LMFDB - Embedded newform 825.2.n.e.526.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			526.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	825.526
Dual form			825.2.n.e.676.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.190983 - 0.587785i) q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.190983 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.190983 - 0.587785i) q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 3.21644i) q^{11} +1.61803 q^{12} +(-1.50000 + 4.61653i) q^{13} +(1.50000 - 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(0.454915 + 1.40008i) q^{17} +(-0.500000 - 0.363271i) q^{18} +(5.85410 - 4.25325i) q^{19} +3.00000 q^{21} +(-2.04508 - 0.138757i) q^{22} -5.38197 q^{23} +(0.690983 - 2.12663i) q^{24} +(2.42705 + 1.76336i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.50000 + 4.61653i) q^{28} +(-1.11803 - 0.812299i) q^{29} +(-0.663119 + 2.04087i) q^{31} +5.61803 q^{32} +(-2.54508 - 2.12663i) q^{33} +0.909830 q^{34} +(1.30902 - 0.951057i) q^{36} +(1.73607 + 1.26133i) q^{37} +(-1.38197 - 4.25325i) q^{38} +(1.50000 + 4.61653i) q^{39} +(-3.42705 + 2.48990i) q^{41} +(0.572949 - 1.76336i) q^{42} -6.23607 q^{43} +(2.00000 - 4.97980i) q^{44} +(-1.02786 + 3.16344i) q^{46} +(9.39919 - 6.82891i) q^{47} +(1.50000 + 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(1.19098 + 0.865300i) q^{51} +(-6.35410 + 4.61653i) q^{52} +(-2.61803 + 8.05748i) q^{53} -0.618034 q^{54} +6.70820 q^{56} +(2.23607 - 6.88191i) q^{57} +(-0.690983 + 0.502029i) q^{58} +(8.78115 + 6.37988i) q^{59} +(-3.16312 - 9.73508i) q^{61} +(1.07295 + 0.779543i) q^{62} +(2.42705 - 1.76336i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +(-1.73607 + 1.08981i) q^{66} -4.70820 q^{67} +(-0.736068 + 2.26538i) q^{68} +(-4.35410 + 3.16344i) q^{69} +(-2.30902 - 7.10642i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(-0.118034 - 0.0857567i) q^{73} +(1.07295 - 0.779543i) q^{74} +11.7082 q^{76} +(3.70820 - 9.23305i) q^{77} +3.00000 q^{78} +(3.88197 - 11.9475i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.809017 + 2.48990i) q^{82} +(-3.89919 - 12.0005i) q^{83} +(3.92705 + 2.85317i) q^{84} +(-1.19098 + 3.66547i) q^{86} -1.38197 q^{87} +(-5.69098 - 4.75528i) q^{88} -17.5623 q^{89} +(-11.7812 + 8.55951i) q^{91} +(-7.04508 - 5.11855i) q^{92} +(0.663119 + 2.04087i) q^{93} +(-2.21885 - 6.82891i) q^{94} +(4.54508 - 3.30220i) q^{96} +(-5.07295 + 15.6129i) q^{97} +1.23607 q^{98} +(-3.30902 - 0.224514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - q^{11} + 2 q^{12} - 6 q^{13} + 6 q^{14} + 9 q^{16} + 13 q^{17} - 2 q^{18} + 10 q^{19} + 12 q^{21} + 3 q^{22} - 26 q^{23} + 5 q^{24} + 3 q^{26} + q^{27} + 6 q^{28} + 13 q^{31} + 18 q^{32} + q^{33} + 26 q^{34} + 3 q^{36} - 2 q^{37} - 10 q^{38} + 6 q^{39} - 7 q^{41} + 9 q^{42} - 16 q^{43} + 8 q^{44} - 22 q^{46} + 13 q^{47} + 6 q^{48} - 2 q^{49} + 7 q^{51} - 12 q^{52} - 6 q^{53} + 2 q^{54} - 5 q^{58} + 15 q^{59} + 3 q^{61} + 11 q^{62} + 3 q^{63} - 7 q^{64} + 2 q^{66} + 8 q^{67} + 6 q^{68} - 4 q^{69} - 7 q^{71} - 5 q^{72} + 4 q^{73} + 11 q^{74} + 20 q^{76} - 12 q^{77} + 12 q^{78} + 20 q^{79} - q^{81} + q^{82} + 9 q^{83} + 9 q^{84} - 7 q^{86} - 10 q^{87} - 25 q^{88} - 30 q^{89} - 27 q^{91} - 17 q^{92} - 13 q^{93} - 29 q^{94} + 7 q^{96} - 27 q^{97} - 4 q^{98} - 11 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - q^11 + 2 * q^12 - 6 * q^13 + 6 * q^14 + 9 * q^16 + 13 * q^17 - 2 * q^18 + 10 * q^19 + 12 * q^21 + 3 * q^22 - 26 * q^23 + 5 * q^24 + 3 * q^26 + q^27 + 6 * q^28 + 13 * q^31 + 18 * q^32 + q^33 + 26 * q^34 + 3 * q^36 - 2 * q^37 - 10 * q^38 + 6 * q^39 - 7 * q^41 + 9 * q^42 - 16 * q^43 + 8 * q^44 - 22 * q^46 + 13 * q^47 + 6 * q^48 - 2 * q^49 + 7 * q^51 - 12 * q^52 - 6 * q^53 + 2 * q^54 - 5 * q^58 + 15 * q^59 + 3 * q^61 + 11 * q^62 + 3 * q^63 - 7 * q^64 + 2 * q^66 + 8 * q^67 + 6 * q^68 - 4 * q^69 - 7 * q^71 - 5 * q^72 + 4 * q^73 + 11 * q^74 + 20 * q^76 - 12 * q^77 + 12 * q^78 + 20 * q^79 - q^81 + q^82 + 9 * q^83 + 9 * q^84 - 7 * q^86 - 10 * q^87 - 25 * q^88 - 30 * q^89 - 27 * q^91 - 17 * q^92 - 13 * q^93 - 29 * q^94 + 7 * q^96 - 27 * q^97 - 4 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	−0.860552	−	0.509363i	$-0.829881\pi$
$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	0.995597	+	0.0937362i	$0.0298810\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.190983	−	0.587785i	−0.0779685	−	0.239962i
$7$	2.42705	+	1.76336i	0.917339	+	0.666486i	0.942860	−	0.333188i	$-0.108125\pi$
$7$	2.42705	+	1.76336i	0.917339	+	0.666486i	−0.0255212	+	0.999674i	$0.508125\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$12$	1.61803			0.467086
$13$	−1.50000	+	4.61653i	−0.416025	+	1.28039i	0.495306	+	0.868719i	$0.335056\pi$
$13$	−1.50000	+	4.61653i	−0.416025	+	1.28039i	−0.911331	+	0.411675i	$0.864944\pi$
$14$	1.50000	−	1.08981i	0.400892	−	0.291265i
$15$		0			0
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	0.454915	+	1.40008i	0.110333	+	0.339570i	0.990945	−	0.134268i	$-0.0428682\pi$
$17$	0.454915	+	1.40008i	0.110333	+	0.339570i	−0.880612	+	0.473838i	$0.842868\pi$
$18$	−0.500000	−	0.363271i	−0.117851	−	0.0856239i
$19$	5.85410	−	4.25325i	1.34302	−	0.975763i	0.343696	−	0.939081i	$-0.388321\pi$
$19$	5.85410	−	4.25325i	1.34302	−	0.975763i	0.999327	−	0.0366825i	$-0.0116790\pi$
$20$		0			0
$21$	3.00000			0.654654
$22$	−2.04508	−	0.138757i	−0.436014	−	0.0295832i
$23$	−5.38197			−1.12222			−0.561109	−	0.827742i	$-0.689625\pi$
$23$	−5.38197			−1.12222			−0.561109	+	0.827742i	$0.689625\pi$
$24$	0.690983	−	2.12663i	0.141046	−	0.434096i
$25$		0			0
$26$	2.42705	+	1.76336i	0.475984	+	0.345823i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	1.50000	+	4.61653i	0.283473	+	0.872441i
$29$	−1.11803	−	0.812299i	−0.207614	−	0.150840i	0.479120	−	0.877750i	$-0.340956\pi$
$29$	−1.11803	−	0.812299i	−0.207614	−	0.150840i	−0.686733	+	0.726909i	$0.740956\pi$
$30$		0			0
$31$	−0.663119	+	2.04087i	−0.119100	+	0.366551i	−0.992780	−	0.119949i	$-0.961727\pi$
$31$	−0.663119	+	2.04087i	−0.119100	+	0.366551i	0.873680	+	0.486500i	$0.161727\pi$
$32$	5.61803			0.993137
$33$	−2.54508	−	2.12663i	−0.443042	−	0.370198i
$34$	0.909830			0.156035
$35$		0			0
$36$	1.30902	−	0.951057i	0.218169	−	0.158509i
$37$	1.73607	+	1.26133i	0.285408	+	0.207361i	0.721273	−	0.692651i	$-0.243557\pi$
$37$	1.73607	+	1.26133i	0.285408	+	0.207361i	−0.435865	+	0.900012i	$0.643557\pi$
$38$	−1.38197	−	4.25325i	−0.224184	−	0.689969i
$39$	1.50000	+	4.61653i	0.240192	+	0.739236i
$40$		0			0
$41$	−3.42705	+	2.48990i	−0.535215	+	0.388857i	−0.822305	−	0.569047i	$-0.807312\pi$
$41$	−3.42705	+	2.48990i	−0.535215	+	0.388857i	0.287090	+	0.957904i	$0.407312\pi$
$42$	0.572949	−	1.76336i	0.0884080	−	0.272092i
$43$	−6.23607			−0.950991			−0.475496	−	0.879718i	$-0.657731\pi$
$43$	−6.23607			−0.950991			−0.475496	+	0.879718i	$0.657731\pi$
$44$	2.00000	−	4.97980i	0.301511	−	0.750733i
$45$		0			0
$46$	−1.02786	+	3.16344i	−0.151550	+	0.466424i
$47$	9.39919	−	6.82891i	1.37101	−	0.996099i	0.373355	−	0.927689i	$-0.378207\pi$
$47$	9.39919	−	6.82891i	1.37101	−	0.996099i	0.997657	−	0.0684102i	$-0.0217927\pi$
$48$	1.50000	+	1.08981i	0.216506	+	0.157301i
$49$	0.618034	+	1.90211i	0.0882906	+	0.271730i
$50$		0			0
$51$	1.19098	+	0.865300i	0.166771	+	0.121166i
$52$	−6.35410	+	4.61653i	−0.881155	+	0.640197i
$53$	−2.61803	+	8.05748i	−0.359615	+	1.10678i	0.593671	+	0.804708i	$0.297678\pi$
$53$	−2.61803	+	8.05748i	−0.359615	+	1.10678i	−0.953285	+	0.302072i	$0.902322\pi$
$54$	−0.618034			−0.0841038
$55$		0			0
$56$	6.70820			0.896421
$57$	2.23607	−	6.88191i	0.296174	−	0.911531i
$58$	−0.690983	+	0.502029i	−0.0907305	+	0.0659196i
$59$	8.78115	+	6.37988i	1.14321	+	0.830590i	0.987563	−	0.157223i	$-0.0502542\pi$
$59$	8.78115	+	6.37988i	1.14321	+	0.830590i	0.155646	+	0.987813i	$0.450254\pi$
$60$		0			0
$61$	−3.16312	−	9.73508i	−0.404996	−	1.24645i	−0.920899	−	0.389802i	$-0.872543\pi$
$61$	−3.16312	−	9.73508i	−0.404996	−	1.24645i	0.515903	−	0.856647i	$-0.327457\pi$
$62$	1.07295	+	0.779543i	0.136265	+	0.0990021i
$63$	2.42705	−	1.76336i	0.305780	−	0.222162i
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$		0			0
$66$	−1.73607	+	1.08981i	−0.213695	+	0.134147i
$67$	−4.70820			−0.575199			−0.287599	−	0.957751i	$-0.592857\pi$
$67$	−4.70820			−0.575199			−0.287599	+	0.957751i	$0.592857\pi$
$68$	−0.736068	+	2.26538i	−0.0892614	+	0.274718i
$69$	−4.35410	+	3.16344i	−0.524172	+	0.380833i
$70$		0			0
$71$	−2.30902	−	7.10642i	−0.274030	−	0.843377i	−0.989474	−	0.144708i	$-0.953776\pi$
$71$	−2.30902	−	7.10642i	−0.274030	−	0.843377i	0.715445	−	0.698670i	$-0.246224\pi$
$72$	−0.690983	−	2.12663i	−0.0814331	−	0.250625i
$73$	−0.118034	−	0.0857567i	−0.0138148	−	0.0100371i	0.580856	−	0.814006i	$-0.302718\pi$
$73$	−0.118034	−	0.0857567i	−0.0138148	−	0.0100371i	−0.594671	+	0.803969i	$0.702718\pi$
$74$	1.07295	−	0.779543i	0.124728	−	0.0906200i
$75$		0			0
$76$	11.7082			1.34302
$77$	3.70820	−	9.23305i	0.422589	−	1.05220i
$78$	3.00000			0.339683
$79$	3.88197	−	11.9475i	0.436755	−	1.34419i	−0.454522	−	0.890736i	$-0.650190\pi$
$79$	3.88197	−	11.9475i	0.436755	−	1.34419i	0.891277	−	0.453459i	$-0.149810\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.809017	+	2.48990i	0.0893410	+	0.274963i
$83$	−3.89919	−	12.0005i	−0.427991	−	1.31722i	−0.900101	−	0.435682i	$-0.856507\pi$
$83$	−3.89919	−	12.0005i	−0.427991	−	1.31722i	0.472109	−	0.881540i	$-0.343493\pi$
$84$	3.92705	+	2.85317i	0.428476	+	0.311306i
$85$		0			0
$86$	−1.19098	+	3.66547i	−0.128427	+	0.395258i
$87$	−1.38197			−0.148162
$88$	−5.69098	−	4.75528i	−0.606661	−	0.506915i
$89$	−17.5623			−1.86160			−0.930800	−	0.365528i	$-0.880888\pi$
$89$	−17.5623			−1.86160			−0.930800	+	0.365528i	$0.880888\pi$
$90$		0			0
$91$	−11.7812	+	8.55951i	−1.23500	+	0.897280i
$92$	−7.04508	−	5.11855i	−0.734501	−	0.533646i
$93$	0.663119	+	2.04087i	0.0687622	+	0.211628i
$94$	−2.21885	−	6.82891i	−0.228857	−	0.704348i
$95$		0			0
$96$	4.54508	−	3.30220i	0.463881	−	0.337029i
$97$	−5.07295	+	15.6129i	−0.515080	+	1.58525i	0.268057	+	0.963403i	$0.413619\pi$
$97$	−5.07295	+	15.6129i	−0.515080	+	1.58525i	−0.783136	+	0.621850i	$0.786381\pi$
$98$	1.23607			0.124862
$99$	−3.30902	−	0.224514i	−0.332569	−	0.0225645i
$100$		0			0
$101$	3.11803	−	9.59632i	0.310256	−	0.954870i	−0.667407	−	0.744693i	$-0.732596\pi$
$101$	3.11803	−	9.59632i	0.310256	−	0.954870i	0.977663	−	0.210177i	$-0.0674040\pi$
$102$	0.736068	−	0.534785i	0.0728816	−	0.0529516i
$103$	−5.80902	−	4.22050i	−0.572379	−	0.415858i	0.263589	−	0.964635i	$-0.415094\pi$
$103$	−5.80902	−	4.22050i	−0.572379	−	0.415858i	−0.835969	+	0.548777i	$0.815094\pi$
$104$	3.35410	+	10.3229i	0.328897	+	1.01224i
$105$		0			0
$106$	4.23607	+	3.07768i	0.411443	+	0.298931i
$107$	−8.42705	+	6.12261i	−0.814674	+	0.591895i	−0.915182	−	0.403041i	$-0.867953\pi$
$107$	−8.42705	+	6.12261i	−0.814674	+	0.591895i	0.100508	+	0.994936i	$0.467953\pi$
$108$	0.500000	−	1.53884i	0.0481125	−	0.148075i
$109$	15.0000			1.43674			0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000			1.43674			0.718370	+	0.695662i	$0.244889\pi$
$110$		0			0
$111$	2.14590			0.203680
$112$	−1.71885	+	5.29007i	−0.162416	+	0.499864i
$113$	−0.381966	+	0.277515i	−0.0359323	+	0.0261064i	−0.605606	−	0.795764i	$-0.707069\pi$
$113$	−0.381966	+	0.277515i	−0.0359323	+	0.0261064i	0.569674	+	0.821871i	$0.307069\pi$
$114$	−3.61803	−	2.62866i	−0.338860	−	0.246196i
$115$		0			0
$116$	−0.690983	−	2.12663i	−0.0641562	−	0.197452i
$117$	3.92705	+	2.85317i	0.363056	+	0.263776i
$118$	5.42705	−	3.94298i	0.499601	−	0.362981i
$119$	−1.36475	+	4.20025i	−0.125106	+	0.385037i
$120$		0			0
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$	−6.32624			−0.572751
$123$	−1.30902	+	4.02874i	−0.118030	+	0.363259i
$124$	−2.80902	+	2.04087i	−0.252257	+	0.183276i
$125$		0			0
$126$	−0.572949	−	1.76336i	−0.0510424	−	0.157092i
$127$	−1.35410	−	4.16750i	−0.120157	−	0.369806i	0.872831	−	0.488023i	$-0.162282\pi$
$127$	−1.35410	−	4.16750i	−0.120157	−	0.369806i	−0.992988	+	0.118218i	$0.962282\pi$
$128$	9.20820	+	6.69015i	0.813898	+	0.591331i
$129$	−5.04508	+	3.66547i	−0.444195	+	0.322727i
$130$		0			0
$131$	−8.32624			−0.727467			−0.363733	−	0.931503i	$-0.618498\pi$
$131$	−8.32624			−0.727467			−0.363733	+	0.931503i	$0.618498\pi$
$132$	−1.30902	−	5.20431i	−0.113935	−	0.452977i
$133$	21.7082			1.88234
$134$	−0.899187	+	2.76741i	−0.0776779	+	0.239068i
$135$		0			0
$136$	2.66312	+	1.93487i	0.228361	+	0.165914i
$137$	3.64590	+	11.2209i	0.311490	+	0.958668i	0.977175	+	0.212435i	$0.0681394\pi$
$137$	3.64590	+	11.2209i	0.311490	+	0.958668i	−0.665685	+	0.746233i	$0.731861\pi$
$138$	1.02786	+	3.16344i	0.0874976	+	0.269290i
$139$	0.690983	+	0.502029i	0.0586084	+	0.0425815i	0.616704	−	0.787195i	$-0.288468\pi$
$139$	0.690983	+	0.502029i	0.0586084	+	0.0425815i	−0.558095	+	0.829777i	$0.688468\pi$
$140$		0			0
$141$	3.59017	−	11.0494i	0.302347	−	0.930528i
$142$	−4.61803			−0.387537
$143$	16.0623	+	1.08981i	1.34320	+	0.0911348i
$144$	1.85410			0.154508
$145$		0			0
$146$	−0.0729490	+	0.0530006i	−0.00603730	+	0.00438636i
$147$	1.61803	+	1.17557i	0.133453	+	0.0969594i
$148$	1.07295	+	3.30220i	0.0881959	+	0.271439i
$149$	−1.90983	−	5.87785i	−0.156459	−	0.481532i	0.841846	−	0.539717i	$-0.181469\pi$
$149$	−1.90983	−	5.87785i	−0.156459	−	0.481532i	−0.998306	+	0.0581846i	$0.981469\pi$
$150$		0			0
$151$	−10.6631	+	7.74721i	−0.867752	+	0.630459i	−0.929983	−	0.367603i	$-0.880179\pi$
$151$	−10.6631	+	7.74721i	−0.867752	+	0.630459i	0.0622306	+	0.998062i	$0.480179\pi$
$152$	5.00000	−	15.3884i	0.405554	−	1.24817i
$153$	1.47214			0.119015
$154$	−4.71885	−	3.94298i	−0.380256	−	0.317735i
$155$		0			0
$156$	−2.42705	+	7.46969i	−0.194320	+	0.598054i
$157$	−5.50000	+	3.99598i	−0.438948	+	0.318914i	−0.785217	−	0.619221i	$-0.787448\pi$
$157$	−5.50000	+	3.99598i	−0.438948	+	0.318914i	0.346269	+	0.938135i	$0.387448\pi$
$158$	−6.28115	−	4.56352i	−0.499702	−	0.363055i
$159$	2.61803	+	8.05748i	0.207624	+	0.639000i
$160$		0			0
$161$	−13.0623	−	9.49032i	−1.02945	−	0.747942i
$162$	−0.500000	+	0.363271i	−0.0392837	+	0.0285413i
$163$	−1.82624	+	5.62058i	−0.143042	+	0.440238i	−0.996754	−	0.0805074i	$-0.974346\pi$
$163$	−1.82624	+	5.62058i	−0.143042	+	0.440238i	0.853712	+	0.520745i	$0.174346\pi$
$164$	−6.85410			−0.535215
$165$		0			0
$166$	−7.79837			−0.605271
$167$	0.944272	−	2.90617i	0.0730700	−	0.224886i	−0.907851	−	0.419293i	$-0.862278\pi$
$167$	0.944272	−	2.90617i	0.0730700	−	0.224886i	0.980921	+	0.194407i	$0.0622781\pi$
$168$	5.42705	−	3.94298i	0.418706	−	0.304208i
$169$	−8.54508	−	6.20837i	−0.657314	−	0.477567i
$170$		0			0
$171$	−2.23607	−	6.88191i	−0.170996	−	0.526273i
$172$	−8.16312	−	5.93085i	−0.622432	−	0.452223i
$173$	2.80902	−	2.04087i	0.213566	−	0.155164i	−0.475860	−	0.879521i	$-0.657863\pi$
$173$	2.80902	−	2.04087i	0.213566	−	0.155164i	0.689425	+	0.724357i	$0.257863\pi$
$174$	−0.263932	+	0.812299i	−0.0200086	+	0.0615802i
$175$		0			0
$176$	5.20820	−	3.26944i	0.392583	−	0.246443i
$177$	10.8541			0.815844
$178$	−3.35410	+	10.3229i	−0.251401	+	0.773731i
$179$	−16.2812	+	11.8290i	−1.21691	+	0.884137i	−0.995840	−	0.0911206i	$-0.970955\pi$
$179$	−16.2812	+	11.8290i	−1.21691	+	0.884137i	−0.221071	+	0.975258i	$0.570955\pi$
$180$		0			0
$181$	3.64590	+	11.2209i	0.270997	+	0.834044i	0.990251	+	0.139296i	$0.0444841\pi$
$181$	3.64590	+	11.2209i	0.270997	+	0.834044i	−0.719253	+	0.694748i	$0.755516\pi$
$182$	2.78115	+	8.55951i	0.206153	+	0.634473i
$183$	−8.28115	−	6.01661i	−0.612160	−	0.444761i
$184$	−9.73607	+	7.07367i	−0.717752	+	0.521478i
$185$		0			0
$186$	1.32624			0.0972445
$187$	4.13525	−	2.59590i	0.302400	−	0.189831i
$188$	18.7984			1.37101
$189$	0.927051	−	2.85317i	0.0674330	−	0.207538i
$190$		0			0
$191$	21.6353	+	15.7189i	1.56547	+	1.13738i	0.931336	+	0.364160i	$0.118644\pi$
$191$	21.6353	+	15.7189i	1.56547	+	1.13738i	0.634136	+	0.773222i	$0.281356\pi$
$192$	0.0729490	+	0.224514i	0.00526464	+	0.0162029i
$193$	−2.94427	−	9.06154i	−0.211933	−	0.652264i	−0.999357	−	0.0358517i	$-0.988586\pi$
$193$	−2.94427	−	9.06154i	−0.211933	−	0.652264i	0.787424	−	0.616412i	$-0.211414\pi$
$194$	8.20820	+	5.96361i	0.589315	+	0.428162i
$195$		0			0
$196$	−1.00000	+	3.07768i	−0.0714286	+	0.219835i
$197$	3.70820			0.264199			0.132099	−	0.991236i	$-0.457828\pi$
$197$	3.70820			0.264199			0.132099	+	0.991236i	$0.457828\pi$
$198$	−0.763932	+	1.90211i	−0.0542903	+	0.135177i
$199$	−21.7082			−1.53885			−0.769427	−	0.638735i	$-0.779458\pi$
$199$	−21.7082			−1.53885			−0.769427	+	0.638735i	$0.779458\pi$
$200$		0			0
$201$	−3.80902	+	2.76741i	−0.268667	+	0.195198i
$202$	−5.04508	−	3.66547i	−0.354971	−	0.257901i
$203$	−1.28115	−	3.94298i	−0.0899193	−	0.276743i
$204$	0.736068	+	2.26538i	0.0515351	+	0.158609i
$205$		0			0
$206$	−3.59017	+	2.60841i	−0.250139	+	0.181737i
$207$	−1.66312	+	5.11855i	−0.115595	+	0.355764i
$208$	−9.00000			−0.624038
$209$	−18.4164	−	15.3884i	−1.27389	−	1.06444i
$210$		0			0
$211$	−2.83688	+	8.73102i	−0.195299	+	0.601068i	0.804674	+	0.593717i	$0.202340\pi$
$211$	−2.83688	+	8.73102i	−0.195299	+	0.601068i	−0.999973	+	0.00735149i	$0.997660\pi$
$212$	−11.0902	+	8.05748i	−0.761676	+	0.553390i
$213$	−6.04508	−	4.39201i	−0.414202	−	0.300936i
$214$	1.98936	+	6.12261i	0.135990	+	0.418533i
$215$		0			0
$216$	−1.80902	−	1.31433i	−0.123088	−	0.0894287i
$217$	−5.20820	+	3.78398i	−0.353556	+	0.256873i
$218$	2.86475	−	8.81678i	0.194025	−	0.597148i
$219$	−0.145898			−0.00985888
$220$		0			0
$221$	−7.14590			−0.480685
$222$	0.409830	−	1.26133i	0.0275060	−	0.0846547i
$223$	0.572949	−	0.416272i	0.0383675	−	0.0278756i	−0.568436	−	0.822727i	$-0.692451\pi$
$223$	0.572949	−	0.416272i	0.0383675	−	0.0278756i	0.606804	+	0.794852i	$0.292451\pi$
$224$	13.6353	+	9.90659i	0.911044	+	0.661912i
$225$		0			0
$226$	0.0901699	+	0.277515i	0.00599802	+	0.0184600i
$227$	4.50000	+	3.26944i	0.298675	+	0.217000i	0.727022	−	0.686614i	$-0.240904\pi$
$227$	4.50000	+	3.26944i	0.298675	+	0.217000i	−0.428347	+	0.903615i	$0.640904\pi$
$228$	9.47214	−	6.88191i	0.627308	−	0.455766i
$229$	−3.09017	+	9.51057i	−0.204204	+	0.628476i	0.795541	+	0.605900i	$0.207187\pi$
$229$	−3.09017	+	9.51057i	−0.204204	+	0.628476i	−0.999745	+	0.0225760i	$0.992813\pi$
$230$		0			0
$231$	−2.42705	−	9.64932i	−0.159688	−	0.634879i
$232$	−3.09017			−0.202880
$233$	−2.88197	+	8.86978i	−0.188804	+	0.581079i	−0.999993	−	0.00370514i	$-0.998821\pi$
$233$	−2.88197	+	8.86978i	−0.188804	+	0.581079i	0.811189	+	0.584784i	$0.198821\pi$
$234$	2.42705	−	1.76336i	0.158661	−	0.115274i
$235$		0			0
$236$	5.42705	+	16.7027i	0.353271	+	1.08726i
$237$	−3.88197	−	11.9475i	−0.252161	−	0.776071i
$238$	2.20820	+	1.60435i	0.143137	+	0.103995i
$239$	−8.61803	+	6.26137i	−0.557454	+	0.405014i	−0.830526	−	0.556979i	$-0.811960\pi$
$239$	−8.61803	+	6.26137i	−0.557454	+	0.405014i	0.273072	+	0.961994i	$0.411960\pi$
$240$		0			0
$241$	1.14590			0.0738138			0.0369069	−	0.999319i	$-0.488250\pi$
$241$	1.14590			0.0738138			0.0369069	+	0.999319i	$0.488250\pi$
$242$	1.20820	+	6.69015i	0.0776663	+	0.430059i
$243$	−1.00000			−0.0641500
$244$	5.11803	−	15.7517i	0.327649	−	1.00840i
$245$		0			0
$246$	2.11803	+	1.53884i	0.135041	+	0.0981130i
$247$	10.8541	+	33.4055i	0.690630	+	2.12554i
$248$	1.48278	+	4.56352i	0.0941566	+	0.289784i
$249$	−10.2082	−	7.41669i	−0.646919	−	0.470014i
$250$		0			0
$251$	−0.135255	+	0.416272i	−0.00853721	+	0.0262748i	−0.955234	−	0.295850i	$-0.904397\pi$
$251$	−0.135255	+	0.416272i	−0.00853721	+	0.0262748i	0.946697	+	0.322125i	$0.104397\pi$
$252$	4.85410			0.305780
$253$	4.35410	+	17.3108i	0.273740	+	1.08832i
$254$	−2.70820			−0.169928
$255$		0			0
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	−15.3992	−	11.1882i	−0.960575	−	0.697899i	−0.00729070	−	0.999973i	$-0.502321\pi$
$257$	−15.3992	−	11.1882i	−0.960575	−	0.697899i	−0.953284	+	0.302075i	$0.902321\pi$
$258$	1.19098	+	3.66547i	0.0741474	+	0.228202i
$259$	1.98936	+	6.12261i	0.123613	+	0.380441i
$260$		0			0
$261$	−1.11803	+	0.812299i	−0.0692046	+	0.0502801i
$262$	−1.59017	+	4.89404i	−0.0982410	+	0.302355i
$263$	−29.1246			−1.79590			−0.897950	−	0.440097i	$-0.854944\pi$
$263$	−29.1246			−1.79590			−0.897950	+	0.440097i	$0.854944\pi$
$264$	−7.39919	−	0.502029i	−0.455388	−	0.0308977i
$265$		0			0
$266$	4.14590	−	12.7598i	0.254201	−	0.782351i
$267$	−14.2082	+	10.3229i	−0.869528	+	0.631749i
$268$	−6.16312	−	4.47777i	−0.376472	−	0.273523i
$269$	−2.92705	−	9.00854i	−0.178465	−	0.549260i	0.821309	−	0.570483i	$-0.193244\pi$
$269$	−2.92705	−	9.00854i	−0.178465	−	0.549260i	−0.999775	+	0.0212230i	$0.993244\pi$
$270$		0			0
$271$	−9.11803	−	6.62464i	−0.553881	−	0.402418i	0.275333	−	0.961349i	$-0.411212\pi$
$271$	−9.11803	−	6.62464i	−0.553881	−	0.402418i	−0.829214	+	0.558931i	$0.811212\pi$
$272$	−2.20820	+	1.60435i	−0.133892	+	0.0972783i
$273$	−4.50000	+	13.8496i	−0.272352	+	0.838214i
$274$	7.29180			0.440514
$275$		0			0
$276$	−8.70820			−0.524172
$277$	7.10081	−	21.8541i	0.426647	−	1.31308i	−0.474762	−	0.880114i	$-0.657466\pi$
$277$	7.10081	−	21.8541i	0.426647	−	1.31308i	0.901409	−	0.432969i	$-0.142534\pi$
$278$	0.427051	−	0.310271i	0.0256128	−	0.0186088i
$279$	1.73607	+	1.26133i	0.103936	+	0.0755137i
$280$		0			0
$281$	3.80902	+	11.7229i	0.227227	+	0.699333i	0.998058	+	0.0622928i	$0.0198413\pi$
$281$	3.80902	+	11.7229i	0.227227	+	0.699333i	−0.770831	+	0.637040i	$0.780159\pi$
$282$	−5.80902	−	4.22050i	−0.345922	−	0.251327i
$283$	12.8713	−	9.35156i	0.765121	−	0.555893i	−0.135356	−	0.990797i	$-0.543218\pi$
$283$	12.8713	−	9.35156i	0.765121	−	0.555893i	0.900477	+	0.434904i	$0.143218\pi$
$284$	3.73607	−	11.4984i	0.221695	−	0.682307i
$285$		0			0
$286$	3.70820	−	9.23305i	0.219271	−	0.545962i
$287$	−12.7082			−0.750142
$288$	1.73607	−	5.34307i	0.102299	−	0.314843i
$289$	12.0000	−	8.71851i	0.705882	−	0.512854i
$290$		0			0
$291$	5.07295	+	15.6129i	0.297382	+	0.915246i
$292$	−0.0729490	−	0.224514i	−0.00426902	−	0.0131387i
$293$	6.00000	+	4.35926i	0.350524	+	0.254670i	0.749089	−	0.662470i	$-0.230492\pi$
$293$	6.00000	+	4.35926i	0.350524	+	0.254670i	−0.398565	+	0.917140i	$0.630492\pi$
$294$	1.00000	−	0.726543i	0.0583212	−	0.0423728i
$295$		0			0
$296$	4.79837			0.278900
$297$	−2.80902	+	1.76336i	−0.162996	+	0.102320i
$298$	−3.81966			−0.221267
$299$	8.07295	−	24.8460i	0.466871	−	1.43688i
$300$		0			0
$301$	−15.1353	−	10.9964i	−0.872382	−	0.633822i
$302$	2.51722	+	7.74721i	0.144850	+	0.445802i
$303$	−3.11803	−	9.59632i	−0.179126	−	0.551294i
$304$	10.8541	+	7.88597i	0.622525	+	0.452291i
$305$		0			0
$306$	0.281153	−	0.865300i	0.0160724	−	0.0494659i
$307$	19.8885			1.13510			0.567550	−	0.823339i	$-0.307892\pi$
$307$	19.8885			1.13510			0.567550	+	0.823339i	$0.307892\pi$
$308$	13.6353	−	8.55951i	0.776941	−	0.487723i
$309$	−7.18034			−0.408475
$310$		0			0
$311$	22.2254	−	16.1477i	1.26029	−	0.915653i	0.261516	−	0.965199i	$-0.415777\pi$
$311$	22.2254	−	16.1477i	1.26029	−	0.915653i	0.998772	+	0.0495460i	$0.0157775\pi$
$312$	8.78115	+	6.37988i	0.497135	+	0.361190i
$313$	−5.34346	−	16.4455i	−0.302030	−	0.929553i	−0.980769	−	0.195173i	$-0.937473\pi$
$313$	−5.34346	−	16.4455i	−0.302030	−	0.929553i	0.678739	−	0.734380i	$-0.262527\pi$
$314$	1.29837	+	3.99598i	0.0732715	+	0.225506i
$315$		0			0
$316$	16.4443	−	11.9475i	0.925063	−	0.672097i
$317$	4.07295	−	12.5352i	0.228760	−	0.704050i	−0.769129	−	0.639094i	$-0.779309\pi$
$317$	4.07295	−	12.5352i	0.228760	−	0.704050i	0.997888	−	0.0649556i	$-0.0206906\pi$
$318$	5.23607			0.293624
$319$	−1.70820	+	4.25325i	−0.0956411	+	0.238137i
$320$		0			0
$321$	−3.21885	+	9.90659i	−0.179659	+	0.552932i
$322$	−8.07295	+	5.86534i	−0.449888	+	0.326863i
$323$	8.61803	+	6.26137i	0.479520	+	0.348392i
$324$	−0.500000	−	1.53884i	−0.0277778	−	0.0854912i
$325$		0			0
$326$	2.95492	+	2.14687i	0.163658	+	0.118904i
$327$	12.1353	−	8.81678i	0.671081	−	0.487569i
$328$	−2.92705	+	9.00854i	−0.161619	+	0.497413i
$329$	34.8541			1.92157
$330$		0			0
$331$	10.4164			0.572538			0.286269	−	0.958149i	$-0.407585\pi$
$331$	10.4164			0.572538			0.286269	+	0.958149i	$0.407585\pi$
$332$	6.30902	−	19.4172i	0.346252	−	1.06565i
$333$	1.73607	−	1.26133i	0.0951359	−	0.0691203i
$334$	−1.52786	−	1.11006i	−0.0836010	−	0.0607397i
$335$		0			0
$336$	1.71885	+	5.29007i	0.0937708	+	0.288597i
$337$	−8.32624	−	6.04937i	−0.453559	−	0.329530i	0.337440	−	0.941347i	$-0.390439\pi$
$337$	−8.32624	−	6.04937i	−0.453559	−	0.329530i	−0.790999	+	0.611817i	$0.790439\pi$
$338$	−5.28115	+	3.83698i	−0.287257	+	0.208704i
$339$	−0.145898	+	0.449028i	−0.00792409	+	0.0243879i
$340$		0			0
$341$	7.10081	+	0.481784i	0.384531	+	0.0260901i
$342$	−4.47214			−0.241825
$343$	4.63525	−	14.2658i	0.250280	−	0.770283i
$344$	−11.2812	+	8.19624i	−0.608239	+	0.441912i
$345$		0			0
$346$	−0.663119	−	2.04087i	−0.0356495	−	0.109718i
$347$	−1.02786	−	3.16344i	−0.0551786	−	0.169822i	0.919669	−	0.392694i	$-0.128457\pi$
$347$	−1.02786	−	3.16344i	−0.0551786	−	0.169822i	−0.974848	+	0.222872i	$0.928457\pi$
$348$	−1.80902	−	1.31433i	−0.0969735	−	0.0704554i
$349$	−8.94427	+	6.49839i	−0.478776	+	0.347851i	−0.800852	−	0.598863i	$-0.795619\pi$
$349$	−8.94427	+	6.49839i	−0.478776	+	0.347851i	0.322076	+	0.946714i	$0.395619\pi$
$350$		0			0
$351$	4.85410			0.259093
$352$	−4.54508	−	18.0701i	−0.242254	−	0.963138i
$353$	−26.8885			−1.43113			−0.715566	−	0.698545i	$-0.753831\pi$
$353$	−26.8885			−1.43113			−0.715566	+	0.698545i	$0.753831\pi$
$354$	2.07295	−	6.37988i	0.110176	−	0.339087i
$355$		0			0
$356$	−22.9894	−	16.7027i	−1.21843	−	0.885244i
$357$	1.36475	+	4.20025i	0.0722300	+	0.222301i
$358$	3.84346	+	11.8290i	0.203133	+	0.625179i
$359$	26.8713	+	19.5232i	1.41821	+	1.03039i	0.992063	+	0.125741i	$0.0401308\pi$
$359$	26.8713	+	19.5232i	1.41821	+	1.03039i	0.426151	+	0.904652i	$0.359869\pi$
$360$		0			0
$361$	10.3090	−	31.7279i	0.542580	−	1.66989i
$362$	7.29180			0.383248
$363$	−4.78115	+	9.90659i	−0.250945	+	0.519961i
$364$	−23.5623			−1.23500
$365$		0			0
$366$	−5.11803	+	3.71847i	−0.267524	+	0.194368i
$367$	28.1803	+	20.4742i	1.47100	+	1.06875i	0.980322	+	0.197405i	$0.0632515\pi$
$367$	28.1803	+	20.4742i	1.47100	+	1.06875i	0.490680	+	0.871340i	$0.336748\pi$
$368$	−3.08359	−	9.49032i	−0.160743	−	0.494717i
$369$	1.30902	+	4.02874i	0.0681447	+	0.209728i
$370$		0			0
$371$	−20.5623	+	14.9394i	−1.06754	+	0.775614i
$372$	−1.07295	+	3.30220i	−0.0556298	+	0.171211i
$373$	9.41641			0.487563			0.243782	−	0.969830i	$-0.421612\pi$
$373$	9.41641			0.487563			0.243782	+	0.969830i	$0.421612\pi$
$374$	−0.736068	−	2.92641i	−0.0380612	−	0.151321i
$375$		0			0
$376$	8.02786	−	24.7072i	0.414005	−	1.27418i
$377$	5.42705	−	3.94298i	0.279507	−	0.203074i
$378$	−1.50000	−	1.08981i	−0.0771517	−	0.0560540i
$379$	8.71885	+	26.8339i	0.447857	+	1.37836i	0.879320	+	0.476232i	$0.157998\pi$
$379$	8.71885	+	26.8339i	0.447857	+	1.37836i	−0.431463	+	0.902131i	$0.642002\pi$
$380$		0			0
$381$	−3.54508	−	2.57565i	−0.181620	−	0.131955i
$382$	13.3713	−	9.71483i	0.684136	−	0.497054i
$383$	9.41641	−	28.9807i	0.481156	−	1.48085i	−0.356316	−	0.934366i	$-0.615967\pi$
$383$	9.41641	−	28.9807i	0.481156	−	1.48085i	0.837472	−	0.546480i	$-0.184033\pi$
$384$	11.3820			0.580834
$385$		0			0
$386$	−5.88854			−0.299719
$387$	−1.92705	+	5.93085i	−0.0979575	+	0.301482i
$388$	−21.4894	+	15.6129i	−1.09096	+	0.792627i
$389$	5.59017	+	4.06150i	0.283433	+	0.205926i	0.720413	−	0.693545i	$-0.243952\pi$
$389$	5.59017	+	4.06150i	0.283433	+	0.205926i	−0.436980	+	0.899471i	$0.643952\pi$
$390$		0			0
$391$	−2.44834	−	7.53521i	−0.123818	−	0.381072i
$392$	3.61803	+	2.62866i	0.182738	+	0.132767i
$393$	−6.73607	+	4.89404i	−0.339790	+	0.246872i
$394$	0.708204	−	2.17963i	0.0356788	−	0.109808i
$395$		0			0
$396$	−4.11803	−	3.44095i	−0.206939	−	0.172914i
$397$	−0.562306			−0.0282213			−0.0141107	−	0.999900i	$-0.504492\pi$
$397$	−0.562306			−0.0282213			−0.0141107	+	0.999900i	$0.504492\pi$
$398$	−4.14590	+	12.7598i	−0.207815	+	0.639589i
$399$	17.5623	−	12.7598i	0.879215	−	0.638787i
$400$		0			0
$401$	7.16312	+	22.0458i	0.357709	+	1.10092i	0.954422	+	0.298461i	$0.0964731\pi$
$401$	7.16312	+	22.0458i	0.357709	+	1.10092i	−0.596713	+	0.802455i	$0.703527\pi$
$402$	0.899187	+	2.76741i	0.0448474	+	0.138026i
$403$	−8.42705	−	6.12261i	−0.419781	−	0.304989i
$404$	13.2082	−	9.59632i	0.657133	−	0.477435i
$405$		0			0
$406$	−2.56231			−0.127165
$407$	2.65248	−	6.60440i	0.131478	−	0.327368i
$408$	3.29180			0.162968
$409$	9.30902	−	28.6502i	0.460301	−	1.41666i	−0.404496	−	0.914540i	$-0.632553\pi$
$409$	9.30902	−	28.6502i	0.460301	−	1.41666i	0.864797	−	0.502122i	$-0.167447\pi$
$410$		0			0
$411$	9.54508	+	6.93491i	0.470824	+	0.342074i
$412$	−3.59017	−	11.0494i	−0.176875	−	0.544365i
$413$	10.0623	+	30.9686i	0.495134	+	1.52386i
$414$	2.69098	+	1.95511i	0.132255	+	0.0960886i
$415$		0			0
$416$	−8.42705	+	25.9358i	−0.413170	+	1.27161i
$417$	0.854102			0.0418256
$418$	−12.5623	+	7.88597i	−0.614442	+	0.385715i
$419$	1.05573			0.0515757			0.0257878	−	0.999667i	$-0.491791\pi$
$419$	1.05573			0.0515757			0.0257878	+	0.999667i	$0.491791\pi$
$420$		0			0
$421$	−21.2533	+	15.4414i	−1.03582	+	0.752569i	−0.969466	−	0.245227i	$-0.921137\pi$
$421$	−21.2533	+	15.4414i	−1.03582	+	0.752569i	−0.0663563	+	0.997796i	$0.521137\pi$
$422$	4.59017	+	3.33495i	0.223446	+	0.162343i
$423$	−3.59017	−	11.0494i	−0.174560	−	0.537241i
$424$	5.85410	+	18.0171i	0.284300	+	0.874986i
$425$		0			0
$426$	−3.73607	+	2.71441i	−0.181013	+	0.131514i
$427$	9.48936	−	29.2052i	0.459222	−	1.41334i
$428$	−16.8541			−0.814674
$429$	13.6353	−	8.55951i	0.658316	−	0.413257i
$430$		0			0
$431$	7.06231	−	21.7355i	0.340179	−	1.04696i	−0.623935	−	0.781476i	$-0.714467\pi$
$431$	7.06231	−	21.7355i	0.340179	−	1.04696i	0.964114	−	0.265488i	$-0.0855330\pi$
$432$	1.50000	−	1.08981i	0.0721688	−	0.0524337i
$433$	−3.89919	−	2.83293i	−0.187383	−	0.136142i	0.490139	−	0.871644i	$-0.336946\pi$
$433$	−3.89919	−	2.83293i	−0.187383	−	0.136142i	−0.677522	+	0.735503i	$0.736946\pi$
$434$	1.22949	+	3.78398i	0.0590174	+	0.181637i
$435$		0			0
$436$	19.6353	+	14.2658i	0.940358	+	0.683210i
$437$	−31.5066	+	22.8909i	−1.50716	+	1.09502i
$438$	−0.0278640	+	0.0857567i	−0.00133140	+	0.00409761i
$439$	27.5623			1.31548			0.657739	−	0.753246i	$-0.271513\pi$
$439$	27.5623			1.31548			0.657739	+	0.753246i	$0.271513\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$	−1.36475	+	4.20025i	−0.0649143	+	0.199786i
$443$	8.50000	−	6.17561i	0.403847	−	0.293412i	−0.367259	−	0.930119i	$-0.619704\pi$
$443$	8.50000	−	6.17561i	0.403847	−	0.293412i	0.771106	+	0.636707i	$0.219704\pi$
$444$	2.80902	+	2.04087i	0.133310	+	0.0968554i
$445$		0			0
$446$	−0.135255	−	0.416272i	−0.00640451	−	0.0197110i
$447$	−5.00000	−	3.63271i	−0.236492	−	0.171821i
$448$	−0.572949	+	0.416272i	−0.0270693	+	0.0196670i
$449$	1.70820	−	5.25731i	0.0806151	−	0.248108i	−0.902624	−	0.430431i	$-0.858362\pi$
$449$	1.70820	−	5.25731i	0.0806151	−	0.248108i	0.983239	+	0.182323i	$0.0583616\pi$
$450$		0			0
$451$	10.7812	+	9.00854i	0.507665	+	0.424195i
$452$	−0.763932			−0.0359323
$453$	−4.07295	+	12.5352i	−0.191364	+	0.588957i
$454$	2.78115	−	2.02063i	0.130526	−	0.0948327i
$455$		0			0
$456$	−5.00000	−	15.3884i	−0.234146	−	0.720629i
$457$	−10.0344	−	30.8828i	−0.469391	−	1.44464i	−0.853375	−	0.521298i	$-0.825448\pi$
$457$	−10.0344	−	30.8828i	−0.469391	−	1.44464i	0.383983	−	0.923340i	$-0.374552\pi$
$458$	5.00000	+	3.63271i	0.233635	+	0.169746i
$459$	1.19098	−	0.865300i	0.0555903	−	0.0403887i
$460$		0			0
$461$	13.1803			0.613870			0.306935	−	0.951731i	$-0.400697\pi$
$461$	13.1803			0.613870			0.306935	+	0.951731i	$0.400697\pi$
$462$	−6.13525	−	0.416272i	−0.285438	−	0.0193667i
$463$	22.7082			1.05534			0.527670	−	0.849450i	$-0.323066\pi$
$463$	22.7082			1.05534			0.527670	+	0.849450i	$0.323066\pi$
$464$	0.791796	−	2.43690i	0.0367582	−	0.113130i
$465$		0			0
$466$	4.66312	+	3.38795i	0.216015	+	0.156944i
$467$	10.5172	+	32.3687i	0.486679	+	1.49784i	0.829534	+	0.558456i	$0.188606\pi$
$467$	10.5172	+	32.3687i	0.486679	+	1.49784i	−0.342855	+	0.939388i	$0.611394\pi$
$468$	2.42705	+	7.46969i	0.112190	+	0.345287i
$469$	−11.4271	−	8.30224i	−0.527652	−	0.383362i
$470$		0			0
$471$	−2.10081	+	6.46564i	−0.0968004	+	0.297921i
$472$	24.2705			1.11714
$473$	5.04508	+	20.0579i	0.231973	+	0.922265i
$474$	−7.76393			−0.356609
$475$		0			0
$476$	−5.78115	+	4.20025i	−0.264979	+	0.192518i
$477$	6.85410	+	4.97980i	0.313828	+	0.228009i
$478$	2.03444	+	6.26137i	0.0930532	+	0.286388i
$479$	−11.5451	−	35.5321i	−0.527508	−	1.62350i	−0.759302	−	0.650739i	$-0.774459\pi$
$479$	−11.5451	−	35.5321i	−0.527508	−	1.62350i	0.231793	−	0.972765i	$-0.425541\pi$
$480$		0			0
$481$	−8.42705	+	6.12261i	−0.384240	+	0.279167i
$482$	0.218847	−	0.673542i	0.00996821	−	0.0306790i
$483$	−16.1459			−0.734664
$484$	−17.6353	−	2.40414i	−0.801602	−	0.109279i
$485$		0			0
$486$	−0.190983	+	0.587785i	−0.00866317	+	0.0266625i
$487$	26.1074	−	18.9681i	1.18304	−	0.859528i	0.190528	−	0.981682i	$-0.438980\pi$
$487$	26.1074	−	18.9681i	1.18304	−	0.859528i	0.992511	+	0.122154i	$0.0389801\pi$
$488$	−18.5172	−	13.4535i	−0.838235	−	0.609014i
$489$	1.82624	+	5.62058i	0.0825853	+	0.254172i
$490$		0			0
$491$	5.78115	+	4.20025i	0.260900	+	0.189555i	0.710544	−	0.703653i	$-0.248449\pi$
$491$	5.78115	+	4.20025i	0.260900	+	0.189555i	−0.449644	+	0.893208i	$0.648449\pi$
$492$	−5.54508	+	4.02874i	−0.249992	+	0.181630i
$493$	0.628677	−	1.93487i	0.0283142	−	0.0871421i
$494$	21.7082			0.976698
$495$		0			0
$496$	−3.97871			−0.178650
$497$	6.92705	−	21.3193i	0.310721	−	0.956300i
$498$	−6.30902	+	4.58377i	−0.282714	+	0.205404i
$499$	33.8435	+	24.5887i	1.51504	+	1.10074i	0.963878	+	0.266345i	$0.0858159\pi$
$499$	33.8435	+	24.5887i	1.51504	+	1.10074i	0.551163	+	0.834397i	$0.314184\pi$
$500$		0			0
$501$	−0.944272	−	2.90617i	−0.0421870	−	0.129838i
$502$	0.218847	+	0.159002i	0.00976762	+	0.00709659i
$503$	−19.0623	+	13.8496i	−0.849946	+	0.617522i	−0.925131	−	0.379648i	$-0.876045\pi$
$503$	−19.0623	+	13.8496i	−0.849946	+	0.617522i	0.0751850	+	0.997170i	$0.476045\pi$
$504$	2.07295	−	6.37988i	0.0923365	−	0.284182i
$505$		0			0
$506$	11.0066	+	0.746787i	0.489302	+	0.0331987i
$507$	−10.5623			−0.469088
$508$	2.19098	−	6.74315i	0.0972092	−	0.299179i
$509$	−7.92705	+	5.75934i	−0.351360	+	0.255278i	−0.749439	−	0.662073i	$-0.769677\pi$
$509$	−7.92705	+	5.75934i	−0.351360	+	0.255278i	0.398079	+	0.917351i	$0.369677\pi$
$510$		0			0
$511$	−0.135255	−	0.416272i	−0.00598333	−	0.0184148i
$512$	5.78115	+	17.7926i	0.255493	+	0.786327i
$513$	−5.85410	−	4.25325i	−0.258465	−	0.187786i
$514$	−9.51722	+	6.91467i	−0.419787	+	0.304993i
$515$		0			0
$516$	−10.0902			−0.444195
$517$	−29.5689	−	24.7072i	−1.30044	−	1.08662i
$518$	3.97871			0.174815
$519$	1.07295	−	3.30220i	0.0470972	−	0.144950i
$520$		0			0
$521$	−30.1353	−	21.8945i	−1.32025	−	0.959217i	−0.999929	−	0.0119081i	$-0.996209\pi$
$521$	−30.1353	−	21.8945i	−1.32025	−	0.959217i	−0.320320	−	0.947309i	$-0.603791\pi$
$522$	0.263932	+	0.812299i	0.0115520	+	0.0355534i
$523$	−4.38854	−	13.5065i	−0.191898	−	0.590600i	−0.999999	−	0.00155643i	$-0.999505\pi$
$523$	−4.38854	−	13.5065i	−0.191898	−	0.590600i	0.808101	−	0.589044i	$-0.200495\pi$
$524$	−10.8992	−	7.91872i	−0.476133	−	0.345931i
$525$		0			0
$526$	−5.56231	+	17.1190i	−0.242528	+	0.746425i
$527$	−3.15905			−0.137611
$528$	2.29180	−	5.70634i	0.0997376	−	0.248337i
$529$	5.96556			0.259372
$530$		0			0
$531$	8.78115	−	6.37988i	0.381070	−	0.276863i
$532$	28.4164	+	20.6457i	1.23201	+	0.895106i
$533$	−6.35410	−	19.5559i	−0.275227	−	0.847061i
$534$	3.35410	+	10.3229i	0.145146	+	0.446714i
$535$		0			0
$536$	−8.51722	+	6.18812i	−0.367888	+	0.267286i
$537$	−6.21885	+	19.1396i	−0.268363	+	0.825937i
$538$	−5.85410			−0.252388
$539$	5.61803	−	3.52671i	0.241986	−	0.151906i
$540$		0			0
$541$	8.90983	−	27.4216i	0.383064	−	1.17895i	−0.554812	−	0.831976i	$-0.687210\pi$
$541$	8.90983	−	27.4216i	0.383064	−	1.17895i	0.937875	−	0.346972i	$-0.112790\pi$
$542$	−5.63525	+	4.09425i	−0.242055	+	0.175863i
$543$	9.54508	+	6.93491i	0.409619	+	0.297605i
$544$	2.55573	+	7.86572i	0.109576	+	0.337240i
$545$		0			0
$546$	7.28115	+	5.29007i	0.311605	+	0.226394i
$547$	28.0795	−	20.4010i	1.20059	−	0.872283i	0.206251	−	0.978499i	$-0.433874\pi$
$547$	28.0795	−	20.4010i	1.20059	−	0.872283i	0.994343	+	0.106217i	$0.0338737\pi$
$548$	−5.89919	+	18.1558i	−0.252001	+	0.775579i
$549$	−10.2361			−0.436865
$550$		0			0
$551$	−10.0000			−0.426014
$552$	−3.71885	+	11.4454i	−0.158285	+	0.487150i
$553$	30.4894	−	22.1518i	1.29654	−	0.941991i
$554$	−11.4894	−	8.34751i	−0.488136	−	0.354652i
$555$		0			0
$556$	0.427051	+	1.31433i	0.0181110	+	0.0557399i
$557$	29.5623	+	21.4783i	1.25260	+	0.910064i	0.998370	−	0.0570813i	$-0.0181794\pi$
$557$	29.5623	+	21.4783i	1.25260	+	0.910064i	0.254226	+	0.967145i	$0.418179\pi$
$558$	1.07295	−	0.779543i	0.0454216	−	0.0330007i
$559$	9.35410	−	28.7890i	0.395636	−	1.21764i
$560$		0			0
$561$	1.81966	−	4.53077i	0.0768261	−	0.191289i
$562$	7.61803			0.321347
$563$	−11.0729	+	34.0790i	−0.466669	+	1.43626i	0.390202	+	0.920729i	$0.372405\pi$
$563$	−11.0729	+	34.0790i	−0.466669	+	1.43626i	−0.856871	+	0.515531i	$0.827595\pi$
$564$	15.2082	−	11.0494i	0.640381	−	0.465264i
$565$		0			0
$566$	−3.03851	−	9.35156i	−0.127718	−	0.393076i
$567$	−0.927051	−	2.85317i	−0.0389325	−	0.119822i
$568$	−13.5172	−	9.82084i	−0.567170	−	0.412073i
$569$	−19.7984	+	14.3844i	−0.829991	+	0.603024i	−0.919557	−	0.392957i	$-0.871452\pi$
$569$	−19.7984	+	14.3844i	−0.829991	+	0.603024i	0.0895658	+	0.995981i	$0.471452\pi$
$570$		0			0
$571$	40.4164			1.69137			0.845687	−	0.533679i	$-0.179191\pi$
$571$	40.4164			1.69137			0.845687	+	0.533679i	$0.179191\pi$
$572$	19.9894	+	16.7027i	0.835797	+	0.698377i
$573$	26.7426			1.11719
$574$	−2.42705	+	7.46969i	−0.101303	+	0.311779i
$575$		0			0
$576$	0.190983	+	0.138757i	0.00795763	+	0.00578155i
$577$	−9.64590	−	29.6870i	−0.401564	−	1.23589i	−0.923730	−	0.383043i	$-0.874876\pi$
$577$	−9.64590	−	29.6870i	−0.401564	−	1.23589i	0.522166	−	0.852844i	$-0.325124\pi$
$578$	−2.83282	−	8.71851i	−0.117830	−	0.362642i
$579$	−7.70820	−	5.60034i	−0.320342	−	0.232742i
$580$		0			0
$581$	11.6976	−	36.0014i	0.485297	−	1.49359i
$582$	10.1459			0.420561
$583$	28.0344	+	1.90211i	1.16107	+	0.0787775i
$584$	−0.326238			−0.0134998
$585$		0			0
$586$	3.70820	−	2.69417i	0.153184	−	0.111295i
$587$	−22.8992	−	16.6372i	−0.945151	−	0.686692i	0.00450435	−	0.999990i	$-0.498566\pi$
$587$	−22.8992	−	16.6372i	−0.945151	−	0.686692i	−0.949655	+	0.313298i	$0.898566\pi$
$588$	1.00000	+	3.07768i	0.0412393	+	0.126922i
$589$	4.79837	+	14.7679i	0.197714	+	0.608500i
$590$		0			0
$591$	3.00000	−	2.17963i	0.123404	−	0.0896579i
$592$	−1.22949	+	3.78398i	−0.0505317	+	0.155521i
$593$	12.5066			0.513584			0.256792	−	0.966467i	$-0.417335\pi$
$593$	12.5066			0.513584			0.256792	+	0.966467i	$0.417335\pi$
$594$	0.500000	+	1.98787i	0.0205152	+	0.0815633i
$595$		0			0
$596$	3.09017	−	9.51057i	0.126578	−	0.389568i
$597$	−17.5623	+	12.7598i	−0.718777	+	0.522222i
$598$	−13.0623	−	9.49032i	−0.534157	−	0.388088i
$599$	7.88854	+	24.2784i	0.322317	+	0.991990i	0.972637	+	0.232330i	$0.0746349\pi$
$599$	7.88854	+	24.2784i	0.322317	+	0.991990i	−0.650320	+	0.759660i	$0.725365\pi$
$600$		0			0
$601$	25.5795	+	18.5846i	1.04341	+	0.758082i	0.970948	−	0.239289i	$-0.0769143\pi$
$601$	25.5795	+	18.5846i	1.04341	+	0.758082i	0.0724623	+	0.997371i	$0.476914\pi$
$602$	−9.35410	+	6.79615i	−0.381245	+	0.276991i
$603$	−1.45492	+	4.47777i	−0.0592487	+	0.182349i
$604$	−21.3262			−0.867752
$605$		0			0
$606$	−6.23607			−0.253323
$607$	−6.84346	+	21.0620i	−0.277767	+	0.854880i	0.710706	+	0.703489i	$0.248375\pi$
$607$	−6.84346	+	21.0620i	−0.277767	+	0.854880i	−0.988474	+	0.151392i	$0.951625\pi$
$608$	32.8885	−	23.8949i	1.33381	−	0.969067i
$609$	−3.35410	−	2.43690i	−0.135915	−	0.0987481i
$610$		0			0
$611$	17.4271	+	53.6349i	0.705023	+	2.16984i
$612$	1.92705	+	1.40008i	0.0778964	+	0.0565951i
$613$	−17.7812	+	12.9188i	−0.718174	+	0.521784i	−0.885800	−	0.464067i	$-0.846390\pi$
$613$	−17.7812	+	12.9188i	−0.718174	+	0.521784i	0.167626	+	0.985851i	$0.446390\pi$
$614$	3.79837	−	11.6902i	0.153290	−	0.471778i
$615$		0			0
$616$	−5.42705	−	21.5765i	−0.218662	−	0.869344i
$617$	−26.9443			−1.08474			−0.542368	−	0.840141i	$-0.682472\pi$
$617$	−26.9443			−1.08474			−0.542368	+	0.840141i	$0.682472\pi$
$618$	−1.37132	+	4.22050i	−0.0551627	+	0.169773i
$619$	−38.3156	+	27.8379i	−1.54003	+	1.11890i	−0.589719	+	0.807608i	$0.700762\pi$
$619$	−38.3156	+	27.8379i	−1.54003	+	1.11890i	−0.950314	+	0.311292i	$0.899238\pi$
$620$		0			0
$621$	1.66312	+	5.11855i	0.0667387	+	0.205400i
$622$	−5.24671	−	16.1477i	−0.210374	−	0.647464i
$623$	−42.6246	−	30.9686i	−1.70772	−	1.24073i
$624$	−7.28115	+	5.29007i	−0.291479	+	0.211772i
$625$		0			0
$626$	−10.6869			−0.427135
$627$	−23.9443	−	1.62460i	−0.956242	−	0.0648802i
$628$	−11.0000			−0.438948
$629$	−0.976201	+	3.00444i	−0.0389237	+	0.119795i
$630$		0			0
$631$	21.6976	+	15.7642i	0.863766	+	0.627563i	0.928907	−	0.370313i	$-0.120750\pi$
$631$	21.6976	+	15.7642i	0.863766	+	0.627563i	−0.0651407	+	0.997876i	$0.520750\pi$
$632$	−8.68034	−	26.7153i	−0.345285	−	1.06268i
$633$	2.83688	+	8.73102i	0.112756	+	0.347027i
$634$	−6.59017	−	4.78804i	−0.261729	−	0.190157i
$635$		0			0
$636$	−4.23607	+	13.0373i	−0.167971	+	0.516962i
$637$	−9.70820			−0.384653
$638$	2.17376	+	1.81636i	0.0860601	+	0.0719102i
$639$	−7.47214			−0.295593
$640$		0			0
$641$	24.3992	−	17.7270i	0.963710	−	0.700176i	0.00970054	−	0.999953i	$-0.496912\pi$
$641$	24.3992	−	17.7270i	0.963710	−	0.700176i	0.954009	+	0.299777i	$0.0969122\pi$
$642$	5.20820	+	3.78398i	0.205551	+	0.149342i
$643$	−6.98936	−	21.5110i	−0.275633	−	0.848312i	−0.989051	−	0.147573i	$-0.952854\pi$
$643$	−6.98936	−	21.5110i	−0.275633	−	0.848312i	0.713418	−	0.700739i	$-0.247146\pi$
$644$	−8.07295	−	24.8460i	−0.318119	−	0.979069i
$645$		0			0
$646$	5.32624	−	3.86974i	0.209558	−	0.152253i
$647$	−11.6803	+	35.9484i	−0.459202	+	1.41328i	0.406929	+	0.913460i	$0.366600\pi$
$647$	−11.6803	+	35.9484i	−0.459202	+	1.41328i	−0.866131	+	0.499817i	$0.833400\pi$
$648$	−2.23607			−0.0878410
$649$	13.4164	−	33.4055i	0.526640	−	1.31128i
$650$		0			0
$651$	−1.98936	+	6.12261i	−0.0779690	+	0.239964i
$652$	−7.73607	+	5.62058i	−0.302968	+	0.220119i
$653$	10.4721	+	7.60845i	0.409806	+	0.297742i	0.773523	−	0.633768i	$-0.218492\pi$
$653$	10.4721	+	7.60845i	0.409806	+	0.297742i	−0.363717	+	0.931509i	$0.618492\pi$
$654$	−2.86475	−	8.81678i	−0.112020	−	0.344763i
$655$		0			0
$656$	−6.35410	−	4.61653i	−0.248086	−	0.180245i
$657$	−0.118034	+	0.0857567i	−0.00460494	+	0.00334569i
$658$	6.65654	−	20.4867i	0.259499	−	0.798656i
$659$	14.0689			0.548046			0.274023	−	0.961723i	$-0.411646\pi$
$659$	14.0689			0.548046			0.274023	+	0.961723i	$0.411646\pi$
$660$		0			0
$661$	−3.00000			−0.116686			−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000			−0.116686			−0.0583432	+	0.998297i	$0.518582\pi$
$662$	1.98936	−	6.12261i	0.0773186	−	0.237962i
$663$	−5.78115	+	4.20025i	−0.224521	+	0.163124i
$664$	−22.8262	−	16.5842i	−0.885830	−	0.643593i
$665$		0			0
$666$	−0.409830	−	1.26133i	−0.0158806	−	0.0488754i
$667$	6.01722	+	4.37177i	0.232988	+	0.169275i
$668$	4.00000	−	2.90617i	0.154765	−	0.112443i
$669$	0.218847	−	0.673542i	0.00846112	−	0.0260406i
$670$		0			0
$671$	−28.7533	+	18.0498i	−1.11001	+	0.696806i
$672$	16.8541			0.650161
$673$	−4.79180	+	14.7476i	−0.184710	+	0.568479i	−0.999943	−	0.0106536i	$-0.996609\pi$
$673$	−4.79180	+	14.7476i	−0.184710	+	0.568479i	0.815233	+	0.579133i	$0.196609\pi$
$674$	−5.14590	+	3.73871i	−0.198213	+	0.144010i
$675$		0			0
$676$	−5.28115	−	16.2537i	−0.203121	−	0.625143i
$677$	5.09017	+	15.6659i	0.195631	+	0.602091i	0.999969	+	0.00791804i	$0.00252042\pi$
$677$	5.09017	+	15.6659i	0.195631	+	0.602091i	−0.804338	+	0.594173i	$0.797480\pi$
$678$	0.236068	+	0.171513i	0.00906614	+	0.00658693i
$679$	−39.8435	+	28.9480i	−1.52905	+	1.11092i
$680$		0			0
$681$	5.56231			0.213148
$682$	1.63932	−	4.08174i	0.0627728	−	0.156298i
$683$	−0.708204			−0.0270987			−0.0135493	−	0.999908i	$-0.504313\pi$
$683$	−0.708204			−0.0270987			−0.0135493	+	0.999908i	$0.504313\pi$
$684$	3.61803	−	11.1352i	0.138339	−	0.425764i
$685$		0			0
$686$	−7.50000	−	5.44907i	−0.286351	−	0.208046i
$687$	3.09017	+	9.51057i	0.117897	+	0.362851i
$688$	−3.57295	−	10.9964i	−0.136217	−	0.419234i
$689$	−33.2705	−	24.1724i	−1.26751	−	0.920897i
$690$		0			0
$691$	−3.48936	+	10.7391i	−0.132741	+	0.408536i	−0.995232	−	0.0975373i	$-0.968903\pi$
$691$	−3.48936	+	10.7391i	−0.132741	+	0.408536i	0.862490	+	0.506073i	$0.168903\pi$
$692$	5.61803			0.213566
$693$	−7.63525	−	6.37988i	−0.290039	−	0.242352i
$694$	−2.05573			−0.0780344
$695$		0			0
$696$	−2.50000	+	1.81636i	−0.0947623	+	0.0688488i
$697$	−5.04508	−	3.66547i	−0.191096	−	0.138840i
$698$	2.11146	+	6.49839i	0.0799198	+	0.245968i
$699$	2.88197	+	8.86978i	0.109006	+	0.335486i
$700$		0			0
$701$	−7.89919	+	5.73910i	−0.298348	+	0.216763i	−0.726881	−	0.686764i	$-0.759031\pi$
$701$	−7.89919	+	5.73910i	−0.298348	+	0.216763i	0.428533	+	0.903526i	$0.359031\pi$
$702$	0.927051	−	2.85317i	0.0349893	−	0.107686i
$703$	15.5279			0.585644
$704$	0.781153	+	0.0530006i	0.0294408	+	0.00199753i
$705$		0			0
$706$	−5.13525	+	15.8047i	−0.193268	+	0.594817i
$707$	24.4894	−	17.7926i	0.921017	−	0.669158i
$708$	14.2082	+	10.3229i	0.533977	+	0.387957i
$709$	−0.163119	−	0.502029i	−0.00612606	−	0.0188541i	0.947947	−	0.318429i	$-0.103155\pi$
$709$	−0.163119	−	0.502029i	−0.00612606	−	0.0188541i	−0.954073	+	0.299575i	$0.903155\pi$
$710$		0			0
$711$	−10.1631	−	7.38394i	−0.381147	−	0.276919i
$712$	−31.7705	+	23.0826i	−1.19065	+	0.865058i
$713$	3.56888	−	10.9839i	0.133656	−	0.411350i
$714$	2.72949			0.102149
$715$		0			0
$716$	−32.5623			−1.21691
$717$	−3.29180	+	10.1311i	−0.122934	+	0.378353i
$718$	16.6074	−	12.0660i	0.619782	−	0.450298i
$719$	35.5517	+	25.8298i	1.32585	+	0.963289i	0.999839	+	0.0179238i	$0.00570564\pi$
$719$	35.5517	+	25.8298i	1.32585	+	0.963289i	0.326014	+	0.945365i	$0.394294\pi$
$720$		0			0
$721$	−6.65654	−	20.4867i	−0.247903	−	0.762966i
$722$	−16.6803	−	12.1190i	−0.620778	−	0.451022i
$723$	0.927051	−	0.673542i	0.0344774	−	0.0250493i
$724$	−5.89919	+	18.1558i	−0.219242	+	0.674756i
$725$		0			0
$726$	4.90983	+	4.70228i	0.182221	+	0.174518i
$727$	4.23607			0.157107			0.0785535	−	0.996910i	$-0.474970\pi$
$727$	4.23607			0.157107			0.0785535	+	0.996910i	$0.474970\pi$
$728$	−10.0623	+	30.9686i	−0.372934	+	1.14777i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−2.83688	−	8.73102i	−0.104926	−	0.322929i
$732$	−5.11803	−	15.7517i	−0.189168	−	0.582199i
$733$	21.4894	+	15.6129i	0.793728	+	0.576677i	0.909067	−	0.416649i	$-0.136796\pi$
$733$	21.4894	+	15.6129i	0.793728	+	0.576677i	−0.115340	+	0.993326i	$0.536796\pi$
$734$	17.4164	−	12.6538i	0.642851	−	0.467059i
$735$		0			0
$736$	−30.2361			−1.11452
$737$	3.80902	+	15.1437i	0.140307	+	0.557824i
$738$	2.61803			0.0963712
$739$	3.31559	−	10.2044i	0.121966	−	0.375373i	−0.871370	−	0.490626i	$-0.836768\pi$
$739$	3.31559	−	10.2044i	0.121966	−	0.375373i	0.993336	+	0.115253i	$0.0367680\pi$
$740$		0			0
$741$	28.4164	+	20.6457i	1.04390	+	0.758440i
$742$	4.85410	+	14.9394i	0.178200	+	0.548442i
$743$	4.57953	+	14.0943i	0.168007	+	0.517071i	0.999245	−	0.0388447i	$-0.0123678\pi$
$743$	4.57953	+	14.0943i	0.168007	+	0.517071i	−0.831239	+	0.555916i	$0.812368\pi$
$744$	3.88197	+	2.82041i	0.142320	+	0.103401i
$745$		0			0
$746$	1.79837	−	5.53483i	0.0658431	−	0.202644i
$747$	−12.6180			−0.461670
$748$	7.88197	+	0.534785i	0.288193	+	0.0195537i
$749$	−31.2492			−1.14182
$750$		0			0
$751$	6.89919	−	5.01255i	0.251755	−	0.182911i	−0.454749	−	0.890619i	$-0.650271\pi$
$751$	6.89919	−	5.01255i	0.251755	−	0.182911i	0.706504	+	0.707709i	$0.250271\pi$
$752$	17.4271	+	12.6615i	0.635499	+	0.461717i
$753$	0.135255	+	0.416272i	0.00492896	+	0.0151698i
$754$	−1.28115	−	3.94298i	−0.0466568	−	0.143595i
$755$		0			0
$756$	3.92705	−	2.85317i	0.142825	−	0.103769i
$757$	3.07953	−	9.47781i	0.111927	−	0.344477i	−0.879366	−	0.476146i	$-0.842034\pi$
$757$	3.07953	−	9.47781i	0.111927	−	0.344477i	0.991294	+	0.131669i	$0.0420335\pi$
$758$	17.4377			0.633366
$759$	13.6976	+	11.4454i	0.497190	+	0.415443i
$760$		0			0
$761$	−11.0902	+	34.1320i	−0.402018	+	1.23729i	0.521341	+	0.853348i	$0.325432\pi$
$761$	−11.0902	+	34.1320i	−0.402018	+	1.23729i	−0.923359	+	0.383937i	$0.874568\pi$
$762$	−2.19098	+	1.59184i	−0.0793709	+	0.0576664i
$763$	36.4058	+	26.4503i	1.31798	+	0.957566i
$764$	13.3713	+	41.1527i	0.483757	+	1.48885i
$765$		0			0
$766$	−15.2361	−	11.0697i	−0.550502	−	0.399963i
$767$	−42.6246	+	30.9686i	−1.53909	+	1.11821i
$768$	2.02786	−	6.24112i	0.0731742	−	0.225207i
$769$	−30.8541			−1.11263			−0.556314	−	0.830972i	$-0.687785\pi$
$769$	−30.8541			−1.11263			−0.556314	+	0.830972i	$0.687785\pi$
$770$		0			0
$771$	−19.0344			−0.685509
$772$	4.76393	−	14.6619i	0.171458	−	0.527692i
$773$	7.80902	−	5.67358i	0.280871	−	0.204065i	−0.438426	−	0.898767i	$-0.644464\pi$
$773$	7.80902	−	5.67358i	0.280871	−	0.204065i	0.719297	+	0.694703i	$0.244464\pi$
$774$	3.11803	+	2.26538i	0.112075	+	0.0814276i
$775$		0			0
$776$	11.3435	+	34.9116i	0.407206	+	1.25325i
$777$	5.20820	+	3.78398i	0.186843	+	0.135750i
$778$	3.45492	−	2.51014i	0.123865	−	0.0899930i
$779$	−9.47214	+	29.1522i	−0.339374	+	1.04449i
$780$		0			0
$781$	−20.9894	+	13.1760i	−0.751058	+	0.471476i
$782$	−4.89667			−0.175105
$783$	−0.427051	+	1.31433i	−0.0152616	+	0.0469702i
$784$	−3.00000	+	2.17963i	−0.107143	+	0.0778438i
$785$		0			0
$786$	1.59017	+	4.89404i	0.0567195	+	0.174565i
$787$	7.22542	+	22.2376i	0.257559	+	0.792684i	0.993315	+	0.115437i	$0.0368269\pi$
$787$	7.22542	+	22.2376i	0.257559	+	0.792684i	−0.735756	+	0.677247i	$0.763173\pi$
$788$	4.85410	+	3.52671i	0.172920	+	0.125634i
$789$	−23.5623	+	17.1190i	−0.838840	+	0.609453i
$790$		0			0
$791$	−1.41641			−0.0503617
$792$	−6.28115	+	3.94298i	−0.223191	+	0.140108i
$793$	49.6869			1.76443
$794$	−0.107391	+	0.330515i	−0.00381116	+	0.0117295i
$795$		0			0
$796$	−28.4164	−	20.6457i	−1.00719	−	0.731768i
$797$	−10.0106	−	30.8096i	−0.354595	−	1.09133i	−0.956244	−	0.292571i	$-0.905489\pi$
$797$	−10.0106	−	30.8096i	−0.354595	−	1.09133i	0.601649	−	0.798761i	$-0.294511\pi$
$798$	−4.14590	−	12.7598i	−0.146763	−	0.451691i
$799$	13.8369	+	10.0531i	0.489514	+	0.355652i
$800$		0			0
$801$	−5.42705	+	16.7027i	−0.191755	+	0.590162i
$802$	14.3262			0.505877
$803$	−0.180340	+	0.449028i	−0.00636406	+	0.0158459i
$804$	−7.61803			−0.268667
$805$		0			0
$806$	−5.20820	+	3.78398i	−0.183451	+	0.133285i
$807$	−7.66312	−	5.56758i	−0.269755	−	0.195988i
$808$	−6.97214	−	21.4580i	−0.245279	−	0.754891i
$809$	−0.690983	−	2.12663i	−0.0242937	−	0.0747682i	0.938175	−	0.346162i	$-0.112515\pi$
$809$	−0.690983	−	2.12663i	−0.0242937	−	0.0747682i	−0.962468	+	0.271394i	$0.912515\pi$
$810$		0			0
$811$	5.09017	−	3.69822i	0.178740	−	0.129862i	−0.494818	−	0.868997i	$-0.664765\pi$
$811$	5.09017	−	3.69822i	0.178740	−	0.129862i	0.673558	+	0.739134i	$0.264765\pi$
$812$	2.07295	−	6.37988i	0.0727462	−	0.223890i
$813$	−11.2705			−0.395274
$814$	−3.37539	−	2.82041i	−0.118307	−	0.0988554i
$815$		0			0
$816$	−0.843459	+	2.59590i	−0.0295270	+	0.0908747i
$817$	−36.5066	+	26.5236i	−1.27720	+	0.927943i
$818$	−15.0623	−	10.9434i	−0.526641	−	0.382627i
$819$	4.50000	+	13.8496i	0.157243	+	0.483943i
$820$		0			0
$821$	14.0729	+	10.2246i	0.491149	+	0.356841i	0.805626	−	0.592424i	$-0.201829\pi$
$821$	14.0729	+	10.2246i	0.491149	+	0.356841i	−0.314477	+	0.949265i	$0.601829\pi$
$822$	5.89919	−	4.28601i	0.205758	−	0.149492i
$823$	1.69098	−	5.20431i	0.0589440	−	0.181411i	−0.917249	−	0.398314i	$-0.869596\pi$
$823$	1.69098	−	5.20431i	0.0589440	−	0.181411i	0.976193	+	0.216903i	$0.0695955\pi$
$824$	−16.0557			−0.559328
$825$		0			0
$826$	20.1246			0.700225
$827$	11.0836	−	34.1118i	0.385414	−	1.18618i	−0.550765	−	0.834660i	$-0.685664\pi$
$827$	11.0836	−	34.1118i	0.385414	−	1.18618i	0.936179	−	0.351523i	$-0.114336\pi$
$828$	−7.04508	+	5.11855i	−0.244834	+	0.177882i
$829$	7.82624	+	5.68609i	0.271816	+	0.197486i	0.715340	−	0.698776i	$-0.246272\pi$
$829$	7.82624	+	5.68609i	0.271816	+	0.197486i	−0.443524	+	0.896263i	$0.646272\pi$
$830$		0			0
$831$	−7.10081	−	21.8541i	−0.246324	−	0.758109i
$832$	−0.927051	−	0.673542i	−0.0321397	−	0.0233509i
$833$	−2.38197	+	1.73060i	−0.0825302	+	0.0599617i
$834$	0.163119	−	0.502029i	0.00564835	−	0.0173838i
$835$		0			0
$836$	−9.47214	−	37.6587i	−0.327601	−	1.30245i
$837$	2.14590			0.0741731
$838$	0.201626	−	0.620541i	0.00696506	−	0.0214362i
$839$	−0.163119	+	0.118513i	−0.00563149	+	0.00409152i	−0.590597	−	0.806966i	$-0.701108\pi$
$839$	−0.163119	+	0.118513i	−0.00563149	+	0.00409152i	0.584966	+	0.811058i	$0.301108\pi$
$840$		0			0
$841$	−8.37132	−	25.7643i	−0.288666	−	0.888424i
$842$	5.01722	+	15.4414i	0.172905	+	0.532146i
$843$	9.97214	+	7.24518i	0.343459	+	0.249537i
$844$	−12.0172	+	8.73102i	−0.413650	+	0.300534i
$845$		0			0
$846$	−7.18034			−0.246865
$847$	−32.6976	−	4.45752i	−1.12350	−	0.153162i
$848$	−15.7082			−0.539422
$849$	4.91641	−	15.1311i	0.168731	−	0.519300i
$850$		0			0
$851$	−9.34346	−	6.78842i	−0.320290	−	0.232704i
$852$	−3.73607	−	11.4984i	−0.127996	−	0.393930i
$853$	−2.06637	−	6.35964i	−0.0707512	−	0.217750i	0.909428	−	0.415860i	$-0.136519\pi$
$853$	−2.06637	−	6.35964i	−0.0707512	−	0.217750i	−0.980180	+	0.198111i	$0.936519\pi$
$854$	−15.3541	−	11.1554i	−0.525407	−	0.381730i
$855$		0			0
$856$	−7.19756	+	22.1518i	−0.246008	+	0.757133i
$857$	−1.09017			−0.0372395			−0.0186197	−	0.999827i	$-0.505927\pi$
$857$	−1.09017			−0.0372395			−0.0186197	+	0.999827i	$0.505927\pi$
$858$	−2.42705	−	9.64932i	−0.0828582	−	0.329422i
$859$	17.5623			0.599218			0.299609	−	0.954062i	$-0.403144\pi$
$859$	17.5623			0.599218			0.299609	+	0.954062i	$0.403144\pi$
$860$		0			0
$861$	−10.2812	+	7.46969i	−0.350381	+	0.254567i
$862$	−11.4271	−	8.30224i	−0.389207	−	0.282775i
$863$	10.0066	+	30.7971i	0.340628	+	1.04834i	0.963883	+	0.266326i	$0.0858098\pi$
$863$	10.0066	+	30.7971i	0.340628	+	1.04834i	−0.623255	+	0.782019i	$0.714190\pi$
$864$	−1.73607	−	5.34307i	−0.0590622	−	0.181775i
$865$		0			0
$866$	−2.40983	+	1.75084i	−0.0818894	+	0.0594961i
$867$	4.58359	−	14.1068i	0.155667	−	0.479094i
$868$	−10.4164			−0.353556
$869$	−41.5689	−	2.82041i	−1.41013	−	0.0956760i
$870$		0			0
$871$	7.06231	−	21.7355i	0.239297	−	0.736481i
$872$	27.1353	−	19.7149i	0.918916	−	0.667631i
$873$	13.2812	+	9.64932i	0.449499	+	0.326580i
$874$	7.43769	+	22.8909i	0.251584	+	0.774295i
$875$		0			0
$876$	−0.190983	−	0.138757i	−0.00645272	−	0.00468817i
$877$	45.6418	−	33.1607i	1.54122	−	1.11976i	0.591647	−	0.806197i	$-0.298478\pi$
$877$	45.6418	−	33.1607i	1.54122	−	1.11976i	0.949568	−	0.313561i	$-0.101522\pi$
$878$	5.26393	−	16.2007i	0.177649	−	0.546748i
$879$	7.41641			0.250149
$880$		0			0
$881$	−11.8197			−0.398214			−0.199107	−	0.979978i	$-0.563804\pi$
$881$	−11.8197			−0.398214			−0.199107	+	0.979978i	$0.563804\pi$
$882$	0.381966	−	1.17557i	0.0128615	−	0.0395835i
$883$	−35.3435	+	25.6785i	−1.18940	+	0.864151i	−0.993201	−	0.116412i	$-0.962861\pi$
$883$	−35.3435	+	25.6785i	−1.18940	+	0.864151i	−0.196201	+	0.980564i	$0.562861\pi$
$884$	−9.35410	−	6.79615i	−0.314612	−	0.228579i
$885$		0			0
$886$	−2.00658	−	6.17561i	−0.0674123	−	0.207474i
$887$	3.38197	+	2.45714i	0.113555	+	0.0825028i	0.643114	−	0.765771i	$-0.277642\pi$
$887$	3.38197	+	2.45714i	0.113555	+	0.0825028i	−0.529558	+	0.848274i	$0.677642\pi$
$888$	3.88197	−	2.82041i	0.130270	−	0.0946469i
$889$	4.06231	−	12.5025i	0.136245	−	0.419320i
$890$		0			0
$891$	−1.23607	+	3.07768i	−0.0414098	+	0.103106i
$892$	1.14590			0.0383675
$893$	25.9787	−	79.9543i	0.869345	−	2.67557i
$894$	−3.09017	+	2.24514i	−0.103351	+	0.0750887i
$895$		0			0
$896$	10.5517	+	32.4747i	0.352506	+	1.08490i
$897$	−8.07295	−	24.8460i	−0.269548	−	0.829583i
$898$	−2.76393	−	2.00811i	−0.0922336	−	0.0670116i
$899$	2.39919	−	1.74311i	0.0800174	−	0.0581360i
$900$		0			0
$901$	−12.4721			−0.415507
$902$	7.35410	−	4.61653i	0.244865	−	0.153713i
$903$	−18.7082			−0.622570
$904$	−0.326238	+	1.00406i	−0.0108505	+	0.0333944i
$905$		0			0
$906$	6.59017	+	4.78804i	0.218944	+	0.159072i
$907$	0.0516628	+	0.159002i	0.00171543	+	0.00527956i	0.951911	−	0.306376i	$-0.0991165\pi$
$907$	0.0516628	+	0.159002i	0.00171543	+	0.00527956i	−0.950195	+	0.311656i	$0.899116\pi$
$908$	2.78115	+	8.55951i	0.0922958	+	0.284057i
$909$	−8.16312	−	5.93085i	−0.270754	−	0.196714i
$910$		0			0
$911$	7.71478	−	23.7437i	0.255602	−	0.786662i	−0.738108	−	0.674682i	$-0.764281\pi$
$911$	7.71478	−	23.7437i	0.255602	−	0.786662i	0.993710	−	0.111980i	$-0.0357193\pi$
$912$	13.4164			0.444262
$913$	−35.4443	+	22.2501i	−1.17303	+	0.736370i
$914$	−20.0689			−0.663820
$915$		0			0
$916$	−13.0902	+	9.51057i	−0.432511	+	0.314238i
$917$	−20.2082	−	14.6821i	−0.667334	−	0.484846i
$918$	−0.281153	−	0.865300i	−0.00927943	−	0.0285591i
$919$	2.82624	+	8.69827i	0.0932290	+	0.286929i	0.986788	−	0.162016i	$-0.0517997\pi$
$919$	2.82624	+	8.69827i	0.0932290	+	0.286929i	−0.893559	+	0.448946i	$0.851800\pi$
$920$		0			0
$921$	16.0902	−	11.6902i	0.530189	−	0.385205i
$922$	2.51722	−	7.74721i	0.0829003	−	0.255141i
$923$	36.2705			1.19386
$924$	6.00000	−	14.9394i	0.197386	−	0.491470i
$925$		0			0
$926$	4.33688	−	13.3475i	0.142519	−	0.438628i
$927$	−5.80902	+	4.22050i	−0.190793	+	0.138619i
$928$	−6.28115	−	4.56352i	−0.206189	−	0.149805i
$929$	−14.0689	−	43.2996i	−0.461585	−	1.42061i	−0.863227	−	0.504816i	$-0.831560\pi$
$929$	−14.0689	−	43.2996i	−0.461585	−	1.42061i	0.401642	−	0.915797i	$-0.368440\pi$
$930$		0			0
$931$	11.7082	+	8.50651i	0.383721	+	0.278790i
$932$	−12.2082	+	8.86978i	−0.399893	+	0.290539i
$933$	8.48936	−	26.1276i	0.277929	−	0.855378i
$934$	21.0344			0.688268
$935$		0			0
$936$	10.8541			0.354777
$937$	−2.96149	+	9.11454i	−0.0967478	+	0.297759i	−0.987705	−	0.156328i	$-0.950034\pi$
$937$	−2.96149	+	9.11454i	−0.0967478	+	0.297759i	0.890957	+	0.454087i	$0.150034\pi$
$938$	−7.06231	+	5.13107i	−0.230592	+	0.167535i
$939$	−13.9894	−	10.1639i	−0.456525	−	0.331685i
$940$		0			0
$941$	−0.927051	−	2.85317i	−0.0302210	−	0.0930107i	0.934808	−	0.355153i	$-0.115571\pi$
$941$	−0.927051	−	2.85317i	−0.0302210	−	0.0930107i	−0.965029	+	0.262142i	$0.915571\pi$
$942$	3.39919	+	2.46965i	0.110751	+	0.0804657i
$943$	18.4443	−	13.4005i	0.600628	−	0.436382i
$944$	−6.21885	+	19.1396i	−0.202406	+	0.622942i
$945$		0			0
$946$	12.7533	+	0.865300i	0.414645	+	0.0281333i
$947$	−59.5066			−1.93370			−0.966852	−	0.255338i	$-0.917813\pi$
$947$	−59.5066			−1.93370			−0.966852	+	0.255338i	$0.917813\pi$
$948$	6.28115	−	19.3314i	0.204002	−	0.627855i
$949$	0.572949	−	0.416272i	0.0185987	−	0.0135128i
$950$		0			0
$951$	−4.07295	−	12.5352i	−0.132074	−	0.406483i
$952$	3.05166	+	9.39205i	0.0989050	+	0.304398i
$953$	27.2812	+	19.8209i	0.883723	+	0.642063i	0.934234	−	0.356661i	$-0.116085\pi$
$953$	27.2812	+	19.8209i	0.883723	+	0.642063i	−0.0505106	+	0.998724i	$0.516085\pi$
$954$	4.23607	−	3.07768i	0.137148	−	0.0996437i
$955$		0			0
$956$	−17.2361			−0.557454
$957$	1.11803	+	4.44501i	0.0361409	+	0.143687i
$958$	−23.0902			−0.746010
$959$	−10.9377	+	33.6628i	−0.353197	+	1.08703i
$960$		0			0
$961$	21.3541	+	15.5147i	0.688842	+	0.500473i
$962$	1.98936	+	6.12261i	0.0641394	+	0.197401i
$963$	3.21885	+	9.90659i	0.103726	+	0.319235i
$964$	1.50000	+	1.08981i	0.0483117	+	0.0351005i
$965$		0			0
$966$	−3.08359	+	9.49032i	−0.0992130	+	0.305346i
$967$	−46.2148			−1.48617			−0.743084	−	0.669199i	$-0.766638\pi$
$967$	−46.2148			−1.48617			−0.743084	+	0.669199i	$0.766638\pi$
$968$	−10.6910	+	22.1518i	−0.343621	+	0.711986i
$969$	10.6525			0.342207
$970$		0			0
$971$	20.6180	−	14.9799i	0.661664	−	0.480727i	−0.205560	−	0.978644i	$-0.565902\pi$
$971$	20.6180	−	14.9799i	0.661664	−	0.480727i	0.867225	+	0.497917i	$0.165902\pi$
$972$	−1.30902	−	0.951057i	−0.0419867	−	0.0305052i
$973$	0.791796	+	2.43690i	0.0253838	+	0.0781234i
$974$	−6.16312	−	18.9681i	−0.197479	−	0.607778i
$975$		0			0
$976$	15.3541	−	11.1554i	0.491473	−	0.357076i
$977$	0.843459	−	2.59590i	0.0269846	−	0.0830502i	−0.936657	−	0.350247i	$-0.886098\pi$
$977$	0.843459	−	2.59590i	0.0269846	−	0.0830502i	0.963642	+	0.267197i	$0.0860975\pi$
$978$	3.65248			0.116793
$979$	14.2082	+	56.4881i	0.454096	+	1.80537i
$980$		0			0
$981$	4.63525	−	14.2658i	0.147992	−	0.455473i
$982$	3.57295	−	2.59590i	0.114017	−	0.0828385i
$983$	−33.2705	−	24.1724i	−1.06116	−	0.770981i	−0.0868610	−	0.996220i	$-0.527684\pi$
$983$	−33.2705	−	24.1724i	−1.06116	−	0.770981i	−0.974303	+	0.225239i	$0.927684\pi$
$984$	2.92705	+	9.00854i	0.0933110	+	0.287182i
$985$		0			0
$986$	−1.01722	−	0.739054i	−0.0323949	−	0.0235363i
$987$	28.1976	−	20.4867i	0.897538	−	0.652100i
$988$	−17.5623	+	54.0512i	−0.558731	+	1.71960i
$989$	33.5623			1.06722
$990$		0			0
$991$	7.45085			0.236684			0.118342	−	0.992973i	$-0.462242\pi$
$991$	7.45085			0.236684			0.118342	+	0.992973i	$0.462242\pi$
$992$	−3.72542	+	11.4657i	−0.118282	+	0.364036i
$993$	8.42705	−	6.12261i	0.267424	−	0.194295i
$994$	−11.2082	−	8.14324i	−0.355503	−	0.258288i
$995$		0			0
$996$	−6.30902	−	19.4172i	−0.199909	−	0.615256i
$997$	1.04508	+	0.759299i	0.0330982	+	0.0240472i	0.604211	−	0.796824i	$-0.293488\pi$
$997$	1.04508	+	0.759299i	0.0330982	+	0.0240472i	−0.571113	+	0.820871i	$0.693488\pi$
$998$	20.9164	−	15.1967i	0.662097	−	0.481042i
$999$	0.663119	−	2.04087i	0.0209802	−	0.0645703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.e.526.1	yes	4
5.2	odd	4		825.2.bx.a.724.2		8
5.3	odd	4		825.2.bx.a.724.1		8
5.4	even	2		825.2.n.a.526.1	✓	4
11.4	even	5		9075.2.a.y.1.2		2
11.5	even	5	inner	825.2.n.e.676.1	yes	4
11.7	odd	10		9075.2.a.bu.1.1		2
55.4	even	10		9075.2.a.bz.1.1		2
55.27	odd	20		825.2.bx.a.49.1		8
55.29	odd	10		9075.2.a.bb.1.2		2
55.38	odd	20		825.2.bx.a.49.2		8
55.49	even	10		825.2.n.a.676.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.n.a.526.1	✓	4	5.4	even	2
825.2.n.a.676.1	yes	4	55.49	even	10
825.2.n.e.526.1	yes	4	1.1	even	1	trivial
825.2.n.e.676.1	yes	4	11.5	even	5	inner
825.2.bx.a.49.1		8	55.27	odd	20
825.2.bx.a.49.2		8	55.38	odd	20
825.2.bx.a.724.1		8	5.3	odd	4
825.2.bx.a.724.2		8	5.2	odd	4
9075.2.a.y.1.2		2	11.4	even	5
9075.2.a.bb.1.2		2	55.29	odd	10
9075.2.a.bu.1.1		2	11.7	odd	10
9075.2.a.bz.1.1		2	55.4	even	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.190983 - 0.587785i) q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.190983 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.190983 - 0.587785i) q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 3.21644i) q^{11} +1.61803 q^{12} +(-1.50000 + 4.61653i) q^{13} +(1.50000 - 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(0.454915 + 1.40008i) q^{17} +(-0.500000 - 0.363271i) q^{18} +(5.85410 - 4.25325i) q^{19} +3.00000 q^{21} +(-2.04508 - 0.138757i) q^{22} -5.38197 q^{23} +(0.690983 - 2.12663i) q^{24} +(2.42705 + 1.76336i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.50000 + 4.61653i) q^{28} +(-1.11803 - 0.812299i) q^{29} +(-0.663119 + 2.04087i) q^{31} +5.61803 q^{32} +(-2.54508 - 2.12663i) q^{33} +0.909830 q^{34} +(1.30902 - 0.951057i) q^{36} +(1.73607 + 1.26133i) q^{37} +(-1.38197 - 4.25325i) q^{38} +(1.50000 + 4.61653i) q^{39} +(-3.42705 + 2.48990i) q^{41} +(0.572949 - 1.76336i) q^{42} -6.23607 q^{43} +(2.00000 - 4.97980i) q^{44} +(-1.02786 + 3.16344i) q^{46} +(9.39919 - 6.82891i) q^{47} +(1.50000 + 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(1.19098 + 0.865300i) q^{51} +(-6.35410 + 4.61653i) q^{52} +(-2.61803 + 8.05748i) q^{53} -0.618034 q^{54} +6.70820 q^{56} +(2.23607 - 6.88191i) q^{57} +(-0.690983 + 0.502029i) q^{58} +(8.78115 + 6.37988i) q^{59} +(-3.16312 - 9.73508i) q^{61} +(1.07295 + 0.779543i) q^{62} +(2.42705 - 1.76336i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +(-1.73607 + 1.08981i) q^{66} -4.70820 q^{67} +(-0.736068 + 2.26538i) q^{68} +(-4.35410 + 3.16344i) q^{69} +(-2.30902 - 7.10642i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(-0.118034 - 0.0857567i) q^{73} +(1.07295 - 0.779543i) q^{74} +11.7082 q^{76} +(3.70820 - 9.23305i) q^{77} +3.00000 q^{78} +(3.88197 - 11.9475i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.809017 + 2.48990i) q^{82} +(-3.89919 - 12.0005i) q^{83} +(3.92705 + 2.85317i) q^{84} +(-1.19098 + 3.66547i) q^{86} -1.38197 q^{87} +(-5.69098 - 4.75528i) q^{88} -17.5623 q^{89} +(-11.7812 + 8.55951i) q^{91} +(-7.04508 - 5.11855i) q^{92} +(0.663119 + 2.04087i) q^{93} +(-2.21885 - 6.82891i) q^{94} +(4.54508 - 3.30220i) q^{96} +(-5.07295 + 15.6129i) q^{97} +1.23607 q^{98} +(-3.30902 - 0.224514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - q^{11} + 2 q^{12} - 6 q^{13} + 6 q^{14} + 9 q^{16} + 13 q^{17} - 2 q^{18} + 10 q^{19} + 12 q^{21} + 3 q^{22} - 26 q^{23} + 5 q^{24} + 3 q^{26} + q^{27} + 6 q^{28} + 13 q^{31} + 18 q^{32} + q^{33} + 26 q^{34} + 3 q^{36} - 2 q^{37} - 10 q^{38} + 6 q^{39} - 7 q^{41} + 9 q^{42} - 16 q^{43} + 8 q^{44} - 22 q^{46} + 13 q^{47} + 6 q^{48} - 2 q^{49} + 7 q^{51} - 12 q^{52} - 6 q^{53} + 2 q^{54} - 5 q^{58} + 15 q^{59} + 3 q^{61} + 11 q^{62} + 3 q^{63} - 7 q^{64} + 2 q^{66} + 8 q^{67} + 6 q^{68} - 4 q^{69} - 7 q^{71} - 5 q^{72} + 4 q^{73} + 11 q^{74} + 20 q^{76} - 12 q^{77} + 12 q^{78} + 20 q^{79} - q^{81} + q^{82} + 9 q^{83} + 9 q^{84} - 7 q^{86} - 10 q^{87} - 25 q^{88} - 30 q^{89} - 27 q^{91} - 17 q^{92} - 13 q^{93} - 29 q^{94} + 7 q^{96} - 27 q^{97} - 4 q^{98} - 11 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - q^11 + 2 * q^12 - 6 * q^13 + 6 * q^14 + 9 * q^16 + 13 * q^17 - 2 * q^18 + 10 * q^19 + 12 * q^21 + 3 * q^22 - 26 * q^23 + 5 * q^24 + 3 * q^26 + q^27 + 6 * q^28 + 13 * q^31 + 18 * q^32 + q^33 + 26 * q^34 + 3 * q^36 - 2 * q^37 - 10 * q^38 + 6 * q^39 - 7 * q^41 + 9 * q^42 - 16 * q^43 + 8 * q^44 - 22 * q^46 + 13 * q^47 + 6 * q^48 - 2 * q^49 + 7 * q^51 - 12 * q^52 - 6 * q^53 + 2 * q^54 - 5 * q^58 + 15 * q^59 + 3 * q^61 + 11 * q^62 + 3 * q^63 - 7 * q^64 + 2 * q^66 + 8 * q^67 + 6 * q^68 - 4 * q^69 - 7 * q^71 - 5 * q^72 + 4 * q^73 + 11 * q^74 + 20 * q^76 - 12 * q^77 + 12 * q^78 + 20 * q^79 - q^81 + q^82 + 9 * q^83 + 9 * q^84 - 7 * q^86 - 10 * q^87 - 25 * q^88 - 30 * q^89 - 27 * q^91 - 17 * q^92 - 13 * q^93 - 29 * q^94 + 7 * q^96 - 27 * q^97 - 4 * q^98 - 11 * q^99

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