LMFDB - Embedded newform 825.2.o.b.631.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(421,825)]

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, 6, 8]))

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

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

chi := DirichletCharacter("825.421");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.o (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			631.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	825.631
Dual form			825.2.o.b.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{4} +(1.80902 + 1.31433i) q^{5} -0.618034 q^{6} +(-0.927051 - 2.85317i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.190983 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{4} +(1.80902 + 1.31433i) q^{5} -0.618034 q^{6} +(-0.927051 - 2.85317i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(1.11803 - 0.812299i) q^{10} +(0.309017 - 3.30220i) q^{11} +(0.500000 - 1.53884i) q^{12} +(1.00000 - 0.726543i) q^{13} -1.85410 q^{14} +(0.690983 - 2.12663i) q^{15} +(0.572949 + 1.76336i) q^{16} -5.23607 q^{17} +(0.190983 + 0.587785i) q^{18} +(2.92705 - 2.12663i) q^{19} +(1.11803 + 3.44095i) q^{20} +(-2.42705 + 1.76336i) q^{21} +(-1.88197 - 0.812299i) q^{22} +(-1.50000 - 4.61653i) q^{23} +(-1.80902 - 1.31433i) q^{24} +(1.54508 + 4.75528i) q^{25} +(-0.236068 - 0.726543i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.50000 - 4.61653i) q^{28} +(8.35410 + 6.06961i) q^{29} +(-1.11803 - 0.812299i) q^{30} +(-1.78115 - 5.48183i) q^{31} +5.61803 q^{32} +(-3.23607 + 0.726543i) q^{33} +(-1.00000 + 3.07768i) q^{34} +(2.07295 - 6.37988i) q^{35} -1.61803 q^{36} -2.14590 q^{37} +(-0.690983 - 2.12663i) q^{38} +(-1.00000 - 0.726543i) q^{39} +5.00000 q^{40} +(8.97214 + 6.51864i) q^{41} +(0.572949 + 1.76336i) q^{42} +6.00000 q^{43} +(3.54508 - 4.02874i) q^{44} -2.23607 q^{45} -3.00000 q^{46} +(-0.336881 - 1.03681i) q^{47} +(1.50000 - 1.08981i) q^{48} +(-1.61803 + 1.17557i) q^{49} +3.09017 q^{50} +(1.61803 + 4.97980i) q^{51} +2.00000 q^{52} -11.2361 q^{53} +(0.500000 - 0.363271i) q^{54} +(4.89919 - 5.56758i) q^{55} +(-5.42705 - 3.94298i) q^{56} +(-2.92705 - 2.12663i) q^{57} +(5.16312 - 3.75123i) q^{58} -14.4721 q^{59} +(2.92705 - 2.12663i) q^{60} +(3.80902 + 2.76741i) q^{61} -3.56231 q^{62} +(2.42705 + 1.76336i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +2.76393 q^{65} +(-0.190983 + 2.04087i) q^{66} +(2.42705 + 1.76336i) q^{67} +(-6.85410 - 4.97980i) q^{68} +(-3.92705 + 2.85317i) q^{69} +(-3.35410 - 2.43690i) q^{70} +(-3.59017 + 11.0494i) q^{71} +(-0.690983 + 2.12663i) q^{72} +(9.35410 - 6.79615i) q^{73} +(-0.409830 + 1.26133i) q^{74} +(4.04508 - 2.93893i) q^{75} +5.85410 q^{76} +(-9.70820 + 2.17963i) q^{77} +(-0.618034 + 0.449028i) q^{78} -5.00000 q^{79} +(-1.28115 + 3.94298i) q^{80} +(0.309017 - 0.951057i) q^{81} +(5.54508 - 4.02874i) q^{82} -7.61803 q^{83} -4.85410 q^{84} +(-9.47214 - 6.88191i) q^{85} +(1.14590 - 3.52671i) q^{86} +(3.19098 - 9.82084i) q^{87} +(-3.78115 - 6.37988i) q^{88} +(0.690983 + 2.12663i) q^{89} +(-0.427051 + 1.31433i) q^{90} +(-3.00000 - 2.17963i) q^{91} +(2.42705 - 7.46969i) q^{92} +(-4.66312 + 3.38795i) q^{93} -0.673762 q^{94} +8.09017 q^{95} +(-1.73607 - 5.34307i) q^{96} +11.4721 q^{97} +(0.381966 + 1.17557i) q^{98} +(1.69098 + 2.85317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{14} + 5 q^{15} + 9 q^{16} - 12 q^{17} + 3 q^{18} + 5 q^{19} - 3 q^{21} - 12 q^{22} - 6 q^{23} - 5 q^{24} - 5 q^{25} + 8 q^{26} + q^{27} + 6 q^{28} + 20 q^{29} + 13 q^{31} + 18 q^{32} - 4 q^{33} - 4 q^{34} + 15 q^{35} - 2 q^{36} - 22 q^{37} - 5 q^{38} - 4 q^{39} + 20 q^{40} + 18 q^{41} + 9 q^{42} + 24 q^{43} + 3 q^{44} - 12 q^{46} - 17 q^{47} + 6 q^{48} - 2 q^{49} - 10 q^{50} + 2 q^{51} + 8 q^{52} - 36 q^{53} + 2 q^{54} - 5 q^{55} - 15 q^{56} - 5 q^{57} + 5 q^{58} - 40 q^{59} + 5 q^{60} + 13 q^{61} + 26 q^{62} + 3 q^{63} - 7 q^{64} + 20 q^{65} - 3 q^{66} + 3 q^{67} - 14 q^{68} - 9 q^{69} + 8 q^{71} - 5 q^{72} + 24 q^{73} - 24 q^{74} + 5 q^{75} + 10 q^{76} - 12 q^{77} + 2 q^{78} - 20 q^{79} + 15 q^{80} - q^{81} + 11 q^{82} - 26 q^{83} - 6 q^{84} - 20 q^{85} + 18 q^{86} + 15 q^{87} + 5 q^{88} + 5 q^{89} + 5 q^{90} - 12 q^{91} + 3 q^{92} - 3 q^{93} - 34 q^{94} + 10 q^{95} + 2 q^{96} + 28 q^{97} + 6 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - q^11 + 2 * q^12 + 4 * q^13 + 6 * q^14 + 5 * q^15 + 9 * q^16 - 12 * q^17 + 3 * q^18 + 5 * q^19 - 3 * q^21 - 12 * q^22 - 6 * q^23 - 5 * q^24 - 5 * q^25 + 8 * q^26 + q^27 + 6 * q^28 + 20 * q^29 + 13 * q^31 + 18 * q^32 - 4 * q^33 - 4 * q^34 + 15 * q^35 - 2 * q^36 - 22 * q^37 - 5 * q^38 - 4 * q^39 + 20 * q^40 + 18 * q^41 + 9 * q^42 + 24 * q^43 + 3 * q^44 - 12 * q^46 - 17 * q^47 + 6 * q^48 - 2 * q^49 - 10 * q^50 + 2 * q^51 + 8 * q^52 - 36 * q^53 + 2 * q^54 - 5 * q^55 - 15 * q^56 - 5 * q^57 + 5 * q^58 - 40 * q^59 + 5 * q^60 + 13 * q^61 + 26 * q^62 + 3 * q^63 - 7 * q^64 + 20 * q^65 - 3 * q^66 + 3 * q^67 - 14 * q^68 - 9 * q^69 + 8 * q^71 - 5 * q^72 + 24 * q^73 - 24 * q^74 + 5 * q^75 + 10 * q^76 - 12 * q^77 + 2 * q^78 - 20 * q^79 + 15 * q^80 - q^81 + 11 * q^82 - 26 * q^83 - 6 * q^84 - 20 * q^85 + 18 * q^86 + 15 * q^87 + 5 * q^88 + 5 * q^89 + 5 * q^90 - 12 * q^91 + 3 * q^92 - 3 * q^93 - 34 * q^94 + 10 * q^95 + 2 * q^96 + 28 * q^97 + 6 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.190983	−	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	$0.0298810\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$	1.80902	+	1.31433i	0.809017	+	0.587785i
$5$	1.80902	+	1.31433i	0.809017	+	0.587785i
$6$	−0.618034			−0.252311
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	−0.958633	−	0.284644i	$-0.908125\pi$
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	0.608241	−	0.793752i	$-0.291875\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.11803	−	0.812299i	0.353553	−	0.256872i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$	0.500000	−	1.53884i	0.144338	−	0.444225i
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	−0.440411	−	0.897796i	$-0.645167\pi$
$13$	1.00000	−	0.726543i	0.277350	−	0.201507i	0.717761	+	0.696290i	$0.245167\pi$
$14$	−1.85410			−0.495530
$15$	0.690983	−	2.12663i	0.178411	−	0.549093i
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	−5.23607			−1.26993			−0.634967	−	0.772540i	$-0.718986\pi$
$17$	−5.23607			−1.26993			−0.634967	+	0.772540i	$0.718986\pi$
$18$	0.190983	+	0.587785i	0.0450151	+	0.138542i
$19$	2.92705	−	2.12663i	0.671512	−	0.487882i	−0.199019	−	0.979996i	$-0.563776\pi$
$19$	2.92705	−	2.12663i	0.671512	−	0.487882i	0.870531	+	0.492114i	$0.163776\pi$
$20$	1.11803	+	3.44095i	0.250000	+	0.769421i
$21$	−2.42705	+	1.76336i	−0.529626	+	0.384796i
$22$	−1.88197	−	0.812299i	−0.401237	−	0.173183i
$23$	−1.50000	−	4.61653i	−0.312772	−	0.962612i	−0.976662	−	0.214782i	$-0.931096\pi$
$23$	−1.50000	−	4.61653i	−0.312772	−	0.962612i	0.663890	−	0.747830i	$-0.268904\pi$
$24$	−1.80902	−	1.31433i	−0.369264	−	0.268286i
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$	−0.236068	−	0.726543i	−0.0462967	−	0.142487i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	1.50000	−	4.61653i	0.283473	−	0.872441i
$29$	8.35410	+	6.06961i	1.55132	+	1.12710i	0.942703	+	0.333632i	$0.108274\pi$
$29$	8.35410	+	6.06961i	1.55132	+	1.12710i	0.608614	+	0.793466i	$0.291726\pi$
$30$	−1.11803	−	0.812299i	−0.204124	−	0.148305i
$31$	−1.78115	−	5.48183i	−0.319905	−	0.984565i	−0.973688	−	0.227884i	$-0.926819\pi$
$31$	−1.78115	−	5.48183i	−0.319905	−	0.984565i	0.653784	−	0.756681i	$-0.273181\pi$
$32$	5.61803			0.993137
$33$	−3.23607	+	0.726543i	−0.563327	+	0.126475i
$34$	−1.00000	+	3.07768i	−0.171499	+	0.527818i
$35$	2.07295	−	6.37988i	0.350392	−	1.07840i
$36$	−1.61803			−0.269672
$37$	−2.14590			−0.352783			−0.176392	−	0.984320i	$-0.556443\pi$
$37$	−2.14590			−0.352783			−0.176392	+	0.984320i	$0.556443\pi$
$38$	−0.690983	−	2.12663i	−0.112092	−	0.344984i
$39$	−1.00000	−	0.726543i	−0.160128	−	0.116340i
$40$	5.00000			0.790569
$41$	8.97214	+	6.51864i	1.40121	+	1.01804i	0.994528	+	0.104472i	$0.0333151\pi$
$41$	8.97214	+	6.51864i	1.40121	+	1.01804i	0.406684	+	0.913569i	$0.366685\pi$
$42$	0.572949	+	1.76336i	0.0884080	+	0.272092i
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$	3.54508	−	4.02874i	0.534442	−	0.607355i
$45$	−2.23607			−0.333333
$46$	−3.00000			−0.442326
$47$	−0.336881	−	1.03681i	−0.0491391	−	0.151235i	0.923476	−	0.383656i	$-0.125335\pi$
$47$	−0.336881	−	1.03681i	−0.0491391	−	0.151235i	−0.972615	+	0.232421i	$0.925335\pi$
$48$	1.50000	−	1.08981i	0.216506	−	0.157301i
$49$	−1.61803	+	1.17557i	−0.231148	+	0.167939i
$50$	3.09017			0.437016
$51$	1.61803	+	4.97980i	0.226570	+	0.697311i
$52$	2.00000			0.277350
$53$	−11.2361			−1.54339			−0.771696	−	0.635991i	$-0.780591\pi$
$53$	−11.2361			−1.54339			−0.771696	+	0.635991i	$0.780591\pi$
$54$	0.500000	−	0.363271i	0.0680414	−	0.0494350i
$55$	4.89919	−	5.56758i	0.660606	−	0.750733i
$56$	−5.42705	−	3.94298i	−0.725220	−	0.526903i
$57$	−2.92705	−	2.12663i	−0.387697	−	0.281679i
$58$	5.16312	−	3.75123i	0.677951	−	0.492560i
$59$	−14.4721			−1.88411			−0.942056	−	0.335456i	$-0.891110\pi$
$59$	−14.4721			−1.88411			−0.942056	+	0.335456i	$0.891110\pi$
$60$	2.92705	−	2.12663i	0.377881	−	0.274546i
$61$	3.80902	+	2.76741i	0.487695	+	0.354331i	0.804297	−	0.594227i	$-0.202542\pi$
$61$	3.80902	+	2.76741i	0.487695	+	0.354331i	−0.316602	+	0.948558i	$0.602542\pi$
$62$	−3.56231			−0.452413
$63$	2.42705	+	1.76336i	0.305780	+	0.222162i
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$	2.76393			0.342824
$66$	−0.190983	+	2.04087i	−0.0235084	+	0.251214i
$67$	2.42705	+	1.76336i	0.296511	+	0.215428i	0.726087	−	0.687603i	$-0.241337\pi$
$67$	2.42705	+	1.76336i	0.296511	+	0.215428i	−0.429576	+	0.903031i	$0.641337\pi$
$68$	−6.85410	−	4.97980i	−0.831182	−	0.603889i
$69$	−3.92705	+	2.85317i	−0.472761	+	0.343481i
$70$	−3.35410	−	2.43690i	−0.400892	−	0.291265i
$71$	−3.59017	+	11.0494i	−0.426075	+	1.31132i	0.475887	+	0.879507i	$0.342127\pi$
$71$	−3.59017	+	11.0494i	−0.426075	+	1.31132i	−0.901961	+	0.431817i	$0.857873\pi$
$72$	−0.690983	+	2.12663i	−0.0814331	+	0.250625i
$73$	9.35410	−	6.79615i	1.09481	−	0.795430i	0.114609	−	0.993411i	$-0.463438\pi$
$73$	9.35410	−	6.79615i	1.09481	−	0.795430i	0.980206	+	0.197981i	$0.0634385\pi$
$74$	−0.409830	+	1.26133i	−0.0476418	+	0.146626i
$75$	4.04508	−	2.93893i	0.467086	−	0.339358i
$76$	5.85410			0.671512
$77$	−9.70820	+	2.17963i	−1.10635	+	0.248392i
$78$	−0.618034	+	0.449028i	−0.0699786	+	0.0508424i
$79$	−5.00000			−0.562544			−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000			−0.562544			−0.281272	+	0.959628i	$0.590756\pi$
$80$	−1.28115	+	3.94298i	−0.143237	+	0.440839i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	5.54508	−	4.02874i	0.612352	−	0.444900i
$83$	−7.61803			−0.836188			−0.418094	−	0.908404i	$-0.637302\pi$
$83$	−7.61803			−0.836188			−0.418094	+	0.908404i	$0.637302\pi$
$84$	−4.85410			−0.529626
$85$	−9.47214	−	6.88191i	−1.02740	−	0.746448i
$86$	1.14590	−	3.52671i	0.123565	−	0.380295i
$87$	3.19098	−	9.82084i	0.342109	−	1.05290i
$88$	−3.78115	−	6.37988i	−0.403072	−	0.680098i
$89$	0.690983	+	2.12663i	0.0732441	+	0.225422i	0.980976	−	0.194128i	$-0.0621878\pi$
$89$	0.690983	+	2.12663i	0.0732441	+	0.225422i	−0.907732	+	0.419550i	$0.862188\pi$
$90$	−0.427051	+	1.31433i	−0.0450151	+	0.138542i
$91$	−3.00000	−	2.17963i	−0.314485	−	0.228487i
$92$	2.42705	−	7.46969i	0.253038	−	0.778770i
$93$	−4.66312	+	3.38795i	−0.483543	+	0.351314i
$94$	−0.673762			−0.0694933
$95$	8.09017			0.830034
$96$	−1.73607	−	5.34307i	−0.177187	−	0.545325i
$97$	11.4721			1.16482			0.582409	−	0.812896i	$-0.302110\pi$
$97$	11.4721			1.16482			0.582409	+	0.812896i	$0.302110\pi$
$98$	0.381966	+	1.17557i	0.0385844	+	0.118751i
$99$	1.69098	+	2.85317i	0.169950	+	0.286754i
$100$	−2.50000	+	7.69421i	−0.250000	+	0.769421i
$101$	−9.28115	−	6.74315i	−0.923509	−	0.670969i	0.0208858	−	0.999782i	$-0.493351\pi$
$101$	−9.28115	−	6.74315i	−0.923509	−	0.670969i	−0.944395	+	0.328813i	$0.893351\pi$
$102$	3.23607			0.320418
$103$	5.04508	+	3.66547i	0.497107	+	0.361169i	0.807911	−	0.589305i	$-0.200598\pi$
$103$	5.04508	+	3.66547i	0.497107	+	0.361169i	−0.310804	+	0.950474i	$0.600598\pi$
$104$	0.854102	−	2.62866i	0.0837516	−	0.257761i
$105$	−6.70820			−0.654654
$106$	−2.14590	+	6.60440i	−0.208428	+	0.641476i
$107$	−2.40983	+	7.41669i	−0.232967	+	0.716999i	0.764418	+	0.644722i	$0.223027\pi$
$107$	−2.40983	+	7.41669i	−0.232967	+	0.716999i	−0.997385	+	0.0722774i	$0.976973\pi$
$108$	0.500000	+	1.53884i	0.0481125	+	0.148075i
$109$	−0.527864	+	1.62460i	−0.0505602	+	0.155608i	−0.973149	−	0.230177i	$-0.926069\pi$
$109$	−0.527864	+	1.62460i	−0.0505602	+	0.155608i	0.922589	+	0.385785i	$0.126069\pi$
$110$	−2.33688	−	3.94298i	−0.222813	−	0.375949i
$111$	0.663119	+	2.04087i	0.0629405	+	0.193711i
$112$	4.50000	−	3.26944i	0.425210	−	0.308933i
$113$	−9.85410	−	7.15942i	−0.926996	−	0.673502i	0.0182595	−	0.999833i	$-0.494187\pi$
$113$	−9.85410	−	7.15942i	−0.926996	−	0.673502i	−0.945255	+	0.326331i	$0.894187\pi$
$114$	−1.80902	+	1.31433i	−0.169430	+	0.123098i
$115$	3.35410	−	10.3229i	0.312772	−	0.962612i
$116$	5.16312	+	15.8904i	0.479384	+	1.47539i
$117$	−0.381966	+	1.17557i	−0.0353128	+	0.108682i
$118$	−2.76393	+	8.50651i	−0.254441	+	0.783088i
$119$	4.85410	+	14.9394i	0.444975	+	1.36949i
$120$	−1.54508	−	4.75528i	−0.141046	−	0.434096i
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	2.35410	−	1.71036i	0.213130	−	0.154848i
$123$	3.42705	−	10.5474i	0.309007	−	0.951025i
$124$	2.88197	−	8.86978i	0.258808	−	0.796530i
$125$	−3.45492	+	10.6331i	−0.309017	+	0.951057i
$126$	1.50000	−	1.08981i	0.133631	−	0.0970883i
$127$	13.2812	+	9.64932i	1.17851	+	0.856239i	0.992003	−	0.126214i	$-0.0402827\pi$
$127$	13.2812	+	9.64932i	1.17851	+	0.856239i	0.186509	+	0.982453i	$0.440283\pi$
$128$	9.20820	+	6.69015i	0.813898	+	0.591331i
$129$	−1.85410	−	5.70634i	−0.163245	−	0.502415i
$130$	0.527864	−	1.62460i	0.0462967	−	0.142487i
$131$	−12.8992	−	9.37181i	−1.12701	−	0.818819i	−0.141751	−	0.989902i	$-0.545273\pi$
$131$	−12.8992	−	9.37181i	−1.12701	−	0.818819i	−0.985256	+	0.171084i	$0.945273\pi$
$132$	−4.92705	−	2.12663i	−0.428845	−	0.185099i
$133$	−8.78115	−	6.37988i	−0.761423	−	0.553206i
$134$	1.50000	−	1.08981i	0.129580	−	0.0941456i
$135$	0.690983	+	2.12663i	0.0594703	+	0.183031i
$136$	−9.47214	+	6.88191i	−0.812229	+	0.590119i
$137$	4.33688	+	13.3475i	0.370525	+	1.14036i	0.946449	+	0.322855i	$0.104642\pi$
$137$	4.33688	+	13.3475i	0.370525	+	1.14036i	−0.575924	+	0.817503i	$0.695358\pi$
$138$	0.927051	+	2.85317i	0.0789158	+	0.242878i
$139$	−3.19098	+	2.31838i	−0.270656	+	0.196643i	−0.714831	−	0.699297i	$-0.753497\pi$
$139$	−3.19098	+	2.31838i	−0.270656	+	0.196643i	0.444176	+	0.895940i	$0.353497\pi$
$140$	8.78115	−	6.37988i	0.742143	−	0.539198i
$141$	−0.881966	+	0.640786i	−0.0742749	+	0.0539639i
$142$	5.80902	+	4.22050i	0.487482	+	0.354176i
$143$	−2.09017	−	3.52671i	−0.174789	−	0.294918i
$144$	−1.50000	−	1.08981i	−0.125000	−	0.0908178i
$145$	7.13525	+	21.9601i	0.592551	+	1.82368i
$146$	−2.20820	−	6.79615i	−0.182752	−	0.562454i
$147$	1.61803	+	1.17557i	0.133453	+	0.0969594i
$148$	−2.80902	−	2.04087i	−0.230900	−	0.167759i
$149$	5.16312	−	3.75123i	0.422979	−	0.307312i	−0.355856	−	0.934541i	$-0.615811\pi$
$149$	5.16312	−	3.75123i	0.422979	−	0.307312i	0.778835	+	0.627228i	$0.215811\pi$
$150$	−0.954915	−	2.93893i	−0.0779685	−	0.239962i
$151$	1.20820	−	3.71847i	0.0983222	−	0.302605i	−0.889783	−	0.456384i	$-0.849144\pi$
$151$	1.20820	−	3.71847i	0.0983222	−	0.302605i	0.988105	+	0.153779i	$0.0491444\pi$
$152$	2.50000	−	7.69421i	0.202777	−	0.624083i
$153$	4.23607	−	3.07768i	0.342466	−	0.248816i
$154$	−0.572949	+	6.12261i	−0.0461695	+	0.493374i
$155$	3.98278	−	12.2577i	0.319905	−	0.984565i
$156$	−0.618034	−	1.90211i	−0.0494823	−	0.152291i
$157$	−1.71885	+	5.29007i	−0.137179	+	0.422193i	−0.995923	−	0.0902121i	$-0.971245\pi$
$157$	−1.71885	+	5.29007i	−0.137179	+	0.422193i	0.858744	+	0.512405i	$0.171245\pi$
$158$	−0.954915	+	2.93893i	−0.0759690	+	0.233808i
$159$	3.47214	+	10.6861i	0.275358	+	0.847466i
$160$	10.1631	+	7.38394i	0.803465	+	0.583752i
$161$	−11.7812	+	8.55951i	−0.928485	+	0.674584i
$162$	−0.500000	−	0.363271i	−0.0392837	−	0.0285413i
$163$	−10.9721	+	7.97172i	−0.859404	+	0.624394i	−0.927723	−	0.373270i	$-0.878237\pi$
$163$	−10.9721	+	7.97172i	−0.859404	+	0.624394i	0.0683187	+	0.997664i	$0.478237\pi$
$164$	5.54508	+	17.0660i	0.432998	+	1.33263i
$165$	−6.80902	−	2.93893i	−0.530081	−	0.228795i
$166$	−1.45492	+	4.47777i	−0.112923	+	0.347542i
$167$	6.89919	+	21.2335i	0.533875	+	1.64310i	0.746067	+	0.665871i	$0.231940\pi$
$167$	6.89919	+	21.2335i	0.533875	+	1.64310i	−0.212192	+	0.977228i	$0.568060\pi$
$168$	−2.07295	+	6.37988i	−0.159931	+	0.492219i
$169$	−3.54508	+	10.9106i	−0.272699	+	0.839281i
$170$	−5.85410	+	4.25325i	−0.448989	+	0.326210i
$171$	−1.11803	+	3.44095i	−0.0854982	+	0.263136i
$172$	7.85410	+	5.70634i	0.598870	+	0.435104i
$173$	5.47214			0.416039			0.208019	−	0.978125i	$-0.433298\pi$
$173$	5.47214			0.416039			0.208019	+	0.978125i	$0.433298\pi$
$174$	−5.16312	−	3.75123i	−0.391415	−	0.284380i
$175$	12.1353	−	8.81678i	0.917339	−	0.666486i
$176$	6.00000	−	1.34708i	0.452267	−	0.101540i
$177$	4.47214	+	13.7638i	0.336146	+	1.03455i
$178$	1.38197			0.103583
$179$	6.80902	+	20.9560i	0.508930	+	1.56632i	0.794062	+	0.607837i	$0.207962\pi$
$179$	6.80902	+	20.9560i	0.508930	+	1.56632i	−0.285132	+	0.958488i	$0.592038\pi$
$180$	−2.92705	−	2.12663i	−0.218169	−	0.158509i
$181$	12.5279			0.931189			0.465594	−	0.884998i	$-0.345841\pi$
$181$	12.5279			0.931189			0.465594	+	0.884998i	$0.345841\pi$
$182$	−1.85410	+	1.34708i	−0.137435	+	0.0998525i
$183$	1.45492	−	4.47777i	0.107550	−	0.331006i
$184$	−8.78115	−	6.37988i	−0.647355	−	0.470331i
$185$	−3.88197	−	2.82041i	−0.285408	−	0.207361i
$186$	1.10081	+	3.38795i	0.0807155	+	0.248417i
$187$	−1.61803	+	17.2905i	−0.118322	+	1.26441i
$188$	0.545085	−	1.67760i	0.0397544	−	0.122351i
$189$	0.927051	−	2.85317i	0.0674330	−	0.207538i
$190$	1.54508	−	4.75528i	0.112092	−	0.344984i
$191$	0.618034			0.0447194			0.0223597	−	0.999750i	$-0.492882\pi$
$191$	0.618034			0.0447194			0.0223597	+	0.999750i	$0.492882\pi$
$192$	0.236068			0.0170367
$193$	−7.61803	+	5.53483i	−0.548358	+	0.398405i	−0.827180	−	0.561937i	$-0.810056\pi$
$193$	−7.61803	+	5.53483i	−0.548358	+	0.398405i	0.278822	+	0.960343i	$0.410056\pi$
$194$	2.19098	−	6.74315i	0.157303	−	0.484130i
$195$	−0.854102	−	2.62866i	−0.0611635	−	0.188242i
$196$	−3.23607			−0.231148
$197$	−7.89919	+	5.73910i	−0.562794	+	0.408894i	−0.832480	−	0.554055i	$-0.813080\pi$
$197$	−7.89919	+	5.73910i	−0.562794	+	0.408894i	0.269687	+	0.962948i	$0.413080\pi$
$198$	2.00000	−	0.449028i	0.142134	−	0.0319110i
$199$	14.7984			1.04903			0.524514	−	0.851402i	$-0.324247\pi$
$199$	14.7984			1.04903			0.524514	+	0.851402i	$0.324247\pi$
$200$	9.04508	+	6.57164i	0.639584	+	0.464685i
$201$	0.927051	−	2.85317i	0.0653891	−	0.201247i
$202$	−5.73607	+	4.16750i	−0.403588	+	0.293224i
$203$	9.57295	−	29.4625i	0.671889	−	2.06786i
$204$	−2.61803	+	8.05748i	−0.183299	+	0.564136i
$205$	7.66312	+	23.5847i	0.535215	+	1.64722i
$206$	3.11803	−	2.26538i	0.217244	−	0.157837i
$207$	3.92705	+	2.85317i	0.272949	+	0.198309i
$208$	1.85410	+	1.34708i	0.128559	+	0.0934035i
$209$	−6.11803	−	10.3229i	−0.423193	−	0.714047i
$210$	−1.28115	+	3.94298i	−0.0884080	+	0.272092i
$211$	7.69098	−	23.6704i	0.529469	−	1.62954i	−0.225836	−	0.974165i	$-0.572511\pi$
$211$	7.69098	−	23.6704i	0.529469	−	1.62954i	0.755305	−	0.655373i	$-0.227489\pi$
$212$	−14.7082	−	10.6861i	−1.01016	−	0.733927i
$213$	11.6180			0.796055
$214$	3.89919	+	2.83293i	0.266543	+	0.193655i
$215$	10.8541	+	7.88597i	0.740244	+	0.537818i
$216$	2.23607			0.152145
$217$	−13.9894	+	10.1639i	−0.949659	+	0.689968i
$218$	0.854102	+	0.620541i	0.0578471	+	0.0420284i
$219$	−9.35410	−	6.79615i	−0.632092	−	0.459241i
$220$	11.7082	−	2.62866i	0.789367	−	0.177224i
$221$	−5.23607	+	3.80423i	−0.352216	+	0.255900i
$222$	1.32624			0.0890113
$223$	−22.4164			−1.50111			−0.750557	−	0.660806i	$-0.770215\pi$
$223$	−22.4164			−1.50111			−0.750557	+	0.660806i	$0.770215\pi$
$224$	−5.20820	−	16.0292i	−0.347988	−	1.07100i
$225$	−4.04508	−	2.93893i	−0.269672	−	0.195928i
$226$	−6.09017	+	4.42477i	−0.405112	+	0.294331i
$227$	−10.6631	+	7.74721i	−0.707736	+	0.514200i	−0.882443	−	0.470420i	$-0.844102\pi$
$227$	−10.6631	+	7.74721i	−0.707736	+	0.514200i	0.174706	+	0.984621i	$0.444102\pi$
$228$	−1.80902	−	5.56758i	−0.119805	−	0.368722i
$229$	−25.0000			−1.65205			−0.826023	−	0.563636i	$-0.809402\pi$
$229$	−25.0000			−1.65205			−0.826023	+	0.563636i	$0.809402\pi$
$230$	−5.42705	−	3.94298i	−0.357849	−	0.259993i
$231$	5.07295	+	8.55951i	0.333776	+	0.563174i
$232$	23.0902			1.51594
$233$	−0.708204	−	2.17963i	−0.0463960	−	0.142792i	0.925175	−	0.379541i	$-0.123918\pi$
$233$	−0.708204	−	2.17963i	−0.0463960	−	0.142792i	−0.971571	+	0.236749i	$0.923918\pi$
$234$	0.618034	+	0.449028i	0.0404021	+	0.0293539i
$235$	0.753289	−	2.31838i	0.0491391	−	0.151235i
$236$	−18.9443	−	13.7638i	−1.23317	−	0.895948i
$237$	1.54508	+	4.75528i	0.100364	+	0.308889i
$238$	9.70820			0.629289
$239$	10.5279			0.680991			0.340495	−	0.940246i	$-0.389405\pi$
$239$	10.5279			0.680991			0.340495	+	0.940246i	$0.389405\pi$
$240$	4.14590			0.267617
$241$	−0.173762	+	0.534785i	−0.0111930	+	0.0344485i	−0.956497	−	0.291742i	$-0.905765\pi$
$241$	−0.173762	+	0.534785i	−0.0111930	+	0.0344485i	0.945304	+	0.326191i	$0.105765\pi$
$242$	−3.26393	+	5.96361i	−0.209813	+	0.383355i
$243$	−1.00000			−0.0641500
$244$	2.35410	+	7.24518i	0.150706	+	0.463825i
$245$	−4.47214			−0.285714
$246$	−5.54508	−	4.02874i	−0.353542	−	0.256863i
$247$	1.38197	−	4.25325i	0.0879324	−	0.270628i
$248$	−10.4271	−	7.57570i	−0.662118	−	0.481057i
$249$	2.35410	+	7.24518i	0.149185	+	0.459145i
$250$	5.59017	+	4.06150i	0.353553	+	0.256872i
$251$	19.1353	+	13.9026i	1.20781	+	0.877523i	0.995030	−	0.0995780i	$-0.0317493\pi$
$251$	19.1353	+	13.9026i	1.20781	+	0.877523i	0.212777	+	0.977101i	$0.431749\pi$
$252$	1.50000	+	4.61653i	0.0944911	+	0.290814i
$253$	−15.7082	+	3.52671i	−0.987566	+	0.221722i
$254$	8.20820	−	5.96361i	0.515029	−	0.374190i
$255$	−3.61803	+	11.1352i	−0.226570	+	0.697311i
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	−5.56231	−	17.1190i	−0.346967	−	1.06785i	−0.960522	−	0.278203i	$-0.910261\pi$
$257$	−5.56231	−	17.1190i	−0.346967	−	1.06785i	0.613555	−	0.789652i	$-0.289739\pi$
$258$	−3.70820			−0.230863
$259$	1.98936	+	6.12261i	0.123613	+	0.380441i
$260$	3.61803	+	2.62866i	0.224381	+	0.163022i
$261$	−10.3262			−0.639178
$262$	−7.97214	+	5.79210i	−0.492520	+	0.357837i
$263$	1.52786	−	4.70228i	0.0942121	−	0.289955i	−0.892835	−	0.450383i	$-0.851287\pi$
$263$	1.52786	−	4.70228i	0.0942121	−	0.289955i	0.987048	+	0.160428i	$0.0512874\pi$
$264$	−4.89919	+	5.56758i	−0.301524	+	0.342661i
$265$	−20.3262	−	14.7679i	−1.24863	−	0.907183i
$266$	−5.42705	+	3.94298i	−0.332754	+	0.241760i
$267$	1.80902	−	1.31433i	0.110710	−	0.0804356i
$268$	1.50000	+	4.61653i	0.0916271	+	0.281999i
$269$	10.5279			0.641895			0.320948	−	0.947097i	$-0.395999\pi$
$269$	10.5279			0.641895			0.320948	+	0.947097i	$0.395999\pi$
$270$	1.38197			0.0841038
$271$	−14.7082	−	10.6861i	−0.893460	−	0.649137i	0.0433180	−	0.999061i	$-0.486207\pi$
$271$	−14.7082	−	10.6861i	−0.893460	−	0.649137i	−0.936778	+	0.349925i	$0.886207\pi$
$272$	−3.00000	−	9.23305i	−0.181902	−	0.559836i
$273$	−1.14590	+	3.52671i	−0.0693529	+	0.213446i
$274$	8.67376			0.524001
$275$	16.1803	−	3.63271i	0.975711	−	0.219061i
$276$	−7.85410			−0.472761
$277$	6.24671	−	19.2254i	0.375328	−	1.15514i	−0.567928	−	0.823078i	$-0.692255\pi$
$277$	6.24671	−	19.2254i	0.375328	−	1.15514i	0.943257	−	0.332064i	$-0.107745\pi$
$278$	0.753289	+	2.31838i	0.0451793	+	0.139047i
$279$	4.66312	+	3.38795i	0.279174	+	0.202832i
$280$	−4.63525	−	14.2658i	−0.277009	−	0.852547i
$281$	−25.3607			−1.51289			−0.756446	−	0.654057i	$-0.773066\pi$
$281$	−25.3607			−1.51289			−0.756446	+	0.654057i	$0.773066\pi$
$282$	0.208204	+	0.640786i	0.0123984	+	0.0381582i
$283$	0.472136	−	0.343027i	0.0280656	−	0.0203908i	−0.573664	−	0.819091i	$-0.694478\pi$
$283$	0.472136	−	0.343027i	0.0280656	−	0.0203908i	0.601730	+	0.798700i	$0.294478\pi$
$284$	−15.2082	+	11.0494i	−0.902441	+	0.655662i
$285$	−2.50000	−	7.69421i	−0.148087	−	0.455766i
$286$	−2.47214	+	0.555029i	−0.146180	+	0.0328196i
$287$	10.2812	−	31.6421i	0.606877	−	1.86778i
$288$	−4.54508	+	3.30220i	−0.267822	+	0.194584i
$289$	10.4164			0.612730
$290$	14.2705			0.837993
$291$	−3.54508	−	10.9106i	−0.207817	−	0.639594i
$292$	18.7082			1.09481
$293$	−1.86475	−	5.73910i	−0.108940	−	0.335282i	0.881695	−	0.471819i	$-0.156403\pi$
$293$	−1.86475	−	5.73910i	−0.108940	−	0.335282i	−0.990635	+	0.136538i	$0.956403\pi$
$294$	1.00000	−	0.726543i	0.0583212	−	0.0423728i
$295$	−26.1803	−	19.0211i	−1.52428	−	1.10745i
$296$	−3.88197	+	2.82041i	−0.225635	+	0.163933i
$297$	2.19098	−	2.48990i	0.127134	−	0.144479i
$298$	−1.21885	−	3.75123i	−0.0706059	−	0.217303i
$299$	−4.85410	−	3.52671i	−0.280720	−	0.203955i
$300$	8.09017			0.467086
$301$	−5.56231	−	17.1190i	−0.320606	−	0.986724i
$302$	−1.95492	−	1.42033i	−0.112493	−	0.0817307i
$303$	−3.54508	+	10.9106i	−0.203660	+	0.626800i
$304$	5.42705	+	3.94298i	0.311263	+	0.226146i
$305$	3.25329	+	10.0126i	0.186283	+	0.573319i
$306$	−1.00000	−	3.07768i	−0.0571662	−	0.175939i
$307$	1.67376			0.0955266			0.0477633	−	0.998859i	$-0.484791\pi$
$307$	1.67376			0.0955266			0.0477633	+	0.998859i	$0.484791\pi$
$308$	−14.7812	−	6.37988i	−0.842234	−	0.363527i
$309$	1.92705	−	5.93085i	0.109626	−	0.337394i
$310$	−6.44427	−	4.68204i	−0.366010	−	0.265922i
$311$	8.38197			0.475298			0.237649	−	0.971351i	$-0.423623\pi$
$311$	8.38197			0.475298			0.237649	+	0.971351i	$0.423623\pi$
$312$	−2.76393			−0.156477
$313$	3.43769	+	10.5801i	0.194310	+	0.598025i	0.999984	+	0.00566537i	$0.00180335\pi$
$313$	3.43769	+	10.5801i	0.194310	+	0.598025i	−0.805674	+	0.592359i	$0.798197\pi$
$314$	2.78115	+	2.02063i	0.156950	+	0.114031i
$315$	2.07295	+	6.37988i	0.116797	+	0.359466i
$316$	−6.54508	−	4.75528i	−0.368190	−	0.267506i
$317$	5.29180	+	16.2865i	0.297217	+	0.914739i	0.982468	+	0.186432i	$0.0596925\pi$
$317$	5.29180	+	16.2865i	0.297217	+	0.914739i	−0.685251	+	0.728307i	$0.740307\pi$
$318$	6.94427			0.389415
$319$	22.6246	−	25.7113i	1.26674	−	1.43956i
$320$	−0.427051	+	0.310271i	−0.0238729	+	0.0173447i
$321$	7.79837			0.435263
$322$	2.78115	+	8.55951i	0.154988	+	0.477003i
$323$	−15.3262	+	11.1352i	−0.852775	+	0.619577i
$324$	1.30902	−	0.951057i	0.0727232	−	0.0528365i
$325$	5.00000	+	3.63271i	0.277350	+	0.201507i
$326$	2.59017	+	7.97172i	0.143456	+	0.441513i
$327$	1.70820			0.0944639
$328$	24.7984			1.36926
$329$	−2.64590	+	1.92236i	−0.145873	+	0.105983i
$330$	−3.02786	+	3.44095i	−0.166678	+	0.189418i
$331$	5.45492	+	3.96323i	0.299829	+	0.217839i	0.727520	−	0.686086i	$-0.240673\pi$
$331$	5.45492	+	3.96323i	0.299829	+	0.217839i	−0.427691	+	0.903925i	$0.640673\pi$
$332$	−9.97214	−	7.24518i	−0.547292	−	0.397631i
$333$	1.73607	−	1.26133i	0.0951359	−	0.0691203i
$334$	13.7984			0.755013
$335$	2.07295	+	6.37988i	0.113257	+	0.348570i
$336$	−4.50000	−	3.26944i	−0.245495	−	0.178363i
$337$	8.90983			0.485349			0.242675	−	0.970108i	$-0.421975\pi$
$337$	8.90983			0.485349			0.242675	+	0.970108i	$0.421975\pi$
$338$	5.73607	+	4.16750i	0.312001	+	0.226682i
$339$	−3.76393	+	11.5842i	−0.204429	+	0.629167i
$340$	−5.85410	−	18.0171i	−0.317483	−	0.977113i
$341$	−18.6525	+	4.18774i	−1.01009	+	0.226779i
$342$	1.80902	+	1.31433i	0.0978204	+	0.0710707i
$343$	−12.1353	−	8.81678i	−0.655242	−	0.476061i
$344$	10.8541	−	7.88597i	0.585214	−	0.425183i
$345$	−10.8541			−0.584365
$346$	1.04508	−	3.21644i	0.0561841	−	0.172917i
$347$	−5.17376	+	15.9232i	−0.277742	+	0.854802i	0.710739	+	0.703456i	$0.248361\pi$
$347$	−5.17376	+	15.9232i	−0.277742	+	0.854802i	−0.988481	+	0.151346i	$0.951639\pi$
$348$	13.5172	−	9.82084i	0.724599	−	0.526452i
$349$	−1.44427	+	4.44501i	−0.0773101	+	0.237936i	−0.982241	−	0.187622i	$-0.939922\pi$
$349$	−1.44427	+	4.44501i	−0.0773101	+	0.237936i	0.904931	+	0.425558i	$0.139922\pi$
$350$	−2.86475	−	8.81678i	−0.153127	−	0.471277i
$351$	1.23607			0.0659764
$352$	1.73607	−	18.5519i	0.0925327	−	0.988817i
$353$	23.1353	−	16.8087i	1.23137	−	0.894639i	0.234374	−	0.972147i	$-0.424696\pi$
$353$	23.1353	−	16.8087i	1.23137	−	0.894639i	0.996992	+	0.0775073i	$0.0246961\pi$
$354$	8.94427			0.475383
$355$	−21.0172	+	15.2699i	−1.11548	+	0.810442i
$356$	−1.11803	+	3.44095i	−0.0592557	+	0.182370i
$357$	12.7082	−	9.23305i	0.672589	−	0.488665i
$358$	13.6180			0.719735
$359$	−13.4164			−0.708091			−0.354045	−	0.935228i	$-0.615194\pi$
$359$	−13.4164			−0.708091			−0.354045	+	0.935228i	$0.615194\pi$
$360$	−4.04508	+	2.93893i	−0.213195	+	0.154895i
$361$	−1.82624	+	5.62058i	−0.0961178	+	0.295820i
$362$	2.39261	−	7.36369i	0.125753	−	0.387027i
$363$	1.39919	+	10.9106i	0.0734383	+	0.572661i
$364$	−1.85410	−	5.70634i	−0.0971813	−	0.299093i
$365$	25.8541			1.35327
$366$	−2.35410	−	1.71036i	−0.123051	−	0.0894017i
$367$	−6.12868	+	18.8621i	−0.319914	+	0.984595i	0.653770	+	0.756693i	$0.273186\pi$
$367$	−6.12868	+	18.8621i	−0.319914	+	0.984595i	−0.973684	+	0.227902i	$0.926814\pi$
$368$	7.28115	−	5.29007i	0.379556	−	0.275764i
$369$	−11.0902			−0.577331
$370$	−2.39919	+	1.74311i	−0.124728	+	0.0906200i
$371$	10.4164	+	32.0584i	0.540793	+	1.66439i
$372$	−9.32624			−0.483543
$373$	−5.87132	−	18.0701i	−0.304006	−	0.935633i	−0.980046	−	0.198769i	$-0.936306\pi$
$373$	−5.87132	−	18.0701i	−0.304006	−	0.935633i	0.676041	−	0.736864i	$-0.263694\pi$
$374$	9.85410	+	4.25325i	0.509543	+	0.219931i
$375$	11.1803			0.577350
$376$	−1.97214	−	1.43284i	−0.101705	−	0.0738931i
$377$	12.7639			0.657376
$378$	−1.50000	−	1.08981i	−0.0771517	−	0.0560540i
$379$	−9.83688	+	30.2748i	−0.505287	+	1.55511i	0.295002	+	0.955497i	$0.404680\pi$
$379$	−9.83688	+	30.2748i	−0.505287	+	1.55511i	−0.800288	+	0.599616i	$0.795320\pi$
$380$	10.5902	+	7.69421i	0.543264	+	0.394705i
$381$	5.07295	−	15.6129i	0.259895	−	0.799875i
$382$	0.118034	−	0.363271i	0.00603914	−	0.0185866i
$383$	0.572949	+	1.76336i	0.0292763	+	0.0901033i	0.964627	−	0.263618i	$-0.0849160\pi$
$383$	0.572949	+	1.76336i	0.0292763	+	0.0901033i	−0.935351	+	0.353722i	$0.884916\pi$
$384$	3.51722	−	10.8249i	0.179487	−	0.552406i
$385$	−20.4271	−	8.81678i	−1.04106	−	0.449345i
$386$	1.79837	+	5.53483i	0.0915348	+	0.281715i
$387$	−4.85410	+	3.52671i	−0.246748	+	0.179273i
$388$	15.0172	+	10.9106i	0.762384	+	0.553904i
$389$	7.92705	−	5.75934i	0.401917	−	0.292010i	−0.368404	−	0.929666i	$-0.620096\pi$
$389$	7.92705	−	5.75934i	0.401917	−	0.292010i	0.770322	+	0.637656i	$0.220096\pi$
$390$	−1.70820			−0.0864983
$391$	7.85410	+	24.1724i	0.397199	+	1.22245i
$392$	−1.38197	+	4.25325i	−0.0697998	+	0.214822i
$393$	−4.92705	+	15.1639i	−0.248537	+	0.764918i
$394$	1.86475	+	5.73910i	0.0939445	+	0.289131i
$395$	−9.04508	−	6.57164i	−0.455108	−	0.330655i
$396$	−0.500000	+	5.34307i	−0.0251259	+	0.268499i
$397$	9.92705	−	7.21242i	0.498224	−	0.361981i	−0.310114	−	0.950699i	$-0.600367\pi$
$397$	9.92705	−	7.21242i	0.498224	−	0.361981i	0.808338	+	0.588718i	$0.200367\pi$
$398$	2.82624	−	8.69827i	0.141667	−	0.436005i
$399$	−3.35410	+	10.3229i	−0.167915	+	0.516790i
$400$	−7.50000	+	5.44907i	−0.375000	+	0.272453i
$401$	8.11803	−	5.89810i	0.405395	−	0.294537i	−0.366340	−	0.930481i	$-0.619389\pi$
$401$	8.11803	−	5.89810i	0.405395	−	0.294537i	0.771735	+	0.635944i	$0.219389\pi$
$402$	−1.50000	−	1.08981i	−0.0748132	−	0.0543550i
$403$	−5.76393	−	4.18774i	−0.287122	−	0.208606i
$404$	−5.73607	−	17.6538i	−0.285380	−	0.878309i
$405$	1.80902	−	1.31433i	0.0898908	−	0.0653095i
$406$	−15.4894	−	11.2537i	−0.768724	−	0.558511i
$407$	−0.663119	+	7.08618i	−0.0328696	+	0.351249i
$408$	9.47214	+	6.88191i	0.468941	+	0.340705i
$409$	4.20820	−	3.05744i	0.208082	−	0.151181i	−0.478863	−	0.877889i	$-0.658951\pi$
$409$	4.20820	−	3.05744i	0.208082	−	0.151181i	0.686946	+	0.726709i	$0.258951\pi$
$410$	15.3262			0.756909
$411$	11.3541	−	8.24924i	0.560057	−	0.406905i
$412$	3.11803	+	9.59632i	0.153615	+	0.472777i
$413$	13.4164	+	41.2915i	0.660178	+	2.03182i
$414$	2.42705	−	1.76336i	0.119283	−	0.0866642i
$415$	−13.7812	−	10.0126i	−0.676490	−	0.491499i
$416$	5.61803	−	4.08174i	0.275447	−	0.200124i
$417$	3.19098	+	2.31838i	0.156263	+	0.113532i
$418$	−7.23607	+	1.62460i	−0.353928	+	0.0794617i
$419$	−17.2984	−	12.5680i	−0.845081	−	0.613987i	0.0787045	−	0.996898i	$-0.474922\pi$
$419$	−17.2984	−	12.5680i	−0.845081	−	0.613987i	−0.923785	+	0.382911i	$0.874922\pi$
$420$	−8.78115	−	6.37988i	−0.428476	−	0.311306i
$421$	4.66312	+	14.3516i	0.227267	+	0.699454i	0.998054	+	0.0623616i	$0.0198632\pi$
$421$	4.66312	+	14.3516i	0.227267	+	0.699454i	−0.770787	+	0.637093i	$0.780137\pi$
$422$	−12.4443	−	9.04129i	−0.605778	−	0.440123i
$423$	0.881966	+	0.640786i	0.0428827	+	0.0311561i
$424$	−20.3262	+	14.7679i	−0.987129	+	0.717191i
$425$	−8.09017	−	24.8990i	−0.392431	−	1.20778i
$426$	2.21885	−	6.82891i	0.107503	−	0.330862i
$427$	4.36475	−	13.4333i	0.211225	−	0.650083i
$428$	−10.2082	+	7.41669i	−0.493432	+	0.358499i
$429$	−2.70820	+	3.07768i	−0.130753	+	0.148592i
$430$	6.70820	−	4.87380i	0.323498	−	0.235035i
$431$	−7.30902	−	22.4948i	−0.352063	−	1.08354i	−0.957693	−	0.287792i	$-0.907079\pi$
$431$	−7.30902	−	22.4948i	−0.352063	−	1.08354i	0.605630	−	0.795746i	$-0.292921\pi$
$432$	−0.572949	+	1.76336i	−0.0275660	+	0.0848395i
$433$	8.43769	−	25.9686i	0.405490	−	1.24797i	−0.514996	−	0.857193i	$-0.672207\pi$
$433$	8.43769	−	25.9686i	0.405490	−	1.24797i	0.920486	−	0.390776i	$-0.127793\pi$
$434$	3.30244	+	10.1639i	0.158522	+	0.487881i
$435$	18.6803	−	13.5721i	0.895654	−	0.650731i
$436$	−2.23607	+	1.62460i	−0.107088	+	0.0778042i
$437$	−14.2082	−	10.3229i	−0.679671	−	0.493810i
$438$	−5.78115	+	4.20025i	−0.276234	+	0.200696i
$439$	−8.84346	−	27.2174i	−0.422075	−	1.29901i	−0.905767	−	0.423776i	$-0.860704\pi$
$439$	−8.84346	−	27.2174i	−0.422075	−	1.29901i	0.483692	−	0.875238i	$-0.339296\pi$
$440$	1.54508	−	16.5110i	0.0736590	−	0.787130i
$441$	0.618034	−	1.90211i	0.0294302	−	0.0905768i
$442$	1.23607	+	3.80423i	0.0587938	+	0.180949i
$443$	6.59017	−	20.2825i	0.313108	−	0.963649i	−0.663418	−	0.748249i	$-0.730895\pi$
$443$	6.59017	−	20.2825i	0.313108	−	0.963649i	0.976526	−	0.215399i	$-0.0691053\pi$
$444$	−1.07295	+	3.30220i	−0.0509199	+	0.156715i
$445$	−1.54508	+	4.75528i	−0.0732441	+	0.225422i
$446$	−4.28115	+	13.1760i	−0.202718	+	0.623903i
$447$	−5.16312	−	3.75123i	−0.244207	−	0.177427i
$448$	0.708204			0.0334595
$449$	−16.6074	−	12.0660i	−0.783751	−	0.569429i	0.122351	−	0.992487i	$-0.460957\pi$
$449$	−16.6074	−	12.0660i	−0.783751	−	0.569429i	−0.906102	+	0.423058i	$0.860957\pi$
$450$	−2.50000	+	1.81636i	−0.117851	+	0.0856239i
$451$	24.2984	−	27.6134i	1.14417	−	1.30026i
$452$	−6.09017	−	18.7436i	−0.286457	−	0.881626i
$453$	−3.90983			−0.183700
$454$	2.51722	+	7.74721i	0.118139	+	0.363595i
$455$	−2.56231	−	7.88597i	−0.120123	−	0.369700i
$456$	−8.09017			−0.378857
$457$	−6.78115	+	4.92680i	−0.317209	+	0.230466i	−0.734984	−	0.678085i	$-0.762810\pi$
$457$	−6.78115	+	4.92680i	−0.317209	+	0.230466i	0.417775	+	0.908551i	$0.362810\pi$
$458$	−4.77458	+	14.6946i	−0.223101	+	0.686635i
$459$	−4.23607	−	3.07768i	−0.197723	−	0.143654i
$460$	14.2082	−	10.3229i	0.662461	−	0.481306i
$461$	3.07953	+	9.47781i	0.143428	+	0.441426i	0.996805	−	0.0798677i	$-0.0254498\pi$
$461$	3.07953	+	9.47781i	0.143428	+	0.441426i	−0.853378	+	0.521293i	$0.825450\pi$
$462$	6.00000	−	1.34708i	0.279145	−	0.0626720i
$463$	−8.47214	+	26.0746i	−0.393734	+	1.21179i	0.536210	+	0.844085i	$0.319856\pi$
$463$	−8.47214	+	26.0746i	−0.393734	+	1.21179i	−0.929943	+	0.367703i	$0.880144\pi$
$464$	−5.91641	+	18.2088i	−0.274662	+	0.845324i
$465$	−12.8885			−0.597692
$466$	−1.41641			−0.0656138
$467$	−19.0557			−0.881794			−0.440897	−	0.897558i	$-0.645340\pi$
$467$	−19.0557			−0.881794			−0.440897	+	0.897558i	$0.645340\pi$
$468$	−1.61803	+	1.17557i	−0.0747936	+	0.0543408i
$469$	2.78115	−	8.55951i	0.128422	−	0.395241i
$470$	−1.21885	−	0.885544i	−0.0562212	−	0.0408471i
$471$	5.56231			0.256298
$472$	−26.1803	+	19.0211i	−1.20505	+	0.875518i
$473$	1.85410	−	19.8132i	0.0852517	−	0.911011i
$474$	3.09017			0.141936
$475$	14.6353	+	10.6331i	0.671512	+	0.487882i
$476$	−7.85410	+	24.1724i	−0.359992	+	1.10794i
$477$	9.09017	−	6.60440i	0.416210	−	0.302394i
$478$	2.01064	−	6.18812i	0.0919647	−	0.283038i
$479$	4.04508	−	12.4495i	0.184825	−	0.568832i	−0.815121	−	0.579291i	$-0.803329\pi$
$479$	4.04508	−	12.4495i	0.184825	−	0.568832i	0.999945	+	0.0104594i	$0.00332941\pi$
$480$	3.88197	−	11.9475i	0.177187	−	0.545325i
$481$	−2.14590	+	1.55909i	−0.0978445	+	0.0710882i
$482$	0.281153	+	0.204270i	0.0128062	+	0.00930422i
$483$	11.7812	+	8.55951i	0.536061	+	0.389471i
$484$	−12.2082	−	12.9515i	−0.554918	−	0.588705i
$485$	20.7533	+	15.0781i	0.942358	+	0.684663i
$486$	−0.190983	+	0.587785i	−0.00866317	+	0.0266625i
$487$	2.85410	+	2.07363i	0.129332	+	0.0939650i	0.650570	−	0.759446i	$-0.274530\pi$
$487$	2.85410	+	2.07363i	0.129332	+	0.0939650i	−0.521239	+	0.853411i	$0.674530\pi$
$488$	10.5279			0.476574
$489$	10.9721	+	7.97172i	0.496177	+	0.360494i
$490$	−0.854102	+	2.62866i	−0.0385844	+	0.118751i
$491$	17.4508			0.787546			0.393773	−	0.919208i	$-0.371170\pi$
$491$	17.4508			0.787546			0.393773	+	0.919208i	$0.371170\pi$
$492$	14.5172	−	10.5474i	0.654487	−	0.475513i
$493$	−43.7426	−	31.7809i	−1.97007	−	1.43134i
$494$	−2.23607	−	1.62460i	−0.100605	−	0.0730941i
$495$	−0.690983	+	7.38394i	−0.0310574	+	0.331883i
$496$	8.64590	−	6.28161i	0.388212	−	0.282053i
$497$	34.8541			1.56342
$498$	4.70820			0.210980
$499$	7.76393	+	23.8949i	0.347561	+	1.06968i	0.960198	+	0.279319i	$0.0901088\pi$
$499$	7.76393	+	23.8949i	0.347561	+	1.06968i	−0.612637	+	0.790364i	$0.709891\pi$
$500$	−14.6353	+	10.6331i	−0.654508	+	0.475528i
$501$	18.0623	−	13.1230i	0.806964	−	0.586294i
$502$	11.8262	−	8.59226i	0.527831	−	0.383492i
$503$	−6.33688	−	19.5029i	−0.282548	−	0.869592i	−0.987123	−	0.159963i	$-0.948863\pi$
$503$	−6.33688	−	19.5029i	−0.282548	−	0.869592i	0.704575	−	0.709629i	$-0.251137\pi$
$504$	6.70820			0.298807
$505$	−7.92705	−	24.3970i	−0.352749	−	1.08565i
$506$	−0.927051	+	9.90659i	−0.0412124	+	0.440402i
$507$	11.4721			0.509495
$508$	8.20820	+	25.2623i	0.364180	+	1.12083i
$509$	17.8262	+	12.9515i	0.790134	+	0.574066i	0.908003	−	0.418963i	$-0.137606\pi$
$509$	17.8262	+	12.9515i	0.790134	+	0.574066i	−0.117869	+	0.993029i	$0.537606\pi$
$510$	5.85410	+	4.25325i	0.259224	+	0.188337i
$511$	−28.0623	−	20.3885i	−1.24140	−	0.901932i
$512$	5.78115	+	17.7926i	0.255493	+	0.786327i
$513$	3.61803			0.159740
$514$	−11.1246			−0.490686
$515$	4.30902	+	13.2618i	0.189878	+	0.584384i
$516$	3.00000	−	9.23305i	0.132068	−	0.406462i
$517$	−3.52786	+	0.792055i	−0.155155	+	0.0348345i
$518$	3.97871			0.174815
$519$	−1.69098	−	5.20431i	−0.0742259	−	0.228444i
$520$	5.00000	−	3.63271i	0.219265	−	0.159305i
$521$	−25.4615	−	18.4989i	−1.11549	−	0.810450i	−0.131969	−	0.991254i	$-0.542130\pi$
$521$	−25.4615	−	18.4989i	−1.11549	−	0.810450i	−0.983519	+	0.180804i	$0.942130\pi$
$522$	−1.97214	+	6.06961i	−0.0863180	+	0.265660i
$523$	−16.9894	−	12.3435i	−0.742893	−	0.539743i	0.150723	−	0.988576i	$-0.451840\pi$
$523$	−16.9894	−	12.3435i	−0.742893	−	0.539743i	−0.893616	+	0.448833i	$0.851840\pi$
$524$	−7.97214	−	24.5357i	−0.348264	−	1.07185i
$525$	−12.1353	−	8.81678i	−0.529626	−	0.384796i
$526$	−2.47214	−	1.79611i	−0.107790	−	0.0783142i
$527$	9.32624	+	28.7032i	0.406257	+	1.25033i
$528$	−3.13525	−	5.29007i	−0.136444	−	0.230221i
$529$	−0.454915	+	0.330515i	−0.0197789	+	0.0143702i
$530$	−12.5623	+	9.12705i	−0.545672	+	0.396454i
$531$	11.7082	−	8.50651i	0.508093	−	0.369151i
$532$	−5.42705	−	16.7027i	−0.235293	−	0.724156i
$533$	13.7082			0.593768
$534$	−0.427051	−	1.31433i	−0.0184803	−	0.0568765i
$535$	−14.1074	+	10.2496i	−0.609916	+	0.443130i
$536$	6.70820			0.289750
$537$	17.8262	−	12.9515i	0.769259	−	0.558899i
$538$	2.01064	−	6.18812i	0.0866850	−	0.266789i
$539$	3.38197	+	5.70634i	0.145672	+	0.245789i
$540$	−1.11803	+	3.44095i	−0.0481125	+	0.148075i
$541$	9.50000	−	6.90215i	0.408437	−	0.296747i	−0.364532	−	0.931191i	$-0.618771\pi$
$541$	9.50000	−	6.90215i	0.408437	−	0.296747i	0.772969	+	0.634444i	$0.218771\pi$
$542$	−9.09017	+	6.60440i	−0.390456	+	0.283683i
$543$	−3.87132	−	11.9147i	−0.166134	−	0.511309i
$544$	−29.4164			−1.26122
$545$	−3.09017	+	2.24514i	−0.132368	+	0.0961712i
$546$	1.85410	+	1.34708i	0.0793482	+	0.0576499i
$547$	−7.10739	−	21.8743i	−0.303890	−	0.935278i	−0.980089	−	0.198558i	$-0.936374\pi$
$547$	−7.10739	−	21.8743i	−0.303890	−	0.935278i	0.676199	−	0.736719i	$-0.263626\pi$
$548$	−7.01722	+	21.5968i	−0.299761	+	0.922569i
$549$	−4.70820			−0.200941
$550$	0.954915	−	10.2044i	0.0407177	−	0.435115i
$551$	37.3607			1.59162
$552$	−3.35410	+	10.3229i	−0.142760	+	0.439370i
$553$	4.63525	+	14.2658i	0.197111	+	0.606646i
$554$	−10.1074	−	7.34345i	−0.429422	−	0.311993i
$555$	−1.48278	+	4.56352i	−0.0629405	+	0.193711i
$556$	−6.38197			−0.270656
$557$	−5.17376	−	15.9232i	−0.219219	−	0.674688i	−0.998827	−	0.0484196i	$-0.984582\pi$
$557$	−5.17376	−	15.9232i	−0.219219	−	0.674688i	0.779608	−	0.626268i	$-0.215418\pi$
$558$	2.88197	−	2.09387i	0.122003	−	0.0886406i
$559$	6.00000	−	4.35926i	0.253773	−	0.184377i
$560$	12.4377			0.525589
$561$	16.9443	−	3.80423i	0.715388	−	0.160615i
$562$	−4.84346	+	14.9066i	−0.204309	+	0.628798i
$563$	27.9336	−	20.2950i	1.17726	−	0.855331i	0.185402	−	0.982663i	$-0.440641\pi$
$563$	27.9336	−	20.2950i	1.17726	−	0.855331i	0.991860	+	0.127332i	$0.0406413\pi$
$564$	−1.76393			−0.0742749
$565$	−8.41641	−	25.9030i	−0.354081	−	1.08975i
$566$	−0.111456	−	0.343027i	−0.00468485	−	0.0144185i
$567$	−3.00000			−0.125988
$568$	8.02786	+	24.7072i	0.336842	+	1.03669i
$569$	18.6803	−	13.5721i	0.783121	−	0.568970i	−0.122793	−	0.992432i	$-0.539185\pi$
$569$	18.6803	−	13.5721i	0.783121	−	0.568970i	0.905914	+	0.423462i	$0.139185\pi$
$570$	−5.00000			−0.209427
$571$	21.8992	−	15.9107i	0.916452	−	0.665842i	−0.0261860	−	0.999657i	$-0.508336\pi$
$571$	21.8992	−	15.9107i	0.916452	−	0.665842i	0.942638	+	0.333815i	$0.108336\pi$
$572$	0.618034	−	6.60440i	0.0258413	−	0.276144i
$573$	−0.190983	−	0.587785i	−0.00797843	−	0.0245551i
$574$	−16.6353	−	12.0862i	−0.694342	−	0.504469i
$575$	19.6353	−	14.2658i	0.818847	−	0.594927i
$576$	−0.0729490	−	0.224514i	−0.00303954	−	0.00935475i
$577$	3.80902	+	2.76741i	0.158571	+	0.115209i	0.664241	−	0.747518i	$-0.268755\pi$
$577$	3.80902	+	2.76741i	0.158571	+	0.115209i	−0.505670	+	0.862727i	$0.668755\pi$
$578$	1.98936	−	6.12261i	0.0827463	−	0.254667i
$579$	7.61803	+	5.53483i	0.316595	+	0.230020i
$580$	−11.5451	+	35.5321i	−0.479384	+	1.47539i
$581$	7.06231	+	21.7355i	0.292994	+	0.901742i
$582$	−7.09017			−0.293897
$583$	−3.47214	+	37.1037i	−0.143801	+	1.53668i
$584$	7.98936	−	24.5887i	0.330602	−	1.01749i
$585$	−2.23607	+	1.62460i	−0.0924500	+	0.0671689i
$586$	−3.72949			−0.154064
$587$	2.72949			0.112658			0.0563291	−	0.998412i	$-0.482060\pi$
$587$	2.72949			0.112658			0.0563291	+	0.998412i	$0.482060\pi$
$588$	1.00000	+	3.07768i	0.0412393	+	0.126922i
$589$	−16.8713	−	12.2577i	−0.695171	−	0.505071i
$590$	−16.1803	+	11.7557i	−0.666134	+	0.483975i
$591$	7.89919	+	5.73910i	0.324929	+	0.236075i
$592$	−1.22949	−	3.78398i	−0.0505317	−	0.155521i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	−1.04508	−	1.76336i	−0.0428804	−	0.0723514i
$595$	−10.8541	+	33.4055i	−0.444975	+	1.36949i
$596$	10.3262			0.422979
$597$	−4.57295	−	14.0741i	−0.187158	−	0.576014i
$598$	−3.00000	+	2.17963i	−0.122679	+	0.0891316i
$599$	2.33688	−	1.69784i	0.0954824	−	0.0693720i	−0.539020	−	0.842293i	$-0.681205\pi$
$599$	2.33688	−	1.69784i	0.0954824	−	0.0693720i	0.634502	+	0.772921i	$0.281205\pi$
$600$	3.45492	−	10.6331i	0.141046	−	0.434096i
$601$	3.48278	+	10.7189i	0.142066	+	0.437233i	0.996622	−	0.0821258i	$-0.0261709\pi$
$601$	3.48278	+	10.7189i	0.142066	+	0.437233i	−0.854556	+	0.519359i	$0.826171\pi$
$602$	−11.1246			−0.453405
$603$	−3.00000			−0.122169
$604$	5.11803	−	3.71847i	0.208250	−	0.151302i
$605$	−16.8713	−	17.8986i	−0.685917	−	0.727680i
$606$	5.73607	+	4.16750i	0.233012	+	0.169293i
$607$	25.2533	+	18.3476i	1.02500	+	0.744706i	0.967302	−	0.253628i	$-0.0816241\pi$
$607$	25.2533	+	18.3476i	1.02500	+	0.744706i	0.0576977	+	0.998334i	$0.481624\pi$
$608$	16.4443	−	11.9475i	0.666903	−	0.484534i
$609$	−30.9787			−1.25532
$610$	6.50658			0.263444
$611$	−1.09017	−	0.792055i	−0.0441036	−	0.0320431i
$612$	8.47214			0.342466
$613$	26.1246	+	18.9806i	1.05516	+	0.766621i	0.973187	−	0.230013i	$-0.0738770\pi$
$613$	26.1246	+	18.9806i	1.05516	+	0.766621i	0.0819757	+	0.996634i	$0.473877\pi$
$614$	0.319660	−	0.983813i	0.0129004	−	0.0397034i
$615$	20.0623	−	14.5761i	0.808990	−	0.587766i
$616$	−14.6976	+	16.7027i	−0.592182	+	0.672973i
$617$	−22.2082	−	16.1352i	−0.894069	−	0.649579i	0.0428670	−	0.999081i	$-0.486351\pi$
$617$	−22.2082	−	16.1352i	−0.894069	−	0.649579i	−0.936936	+	0.349502i	$0.886351\pi$
$618$	−3.11803	−	2.26538i	−0.125426	−	0.0911271i
$619$	−32.4615	+	23.5847i	−1.30474	+	0.947947i	−0.999990	−	0.00448582i	$-0.998572\pi$
$619$	−32.4615	+	23.5847i	−1.30474	+	0.947947i	−0.304748	+	0.952433i	$0.598572\pi$
$620$	16.8713	−	12.2577i	0.677569	−	0.492282i
$621$	1.50000	−	4.61653i	0.0601929	−	0.185255i
$622$	1.60081	−	4.92680i	0.0641868	−	0.197547i
$623$	5.42705	−	3.94298i	0.217430	−	0.157972i
$624$	0.708204	−	2.17963i	0.0283508	−	0.0872549i
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	6.87539			0.274796
$627$	−7.92705	+	9.00854i	−0.316576	+	0.359766i
$628$	−7.28115	+	5.29007i	−0.290550	+	0.211097i
$629$	11.2361			0.448011
$630$	4.14590			0.165177
$631$	−0.274575	+	0.845055i	−0.0109307	+	0.0336411i	−0.956373	−	0.292148i	$-0.905630\pi$
$631$	−0.274575	+	0.845055i	−0.0109307	+	0.0336411i	0.945442	+	0.325789i	$0.105630\pi$
$632$	−9.04508	+	6.57164i	−0.359794	+	0.261406i
$633$	−24.8885			−0.989231
$634$	10.5836			0.420328
$635$	11.3435	+	34.9116i	0.450151	+	1.38542i
$636$	−5.61803	+	17.2905i	−0.222770	+	0.685614i
$637$	−0.763932	+	2.35114i	−0.0302681	+	0.0931556i
$638$	−10.7918	−	18.2088i	−0.427251	−	0.720895i
$639$	−3.59017	−	11.0494i	−0.142025	−	0.437108i
$640$	7.86475	+	24.2052i	0.310881	+	0.956794i
$641$	37.2877	+	27.0911i	1.47278	+	1.07003i	0.979797	+	0.199994i	$0.0640923\pi$
$641$	37.2877	+	27.0911i	1.47278	+	1.07003i	0.492980	+	0.870041i	$0.335908\pi$
$642$	1.48936	−	4.58377i	0.0587802	−	0.180907i
$643$	32.2426	−	23.4257i	1.27153	−	0.923818i	0.272264	−	0.962223i	$-0.412228\pi$
$643$	32.2426	−	23.4257i	1.27153	−	0.923818i	0.999262	+	0.0384051i	$0.0122277\pi$
$644$	−23.5623			−0.928485
$645$	4.14590	−	12.7598i	0.163245	−	0.502415i
$646$	3.61803	+	11.1352i	0.142350	+	0.438107i
$647$	−10.0344			−0.394495			−0.197247	−	0.980354i	$-0.563200\pi$
$647$	−10.0344			−0.394495			−0.197247	+	0.980354i	$0.563200\pi$
$648$	−0.690983	−	2.12663i	−0.0271444	−	0.0835418i
$649$	−4.47214	+	47.7899i	−0.175547	+	1.87592i
$650$	3.09017	−	2.24514i	0.121206	−	0.0880616i
$651$	13.9894	+	10.1639i	0.548286	+	0.398353i
$652$	−21.9443			−0.859404
$653$	−0.708204	−	0.514540i	−0.0277142	−	0.0201355i	0.573842	−	0.818966i	$-0.305452\pi$
$653$	−0.708204	−	0.514540i	−0.0277142	−	0.0201355i	−0.601556	+	0.798831i	$0.705452\pi$
$654$	0.326238	−	1.00406i	0.0127569	−	0.0392617i
$655$	−11.0172	−	33.9075i	−0.430478	−	1.32488i
$656$	−6.35410	+	19.5559i	−0.248086	+	0.763530i
$657$	−3.57295	+	10.9964i	−0.139394	+	0.429011i
$658$	0.624612	+	1.92236i	0.0243499	+	0.0749413i
$659$	9.96149	−	30.6583i	0.388045	−	1.19428i	−0.546203	−	0.837653i	$-0.683927\pi$
$659$	9.96149	−	30.6583i	0.388045	−	1.19428i	0.934247	−	0.356626i	$-0.116073\pi$
$660$	−6.11803	−	10.3229i	−0.238144	−	0.401817i
$661$	−12.7984	−	39.3893i	−0.497799	−	1.53207i	−0.812549	−	0.582893i	$-0.801921\pi$
$661$	−12.7984	−	39.3893i	−0.497799	−	1.53207i	0.314750	−	0.949175i	$-0.398079\pi$
$662$	3.37132	−	2.44941i	0.131030	−	0.0951990i
$663$	5.23607	+	3.80423i	0.203352	+	0.147744i
$664$	−13.7812	+	10.0126i	−0.534812	+	0.388564i
$665$	−7.50000	−	23.0826i	−0.290838	−	0.895106i
$666$	−0.409830	−	1.26133i	−0.0158806	−	0.0488754i
$667$	15.4894	−	47.6713i	0.599750	−	1.84584i
$668$	−11.1631	+	34.3565i	−0.431914	+	1.32929i
$669$	6.92705	+	21.3193i	0.267815	+	0.824251i
$670$	4.14590			0.160170
$671$	10.3156	−	11.7229i	0.398229	−	0.452559i
$672$	−13.6353	+	9.90659i	−0.525991	+	0.382155i
$673$	−13.4721	+	41.4630i	−0.519313	+	1.59828i	0.255983	+	0.966681i	$0.417601\pi$
$673$	−13.4721	+	41.4630i	−0.519313	+	1.59828i	−0.775295	+	0.631599i	$0.782399\pi$
$674$	1.70163	−	5.23707i	0.0655442	−	0.201724i
$675$	−1.54508	+	4.75528i	−0.0594703	+	0.183031i
$676$	−15.0172	+	10.9106i	−0.577585	+	0.419640i
$677$	−7.14590	−	5.19180i	−0.274639	−	0.199537i	0.441937	−	0.897046i	$-0.354292\pi$
$677$	−7.14590	−	5.19180i	−0.274639	−	0.199537i	−0.716576	+	0.697509i	$0.754292\pi$
$678$	6.09017	+	4.42477i	0.233892	+	0.169932i
$679$	−10.6353	−	32.7319i	−0.408144	−	1.25614i
$680$	−26.1803			−1.00397
$681$	10.6631	+	7.74721i	0.408612	+	0.296874i
$682$	−1.10081	+	11.7634i	−0.0421523	+	0.450445i
$683$	21.3262	+	15.4944i	0.816026	+	0.592877i	0.915571	−	0.402156i	$-0.131739\pi$
$683$	21.3262	+	15.4944i	0.816026	+	0.592877i	−0.0995455	+	0.995033i	$0.531739\pi$
$684$	−4.73607	+	3.44095i	−0.181088	+	0.131568i
$685$	−9.69756	+	29.8460i	−0.370525	+	1.14036i
$686$	−7.50000	+	5.44907i	−0.286351	+	0.208046i
$687$	7.72542	+	23.7764i	0.294743	+	0.907127i
$688$	3.43769	+	10.5801i	0.131061	+	0.403364i
$689$	−11.2361	+	8.16348i	−0.428060	+	0.311004i
$690$	−2.07295	+	6.37988i	−0.0789158	+	0.242878i
$691$	−13.1631	+	9.56357i	−0.500749	+	0.363815i	−0.809303	−	0.587392i	$-0.800155\pi$
$691$	−13.1631	+	9.56357i	−0.500749	+	0.363815i	0.308554	+	0.951207i	$0.400155\pi$
$692$	7.16312	+	5.20431i	0.272301	+	0.197838i
$693$	6.57295	−	7.46969i	0.249686	−	0.283750i
$694$	8.37132	+	6.08212i	0.317771	+	0.230874i
$695$	−8.81966			−0.334549
$696$	−7.13525	−	21.9601i	−0.270461	−	0.832394i
$697$	−46.9787	−	34.1320i	−1.77945	−	1.29284i
$698$	2.33688	+	1.69784i	0.0884523	+	0.0642643i
$699$	−1.85410	+	1.34708i	−0.0701286	+	0.0509514i
$700$	24.2705			0.917339
$701$	0.517221	−	1.59184i	0.0195352	−	0.0601231i	−0.940814	−	0.338924i	$-0.889937\pi$
$701$	0.517221	−	1.59184i	0.0195352	−	0.0601231i	0.960349	+	0.278801i	$0.0899370\pi$
$702$	0.236068	−	0.726543i	0.00890981	−	0.0274216i
$703$	−6.28115	+	4.56352i	−0.236898	+	0.172117i
$704$	0.718847	+	0.310271i	0.0270926	+	0.0116938i
$705$	−2.43769			−0.0918089
$706$	−5.46149	−	16.8087i	−0.205546	−	0.632606i
$707$	−10.6353	+	32.7319i	−0.399980	+	1.23101i
$708$	−7.23607	+	22.2703i	−0.271948	+	0.836970i
$709$	8.12868	+	25.0175i	0.305279	+	0.939552i	0.979573	+	0.201089i	$0.0644480\pi$
$709$	8.12868	+	25.0175i	0.305279	+	0.939552i	−0.674294	+	0.738463i	$0.735552\pi$
$710$	4.96149	+	15.2699i	0.186202	+	0.573069i
$711$	4.04508	−	2.93893i	0.151703	−	0.110218i
$712$	4.04508	+	2.93893i	0.151596	+	0.110141i
$713$	−22.6353	+	16.4455i	−0.847697	+	0.615888i
$714$	−3.00000	−	9.23305i	−0.112272	−	0.345538i
$715$	0.854102	−	9.12705i	0.0319416	−	0.341332i
$716$	−11.0172	+	33.9075i	−0.411733	+	1.26718i
$717$	−3.25329	−	10.0126i	−0.121496	−	0.373927i
$718$	−2.56231	+	7.88597i	−0.0956244	+	0.294302i
$719$	−5.52786	+	17.0130i	−0.206155	+	0.634478i	0.793509	+	0.608558i	$0.208252\pi$
$719$	−5.52786	+	17.0130i	−0.206155	+	0.634478i	−0.999664	+	0.0259205i	$0.991748\pi$
$720$	−1.28115	−	3.94298i	−0.0477458	−	0.146946i
$721$	5.78115	−	17.7926i	0.215301	−	0.662630i
$722$	2.95492	+	2.14687i	0.109971	+	0.0798983i
$723$	0.562306			0.0209124
$724$	16.3992	+	11.9147i	0.609471	+	0.442807i
$725$	−15.9549	+	49.1042i	−0.592551	+	1.82368i
$726$	6.68034	+	1.26133i	0.247931	+	0.0468122i
$727$	−8.75329	−	26.9399i	−0.324642	−	0.999144i	−0.971602	−	0.236620i	$-0.923960\pi$
$727$	−8.75329	−	26.9399i	−0.324642	−	0.999144i	0.646961	−	0.762523i	$-0.276040\pi$
$728$	−8.29180			−0.307314
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	4.93769	−	15.1967i	0.182752	−	0.562454i
$731$	−31.4164			−1.16198
$732$	6.16312	−	4.47777i	0.227795	−	0.165503i
$733$	6.26393	−	19.2784i	0.231364	−	0.712064i	−0.766219	−	0.642579i	$-0.777864\pi$
$733$	6.26393	−	19.2784i	0.231364	−	0.712064i	0.997583	−	0.0694849i	$-0.0221356\pi$
$734$	9.91641	+	7.20469i	0.366021	+	0.265930i
$735$	1.38197	+	4.25325i	0.0509746	+	0.156884i
$736$	−8.42705	−	25.9358i	−0.310625	−	0.956006i
$737$	6.57295	−	7.46969i	0.242118	−	0.275150i
$738$	−2.11803	+	6.51864i	−0.0779659	+	0.239954i
$739$	−0.489357	+	1.50609i	−0.0180013	+	0.0554023i	−0.959654	−	0.281185i	$-0.909273\pi$
$739$	−0.489357	+	1.50609i	−0.0180013	+	0.0554023i	0.941652	+	0.336587i	$0.109273\pi$
$740$	−2.39919	−	7.38394i	−0.0881959	−	0.271439i
$741$	−4.47214			−0.164288
$742$	20.8328			0.764797
$743$	25.3713	−	18.4333i	0.930784	−	0.676254i	−0.0154010	−	0.999881i	$-0.504902\pi$
$743$	25.3713	−	18.4333i	0.930784	−	0.676254i	0.946185	+	0.323628i	$0.104902\pi$
$744$	−3.98278	+	12.2577i	−0.146016	+	0.449390i
$745$	14.2705			0.522831
$746$	−11.7426			−0.429929
$747$	6.16312	−	4.47777i	0.225497	−	0.163833i
$748$	−18.5623	+	21.0948i	−0.678705	+	0.771301i
$749$	23.3951			0.854839
$750$	2.13525	−	6.57164i	0.0779685	−	0.239962i
$751$	11.4336	−	35.1891i	0.417219	−	1.28407i	−0.493032	−	0.870011i	$-0.664111\pi$
$751$	11.4336	−	35.1891i	0.417219	−	1.28407i	0.910251	−	0.414057i	$-0.135889\pi$
$752$	1.63525	−	1.18808i	0.0596316	−	0.0433249i
$753$	7.30902	−	22.4948i	0.266355	−	0.819758i
$754$	2.43769	−	7.50245i	0.0887756	−	0.273223i
$755$	7.07295	−	5.13880i	0.257411	−	0.187020i
$756$	3.92705	−	2.85317i	0.142825	−	0.103769i
$757$	−23.5902	−	17.1393i	−0.857399	−	0.622937i	0.0697769	−	0.997563i	$-0.477771\pi$
$757$	−23.5902	−	17.1393i	−0.857399	−	0.622937i	−0.927176	+	0.374626i	$0.877771\pi$
$758$	15.9164	+	11.5639i	0.578110	+	0.420021i
$759$	8.20820	+	13.8496i	0.297939	+	0.502708i
$760$	14.6353	−	10.6331i	0.530876	−	0.385704i
$761$	7.36475	−	22.6664i	0.266972	−	0.821655i	−0.724261	−	0.689526i	$-0.757819\pi$
$761$	7.36475	−	22.6664i	0.266972	−	0.821655i	0.991233	−	0.132129i	$-0.0421812\pi$
$762$	−8.20820	−	5.96361i	−0.297352	−	0.216039i
$763$	5.12461			0.185523
$764$	0.809017	+	0.587785i	0.0292692	+	0.0212653i
$765$	11.7082			0.423311
$766$	1.14590			0.0414030
$767$	−14.4721	+	10.5146i	−0.522559	+	0.379661i
$768$	−5.30902	−	3.85723i	−0.191573	−	0.139186i
$769$	5.00000	+	3.63271i	0.180305	+	0.130999i	0.674277	−	0.738479i	$-0.264456\pi$
$769$	5.00000	+	3.63271i	0.180305	+	0.130999i	−0.493972	+	0.869478i	$0.664456\pi$
$770$	−9.08359	+	10.3229i	−0.327350	+	0.372010i
$771$	−14.5623	+	10.5801i	−0.524449	+	0.381034i
$772$	−15.2361			−0.548358
$773$	−32.8673			−1.18215			−0.591077	−	0.806615i	$-0.701297\pi$
$773$	−32.8673			−1.18215			−0.591077	+	0.806615i	$0.701297\pi$
$774$	1.14590	+	3.52671i	0.0411885	+	0.126765i
$775$	23.3156	−	16.9398i	0.837521	−	0.608495i
$776$	20.7533	−	15.0781i	0.745000	−	0.541274i
$777$	5.20820	−	3.78398i	0.186843	−	0.135750i
$778$	−1.87132	−	5.75934i	−0.0670902	−	0.206482i
$779$	40.1246			1.43761
$780$	1.38197	−	4.25325i	0.0494823	−	0.152291i
$781$	35.3779	+	15.2699i	1.26592	+	0.546400i
$782$	15.7082			0.561724
$783$	3.19098	+	9.82084i	0.114036	+	0.350968i
$784$	−3.00000	−	2.17963i	−0.107143	−	0.0778438i
$785$	−10.0623	+	7.31069i	−0.359139	+	0.260930i
$786$	7.97214	+	5.79210i	0.284357	+	0.206597i
$787$	−1.41641	−	4.35926i	−0.0504895	−	0.155391i	0.922633	−	0.385679i	$-0.126033\pi$
$787$	−1.41641	−	4.35926i	−0.0504895	−	0.155391i	−0.973122	+	0.230289i	$0.926033\pi$
$788$	−15.7984			−0.562794
$789$	−4.94427			−0.176021
$790$	−5.59017	+	4.06150i	−0.198889	+	0.144502i
$791$	−11.2918	+	34.7526i	−0.401490	+	1.23566i
$792$	6.80902	+	2.93893i	0.241948	+	0.104430i
$793$	5.81966			0.206662
$794$	−2.34346	−	7.21242i	−0.0831662	−	0.255959i
$795$	−7.76393	+	23.8949i	−0.275358	+	0.847466i
$796$	19.3713	+	14.0741i	0.686598	+	0.498843i
$797$	3.87132	−	11.9147i	0.137129	−	0.422041i	−0.858786	−	0.512335i	$-0.828781\pi$
$797$	3.87132	−	11.9147i	0.137129	−	0.422041i	0.995915	+	0.0902942i	$0.0287807\pi$
$798$	5.42705	+	3.94298i	0.192116	+	0.139580i
$799$	1.76393	+	5.42882i	0.0624034	+	0.192058i
$800$	8.68034	+	26.7153i	0.306896	+	0.944530i
$801$	−1.80902	−	1.31433i	−0.0639185	−	0.0464395i
$802$	−1.91641	−	5.89810i	−0.0676707	−	0.208269i
$803$	−19.5517	−	32.9892i	−0.689963	−	1.16416i
$804$	3.92705	−	2.85317i	0.138496	−	0.100624i
$805$	−32.5623			−1.14767
$806$	−3.56231	+	2.58817i	−0.125477	+	0.0911643i
$807$	−3.25329	−	10.0126i	−0.114521	−	0.352460i
$808$	−25.6525			−0.902451
$809$	12.0344	+	37.0382i	0.423108	+	1.30219i	0.904794	+	0.425850i	$0.140025\pi$
$809$	12.0344	+	37.0382i	0.423108	+	1.30219i	−0.481685	+	0.876344i	$0.659975\pi$
$810$	−0.427051	−	1.31433i	−0.0150050	−	0.0461808i
$811$	22.4508			0.788356			0.394178	−	0.919034i	$-0.371029\pi$
$811$	22.4508			0.788356			0.394178	+	0.919034i	$0.371029\pi$
$812$	40.5517	−	29.4625i	1.42308	−	1.03393i
$813$	−5.61803	+	17.2905i	−0.197033	+	0.606405i
$814$	4.03851	+	1.74311i	0.141550	+	0.0610960i
$815$	−30.3262			−1.06228
$816$	−7.85410	+	5.70634i	−0.274949	+	0.199762i
$817$	17.5623	−	12.7598i	0.614427	−	0.446408i
$818$	−0.993422	−	3.05744i	−0.0347342	−	0.106901i
$819$	3.70820			0.129575
$820$	−12.3992	+	38.1608i	−0.432998	+	1.33263i
$821$	36.2705	+	26.3521i	1.26585	+	0.919694i	0.999029	−	0.0440528i	$-0.0140270\pi$
$821$	36.2705	+	26.3521i	1.26585	+	0.919694i	0.266820	+	0.963746i	$0.414027\pi$
$822$	−2.68034	−	8.24924i	−0.0934876	−	0.287725i
$823$	−1.01064	+	3.11044i	−0.0352288	+	0.108423i	−0.967125	−	0.254303i	$-0.918154\pi$
$823$	−1.01064	+	3.11044i	−0.0352288	+	0.108423i	0.931896	+	0.362726i	$0.118154\pi$
$824$	13.9443			0.485772
$825$	−8.45492	−	14.2658i	−0.294362	−	0.496673i
$826$	26.8328			0.933633
$827$	−10.9656	+	33.7485i	−0.381310	+	1.17355i	0.557812	+	0.829967i	$0.311641\pi$
$827$	−10.9656	+	33.7485i	−0.381310	+	1.17355i	−0.939122	+	0.343584i	$0.888359\pi$
$828$	2.42705	+	7.46969i	0.0843459	+	0.259590i
$829$	−28.8435	−	20.9560i	−1.00177	−	0.727832i	−0.0393067	−	0.999227i	$-0.512515\pi$
$829$	−28.8435	−	20.9560i	−1.00177	−	0.727832i	−0.962468	+	0.271395i	$0.912515\pi$
$830$	−8.51722	+	6.18812i	−0.295637	+	0.214793i
$831$	−20.2148			−0.701243
$832$	0.0901699	+	0.277515i	0.00312608	+	0.00962109i
$833$	8.47214	−	6.15537i	0.293542	−	0.213271i
$834$	1.97214	−	1.43284i	0.0682895	−	0.0496152i
$835$	−15.4271	+	47.4796i	−0.533875	+	1.64310i
$836$	1.80902	−	19.3314i	0.0625662	−	0.668590i
$837$	1.78115	−	5.48183i	0.0615657	−	0.189480i
$838$	−10.6910	+	7.76745i	−0.369314	+	0.268322i
$839$	53.8673			1.85970			0.929852	−	0.367933i	$-0.119935\pi$
$839$	53.8673			1.85970			0.929852	+	0.367933i	$0.119935\pi$
$840$	−12.1353	+	8.81678i	−0.418706	+	0.304208i
$841$	23.9894	+	73.8316i	0.827219	+	2.54592i
$842$	9.32624			0.321403
$843$	7.83688	+	24.1194i	0.269917	+	0.830718i
$844$	32.5795	−	23.6704i	1.12143	−	0.814769i
$845$	−20.7533	+	15.0781i	−0.713935	+	0.518704i
$846$	0.545085	−	0.396027i	0.0187404	−	0.0136157i
$847$	4.19756	+	32.7319i	0.144230	+	1.12468i
$848$	−6.43769	−	19.8132i	−0.221071	−	0.680388i
$849$	−0.472136	−	0.343027i	−0.0162037	−	0.0117727i
$850$	−16.1803			−0.554981
$851$	3.21885	+	9.90659i	0.110341	+	0.339594i
$852$	15.2082	+	11.0494i	0.521024	+	0.378546i
$853$	2.70820	−	8.33499i	0.0927271	−	0.285385i	−0.893928	−	0.448211i	$-0.852061\pi$
$853$	2.70820	−	8.33499i	0.0927271	−	0.285385i	0.986655	+	0.162827i	$0.0520611\pi$
$854$	−7.06231	−	5.13107i	−0.241667	−	0.175581i
$855$	−6.54508	+	4.75528i	−0.223837	+	0.162627i
$856$	5.38854	+	16.5842i	0.184177	+	0.566837i
$857$	10.4164			0.355818			0.177909	−	0.984047i	$-0.443067\pi$
$857$	10.4164			0.355818			0.177909	+	0.984047i	$0.443067\pi$
$858$	1.29180	+	2.17963i	0.0441012	+	0.0744113i
$859$	6.18034	−	19.0211i	0.210870	−	0.648993i	−0.788551	−	0.614970i	$-0.789168\pi$
$859$	6.18034	−	19.0211i	0.210870	−	0.648993i	0.999421	−	0.0340227i	$-0.0108319\pi$
$860$	6.70820	+	20.6457i	0.228748	+	0.704014i
$861$	−33.2705			−1.13386
$862$	−14.6180			−0.497892
$863$	−8.10739	−	24.9520i	−0.275979	−	0.849375i	−0.988959	−	0.148191i	$-0.952655\pi$
$863$	−8.10739	−	24.9520i	−0.275979	−	0.849375i	0.712980	−	0.701184i	$-0.247345\pi$
$864$	4.54508	+	3.30220i	0.154627	+	0.112343i
$865$	9.89919	+	7.19218i	0.336582	+	0.244541i
$866$	−13.6525	−	9.91910i	−0.463930	−	0.337065i
$867$	−3.21885	−	9.90659i	−0.109318	−	0.336446i
$868$	−27.9787			−0.949659
$869$	−1.54508	+	16.5110i	−0.0524134	+	0.560097i
$870$	−4.40983	−	13.5721i	−0.149507	−	0.460136i
$871$	3.70820			0.125648
$872$	1.18034	+	3.63271i	0.0399714	+	0.123019i
$873$	−9.28115	+	6.74315i	−0.314119	+	0.228221i
$874$	−8.78115	+	6.37988i	−0.297027	+	0.215803i
$875$	33.5410			1.13389
$876$	−5.78115	−	17.7926i	−0.195327	−	0.601155i
$877$	−13.9787			−0.472028			−0.236014	−	0.971750i	$-0.575841\pi$
$877$	−13.9787			−0.472028			−0.236014	+	0.971750i	$0.575841\pi$
$878$	−17.6869			−0.596905
$879$	−4.88197	+	3.54696i	−0.164665	+	0.119636i
$880$	12.6246	+	5.44907i	0.425576	+	0.183688i
$881$	−23.1631	−	16.8290i	−0.780385	−	0.566983i	0.124709	−	0.992193i	$-0.460200\pi$
$881$	−23.1631	−	16.8290i	−0.780385	−	0.566983i	−0.905095	+	0.425210i	$0.860200\pi$
$882$	−1.00000	−	0.726543i	−0.0336718	−	0.0244640i
$883$	12.8090	−	9.30630i	0.431058	−	0.313182i	−0.351014	−	0.936370i	$-0.614163\pi$
$883$	12.8090	−	9.30630i	0.431058	−	0.313182i	0.782072	+	0.623188i	$0.214163\pi$
$884$	−10.4721			−0.352216
$885$	−10.0000	+	30.7768i	−0.336146	+	1.03455i
$886$	−10.6631	−	7.74721i	−0.358234	−	0.260273i
$887$	−47.3951			−1.59137			−0.795686	−	0.605709i	$-0.792890\pi$
$887$	−47.3951			−1.59137			−0.795686	+	0.605709i	$0.792890\pi$
$888$	3.88197	+	2.82041i	0.130270	+	0.0946469i
$889$	15.2188	−	46.8388i	0.510424	−	1.57092i
$890$	2.50000	+	1.81636i	0.0838002	+	0.0608844i
$891$	−3.04508	−	1.31433i	−0.102014	−	0.0440316i
$892$	−29.3435	−	21.3193i	−0.982492	−	0.713822i
$893$	−3.19098	−	2.31838i	−0.106782	−	0.0775818i
$894$	−3.19098	+	2.31838i	−0.106722	+	0.0775384i
$895$	−15.2254	+	46.8590i	−0.508930	+	1.56632i
$896$	10.5517	−	32.4747i	0.352506	−	1.08490i
$897$	−1.85410	+	5.70634i	−0.0619067	+	0.190529i
$898$	−10.2639	+	7.45718i	−0.342512	+	0.248849i
$899$	18.3926	−	56.6066i	0.613428	−	1.88794i
$900$	−2.50000	−	7.69421i	−0.0833333	−	0.256474i
$901$	58.8328			1.96001
$902$	−11.5902	−	19.5559i	−0.385910	−	0.651141i
$903$	−14.5623	+	10.5801i	−0.484603	+	0.352085i
$904$	−27.2361			−0.905858
$905$	22.6631	+	16.4657i	0.753348	+	0.547339i
$906$	−0.746711	+	2.29814i	−0.0248078	+	0.0763506i
$907$	−39.6074	+	28.7765i	−1.31514	+	0.955506i	−0.315163	+	0.949038i	$0.602059\pi$
$907$	−39.6074	+	28.7765i	−1.31514	+	0.955506i	−0.999979	+	0.00646883i	$0.997941\pi$
$908$	−21.3262			−0.707736
$909$	11.4721			0.380507
$910$	−5.12461			−0.169879
$911$	−1.22949	+	3.78398i	−0.0407348	+	0.125369i	−0.969356	−	0.245661i	$-0.920995\pi$
$911$	−1.22949	+	3.78398i	−0.0407348	+	0.125369i	0.928621	+	0.371030i	$0.120995\pi$
$912$	2.07295	−	6.37988i	0.0686422	−	0.211259i
$913$	−2.35410	+	25.1563i	−0.0779094	+	0.832550i
$914$	1.60081	+	4.92680i	0.0529502	+	0.162964i
$915$	8.51722	−	6.18812i	0.281571	−	0.204573i
$916$	−32.7254	−	23.7764i	−1.08128	−	0.785595i
$917$	−14.7812	+	45.4917i	−0.488117	+	1.50227i
$918$	−2.61803	+	1.90211i	−0.0864080	+	0.0627791i
$919$	6.70820			0.221283			0.110642	−	0.993860i	$-0.464709\pi$
$919$	6.70820			0.221283			0.110642	+	0.993860i	$0.464709\pi$
$920$	−7.50000	−	23.0826i	−0.247268	−	0.761012i
$921$	−0.517221	−	1.59184i	−0.0170430	−	0.0524530i
$922$	6.15905			0.202838
$923$	4.43769	+	13.6578i	0.146068	+	0.449553i
$924$	−1.50000	+	16.0292i	−0.0493464	+	0.527322i
$925$	−3.31559	−	10.2044i	−0.109016	−	0.335517i
$926$	13.7082	+	9.95959i	0.450480	+	0.327293i
$927$	−6.23607			−0.204819
$928$	46.9336	+	34.0993i	1.54067	+	1.11936i
$929$	7.09675	−	21.8415i	0.232837	−	0.716598i	−0.764564	−	0.644548i	$-0.777046\pi$
$929$	7.09675	−	21.8415i	0.232837	−	0.716598i	0.997401	−	0.0720503i	$-0.0229542\pi$
$930$	−2.46149	+	7.57570i	−0.0807155	+	0.248417i
$931$	−2.23607	+	6.88191i	−0.0732842	+	0.225545i
$932$	1.14590	−	3.52671i	0.0375351	−	0.115521i
$933$	−2.59017	−	7.97172i	−0.0847984	−	0.260983i
$934$	−3.63932	+	11.2007i	−0.119082	+	0.366497i
$935$	−25.6525	+	29.1522i	−0.838926	+	0.953380i
$936$	0.854102	+	2.62866i	0.0279172	+	0.0859203i
$937$	−12.5729	+	9.13478i	−0.410740	+	0.298420i	−0.773901	−	0.633306i	$-0.781697\pi$
$937$	−12.5729	+	9.13478i	−0.410740	+	0.298420i	0.363161	+	0.931726i	$0.381697\pi$
$938$	−4.50000	−	3.26944i	−0.146930	−	0.106751i
$939$	9.00000	−	6.53888i	0.293704	−	0.213388i
$940$	3.19098	−	2.31838i	0.104078	−	0.0756174i
$941$	−5.56231	−	17.1190i	−0.181326	−	0.558064i	0.818540	−	0.574450i	$-0.194784\pi$
$941$	−5.56231	−	17.1190i	−0.181326	−	0.558064i	−0.999866	+	0.0163859i	$0.994784\pi$
$942$	1.06231	−	3.26944i	0.0346118	−	0.106524i
$943$	16.6353	−	51.1981i	0.541718	−	1.66724i
$944$	−8.29180	−	25.5195i	−0.269875	−	0.830590i
$945$	5.42705	−	3.94298i	0.176542	−	0.128265i
$946$	−11.2918	−	4.87380i	−0.367128	−	0.158461i
$947$	−9.70820	+	7.05342i	−0.315474	+	0.229205i	−0.734242	−	0.678888i	$-0.762462\pi$
$947$	−9.70820	+	7.05342i	−0.315474	+	0.229205i	0.418768	+	0.908093i	$0.362462\pi$
$948$	−2.50000	+	7.69421i	−0.0811962	+	0.249896i
$949$	4.41641	−	13.5923i	0.143363	−	0.441225i
$950$	9.04508	−	6.57164i	0.293461	−	0.213212i
$951$	13.8541	−	10.0656i	0.449250	−	0.326399i
$952$	28.4164	+	20.6457i	0.920981	+	0.669132i
$953$	−29.6525	−	21.5438i	−0.960538	−	0.697872i	−0.00726230	−	0.999974i	$-0.502312\pi$
$953$	−29.6525	−	21.5438i	−0.960538	−	0.697872i	−0.953276	+	0.302102i	$0.902312\pi$
$954$	−2.14590	−	6.60440i	−0.0694760	−	0.213825i
$955$	1.11803	+	0.812299i	0.0361787	+	0.0262854i
$956$	13.7812	+	10.0126i	0.445714	+	0.323830i
$957$	−31.4443	−	13.5721i	−1.01645	−	0.438722i
$958$	−6.54508	−	4.75528i	−0.211462	−	0.153636i
$959$	34.0623	−	24.7477i	1.09993	−	0.799145i
$960$	0.427051	+	0.310271i	0.0137830	+	0.0100139i
$961$	−1.79837	+	1.30660i	−0.0580121	+	0.0421482i
$962$	0.506578	+	1.55909i	0.0163327	+	0.0502670i
$963$	−2.40983	−	7.41669i	−0.0776557	−	0.239000i
$964$	−0.736068	+	0.534785i	−0.0237072	+	0.0172243i
$965$	−21.0557			−0.677808
$966$	7.28115	−	5.29007i	0.234267	−	0.170205i
$967$	−1.51722	−	1.10233i	−0.0487905	−	0.0354484i	0.563123	−	0.826373i	$-0.309600\pi$
$967$	−1.51722	−	1.10233i	−0.0487905	−	0.0354484i	−0.611913	+	0.790925i	$0.709600\pi$
$968$	−22.2361	+	10.5146i	−0.714694	+	0.337953i
$969$	15.3262	+	11.1352i	0.492350	+	0.357713i
$970$	12.8262	−	9.31881i	0.411826	−	0.299209i
$971$	7.69098	+	23.6704i	0.246815	+	0.759620i	0.995333	+	0.0965043i	$0.0307661\pi$
$971$	7.69098	+	23.6704i	0.246815	+	0.759620i	−0.748517	+	0.663115i	$0.769234\pi$
$972$	−1.30902	−	0.951057i	−0.0419867	−	0.0305052i
$973$	9.57295	+	6.95515i	0.306895	+	0.222972i
$974$	1.76393	−	1.28157i	0.0565200	−	0.0410642i
$975$	1.90983	−	5.87785i	0.0611635	−	0.188242i
$976$	−2.69756	+	8.30224i	−0.0863468	+	0.265748i
$977$	13.6459	−	41.9978i	0.436571	−	1.34363i	−0.454897	−	0.890544i	$-0.650324\pi$
$977$	13.6459	−	41.9978i	0.436571	−	1.34363i	0.891468	−	0.453083i	$-0.149676\pi$
$978$	6.78115	−	4.92680i	0.216837	−	0.157542i
$979$	7.23607	−	1.62460i	0.231266	−	0.0519224i
$980$	−5.85410	−	4.25325i	−0.187002	−	0.135865i
$981$	−0.527864	−	1.62460i	−0.0168534	−	0.0518694i
$982$	3.33282	−	10.2574i	0.106354	−	0.327325i
$983$	−15.5451	+	47.8429i	−0.495811	+	1.52595i	0.319877	+	0.947459i	$0.396358\pi$
$983$	−15.5451	+	47.8429i	−0.495811	+	1.52595i	−0.815689	+	0.578491i	$0.803642\pi$
$984$	−7.66312	−	23.5847i	−0.244291	−	0.751851i
$985$	−21.8328			−0.695651
$986$	−27.0344	+	19.6417i	−0.860952	+	0.625518i
$987$	2.64590	+	1.92236i	0.0842199	+	0.0611893i
$988$	5.85410	−	4.25325i	0.186244	−	0.135314i
$989$	−9.00000	−	27.6992i	−0.286183	−	0.880782i
$990$	4.20820	+	1.81636i	0.133746	+	0.0577276i
$991$	6.79837	−	20.9232i	0.215957	−	0.664649i	−0.783127	−	0.621862i	$-0.786376\pi$
$991$	6.79837	−	20.9232i	0.215957	−	0.664649i	0.999084	−	0.0427866i	$-0.0136236\pi$
$992$	−10.0066	−	30.7971i	−0.317709	−	0.977808i
$993$	2.08359	−	6.41264i	0.0661208	−	0.203499i
$994$	6.65654	−	20.4867i	0.211133	−	0.649800i
$995$	26.7705	+	19.4499i	0.848682	+	0.616604i
$996$	−3.80902	+	11.7229i	−0.120693	+	0.371456i
$997$	33.0795	+	24.0337i	1.04764	+	0.761154i	0.971762	−	0.235963i	$-0.0758244\pi$
$997$	33.0795	+	24.0337i	1.04764	+	0.761154i	0.0758770	+	0.997117i	$0.475824\pi$
$998$	15.5279			0.491526
$999$	−1.73607	−	1.26133i	−0.0549268	−	0.0399066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.o.b.631.1	yes	4
11.3	even	5		825.2.m.a.256.1	✓	4
25.21	even	5		825.2.m.a.796.1	yes	4
275.146	even	5	inner	825.2.o.b.421.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.m.a.256.1	✓	4	11.3	even	5
825.2.m.a.796.1	yes	4	25.21	even	5
825.2.o.b.421.1	yes	4	275.146	even	5	inner
825.2.o.b.631.1	yes	4	1.1	even	1	trivial

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.o (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{4} +(1.80902 + 1.31433i) q^{5} -0.618034 q^{6} +(-0.927051 - 2.85317i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.190983 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{4} +(1.80902 + 1.31433i) q^{5} -0.618034 q^{6} +(-0.927051 - 2.85317i) q^{7} +(1.80902 - 1.31433i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(1.11803 - 0.812299i) q^{10} +(0.309017 - 3.30220i) q^{11} +(0.500000 - 1.53884i) q^{12} +(1.00000 - 0.726543i) q^{13} -1.85410 q^{14} +(0.690983 - 2.12663i) q^{15} +(0.572949 + 1.76336i) q^{16} -5.23607 q^{17} +(0.190983 + 0.587785i) q^{18} +(2.92705 - 2.12663i) q^{19} +(1.11803 + 3.44095i) q^{20} +(-2.42705 + 1.76336i) q^{21} +(-1.88197 - 0.812299i) q^{22} +(-1.50000 - 4.61653i) q^{23} +(-1.80902 - 1.31433i) q^{24} +(1.54508 + 4.75528i) q^{25} +(-0.236068 - 0.726543i) q^{26} +(0.809017 + 0.587785i) q^{27} +(1.50000 - 4.61653i) q^{28} +(8.35410 + 6.06961i) q^{29} +(-1.11803 - 0.812299i) q^{30} +(-1.78115 - 5.48183i) q^{31} +5.61803 q^{32} +(-3.23607 + 0.726543i) q^{33} +(-1.00000 + 3.07768i) q^{34} +(2.07295 - 6.37988i) q^{35} -1.61803 q^{36} -2.14590 q^{37} +(-0.690983 - 2.12663i) q^{38} +(-1.00000 - 0.726543i) q^{39} +5.00000 q^{40} +(8.97214 + 6.51864i) q^{41} +(0.572949 + 1.76336i) q^{42} +6.00000 q^{43} +(3.54508 - 4.02874i) q^{44} -2.23607 q^{45} -3.00000 q^{46} +(-0.336881 - 1.03681i) q^{47} +(1.50000 - 1.08981i) q^{48} +(-1.61803 + 1.17557i) q^{49} +3.09017 q^{50} +(1.61803 + 4.97980i) q^{51} +2.00000 q^{52} -11.2361 q^{53} +(0.500000 - 0.363271i) q^{54} +(4.89919 - 5.56758i) q^{55} +(-5.42705 - 3.94298i) q^{56} +(-2.92705 - 2.12663i) q^{57} +(5.16312 - 3.75123i) q^{58} -14.4721 q^{59} +(2.92705 - 2.12663i) q^{60} +(3.80902 + 2.76741i) q^{61} -3.56231 q^{62} +(2.42705 + 1.76336i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +2.76393 q^{65} +(-0.190983 + 2.04087i) q^{66} +(2.42705 + 1.76336i) q^{67} +(-6.85410 - 4.97980i) q^{68} +(-3.92705 + 2.85317i) q^{69} +(-3.35410 - 2.43690i) q^{70} +(-3.59017 + 11.0494i) q^{71} +(-0.690983 + 2.12663i) q^{72} +(9.35410 - 6.79615i) q^{73} +(-0.409830 + 1.26133i) q^{74} +(4.04508 - 2.93893i) q^{75} +5.85410 q^{76} +(-9.70820 + 2.17963i) q^{77} +(-0.618034 + 0.449028i) q^{78} -5.00000 q^{79} +(-1.28115 + 3.94298i) q^{80} +(0.309017 - 0.951057i) q^{81} +(5.54508 - 4.02874i) q^{82} -7.61803 q^{83} -4.85410 q^{84} +(-9.47214 - 6.88191i) q^{85} +(1.14590 - 3.52671i) q^{86} +(3.19098 - 9.82084i) q^{87} +(-3.78115 - 6.37988i) q^{88} +(0.690983 + 2.12663i) q^{89} +(-0.427051 + 1.31433i) q^{90} +(-3.00000 - 2.17963i) q^{91} +(2.42705 - 7.46969i) q^{92} +(-4.66312 + 3.38795i) q^{93} -0.673762 q^{94} +8.09017 q^{95} +(-1.73607 - 5.34307i) q^{96} +11.4721 q^{97} +(0.381966 + 1.17557i) q^{98} +(1.69098 + 2.85317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + 2 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{14} + 5 q^{15} + 9 q^{16} - 12 q^{17} + 3 q^{18} + 5 q^{19} - 3 q^{21} - 12 q^{22} - 6 q^{23} - 5 q^{24} - 5 q^{25} + 8 q^{26} + q^{27} + 6 q^{28} + 20 q^{29} + 13 q^{31} + 18 q^{32} - 4 q^{33} - 4 q^{34} + 15 q^{35} - 2 q^{36} - 22 q^{37} - 5 q^{38} - 4 q^{39} + 20 q^{40} + 18 q^{41} + 9 q^{42} + 24 q^{43} + 3 q^{44} - 12 q^{46} - 17 q^{47} + 6 q^{48} - 2 q^{49} - 10 q^{50} + 2 q^{51} + 8 q^{52} - 36 q^{53} + 2 q^{54} - 5 q^{55} - 15 q^{56} - 5 q^{57} + 5 q^{58} - 40 q^{59} + 5 q^{60} + 13 q^{61} + 26 q^{62} + 3 q^{63} - 7 q^{64} + 20 q^{65} - 3 q^{66} + 3 q^{67} - 14 q^{68} - 9 q^{69} + 8 q^{71} - 5 q^{72} + 24 q^{73} - 24 q^{74} + 5 q^{75} + 10 q^{76} - 12 q^{77} + 2 q^{78} - 20 q^{79} + 15 q^{80} - q^{81} + 11 q^{82} - 26 q^{83} - 6 q^{84} - 20 q^{85} + 18 q^{86} + 15 q^{87} + 5 q^{88} + 5 q^{89} + 5 q^{90} - 12 q^{91} + 3 q^{92} - 3 q^{93} - 34 q^{94} + 10 q^{95} + 2 q^{96} + 28 q^{97} + 6 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + 2 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - q^11 + 2 * q^12 + 4 * q^13 + 6 * q^14 + 5 * q^15 + 9 * q^16 - 12 * q^17 + 3 * q^18 + 5 * q^19 - 3 * q^21 - 12 * q^22 - 6 * q^23 - 5 * q^24 - 5 * q^25 + 8 * q^26 + q^27 + 6 * q^28 + 20 * q^29 + 13 * q^31 + 18 * q^32 - 4 * q^33 - 4 * q^34 + 15 * q^35 - 2 * q^36 - 22 * q^37 - 5 * q^38 - 4 * q^39 + 20 * q^40 + 18 * q^41 + 9 * q^42 + 24 * q^43 + 3 * q^44 - 12 * q^46 - 17 * q^47 + 6 * q^48 - 2 * q^49 - 10 * q^50 + 2 * q^51 + 8 * q^52 - 36 * q^53 + 2 * q^54 - 5 * q^55 - 15 * q^56 - 5 * q^57 + 5 * q^58 - 40 * q^59 + 5 * q^60 + 13 * q^61 + 26 * q^62 + 3 * q^63 - 7 * q^64 + 20 * q^65 - 3 * q^66 + 3 * q^67 - 14 * q^68 - 9 * q^69 + 8 * q^71 - 5 * q^72 + 24 * q^73 - 24 * q^74 + 5 * q^75 + 10 * q^76 - 12 * q^77 + 2 * q^78 - 20 * q^79 + 15 * q^80 - q^81 + 11 * q^82 - 26 * q^83 - 6 * q^84 - 20 * q^85 + 18 * q^86 + 15 * q^87 + 5 * q^88 + 5 * q^89 + 5 * q^90 - 12 * q^91 + 3 * q^92 - 3 * q^93 - 34 * q^94 + 10 * q^95 + 2 * q^96 + 28 * q^97 + 6 * q^98 + 9 * q^99

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