LMFDB - Embedded newform 375.2.i.c.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, 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 $\Q(\zeta_{10})$
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:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.4
Root			$-1.53767i$ of defining polynomial
Character	$\chi$	$=$	375.49
Dual form			375.2.i.c.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.903822 - 1.24400i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.112618 - 0.346603i) q^{4} +(0.475167 - 1.46241i) q^{6} -1.68601i q^{7} +(2.39187 + 0.777165i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.903822 - 1.24400i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.112618 - 0.346603i) q^{4} +(0.475167 - 1.46241i) q^{6} -1.68601i q^{7} +(2.39187 + 0.777165i) q^{8} +(0.809017 - 0.587785i) q^{9} +(2.40891 + 1.75017i) q^{11} +(-0.214212 - 0.294838i) q^{12} +(-0.136890 - 0.188414i) q^{13} +(-2.09740 - 1.52385i) q^{14} +(3.71829 - 2.70150i) q^{16} +(-7.09394 - 2.30496i) q^{17} -1.53767i q^{18} +(-0.232853 + 0.716646i) q^{19} +(-0.521005 - 1.60349i) q^{21} +(4.35444 - 1.41484i) q^{22} +(0.512972 - 0.706046i) q^{23} +2.51496 q^{24} -0.358112 q^{26} +(0.587785 - 0.809017i) q^{27} +(-0.584375 + 0.189875i) q^{28} +(-2.12444 - 6.53835i) q^{29} +(-3.03433 + 9.33870i) q^{31} -2.03733i q^{32} +(2.83184 + 0.920120i) q^{33} +(-9.27904 + 6.74162i) q^{34} +(-0.294838 - 0.214212i) q^{36} +(5.95259 + 8.19304i) q^{37} +(0.681054 + 0.937390i) q^{38} +(-0.188414 - 0.136890i) q^{39} +(-3.07210 + 2.23201i) q^{41} +(-2.46564 - 0.801135i) q^{42} -5.27322i q^{43} +(0.335328 - 1.03203i) q^{44} +(-0.414688 - 1.27628i) q^{46} +(-8.14814 + 2.64749i) q^{47} +(2.70150 - 3.71829i) q^{48} +4.15738 q^{49} -7.45901 q^{51} +(-0.0498883 + 0.0686654i) q^{52} +(-5.68614 + 1.84754i) q^{53} +(-0.475167 - 1.46241i) q^{54} +(1.31031 - 4.03270i) q^{56} +0.753527i q^{57} +(-10.0538 - 3.26669i) q^{58} +(-3.11564 + 2.26365i) q^{59} +(3.55679 + 2.58416i) q^{61} +(8.87488 + 12.2152i) q^{62} +(-0.991010 - 1.36401i) q^{63} +(4.90214 + 3.56161i) q^{64} +(3.70411 - 2.69119i) q^{66} +(-1.70508 - 0.554013i) q^{67} +2.71836i q^{68} +(0.269686 - 0.830007i) q^{69} +(-1.35179 - 4.16039i) q^{71} +(2.39187 - 0.777165i) q^{72} +(-8.84783 + 12.1780i) q^{73} +15.5723 q^{74} +0.274615 q^{76} +(2.95080 - 4.06143i) q^{77} +(-0.340585 + 0.110663i) q^{78} +(-2.27926 - 7.01484i) q^{79} +(0.309017 - 0.951057i) q^{81} +5.83904i q^{82} +(4.13188 + 1.34253i) q^{83} +(-0.497099 + 0.361163i) q^{84} +(-6.55991 - 4.76605i) q^{86} +(-4.04092 - 5.56185i) q^{87} +(4.40161 + 6.05830i) q^{88} +(9.79170 + 7.11409i) q^{89} +(-0.317667 + 0.230798i) q^{91} +(-0.302487 - 0.0982841i) q^{92} +9.81929i q^{93} +(-4.07098 + 12.5292i) q^{94} +(-0.629569 - 1.93761i) q^{96} +(9.01055 - 2.92771i) q^{97} +(3.75753 - 5.17180i) q^{98} +2.97757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	0.903822	−	1.24400i	0.639099	−	0.879644i	−0.359469	−	0.933157i	$-0.617042\pi$
$2$	0.903822	−	1.24400i	0.639099	−	0.879644i	0.998567	+	0.0535136i	$0.0170420\pi$
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	−0.112618	−	0.346603i	−0.0563090	−	0.173301i
$5$		0			0
$5$		0			0
$6$	0.475167	−	1.46241i	0.193986	−	0.597028i
$7$		−	1.68601i		−	0.637251i	−0.947881	−	0.318625i	$-0.896779\pi$
$7$		−	1.68601i		−	0.637251i	0.947881	−	0.318625i	$-0.103221\pi$
$8$	2.39187	+	0.777165i	0.845653	+	0.274769i
$9$	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	$0.551821\pi$
$12$	−0.214212	−	0.294838i	−0.0618377	−	0.0851123i
$13$	−0.136890	−	0.188414i	−0.0379666	−	0.0522565i	0.789612	−	0.613607i	$-0.210282\pi$
$13$	−0.136890	−	0.188414i	−0.0379666	−	0.0522565i	−0.827578	+	0.561350i	$0.810282\pi$
$14$	−2.09740	−	1.52385i	−0.560554	−	0.407266i
$15$		0			0
$16$	3.71829	−	2.70150i	0.929573	−	0.675375i
$17$	−7.09394	−	2.30496i	−1.72053	−	0.559035i	−0.728505	−	0.685041i	$-0.759784\pi$
$17$	−7.09394	−	2.30496i	−1.72053	−	0.559035i	−0.992030	+	0.126005i	$0.959784\pi$
$18$		−	1.53767i		−	0.362433i
$19$	−0.232853	+	0.716646i	−0.0534200	+	0.164410i	−0.974207	−	0.225656i	$-0.927548\pi$
$19$	−0.232853	+	0.716646i	−0.0534200	+	0.164410i	0.920787	+	0.390065i	$0.127548\pi$
$20$		0			0
$21$	−0.521005	−	1.60349i	−0.113693	−	0.349910i
$22$	4.35444	−	1.41484i	0.928370	−	0.301646i
$23$	0.512972	−	0.706046i	0.106962	−	0.147221i	−0.752180	−	0.658958i	$-0.770998\pi$
$23$	0.512972	−	0.706046i	0.106962	−	0.147221i	0.859142	+	0.511737i	$0.170998\pi$
$24$	2.51496			0.513364
$25$		0			0
$26$	−0.358112			−0.0702315
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−0.584375	+	0.189875i	−0.110436	+	0.0358830i
$29$	−2.12444	−	6.53835i	−0.394498	−	1.21414i	−0.929352	−	0.369195i	$-0.879633\pi$
$29$	−2.12444	−	6.53835i	−0.394498	−	1.21414i	0.534854	−	0.844945i	$-0.320367\pi$
$30$		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	$0.756333\pi$
$32$		−	2.03733i		−	0.360152i
$33$	2.83184	+	0.920120i	0.492960	+	0.160172i
$34$	−9.27904	+	6.74162i	−1.59134	+	1.15618i
$35$		0			0
$36$	−0.294838	−	0.214212i	−0.0491396	−	0.0357020i
$37$	5.95259	+	8.19304i	0.978600	+	1.34693i	0.937580	+	0.347769i	$0.113061\pi$
$37$	5.95259	+	8.19304i	0.978600	+	1.34693i	0.0410198	+	0.999158i	$0.486939\pi$
$38$	0.681054	+	0.937390i	0.110482	+	0.152065i
$39$	−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	$0.395826\pi$
$42$	−2.46564	−	0.801135i	−0.380457	−	0.123618i
$43$		−	5.27322i		−	0.804159i	−0.915605	−	0.402079i	$-0.868288\pi$
$43$		−	5.27322i		−	0.804159i	0.915605	−	0.402079i	$-0.131712\pi$
$44$	0.335328	−	1.03203i	0.0505526	−	0.155585i
$45$		0			0
$46$	−0.414688	−	1.27628i	−0.0611425	−	0.188177i
$47$	−8.14814	+	2.64749i	−1.18853	+	0.386176i	−0.835529	−	0.549447i	$-0.814839\pi$
$47$	−8.14814	+	2.64749i	−1.18853	+	0.386176i	−0.353000	+	0.935623i	$0.614839\pi$
$48$	2.70150	−	3.71829i	0.389928	−	0.536689i
$49$	4.15738			0.593911
$50$		0			0
$51$	−7.45901			−1.04447
$52$	−0.0498883	+	0.0686654i	−0.00691826	+	0.00952217i
$53$	−5.68614	+	1.84754i	−0.781051	+	0.253779i	−0.672289	−	0.740289i	$-0.734689\pi$
$53$	−5.68614	+	1.84754i	−0.781051	+	0.253779i	−0.108762	+	0.994068i	$0.534689\pi$
$54$	−0.475167	−	1.46241i	−0.0646621	−	0.199009i
$55$		0			0
$56$	1.31031	−	4.03270i	0.175097	−	0.538893i
$57$			0.753527i			0.0998070i
$58$	−10.0538	−	3.26669i	−1.32013	−	0.428937i
$59$	−3.11564	+	2.26365i	−0.405622	+	0.294702i	−0.771827	−	0.635833i	$-0.780657\pi$
$59$	−3.11564	+	2.26365i	−0.405622	+	0.294702i	0.366205	+	0.930534i	$0.380657\pi$
$60$		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	$0.609184\pi$
$62$	8.87488	+	12.2152i	1.12711	+	1.55134i
$63$	−0.991010	−	1.36401i	−0.124856	−	0.171849i
$64$	4.90214	+	3.56161i	0.612768	+	0.445202i
$65$		0			0
$66$	3.70411	−	2.69119i	0.455944	−	0.331263i
$67$	−1.70508	−	0.554013i	−0.208308	−	0.0676835i	0.203004	−	0.979178i	$-0.434930\pi$
$67$	−1.70508	−	0.554013i	−0.208308	−	0.0676835i	−0.411312	+	0.911494i	$0.634930\pi$
$68$			2.71836i			0.329650i
$69$	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	$0.983584\pi$
$72$	2.39187	−	0.777165i	0.281884	−	0.0915897i
$73$	−8.84783	+	12.1780i	−1.03556	+	1.42533i	−0.134870	+	0.990863i	$0.543062\pi$
$73$	−8.84783	+	12.1780i	−1.03556	+	1.42533i	−0.900690	+	0.434463i	$0.856938\pi$
$74$	15.5723			1.81024
$75$		0			0
$76$	0.274615			0.0315005
$77$	2.95080	−	4.06143i	0.336275	−	0.462843i
$78$	−0.340585	+	0.110663i	−0.0385636	+	0.0125301i
$79$	−2.27926	−	7.01484i	−0.256437	−	0.789232i	−0.993543	−	0.113455i	$-0.963808\pi$
$79$	−2.27926	−	7.01484i	−0.256437	−	0.789232i	0.737106	−	0.675777i	$-0.236192\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$			5.83904i			0.644814i
$83$	4.13188	+	1.34253i	0.453532	+	0.147362i	0.526871	−	0.849946i	$-0.323365\pi$
$83$	4.13188	+	1.34253i	0.453532	+	0.147362i	−0.0733383	+	0.997307i	$0.523365\pi$
$84$	−0.497099	+	0.361163i	−0.0542379	+	0.0394061i
$85$		0			0
$86$	−6.55991	−	4.76605i	−0.707373	−	0.513937i
$87$	−4.04092	−	5.56185i	−0.433232	−	0.596293i
$88$	4.40161	+	6.05830i	0.469213	+	0.645817i
$89$	9.79170	+	7.11409i	1.03792	+	0.754092i	0.969878	−	0.243591i	$-0.0783255\pi$
$89$	9.79170	+	7.11409i	1.03792	+	0.754092i	0.0680399	+	0.997683i	$0.478325\pi$
$90$		0			0
$91$	−0.317667	+	0.230798i	−0.0333005	+	0.0241942i
$92$	−0.302487	−	0.0982841i	−0.0315365	−	0.0102468i
$93$			9.81929i			1.01821i
$94$	−4.07098	+	12.5292i	−0.419889	+	1.29229i
$95$		0			0
$96$	−0.629569	−	1.93761i	−0.0642551	−	0.197757i
$97$	9.01055	−	2.92771i	0.914883	−	0.297264i	0.186517	−	0.982452i	$-0.440280\pi$
$97$	9.01055	−	2.92771i	0.914883	−	0.297264i	0.728366	+	0.685188i	$0.240280\pi$
$98$	3.75753	−	5.17180i	0.379568	−	0.522430i
$99$	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	$0.605570\pi$
$102$	−6.74162	+	9.27904i	−0.667520	+	0.918762i
$103$	0.666504	−	0.216560i	0.0656726	−	0.0213383i	−0.275996	−	0.961159i	$-0.589008\pi$
$103$	0.666504	−	0.216560i	0.0656726	−	0.0213383i	0.341669	+	0.939820i	$0.389008\pi$
$104$	−0.180995	−	0.557047i	−0.0177481	−	0.0546229i
$105$		0			0
$106$	−2.84091	+	8.74342i	−0.275934	+	0.849236i
$107$		−	12.5288i		−	1.21120i	−0.795768	−	0.605602i	$-0.792933\pi$
$107$		−	12.5288i		−	1.21120i	0.795768	−	0.605602i	$-0.207067\pi$
$108$	−0.346603	−	0.112618i	−0.0333519	−	0.0108367i
$109$	3.46541	−	2.51776i	0.331926	−	0.241158i	−0.409322	−	0.912390i	$-0.634235\pi$
$109$	3.46541	−	2.51776i	0.331926	−	0.241158i	0.741247	+	0.671232i	$0.234235\pi$
$110$		0			0
$111$	8.19304	+	5.95259i	0.777649	+	0.564995i
$112$	−4.55474	−	6.26907i	−0.430383	−	0.592371i
$113$	−4.83607	−	6.65628i	−0.454939	−	0.626170i	0.518511	−	0.855071i	$-0.326487\pi$
$113$	−4.83607	−	6.65628i	−0.454939	−	0.626170i	−0.973450	+	0.228901i	$0.926487\pi$
$114$	0.937390	+	0.681054i	0.0877946	+	0.0637865i
$115$		0			0
$116$	−2.02696	+	1.47267i	−0.188198	+	0.136734i
$117$	−0.221493	−	0.0719676i	−0.0204771	−	0.00665340i
$118$			5.92180i			0.545146i
$119$	−3.88618	+	11.9604i	−0.356246	+	1.09641i
$120$		0			0
$121$	−0.659464	−	2.02962i	−0.0599512	−	0.184511i
$122$	6.42940	−	2.08904i	0.582091	−	0.189133i
$123$	−2.23201	+	3.07210i	−0.201253	+	0.277002i
$124$	3.57854			0.321362
$125$		0			0
$126$	−2.59253			−0.230961
$127$	−7.02296	+	9.66627i	−0.623187	+	0.857743i	−0.997580	−	0.0695269i	$-0.977851\pi$
$127$	−7.02296	+	9.66627i	−0.623187	+	0.857743i	0.374393	+	0.927270i	$0.377851\pi$
$128$	12.7366	−	4.13836i	1.12576	−	0.365783i
$129$	−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	$-0.286746\pi$
$132$		−	1.08514i		−	0.0944497i
$133$	1.20827	+	0.392591i	0.104770	+	0.0340420i
$134$	−2.23028	+	1.62039i	−0.192667	+	0.139981i
$135$		0			0
$136$	−15.1764	−	11.0263i	−1.30137	−	0.945500i
$137$	5.88914	+	8.10570i	0.503143	+	0.692517i	0.982744	−	0.184970i	$-0.0592187\pi$
$137$	5.88914	+	8.10570i	0.503143	+	0.692517i	−0.479601	+	0.877487i	$0.659219\pi$
$138$	−0.788784	−	1.08567i	−0.0671458	−	0.0924182i
$139$	−5.31902	−	3.86450i	−0.451154	−	0.327782i	0.338897	−	0.940823i	$-0.389946\pi$
$139$	−5.31902	−	3.86450i	−0.451154	−	0.327782i	−0.790051	+	0.613041i	$0.789946\pi$
$140$		0			0
$141$	−6.93123	+	5.03583i	−0.583714	+	0.424093i
$142$	−6.39733	−	2.07862i	−0.536852	−	0.174434i
$143$		−	0.693452i		−	0.0579894i
$144$	1.42026	−	4.37112i	0.118355	−	0.364260i
$145$		0			0
$146$	7.15261	+	22.0135i	0.591954	+	1.82185i
$147$	3.95390	−	1.28470i	0.326112	−	0.105960i
$148$	2.16936	−	2.98587i	0.178320	−	0.245437i
$149$	−10.9143			−0.894132			−0.447066	−	0.894501i	$-0.647531\pi$
$149$	−10.9143			−0.894132			−0.447066	+	0.894501i	$0.647531\pi$
$150$		0			0
$151$	20.4128			1.66117			0.830584	−	0.556894i	$-0.188007\pi$
$151$	20.4128			1.66117			0.830584	+	0.556894i	$0.188007\pi$
$152$	−1.11390	+	1.53316i	−0.0903496	+	0.124356i
$153$	−7.09394	+	2.30496i	−0.573511	+	0.186345i
$154$	−2.38544	−	7.34162i	−0.192224	−	0.591605i
$155$		0			0
$156$	−0.0262278	+	0.0807210i	−0.00209991	+	0.00646285i
$157$		−	3.49944i		−	0.279286i	−0.990202	−	0.139643i	$-0.955405\pi$
$157$		−	3.49944i		−	0.279286i	0.990202	−	0.139643i	$-0.0445954\pi$
$158$	−10.7865	−	3.50476i	−0.858131	−	0.278824i
$159$	−4.83692	+	3.51423i	−0.383592	+	0.278696i
$160$		0			0
$161$	−1.19040	−	0.864875i	−0.0938165	−	0.0681617i
$162$	−0.903822	−	1.24400i	−0.0710109	−	0.0977382i
$163$	−3.51118	−	4.83272i	−0.275017	−	0.378528i	0.649059	−	0.760738i	$-0.275163\pi$
$163$	−3.51118	−	4.83272i	−0.275017	−	0.378528i	−0.924075	+	0.382210i	$0.875163\pi$
$164$	1.11959	+	0.813432i	0.0874256	+	0.0635184i
$165$		0			0
$166$	5.40459	−	3.92666i	0.419477	−	0.304768i
$167$	2.22326	+	0.722381i	0.172041	+	0.0558995i	0.393771	−	0.919209i	$-0.371170\pi$
$167$	2.22326	+	0.722381i	0.172041	+	0.0558995i	−0.221730	+	0.975108i	$0.571170\pi$
$168$		−	4.24024i		−	0.327141i
$169$	4.00046	−	12.3122i	0.307728	−	0.947089i
$170$		0			0
$171$	0.232853	+	0.716646i	0.0178067	+	0.0548033i
$172$	−1.82771	+	0.593860i	−0.139362	+	0.0452814i
$173$	3.56844	−	4.91154i	0.271303	−	0.373417i	−0.651526	−	0.758626i	$-0.725871\pi$
$173$	3.56844	−	4.91154i	0.271303	−	0.373417i	0.922829	+	0.385209i	$0.125871\pi$
$174$	−10.5712			−0.801403
$175$		0			0
$176$	13.6851			1.03155
$177$	−2.26365	+	3.11564i	−0.170146	+	0.234186i
$178$	17.6999	−	5.75105i	1.32666	−	0.431059i
$179$	−3.53007	−	10.8644i	−0.263850	−	0.812045i	−0.991956	−	0.126581i	$-0.959599\pi$
$179$	−3.53007	−	10.8644i	−0.263850	−	0.812045i	0.728107	−	0.685464i	$-0.240401\pi$
$180$		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	$0.194236\pi$
$182$			0.603779i			0.0447551i
$183$	4.18125	+	1.35857i	0.309087	+	0.100428i
$184$	1.77568	−	1.29010i	0.130905	−	0.0951077i
$185$		0			0
$186$	12.2152	+	8.87488i	0.895664	+	0.650738i
$187$	−13.0546	−	17.9681i	−0.954644	−	1.31395i
$188$	1.83526	+	2.52601i	0.133850	+	0.184228i
$189$	−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	$0.450202\pi$
$192$	5.76281	+	1.87245i	0.415895	+	0.135133i
$193$		−	10.1437i		−	0.730161i	−0.930976	−	0.365081i	$-0.881041\pi$
$193$		−	10.1437i		−	0.730161i	0.930976	−	0.365081i	$-0.118959\pi$
$194$	4.50186	−	13.8553i	0.323214	−	0.994752i
$195$		0			0
$196$	−0.468196	−	1.44096i	−0.0334426	−	0.102926i
$197$	−1.94684	+	0.632566i	−0.138706	+	0.0450685i	−0.377547	−	0.925990i	$-0.623233\pi$
$197$	−1.94684	+	0.632566i	−0.138706	+	0.0450685i	0.238841	+	0.971059i	$0.423233\pi$
$198$	2.69119	−	3.70411i	0.191255	−	0.263240i
$199$	−3.57125			−0.253159			−0.126580	−	0.991956i	$-0.540400\pi$
$199$	−3.57125			−0.253159			−0.126580	+	0.991956i	$0.540400\pi$
$200$		0			0
$201$	−1.79282			−0.126456
$202$	−5.91522	+	8.14161i	−0.416194	+	0.572842i
$203$	−11.0237	+	3.58182i	−0.773712	+	0.251394i
$204$	0.840020	+	2.58531i	0.0588131	+	0.181008i
$205$		0			0
$206$	0.332999	−	1.02487i	0.0232011	−	0.0714058i
$207$		−	0.872721i		−	0.0606583i
$208$	−1.01800	−	0.330767i	−0.0705854	−	0.0229346i
$209$	−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	$0.740942\pi$
$212$	1.28072	+	1.76276i	0.0879604	+	0.121067i
$213$	−2.57126	−	3.53904i	−0.176180	−	0.242491i
$214$	−15.5859	−	11.3238i	−1.06543	−	0.774078i
$215$		0			0
$216$	2.03464	−	1.47826i	0.138440	−	0.100583i
$217$	15.7451	+	5.11590i	1.06885	+	0.347290i
$218$		−	6.58659i		−	0.446100i
$219$	−4.65158	+	14.3161i	−0.314325	+	0.967391i
$220$		0			0
$221$	0.536807	+	1.65212i	0.0361096	+	0.111134i
$222$	14.8101	−	4.81209i	0.993988	−	0.322966i
$223$	15.4287	−	21.2357i	1.03318	−	1.42205i	0.130647	−	0.991429i	$-0.458294\pi$
$223$	15.4287	−	21.2357i	1.03318	−	1.42205i	0.902533	−	0.430622i	$-0.141706\pi$
$224$	−3.43495			−0.229507
$225$		0			0
$226$	−12.6514			−0.841557
$227$	2.63981	−	3.63338i	0.175210	−	0.241156i	−0.712376	−	0.701798i	$-0.752381\pi$
$227$	2.63981	−	3.63338i	0.175210	−	0.241156i	0.887586	+	0.460642i	$0.152381\pi$
$228$	0.261174	−	0.0848607i	0.0172967	−	0.00562004i
$229$	2.32979	+	7.17035i	0.153957	+	0.473830i	0.998054	−	0.0623605i	$-0.0198629\pi$
$229$	2.32979	+	7.17035i	0.153957	+	0.473830i	−0.844097	+	0.536191i	$0.819863\pi$
$230$		0			0
$231$	1.55133	−	4.77450i	0.102070	−	0.314139i
$232$		−	17.2899i		−	1.13514i
$233$	9.85679	+	3.20266i	0.645740	+	0.209814i	0.613535	−	0.789668i	$-0.289747\pi$
$233$	9.85679	+	3.20266i	0.645740	+	0.209814i	0.0322049	+	0.999481i	$0.489747\pi$
$234$	−0.289719	+	0.210493i	−0.0189395	+	0.0137603i
$235$		0			0
$236$	1.13546	+	0.824962i	0.0739124	+	0.0537005i
$237$	−4.33541	−	5.96718i	−0.281615	−	0.387610i
$238$	11.3664	+	15.6445i	0.736775	+	1.01408i
$239$	−15.0265	−	10.9174i	−0.971985	−	0.706188i	−0.0160815	−	0.999871i	$-0.505119\pi$
$239$	−15.0265	−	10.9174i	−0.971985	−	0.706188i	−0.955903	+	0.293683i	$0.905119\pi$
$240$		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	$0.243987\pi$
$242$	−3.12089	−	1.01404i	−0.200619	−	0.0651849i
$243$		−	1.00000i		−	0.0641500i
$244$	0.495117	−	1.52381i	0.0316966	−	0.0975522i
$245$		0			0
$246$	1.80436	+	5.55325i	0.115042	+	0.354063i
$247$	0.166901	−	0.0542295i	0.0106197	−	0.00345054i
$248$	−14.5154	+	19.9787i	−0.921729	+	1.26865i
$249$	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	$0.236166\pi$
$252$	−0.361163	+	0.497099i	−0.0227511	+	0.0313143i
$253$	2.47140	−	0.803008i	0.155376	−	0.0504847i
$254$	5.67738	+	17.4732i	0.356230	+	1.09636i
$255$		0			0
$256$	2.61854	−	8.05903i	0.163659	−	0.503690i
$257$		−	4.48380i		−	0.279692i	−0.990173	−	0.139846i	$-0.955339\pi$
$257$		−	4.48380i		−	0.279692i	0.990173	−	0.139846i	$-0.0446607\pi$
$258$	−7.71163	−	2.50566i	−0.480105	−	0.155996i
$259$	13.8135	−	10.0361i	0.858330	−	0.623614i
$260$		0			0
$261$	−5.56185	−	4.04092i	−0.344270	−	0.250127i
$262$	−19.3936	−	26.6930i	−1.19814	−	1.64910i
$263$	4.54093	+	6.25006i	0.280006	+	0.385395i	0.925736	−	0.378171i	$-0.123447\pi$
$263$	4.54093	+	6.25006i	0.280006	+	0.385395i	−0.645730	+	0.763566i	$0.723447\pi$
$264$	6.05830	+	4.40161i	0.372862	+	0.270900i
$265$		0			0
$266$	1.58045	−	1.14826i	0.0969034	−	0.0704044i
$267$	11.5108	+	3.74010i	0.704451	+	0.228890i
$268$			0.653376i			0.0399113i
$269$	−3.31865	+	10.2138i	−0.202342	+	0.622743i	0.797470	+	0.603358i	$0.206171\pi$
$269$	−3.31865	+	10.2138i	−0.202342	+	0.622743i	−0.999812	+	0.0193855i	$0.993829\pi$
$270$		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	$-0.385272\pi$
$272$	−32.6042	+	10.5938i	−1.97692	+	0.642341i
$273$	−0.230798	+	0.317667i	−0.0139685	+	0.0192261i
$274$	15.4063			0.930726
$275$		0			0
$276$	−0.318054			−0.0191446
$277$	−5.65712	+	7.78635i	−0.339903	+	0.467837i	−0.944413	−	0.328761i	$-0.893369\pi$
$277$	−5.65712	+	7.78635i	−0.339903	+	0.467837i	0.604510	+	0.796598i	$0.293369\pi$
$278$	−9.61490	+	3.12407i	−0.576663	+	0.187369i
$279$	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	$0.126927\pi$
$282$			13.1740i			0.784498i
$283$	22.5052	+	7.31238i	1.33780	+	0.434676i	0.888569	−	0.458742i	$-0.151700\pi$
$283$	22.5052	+	7.31238i	1.33780	+	0.434676i	0.449226	+	0.893418i	$0.351700\pi$
$284$	−1.28977	+	0.937071i	−0.0765336	+	0.0556049i
$285$		0			0
$286$	−0.862658	−	0.626757i	−0.0510100	−	0.0370609i
$287$	3.76318	+	5.17958i	0.222134	+	0.305741i
$288$	−1.19751	−	1.64823i	−0.0705640	−	0.0971231i
$289$	31.2579	+	22.7102i	1.83870	+	1.33589i
$290$		0			0
$291$	7.66483	−	5.56883i	0.449321	−	0.326450i
$292$	5.21735	+	1.69522i	0.305322	+	0.0992052i
$293$			23.2376i			1.35755i	0.734345	+	0.678777i	$0.237490\pi$
$293$			23.2376i			1.35755i	−0.734345	+	0.678777i	$0.762510\pi$
$294$	1.97545	−	6.07981i	0.115211	−	0.354582i
$295$		0			0
$296$	7.87047	+	24.2228i	0.457462	+	1.40792i
$297$	2.83184	−	0.920120i	0.164320	−	0.0533908i
$298$	−9.86455	+	13.5774i	−0.571438	+	0.786517i
$299$	−0.203250			−0.0117542
$300$		0			0
$301$	−8.89069			−0.512451
$302$	18.4495	−	25.3936i	1.06165	−	1.46124i
$303$	−6.22436	+	2.02242i	−0.357580	+	0.116185i
$304$	1.07020	+	3.29375i	0.0613805	+	0.188910i
$305$		0			0
$306$	−3.54428	+	10.9082i	−0.202613	+	0.623579i
$307$			21.8131i			1.24494i	0.782643	+	0.622470i	$0.213871\pi$
$307$			21.8131i			1.24494i	−0.782643	+	0.622470i	$0.786129\pi$
$308$	−1.74002	−	0.565366i	−0.0991467	−	0.0322147i
$309$	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	$0.791893\pi$
$312$	−0.344274	−	0.473852i	−0.0194907	−	0.0268266i
$313$	−3.55825	−	4.89752i	−0.201124	−	0.276824i	0.696527	−	0.717531i	$-0.254728\pi$
$313$	−3.55825	−	4.89752i	−0.201124	−	0.276824i	−0.897651	+	0.440707i	$0.854728\pi$
$314$	−4.35332	−	3.16287i	−0.245672	−	0.178491i
$315$		0			0
$316$	−2.17468	+	1.58000i	−0.122335	+	0.0888817i
$317$	8.08309	+	2.62636i	0.453992	+	0.147511i	0.527082	−	0.849814i	$-0.323286\pi$
$317$	8.08309	+	2.62636i	0.453992	+	0.147511i	−0.0730902	+	0.997325i	$0.523286\pi$
$318$			9.19338i			0.515539i
$319$	6.32566	−	19.4684i	0.354169	−	1.09002i
$320$		0			0
$321$	−3.87161	−	11.9156i	−0.216092	−	0.665063i
$322$	−2.15182	+	0.699167i	−0.119916	+	0.0389631i
$323$	3.30369	−	4.54713i	0.183822	−	0.253009i
$324$	−0.364440			−0.0202466
$325$		0			0
$326$	−9.18540			−0.508733
$327$	2.51776	−	3.46541i	0.139233	−	0.191637i
$328$	−9.08268	+	2.95114i	−0.501507	+	0.162950i
$329$	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	$-0.0477966\pi$
$332$		−	1.58331i		−	0.0868955i
$333$	9.63150	+	3.12946i	0.527803	+	0.171493i
$334$	2.90808	−	2.11284i	0.159123	−	0.115610i
$335$		0			0
$336$	−6.26907	−	4.55474i	−0.342006	−	0.248482i
$337$	14.5161	+	19.9796i	0.790740	+	1.08836i	0.994015	+	0.109239i	$0.0348414\pi$
$337$	14.5161	+	19.9796i	0.790740	+	1.08836i	−0.203275	+	0.979122i	$0.565159\pi$
$338$	−11.7007	−	16.1046i	−0.636432	−	0.875974i
$339$	−6.65628	−	4.83607i	−0.361519	−	0.262659i
$340$		0			0
$341$	−23.6537	+	17.1854i	−1.28092	+	0.930644i
$342$	1.10197	+	0.358051i	0.0595876	+	0.0193612i
$343$		−	18.8114i		−	1.01572i
$344$	4.09816	−	12.6128i	0.220958	−	0.680039i
$345$		0			0
$346$	−2.88474	−	8.87831i	−0.155084	−	0.477301i
$347$	−13.2640	+	4.30975i	−0.712051	+	0.231359i	−0.642573	−	0.766224i	$-0.722133\pi$
$347$	−13.2640	+	4.30975i	−0.712051	+	0.231359i	−0.0694775	+	0.997584i	$0.522133\pi$
$348$	−1.47267	+	2.02696i	−0.0789435	+	0.108656i
$349$	−18.4966			−0.990099			−0.495049	−	0.868865i	$-0.664850\pi$
$349$	−18.4966			−0.990099			−0.495049	+	0.868865i	$0.664850\pi$
$350$		0			0
$351$	−0.232892			−0.0124309
$352$	3.56568	−	4.90773i	0.190051	−	0.261583i
$353$	0.420113	−	0.136503i	0.0223604	−	0.00726532i	−0.297815	−	0.954623i	$-0.596258\pi$
$353$	0.420113	−	0.136503i	0.0223604	−	0.00726532i	0.320176	+	0.947358i	$0.396258\pi$
$354$	1.82994	+	5.63197i	0.0972601	+	0.299336i
$355$		0			0
$356$	1.36304	−	4.19500i	0.0722409	−	0.222335i
$357$			12.5760i			0.665590i
$358$	−16.7059	−	5.42809i	−0.882936	−	0.286883i
$359$	3.73869	−	2.71631i	0.197320	−	0.143362i	−0.484738	−	0.874659i	$-0.661085\pi$
$359$	3.73869	−	2.71631i	0.197320	−	0.143362i	0.682058	+	0.731298i	$0.261085\pi$
$360$		0			0
$361$	14.9120	+	10.8342i	0.784840	+	0.570220i
$362$	7.09506	+	9.76552i	0.372908	+	0.513264i
$363$	−1.25437	−	1.72650i	−0.0658376	−	0.0906176i
$364$	0.115770	+	0.0841120i	0.00606801	+	0.00440867i
$365$		0			0
$366$	5.46917	−	3.97359i	0.285878	−	0.207703i
$367$	−8.34738	−	2.71223i	−0.435730	−	0.141577i	0.0829348	−	0.996555i	$-0.473571\pi$
$367$	−8.34738	−	2.71223i	−0.435730	−	0.141577i	−0.518665	+	0.854978i	$0.673571\pi$
$368$		−	4.01108i		−	0.209092i
$369$	−1.17344	+	3.61147i	−0.0610867	+	0.188005i
$370$		0			0
$371$	3.11496	+	9.58687i	0.161721	+	0.497725i
$372$	3.40339	−	1.10583i	0.176458	−	0.0573345i
$373$	−9.10804	+	12.5361i	−0.471596	+	0.649097i	−0.976863	−	0.213867i	$-0.931394\pi$
$373$	−9.10804	+	12.5361i	−0.471596	+	0.649097i	0.505266	+	0.862963i	$0.331394\pi$
$374$	−34.1513			−1.76592
$375$		0			0
$376$	−21.5468			−1.11119
$377$	−0.941098	+	1.29531i	−0.0484690	+	0.0667118i
$378$	−2.46564	+	0.801135i	−0.126819	+	0.0412060i
$379$	8.43404	+	25.9573i	0.433227	+	1.33334i	0.894892	+	0.446282i	$0.147252\pi$
$379$	8.43404	+	25.9573i	0.433227	+	1.33334i	−0.461665	+	0.887054i	$0.652748\pi$
$380$		0			0
$381$	−3.69219	+	11.3634i	−0.189157	+	0.582164i
$382$			19.3196i			0.988474i
$383$	−12.4628	−	4.04941i	−0.636820	−	0.206915i	−0.0272261	−	0.999629i	$-0.508667\pi$
$383$	−12.4628	−	4.04941i	−0.636820	−	0.206915i	−0.609594	+	0.792714i	$0.708667\pi$
$384$	10.8344	−	7.87162i	0.552889	−	0.401697i
$385$		0			0
$386$	−12.6188	−	9.16812i	−0.642282	−	0.466645i
$387$	−3.09952	−	4.26612i	−0.157558	−	0.216859i
$388$	−2.02950	−	2.79337i	−0.103032	−	0.141812i
$389$	13.6769	+	9.93685i	0.693447	+	0.503818i	0.877791	−	0.479043i	$-0.159016\pi$
$389$	13.6769	+	9.93685i	0.693447	+	0.503818i	−0.184345	+	0.982862i	$0.559016\pi$
$390$		0			0
$391$	−5.26641	+	3.82627i	−0.266334	+	0.193503i
$392$	9.94390	+	3.23097i	0.502243	+	0.163189i
$393$		−	21.4573i		−	1.08238i
$394$	−0.972680	+	2.99360i	−0.0490029	+	0.150815i
$395$		0			0
$396$	−0.335328	−	1.03203i	−0.0168509	−	0.0518617i
$397$	9.89842	−	3.21619i	0.496787	−	0.161416i	−0.0498977	−	0.998754i	$-0.515890\pi$
$397$	9.89842	−	3.21619i	0.496787	−	0.161416i	0.546685	+	0.837338i	$0.315890\pi$
$398$	−3.22778	+	4.44265i	−0.161794	+	0.222690i
$399$	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	$0.505522\pi$
$402$	−1.62039	+	2.23028i	−0.0808179	+	0.111236i
$403$	2.17491	−	0.706670i	0.108340	−	0.0352017i
$404$	0.737049	+	2.26840i	0.0366696	+	0.112857i
$405$		0			0
$406$	−5.50766	+	16.9508i	−0.273341	+	0.841256i
$407$			30.1543i			1.49469i
$408$	−17.8410	−	5.79688i	−0.883260	−	0.286988i
$409$	−0.962002	+	0.698936i	−0.0475680	+	0.0345601i	−0.611315	−	0.791387i	$-0.709359\pi$
$409$	−0.962002	+	0.698936i	−0.0475680	+	0.0345601i	0.563747	+	0.825947i	$0.309359\pi$
$410$		0			0
$411$	8.10570	+	5.88914i	0.399825	+	0.290490i
$412$	−0.150121	−	0.206623i	−0.00739592	−	0.0101796i
$413$	3.81652	+	5.25299i	0.187799	+	0.258483i
$414$	−1.08567	−	0.788784i	−0.0533577	−	0.0387666i
$415$		0			0
$416$	−0.383860	+	0.278891i	−0.0188203	+	0.0136737i
$417$	−6.25289	−	2.03169i	−0.306205	−	0.0994921i
$418$			3.45005i			0.168747i
$419$	−0.611361	+	1.88158i	−0.0298670	+	0.0919210i	−0.964879	−	0.262695i	$-0.915389\pi$
$419$	−0.611361	+	1.88158i	−0.0298670	+	0.0919210i	0.935012	+	0.354616i	$0.115389\pi$
$420$		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	$0.812955\pi$
$422$	−5.44958	+	1.77068i	−0.265281	+	0.0861951i
$423$	−5.03583	+	6.93123i	−0.244850	+	0.337008i
$424$	−15.0363			−0.730229
$425$		0			0
$426$	−6.72655			−0.325902
$427$	4.35690	−	5.99677i	0.210845	−	0.290204i
$428$	−4.34251	+	1.41097i	−0.209903	+	0.0682017i
$429$	−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	$0.180695\pi$
$432$		−	4.59606i		−	0.221128i
$433$	9.76195	+	3.17185i	0.469129	+	0.152429i	0.534035	−	0.845462i	$-0.320675\pi$
$433$	9.76195	+	3.17185i	0.469129	+	0.152429i	−0.0649063	+	0.997891i	$0.520675\pi$
$434$	20.5950	−	14.9631i	0.988590	−	0.718253i
$435$		0			0
$436$	−1.26293	−	0.917573i	−0.0604834	−	0.0439438i
$437$	0.386538	+	0.532024i	0.0184906	+	0.0254502i
$438$	13.6051	+	18.7258i	0.650075	+	0.894752i
$439$	−19.9920	−	14.5251i	−0.954168	−	0.693244i	−0.00237925	−	0.999997i	$-0.500757\pi$
$439$	−19.9920	−	14.5251i	−0.954168	−	0.693244i	−0.951789	+	0.306753i	$0.900757\pi$
$440$		0			0
$441$	3.36339	−	2.44365i	0.160161	−	0.116364i
$442$	2.54043	+	0.825434i	0.120836	+	0.0392619i
$443$		−	7.52935i		−	0.357730i	−0.983874	−	0.178865i	$-0.942757\pi$
$443$		−	7.52935i		−	0.357730i	0.983874	−	0.178865i	$-0.0572426\pi$
$444$	1.14050	−	3.51010i	0.0541257	−	0.166582i
$445$		0			0
$446$	−12.4726	−	38.3867i	−0.590594	−	1.81766i
$447$	−10.3801	+	3.37269i	−0.490961	+	0.159523i
$448$	6.00491	−	8.26505i	0.283705	−	0.390487i
$449$	31.6627			1.49426			0.747128	−	0.664681i	$-0.231432\pi$
$449$	31.6627			1.49426			0.747128	+	0.664681i	$0.231432\pi$
$450$		0			0
$451$	−11.3068			−0.532416
$452$	−1.76245	+	2.42581i	−0.0828989	+	0.114101i
$453$	19.4137	−	6.30789i	0.912135	−	0.296371i
$454$	−2.13403	−	6.56786i	−0.100155	−	0.308245i
$455$		0			0
$456$	−0.585614	+	1.80234i	−0.0274239	+	0.0844021i
$457$			2.95742i			0.138342i	0.997605	+	0.0691712i	$0.0220355\pi$
$457$			2.95742i			0.138342i	−0.997605	+	0.0691712i	$0.977965\pi$
$458$	11.0257	+	3.58245i	0.515195	+	0.167397i
$459$	−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	$0.565570\pi$
$462$	−4.53737	−	6.24516i	−0.211098	−	0.290551i
$463$	−15.4835	−	21.3112i	−0.719578	−	0.990414i	−0.999538	−	0.0304024i	$-0.990321\pi$
$463$	−15.4835	−	21.3112i	−0.719578	−	0.990414i	0.279960	−	0.960012i	$-0.409679\pi$
$464$	−25.5626	−	18.5723i	−1.18671	−	0.862198i
$465$		0			0
$466$	12.8929	−	9.36724i	0.597252	−	0.433929i
$467$	−6.99888	−	2.27408i	−0.323870	−	0.105232i	0.142570	−	0.989785i	$-0.454463\pi$
$467$	−6.99888	−	2.27408i	−0.323870	−	0.105232i	−0.466439	+	0.884553i	$0.654463\pi$
$468$			0.0848751i			0.00392335i
$469$	−0.934070	+	2.87477i	−0.0431313	+	0.132745i
$470$		0			0
$471$	−1.08139	−	3.32816i	−0.0498276	−	0.153354i
$472$	−9.21143	+	2.99297i	−0.423990	+	0.137763i
$473$	9.22905	−	12.7027i	0.424352	−	0.584070i
$474$	−11.3416			−0.520939
$475$		0			0
$476$	4.58317			0.210069
$477$	−3.51423	+	4.83692i	−0.160905	+	0.221467i
$478$	−27.1626	+	8.82566i	−1.24239	+	0.403676i
$479$	8.79679	+	27.0737i	0.401936	+	1.23703i	0.923427	+	0.383774i	$0.125376\pi$
$479$	8.79679	+	27.0737i	0.401936	+	1.23703i	−0.521491	+	0.853257i	$0.674624\pi$
$480$		0			0
$481$	0.728827	−	2.24310i	0.0332316	−	0.102276i
$482$		−	8.35791i		−	0.380692i
$483$	−1.39940	−	0.454692i	−0.0636748	−	0.0206892i
$484$	−0.629204	+	0.457144i	−0.0286002	+	0.0207793i
$485$		0			0
$486$	−1.24400	−	0.903822i	−0.0564292	−	0.0409982i
$487$	1.40132	+	1.92875i	0.0634998	+	0.0873999i	0.839586	−	0.543227i	$-0.182798\pi$
$487$	1.40132	+	1.92875i	0.0634998	+	0.0873999i	−0.776086	+	0.630627i	$0.782798\pi$
$488$	6.49904	+	8.94516i	0.294198	+	0.404929i
$489$	−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	$0.102883\pi$
$492$	1.31616	+	0.427647i	0.0593371	+	0.0192798i
$493$			51.2794i			2.30951i
$494$	0.0833872	−	0.256640i	0.00375177	−	0.0115468i
$495$		0			0
$496$	13.9460	+	42.9212i	0.626192	+	1.92722i
$497$	−7.01445	+	2.27913i	−0.314641	+	0.102233i
$498$	3.92666	−	5.40459i	0.175958	−	0.242185i
$499$	−29.9989			−1.34293			−0.671467	−	0.741035i	$-0.734335\pi$
$499$	−29.9989			−1.34293			−0.671467	+	0.741035i	$0.734335\pi$
$500$		0			0
$501$	2.33767			0.104440
$502$	21.1112	−	29.0570i	0.942238	−	1.29688i
$503$	13.1483	−	4.27216i	0.586256	−	0.190486i	−0.000845408	−	1.00000i	$-0.500269\pi$
$503$	13.1483	−	4.27216i	0.586256	−	0.190486i	0.587101	+	0.809514i	$0.300269\pi$
$504$	−1.31031	−	4.03270i	−0.0583656	−	0.179631i
$505$		0			0
$506$	1.23476	−	3.80021i	0.0548920	−	0.168940i
$507$		−	12.9458i		−	0.574941i
$508$	4.14127	+	1.34558i	0.183739	+	0.0597004i
$509$	25.8511	−	18.7819i	1.14583	−	0.832493i	0.157908	−	0.987454i	$-0.449525\pi$
$509$	25.8511	−	18.7819i	1.14583	−	0.832493i	0.987921	+	0.154960i	$0.0495250\pi$
$510$		0			0
$511$	20.5322	+	14.9175i	0.908290	+	0.659911i
$512$	8.08447	+	11.1273i	0.357286	+	0.491763i
$513$	0.442912	+	0.609616i	0.0195550	+	0.0269152i
$514$	−5.57787	−	4.05256i	−0.246029	−	0.178751i
$515$		0			0
$516$	−1.55474	+	1.12959i	−0.0684438	+	0.0497273i
$517$	−24.2617	−	7.88310i	−1.06703	−	0.346698i
$518$		−	26.2549i		−	1.15358i
$519$	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	$-0.423313\pi$
$522$	−10.0538	+	3.26669i	−0.440045	+	0.142979i
$523$	13.9389	−	19.1853i	0.609507	−	0.838914i	−0.387030	−	0.922067i	$-0.626499\pi$
$523$	13.9389	−	19.1853i	0.609507	−	0.838914i	0.996537	+	0.0831532i	$0.0264991\pi$
$524$	−7.81991			−0.341614
$525$		0			0
$526$	11.8793			0.517962
$527$	43.0507	−	59.2542i	1.87532	−	2.58115i
$528$	13.0153	−	4.22893i	0.566419	−	0.184041i
$529$	6.87203	+	21.1499i	0.298784	+	0.919562i
$530$		0			0
$531$	−1.19007	+	3.66266i	−0.0516446	+	0.158946i
$532$		−	0.463003i		−	0.0200737i
$533$	0.841081	+	0.273284i	0.0364313	+	0.0118372i
$534$	15.0564	−	10.9391i	0.651556	−	0.473383i
$535$		0			0
$536$	−3.64776	−	2.65025i	−0.157559	−	0.114473i
$537$	−6.71458	−	9.24183i	−0.289756	−	0.398815i
$538$	9.70648	+	13.3598i	0.418476	+	0.575983i
$539$	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	$0.319292\pi$
$542$	−37.6025	−	12.2178i	−1.61516	−	0.524799i
$543$			7.85007i			0.336879i
$544$	−4.69597	+	14.4527i	−0.201338	+	0.619654i
$545$		0			0
$546$	0.186578	+	0.574228i	0.00798480	+	0.0245747i
$547$	−4.20728	+	1.36703i	−0.179890	+	0.0584499i	−0.397577	−	0.917569i	$-0.630149\pi$
$547$	−4.20728	+	1.36703i	−0.179890	+	0.0584499i	0.217687	+	0.976019i	$0.430149\pi$
$548$	2.14623	−	2.95404i	0.0916826	−	0.126190i
$549$	4.39643			0.187635
$550$		0			0
$551$	5.18036			0.220691
$552$	1.29010	−	1.77568i	0.0549105	−	0.0755778i
$553$	−11.8271	+	3.84285i	−0.502938	+	0.163415i
$554$	4.57323	+	14.0749i	0.194298	+	0.597987i
$555$		0			0
$556$	−0.740427	+	2.27880i	−0.0314011	+	0.0966426i
$557$		−	7.20182i		−	0.305151i	−0.988292	−	0.152575i	$-0.951243\pi$
$557$		−	7.20182i		−	0.305151i	0.988292	−	0.152575i	$-0.0487567\pi$
$558$	14.3599	+	4.66580i	0.607902	+	0.197519i
$559$	−0.993546	+	0.721854i	−0.0420225	+	0.0305312i
$560$		0			0
$561$	−17.9681	−	13.0546i	−0.758612	−	0.551164i
$562$	2.56030	+	3.52395i	0.108000	+	0.148649i
$563$	13.6665	+	18.8103i	0.575975	+	0.792761i	0.993247	−	0.116020i	$-0.0370137\pi$
$563$	13.6665	+	18.8103i	0.575975	+	0.792761i	−0.417272	+	0.908782i	$0.637014\pi$
$564$	2.52601	+	1.83526i	0.106364	+	0.0772782i
$565$		0			0
$566$	29.4373	−	21.3875i	1.23734	−	0.898982i
$567$	−1.60349	−	0.521005i	−0.0673402	−	0.0218801i
$568$		−	11.0017i		−	0.461620i
$569$	6.37307	−	19.6143i	0.267173	−	0.822273i	−0.724012	−	0.689787i	$-0.757704\pi$
$569$	6.37307	−	19.6143i	0.267173	−	0.822273i	0.991185	−	0.132486i	$-0.0422960\pi$
$570$		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	$0.887984\pi$
$572$	−0.240352	+	0.0780952i	−0.0100496	+	0.00326533i
$573$	−7.38502	+	10.1646i	−0.308514	+	0.424633i
$574$	9.84466			0.410908
$575$		0			0
$576$	6.05938			0.252474
$577$	9.69043	−	13.3377i	0.403418	−	0.555257i	−0.558180	−	0.829720i	$-0.688500\pi$
$577$	9.69043	−	13.3377i	0.403418	−	0.555257i	0.961598	+	0.274463i	$0.0885001\pi$
$578$	56.5032	−	18.3590i	2.35022	−	0.763633i
$579$	−3.13458	−	9.64725i	−0.130269	−	0.400926i
$580$		0			0
$581$	2.26351	−	6.96637i	0.0939063	−	0.289014i
$582$		−	14.5683i		−	0.603876i
$583$	−16.9309	−	5.50118i	−0.701205	−	0.227835i
$584$	−30.6271	+	22.2519i	−1.26736	+	0.920791i
$585$		0			0
$586$	28.9076	+	21.0026i	1.19416	+	0.867610i
$587$	−4.27415	−	5.88286i	−0.176413	−	0.242811i	0.711649	−	0.702535i	$-0.247949\pi$
$587$	−4.27415	−	5.88286i	−0.176413	−	0.242811i	−0.888062	+	0.459723i	$0.847949\pi$
$588$	−0.890562	−	1.22575i	−0.0367261	−	0.0505492i
$589$	−5.98599	−	4.34908i	−0.246649	−	0.179201i
$590$		0			0
$591$	−1.65608	+	1.20321i	−0.0681220	+	0.0494935i
$592$	44.2670	+	14.3832i	1.81936	+	0.591146i
$593$			2.47898i			0.101800i	0.998704	+	0.0508998i	$0.0162089\pi$
$593$			2.47898i			0.101800i	−0.998704	+	0.0508998i	$0.983791\pi$
$594$	1.41484	−	4.35444i	0.0580518	−	0.178665i
$595$		0			0
$596$	1.22914	+	3.78291i	0.0503477	+	0.154954i
$597$	−3.39646	+	1.10358i	−0.139008	+	0.0451664i
$598$	−0.183701	+	0.252843i	−0.00751211	+	0.0103395i
$599$	−30.2951			−1.23782			−0.618912	−	0.785460i	$-0.712426\pi$
$599$	−30.2951			−1.23782			−0.618912	+	0.785460i	$0.712426\pi$
$600$		0			0
$601$	4.46130			0.181980			0.0909900	−	0.995852i	$-0.470997\pi$
$601$	4.46130			0.181980			0.0909900	+	0.995852i	$0.470997\pi$
$602$	−8.03560	+	11.0600i	−0.327506	+	0.450774i
$603$	−1.70508	+	0.554013i	−0.0694361	+	0.0225612i
$604$	−2.29885	−	7.07512i	−0.0935387	−	0.287882i
$605$		0			0
$606$	−3.10982	+	9.57103i	−0.126328	+	0.388797i
$607$		−	17.2931i		−	0.701906i	−0.936393	−	0.350953i	$-0.885858\pi$
$607$		−	17.2931i		−	0.701906i	0.936393	−	0.350953i	$-0.114142\pi$
$608$	1.46004	+	0.474397i	0.0592126	+	0.0192393i
$609$	−9.37732	+	6.81302i	−0.379988	+	0.276077i
$610$		0			0
$611$	1.61423	+	1.17280i	0.0653046	+	0.0474466i
$612$	1.59781	+	2.19920i	0.0645877	+	0.0888974i
$613$	−8.41293	−	11.5794i	−0.339795	−	0.467688i	0.604587	−	0.796539i	$-0.293338\pi$
$613$	−8.41293	−	11.5794i	−0.339795	−	0.467688i	−0.944382	+	0.328852i	$0.893338\pi$
$614$	27.1356	+	19.7152i	1.09510	+	0.795640i
$615$		0			0
$616$	10.2143	−	7.42115i	0.411547	−	0.299006i
$617$	25.0669	+	8.14472i	1.00915	+	0.327894i	0.766518	−	0.642223i	$-0.221988\pi$
$617$	25.0669	+	8.14472i	1.00915	+	0.327894i	0.242637	+	0.970117i	$0.421988\pi$
$618$		−	1.07761i		−	0.0433477i
$619$	0.864708	−	2.66130i	0.0347555	−	0.106967i	−0.932174	−	0.362011i	$-0.882090\pi$
$619$	0.864708	−	2.66130i	0.0347555	−	0.106967i	0.966929	+	0.255045i	$0.0820902\pi$
$620$		0			0
$621$	−0.269686	−	0.830007i	−0.0108221	−	0.0333070i
$622$	−14.6846	+	4.77133i	−0.588800	+	0.191313i
$623$	11.9944	−	16.5089i	0.480545	−	0.661414i
$624$	−1.07039			−0.0428497
$625$		0			0
$626$	−9.30856			−0.372045
$627$	−1.31880	+	1.81517i	−0.0526679	+	0.0724911i
$628$	−1.21291	+	0.394100i	−0.0484006	+	0.0157263i
$629$	−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	$-0.148916\pi$
$632$		−	18.5499i		−	0.737877i
$633$	−3.54404	−	1.15153i	−0.140863	−	0.0457692i
$634$	10.5729	−	7.68164i	0.419902	−	0.305077i
$635$		0			0
$636$	1.76276	+	1.28072i	0.0698981	+	0.0507840i
$637$	−0.569106	−	0.783307i	−0.0225488	−	0.0310357i
$638$	−18.5015	−	25.4651i	−0.732481	−	1.00817i
$639$	−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	$0.408539\pi$
$642$	−18.3223	−	5.95327i	−0.723122	−	0.234957i
$643$			25.9118i			1.02186i	0.859622	+	0.510931i	$0.170699\pi$
$643$			25.9118i			1.02186i	−0.859622	+	0.510931i	$0.829301\pi$
$644$	−0.165708	+	0.509996i	−0.00652980	+	0.0200966i
$645$		0			0
$646$	−2.67071	−	8.21960i	−0.105078	−	0.323396i
$647$	10.3911	−	3.37629i	0.408518	−	0.132736i	−0.0975468	−	0.995231i	$-0.531100\pi$
$647$	10.3911	−	3.37629i	0.408518	−	0.132736i	0.506065	+	0.862495i	$0.331100\pi$
$648$	1.47826	−	2.03464i	0.0580713	−	0.0799283i
$649$	−11.4671			−0.450121
$650$		0			0
$651$	16.5554			0.648857
$652$	−1.27961	+	1.76124i	−0.0501135	+	0.0689753i
$653$	−13.5602	+	4.40596i	−0.530650	+	0.172419i	−0.562073	−	0.827088i	$-0.689996\pi$
$653$	−13.5602	+	4.40596i	−0.530650	+	0.172419i	0.0314233	+	0.999506i	$0.489996\pi$
$654$	−2.03537	−	6.26422i	−0.0795892	−	0.244950i
$655$		0			0
$656$	−5.39319	+	16.5985i	−0.210569	+	0.648063i
$657$			15.0528i			0.587267i
$658$	21.1243	+	6.86370i	0.823511	+	0.267575i
$659$	18.5179	−	13.4540i	0.721355	−	0.524095i	−0.165462	−	0.986216i	$-0.552912\pi$
$659$	18.5179	−	13.4540i	0.721355	−	0.524095i	0.886817	+	0.462121i	$0.152912\pi$
$660$		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	$0.417214\pi$
$662$	−14.7273	−	20.2704i	−0.572392	−	0.787830i
$663$	1.02107	+	1.40538i	0.0396550	+	0.0545804i
$664$	8.83953	+	6.42230i	0.343040	+	0.249233i
$665$		0			0
$666$	12.5982	−	9.15314i	0.488171	−	0.354677i
$667$	−5.70615	−	1.85404i	−0.220943	−	0.0717887i
$668$		−	0.851941i		−	0.0329626i
$669$	8.11133	−	24.9641i	0.313602	−	0.965168i
$670$		0			0
$671$	4.04524	+	12.4500i	0.156165	+	0.480626i
$672$	−3.26683	+	1.06146i	−0.126021	+	0.0409466i
$673$	−1.26872	+	1.74624i	−0.0489054	+	0.0673126i	−0.832769	−	0.553620i	$-0.813246\pi$
$673$	−1.26872	+	1.74624i	−0.0489054	+	0.0673126i	0.783864	+	0.620933i	$0.213246\pi$
$674$	37.9747			1.46273
$675$		0			0
$676$	−4.71795			−0.181460
$677$	−24.6717	+	33.9577i	−0.948210	+	1.30510i	0.00410738	+	0.999992i	$0.498693\pi$
$677$	−24.6717	+	33.9577i	−0.948210	+	1.30510i	−0.952318	+	0.305108i	$0.901307\pi$
$678$	−12.0322	+	3.90949i	−0.462093	+	0.150143i
$679$	−4.93613	−	15.1919i	−0.189431	−	0.583010i
$680$		0			0
$681$	1.38783	−	4.27129i	0.0531817	−	0.163676i
$682$			44.9579i			1.72153i
$683$	−27.7767	−	9.02521i	−1.06285	−	0.345340i	−0.275149	−	0.961401i	$-0.588727\pi$
$683$	−27.7767	−	9.02521i	−1.06285	−	0.345340i	−0.787698	+	0.616061i	$0.788727\pi$
$684$	0.222168	−	0.161415i	0.00849481	−	0.00617184i
$685$		0			0
$686$	−23.4015	−	17.0022i	−0.893473	−	0.649146i
$687$	4.43152	+	6.09946i	0.169073	+	0.232709i
$688$	−14.2456	−	19.6074i	−0.543108	−	0.747524i
$689$	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	$0.978455\pi$
$692$	−2.10422	−	0.683703i	−0.0799905	−	0.0259905i
$693$		−	5.02021i		−	0.190702i
$694$	−6.62698	+	20.3958i	−0.251557	+	0.774212i
$695$		0			0
$696$	−5.34287	−	16.4437i	−0.202521	−	0.623295i
$697$	26.9380	−	8.75268i	1.02035	−	0.331531i
$698$	−16.7176	+	23.0098i	−0.632771	+	0.870934i
$699$	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	$0.527117\pi$
$702$	−0.210493	+	0.289719i	−0.00794454	+	0.0109347i
$703$	−7.25759	+	2.35813i	−0.273725	+	0.0889387i
$704$	5.57536	+	17.1592i	0.210129	+	0.646711i
$705$		0			0
$706$	0.209897	−	0.645997i	0.00789958	−	0.0243124i
$707$			11.0344i			0.414990i
$708$	1.33482	+	0.433708i	0.0501655	+	0.0162998i
$709$	−41.4788	+	30.1361i	−1.55777	+	1.13178i	−0.619959	+	0.784634i	$0.712851\pi$
$709$	−41.4788	+	30.1361i	−1.55777	+	1.13178i	−0.937809	+	0.347151i	$0.887149\pi$
$710$		0			0
$711$	−5.96718	−	4.33541i	−0.223787	−	0.162591i
$712$	17.8916	+	24.6257i	0.670517	+	0.922887i
$713$	5.03702	+	6.93287i	0.188638	+	0.259638i
$714$	15.6445	+	11.3664i	0.585482	+	0.425378i
$715$		0			0
$716$	−3.36809	+	2.44706i	−0.125871	+	0.0914509i
$717$	−17.6647	−	5.73962i	−0.659701	−	0.214350i
$718$		−	7.10600i		−	0.265194i
$719$	−10.8976	+	33.5393i	−0.406411	+	1.25080i	0.513301	+	0.858209i	$0.328422\pi$
$719$	−10.8976	+	33.5393i	−0.406411	+	1.25080i	−0.919712	+	0.392595i	$0.871578\pi$
$720$		0			0
$721$	−0.365122	−	1.12373i	−0.0135979	−	0.0418499i
$722$	26.9555	−	8.75838i	1.00318	−	0.325953i
$723$	3.19486	−	4.39735i	0.118818	−	0.163539i
$724$	2.86088			0.106324
$725$		0			0
$726$	−3.28150			−0.121788
$727$	−25.8648	+	35.5998i	−0.959271	+	1.32032i	−0.0119876	+	0.999928i	$0.503816\pi$
$727$	−25.8648	+	35.5998i	−0.959271	+	1.32032i	−0.947284	+	0.320396i	$0.896184\pi$
$728$	−0.939184	+	0.305160i	−0.0348085	+	0.0113100i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	−12.1546	+	37.4079i	−0.449553	+	1.38358i
$732$		−	1.60223i		−	0.0592202i
$733$	−26.5098	−	8.61356i	−0.979162	−	0.318149i	−0.224653	−	0.974439i	$-0.572125\pi$
$733$	−26.5098	−	8.61356i	−0.979162	−	0.318149i	−0.754509	+	0.656290i	$0.772125\pi$
$734$	−10.9186	+	7.93281i	−0.403012	+	0.292805i
$735$		0			0
$736$	−1.43845	−	1.04509i	−0.0530219	−	0.0385226i
$737$	−3.13775	−	4.31874i	−0.115581	−	0.159083i
$738$	3.43210	+	4.72388i	0.126337	+	0.173888i
$739$	−26.2456	−	19.0685i	−0.965459	−	0.701447i	−0.0110469	−	0.999939i	$-0.503516\pi$
$739$	−26.2456	−	19.0685i	−0.965459	−	0.701447i	−0.954412	+	0.298492i	$0.903516\pi$
$740$		0			0
$741$	0.141975	−	0.103151i	0.00521557	−	0.00378933i
$742$	14.7415	+	4.78979i	0.541176	+	0.175839i
$743$			9.09256i			0.333574i	0.985993	+	0.166787i	$0.0533392\pi$
$743$			9.09256i			0.333574i	−0.985993	+	0.166787i	$0.946661\pi$
$744$	−7.63120	+	23.4864i	−0.279773	+	0.861054i
$745$		0			0
$746$	7.36297	+	22.6609i	0.269577	+	0.829674i
$747$	4.13188	−	1.34253i	0.151177	−	0.0491205i
$748$	−4.75760	+	6.54827i	−0.173955	+	0.239429i
$749$	−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	$0.864061\pi$
$752$	−23.1450	+	31.8563i	−0.844011	+	1.16168i
$753$	22.2145	−	7.21792i	0.809540	−	0.263036i
$754$	0.760786	+	2.34146i	0.0277062	+	0.0852709i
$755$		0			0
$756$	−0.189875	+	0.584375i	−0.00690568	+	0.0212535i
$757$		−	31.1239i		−	1.13122i	−0.824674	−	0.565608i	$-0.808642\pi$
$757$		−	31.1239i		−	1.13122i	0.824674	−	0.565608i	$-0.191358\pi$
$758$	39.9138	+	12.9688i	1.44974	+	0.471048i
$759$	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	$0.950933\pi$
$762$	10.7990	+	14.8636i	0.391207	+	0.538450i
$763$	−4.24497	−	5.84270i	−0.153678	−	0.211520i
$764$	3.70438	+	2.69139i	0.134020	+	0.0973712i
$765$		0			0
$766$	−16.3016	+	11.8438i	−0.589002	+	0.427935i
$767$	0.853003	+	0.277158i	0.0308002	+	0.0100076i
$768$		−	8.47377i		−	0.305771i
$769$	−4.43076	+	13.6365i	−0.159777	+	0.491744i	−0.998614	−	0.0526398i	$-0.983236\pi$
$769$	−4.43076	+	13.6365i	−0.159777	+	0.491744i	0.838836	+	0.544384i	$0.183236\pi$
$770$		0			0
$771$	−1.38557	−	4.26435i	−0.0499001	−	0.153577i
$772$	−3.51584	+	1.14237i	−0.126538	+	0.0411146i
$773$	−2.49807	+	3.43830i	−0.0898493	+	0.123667i	−0.851575	−	0.524232i	$-0.824352\pi$
$773$	−2.49807	+	3.43830i	−0.0898493	+	0.123667i	0.761726	+	0.647899i	$0.224352\pi$
$774$	−8.10849			−0.291454
$775$		0			0
$776$	23.8274			0.855352
$777$	10.0361	−	13.8135i	0.360043	−	0.495557i
$778$	24.7230	−	8.03298i	0.886361	−	0.287996i
$779$	−0.884215	−	2.72134i	−0.0316803	−	0.0975020i
$780$		0			0
$781$	4.02506	−	12.3879i	0.144028	−	0.443273i
$782$			10.0097i			0.357946i
$783$	−6.53835	−	2.12444i	−0.233661	−	0.0759212i
$784$	15.4584	−	11.2312i	0.552084	−	0.401113i
$785$		0			0
$786$	−26.6930	−	19.3936i	−0.952109	−	0.691747i
$787$	−15.9464	−	21.9483i	−0.568428	−	0.782374i	0.423940	−	0.905690i	$-0.360647\pi$
$787$	−15.9464	−	21.9483i	−0.568428	−	0.782374i	−0.992367	+	0.123317i	$0.960647\pi$
$788$	0.438498	+	0.603541i	0.0156208	+	0.0215002i
$789$	6.25006	+	4.54093i	0.222508	+	0.161662i
$790$		0			0
$791$	−11.2225	+	8.15364i	−0.399027	+	0.289910i
$792$	7.12195	+	2.31406i	0.253068	+	0.0822267i
$793$		−	1.02389i		−	0.0363595i
$794$	4.94545	−	15.2205i	0.175507	−	0.540156i
$795$		0			0
$796$	0.402187	+	1.23781i	0.0142552	+	0.0438729i
$797$	−12.0000	+	3.89902i	−0.425060	+	0.138111i	−0.513733	−	0.857950i	$-0.671738\pi$
$797$	−12.0000	+	3.89902i	−0.425060	+	0.138111i	0.0886722	+	0.996061i	$0.471738\pi$
$798$	1.14826	−	1.58045i	0.0406480	−	0.0559472i
$799$	63.9049			2.26079
$800$		0			0
$801$	12.1032			0.427646
$802$	−0.627976	+	0.864334i	−0.0221746	+	0.0305207i
$803$	−42.6272	+	13.8504i	−1.50428	+	0.488770i
$804$	0.201904	+	0.621398i	0.00712062	+	0.0219150i
$805$		0			0
$806$	1.08663	−	3.34430i	0.0382748	−	0.117798i
$807$			10.7394i			0.378044i
$808$	−15.6540	−	5.08629i	−0.550706	−	0.178935i
$809$	−30.2684	+	21.9913i	−1.06418	+	0.773172i	−0.974857	−	0.222831i	$-0.928470\pi$
$809$	−30.2684	+	21.9913i	−1.06418	+	0.773172i	−0.0893229	+	0.996003i	$0.528470\pi$
$810$		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	$0.926540\pi$
$812$	2.48293	+	3.41747i	0.0871339	+	0.119930i
$813$	−15.1135	−	20.8019i	−0.530053	−	0.729555i
$814$	37.5121	+	27.2541i	1.31480	+	0.955257i
$815$		0			0
$816$	−27.7348	+	20.1505i	−0.970912	+	0.705409i
$817$	3.77903	+	1.22788i	0.132212	+	0.0429582i
$818$			1.82845i			0.0639302i
$819$	−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	$0.740845\pi$
$822$	14.6522	−	4.76080i	0.511055	−	0.166052i
$823$	−13.7698	+	18.9526i	−0.479987	+	0.660645i	−0.978502	−	0.206236i	$-0.933879\pi$
$823$	−13.7698	+	18.9526i	−0.479987	+	0.660645i	0.498516	+	0.866881i	$0.333879\pi$
$824$	1.76249			0.0613993
$825$		0			0
$826$	9.98420			0.347395
$827$	−19.0778	+	26.2583i	−0.663399	+	0.913090i	−0.999588	−	0.0287047i	$-0.990862\pi$
$827$	−19.0778	+	26.2583i	−0.663399	+	0.913090i	0.336189	+	0.941794i	$0.390862\pi$
$828$	−0.302487	+	0.0982841i	−0.0105122	+	0.00341561i
$829$	0.0476213	+	0.146563i	0.00165395	+	0.00509035i	0.951880	−	0.306471i	$-0.0991482\pi$
$829$	0.0476213	+	0.146563i	0.00165395	+	0.00509035i	−0.950226	+	0.311561i	$0.899148\pi$
$830$		0			0
$831$	−2.97412	+	9.15340i	−0.103171	+	0.317528i
$832$		−	1.41118i		−	0.0489239i
$833$	−29.4922	−	9.58260i	−1.02185	−	0.332018i
$834$	−8.17892	+	5.94233i	−0.283213	+	0.205766i
$835$		0			0
$836$	0.661522	+	0.480624i	0.0228792	+	0.0166227i
$837$	5.77163	+	7.94397i	0.199497	+	0.274584i
$838$	1.78813	+	2.46115i	0.0617698	+	0.0850189i
$839$	−28.6568	−	20.8204i	−0.989342	−	0.718799i	−0.0295652	−	0.999563i	$-0.509412\pi$
$839$	−28.6568	−	20.8204i	−0.989342	−	0.718799i	−0.959777	+	0.280764i	$0.909412\pi$
$840$		0			0
$841$	−14.7752	+	10.7348i	−0.509491	+	0.370167i
$842$	16.2072	+	5.26602i	0.558535	+	0.181479i
$843$			2.83275i			0.0975651i
$844$	−0.419663	+	1.29159i	−0.0144454	+	0.0444583i
$845$		0			0
$846$	4.07098	+	12.5292i	0.139963	+	0.430762i
$847$	−3.42195	+	1.11186i	−0.117580	+	0.0382040i
$848$	−16.1516	+	22.2308i	−0.554648	+	0.763408i
$849$	23.6634			0.812125
$850$		0			0
$851$	8.83818			0.302969
$852$	−0.937071	+	1.28977i	−0.0321035	+	0.0441867i
$853$	−34.8150	+	11.3121i	−1.19204	+	0.387318i	−0.836828	−	0.547467i	$-0.815592\pi$
$853$	−34.8150	+	11.3121i	−1.19204	+	0.387318i	−0.355215	+	0.934785i	$0.615592\pi$
$854$	−3.52213	−	10.8400i	−0.120525	−	0.370938i
$855$		0			0
$856$	9.73693	−	29.9672i	0.332801	−	1.02426i
$857$		−	2.04867i		−	0.0699813i	−0.999388	−	0.0349907i	$-0.988860\pi$
$857$		−	2.04867i		−	0.0699813i	0.999388	−	0.0349907i	$-0.0111402\pi$
$858$	−1.01411	−	0.329506i	−0.0346213	−	0.0112491i
$859$	11.4736	−	8.33605i	0.391474	−	0.284422i	−0.374585	−	0.927192i	$-0.622215\pi$
$859$	11.4736	−	8.33605i	0.391474	−	0.284422i	0.766059	+	0.642770i	$0.222215\pi$
$860$		0			0
$861$	5.17958	+	3.76318i	0.176519	+	0.128249i
$862$	9.41209	+	12.9546i	0.320577	+	0.441237i
$863$	25.3546	+	34.8976i	0.863081	+	1.18793i	0.980826	+	0.194885i	$0.0624333\pi$
$863$	25.3546	+	34.8976i	0.863081	+	1.18793i	−0.117745	+	0.993044i	$0.537567\pi$
$864$	−1.64823	−	1.19751i	−0.0560740	−	0.0407402i
$865$		0			0
$866$	12.7689	−	9.27711i	0.433903	−	0.315249i
$867$	36.7459	+	11.9395i	1.24796	+	0.405485i
$868$		−	6.03344i		−	0.204788i
$869$	6.78666	−	20.8872i	0.230222	−	0.708550i
$870$		0			0
$871$	0.129025	+	0.397099i	0.00437185	+	0.0134552i
$872$	10.2455	−	3.32897i	0.346957	−	0.112733i
$873$	5.56883	−	7.66483i	0.188476	−	0.259415i
$874$	1.01120			0.0342044
$875$		0			0
$876$	5.48584			0.185350
$877$	−3.96567	+	5.45827i	−0.133911	+	0.184313i	−0.870707	−	0.491803i	$-0.836338\pi$
$877$	−3.96567	+	5.45827i	−0.133911	+	0.184313i	0.736795	+	0.676116i	$0.236338\pi$
$878$	−36.1385	+	11.7421i	−1.21962	+	0.396277i
$879$	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	$0.00655221\pi$
$882$		−	6.39269i		−	0.215253i
$883$	54.0787	+	17.5712i	1.81989	+	0.591319i	0.999818	+	0.0190624i	$0.00606811\pi$
$883$	54.0787	+	17.5712i	1.81989	+	0.591319i	0.820075	+	0.572257i	$0.193932\pi$
$884$	0.512176	−	0.372118i	0.0172263	−	0.0125157i
$885$		0			0
$886$	−9.36654	−	6.80519i	−0.314675	−	0.228625i
$887$	−21.7067	−	29.8768i	−0.728841	−	1.00316i	−0.999184	−	0.0403995i	$-0.987137\pi$
$887$	−21.7067	−	29.8768i	−0.728841	−	1.00316i	0.270342	−	0.962764i	$-0.412863\pi$
$888$	14.9705	+	20.6051i	0.502378	+	0.691463i
$889$	16.2974	+	11.8408i	0.546597	+	0.397126i
$890$		0			0
$891$	2.40891	−	1.75017i	0.0807014	−	0.0586330i
$892$	−9.09791	−	2.95609i	−0.304621	−	0.0989772i
$893$		−	6.45581i		−	0.216036i
$894$	−5.18610	+	15.9612i	−0.173449	+	0.533822i
$895$		0			0
$896$	−6.97730	−	21.4739i	−0.233095	−	0.717393i
$897$	−0.193302	+	0.0628076i	−0.00645416	+	0.00209708i
$898$	28.6174	−	39.3885i	0.954976	−	1.31441i
$899$	67.5058			2.25145
$900$		0			0
$901$	44.5956			1.48570
$902$	−10.2193	+	14.0657i	−0.340266	+	0.468336i
$903$	−8.45555	+	2.74737i	−0.281383	+	0.0914269i
$904$	−6.39421	−	19.6793i	−0.212668	−	0.654525i
$905$		0			0
$906$	9.69948	−	29.8519i	0.322244	−	0.991764i
$907$		−	25.7833i		−	0.856120i	−0.903750	−	0.428060i	$-0.859197\pi$
$907$		−	25.7833i		−	0.856120i	0.903750	−	0.428060i	$-0.140803\pi$
$908$	−1.55663	−	0.505779i	−0.0516585	−	0.0167849i
$909$	−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	$0.552356\pi$
$912$	2.03565	+	2.80183i	0.0674071	+	0.0927780i
$913$	7.60364	+	10.4655i	0.251644	+	0.346358i
$914$	3.67905	+	2.67298i	0.121692	+	0.0884145i
$915$		0			0
$916$	2.22289	−	1.61502i	0.0734462	−	0.0533618i
$917$	−34.4066	−	11.1794i	−1.13621	−	0.369176i
$918$			11.4695i			0.378551i
$919$	8.01412	−	24.6649i	0.264362	−	0.813621i	−0.727478	−	0.686131i	$-0.759308\pi$
$919$	8.01412	−	24.6649i	0.264362	−	0.813621i	0.991840	−	0.127490i	$-0.0406922\pi$
$920$		0			0
$921$	6.74062	+	20.7455i	0.222111	+	0.683588i
$922$	25.7401	−	8.36347i	0.847705	−	0.275436i
$923$	−0.598827	+	0.824214i	−0.0197106	+	0.0271293i
$924$	−1.82956			−0.0601882
$925$		0			0
$926$	−40.5055			−1.33109
$927$	0.411922	−	0.566962i	0.0135293	−	0.0186215i
$928$	−13.3208	+	4.32818i	−0.437275	+	0.142079i
$929$	−4.66201	−	14.3482i	−0.152955	−	0.470749i	0.844993	−	0.534778i	$-0.179605\pi$
$929$	−4.66201	−	14.3482i	−0.152955	−	0.470749i	−0.997948	+	0.0640296i	$0.979605\pi$
$930$		0			0
$931$	−0.968057	+	2.97937i	−0.0317268	+	0.0976450i
$932$		−	3.77707i		−	0.123722i
$933$	−9.54991	−	3.10295i	−0.312650	−	0.101586i
$934$	−9.15470	+	6.65128i	−0.299551	+	0.217637i
$935$		0			0
$936$	−0.473852	−	0.344274i	−0.0154883	−	0.0112529i
$937$	−0.385330	−	0.530361i	−0.0125882	−	0.0173262i	0.802677	−	0.596415i	$-0.203409\pi$
$937$	−0.385330	−	0.530361i	−0.0125882	−	0.0173262i	−0.815265	+	0.579088i	$0.803409\pi$
$938$	2.73199	+	3.76027i	0.0892028	+	0.122777i
$939$	−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	$0.0977333\pi$
$942$	−5.11763	−	1.66282i	−0.166741	−	0.0541776i
$943$			3.31400i			0.107919i
$944$	−5.46963	+	16.8338i	−0.178021	+	0.547893i
$945$		0			0
$946$	−7.46079	−	22.9619i	−0.242571	−	0.746557i
$947$	43.1901	−	14.0333i	1.40349	−	0.456021i	0.493171	−	0.869932i	$-0.335838\pi$
$947$	43.1901	−	14.0333i	1.40349	−	0.456021i	0.910317	+	0.413911i	$0.135838\pi$
$948$	−1.58000	+	2.17468i	−0.0513159	+	0.0706302i
$949$	3.50568			0.113799
$950$		0			0
$951$	8.49907			0.275601
$952$	−18.5905	+	25.5876i	−0.602520	+	0.829298i
$953$	43.9898	−	14.2932i	1.42497	−	0.463001i	0.507793	−	0.861479i	$-0.330462\pi$
$953$	43.9898	−	14.2932i	1.42497	−	0.463001i	0.917178	+	0.398478i	$0.130462\pi$
$954$	2.84091	+	8.74342i	0.0919779	+	0.283079i
$955$		0			0
$956$	−2.09174	+	6.43773i	−0.0676518	+	0.208211i
$957$		−	20.4703i		−	0.661710i
$958$	41.6306	+	13.5266i	1.34502	+	0.437024i
$959$	13.6663	−	9.92913i	0.441307	−	0.320628i
$960$		0			0
$961$	−52.9246	−	38.4520i	−1.70724	−	1.24039i
$962$	−2.13169	−	2.93402i	−0.0687285	−	0.0945967i
$963$	−7.36423	−	10.1360i	−0.237309	−	0.326628i
$964$	−1.60257	−	1.16433i	−0.0516153	−	0.0375007i
$965$		0			0
$966$	−1.83044	+	1.32990i	−0.0588936	+	0.0427887i
$967$	2.77461	+	0.901526i	0.0892255	+	0.0289911i	0.353290	−	0.935514i	$-0.385063\pi$
$967$	2.77461	+	0.901526i	0.0892255	+	0.0289911i	−0.264064	+	0.964505i	$0.585063\pi$
$968$		−	5.36709i		−	0.172505i
$969$	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	$0.906222\pi$
$972$	−0.346603	+	0.112618i	−0.0111173	+	0.00361222i
$973$	−6.51557	+	8.96791i	−0.208879	+	0.287498i
$974$	3.66591			0.117463
$975$		0			0
$976$	20.2063			0.646787
$977$	−26.2575	+	36.1404i	−0.840053	+	1.15623i	0.145915	+	0.989297i	$0.453387\pi$
$977$	−26.2575	+	36.1404i	−0.840053	+	1.15623i	−0.985968	+	0.166936i	$0.946613\pi$
$978$	−8.73584	+	2.83845i	−0.279341	+	0.0907635i
$979$	11.1364	+	34.2743i	0.355921	+	1.09541i
$980$		0			0
$981$	1.32367	−	4.07383i	0.0422614	−	0.130067i
$982$		−	39.5538i		−	1.26221i
$983$	−34.3627	−	11.1651i	−1.09600	−	0.356112i	−0.295437	−	0.955362i	$-0.595465\pi$
$983$	−34.3627	−	11.1651i	−1.09600	−	0.356112i	−0.800561	+	0.599251i	$0.795465\pi$
$984$	−7.72619	+	5.61341i	−0.246302	+	0.178949i
$985$		0			0
$986$	63.7918	+	46.3474i	2.03154	+	1.47600i
$987$	8.49044	+	11.6861i	0.270254	+	0.371972i
$988$	−0.0375922	−	0.0517412i	−0.00119597	−	0.00164611i
$989$	−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	$0.0807399\pi$
$992$	19.0260	+	6.18192i	0.604076	+	0.196276i
$993$		−	16.2945i		−	0.517089i
$994$	−3.50456	+	10.7859i	−0.111158	+	0.342109i
$995$		0			0
$996$	−0.489270	−	1.50582i	−0.0155031	−	0.0477137i
$997$	3.08464	−	1.00226i	0.0976915	−	0.0317419i	−0.259763	−	0.965672i	$-0.583645\pi$
$997$	3.08464	−	1.00226i	0.0976915	−	0.0317419i	0.357455	+	0.933930i	$0.383645\pi$
$998$	−27.1136	+	37.3187i	−0.858267	+	1.18130i
$999$	10.1272			0.320409

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.1	✓	16	5.4	even	2
75.2.i.a.64.1	yes	16	25.11	even	5
225.2.m.b.64.4		16	75.11	odd	10
225.2.m.b.109.4		16	15.14	odd	2
375.2.g.d.76.4		16	5.2	odd	4
375.2.g.d.301.4		16	25.2	odd	20
375.2.g.e.76.1		16	5.3	odd	4
375.2.g.e.301.1		16	25.23	odd	20
375.2.i.c.49.4		16	1.1	even	1	trivial
375.2.i.c.199.4		16	25.14	even	10	inner
1875.2.a.m.1.8		8	25.8	odd	20
1875.2.a.p.1.1		8	25.17	odd	20
1875.2.b.h.1249.3		16	25.19	even	10
1875.2.b.h.1249.14		16	25.6	even	5
5625.2.a.t.1.8		8	75.17	even	20
5625.2.a.bd.1.1		8	75.8	even	20

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.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.903822 - 1.24400i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.112618 - 0.346603i) q^{4} +(0.475167 - 1.46241i) q^{6} -1.68601i q^{7} +(2.39187 + 0.777165i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.903822 - 1.24400i) q^{2} +(0.951057 - 0.309017i) q^{3} +(-0.112618 - 0.346603i) q^{4} +(0.475167 - 1.46241i) q^{6} -1.68601i q^{7} +(2.39187 + 0.777165i) q^{8} +(0.809017 - 0.587785i) q^{9} +(2.40891 + 1.75017i) q^{11} +(-0.214212 - 0.294838i) q^{12} +(-0.136890 - 0.188414i) q^{13} +(-2.09740 - 1.52385i) q^{14} +(3.71829 - 2.70150i) q^{16} +(-7.09394 - 2.30496i) q^{17} -1.53767i q^{18} +(-0.232853 + 0.716646i) q^{19} +(-0.521005 - 1.60349i) q^{21} +(4.35444 - 1.41484i) q^{22} +(0.512972 - 0.706046i) q^{23} +2.51496 q^{24} -0.358112 q^{26} +(0.587785 - 0.809017i) q^{27} +(-0.584375 + 0.189875i) q^{28} +(-2.12444 - 6.53835i) q^{29} +(-3.03433 + 9.33870i) q^{31} -2.03733i q^{32} +(2.83184 + 0.920120i) q^{33} +(-9.27904 + 6.74162i) q^{34} +(-0.294838 - 0.214212i) q^{36} +(5.95259 + 8.19304i) q^{37} +(0.681054 + 0.937390i) q^{38} +(-0.188414 - 0.136890i) q^{39} +(-3.07210 + 2.23201i) q^{41} +(-2.46564 - 0.801135i) q^{42} -5.27322i q^{43} +(0.335328 - 1.03203i) q^{44} +(-0.414688 - 1.27628i) q^{46} +(-8.14814 + 2.64749i) q^{47} +(2.70150 - 3.71829i) q^{48} +4.15738 q^{49} -7.45901 q^{51} +(-0.0498883 + 0.0686654i) q^{52} +(-5.68614 + 1.84754i) q^{53} +(-0.475167 - 1.46241i) q^{54} +(1.31031 - 4.03270i) q^{56} +0.753527i q^{57} +(-10.0538 - 3.26669i) q^{58} +(-3.11564 + 2.26365i) q^{59} +(3.55679 + 2.58416i) q^{61} +(8.87488 + 12.2152i) q^{62} +(-0.991010 - 1.36401i) q^{63} +(4.90214 + 3.56161i) q^{64} +(3.70411 - 2.69119i) q^{66} +(-1.70508 - 0.554013i) q^{67} +2.71836i q^{68} +(0.269686 - 0.830007i) q^{69} +(-1.35179 - 4.16039i) q^{71} +(2.39187 - 0.777165i) q^{72} +(-8.84783 + 12.1780i) q^{73} +15.5723 q^{74} +0.274615 q^{76} +(2.95080 - 4.06143i) q^{77} +(-0.340585 + 0.110663i) q^{78} +(-2.27926 - 7.01484i) q^{79} +(0.309017 - 0.951057i) q^{81} +5.83904i q^{82} +(4.13188 + 1.34253i) q^{83} +(-0.497099 + 0.361163i) q^{84} +(-6.55991 - 4.76605i) q^{86} +(-4.04092 - 5.56185i) q^{87} +(4.40161 + 6.05830i) q^{88} +(9.79170 + 7.11409i) q^{89} +(-0.317667 + 0.230798i) q^{91} +(-0.302487 - 0.0982841i) q^{92} +9.81929i q^{93} +(-4.07098 + 12.5292i) q^{94} +(-0.629569 - 1.93761i) q^{96} +(9.01055 - 2.92771i) q^{97} +(3.75753 - 5.17180i) q^{98} +2.97757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Introduction

L-functions

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