LMFDB - Embedded newform 325.2.l.a.261.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(66,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("325.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.l (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:	$2.59513806569$
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			261.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	325.261
Dual form			325.2.l.a.66.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 - 0.951057i) q^{2} +(-0.118034 + 0.363271i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(0.190983 + 0.587785i) q^{6} +2.85410 q^{7} +(0.690983 + 2.12663i) q^{8} +(2.30902 + 1.67760i) q^{9} +O(q^{10})$	\(q+(1.30902 - 0.951057i) q^{2} +(-0.118034 + 0.363271i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(0.190983 + 0.587785i) q^{6} +2.85410 q^{7} +(0.690983 + 2.12663i) q^{8} +(2.30902 + 1.67760i) q^{9} +(-1.11803 + 3.44095i) q^{10} +(0.190983 - 0.138757i) q^{11} +(0.190983 + 0.138757i) q^{12} +(0.809017 + 0.587785i) q^{13} +(3.73607 - 2.71441i) q^{14} +(-0.263932 - 0.812299i) q^{15} +(3.92705 + 2.85317i) q^{16} +(-1.61803 - 4.97980i) q^{17} +4.61803 q^{18} +(-1.54508 - 4.75528i) q^{19} +(0.427051 + 1.31433i) q^{20} +(-0.336881 + 1.03681i) q^{21} +(0.118034 - 0.363271i) q^{22} +(-3.30902 + 2.40414i) q^{23} -0.854102 q^{24} +(1.54508 - 4.75528i) q^{25} +1.61803 q^{26} +(-1.80902 + 1.31433i) q^{27} +(0.545085 - 1.67760i) q^{28} +(-1.11803 - 0.812299i) q^{30} +(2.42705 + 7.46969i) q^{31} +3.38197 q^{32} +(0.0278640 + 0.0857567i) q^{33} +(-6.85410 - 4.97980i) q^{34} +(-5.16312 + 3.75123i) q^{35} +(1.42705 - 1.03681i) q^{36} +(1.73607 + 1.26133i) q^{37} +(-6.54508 - 4.75528i) q^{38} +(-0.309017 + 0.224514i) q^{39} +(-4.04508 - 2.93893i) q^{40} +(-4.54508 - 3.30220i) q^{41} +(0.545085 + 1.67760i) q^{42} -3.47214 q^{43} +(-0.0450850 - 0.138757i) q^{44} -6.38197 q^{45} +(-2.04508 + 6.29412i) q^{46} +(2.26393 - 6.96767i) q^{47} +(-1.50000 + 1.08981i) q^{48} +1.14590 q^{49} +(-2.50000 - 7.69421i) q^{50} +2.00000 q^{51} +(0.500000 - 0.363271i) q^{52} +(2.28115 - 7.02067i) q^{53} +(-1.11803 + 3.44095i) q^{54} +(-0.163119 + 0.502029i) q^{55} +(1.97214 + 6.06961i) q^{56} +1.90983 q^{57} +(-1.80902 - 1.31433i) q^{59} -0.527864 q^{60} +(-0.236068 + 0.171513i) q^{61} +(10.2812 + 7.46969i) q^{62} +(6.59017 + 4.78804i) q^{63} +(-3.42705 + 2.48990i) q^{64} -2.23607 q^{65} +(0.118034 + 0.0857567i) q^{66} +(-2.57295 - 7.91872i) q^{67} -3.23607 q^{68} +(-0.482779 - 1.48584i) q^{69} +(-3.19098 + 9.82084i) q^{70} +(0.354102 - 1.08981i) q^{71} +(-1.97214 + 6.06961i) q^{72} +(8.66312 - 6.29412i) q^{73} +3.47214 q^{74} +(1.54508 + 1.12257i) q^{75} -3.09017 q^{76} +(0.545085 - 0.396027i) q^{77} +(-0.190983 + 0.587785i) q^{78} +(3.35410 - 10.3229i) q^{79} -10.8541 q^{80} +(2.38197 + 7.33094i) q^{81} -9.09017 q^{82} +(-1.60081 - 4.92680i) q^{83} +(0.545085 + 0.396027i) q^{84} +(9.47214 + 6.88191i) q^{85} +(-4.54508 + 3.30220i) q^{86} +(0.427051 + 0.310271i) q^{88} +(-9.04508 + 6.57164i) q^{89} +(-8.35410 + 6.06961i) q^{90} +(2.30902 + 1.67760i) q^{91} +(0.781153 + 2.40414i) q^{92} -3.00000 q^{93} +(-3.66312 - 11.2739i) q^{94} +(9.04508 + 6.57164i) q^{95} +(-0.399187 + 1.22857i) q^{96} +(3.28115 - 10.0984i) q^{97} +(1.50000 - 1.08981i) q^{98} +0.673762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} + 5 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 + 5 * q^8 + 7 * q^9	\( 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} + 5 q^{8} + 7 q^{9} + 3 q^{11} + 3 q^{12} + q^{13} + 6 q^{14} - 10 q^{15} + 9 q^{16} - 2 q^{17} + 14 q^{18} + 5 q^{19} - 5 q^{20} - 17 q^{21} - 4 q^{22} - 11 q^{23} + 10 q^{24} - 5 q^{25} + 2 q^{26} - 5 q^{27} - 9 q^{28} + 3 q^{31} + 18 q^{32} + 18 q^{33} - 14 q^{34} - 5 q^{35} - q^{36} - 2 q^{37} - 15 q^{38} + q^{39} - 5 q^{40} - 7 q^{41} - 9 q^{42} + 4 q^{43} + 11 q^{44} - 30 q^{45} + 3 q^{46} + 18 q^{47} - 6 q^{48} + 18 q^{49} - 10 q^{50} + 8 q^{51} + 2 q^{52} - 11 q^{53} + 15 q^{55} - 10 q^{56} + 30 q^{57} - 5 q^{59} - 20 q^{60} + 8 q^{61} + 21 q^{62} + 4 q^{63} - 7 q^{64} - 4 q^{66} - 17 q^{67} - 4 q^{68} - 31 q^{69} - 15 q^{70} - 12 q^{71} + 10 q^{72} + 19 q^{73} - 4 q^{74} - 5 q^{75} + 10 q^{76} - 9 q^{77} - 3 q^{78} - 30 q^{80} + 14 q^{81} - 14 q^{82} - 31 q^{83} - 9 q^{84} + 20 q^{85} - 7 q^{86} - 5 q^{88} - 25 q^{89} - 20 q^{90} + 7 q^{91} - 17 q^{92} - 12 q^{93} + q^{94} + 25 q^{95} + 23 q^{96} - 7 q^{97} + 6 q^{98} + 34 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 + 5 * q^8 + 7 * q^9 + 3 * q^11 + 3 * q^12 + q^13 + 6 * q^14 - 10 * q^15 + 9 * q^16 - 2 * q^17 + 14 * q^18 + 5 * q^19 - 5 * q^20 - 17 * q^21 - 4 * q^22 - 11 * q^23 + 10 * q^24 - 5 * q^25 + 2 * q^26 - 5 * q^27 - 9 * q^28 + 3 * q^31 + 18 * q^32 + 18 * q^33 - 14 * q^34 - 5 * q^35 - q^36 - 2 * q^37 - 15 * q^38 + q^39 - 5 * q^40 - 7 * q^41 - 9 * q^42 + 4 * q^43 + 11 * q^44 - 30 * q^45 + 3 * q^46 + 18 * q^47 - 6 * q^48 + 18 * q^49 - 10 * q^50 + 8 * q^51 + 2 * q^52 - 11 * q^53 + 15 * q^55 - 10 * q^56 + 30 * q^57 - 5 * q^59 - 20 * q^60 + 8 * q^61 + 21 * q^62 + 4 * q^63 - 7 * q^64 - 4 * q^66 - 17 * q^67 - 4 * q^68 - 31 * q^69 - 15 * q^70 - 12 * q^71 + 10 * q^72 + 19 * q^73 - 4 * q^74 - 5 * q^75 + 10 * q^76 - 9 * q^77 - 3 * q^78 - 30 * q^80 + 14 * q^81 - 14 * q^82 - 31 * q^83 - 9 * q^84 + 20 * q^85 - 7 * q^86 - 5 * q^88 - 25 * q^89 - 20 * q^90 + 7 * q^91 - 17 * q^92 - 12 * q^93 + q^94 + 25 * q^95 + 23 * q^96 - 7 * q^97 + 6 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	1.30902	−	0.951057i	0.925615	−	0.672499i	−0.0193004	−	0.999814i	$-0.506144\pi$
$2$	1.30902	−	0.951057i	0.925615	−	0.672499i	0.944915	+	0.327315i	$0.106144\pi$
$3$	−0.118034	+	0.363271i	−0.0681470	+	0.209735i	−0.979331	−	0.202265i	$-0.935170\pi$
$3$	−0.118034	+	0.363271i	−0.0681470	+	0.209735i	0.911184	+	0.412000i	$0.135170\pi$
$4$	0.190983	−	0.587785i	0.0954915	−	0.293893i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$6$	0.190983	+	0.587785i	0.0779685	+	0.239962i
$7$	2.85410			1.07875			0.539375	−	0.842066i	$-0.318661\pi$
$7$	2.85410			1.07875			0.539375	+	0.842066i	$0.318661\pi$
$8$	0.690983	+	2.12663i	0.244299	+	0.751876i
$9$	2.30902	+	1.67760i	0.769672	+	0.559200i
$10$	−1.11803	+	3.44095i	−0.353553	+	1.08813i
$11$	0.190983	−	0.138757i	0.0575835	−	0.0418369i	−0.558621	−	0.829423i	$-0.688669\pi$
$11$	0.190983	−	0.138757i	0.0575835	−	0.0418369i	0.616205	+	0.787586i	$0.288669\pi$
$12$	0.190983	+	0.138757i	0.0551320	+	0.0400558i
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i
$13$	0.809017	+	0.587785i	0.224381	+	0.163022i
$14$	3.73607	−	2.71441i	0.998506	−	0.725457i
$15$	−0.263932	−	0.812299i	−0.0681470	−	0.209735i
$16$	3.92705	+	2.85317i	0.981763	+	0.713292i
$17$	−1.61803	−	4.97980i	−0.392431	−	1.20778i	−0.930944	−	0.365161i	$-0.881014\pi$
$17$	−1.61803	−	4.97980i	−0.392431	−	1.20778i	0.538513	−	0.842617i	$-0.318986\pi$
$18$	4.61803			1.08848
$19$	−1.54508	−	4.75528i	−0.354467	−	1.09094i	−0.956318	−	0.292328i	$-0.905570\pi$
$19$	−1.54508	−	4.75528i	−0.354467	−	1.09094i	0.601851	−	0.798608i	$-0.294430\pi$
$20$	0.427051	+	1.31433i	0.0954915	+	0.293893i
$21$	−0.336881	+	1.03681i	−0.0735135	+	0.226251i
$22$	0.118034	−	0.363271i	0.0251649	−	0.0774497i
$23$	−3.30902	+	2.40414i	−0.689978	+	0.501298i	−0.876653	−	0.481124i	$-0.840229\pi$
$23$	−3.30902	+	2.40414i	−0.689978	+	0.501298i	0.186675	+	0.982422i	$0.440229\pi$
$24$	−0.854102			−0.174343
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	1.61803			0.317323
$27$	−1.80902	+	1.31433i	−0.348145	+	0.252942i
$28$	0.545085	−	1.67760i	0.103011	−	0.317036i
$29$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$29$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$30$	−1.11803	−	0.812299i	−0.204124	−	0.148305i
$31$	2.42705	+	7.46969i	0.435911	+	1.34160i	0.892150	+	0.451739i	$0.149196\pi$
$31$	2.42705	+	7.46969i	0.435911	+	1.34160i	−0.456239	+	0.889857i	$0.650804\pi$
$32$	3.38197			0.597853
$33$	0.0278640	+	0.0857567i	0.00485051	+	0.0149283i
$34$	−6.85410	−	4.97980i	−1.17547	−	0.854028i
$35$	−5.16312	+	3.75123i	−0.872726	+	0.634073i
$36$	1.42705	−	1.03681i	0.237842	−	0.172802i
$37$	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	$0.643557\pi$
$38$	−6.54508	−	4.75528i	−1.06175	−	0.771409i
$39$	−0.309017	+	0.224514i	−0.0494823	+	0.0359510i
$40$	−4.04508	−	2.93893i	−0.639584	−	0.464685i
$41$	−4.54508	−	3.30220i	−0.709823	−	0.515717i	0.173294	−	0.984870i	$-0.444559\pi$
$41$	−4.54508	−	3.30220i	−0.709823	−	0.515717i	−0.883117	+	0.469154i	$0.844559\pi$
$42$	0.545085	+	1.67760i	0.0841084	+	0.258859i
$43$	−3.47214			−0.529496			−0.264748	−	0.964318i	$-0.585289\pi$
$43$	−3.47214			−0.529496			−0.264748	+	0.964318i	$0.585289\pi$
$44$	−0.0450850	−	0.138757i	−0.00679682	−	0.0209184i
$45$	−6.38197			−0.951367
$46$	−2.04508	+	6.29412i	−0.301531	+	0.928018i
$47$	2.26393	−	6.96767i	0.330228	−	1.01634i	−0.638797	−	0.769376i	$-0.720567\pi$
$47$	2.26393	−	6.96767i	0.330228	−	1.01634i	0.969025	−	0.246963i	$-0.0794326\pi$
$48$	−1.50000	+	1.08981i	−0.216506	+	0.157301i
$49$	1.14590			0.163700
$50$	−2.50000	−	7.69421i	−0.353553	−	1.08813i
$51$	2.00000			0.280056
$52$	0.500000	−	0.363271i	0.0693375	−	0.0503767i
$53$	2.28115	−	7.02067i	0.313340	−	0.964363i	−0.663092	−	0.748538i	$-0.730756\pi$
$53$	2.28115	−	7.02067i	0.313340	−	0.964363i	0.976432	−	0.215825i	$-0.0692439\pi$
$54$	−1.11803	+	3.44095i	−0.152145	+	0.468255i
$55$	−0.163119	+	0.502029i	−0.0219950	+	0.0676935i
$56$	1.97214	+	6.06961i	0.263538	+	0.811086i
$57$	1.90983			0.252963
$58$		0			0
$59$	−1.80902	−	1.31433i	−0.235514	−	0.171111i	0.463768	−	0.885956i	$-0.346497\pi$
$59$	−1.80902	−	1.31433i	−0.235514	−	0.171111i	−0.699282	+	0.714846i	$0.746497\pi$
$60$	−0.527864			−0.0681470
$61$	−0.236068	+	0.171513i	−0.0302254	+	0.0219600i	−0.602795	−	0.797896i	$-0.705946\pi$
$61$	−0.236068	+	0.171513i	−0.0302254	+	0.0219600i	0.572570	+	0.819856i	$0.305946\pi$
$62$	10.2812	+	7.46969i	1.30571	+	0.948652i
$63$	6.59017	+	4.78804i	0.830283	+	0.603236i
$64$	−3.42705	+	2.48990i	−0.428381	+	0.311237i
$65$	−2.23607			−0.277350
$66$	0.118034	+	0.0857567i	0.0145290	+	0.0105559i
$67$	−2.57295	−	7.91872i	−0.314336	−	0.967426i	−0.976027	−	0.217650i	$-0.930161\pi$
$67$	−2.57295	−	7.91872i	−0.314336	−	0.967426i	0.661691	−	0.749776i	$-0.269839\pi$
$68$	−3.23607			−0.392431
$69$	−0.482779	−	1.48584i	−0.0581198	−	0.178874i
$70$	−3.19098	+	9.82084i	−0.381395	+	1.17381i
$71$	0.354102	−	1.08981i	0.0420242	−	0.129337i	−0.927843	−	0.372970i	$-0.878339\pi$
$71$	0.354102	−	1.08981i	0.0420242	−	0.129337i	0.969867	+	0.243633i	$0.0783393\pi$
$72$	−1.97214	+	6.06961i	−0.232418	+	0.715310i
$73$	8.66312	−	6.29412i	1.01394	−	0.736672i	0.0489093	−	0.998803i	$-0.484425\pi$
$73$	8.66312	−	6.29412i	1.01394	−	0.736672i	0.965032	+	0.262132i	$0.0844255\pi$
$74$	3.47214			0.403628
$75$	1.54508	+	1.12257i	0.178411	+	0.129623i
$76$	−3.09017			−0.354467
$77$	0.545085	−	0.396027i	0.0621182	−	0.0451315i
$78$	−0.190983	+	0.587785i	−0.0216246	+	0.0665536i
$79$	3.35410	−	10.3229i	0.377366	−	1.16141i	−0.564503	−	0.825431i	$-0.690932\pi$
$79$	3.35410	−	10.3229i	0.377366	−	1.16141i	0.941869	−	0.335982i	$-0.109068\pi$
$80$	−10.8541			−1.21353
$81$	2.38197	+	7.33094i	0.264663	+	0.814549i
$82$	−9.09017			−1.00384
$83$	−1.60081	−	4.92680i	−0.175712	−	0.540786i	0.823953	−	0.566658i	$-0.191764\pi$
$83$	−1.60081	−	4.92680i	−0.175712	−	0.540786i	−0.999665	+	0.0258717i	$0.991764\pi$
$84$	0.545085	+	0.396027i	0.0594736	+	0.0432101i
$85$	9.47214	+	6.88191i	1.02740	+	0.746448i
$86$	−4.54508	+	3.30220i	−0.490109	+	0.356085i
$87$		0			0
$88$	0.427051	+	0.310271i	0.0455238	+	0.0330750i
$89$	−9.04508	+	6.57164i	−0.958777	+	0.696592i	−0.952866	−	0.303390i	$-0.901881\pi$
$89$	−9.04508	+	6.57164i	−0.958777	+	0.696592i	−0.00591068	+	0.999983i	$0.501881\pi$
$90$	−8.35410	+	6.06961i	−0.880600	+	0.639793i
$91$	2.30902	+	1.67760i	0.242051	+	0.175860i
$92$	0.781153	+	2.40414i	0.0814408	+	0.250649i
$93$	−3.00000			−0.311086
$94$	−3.66312	−	11.2739i	−0.377822	−	1.16282i
$95$	9.04508	+	6.57164i	0.928006	+	0.674236i
$96$	−0.399187	+	1.22857i	−0.0407418	+	0.125391i
$97$	3.28115	−	10.0984i	0.333151	−	1.02533i	−0.634475	−	0.772943i	$-0.718784\pi$
$97$	3.28115	−	10.0984i	0.333151	−	1.02533i	0.967626	−	0.252389i	$-0.0812162\pi$
$98$	1.50000	−	1.08981i	0.151523	−	0.110088i
$99$	0.673762			0.0677156
$100$	−2.50000	−	1.81636i	−0.250000	−	0.181636i
$101$	−9.70820			−0.966002			−0.483001	−	0.875620i	$-0.660453\pi$
$101$	−9.70820			−0.966002			−0.483001	+	0.875620i	$0.660453\pi$
$102$	2.61803	−	1.90211i	0.259224	−	0.188337i
$103$	2.97214	−	9.14729i	0.292853	−	0.901310i	−0.691081	−	0.722777i	$-0.742865\pi$
$103$	2.97214	−	9.14729i	0.292853	−	0.901310i	0.983934	−	0.178532i	$-0.0571349\pi$
$104$	−0.690983	+	2.12663i	−0.0677565	+	0.208533i
$105$	−0.753289	−	2.31838i	−0.0735135	−	0.226251i
$106$	−3.69098	−	11.3597i	−0.358500	−	1.10335i
$107$	−15.2361			−1.47293			−0.736463	−	0.676478i	$-0.763506\pi$
$107$	−15.2361			−1.47293			−0.736463	+	0.676478i	$0.763506\pi$
$108$	0.427051	+	1.31433i	0.0410930	+	0.126471i
$109$	10.8541	+	7.88597i	1.03963	+	0.755339i	0.970214	−	0.242249i	$-0.0778851\pi$
$109$	10.8541	+	7.88597i	1.03963	+	0.755339i	0.0694203	+	0.997588i	$0.477885\pi$
$110$	0.263932	+	0.812299i	0.0251649	+	0.0774497i
$111$	−0.663119	+	0.481784i	−0.0629405	+	0.0457289i
$112$	11.2082	+	8.14324i	1.05908	+	0.769464i
$113$	9.35410	+	6.79615i	0.879960	+	0.639328i	0.933241	−	0.359251i	$-0.116968\pi$
$113$	9.35410	+	6.79615i	0.879960	+	0.639328i	−0.0532810	+	0.998580i	$0.516968\pi$
$114$	2.50000	−	1.81636i	0.234146	−	0.170117i
$115$	2.82624	−	8.69827i	0.263548	−	0.811117i
$116$		0			0
$117$	0.881966	+	2.71441i	0.0815378	+	0.250948i
$118$	−3.61803			−0.333067
$119$	−4.61803	−	14.2128i	−0.423334	−	1.30289i
$120$	1.54508	−	1.12257i	0.141046	−	0.102476i
$121$	−3.38197	+	10.4086i	−0.307451	+	0.946238i
$122$	−0.145898	+	0.449028i	−0.0132090	+	0.0406531i
$123$	1.73607	−	1.26133i	0.156536	−	0.113730i
$124$	4.85410			0.435911
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$	13.1803			1.17420
$127$	−3.69098	+	2.68166i	−0.327522	+	0.237959i	−0.739378	−	0.673290i	$-0.764880\pi$
$127$	−3.69098	+	2.68166i	−0.327522	+	0.237959i	0.411857	+	0.911249i	$0.364880\pi$
$128$	−4.20820	+	12.9515i	−0.371956	+	1.14476i
$129$	0.409830	−	1.26133i	0.0360835	−	0.111054i
$130$	−2.92705	+	2.12663i	−0.256719	+	0.186518i
$131$	3.38197	+	10.4086i	0.295484	+	0.909405i	0.983059	+	0.183292i	$0.0586753\pi$
$131$	3.38197	+	10.4086i	0.295484	+	0.909405i	−0.687575	+	0.726114i	$0.741325\pi$
$132$	0.0557281			0.00485051
$133$	−4.40983	−	13.5721i	−0.382381	−	1.17685i
$134$	−10.8992	−	7.91872i	−0.941546	−	0.684073i
$135$	1.54508	−	4.75528i	0.132980	−	0.409270i
$136$	9.47214	−	6.88191i	0.812229	−	0.590119i
$137$	16.8992	+	12.2780i	1.44379	+	1.04898i	0.987232	+	0.159287i	$0.0509196\pi$
$137$	16.8992	+	12.2780i	1.44379	+	1.04898i	0.456563	+	0.889691i	$0.349080\pi$
$138$	−2.04508	−	1.48584i	−0.174089	−	0.126483i
$139$	−9.89919	+	7.19218i	−0.839638	+	0.610033i	−0.922270	−	0.386547i	$-0.873668\pi$
$139$	−9.89919	+	7.19218i	−0.839638	+	0.610033i	0.0826315	+	0.996580i	$0.473668\pi$
$140$	1.21885	+	3.75123i	0.103011	+	0.317036i
$141$	2.26393	+	1.64484i	0.190657	+	0.138521i
$142$	−0.572949	−	1.76336i	−0.0480808	−	0.147978i
$143$	0.236068			0.0197410
$144$	4.28115	+	13.1760i	0.356763	+	1.09800i
$145$		0			0
$146$	5.35410	−	16.4782i	0.443109	−	1.36375i
$147$	−0.135255	+	0.416272i	−0.0111556	+	0.0343335i
$148$	1.07295	−	0.779543i	0.0881959	−	0.0640780i
$149$	−7.23607			−0.592802			−0.296401	−	0.955064i	$-0.595786\pi$
$149$	−7.23607			−0.592802			−0.296401	+	0.955064i	$0.595786\pi$
$150$	3.09017			0.252311
$151$	7.32624			0.596201			0.298100	−	0.954535i	$-0.403647\pi$
$151$	7.32624			0.596201			0.298100	+	0.954535i	$0.403647\pi$
$152$	9.04508	−	6.57164i	0.733653	−	0.533030i
$153$	4.61803	−	14.2128i	0.373346	−	1.14904i
$154$	0.336881	−	1.03681i	0.0271466	−	0.0835488i
$155$	−14.2082	−	10.3229i	−1.14123	−	0.829152i
$156$	0.0729490	+	0.224514i	0.00584060	+	0.0179755i
$157$	−5.56231			−0.443920			−0.221960	−	0.975056i	$-0.571245\pi$
$157$	−5.56231			−0.443920			−0.221960	+	0.975056i	$0.571245\pi$
$158$	−5.42705	−	16.7027i	−0.431753	−	1.32880i
$159$	2.28115	+	1.65735i	0.180907	+	0.131437i
$160$	−6.11803	+	4.44501i	−0.483673	+	0.351409i
$161$	−9.44427	+	6.86167i	−0.744313	+	0.540775i
$162$	10.0902	+	7.33094i	0.792759	+	0.575973i
$163$	1.16312	+	0.845055i	0.0911025	+	0.0661898i	0.632404	−	0.774639i	$-0.282068\pi$
$163$	1.16312	+	0.845055i	0.0911025	+	0.0661898i	−0.541302	+	0.840829i	$0.682068\pi$
$164$	−2.80902	+	2.04087i	−0.219347	+	0.159365i
$165$	−0.163119	−	0.118513i	−0.0126988	−	0.00922621i
$166$	−6.78115	−	4.92680i	−0.526320	−	0.382394i
$167$	−1.71885	−	5.29007i	−0.133008	−	0.409358i	0.862267	−	0.506455i	$-0.169044\pi$
$167$	−1.71885	−	5.29007i	−0.133008	−	0.409358i	−0.995275	+	0.0970971i	$0.969044\pi$
$168$	−2.43769			−0.188072
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	18.9443			1.45296
$171$	4.40983	−	13.5721i	0.337228	−	1.03788i
$172$	−0.663119	+	2.04087i	−0.0505623	+	0.155615i
$173$	13.1353	−	9.54332i	0.998655	−	0.725565i	0.0368556	−	0.999321i	$-0.488266\pi$
$173$	13.1353	−	9.54332i	0.998655	−	0.725565i	0.961799	+	0.273755i	$0.0882659\pi$
$174$		0			0
$175$	4.40983	−	13.5721i	0.333352	−	1.02595i
$176$	1.14590			0.0863753
$177$	0.690983	−	0.502029i	0.0519375	−	0.0377348i
$178$	−5.59017	+	17.2048i	−0.419001	+	1.28955i
$179$	−6.70820	+	20.6457i	−0.501395	+	1.54313i	0.305354	+	0.952239i	$0.401225\pi$
$179$	−6.70820	+	20.6457i	−0.501395	+	1.54313i	−0.806748	+	0.590895i	$0.798775\pi$
$180$	−1.21885	+	3.75123i	−0.0908475	+	0.279600i
$181$	1.40983	+	4.33901i	0.104792	+	0.322516i	0.989682	−	0.143284i	$-0.0457664\pi$
$181$	1.40983	+	4.33901i	0.104792	+	0.322516i	−0.884890	+	0.465801i	$0.845766\pi$
$182$	4.61803			0.342311
$183$	−0.0344419	−	0.106001i	−0.00254602	−	0.00783583i
$184$	−7.39919	−	5.37582i	−0.545475	−	0.396311i
$185$	−4.79837			−0.352783
$186$	−3.92705	+	2.85317i	−0.287945	+	0.209205i
$187$	−1.00000	−	0.726543i	−0.0731272	−	0.0531301i
$188$	−3.66312	−	2.66141i	−0.267160	−	0.194103i
$189$	−5.16312	+	3.75123i	−0.375562	+	0.272862i
$190$	18.0902			1.31240
$191$	−19.6074	−	14.2456i	−1.41874	−	1.03078i	−0.991978	−	0.126412i	$-0.959654\pi$
$191$	−19.6074	−	14.2456i	−1.41874	−	1.03078i	−0.426763	−	0.904363i	$-0.640346\pi$
$192$	−0.500000	−	1.53884i	−0.0360844	−	0.111056i
$193$	26.1246			1.88049			0.940245	−	0.340498i	$-0.110596\pi$
$193$	26.1246			1.88049			0.940245	+	0.340498i	$0.110596\pi$
$194$	−5.30902	−	16.3395i	−0.381165	−	1.17311i
$195$	0.263932	−	0.812299i	0.0189006	−	0.0581700i
$196$	0.218847	−	0.673542i	0.0156319	−	0.0481101i
$197$	−1.88197	+	5.79210i	−0.134085	+	0.412670i	−0.995446	−	0.0953220i	$-0.969612\pi$
$197$	−1.88197	+	5.79210i	−0.134085	+	0.412670i	0.861362	+	0.507992i	$0.169612\pi$
$198$	0.881966	−	0.640786i	0.0626786	−	0.0455387i
$199$	17.5623			1.24496			0.622479	−	0.782636i	$-0.286125\pi$
$199$	17.5623			1.24496			0.622479	+	0.782636i	$0.286125\pi$
$200$	11.1803			0.790569
$201$	3.18034			0.224324
$202$	−12.7082	+	9.23305i	−0.894146	+	0.649635i
$203$		0			0
$204$	0.381966	−	1.17557i	0.0267430	−	0.0823064i
$205$	12.5623			0.877390
$206$	−4.80902	−	14.8006i	−0.335060	−	1.03121i
$207$	−11.6738			−0.811383
$208$	1.50000	+	4.61653i	0.104006	+	0.320098i
$209$	−0.954915	−	0.693786i	−0.0660529	−	0.0479902i
$210$	−3.19098	−	2.31838i	−0.220199	−	0.159984i
$211$	−17.2082	+	12.5025i	−1.18466	+	0.860707i	−0.992690	−	0.120693i	$-0.961488\pi$
$211$	−17.2082	+	12.5025i	−1.18466	+	0.860707i	−0.191972	+	0.981400i	$0.561488\pi$
$212$	−3.69098	−	2.68166i	−0.253498	−	0.184177i
$213$	0.354102	+	0.257270i	0.0242627	+	0.0176279i
$214$	−19.9443	+	14.4904i	−1.36336	+	0.990541i
$215$	6.28115	−	4.56352i	0.428371	−	0.311230i
$216$	−4.04508	−	2.93893i	−0.275233	−	0.199969i
$217$	6.92705	+	21.3193i	0.470239	+	1.44725i
$218$	21.7082			1.47027
$219$	1.26393	+	3.88998i	0.0854086	+	0.262861i
$220$	0.263932	+	0.191758i	0.0177943	+	0.0129283i
$221$	1.61803	−	4.97980i	0.108841	−	0.334977i
$222$	−0.409830	+	1.26133i	−0.0275060	+	0.0846547i
$223$	−4.69098	+	3.40820i	−0.314131	+	0.228230i	−0.733667	−	0.679509i	$-0.762193\pi$
$223$	−4.69098	+	3.40820i	−0.314131	+	0.228230i	0.419536	+	0.907739i	$0.362193\pi$
$224$	9.65248			0.644933
$225$	11.5451	−	8.38800i	0.769672	−	0.559200i
$226$	18.7082			1.24445
$227$	4.50000	−	3.26944i	0.298675	−	0.217000i	−0.428347	−	0.903615i	$-0.640904\pi$
$227$	4.50000	−	3.26944i	0.298675	−	0.217000i	0.727022	+	0.686614i	$0.240904\pi$
$228$	0.364745	−	1.12257i	0.0241558	−	0.0743440i
$229$	−7.76393	+	23.8949i	−0.513055	+	1.57902i	0.273738	+	0.961804i	$0.411740\pi$
$229$	−7.76393	+	23.8949i	−0.513055	+	1.57902i	−0.786793	+	0.617217i	$0.788260\pi$
$230$	−4.57295	−	14.0741i	−0.301531	−	0.928018i
$231$	0.0795268	+	0.244758i	0.00523248	+	0.0161039i
$232$		0			0
$233$	8.07295	+	24.8460i	0.528876	+	1.62771i	0.756520	+	0.653970i	$0.226898\pi$
$233$	8.07295	+	24.8460i	0.528876	+	1.62771i	−0.227644	+	0.973744i	$0.573102\pi$
$234$	3.73607	+	2.71441i	0.244234	+	0.177447i
$235$	5.06231	+	15.5802i	0.330228	+	1.01634i
$236$	−1.11803	+	0.812299i	−0.0727778	+	0.0528762i
$237$	3.35410	+	2.43690i	0.217872	+	0.158294i
$238$	−19.5623	−	14.2128i	−1.26804	−	0.921282i
$239$	20.9164	−	15.1967i	1.35297	−	0.982990i	0.354112	−	0.935203i	$-0.384783\pi$
$239$	20.9164	−	15.1967i	1.35297	−	0.982990i	0.998858	−	0.0477873i	$-0.0152170\pi$
$240$	1.28115	−	3.94298i	0.0826981	−	0.254518i
$241$	9.13525	+	6.63715i	0.588453	+	0.427536i	0.841762	−	0.539849i	$-0.181519\pi$
$241$	9.13525	+	6.63715i	0.588453	+	0.427536i	−0.253308	+	0.967386i	$0.581519\pi$
$242$	5.47214	+	16.8415i	0.351762	+	1.08261i
$243$	−9.65248			−0.619207
$244$	0.0557281	+	0.171513i	0.00356763	+	0.0109800i
$245$	−2.07295	+	1.50609i	−0.132436	+	0.0962203i
$246$	1.07295	−	3.30220i	0.0684087	−	0.210540i
$247$	1.54508	−	4.75528i	0.0983114	−	0.302571i
$248$	−14.2082	+	10.3229i	−0.902222	+	0.655503i
$249$	1.97871			0.125396
$250$	14.6353	+	10.6331i	0.925615	+	0.672499i
$251$	−11.6180			−0.733324			−0.366662	−	0.930354i	$-0.619499\pi$
$251$	−11.6180			−0.733324			−0.366662	+	0.930354i	$0.619499\pi$
$252$	4.07295	−	2.95917i	0.256572	−	0.186410i
$253$	−0.298374	+	0.918300i	−0.0187586	+	0.0577330i
$254$	−2.28115	+	7.02067i	−0.143132	+	0.440516i
$255$	−3.61803	+	2.62866i	−0.226570	+	0.164613i
$256$	4.19098	+	12.8985i	0.261936	+	0.806157i
$257$	−23.1246			−1.44247			−0.721237	−	0.692689i	$-0.756426\pi$
$257$	−23.1246			−1.44247			−0.721237	+	0.692689i	$0.756426\pi$
$258$	−0.663119	−	2.04087i	−0.0412840	−	0.127059i
$259$	4.95492	+	3.59996i	0.307883	+	0.223690i
$260$	−0.427051	+	1.31433i	−0.0264846	+	0.0815111i
$261$		0			0
$262$	14.3262	+	10.4086i	0.885078	+	0.643047i
$263$	−1.07295	−	0.779543i	−0.0661609	−	0.0480687i	0.554213	−	0.832375i	$-0.313019\pi$
$263$	−1.07295	−	0.779543i	−0.0661609	−	0.0480687i	−0.620374	+	0.784306i	$0.713019\pi$
$264$	−0.163119	+	0.118513i	−0.0100393	+	0.00729396i
$265$	5.10081	+	15.6987i	0.313340	+	0.964363i
$266$	−18.6803	−	13.5721i	−1.14537	−	0.832156i
$267$	−1.31966	−	4.06150i	−0.0807619	−	0.248560i
$268$	−5.14590			−0.314336
$269$	−3.45492	−	10.6331i	−0.210650	−	0.648314i	−0.999434	−	0.0336432i	$-0.989289\pi$
$269$	−3.45492	−	10.6331i	−0.210650	−	0.648314i	0.788784	−	0.614670i	$-0.210711\pi$
$270$	−2.50000	−	7.69421i	−0.152145	−	0.468255i
$271$	6.57295	−	20.2295i	0.399278	−	1.22885i	−0.526301	−	0.850298i	$-0.676422\pi$
$271$	6.57295	−	20.2295i	0.399278	−	1.22885i	0.925579	−	0.378554i	$-0.123578\pi$
$272$	7.85410	−	24.1724i	0.476225	−	1.46567i
$273$	−0.881966	+	0.640786i	−0.0533790	+	0.0387821i
$274$	33.7984			2.04183
$275$	−0.364745	−	1.12257i	−0.0219950	−	0.0676935i
$276$	−0.965558			−0.0581198
$277$	−12.3713	+	8.98829i	−0.743321	+	0.540054i	−0.893749	−	0.448567i	$-0.851935\pi$
$277$	−12.3713	+	8.98829i	−0.743321	+	0.540054i	0.150429	+	0.988621i	$0.451935\pi$
$278$	−6.11803	+	18.8294i	−0.366935	+	1.12931i
$279$	−6.92705	+	21.3193i	−0.414712	+	1.27635i
$280$	−11.5451	−	8.38800i	−0.689951	−	0.501279i
$281$	−1.51722	−	4.66953i	−0.0905098	−	0.278561i	0.895548	−	0.444966i	$-0.146784\pi$
$281$	−1.51722	−	4.66953i	−0.0905098	−	0.278561i	−0.986057	+	0.166405i	$0.946784\pi$
$282$	4.52786			0.269630
$283$	−9.16312	−	28.2012i	−0.544691	−	1.67639i	−0.721724	−	0.692181i	$-0.756650\pi$
$283$	−9.16312	−	28.2012i	−0.544691	−	1.67639i	0.177033	−	0.984205i	$-0.443350\pi$
$284$	−0.572949	−	0.416272i	−0.0339983	−	0.0247012i
$285$	−3.45492	+	2.51014i	−0.204652	+	0.148688i
$286$	0.309017	−	0.224514i	0.0182726	−	0.0132758i
$287$	−12.9721	−	9.42481i	−0.765721	−	0.556329i
$288$	7.80902	+	5.67358i	0.460151	+	0.334319i
$289$	−8.42705	+	6.12261i	−0.495709	+	0.360154i
$290$		0			0
$291$	3.28115	+	2.38390i	0.192345	+	0.139747i
$292$	−2.04508	−	6.29412i	−0.119680	−	0.368336i
$293$	−7.41641			−0.433271			−0.216636	−	0.976253i	$-0.569508\pi$
$293$	−7.41641			−0.433271			−0.216636	+	0.976253i	$0.569508\pi$
$294$	0.218847	+	0.673542i	0.0127634	+	0.0392818i
$295$	5.00000			0.291111
$296$	−1.48278	+	4.56352i	−0.0861848	+	0.265249i
$297$	−0.163119	+	0.502029i	−0.00946512	+	0.0291307i
$298$	−9.47214	+	6.88191i	−0.548706	+	0.398658i
$299$	−4.09017			−0.236541
$300$	0.954915	−	0.693786i	0.0551320	−	0.0400558i
$301$	−9.90983			−0.571193
$302$	9.59017	−	6.96767i	0.551852	−	0.400944i
$303$	1.14590	−	3.52671i	0.0658301	−	0.202604i
$304$	7.50000	−	23.0826i	0.430155	−	1.32388i
$305$	0.201626	−	0.620541i	0.0115451	−	0.0355321i
$306$	−7.47214	−	22.9969i	−0.427154	−	1.31464i
$307$	−28.1246			−1.60516			−0.802578	−	0.596547i	$-0.796539\pi$
$307$	−28.1246			−1.60516			−0.802578	+	0.596547i	$0.796539\pi$
$308$	−0.128677	−	0.396027i	−0.00733206	−	0.0225658i
$309$	2.97214	+	2.15938i	0.169079	+	0.122843i
$310$	−28.4164			−1.61394
$311$	−20.9894	+	15.2497i	−1.19020	+	0.864729i	−0.993285	−	0.115692i	$-0.963091\pi$
$311$	−20.9894	+	15.2497i	−1.19020	+	0.864729i	−0.196912	+	0.980421i	$0.563091\pi$
$312$	−0.690983	−	0.502029i	−0.0391192	−	0.0284218i
$313$	15.2082	+	11.0494i	0.859619	+	0.624549i	0.927781	−	0.373125i	$-0.121714\pi$
$313$	15.2082	+	11.0494i	0.859619	+	0.624549i	−0.0681626	+	0.997674i	$0.521714\pi$
$314$	−7.28115	+	5.29007i	−0.410899	+	0.298536i
$315$	−18.2148			−1.02629
$316$	−5.42705	−	3.94298i	−0.305295	−	0.221810i
$317$	−7.63525	−	23.4989i	−0.428839	−	1.31983i	−0.899270	−	0.437393i	$-0.855902\pi$
$317$	−7.63525	−	23.4989i	−0.428839	−	1.31983i	0.470432	−	0.882436i	$-0.344098\pi$
$318$	4.56231			0.255841
$319$		0			0
$320$	2.92705	−	9.00854i	0.163627	−	0.503593i
$321$	1.79837	−	5.53483i	0.100375	−	0.308924i
$322$	−5.83688	+	17.9641i	−0.325277	+	1.00110i
$323$	−21.1803	+	15.3884i	−1.17851	+	0.856234i
$324$	4.76393			0.264663
$325$	4.04508	−	2.93893i	0.224381	−	0.163022i
$326$	2.32624			0.128838
$327$	−4.14590	+	3.01217i	−0.229269	+	0.166573i
$328$	3.88197	−	11.9475i	0.214346	−	0.659688i
$329$	6.46149	−	19.8864i	0.356234	−	1.09637i
$330$	−0.326238			−0.0179588
$331$	5.15248	+	15.8577i	0.283206	+	0.871617i	0.986931	+	0.161145i	$0.0515187\pi$
$331$	5.15248	+	15.8577i	0.283206	+	0.871617i	−0.703725	+	0.710472i	$0.748481\pi$
$332$	−3.20163			−0.175712
$333$	1.89261	+	5.82485i	0.103714	+	0.319200i
$334$	−7.28115	−	5.29007i	−0.398407	−	0.289460i
$335$	15.0623	+	10.9434i	0.822942	+	0.597902i
$336$	−4.28115	+	3.11044i	−0.233556	+	0.169688i
$337$	−16.0902	−	11.6902i	−0.876487	−	0.636805i	0.0558324	−	0.998440i	$-0.482219\pi$
$337$	−16.0902	−	11.6902i	−0.876487	−	0.636805i	−0.932320	+	0.361635i	$0.882219\pi$
$338$	1.30902	+	0.951057i	0.0712011	+	0.0517307i
$339$	−3.57295	+	2.59590i	−0.194056	+	0.140990i
$340$	5.85410	−	4.25325i	0.317483	−	0.230665i
$341$	1.50000	+	1.08981i	0.0812296	+	0.0590167i
$342$	−7.13525	−	21.9601i	−0.385830	−	1.18746i
$343$	−16.7082			−0.902158
$344$	−2.39919	−	7.38394i	−0.129355	−	0.398115i
$345$	2.82624	+	2.05338i	0.152160	+	0.110550i
$346$	8.11803	−	24.9847i	0.436428	−	1.34319i
$347$	8.01722	−	24.6745i	0.430387	−	1.32459i	−0.467354	−	0.884070i	$-0.654793\pi$
$347$	8.01722	−	24.6745i	0.430387	−	1.32459i	0.897741	−	0.440524i	$-0.145207\pi$
$348$		0			0
$349$	22.2361			1.19027			0.595135	−	0.803626i	$-0.297099\pi$
$349$	22.2361			1.19027			0.595135	+	0.803626i	$0.297099\pi$
$350$	−7.13525	−	21.9601i	−0.381395	−	1.17381i
$351$	−2.23607			−0.119352
$352$	0.645898	−	0.469272i	0.0344265	−	0.0250123i
$353$	−4.75329	+	14.6291i	−0.252992	+	0.778629i	0.741227	+	0.671255i	$0.234244\pi$
$353$	−4.75329	+	14.6291i	−0.252992	+	0.778629i	−0.994219	+	0.107375i	$0.965756\pi$
$354$	0.427051	−	1.31433i	0.0226975	−	0.0698557i
$355$	0.791796	+	2.43690i	0.0420242	+	0.129337i
$356$	2.13525	+	6.57164i	0.113168	+	0.348296i
$357$	5.70820			0.302110
$358$	10.8541	+	33.4055i	0.573657	+	1.76554i
$359$	−3.19098	−	2.31838i	−0.168414	−	0.122360i	0.500386	−	0.865803i	$-0.333192\pi$
$359$	−3.19098	−	2.31838i	−0.168414	−	0.122360i	−0.668799	+	0.743443i	$0.733192\pi$
$360$	−4.40983	−	13.5721i	−0.232418	−	0.715310i
$361$	−4.85410	+	3.52671i	−0.255479	+	0.185616i
$362$	5.97214	+	4.33901i	0.313888	+	0.228053i
$363$	−3.38197	−	2.45714i	−0.177507	−	0.128967i
$364$	1.42705	−	1.03681i	0.0747978	−	0.0543438i
$365$	−7.39919	+	22.7724i	−0.387291	+	1.19196i
$366$	−0.145898	−	0.106001i	−0.00762621	−	0.00554077i
$367$	−3.65248	−	11.2412i	−0.190658	−	0.586784i	0.809342	−	0.587337i	$-0.199824\pi$
$367$	−3.65248	−	11.2412i	−0.190658	−	0.586784i	−1.00000		0.000553415i	$0.999824\pi$
$368$	−19.8541			−1.03497
$369$	−4.95492	−	15.2497i	−0.257943	−	0.793866i
$370$	−6.28115	+	4.56352i	−0.326542	+	0.237246i
$371$	6.51064	−	20.0377i	0.338016	−	1.04031i
$372$	−0.572949	+	1.76336i	−0.0297060	+	0.0914257i
$373$	−22.2533	+	16.1680i	−1.15223	+	0.837145i	−0.988776	−	0.149405i	$-0.952264\pi$
$373$	−22.2533	+	16.1680i	−1.15223	+	0.837145i	−0.163456	+	0.986551i	$0.552264\pi$
$374$	−2.00000			−0.103418
$375$	−4.27051			−0.220528
$376$	16.3820			0.844835
$377$		0			0
$378$	−3.19098	+	9.82084i	−0.164126	+	0.505129i
$379$	−3.84346	+	11.8290i	−0.197425	+	0.607612i	0.802515	+	0.596633i	$0.203495\pi$
$379$	−3.84346	+	11.8290i	−0.197425	+	0.607612i	−0.999940	+	0.0109797i	$0.996505\pi$
$380$	5.59017	−	4.06150i	0.286770	−	0.208350i
$381$	−0.538507	−	1.65735i	−0.0275886	−	0.0849088i
$382$	−39.2148			−2.00640
$383$	11.8541	+	36.4832i	0.605716	+	1.86420i	0.491790	+	0.870714i	$0.336343\pi$
$383$	11.8541	+	36.4832i	0.605716	+	1.86420i	0.113927	+	0.993489i	$0.463657\pi$
$384$	−4.20820	−	3.05744i	−0.214749	−	0.156024i
$385$	−0.465558	+	1.43284i	−0.0237270	+	0.0730243i
$386$	34.1976	−	24.8460i	1.74061	−	1.26463i
$387$	−8.01722	−	5.82485i	−0.407538	−	0.296094i
$388$	−5.30902	−	3.85723i	−0.269525	−	0.195821i
$389$	25.2254	−	18.3273i	1.27898	−	0.929233i	0.279458	−	0.960158i	$-0.409845\pi$
$389$	25.2254	−	18.3273i	1.27898	−	0.929233i	0.999522	+	0.0309247i	$0.00984520\pi$
$390$	−0.427051	−	1.31433i	−0.0216246	−	0.0665536i
$391$	17.3262	+	12.5882i	0.876226	+	0.636615i
$392$	0.791796	+	2.43690i	0.0399917	+	0.123082i
$393$	−4.18034			−0.210870
$394$	3.04508	+	9.37181i	0.153409	+	0.472145i
$395$	7.50000	+	23.0826i	0.377366	+	1.16141i
$396$	0.128677	−	0.396027i	0.00646627	−	0.0199011i
$397$	−3.85410	+	11.8617i	−0.193432	+	0.595322i	0.806559	+	0.591153i	$0.201327\pi$
$397$	−3.85410	+	11.8617i	−0.193432	+	0.595322i	−0.999991	+	0.00416902i	$0.998673\pi$
$398$	22.9894	−	16.7027i	1.15235	−	0.837233i
$399$	5.45085			0.272884
$400$	19.6353	−	14.2658i	0.981763	−	0.713292i
$401$	2.52786			0.126236			0.0631178	−	0.998006i	$-0.479896\pi$
$401$	2.52786			0.126236			0.0631178	+	0.998006i	$0.479896\pi$
$402$	4.16312	−	3.02468i	0.207638	−	0.150857i
$403$	−2.42705	+	7.46969i	−0.120900	+	0.372092i
$404$	−1.85410	+	5.70634i	−0.0922450	+	0.283901i
$405$	−13.9443	−	10.1311i	−0.692896	−	0.503419i
$406$		0			0
$407$	0.506578			0.0251101
$408$	1.38197	+	4.25325i	0.0684175	+	0.210567i
$409$	17.5623	+	12.7598i	0.868400	+	0.630930i	0.930157	−	0.367162i	$-0.119670\pi$
$409$	17.5623	+	12.7598i	0.868400	+	0.630930i	−0.0617570	+	0.998091i	$0.519670\pi$
$410$	16.4443	−	11.9475i	0.812125	−	0.590043i
$411$	−6.45492	+	4.68977i	−0.318397	+	0.231329i
$412$	−4.80902	−	3.49396i	−0.236923	−	0.172135i
$413$	−5.16312	−	3.75123i	−0.254060	−	0.184586i
$414$	−15.2812	+	11.1024i	−0.751028	+	0.545654i
$415$	9.37132	+	6.80866i	0.460020	+	0.334224i
$416$	2.73607	+	1.98787i	0.134147	+	0.0974633i
$417$	−1.44427	−	4.44501i	−0.0707263	−	0.217673i
$418$	−1.90983			−0.0934128
$419$	3.25329	+	10.0126i	0.158934	+	0.489147i	0.998538	−	0.0540508i	$-0.0172133\pi$
$419$	3.25329	+	10.0126i	0.158934	+	0.489147i	−0.839605	+	0.543198i	$0.817213\pi$
$420$	−1.50658			−0.0735135
$421$	−11.5172	+	35.4464i	−0.561315	+	1.72755i	0.117339	+	0.993092i	$0.462564\pi$
$421$	−11.5172	+	35.4464i	−0.561315	+	1.72755i	−0.678654	+	0.734458i	$0.737436\pi$
$422$	−10.6353	+	32.7319i	−0.517716	+	1.59337i
$423$	16.9164	−	12.2905i	0.822504	−	0.597584i
$424$	16.5066			0.801630
$425$	−26.1803			−1.26993
$426$	0.708204			0.0343126
$427$	−0.673762	+	0.489517i	−0.0326056	+	0.0236894i
$428$	−2.90983	+	8.95554i	−0.140652	+	0.432882i
$429$	−0.0278640	+	0.0857567i	−0.00134529	+	0.00414037i
$430$	3.88197	−	11.9475i	0.187205	−	0.576158i
$431$	−2.14590	−	6.60440i	−0.103364	−	0.318123i	0.885979	−	0.463726i	$-0.153488\pi$
$431$	−2.14590	−	6.60440i	−0.103364	−	0.318123i	−0.989343	+	0.145603i	$0.953488\pi$
$432$	−10.8541			−0.522218
$433$	−11.5000	−	35.3934i	−0.552655	−	1.70090i	−0.702058	−	0.712120i	$-0.747735\pi$
$433$	−11.5000	−	35.3934i	−0.552655	−	1.70090i	0.149403	−	0.988776i	$-0.452265\pi$
$434$	29.3435	+	21.3193i	1.40853	+	1.02336i
$435$		0			0
$436$	6.70820	−	4.87380i	0.321265	−	0.233412i
$437$	16.5451	+	12.0207i	0.791459	+	0.575028i
$438$	5.35410	+	3.88998i	0.255829	+	0.185871i
$439$	4.73607	−	3.44095i	0.226040	−	0.164228i	−0.469001	−	0.883198i	$-0.655386\pi$
$439$	4.73607	−	3.44095i	0.226040	−	0.164228i	0.695041	+	0.718970i	$0.255386\pi$
$440$	−1.18034			−0.0562705
$441$	2.64590	+	1.92236i	0.125995	+	0.0915408i
$442$	−2.61803	−	8.05748i	−0.124527	−	0.383255i
$443$	−1.96556			−0.0933865			−0.0466932	−	0.998909i	$-0.514868\pi$
$443$	−1.96556			−0.0933865			−0.0466932	+	0.998909i	$0.514868\pi$
$444$	0.156541	+	0.481784i	0.00742911	+	0.0228645i
$445$	7.72542	−	23.7764i	0.366220	−	1.12711i
$446$	−2.89919	+	8.92278i	−0.137280	+	0.422506i
$447$	0.854102	−	2.62866i	0.0403976	−	0.124331i
$448$	−9.78115	+	7.10642i	−0.462116	+	0.335747i
$449$	−5.12461			−0.241845			−0.120923	−	0.992662i	$-0.538585\pi$
$449$	−5.12461			−0.241845			−0.120923	+	0.992662i	$0.538585\pi$
$450$	7.13525	−	21.9601i	0.336359	−	1.03521i
$451$	−1.32624			−0.0624501
$452$	5.78115	−	4.20025i	0.271923	−	0.197563i
$453$	−0.864745	+	2.66141i	−0.0406293	+	0.125044i
$454$	2.78115	−	8.55951i	0.130526	−	0.401718i
$455$	−6.38197			−0.299191
$456$	1.31966	+	4.06150i	0.0617987	+	0.190197i
$457$	−10.2361			−0.478823			−0.239412	−	0.970918i	$-0.576955\pi$
$457$	−10.2361			−0.478823			−0.239412	+	0.970918i	$0.576955\pi$
$458$	12.5623	+	38.6628i	0.586998	+	1.80659i
$459$	9.47214	+	6.88191i	0.442121	+	0.321220i
$460$	−4.57295	−	3.32244i	−0.213215	−	0.154910i
$461$	29.5623	−	21.4783i	1.37685	−	1.00034i	0.379687	−	0.925115i	$-0.376032\pi$
$461$	29.5623	−	21.4783i	1.37685	−	1.00034i	0.997166	−	0.0752281i	$-0.0239685\pi$
$462$	0.336881	+	0.244758i	0.0156731	+	0.0113872i
$463$	−11.5623	−	8.40051i	−0.537346	−	0.390405i	0.285752	−	0.958303i	$-0.407756\pi$
$463$	−11.5623	−	8.40051i	−0.537346	−	0.390405i	−0.823098	+	0.567899i	$0.807756\pi$
$464$		0			0
$465$	5.42705	−	3.94298i	0.251673	−	0.182851i
$466$	34.1976	+	24.8460i	1.58417	+	1.15097i
$467$	−1.41641	−	4.35926i	−0.0655435	−	0.201722i	0.912921	−	0.408135i	$-0.133821\pi$
$467$	−1.41641	−	4.35926i	−0.0655435	−	0.201722i	−0.978465	+	0.206413i	$0.933821\pi$
$468$	1.76393			0.0815378
$469$	−7.34346	−	22.6008i	−0.339089	−	1.04361i
$470$	21.4443	+	15.5802i	0.989151	+	0.718660i
$471$	0.656541	−	2.02063i	0.0302518	−	0.0931055i
$472$	1.54508	−	4.75528i	0.0711183	−	0.218880i
$473$	−0.663119	+	0.481784i	−0.0304902	+	0.0221525i
$474$	6.70820			0.308118
$475$	−25.0000			−1.14708
$476$	−9.23607			−0.423334
$477$	17.0451	−	12.3840i	0.780441	−	0.567023i
$478$	12.9271	−	39.7854i	0.591270	−	1.81974i
$479$	−1.64590	+	5.06555i	−0.0752030	+	0.231451i	−0.981591	−	0.190995i	$-0.938828\pi$
$479$	−1.64590	+	5.06555i	−0.0752030	+	0.231451i	0.906388	+	0.422446i	$0.138828\pi$
$480$	−0.892609	−	2.74717i	−0.0407418	−	0.125391i
$481$	0.663119	+	2.04087i	0.0302356	+	0.0930557i
$482$	18.2705			0.832199
$483$	−1.37790	−	4.24074i	−0.0626967	−	0.192960i
$484$	5.47214	+	3.97574i	0.248733	+	0.180715i
$485$	7.33688	+	22.5806i	0.333151	+	1.02533i
$486$	−12.6353	+	9.18005i	−0.573147	+	0.416416i
$487$	27.4894	+	19.9722i	1.24566	+	0.905026i	0.997962	−	0.0638107i	$-0.0203254\pi$
$487$	27.4894	+	19.9722i	1.24566	+	0.905026i	0.247700	+	0.968837i	$0.420325\pi$
$488$	−0.527864	−	0.383516i	−0.0238953	−	0.0173609i
$489$	−0.444272	+	0.322782i	−0.0200907	+	0.0145967i
$490$	−1.28115	+	3.94298i	−0.0578766	+	0.178126i
$491$	−14.7082	−	10.6861i	−0.663772	−	0.482259i	0.204163	−	0.978937i	$-0.434553\pi$
$491$	−14.7082	−	10.6861i	−0.663772	−	0.482259i	−0.867935	+	0.496678i	$0.834553\pi$
$492$	−0.409830	−	1.26133i	−0.0184766	−	0.0568650i
$493$		0			0
$494$	−2.50000	−	7.69421i	−0.112480	−	0.346179i
$495$	−1.21885	+	0.885544i	−0.0547831	+	0.0398023i
$496$	−11.7812	+	36.2587i	−0.528989	+	1.62806i
$497$	1.01064	−	3.11044i	0.0453335	−	0.139522i
$498$	2.59017	−	1.88187i	0.116068	−	0.0843285i
$499$	43.5410			1.94916			0.974582	−	0.224032i	$-0.0719219\pi$
$499$	43.5410			1.94916			0.974582	+	0.224032i	$0.0719219\pi$
$500$	6.90983			0.309017
$501$	2.12461			0.0949207
$502$	−15.2082	+	11.0494i	−0.678775	+	0.493159i
$503$	−5.70820	+	17.5680i	−0.254516	+	0.783320i	0.739408	+	0.673257i	$0.235105\pi$
$503$	−5.70820	+	17.5680i	−0.254516	+	0.783320i	−0.993925	+	0.110063i	$0.964895\pi$
$504$	−5.62868	+	17.3233i	−0.250721	+	0.771641i
$505$	17.5623	−	12.7598i	0.781512	−	0.567802i
$506$	0.482779	+	1.48584i	0.0214621	+	0.0660537i
$507$	−0.381966			−0.0169637
$508$	0.871323	+	2.68166i	0.0386587	+	0.118979i
$509$	12.6631	+	9.20029i	0.561283	+	0.407796i	0.831928	−	0.554883i	$-0.187237\pi$
$509$	12.6631	+	9.20029i	0.561283	+	0.407796i	−0.270645	+	0.962679i	$0.587237\pi$
$510$	−2.23607	+	6.88191i	−0.0990148	+	0.304736i
$511$	24.7254	−	17.9641i	1.09379	−	0.794684i
$512$	−4.28115	−	3.11044i	−0.189202	−	0.137463i
$513$	9.04508	+	6.57164i	0.399350	+	0.290145i
$514$	−30.2705	+	21.9928i	−1.33517	+	0.970061i
$515$	6.64590	+	20.4540i	0.292853	+	0.901310i
$516$	−0.663119	−	0.481784i	−0.0291922	−	0.0212094i
$517$	−0.534442	−	1.64484i	−0.0235047	−	0.0723401i
$518$	9.90983			0.435413
$519$	1.91641	+	5.89810i	0.0841210	+	0.258898i
$520$	−1.54508	−	4.75528i	−0.0677565	−	0.208533i
$521$	−11.8820	+	36.5689i	−0.520558	+	1.60211i	0.252377	+	0.967629i	$0.418788\pi$
$521$	−11.8820	+	36.5689i	−0.520558	+	1.60211i	−0.772935	+	0.634485i	$0.781212\pi$
$522$		0			0
$523$	2.54508	−	1.84911i	0.111289	−	0.0808560i	−0.530749	−	0.847529i	$-0.678089\pi$
$523$	2.54508	−	1.84911i	0.111289	−	0.0808560i	0.642038	+	0.766673i	$0.278089\pi$
$524$	6.76393			0.295484
$525$	4.40983	+	3.20393i	0.192461	+	0.139831i
$526$	−2.14590			−0.0935656
$527$	33.2705	−	24.1724i	1.44929	−	1.05297i
$528$	−0.135255	+	0.416272i	−0.00588621	+	0.0181159i
$529$	−1.93769	+	5.96361i	−0.0842476	+	0.259287i
$530$	21.6074	+	15.6987i	0.938565	+	0.681907i
$531$	−1.97214	−	6.06961i	−0.0855834	−	0.263399i
$532$	−8.81966			−0.382381
$533$	−1.73607	−	5.34307i	−0.0751975	−	0.231434i
$534$	−5.59017	−	4.06150i	−0.241910	−	0.175758i
$535$	27.5623	−	20.0252i	1.19162	−	0.865764i
$536$	15.0623	−	10.9434i	0.650593	−	0.472683i
$537$	−6.70820	−	4.87380i	−0.289480	−	0.210320i
$538$	−14.6353	−	10.6331i	−0.630971	−	0.458427i
$539$	0.218847	−	0.159002i	0.00942641	−	0.00684869i
$540$	−2.50000	−	1.81636i	−0.107583	−	0.0781635i
$541$	−12.3713	−	8.98829i	−0.531885	−	0.386437i	0.289178	−	0.957275i	$-0.406618\pi$
$541$	−12.3713	−	8.98829i	−0.531885	−	0.386437i	−0.821062	+	0.570839i	$0.806618\pi$
$542$	−10.6353	−	32.7319i	−0.456823	−	1.40596i
$543$	−1.74265			−0.0747841
$544$	−5.47214	−	16.8415i	−0.234616	−	0.722073i
$545$	−30.0000			−1.28506
$546$	−0.545085	+	1.67760i	−0.0233275	+	0.0717946i
$547$	1.93769	−	5.96361i	0.0828498	−	0.254986i	−0.901047	−	0.433721i	$-0.857200\pi$
$547$	1.93769	−	5.96361i	0.0828498	−	0.254986i	0.983897	+	0.178735i	$0.0572005\pi$
$548$	10.4443	−	7.58821i	0.446157	−	0.324152i
$549$	−0.832816			−0.0355437
$550$	−1.54508	−	1.12257i	−0.0658826	−	0.0478665i
$551$		0			0
$552$	2.82624	−	2.05338i	0.120293	−	0.0873977i
$553$	9.57295	−	29.4625i	0.407083	−	1.25287i
$554$	−7.64590	+	23.5317i	−0.324843	+	0.999764i
$555$	0.566371	−	1.74311i	0.0240411	−	0.0739910i
$556$	2.33688	+	7.19218i	0.0991058	+	0.305016i
$557$	25.7426			1.09075			0.545375	−	0.838192i	$-0.316387\pi$
$557$	25.7426			1.09075			0.545375	+	0.838192i	$0.316387\pi$
$558$	11.2082	+	34.4953i	0.474481	+	1.46030i
$559$	−2.80902	−	2.04087i	−0.118809	−	0.0863196i
$560$	−30.9787			−1.30909
$561$	0.381966	−	0.277515i	0.0161266	−	0.0117167i
$562$	−6.42705	−	4.66953i	−0.271109	−	0.196972i
$563$	15.7984	+	11.4782i	0.665822	+	0.483748i	0.868624	−	0.495472i	$-0.165005\pi$
$563$	15.7984	+	11.4782i	0.665822	+	0.483748i	−0.202802	+	0.979220i	$0.565005\pi$
$564$	1.39919	−	1.01657i	0.0589164	−	0.0428053i
$565$	−25.8541			−1.08769
$566$	−38.8156	−	28.2012i	−1.63154	−	1.18538i
$567$	6.79837	+	20.9232i	0.285505	+	0.878694i
$568$	2.56231			0.107512
$569$	−10.2639	−	31.5891i	−0.430286	−	1.32429i	−0.897840	−	0.440321i	$-0.854865\pi$
$569$	−10.2639	−	31.5891i	−0.430286	−	1.32429i	0.467554	−	0.883964i	$-0.345135\pi$
$570$	−2.13525	+	6.57164i	−0.0894360	+	0.275256i
$571$	9.86475	−	30.3606i	0.412827	−	1.27055i	−0.501354	−	0.865242i	$-0.667164\pi$
$571$	9.86475	−	30.3606i	0.412827	−	1.27055i	0.914180	−	0.405308i	$-0.132836\pi$
$572$	0.0450850	−	0.138757i	0.00188510	−	0.00580173i
$573$	7.48936	−	5.44134i	0.312872	−	0.227315i
$574$	−25.9443			−1.08289
$575$	6.31966	+	19.4499i	0.263548	+	0.811117i
$576$	−12.0902			−0.503757
$577$	−13.1631	+	9.56357i	−0.547988	+	0.398136i	−0.827043	−	0.562139i	$-0.809979\pi$
$577$	−13.1631	+	9.56357i	−0.547988	+	0.398136i	0.279055	+	0.960275i	$0.409979\pi$
$578$	−5.20820	+	16.0292i	−0.216633	+	0.666727i
$579$	−3.08359	+	9.49032i	−0.128150	+	0.394404i
$580$		0			0
$581$	−4.56888	−	14.0616i	−0.189549	−	0.583373i
$582$	6.56231			0.272016
$583$	−0.538507	−	1.65735i	−0.0223027	−	0.0686406i
$584$	19.3713	+	14.0741i	0.801591	+	0.582390i
$585$	−5.16312	−	3.75123i	−0.213469	−	0.155094i
$586$	−9.70820	+	7.05342i	−0.401042	+	0.291374i
$587$	−14.7082	−	10.6861i	−0.607073	−	0.441064i	0.241310	−	0.970448i	$-0.422423\pi$
$587$	−14.7082	−	10.6861i	−0.607073	−	0.441064i	−0.848382	+	0.529384i	$0.822423\pi$
$588$	0.218847	+	0.159002i	0.00902510	+	0.00655712i
$589$	31.7705	−	23.0826i	1.30908	−	0.951103i
$590$	6.54508	−	4.75528i	0.269457	−	0.195772i
$591$	−1.88197	−	1.36733i	−0.0774137	−	0.0562444i
$592$	3.21885	+	9.90659i	0.132294	+	0.407158i
$593$	13.7639			0.565217			0.282608	−	0.959235i	$-0.408800\pi$
$593$	13.7639			0.565217			0.282608	+	0.959235i	$0.408800\pi$
$594$	0.263932	+	0.812299i	0.0108293	+	0.0333290i
$595$	27.0344	+	19.6417i	1.10830	+	0.805230i
$596$	−1.38197	+	4.25325i	−0.0566075	+	0.174220i
$597$	−2.07295	+	6.37988i	−0.0848402	+	0.261111i
$598$	−5.35410	+	3.88998i	−0.218946	+	0.159073i
$599$	−6.38197			−0.260760			−0.130380	−	0.991464i	$-0.541620\pi$
$599$	−6.38197			−0.260760			−0.130380	+	0.991464i	$0.541620\pi$
$600$	−1.31966	+	4.06150i	−0.0538749	+	0.165810i
$601$	−8.72949			−0.356083			−0.178042	−	0.984023i	$-0.556976\pi$
$601$	−8.72949			−0.356083			−0.178042	+	0.984023i	$0.556976\pi$
$602$	−12.9721	+	9.42481i	−0.528705	+	0.384127i
$603$	7.34346	−	22.6008i	0.299049	−	0.920377i
$604$	1.39919	−	4.30625i	0.0569321	−	0.175219i
$605$	−7.56231	−	23.2744i	−0.307451	−	0.946238i
$606$	−1.85410	−	5.70634i	−0.0753177	−	0.231804i
$607$	13.3820			0.543157			0.271579	−	0.962416i	$-0.412454\pi$
$607$	13.3820			0.543157			0.271579	+	0.962416i	$0.412454\pi$
$608$	−5.22542	−	16.0822i	−0.211919	−	0.652219i
$609$		0			0
$610$	−0.326238	−	1.00406i	−0.0132090	−	0.0406531i
$611$	5.92705	−	4.30625i	0.239783	−	0.174212i
$612$	−7.47214	−	5.42882i	−0.302043	−	0.219447i
$613$	19.4164	+	14.1068i	0.784221	+	0.569770i	0.906243	−	0.422757i	$-0.138938\pi$
$613$	19.4164	+	14.1068i	0.784221	+	0.569770i	−0.122022	+	0.992527i	$0.538938\pi$
$614$	−36.8156	+	26.7481i	−1.48576	+	1.07947i
$615$	−1.48278	+	4.56352i	−0.0597914	+	0.184019i
$616$	1.21885	+	0.885544i	0.0491087	+	0.0356796i
$617$	−2.27051	−	6.98791i	−0.0914073	−	0.281323i	0.894893	−	0.446280i	$-0.147251\pi$
$617$	−2.27051	−	6.98791i	−0.0914073	−	0.281323i	−0.986301	+	0.164957i	$0.947251\pi$
$618$	5.94427			0.239114
$619$	−2.23607	−	6.88191i	−0.0898752	−	0.276607i	0.896009	−	0.444036i	$-0.146454\pi$
$619$	−2.23607	−	6.88191i	−0.0898752	−	0.276607i	−0.985884	+	0.167428i	$0.946454\pi$
$620$	−8.78115	+	6.37988i	−0.352660	+	0.256222i
$621$	2.82624	−	8.69827i	0.113413	−	0.349049i
$622$	−12.9721	+	39.9241i	−0.520135	+	1.60081i
$623$	−25.8156	+	18.7561i	−1.03428	+	0.751448i
$624$	−1.85410			−0.0742235
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$	30.4164			1.21568
$627$	0.364745	−	0.265003i	0.0145665	−	0.0105832i
$628$	−1.06231	+	3.26944i	−0.0423906	+	0.130465i
$629$	3.47214	−	10.6861i	0.138443	−	0.426084i
$630$	−23.8435	+	17.3233i	−0.949946	+	0.690176i
$631$	−13.8541	−	42.6385i	−0.551523	−	1.69741i	−0.704953	−	0.709254i	$-0.749032\pi$
$631$	−13.8541	−	42.6385i	−0.551523	−	1.69741i	0.153430	−	0.988160i	$-0.450968\pi$
$632$	24.2705			0.965429
$633$	−2.51064	−	7.72696i	−0.0997891	−	0.307119i
$634$	−32.3435	−	23.4989i	−1.28452	−	0.933260i
$635$	3.15248	−	9.70232i	0.125102	−	0.385025i
$636$	1.40983	−	1.02430i	0.0559034	−	0.0406162i
$637$	0.927051	+	0.673542i	0.0367311	+	0.0266867i
$638$		0			0
$639$	2.64590	−	1.92236i	0.104670	−	0.0760473i
$640$	−9.40983	−	28.9605i	−0.371956	−	1.14476i
$641$	27.9164	+	20.2825i	1.10263	+	0.801109i	0.981488	−	0.191526i	$-0.0613436\pi$
$641$	27.9164	+	20.2825i	1.10263	+	0.801109i	0.121144	+	0.992635i	$0.461344\pi$
$642$	−2.90983	−	8.95554i	−0.114842	−	0.353447i
$643$	−27.9443			−1.10201			−0.551007	−	0.834500i	$-0.685756\pi$
$643$	−27.9443			−1.10201			−0.551007	+	0.834500i	$0.685756\pi$
$644$	2.22949	+	6.86167i	0.0878542	+	0.270387i
$645$	0.916408	+	2.82041i	0.0360835	+	0.111054i
$646$	−13.0902	+	40.2874i	−0.515026	+	1.58509i
$647$	−15.1353	+	46.5815i	−0.595028	+	1.83131i	−0.0404429	+	0.999182i	$0.512877\pi$
$647$	−15.1353	+	46.5815i	−0.595028	+	1.83131i	−0.554585	+	0.832127i	$0.687123\pi$
$648$	−13.9443	+	10.1311i	−0.547783	+	0.397987i
$649$	−0.527864			−0.0207205
$650$	2.50000	−	7.69421i	0.0980581	−	0.301792i
$651$	−8.56231			−0.335583
$652$	0.718847	−	0.522273i	0.0281522	−	0.0204538i
$653$	−2.65654	+	8.17599i	−0.103958	+	0.319951i	−0.989485	−	0.144638i	$-0.953798\pi$
$653$	−2.65654	+	8.17599i	−0.103958	+	0.319951i	0.885526	+	0.464590i	$0.153798\pi$
$654$	−2.56231	+	7.88597i	−0.100194	+	0.308366i
$655$	−19.7984	−	14.3844i	−0.773586	−	0.562043i
$656$	−8.42705	−	25.9358i	−0.329021	−	1.01262i
$657$	30.5623			1.19235
$658$	−10.4549	−	32.1769i	−0.407575	−	1.25439i
$659$	−3.35410	−	2.43690i	−0.130657	−	0.0949281i	0.520537	−	0.853839i	$-0.325732\pi$
$659$	−3.35410	−	2.43690i	−0.130657	−	0.0949281i	−0.651194	+	0.758911i	$0.725732\pi$
$660$	−0.100813	+	0.0732450i	−0.00392414	+	0.00285106i
$661$	−9.87132	+	7.17194i	−0.383950	+	0.278956i	−0.762972	−	0.646432i	$-0.776261\pi$
$661$	−9.87132	+	7.17194i	−0.383950	+	0.278956i	0.379022	+	0.925388i	$0.376261\pi$
$662$	21.8262	+	15.8577i	0.848301	+	0.616327i
$663$	1.61803	+	1.17557i	0.0628392	+	0.0456554i
$664$	9.37132	−	6.80866i	0.363678	−	0.264227i
$665$	25.8156	+	18.7561i	1.00109	+	0.727331i
$666$	8.01722	+	5.82485i	0.310661	+	0.225708i
$667$		0			0
$668$	−3.43769			−0.133008
$669$	−0.684405	−	2.10638i	−0.0264606	−	0.0814375i
$670$	30.1246			1.16382
$671$	−0.0212862	+	0.0655123i	−0.000821746	+	0.00252907i
$672$	−1.13932	+	3.50647i	−0.0439502	+	0.135265i
$673$	−4.42705	+	3.21644i	−0.170650	+	0.123985i	−0.669832	−	0.742513i	$-0.733634\pi$
$673$	−4.42705	+	3.21644i	−0.170650	+	0.123985i	0.499182	+	0.866497i	$0.333634\pi$
$674$	−32.1803			−1.23954
$675$	3.45492	+	10.6331i	0.132980	+	0.409270i
$676$	0.618034			0.0237705
$677$	17.1631	−	12.4697i	0.659632	−	0.479251i	−0.206906	−	0.978361i	$-0.566340\pi$
$677$	17.1631	−	12.4697i	0.659632	−	0.479251i	0.866539	+	0.499110i	$0.166340\pi$
$678$	−2.20820	+	6.79615i	−0.0848056	+	0.261005i
$679$	9.36475	−	28.8217i	0.359386	−	1.10608i
$680$	−8.09017	+	24.8990i	−0.310244	+	0.954832i
$681$	0.656541	+	2.02063i	0.0251587	+	0.0774306i
$682$	3.00000			0.114876
$683$	−6.23607	−	19.1926i	−0.238617	−	0.734386i	−0.996621	−	0.0821368i	$-0.973826\pi$
$683$	−6.23607	−	19.1926i	−0.238617	−	0.734386i	0.758005	−	0.652249i	$-0.226174\pi$
$684$	−7.13525	−	5.18407i	−0.272823	−	0.198218i
$685$	−46.7082			−1.78463
$686$	−21.8713	+	15.8904i	−0.835051	+	0.606700i
$687$	−7.76393	−	5.64083i	−0.296212	−	0.215211i
$688$	−13.6353	−	9.90659i	−0.519839	−	0.377685i
$689$	5.97214	−	4.33901i	0.227520	−	0.165303i
$690$	5.65248			0.215186
$691$	−22.2082	−	16.1352i	−0.844840	−	0.613812i	0.0788785	−	0.996884i	$-0.474866\pi$
$691$	−22.2082	−	16.1352i	−0.844840	−	0.613812i	−0.923718	+	0.383072i	$0.874866\pi$
$692$	−3.10081	−	9.54332i	−0.117875	−	0.362783i
$693$	1.92299			0.0730482
$694$	−12.9721	−	39.9241i	−0.492416	−	1.51550i
$695$	8.45492	−	26.0216i	0.320713	−	0.987054i
$696$		0			0
$697$	−9.09017	+	27.9767i	−0.344315	+	1.05969i
$698$	29.1074	−	21.1478i	1.10173	−	0.800454i
$699$	−9.97871			−0.377430
$700$	−7.13525	−	5.18407i	−0.269687	−	0.195939i
$701$	10.6180			0.401038			0.200519	−	0.979690i	$-0.435737\pi$
$701$	10.6180			0.401038			0.200519	+	0.979690i	$0.435737\pi$
$702$	−2.92705	+	2.12663i	−0.110474	+	0.0802644i
$703$	3.31559	−	10.2044i	0.125050	−	0.384864i
$704$	−0.309017	+	0.951057i	−0.0116465	+	0.0358443i
$705$	−6.25735			−0.235666
$706$	7.69098	+	23.6704i	0.289454	+	0.890848i
$707$	−27.7082			−1.04207
$708$	−0.163119	−	0.502029i	−0.00613039	−	0.0188674i
$709$	−21.6074	−	15.6987i	−0.811483	−	0.589577i	0.102777	−	0.994704i	$-0.467227\pi$
$709$	−21.6074	−	15.6987i	−0.811483	−	0.589577i	−0.914260	+	0.405128i	$0.867227\pi$
$710$	3.35410	+	2.43690i	0.125877	+	0.0914551i
$711$	25.0623	−	18.2088i	0.939910	−	0.682885i
$712$	−20.2254	−	14.6946i	−0.757980	−	0.550705i
$713$	−25.9894	−	18.8824i	−0.973309	−	0.707150i
$714$	7.47214	−	5.42882i	0.279638	−	0.203169i
$715$	−0.427051	+	0.310271i	−0.0159708	+	0.0116035i
$716$	10.8541	+	7.88597i	0.405637	+	0.294712i
$717$	3.05166	+	9.39205i	0.113966	+	0.350753i
$718$	−6.38197			−0.238173
$719$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$719$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$720$	−25.0623	−	18.2088i	−0.934017	−	0.678603i
$721$	8.48278	−	26.1073i	0.315915	−	0.972287i
$722$	−3.00000	+	9.23305i	−0.111648	+	0.343619i
$723$	−3.48936	+	2.53517i	−0.129771	+	0.0942838i
$724$	2.81966			0.104792
$725$		0			0
$726$	−6.76393			−0.251033
$727$	−19.6074	+	14.2456i	−0.727198	+	0.528340i	−0.888676	−	0.458536i	$-0.848374\pi$
$727$	−19.6074	+	14.2456i	−0.727198	+	0.528340i	0.161478	+	0.986876i	$0.448374\pi$
$728$	−1.97214	+	6.06961i	−0.0730922	+	0.224955i
$729$	−6.00658	+	18.4863i	−0.222466	+	0.684679i
$730$	11.9721	+	36.8464i	0.443109	+	1.36375i
$731$	5.61803	+	17.2905i	0.207790	+	0.639513i
$732$	−0.0688837			−0.00254602
$733$	−8.63525	−	26.5766i	−0.318950	−	0.981628i	−0.974098	−	0.226127i	$-0.927393\pi$
$733$	−8.63525	−	26.5766i	−0.318950	−	0.981628i	0.655147	−	0.755501i	$-0.272607\pi$
$734$	−15.4721	−	11.2412i	−0.571087	−	0.414919i
$735$	−0.302439	−	0.930812i	−0.0111556	−	0.0343335i
$736$	−11.1910	+	8.13073i	−0.412505	+	0.299703i
$737$	−1.59017	−	1.15533i	−0.0585747	−	0.0425570i
$738$	−20.9894	−	15.2497i	−0.772629	−	0.561348i
$739$	3.71885	−	2.70190i	0.136800	−	0.0993910i	−0.517281	−	0.855816i	$-0.673056\pi$
$739$	3.71885	−	2.70190i	0.136800	−	0.0993910i	0.654081	+	0.756425i	$0.273056\pi$
$740$	−0.916408	+	2.82041i	−0.0336878	+	0.103680i
$741$	1.54508	+	1.12257i	0.0567601	+	0.0412386i
$742$	−10.5344	−	32.4217i	−0.386732	−	1.19024i
$743$	22.9098			0.840480			0.420240	−	0.907413i	$-0.361946\pi$
$743$	22.9098			0.840480			0.420240	+	0.907413i	$0.361946\pi$
$744$	−2.07295	−	6.37988i	−0.0759980	−	0.233898i
$745$	13.0902	−	9.51057i	0.479587	−	0.348440i
$746$	−13.7533	+	42.3283i	−0.503544	+	1.54975i
$747$	4.56888	−	14.0616i	0.167167	−	0.514486i
$748$	−0.618034	+	0.449028i	−0.0225976	+	0.0164181i
$749$	−43.4853			−1.58892
$750$	−5.59017	+	4.06150i	−0.204124	+	0.148305i
$751$	−53.3262			−1.94590			−0.972951	−	0.231011i	$-0.925797\pi$
$751$	−53.3262			−1.94590			−0.972951	+	0.231011i	$0.925797\pi$
$752$	28.7705	−	20.9030i	1.04915	−	0.762254i
$753$	1.37132	−	4.22050i	0.0499738	−	0.153803i
$754$		0			0
$755$	−13.2533	+	9.62908i	−0.482337	+	0.350438i
$756$	1.21885	+	3.75123i	0.0443290	+	0.136431i
$757$	40.8673			1.48535			0.742673	−	0.669654i	$-0.233558\pi$
$757$	40.8673			1.48535			0.742673	+	0.669654i	$0.233558\pi$
$758$	6.21885	+	19.1396i	0.225879	+	0.695183i
$759$	−0.298374	−	0.216781i	−0.0108303	−	0.00786866i
$760$	−7.72542	+	23.7764i	−0.280231	+	0.862461i
$761$	−35.2984	+	25.6458i	−1.27957	+	0.929658i	−0.999540	−	0.0303342i	$-0.990343\pi$
$761$	−35.2984	+	25.6458i	−1.27957	+	0.929658i	−0.280025	+	0.959993i	$0.590343\pi$
$762$	−2.28115	−	1.65735i	−0.0826375	−	0.0600396i
$763$	30.9787	+	22.5074i	1.12150	+	0.814821i
$764$	−12.1180	+	8.80427i	−0.438415	+	0.318527i
$765$	10.3262	+	31.7809i	0.373346	+	1.14904i
$766$	50.2148	+	36.4832i	1.81433	+	1.31819i
$767$	−0.690983	−	2.12663i	−0.0249500	−	0.0767881i
$768$	−5.18034			−0.186929
$769$	11.7082	+	36.0341i	0.422209	+	1.29942i	0.905642	+	0.424043i	$0.139390\pi$
$769$	11.7082	+	36.0341i	0.422209	+	1.29942i	−0.483433	+	0.875381i	$0.660610\pi$
$770$	0.753289	+	2.31838i	0.0271466	+	0.0835488i
$771$	2.72949	−	8.40051i	0.0983002	−	0.302537i
$772$	4.98936	−	15.3557i	0.179571	−	0.552662i
$773$	38.1976	−	27.7522i	1.37387	−	0.998176i	0.376447	−	0.926438i	$-0.377146\pi$
$773$	38.1976	−	27.7522i	1.37387	−	0.998176i	0.997424	−	0.0717375i	$-0.0228544\pi$
$774$	−16.0344			−0.576346
$775$	39.2705			1.41064
$776$	23.7426			0.852311
$777$	−1.89261	+	1.37506i	−0.0678970	+	0.0493300i
$778$	15.5902	−	47.9816i	0.558935	−	1.72022i
$779$	−8.68034	+	26.7153i	−0.311005	+	0.957176i
$780$	−0.427051	−	0.310271i	−0.0152909	−	0.0111095i
$781$	−0.0835921	−	0.257270i	−0.00299116	−	0.00920585i
$782$	34.6525			1.23917
$783$		0			0
$784$	4.50000	+	3.26944i	0.160714	+	0.116766i
$785$	10.0623	−	7.31069i	0.359139	−	0.260930i
$786$	−5.47214	+	3.97574i	−0.195185	+	0.141810i
$787$	22.7533	+	16.5312i	0.811067	+	0.589275i	0.914140	−	0.405399i	$-0.132867\pi$
$787$	22.7533	+	16.5312i	0.811067	+	0.589275i	−0.103073	+	0.994674i	$0.532867\pi$
$788$	3.04508	+	2.21238i	0.108477	+	0.0788129i
$789$	0.409830	−	0.297759i	0.0145903	−	0.0106005i
$790$	31.7705	+	23.0826i	1.13034	+	0.821243i
$791$	26.6976	+	19.3969i	0.949256	+	0.689675i
$792$	0.465558	+	1.43284i	0.0165429	+	0.0509138i
$793$	−0.291796			−0.0103620
$794$	6.23607	+	19.1926i	0.221310	+	0.681121i
$795$	−6.30495			−0.223614
$796$	3.35410	−	10.3229i	0.118883	−	0.365884i
$797$	−5.50000	+	16.9273i	−0.194820	+	0.599594i	0.805159	+	0.593059i	$0.202080\pi$
$797$	−5.50000	+	16.9273i	−0.194820	+	0.599594i	−0.999979	+	0.00653481i	$0.997920\pi$
$798$	7.13525	−	5.18407i	0.252585	−	0.183514i
$799$	−38.3607			−1.35710
$800$	5.22542	−	16.0822i	0.184747	−	0.568592i
$801$	−31.9098			−1.12748
$802$	3.30902	−	2.40414i	0.116845	−	0.0848932i
$803$	0.781153	−	2.40414i	0.0275663	−	0.0848403i
$804$	0.607391	−	1.86936i	0.0214210	−	0.0659271i
$805$	8.06637	−	24.8257i	0.284302	−	0.874992i
$806$	3.92705	+	12.0862i	0.138324	+	0.425719i
$807$	4.27051			0.150329
$808$	−6.70820	−	20.6457i	−0.235994	−	0.726314i
$809$	−10.8541	−	7.88597i	−0.381610	−	0.277256i	0.380399	−	0.924823i	$-0.375787\pi$
$809$	−10.8541	−	7.88597i	−0.381610	−	0.277256i	−0.762009	+	0.647567i	$0.775787\pi$
$810$	−27.8885			−0.979904
$811$	9.82624	−	7.13918i	0.345046	−	0.250691i	−0.401742	−	0.915753i	$-0.631595\pi$
$811$	9.82624	−	7.13918i	0.345046	−	0.250691i	0.746788	+	0.665062i	$0.231595\pi$
$812$		0			0
$813$	6.57295	+	4.77553i	0.230523	+	0.167485i
$814$	0.663119	−	0.481784i	0.0232423	−	0.0168865i
$815$	−3.21478			−0.112609
$816$	7.85410	+	5.70634i	0.274949	+	0.199762i
$817$	5.36475	+	16.5110i	0.187689	+	0.577646i
$818$	35.1246			1.22810
$819$	2.51722	+	7.74721i	0.0879588	+	0.270709i
$820$	2.39919	−	7.38394i	0.0837832	−	0.257858i
$821$	−3.36475	+	10.3556i	−0.117430	+	0.361414i	−0.992446	−	0.122681i	$-0.960851\pi$
$821$	−3.36475	+	10.3556i	−0.117430	+	0.361414i	0.875016	+	0.484094i	$0.160851\pi$
$822$	−3.98936	+	12.2780i	−0.139145	+	0.428244i
$823$	1.95492	−	1.42033i	0.0681441	−	0.0495096i	−0.553192	−	0.833054i	$-0.686590\pi$
$823$	1.95492	−	1.42033i	0.0681441	−	0.0495096i	0.621336	+	0.783544i	$0.286590\pi$
$824$	21.5066			0.749217
$825$	0.450850			0.0156966
$826$	−10.3262			−0.359296
$827$	2.59017	−	1.88187i	0.0900690	−	0.0654390i	−0.541839	−	0.840482i	$-0.682272\pi$
$827$	2.59017	−	1.88187i	0.0900690	−	0.0654390i	0.631908	+	0.775043i	$0.282272\pi$
$828$	−2.22949	+	6.86167i	−0.0774801	+	0.238459i
$829$	10.3647	−	31.8994i	0.359982	−	1.10791i	−0.593081	−	0.805143i	$-0.702089\pi$
$829$	10.3647	−	31.8994i	0.359982	−	1.10791i	0.953064	−	0.302770i	$-0.0979113\pi$
$830$	18.7426			0.650567
$831$	−1.80495	−	5.55507i	−0.0626131	−	0.192703i
$832$	−4.23607			−0.146859
$833$	−1.85410	−	5.70634i	−0.0642408	−	0.197713i
$834$	−6.11803	−	4.44501i	−0.211850	−	0.153918i
$835$	10.0623	+	7.31069i	0.348220	+	0.252997i
$836$	−0.590170	+	0.428784i	−0.0204115	+	0.0148298i
$837$	−14.2082	−	10.3229i	−0.491107	−	0.356810i
$838$	13.7812	+	10.0126i	0.476062	+	0.345879i
$839$	−22.9894	+	16.7027i	−0.793681	+	0.576643i	−0.909053	−	0.416679i	$-0.863194\pi$
$839$	−22.9894	+	16.7027i	−0.793681	+	0.576643i	0.115373	+	0.993322i	$0.463194\pi$
$840$	4.40983	−	3.20393i	0.152154	−	0.110546i
$841$	23.4615	+	17.0458i	0.809017	+	0.587785i
$842$	18.6353	+	57.3534i	0.642213	+	1.97653i
$843$	1.87539			0.0645918
$844$	4.06231	+	12.5025i	0.139830	+	0.430354i
$845$	−1.80902	−	1.31433i	−0.0622321	−	0.0452143i
$846$	10.4549	−	32.1769i	0.359447	−	1.10627i
$847$	−9.65248	+	29.7073i	−0.331663	+	1.02075i
$848$	28.9894	−	21.0620i	0.995499	−	0.723272i
$849$	11.3262			0.388715
$850$	−34.2705	+	24.8990i	−1.17547	+	0.854028i
$851$	−8.77709			−0.300875
$852$	0.218847	−	0.159002i	0.00749758	−	0.00544731i
$853$	0.347524	−	1.06957i	0.0118990	−	0.0366214i	−0.944931	−	0.327270i	$-0.893871\pi$
$853$	0.347524	−	1.06957i	0.0118990	−	0.0366214i	0.956830	+	0.290649i	$0.0938712\pi$
$854$	−0.416408	+	1.28157i	−0.0142492	+	0.0438545i
$855$	9.86068	+	30.3481i	0.337228	+	1.03788i
$856$	−10.5279	−	32.4014i	−0.359835	−	1.10746i
$857$	18.9098			0.645947			0.322974	−	0.946408i	$-0.395317\pi$
$857$	18.9098			0.645947			0.322974	+	0.946408i	$0.395317\pi$
$858$	0.0450850	+	0.138757i	0.00153918	+	0.00473710i
$859$	−16.7082	−	12.1392i	−0.570077	−	0.414185i	0.265056	−	0.964233i	$-0.414609\pi$
$859$	−16.7082	−	12.1392i	−0.570077	−	0.414185i	−0.835133	+	0.550048i	$0.814609\pi$
$860$	−1.48278	−	4.56352i	−0.0505623	−	0.155615i
$861$	4.95492	−	3.59996i	0.168863	−	0.122686i
$862$	−9.09017	−	6.60440i	−0.309612	−	0.224947i
$863$	−8.20820	−	5.96361i	−0.279411	−	0.203004i	0.439250	−	0.898365i	$-0.355244\pi$
$863$	−8.20820	−	5.96361i	−0.279411	−	0.203004i	−0.718660	+	0.695361i	$0.755244\pi$
$864$	−6.11803	+	4.44501i	−0.208140	+	0.151222i
$865$	−11.2188	+	34.5281i	−0.381452	+	1.17399i
$866$	−48.7148	−	35.3934i	−1.65540	−	1.20272i
$867$	−1.22949	−	3.78398i	−0.0417557	−	0.128511i
$868$	13.8541			0.470239
$869$	−0.791796	−	2.43690i	−0.0268598	−	0.0826661i
$870$		0			0
$871$	2.57295	−	7.91872i	0.0871811	−	0.268316i
$872$	−9.27051	+	28.5317i	−0.313939	+	0.966205i
$873$	24.5172	−	17.8128i	0.829782	−	0.602872i
$874$	33.0902			1.11929
$875$	9.86068	+	30.3481i	0.333352	+	1.02595i
$876$	2.52786			0.0854086
$877$	9.33688	−	6.78364i	0.315284	−	0.229067i	−0.418876	−	0.908043i	$-0.637576\pi$
$877$	9.33688	−	6.78364i	0.315284	−	0.229067i	0.734161	+	0.678976i	$0.237576\pi$
$878$	2.92705	−	9.00854i	0.0987832	−	0.304023i
$879$	0.875388	−	2.69417i	0.0295261	−	0.0908720i
$880$	−2.07295	+	1.50609i	−0.0698791	+	0.0507701i
$881$	−3.20163	−	9.85359i	−0.107866	−	0.331976i	0.882527	−	0.470262i	$-0.155841\pi$
$881$	−3.20163	−	9.85359i	−0.107866	−	0.331976i	−0.990392	+	0.138286i	$0.955841\pi$
$882$	5.29180			0.178184
$883$	4.41641	+	13.5923i	0.148624	+	0.457418i	0.997459	−	0.0712400i	$-0.0226956\pi$
$883$	4.41641	+	13.5923i	0.148624	+	0.457418i	−0.848835	+	0.528657i	$0.822696\pi$
$884$	−2.61803	−	1.90211i	−0.0880540	−	0.0639750i
$885$	−0.590170	+	1.81636i	−0.0198383	+	0.0610561i
$886$	−2.57295	+	1.86936i	−0.0864399	+	0.0628023i
$887$	14.5623	+	10.5801i	0.488954	+	0.355246i	0.804782	−	0.593570i	$-0.202282\pi$
$887$	14.5623	+	10.5801i	0.488954	+	0.355246i	−0.315828	+	0.948817i	$0.602282\pi$
$888$	−1.48278	−	1.07730i	−0.0497588	−	0.0361519i
$889$	−10.5344	+	7.65372i	−0.353314	+	0.256698i
$890$	−12.5000	−	38.4710i	−0.419001	−	1.28955i
$891$	1.47214	+	1.06957i	0.0493184	+	0.0358319i
$892$	1.10739	+	3.40820i	0.0370782	+	0.114115i
$893$	−36.6312			−1.22582
$894$	−1.38197	−	4.25325i	−0.0462199	−	0.142250i
$895$	−15.0000	−	46.1653i	−0.501395	−	1.54313i
$896$	−12.0106	+	36.9650i	−0.401247	+	1.23491i
$897$	0.482779	−	1.48584i	0.0161195	−	0.0496108i
$898$	−6.70820	+	4.87380i	−0.223856	+	0.162641i
$899$		0			0
$900$	−2.72542	−	8.38800i	−0.0908475	−	0.279600i
$901$	−38.6525			−1.28770
$902$	−1.73607	+	1.26133i	−0.0578047	+	0.0419976i
$903$	1.16970	−	3.59996i	0.0389251	−	0.119799i
$904$	−7.98936	+	24.5887i	−0.265722	+	0.817808i
$905$	−8.25329	−	5.99637i	−0.274349	−	0.199326i
$906$	1.39919	+	4.30625i	0.0464849	+	0.143066i
$907$	27.5279			0.914048			0.457024	−	0.889454i	$-0.348915\pi$
$907$	27.5279			0.914048			0.457024	+	0.889454i	$0.348915\pi$
$908$	−1.06231	−	3.26944i	−0.0352539	−	0.108500i
$909$	−22.4164	−	16.2865i	−0.743505	−	0.540188i
$910$	−8.35410	+	6.06961i	−0.276936	+	0.201206i
$911$	31.5967	−	22.9564i	1.04685	−	0.760579i	0.0752366	−	0.997166i	$-0.476029\pi$
$911$	31.5967	−	22.9564i	1.04685	−	0.760579i	0.971610	+	0.236587i	$0.0760288\pi$
$912$	7.50000	+	5.44907i	0.248350	+	0.180437i
$913$	−0.989357	−	0.718810i	−0.0327429	−	0.0237891i
$914$	−13.3992	+	9.73508i	−0.443206	+	0.322008i
$915$	0.201626	+	0.146490i	0.00666555	+	0.00484281i
$916$	12.5623	+	9.12705i	0.415070	+	0.301566i
$917$	9.65248	+	29.7073i	0.318753	+	0.981020i
$918$	18.9443			0.625254
$919$	0.791796	+	2.43690i	0.0261189	+	0.0803858i	0.963266	−	0.268548i	$-0.0865438\pi$
$919$	0.791796	+	2.43690i	0.0261189	+	0.0803858i	−0.937147	+	0.348934i	$0.886544\pi$
$920$	20.4508			0.674245
$921$	3.31966	−	10.2169i	0.109387	−	0.336657i
$922$	18.2705	−	56.2308i	0.601707	−	1.85186i
$923$	0.927051	−	0.673542i	0.0305143	−	0.0221699i
$924$	0.159054			0.00523248
$925$	8.68034	−	6.30664i	0.285408	−	0.207361i
$926$	−23.1246			−0.759922
$927$	22.2082	−	16.1352i	0.729413	−	0.529950i
$928$		0			0
$929$	6.21885	−	19.1396i	0.204034	−	0.627951i	−0.795718	−	0.605667i	$-0.792906\pi$
$929$	6.21885	−	19.1396i	0.204034	−	0.627951i	0.999752	−	0.0222839i	$-0.00709379\pi$
$930$	3.35410	−	10.3229i	0.109985	−	0.338500i
$931$	−1.77051	−	5.44907i	−0.0580261	−	0.178586i
$932$	16.1459			0.528876
$933$	−3.06231	−	9.42481i	−0.100255	−	0.308554i
$934$	−6.00000	−	4.35926i	−0.196326	−	0.142639i
$935$	2.76393			0.0903902
$936$	−5.16312	+	3.75123i	−0.168762	+	0.122613i
$937$	−31.3156	−	22.7521i	−1.02304	−	0.743279i	−0.0561329	−	0.998423i	$-0.517877\pi$
$937$	−31.3156	−	22.7521i	−1.02304	−	0.743279i	−0.966903	+	0.255144i	$0.917877\pi$
$938$	−31.1074	−	22.6008i	−1.01569	−	0.737944i
$939$	−5.80902	+	4.22050i	−0.189570	+	0.137731i
$940$	10.1246			0.330228
$941$	23.8713	+	17.3435i	0.778183	+	0.565383i	0.904433	−	0.426615i	$-0.140294\pi$
$941$	23.8713	+	17.3435i	0.778183	+	0.565383i	−0.126250	+	0.991998i	$0.540294\pi$
$942$	−1.06231	−	3.26944i	−0.0346118	−	0.106524i
$943$	22.9787			0.748290
$944$	−3.35410	−	10.3229i	−0.109167	−	0.335981i
$945$	4.40983	−	13.5721i	0.143452	−	0.441499i
$946$	−0.409830	+	1.26133i	−0.0133247	+	0.0410093i
$947$	1.61146	−	4.95955i	0.0523653	−	0.161164i	−0.921454	−	0.388488i	$-0.872998\pi$
$947$	1.61146	−	4.95955i	0.0523653	−	0.161164i	0.973819	+	0.227324i	$0.0729976\pi$
$948$	2.07295	−	1.50609i	0.0673263	−	0.0489154i
$949$	10.7082			0.347603
$950$	−32.7254	+	23.7764i	−1.06175	+	0.771409i
$951$	9.43769			0.306038
$952$	27.0344	−	19.6417i	0.876191	−	0.636590i
$953$	0.712269	−	2.19214i	0.0230727	−	0.0710104i	−0.938857	−	0.344307i	$-0.888114\pi$
$953$	0.712269	−	2.19214i	0.0230727	−	0.0710104i	0.961930	+	0.273296i	$0.0881140\pi$
$954$	10.5344	−	32.4217i	0.341065	−	1.04969i
$955$	54.1935			1.75366
$956$	−4.93769	−	15.1967i	−0.159696	−	0.491495i
$957$		0			0
$958$	2.66312	+	8.19624i	0.0860415	+	0.264808i
$959$	48.2320	+	35.0426i	1.55749	+	1.13158i
$960$	2.92705	+	2.12663i	0.0944702	+	0.0686366i
$961$	−24.8262	+	18.0373i	−0.800846	+	0.581849i
$962$	2.80902	+	2.04087i	0.0905663	+	0.0658003i
$963$	−35.1803	−	25.5600i	−1.13367	−	0.823660i
$964$	5.64590	−	4.10199i	0.181842	−	0.132116i
$965$	−47.2599	+	34.3363i	−1.52135	+	1.10532i
$966$	−5.83688	−	4.24074i	−0.187799	−	0.136444i
$967$	−14.6459	−	45.0754i	−0.470980	−	1.44953i	−0.851303	−	0.524675i	$-0.824187\pi$
$967$	−14.6459	−	45.0754i	−0.470980	−	1.44953i	0.380323	−	0.924854i	$-0.375813\pi$
$968$	−24.4721			−0.786564
$969$	−3.09017	−	9.51057i	−0.0992706	−	0.305523i
$970$	31.0795	+	22.5806i	0.997903	+	0.725019i
$971$	−6.45492	+	19.8662i	−0.207148	+	0.637536i	0.792470	+	0.609911i	$0.208795\pi$
$971$	−6.45492	+	19.8662i	−0.207148	+	0.637536i	−0.999618	+	0.0276257i	$0.991205\pi$
$972$	−1.84346	+	5.67358i	−0.0591290	+	0.181980i
$973$	−28.2533	+	20.5272i	−0.905759	+	0.658072i
$974$	54.9787			1.76163
$975$	0.590170	+	1.81636i	0.0189006	+	0.0581700i
$976$	−1.41641			−0.0453381
$977$	27.2254	−	19.7804i	0.871019	−	0.632832i	−0.0598416	−	0.998208i	$-0.519060\pi$
$977$	27.2254	−	19.7804i	0.871019	−	0.632832i	0.930860	+	0.365376i	$0.119060\pi$
$978$	−0.274575	+	0.845055i	−0.00877994	+	0.0270219i
$979$	−0.815595	+	2.51014i	−0.0260665	+	0.0802245i
$980$	0.489357	+	1.50609i	0.0156319	+	0.0481101i
$981$	11.8328	+	36.4177i	0.377793	+	1.16273i
$982$	−29.4164			−0.938715
$983$	−12.8197	−	39.4549i	−0.408884	−	1.25841i	−0.917609	−	0.397485i	$-0.869883\pi$
$983$	−12.8197	−	39.4549i	−0.408884	−	1.25841i	0.508725	−	0.860929i	$-0.330117\pi$
$984$	3.88197	+	2.82041i	0.123753	+	0.0899115i
$985$	−4.20820	−	12.9515i	−0.134085	−	0.412670i
$986$		0			0
$987$	6.46149	+	4.69455i	0.205672	+	0.149429i
$988$	−2.50000	−	1.81636i	−0.0795356	−	0.0577860i
$989$	11.4894	−	8.34751i	0.365340	−	0.265435i
$990$	−0.753289	+	2.31838i	−0.0239411	+	0.0736831i
$991$	−8.75329	−	6.35964i	−0.278057	−	0.202021i	0.440012	−	0.897992i	$-0.354974\pi$
$991$	−8.75329	−	6.35964i	−0.278057	−	0.202021i	−0.718070	+	0.695971i	$0.754974\pi$
$992$	8.20820	+	25.2623i	0.260611	+	0.802077i
$993$	−6.36881			−0.202108
$994$	−1.63525	−	5.03280i	−0.0518671	−	0.159631i
$995$	−31.7705	+	23.0826i	−1.00719	+	0.731768i
$996$	0.377901	−	1.16306i	0.0119742	−	0.0368529i
$997$	−16.0902	+	49.5205i	−0.509581	+	1.56833i	0.283350	+	0.959017i	$0.408554\pi$
$997$	−16.0902	+	49.5205i	−0.509581	+	1.56833i	−0.792931	+	0.609312i	$0.791446\pi$
$998$	56.9959	−	41.4100i	1.80417	−	1.31081i
$999$	−4.79837			−0.151814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.l.a.261.1	yes	4
25.4	even	10		8125.2.a.b.1.2		2
25.16	even	5	inner	325.2.l.a.66.1	✓	4
25.21	even	5		8125.2.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.l.a.66.1	✓	4	25.16	even	5	inner
325.2.l.a.261.1	yes	4	1.1	even	1	trivial
8125.2.a.a.1.1		2	25.21	even	5
8125.2.a.b.1.2		2	25.4	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 - 0.951057i) q^{2} +(-0.118034 + 0.363271i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(0.190983 + 0.587785i) q^{6} +2.85410 q^{7} +(0.690983 + 2.12663i) q^{8} +(2.30902 + 1.67760i) q^{9} +O(q^{10})\)	\(q+(1.30902 - 0.951057i) q^{2} +(-0.118034 + 0.363271i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(0.190983 + 0.587785i) q^{6} +2.85410 q^{7} +(0.690983 + 2.12663i) q^{8} +(2.30902 + 1.67760i) q^{9} +(-1.11803 + 3.44095i) q^{10} +(0.190983 - 0.138757i) q^{11} +(0.190983 + 0.138757i) q^{12} +(0.809017 + 0.587785i) q^{13} +(3.73607 - 2.71441i) q^{14} +(-0.263932 - 0.812299i) q^{15} +(3.92705 + 2.85317i) q^{16} +(-1.61803 - 4.97980i) q^{17} +4.61803 q^{18} +(-1.54508 - 4.75528i) q^{19} +(0.427051 + 1.31433i) q^{20} +(-0.336881 + 1.03681i) q^{21} +(0.118034 - 0.363271i) q^{22} +(-3.30902 + 2.40414i) q^{23} -0.854102 q^{24} +(1.54508 - 4.75528i) q^{25} +1.61803 q^{26} +(-1.80902 + 1.31433i) q^{27} +(0.545085 - 1.67760i) q^{28} +(-1.11803 - 0.812299i) q^{30} +(2.42705 + 7.46969i) q^{31} +3.38197 q^{32} +(0.0278640 + 0.0857567i) q^{33} +(-6.85410 - 4.97980i) q^{34} +(-5.16312 + 3.75123i) q^{35} +(1.42705 - 1.03681i) q^{36} +(1.73607 + 1.26133i) q^{37} +(-6.54508 - 4.75528i) q^{38} +(-0.309017 + 0.224514i) q^{39} +(-4.04508 - 2.93893i) q^{40} +(-4.54508 - 3.30220i) q^{41} +(0.545085 + 1.67760i) q^{42} -3.47214 q^{43} +(-0.0450850 - 0.138757i) q^{44} -6.38197 q^{45} +(-2.04508 + 6.29412i) q^{46} +(2.26393 - 6.96767i) q^{47} +(-1.50000 + 1.08981i) q^{48} +1.14590 q^{49} +(-2.50000 - 7.69421i) q^{50} +2.00000 q^{51} +(0.500000 - 0.363271i) q^{52} +(2.28115 - 7.02067i) q^{53} +(-1.11803 + 3.44095i) q^{54} +(-0.163119 + 0.502029i) q^{55} +(1.97214 + 6.06961i) q^{56} +1.90983 q^{57} +(-1.80902 - 1.31433i) q^{59} -0.527864 q^{60} +(-0.236068 + 0.171513i) q^{61} +(10.2812 + 7.46969i) q^{62} +(6.59017 + 4.78804i) q^{63} +(-3.42705 + 2.48990i) q^{64} -2.23607 q^{65} +(0.118034 + 0.0857567i) q^{66} +(-2.57295 - 7.91872i) q^{67} -3.23607 q^{68} +(-0.482779 - 1.48584i) q^{69} +(-3.19098 + 9.82084i) q^{70} +(0.354102 - 1.08981i) q^{71} +(-1.97214 + 6.06961i) q^{72} +(8.66312 - 6.29412i) q^{73} +3.47214 q^{74} +(1.54508 + 1.12257i) q^{75} -3.09017 q^{76} +(0.545085 - 0.396027i) q^{77} +(-0.190983 + 0.587785i) q^{78} +(3.35410 - 10.3229i) q^{79} -10.8541 q^{80} +(2.38197 + 7.33094i) q^{81} -9.09017 q^{82} +(-1.60081 - 4.92680i) q^{83} +(0.545085 + 0.396027i) q^{84} +(9.47214 + 6.88191i) q^{85} +(-4.54508 + 3.30220i) q^{86} +(0.427051 + 0.310271i) q^{88} +(-9.04508 + 6.57164i) q^{89} +(-8.35410 + 6.06961i) q^{90} +(2.30902 + 1.67760i) q^{91} +(0.781153 + 2.40414i) q^{92} -3.00000 q^{93} +(-3.66312 - 11.2739i) q^{94} +(9.04508 + 6.57164i) q^{95} +(-0.399187 + 1.22857i) q^{96} +(3.28115 - 10.0984i) q^{97} +(1.50000 - 1.08981i) q^{98} +0.673762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} + 5 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 + 5 * q^8 + 7 * q^9	\( 4 q + 3 q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} + 5 q^{8} + 7 q^{9} + 3 q^{11} + 3 q^{12} + q^{13} + 6 q^{14} - 10 q^{15} + 9 q^{16} - 2 q^{17} + 14 q^{18} + 5 q^{19} - 5 q^{20} - 17 q^{21} - 4 q^{22} - 11 q^{23} + 10 q^{24} - 5 q^{25} + 2 q^{26} - 5 q^{27} - 9 q^{28} + 3 q^{31} + 18 q^{32} + 18 q^{33} - 14 q^{34} - 5 q^{35} - q^{36} - 2 q^{37} - 15 q^{38} + q^{39} - 5 q^{40} - 7 q^{41} - 9 q^{42} + 4 q^{43} + 11 q^{44} - 30 q^{45} + 3 q^{46} + 18 q^{47} - 6 q^{48} + 18 q^{49} - 10 q^{50} + 8 q^{51} + 2 q^{52} - 11 q^{53} + 15 q^{55} - 10 q^{56} + 30 q^{57} - 5 q^{59} - 20 q^{60} + 8 q^{61} + 21 q^{62} + 4 q^{63} - 7 q^{64} - 4 q^{66} - 17 q^{67} - 4 q^{68} - 31 q^{69} - 15 q^{70} - 12 q^{71} + 10 q^{72} + 19 q^{73} - 4 q^{74} - 5 q^{75} + 10 q^{76} - 9 q^{77} - 3 q^{78} - 30 q^{80} + 14 q^{81} - 14 q^{82} - 31 q^{83} - 9 q^{84} + 20 q^{85} - 7 q^{86} - 5 q^{88} - 25 q^{89} - 20 q^{90} + 7 q^{91} - 17 q^{92} - 12 q^{93} + q^{94} + 25 q^{95} + 23 q^{96} - 7 q^{97} + 6 q^{98} + 34 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 4 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 + 5 * q^8 + 7 * q^9 + 3 * q^11 + 3 * q^12 + q^13 + 6 * q^14 - 10 * q^15 + 9 * q^16 - 2 * q^17 + 14 * q^18 + 5 * q^19 - 5 * q^20 - 17 * q^21 - 4 * q^22 - 11 * q^23 + 10 * q^24 - 5 * q^25 + 2 * q^26 - 5 * q^27 - 9 * q^28 + 3 * q^31 + 18 * q^32 + 18 * q^33 - 14 * q^34 - 5 * q^35 - q^36 - 2 * q^37 - 15 * q^38 + q^39 - 5 * q^40 - 7 * q^41 - 9 * q^42 + 4 * q^43 + 11 * q^44 - 30 * q^45 + 3 * q^46 + 18 * q^47 - 6 * q^48 + 18 * q^49 - 10 * q^50 + 8 * q^51 + 2 * q^52 - 11 * q^53 + 15 * q^55 - 10 * q^56 + 30 * q^57 - 5 * q^59 - 20 * q^60 + 8 * q^61 + 21 * q^62 + 4 * q^63 - 7 * q^64 - 4 * q^66 - 17 * q^67 - 4 * q^68 - 31 * q^69 - 15 * q^70 - 12 * q^71 + 10 * q^72 + 19 * q^73 - 4 * q^74 - 5 * q^75 + 10 * q^76 - 9 * q^77 - 3 * q^78 - 30 * q^80 + 14 * q^81 - 14 * q^82 - 31 * q^83 - 9 * q^84 + 20 * q^85 - 7 * q^86 - 5 * q^88 - 25 * q^89 - 20 * q^90 + 7 * q^91 - 17 * q^92 - 12 * q^93 + q^94 + 25 * q^95 + 23 * q^96 - 7 * q^97 + 6 * q^98 + 34 * q^99

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