$
$137$	−8.10570	+	5.88914i	−0.692517	+	0.503143i	0.184970	+	0.982744i	$0.440781\pi$
$138$	−1.08567	+	0.788784i	−0.0924182	+	0.0671458i
$139$	5.31902	+	3.86450i	0.451154	+	0.327782i	0.790051	−	0.613041i	$-0.210054\pi$
$139$	5.31902	+	3.86450i	0.451154	+	0.327782i	−0.338897	+	0.940823i	$0.610054\pi$
$140$		0			0
$141$	−6.93123	+	5.03583i	−0.583714	+	0.424093i
$142$	2.07862	−	6.39733i	0.174434	−	0.536852i
$143$	−0.693452			−0.0579894
$144$	−1.42026	+	4.37112i	−0.118355	+	0.364260i
$145$		0			0
$146$	7.15261	+	22.0135i	0.591954	+	1.82185i
$147$	1.28470	+	3.95390i	0.105960	+	0.326112i
$148$	−2.98587	−	2.16936i	−0.245437	−	0.178320i
$149$	10.9143			0.894132			0.447066	−	0.894501i	$-0.352469\pi$
$149$	10.9143			0.894132			0.447066	+	0.894501i	$0.352469\pi$
$150$		0			0
$151$	20.4128			1.66117			0.830584	−	0.556894i	$-0.188007\pi$
$151$	20.4128			1.66117			0.830584	+	0.556894i	$0.188007\pi$
$152$	−1.53316	−	1.11390i	−0.124356	−	0.0903496i
$153$	2.30496	+	7.09394i	0.186345	+	0.573511i
$154$	2.38544	+	7.34162i	0.192224	+	0.591605i
$155$		0			0
$156$	−0.0262278	+	0.0807210i	−0.00209991	+	0.00646285i
$157$	3.49944			0.279286			0.139643	−	0.990202i	$-0.455405\pi$
$157$	3.49944			0.279286			0.139643	+	0.990202i	$0.455405\pi$
$158$	−3.50476	+	10.7865i	−0.278824	+	0.858131i
$159$	4.83692	−	3.51423i	0.383592	−	0.278696i
$160$		0			0
$161$	−1.19040	−	0.864875i	−0.0938165	−	0.0681617i
$162$	1.24400	−	0.903822i	0.0977382	−	0.0710109i
$163$	−4.83272	+	3.51118i	−0.378528	+	0.275017i	−0.760738	−	0.649059i	$-0.775163\pi$
$163$	−4.83272	+	3.51118i	−0.378528	+	0.275017i	0.382210	+	0.924075i	$0.375163\pi$
$164$	−1.11959	−	0.813432i	−0.0874256	−	0.0635184i
$165$		0			0
$166$	5.40459	−	3.92666i	0.419477	−	0.304768i
$167$	−0.722381	+	2.22326i	−0.0558995	+	0.172041i	−0.975108	−	0.221730i	$-0.928830\pi$
$167$	−0.722381	+	2.22326i	−0.0558995	+	0.172041i	0.919209	+	0.393771i	$0.128830\pi$
$168$	−4.24024			−0.327141
$169$	−4.00046	+	12.3122i	−0.307728	+	0.947089i
$170$		0			0
$171$	0.232853	+	0.716646i	0.0178067	+	0.0548033i
$172$	−0.593860	−	1.82771i	−0.0452814	−	0.139362i
$173$	−4.91154	−	3.56844i	−0.373417	−	0.271303i	0.385209	−	0.922829i	$-0.374129\pi$
$173$	−4.91154	−	3.56844i	−0.373417	−	0.271303i	−0.758626	+	0.651526i	$0.774129\pi$
$174$	10.5712			0.801403
$175$		0			0
$176$	13.6851			1.03155
$177$	−3.11564	−	2.26365i	−0.234186	−	0.170146i
$178$	−5.75105	−	17.6999i	−0.431059	−	1.32666i
$179$	3.53007	+	10.8644i	0.263850	+	0.812045i	0.991956	+	0.126581i	$0.0404005\pi$
$179$	3.53007	+	10.8644i	0.263850	+	0.812045i	−0.728107	+	0.685464i	$0.759599\pi$
$180$		0			0
$181$	−2.42581	+	7.46586i	−0.180309	+	0.554933i	−0.999836	−	0.0181070i	$-0.994236\pi$
$181$	−2.42581	+	7.46586i	−0.180309	+	0.554933i	0.819527	+	0.573040i	$0.194236\pi$
$182$	−0.603779			−0.0447551
$183$	1.35857	−	4.18125i	0.100428	−	0.309087i
$184$	−1.77568	+	1.29010i	−0.130905	+	0.0951077i
$185$		0			0
$186$	12.2152	+	8.87488i	0.895664	+	0.650738i
$187$	17.9681	−	13.0546i	1.31395	−	0.954644i
$188$	2.52601	−	1.83526i	0.184228	−	0.133850i
$189$	1.36401	+	0.991010i	0.0992170	+	0.0720854i
$190$		0			0
$191$	−10.1646	+	7.38502i	−0.735485	+	0.534361i	−0.891294	−	0.453426i	$-0.850202\pi$
$191$	−10.1646	+	7.38502i	−0.735485	+	0.534361i	0.155809	+	0.987787i	$0.450202\pi$
$192$	−1.87245	+	5.76281i	−0.135133	+	0.415895i
$193$	−10.1437			−0.730161			−0.365081	−	0.930976i	$-0.618959\pi$
$193$	−10.1437			−0.730161			−0.365081	+	0.930976i	$0.618959\pi$
$194$	−4.50186	+	13.8553i	−0.323214	+	0.994752i
$195$		0			0
$196$	−0.468196	−	1.44096i	−0.0334426	−	0.102926i
$197$	−0.632566	−	1.94684i	−0.0450685	−	0.138706i	0.925990	−	0.377547i	$-0.123233\pi$
$197$	−0.632566	−	1.94684i	−0.0450685	−	0.138706i	−0.971059	+	0.238841i	$0.923233\pi$
$198$	−3.70411	−	2.69119i	−0.263240	−	0.191255i
$199$	3.57125			0.253159			0.126580	−	0.991956i	$-0.459600\pi$
$199$	3.57125			0.253159			0.126580	+	0.991956i	$0.459600\pi$
$200$		0			0
$201$	−1.79282			−0.126456
$202$	−8.14161	−	5.91522i	−0.572842	−	0.416194i
$203$	3.58182	+	11.0237i	0.251394	+	0.773712i
$204$	−0.840020	−	2.58531i	−0.0588131	−	0.181008i
$205$		0			0
$206$	0.332999	−	1.02487i	0.0232011	−	0.0714058i
$207$	0.872721			0.0606583
$208$	−0.330767	+	1.01800i	−0.0229346	+	0.0705854i
$209$	1.81517	−	1.31880i	0.125558	−	0.0912234i
$210$		0			0
$211$	−3.01474	−	2.19034i	−0.207543	−	0.150789i	0.479158	−	0.877729i	$-0.340942\pi$
$211$	−3.01474	−	2.19034i	−0.207543	−	0.150789i	−0.686701	+	0.726940i	$0.740942\pi$
$212$	−1.76276	+	1.28072i	−0.121067	+	0.0879604i
$213$	−3.53904	+	2.57126i	−0.242491	+	0.176180i
$214$	15.5859	+	11.3238i	1.06543	+	0.774078i
$215$		0			0
$216$	2.03464	−	1.47826i	0.138440	−	0.100583i
$217$	−5.11590	+	15.7451i	−0.347290	+	1.06885i
$218$	−6.58659			−0.446100
$219$	4.65158	−	14.3161i	0.314325	−	0.967391i
$220$		0			0
$221$	0.536807	+	1.65212i	0.0361096	+	0.111134i
$222$	4.81209	+	14.8101i	0.322966	+	0.993988i
$223$	−21.2357	−	15.4287i	−1.42205	−	1.03318i	−0.991429	−	0.130647i	$-0.958294\pi$
$223$	−21.2357	−	15.4287i	−1.42205	−	1.03318i	−0.430622	−	0.902533i	$-0.641706\pi$
$224$	3.43495			0.229507
$225$		0			0
$226$	−12.6514			−0.841557
$227$	3.63338	+	2.63981i	0.241156	+	0.175210i	0.701798	−	0.712376i	$-0.252381\pi$
$227$	3.63338	+	2.63981i	0.241156	+	0.175210i	−0.460642	+	0.887586i	$0.652381\pi$
$228$	−0.0848607	−	0.261174i	−0.00562004	−	0.0172967i
$229$	−2.32979	−	7.17035i	−0.153957	−	0.473830i	0.844097	−	0.536191i	$-0.180137\pi$
$229$	−2.32979	−	7.17035i	−0.153957	−	0.473830i	−0.998054	+	0.0623605i	$0.980137\pi$
$230$		0			0
$231$	1.55133	−	4.77450i	0.102070	−	0.314139i
$232$	17.2899			1.13514
$233$	3.20266	−	9.85679i	0.209814	−	0.645740i	−0.789668	−	0.613535i	$-0.789747\pi$
$233$	3.20266	−	9.85679i	0.209814	−	0.645740i	0.999481	−	0.0322049i	$-0.0102529\pi$
$234$	0.289719	−	0.210493i	0.0189395	−	0.0137603i
$235$		0			0
$236$	1.13546	+	0.824962i	0.0739124	+	0.0537005i
$237$	5.96718	−	4.33541i	0.387610	−	0.281615i
$238$	15.6445	−	11.3664i	1.01408	−	0.736775i
$239$	15.0265	+	10.9174i	0.971985	+	0.706188i	0.955903	−	0.293683i	$-0.0948809\pi$
$239$	15.0265	+	10.9174i	0.971985	+	0.706188i	0.0160815	+	0.999871i	$0.494881\pi$
$240$		0			0
$241$	4.39735	−	3.19486i	0.283258	−	0.205799i	−0.437079	−	0.899423i	$-0.643987\pi$
$241$	4.39735	−	3.19486i	0.283258	−	0.205799i	0.720337	+	0.693624i	$0.243987\pi$
$242$	1.01404	−	3.12089i	0.0651849	−	0.200619i
$243$	−1.00000			−0.0641500
$244$	−0.495117	+	1.52381i	−0.0316966	+	0.0975522i
$245$		0			0
$246$	1.80436	+	5.55325i	0.115042	+	0.354063i
$247$	0.0542295	+	0.166901i	0.00345054	+	0.0106197i
$248$	19.9787	+	14.5154i	1.26865	+	0.921729i
$249$	−4.34451			−0.275322
$250$		0			0
$251$	23.3577			1.47432			0.737162	−	0.675716i	$-0.236166\pi$
$251$	23.3577			1.47432			0.737162	+	0.675716i	$0.236166\pi$
$252$	−0.497099	−	0.361163i	−0.0313143	−	0.0227511i
$253$	−0.803008	−	2.47140i	−0.0504847	−	0.155376i
$254$	−5.67738	−	17.4732i	−0.356230	−	1.09636i
$255$		0			0
$256$	2.61854	−	8.05903i	0.163659	−	0.503690i
$257$	4.48380			0.279692			0.139846	−	0.990173i	$-0.455339\pi$
$257$	4.48380			0.279692			0.139846	+	0.990173i	$0.455339\pi$
$258$	−2.50566	+	7.71163i	−0.155996	+	0.480105i
$259$	−13.8135	+	10.0361i	−0.858330	+	0.623614i
$260$		0			0
$261$	−5.56185	−	4.04092i	−0.344270	−	0.250127i
$262$	26.6930	−	19.3936i	1.64910	−	1.19814i
$263$	6.25006	−	4.54093i	0.385395	−	0.280006i	−0.378171	−	0.925736i	$-0.623447\pi$
$263$	6.25006	−	4.54093i	0.385395	−	0.280006i	0.763566	+	0.645730i	$0.223447\pi$
$264$	−6.05830	−	4.40161i	−0.372862	−	0.270900i
$265$		0			0
$266$	1.58045	−	1.14826i	0.0969034	−	0.0704044i
$267$	−3.74010	+	11.5108i	−0.228890	+	0.704451i
$268$	0.653376			0.0399113
$269$	3.31865	−	10.2138i	0.202342	−	0.622743i	−0.797470	−	0.603358i	$-0.793829\pi$
$269$	3.31865	−	10.2138i	0.202342	−	0.622743i	0.999812	−	0.0193855i	$-0.00617097\pi$
$270$		0			0
$271$	−7.94563	−	24.4541i	−0.482662	−	1.48548i	−0.835338	−	0.549737i	$-0.814728\pi$
$271$	−7.94563	−	24.4541i	−0.482662	−	1.48548i	0.352676	−	0.935746i	$-0.385272\pi$
$272$	−10.5938	−	32.6042i	−0.642341	−	1.97692i
$273$	0.317667	+	0.230798i	0.0192261	+	0.0139685i
$274$	−15.4063			−0.930726
$275$		0			0
$276$	−0.318054			−0.0191446
$277$	−7.78635	−	5.65712i	−0.467837	−	0.339903i	0.328761	−	0.944413i	$-0.393369\pi$
$277$	−7.78635	−	5.65712i	−0.467837	−	0.339903i	−0.796598	+	0.604510i	$0.793369\pi$
$278$	3.12407	+	9.61490i	0.187369	+	0.576663i
$279$	−3.03433	−	9.33870i	−0.181660	−	0.559093i
$280$		0			0
$281$	−0.875368	+	2.69411i	−0.0522201	+	0.160717i	−0.973766	−	0.227553i	$-0.926927\pi$
$281$	−0.875368	+	2.69411i	−0.0522201	+	0.160717i	0.921545	+	0.388270i	$0.126927\pi$
$282$	−13.1740			−0.784498
$283$	7.31238	−	22.5052i	0.434676	−	1.33780i	−0.458742	−	0.888569i	$-0.651700\pi$
$283$	7.31238	−	22.5052i	0.434676	−	1.33780i	0.893418	−	0.449226i	$-0.148300\pi$
$284$	1.28977	−	0.937071i	0.0765336	−	0.0556049i
$285$		0			0
$286$	−0.862658	−	0.626757i	−0.0510100	−	0.0370609i
$287$	−5.17958	+	3.76318i	−0.305741	+	0.222134i
$288$	−1.64823	+	1.19751i	−0.0971231	+	0.0705640i
$289$	−31.2579	−	22.7102i	−1.83870	−	1.33589i
$290$		0			0
$291$	7.66483	−	5.56883i	0.449321	−	0.326450i
$292$	−1.69522	+	5.21735i	−0.0992052	+	0.305322i
$293$	23.2376			1.35755			0.678777	−	0.734345i	$-0.262510\pi$
$293$	23.2376			1.35755			0.678777	+	0.734345i	$0.262510\pi$
$294$	−1.97545	+	6.07981i	−0.115211	+	0.354582i
$295$		0			0
$296$	7.87047	+	24.2228i	0.457462	+	1.40792i
$297$	0.920120	+	2.83184i	0.0533908	+	0.164320i
$298$	13.5774	+	9.86455i	0.786517	+	0.571438i
$299$	0.203250			0.0117542
$300$		0			0
$301$	−8.89069			−0.512451
$302$	25.3936	+	18.4495i	1.46124	+	1.06165i
$303$	2.02242	+	6.22436i	0.116185	+	0.357580i
$304$	−1.07020	−	3.29375i	−0.0613805	−	0.188910i
$305$		0			0
$306$	−3.54428	+	10.9082i	−0.202613	+	0.623579i
$307$	−21.8131			−1.24494			−0.622470	−	0.782643i	$-0.713871\pi$
$307$	−21.8131			−1.24494			−0.622470	+	0.782643i	$0.713871\pi$
$308$	−0.565366	+	1.74002i	−0.0322147	+	0.0991467i
$309$	−0.566962	+	0.411922i	−0.0322533	+	0.0234334i
$310$		0			0
$311$	−8.12364	−	5.90217i	−0.460649	−	0.334681i	0.333137	−	0.942879i	$-0.391893\pi$
$311$	−8.12364	−	5.90217i	−0.460649	−	0.334681i	−0.793786	+	0.608197i	$0.791893\pi$
$312$	0.473852	−	0.344274i	0.0268266	−	0.0194907i
$313$	−4.89752	+	3.55825i	−0.276824	+	0.201124i	−0.717531	−	0.696527i	$-0.754728\pi$
$313$	−4.89752	+	3.55825i	−0.276824	+	0.201124i	0.440707	+	0.897651i	$0.354728\pi$
$314$	4.35332	+	3.16287i	0.245672	+	0.178491i
$315$		0			0
$316$	−2.17468	+	1.58000i	−0.122335	+	0.0888817i
$317$	−2.62636	+	8.08309i	−0.147511	+	0.453992i	−0.997325	−	0.0730902i	$-0.976714\pi$
$317$	−2.62636	+	8.08309i	−0.147511	+	0.453992i	0.849814	+	0.527082i	$0.176714\pi$
$318$	9.19338			0.515539
$319$	−6.32566	+	19.4684i	−0.354169	+	1.09002i
$320$		0			0
$321$	−3.87161	−	11.9156i	−0.216092	−	0.665063i
$322$	−0.699167	−	2.15182i	−0.0389631	−	0.119916i
$323$	−4.54713	−	3.30369i	−0.253009	−	0.183822i
$324$	0.364440			0.0202466
$325$		0			0
$326$	−9.18540			−0.508733
$327$	3.46541	+	2.51776i	0.191637	+	0.139233i
$328$	2.95114	+	9.08268i	0.162950	+	0.501507i
$329$	−4.46369	−	13.7378i	−0.246091	−	0.757391i
$330$		0			0
$331$	5.03526	−	15.4969i	0.276763	−	0.851789i	−0.711984	−	0.702195i	$-0.752203\pi$
$331$	5.03526	−	15.4969i	0.276763	−	0.851789i	0.988748	−	0.149594i	$-0.0477966\pi$
$332$	1.58331			0.0868955
$333$	3.12946	−	9.63150i	0.171493	−	0.527803i
$334$	−2.90808	+	2.11284i	−0.159123	+	0.115610i
$335$		0			0
$336$	−6.26907	−	4.55474i	−0.342006	−	0.248482i
$337$	−19.9796	+	14.5161i	−1.08836	+	0.790740i	−0.979122	−	0.203275i	$-0.934841\pi$
$337$	−19.9796	+	14.5161i	−1.08836	+	0.790740i	−0.109239	+	0.994015i	$0.534841\pi$
$338$	−16.1046	+	11.7007i	−0.875974	+	0.636432i
$339$	6.65628	+	4.83607i	0.361519	+	0.262659i
$340$		0			0
$341$	−23.6537	+	17.1854i	−1.28092	+	0.930644i
$342$	−0.358051	+	1.10197i	−0.0193612	+	0.0595876i
$343$	−18.8114			−1.01572
$344$	−4.09816	+	12.6128i	−0.220958	+	0.680039i
$345$		0			0
$346$	−2.88474	−	8.87831i	−0.155084	−	0.477301i
$347$	−4.30975	−	13.2640i	−0.231359	−	0.712051i	−0.997584	−	0.0694775i	$-0.977867\pi$
$347$	−4.30975	−	13.2640i	−0.231359	−	0.712051i	0.766224	−	0.642573i	$-0.222133\pi$
$348$	2.02696	+	1.47267i	0.108656	+	0.0789435i
$349$	18.4966			0.990099			0.495049	−	0.868865i	$-0.335150\pi$
$349$	18.4966			0.990099			0.495049	+	0.868865i	$0.335150\pi$
$350$		0			0
$351$	−0.232892			−0.0124309
$352$	4.90773	+	3.56568i	0.261583	+	0.190051i
$353$	−0.136503	−	0.420113i	−0.00726532	−	0.0223604i	0.947358	−	0.320176i	$-0.103742\pi$
$353$	−0.136503	−	0.420113i	−0.00726532	−	0.0223604i	−0.954623	+	0.297815i	$0.903742\pi$
$354$	−1.82994	−	5.63197i	−0.0972601	−	0.299336i
$355$		0			0
$356$	1.36304	−	4.19500i	0.0722409	−	0.222335i
$357$	−12.5760			−0.665590
$358$	−5.42809	+	16.7059i	−0.286883	+	0.882936i
$359$	−3.73869	+	2.71631i	−0.197320	+	0.143362i	−0.682058	−	0.731298i	$-0.738915\pi$
$359$	−3.73869	+	2.71631i	−0.197320	+	0.143362i	0.484738	+	0.874659i	$0.338915\pi$
$360$		0			0
$361$	14.9120	+	10.8342i	0.784840	+	0.570220i
$362$	−9.76552	+	7.09506i	−0.513264	+	0.372908i
$363$	−1.72650	+	1.25437i	−0.0906176	+	0.0658376i
$364$	−0.115770	−	0.0841120i	−0.00606801	−	0.00440867i
$365$		0			0
$366$	5.46917	−	3.97359i	0.285878	−	0.207703i
$367$	2.71223	−	8.34738i	0.141577	−	0.435730i	−0.854978	−	0.518665i	$-0.826429\pi$
$367$	2.71223	−	8.34738i	0.141577	−	0.435730i	0.996555	+	0.0829348i	$0.0264293\pi$
$368$	−4.01108			−0.209092
$369$	1.17344	−	3.61147i	0.0610867	−	0.188005i
$370$		0			0
$371$	3.11496	+	9.58687i	0.161721	+	0.497725i
$372$	1.10583	+	3.40339i	0.0573345	+	0.176458i
$373$	12.5361	+	9.10804i	0.649097	+	0.471596i	0.862963	−	0.505266i	$-0.168606\pi$
$373$	12.5361	+	9.10804i	0.649097	+	0.471596i	−0.213867	+	0.976863i	$0.568606\pi$
$374$	34.1513			1.76592
$375$		0			0
$376$	−21.5468			−1.11119
$377$	−1.29531	−	0.941098i	−0.0667118	−	0.0484690i
$378$	0.801135	+	2.46564i	0.0412060	+	0.126819i
$379$	−8.43404	−	25.9573i	−0.433227	−	1.33334i	−0.894892	−	0.446282i	$-0.852748\pi$
$379$	−8.43404	−	25.9573i	−0.433227	−	1.33334i	0.461665	−	0.887054i	$-0.347252\pi$
$380$		0			0
$381$	−3.69219	+	11.3634i	−0.189157	+	0.582164i
$382$	−19.3196			−0.988474
$383$	−4.04941	+	12.4628i	−0.206915	+	0.636820i	0.792714	+	0.609594i	$0.208667\pi$
$383$	−4.04941	+	12.4628i	−0.206915	+	0.636820i	−0.999629	+	0.0272261i	$0.991333\pi$
$384$	−10.8344	+	7.87162i	−0.552889	+	0.401697i
$385$		0			0
$386$	−12.6188	−	9.16812i	−0.642282	−	0.466645i
$387$	4.26612	−	3.09952i	0.216859	−	0.157558i
$388$	−2.79337	+	2.02950i	−0.141812	+	0.103032i
$389$	−13.6769	−	9.93685i	−0.693447	−	0.503818i	0.184345	−	0.982862i	$-0.440984\pi$
$389$	−13.6769	−	9.93685i	−0.693447	−	0.503818i	−0.877791	+	0.479043i	$0.840984\pi$
$390$		0			0
$391$	−5.26641	+	3.82627i	−0.266334	+	0.193503i
$392$	−3.23097	+	9.94390i	−0.163189	+	0.502243i
$393$	−21.4573			−1.08238
$394$	0.972680	−	2.99360i	0.0490029	−	0.150815i
$395$		0			0
$396$	−0.335328	−	1.03203i	−0.0168509	−	0.0518617i
$397$	3.21619	+	9.89842i	0.161416	+	0.496787i	0.998754	−	0.0498977i	$-0.0158895\pi$
$397$	3.21619	+	9.89842i	0.161416	+	0.496787i	−0.837338	+	0.546685i	$0.815890\pi$
$398$	4.44265	+	3.22778i	0.222690	+	0.161794i
$399$	−1.27045			−0.0636021
$400$		0			0
$401$	−0.694800			−0.0346967			−0.0173483	−	0.999850i	$-0.505522\pi$
$401$	−0.694800			−0.0346967			−0.0173483	+	0.999850i	$0.505522\pi$
$402$	−2.23028	−	1.62039i	−0.111236	−	0.0808179i
$403$	−0.706670	−	2.17491i	−0.0352017	−	0.108340i
$404$	−0.737049	−	2.26840i	−0.0366696	−	0.112857i
$405$		0			0
$406$	−5.50766	+	16.9508i	−0.273341	+	0.841256i
$407$	−30.1543			−1.49469
$408$	−5.79688	+	17.8410i	−0.286988	+	0.883260i
$409$	0.962002	−	0.698936i	0.0475680	−	0.0345601i	−0.563747	−	0.825947i	$-0.690641\pi$
$409$	0.962002	−	0.698936i	0.0475680	−	0.0345601i	0.611315	+	0.791387i	$0.290641\pi$
$410$		0			0
$411$	8.10570	+	5.88914i	0.399825	+	0.290490i
$412$	0.206623	−	0.150121i	0.0101796	−	0.00739592i
$413$	5.25299	−	3.81652i	0.258483	−	0.187799i
$414$	1.08567	+	0.788784i	0.0533577	+	0.0387666i
$415$		0			0
$416$	−0.383860	+	0.278891i	−0.0188203	+	0.0136737i
$417$	2.03169	−	6.25289i	0.0994921	−	0.306205i
$418$	3.45005			0.168747
$419$	0.611361	−	1.88158i	0.0298670	−	0.0919210i	−0.935012	−	0.354616i	$-0.884611\pi$
$419$	0.611361	−	1.88158i	0.0298670	−	0.0919210i	0.964879	+	0.262695i	$0.0846114\pi$
$420$		0			0
$421$	3.42467	+	10.5400i	0.166908	+	0.513690i	0.999172	−	0.0406895i	$-0.0129554\pi$
$421$	3.42467	+	10.5400i	0.166908	+	0.513690i	−0.832264	+	0.554380i	$0.812955\pi$
$422$	−1.77068	−	5.44958i	−0.0861951	−	0.265281i
$423$	6.93123	+	5.03583i	0.337008	+	0.244850i
$424$	15.0363			0.730229
$425$		0			0
$426$	−6.72655			−0.325902
$427$	5.99677	+	4.35690i	0.290204	+	0.210845i
$428$	1.41097	+	4.34251i	0.0682017	+	0.209903i
$429$	0.214289	+	0.659512i	0.0103460	+	0.0318416i
$430$		0			0
$431$	−3.21800	+	9.90398i	−0.155005	+	0.477058i	−0.998161	−	0.0606112i	$-0.980695\pi$
$431$	−3.21800	+	9.90398i	−0.155005	+	0.477058i	0.843156	+	0.537669i	$0.180695\pi$
$432$	4.59606			0.221128
$433$	3.17185	−	9.76195i	0.152429	−	0.469129i	−0.845462	−	0.534035i	$-0.820675\pi$
$433$	3.17185	−	9.76195i	0.152429	−	0.469129i	0.997891	+	0.0649063i	$0.0206749\pi$
$434$	−20.5950	+	14.9631i	−0.988590	+	0.718253i
$435$		0			0
$436$	−1.26293	−	0.917573i	−0.0604834	−	0.0439438i
$437$	−0.532024	+	0.386538i	−0.0254502	+	0.0184906i
$438$	18.7258	−	13.6051i	0.894752	−	0.650075i
$439$	19.9920	+	14.5251i	0.954168	+	0.693244i	0.951789	−	0.306753i	$-0.0992427\pi$
$439$	19.9920	+	14.5251i	0.954168	+	0.693244i	0.00237925	+	0.999997i	$0.499243\pi$
$440$		0			0
$441$	3.36339	−	2.44365i	0.160161	−	0.116364i
$442$	−0.825434	+	2.54043i	−0.0392619	+	0.120836i
$443$	−7.52935			−0.357730			−0.178865	−	0.983874i	$-0.557243\pi$
$443$	−7.52935			−0.357730			−0.178865	+	0.983874i	$0.557243\pi$
$444$	−1.14050	+	3.51010i	−0.0541257	+	0.166582i
$445$		0			0
$446$	−12.4726	−	38.3867i	−0.590594	−	1.81766i
$447$	−3.37269	−	10.3801i	−0.159523	−	0.490961i
$448$	−8.26505	−	6.00491i	−0.390487	−	0.283705i
$449$	−31.6627			−1.49426			−0.747128	−	0.664681i	$-0.768568\pi$
$449$	−31.6627			−1.49426			−0.747128	+	0.664681i	$0.768568\pi$
$450$		0			0
$451$	−11.3068			−0.532416
$452$	−2.42581	−	1.76245i	−0.114101	−	0.0828989i
$453$	−6.30789	−	19.4137i	−0.296371	−	0.912135i
$454$	2.13403	+	6.56786i	0.100155	+	0.308245i
$455$		0			0
$456$	−0.585614	+	1.80234i	−0.0274239	+	0.0844021i
$457$	−2.95742			−0.138342			−0.0691712	−	0.997605i	$-0.522035\pi$
$457$	−2.95742			−0.138342			−0.0691712	+	0.997605i	$0.522035\pi$
$458$	3.58245	−	11.0257i	0.167397	−	0.515195i
$459$	6.03447	−	4.38430i	0.281665	−	0.204642i
$460$		0			0
$461$	14.2396	+	10.3457i	0.663204	+	0.481846i	0.867743	−	0.497012i	$-0.165570\pi$
$461$	14.2396	+	10.3457i	0.663204	+	0.481846i	−0.204539	+	0.978858i	$0.565570\pi$
$462$	6.24516	−	4.53737i	0.290551	−	0.211098i
$463$	−21.3112	+	15.4835i	−0.990414	+	0.719578i	−0.960012	−	0.279960i	$-0.909679\pi$
$463$	−21.3112	+	15.4835i	−0.990414	+	0.719578i	−0.0304024	+	0.999538i	$0.509679\pi$
$464$	25.5626	+	18.5723i	1.18671	+	0.862198i
$465$		0			0
$466$	12.8929	−	9.36724i	0.597252	−	0.433929i
$467$	2.27408	−	6.99888i	0.105232	−	0.323870i	−0.884553	−	0.466439i	$-0.845537\pi$
$467$	2.27408	−	6.99888i	0.105232	−	0.323870i	0.989785	+	0.142570i	$0.0455365\pi$
$468$	0.0848751			0.00392335
$469$	0.934070	−	2.87477i	0.0431313	−	0.132745i
$470$		0			0
$471$	−1.08139	−	3.32816i	−0.0498276	−	0.153354i
$472$	−2.99297	−	9.21143i	−0.137763	−	0.423990i
$473$	−12.7027	−	9.22905i	−0.584070	−	0.424352i
$474$	11.3416			0.520939
$475$		0			0
$476$	4.58317			0.210069
$477$	−4.83692	−	3.51423i	−0.221467	−	0.160905i
$478$	8.82566	+	27.1626i	0.403676	+	1.24239i
$479$	−8.79679	−	27.0737i	−0.401936	−	1.23703i	−0.923427	−	0.383774i	$-0.874624\pi$
$479$	−8.79679	−	27.0737i	−0.401936	−	1.23703i	0.521491	−	0.853257i	$-0.325376\pi$
$480$		0			0
$481$	0.728827	−	2.24310i	0.0332316	−	0.102276i
$482$	8.35791			0.380692
$483$	−0.454692	+	1.39940i	−0.0206892	+	0.0636748i
$484$	0.629204	−	0.457144i	0.0286002	−	0.0207793i
$485$		0			0
$486$	−1.24400	−	0.903822i	−0.0564292	−	0.0409982i
$487$	−1.92875	+	1.40132i	−0.0873999	+	0.0634998i	−0.630627	−	0.776086i	$-0.717202\pi$
$487$	−1.92875	+	1.40132i	−0.0873999	+	0.0634998i	0.543227	+	0.839586i	$0.317202\pi$
$488$	8.94516	−	6.49904i	0.404929	−	0.294198i
$489$	4.83272	+	3.51118i	0.218543	+	0.158781i
$490$		0			0
$491$	20.8105	−	15.1197i	0.939163	−	0.682342i	−0.00905626	−	0.999959i	$-0.502883\pi$
$491$	20.8105	−	15.1197i	0.939163	−	0.682342i	0.948219	+	0.317617i	$0.102883\pi$
$492$	−0.427647	+	1.31616i	−0.0192798	+	0.0593371i
$493$	51.2794			2.30951
$494$	−0.0833872	+	0.256640i	−0.00375177	+	0.0115468i
$495$		0			0
$496$	13.9460	+	42.9212i	0.626192	+	1.92722i
$497$	−2.27913	−	7.01445i	−0.102233	−	0.314641i
$498$	−5.40459	−	3.92666i	−0.242185	−	0.175958i
$499$	29.9989			1.34293			0.671467	−	0.741035i	$-0.265665\pi$
$499$	29.9989			1.34293			0.671467	+	0.741035i	$0.265665\pi$
$500$		0			0
$501$	2.33767			0.104440
$502$	29.0570	+	21.1112i	1.29688	+	0.942238i
$503$	−4.27216	−	13.1483i	−0.190486	−	0.586256i	0.809514	−	0.587101i	$-0.199731\pi$
$503$	−4.27216	−	13.1483i	−0.190486	−	0.586256i	−1.00000		0.000845408i	$0.999731\pi$
$504$	1.31031	+	4.03270i	0.0583656	+	0.179631i
$505$		0			0
$506$	1.23476	−	3.80021i	0.0548920	−	0.168940i
$507$	12.9458			0.574941
$508$	1.34558	−	4.14127i	0.0597004	−	0.183739i
$509$	−25.8511	+	18.7819i	−1.14583	+	0.832493i	−0.987921	−	0.154960i	$-0.950475\pi$
$509$	−25.8511	+	18.7819i	−1.14583	+	0.832493i	−0.157908	+	0.987454i	$0.550475\pi$
$510$		0			0
$511$	20.5322	+	14.9175i	0.908290	+	0.659911i
$512$	−11.1273	+	8.08447i	−0.491763	+	0.357286i
$513$	0.609616	−	0.442912i	0.0269152	−	0.0195550i
$514$	5.57787	+	4.05256i	0.246029	+	0.178751i
$515$		0			0
$516$	−1.55474	+	1.12959i	−0.0684438	+	0.0497273i
$517$	7.88310	−	24.2617i	0.346698	−	1.06703i
$518$	−26.2549			−1.15358
$519$	−1.87604	+	5.77386i	−0.0823490	+	0.253444i
$520$		0			0
$521$	−11.9889	−	36.8979i	−0.525242	−	1.61653i	−0.763837	−	0.645409i	$-0.776687\pi$
$521$	−11.9889	−	36.8979i	−0.525242	−	1.61653i	0.238595	−	0.971119i	$-0.423313\pi$
$522$	−3.26669	−	10.0538i	−0.142979	−	0.440045i
$523$	−19.1853	−	13.9389i	−0.838914	−	0.609507i	0.0831532	−	0.996537i	$-0.473501\pi$
$523$	−19.1853	−	13.9389i	−0.838914	−	0.609507i	−0.922067	+	0.387030i	$0.873501\pi$
$524$	7.81991			0.341614
$525$		0			0
$526$	11.8793			0.517962
$527$	59.2542	+	43.0507i	2.58115	+	1.87532i
$528$	−4.22893	−	13.0153i	−0.184041	−	0.566419i
$529$	−6.87203	−	21.1499i	−0.298784	−	0.919562i
$530$		0			0
$531$	−1.19007	+	3.66266i	−0.0516446	+	0.158946i
$532$	0.463003			0.0200737
$533$	0.273284	−	0.841081i	0.0118372	−	0.0364313i
$534$	−15.0564	+	10.9391i	−0.651556	+	0.473383i
$535$		0			0
$536$	−3.64776	−	2.65025i	−0.157559	−	0.114473i
$537$	9.24183	−	6.71458i	0.398815	−	0.289756i
$538$	13.3598	−	9.70648i	0.575983	−	0.418476i
$539$	−10.0147	−	7.27613i	−0.431365	−	0.313405i
$540$		0			0
$541$	−2.27953	+	1.65618i	−0.0980046	+	0.0712045i	−0.635708	−	0.771929i	$-0.719292\pi$
$541$	−2.27953	+	1.65618i	−0.0980046	+	0.0712045i	0.537704	+	0.843134i	$0.319292\pi$
$542$	12.2178	−	37.6025i	0.524799	−	1.61516i
$543$	7.85007			0.336879
$544$	4.69597	−	14.4527i	0.201338	−	0.619654i
$545$		0			0
$546$	0.186578	+	0.574228i	0.00798480	+	0.0245747i
$547$	−1.36703	−	4.20728i	−0.0584499	−	0.179890i	0.917569	−	0.397577i	$-0.130149\pi$
$547$	−1.36703	−	4.20728i	−0.0584499	−	0.179890i	−0.976019	+	0.217687i	$0.930149\pi$
$548$	−2.95404	−	2.14623i	−0.126190	−	0.0916826i
$549$	−4.39643			−0.187635
$550$		0			0
$551$	5.18036			0.220691
$552$	1.77568	+	1.29010i	0.0755778	+	0.0549105i
$553$	3.84285	+	11.8271i	0.163415	+	0.502938i
$554$	−4.57323	−	14.0749i	−0.194298	−	0.597987i
$555$		0			0
$556$	−0.740427	+	2.27880i	−0.0314011	+	0.0966426i
$557$	7.20182			0.305151			0.152575	−	0.988292i	$-0.451243\pi$
$557$	7.20182			0.305151			0.152575	+	0.988292i	$0.451243\pi$
$558$	4.66580	−	14.3599i	0.197519	−	0.607902i
$559$	0.993546	−	0.721854i	0.0420225	−	0.0305312i
$560$		0			0
$561$	−17.9681	−	13.0546i	−0.758612	−	0.551164i
$562$	−3.52395	+	2.56030i	−0.148649	+	0.108000i
$563$	18.8103	−	13.6665i	0.792761	−	0.575975i	−0.116020	−	0.993247i	$-0.537014\pi$
$563$	18.8103	−	13.6665i	0.792761	−	0.575975i	0.908782	+	0.417272i	$0.137014\pi$
$564$	−2.52601	−	1.83526i	−0.106364	−	0.0772782i
$565$		0			0
$566$	29.4373	−	21.3875i	1.23734	−	0.898982i
$567$	0.521005	−	1.60349i	0.0218801	−	0.0673402i
$568$	−11.0017			−0.461620
$569$	−6.37307	+	19.6143i	−0.267173	+	0.822273i	0.724012	+	0.689787i	$0.242296\pi$
$569$	−6.37307	+	19.6143i	−0.267173	+	0.822273i	−0.991185	+	0.132486i	$0.957704\pi$
$570$		0			0
$571$	0.557381	+	1.71544i	0.0233257	+	0.0717890i	0.962042	−	0.272902i	$-0.0879836\pi$
$571$	0.557381	+	1.71544i	0.0233257	+	0.0717890i	−0.938716	+	0.344691i	$0.887984\pi$
$572$	−0.0780952	−	0.240352i	−0.00326533	−	0.0100496i
$573$	10.1646	+	7.38502i	0.424633	+	0.308514i
$574$	−9.84466			−0.410908
$575$		0			0
$576$	6.05938			0.252474
$577$	13.3377	+	9.69043i	0.555257	+	0.403418i	0.829720	−	0.558180i	$-0.188500\pi$
$577$	13.3377	+	9.69043i	0.555257	+	0.403418i	−0.274463	+	0.961598i	$0.588500\pi$
$578$	−18.3590	−	56.5032i	−0.763633	−	2.35022i
$579$	3.13458	+	9.64725i	0.130269	+	0.400926i
$580$		0			0
$581$	2.26351	−	6.96637i	0.0939063	−	0.289014i
$582$	14.5683			0.603876
$583$	−5.50118	+	16.9309i	−0.227835	+	0.701205i
$584$	30.6271	−	22.2519i	1.26736	−	0.920791i
$585$		0			0
$586$	28.9076	+	21.0026i	1.19416	+	0.867610i
$587$	5.88286	−	4.27415i	0.242811	−	0.176413i	−0.459723	−	0.888062i	$-0.652051\pi$
$587$	5.88286	−	4.27415i	0.242811	−	0.176413i	0.702535	+	0.711649i	$0.252051\pi$
$588$	−1.22575	+	0.890562i	−0.0505492	+	0.0367261i
$589$	5.98599	+	4.34908i	0.246649	+	0.179201i
$590$		0			0
$591$	−1.65608	+	1.20321i	−0.0681220	+	0.0494935i
$592$	−14.3832	+	44.2670i	−0.591146	+	1.81936i
$593$	2.47898			0.101800			0.0508998	−	0.998704i	$-0.483791\pi$
$593$	2.47898			0.101800			0.0508998	+	0.998704i	$0.483791\pi$
$594$	−1.41484	+	4.35444i	−0.0580518	+	0.178665i
$595$		0			0
$596$	1.22914	+	3.78291i	0.0503477	+	0.154954i
$597$	−1.10358	−	3.39646i	−0.0451664	−	0.139008i
$598$	0.252843	+	0.183701i	0.0103395	+	0.00751211i
$599$	30.2951			1.23782			0.618912	−	0.785460i	$-0.287574\pi$
$599$	30.2951			1.23782			0.618912	+	0.785460i	$0.287574\pi$
$600$		0			0
$601$	4.46130			0.181980			0.0909900	−	0.995852i	$-0.470997\pi$
$601$	4.46130			0.181980			0.0909900	+	0.995852i	$0.470997\pi$
$602$	−11.0600	−	8.03560i	−0.450774	−	0.327506i
$603$	0.554013	+	1.70508i	0.0225612	+	0.0694361i
$604$	2.29885	+	7.07512i	0.0935387	+	0.287882i
$605$		0			0
$606$	−3.10982	+	9.57103i	−0.126328	+	0.388797i
$607$	17.2931			0.701906			0.350953	−	0.936393i	$-0.385858\pi$
$607$	17.2931			0.701906			0.350953	+	0.936393i	$0.385858\pi$
$608$	0.474397	−	1.46004i	0.0192393	−	0.0592126i
$609$	9.37732	−	6.81302i	0.379988	−	0.276077i
$610$		0			0
$611$	1.61423	+	1.17280i	0.0653046	+	0.0474466i
$612$	−2.19920	+	1.59781i	−0.0888974	+	0.0645877i
$613$	−11.5794	+	8.41293i	−0.467688	+	0.339795i	−0.796539	−	0.604587i	$-0.793338\pi$
$613$	−11.5794	+	8.41293i	−0.467688	+	0.339795i	0.328852	+	0.944382i	$0.393338\pi$
$614$	−27.1356	−	19.7152i	−1.09510	−	0.795640i
$615$		0			0
$616$	10.2143	−	7.42115i	0.411547	−	0.299006i
$617$	−8.14472	+	25.0669i	−0.327894	+	1.00915i	0.642223	+	0.766518i	$0.278012\pi$
$617$	−8.14472	+	25.0669i	−0.327894	+	1.00915i	−0.970117	+	0.242637i	$0.921988\pi$
$618$	−1.07761			−0.0433477
$619$	−0.864708	+	2.66130i	−0.0347555	+	0.106967i	−0.966929	−	0.255045i	$-0.917910\pi$
$619$	−0.864708	+	2.66130i	−0.0347555	+	0.106967i	0.932174	+	0.362011i	$0.117910\pi$
$620$		0			0
$621$	−0.269686	−	0.830007i	−0.0108221	−	0.0333070i
$622$	−4.77133	−	14.6846i	−0.191313	−	0.588800i
$623$	−16.5089	−	11.9944i	−0.661414	−	0.480545i
$624$	1.07039			0.0428497
$625$		0			0
$626$	−9.30856			−0.372045
$627$	−1.81517	−	1.31880i	−0.0724911	−	0.0526679i
$628$	0.394100	+	1.21291i	0.0157263	+	0.0484006i
$629$	23.3427	+	71.8415i	0.930735	+	2.86451i
$630$		0			0
$631$	10.9403	−	33.6707i	0.435526	−	1.34041i	−0.457021	−	0.889456i	$-0.651084\pi$
$631$	10.9403	−	33.6707i	0.435526	−	1.34041i	0.892547	−	0.450955i	$-0.148916\pi$
$632$	18.5499			0.737877
$633$	−1.15153	+	3.54404i	−0.0457692	+	0.140863i
$634$	−10.5729	+	7.68164i	−0.419902	+	0.305077i
$635$		0			0
$636$	1.76276	+	1.28072i	0.0698981	+	0.0507840i
$637$	0.783307	−	0.569106i	0.0310357	−	0.0225488i
$638$	−25.4651	+	18.5015i	−1.00817	+	0.732481i
$639$	3.53904	+	2.57126i	0.140002	+	0.101718i
$640$		0			0
$641$	−13.6994	+	9.95321i	−0.541094	+	0.393128i	−0.824491	−	0.565875i	$-0.808539\pi$
$641$	−13.6994	+	9.95321i	−0.541094	+	0.393128i	0.283397	+	0.959003i	$0.408539\pi$
$642$	5.95327	−	18.3223i	0.234957	−	0.723122i
$643$	25.9118			1.02186			0.510931	−	0.859622i	$-0.329301\pi$
$643$	25.9118			1.02186			0.510931	+	0.859622i	$0.329301\pi$
$644$	0.165708	−	0.509996i	0.00652980	−	0.0200966i
$645$		0			0
$646$	−2.67071	−	8.21960i	−0.105078	−	0.323396i
$647$	3.37629	+	10.3911i	0.132736	+	0.408518i	0.995231	−	0.0975468i	$-0.0310996\pi$
$647$	3.37629	+	10.3911i	0.132736	+	0.408518i	−0.862495	+	0.506065i	$0.831100\pi$
$648$	−2.03464	−	1.47826i	−0.0799283	−	0.0580713i
$649$	11.4671			0.450121
$650$		0			0
$651$	16.5554			0.648857
$652$	−1.76124	−	1.27961i	−0.0689753	−	0.0501135i
$653$	4.40596	+	13.5602i	0.172419	+	0.530650i	0.999506	−	0.0314233i	$-0.0100040\pi$
$653$	4.40596	+	13.5602i	0.172419	+	0.530650i	−0.827088	+	0.562073i	$0.810004\pi$
$654$	2.03537	+	6.26422i	0.0795892	+	0.244950i
$655$		0			0
$656$	−5.39319	+	16.5985i	−0.210569	+	0.648063i
$657$	−15.0528			−0.587267
$658$	6.86370	−	21.1243i	0.267575	−	0.823511i
$659$	−18.5179	+	13.4540i	−0.721355	+	0.524095i	−0.886817	−	0.462121i	$-0.847088\pi$
$659$	−18.5179	+	13.4540i	−0.721355	+	0.524095i	0.165462	+	0.986216i	$0.447088\pi$
$660$		0			0
$661$	32.2838	+	23.4556i	1.25570	+	0.912316i	0.998538	−	0.0540529i	$-0.0172140\pi$
$661$	32.2838	+	23.4556i	1.25570	+	0.912316i	0.257158	+	0.966369i	$0.417214\pi$
$662$	20.2704	−	14.7273i	0.787830	−	0.572392i
$663$	1.40538	−	1.02107i	0.0545804	−	0.0396550i
$664$	−8.83953	−	6.42230i	−0.343040	−	0.249233i
$665$		0			0
$666$	12.5982	−	9.15314i	0.488171	−	0.354677i
$667$	1.85404	−	5.70615i	0.0717887	−	0.220943i
$668$	−0.851941			−0.0329626
$669$	−8.11133	+	24.9641i	−0.313602	+	0.965168i
$670$		0			0
$671$	4.04524	+	12.4500i	0.156165	+	0.480626i
$672$	−1.06146	−	3.26683i	−0.0409466	−	0.126021i
$673$	1.74624	+	1.26872i	0.0673126	+	0.0489054i	0.620933	−	0.783864i	$-0.286754\pi$
$673$	1.74624	+	1.26872i	0.0673126	+	0.0489054i	−0.553620	+	0.832769i	$0.686754\pi$
$674$	−37.9747			−1.46273
$675$		0			0
$676$	−4.71795			−0.181460
$677$	−33.9577	−	24.6717i	−1.30510	−	0.948210i	−0.305108	−	0.952318i	$-0.598693\pi$
$677$	−33.9577	−	24.6717i	−1.30510	−	0.948210i	−0.999992	+	0.00410738i	$0.998693\pi$
$678$	3.90949	+	12.0322i	0.150143	+	0.462093i
$679$	4.93613	+	15.1919i	0.189431	+	0.583010i
$680$		0			0
$681$	1.38783	−	4.27129i	0.0531817	−	0.163676i
$682$	−44.9579			−1.72153
$683$	−9.02521	+	27.7767i	−0.345340	+	1.06285i	0.616061	+	0.787698i	$0.288727\pi$
$683$	−9.02521	+	27.7767i	−0.345340	+	1.06285i	−0.961401	+	0.275149i	$0.911273\pi$
$684$	−0.222168	+	0.161415i	−0.00849481	+	0.00617184i
$685$		0			0
$686$	−23.4015	−	17.0022i	−0.893473	−	0.649146i
$687$	−6.09946	+	4.43152i	−0.232709	+	0.169073i
$688$	−19.6074	+	14.2456i	−0.747524	+	0.543108i
$689$	−1.12648	−	0.818435i	−0.0429154	−	0.0311799i
$690$		0			0
$691$	−36.0221	+	26.1716i	−1.37034	+	0.995614i	−0.372634	+	0.927978i	$0.621545\pi$
$691$	−36.0221	+	26.1716i	−1.37034	+	0.995614i	−0.997710	+	0.0676353i	$0.978455\pi$
$692$	0.683703	−	2.10422i	0.0259905	−	0.0799905i
$693$	−5.02021			−0.190702
$694$	6.62698	−	20.3958i	0.251557	−	0.774212i
$695$		0			0
$696$	−5.34287	−	16.4437i	−0.202521	−	0.623295i
$697$	8.75268	+	26.9380i	0.331531	+	1.02035i
$698$	23.0098	+	16.7176i	0.870934	+	0.632771i
$699$	−10.3640			−0.392004
$700$		0			0
$701$	−4.50567			−0.170177			−0.0850884	−	0.996373i	$-0.527117\pi$
$701$	−4.50567			−0.170177			−0.0850884	+	0.996373i	$0.527117\pi$
$702$	−0.289719	−	0.210493i	−0.0109347	−	0.00794454i
$703$	2.35813	+	7.25759i	0.0889387	+	0.273725i
$704$	−5.57536	−	17.1592i	−0.210129	−	0.646711i
$705$		0			0
$706$	0.209897	−	0.645997i	0.00789958	−	0.0243124i
$707$	−11.0344			−0.414990
$708$	0.433708	−	1.33482i	0.0162998	−	0.0501655i
$709$	41.4788	−	30.1361i	1.55777	−	1.13178i	0.619959	−	0.784634i	$-0.287149\pi$
$709$	41.4788	−	30.1361i	1.55777	−	1.13178i	0.937809	−	0.347151i	$-0.112851\pi$
$710$		0			0
$711$	−5.96718	−	4.33541i	−0.223787	−	0.162591i
$712$	−24.6257	+	17.8916i	−0.922887	+	0.670517i
$713$	6.93287	−	5.03702i	0.259638	−	0.188638i
$714$	−15.6445	−	11.3664i	−0.585482	−	0.425378i
$715$		0			0
$716$	−3.36809	+	2.44706i	−0.125871	+	0.0914509i
$717$	5.73962	−	17.6647i	0.214350	−	0.659701i
$718$	−7.10600			−0.265194
$719$	10.8976	−	33.5393i	0.406411	−	1.25080i	−0.513301	−	0.858209i	$-0.671578\pi$
$719$	10.8976	−	33.5393i	0.406411	−	1.25080i	0.919712	−	0.392595i	$-0.128422\pi$
$720$		0			0
$721$	−0.365122	−	1.12373i	−0.0135979	−	0.0418499i
$722$	8.75838	+	26.9555i	0.325953	+	1.00318i
$723$	−4.39735	−	3.19486i	−0.163539	−	0.118818i
$724$	−2.86088			−0.106324
$725$		0			0
$726$	−3.28150			−0.121788
$727$	−35.5998	−	25.8648i	−1.32032	−	0.959271i	−0.999928	−	0.0119876i	$-0.996184\pi$
$727$	−35.5998	−	25.8648i	−1.32032	−	0.959271i	−0.320396	−	0.947284i	$-0.603816\pi$
$728$	0.305160	+	0.939184i	0.0113100	+	0.0348085i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−12.1546	+	37.4079i	−0.449553	+	1.38358i
$732$	1.60223			0.0592202
$733$	−8.61356	+	26.5098i	−0.318149	+	0.979162i	0.656290	+	0.754509i	$0.272125\pi$
$733$	−8.61356	+	26.5098i	−0.318149	+	0.979162i	−0.974439	+	0.224653i	$0.927875\pi$
$734$	10.9186	−	7.93281i	0.403012	−	0.292805i
$735$		0			0
$736$	−1.43845	−	1.04509i	−0.0530219	−	0.0385226i
$737$	4.31874	−	3.13775i	0.159083	−	0.115581i
$738$	4.72388	−	3.43210i	0.173888	−	0.126337i
$739$	26.2456	+	19.0685i	0.965459	+	0.701447i	0.954412	−	0.298492i	$-0.0964836\pi$
$739$	26.2456	+	19.0685i	0.965459	+	0.701447i	0.0110469	+	0.999939i	$0.496484\pi$
$740$		0			0
$741$	0.141975	−	0.103151i	0.00521557	−	0.00378933i
$742$	−4.78979	+	14.7415i	−0.175839	+	0.541176i
$743$	9.09256			0.333574			0.166787	−	0.985993i	$-0.446661\pi$
$743$	9.09256			0.333574			0.166787	+	0.985993i	$0.446661\pi$
$744$	7.63120	−	23.4864i	0.279773	−	0.861054i
$745$		0			0
$746$	7.36297	+	22.6609i	0.269577	+	0.829674i
$747$	1.34253	+	4.13188i	0.0491205	+	0.151177i
$748$	6.54827	+	4.75760i	0.239429	+	0.173955i
$749$	21.1236			0.771840
$750$		0			0
$751$	−49.8861			−1.82037			−0.910185	−	0.414202i	$-0.864061\pi$
$751$	−49.8861			−1.82037			−0.910185	+	0.414202i	$0.864061\pi$
$752$	−31.8563	−	23.1450i	−1.16168	−	0.844011i
$753$	−7.21792	−	22.2145i	−0.263036	−	0.809540i
$754$	−0.760786	−	2.34146i	−0.0277062	−	0.0852709i
$755$		0			0
$756$	−0.189875	+	0.584375i	−0.00690568	+	0.0212535i
$757$	31.1239			1.13122			0.565608	−	0.824674i	$-0.308642\pi$
$757$	31.1239			1.13122			0.565608	+	0.824674i	$0.308642\pi$
$758$	12.9688	−	39.9138i	0.471048	−	1.44974i
$759$	−2.10230	+	1.52741i	−0.0763087	+	0.0554415i
$760$		0			0
$761$	−31.6544	−	22.9982i	−1.14747	−	0.833686i	−0.159327	−	0.987226i	$-0.550933\pi$
$761$	−31.6544	−	22.9982i	−1.14747	−	0.833686i	−0.988142	+	0.153540i	$0.950933\pi$
$762$	−14.8636	+	10.7990i	−0.538450	+	0.391207i
$763$	−5.84270	+	4.24497i	−0.211520	+	0.153678i
$764$	−3.70438	−	2.69139i	−0.134020	−	0.0973712i
$765$		0			0
$766$	−16.3016	+	11.8438i	−0.589002	+	0.427935i
$767$	−0.277158	+	0.853003i	−0.0100076	+	0.0308002i
$768$	−8.47377			−0.305771
$769$	4.43076	−	13.6365i	0.159777	−	0.491744i	−0.838836	−	0.544384i	$-0.816764\pi$
$769$	4.43076	−	13.6365i	0.159777	−	0.491744i	0.998614	+	0.0526398i	$0.0167635\pi$
$770$		0			0
$771$	−1.38557	−	4.26435i	−0.0499001	−	0.153577i
$772$	−1.14237	−	3.51584i	−0.0411146	−	0.126538i
$773$	3.43830	+	2.49807i	0.123667	+	0.0898493i	0.647899	−	0.761726i	$-0.275648\pi$
$773$	3.43830	+	2.49807i	0.123667	+	0.0898493i	−0.524232	+	0.851575i	$0.675648\pi$
$774$	8.10849			0.291454
$775$		0			0
$776$	23.8274			0.855352
$777$	13.8135	+	10.0361i	0.495557	+	0.360043i
$778$	−8.03298	−	24.7230i	−0.287996	−	0.886361i
$779$	0.884215	+	2.72134i	0.0316803	+	0.0975020i
$780$		0			0
$781$	4.02506	−	12.3879i	0.144028	−	0.443273i
$782$	−10.0097			−0.357946
$783$	−2.12444	+	6.53835i	−0.0759212	+	0.233661i
$784$	−15.4584	+	11.2312i	−0.552084	+	0.401113i
$785$		0			0
$786$	−26.6930	−	19.3936i	−0.952109	−	0.691747i
$787$	21.9483	−	15.9464i	0.782374	−	0.568428i	−0.123317	−	0.992367i	$-0.539353\pi$
$787$	21.9483	−	15.9464i	0.782374	−	0.568428i	0.905690	+	0.423940i	$0.139353\pi$
$788$	0.603541	−	0.438498i	0.0215002	−	0.0156208i
$789$	−6.25006	−	4.54093i	−0.222508	−	0.161662i
$790$		0			0
$791$	−11.2225	+	8.15364i	−0.399027	+	0.289910i
$792$	−2.31406	+	7.12195i	−0.0822267	+	0.253068i
$793$	−1.02389			−0.0363595
$794$	−4.94545	+	15.2205i	−0.175507	+	0.540156i
$795$		0			0
$796$	0.402187	+	1.23781i	0.0142552	+	0.0438729i
$797$	−3.89902	−	12.0000i	−0.138111	−	0.425060i	0.857950	−	0.513733i	$-0.171738\pi$
$797$	−3.89902	−	12.0000i	−0.138111	−	0.425060i	−0.996061	+	0.0886722i	$0.971738\pi$
$798$	−1.58045	−	1.14826i	−0.0559472	−	0.0406480i
$799$	−63.9049			−2.26079
$800$		0			0
$801$	12.1032			0.427646
$802$	−0.864334	−	0.627976i	−0.0305207	−	0.0221746i
$803$	13.8504	+	42.6272i	0.488770	+	1.50428i
$804$	−0.201904	−	0.621398i	−0.00712062	−	0.0219150i
$805$		0			0
$806$	1.08663	−	3.34430i	0.0382748	−	0.117798i
$807$	−10.7394			−0.378044
$808$	−5.08629	+	15.6540i	−0.178935	+	0.550706i
$809$	30.2684	−	21.9913i	1.06418	−	0.773172i	0.0893229	−	0.996003i	$-0.471530\pi$
$809$	30.2684	−	21.9913i	1.06418	−	0.773172i	0.974857	+	0.222831i	$0.0715297\pi$
$810$		0			0
$811$	−30.0948	−	21.8651i	−1.05677	−	0.767789i	−0.0832825	−	0.996526i	$-0.526540\pi$
$811$	−30.0948	−	21.8651i	−1.05677	−	0.767789i	−0.973488	+	0.228737i	$0.926540\pi$
$812$	−3.41747	+	2.48293i	−0.119930	+	0.0871339i
$813$	−20.8019	+	15.1135i	−0.729555	+	0.530053i
$814$	−37.5121	−	27.2541i	−1.31480	−	0.955257i
$815$		0			0
$816$	−27.7348	+	20.1505i	−0.970912	+	0.705409i
$817$	−1.22788	+	3.77903i	−0.0429582	+	0.132212i
$818$	1.82845			0.0639302
$819$	0.121338	−	0.373439i	0.00423989	−	0.0130490i
$820$		0			0
$821$	8.48994	+	26.1294i	0.296301	+	0.911921i	0.982781	+	0.184772i	$0.0591548\pi$
$821$	8.48994	+	26.1294i	0.296301	+	0.911921i	−0.686480	+	0.727148i	$0.740845\pi$
$822$	4.76080	+	14.6522i	0.166052	+	0.511055i
$823$	18.9526	+	13.7698i	0.660645	+	0.479987i	0.866881	−	0.498516i	$-0.166121\pi$
$823$	18.9526	+	13.7698i	0.660645	+	0.479987i	−0.206236	+	0.978502i	$0.566121\pi$
$824$	−1.76249			−0.0613993
$825$		0			0
$826$	9.98420			0.347395
$827$	−26.2583	−	19.0778i	−0.913090	−	0.663399i	0.0287047	−	0.999588i	$-0.490862\pi$
$827$	−26.2583	−	19.0778i	−0.913090	−	0.663399i	−0.941794	+	0.336189i	$0.890862\pi$
$828$	0.0982841	+	0.302487i	0.00341561	+	0.0105122i
$829$	−0.0476213	−	0.146563i	−0.00165395	−	0.00509035i	0.950226	−	0.311561i	$-0.100852\pi$
$829$	−0.0476213	−	0.146563i	−0.00165395	−	0.00509035i	−0.951880	+	0.306471i	$0.900852\pi$
$830$		0			0
$831$	−2.97412	+	9.15340i	−0.103171	+	0.317528i
$832$	1.41118			0.0489239
$833$	−9.58260	+	29.4922i	−0.332018	+	1.02185i
$834$	8.17892	−	5.94233i	0.283213	−	0.205766i
$835$		0			0
$836$	0.661522	+	0.480624i	0.0228792	+	0.0166227i
$837$	−7.94397	+	5.77163i	−0.274584	+	0.199497i
$838$	2.46115	−	1.78813i	0.0850189	−	0.0617698i
$839$	28.6568	+	20.8204i	0.989342	+	0.718799i	0.959777	−	0.280764i	$-0.0905877\pi$
$839$	28.6568	+	20.8204i	0.989342	+	0.718799i	0.0295652	+	0.999563i	$0.490588\pi$
$840$		0			0
$841$	−14.7752	+	10.7348i	−0.509491	+	0.370167i
$842$	−5.26602	+	16.2072i	−0.181479	+	0.558535i
$843$	2.83275			0.0975651
$844$	0.419663	−	1.29159i	0.0144454	−	0.0444583i
$845$		0			0
$846$	4.07098	+	12.5292i	0.139963	+	0.430762i
$847$	−1.11186	−	3.42195i	−0.0382040	−	0.117580i
$848$	22.2308	+	16.1516i	0.763408	+	0.554648i
$849$	−23.6634			−0.812125
$850$		0			0
$851$	8.83818			0.302969
$852$	−1.28977	−	0.937071i	−0.0441867	−	0.0321035i
$853$	11.3121	+	34.8150i	0.387318	+	1.19204i	0.934785	+	0.355215i	$0.115592\pi$
$853$	11.3121	+	34.8150i	0.387318	+	1.19204i	−0.547467	+	0.836828i	$0.684408\pi$
$854$	3.52213	+	10.8400i	0.120525	+	0.370938i
$855$		0			0
$856$	9.73693	−	29.9672i	0.332801	−	1.02426i
$857$	2.04867			0.0699813			0.0349907	−	0.999388i	$-0.488860\pi$
$857$	2.04867			0.0699813			0.0349907	+	0.999388i	$0.488860\pi$
$858$	−0.329506	+	1.01411i	−0.0112491	+	0.0346213i
$859$	−11.4736	+	8.33605i	−0.391474	+	0.284422i	−0.766059	−	0.642770i	$-0.777785\pi$
$859$	−11.4736	+	8.33605i	−0.391474	+	0.284422i	0.374585	+	0.927192i	$0.377785\pi$
$860$		0			0
$861$	5.17958	+	3.76318i	0.176519	+	0.128249i
$862$	−12.9546	+	9.41209i	−0.441237	+	0.320577i
$863$	34.8976	−	25.3546i	1.18793	−	0.863081i	0.194885	−	0.980826i	$-0.437567\pi$
$863$	34.8976	−	25.3546i	1.18793	−	0.863081i	0.993044	+	0.117745i	$0.0375667\pi$
$864$	1.64823	+	1.19751i	0.0560740	+	0.0407402i
$865$		0			0
$866$	12.7689	−	9.27711i	0.433903	−	0.315249i
$867$	−11.9395	+	36.7459i	−0.405485	+	1.24796i
$868$	−6.03344			−0.204788
$869$	−6.78666	+	20.8872i	−0.230222	+	0.708550i
$870$		0			0
$871$	0.129025	+	0.397099i	0.00437185	+	0.0134552i
$872$	3.32897	+	10.2455i	0.112733	+	0.346957i
$873$	−7.66483	−	5.56883i	−0.259415	−	0.188476i
$874$	−1.01120			−0.0342044
$875$		0			0
$876$	5.48584			0.185350
$877$	−5.45827	−	3.96567i	−0.184313	−	0.133911i	0.491803	−	0.870707i	$-0.336338\pi$
$877$	−5.45827	−	3.96567i	−0.184313	−	0.133911i	−0.676116	+	0.736795i	$0.736338\pi$
$878$	11.7421	+	36.1385i	0.396277	+	1.21962i
$879$	−7.18080	−	22.1002i	−0.242202	−	0.745423i
$880$		0			0
$881$	5.30839	−	16.3375i	0.178844	−	0.550426i	−0.820944	−	0.571009i	$-0.806552\pi$
$881$	5.30839	−	16.3375i	0.178844	−	0.550426i	0.999788	+	0.0205829i	$0.00655221\pi$
$882$	6.39269			0.215253
$883$	17.5712	−	54.0787i	0.591319	−	1.81989i	0.0190624	−	0.999818i	$-0.493932\pi$
$883$	17.5712	−	54.0787i	0.591319	−	1.81989i	0.572257	−	0.820075i	$-0.306068\pi$
$884$	−0.512176	+	0.372118i	−0.0172263	+	0.0125157i
$885$		0			0
$886$	−9.36654	−	6.80519i	−0.314675	−	0.228625i
$887$	29.8768	−	21.7067i	1.00316	−	0.728841i	0.0403995	−	0.999184i	$-0.487137\pi$
$887$	29.8768	−	21.7067i	1.00316	−	0.728841i	0.962764	+	0.270342i	$0.0871369\pi$
$888$	20.6051	−	14.9705i	0.691463	−	0.502378i
$889$	−16.2974	−	11.8408i	−0.546597	−	0.397126i
$890$		0			0
$891$	2.40891	−	1.75017i	0.0807014	−	0.0586330i
$892$	2.95609	−	9.09791i	0.0989772	−	0.304621i
$893$	−6.45581			−0.216036
$894$	5.18610	−	15.9612i	0.173449	−	0.533822i
$895$		0			0
$896$	−6.97730	−	21.4739i	−0.233095	−	0.717393i
$897$	−0.0628076	−	0.193302i	−0.00209708	−	0.00645416i
$898$	−39.3885	−	28.6174i	−1.31441	−	0.954976i
$899$	−67.5058			−2.25145
$900$		0			0
$901$	44.5956			1.48570
$902$	−14.0657	−	10.2193i	−0.468336	−	0.340266i
$903$	2.74737	+	8.45555i	0.0914269	+	0.281383i
$904$	6.39421	+	19.6793i	0.212668	+	0.654525i
$905$		0			0
$906$	9.69948	−	29.8519i	0.322244	−	0.991764i
$907$	25.7833			0.856120			0.428060	−	0.903750i	$-0.359197\pi$
$907$	25.7833			0.856120			0.428060	+	0.903750i	$0.359197\pi$
$908$	−0.505779	+	1.55663i	−0.0167849	+	0.0516585i
$909$	5.29476	−	3.84687i	0.175616	−	0.127593i
$910$		0			0
$911$	21.8488	+	15.8741i	0.723882	+	0.525931i	0.887622	−	0.460572i	$-0.152356\pi$
$911$	21.8488	+	15.8741i	0.723882	+	0.525931i	−0.163740	+	0.986504i	$0.552356\pi$
$912$	−2.80183	+	2.03565i	−0.0927780	+	0.0674071i
$913$	10.4655	−	7.60364i	0.346358	−	0.251644i
$914$	−3.67905	−	2.67298i	−0.121692	−	0.0884145i
$915$		0			0
$916$	2.22289	−	1.61502i	0.0734462	−	0.0533618i
$917$	11.1794	−	34.4066i	0.369176	−	1.13621i
$918$	11.4695			0.378551
$919$	−8.01412	+	24.6649i	−0.264362	+	0.813621i	0.727478	+	0.686131i	$0.240692\pi$
$919$	−8.01412	+	24.6649i	−0.264362	+	0.813621i	−0.991840	+	0.127490i	$0.959308\pi$
$920$		0			0
$921$	6.74062	+	20.7455i	0.222111	+	0.683588i
$922$	8.36347	+	25.7401i	0.275436	+	0.847705i
$923$	0.824214	+	0.598827i	0.0271293	+	0.0197106i
$924$	1.82956			0.0601882
$925$		0			0
$926$	−40.5055			−1.33109
$927$	0.566962	+	0.411922i	0.0186215	+	0.0135293i
$928$	4.32818	+	13.3208i	0.142079	+	0.437275i
$929$	4.66201	+	14.3482i	0.152955	+	0.470749i	0.997948	−	0.0640296i	$-0.0203952\pi$
$929$	4.66201	+	14.3482i	0.152955	+	0.470749i	−0.844993	+	0.534778i	$0.820395\pi$
$930$		0			0
$931$	−0.968057	+	2.97937i	−0.0317268	+	0.0976450i
$932$	3.77707			0.123722
$933$	−3.10295	+	9.54991i	−0.101586	+	0.312650i
$934$	9.15470	−	6.65128i	0.299551	−	0.217637i
$935$		0			0
$936$	−0.473852	−	0.344274i	−0.0154883	−	0.0112529i
$937$	0.530361	−	0.385330i	0.0173262	−	0.0125882i	−0.579088	−	0.815265i	$-0.696591\pi$
$937$	0.530361	−	0.385330i	0.0173262	−	0.0125882i	0.596415	+	0.802677i	$0.296591\pi$
$938$	3.76027	−	2.73199i	0.122777	−	0.0892028i
$939$	4.89752	+	3.55825i	0.159824	+	0.116119i
$940$		0			0
$941$	29.4596	−	21.4036i	0.960354	−	0.697738i	0.00712112	−	0.999975i	$-0.497733\pi$
$941$	29.4596	−	21.4036i	0.960354	−	0.697738i	0.953233	+	0.302237i	$0.0977333\pi$
$942$	1.66282	−	5.11763i	0.0541776	−	0.166741i
$943$	3.31400			0.107919
$944$	5.46963	−	16.8338i	0.178021	−	0.547893i
$945$		0			0
$946$	−7.46079	−	22.9619i	−0.242571	−	0.746557i
$947$	14.0333	+	43.1901i	0.456021	+	1.40349i	0.869932	+	0.493171i	$0.164162\pi$
$947$	14.0333	+	43.1901i	0.456021	+	1.40349i	−0.413911	+	0.910317i	$0.635838\pi$
$948$	2.17468	+	1.58000i	0.0706302	+	0.0513159i
$949$	−3.50568			−0.113799
$950$		0			0
$951$	8.49907			0.275601
$952$	−25.5876	−	18.5905i	−0.829298	−	0.602520i
$953$	−14.2932	−	43.9898i	−0.463001	−	1.42497i	−0.861479	−	0.507793i	$-0.830462\pi$
$953$	−14.2932	−	43.9898i	−0.463001	−	1.42497i	0.398478	−	0.917178i	$-0.369538\pi$
$954$	−2.84091	−	8.74342i	−0.0919779	−	0.283079i
$955$		0			0
$956$	−2.09174	+	6.43773i	−0.0676518	+	0.208211i
$957$	20.4703			0.661710
$958$	13.5266	−	41.6306i	0.437024	−	1.34502i
$959$	−13.6663	+	9.92913i	−0.441307	+	0.320628i
$960$		0			0
$961$	−52.9246	−	38.4520i	−1.70724	−	1.24039i
$962$	2.93402	−	2.13169i	0.0945967	−	0.0687285i
$963$	−10.1360	+	7.36423i	−0.326628	+	0.237309i
$964$	1.60257	+	1.16433i	0.0516153	+	0.0375007i
$965$		0			0
$966$	−1.83044	+	1.32990i	−0.0588936	+	0.0427887i
$967$	−0.901526	+	2.77461i	−0.0289911	+	0.0892255i	−0.964505	−	0.264064i	$-0.914937\pi$
$967$	−0.901526	+	2.77461i	−0.0289911	+	0.0892255i	0.935514	+	0.353290i	$0.114937\pi$
$968$	−5.36709			−0.172505
$969$	−1.73685	+	5.34548i	−0.0557957	+	0.171721i
$970$		0			0
$971$	−0.376445	−	1.15858i	−0.0120807	−	0.0371806i	0.944834	−	0.327548i	$-0.106222\pi$
$971$	−0.376445	−	1.15858i	−0.0120807	−	0.0371806i	−0.956915	+	0.290368i	$0.906222\pi$
$972$	−0.112618	−	0.346603i	−0.00361222	−	0.0111173i
$973$	8.96791	+	6.51557i	0.287498	+	0.208879i
$974$	−3.66591			−0.117463
$975$		0			0
$976$	20.2063			0.646787
$977$	−36.1404	−	26.2575i	−1.15623	−	0.840053i	−0.166936	−	0.985968i	$-0.553387\pi$
$977$	−36.1404	−	26.2575i	−1.15623	−	0.840053i	−0.989297	+	0.145915i	$0.953387\pi$
$978$	2.83845	+	8.73584i	0.0907635	+	0.279341i
$979$	−11.1364	−	34.2743i	−0.355921	−	1.09541i
$980$		0			0
$981$	1.32367	−	4.07383i	0.0422614	−	0.130067i
$982$	39.5538			1.26221
$983$	−11.1651	+	34.3627i	−0.356112	+	1.09600i	0.599251	+	0.800561i	$0.295465\pi$
$983$	−11.1651	+	34.3627i	−0.356112	+	1.09600i	−0.955362	+	0.295437i	$0.904535\pi$
$984$	7.72619	−	5.61341i	0.246302	−	0.178949i
$985$		0			0
$986$	63.7918	+	46.3474i	2.03154	+	1.47600i
$987$	−11.6861	+	8.49044i	−0.371972	+	0.270254i
$988$	−0.0517412	+	0.0375922i	−0.00164611	+	0.00119597i
$989$	3.72314	+	2.70502i	0.118389	+	0.0860145i
$990$		0			0
$991$	32.3765	−	23.5229i	1.02847	−	0.747229i	0.0604705	−	0.998170i	$-0.480740\pi$
$991$	32.3765	−	23.5229i	1.02847	−	0.747229i	0.968002	+	0.250941i	$0.0807399\pi$
$992$	−6.18192	+	19.0260i	−0.196276	+	0.604076i
$993$	−16.2945			−0.517089
$994$	3.50456	−	10.7859i	0.111158	−	0.342109i
$995$		0			0
$996$	−0.489270	−	1.50582i	−0.0155031	−	0.0477137i
$997$	1.00226	+	3.08464i	0.0317419	+	0.0976915i	0.965672	−	0.259763i	$-0.0836446\pi$
$997$	1.00226	+	3.08464i	0.0317419	+	0.0976915i	−0.933930	+	0.357455i	$0.883645\pi$
$998$	37.3187	+	27.1136i	1.18130	+	0.858267i
$999$	−10.1272			−0.320409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.d.76.4		16
5.2	odd	4		75.2.i.a.34.1	✓	16
5.3	odd	4		375.2.i.c.49.4		16
5.4	even	2		375.2.g.e.76.1		16
15.2	even	4		225.2.m.b.109.4		16
25.2	odd	20		375.2.i.c.199.4		16
25.6	even	5		1875.2.a.p.1.1		8
25.8	odd	20		1875.2.b.h.1249.14		16
25.11	even	5	inner	375.2.g.d.301.4		16
25.14	even	10		375.2.g.e.301.1		16
25.17	odd	20		1875.2.b.h.1249.3		16
25.19	even	10		1875.2.a.m.1.8		8
25.23	odd	20		75.2.i.a.64.1	yes	16
75.23	even	20		225.2.m.b.64.4		16
75.44	odd	10		5625.2.a.bd.1.1		8
75.56	odd	10		5625.2.a.t.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.1	✓	16	5.2	odd	4
75.2.i.a.64.1	yes	16	25.23	odd	20
225.2.m.b.64.4		16	75.23	even	20
225.2.m.b.109.4		16	15.2	even	4
375.2.g.d.76.4		16	1.1	even	1	trivial
375.2.g.d.301.4		16	25.11	even	5	inner
375.2.g.e.76.1		16	5.4	even	2
375.2.g.e.301.1		16	25.14	even	10
375.2.i.c.49.4		16	5.3	odd	4
375.2.i.c.199.4		16	25.2	odd	20
1875.2.a.m.1.8		8	25.19	even	10
1875.2.a.p.1.1		8	25.6	even	5
1875.2.b.h.1249.3		16	25.17	odd	20
1875.2.b.h.1249.14		16	25.8	odd	20
5625.2.a.t.1.8		8	75.56	odd	10
5625.2.a.bd.1.1		8	75.44	odd	10

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24400 + 0.903822i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.112618 + 0.346603i) q^{4} +(0.475167 - 1.46241i) q^{6} +1.68601 q^{7} +(0.777165 - 2.39187i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.24400 + 0.903822i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.112618 + 0.346603i) q^{4} +(0.475167 - 1.46241i) q^{6} +1.68601 q^{7} +(0.777165 - 2.39187i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(2.40891 + 1.75017i) q^{11} +(0.294838 - 0.214212i) q^{12} +(-0.188414 + 0.136890i) q^{13} +(2.09740 + 1.52385i) q^{14} +(3.71829 - 2.70150i) q^{16} +(2.30496 - 7.09394i) q^{17} -1.53767 q^{18} +(0.232853 - 0.716646i) q^{19} +(-0.521005 - 1.60349i) q^{21} +(1.41484 + 4.35444i) q^{22} +(-0.706046 - 0.512972i) q^{23} -2.51496 q^{24} -0.358112 q^{26} +(0.809017 + 0.587785i) q^{27} +(0.189875 + 0.584375i) q^{28} +(2.12444 + 6.53835i) q^{29} +(-3.03433 + 9.33870i) q^{31} +2.03733 q^{32} +(0.920120 - 2.83184i) q^{33} +(9.27904 - 6.74162i) q^{34} +(-0.294838 - 0.214212i) q^{36} +(-8.19304 + 5.95259i) q^{37} +(0.937390 - 0.681054i) q^{38} +(0.188414 + 0.136890i) q^{39} +(-3.07210 + 2.23201i) q^{41} +(0.801135 - 2.46564i) q^{42} -5.27322 q^{43} +(-0.335328 + 1.03203i) q^{44} +(-0.414688 - 1.27628i) q^{46} +(-2.64749 - 8.14814i) q^{47} +(-3.71829 - 2.70150i) q^{48} -4.15738 q^{49} -7.45901 q^{51} +(-0.0686654 - 0.0498883i) q^{52} +(1.84754 + 5.68614i) q^{53} +(0.475167 + 1.46241i) q^{54} +(1.31031 - 4.03270i) q^{56} -0.753527 q^{57} +(-3.26669 + 10.0538i) q^{58} +(3.11564 - 2.26365i) q^{59} +(3.55679 + 2.58416i) q^{61} +(-12.2152 + 8.87488i) q^{62} +(-1.36401 + 0.991010i) q^{63} +(-4.90214 - 3.56161i) q^{64} +(3.70411 - 2.69119i) q^{66} +(0.554013 - 1.70508i) q^{67} +2.71836 q^{68} +(-0.269686 + 0.830007i) q^{69} +(-1.35179 - 4.16039i) q^{71} +(0.777165 + 2.39187i) q^{72} +(12.1780 + 8.84783i) q^{73} -15.5723 q^{74} +0.274615 q^{76} +(4.06143 + 2.95080i) q^{77} +(0.110663 + 0.340585i) q^{78} +(2.27926 + 7.01484i) q^{79} +(0.309017 - 0.951057i) q^{81} -5.83904 q^{82} +(1.34253 - 4.13188i) q^{83} +(0.497099 - 0.361163i) q^{84} +(-6.55991 - 4.76605i) q^{86} +(5.56185 - 4.04092i) q^{87} +(6.05830 - 4.40161i) q^{88} +(-9.79170 - 7.11409i) q^{89} +(-0.317667 + 0.230798i) q^{91} +(0.0982841 - 0.302487i) q^{92} +9.81929 q^{93} +(4.07098 - 12.5292i) q^{94} +(-0.629569 - 1.93761i) q^{96} +(2.92771 + 9.01055i) q^{97} +(-5.17180 - 3.75753i) q^{98} -2.97757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 - 6 * q^8 - 4 * q^9	\( 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9} - 6 q^{11} + 2 q^{12} - 8 q^{13} + 12 q^{14} - 10 q^{16} - 8 q^{17} + 8 q^{18} + 2 q^{19} + 4 q^{21} + 4 q^{22} - 2 q^{23} - 24 q^{24} + 12 q^{26} + 4 q^{27} - 28 q^{28} - 16 q^{29} + 6 q^{31} - 4 q^{32} - 4 q^{33} + 36 q^{34} - 2 q^{36} - 24 q^{37} + 38 q^{38} + 8 q^{39} - 14 q^{41} + 18 q^{42} + 40 q^{43} - 26 q^{44} + 16 q^{46} + 10 q^{47} + 10 q^{48} - 32 q^{51} - 48 q^{52} - 12 q^{53} + 2 q^{54} + 28 q^{57} - 44 q^{58} - 12 q^{59} - 28 q^{62} - 4 q^{63} - 8 q^{64} + 16 q^{66} + 12 q^{67} - 4 q^{68} + 12 q^{69} - 8 q^{71} - 6 q^{72} + 8 q^{73} + 52 q^{74} - 32 q^{76} - 18 q^{77} - 32 q^{78} + 20 q^{79} - 4 q^{81} + 32 q^{82} - 6 q^{83} - 12 q^{84} - 36 q^{86} - 14 q^{87} - 16 q^{88} - 18 q^{89} + 26 q^{91} + 36 q^{92} + 44 q^{93} + 38 q^{94} - 26 q^{96} - 8 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 + 2 * q^6 + 16 * q^7 - 6 * q^8 - 4 * q^9 - 6 * q^11 + 2 * q^12 - 8 * q^13 + 12 * q^14 - 10 * q^16 - 8 * q^17 + 8 * q^18 + 2 * q^19 + 4 * q^21 + 4 * q^22 - 2 * q^23 - 24 * q^24 + 12 * q^26 + 4 * q^27 - 28 * q^28 - 16 * q^29 + 6 * q^31 - 4 * q^32 - 4 * q^33 + 36 * q^34 - 2 * q^36 - 24 * q^37 + 38 * q^38 + 8 * q^39 - 14 * q^41 + 18 * q^42 + 40 * q^43 - 26 * q^44 + 16 * q^46 + 10 * q^47 + 10 * q^48 - 32 * q^51 - 48 * q^52 - 12 * q^53 + 2 * q^54 + 28 * q^57 - 44 * q^58 - 12 * q^59 - 28 * q^62 - 4 * q^63 - 8 * q^64 + 16 * q^66 + 12 * q^67 - 4 * q^68 + 12 * q^69 - 8 * q^71 - 6 * q^72 + 8 * q^73 + 52 * q^74 - 32 * q^76 - 18 * q^77 - 32 * q^78 + 20 * q^79 - 4 * q^81 + 32 * q^82 - 6 * q^83 - 12 * q^84 - 36 * q^86 - 14 * q^87 - 16 * q^88 - 18 * q^89 + 26 * q^91 + 36 * q^92 + 44 * q^93 + 38 * q^94 - 26 * q^96 - 8 * q^97 + 18 * q^98 + 4 * q^99

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